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EUROPEAN  THOUGHT  IN  THE  NINETEENTH 

CENTURY 


TotovTOs  ovv  fiOi  6  (rvyypa(fiev<;  earw,  .  .  . 

$€VO<i  iv  TOtS  /3ty8Xt'otS  KOI  aTToAtS. 

— LUCIAN. 


A   HISTORY 


OF 


EUROPEAN    THOUGHT 


IN    THE 


NINETEENTH   CENTURY 


BY 


JOHN  thp:odoiie  mekz 


VOL.   II. 


WILLIAM     BLACKWOOD    AND    SONS 

EDINBDilGH     AND     LONDON 

M  C  M  1  I  1 


All  liiohU  rrsfrveit 


^llY  OF  TO525. 

79787' 


PREFACE. 


In  this  second  volume  I  have  carried  out  the  programme 
which  I  put  forward  in  the  preface  to  the  first  volume,  thus 
finishing  the  first  portion  of  my  undertakiui,' — Tlie  History 
of  Scientific  Thought  in  the  Nineteenth  Century.  The 
two  volumes  form  a  work  complete  in  itself,  and  for  this 
reason  I  have  attached  an  alphabetical  index. 

In  addition  to  the  names  I  mentioned  in  the  preface  to 
the  first  volume,  I  have  to  add  those  of  other  friends 
who  have  been  of  great  help  to  me  in  the  course  of 
my  work.  With  Professor  Sampson,  F.K.S.,  of  Durham 
University,  I  have  liad  many  helpful  discussions  on  the 
subjects  of  this  volume,  notably  on  chapters  viii.  and 
xiii.,  which  he  read  in  proof.  Mr  Arthur  Berry,  M.A., 
of  King's  College,  Cambridge,  has  read  over  chapter 
xiii.,  and  made  valuable  suggestions.  Mr  Archibald  S. 
Percival,  M.B.,  of  Cambridge,  has  read  over  chapters 
vi.  and  x.  Professor  F.  G.  Weiss,  D.Sc,  of  Victoria 
University,  has  read  chapters  viii.  and  i.v.  Mr  Thomas 
Whittaker  has  continued  his  revision,  much  to  the  bonetit 
of  the  book ;  and  Dr  Spence  Watson  has  given  the  finishing 


VI  PREFACE. 

touches  to  the  last  pages,  in  which  I  endeavour  to  secure 
in  advance  the  interest  of  my  readers  for  the  subsequent 
portions  of  this  work.  To  all  these  friends  I  wish  to 
express  my  sense  of  obligation  and  my  sincere  thanks. 
I  find  it  impossible  to  express  how  much  this  book  owes 
to  my  beloved  wife,  my  constant  helpmate  on  the  long 
course  of  this  arduous  enterprise. 

It  is  unnecessary  for  me  to  lighten  the  work  of  my 
critics  by  pointing  out  the  many  defects  of  which  I  myself 
am  painfully  conscious ;  but,  in  the  case  of  the  last  chapter 
on  "  The  Development  of  Mathematical  Thought,"  I  wish 
to  say  that  this  is — so  far  as  I  know — the  first  attempt 
to  give  to  this  abstract  region  of  thought  a  place  in  a 
general  history  of  intellectual  progress.  I  sincerely  hope 
that  it  will  be  followed  by  other  and  more  successful 
attempts  to  perform  this  very  difficult  task.  It  is  now 
abundantly  clear  that  mathematical  thought  will  play  an 
increasingly  important  part  in  the  progress  of  science  and 
culture,  and  it  is  no  longer  permissible  to  consider  it  merely 
an  interesting  specialty  apart  from  the  general  course  of 
intellectual  development.  A  due  appreciation  of  its  im- 
portance and  power  will  in  future  be  expected,  not  only 
from  the  practical  thinker  who  applies  science,  but  likewise 
from  the  philosopher  who  assigns  to  science  its  place  in 
the  comprehensive  scheme  of  human  culture. 


J.    THEO.    MEEZ, 


The  Qpabbies, 
Nkwcastle-upon-Ttne,  October  1903. 


CONTENTS  OF  THE  SECOND  YOIXME. 


CHAPTER    VI. 

ON    THE    KINETIC    OK    MECHANICAL    VIEW    OF    NATURE. 

The  idea  of  motion  in  ancient  philosophy,  3  ;  Descartes'  development  of  the 
kinetic  view,  6  ;  Huygens  and  Newton,  7  ;  Revival  of  the  kinetic  view 
in  the  nineteenth  century,  7  ;  Young  and  Fresnel,  8  ;  UnduLttorj-  and 
emission  theories,  11  ;  Doth  theories  kinetic,  11  ;  Undulatory  theory 
prepared  by  acoustics,  12  ;  Newton's  authority  on  the  side  of  the  emission 
theory,  14;  But  also  suggests  the  other  theory,  15;  Biot,  BrewHter, 
and  Laplace  against  the  undulatory  theory,  16  ;  Euler  the  suceeabor  of 
Huygens,  16;  Young,  16;  His  "general  law  of  the  interference  of 
light,"  18  ;  Theory  of  the  luminiferous  ether,  18  ;  Brougham's  attack  on 
Young,  19  ;  Augustin  Fresnel,  21  ;  Difficulties  presented  by  the  jwliir- 
isation  of  light,  22  ;  Fresnel's  Memoir  on  Ditfi-action,  25  ;  Young  and 
Fresnel  introduce  the  conception  of  transverse  vibrations,  28  ;  Mechani- 
cal difference  between  light  and  sound,  30  ;  The  proi)ertie8  of  the  ether, 
31  ;  Other  kinetic  theories,  34  ;  Kinetic  theory  of  ga.ses,  34  ;  Vortex 
motion,  35  ;  Faraday's  researches,  35  ;  Problems  aa  to  tlie  nature  of  the 
ether,  36  ;  The  theory  of  elasticity,  40  ;  The  problem  of  the  ether  may 
be  treated  mathematically,  44  ;  or  experimentally,  44  ;  Necessity  of 
combining  the  two  methods,  44  ;  Spectrum  analysis,  45  ;  Tl>e  rlue 
furnished  by  the  phenomena  on  which  it  depends,  47  ;  Sir  0.  St<>ki>«, 
47  ;  (iustav  KirchhofF,  48  ;  Explanation  of  fluorescence,  52  ;  View  of  (he 
ether  as  an  "elastic  solid,"  54  ;  Lord  Kelvin's  rcseiux-lies,  55  ;  Tyndull'* 
'  Heat,'  57  ;  Lord  Kelvin's  vortex  theory  of  rnalltT,  57  ;  Heiuiholi*'* 
investigations,  58 ;  Earlier  researches  on  vortex  motion,  (51  ;  IufluoiKX» 
of  Helmholtz's  investigations  in  England,  62  ;  Difl^icultjos  of  liio  vort<«x 
ring  theory,  64  ;  Modern  view  of  electrical  plienomcna  :  KanuUy,  6«3  ; 


Vlll  CONTENTS. 

"  Lines  of  force,"  68  ;  Development  of  the  conception  by  Lord  Kelvin, 
71  ;  Clerk-Maxwell,  76  ;  His  series  of  works  on  the  theory  of  electricity, 
78;  His  conception  of  "tubes  of  force,"  80;  " Electrotonic  state"  of 
matter,  81  ;  Correspondence  between  velocities  of  light  and  electricity, 
84  ;  "  Elastic  disturbances  "  of  the  same  medium,  85  ;  Consequences  on 
the  lines  of  the  theory  of  Energy,  87  ;  Destructive  effect  of  the  new 
theories  on  the  astronomical  view,  89  ;  Lord  Kelvin  on  the  vibrations 
of  the  ether,  91  ;  Indefiniteness  of  the  electro-magnetic  theory,  93. 


CHAPTER    VII. 

ON   THE   PHYSICAL   VIEW   OF   NATDRE. 

Recapitulation,  95 ;  Insufficiency  of  the  astronomical,  atomic,  and  kinetic 
views,  96  ;  The  conception  of  energy,  96  ;  The  term  first  used  by  Young, 
98  ;  Watt  introduces  the  term  "  power,"  99  ;  Poncelet  introduces  the 
term  "mechanical  work,"  101  ;  Black,  Rumford,  and  Davy,  102;  Cor- 
relation of  forces,  105  ;  Liebig,  105 ;  Johannes  Miiller,  106  ;  F.  Mohr, 
107  ;  Mayer,  108  ;  Joule,  110  ;  Helmholtz,  112  ;  "Work"  and  "energy" 
introduced  by  Clausius  and  Thomson,  115;  Sadi  Carnot,  117;  Carnot 
introduces  the  idea  of  "availability,"  119  ;  Thomson  introduces  the  idea 
of  "dissipation,"  119;  Fourier,  120;  His  influence  on  Carnot,  122; 
Clapeyron's  graphical  method,  123 ;  Perpetual  motion  impossible,  124  ; 
Application  by  William  and  James  Thomson,  126  ;  The  two  laws  of 
thermodynamics,  128  ;  Summary  statement  of  Thomson  (Lord  Kelvin), 
132  ;  Rankine,  Zeuuer,  and  Hirn,  133  ;  Revolutions  brought  about  by 
idea  of  energy,  137;  Helmholtz  on  "tension,"  138;  "Potential"  and 
"actual"  energy,  139  ;  The  Scotch  school,  141  ;  Thomson  and  Tait,  144; 
Clerk  -  Maxwell,  145  ;  Faraday,  146  ;  Helmholtz  on  electro-dynamics, 
149;  Ostwald's  physical  chemistry,  153;  The  factor  of  "cost"  in 
industry,  155  ;  Berthelot  and  Ostwald,  157  ;  Arrhenius,  159  ;  Graham 
and  Andrews,  161  ;  Dissociation,  163  ;  Hittorf  and  Kohlrausch,  164  ; 
Victor  Meyer  on  change  of  chemical  views,  165  ;  Ostwald's  journal,  166  ; 
Willard  Gibbs,  167  ;  Entropy,  169  ;  Horstmann,  170  ;  Helmholtz's  "free 
energy,"  173  ;  Kelvin's  "available  energy,"  174  ;  Ostwald's  '  Allgemeine 
Chemie,'  176  ;  "  Kinetics"  and  "energetics,"  180  ;  Criticism  of  mechani- 
cal view,  183  ;  The  outcome,  187  ;  Recent  triumphs  of  atomic  view,  188  ; 
Modern  electrical  researches,  189;  The  term  "electron,"  193;  Diffi- 
culties of  Clerk-Maxwell's  theory,  194 ;  What  are  electric  charges  1 
195  ;  Dr  Larmor's  position,  195  ;  Objections  raised  by  atomists,  198  ; 
Artificial  character  of  modern  dynamical  explanations,  199;  The  phil- 
osophic problem  raised,  199. 


CONTENTS.  ix 

CHAPTEE    VIII. 

ON  THE  MORPHOLOGICAL  VIEW  OK  NATURE. 

The  abstract  sciences,  200  ;  Convenience  and  usefulness  of  the  process  of 
abstraction,  "201  ;  Interest  opposed  to  the  spirit  of  abstraction,  '202  ; 
Tlie  descriptive  sciences,  203  ;  The  breaking  down  of  old  landmarks, 
204  ;  The  spirit  of  exploration,  206  ;  The  medical  interest,  207  ;  Physical 
science  applied  to  medicine,  208  ;  Schwann,  209  ;  Darwin,  209  ;  Herbert 
Spencer,  210  LJ^Hiewell's  divisions  abandoned.  210  ;  Divisions  of  natural 
history,  211  ;  Morphology  and  genetics,  213;  Other  aspects,  215;  Life 
and  mind,  216  ;  Vitalistic  and  psycho-physical  aspects,  218  ;  Morphology 
defined,  219  ;  Artificial  and  natural  systems,  220  ;  Linnaeus  and  liuffon, 
221  ;  Morphology  of  crystals,  222  ;  Morphology  on  a  large  scale,  224  ; 
Humboldt,  225  ;  Morphology  on  a  minute  scale,  227  ;  Its  improvement, 
230  ;  Morphology  and  classification,  231  ;  Study  of  separate  organs,  233  ; 
Outdoor  studies,  234  ;  Jussieu,  235 ;  Problem  of  organisation,  236  ; 
Cuvier,  237;  "Types,"  238;  De  Candolle,  239;  Regularity  and  sym- 
metry, 241  ;  Goethe's  metamorphosis,  243;  The  ideal  type,  245;  Paltcon- 
tology,  247  ;  Cuvier's  catastrophism,  250  ;  Study  of  analogies,  250  ; 
Geoffroy  Saint-Hilaire,  253  ;  Cuvier  and  Geoffroy,  255  ;  Richard  Owen, 
257  ;  Study  of  homology,  258  ;  The  cellular  theory,  260  ;  Hugo  von 
Mohl,  262  ;  Schleiden  and  Schwann,  263  ;  Transition  to  tlie  study  of 
development,  264  ;  Affinity,  267  ;  Insufficiency  of  the  morphological 
view,  270;  Herbert  Spencer's  "physiological  units,"  272;  Change  of 
scientific  interests,  273  ;   The  morphological  period,  274. 

CHAPTER    IX. 

ON   THE   GENETIC   VIEW   OP   NATURE. 

Statics  and  dynamics  of  living  forms,  276;  "Evolution,"  278;  "Genesis," 
279  ;  Leibniz's  '  Protogaa,'  280  ;  Kant's  nebular  theory,  282  ;  Laplace, 
284;  "Cyclical"  view,  286;  Supplanted  by  genetic  view,  290;  Geology, 
290  ;  Hutton,  292  ;  Lyell,  293  ;  Embryology,  296  ;  Epigenesis  and  evolu- 
tion, 298;  C.  F.  Wolff,  298;  Pander  and  K.  E.  von  Baer,  299;  Von 
Baer's  comprehensive  views,  302  ;  Von  Baer's  views  in  modern  terms, 
306  ;  Phylotaxy  and  phylogenesis,  308  ;  Lamarck,  309 ;  The  term 
"Biology,"  312  ;  "Environment,"  314  ;  The  "Natur-philosophie,"  315  ; 
Lamarck  and  Von  Baer,  816;  The  'Vestiges,'  318;  Popular  influence, 
320  ;  Genetic  view  in  Germany  and  France,  321  ;  Apologetic  literature 
in  England,  324  ;  Mansel  and  Darwin,  326 ;  Triumph  of  the  genetic 
view,   328;    Humboldt's   'Kosmos'  and  the   'Origin  of  Species,'   329; 


CONTENTS. 

"Variation,"  331  ;  Malthus,  332  ;  "Struggle  for  existence,"  333  ;  Out- 
door studies,  334;  "Natural  selection"  and  "sexual  selection,"  336; 
Meaning  of  natural  classification,  336 ;  Fertilisation  of  plants  and 
"Mimicry,"  338;  The  judicial  method,  339;  Darwin  and  Newton 
compared,  341  ;  Unsolved  problems,  343  ;  Genetic  view  on  a  large 
scale,  345  ;  Phi1nsophica1  theories,  346  ;  Herbert  Spencer,  346  ;  Haeckel, 
347  ;  CombinesTTarwin  and  Lamarck,  350  ;  Philosophical  problems,  352  ; 
Problem  of  life,  352  ;  Genetic  view  strengthened  by  physics  and  chem- 
istry, 355  ;  The  heat  of  the  sun,  357  ;  Spectrum  Analysis,  359  ;  Genesis 
of  the  cosmos — Faye  and  Lockyer,  360  ;  Palseontology  and  geophysics, 
363  ;  Dissipation  of  energy,  364  ;  Mystery  of  the  actual  processes  of 
Nature,  366.  '  "^ 


CHAPTER    X. 

ON   THE  VITALISTIC   VIEW   OF   NATURE. 

The  cosmical  and  the  terrestrial  views,  369  ;  Vagueness  of  biological  theories, 
370  ;  Impossibility  of  prediction,  372  ;  Oscillation  of  biological  thought, 
374  ;  The  unknown  factor,  375  ;  The  purely  scientific  aspect,  377  ;  In- 
fluence of  medicine,  379 ;  Practice  urges  the  question  :  What  is  life  ? 
381  ;  Bichat,  381 ;  His  Vitalism,  383  ;  His  definition  of  life,  383  ;  Vital- 
ism and  Darwinism,  386  ;  The  extreme  vitalism,  388  ;  Attack  from  the 
side  of  chemi.stry,  389  ;  Change  in  organic  chemistry,  393  ;  Influence  of 
Liebig,  394  ;  " Stoflwechsel"  and  "Kreislauf  des  Lebens,"  395  ;  "Auto- 
nomy of  the  Cell,"  395;  "Division  of  Physiological  Labour,"  396; 
Johannes  Miiller,  397  ;  Influence  of  doctrine  of  energy,  399  ;  Mechanism, 
399  ;  Lotze  and  Du  Bois-Reymond,  401 ;  Liebig's  vitalism,  405  ;  Darwin, 
406  ;  Lotze  and  Claude  Bernard,  409  ;  Darwinism  and  final  causes,  411  ; 
"Natural  result"  against  "purpose,"  413;  Organisation  and  individua- 
tion, 415  ;  Biology  and  economics,  415 ;  The  cellular  theory,  417  ; 
Schwann,  419;  Circulation  of  matter  and  energy,  420;  "Metabolism," 
422 ;  Structural  analysis  of  morphological  elements,  423  ;  Synthesis  of 
organic  substances,  425;  The  "physical"  method,  428;  Properties  of 
the  living  substance,  429  ;  Environment,  430  ;  The  "internal  medium," 
432;  Natural  selection  within  the  organism,  435  ;  Mobility  of  living 
matter,  438  ;  Anabolism  and  Catabolism,  442 ;  Reproduction,  443  ;  The 
protoplasmic  theory,  444  ;  Spencers  law  of  limit  of  growth,  445  ;  Fusion 
of  two  elements,  446  ;  New  problems,  448  ;  Weismann  on  heredity,  450  ; 
Biogenesis,  451  ;  The  ubiquity  of  life,  452  ;  The  continuity  of  living 
forms,  453  ;  "  Pangenesis,"  454  ;  Germ-substance  and  body-substance, 
457 ;  Germ-plasma  and  body-plasma,  458  ;  DiSerentiation  of  germ- 
plasma,  459  ;  Weismann  v.  Lamarck,  460  ;  Two  aspects  of  the  problem 
of  life,  462  ;  Transition  to  psycho-physics,  464. 


C'UN  TENTS.  Xi 

CHAPTER    XI. 

ON   THE    rSYCHO-PHYSICAL   VIEW   OF   NATURE. 

Abstract  and  concrete  sciences,  405  ;  Their  different  nieth<Hl«,  466  ;  Inner 
experience,  468  ;  P.sycho-physics,  469  ;  Cabaniw'rt  simile,  470  ;  Preporcl 
by  Locke  and  Haller,  471  ;  Berkeley's  'Theory  of  Vision,'  472  ;  BcruouUi 
and  Euler,  474  ;  Animal  electricity,  475  ;  Phrenology,  476  ;  Dr  Young'* 
colour  theory,  480  ;  Charles  Bell,  481  ;  Miiller's  "8i>ecific  ener><ie»,"  482  ; 
Hehnholtz,  485;  "Timbre"  defined,  488;  Analogy  between  h'>un<l  and 
colour,  489 ;  Helmholtz  and  Kant,  491  ;  The  brothers  Wel)er,  492 ; 
Fechner's  Psycho-physics,  493  ;  Influence  of  Herbart,  494  ;  I  lis  attitck 
on  the  "faculty-psychology,"  495;  Unity  of  mental  life,  496;  Mathe- 
matical psychology,  498  ;  Lotze's  physiology  of  the  soul,  500  ;  Two  nidf* 
of  Lotze's  doctrine,  502 ;  The  p.sycho-physics  of  vision,  504  ;  Wheat- 
stone's  stereoscope,  505  ;  Localisation  of  sensations,  507  ;  Lotze's  "  local 
signs,"  508  ;  Fechner,  508  ;  Wundt,  511  ;  Physiological  i)8ychology,  512  ; 
Wundt,  Fechner,  and  Lotze  compared,  515  ;  The  unity  of  consciouHnew. 
516 ;  Doctrine  of  parallelism,  518  ;  Miinsterberg,  521  ;  Phenomenon  of 
centrali-sation,  524  ;  Externali.sation  and  growth  of  mind,  525;  Wundt's 
treatment  of  central  problem,  525  ;  Introspective  nietlKKl,  527  ;  Tlie 
"objective  mind,"  529;  Its  study  prepared  by  Herder,  5:51;  His 
'History  of  Mankind,'  534;  Separation  of  natural  and  mental  sciences, 
534  ;  The  problem  of  language,  536  ;  The  exact  treatment,  53S  ; 
Phonetics,  539;  The  dividing  line  between  man  and  brute,  541  ;  Sum- 
mary, 543  ;  The  three  facts  impressed  by  psycho-physics,  545  ;  Trani>i- 
tiou  to  statistics,  546. 

CHAPTER    XII. 

ON    THE   STATISTICAL   VIEW   OF   NATURE. 

Life  and  Mind  as  limiting  conceptions,  548  ;  Results  of  abstract  science,  550  ; 
.  Uncertainty  in  the  concrete,  552  ;  Scientific  spirit  in  businetw,  553  ;  The 
science  of  large  numbers,  555  ;  Belief  in  general  order,  556j  Rju-onj«_ 
"  Method  of  In.stances,"  557j  General  idea  underlying  enumci-ation, 
561  ;  Doctrine  of  averages,  561  ;~ Statistics  in  France,  Germany,  an<l 
England,  562  ;  John  Graunt  and  Halley,  564  ;  Probability,  Co-oiKration, 
E.iuitable  Distribution,  566  ;  The  Science  of  Chances,  568  ;  Condorcet, 
570  ;  Laplace,  572  ;  Four  applications,  574  ;  Theory  of  Krn.r,  574  ; 
Method  of  Least  Squares :  Gauss,  576  ;  Laplace,  578  ;  guetolet,  579  ; 
The    "mean  man,"  580;  Social   statistics   and    freewill,   5S3  ;    Buckle, 


Xll  CONTENTS. 

584 ;  Criticism  of  pretension  of  statistics,  586  ;  Historical  criticism, 
588  ;  Application  in  physics,  589  ;  Clausius  and  Clerk  -  Maxwell,  590  ; 
Mathematical  representation  of  experimental  laws,  592  ;  Irreversibility 
of  natural  processes,  593  ;  Lord  Kelvin,  594  ;  "  Availability  "  a  theorem 
in  probability,  597;  "Selection"  as  conceived  by  Clerk-Maxwell,  598; 
Statistical  knowledge  of  nature,  600 ;  As  opposed  to  historical  and 
mechanical  knowledge,  603 ;  Sameness  and  variation,  607 ;  Darwin, 
608;  Galton,  609;  "Pangenesis,"  610;  Lends  itself  to  statistical 
treatment,  611  ;  Problem  of  Heredity,  613  ;  Mr  Bateson's  historical 
treatment,  615;  "Particulate"  descent,  615;  Application  of  theory 
of  error,  618  ;  Difference  in  application  to  living  and  lifeless  units, 
620 ;  Professor  Pearson  :  The  mathematical  problem,  621  ;  Statistical 
knowledge  one-sided,  624  ;  Critical  methods,  626  ;  The  instrument 
of  exact  research,  626. 

CHAPTER    XIII. 

ON   THE   DEVELOPMENT   OF   MATHEMATICAL   THOUGHT  DURING 
THE   NINETEENTH   CENTURY. 

History  of  thought,  627 ;  Difference  between  thought  and  knowledge,  628  ; 
Pojjular  prejudices  regarding  mathematics,  628  ;  Use  of  mathematics, 
630 ;  Twofold  interest  in  mathematics,  632 ;  Origin  of  mathematics, 
634  ;  Gauss,  636  ;  Cauchy,  636  ;  Process  of  generalisation,  638  ;  Inverse 
operations,  639  ;  Modern  terms  indicative  of  modern  thought,  643  ; 
Complex  quantities,  644 ;  The  continuous,  644 ;  The  infinite,  644  ; 
Doctrine  of  series :  Gauss,  645  ;  Cauchy's  Analysis,  647  ;  Revision  of 
fundamentals,  649  ;  Extension  of  conception  of  number,  650  ;  The 
geometrical  and  the  logical  problems,  651  ;  Quaternions,  654 ;  Founda- 
tions of  geometry,  656  ;  Descriptive  geometry,  658  ;  Poncelet,  659 ; 
Cliaracter  of  modern  geometry,  662 ;  Method  of  projection,  663 ;  Law 
of  continuity,  664  ;  Ideal  elements,  664  ;  Principle  of  duality,  665  ; 
Reciprocity,  666 ;  Steiuer,  667-;  Mutual  influence  of  metrical  and  pro- 
jective geometry,  668  ;  Pliicker,  Chasles,  Cayley,  671  ;  Historical  aqd 
logical  foundations,  671  ;  Generalised  co-ordinates,  673  ;  Ideal  elements, 
674  ;  Invariants,  676  ;  Theory  of  forms,  678  ;  Theory  of  numbers,  680  ; 
Symmetry,  681  ;  Determinants,  682  ;  Calculus  of  operations,  684  ;  Prin- 
ciple of  substitution,  686  ;  General  solution  of  equations,  687  ;  Theory 
of  groups,  689  ;  Continuous  and  discontinuous  groups,  691  ;  Theory  of 
functions,  693 ;  Physical  analogies,  696 ;  The  potential,  698  ;  Riemann, 
700 ;  Weierstrass,  702  ;  Riemann  and  Weierstrass  compared,  707  ;  Ex- 
amination of  foundations,  709  ;  Non-Euclidean  geometry,  712 ;   Curva- 


CONTENTS.  Xlll 

ture  of  space,  715  ;  Generalised  conceptions,  717  ;  Klein's  exposition, 
718;  Sophus  Lie,  719;  Theory  of  numbers,  721;  Gauss's  tlie<>ry  of 
congruences,  723  ;  Generalised  conception  of  number,  726  ;  Process  of 
inversion,  727  ;  Rummer's  ideal  numbers,  728  ;  Modern  algebra,  730  ; 
Algebraical  and  transcendental  numbers,  730  ;  Counting  and  measuring, 
732 ;  Georg  Cantor's  theory  of  the  transfinite,  735  ;  Corresix)ndence, 
736  ;  Arithmetising  tendency  in  mathematics,  738. 


RETROSPECT  AND  PROSPECT. 

Order  and  Unity,  742 ;  Philosophical  problems,  743 ;  Individuality,  746 ; 
Practical  interests  attaching  to  Order  and  Unity,  748  ;  The  geographical 
centre  of  philosophic  thought,  750. 


Index      .........       753 


ERRATA. 


p. 


Y  Read  Miller  instead  of  Millar. 


47  ;  text,  1.  4  from  below 

48  ;  2nd  col.  of  notes,  1.  8  from  below 

100  ;  2nd  col.  of  notes,  1. 10  from  below   \  „     ,  ^,     ,      •    .     ,    /■  r..      i 

>  Read  Chasles  instead  of  Charles. 

101  ;  2nd  col.  of  notes,  1.  2  from  below     J 

361  ;  1st  col.  of  notes,  1.  5  from  above  .  Read  Secchi  instead  o/Seechi. 

f  Read  C.  Hauptmann  instead  of 
407  ;  2nd  col.  of  notes,  last  word           .    |       Kaufmann. 

572  ;  text,  1.  5  from  above    .         .         .  .Read  Stirling  instead  o/ Sterling. 


CHAPTER   VI. 

ON    THE    KINETIC    OR    MECHANICAL    VIEW    OF    NATURE. 

It  was  a  favourite  idea  witli  the  philosophers  of  antiquity        i- 
that  every  thing  is  in  motion,  that  rest  is  to  be  found  '""tionin 
nowhere  in  nature,  and  that  the  entire  process  of  life  and  i''"'''*op'^>- 
sensation  in  particular  is  Ijrought  about  by  the  communi- 
cation and  transference  of  minute  movements  of  a  purely 
mechanical  kind.      Out  of  the  deep  conviction  that  every- 
thing around  us  and  in  us  is  in  a  perpetual  flux — a  doc- 
trme  which  is  usually  fathered  upon  Heraclitus  of  Ephe- 
sus  ^ — two  distinct  problems  resulted,  and  occupied  the 
thinkers   of   antiquity :    the  problem   of   explaining   the 
apparent  rest  and  permanency  of  many  observable  pheno- 


^  Tlie  doctrine  of  Heraclitus  (b.c. 
500;  is  placed  by  Zeller  (' Philo- 
sophie  der  Griechen,'  vol.  i.)  in 
direct  o])po.sition  to  that  of  the 
Eleatic  School  (Parmenides,  Zeno) 
and  of  Pythagorais.  The  Eleatics 
argued  from  the  unity  of  all  exist- 
ence to  the  impossibility  of  the  mul- 
tiplieity  and  the  change  of  things. 
Heraclitus  sets  out  from  the  concep- 
tion that  everything  is  in  continual 
motion  and  flow  {Ki.vii(T%ai,  iv  Kivr\aii 
tlvai).  Our  knowledge  of  Herac- 
litus is  derived  mainly  from  refer- 
ences in  tlie  writings  of  Plato  and 
Ari8t<jtle.     K  very  full  account  i'^ 


given  by  Zeller,  and  by  E.  Pfleiderer 
( '  Die  Philosophic  des  Heraklit  von 
Ephesus,'  Berlin,  1S8C),  who  sums 
up  the  fundamental  idea  in  the 
beautiful  versesof  i;oethe(Gedichte, 
"  Eins  und  Alles  ")  :— 

"  Uiul  uiMZUscliiifft'ii  (las  Gfschall'iie 
Daiiiit  sicli's  niclit  zuiii  .Starien  wall'ne, 
Wiikt  fwigts,  UlifiiHii^;f.s  Thuii. 
Und  was  iiiclit  war,  nun  will  es  werdeu, 
Zu  reincn  .Sinmen,  farbij,'en  Erden. 
In  keineni  Fallo  darl' I's  rulin. 

Es  soil  sicli  regen,  scliatletid  liandtdn, 
Erst  sich  gcstalteii,  dann  verwandk-n  ; 
Nur  sclieinbar  stclit's  Monieute  still. 
Uas  Ewige  regt  sich  fort  in  Allen  : 
Denn  Alles  muss  in  Niclits  zerfullen, 
Wenn  es  im  Sein  V>eharren  will." 


4  SCIENTIFIC    THOUGHT. 

mena  and  properties  of  natural  objects,  and  the  higher 
ethical  problem  of  fixing  upon  that  which  is  lastingly 
real  and  important  in  the  continuous  change  of  sensation 
and  opinion.  The  latter  formed  the  central  interest  of 
that  course  of  reasoning  which  began  with  Socrates  and 
culminated  in  Plato  and  Aristotle ;  the  former  was  the 
problem  of  natural  philosophy  of  which  Epicurus  and 
Lucretius  stand  out  as  the  great  representatives.  In 
a  well-known  passage  of  the  second  book  of  his  great 
poem,  Lucretius  explains  the  apparent  rest  of  natural 
things  by  the  simile  of  a  flock  of  lustily  dancing  sheep, 
which  at  a  distance  looks  like  a  white  spot  on  a  green 
hillside/  This  tendency  of  philosophic  reasoning  to  see 
motion  where  common-sense  only  sees  rest,  to  reduce 
theoretically  the  apparently  permanent  properties  of 
things  to  a  play  of  intricate  but  imperceptible  modes 
of  motion,  has  governed  still  more  markedly  modern 
scientific  thought.  I  shall  comprise  all  efforts  to  give 
more    definite "    expression    to    this   general   idea    under 

1  '  De  Natura  Rerum,'  ii.  308—  Omnia  qute  nobis  longe  eonfusa  videntur 

Et    velut   in    viridi    candor    oonsistere 

"Illud  in  his  rebus  non  est  mirabile,  colli." 

quare, 

Omnia cuni rerum primordiasint  inmotu,  o  rpj^j^  ^^^^^  definite  expression  is 

Sumnia    tamen    summa  videatur    stare  ;          ...                    .          .         ', 

quigtg  !    entn-ely  a  que.stion  or  niatneniatics. 

Prseterquam  siquid  proprio  dat  corpora    ;    It   is   interesting  to  note    how    Le 

™ot"s.  ,  .       ^  .,  ^aEre,  in   his   '  Lucrece  Neutonien ' 

Omms^^en.m  longe  nostris    ab  seHsibus    ^    ^g^^^.^  ^^^^     ^-gg^^  ..^^.g^^^  ^j^^^ 

Primorum  natura  jacet ;  quapropter,  ubi    [    if  Epicurus  bad  had  but  a  part  of 

the  geometrical  knowledge  of  his 
contemporary  Euclid,  and  concep- 
tions of  cosmography  the  same  as 
those  of  many  then  living,  he  might 


ipsa 
Cernere  jam  nequeas,  motus  quoque  sur- 

pere  debent ; 
Prsesertim  cum,  qu»  possimus  cernere, 

celent  ^                      ^.             ^ 

Ssepe   tamen  motus    spatio  diducta  lo-  ;    Y^^ye    discovCTed    the   laws  of  imi- 

Nan?sa"i"'in  colli  toiidentes  pabula  l»ta  ;    versal    gravity,    and    not   only  _  the 

Lanigerse  reptant  pecudes  quo  quamque  laws,  but,  what  was  the  despair  of 

vncantes  Newton,    its     mechanical    cau.se  " 

Invitai.t  herb*  pemraantes  rore  recenti,  /'ATinirn    '  T.noretiu*  '  vol   ii   n   13.5^ 

Et  satiati  agni  ludunt  blaudeque  coru«-  (Munro      i^ucretius    ^ol  u  p.  i60). 

cant;  I    Lionardo  da  Vinci  (1452-1519)  says  : 


KINETIC    OK    MECHANICAL    VIEW    OF    NATURE.        5 

the  name  of  the  kinetic  ^  theory  or  view  oi  uaiuie. 
It  has  frequently  been  phiced  in  opposition  to  the  atomic 
theory,  and  the  history  of  the  natural  philosophy  of  the 
earlier  ages,  down  to  Newton,  has  in  recent  years  been 
written  from  this  point  of  view.^  If  everything  is 
motion,  there  must  still  be  something  that  moves,  and 
the  question  arises,  What  is  it  that  moves  ?  The 
system  of  Epicurus,  and  the  great  poem  in  which  it  has 
found  a  classical  expression,  are  really  more  occupied  with 
describing  the  final  elements  of  matter — the  so-called 
nature  of  things — than  with  studying  the  different  modes 
of  their  motion.  In  the  atomic  theory,  in  the  conception 
of  an  infinite  number  of  moving  particles,  the  kinetic 
tendency   of   thought    repeatedly   found    botli   in   auricnt 


"  There  is  no  certainty  in  science 
■where  some  mathematics  are  not 
appHcable "'  (quoted  by  Lasswitz, 
'  Geschichte  der  Atomistik,'  1890, 
vol.  ii.  p.  11)  ;  and  Leibniz,  in  a 
letter  to  Foucher  dated  1693,  con- 
demns his  earlier  tract  entitled 
'  Hypothesis  Physica  '  as  a  ''juvenile 
attempt  of  one  who  had  not  yet 
fathomed  mathematics "  (Ger- 
hardt's  edition  of  Leibniz's  '  Philo- 
so])hische  Schriften,'  vol.  i.  p.  415). 
1  The  word  "  kinetic "  seems  to 
have  been  introduced  into  scientific- 
literature  Ijy  Ampere,  who  uses  the 
term  "  cin(5mati([ue  "  to  denote  that 
portion  of  mechanics  where  ' '  les 
mouvements  sont  considores  en  eux- 
memes,  tels  que  nous  les  observons 
dans  les  corps  qui  nous  environ - 
nent,  et  sjiecialement  dans  les 
appareils  appek's  machines  "  (  '  Essai 
sur  la  Philosojihie  des  Sciences,' 
1834).  In  English  text-books  the 
term  kinematics,  following  Thom- 
son and  Tait  ( '  Natural  Philnsophy,' 
Preface),  is  used  to  dcuDte  what 
PVench  writers   call  "  cincmatique 


pure,"  formerly  called  "phoro- 
nomie,"  the  doctrine  of  the  purely 
geometrical  properties  of  motion, 
without  reference  to  the  cause  of 
motion ;  the  consideration  of  the 
latter  being  the  special  study  of 
"kinetics,"  which,  together  with 
"  statics,"  is  comprised  in  the  term 
"dynamics."  The  acceptance  of 
the  word  "  kinetic  "  to  denote  the 
view  that  motion  is  at  the  bottom 
of  all  natural  jirocesses  dates  prob- 
ably from  the  writings  of  Thomson 
(Lord  Kelvin),  Tait,  and  Clerk 
Maxwell,  who,  under  the  influence 
of  Newton  and  the  great  French 
school  of  Lagrange,  Ampere,  Poin- 
sot,  Poncelet,  and  others,  have  re- 
formed English,  and  subse<iuently 
also  German,  thought  and  nomen- 
clature in  these  subject-s. 

-  I  refer  to  the  highly  interesting 
and  important  work  of  Professor 
Kurd  Liisswiti!,  '  (Jcschichte  der 
Atomistik  vnm  ^littelalter  bis 
Newton,'  2  vols.,  Hamburg  and 
Leipzig,  1890. 


SCIENTIFIC    THOUGHT. 


Descartes' 
develop- 
ment of 
the  kinetic 
view. 


and  modern  times  a  convenient  resting-place ;    but  the 
repose  which  it  afforded  has  never  l^een  long  enjoyed ; 
every  new   attempt  to   attach    permanent,   ultimate,   or 
intrinsic  properties  to  matter,  or  to  its  particles,  has  pro- 
voked the  desire  to  explain  these  properties  by  going  still 
farther  back,  and  to  see  in  them,  through  the  dissecting 
microscope  of  the  mind's  eye,  a  still  more  hidden  motion. 
Two    of    the  most  suggestive   ideas    by   which  physical 
science  has  benefited  in  the  nineteenth  century  are  the 
successful  explanation  of  the  dead  pressure  of  gases  by 
a  rapid  translational,  and  of  the  rigidity  of  solid  bodies 
by  a  rapid   rotational,   motion   of  matter.      The   second 
of  these  suggestions  is  far  from  being  exhausted  in  its 
capabilities ;  the  working  out  of  the  ultimate  problems 
which  it  suggests  will  be  one  of  the  principal  tasks  of 
the  coming  acre. 

The  kinetic  view  of  nature,  however  useful  and  suggest- 
ive it  may  have  shown  itself  to  be  in  recent  times,  did  not 
yield  any  fruits  of  real  knowledge  either  in  the  hands  of 
the  ancients  or  even  in  those  of  the  first  great  philoso- 
pher of  modern  times,  in  those  of  Descartes.  Just  like 
attraction  and  atomism,  the  kinetic  theory  had  to  be 
worked  out  by  the  instruments  of  measurement  and  calcu- 
lation, by  the  exact  method,  before  it  led  to  any  actual 
results.  The  kinetic  view  of  nature  was  made  scientifi- 
cally possible  when  Newton,  in  the  First  Book  of  the 
'  Principia,'  laid  down  for  all  time  the  laws  of  motion. 
And  yet  we  can  hardly  say  that  Newton  himself  developed 
this  promising  vein  of  exploration ;  for,  even  while  open- 
ing out  an  endless  vista  of  research,  he  also,  in  the  enun- 
ciation of  the  so-called  law  of  gravitation,  afforded  only 


KINETIC    OR    MECHANICAL    VIEW    OF    NATUKK. 


one  of  those  convenient  resting-places,  those  preliminary 
or  provisional  bases  of  thought,  from  which  definite  prob- 
lems could  be  attacked  and  solved.  His  immediate 
intluence  lay,  therefore,  rather  in  discountenancing  the 
attempts  towards  a  kinetic  view  of  nature,  which  belonged 
to  the  school  of  Descartes,  and  found  an  eminent  exponent 
in  Huvsens  as  well  as  in  others  of  his  contemporaries  and  ■.'.. 
rivals ;  ^  in  fact,  he  launched  into  existence  what  I  have  an.i  n.  wto.,. 
termed  the  astronomical  view  of  nature,  under  the  sway 
of  which  the  promising  beginnings  of  the  kinetic  view 
were  for  a  long  period  almost  forgotten,  but  which  has 
the  merit  of  having  built  up  the  most  perfect  of  all 
physical  sciences,  namely,  physical  astronomy. 

The  sporadic  beginnings  of  a  genuine  kinetic  view  of  ^^^..J^^  ^^ 
natural  phenomena,  after  having  been  cultivated  with  "eJ'!" tile 
more  or  less  success  by  Huygens  and  Euler,"  and  early  ccntun-. 


'  Among  these,  of  whom  Lasswitz 
gives  an  exhaustive  account,  must 
be  mentioned  specially  Robert 
Hooke  (1635-1703).  "In  the  his- 
tory of  tlie  corpuscular  theory  Hooke 
represents  quite  an  original  idea, 
which  would  have  been  of  the  most 
far-reaching  importance  if  Hooke 
himself  had  got  beyond  a  mere 
sketch  to  an  exhaustive  theory,  or 
if  his  conceptions  had,  through 
Huygens'  principles  of  dynamics, 
been  domiciled  in  science.  Tiie 
deviation  from  kinetic  theories 
caused  by  Newton's  discoveries 
brushed  away,  with  much  useless 
hypothetical  rubbish,  likewise 
Hooke's  more  valuable  and  legiti- 
mate suggestions.  The  doctrine 
owing  to  which  we  place  Hooke 
between  Borelli  and  Huygens  is  his 
vibratory  theory  of  matter.  It  is 
given  in  various  writings,  but  most 
clearly  in  his  Lectures  '  l)e  Potentia 
Restitutiva,  or  of  Spring  explaining 


the  Power  of  Springing  Bodies,' 
London,  1678  "  {op.  cit.,  vol.  ii.  p. 
329  sq.) 

-  Leonhard  Euler  (1707-83), 
one  of  the  greatest  analytical 
talents  of  all  times,  whose  writings 
contain  the  beginnings  of  a  very 
large  portion  of  subsequent  mathe- 
matical work  in  pure  and  applied 
science,  was  in  physics  a  great 
opponent  of  Newton's  philosophy 
as  it  was  then  generally  expounded 
on  the  continent  of  Europe.  There 
it  was  identified  in  mechauios 
with  the  theory  of  action  at  a 
distance,  and,  in  optics,  with  the 
corpuscular  theory  of  light.  To 
both  Euler  opposed  his  ether 
theory,  of  which  he  gave  a  popular 
account  in  his  celel)rated  '  Lettres  ii 
une  princesse  d'Allemagne [Princess 
of  Anhalt  -  Dessau]  sur  quelques 
sujets  de  physique  et  de  philoso- 
phie"  (Petersburg,  176S-7'2,  3  parts). 
He   had   given  a  seientirtc  exposi- 


8 


SCIENTIFIC    THOUGHT. 


Young  and 
Fresnel. 


in  the  nineteenth  century  by  Eumford  and  Young,  were 
united  into  a  consistent  physical  theory  by  Augustin 
Fresnel,  who  has  been  termed  the  Newton  of  optics,  and 
who  consistently,  and  all  but  completely,  worked  out  one 
great  example  of  this  kind  of  reasoning.  He  has  the 
glory  of  having  not  only  established  the  undulatory 
theory  of  light  on  a  firm  foundation,  but  still  more  of 
having  impressed  natural  philosophers  with  the  import- 
ance of  studying  the  laws  of  regular  vibratory  motion  and 
the  phenomena  of  periodicity  in  the  most  general  manner. 
His  work  was  carried  through,  as  was  that  of  Newton, 
by  a  combination  of  observation,  measurement,  and  calcu- 
lation ;  of  experimental  skill  with  mathematical  ability. 


tion  of  the  same  twenty-five  years 
before  in  his  Berhn  memoir,  "  Sur 
la  lumiere  et  les  eouleurs"  (1745). 
Euler  was  as  much  opposed  to 
Descartes'  and  Leibniz's  views  as 
he  was  to  those  of  Newton,  and 
though  he  admits  having  forerun- 
ners, he  hardly  refers  to  the 
principal  one,  viz.,  Huygens,  whose 
well  -  known  and  useful  prin- 
ciple he  absolutely  ignores.  In 
fact,  in  spite  of  his  great  name  and 
reputation,  his  ideas  on  the  ether  as 
continuously  filling  space,  and  his 
attempts  to  explain  the  phenomena 
of  light,  heat,  magnetism,  and 
even  gravitation  by  means  of  this 
continuum  remained  isolated,  and 
had  hardly  any  influence  on  physi- 
cal science.  His  great  friend  and 
correspondent,  Daniel  Bernoulli, 
remained  a  firm  believer  in  action 
at  a  distance,  and  thought  Euler 
had  put  forward  his  hypotheses 
with  too  much  assurance.  It  is, 
nevertheless,  remarkable  how 
closelj-  the  terms  in  which  Euler,  in 
his  posthumous  work  '  Auleitung 
zur  Naturlehre'  (edited  by  the 
Petersburg  Academy  in  the  second 


volume  of  the  ' '  Opera  posthuma 
.  .  .  anno  1844  detecta,"  1862), 
describes  his  ether  as  continuously 
filling  empty  space  and  existing  in 
a  strained  (gcwaltsam)  condition, 
agree  with  quite  modern  ideas  on 
the  subject.  Accordingly  Euler's 
ether  theory  has  in  recent  times 
been  studied  again  by  several 
writers  abroad,  of  whom  I  will  only 
mention  E.  Cherbuliez,  '  Ueber 
physikalische  Arbeiten 
(Bern,  1872)  ;  F.  Rosen- 
'  Die       Geschichte      der 

(vol.  ii.,  1884,  p.  333  sqq.); 
C.  Isenkrahe  in  '  Zeitschrift  fiir 
Mathematik  und  Physik  '  (Hist.  Lit. 
Abth.,   vol.    xxvi.)    and    '  Abhand- 

zur  Geschichte  der  Mathe- 

vi. ;  and  E.  Miething,  '  L. 
Lehre  vom  Aether  '  (Berlin, 

The  first-mentioned  author 
tries  to  answer  the  question  why 
Euler's  ideas  remained  so  isolated. 
He  says  (p.  49):  "If  we  combine 
the  results  of  Huygens'  and  Euler's 
investigations,  we  see  that  in  the 
'fifties  of  the  eighteenth  century  the 
undulatory  system  formed  a  largely 
developed  scientific  doctrine.    ,   .  . 


eniige 
Eulers ' 
berger, 
Physik' 


lungen 
matik, 
Eulers 
1894) 


KINETIC    OR    MECHANICAL    VIEW    OF    NATURE.        9 

There  is  not,  indeed,  to  be  found  in  Fresnel's  work  .my 
central  and  simple  formula — like  the  gravitation  formuhi 
of  Newton — out  of  which  everything  else  Hows  with 
mathematical  necessity.  His  work  lay  rather  in  combin- 
ing u  number  of  fruitful  suggestions  thrown  out  by 
contemporary  or  earlier  writers  into  a  consistent  whole, 
correcting  and  enlarging  them  as  was  found  necessary, 
and  following  them  out  into  their  logical  consequences. 
Thus  he  was  able  to  reveal  in  a  special  branch  of  physical 
science  new  phenomena  which  had  remained  unoljserved 
or  unexplained  till  that  time.  In  order  to  understand 
how  the  kinetic  view  of  nature  has  become  firmly  estab- 
lished in  the  minds  of  physicists,  it  will  l)e  useful  to  enum- 


In  a  certain  sense  Euler  carried 
further  the  work  of  Huygeus,  .  .  . 
but  as  he  neglected  the  useful  idea 
of  a  wave-surface  and  anxiously 
avoided  Huygens'  principle,  lie 
made  the  theory  which  he  wished 
to  defend  unfruitful.  .  .  .  We  think 
that  Euler  did  more  harm  than 
good  to  the  progress  of  that  theory. 
.  .  .  Euler's  theory  of  light  had  no 
great  number  of  followers."  In 
England  Euler's  theory  was  known 
and  generally  condemned.  Priest- 
ley, in  his  '  History  of  Optics ' 
(1772),  refers  to  it  at  some  length. 
In  the  well-known  attacks  in  which 
Lord  Brougham  treated  so  unfairly 
and  superficially  the  discoveries  of 
Dr  Young,  it  is  suggested  that  the 
latter  borrowed  his  ideas  from 
Euler,  whose  natural  philoso])hy  is 
held  in  little  esteem.  The  fact  is 
that  Young  really  went  back  to 
Huygens  and  Newton,  and  that  he 
well  knew  that  his  own  opinion, 
as  stated  in  the  first  Bakerian 
Lecture  (1802),  "was  precisely  the 
theory  of  Hooke  and  Huygens,  with 
the  adoption  of  some  suggestions 


made  by  Newton  himself  as  not  in 
themselves  improbable "  (Young's 
'Miscellaneous  Works,' ed.  Peacock, 
vol.  i.  p.  200).  In  spite  of  the 
great  admiration  which  Young  had 
for  Euler  as  a  mathematician,  he 
admits  that  Euler  "added  no 
argumentative  evidence  whatever  to 
the  [uudulatoryj  theory,  but  has 
done  a  real  injury  to  the  cau.se 
which  he  endeavoured  to  support  " 
('  Lectures  on  Natural  Philosophy,' 
ed.  Kelland,  vol.  i.  p.  380).  A  more 
recent  and  well-informed  writer  on 
this  subject,  M.  Verdet,  says  of 
Euler  :  "  Bien  qu'il  a  donnc?  de  la 
plupart  des  pln^nomcnes  connus  de 
son  temps  les  explications  les  plus 
inexactes,  il  ne  m3rite  pas  moins  de 
conserver  dans  I'histoire  de  I'ojitique 
une  place  ominente  jiour  avoir  dit 
d'une  maniore  exjjrcssc  que  les 
ondulations  lumineusessont  ])Oriod- 
iques  comnie  les  vibrations  sonores, 
et  ([ue  la  cause  des  differences  de 
coloration  est  au  fond  la  monie,  que 
la  cause  des  differences  de  toualit«5  " 
('(Kuvres  de  Fresnel,'  vol.  i.  p. 
xix). 


10 


SCIENTIFIC    THOUGHT. 


erate  shortly  the  different  suggestions  which  Fresnel 
assimilated  and  worked  up  into  his  celebrated  physical 
theory  of  light. 

That  light  consisted  in  the  motion  of  something  was 
in  the  beginning  of  the  nineteenth  century  a  generally 
accepted  notion  among  natural  philosaphers.  It  had 
been  so  ever  since  Olaus  Eomer^  in  the  seventeenth 
century,  from  the  observation  of  the  hitherto  unexplained 
delay  in  the  disappearance  of  Jupiter's  satellites  during 
eclipses,  had  inferred,  and  Bradley'^  had  later  on  con- 


^  The  moons  of  Jupiter,  of  which 
two  are  visible  to  the  naked  eye, 
were  clearly  seen  and  described  as 
one  of  the  first  discoveries  with  his 
telescope  by  Gahleo  in  1610,  and 
published  in  his  '  Sidereus  Nuncius.' 
Owing  to  their  continual  and  rapid 
change  of  position  and  their  fre- 
quent eclipses,  they  were  very  soon 
considered  to  furnish  a  valuable 
means  of  determining  the  longi- 
tude at  sea,  and  were  repeatedly 
and  very  minutely  observed.  In 
the  course  of  such  observations  by 
Cassini  and  Romer  at  Paris,  the 
latter  found,  in  1675,  that  the  period 
of  occultation  of  the  nearest  moon 
varied.  This  variation  he  traced 
to  the  fact  that  the  earth  was 
moving  towards  or  away  from 
Jupiter.  If  light  takes  time  to 
travel,  the  visibility  of  the  pheno- 
menon is  necessarily  thus  antici- 
pated or  postj^oned.  This  was  the 
first  occasion  on  which  data  for  the 
calculation  of  the  velocity  of  light 
were  forthcoming ;  the  terrestrial 
experiments  of  Galileo  having  been 
inconclusive.  Romer's  explanation 
and  calculation  were  accepted  by 
most  astronomers  ;  they  were  con- 
firmed by 

-  the  phenomenon  of  aberration, 
discovered  by  Bradley.  It  is  ana- 
logous to  the   observation    we  can 


make  in  a  moving  railway  train 
if  it  rains  ;  the  drops  at  the  win- 
dow, though  they  be  descending 
perpendicularly,  yet  appearing  in 
a  slanting  direction,  in  propor- 
tion to  the  velocity  of  the  train. 
Both  phenomena  involve  the  mo- 
tion of  light  itself  and  the  motion 
of  the  observer,  who  receives  the 
luminous  impression  and  locates  it 
in  space  and  time.  The  principle 
involved  in  Romer's  discovery  was 
later  enunciated  by  Doppler,  who 
maintained  that  the  very  shoi-t 
periods  which  belong  to  different 
coloui's  of  the  spectrum,  according 
to  the  undulatory  theory,  must 
suffer  (like  the  longer  periods  in 
Riimer's  occultations)  by  the  mo- 
tion of  the  luminous  object  or  of 
the  observer  in  the  line  of  sight.  Al- 
though this  theory  was  admitted 
in  acoustics,  it  took  some  time 
before  it  was  admitted  in  optics. 
Bolzano,  Professor  of  Religious  Phil- 
osophj'  and  a  colleague  of  Doppler 
at  Prague,  foretold  as  early  as  1842 
the  great  utility  of  the  principle, 
and  wrote :  "I  foresee  with  con- 
fidence that  use  will  be  hereafter 
made  of  it  in  order  to  solve — by 
observing  the  changes  which  the 
colour  of  stars  undergoes  in  time 
— the  questions  whether  and  in 
which     direction    and    with    what 


KINETIC    OK    MECHANICAL    VIEW    OF    NATLKE.        11 

firmed,  tliat  light  takes  time  to  travel  from  one  point 
ill  space  to  another.  Wherever  time  is  involved  in  a 
phenomenon,  motion  of  something  is  suggested,  and 
this  something,  as  well  as  the  nature  of  its  motion, 
become  subjects  of  speculation.  At  the  beginning  of  5. 
the    nineteenth    century    two    distinct    theories    existed  andemusion 

theoriea. 

regarding  these  matters.  Both  had  succeeded  in  ex- 
])laining  and  calculating  satisfactorily  a  large  number 
of  the  phenomena  of  light  as  exhibited  by  mirrors  and 
lenses,  as  well  as  in  optical  instruments  and  crystals. 
One  of  these  theories,  the  so-called  emission,  emanation, 
or  corpuscular  theory  of  light,  held  that  luminous 
bodies  send  out  minute  particles  which  travel  in 
straight  lines,  and,  impinging  upon  the  eye,  create  the 
sensation  of  light.  The  rival  hypothesis,  the  undul- 
atory  or  vibratory  theory,  held  light  to  consist  in 
the  periodic  wave-motion  of  a  substance  called  ether, 
which  was  supposed  to  exist  everywhere,  filling  all 
space  and  interpenetrating  all  ponderable  matter.  Both  e. 
theories  are  kinetic  or  mechanical  theories,  and  for  their  theories 

kinetic. 

development  require  the  analysis  of  certain  modes  of 
motion.  Both  liad  to  formulate  their  respective 
notions  as  to  the  something  that  moved.  Both  could 
point  to  analogies  in  other  domains  of  natural  science. 
There  existed  at  that  time  similar  corpuscular  ex- 
planations   of    the    phenomena    of    heat,    of    electricity 

velocity    tliey   move,    how    (li.staut  William   Huggins  (1S6S),   Kox-Tiil- 

they  are  from  u.s,  and    mucli    else  '    bot,   and   others.     That   Doppler's 

he-sidex,"  a  jjrediction  which,  since  principle  i.s  really  none  otiier  than 

the  invention  of  spectrum  analysis  U()mer".s    was    )-emarked    by    P.   G. 

and  various  controversies  connected  Tait  in  'Light'  ^•2nd  eil.,   p.   '220). 

witli  the  subject,  has  been  brilliantly  ^    See    also    Hoscnborgor,   '  Gescli.   d. 

verified    by  the  discoveries  of  Sir  Physik,'  vol.  iii.  p.  708  Kq(j. 


prepared  by 
acoustics. 


12  SCIENTIFIC    THOUGHT. 

and  of  magnetism.  On  the  other  side  there  was  the 
highly  developed  theory  of  sound,  which  had  succeeded 
in  explaining  and  analysing  the  properties  of  sound- 
ing bodies  by  studying  experimentally  and  mathe- 
matically the  vibrations  of  sounding  strings,  membranes 
and  plates,  and  also  of  the  air  in  organ-pipes  and  other 
7.        musical   instruments.     Acoustics,  the  branch  of  science 

Undulatory 

DreuSed  bv  ^^hich  treats  of  these  phenomena,  was,  next  to  physical 
astronomy,  the  furthest  developed  and  best  founded  of 
the  physical  sciences.  By  following  up  the  elemen- 
tary and  primitive  experience,  known  already  to  the 
ancients,  that  sound  is  everywhere  to  be  traced  to  the 
vibrations  or  the  tremor  of  some  body  which  has  been 
struck  or  otherwise  excited,  a  very  complete  theory, 
substantiated  by  many  experiments,  had  been  built  up. 
Common-sense  and  everyday  experience  had  originally 
suggested  this  line  of  inquiry  and  explanation.-^  No 
other  physical  science  was  so  early  in  possession  of  the 
right  road  of  inquiry.  In  astronomy  and  optics  the 
suggestion  of  common-sense,  which  regards  the  earth 
as  stationary  and  light  as  an  emission  travelling  in 
straight  lines,  had  indeed  allowed  a  certain  amount  of 
definite   knowledge,  based   upon   measurement   and   cal- 

1  Acoustics  is  probably  the  only  I    covery,  like  universal  gravitation,  or 

phj'sical    science    where    this     has  luminiferous  undulations,  we  take 

been     the     case;     as    is    well    re-  our  stand  upon  acknowledged  truths, 

marked  by  "\Miewell  in  his  '  History  the  production  and  propagation  of 

of    the    Inductive    Sciences.'      He  sound    by   the    motion    of    bodies 

there  contrasts  acoustics   with   as-  ;    and  of  air;  and  we  connect  these 

tronomy   and    optics.       He    might  i    with    other    truths,    the    laws    of 

have  added  dynamics,  where  Gal-  motion,  and  the   known  properties 

ileo's  principle  of  inertia  similarly  of    bodies,    as    for    instance   their 

reversed  the  dicta  of  common-sense.  elasticitj\       Instead    of    epochs    of 

Whewell   says   (vol.   ii.   p.  237)   of  i   discovery,    we    have    solutions    of 

acoustics  :    "  Instead  of   having  to  problems. " 
travel  gradually  towards  a  great  dis- 


kine:tic  or  mechanical  view  of  nature.     13 

dilation,  to  be  accumulated.  A  real  physical  theory, 
however,  was  impossible  until  the  notions  suggested 
by  common  -  sense  were  completely  reversed,  and  an 
ideal  construction  put  in  the  place  of  a  seemingly 
obvious  theory.  This  was  done  in  astronomy  at  one 
stroke  by  Copernicus ;  in  optics  only  gradually,  tenta- 
tively, and  hesitatingly.  The  purely  geometrical  rela- 
tions of  straight  lines,  which  light  seemed  to  resemble ; 
of  pencils  of  rays,  which  were  bent  back  or  altered  in 
their  direction  at  the  surface  of  plane  or  curved  mirrors 
and  of  transparent  bodies ;  seemed  to  flow  quite  easily 
and  naturally  when  in  the  seventeenth  century  the 
simple  law  of  refraction  had  been  added  to  that  of 
reflexion,  known  already  to  the  ancients.  The  sciences 
of  catoptrics  and  dioptrics,  with  their  application  to  the 
telescope  and  microscope,  were  thus  so  complete  and 
useful  that  to  many  it  must  have  seemed  ditticult  and 
unnecessary  to  plunge  into   a    new  theory ;  ^    especially 

'   It  has  always  been  the  aim  of  process"  (Tait,  'Light,'  "ind  ed..  p. 

"  geometrical  optics  "  to  free  itself  160).  Owing  to  the  difBculties 
from  every  hyi)othesis  on  the  physi-  i  which  liave  more  and  more  jire- 
cal  nature  of  light,  and  to  deduce   '   sented  themselves  in  the  fundamen- 

properties  of  light  from  a  tew  simple  tal  conceptions  f)f  the  wave-theory 

geometrical  const  ructions.  Precisely  and  the  vibrating  ether,  of  whicli 

in  the  same  way  all  geometrical  and  we  shall  learn  more  in  the  sequel  of 

many    jjhysical    i)roperties    of    the  this  chapter,  the  desire  to  bring  the 

stellar  system  can  be  deduced  from  j)henomena    of  refraction   under    a 

the  kinematical  formula  of  attrac-  purely  geometrical  formula,  and  to 

tion,  without  discussing  the  nature  emancipate  the    optics   of   crj'stals 

of  gravitation.      This  desideratum  from    physical  hypotheses,   has  be- 

— so  far    as  optics    is  concerned —  come  very  pronounced.      Huygens' 

was  before  the  mind  of  .Sir  W.  U.  geometiical     coustiut-tioM    of     the 

Hamilton,  when,   during  tlie  yeai's  ordinary  and  extraordinary  raj'.s  in 

1824-33,  he  discovered  and  elabor-  uniaxial     crystals    answered     well, 

ated  the  theory  of  the  "  character-  For  luaxial  crystals  Fresnel  had  in- 

istic  function,  by  the  helj)  of  which  troduced  the  wave-surface,  towliicli 

all  optical  problems,  whether  on  the  corresponds   Hamilton's    i-haracter- 
corjmscular  or    on  the    uiidulatory    '    istic  function.     For   didactic    pur- 

tlieory,  are  solved  by  one  coniiium  poses,  and  for  the  practical  applica- 


14 


SCIENTIFIC    THOUGHT. 


8. 
Newton's 
authority 
on  the 
Bide  of  the 
emission 
theory, 


as  that  theory  failed  for  a  long  time  to  explain  the 
apparently  fundamental  fact,  viz.,  that  light  travels  in 
straight  hnes,  accompanied  by  well  -  marked  shadows. 
The  contrary  view,  according  to  which  light  is  a  tremor 
propagated  like  sound,  was  unable  to  explain  the  ex- 
istence of  clearly  marked  shadows.  And  so  it  came 
about  that  Newton,  to  whom  both  theories  were  qiute 
familiar,  and  to  whom  we  owe  great  discoveries  telling 
severally  in  favour  of  each  of  these  theories,  in  the 
end  threw  the  weight  of  his  authority  into  the  scale 
of  the  corpuscular  or  emission  theory.  For  many  this 
was  quite  sufficient  to  suppress  for  a  long  time  all 
claims  which  the  tremor  or  wave  theory  put  forward, 
the  fact  being  forgotten  or  overlooked  that  Newton 
himself  had  pronounced  the  pure  emission  theory  to 
be  insufficient,  and  had  modified  and  complicated  it  by 


tion  to  crystallography,  it  became  a 
desideratum  to  reach  the  geometri- 
cal conception  of  the  wave-surface 
by  purely  geometrical  methods. 
This  has  been  done  in  an  admir- 
able treatise  entitled  '  The  Optical 
Indicati-ix,'  by  Mr  L.  Fletcher.  He 
has  shown  that  the  construction  of 
the  ray,  a  conception  easily  defined 
geometrically,  gives  an  easier  ap- 
proach than  the  construction  of 
the  wave,  which  introduces  phj'si- 
cally  doubtful  definitions ;  and 
he  demonstrates  how  "  a  simple 
generalisation,  involving  no  refer- 
ence either  to  the  constitution 
of  the  luminiferous  ether  or  to 
the  nature  of  the  physical  change 
involved  in  the  transmission  of 
light,"  will  lead  to  the  ray  surface 
(p.  IS).  For  his  purpose  he  starts 
from  a  surface  of  reference,  which 
in  singly  refractive  substances  is 
a    sphere,   in   uniaxial    crystals    a 


spheroid,  and  by  inference  in  biaxial 
crystals  an  ellipsoid  with  three  un- 
equal axes.  This  beautiful  con- 
struction was  arrived  at,  as  the 
author  tells  us,  before  the  detailed 
history  of  Fresnel's  theorj'  had 
come  to  his  notice.  It  is  now 
known  through  Verdet,  one  of  the 
editors  of  Fresnel's  '  Works  '  (1868), 
that  Fresnel  arrived  at  his  wave- 
surface  by  a  purelj'  geometiical 
generalisation  of  Huygens'  con- 
struction, and  that  the  conception 
of  the  ether  was  subsequently 
fixed  so  as  to  allow  the  wave  surface 
to  be  deduced  therefrom  (p.  24) ; 
surely  an  interesting  case  in  the 
history  of  scientific  thought.  As 
to  the  insufficiency  of  purely  geo- 
metrical optics  for  explaining  the 
phenomena  connected  with  optical 
instruments,  see  Czapski,  '  Theorie 
der  optischen  Instrumente,'  Bres- 
lau,  1893,  p.  2. 


KINETIC    OK    MECHANICAL    VIEW    OF    NATURE.       15 

suggesting  tluiL  the  rays  of  light  were  possessed  of  tits  of 
eusy  transmission  and  reflexion,  i.e.,  of  regular  periodic 
changes  which  could  be  measured  and  numbered.  To 
this  amplification  of  the  simple  geometrical  emission 
theory  Newton  was  driven  by  his  own  immortal  researches, 
which  revealed  the  wonderful  regularly  arranged  colours 
of  thin  plates  known  as  Newton's  rings.  In  reading, 
after  the  lapse  of  nearly  two  centuries,  the  reflections  of 
Newton  on  the  nature  of  light,  reflections  which  he  never  9. 
gathered  up  mto  a  compact  and  exhaustive  treatise,  as  he  minpests 
did  the  theory  of  gravitation,^  we  recognise  that  he  had  t'-eory. 
clearly  before  his  mind  the  two  fundamental  phenomena 
peculiar  to  light,  namely,  its  property  of  travelling  in 
straight  lines,  and  its  periodicity,  as  revealed  by  certain 
delicate  experiments  of  his  own.  Which  of  the  two 
theories  should  in  the  end  prevail  depended  on  the  more 
intimate  knowledge — to  be  gained  by  experiment  and 
calculation — of  the  two  kinds  of  motion  involved  ;  of 
rectilinear  motion  of  particles  under  the  influence  of 
contending  forces,  and  of  the  more  complicated  periodic 
motion  pecuhar  to  waves,  tremors,  or  oscillations.  The 
first  kind  of  motion,  being  more  easily  studied  and 
also  more  nearly  related  to  other  prevailing  studies, 
received   earlier    attention  ;    the    second  —  especially   so 


^  It  is  now  sufficiently  known 
and  recognised  that  Newton,  both 
in  the  theory  of  gravitation  and 
that  of  Hglit,  did  not  pro[io8e  to  do 
more  than  give  a  preliminary  formu- 
lation which  was  applicable  as  a 
ba-sis  for  e.\perimentand  calculation. 
His  further  speculations  are  con- 
tained mostly  in  the  well  -  known 
'yu<?riea'  to   the  'Opticks,'  which 


were  extended  in  later  editions,  and 
among  which,  "  to  show  that "  he 
"  did  not  take  gravity  for  an  esseu- 
tial  property  of  bodies,"  he  adiled 
one  (juestion  concerning  its  cause, 
choosing  to  projiose  it  by  way  of  a 
question,  because  "  he  was  not  yet 
satisfied  about  it  for  want  of  experi- 
ments" (Advertisement  to  second 
edition,  1717). 


16 


SCIENTIFIC    THOUGHT. 


10. 
Biot, 
Brewster, 
and  Laplace 

against  the 
undulatory 
theory. 


11. 
Euler  the 
successor 
of  Huygens. 


12. 
Young. 


far    as    the    mathematical    side    was    concerned  —  was 
studied  later.     The   former   theory   has   been   furthered 
more    by    the     ingenuity     of     physical     observers,    the 
latter   more   by  mathematical  reasoning  applied  to   the 
invention   of   crucial   experiments    which   pure    observa- 
tion would  probably  never  have  suggested.      Since  the 
time  of  Newton,  whose  name  has  been  used  in  a  one- 
sided way   to   discredit   the  vibratory  theory,  although, 
as  already  stated,  his  discoveries  contributed  equally  to 
the   formation   of   both  views,   the   development   of   the 
corpuscular     theory    owes     most    to    the     experimental 
labours  of  Biot  in  France  and  Brewster  in  this  country ; 
whilst  no  doubt  Laplace's  great  predilection  for  atomic 
and  astronomical  explanation  of  all  natural  phenomena 
gave  it  great  support  in  the  eyes  of  his  many  followers 
and    admirers.       The   vibratory    theory   was   first   made 
the    subject    of    detailed    study    by   Huygens,   Newton's 
contemporary ;   it  was  accepted  on  purely  mathematical 
grounds  by  Euler :  the  lines  of  reasoning  on  which   its 
ultimate  success  depended  were  elaborated  by  Lagrange's 
and  d'Alembert's  mathematical  study  of  \dbrations ;   but 
the  first  great  step  in  advance,  based  upon  experiment 
and   calculation    alike,   was   taken   by   Dr   Young,   who 
from    1793    onward   studied   the    subject,   and   who    in 
1801  published  his  'Principle  of  Interferences.'     Young 
was  led  to  his  reflections  on  the  phenomena  of  light  by 
an  inquiry  into  the  nature  of  sound,^  a  province  where 

^  In  his  '  Reply  to  the  Edinburgh  degree    in    physic  at  Gottiugen,   it 

Reviewers '   (published  as    a   pam-  was  necessary,  besides  publishing  a 

phlet    in     1804,     see    Works,    ed.  medical    dissertation,    to    deliver  a 

Peacock,  vol.  i.  pp.  192-215),  Young  lecture  upon  some  subject  connected 

gives  the  following  history  of    his  with  medical   studies,  and  I  chose 

speculations:     "When    I    took    a  for  this  the  Formation  of  the  Human 


KINETIC    OR    MECHANICAL    VIEW    OF    NATURE.        17 

the  theory  of  vibrations  iuid  idready  acliieved  so  much. 
He  was  thus  more  interested  in  the  physical  nature  than 
in  the  geometrical  properties  of  rays  of  light.  He  was 
imp«ressed  by  the  analogies  which  exist  between  many 
phenomena  of  sound  and  light,  and  acquainted  with  the 
writings  of  the  Continental  mathematicians,  among  whom 
Euler  was  conspicuous  as  favouring  the  undulatory  or 
ether  theory  of  Huygeus.  He  noticed  that  in  Xewton's 
writings  were  to  be  found  the  germs  of  both  theories, 
also  that  the  arguments  by  which  Newton  convinced  him- 
self that  a  theory  of  undulations  could  not  explain  the 
rectilinear  propagation  of  light,  were  untenable.^  On  re- 
flecting in  May  1801  on  Xewton's  beautiful  experiments, 


Voice.  .  .  .  Wheu  I  began  the  out- 
line of  an  essay  on  the  human  voice, 
I  found  myself  at  a  loss  for  a  per- 
fect conception  of  what  sound  was, 
and  during  the  three  years  that  I 
passed  at  Emmanuel  College,  Cam- 
bridge, I  collected  all  the  informa- 
tion relating  to  it  that  I  could 
procure  from  books,  and  I  made  a 
variety  of  original  experiments  on 
sounds  of  all  kinds,  and  on  the 
motions  of  fluids  in  general.  In 
the  course  of  these  inquiries  1 
learned  to  my  surprise  how  much 
further  our  neighbours  on  the 
Continent  were  advanced  in  the 
investigation  of  tlie  motions  of 
sounding  bodies  and  of  elastic  fluids 
than  any  of  our  countrymen  ;  and 
in  making  some  experiments  on  the 
production  of  sounds,  I  was  so 
forcibly  impressed  with  tlie  resem- 
blance of  the  phenomena  that  I  saw 
to  those  of  the  colours  of  thin  plates, 
with  which  1  was  already  acquainted, 
tliat  I  began  to  suspect  the  exist- 
ence of  a  closer  analogy  between 
tliem  than  I  could  before  have 
easily  believed  "  (p.  199).     This  led 

VOL.  II. 


to  his  'Outlines  of  Experiments 
and  Inquiries  respecting  Sound  and 
Light '  (ibid.,  p.  64). 

i  Works,  vol.  i.  p.  200.  "  New- 
ton's arguments  from  experiment 
appear  to  me  to  have  been  sutti- 
ciently  obviated  by  what  Lambert 
has  advanced  in  the  '  Memoirs  of 
Berlin.'  .  .  .  The  demonstration  is 
attempted  in  the  '  Principia' :  to  me 
it  appears  to  be  defective.  .  .  . 
The  celebrated  Laplace,  in  com- 
paring the  opinions  respecting 
light,  is  contented  to  call  the 
Newtonian  doctrine  a  hypothesis, 
which,  on  account  of  the  facility 
of  its  application  to  the  plienomena, 
is  extremely  probable.  If  he  had 
considered  the  undulatory  system 
as  demonstrably  absurd,  he  would 
not  have  expressed  himself  in  so 
undecided  a  maimer.  .  .  .  !Mucli 
as  I  venerate  tiio  name  of  Newton, 
1  am  not  tiierefore  obliged  to  be- 
lieve that  he  was  infallible.  I  see 
.  .  .  with  regret  that  he  was  liable 
to  err,  and  that  his  autliority  hn.s, 
j)erhaps,  sometimes  even  retarded 
the  progress  of  science,"  &c.,  &c. 

B 


18 


SCIENTIFIC    THOUGHT. 


13. 
His 

' '  general 
law  of  the 


he  "  discovered  a  law  which  appeared  to  account  for  a 
greater  variety  of  interesting  phenomena  than  any  other 
optical  principle  that  had  yet  been  made  known."  ^  This 
principle  he  familiarly  illustrated  by  the  well  -  known 
observation  that  two  series  of  waves  of  water  entering  a 
channel  reinforce  or  destroy  each  other  according  as  their 
elevations  coincide  or  alternate  in  time.  He  main- 
tained that  similar  effects  take  place  whenever  two 
portions  of  light  are  thus  mixed,  and  this  he  called 
"  the  general  law  of  the  interference  of  light."  He 
SYight.^^*^^  showed "  "  that  this  law  agrees  most  accurately  with 
the  measures  recorded  in  Newton's  '  Opticks,'  relative  to 
the  colours  of  transparent  substances,  and  with  a  great 
diversity  of  other  experiments  never  before  explained."  ^ 
In  three  papers  Young  entered  "  minutely  into  the  con- 
sequences of  the  law  of  the  interference  of  light.' 
Especially  in  the  case  of  the  remarkable  phenomena 
discovered  by  Grimaldi,  where  Ught  seems  to  bend  round 
the  edge  of  screening  surfaces,  he  showed  how  under 
certain  conditions  light  added  to  light  would  create 
darkness,  and,  if  removed,  would  leave  light ;  and  he 
^^  boldly  generalised  the  undulatory  theory  by  maintaining 
^t^7  that  *  "  a  luminiferous  ether  pervades  the  universe,  rare 
ether!'  ^™"*'  and    clastic   in   a   high    degree,"   that    the    sensation    of 


»/ 


1  Works,  vol.  i.  p.  202. 

-  Ibid.,  p.  203. 

'  ' '  This,  I  assert,  is  a  most 
powerful  argument  in  favour  of 
the  theory  which  I  had  before 
revived :  there  was  nothing  that 
could  have  led  to  it  in  auj^  author 
with  whom  I  am  acquainted,  ex- 
cept some  imperfect  hints  in  those 
inexhaustible  but  neglected  mines 


of  nascent  inventions,  the  works  of 
the  great  Dr  Robert  Hooke,  which 
had  never  occurred  to  me  at  the 
time  that  I  discovered  the  law " 
(ibid.,  p.   203). 

■^  The  sentences  in  quotation 
marks  are  the  headings  of  the 
different  paragraphs  in  the  "  Baker- 
ian  Lecture  "  of  November  12,  ISOl. 
Works,  vol.  i.   p.    140  sqq. 


KINETIC    OR    MECHANICAL    VIEW    OF    NATURE.        10 


different  colours  depends  on  tlie  difterent  frequency  of 
vibrations  excited  by  light  in  the  retina,  and  "  that  all 
material  bodies  have  an  attraction  for  the  ethereal 
medium  by  means  of  which  it  is  accumulated  within 
their  substance."  In  all  his  conclusions,  while  differing 
from  Xewton's  doctrines,  he  sees  the  strongest  proofs  of 
llie  admirable  accuracy  of  Newton's  experiments,  "  but 
scarcely  any  remaining  hope  to  explain  the  affections 
of  light  by  a  comparison  with  the  motions  of  projectiles."  ^ 
Although  Young  thus  estabhshed  "  a  theory  of  the  nature 
of  light  which  satisfactorily  removes  almost  every  diffi- 
culty that  has  hitherto  attended  the  subject," "'  his  view 
was  only  tardily  accepted.  Wollaston,^  with  the  hesi- 
tancy which  also  characterised  liis  adhesion  to  the 
atomic  theory  of  Dalton,  did  not  avowedly  adopt  Young's 
views,  though  he  furnished  some  capital  experimental 
support  for  the  vibratory  theory  of  light.'' 

Brougham,    in     the     '  Edinburgh     Eeview,'     ridiculed  , 

O  '  o  '  Brougliani  s 

Young's  theories,  and  persuaded  the  public  that  they  yo^ng"'' 
stood  in  contradiction  with  Newton's  discoveries,  on 
which  they  were  really  as  much  founded  as  those  of 
the  opposite  school.  Through  such  disfavour,  arising 
largely  from  a  want  of  skill  in  grasping  the  intricate 
mathematical  problems  whicli  were  involved,  the  doctrine 
of  the  interference  of  light,  the  mainstay  of  the  undula- 


Vj. 


1  Works,  vol.  i.  p.  169. 

-  '  Lectures,' ed.  Kelland,  Preface, 
p.  ix. 

'  "  Whatever  disposition  Dr  Wol- 
laston  may  liave  felt  to  view  this 
theory  with  favour,  lie  was  re- 
strained from  adopting  its  con- 
clusions   by    the    habitual    caution 


of  his  character,  or  rather  by  the 
want  of  that  bold  and  enterprising 
spirit  of  speculation  which  is  more 
or  less  essential  to  those  who 
make  great  revolutions  in  science" 
(Peacock,  '  Life  of  Young,"  p.  375). 
*  Ibid.,  p.  374. 


20 


SCIENTIFIC    THOUGHT. 


tory  theory  was,  like  the  atomic  theory  of  Dalton,  driven 
ovit  of  the  country.  Little  was  heard  of  it,  or  of  Young's 
great  contribution,  till  it  was  taken  up  abroad,  and  in  the 
very  place  where  the  brilliant  development  by  Laplace  of 
one  side  of  Newton's  suggestions  had  given  plausibility 
to  that  form  of  the  projectile  theory  of  light  accord- 
ing to  which  its  material  particles  were  supposed  sub- 
ject to  attractive  forces  when  they  arrived  in  the 
neighbourhood  of  ponderable  matter.  Young  had 
indeed  shown  that  the  introduction  of  such  forces 
could  easily  be  dispensed  with  as  a  basis  of  many  of 
Laplace's  calculations,  and  that  the  results  could  be 
got  without  making  use  of  molecular  attraction.  He  had 
emancipated  himself  from  a  belief  in  the  infallibility  of 
Laplace's  methods.^     He  was   also   one   of  the   first   to 


s/ 


1  On  the  20th  December  1804, 
Young  presented  to  the  Royal 
Society  his  important  "  Memoir  on 
the  Cohesion  of  the  Fluids. "  It  was 
printed  in  the  '  Transactions'  in  1 805. 
In  December  1805  Laplace  read 
before  the  Institute  of  France,  and 
subsequently  published  in  a  supple- 
ment to  the  '  Mecanique  celeste,'  his 
celebrated  theory  of  capillary 
attraction.  Young  bases  his  inves- 
tigation entirely  on  the  existence 
of  a  surface  tension,  an  ojbservable 
and  measurable  property  ;  whereas 
Laplace  falls  back  upon  the  hypo- 
thesis of  an  attraction  of  the 
smallest  particles  of  matter,  just 
as  he  had  employed  the  idea  of 
an  attraction  of  matter  on  the 
smallest  particles  of  light  to  explain 
atmospheric  refraction  according  to 
the  projectile  theory  adopted  by 
him.  In  the  sequel  this  attraction 
is  reduced  to  an  action  which  is 
insensible  at  sensible  distances.  In 
a  supplement  to  his  memoir,  which 


appeared  anonymously  in  the  fii'st 
number  of  the  '  Quarterly  Review  ' 
(1809),  Young,  evidently  annoj-ed 
that  some  of  his  results  had  been 
reproduced  without  acknowledg- 
ment (see  Peacock, '  Life  of  Young,' 
p.  205),  reviewed  the  treatise  of 
Laplace  "  with  a  severity  which, 
though  excessive,  can  hardly  be 
considered  unprovoked  or  un- 
merited" (ibid.,  p.  206).  Inter 
alia  he  says  :  "  The  point  on  which 
M.  Laplace  seems  to  rest  the  most 
material  part  of  his  claim  to  origi- 
nality is  the  deduction  of  all  the 
phenomena  of  capillary  action  from 
the  simple  consideration  of  molec- 
ular attraction.  To  us  it;  does 
not  appear  that  the  fundamental 
principle  from  which  he  sets  out 
is  at  all  a  necessary  consequence 
of  the  established  properties  of 
matter  ;  and  we  conceive  that  this 
mode  of  stating  the  question  is  but 
partially  justified  by  the  coincidence 
of  the  results  derived  from  it  with 


KINETIC    OR    MECHANICAL    VIEW    OF    NATURE.       21 


emancipate  himself  from  the  astronomical  view  of 
phenomena.  In  France  the  matter  stood  quite  difierently, 
and  nothing  hetter  proves  the  genius  of  Augustin  Fresnel        1.5. 

.  .    .  AuKUBtin 

than  the  fact  that  he  ventured  against  the  opp(Jsition  of  FrcHnei. 
great  authorities  to  go  his  own  way,  starting  from  the 
beginning  and  devising  many  ingenious  appeals  to  nature 
herself — i.e.,  to  experiment — in  order  to  establish  a 
correct  view.  It  is  well  known  that  his  labours  had  to 
wait  many  years  for  their  deserved  appreciation.^  It  is, 
however,  only  just  to  remark  that  Arago,  an  admirer  of 
Laplace  and  an  intimate  friend  of  Biot,  the  great 
supporter  of  the  projectile  theory  of  light,  was  the  first 
to  recognise  the  importance  of  Fresnel's  work,  and  that 
it  was  largely  owing  to  his  co-operation  and  influence 
that  the  undulatory  theory  of  light  trimnplied  in  the  end. 
Fresnel's  own  labours  began  with  the  study  of  the 
same  phenomena  which  had  led  Young  to  the  discovery 
of  "  interference  " — -viz.,  the  bands  and  coloured  fringes 
observable  round  the  shadows  of  small  screening  objects, 
or  the  images  of  small  apertures  through  which  rays  of 
light  are  allowed  to  enter :  the  phenomena  of  diftraction 
or  inflection  of  light.  But  whilst  Young  still  explained 
these  phenomena  as  arising  from  the  interference  of 
direct  "  portions  "  of  light  and  such  as  were  reflected  at 
the  edge  of  the  screening  obstacle,  Fresnel  showed  th.iL  the 
principle  of  interference  had  a  much  wider  application,  that 
it  was  adequate  to  exphiin  why  a  periodic  wave-motion, 
such  as  was  conceived  by  Huygens,  only  sent  out  rays  of 


experiment,  since  he  has  not  de- 
monsstratod  that  a  similar  coinci- 
dence might  not  be  obtained  by 
proceeding     on     totally      different 


grounds"  ('Quarterly  Review,'  No. 
l,p.  109). 

'  See   the    first    volume    of    this 
work,  p.  241  note'-. 


22 


SCIENTIFIC    THOUGHT. 


light  in  the  direction  which  was  in  a  straight  line  from 
the  origin  or  centre  of  light ;  that  the  lateral  or  secondary 
waves  destroyed  each  other  almost  entirely  by  interference 
or  overlapping ;  and  that  the  so-called  inflection,  bending, 
or  lateral  spreading  of  light,  was  occasioned  by  an  incom- 
plete coincidence  or  overlapping  of  these  lateral  undula- 
tions. It  appears  that  about  the  year  1815  Fresnel  had, 
through  a  study  of  the  phenomena  of  diffraction,  arrived 
at  a  conviction,  entertained  by  Young  fifteen  years  earher, 
that  the  projectile  theory  of  light  could  not  explain 
them.  He  had  also,  by  a  more  rigorous  and  minute 
study  of  Young's  principle  of  interference,  explained  the 
reason  of  the  rectilinear  propagation  of  light.  Yet  these 
presented      rcsults   did  uot  materially  affect   the   adherents  of  the 

by  the  '' 

ofughf '^'^  projectile  theory,  who  had  been  during  late  years  very 
active  in  studying  another  class  of  optical  phenomena, 
those  of  polarisation — the  power  which  light  possesses 
of  acquiring,  either  by  refraction  or  reflexion,  a  difter- 
ence  not  discernible  merely  by  the  eye.  This  differ- 
ence consists  in  the  fact  that  a  ray  of  light  very  fre- 
quently— as  Newton  had  already  expressed  it — possesses 
I  "  sides,"  just  as  a  flat  strip  or  narrow  tape  has  sides  if 
compared  with  an  ordinary  thread  or  wire,  which  has  no 
sides ;  or  as  a  wire  drawn  through  a  specially  shaped  die 
acquires  sides  or  edges.  This  property  was  later  termed 
polarity,^  a  term  which  implies  that  the  particles  of  light 


17. 
Difficulties 


1  The  word  "polarity"  was  in- 
troduced by  Malus  in  1810.  It  is 
unfortunate,  as  it  suggests  the  cor- 
puscular nature  of  light.  Newton's 
conception  of  "sidedness"  ("later- 
ality," formed  by  analogy  on  Lord 
Kelvin's  term  "  chirality  "  to  de- 
scribe   right-    or   left  -  handedness, 


see  vol.  i.  p.  432)  is  a  better  de- 
scription of  the  phenomenon.  It  is 
contained  in  the  26th  query  to  the 
second  edition  of  the  '  Opticks ' 
(1717).  Huygens  had  long  before, 
in  his  '  Traite  de  la  Lumiere ' 
(written  in  1678,  published  in  1690), 
after  having  given  a  correct  rule  for 


KINETIC    OR    MECHANICAL    VIEW    OF    NATURE.       23 

have  unequal  properties  in  different  directions ;  and  ilie 
process  of  revealing  it  was  termed  polarisation.  Huygens 
had  discovered  this  property,  which  he  found  was  given 
to  rays  of  light  if  they  passed  through  certain  crystals, 
notaljly  througli  Iceland  spar,  which  has  the  capacity 
of  di^^ding  the  rays  so  that  objects  seen  througli  tliem 
appear  double.  He  could  not  explain  it  on  his 
hypothesis  of  undulations,  though  he  had  invented  a  geo- 
metrical construction  of  the  double  refraction  which  had 
led  him  to  its  discovery.  Malus  showed  in  1808  that 
double  refraction  was  not  a  necessary  accompaniment  of 
polarisation,  l)ut  that  ordinary  reflexion  was  enough  tu 
give  these  sides  to  rays  of  light.  Although  the  projectile 
theory  gave  no  complete  explanation  of  this  property, 
still  the  supposition  that  this  one-  or  many-sitledness 
was  owing  to  certain  geometrical  shapes  of  the  i»ro- 
jected  particles  suggested  that  double  refraction  might 
be  explained  by  the  different  attraction  or  repulsion 
which  these   particles  suffered   according    to   tlie  aspect 

determining  the  course  of  the  ordl-  liglit  "  (Works,  vol.  i.    |i.  247).    And 

uary  and  extraordinary  rays  in  Ice-  Plains  himself,  in  writing  to  Young 

land    spar,    described    the    pheno-  as  Foreign  Secretary  of  the   Royal 

menon  fully,  admitting  at  the  same  Society,   by   whom    he    had    been 

time  that  he  could  not  explain  it.  awarded  the  Rumford  Medal,  >ay8  : 

When  Malus  discovered  that  light  "  Je  ne  regarde  pa.s  la  connaissance 
might   acquire    this    peculiar    pro-    ,    de    ces    phononienes    counue    plus 


perty  by  reflexion,  Young  wrote 
in  a  review  ('Quarterly  Review,' 
May  1810):  "The  discovery  .  .  . 
appears  to  us  to  be  by  far  the  most 
important  and  interesting  that  has 
been    made    in    France,  concerning 


favorable  au  sj'stome  de  roniis.sion 
qu'h  celui  des  ondulations.  lis  do- 
montrent  ^galement  linsuffisanoe 
des  deux  hypotheses  ;  en  etlet  com- 
ment expliijuer  dan.s  I'une  ou  dans 
I'autre  pounjuoi  un  rayon  polarii«^ 


the  properties  of  light,  at  least  since    '    pent  traverser   sous    uiie    certaine 

the  time  of  Huygens ;  and  it  is  so  inelinaison  uu  corps  diaphnne,  eu 

much  the  more  deserving  of  notice,  se   ddrobant    totalement    k    la    n.^- 

as  it  greatly  influences  the  general  flexion  partielle  qui  a  lieu  h  la  sur- 

balance    of    evidence    in    the   com-  face  de  ces  corps  dans  les  ciui  ordi- 

parison  of  the  undulatory  and  the  naires  ?"  (quoted  l>y  Peacock,  'Life 

projectile  theories  of  the  nature  of  of  Young,'  p.  248  note). 


24  SCIENTIFIC    THOUGHT. 

which  they  presented  when  approaching  ponderable  or 
attracting  substances.  Nothing  of  this  kind  seemed 
imaginable  on  the  undulatory  theory,  which,  reasoning 
from  the  analogy  of  sound,  considered  light  to  consist 
in  a  rapid  to-and-fro  motion  of  the  ether  in  the  direc- 
tion of  the  rays  of  light.  Sidedness  or  "  laterahty " 
seemed  inconceivable.  Eays  of  light  possessing  this 
property  would  (as  Fresnel  and  Arago  showed  in  1816) 
eventually  even  lose  their  capabihty  of  interference,  that 
main  property  discovered  by  Young,  the  principal  argu- 
ment for  the  vibratory  theory.  "  Every  day  in  that 
remarkable  period — when  so  many  great  observers  were 
endeavouring  to  outstrip  each  other  in  the  career  of 
discovery — was  making  known  modifications  and  phe- 
nomena of  polarised  light  which  no  existing  theory  was 
yet  competent  to  explain.  It  was  polarisation  which 
still  continued  to  cast  a  dark  cloud  over  the  hopes  and 
fortunes  of  the  undulating  theory."  ^  Thus  it  was 
natural  that  the  representatives  of  the  astronomical  view 
of  nature,  who,  headed  by  Laplace,  had  given  so  many 
real  and  some  apparent  explanations  of  complicated  phe- 
nomena, and  to  whom  the  conceptions  of  the  projectile 
theory  of  light  seemed  more  promising,  should  think  it 
time  to  attack  the  very  stronghold  of  the  \abratory  theory, 
namely,  the  phenomena  of  interference,  exhibited  mainly 
in  diffraction,  and,  by  a  minute  experimental  and  mathe- 
matical analysis,  show  whether  these  phenomena  could 
not  be  brought  within  the  pale  of  their  fundamental  con- 
ceptions. For  the  discoveries  of  Young  and  Fresnel  had 
not  shaken    them.     Accordingly  the  Paris  Academy  of 

1  Peacock  in  '  Life  of  Young,'  p.  383. 


KINETIC    OR    MECHANICAL    VIEW    OF    NATURE.       25 


Sciences  in  1817  issued  for  the  competition  on  the  j^iand 
mathematical  prize  for  1  S  1  0  the  subject  of  DilTraction, 
"  jiersuaded  that  a  deeper  investigation  of  these  phenijmena, 
which  seemed  opposed  to  their  cherished  doctrine,  wcjidd 
give  occasion  for  new  triumphs."  ^  In  this  lliey  were 
doomed  to  disappointment.  At  the  request  of  Arag(j  and 
Ampere,  Fresnel  entered  for  this  competition,  and  his 
*  Meinoire  sur  la  Diffraction '  was  crowned  the  following 
year.  In  it  he  viewed  the  subject  from  a  much  more 
general  point  of  view,  examining  the  two  rival  systems — 
that  of  emission  and  that  of  undulations — as  to  their 
capacity  for  explaining  the  phenomena  of  diffraction. 
The  result  seemed  decisive  in  favour  of  the  latter  theory, 
and  the  impression  produced  was  all  the  greater  because 
Poisson,"  one  of  the  judges  and  a  believer  in  the  emission 
theory,  drew  certain  apparently  very  paradoxical  conse- 


18. 


1  Yerdet  in  '  Qiuvres  de  Fresnel,' 
vol.  i..  Preface,  p.  xxxv.,  &c. 

-  The  commissinn  cousisted  of 
Biot,  Arago,  Laplace,  Gay-Lussac, 
and  Poissuii.  Arago  drew  up  the 
report,  which  is  published  in  the 
first  volume  of  the  '  Oiuvres  de 
Fresnel,'  No.  13.  It  closes  with 
the  following  note:  "M.  Poisson, 
depuis  le  rajjport  de  la  commission, 
ayant  fait  remarquer  ii  M.  Fresnel 
que  I'intdgrale  qui  represente 
rintensit(5  de  la  luniicre  difYractie 
peut  aisomeut  s'obtenir  pour  le 
centre  de  I'ombre  d'un  ecran  ou 
d'une  ouverture  circulaires,  celui-ci 
fit  le  calcul  pour  ce  dernier  cas,  et 
trouva  (|ue  I'expression  gendi-ale 
d'intensite  devenait  alors  seinlilable 
h  celle  de  la  lumierc  reflechie  dans 
le  phononiene  des  anneaux  colorcs  ; 
que  868  minima  dtaient  tout  h  fait 
nul  et  devaient  presenter  ainsi  un 
jioir   h.   peu  prds  parfait  dans  une 


lumicre  sensiblenient  honn)g6ne  ;  du 
moins  pour  les  trois  premiers  ordres, 
oil  le  d^faut  d'homogoneitA?  de  la 
lumi6re  rouge  employee  ne  se  fais- 
ait  pas  encore  trop  sentir :  c'est 
aussi  ce  que  Texperience  a  confirmo  ; 
en  plarant  le  foyer  de  la  loupe  du 
micrometre  aux  distances  calculoes 
ou  appercevait  comme  une  tache 
d'encre  au  centre  de  I'ouverture 
circulaire.  .  .  .  Ou  peut  rcgarder 
cette  experience  comme  une  verifi- 
cation des  foi-mules  de  M.  Fresnel," 
&c.  ('Qiuvres,'  vol.  i.  p.  245). 
See  also  the  note  which  Fresnel 
attached  to  his  memoir  (il>id.,  p. 
365).  The  memoir  was  crowned  in 
1819,  Imt  not  publislied  till  1826. 
An  abstract  of  the  first  and  a  re- 
print of  the  second  ]>art  had  been 
publislied  in  tiie  11th  vol  uf  the 
'  Annales  de  Chimie  et  ile  Pliysique.' 
Fresnel  sent  two  co]iie8  to  Vounp, 
19th  September  1819. 


26 


SCIENTIFIC    THOUGHT. 


quences  from  Fresnel's  calculations  :  Fresnel  was  invited 
to  prove  by  experiment  these  astonishing  results,  and  he 
found  them  actually  confirmed.  So  far  as  the  phenomena 
of  diffraction — erroneously  termed  infiection — are  con- 
cerned, this  work  of  Fresnel  established  the  fact  "  that 
the  theory  of  undulations  foretells  the  phenomena  as 
exactly  as  the  theory  of  gravitation  foretells  the  move- 
ments of  the  heavenly  bodies."^  It  was,  however, 
quite  different  if  we  consider  that  other  larger  class  of 
phenomena^  which  revealed  the  fact  that  rays  of  light 


1  See  Schwerd,  '  Die  Beugungs- 
erscheinnugenausdeuFundamental- 
gesetzen  der  Undulations  -  theorie 
aualytisch  entwickelt '  (Mannheim, 
1835),  Preface,  p.  x. 

-  The  history  of  the  final  estab- 
lishment of  the  wave  theory  of 
light  has  been  written  by  Whewell 
in  the  second  volume  of  the 
'  History  of  the  Inductive  Sciences. ' 
The  main  sources  which  existed  at 
that  time  were  the  memoirs  of 
Young  and  Fresnel,  and  the  '  Life 
of  Dr  Young '  by  Peacock.  This 
^  history  has  been  written  again  with 
ampler  materials  by  M.  Verdet  as 
an  introduction  to  the  edition  of 
the  complete  works  of  Fresnel,  pub- 
lished in  1866.  It  is  well  to  read 
both  accounts,  as  some  points  which 
remain  obscure  in  the  earlier  are 
fully  explained  in  the  later.  There 
is  no  doubt  that  Young  suggested 
that  the  phenomena  of  "  sided- 
ness,"  which  rays  of  light  exhibit, 
lead  to  the  conception  of  a  lateral 
or  transverse  movement ;  he  also 
hinted  that  in  biaxial  crystals  the 
shape  of  the  wave  might  be  that 
of  an  almond  or  an  amygdaloid 
(article  "  Chromatics,"  reprinted  in 
Works,  vol.  i.  pp.  317,  322),  v?hat  we 
now  call  an  ellipsoid  ;  but  M.  Ver- 
det is  right  in  characterising  Young's 
suggestions  as  vague,  and  vindicat- 


ing for  Fresnel  the  full  merit  of 
having  defined  transverse  vibrations 
and  of  having  introduced  the  ellip- 
soid of  elasticity  as  a  geometrically 
perfect  means  of  finding  by  con- 
struction the  paths  of  rays  in  biaxial 
crystals.  The  method  was  quite 
independent  of  the  theoretical  views 
regarding  light  which  were  con- 
tained in  the  same  memoir,  the 
consideration  of  which  was  referred 
to  a  commission  consisting  of 
Ampere,  Arago,  Fourier,  and  Pois- 
son.  Of  these  Ampere  had  sug- 
gested transverse  vibrations  as  a 
means  of  explaining  the  phenomena 
of  polarisation  ( '  CEuvres  de  Fresnel,  * 
vol.  i.  p.  394).  Arago,  though  a  great 
friend  of  Fresnel  and  a  believer 
in  the  wave  theory,  never  to  the 
end  of  his  life  accepted  the 
hypothesis  of  transverse  vibrations 
(ibid.,  p.  Iv.)  Poisson,  a  supporter 
of  Laplace's  molecular  theorj%  re- 
tired from  the  commission  ;  and 
Arago,  who  composed  the  Report 
to  the  Academy,  confined  himself 
to  pronouncing  on  the  experimental 
portion,  which  fully  confirmed  the 
general  law  of  double  refraction  an- 
nounced by  the  author  ;  refraining 
from  the  expression  of  any  opinion  as 
to  the  theoretical  portion,  it  being 
premature  to  do  so  (see  '  CEuvres 
de  Fresnel,'  vol.  ii.   p.  463).      Im- 


KINETIC    OK    MECHANICAL    VIEW    OF    NA'ITKK.       2 


~  I 


have  sides,  the  phenomena  of  "  laterality  "  (niLsleacUngly 
called  polarisation).  The  believers  in  the  emission  theory 
studied  them  wiih  predilection,  l>iot  at  their  head.  Al- 
though to  Yoinig  their  explanati<jns  were  unconvincing, 
their  results  were  so  perplexing  that  he  wrote  to  l^rewster 
in  September  1815,  "With  respect  to  my  own  funda- 
mental hypotheses  respecting  the  nature  of  light,  1  be- 
come less  and  less  fond  of  dwelling  on  them,  as  1  learn 
more  and  more  facts  like  those  which  j\lr  Malus  dis- 
covered ;  because,  although  they  may  not  Ite  incompat- 
il)le  with  these  facts,  they  certainly  give  us  no  assistance 
in  explaining  them."  ^  "When  Young  wrote  this,  Fresnel 
had  not  yet  presented  his  first  memoir  on  DiHraction  to 
the  Institute  ;  his  own  labours  on  that  matter  were  more 
than  ten  years  old ;  the  phenomena  of  polarisation  had 
meantime  absorbed  the  attention  of  opticians.  In  the 
summer  of   1816  Arago  and  Gay-Lussac  paid  a  visit  to 

mediately    after     the     reading    of  fraction,    ils    font    disiKiraitre    une 

Arago's  report,  Laplace,  "  who  had  ^    difficulte  qui  ne  pouvait  luauquer  de 

thought  for  a  long   time   that    his  rcsulter  de  toute  dtudetaut  soit  ])eu 

analysis  had   made  the  phenomena  approfondie  de  ses  ecrits  imprimos. 

of  double  refraction  depend  on  his  ...    Un  a  vu  au  contraire  que  cette 

emission    theory,"   proclaimed    the  loi  s'est  manifesto  Ji  Fresnel  coniiue 

great  importance   of    the    memoir,  ,    le  rdsultatd'une  generalisation  toute 

and  declared  that  he  placed  these  semblable    aux    g(?n<5ralisations  iiui 

researches  above  anything  that  had  ont  ameue  la   plupart  dcs  grandes 

for  a  long  time  been  communicated  ,    ducouvertes.      Lorsqu'il     a      voulu 

to  the  Academy  (  'Qiuvres  de  Fres-  ensuite  se  renclre    compte  de  la  loi 

nel',  vol.  i.  p.  Lxxxvi.,  and  vol.  ii.  par  une  thdorie  mecanique,  il  n'e.st 


p.  459).  We  are  indebted  to  M. 
Verdet  for  having  shown  that  the 
discovery  of  this  law  by  Fresnel  is 
independent  of  the  theoretical  con- 
siderations    by    which      he     tried 


pas  etonnant  qu'il  ait,  [leut-ctre  h 
son  insu,  conduit  cette  thoorie  vers 
le  but  qu'il  couuaissj\it  il'avance, 
et  qu'il  ait  itc  determine,  dans  le 
choix     dcs     hyp<'th^ses    au.viliaiies 


synthetically  to  prove  it.     On  this  moins  par  leur  vraisemblance  intriu- 

point    he   says  :    "  En   r(5vdlant  la  suque  tiue  par  leur  accord  avec  ce 

sdrie  de  generalisations  et  de  con-  qu'il    utait   en  droit   de  considiVer 

jectures  par  lesquelles  Fresnel  est  comme  la  verito  "  (ibid.,  vol.  ii,  p. 

arrive   peu    ii  j)eu  a    la   ducouverte  327.      Cf.  vol.  i.  p.  Ixxxiv. ) 
dea  lois  g(5n(jrales  de  la  double  re-  '  Works,  vol.  i.  p.  36 L 


28 


SCIENTIFIC    THOUGHT. 


10. 
Young  and 
Fresnel 
introduce 
the  concep- 
tion of 
transverse 
vibrations. 


England  and  to  Young,  who  learnt  from  them  that, 
mainly  owing  to  Fresnel's  labours,  his  own  researches 
had  "  attracted  much  more  notice  in  Paris  than  in 
London,  .  .  .  leading  to  some  very  warm  discussions 
among  the  members  of  the  Institute  on  some  public 
occasions."  ^  It  is  likely  that  this  visit,  as  well  as  the 
discovery  of  Arago  that  rays  of  light  when  polarised 
— i.e.,  possessed  of  laterality — lose  under  certain  condi- 
tions their  power  of  interference,  induced  Young  to 
resume  seriously  the  consideration  of  the  subject.  In 
January  1817,  long  before  Fresnel  had  made  up  his 
mind  to  adopt  a  similar  conclusion  (suggested  to  him 
by  Ampere),  Young  announced  in  a  letter  to  Arago 
that  in  the  assumption  of  transverse  vibrations,  after  the 
manner  of  the  vibrations  of  a  stretched  string,  lay  the 
possibility  of  explaining  polarisation  or  "  laterality,"  and 
the  non  -  interference  of  rays  whose  sides  are  perpen- 
dicular to  each  other.  By  introducing  this  conception 
of  a  lateral  or  transverse  movement  into  physical  optics 
—  a  conception  shortly  afterwards  adopted  by  Fresnel — 
the  data  were  provided  for  a  complete  mechanical  or 
kinetic  explanation  of  all  phenomena  of  homogeneous 
rays  of  light — i.e.,  of  such  rays  as,  on  passing  through 
refracting  substances,  are  not  divided  into  several 
colours. 

Two  great  problems  now  presented  themselves,  one  of 
which  Fresnel  attacked  with  great  success.  The  other  is 
hardly  yet  solved.  Inasmuch  as  these  tw^o  problems 
have  largely  occupied  physicists  and  mathematicians  all 
through  the  century,  and  guided  their  reasonings  in  other 

1  Peacock,  '  Life  of  Young,'  p.  389. 


KINETIC    OR    MECHANICAL    VIEW    OF    NATL'UE.       29 

l)ianches  of  research,  it   will   l)e   useful   to  deHue  them 
more  clearly. 

Ever  since  Newton  laid  down  the  general  laws  of 
motion,  it  has  been  seen  with  increasing  clearness  t<i  Yte 
the  object  of  mathematical  physics  to  describe  the  exist- 
ing- ol)servable  or  supposed  forms  of  miitJMii  in  nature  by 
having  recourse  to  the  fundamental  laws  of  motion 
coupled  with  the  smallest  possible  number  of  assumptions 
as  to  the  ultimate  constitution  of  matter  or  of  the 
iniiving  substance.  As  soon  as  any  definite  assumption 
was  made,  it  became  necessary  to  follow  it  into  all 
possible  consequences,  and  not  to  make  any  new  assump- 
tions so  long  as  the  capabilities  of  the  old  ones  were  un- 
exhausted, or  so  long  as  it  was  not  shown  either  that  the 
new  assumption  w^as  based  upon  observable  facts,  or 
did  not  involve  latent  contradictions  with  those  already 
admitted.  Newton  had  led  the  way  by  making  one 
great  assumption  in  addition  to  laying  down  the  laws  of 
motion.  This  was  the  property  of  gravitation.  Heed- 
less of  Newton's  warning  that  this  assumption,  though 
proved  by  experiment,  did  involve  certain  seeming 
absurdities  which  called  for  further  examination,  philo- 
sophers like  Boscovich,  and  mathematicians  like  Laplace, 
busied  themselves  with  drawing  all  the  consequences  of 
the  assumption,  and  they  saw  the  most  hopeful  way  of 
further  progress  in  an  extension  of  it  into  the  realm 
of  molecular  physics.  Young  was  probably  one  of  the 
first  to  see  the  futility  or  the  mere  semblance  of  truth 
in  the  astronomical  view  of  nature.  He  approached  both 
by  experiment  and  mathematically  the  great  class  of 
phenomena    of    small,   extremely   rapid,   periodic    move- 


30 


SCIENTIFIC    THOUGHT. 


20. 
Mechanical 
difference 
between 
light  and 
sound. 


ments ;  and  he  applied  his  results  for  the  purpose  of 
gaining  a  new  basis  for  the  theory  of  light.  His  specu- 
lations were,  however,  not  confined  to  this.  He  had 
started  by  studying  sound  and  had  shown  its  analogy 
with  light ;  but  when  he  ultimately  ventured  on  the  bold 
assumption  of  a  lateral  to-and-fro  tremor,  he  showed 
where  the  nature  of  light  differed  from  that  of  sound. 
It  was  in  this :  that  the  tremor  of  sound  was  that  of  an 
elastic  fluid  such  as  air,  or  of  any  substance  in  which  the 
movement  is  carried  forward  by  alternate  compression 
and  expansion.  But  the  phenomena  of  light  seemed  to 
require  for  their  explanation  two  seemingly  incompatible 
assmnptions  :  first,  a  substance  more  subtle  than  air,  incap- 
able of  impeding  the  motion  of  matter  in  it ;  and,  secondly, 
a  substance  having  vibrations  resembling  the  tremors 
of  what  we  term  sohd  bodies,  e.g.,  stretched  strings. 
Young  is  one  of  the  founders  of  the  theory  of  elasticity.-^ 


^  The  hi.story  of  the  theories  of 
elasticity  has  been  written  by  Isaac 
Todhunter  and  continued  by  Pro- 
fessor Karl  Pearson.  A  perusal  of 
the  earlier  portion  of  the  work 
shows  how  imperfect  were  the  ideas 
which  existed  at  the  time  when 
Fresnel  approached  the  problem  in 
the  interest  of  the  wave  theoi-y 
of  light.  The  greatest  mathemat- 
icians, like  Euler,  had  handled  the 
subject,  and  had  damaged  their  rep- 
utation, especially  in  this  country, 
by  serious  errors  or  by  conclusions 
which  agreed  ill  with  experience. 
Young  was  one  of  the  earliest  writers 
on  elasticity  in  the  nineteenth  cen- 
tury ;  having  given  considerable  at- 
telition  to  the  subject  in  his  Lec- 
tures on  Natural  Philosophy  (de- 
livered in  1802,  published  in  1807). 
He  there  introduces  the  modulus  of 
elasticity,  a  term  which,  with  some 


change  of  meaning,  survives  in  mod- 
ern treatises.  His  name,  as  well  as 
that  of  Hooke  ("  Ut  tensio  sic  vis  '"), 
appears  accordingly  at  the  portal  of 
the  science.  Young,  though  Tod- 
hunter has  a  significant  remark  on 
his  obscurity  of  style,  stands  out 
prominently,  if  compared  with  con- 
temjDorary  writers  in  this  country, 
by  his  thorough  knowledge  of  the 
labours  of  Continental  mathemati- 
cians, among  whom  he  assigns  special 
merit  to  Coulomb.  In  general,  Tod- 
hunter has  little  to  say  in  praise  of 
English  science  in  this  department 
during  the  earlier  part  of  the  cen- 
turj',  and  he  considers  the  "  perusal 
of  English  text-books  on  practical 
mechanics  published  in  the  first 
half  of  the  century  a  dispiriting 
task,"  in  consequence  of  a  "  want  of 
clear  thinking,  of  scientific  accuracy, 
and  of  knowledge  of  the  work  ac- 


'!' 


KINETIC    OR    MECHANICAL    VIEW    OF    NATURE.       31 

He  must  have  fully  realised  the  difticulty  of  imagining  a 
substance  more  subtle  than  air  and  yet  endowed  with  the 
property  of  rigidity,  known  to  us  only  in  solid  Ixidies. 
The  elaboration  of  the  theory  of  light  pressed  upon 
physicists  and  mathematicians  a  more  careful  study  of 
the  different  states  in  which  matter  can  exist.  The 
different  properties  which  this  hypothetical  substance  21. 
called  ether  must  possess  had  to  be  mathematically  de- 
fined ;  and,  further,  it  had  to  be  shown  whether  it 
would  be  physically  possible  for  a  body,  subject  to  the 
empirical  laws  of  motion,  to  possess  certain  of  the  pro- 
perties of  what  we  term  solids,  and  yet  to  be  in  other 
respects  the  very  opposite  of  a  solid.  Tlie  solution  of  the 
first  problem  was  a  purely  mathematical  performance,  in 
which  many  eminent  mathematicians,  such  as  Cauchy, 
Neumann,    Green,   M'Cullagh,    and    Stokes,^    have    been 


complished  abroad  "  (vol.  i.  p.  10.')).  :    brothers  Weber,  whose  '  Wellenlehre 

"It  is  difficult  to  picture  the  re-  auf    Experimente    gegriindet'    ap- 

markable    scientific     ignorance    of  peared  in  1825.    In  it  wave-motion, 

practical    men    iu    England   in   the  '    such   a,s  the  theories  of  sound  and 

first  quarter  of  the  century.      One  light  had  made  specially  interesting 

can  only  trust  that  there  may  be  a  and  important,  was  experimentally 

closer  union  of  practice  and  theory  examined     and     illustrated.       The 

in  our  own  day  "  (p.  106).      This  I    theory  of  elasticity  now  received  a 

passage  was  probably  written  iu  the  '   new  ally,   viz.,    tlie  ela-stic   theory 

'seventies.                   "  of  light  or  of  the  ether.     Thougli 

According  to  Todhuntor,  the  true  ,    suggested     by     Fresnel,     its     real 

theory    of    elasticity    was    founded  founder  was  Cauchy. 

in   France  between  the  years  1820  j       ^  The  natural  philosojiher  to  whiun 

and  1830,  by  Xavier,  Poisson,  and  ,    we  are  most  indebted  for  l>ringing 

Cauchy  on  the  one  side  ;  by  the  ex-  clearness  and  definiteness  into  our 

perimeutal  work  of  Savart  on  the  |    ideas   and    our   language   in    these 

other.      It    had    been    allied   with  very  intricate  subjects  is  Sir  Ceoi-ge 

theoretical    acoustics    since  Euler's  Stokes.      In  two  ])apers,   |)ublishcd 

time.       Chladni    in    Germany    fur-  respectively  in  184.')  and   1849  (see 

thered  that  branch  of  the  subject  in  '  Matliematical  and  Thysical  I'ajwrs,' 

three   celebrated   works:  '  Theorie  vol.   i.  pp.  In-l'ld,  and  vol.   ii.   pp. 

des    Klanges'    (1787),     '  Akustik  '  8-13),  he  haa  done  more  than  any 

(1802),     'Beitriige     zur     Akustik'  other  writer  to  fix  for  nearly  half 

(1817).       Chladni     infiuenced    the  a  century  the  conceptionn  and  tlie 


32 


SCIENTIFIC    THOUGHT. 


engaged.  The  solution  of  the  latter  prohlem  involved 
experiment  as  well  as  calculation.  The  different  states 
and  properties  of  matter  had  to  be  studied  from  quite 
novel  points  of  view :  they  had  to  be  defined  in  terms 
of  the  different  kinds  of  motion  and  of  inertia,  i.e., 
resistance  to  motion  or  capacity  for  motion.  The  popular 
conceptions  of  solidity,  rigidity,  fluidity,  expansion,  pres- 
sure, weight,  required  to  be  translated  into  the  language 
of    ordinary   dynamics,    that    it    might   appear   to  what 


vocabulary  of  physical  optics.  He 
has,  however,  whilst  working  inde- 
pendently, been  careful  to  point 
out  to  what  extent  his  views 
agree  with  or  are  anticipated  by 
the  important  writings  of  Cauchy 
and  Poisson  in  France.  Up  to  his 
time  the  ether  was  universally 
spoken  of  as  a  fluid.  Stokes  led 
up  to  the  "elastic  solid"  and  the 
"  jelly  "  theory  of  the  ether.  "Un- 
doubtedly," he  says,  "  it  does  vio- 
lence to  the  ideas  that  we  should 
have  been  likely  to  form  a  priori 
of  the  nature  of  the  ether  to  assert 
that  it  must  be  regarded  as  an 
elastic  solid  in  treating  of  the 
vibrations  of  light.  When,  how- 
ever, we  consider  .  .  .  the  diffi- 
culty of  explaining  these  phenomena 
by  any  vibrations  due  to  the  con- 
densation and  rarefaction  of  an 
elastic  fluid  such  as  air,  it  seems 
reasonable  to  suspend  our  judg- 
ment and  be  content  to  learn  from 
phenomena  the  existence  of  forces 
which  we  should  not  beforehand 
have  expected.  .  .  .  The  following 
illustration  is  advanced,  not  so 
much  as  explaining  the  real  nature 
of  the  ether,  as  for  the  sake  of 
offering  a  plausible  mode  of  con- 
ceiving how  the  apparently  opposite 
properties  of  solidity  and  fluidity 
which  we  must  attribute  to  the 
ether  may  be  reconciled.  Suppose 
a  small  quantity  of  glue  dissolved 


in  a  little  water  so  as  to  form  a 
stiff  jelly.  This  jelly  forms,  in  fact, 
an  elastic  solid :  it  may  be  con- 
strained .  .  .  and  return  to  its 
original  form  when  the  constraining 
force  is  removed,  by  virtue  of  its 
elasticity  ;  but  if  we  constrain  it 
too  far  it  will  break.  Suppose  now 
the  quantity  of  water  to  be  '  in- 
creased '  .  .  .  till  we  have  a  pint 
or  a  quart  of  glue-water.  The  jelly 
will  then  become  thinner.  .  .  .  At 
last  it  will  become  so  far  fluid  as  to 
mend  itself  again  as  soon  as  it  is 
dislocated.  Yet  there  seems  hardly 
sufficient  reason  for  supposing  that 
at  a  certain  stage  of  the  dilution  the 
tangential  force  whereby  it  resists 
constraint  ceases  all  of  a  sudden. 
In  order  that  the  medium  .  .  . 
should  have  to  be  treated  as  an 
elastic  solid,  it  is  only  necessary  that 
the  amount  of  constraint  should 
be  very  small.  The  medium  would, 
however,  be  what  we  should  call  a 
fluid  as  regards  the  motion  of  solid 
bodies  through  it.  .  .  .  Conceive 
now  a  medium  having  similar  pro- 
perties, but  incomparably  rarer 
than  air,  and  we  have  a  medium 
such  as  we  may  conceive  the  ether 
to  be,  a  fluid  as  regards  the  motion 
of  the  earth  and  planets  through  it, 
an  elastic  solid  as  regards  the  small 
vibrations  which  constitute  light " 
(  '  Papers,'  vol.  ii.  p.  11  sqq.) 


KINETIC    OR    iVIECHANICAL    VIEW    oF    NAnUK.       MM 


extent  these  various  properties  could  exist  separately  or 
were  mutually  dependent.^ 

In  the  domain  of  sound  and  light  the  early  part  of 
the  century  was  thus,  as  we  have  seen,  witness  of  a 
useful  interpretation  of  these  various  modifications  as 
merely  different  kinds  of  motion  :  both  were  considered 
to  be  vibrations,  the  frequency  of  which  marked  the 
position  of  a  note  or  a  tint  in  the  musical  or  chromatic 


'  That  is  to  say,  the  number  of 
independent  constants  hiid  to  Ije 
fixed  which  would  permit  isotropic 
or  anisotropic  bodies  (i.e.,  bodies 
which  are  either  equal  in  all  direc- 
tions, or  unequal  in  the  three  direc- 
tions) to  be  mathematically  defined, 
and  in  consequence  their  behaviour 
studied,  if  subjected  to  strains  and 
displacements.  Over  these  defini- 
tions there  arose  the  gi-eat  contro- 
versies of  those  who  believed  in  a 
small  number  of  constants  (one 
constant  in  isotropic  and  fifteen  in 
anisotropic  bodies  against  two  and 
twenty-one  respectively).  A  good 
account  of  these  controversies  and  of 
their  mathematical  and  physical  sig- 
nificance will  be  found  in  the  first 
volume  of  Todhunter's  '  History  of 
Elasticity,'  by  Professor  Karl  Pear- 
son, p.  496  sqq.  The  former  theory 
is  termed  the  rari-  (few)  constant 
theory,  the  latter  the  multi-  (many) 
constant  theory.  The  rari-constant 
theory  is  based  upon  the  assump- 
tion that  a  body  consists  of  mole- 
cules, and  that  the  action  between 
two  molecules  ...  is  in  the  line 
joining  them.  It  is  an  outcome  of 
the  atomic  and  action  -  at  -  a  -  dis- 
tance theory  in  vogue  on  the  Conti- 
nent, and  is  accordingly  mainly 
represented  by  Navier,  Poisson, 
Cauchy,  and  others,  notably  Saint- 
Venant.  The  other  school,  mainly 
represented  by  mathematical  physi- 
cists in  this  countrj',  starts  not  from 
a    mathematical    formula    (which, 

VOL.    II. 


after  all,  loses  its  precision  as  the 
active  forces  are  reduced  to  the 
vague  statement  that  they  act  t-en- 
sibly  only  at  insensible  distances) 
but  from  physical  data.  It  is  an 
analogue  to  Young's  theory  of  cap- 
illarity as  against  Laplace  (see 
above,  p.  20,  note).  '"The  .some- 
what unsatisfactory  nature  of  the 
results  of  those  investigations  pro- 
duced, especiallj'  in  this  country,  a 
reaction  in  favour  of  the  opiXM-ite 
method  of  treating  bodies  as  if  they 
were,  so  far  at  least  as  our  experi- 
ments are  concerned,  truly  continu- 
ous. This  method,  in  the  hands  of 
Green,  Stokes,  and  others,  has  led 
to  results  the  value  of  which  does 
not  at  all  depend  on  what  theory 
we  adopt  as  to  the  ultimate  con- 
stitution of  bodies  "  (Clerk  Maxwell, 
'Scientific  Papers,' vol.  ii.  p.  253). 
"  After  the  French  mathematicians 
had  attempted,  with  more  or  less 
ingenuity,  to  construct  a  theory  of 
elastic  solids  from  the  hypothesis 
that  they  consist  of  atoms  in  equi- 
librium under  the  action  of  their 
mutual  forces,  Stokes  and  otiiers 
showed  that  all  the  results  of  this 
hypothesis,  so  far  at  least  as  they 
agreed  with  facts,  miglit  be  deduced 
from  the  postulate  that  ehu-itic 
bodies  exist,  and  from  the  liyi)oth- 
esis  that  the  smallest  portions  into 
which  we  can  divide  tliem  are 
sensiblj'  homogeneous"  (id.  ibid., 
p.   449). 


34  SCIENTIFIC    THOUGHT. 

scale,  and  the  amplitude  or  height  of  the  wave-motion 

22.  of  which  decided  its  intensity.     There  was  floating  about 

other  " 

theories  ^^®  vaguc  idea  that  heat  also  was  to  be  interpreted 
as  a  mode  of  motion ;  still  vaguer  were  the  kinetic 
notions  as  to  electricity  and  magnetism ;  whilst  some 
early  attempts  to  explain  gravity,  not  as  an  inherent 
property  of  matter,  but  as  a  consequence  of  the  motion 
of  matter  itself,  which  was  possessed  merely  of  inertia, 
had  been  half  forgotten. 

There  is  no  doubt  that  the  successful  development  of 
the  undulatory  theory  of  hght  induced  many  minds  to 
dream  of  an  ultimate  kinetic  explanation  or  interpretation 
of  all  natural  phenomena,  when  in  the  course  of  the 
tliird  quarter  of  the  century  this  direction  of  thought 
received  a  great  impetus  through  three  independent 
branches  of  research  of  a  purely  theoretical  kind.  These 
have  led  to  a  very  remarkable  development  of  the  kinetic 
view  of  natui^e ;  in  fact  it  is  mainly  through  them  that 
this  view  has  become  possible  not  only  in  special  depart- 
ments, but  on  a  universal  scale.  They  have,  each  in 
its  own  way,  led  to  a  great  extension  of  our  experi- 
mental knowledge  ;  one  of  them  has  likewise  led  to  many 
practical  appHcations.  AMiat  most  interests  us  here  is 
the  peculiar  direction  which  they  have  given  to  a  great 
volume  of  mathematical  and  physical  thought  of  our  day. 

23.  The  first  of  these  hues  of  research  was  connected  with 

Kmetic  ' 

theoiyof  and  grew  out  of,  the  atomic  hypothesis.  It  cuhninated 
in  the  kinetic  theory  of  gases,  in  which  the  names  of 
Joule,  Clausius,  and  Clerk  Maxwell  are  prominent.  Of 
this  I  have  treated  already  in  the  fifth  chapter.  It 
rests  on  a  study   of   the  average  effect  produced   by  a 


KINETIC    OR    MECHANICAL    VIEW    OF    NATURE.       35 

swarm  of  Ijodies,  subject  to  a  transverse  movement  in 
straight  lines  like  projectiles,  and  continually  encounter- 
ing each  other  on  their  way.     Tlie  second  line  of  research        2*. 

Voricx 

in  ((ucstioii  is  the  study  of  bodies  subject  to  rapid  move-  '""»j<'«». 
nient  round  an  axis,  but  immersed  in  ;i  medium  which 
is  itself  movable  like  water,  but  not  in  a  r(jt;iry  but 
merely  in  a  flowing  motion.  The  whole  .series  of  in- 
vestigations which  started  1)}'  detining  vortex  or  whirUng 
motion  as  distinct  from  transverse,  Howing,  or  projectile 
motion,  and  from  vibratory  to  -  and  -  fro  motion,  was 
initiated  by  Helmholt/^  in  1857  in  a  purely  mathe- 
matical paper,  and  then  applied  and  greatly  extended 
by  Sir  William  Thomson  in  the  conception  of  the  vortex 
atom.  The  third  branch  of  research  had  its  origin  in  2i. 
experimental  investigations  carried  on  for  many  yeare  on  r^-starehe*. 
peculiar  lines,  and  quite  independently,  by  Faraday:  it 
was  put  into  mathematical  language  by  (Jlerk  Maxwell 
in  his  celebrated  treatise  on  electricity  and  magnetism 
which  appeared  in  1872.  It  will  be  my  object  to  show 
in  how  far  these  ditferent  investigations  have  confirmed 
and  developed  the  kinetic  view  of  natural  phenomena. 
But  before  doing  this  it  will  be  well  to  realise  what 
specific  problems  presented  themselves  to  theoretical 
physicists  when  once  the  undulatory  conception  of  light 
had  taken  hold  of  their  minds ;  what  pecuhar  dithculties 
were  involved ;  and  into  what  distinct  new  lines  of 
reasoning  they  were  conducted. 

We  saw  above  that  when  the  gravitational  explana- 
tion of  a  large  class  of  phenomena  had  a  century  earlier 
gradually  gained  ground,  a  great  variety  of  researches 
was  suggested  by  it,  and  new  lines  of  reasoning  opened 


36  SCIENTIFIC    THOUGHT. 

out,  which  in  the  course  of  the  eighteenth  century  com- 
bined to  estabhsh  what  I  termed  the  astronomical  view 
of  nature.  The  undulatory  theory  of  hght,  estabhshed 
by  Young  and  Fresnel  during  the  first  quarter  of  the 
nineteenth  century,  was  a  breaking  away  from  what 
then  seemed  to  many  Continental  philosophers  a  prom- 
ising line  of  thought,  a  unifying  principle  in  natural 
philosophy.  As  long  as  light  was  thought  to  consist  of 
particles,  however  minute,  which  were  projected  from 
luminous  centres,  the  mechanical  laws  of  impact,  of  at- 
traction and  repulsion,  could  be  applied ;  and  they  went 
a  considerable  way  in  apparently  explaining  the  ordinary 
phenomena  of  light,  such  as  motion  in  straight  lines,  re- 
liexion,  and  refraction.  They  failed  indeed  in  the  case 
of  diffraction  or  inflection,  and  still  more  in  those  pheno- 
mena which  were  misleadingly  grouped  under  the  term 
polarisation.  The  new  theory  seemed  specially  adapted 
to  these  more  recently  discovered  phenomena,  but  it  had 
to  be  admitted  that  the  explanation  of  reflexion  and 
refraction  of  light  at  the  surface  of  polished,  transparent, 
•2«.        or  opaque  bodies  met  with  considerable  difficulties.      The 

Problems 

uature'of      ^^^  theory  had   introduced   the   conception   of   an   all- 

the  ether,     pervading,  apparently  imponderable  substance,  the  ether. 

The    reintroduction    of     this     conception    into    physical 

science   was   repugnant    to    many    thinkers    of   the   then 

prevailing  school,^  and  it  became  more  so  when  it  hhd — 

1  One    of    the    crucial    tests    for    i    measured    the    speed    of    light    in 
deciding   between  the   corpuscular       various    media.       He   proved    that 


and  the  wave  theory  of  light  was 
the  relative  speed  with  which  light 
travels  in  air  and  in  water,  i.e.,  in 
a  refracting  substance.  Foucault, 
in  1850,  by  a  very  ingenious  method, 
improved     since     by     Mitchelson, 


light  moves  faster  in  air  than  in 
water,  whereas  on  the  corpuscular 
theory  the  speed  of  light  in  water 
must  be  to  its  speed  in  air  as  4  to  3 
approximately.  "This  finally  dis- 
posed of  the  corpuscular  theory  " 


KINETIC    OR    MECHANICAL    VIEW    OF    NATUUH       37 


for  the  purpose  of  serving  as  the  carrier  of  a  definite 
kind  of  wave  -  motion — to  he  endowed  with  most  mys- 
terious, seemingly  contra(Hctory  properties.^  Neverthe- 
less the  development  of  this  conception,  the  desire  to 
define  more  minutely  the  properties  of  this  fictitious 
sul)stance  of  wliich  we  have  no  direct  perception,  wime 
in  the  course  of  the  century  to  guide  more  and  more  the 
work  of  experimentalists  as  well  as  theorists.  We  meet 
with  objections  in  the  beginning,  when  the  conception  was 
first  introduced,  such  as  were  urged  by  many  chemical 
philosophers  when   Dal  ton  reintroduced  and  formulated 


(Tait,  'Light,'  p.  192).  Sir  G.  G. 
Stokes  tells  us  "  that  in  a  course 
of  conversation  with  Sir  David 
Brewster,  who  had  just  returned 
from  France,  where  lie  witnessed 
the  celebrated  experiment  by  which 
F(»ucault  had  just  proved  experi- 
mentally that  light  travels  faster 
in  air  than  in  water,  he  asked  him 
wliat  his  objection  was  to  the 
theory  of  undulations,  and  he 
found  he  was  staggered  by  the 
idea  in  limine  of  filling  space  with 
some  substance  merely  in  order 
that  'that  little  twinkling  star,' 
as  he  expressed  himself,  should  be 
able  to  send  his  light  to  us" 
('Burnett  Lectures  on  Light,'  p. 
15). 

^  It  is  known  that  the  two  phil- 
osophers who  in  the  middle  of  the 
century  did  more  than  any  others  to 
introduce  the  positive  or  exact  spirit 
into  general  thinking  and  into 
philosophical  literature,  Auguste 
Comte  and  John  Stuart  Mill,  were 
both  opposed  to  the  theory  of  an 
ether.  Huxley,  in  speaking  of 
Comte,  exclaims  :  "  What  is  to  be 
thought  of  the  contemporary  of 
Young  and  of  Fresnel  who  never 
misses  an  opportunity  of  casting 
scorn  upon  the  hypothesis  of  an 
ether — the  fundamental  basis  not 


only  of  the  undulatory  theory  of 
light,  but  of  so  much  else  in 
modern  physics,  and  whose  con- 
tempt for  the  intellects  of  .some  of 
the  strongest  men  of  his  generation 
was  such  that  he  puts  forward  the 
mere  existence  of  niglit :«  a  refuta- 
tion of  the  undulatory  theory  ? " 
(See  'Philosophic  Positive,'  vol.  ii. 
p.  440,  anil  Huxley,  '  Lay  Sermons,' 
J).  134.^  The  fourteenth  chapter 
of  Mill's  'System  of  Logic,'  written 
originally  in  the  beginning  of  the 
'forties,  but  subsequently  anno- 
tated with  reference  to  some  of 
AVliewell's  criticisms,  contains  a 
lengthy  discussion  of  the  hypoth- 
esis of  an  ether.  Mill  says  (vol.  ii. 
]).  21,  seventh  edition):  "  What  has 
most  contributed  to  accredit  the 
hypothesis  of  a  physical  medium 
for  the  conveyance  of  light  is  the 
certiiin  fact  that  light  travels,  that 
its  communication  is  not  instan- 
taneous but  requires  time,  and  that 
it  is  intercepted  by  intervening 
objects.  There  are  analogies  be- 
tween its  j)henomena  iind  those  of 
the  mechanical  motion  of  a  solid  or 
fluid  substance.  But  we  are  not 
entitled  to  ivs^iume  that  mechanical 
motion  is  the  only  i)owcr  in  nature 
capable  of  exhibiting  the.se  attri- 
butes." 


38  SCIENTIFIC    THOUGHT. 

the  atomic  view  of  matter.  Similar  uncertainties  in 
the  definitions  exist  in  both  theories  all  through  the 
century,  down  to  the  most  recent  times.  There  are 
those  who  still  look  upon  both  conceptions  as  merely 
convenient  symbolisms,  as  ideal  instruments  of  thought 
or  scientific  shorthand ;  and  on  the  other  side  we  have  it 
as  emphatically  stated,  that  the  question,  What  is  ether  ? 
"  is  the  question  of  the  physical  world  at  the  present 
time,"  "  that  it  is  not  unanswerable,"  in  fact,  "  that  it 
is  not  far  from  being  answered,"  that  "  it  is  probably 
a  simpler  question  "  than  the  other  question.  What  is 
matter  ?  ^  The  whole  domain  of  physical  science  is  even 
divided  into  two  portions,  the  physics  of  matter  and  the 
physics  of  ether,^  and  the  older,  more  empirical,  and 
common  -  sense  divisions,  treating  separately  of  light, 
electricity,  and  magnetism,  are  assembled  in  one  great 
doctrine,  the  "  doctrine  of  the  ether."  It  is,  indeed, 
somewhat  astounding,  if  not  disheartening,  to  hear  at  the 
same  time  from  an  authority  who  has  done  more  than 
any  other  living  philosopher   to   enlighten    us   in   these 


^  Professor  0.  Lodge,  in  the  |  -  See  inter  alia  Professor  Paul 
Preface  to  the  first  edition  of  \  Drude's  '  Physik  des  Aethers ' 
'  Modern  Views  of  Electricity,'  i  (Stuttgart,  1894).  In  the  Preface, 
\>.  xi.  "  It  is  simpler,"  he  con-  p.  vi,  he  speaks  of  the  philosophical 
tiuues,  "partly  because  ether  is  "desire  of  using  the  i<ame  funda- 
one,  while  matter  is  apparently  mental  conceptions  for  the  physics 
mauj'  ;  partly  because  the  presence  of  the  Pother  as  for  the  physics  of 
of  matter  so  modifies  the  ether  that  matter,  whereby  it  remains  an  open 
no  complete  theory  of  the  properties  question  whether  it  is  more  service- 
of  matter  can  possibly  be  given  ,  able  to  reduce  the  equations  in  the 
without  a  preliminary  and  fairly  '  physics  of  the  sether  to  those  ex- 
complete  knowledge  of  the  pro-  i  pressions  which  can  be  got  from  the 
perties  and  constitution  of  undis-  |  observable  phenomena  in  the 
turbed  ether  in  free  space.  When  |  physics  of  matter  (the  equations 
this  has  been  attained,  the  resultant  of  dynamics),  or  whether  the 
and  combined  effect  we  call  matter  i  opposite  road  can  be  chosen  with 
may  begin  to  be  understood."  '    advantage." 


KINETIC    OK    MECHANICAL    VIEW    UF    NATURE.       39 

matters,  that  at  llie  present  iiKJiiient  he  knows  us  little 
as  to  the  true  nature  of  these  agencies  or  substances  as 
he  did  fifty  years  ago.^ 

Viewed  from  the  position  which  we  occupy  in  this 
history  of  thought — i.e.,  in  relation  to  the  development 
of  ideas — the  conception  of  an  ether  has,  however,  like 
the  atomic  theory,  had  the  most  marked  influence  on 
scientific  research  and  reasoning.  In  digging  for  a  hidden 
treasure,  in  trying  to  describe  the  atoms  or  the  ether, 
many  practically  useful  conceptions,  applicable  to  tangible 
phenomena,  have  been  discovered.  The  atomic  theory 
led  at  once  to  an  enormous  increase  of  our  knowledge  of 
difierent  forms  of  matter,  the  knowledge  of  the  elements, 
and  of  their  ininiiuerable  possible  compounds.  The  con- 
ception of  the  ether  has  led  similarly  to  an  enormous  ex- 
tension of  knowledge  of  the  difierent  possible  forms  of 
motion.  It  is  in  this  sense  that  we  are  greatly  indebted 
to  these  abstract  conceptions  :  both  have  guided  our  ideas 
in  trying  to  uudcrstaud  and  grasp  the  endless  variety 
of  phenomena.  Let  us  see  how  from  the  early  years 
of  the  undulatory  theory  of  light  our  knowledge 
regarding  the  different  forms  of  motion  has  grown,  how 
that  theory  has  contributed  to  the  kinetic  view  of  nature. 


^  Lord  Kelvin,  in  referring  to  first  session  as  professor.  Some- 
fifty  years  of  scientific  labour,  said  thing  of  .sadness  must  come  of 
(see     the     publication     by     James       failure  ;    but    .   .    .    wliat  splendid 


Maclehose  &  Sons  of  tiie  proceedings 
at  his  jubilee  in  1896,  p.  70)  :  "I 
know  no  more  of  electric  and 
magnetic  force,  or  of  the  relation 
between  ether,  electricity,  and 
ponderaljle  matter,  or  of  chemical 
affinity,  than  I  knew  and  tried  to 


compensation  for  j)hilosophical  fail- 
ures we  have  had  iu  the  admirable 
discoveries  by  observation  and  ex- 
periment on  the  proi)ertie8  of 
matter,  and  in  the  exquisitely 
beneficent  applications  of  science  t4) 
the    use    of    mankind    with    which 


teach  to    my    students    of   natural       these  fifty  years  have  so  abounded.' 
philosophy   fifty   years  ago  in   my   . 


40  SCIENTIFIC    THOUGHT. 

It  was  recognised  by  Young,  and  still  more  clearly  by 
Fresnel,  that  the  medium  which  they  supposed  to  be  the 
carrier  of  light  could  not  have  the  ordinary  properties  of 
either  a  solid,  a  liquid,  or  a  gas.      It  offered  apparently 
no  resistance  to  the  motion  of  the  heavenly  bodies,  its 
waves  were  not  like  those  which  in  air  produced  sound  ;  it 
propagated  its  waves  at  a  speed  much  greater  than  any 
other  velocity  known  at  that  time ;  at  the  same  time  the 
wave-motion  was  not  that  of  a  body  possessing  the  pro- 
perties of  a  gas — i.e.,  an  elastic,  compressible  fluid  :  it  was 
that  of  a  body  offering  resistance  to  change  of  form  rather 
than  to  change  of  bulk.      It  was  evident  that  the  different 
properties,  which  we  see  roughly  assembled  to  constitute 
the   three   forms   of   ponderable   matter  with  which  we 
are  practically  acquainted,  the  solid,  the  liquid,  and  the 
gaseous,  cannot  be  assembled  in  any  similar  manner  in 
this  imponderable  substance,  the  ether.      It  was  bound  to 
'^    have  inertia — i.e.,  mass — otherwise  the  laws  of  motion  could 
not  be  employed  in  dealing  with  it,  and  mathematical 
thinking  about  it  would  be  impossible.     A  more  perfect 
description   of   the   elementary   movements    which    con- 
stituted light  evidently  required  a  minute  experimental 
study,  and  a  closer  mathematical  definition  of  the  dif- 
ferent  properties   of   matter,  known   popularly   but   not 
very   clearly  under   the   terms   compressibility,   rigidity, 
27.        mobility,  elasticity,  viscosity,  &c.,  and   of  the  inter-de- 

The  theory 

of  elasticity,  pendcucc  of  thcsc  clearly  defined  properties  one  on  the 
other.  Just  about  the  time  when  the  vibratory  theory 
of  light  began  to  be  seriously  entertained  by  natural 
philosophers,  a  beginning  had  also  been  made  in  this 
study :  the   theory   of   elasticity   had    been    founded    in 


KINETIC    OR    MFX'HANICAL    VIEW    OF    NATIKK.       41 

France  by  Na\'ier  and  I'oisson.  One  of  the  greatest 
analysts  of  the  century,  Augustin  L'auchy,  had  like- 
wise applied  himself  to  it;  and  when  Fi-esnel,  in  ihe 
\ear  1S26,  brought  out  his  great  memoir  on  double 
refraction  in  crystals,  in  which  he  was  obliged  to  enter 
more  closely  into  the  properties  of  the  luminiferous  ether 
and  its  relation  to  ponderable  matter,  Cauchy  was  induced 
to  devote  himself  more  specially  to  the  mathematical 
problems  which  presented  themselves.  Before  his  time 
the  theory  of  elasticity  had  been  studied  more  as  con- 
nected with  questions  of  practical  engineering,  such  as 
the  strength  of  materials,  the  stability  of  buildings,  the 
construction  of  macliines,  or  with  the  properties  of  nnisical 
and  sounding  bodies.  A  new  interest  was  created  by 
Fresnel's  researches.^  The  ([uestion  arose,  \hi\\  mv  we 
to  describe  the  vibrations  of  an  imponderable  substance, 
endowed  with  mass  (density)  and  rigidity,  and  what  con- 
ceptions can  we  form  of  the  change  of  these  vibrations 
if  there  is  present  likewise  ponderable  matter  ?  Evi- 
dently upon  the  clearness  and  correctness  of  these 
notions  depends  the  explanation  of  the  phenomena  observ- 
able when  rays  of  light  fall  upon  the  surfaces  of  trans- 
parent or  opaque  bodies.  We  have  to  ask:  In  wliat 
terms  (viz.,  of  different  kinds  of  motion)  can  we  define 
and  describe,  and  accordingly  calculate  the  phenomena 
of  reflexion,  refraction,  scattering  (i.e.,  dispersion),  and 
absorption  (i.r.,  extinction)  of  light  ?      A  tolerably  clear 


1  See  Verdet  iu  '  ffiuvres  de 
Fresnel,'  vol.  i.  p.  Ixxx :  "  Les 
seuls  ecrits  antdrieurs  a  Fresnel 
oil  I'on  trouve  des  notions  justes 
8ur  les  in(5galites  d't'^liisticito  qui 
peuvent  exister  dans  les  corps  et 


sur  leur  repartition  rt^Kuli6re  ]mr 
rapport  h,  certains  axes  ou  plans  de 
symdtrie  sont  ceux  du  grand  miiu'"- 
ralogiste  allemand  Samuel  Christian 
Weis"  ('  Mdm.  de  I'AwkI.  dc  Herlin.' 
ISl.'i). 


42 


SCIENTIFIC    THOUGHT. 


definition  of  the  kind  of  motion  constituting  a  pencil  of 
homogeneous  Hght  in  the  free  ether  or  in  atmospheric 
air  had  been  given  by  Fresnel.  Experimentally  the 
velocity  of  a  wave  motion  of  this  kind  was  known ;  it 
was  subsequently  ascertained  that  this  speed  was  not 
the  same  in  air  as  in  the  free  ether,  the  so-called 
vacuum.  It  was  also  known  that  this  speed  in  an 
elastic  medium,  such  as  the  ether  was  supposed  to  be, 
depends  upon  the  density  and  the  rigidity  of  the  medium. 
But  when  rays  of  light — i.e.,  the  wave-motions  of  the 
ether — arrive  at  the  surface  of  liquid  or  solid  bodies, 
various  changes  are  known  to  take  place.  These  changes 
had  been  to  some  extent  described  and  brought  into 
measurable  terms  by  experiment,  and  it  had  been  shown 
in  a  general  way  by  Huygens,  and  more  completely  by 
Fresnel,  how  these  observed  changes  of  reflexion,  refrac- 
tion, and  dispersion  could  be  translated  into  the  language 
of  the  vibratory  theory.  Complicated  and  yet  very  elegant 
geometrical  constructions,  at  which  Fresnel  arrived  by  an 
intuitive  or  tentative  process/  enabled  the  course  of  rays 
inside  transparent,  doubly-refracting  substances,  such  as 
crystals,  to  be  calculated ;  a  whole  geometry  of  rays  was 
developed  out  of  these  representations ;  new  phenomena 


^  The  equation  of  the  wave-sur- 
face was  not  expHcitly  given  by 
Fresnel  himself.  M.  Verdet  says 
(' CEuvres  de  Fresnel,'  vol.  i.  p. 
Ixxv)  :  "  Fresnel  n'a  pu  lui-meme 
venir  a  bout  de  ces  ditficulles  et  n'a 
su  obtenir  I'equation  de  la  surface 
del'onde  qu'eu  la  supposant  a  priori 
du  quatrieme  degre,  et  calculant  la 
valeur  de  ses  coefficients  de  maniere 
qu'ils  satisfissent  ti  certaines  condi- 
tions faciles   h  d^duire  de  la  con- 


sideration des  ondes  planes  normales 
aux  trois  plans  de  sym(5tiie  du 
milieu.  Ampere  est  le  premier  qui 
ait  eSectue  le  calcul  d'une  maniere 
rigoureuse."  However,  "the  con- 
struction yields  the  wave-surface  in 
sucli  a  way  that  its  singularities 
are  not  obvious,  and  were  only  I'e- 
marked  by  Sir  W.  R.  Hamilton 
several  years  after  Fresnel's  death  " 
(Fletcher,  'The  Optical  Indicat- 
rix,'  p.  31). 


KINETIC    UK    MECHANICAL    VIEW    OF    NATCRE.       4:'. 

of  refraction,  such  as  conical  refraction,  were  mathe- 
matically foretold  and  experimentally  verified.'  The 
real  ]ihysical  question,  however,  remained  unanswered; 
and  it  remains  only  partially  answered  up  to  the  present 
day."  How  is  it  tliat  the  luminiferous  ether,  wlien  ex- 
isting inside  ponderable  matter,  like  air  permeating  a 
grove  of  trees — as  Young  put  it — is  so  changed  that  its 
waves  travel  with  variously  altered  speeds,  that  in 
different  directions  the  rays  acquire  diftierent  pro- 
perties, are  differently  maintained  or  partially  extin- 
guished (absorbed)  ?  It  was  natural  to  suppose  that 
the  particles  of  ponderable  matter  must  in  some  way 
affect  the  ether,  changing  its  density  or  its  rigidity,  and 
that  they  themselves  are  affected  by  the  movements 
of  the  ether  which  tills  their  interstices.  The  question 
can  only  be  exhaustively  answered  l)y  a  complete  know- 


^  The  subsequent  sug2;estioii  of 
the  phenomena  of  inner  and  outer 
conical  refraction,  experimentally 
verified  by  Hum]>Iirey  Lloyd  in 
1833  (see  his  'Miscellaneous  Pajiers,' 
No.  1,  or  Transactions,  Royal  Irish 
Academy,  vol.  xvii.),  was  jjopularly 
regarded  as  a  complete  proof  of 
the  correctness  of  the  wave-surface, 
and  of  Fresnel's  entire  theory.  But 
as  to  the  first  point,  Sir  G.  G. 
Stokes  showed  (Brit.  Assoc.  Repoi-t 
on  Double  Refraction,  1862,  p. 
270)  that  conical  refraction  "  must 
be  a  property  of  the  wave-sur- 
face resulting  from  any  reasonable 
theory."  And  as  the  wave-surface 
itself  can  Ijo  geometrically  con- 
structed without  any  reference  to 
the  mechanical  theory  of  the  ether 
(as  Mr  Fletcher  has  most  exhaus- 
tively shown),  the  prediction  of 
conical  refraction  cannot  be  re- 
garded   as    a    proof    of     Fresnel's 


theory.  Todhunter- Pearson  says  : 
"  But  for  Cauchy's  magnificent 
molecular  researches,  it  might  have 
been  possible  for  Fresnel  to  com- 
pletely sacriticc  the  infant  theorj* 
of  elasticitj-  to  that  fiimsy  sujx?r- 
stition,  the  mechanical  dogma,  ou 
which  he  has  endeavoured  to  base 
his  great  discoveries  in  light. 
Cauchy  inspired  Green,  and  Green 
and  his  followers  have  done  soiue- 
thing,  if  not  all,  to  reconcile  Fres- 
nel's I'e.sults  with  the  now  fully 
developed  theory  of  elasticity,  the 
growth  of  which  his  dogma  at  one 
time  seriou.sIy  threatened  to  check  " 
('  Hist,  of  Elasticit}-,'  vol.  i.  p. 
167). 

-  In  1862  Sir  G.  G.  Stokes  "ex- 
pressed his  belief  that  the  true 
dynamical  theory  of  double  refrac- 
tion had  yet  to  be  found  "  (Report, 
I-.  268). 


44  SCIENTIFIC    THOUGHT. 

ledge  of  the  mechanism  of  the  ether  on  the  one  side,  of 
ponderable  matter  on  the  other.  Two  ways  are  open  by 
which  a  solution  of  this  ultimate  or  fundamental  problem 

28.  can    be   solved.     The   one   is    purely   mathematical.      It 

The  problem 

of  the  ether  meaus  the  analysis  of  all  the  possible  modes  of  motion  of 

may  be  ^  x 

mlthe**  a  given  mechanical  system,  and  of  the  mutual  iniiuence 
niaticaiiy,  ^j-j^gj-^  ^-^q  interconnected  mechanical  systems,  that  of  the 
ether  and  that  of  ponderable  matter,  exert  on  each  other. 
This  is  a  perfectly  definite  though  a  very  intricate  prob- 
lem. It  is  a  problem  which  can  be  compared  with — 
though  it  transcends  in  complexity — the  analytical  prob- 
lem suggested  by  the  gravitational  view  of  physical 
astronomy :  to  calculate  mathematically  the  movements 
of  any  number  of  bodies  attracting  each  other  according 

29.  to    Newton's    formula.      The   other   way   is   the   experi- 

or  experi- 
mentally,     mental    method  —  to    observe    how    under    methodically 

altered  conditions  rays  of  light  are  modified  in  colour 
(wave-frequency),  in  direction,  in  intensity  (amplitude  of 
wave-motion),  in  laterality  (polarisation),  and  in  other 
ways ;  and  then  to  translate  these  conditions  and  altera- 
tions into  the  now  fairly  well-established  language  of 
the  vibratory  theory ;  gaining  in  this  way  indications  as 
to  the  changes  which  the  wave-motion  is  capable  of,  and 
inferring  from  these  possible  changes  the  original  con- 
stitution (usvially  called  the  constants)  of  the  primary 
substances — the  ether  and  the  ponderable  matter  which 
come  into  interaction. 

30.  It  may  in  general  be  stated  that  neither  of  these  two 

Necessity  of  . 

combining     mcthods  has  for  any  length  of  time  been  pursued  alone, 

the  two  J  >=>  f  ' 

methods.      ij^^  ^j^^^  progrcss  lias  nearly  always  depended  upon  an 
alternating  employment  or  a  combination  of  both.      On 


KINETIC    OK    MhXHANICAL    VIEW    OF    NATLllK.       45 

the  one  side  we  have  a  great  volume  of  purely  analytical 
reasoning  begun  l>y  Cauchy  in  1- ranee,  and  purHued 
under  varying  assumptions  by  Green  and  MacCJuUagh  in 
England,  by  F.  Neumann  and  others  in  (Jermany.  On 
the  other  side  we  have  the  purely  experimental  work 
beginning  with  WoUaston  and  Brewster  in  England,  the 
refined  methods  for  measuring  the  speed  of  light  invented 
]jy  Fizeau  and  Foucault,  the  beautiful  contrivances  for 
experimental  research  and  verification  of  Jamin  and 
nianv  others.  Out  of  so  many  fruitful  conceptions 
which  have  resulted  in  an  enormous  accumulati(jn  of  new 
knowledge  of  actual  phenomena  of  light  and  wave-motion 
— the  real  and  sole  end  and  aim  of  all  theory — I  will  for 
the  purpose  of  illustration  single  out  one  which  in  llie 
middle  of  the  century  opened  out  an  entirely  new  field 
of  iniiuirv,  formino-  almost  a  new  science  by  itself.      I        8i. 

^        ■'  ■"  Spectrum 

refer  to  spectrum  analysis.  analysis. 

The  phenomena  of  dispersion  (rainbow  scattering)  and 
absorption  (partial  or  complete  extinction)  of  light  were 
among  the  earliest  known,  and  had  been  among  the 
longest  studied,  properties  of  bodies.  I>eing,  besides, 
connected  with  the  physiological,  subjective,  and  artistic 
effects  of  light,  they  have  always  commanded  special 
interest.  And  yet,  so  far  as  either  the  emission  or 
the  undulatory  theory  is  concerned,  they  have  always 
presented  special  ditticulties.  When  the  wave  theory 
was  first  propounded,  it  was  generally  understood  on 
the  analogy  of  the  phenomenon  of  sound  that  diflerence 
of  colour  depends  upon  difierence  of  frequency,  or  where 
the  velocity  of  propagation  (as  in  vacuo  or  in  atmospheric 
air)  is  the  same,  on  the  length  of  the  waves.      Thr  ditli- 


46 


SCIENTIFIC    THOUGHT. 


ciUty  arose  of  explaining  how  in  refracting  substances, 
be  they  fluid,  amorphous  (singly  refracting),  or  crystalline 
(including  doubly  refracting),  these  different  rays,  with 
different  wave-lengths,  come  to  travel  with  different 
velocities,  and  hence  take  different  courses  ;  how,  further, 
some  of  these  rays  come  to  be  extinguished  or  reflected 
(or  both)  in  varying  degrees. 

Now,  although  the  complete  answer  to  this  general 
question  has  not  yet  been  given,  a  principle  has  been 
recognised  which  gives  us  a  clue  to  the  possible  explana- 
tion of  a  large  class  of  phenomena,  and  wliich  is  thus  of 
remarkable  fruitfulness.  It  was  first  laid  down  by 
Euler,-^  a  pure  mathematician,  whose  physical  reasoning- 
was  frequently  suggestive  but  never  particularly  clear  and 
definite;  it  was  probably  first  applied  to  optical  phenomena 
by  Sir  George  Stokes ; '  and  it  was  later  on  used  by  him 


^  In  the  last  section  of  his  treatise 
on  light  and  colours  ( '  Berlin  Me- 
moirs,' 1745  ;  published  in  Latin, 
1746),  Euler  treats  of  luminous, 
reflecting,  refracting,  and  opaque 
bodies,  and  he  there  mentions  the 
analogy  which  exists  with  musical 
resonance.  "  The  smallest  particles 
[of  opaque  bodies]  are  similar  to 
Stretched  strings,  which  are,  as  it 
were,  specially  receptive  for  certain 
vibrations,  which  they  can  assume 
without  being  struck,  if  only  they 
are  afifected  by  the  undulatory 
movement  of  the  air."  "In  his 
expositions  upon  light  and  colours, 
Euler  always  starts  with  the  analogy 
of  sound  and  light ;  he  follows  it 
with  absolute  consistency  "  (Cher- 
buliez,  '  Eulers  physicalische  Ar- 
beiten,'  p.  44).  This  analogy  was 
exactly  what  was  absent  in  the  in- 
vestigations of  Brewster,  who  re- 
mained to  the  end  an  adherent  of  the 


projectile  theory.  Balfour  Stewart 
came  nearest  to  the  true  explana- 
tion in  his  memoir  of  1858  ( '  Trans, 
of  the  Royal  Societj*  of  Edin- 
burgh,' 1861);  but  this  referred  to 
radiant  heat  and  to  Provost's  theory 
of  exchanges.  It  contains  the 
words  :  "  The  absorption  of  a  plate 
equals  its  radiation,  and  that  for 
every  description  of  heat "  (p.  13). 
Had  this  statement  been  distinctly 
applied  to  luminous  rays,  spectrum 
analysis  would  have  been  his  dis- 
covery, although  his  theoretical 
proof  might  be  regarded  as  in- 
sufficient (see  Scheiner's  treatise 
on  Astronomical  Spectroscopy, 
transl.  by  Frost,  1894,  p.  112;  also 
Rosen  berger's  '  Geschichte  der 
Physik,'  vol.  iii.,  1890,  p.  iS2'sq.) 

^  See  the  references  given  on 
p.  277  of  the  first  volume  of  tliis 
history. 


KINETIC    OR    MECHANICAL    VI KW    OF    NATfl'.K.       47 

in  giving  a  mechanical  explanation  of  the  dark  and  bright 

lines  of  the  spectrum,  upon  which  Kirchhoff  and  liunseu  [^',^1'/'*** 

founded  spectrum  analysis  about  the  year  1860.  ',. 

Wollaston  ^  had  in  1802,  on  examining  the  solar  "^^ 
spectrum  (the  succession  of  rainbow  coloui-s  expanded  on 
a  white  screen  placed  behind  a  prism  uf  white  glass 
through  which  a  narrow  beam  of  sunlight  is  made  t(j  pasij), 
noticed  that  with  a  sufficient  enlargement  black  lines  in 
great  number  could  be  detected.  Fraunhofer,'-  in  ^lunich, 
made  a  special  study  of  them,  named  them  by  letters  of 
the  alphabet,  and  compared  the  solar  spectrum  with  the 
spectra  of  artificial  terrestrial  sources  where  light  is 
created  by  combustion  or  incandescence.  He  found  that 
these  spectra  differed,  the  peculiar  colour  exhibited  by 
various  flames  being  defined  in  the  spectra  by  special 
bright  lines  of  different  colours.  Thus  notably  the  two 
dark  lines  called  by  him  D  in  the  solar  spectrum  were 
replaced  in  the  spectrum  of  a  flame  in  which  a  volatile 
salt  of  sodium  was  present,  by  two  bright  lines  :  Brewster 
found  the  same  coincidence  of  others  of  Fraunhofer's 
lines  with  the  bright  lines  of  a  flame  in  which  nitre  was 
volatilised.  Very  similar  and  very  accurate  observations 
of  A.  Millar  as  to  the  identity  of  the  dark  Hues  D  in  the 
solar  spectrimi  with  the  two  bright  lines  of  the  sodium 
flame  were  explained  by  Sir  G.   Stokes  about  the  year       ss. 

^  '  Sir  G. 

1850  by  the  following  theoretical  reasoning:  The  sodium  stokes. 

1   "A  method  of  examining  re-  after  him  in   his   investigations  of 

fractive  and  dispersive   powers  by  the      "refractive     and     dispersive 

prismatic   reflection"   ('Trans,   of  i)o\vers  of  various  kinds  of  gbss" 

the  Royal  Society,'  1802).  tor  the  purpose  of  improving  the 

3  Fraunhofer,     whose     epitaph,  achromatic  telescoiie  (' Denkschrif- 

"  approximavit     sidera,"    describes  ten  der  Miinchener  Akadcmie,' vol. 

beautifully  his  life-work,  was  led  to  i.,  1814-15). 
the  discovery  of   the  lines  named 


48 


SCIENTIFIC    THOUGHT. 


34. 
Gustav 
Kirchhofl. 


flame  which  emits  the  two  bright  lines  in  its  own  spectrum 

destroys  them  (replacing  them  by  two  dark  lines)  in  the 

spectrum   of   a   ray  of    light  which  passes  through   the 

sodium  tiame.^      Foucault  had   in   1849   already  shown 

the  direct  reversal  of  the  sodium  line  in  the  spectrum  of 

the   electric   arc.      These   earlier   anticipations  remained 

partly  unnoticed,  partly  unknown,  or  were  looked  upon 

as  isolated  cases,  and  it  was  reserved  for  Gustav  Kirch- 

hoff  to  put   this  remarkable   property  of   emission  and 

absorption    of    special    colours  by   coloured   flames  into 

practical  language,  and  express  it  in  a  general  way.     He 

wrote  in   1859:^    "I   conclude    that  coloured  flames  in 

the  spectra  of  which  bright  lines  present  themselves,  so 

weaken  rays  of  the  colour  of  these  lines,  when  such  rays 

pass  through  them,  that  in  place  of  the  bright  lines,  dark 

ones  appear  as  soon  as  there  is  brought  behind  the  flame 

a  source  of  light  of  sufflcient  intensity,  in  which  these 

lines  are  otherwise  wanting."     And  when  he  concluded 

further  that  the  dark  lines  of  the  solar  spectrum  which 

are  not  evoked   by   the   atmosphere  of  the  earth,  exist 

in  consequence  of  the  presence  in  the  sun's  atmosphere 

of   those  substances  which   in  the  spectrum  of  a  flame 

produce  bright  lines  at  the  same  place,  "  he  at  once  gave 


^  From  this  lie  inferred  that  the 
presence  of  sodium  vapour  in  the  at- 
mosphere of  the  sun  wt)uld  explain 
by  absorption  the  two  dark  lines  in 
the  solar  spectrum.  Lord  Kelvin 
reports  that  in  consequence  of  this 
observation  of  Stokes  he  regularly 
taught  his  Glasgow  students  that 
sodium  must  be  in  the  sun's  at- 
mosphere. See  the  reprint  of  the 
correspondence  ou  this  subject  in 
the  '  Gesammelte  Abhandlungen  '  of 


Kirehhoff,  1882,  p.  639,  where  it 
will  also  be  seen  that  Sir  W. 
Crookes  claimed  a  similar  anticipa- 
tion for  Millar  in  1846.  See  also 
Sir  W.  Thomson's  ninth  Baltimore 
Lecture. 

"  See  the  translations  of  Fou- 
cault's  and  Kirchhoif's  memoirs 
sent  by  Sir  G.  Stokes  to  the 
'  Philosophical  Magazine '  of  March. 
1860,  p.  194  sqq. 


KINETIC    OR    MECHANICAL    VIEW    uF    NAT!  KK.       49 

birth  to  two  great  applications  of  lii.s  principle  —  tlie 
search,  through  the  study  of  the  spectra  of  distant  stellar 
sources  of  light,  after  the  ingredients  which  are  jtresent 
in  those  distant  luminaries,  and  the  search,  through  the 
study  of  the  flames  of  terrestrial  substances,  for  new 
sj)ectral  lines  announcing  yet  undiscovered  elements."  ' 
AMiilst  in  these  two  independent  directions  an  enormous 
amount  of  new  knnwledge  has  been  accumulated,  the 
mechanical  explanation  througli  which  Sir  (!.  Stokes 
anticipated  these  phenomena,  and  llie  further  applications 
of  this  principle  by  him,  have  done  much  to  confirm  the 
conviction,  that  in  looking  upon  liglit  as  a  vibratory  mode 
of  motion,  we  are  on  the  road  towards  an  adequate 
description   of  these  phenomena. 


'  To  this  principle  we  owe  the 
spectrum  analysis  of  stellar  at- 
mospheres and  the  discovery  of 
new  chemical  elements,  of  which 
no  fewer  than  six  have  been  iden- 
tified by  tliis  method,  lieginning 
with  cicsium  and  rubidium  (found 
by  Kirchhoff  and  Bunsen  in  the 
waters  of  some  mineral  springs). 
The  suggestion  of  Doppler,  men- 
tioned above  (p.  10,  note),  has  only 
become  fruitful  through  the  inven- 
tion of  the  sjiectroscope.  Colour 
differences  originating  through  the 
change  of  the  frecjuency  of  vibra- 
tions depending  on  cosmical  veloc- 
ities in  the  line  of  sight,  could 
not  be  discovered  by  the  most 
sensitive  eye.  In  the  spectrum, 
however,  shown  by  the  spectro- 
scope, "not  only  tiie  colours  of  the 
bright  lines  have  been  altered,  but 
their  position  in  the  spectrum 
relatively  to  a  fixed  point  of 
reference  as  well.  .  .  .  The  measure- 
ment of  the  displacement  of  spectral 
lines  in  conseciuence  of  the  altere<l 
refraiigiljility  of  the  rays  is  the  only 

VOL.  II. 


method  yet  known  which  possesses 
sufficient  accuracy  for  determining 
the  motions  of  objects  in  the  line 
of  sight.  Thus  far  it  has  not  been 
possible  to  produce  in  the  laboratory 
velocities  high  enough  to  occasion 
a  perceptible  displacement  of  the 
lines"  (Scheiner, /oc.  cit.,  p.  148). 
And  as  Doppler's  principle  in 
acoustics  was  proved  directly  bj- 
Buys  Ballot  through  the  whistle  on 
moving  railway  trains,  so  it  has 
been  proved  directly  in  optics  by 
observing  the  displacetnent  in  the 
lines  of  the  solar  spectrum,  wlieu 
this  is  deiived  from  the  nuter  rays 
of  the  sun's  disc,  the  light-giving 
parts  moving  in  the  line  of  sight 
towards  or  away  from  tiie  observer 
in  consec|uence  of  the  rotation  of 
the  .sun  round  its  axis.  "  The  re- 
sulting velocity  of  the  surface  of 
the  sun  is  found  to  agree  very 
closely  with  the  results  of  direct 
observations  of  the  revolution  of 
the  spots,  thus  practically  furnish- 
ing a  ])roof  of  the  correctness  of 
Doppler's  principle"  (ibid.,  p.  149). 

D 


50  SCIENTIFIC    THOUGHT. 

We  have  seen  above  how  the  vibratory  theory  of  light 
was  arrived  at — mainly  in  the  hands  of  Young — through 
dwellincr  on  the  analogy  of  certain  optical  phenomena, 
notably  those  of  interference,  with  the  properties  exhibited 
bv  sound.  Amons  the  latter  none  were  more  remarkable 
than  those  known  popularly  as  consonance  and  resonance. 
Sir  George  Stokes,  on  the  appearance  of  Kirchhoff  s  memoir 
on  the  relation  of  emission  and  absorption  of  certain  rays 
of  light,  gave  the  mechanical  explanation  in  the  following 
words  :  1  "  In  describing  the  result  of  a  prismatic  analysis 
of  the  voltaic  aixj  formed  between  charcoal  poles,  ]\I. 
Foucault  '  found  that  the  arc  presents  us  with  a  mediimi 
which  emits  the  rays  D  on  its  own  account,  and  which  at 
the  same  time  absorbs  them  when  they  come  from  another 
quarter.'  .  .  .  The  remarkable  phenomena  discovered  by 
Foucault,  and  rediscovered  and  extended  by  Kirchhoff, 
that  a  bodv  mav  be  at  the  s:ime  time  a  source  of  lisht, 
giving  out  rays  of  a  definite  refrangibility,  and  an  ab- 
sorbincf  medium  extinguishing  ravs  of  the  same  refransri- 
bOity  which  traverse  it,  seems  readily  to  admit  of  a 
d3mamical  illustration  borrowed  from  sound.  "We  know 
that  a  stretched  sti-ins  which  on  being  struck  gives  out  a 
certain  note,  is  capable  of  being  thrown  into  the  same 
state  of  vibration  by  aerial  vibrations  corresponding  to  the 
same  note.  Suppose  now  a  portion  of  space  to  contain  a 
great  number  of  such  stretched  stiings,  forming  thus  the 
analogue  of  a  'medium."  It  is  evident  that  such  a 
medium,  on  being  agitated,  would  give  out  the  note  above 
mentioned,  while  on  the  other  hand,  if  that  note  were 
sounded  in  air  at  a  distance,  the  incident  A"ibrations  would 

1  'Phil.  Mag.,'  March  1860,  pp.  194,  196. 


KINETIC    OR    MECHANICAL    VIEW    OF    NATURE.       51 

throw  the  strings  into  vibration,  and  consequently  wouM 
themselves  be  gradually  extinguished,  since  otherwise 
there  would  be  a  creation  of  vis  viva.  The  optical  applica- 
tion of  this  illustration  is  too  obvious  to  need  comment." 
Already  ten  years  before  Kircldiofl"  gave  t(j  the 
researches  into  the  spectrum  their  popular  celebrity  and 
practical  importance,  Stokes  ^   had  made  an  extensive  ex- 


'  The  memoir  of  Sir  G.  Stokes 
"  on  the  chauge  of  the  refrangi- 
ViiHty  of  light,"  iu  the  '  Phiios. 
Transactions'  (Maj'  1852),  forms  a 
landmark  in  optical  science,  and 
wliilst  dealing  with  the  less  obvious 
— though  very  frequent  and  general 
— phenomena  of  fluorescence  and 
phosphorescence,  really  indicated 
the  line  of  reasoning  which  has 
become  so  fruitful  and  suggestive 
in  his  own  hands  and  in  those 
of  other  eminent  natural  phil- 
osophers. On  page  r)4!}  of  that 
meinoii-  he  wrote :  ''  All  believers 
in  the  undulatory  theory  of  light 
are  agreed  in  regarding  the  pro- 
duction of  light  in  the  first  instance 
as  due  to  vibratory  movements 
among  the  molecules  of  the  self- 
luminous  body.  .  .  .  Nothing  then 
seems  more  natural  than  to  suppose 
that  the  incident  vibrations  of  the 
luminiferous  ether  produce  vibra- 
tory movements  among  the  ultimate 
molecules  of  sensitive  substances, 
and  that  the  molecules  in  turn, 
swinging  on  their  own  account,  pro- 
duce vibrations  in  the  luminiferous 
ether,  and  thus  cause  the  sensation 
of  light.  The  periodic  times  of 
these  vibrations  depend  upon  the 
j)eriods  in  which  the  molecules  are 
disjiosed  to  swing,  not  upon  the 
jjeriodic  time  of  the  incident  vibra- 
tions." Referring,  then,  to  the 
dynamical  difficulties  which  attach 
to  such  a  view,  he  proceeds  to  point 
out  "  that  we  have  no  right  to  re- 
gard the    molecular  vibrations    as 


indefinitely  small.  The  excursions 
of  the  atoms  may  be,  and  d(jubtles8 
are,  e.\cessively  small  compared 
with  the  linear  dimensions  of  a 
complex  molecule.  It  is  well 
known  that  chemical  changes  take 
place  under  the  influence  of  light, 
especially  the  more  refrangible  rays, 
which  would  not  otherwise  happen. 
In  such  cases  it  is  plain  that  the 
molecular  disturbances  nmst  not  be 
regarded  as  indefinitely  small. 
But  vibrations  may  very  well  take 
place  which  do  not  go  to  the 
length  of  complete  disruption  and 
yet  which  ought  by  no  means  to  be 
regarded  as  indefinitely  small.  .  .  . 
Certainly  we  cannot  affirm  that  in 
the  disturbance  comrauniciited  back 
again  to  the  luminiferous  ether 
none  but  periodic  vibrations  would 
be  produced  having  the  same 
period  as  the  incident  vibrations. 
Ilather,  it  seems  that  a  sort  of 
irregular  motion  must  be  produced 
in  the  molecules,  periodic  only  in 
the  sense  that  the  molecules  ret;iin 
the  same  mean  state  ;  and  thattlie 
disturbance  which  the  molecules  in 
turn  communicate  to  the  ctiier 
must  be  such  as  cannot  be  expreseetl 
by  circular  functions  of  a  given 
peritxl,  namely,  that  of  the  incident 
vibrations."  St<jkes  then  refers  to 
the  probable  internal  vibration  of 
the  atoms  in  the  compound  mole- 
cules, as  "  it  is  chiefly  among  organic 
compounds  .  .  .  having  a  compli- 
cated  structure  that  internal  dis- 
persion (fluorescence)  is  found." 


52  SCIENTIFIC    THOUGHT. 

amination  into  the  question  how  vibrations  of  the 
hmiiniferous  medium  can  be  mechanically  transferred  to 
the  compound  molecules  of  a  transparent  body,  and 
retransf erred  again  to  those  of  the  ether  itself  —  t.^., 
the  question  of  the  absorption  and  emission  of  light.  He 
showed  that  vibrations  of  a  certain  period,  corresponding 
to  a  definite  tint  of  colour,  could  eventually  give  rise  to 
vibrations  of  altered  period  in  the  emitted  light ;  that 
this  period,  however,  must  always  be  longer — i.e.,  that 
the  new  colour  must  always  be  of  a  lower  order  in  the 
35.  scale  of  refrangibility.  He  was  thus  not  only  able  to 
tionor'      explain  mechanically  the  peculiar  luminosity  which  he 

flUOr6SC6IlC6 

*  termed  fluorescence,^  and  which  had  been  observed  by 
Herschel  and  Brewster  in  certain  minerals  and  solutions, 
and  independently  studied  by  E.  Becquerel  in  France, 
but  he  also  showed  how,  by  means  of  such  substances, 
rays  of  light  which,  owing  to  the  frequency  of  their 
vibrations,  transcend  the  perceptive  powers  of  the 
•  human  eye,  can  be  made  visible  by  giving  rise  to 
secondary  waves  of  less  frequency.     The  line  of  reason- 


1  The  term  fluorescence  was 
coined  by  Sir  G.  Stokes  by  analogy 
with    opalescence   as  involving    no 


the  term  radiation  was  not  yet 
generally  used  to  embrace  the 
invisible  chemical  (ultra-violet)  and 


theoretical  suggestion,  in   place  of       caloric  (infra-red)  rays;  that  photo 
the    earlier    names     of     "  internal    i    graphy,  which  more  than  any  other 


dispersion"  or  "  epipolised  light  " 
used  by  Brewster  and  Herschel. 
He,  however,  very  soon  favoured 
the  term  "  degraded  light,"  sug- 
gested by  William  Thomson  (Lord 
Kelvin)  (see  the  second  memoir, 
1853,  p.  387).  The  latter  was  at 
that  time  occupied  with  his  cele- 
brated and  not  less  epoch-making 
researches  referiing  to  the  dissipa- 
tion or  degradation  of  energy,  of 
which  more  in  the  next  chapter.    If 


we  remember  that  fifty  yeai's  ago   '   times. 


process  has  familiarised  us  with 
chemical  radiation,  was  a  compara- 
tively recent  invention  ;  that  the 
ideas  of  conservation,  conversion, 
and  degradation  of  energy  were 
quite  new  ;  that  the  general  term 
energy  had  not  even  been  invented, 
— we  must  indeed  regard  the  words 
of  Sir  G.  Stokes  as  containing  a 
prophetic  programme  of  the  ideas 
and  problems  of  the  whole  subse- 
quent period  down  to  quite  recent 


KINETIC    OR    MECHANICAl-    MKW    OF    NATUUK.       53 

in!4  liere  employed  gave  tlie  ehie  to  all  subseiiuent 
attempts  to  deal  with  the  ditticult  problem  of  the  inter- 
action of  the  ether  and  ponderable  matter ;  uf  ihe  pos- 
sible alteration  of  the  density  or  the  rijj^iility  (called  the 
elastic  constants)  of  the  ether  when  Hllinj^  the  interstices 
of  transparent  bodies  ;  of  the  meciianical  differences  which 
make  some  bodies  transparent  for  some  and  opa([ue  for 
other  rays  of  light.  ]\Iany  possible  modiKcations  were 
tlieoretically  foreseen,  giving  rise  to  remarkaltle  unex- 
pected phenomena,  and  these  were  frequently  verified  by 
subsequent  experience.  The  whole  theory  of  light 
entered  upon  a  new  phase  as  it  became  more  and  more 
evident  that  the  study  of  the  vibrations  of  the  elastic 
medium  was  not  suilicient,  but  that  it  must  be  supple- 
mented by  that  of  the  interaction  of  two  vibrating 
systems,  the  ether  and  the  molecules  of  the  ponderable 
substance,  which  give  rise  to  tlie  phenomena  of  })arlial 
reflexion,  refraction,  dispersion,  and  partial  or  eomjilete 
absorption.  This  more  complicated  problem  in  the 
theory  of  elasticity  had  already  presented  itself  in  its 
simpler  form  in  the  tlieory  of  the  pendulum.  To  the 
principle  of  optical  consonance  which  had  been  employed 
to  explain  the  phenomena  of  absorption  of  liglit  was 
added,  in  order  to  explain  the  phenomena  of  tUsper- 
sion,  the  principle  of  tlie  free  and  forced  vibrations 
of  a  vibrating  system.^ 

1  "  If  to  the  l)ob  of  a  pendulum,  Anomalous  dispersion  such  as  wiu 

executing      horizontal      vibrations,  foreseen    by    Sellmciei-    and     Lord 

another  pendulum  be  attached,  exe-  Kelvin  and  discovered   by  Christi- 

cuting     vibrations     of     a    slightly  ansen  and    Kundt   dejiends  on   the 

shorter    [)eriod,    the   effect   of    the  change  of  wave  fre(|uency  indei)en 


latter  will  be  to  increase  the  period 
of  the  former  and  rice  vcr.id  "  (see 
A.  S.  Percival, '  Optics,"  1 899,  p.  1 81 ). 


dent  of  the  change  of  wave  length 
in  refracting  media. 


54 


SCIENTIFIC    THOUGHT. 


3G. 
View  of  the 


The  latest  discussion  of  this  form  of  the  elastic-solid 

ether  as  an    theory   of    light,   which    was    gradually   developed  from 

independent'  beginnings  in  the  three  countries/  is  to  be 


'  elastic 
solid. 


1  In  France  and  Gernaany,  where 
even  in  the  middle  of  the  century 
the  labours  of  English  natural  phil- 
osophers like  Green,  M'CuUagh, 
Stokes,  were  only  very  imperfectly 
known,  the  necessity  was  equally 
felt  of  studying  the  interaction  of 
the  ether  and  ponderable  matter. 
In  France  the  school  of  the  eminent 
"elastician,"  Barre  de  St  Venant, 
produced  in  M.  Boussiuesqtheauthor 
of  the  earliest  published  attempt  to 
solve  the  difficulties  which  the  older 
methods  of  Cauchy  had  not  over- 
come. In  a  lucid  review  of  the  state 
of  physical  optics.  Saint  Venant 
himself  ('Ann.  de  Chimie  et  de 
Physique,'  4™^  serie,  vol.  25,  1872) 
hails  with  delight  the  researches  of 
M.  Boussinesq  from  1865  onward, 
where  the  idea  that  the  ether  in  the 
interstices  of  transparent  bodies  has 
different  elastic  constants  is  given 
up,  and  the  participation  of  the 
ponderable  matter  in  the  vibrations 
is  introduced  in  its  place.  "En 
effet,"  he  says,  "  il  est  bien  difficile 
de  concevoir,  d'une  part,  que  Tether 
puisse  etre  agile  au  sein  cl'un  corps 
dont  la  densite  est  probablement 
bien  sup&ieure  ii  la  sienne,  sans 
lui  communiquer  une  fraction  sens- 
ible de  sa  quantite  de  mouvement, 
et  d'autre  part,  que  les  ondes  ne 
soient  pas  bientot  eteintes  par  cette 
participation  de  la  matiere  ponder- 
able au  mouvement  s'il  n'y  a  pas 
concordance  entre  les  oscillations 
imprimees  k  chaque  molecule  de 
cette  matiere  et  celles  de  I'ether 
qui  I'environne."  It  was  the 
problem  of  the  continuity  at  the 
interface  of  reflecting  and  refracting 
substances  and  the  problem  of  ab- 
sorption which  the  older  simple 
ether   theories    could   not   explain. 


In  Germany  a  similar  impulse  was 
given  to  the  study  of  the  inter- 
action of  elastic  systems — as  indeed 
to  many  problems  of  mathematical 
physics — by  Franz  Neumann,  who 
was  the  centre  of  a  numerous  and 
influential  school.  He  taught  at 
Kcinigsberg  together  with  Richelot 
and  Bessel.  His  lectures  have  been 
edited  by  his  pupils.  Prof.  Karl 
Pearson,  in  his  continuation  of  Tod- 
hunter's  '  History  of  the  Theory  of 
Elasticity,'  does  ample  justice  to  the 
labours  of  Neumann,  who,  "in  his 
investigations  on  photo  -  elasticity 
and  the  elasticitj-  of  crystals,  breaks 
almost  untrodden  ground,  which 
both  physicists  and  mathematicians 
have  hardly  j^et  exhausted  "  [loc.  cit. , 
vol.  ii.  2,  p.  183).  "Neumann  was 
among  the  first  (1841, '  Abh.  der  Ber- 
liner Akademie')  to  attribute  disper- 
sion to  the  influence  of  the  ponder- 
able particles  on  the  particles  of  the 
ether"  (ibid.,  p.  31).  The  most 
important  original  contrilmtions  of 
Neumann's  pupils  are  the  researches 
of  Sellmeier,  who  had  been  led  by 
theoretical  considerations  in  1866 
to  expect  certain  anomalies  in  the 
phenomena  of  dispersion,  such  as 
were  in  1870  actually  discovered  by 
Christiansen,  and  fully  investigated 
by  Kundt.  Surface  coloration  was 
shown  to  be  intimately  connected 
with  the  absorptive  powers  in  sub- 
stances showing  these  anomalous 
phenomena.  A  full  report  on  these 
and  other  theories,  based  upon  what 
has  been  termed  abroad  the  "Bessel- 
Sellmeier  hypothesis "  (see  Ket- 
teler,  '  Theoretische  Optik,' 1885), 
will  be  found  in  Prof.  Glazebrook's 
"  Report  on  Optical  Theories," 
Brit.  Assoc.  Reports,  1885. 


KINKTIC    OR    MECHANICAL    VIEW    OF    XATUKE.       55 

found  in  Lord  Kelvin's  celebrated  lialtinuiie  l>.'eture8  ^ 
where  with  unhinittMl  resourcefulness  the  methods  of  ' 
analogy,  analysis,  and  experiment  are  employed  to  solve 
or  to  define  the  intricate  problems  of  pliysical  optics. 
Nor  is  it  a  merely  fortuitous  coincidence  for  the  history 
of  thought  that,  whilst  his  mind  must  have  been  filled 
with  the  many  illustrations  and  mechanical  devices,  and 
all  the  wealth  of  suggestions  contained  in  the  Baltimore 
Lectures,  Lord  Kelvin  should  have  delivered  the  opening 
address  to  the  mathematical  section  of  the  Ihitish  Asso- 
ciation, entitled,  "  Steps  towards  a  Kinetic  Theory  of 
]\Iatter."  Following — as  did  also  Clerk  Maxwell — on 
the  lines  indicated  by  Stokes's  earlier  papers,  he  has  done 
much  to  change  our  fundamental  conceptions  as  to  the 
properties  of  matter,  and  this  in  two  distinct  ways. 
The  first  consisted  in  breaking  down  the  rigid  barriei-s 
which  popular  definitions  had  set  up  between  the  dif- 
ferent forms  of  aggregation — the  solid,  liquid,  and  gaseous 
states  of  matter ;  whilst  the  second  tended  to  show  how 


^  The  Baltimore  Lectures  were 
delivered  by  Lord  Kelvin  (then  Sir 
\V.  Thomson)  after  the  meeting  of 
the  British  A.ssociation  at  Montreal 
in  the  month  of  October  1884,  at 
the  Johns  Hopkins  University,  be- 
fore a  company  of  physicists.  The 
final  edition  of  these  important  and 
highly  suggestive  conferences  is  in 
the  press  as  the  fourtli  volume  of 
the  collected  mathematical  and 
physical  pajiers.  The  comjjletion 
of  this  publication  is  eagerly  ex- 
pected, as  containing  the  most 
mature  exposition  of  the  elastic- 
solid  tlieory  of  light,  towards  which 
the  author  has  in  the  course  of  the 
last  fifteen  years  made  various  valu- 
able additions.     Notably  in  a  paper 


dated  1888,  published  in  the  '  I'liil- 
osophical  Magazine,'  he  has,  as  it 
has  been  said,  "  extricated  the 
elastic  theory  from  the  position  of 
deadlock,  according  to  which  the 
ether  must  be  botii  compressible 
and  incompressiljle,"  by  showing 
that  the  difficulty  can  be  met,  "  pro- 
vided we  either  sujjpose  the  medium 
to  extend  all  through  boundless 
space,  or  give  it  a  fixed  containing 
vessel  as  its  boundary."  I'mf. 
Glazebrook  has  further  worked  out 
the  consequences  of  this  suggestion. 
See  vols.  26  and  27  of  the  .'ith  series 
of  the  '  Phil.  Mag.,'  also  ^  Nature.' 
vol.  40,  1889,  i>.  32,  and  Fletcher, 
the  '  Optical  Indicutrix,'  p.  (J,  ic. 


56 


SCIENTIFIC    THOUGHT. 


the  supposed  static  properties  of  matter  could  be  ex- 
plained by  different  modes  of  motion,  translational, 
periodic,  or  rotational.  The  mathematical  and  experi- 
mental investigations  connected  with  the  theory  of 
radiations  and  vibrations  had  thus  an  influence  ^  on 
our  general  views  of  the  nature  of  physical  processes 
whicii  far  exceeded  the  aims  for  which  they  were  origi- 
nally undertaken.  That  a  substance  so  attenuated  as  the 
ether  should  have  the  properties  of  a  solid ;  that  brittle 
substances  like  pitch  should  flow  like  liquids,  if  only 
sufficient  time  were  given ;  that  towards  very  rapid 
impulses  gases  and  liquids  might  behave  as  solids — all 
these  observations  resulted  in  a  complete  revolution  of 
our  scientific  notions  as  well  as  of  our  vocabulary.  The 
great  turning-point,  indeed,  lay  in  the  kinetic  theory  of 
gases,  which  about  the  middle  of  the  century  had  intro- 
duced quite  novel  considerations  by  showing  how  the 
dead  pressure  of  gases  and  vapours  could  be  explained  on 
the  hypothesis  of  a  very  rapid  but  disorderly  transla- 
tional movement  of  the  smallest  particles  in  every 
possible  direction.  Pressure  of  gases  ha^ang  been  ex- 
plained by  a  very  rapid  motion  of  the  minute  par- 
ticles of  matter,  heat  was  mimediately  conceived  to  be 
merely  a  "  mode  of  motion."  As  no  event  did  more  to 
spread  modern  views  in  the  theory  of  light,  and  to 
popularise   modern   scientific   methods,   than   Kirchhoff's 


^  It  has  been  asserted  that  the 
theory  of  elasticity  received  a  great 
impulse  when  Fresnel  was  forced  to 
make  assumptions  as  to  the  mode  of 
vibrations  of  the  ether  which  were 
quite  incompatible  with  the  then 
accepted  laws  of  the  vibrations  of 


an  elastic  medium.  To  this  view  of 
the  origin  of  the  modern  theory  of 
elasticity  Prof.  Karl  Pearson  takes 
exception,  as  Navier's  memoir  of 
1827  was  not  suggested  by  optical 
investigations  (Todhunter-Pearson, 
vol.  ii.  2,  p.  5). 


KINKTIC    OR    MECHANICAL    VIKVV    OF    NATLRE.       57 


and  Bunsen's  spectrum  analysis,  so  in  the  closely  related 
<l(»ctrine  of  heat,  piol)aljly  no  puhlication  di<l  niore  to 
estal)lish  a  general  kinetic  view  of  matter  and  of  natural 
phenomena  than  Tyndall's  celebrated  treatise,  '  Heat  as  a 
Mode  of  Motion.'  In  spite  of  the  criticisms  which 
have  been  levelled  against  this  expression,^  the  lj<jok, 
which  appeared  in  186."'),  was  to  the  jjopular  nnnd  a 
revelation  ;  it  was  translated  into  many  foreign  languages, 
ran  through  many  editions,  was  recommended  Ijy  thinkers 
of  the  first  order,  and  the  title  coveted  as  "  manifesting 
far  and  wide  through  the  world  one  of  the  gi-eatest 
discoveries  of  modern  philosophy." ""  It  is  the  popular 
herald  of  the  kinetic  or  mechanical  view  of  nature. 

The  same  great  authority  who  has  so  generously 
referred  to  Tyndall's  treatise — Lord  Kelvin — had  been 
inspired  from  (juite  a  different  quarter  to  suggest  the 
most  advanced  conception,  in  tliis  line  of  thought,  of 
which  the  human  mind  has  so    far   been    capable :    the 


as. 
Tvndairi 


39. 
Lor<J 
Ki-lvin'8 
vcirtex 
theory  of 
matter. 


1  Notably  by  Prof.  P.  G.  Tait ; 
see  his  volume  on  '  Heat,'  p.  350, 
also  his  '  Recent  Advances  of 
Physical  Science,'  which  contains 
as  an  appendix  his  lecture  on 
"  Force,"  delivered  in  Glasgow  on 
the  occasion  of  the  meeting  of 
the  British  Association.  He  says 
there :  "  Heat  and  kinetic  energy 
in  general  are  no  more  modes  of 
motion  than  potential  energy  of 
every  kind  is  a  vuxle  of  rest.'' 
"  Heat  is  not  the  mere  motions, 
but  the  energj'  of  these  motions." 
There  is  no  doubt  that  the  terms 
force  and  motion  can  be  used  in 
very  different  meanings,  and  that 
the  early  expounders  of  the  me- 
chanical theory  of  heat  have  not 
been  always  consistent  in  the  use 
of  words  ;  though  their  ideas,  wher- 
ever they  appeared  in  mathematical 


expressions,  were  definite  enough. 
A  good  deal  of  vagueness  has  ac- 
cordingly crept  into  popular  text- 
books and  into  philosophical  treat- 
ises, and  criticisms  such  ivs  those 
of  Prof.  Tait  have  been  useful  in 
helping  us  towards  clearer  con- 
ceptions. We  shall  come  across 
more  of  these  instances  in  the  next 
chapter  when  dealing  with  the 
gradual  evolution  of  the  conception 
of  energy. 

-  See  Lord  Kelvin's  abstract  of 
lecture,  "Elasticity  viewed  as 
possil)iy  a  Mode  of  Motion,"  1881; 
'Popular  Lectures,' &c.,  vol.  i.  p. 
142.  "I  have  always  a<lmire<l  it" 
(viz.,  Tyndall's  title)  ;  "1  have  long 
coveted  it  for  elasticity,  and  now, 
by  kind  permission  of  its  Inventor, 
I  have  borrowed  it  for  this  dis- 
course." 


58 


SCIENTIFIC    THOUGHT. 


40. 
Helniholtzs 
investiga- 
tions. 


vortex  theory  of  matter.  As  this  is  one  of  the  most 
remarkable  instances  of  the  fruitful  reaction  of  abstract 
mathematical  reasoning  on  the  progress  of  physical  re- 
search, it  will  be  useful  to  consider  for  a  moment  by 
what  gradual  steps  this  novel  idea  was  evolved  or 
suggested.  The  immediate  occasion  which  led  to  it  was 
the  publication,  in  1858,  by  Helmholtz  of  a  purely 
mathematical  investigation  of  some  peculiar  forms  of 
lluid  motion.-^  About  a  hundred  years  before  Helmholtz 
published  his  memoir,  Euler  had  laid  the  foundation  of 
theoretical  hydrodynamics  —  i.e.,  of  the  theory  of  the 
motion  of  fluids.      In  doing  so,  it  was  necessary  to  define 


^  Helmholtz's  memoir,  "  Ueber 
Integrale  der  hydrodj'Dami.schen 
Gleichungen  welche  den  Wirbel- 
bewegungeu  entsprechen,"  appeared 
in  the  55th  volume  of  Crelle's 
'  Journal  f  iir  die  reine  uud  ange- 
wandte  Mathematik. '  It  was  trans- 
lated into  English  by  Prof.  Tait  in 
the  '  Philosophical  Magazine '  for 
1867.  Helmholtz's  occupation  with 
the  subject  had  originated  in  the 
acoustical  researches  which  he  was 
carrying  on  at  the  time.  These 
necessitated  an  analysis  of  the 
more  complicated  conditions  which 
the  motion  of  incompressible  and 
elastic  fluids  presents  in  actual 
experience.  The  hydrodynamical 
equations  had  been  solved  under 
certain  simplifying  assumptions. 
Discontinuity  of  motion  and  in- 
ternal friction  had  been  left  out 
of  considei'ation.  Helmholtz's  re- 
searches led  him  to  the  study  of 
these  more  complicated  phenomena ; 
and  he  successfully  applied  the 
mathematical  methods  which  had 
proved  useful  in  other  branches  of 
physical  science  for  the  solution  of 
these  problems.  Notably  in  the 
paper  on  whirling  motion,  he  came 


I  upon  very  remarkable  and  unex- 
I  pected  results,  which  ten  years  later 
!  led  in  this  country  to  the  novel 
speculations  of  Lord  Kelvin.  It  is 
interesting  to  note  how  at  that 
time  researches  in  England  or  Ger- 
many could  for  many  years  remain 
unnoticed  in  the  other  country. 
The  result  was  that  the  same  prob- 
lems were  frequently  taken  up  in 
ignorance  of  the  fact  that  they  had 
been  treated  before.  See  Hicks's 
"  Report  on  Hydrodynamics,"  'Brit. 
Assoc.  Reports,'  1881-82.  Especially 
the  labours  of  Stokes  seem  to  have 
been  little  known  to  German 
writers,  who  usually  started  from 
the  better-known  French  researches. 
Stokes  had  anticipated  some  of 
Helmholtz's  results  referring  to 
whirling  and  discontinuous  motion 
of  fluids.  About  the  middle  of  the 
century  the  periodical  "  Fort.schritte 
der  Physik "  was  .started  by  the 
"  Physikalische  Gesellschaft "  of 
Berlin.  Helmholtz  himself  contrib- 
uted several  valuable  reports  on 
acoustical  subjects.  See  the 
'  Wissenschaf tliche  Abhandlungen,' 
vol.  i.  passim. 


KINETIC    OR    MECHANICAL    VIEW    OF    NATCRE,       59 

mathematically  what  is  nifaiit  l>v  a  lluid.  The  chief 
property  of  a  tluid,  as  compared  with  a  soliil  body,  is 
the  perfect  mobility  of  its  parts,  the  absence  of  rigidity. 
Tluis  there  were  two  possible  kinds  of  Huids — those 
which  retained  their  bidk  or  volume,  whilst  ottering  no 
resistance  to  change  of  shape,  and  those  whicii  tried  to 
expand,  and  could  be  compressed  by  means  of  external 
forces.  These  latter  were  called  gases.  In  dealing  wiib 
the  former,  incompressibility  had  to  l)e  defined  mathe- 
matically, as  also  perfect  mobility.  These  properties 
constitute  what  is  called  a  perfect  fluid.  Sucii  perfect 
tluids  do  not  exist  in  nature ;  Imt  the  methud  of 
reasoning  was  to  begin  with  an  ideal,  simple  case,  and 
approach  the  explanation  of  natural  phenomena  by  a 
process  of  correction,  introducing  more  and  more  com- 
plications. The  phenomena  of  the  How  of  liquids, 
practically  by  far  the  most  important,  could  be  studied 
to  a  great  extent  by  means  of  the  simplest  form  of  the 
hydrodynamical  conception,  and  up  to  I  he  middle  of  the 
century  such  problems,  as  well  as  those  of  the  propa- 
gation of  small  displacements  under  the  action  of  external 
forces, — notably  the  motion  of  waves,— formed  the  prin- 
cipal problems  whicli  were  treated  mathematically.  The 
idea  of  the  friction  of  fluids,  also  called  viscosity,  had  been 
excluded  in  the  definition  of  a  fluid,  inasmuch  as  friction 
opposed  the  notion  of  perfect  mobility  of  the  parts,  which 
was  the  mathematical  definition  of  a  fluid.  Now  it  is  a 
matter  of  experience  that  in  all  liquids  wiib  which  we 
are  acquainted  friction  can  produce  rotational  moliou, 
such  as  whirls  and  eddies ;  it  was  also  found  that  other 
forces,  such  as  magnetic  forces,  are,  under  cerl^un  con- 


60  SCIENTIFIC    THOUGHT. 

clitions,  able  to  produce  these  rotations.      It  was  therefore 
of  interest  to  study  the  nature  of  rotational  or  whirling 
motion,  if  such  could  exist  in  a  perfect  liquid,  and  to  see 
what  would  be  likely  to  happen  to  these  whirls.     Though 
it  might  be  ditticult  to  understand  how  in  a  perfect  liquid 
rotation  of   any  portion  could   be  produced,  calculation 
misfht  determine  what  would  be  the  nature  and  fate  of 
such   whirls,   if    they   did   exist.       The   problem   was   a 
purely  mathematical  one.       Can  a  rotational  motion,  a 
whirl,  exist  in  a  perfect  fluid,  as  defined  by  the  mathe- 
matical conception  ?    If  it  can,  what  are  the  properties  of 
such  whirls,   and  what    becomes   of   them  ?     Helmholtz 
fiolved   these   questions   in   his   now  celebrated   treatise, 
showing  that  whirls  (called  by  English  waiters  vortices) 
can  exist,   but   only   under   certain   conditions,   such   as 
can  be  experimentally  represented  by  smoke-rings  issuing 
from  an  orifice ;  that,  if  they  existed  in  a  perfect  liquid, 
they  would  be  indestructible  and  would  possess  a  motion 
of  their  own,  giving  them  a  special  individual  character 
as  to  permanence  and  movement.      The  treatise,  like  the 
problem,  was  a  purely  mathematical   one,^  and   in   the 
mind  of  the  celebrated  author  was  probably  connected 
more  with   the  problem  of  the  formation  of  drops,  and 
with  that   of   the  friction  or  viscosity  of   fluids,  which 
he    attacked   subsequently,    than    with    the    nature     of 
matter.      In    this    country   vortex    motion    had    already 
been  studied  by  natural  philosophers  with  very  different 
ends  in  view. 

It  was  known  that  solid  bodies  which  are  in  a  rapid 

'  It  revealed  incidentally  the  analogy  of  hydrodynamical  and  electrical 
phenomena. 


KINETIC    OR    MEC'HANKAl-    VIKW    OK    NA'iritK.        61 

rotary  motion  acquire  i)roperties  which  they  do  not 
possess  otherwise — viz.,  rigidity — i.r.,  reaction  against 
change  of  shape  (the  stifiness  of  a  travelhng  rope  thrcjwn 
off'  a  pulley  is  a  familiar  illustration);  stability — i.r.,  re- 
action against  change  of  position  and  motion,  as  in  a  sjiin- 
ning-top  or  a  bicycle  ;  elasticity — i.e.,  tendency  to  revert  to 
the  same  position,  if  violently  disturbed.  'I'he  gyroscope^ 
had  been  invented  in  1852  by  Foucault,  and  used  by 
him  and  other  physicists  in  France  and  Germany  to 
illustrate  the  rotation  of  the  earth.  It  was  nr)w  shown 
that  portions  of  a  perfect  Huid- — i.e.,  of  a  liody  which 
possesses  neither  rigidity,  nor  stal)ility,  nor  elasticity 
— when  in  a  state  of  rapid  rotational  motion,  acquire 
these  gyrostatic  properties ;  that  whirling  portions  can- 
not be  naturalh'  created,  but  that  if  once  in  existence 
they  preserve  their  identity,  being  permanently  differ- 
entiated from  the  surrounding  ffuid,  which  may  be  at  rest 
or  in  the  state  of  ffow.  These  differentiated  portions  of 
the  liquid  were  called  by  Helmholtz  vortex  filaments ; 
he  showed  that  in  a  lit^uid  without  a  boundary  they 
must  run  back  into  themselves,  foniiing  rings  which 
might  be  knotted  and  linked  together  in   many  ways. 

^  A   much   older   invention    was  j   of    this    work,    and    through    the 

that  of  Bohnenberger  (1817),  known  inexhaustible    wealth     of    esj)eri- 

by   his  name.      The  name  "gyro-  mental    illustrations   contained    in 

scope "    was    introduced    by    Fou-  I    many   of  Lord    Kelvin's   addresses 

cault  ;   and  that  of  "  gyrostat,"  as  j    (see    '  Popular    Lectures    and    Ad- 


defining  an  apparatus  which  ac- 
quires stability  through  rotational 
(whirling  or  gyrating)  motion,  was 
used  first  by  Lord  Kelvin.  An 
extensive  treatment  of  the  subject 
is  to  be  found  in  the  first  part 
of  Thomson  and  Tait's  '  Natural 
Pliilosophy'  C^nd  ed.),  i)p.  SH-il.'i. 
It  is  mainly  through  tlie  influence 


dresses,'  vol.  i.  i)p.  143  ■'«/'/.,  218 
S(jq.  ;  iii.  165  .^'jq.,  245),  that  gj'ro- 
static  and  vortex  motion  has  l>ecome 
in  this  countrj"  a  favourite  study  of 
matiiematicians  and  natural  j>hil- 
o.sophers,  and  forms  an  iuiiH)rtant 
feature  in  almost  every  recent 
attempt  t<>  de.'icril>e  the  proi>ertie» 
of  matter  and  ether. 


62 


SCIENTIFIC    THOUGHT. 


42.  It  does  not  seem  that  Helmholtz's  speculations  were 

Influence  of 

Helmholtz's  much  taken  up  abroad  ;  in  this  country,  however,  they 

speculations  ^                       '                                           "^                           '           ^ 

in  England.  fg||   ^^^    ^^^.^  fruitful   soil :  ^    they   led  first    of    all    to 


^  It  is  a  remarkable  fact  that  the 
country  which  produced  the  great 
theory  that  finally  destroyed  the 
older  vortex  theory  of  Descartes, 
was  the  one  in  wliich,  a  century 
after  Newton,  the  modern  views  on 
vortex-motion  were  first  and  almost 
exclusively  developed.  Notably 
the  scientific  atmosphere  in  which 
Thomson  and  Tait  moved  was,  inter 
alia,  charged  with  the  bold  ideas 
and  the  suggestive  nomenclature  of 
Macquorn  Rankine.  He  owes  his 
permanent  place  in  the  history  of 
science  to  being  side  by  side  with 
Lord  Kelvin  and  Clausius,  one  of  the 
threefoundersof  theoretical  thermo- 
dynamics. But  he  was  in  addition 
to  this  perhaps  the  earliest  and 
purest  representative  of  the  kinetic 
or  mechanical  view  of  natural 
phenomena,  and  of  the  scientific 
tendency  or  habit — derived  from  his 
profession  as  an  engineer — of  con- 
structing for  everj'  phenomenon  to 
be  explained  a  mechanical  model. 
In  a  succession  of  memoirs  beginning 
in  1850,  Rankine  put  forward  his 
theory  of  ' '  molecular  vortices,' ' 
' '  which  assumes  that  each  atom  of 
matter  consists  of  a  nucleus  or 
central  point  enveloped  by  an 
elastic  atmosphere"  ('Scientific 
Papers  of  Macquorn  Rankine,'  ed. 
Miller,  Loudon,  1881,  p.  17).  Clerk 
Maxwell  in  1878  wrote  of  Rankine's 
theory:  "Whatever  he  imagined 
about  molecular  vortices  was  so 
clearly  imaged  in  his  mind's  ej'e 
that  he,  as  a  practical  engineer, 
could  see  how  it  would  work.  How- 
ever intricate.  therefore,  the 
machinery  might  be  which  he 
imagined  to  exist  in  the  minute 
parts  of  bodies,  there  was  no  danger 
of  his  going  on  to  explain  natural 
phenomena  by  any  mode  of  action 


of  this  machinery  which  was  not 
consistent  with  the  general  laws  of 
mechanism.  Hence,  though  the 
construction  and  distribution  of  his 
vortices  may  seem  to  us  as  compli- 
cated and  arbitrary  as  the  Cartesian 
system,  his  final  deductions  are 
simple,  necessary,  and  consistent 
with  facts.  Certain  phenomena  were 
to  be  explained.  Rankine  set  himself 
to  imagine  the  mechanism  by  which 
they  might  be  produced.  Being  an 
accomplished  engineer,  he  succeeded 
in  specifying  a  particular  arrange- 
ment of  mechanism  competent  to 
do  the  work."  Maxwell  goes  on  to 
say  :  "As  long  as  the  training  of 
the  naturalist  enables  him  to  trace 
the  action  only  of  particular 
material  systems,  without  giving 
him  the  power  of  dealing  with  the 
general  properties  of  all  such 
systems,  he  must  proceed  by  the 
method  .so  often  described  in 
histories  of  science  — ■  he  must 
imagine  model  after  model  of  hypo- 
thetical apparatus,  till  he  finds  one 
which  will  do  the  required  work. 
.  .  .  The  theory  of  molecular 
vortices  was  distinguished  from 
other  theories  which  attribute 
motion  to  bodies  apparently  at  rest, 
by  the  further  assumption  that  this 
motion  is  like  that  of  very  small 
vortices,  each  whirling  about  its 
own  axis  "  (Clei-k  Maxwell  in 
'  Nature,'  1878  ;  '  Scientific  Papers,' 
vol.  ii.  p.  662,  &c.  ;  and  Prof. 
Tait's  memoir  of  Rankine  in  the 
'  Collected  Papers,'  p.  xxix).  In  the 
most  recent  attempt  to  reconcile 
the  two  fundamental  ideas  with- 
out which  we  do  not  seem  to  be 
able  to  proceed  in  a  description  of 
natural  phenomena  —  viz.,  that 
space  is  a  plenum,  filled  bj'  a  con- 
tinuous something,  and  that  matter 


KINETIC    OR    MECHANICAL    VIEW    (iF    NATIHF:.       63 


many  experiiiiental  contrivanceB,  by  which  tlie  it- 
iiiaikable  phenomena  known  as  "  ^yrostatic "  —  ix., 
the  stiible  properties  of  liodies  in  rapid  rotary  motion  ' 
— could  be  studied,  as  also  to  the  development  of  tlie 
theory  of  knots  and  linkage."      In  llie  resourceful  brain 


(and  electricity)  is  atomic  (discrete, 
grained),  Dr  Larnior  has  traced 
the  modern  vortex  theory  further 
back  beyond  Raukine  to  James 
MiicCuilagh,  who  in  his  '  Essay 
towards  a  Dynamical  Theory  of 
Crystalline  Reflexion  and  Refrac- 
tion'(Trans.  Irish  Academy,  1839), 
"arrived  at  a  type  of  elasticity  (of 
the  ether)  which  was  win  illy  rota- 
tional, .  .  .  somewhat  after  the 
manner  that  a  spinning  flywheel 
resists  any  angular  deflection  of  its 
axis "  (p.  26  of  his  Adams  prize 
essay,  '  -Ether  and  Matter,'  1900). 
"  Rankine,  never  timid  in  his  specu- 
lations, expounded  I\IacCullagh's  an- 
alytical scheme  soundly  and  clearly, 
in  full  contrast  with  the  elastic 
properties  of  matter,  as  represent- 
ing a  uniform  medium  or  plenum 
endowed  with  ordinary  inertia,  but 
with  elasticitj'  of  purely  rotational 
type"  (iV)id.,p.  77  ;  cf.  p.  73)  ;  but 
he  also  remarks  that  "up  to  the 
period  of  Lord  Kelvin's  vortex 
atoms  .  .  .  the  earlier  theories  .  .  . 
could  only  have  l)een  hypothetical 
speculations  "  (p.  25  note). 

1  Helmholtz  himself  did  not  give 
many  practical  illustrations  of  his 
remarkable  theories.  Such  were 
first  given  by  W.  B.  Rogers  ('  Amer. 
Journ.  of  Science '  (2),  vol.  26,  p. 
246)  in  I8.08,  without  knowledge  of 
Helmholtz's  theoretical  investiga- 
tions. In  this  country  such  illusti-a- 
tions  have  become  quite  favourite 
popular  lecture  experiments  (see 
Sir  Rob.  S.  Ball's  memoir).  Smoke- 
rings,  solid  and  liquid  gyrostats,  and 
a  host  of  similar  contrivances,  have 
impressed  on  us  the  hidden  re- 
sources of  whirling  motion.     Prof. 


Tait,  in  his  '  Recent  Advances  of 
Physical  Science'  (3rd  ed.,  18S."),  p. 
296),  states  that  experiments  on 
smoke-rings  which  he  performed, 
suggested  to  Lord  Kelvin  the 
vortex  theory  of  matter.  Tlie 
various  papers  of  the  latter  have, 
so  far,  not  been  collected  in  a  con- 
venient form.  The  earliest  is  con- 
tained in  the  '  Proceedings  of  the 
Royal  Society  of  Edinburgh,'  Feb- 
ruary 1867.  Then  followed  a 
memoir  in  the  '  Transactions  '  (April 
1867)  on  vortex  statics  (Proc. 
R.  S.  E.,  December  1875)  ;  "  Vibra- 
tions of  a  Columnar  Vortex  "  (Proc, 
March  1880).  Prof.  Hicks,  and 
especially  Prof.  J.  J.  Thomson 
(Trans.  R.  Soc,  1884  ;  1881),  have 
contributed  to  the  theory,  and  the 
latter,  in  his  Adams  prize  essay  for 
1882,  has  further  tested  the  concep- 
tion in  its  application  to  chemical 
statics.  See  Hicks,  '  Recent  Pro- 
gress in  Hydrodynamics '  (Brit. 
Assoc.  Rep.,  1881,  p.  63,  kc),  and 
J.  J.  Thomson  '  On  the  ilotion  of 
Vortex  Rings'  (1883,  p.  114,  kc.) 

-  The  creator  of  this  branch  of 
purely  positional  geometry  is  doubt- 
less Johann  Benedict  Listing,  who 
was  led  to  his  researches  by  some 
suggestions  of  Gauss.  Gauss  refers 
to  the  subject  in  connection  with  his 
unpublislied  researches  into  electro- 
dvnamics  (1833,  posthumously  pub- 
lished in  '  Werke,'  vol.  v.  p."  605). 
Listing  called  this  branch  of 
geometry  "  Topologie  "  (cf.  Listing, 
'  Vorstudien  zur  'rojiologie,'  Giit- 
tingen,  1847).  In  the  meantime 
Riemann  had  been  (1851)  led  in  his 
mathematical  representation  of 
functions    on    tlie    surface    uiUcd 


64 


SCIENTIFIC   THOUGHT. 


of  Lord  Kelvin  this  theory  led  to  the  conception  that 
in  an  all-pervading,  boundless  fluid,  such  as  physicists 
imagined  for  the  purposes  of  the  theory  of  light,  dif- 
ferentiated portions  might  exist  in  the  form  of  whirling 
rings  (vortex  rings),  which  would  possess  most  of  the 
properties  of  ponderable  matter — identity  and  perman- 
ence of  quantity  of  substance,  stability,  rigidity,  elasticity. 
43.        It  was  indeed   soon  found  that  although  eminently  sug- 

Difficulties 

of  the  vortex  gestive  in  this  way,  and  pointing  in  the  direction  of  a 
general  kinetic  theory  of  natural  phenomena,  the  vortex 
ring  theory  presented  two  fundamental  difficulties.  How 
does  whirling  matter  acquire  weight,  and  how  does  it 
acquire  immensely  increased  inertia  ?  In  the  explana- 
tion of  these  two  properties  the  progress  has  been  small, 
— if  indeed  any  glimpse  at  all  has  as  yet  been  got.^ 
But  by  suggesting  numberless  experiments  through  which 
our  knowledge  of  things  natural  has  been  enormously  in- 
creased, by  placing  before  the  minds  of  mathematicians 
a  great  number  of  problems  of  practical  importance  and 
physical  interest,  and  generally  by  familiarising  the  minds 
of  philosophers  with  an  ultimate  kinetic  explanation  of 
nature,^  the  vortex -atom  theory  has  marked  an  epoch  in 


after  him,  to  distinguish  between 
singly,  doubly,  triply,  &c.,  con- 
nected surfaces  ('Werke, '  1876, 
pp.  18,  88,  448).  These  studies, 
which  for  a  long  time  were  looked 
upon  merely  as  curiosa  or-  of  purely 
abstract  interest,  were  indepen- 
dently taken  up  in  the  practical 
interest  of  tlie  vortes,-atom  theory 
by  Prof.  Taitin  1876  ("  On  Knots," 
Trans.  Roy.  Soc.  Edinb.,  1877,  vol. 
28,  p.  145,  &c. ),  and  continued  in 
1884-85.  To  him  we  owe  a  con- 
venient notation  and  vocabulary. 
For  the  history  of  the  subject  and 


further  developments,  see  Diu- 
geldey,  '  Topologische  Studien,' 
Leipzig,   1890. 

^  See  Clerk  Maxwell's  article 
"Atom"  in  the  9th  ed.  of  the 
'  Ency.  Brit.,'  reprinted  in  'Scien- 
tific Papers,'  vol.  ii.,  and  the  account 
given  there  of  Le  Sage's  theory. 

'■^  See  Dr  Larmor's  Address  to 
Section  A  of  the  Brit.  Assoc,  at 
Bradford  in  1890  (Report,  p.  625) : 
"  The  vortex-atom  theory  has  been 
a  main  source  of  physical  suggestion, 
because  it  presents,  on  a  simple 
basis,   a   dynamical  picture   of   an 


KINETIC    OR    MECHANICAL    VIEW    UF    NATL'KE,       65 

the  history  of  thought.  As  tlie  study  of  stiible  motion 
or  dynamical  equilibrium,  it  has  joined  hands  with  the 
kinetic  theory  of  gases — i.e.,  the  study  of  the  motion  of 
a  swarm  of  bodies  in  rectihnear  motion,  and  with  the 
mechanical  theory  of  lieat — i.e.,  of  irregular  intinitesimal 
motion  of  any  kind ;  and  it  has  certainly,  through  the 
remarkable  results  gained  by  Professor  J.  .1.  Thomson, 
afforded  a  clue  to  tlie  explanation  of  chemical  linkage, 
showing  how  it  conies  about  that  stability  of  chemical 
compounds  is  dependent  on,  and  limited  to,  a  small 
number  of  combinations  or  linkages.^  The  mathematiciil 
difficulties  in  the  way  of  progress  are  enormous,  sufKcient 
to  tax  the  brains  of  many  generations  to  come,  l)Ut  as  it 


ideal  material  system,  atomically 
constitatcd,  which  could  go  on 
automatically  without  extraneous 
support.  The  value  of  such  a 
picture  may  be  held  to  lie,  not  in 
any  supposition  that  this  is  the 
mechanism  of  the  actual  world  laid 
bare,  but  in  the  vivid  illustration  it 
affords  of  the  fundamental  postulate 
of  physical  science,  that  mechanical 
phenomena  are  not  parts  of  a 
sclienie  too  involved  for  us  to 
explore,  but  rather  present  them- 
selves in  definite  and  consistent 
correlations,  which  we  are  able  to 
disentangle  and  apprehend  with 
continually  increasing  precision." 

^  See  his  essay  on  the  "  Motion  of 
Vortex  Rings":  "Let  us  suppose 
that  the  atoms  of  the  different 
chemical  elements  are  m.ade  up  of 
vortex  rings  all  of  the  same  strength, 
but  that  some  of  these  elements 
consist  of  only  one  of  these  rings, 
others  of  two  of  the  rings  linked 
together,  or  else  of  a  continuous 
curve  with  two  loops,  others  of 
three,  and  so  on.  Our  investigation 
shows  that  no  element  can  consist 

VOL.   If. 


of  more  than  six  of  these  rings  if 
they  are  arranged  in  the  .sym- 
metrical way  there  described  "  (p. 
119).  "Each  vortex  ring  in  the 
atom  would  correspond  to  a  unit  of 
affinity  in  the  chemical  theoiy  of 
quanlivalence.  If  we  regard  the 
vortex  rings  in  those  atoms  con- 
sisting of  more  vortex  rings  than 
one  as  linked  together  in  the  most 
symmetrical  way,  then  no  element 
could  have  an  atom  consisting  of 
more  than  six  vortex  rings  at  the 
most,  so  that  no  single  atom  would 
be  capable  of  uniting  with  more 
than  six  atoms  of  another  element 
so  as  to  form  a  stable  conijiound. 
This  agrees  witli  chemical  facts, 
as  Lothar  Meyer  in  his  '  Moderne 
Theorien  der  Chemie,'  4th  ed.,  p. 
196,  states  that  no  compound  con- 
sisting of  more  than  six  atoms  of 
one  element  combined  with  only 
one  of  another  is  known  to  exist  in 
the  gaseous  state,  and  that  a 
gaseous  comjjound  of  tungsten, 
consisting  of  si.x  atoms  of  chlorine 
united  to  one  of  tungsten,  does 
exist"  (p.  120). 

E 


66 


SCIENTIFIC    THOUGHT. 


44. 

Modem 
view  of 
electrical 


has  been  remarked,  "  the  glory  of  surmounting  them  would 

be  unique."  ^ 

The  vortex-atom  theory  is  the  most  advanced  chapter 
in  the  kinetic  theory  of  matter,  the  most  exalted  glimpse 
into  the  mechanical  view  of  nature.  Though  suggested 
by  Helmholtz,  it  has,  as  already  stated,  been  limited 
almost  exclusively  to  this  covmtry.  If  science  still 
shows  international  differences  and  patriotic  predilections, 
this  affords  one  of  the  few  remaining  examples.  Another 
step  first  taken  in  this  country,  the  last  and  most  im- 
portant contribution  to  the  science  of  physical  motion, 
the  greatest  support  of  the  kinetic  or  mechanical  view 
of  nature,  has,  in  union  with  the  undulatory  theory  of 
light,  been  now  all  but  universally  accepted  in  the 
scientific  world:  I  refer  to  the  modern  view  of  electric 
phenomena,  which  for  a  long  time  was  supported  by  the 


phenomena:  solitary  labours  and  genius  of  Faraday 


Faraday 


His  great  discoveries  of  magneto-electricity,  of  induc- 
tion, of  the  electrification  of  light,  to  which  I  have  had 
repeated  occasion  to  refer,  made  his  name  familiar  to 
the  whole  scientific  world  ;  but  the  processes  of  reasoning 
by  which  he  arrived  at  them,  or  to  which  in  his  mind 
they  gave  rise,  were  ignored  or  not  understood."     Whilst 


^  Tait,  in  '  Recent  Advances  of 
Phj'sical  Science,'  p.  302,  and  Clerk 
Maxwell,  in  article  "  Atom  "  ('  En- 
cy.  Brit.,'  9th  ed.,  or  'Col- 
lected Scientific  Papers,'  vol.  ii.  p. 
472). 

-  See  Helmlioltz's  '  Faraday  Lec- 
ture,' delivered  before  the  Chemical 
Society  on  April  5,  1881,  reprinted 
in  his  '  Vortriigeund  Reden,'  vol.  ii. 
p.  275,  &c.  "Since  the  mathe- 
matical interpretation  of  Faraday's 
theorems    by    Clerk    Maxwell    has 


been  given,  we  see  indeed  how 
sharply  defined  the  conceptions  are 
and  how  consistent  the  reasoning 
which  lay  concealed  in  Faraday's 
words,  which  to  his  contemporaries 
appeared  so  indefinite  and  obscure  ; 
and  it  is  in  the  highest  degree  re- 
markable to  see  how  a  large  number 
of  comprehensive  theorems,  the 
proof  of  which  taxes  the  highest 
powers  of  mathematical  analysis, 
were  found  by  him  without  the  u.se 
of  a  single  mathematical  formula, 


KINETIC    OR    MECHANICAL    VIEW    OF    NATURE.       67 


Continental  philosophers,  following  Coulomb,  tried  to  put 
into  mathematical  language  the  action  at  measurable  dis- 
tances of  magnetic  masses  and  elements  of  electrical 
circuits,^  Faraday  fastened  upon  tlie  pecuUar  lines  in 
which  iron  tilings  arranged  themselves  in  the  neighbour- 


by  a  kind  of  intuition  with  iu.slinc- 
tive  certiiinty.  I  would  not  de- 
preciate Faraday's  contemporaries 
because  they  did  not  see  this.  I 
know  myself  too  well  how  often  I 
sat  hopeless,  gazing  at  one  of  his 
descriptions  of  lines  of  force  with 
their  numbers  and  tension,  or  look- 
ing for  the  meaning  of  statements 
where  the  galvanic  current  is  re- 
garded as  an  axis  of  force  and  much 
the  like"  (p.  277).  Rosenberger 
tells  us  that  it  may  be  in  part  attrib- 
uted to  the  displeasure  and  annoy- 
ance with  which  foreign  philoso- 
phers received  l<araday's  theoretical 
views,  that Poggendortf,  who  printed 
Faraday's  earlier  memoirs  in  extenso 
in  his  '  Annalen,'  only  gave  a  short 
abstract  of  the  later  series.  See 
Rosenberger,  '  Die  moderne  Ent- 
wickelung  der  elektrischen  Princi- 
pien,'  Leipzig,  1898,  p.  105. 

'  These  researches,  of  which  the 
fourth  chapter  of  this  work  gave 
some  account,  and  which  culminated 
in  Weber's  well-known  law  of  electro- 
dynamic  action  of  electrical  particles 
at  a  distance,  absorbed  almo^^t  ex- 
clusively the  attention  of  natural 
philosophers  abroad.  Mathema- 
ticians of  the  highest  rank,  such 
as  Laplace,  Gauss,  and  Riemann, 
worked  at  the  subject.  It  is,  how- 
ever, interesting  to  note  that  Gauss, 
with  that  remarkable  instinct  for 
physical  adaptation  of  mathematical 
ideas  which  characterised  also  the 
magnetic  researches  which  he 
carried  on  between  1830  and  1840, 
refrained  from  the  development  of 
a  mathematical  theory  of  electro- 
dynamic  action  for  reasons  which 
he  later  explained  to  Weber.    When 


the  latter  prepared  for  publication 
that  elaborate  series  of  exact  mea- 
surements which,  irrespective  of  the 
theory  attached  to  them,  formed 
the  foundation  of  modern  electrical 
science  and  of  the  correlation  of  the 
phenomena  of  magnetism,  of  elec- 
tricity at  rest  and  in  motion,  of 
induction  and  of  diamagnetism, 
Gauss  wrote  as  follows  under  date 
19th  March  1845:  "The  subject 
belongs  to  those  investigations 
which  occupied  me  very  extensively 
about  ten  years  ago  (especially 
1834-36).  .  .  .  Perhaps  I  may  be 
able  to  think  myself  again  into  these 
matters,  which  have  now  become  so 
foreign  to  me.  ...  I  should  no 
doubt  have  long  ago  published  my 
researches ;  but  at  the  time  when 
I  broke  them  off,  that  was  want- 
ing which  1  then  considered  to 
be  the  very  keystone  —  nil  actum 
reputans  si  quid  superesset  agen- 
dum— namely,  the  deduction  of  the 
additional  forces  (which  have  to  be 
added  on  to  the  mutual  action  of 
particles  of  electricity  at  rest,  if 
they  are  in  relative  motion)  from 
action,  not  instantaneous,  but 
(like  that  of  light)  projjagated  in 
time.  With  this  I  could  not  suc- 
ceed at  the  moment,  but  so  far 
as  I  can  remember  I  left  the  subject 
not  entirely  without  hope  that  this 
might  later  be  possible;  yet,  if  I  re- 
member aright,  with  the  subject- 
ive conviction  that  it  would  previ- 
ously be  necessary  to  form  for  one- 
self a  workable  representation  (cine 
construirbarc  Vorstcl/uiig)  of  the 
manner  in  which  the  jn-opagatiou 
takes  place  "  ((iauss,  '  Werke,'  vol. 
v.  p.  627,  &c.) 


68 


SCIENTIFIC    THOUGHT. 


45. 


"  Line 
force. 


of 


hood  of  the  poles  of  magnets ;  ^  inquired  into  the  nature 
and  condition  of  the  region — afterwards  termed  the  "  field  " 
— which  surrounded  magnetised  and  electrified  bodies ; 
invented  the  term  "  electrotonic  state"  and  "  dielectric" "  to 
describe  the  part  which  the  surrounding  medium  played 
in  the  so-called  actions  at  a  distance ;  and  conceived  it  to 
be  in  a  state  of  tension,  which  he  further  described  by 
filling  it  with  so-called  "  lines  of  force."  The  region  or 
"  field "  ^  of  magnetic  and  electric  action,  filled  with 
these  curved  lines  of  force,  possessing  definite  direc- 
tion and  frequency,  gave  him  a  clear  mental  repre- 
sentation of  the  direction  and  intensity  of  magnetic  and 
electric  forces  at  any  point  in  space  in  the  neighbour- 
hood of  magnets  or  of  electric  currents.  For  Faraday, 
the  lines  of  force  in  the  magnetic  field,  from  being 
originally  merely  a   convenient  geometrical  device,*  ac- 


^  "  By  magnetic  curve.s  1  mean 
the  lines  of  magnetic  forces,  how- 
ever modified  by  the  juxtaposition 
of  poles,  which  would  be  depicted 
by  iron  filings,  or  those  to  which 
a  very  small  magnetic  needle  would 
form  a  tangent"  (Faraday,  'Ex- 
perimental Researches  on  Elec- 
tricity,' 1st  series,  November  1831, 
No.  114  note).  "  When  an  electrical 
current  is  passed  through  a  wire,  that 
wire  is  surrounded  at  every  part  by 
magnetic  curves,  diminishing  in 
intensity  according  to  their  distance 
from  the  wire.  .  .  .  These  curves, 
although  different  in  form,  are  per- 
fectly analogous  to  those  existing 
between  two  contrary  magnetic 
poles  opposed  to  each  other"  (ibid., 
2nd  series,  January  1832,  No.  232). 

^  The  term  "electrotonic  state" 
was  introduced  in  1831  to  describe 
the  condition  of  matter  in  the 
neighbourhood  of  electric  bodies. 
"  It  is  probable  that  what  will  affect 


a  conductor  will  affect  an  insulator 
also,  producing,  perhaps,  what  may 
deserve  the  term  of  the  electro- 
tonic state"  (ibid..  No.  1661, 
1838),  "  the  intervening  particles 
assuming  for  the  time  more  or  less 
of  a  peculiar  condition,  which 
(though  with  a  very  imperfect  idea) 
I  have  several  times  expressed  bj' 
the  term  electrotonic  state"  (ibid., 
No.  1729).  "I  use  the  word  'di- 
electric '  to  express  that  substance 
through  or  across  which  the  electric 
forces  are  acting  "  (December  1838, 
ibid.,  No.  1168,  note). 

■*  The  term  "  magnetic  field " 
seems  to  have  been  used  for  the 
first  time  in  the  year  1845  (see 
'  Exp.  Res.,'  No.  2252,  vol.  iii.  p.  30). 

*  November  1837:  "I  use  the 
term  line  of  inductive  force  merely 
as  a  temporary  conventional  mode 
of  expressing  the  direction  of  the 
power  in  cases  of  induction.  .  .  . 
The   power,  instead  of  being   like 


KINETIC    OK    MECHANICAL    VIEW    OF    NATL  Ut.       09 


([uired    gradually   a    physical*   signiHcance,    for   he    had 
very  early  couviriced  himself  of  the  fact,  known  already 


that  of  gravity,  which  causes 
particles  to  act  on  each  otlier 
through  straight  lines,  ...  is  more 
analogous  to  that  of  a  series  of  mag- 
netic needles.  .  .  .  So  that  in  wliat- 
ever  way  I  view  it,  and  with  great 
suspicion  of  the  influence  of  favourite 
notions  over  myself,  I  cannot  per- 
ceive how  the  ordinary  theory  .  .  . 
can  be  a  correct  representation  cf 
that  great  natural  principle  of  elec- 
trical action"  ('Exp.  Res.,'  No. 
r2:}l ).  "1  have  used  tlie  phrases  lines 
of  inductive  force  and  curved  linesoi 
force  in  a  general  sense  only.  .  .  . 
All  I  am  anxious  about  at  present 
is,  that  a  more  particular  meaning 
should  not  be  attached  to  the  ex- 
pressions used  tlian  I  contemplate  " 
(ibid.,  No.  1304).  And  after  hav- 
ing referred  to  the  agreement  of  his 
results  with  those  of  Poisson,  ar- 
rived at  by  starting  from  "  a  very 
different  mode  of  action,"  and  with 
the  experimental  results  of  Snow 
Harris,  he  concludes  by  .saying, 
"  I  put  forth  mj'  particular  view 
with  doubt  and  fear,  lest  it  should 
not  bear  the  test  of  general  examina- 
tion," &c.  (No.  1300). 

^  It  took  more  than  ten  j'ears 
before  the  purely  geometrical  or 
conventional  use  of  the  term  "  lines 
of  force "  ripened  into  a  pliysical 
conception.  The  latter  is  definitely 
expounded  in  a  i)apcr  in  the  '  Philos. 
Magazine'  for  June  1852.  We  can 
compare  this  gradual  development 
of  a  symbolical  into  a  physical 
theorj'  with  the  gradual  develop- 
ment of  the  atomic  theory ;  atoms 
and  molecules  becoming  a  physical 
necessity  to  chemists  long  after 
they  had  been  used  simply  as  a 
convenient  representation  of  the 
laws  of  equivalence  and  of  the  fixed 
proportions  of  combination  (see 
vol.  i.  of  this  work,  chap,  v.,  p. 
432,    &c.)       Faraday,    during    the 


years  1810  to  18o0,  la»j<)uretl  at  two 
great  problemn  :  the  one  he  iiolve<i 
brilliantly  and  in  tlie  direction  he 
anticipated  ;  the  otlier  remains  a 
problem  to  this  day.  The  first 
refers  to  the  action  of  magnetic  on 
the  dielectric.  The  dielectric,  the 
space  which  Continental  philo- 
sophers considered  as  a  vacuum  no 
far  as  magnetic  and  electrical  i.henu- 
mena  are  concerned,  had  Ijeen  filled 
by  Young  and  Fresnel  with  the 
luminifennis  ether.  Faraday  sus- 
pected that  this  luminiferous  ether 
cannot  be  insensible  U)  magnetic 
action,  and  he  .sought  in  the  exi>eri- 
mental  proof  of  the  action  of  mag- 
nets on  rays  of  light  in  the  sur- 
rounding space  a  support  for  his 
view  of  the  part  which  the  dielectric 
plays  in  the  transmission  of  electric 
and  magnetic  action.  After  many 
ineffectual  attemjjts  to  prove  this, 
he  could  at  last  (November  1845) 
announce  his  results  to  the  Royal 
Society  iis  follows:  "These  inef- 
fectual exertions  .  .  .  could  not 
remove  my  strong  jiersuasion  de- 
rived from  philo3oi)hical  considera- 
tions ;  and  therefore  I  recently 
resumed  the  inquiry  by  exf>erinient 
in  a  most  strict  and  searching 
manner,  and  have  at  last  succeeded 
in  magnetising  and  electrifijing  a 
ray  of  light,  and  in  illumiiuitiixg  a 
magnetic  line  of  force.  .  .  .  Em- 
ploying a  ray  of  light,  we  can  tell, 
by  the  eye,  the  direction  of  the 
magnetic  lines  througli  a  body  ;  and 
by  the  alteration  of  the  ray  and  it* 
optical  effect  on  the  eye,  can  sec 
tlie  course  of  the  lines  just  as  we 
can  see  the  course  of  a  thread  of 
glass  or  any  other  trans|)arent  sub- 
stance, rendereil  visible  bv  the 
light "  ('  Exp.  Res.,'  vol.  iii.,  N.').  2148 
and  note).  The  second  problem 
which  Faraday  attjicked  was  to 
prove    a    similar    "connection    l>e- 


70 


SCIENTIFIC    THOUGHT. 


to  Cavendish,  that  in  the  case  of  electric  attraction  and 
repulsion,  the  nature  of  the  intervening  medium  was  of 
importance :  it  played  a  part  in  the  electric  phenomena 
in  the  same  way  as  in  the  propagation  of  light  and  heat 
the  intervening  medium  played  a  definite  part.  This 
part  had  been  entirely  overlooked  by  Continental  philos- 
ophers, who  worked  on  the  hypothesis  of  an  immediate 
action  at  a  distance,  based  upon  the  analogy  of  gravi- 
tation. Their  researches,  carried  on  by  methods  similar 
to  those  invented  by  Laplace  and  his  school  for  the  cal- 
culation of  the  combined  effect  of  gravitational  forces  at 
various  points  in  space,  entirely  ignored  the  question  how 
such  effects  were  brought  about.  As  time  did  not  seem 
to  enter  as  an  appreciable  factor,  the  investigation  of  the 
mechanism  by  which  action  at  a  distance  was  communi- 
cated was  set  aside  as  unnecessary  or  impossible :  the 
astronomical  view  of  the  phenomena  sufficed.  For 
Faraday,  the  intervening  medium,  which — as  in  the  com- 
munication of  light  and  heat — took  an  active  part,  the 
question  of  its  nature  and  mode  of  action  was  very 
important ;  he  accordingly  first  of  all  gave  it  a  name. 
As  in  optics  the  term  luminiferous  ether  had  been 
recently  revived,  and  had  become  familiar  through 
Young  and  Fresnel,  so  through  Faraday  were  intro- 
duced the  terms  "  dielectric "  and  "  magnetic  field," 
as  the  carriers  of  ejectric  and  magnetic  action ;  and 
though    for    a    long    time    used   only   by   himself,   they 


tween  gravity  and  electricity."  On 
the  failure  of  this  attempt  he  fully 
reported  in  his  Bakerian  Lecture, 
November  1850  ('Exp.  Res.,'  vol. 
iii.  p.  161).  But  the  former  results 
were  sufHcient  to  ripen    gradually 


in  his  mind  the  idea  of  the  physical 
nature  of  the  lines  of  force,  which 
he  expounded  with  increasing  pre- 
cision from  1851  onward.  (See 
'  Exp.  Res.,'  28th  series,  vol.  iii.  p. 
328  ;  also  pp.  402,  438.) 


KINETIC    OR    MECHANICAL    VIEW    OF    NATURE.       71 

liave  been  the  means  of  keeping  l>efore  the  minds  of 
natural  philosophers  the  question  h«iw  these  actions 
are  mechanically  communicated,  a  problem  which  lay 
outside  of  the  astronomical  view  of  tlie  phenomena. 
To  Faraday  himself  the  analogy  between  the  phenomena 
of  these  actions  meant  also  a  real  physical  relation 
or  even  identity,  a  supposition  which  he  followed  up 
with  unwearying  patience  and  all  the  experimental 
resources  of  his  inventive  mind,  till  lie  succeeded  in 
showing  by  experiment  that  magnets  in  the  neighbour- 
ho(jd  of  transparent  substances  which  ]ia\e  a  polarising 
effect  on  rays  of  light  possessed  the  jiroperty  of  altering 
the  direction  in  which  the  jjolarised  rays  show  their 
laterality.  Faraday's  conception  of  "  lines  of  force " 
filling  all  space  and  explaining  electric  and  magnetic 
action,  radiation,  and  possibly  also  gravitation,  was 
elaborated  during  the  years  1830  to  ISoO.  An  opinion 
then  prevailed  that  his  discoveries  stood  in  opposition  to 
the  views  elaborated  and  experimentally  verified  by 
Continental   philosophers.       The   first   who   showed    the        46. 

Devplop- 

analogy  and  threw  out  a  hint  how  the  two  views  could  imntofthe 

^^  conception 

be  brought  into  harmony  was  William  Thomson  (Lord  ^J^"^ 
Kelvin).      As   early  as   1842,^  when   scarcely  eighteen 

^  "  On   the   uniform   motion   of  [   heat   in    certain    perfectly   defined 

Heat  in  homogeneous  solid  bodies,  circumstances.    With  developments 

and  its  connexion  with  the  niathe-  and    apijlications    contained    in    a 

matical     theory     of     Electricity,"  subsequent  paper  (1845),  they  con- 

'  Cambridge    Mathematical    Jour-  '.    stitute   a  full  tlieory  of  the  cliar- 

nal,' February  1842.    The  following  acteristics  of  lines  of  force,  which 

note  is  attached  to  the  reprint  in  have  been  so  admirably  investigated 

the    '  Philosophical    Magazine '    of  experimentally    by     Faraday,    and 

1854  :    "  The    general    conclusions  complete    the    analogy    with     the 

established   show   that  the  laws  of  theory  of   the  conduction  of  iieat, 

distribution  of  electric  or  magnetic  of  which   such  terms  as  'conduct- 


force  in  any  case  whatever  must  be 
identical  with  the  laws  of  distri- 
bution   of   the  lines  of    motion    of 


ing  power  of  lines  of  force '  ('  Exp. 
Re8.,'Noa.  2797-2802)  involve  the 
idea. " 


72 


SCIENTIFIC   THOUGHT. 


years  old,  but  already  acquainted  with  English  experi- 
mental and  French  mathematical  researches,  he  pointed 
out  how  phenomena  of  flow — i.e.,  of  motion — could  be 
mathematically  grasped  by  a  formula  quite  similar  to 
that  of  the  distribution  of  masses  at  rest  and  appar- 
ently governed  by  attractive  forces  at  a  distance.  For 
instance,  the  distribution  of  temperature  at  various  dis- 
tinct points  in  a  space  in  which  a  flow  of  heat  from  an 
origin  had  brought  about  a  stationary  condition  (the 
equilibrium  being  dynamical,  not  statical),  was  mathe- 
matically expressed  by  a  formula  identical  with  that 
which,  according  to  Poisson  and  others,  gave  the  dis- 
tribution of  electrical  or  attracting  masses.  Now  we 
know  that  in  the  former  case  the  equilibrium  is  main- 
tained by  a  flow  across  the  intervening  space,  which  takes 
time.  This  suggests,  therefore,  the  possibility  of  ex- 
plaining the  so-called  statical  effects  of  attracting  or 
repelling  masses  kinetically  by  a  process  of  flow  or  motion 
going  on  in  the  intervening  medium,  a  notion  to  which 
Faraday  clung  tenaciously.  In  1845  Thomson  reverted 
to  this  subject,  and  after  harmonising  the  two  views, 
concluded  by  stating  that  the  latter  "  method  of  establish- 
ing the  mathematical  theory  would  be  even  more  simple 
if  possible  than  that  of  Coulomb."  ^ 


^  "  On  the  Mathematical  Theory 
of  Electricity  in  Equilibrium," 
1845.  See  '  Reprint  of  Papers  on 
Electrostatics  and  Magnetism,'  2nd 
ed. ,  p.  29.  A  study  of  these  mathe- 
matical researches  of  Lord  Kelvin, 
beginning  early  in  the  'forties  and 
extending  over  more  than  twenty 
years,  is  of  special  historical  in- 
terest, as  showing  the  gradual 
growth  of  a  physical  out  of  a  purely 


mathematical  theory  :  most  of  the 
conceptions  which  have  since  be- 
come general  through  Maxwell's 
electro-magnetic  theory,  as  it  has 
been  developed  and  popularised 
by  subsequent  writers  (notably 
Prof.  Poynting,  Prof.  Oliver  Lodge, 
and  Mr  Oliver  Heaviside),  being 
already  contained  in  Thomson's 
papers  as  mathematical  notions. 
Thomson  is  throughout  careful  to 


KINETIC    OR    MECHANICAL    VIEW    OF    NATUUE.       73 


This  suggestion  was  not  carried  out  for  some  time, 
and  then  not  l>y  Thomson  himself,  but,  at  his  instiga- 
tion, by  Clerk  Maxwell.  In  the  meantime,  however, 
Tiiomson  added  another  step  to  the  one  already  taken,  by 
bringing   recent   discoveries   of   Faraday,  as   well  as   his 


point  uut  how  the  elementary  ex- 
perimental data  referring  to  elec- 
trical charges,  as  well  as  to  mag- 
netic bodies,  can  be  mathematically 
expressed  equally  well  by  the  con- 
ceptions of  Cf)ulomb  and  Poisson 
ami  by  those  of  conducti(^n  and  How, 
which  are  more  in  conformity  with 
Faraday's  physical  ideas :  neither 
of  the  mathematical  analogies,  of 
attraction  at  a  distance  or  of  con- 
duction through  an  intervening 
medium,  being  sufficient  for  a 
physical  theory.  These  papers  con- 
tain further  the  record  of  the 
gradual  growth  in  the  author's 
mind  of  the  kinetic  out  of  the 
statical  view  of  natural  phenomena. 
Thomson  was  the  first  (18.51)  to 
introduce  the  terms  "field"  and 
"lines  of  force"'  into  mathemati- 
cal literature,  adopting  them  from 
Faraday.  They  have  since  become 
indispensable  not  only  to  the  electri- 
cian but  likewise  to  the  mathema- 
tician ;  forming,  as  it  were,  a  unify- 
ing term  for  apparently  distant 
regions  of  physical  phenomena,  and 
being  introduced  as  fundamental 
notions  at  the  beginning  of  dynami- 
cal treatises.  See,  for  instance,  the 
article  by  M.  Abraham  entitled 
"  Geometrische  Grundbegrifre,"  in 
the  second  part  of  the  fourth  volume 
of  the  '  Encyclopildie  der  mathe- 
matischen  Wissenschaften,'  Leipzig, 
Teubner,  190L  Independently  and 
quite  unknown  to  Faraday,  or  to 
each  other,  two  eminent  mathe- 
maticians. Sir  W.  K.  Hamilton  at 
Dublin  and  Herrmann  Grassmann 
at  Stettin,  were  elaborating,  be- 
tween 1835  and  1845,  the  geo- 
metrical conceptions  and  vocabulary 


wliiL-h  are  required  in  the  repre- 
sentation of  "directed"  quantities. 
Their  exijositions  have  since  become 
much  simplified,  and  now  font), 
under  the  title  of  "  vector  an- 
alysis," an  indispensable  geometrical 
instrument.  Tlie  gradual  evolution 
of  the  kinetic  view  of  jiliyiiical 
phenomena  (which  here  concerns  us 
most)  in  the  memoirs  of  Thomson 
is  most  remarkable.  Inter  alia,  he 
made  a  communication  in  1847  to 
the  British  As.'-ociation  at  Oxford, 
in  whicli  he  dealt  with  the  phe- 
nomena of  terrestrial  magnetism, 
stating  that  "it  becomes  an  in- 
teresting question  whether  mere 
electric  currents  could  produce  the 
actual  j(hen(jmena  observed.  Am- 
pere's electro-magnetic  theory  leads 
us  to  an  affirmative  answer  which 
must  be  regarded  as  merely  theor- 
etical ;  for  it  is  absolutely  impossible 
to  conceive  of  the  currents  which  he 
descriljes  round  the  molecules  of 
matter  as  having  a  physical  exist- 
ence "  (Reprint,  2nd  cd.,  p.  469). 
On  this  pas.sage  he  himself  remark-* 
in  1872  :  "  From  twenty  to  twenty- 
five  years  ago,  I  had  no  belief 
in  the  reality  of  this  [AmJ>^re's] 
theory  ;  but  I  did  not  then  know 
that  motion  is  the  very  es.sence  of 
what  has  hitherto  been  called 
matter.  At  the  1847  meeting  of 
the  British  Association  in  Oxfortl 
I  learned  from  Joule  tlie  dynamical 
theory  of  heat,  and  was  forced  to 
abandon  at  once  many,  and  gi-adu- 
aliy  from  year  to  year  all  other, 
statical  preconcci)tions  regarding 
the  ultimate  causes  of  apparently 
statical  phenomena"  (ibid.,  p.  423 
note). 


74 


SCIENTIFIC    THOUGHT. 


unique  conception  of  the  communication  of  electric  and 
magnetic  phenomena,  into  connection  with  the  mathe- 
matical theory  which  had  been  founded  and  worked  out 
by  Poisson  and  Green.  Without  attempting  to  give 
a  physical  explanation  of  Faraday's  lines  of  force,  he 
showed  how  they  could  be  utilised  in  calculating  the 
complicated  action  of  magnetic  push -and -pull  forces; 
suggested  that  the  newly  discovered  property  called  dia- 
magnetism,  in  virtue  of  which  bodies  in  the  neighbour- 
hood of  powerful  magnets  appeared  to  be  repelled,  not 
attracted,  could  be  explained  as  a  differential  ^  effect  of 


1  It  was  in  the  year  1845  that 
Faraday,  after  having  discovered 
the  "magnetisation  of  light,"  and 
made  visible  the  "  magnetic  lines 
of  force"  ('Exp.  Res.,'  Nos.  2146- 
2242),  entered  upon  that  remark- 
able series  of  experiments  and 
speculations  which  led  him  to  the 
discovery  of  diamagnetism  and  to 
the  assertion  of  the  "  magnetic  con- 
dition of  all  matter"  (ibid.,  Nos. 
2243,  &c.)  In  1847  Thomson  wrote  : 
"  According  to  Mr  Faraday's  recent 
researches  it  appears  that  there  are 
a  great  many  substances  susceptible 
of  magnetic  induction,  of  such  a 
kind  that  for  them  the  value  of  the 
coefficient  i  is  negative.  These  he 
calls  diamagnetic  substances,  and 
in  describing  the  remarkable  re- 
sults to  which  his  experiments 
conducted  him  with  reference  to 
induction  in  diamagnetic  matter, 
he  says,  '  All  the  phenomena  re- 
solve themselves  into  this,  that  a 
portion  of  such  matter,  When  under 
magnetic  action,  tends  to  move 
from  stronger  to  weaker  places  or 
points  of  force.'  This  is  entirely 
in  accordance  with  the  result  ob- 
tained above  ;  and  it  appears  that 
the  law  of  all  the  phenomena  of 
induction  discovered  by  Faraday 
with  reference  to  diamagnetics  may 
be  expressed  in  the  same  terms  as 


in  the  case  of  ordinary  magnetic 
induction,  by  merely  supposing 
the  coefficient  i  to  have  a  nega- 
tive value  "  (Reprint,  p.  502).  In 
the  Reprint  (1854)  of  his  early 
papers  (1842)  on  the  corresponding 
problems  of  magnetism  and  heat 
(Reprint,  p.  18)  he  added  a  note  to 
the  effect  that  the  "same  demon- 
stration is  applicable  to  the  in- 
fluence of  a  piece  of  soft  iron,  or 
other  paramagnetic,  or  to  the  re- 
verse influence  of  a  diamagnetic 
on  the  magnetic  force  in  any 
locality  near  a  magnet  in  which  it 
can  be  placed,  and  shows  that  the 
lines  of  magnetic  force  will  be 
altered  by  it  pi-ecisely  as  the  lines 
of  motion  of  heat  in  corresponding 
thermal  circumstances  would  be 
altei-ed  by  introducing  a  body  of 
greater  or  less  conducting  power  of 
heat.  Hence  we  see  how  strict 
is  the  foundation  for  an  analogy  on 
which  the  conducting  power  of  a 
magnetic  medium  for  lines  of  force 
may  be  spoken  of,  and  we  have  a 
perfect  explanation  of  the  con- 
densing action  of  a  paramagnetic, 
and  the  repulsive  eSect  of  a  dia- 
magnetic upon  the  lines  of  force  of 
a  magnetic  field,  which  have  been 
described  by  Faraday "  (Reprint, 
p.  33  note  ;  cf .  Faraday,  '  Exp. 
Res.,'  Nos.  2807,  2808). 


KINETIC    OR   MECHANICAL    VIEW    OF    NATURE.       75 


the  magnetic  actions  which  liclong  to  all  Kubstances ; 
introduced  the  term  magnetic  "  permealjilily  "  '  as  de- 
scriptive of  the  degree  in  which  various  substances 
acquire  magnetic  properties  and  conduct  the  lines  of 
magnetic  force  in  the  neighbourhood  of  powerful  mag- 
nets ;  and  finally  demonstrated  how,  if  these  properties 
were  considered  as  having  different  degrees  in  the  dif- 
ferent axes  of  crystals,  in  analogy  with  the  dillerent 
elasticities  which  they  exhibited,  the  consequence  would 
be  a  turning  effect  which  would  explain  the  changed 
optical    properties    of    crystals    under    the    influence    of 


magnetic   action. 


Tn   these  investigations  the  ideas  of 


'  Tliis  property  was  afterward.s 
termed  "  permeabifity  "  by  Thom- 
son (Reprint,  p.  489,  1872).  The 
general  rule  of  magnetic  action  can 
then  be  expressed  by  saying  that 
"  by  virtue  of  differential  action  a 
body  may  behave  paramagnetically 
or  diamagnetically  according  as  it 
is  j)laced  in  a  less  or  a  more  perme- 
able medium  than  itself  "  (Clirystal 
in  article  "  Magnetism,"  '  Ency. 
Brit.,'  9th  ed.,  vol.  xv.  p.  248). 

-  "On  Ihe  Theory  of  Magnetic 
Induction  in  Crystalline  and  Non- 
crystalline Substances  "  (  '  Philos. 
Mag.,'  March  18.57  ;  also  Reprint, 
2nd  ed.,  p.  471,  <&c.)  Poisson  had 
alreadj'  foreseen  the  mathematical 
possibility  of  wliat  Faraday  termed 
magne-  (correctly  magneto-)  crys- 
tallic  action,  but  "  ce  cas  singulier 
ne  s'ctant  pas  encore  prdsente  h. 
I'observation,  nous  I'exclurons  de 
nos  recherches  "  ("  Mumoire  sur  la 
Thcorie  du  Magndt.isme,"  '  Mem.  de 
I'Institut,  Paris,  1826,'  quoted  by 
Thomson,  Reprint,  p.  484).  .Stimu- 
lated by  the  discoveries  of  Faraday, 
Pliicker  at  Bonn,  during  the  extra- 
ordinary interval  wliicli  separated 
the  second  from  tlie  first  jjcriod  of 
his  original  geometrical  speculations 
(see  vol.  i.  ]>.  242  of  this  work),  de- 


voted himself  to  the  study  of  the 
electric  and  magnetic  jirnjierties  of 
givses  and  crystals,  and  in  1847 
commenced  that  remarkalile  series 
of  physical  memoirs  through  which 
he  became  the  fellow-worker,  if  not 
the  rival,  of  Faradaj-.  One  of  hia 
first  discoveries  wa.s  the  action  of 
magnets  on  crystals,  published  in 
1847  (Pogg.  Ann.,  or  Pliicker's 
'  Physicalische  Abhandlungen,'  ed. 
Pockels,  Leij)zig,  1896,  p.  6,  &c.), 
which  supplied  to  Thomson  "the 
verj'  circumstance  the  observation 
of  which  wa.s  wanting  to  induce 
Poisson  to  enter  ujion  a  full  treat- 
ment of  the  subject,  and  made  the 
working  out  of  a  mathematical 
theory  of  magnetic  induction  .  .  . 
independently  of  any  hyjwthesis 
.  .  .  ujion  a  purely  exjierimental 
foundation  .  .  .  imjwrtant "  (Tliom- 
son,  loc.  cit.,  p.  471).  Pliicker  was 
an  original  thinker,  and  mainly  a 
self-taught  geniu.-s,  imjierfectly  ac- 
quainted with  the  labours  of  liis 
contemi)oraries  or  predecessors. 
Thi.s  has  been  noted  i>y  his  biog- 
raphers as  much  in  liis  geometrical 
as  in  his  physical  researches  (.see 
tlic  memoirs  of  Cleb.sch  and  of  Prof. 
Riecke,  jncfixed  to  the  two  volumes 
of  the'Gesammclte  Abliandlungen '). 


76 


SCIENTIFIC    THOUGHT. 


47. 
Clerk 
Maxwell. 


Faraday  are  used  merely  for  the  sake  of  describing  and 
calculating  in  the  simplest  manner  phenomena  which 
had  been  experimentally  discovered  :  no  attempt  was 
made  to  explain  physically  how  these  actions  come 
about.  In  fact,  under  the  hands  of  Thomson  the  con- 
ceptions of  Faraday  were  formulated  as  Dalton's  atomic 
theory  had  been  elaborated  by  chemists  in  the  first  half 
of  the  century,  for  the  purpose  of  symbolically  represent- 
ing and  calculating  observed  phenomena. 

But  the  "  lines  of  force  "  of  Faraday  were  not  to  remain 
a  mere  symbolical  representation,  any  more  than  Dalton's 
atoms  were  to  remain  merely  counters  of  a  chemical  arith- 
metic. Both  theories  were  to  be  raised  to  the  rank  of 
physical  theories.  What  the  kinetic  theory  of  gases  did 
for  the  atomic  theory  was  done  for  Faraday's  symbolism 
by  the  researches  of  Clerk  Maxwell.  And  as  the  fact 
that  the  molecules  of  matter  could  be  really  counted, 
and  their  distances  and  velocities  measured,  gave  life  and 
actual  meaning  to  the  atomic  view  of  natural  phenomena, 


In  his  early  geometrical  researches 
he  worked  in  ignorance  of  the  re- 
markable '  Traite '  of  Poncelet, 
which  had  been  published  in  1822 
{loc.  cit.,  vol.  i.  p.  594,  &c.)  :  even 
the  writings  of  his  countryman 
Mobius  were  unknown  to  him. 
Still  more  extraordinary  was  his 
comparative  unacquaintance  with 
the  electrical  measurements  and 
theories  which  dominated  German 
research  when  he  commenced  his 
physical  labours,  and  which  eman- 
ated from  the  school  of  Gauss  and 
Weber.  But  he  was  equally  ignor- 
ant of  the  purely  mathematical 
theories  of  Poisson  and  Thomson, 
which,  as  he  himself  candidly  con- 
fessed,    might     have     saved    him 


from  important  errors  {loc.  cit.,  vol. 
ii.  p.  460),  and  which  were  later 
made  more  widely  known  in  Ger- 
many by  the  excellent  treatise  of 
his  pupil  Beer  ( '  Einleitung  in  die 
Elektrostatik,'  &c.,  Braunschweig, 
1869),  posthumously  edited  by 
Plucker  himself.  The  fact  that 
Pliicker  was  not  influenced  by  the 
spirit  of  Weber's  researches  prob- 
ably made  him  more  appreciative  of 
Faraday's  purely  physical  methods. 
In  such  names  as  Beer,  Clebsch, 
Klein,  Fessel,  Geissler,  and  Hittorf, 
Pliicker  counts  an  illustrious  array 
of  pupils  and  fellow-workers.  See 
Clebsch's  characteristic  of  Plucker, 
loc.  cit.,  vol.  i.  p.  xii,  &c 


KINETIC    OR    MECHANICAL    VIEW    OF    NATURE.       77 

SO  the  rays  of  electric  and  magnetic  force  seen  by  Faraday 
ill  tlie  abstraction  of  bis  intuitive  mind  became  a  reality 
for  every  experimentalist  when  Hertz  in  1888  actually 
showed  the  wonderful  action  of  electric  waves  at  a  dis- 
tance. Atoms  and  lines  of  force  have  become  a  practical 
— shall  I  say  a  popular  ? — reality,  whereas  they  were  once 
only  the  convenient  method  of  a  single  original  mind  for 
gathering  together  aiul  unifying  in  thought  a  bewildering 
mass  of  observed  phenomena,  or  at  most  capable  of  being 
utilised  for  a  mathematical  description  and  calculation  of 
actual  effects. 

For  a  (juarter  of  a  century  after  Faraday  had  conceived 
the  notion  of  looking  upon  electric  and  magnetic 
phenomena  as  depending  on  a  property  belonging  to 
all  matter,  and  pervading  all  space,  like  radiation  and 
gravity,  the  only  natural  ])hilosopher  wlio  to  any  extent 
entered  into  his  ideas  was  Thomson.  Even  Tyndall,  who 
came  more  than  any  other  prominent  physicist  under 
Faraday's  immediate  and  personal  inlluence,  and  contrib- 
uted largely  to  our  knowledge  of  the  new  phenomena 
discovered  by  his  great  master,  does  not  seem  to  have 
assimilated  his  scientific  language  and  reasoning.  It 
required  a  mathematical  mind  really  to  grasp  and  put 
into  form  Faraday's  notions.  Encouraged  by  Thomson, 
and  soon  after  the  publication  of  'i1ioins(ni's  mathe- 
luatical  theory  of  magnetism,  (Terk  jMaxwell  devoted 
himself  to  a  theoretical  study  of  electricity  and  allicil 
subjects,  a  field  wliich  Thomson  bail  tlicii  ahnost  mon- 
opohsed  in  this  country.^      The  first  of  Maxwell's  revolu- 

'  See  Professor  Glazebrook's  little  "Century  Science  Scries."  1901. 
book  on  '  James  Clerk  Maxwell  and  On  page  42  a  letter  of  Maxwell  i6 
Modern  Pliysics,'  published  in  tlie       (juoted,    in    which    he    speaks    of 


78 


SCIENTIFIC    THOUGHT. 


48. 
His  series 
of  works 
on  the 
theory  of 
electricity. 


tionaiy  series  of  works,  '  On  Faraday's  Lines  of  Force,' 
was  published  in  December  1855.  The  series  was 
completed  by  the  appearance  in  1873  of  his  great  work 
on  '  Electricity  and  Magnetism,'  which  has  formed  the 
centre  of  a  large  literature  to  which  all  the  scientific 
schools  of  Europe  and  America  have  contributed.  Histori- 
cally, Maxwell  brought  together  two  distinct  and  very 
fruitful  lines  of  reasoning,  due  to  Faraday  and  Thomson.^ 
He  was  impressed  with  the  desideratum  of  every  physical 
theory  bearing  on  any  large  class  of  phenomena — viz., 
that  it  must  be  mathematical  and  physical  at  the  same 
time.  His  own  theory  had  to  embrace  and  unite  all  the 
purely  arithmetical  and  geometrical  regularities  which 
had  been  discovered,  and  which  at  that  time  were 
known  to  describe  correctly  the  facts  of  electric,  mag- 


"  poaching  upon  Thomson's  electri- 
cal preserves."  In  the  preface  to  the 
treatise  on  electricity  and  magnet- 
ism, he  refers  to  the  apparent  dis- 
crepancy between  the  views  of 
Faraday  and  the  mathematicians, 
and  he  states  that  he  had  arrived 
at  "  the  conviction  that  this  dis- 
crepancy did  not  arise  from  either 
party  being  wrong.  I  was  first 
convinced  of  this,"  he  proceeds,  "  by 
Sir  William  Thomson,  to  whose 
advice  and  assistance,  as  well  as  to 
his  published  papers,  I  owe  most  of 
what  I  have  learned  on  the  subject. 
^  In  a  different  reference  we  may 
say  that  Maxwell's  theory  was  pre- 
pared by  three  independent  lines  of 
research,  starting  respectively  in 
France,  Germany,  and  England :  (1) 
The  investigation  of  the  actions  at 
a  distance  of  electrified  and  mag- 
netised bodies,  and  of  electric 
currents,  which  found  mathemati- 
cal expression  in  the  formula  of 
Coulomb    and   Ampere.     The   full 


significance  and  capabilities  of  the 
formula)  of  electrostatic  and  mag- 
netic action  had  been  demonstrated 
by  Thomson,  who  especially  showed 
that  these  relations  were  not 
necessarily  confined  to  the  physical 
theory  which  had  been  elaborated 
on  the  Continent,  but  that,  mutatis 
mutandis,  they  lent  themselves 
equally  well  to  the  physical  ideas  of 
Faraday.  (2)  The  exact  measure- 
ments of  magnetic,  electro-dynamic, 
and  galvanic  action  started  bj'  Ohm 
and  Gauss  in  Germany,  and  much 
extended  by  Weber.  (3)  The  idea 
of  physical  lines  of  force,  filling 
space  and  representing  action 
through  contiguous  particles,  not 
at  a  distance,  elaborated  by  Fara- 
day. These  tliree  lines  of  research 
were  brought  together  in  the 
theory  of  Maxwell,  which  in  the 
beginning  professed  to  be  only  a 
mathematical  but  ended  by  being  a 
physical  theory. 


KINETIC    OK    MECHANICAL    VIEW    OF    NATLllK.       79 

iietic,  and  galvanic  phenomena,  such  as  Coulomb's  electro- 
static and  magnetic  laws,  Ampere's  electro-dynamic  and 
electro-magnetic  formulie,  and  Ohm's  anil  Faraiiay's  laws 
referring  to  galvanic  currents,  and  many  othei-s.  It 
liad  also  to  give  an  intelligible  representation  of  t!ie 
elementary  actions  of  which  these  complicated  plienom- 
ena  are  made  np.  In  mder  to  arrive  at  the  latter,  the 
method  usually  employed  is  to  look  for  anabjgies  in 
other  provinces  of  science  where  the  desired  uniticatiun 
has  already  I'cen  brought  about.  The  great  natural 
philosophers  of  the  French  school  who  had  so  success- 
fully accomplished  the  most  extensive  unification  yet 
attempted  in  any  large  branch  of  knowledge — tlie  uni- 
fication of  physical  astronomy  under  Newton's  gravita- 
tion formula — had  tried  to  follow  up  this  analogy  in 
Dther  realms  of  research,  and  had  developed  what  I 
called  in  a  former  chapter  tlie  astronomical  view  of 
natural  phenomena.  Ampere,  and  notably  "Weber,  had 
extended  this  analogy  so  as  to  embrace  electric  and 
magnetic  phenomena.  There  was,  however,  another 
analogy  which  was  more  familiar  to  the  great  experi- 
mentahsts  in  this  country,  notal)ly  to  Faraday — namely, 
the  analogy  of  those  various  phenomena  which  depend 
on  processes  of  emanation,  of  a  gradual  spreading  out, 
of  a  How  or  conduction:  tliose  plieiumiena  where  the 
factor  of  time  comes  in,  and  where  an  apparently  sta- 
tionary condition  is  brought  about  by  a  mode  of  motion, 
or  what  has  been  termed  a  "  dynamic  equilibrium." 
Thomson,  starting  from  Fourier's  mathematical  analysis 
of  sucli  processes,  had  been  led  to  sec  bow  far-reaching 
this  analogy  is,  and   bad  latterly  (1852)  extemied   it  to 


80 


SCIENTIFIC    THOUGHT. 


49. 

His  con- 
ception of 
"tubes  of 
force." 


embrace  the  processes  of  the  flow  of  heat,  of  electricity, 
magnetic  and  diamagnetic,  and  of  Huid  motion.  "  He 
called  attention  to  the  remarkable  resemblance  which 
the  diagrams  of  flow  bore  to  those  which  Mr  Faraday 
had  recently  shown  at  the  Eoyal  Institution  to  illus- 
trate his  views  regarding  the  action  of  ferro-magnetics 
and  diamagnetics  in  influencing  the  field  of  force  in 
which  they  are  placed,  and  justified  and  illustrated  the 
expression  '  conducting  power  for  the  lines  of  force '  by 
referring  to  rigorous  mathematical  analogies  presented 
by  the  theory  of  heat."  ^ 

This  view,  which  Thomson  had  merely  shadowed  forth, 
was  more  fully  worked  out  by  Maxwell  in  1855  and 
1861.  His  methods  ^  were  "  generally  those  suggested  by 
the  processes  of  reasoning  which  are  found  in  the  re- 
searches of  Faraday,  and  which,  though  they  had  l^een 
interpreted  mathematically  by  Prof.  Thomson  and  others, 
are  very  generally  supposed  to  be  of  an  indefinite  and 
unmathematical  character  when  compared  with  those 
employed  by  the  professed  mathematicians."  The  first 
addition  which  he  introduced,  by  which  he  made  Fara- 
day's "  lines  of  force  "  mathematically  more  definite,  was 
to  change  them  into  "  tubes  of  force,"  which  represented 
not  only  the  direction  of  force  at  every  point  of  space, 
but  also — according  to  their  sectional  dimensions — the 
intensity  of  the  force.     These  tubes  were  supposed  to  be 


^  Abstracts  of  two  communica- 
tions to  the  British  Association  at 
Belfast  in  1852,  "  On  certain  Mag- 
netic Curves  :  with  Applications  to 
Problems  in  the  Theories  of  Heat, 
Electricity,  and  Fluid  Motion " 
(Reprint  of  Papers,  &c. ,  p.  519,  &c.) 


-  James  Clerk  Maxwell  "  On 
Faraday's  Lines  of  Force,"  '  Trans- 
actions of  the  Cambridge  Philo- 
sophical Society,'  1855.  See  'Col- 
lected Scientific  Papers,'  vol.  i.  p. 
157. 


KINETIC    Oil    MECHANICAL    VIEW    UF    NATURE.       81 


filled  with  a  moving  tiuid,  and  the  velocity  of  the  How  — 
inversely  proportional  to  the  sectional  area  of  the  tuljes 
— represented  the  intensity  of  the  force  at  any  point  in 
space.  He  also  showed  how  very  much  simpler  the  con- 
ception becomes,  if  the  law  of  tlie  acting  forces  is  the 
experimentally  established  law  of  the  inverse  square  of 
the  distance. 

This  thought  of  "  referring  to  the  purely  geometrical 
idea  of  the  motion  of  an  imaginary  tluid "  ^  was  tlie 
beginning  of  the  now  universally  adopted  view  of  a 
very  large  class  of  plienomena,  and  it  was  at  the  same 
time  a  great  step  in  the  development  of  tlie  kinetic 
or  mechanical  view  of  natural  processes.  These  lines  or 
tubes  of  force,"^  with  which  all  space  surrounding  magnets 
or  electrified  bodies  was  supposed  to  be  filled,  enal)led 
Maxwell  further  to  give  a  definite  representation  of  that 

peculiar   state   of    matter   of   which    Faradav   had    very        so. 
^  ^  J  "Electro- 

early    formed    an    indefinite    conception,   and   wliich    he  oj'jj^'t^r'* 

called    the  "  electrotonic  state."     Thomson   had   already 

in  1847  ^  shown  how  the  ideas  of  Faraday,  who  as  early 


^  How  little  ]\laxwell  originally 
intended  to  give  a  physical  theory 
is  seen  from  the  concluding  sen- 
tences of  the  introduction  to  his 
first  paper  {!oc.  cit.,  vol.  i.  p.  159)  : 
"  By  referring  everything  to  the 
purely  geometrical  idea  of  the 
motion  of  an  imaginary  fluid,  I 
hope  to  attain  generality  and  pre- 
cision, and  to  avoid  the  dangers 
arising  from  a  premature  theory 
professing  to  explain  the  cause  of 
the  phenomena.  If  the  results  of 
mere  speculation  which  I  have 
collected  are  found  to  be  of  any 
use  to  experimental  philosophers, 
in  arranging  and  interpreting  their 
results,  they  will  have  served  their 

VOL.  II. 


purpose,  and  a  mature  theory,  in 
which  physical  facts  will  be  physi- 
cally explained,  will  be  formed  by 
those  who  by  interrogating  Nature 
herself  can  obtain  tlie  only  true 
solution  of  the  (luestions  which  the 
mathematical  theory  suggests." 

-'  Faraday  had  already  in  1852 
spoken  of  shells  and  tubes  of  force, 
and  invented  the  term  sphondyloid 
to  denote  the  portion  of  space  en- 
closed between  such  shells  of  force 
('Exp.  Kes.,'  vol.  iii..  No.  3271). 

2  In  1847  ('Cambr.  and  Dubl. 
Math.  Journal,'  lepriiited  in  '  Matli. 
and  Phys.  Pai>ers,'  vol.  i.  p.  76) 
Thomson  wrote  tlmt  Faraday's 
theory    of    electrostatic    inductii>n 


82 


SCIENTIFIC    THOUGHT. 


as  1831  conceived  this  peculiar  condition  of  matter  to 
be  equivalent  to  a  state  of  strain,  could  be  represented 
by  the  mechanical  analogy  of  the  strains  existing  in  an 
elastic  solid.  He  had  distinguished  three  distinct  forms 
of  this  elastic  strain,  and  had  identified  these  three 
forms  severally  with  electrostatic,  magnetic,  and  galvanic 
forces.  He  had  not  given  a  physical  explanation  of  the 
origin  of  these  forces,  but  had  merely  used  the  "  mathe- 
matical analogies  of  the  two  problems  (the  electrical  and 
the  elastic)  to  assist  the  imagination  in  the  study  of 
both."  ^  Maxwell  now  took  a  further  step  and  pro- 
ceeded to  give  a  physical  or  mechanical  description  of  the 
nature  of  this  state  of  stress,  of  the  electrotonic  state  of 
matter.  With  this  object  in  view  he  conceives  of  a 
medium  which  is  capable  of  exerting  force  on  material 
bodies    by    being    itself    strained,    and    exhibiting     the 


"  suggests  the  idea  that  there  may 
be  a  problem  in  the  theory  of 
elastic  solids  corresponding  to  every 
problem  connected  with  the  distri- 
bution of  electricity  on  conductors, 
or  with  the  forces  of  attraction  and 
repulsion  exercised  by  electrified 
bodies.  The  clue  to  a  similar  re- 
presentation of  magnetic  and  gal- 
vanic forces  is  afforded  by  Mr 
Faraday's  recent  discovery  of  the 
affection,  with  reference  to  polarised 
light,  of  transparent  solids  sub- 
jected to  magnetic  or  electro- 
magnetic forces." 

^  Quoted  from  Maxwell's  paper 
"  On  Physical  Lines  of  Force,"  in 
the  'Philos.  Mag.,'  1861  (see  '  Coll. 
Papers,'  vol.  i.  p.  453),  in  which 
Maxwell  applies  Rankine's  concep- 
tion of  molecular  vortices  to  the 
representation  of  magnetic  pheno- 
mena. He  refers  to  his  earlier  paper 
(1855)   on  (geometrical)    "  lines   of 


force"  in  which  he  had  "shown 
the  geometrical  significance  of  the 
electrotonic  state,"  and  had  used 
"  mechanical  illustrations  to  assist 
the  imagination,  but  not  to  ac- 
count for  the  phenomena."  "  I 
now,"  he  says,  "propose  to  examine 
magnetic  phenomena  from  a  me- 
chanical point  of  view,  and  to 
determine  what  tensions  in,  or 
motions  of,  a  medium  are  capable 
of  producing  the  mechanical  pheno- 
mena observed.  If  by  the  same 
hypothesis  we  can  connect  the 
phenomena  of  magnetic  attraction 
with  electro-magnetic  phenomena, 
and  with  those  of  induced  cur- 
rents, we  shall  have  found  a  theory 
which,  if  not  true,  can  only  be 
proved  to  be  erroneous  by  experi- 
ments which  will  greatly  enlarge 
our  knowledge  of  this  part  of 
physics"  (ibid.,    p.  452). 


KINETIC    OR    MECHANICAL    VIEW    OF    NATUHP:.       83 

phenomena  of  tension  and  pressure  (magnetic  uctiun) 
as  also  of  motion  of  its  parts  (electro-magnetic  action). 
Now  in  a  medium  whicli  is  so  constituted — i.e.,  which 
possesses  elastic  mobility  of  its  parts — we  know  that 
by  a  whirling  or  vortex  motion  phenomena  of  pressure 
and  tension  can  be  produced  in  certain  parts,  and  the 
questions  accordingly  presented  tliemselves  to  Maxwell, 
How  Ijy  such  tension  and  pressure  in  certain  parts  of  the 
medium  can  magnetic  phenomena  be  represented  ?  and 
How  can  the  vortices  communicate  motion  to,  or  receive 
motion  from,  the  interlying  movable  particles  of  the 
medium  ?  He  succeeded  in  working  out  a  very  complete 
model  of  such  a  medium,  representing  Ijy  its  mechanical 
motions  both  magnetic  and  electro-magnetic  phenomena. 
Especially  was  he  successful  in  visualising  Faraday's 
lines  or  tubes  of  force,  and  endowing  them  with  me- 
chanically measurable  forces.  Maxwell  admits  that  "  his 
conception  .  .  .  may  appear  somewhat  awkward.  1 
do  not,"  he  says,  "  bring  it  forward  as  a  mode  of  con- 
nection existing  in  nature.  ...  It  is,  however,  a  mode 
of  connection  which  is  mechanically  conceivable  and 
easily  investigated ;  ...  so  that  I  venture  to  say  that 
any  one  who  understands  the  provisional  and  temporary 
character  of  this  hypothesis  will  find  liimself  rather 
helped  than  hindered  by  it  in  his  search  after  the  true 
interpretation  of  the  phenomena."  ^ 


1  '  Collected  Papers,'  vol.  i.  p.  486. 
At  the  end  of  his  paper  on  physical 
lines  of  force.  Maxwell  touches  on 
the  philosoiihical  question,  "  how 
much  evidence  the  explanation  of 
phenomena  lends  to  the  cr^dihility 
of  a  theory,  or  how  far  we  ought  to 


regard  a  coincidence  in  the  mathe- 
matical expression  of  two  seUs  i>f 
phenomena  as  an  indication  tlwt 
these  phenomena  are  of  the  8umc 
kind.  We  know  that  partial  co- 
incidences of  tliis  kind  have  l>efn 
discovered  ;  and  the  fact  that  ihcy 


84 


SCIENTIFIC    THOUGHT. 


51. 

Corre- 
spondence 
between 
velocities 
of  light 
and  of 
electricity. 


The  idea  of  a  medium  of  extreme  rarity,  pervading  all 
space  and  interpenetrating  all  matter,  capable  also  of  the 
elastic  reactions  of  a  solid  body,  was  not  repugnant  to 
physicists  at  the  time  when  Maxwell  wrote.  Though 
violently  opposed  forty  years  earlier  when  proposed  by 
Fresnel  and  Young,  it  had  gradually,  through  the  de- 
velopment of  optical  theories,  become  a  well-recognised 
instrument  of  scientific  thought.  In  such  a  medium  a 
disturbance  or  displacement  is  propagated  with  a  certain 
velocity  dependent  on  its  elastic  nature — the  so-called 
constants  of  density  and  rigidity.  Now,  looking  upon  a 
charge  of  electricity  not  as  a  material  something — an 
imponderable — but  as  a  displacement  of  the  medium, 
the  question  arose.  Does  the  velocity  with  which  such  a 
displacement  travels  compare  at  all  with  the  known 
velocities  of  other  elastic  disturbances,  such  as  light  is 
conceived  to  be  ?  It  was  known  to  electricians  that 
an  amount  or  charge  of  electricity  can  be  either  station- 
ary (called  statical  electricity)  or  in  motion  (called 
an  electric  current) ;  and  Weber  and  Kohlrausch  had  in 
1856  actually  measured  the  number  of  units  of  statical 
electricity  which  must  flow  through  an  electric  circuit  in 
order  to  produce  the  known  mechanical  effect  of  a  unit 
of  electric  current.  The  quantity  which  they  found,  and 
which  corresponded  to  a  velocity,  was  of  the  same  order 
as  the  velocity  with  which  the  elastic  disturbance  which 
we  call  light  is  known  to  travel.     Maxwell  was  the  first 


are  only  partial  is  proved  by  the 
divergence  of  the  laws  of  the  two 
sets  of  phenomena  in  other  respects. 
We  may  chance  to  find,  in  the 
higher  parts  of  physics,  instances  of 


more  complete  coincidence  which 
may  require  much  investigation  to 
detect  their  ultimate  divergence  " 

(p.  188). 


KINETIC    OR    MECHANICAL    VIEW    uF    NATURE.       85 


,02. 
Elastic  di«- 


to  see  the  physical  signiticance  of  this  correspondence.* 
"  I  have  deduced  the  relation  between  the  statical  ami 
dynamical  measures  of  electricity,  and  have  shown  by  a 
comparison  of  the  electro-magnetic  experiments  of  .MM. 
Kohlrausch  and  Weber  willi  the  velocity  of  light  as 
found  by  M.  Fizeau,  that  the  elasticity  of  the  magnetic 
medium  in  air  is  the  same  as  that  of  the  luminiferous 
medium,  if  these  two  coexistent,  coextensive,  and  equally 
elastic  media  are  not  rather  one  medium."  - 

After  having  pointed  out  this  remarkable  correspond- 
ence and  other  analogies  between  electrical  and  optical 
properties  which  could  be  verified  by  experiment,  Max- 
well  seems   to  have   felt  satisfied   tliat  a  dynamical  or  turtai.cea 

"  of  tnt;  same 

kinetic  explanation  of  electric  and  magnetic  phenomena  'nedium. 
based  upon  rotary  and  translational  motions  and  elastic 
strains  in  the  magnetic  field  was  quite  possiljle.  The 
detailed  descriptions  given  in  his  earlier  papers  he  looked 
upon  merely  as  crude  mechanical  devices  by  which  some 
of  the  known  effects  of  magnets  and  currents  could  be 
described.  The  valuable  result  was,  that  the  electro- 
magnetic field  could  1)6  looked  upon  as  a  mechanical 
system ;  that  the  observed  actions  at  a  distance  could 
be  conceived  as  communicated  through  this  mechanical 
system  in  definite  measurable  time ;  and  that  certain 
analogies    had    been    pointed    out    as    existing   between 


^ '  Philos.  Mag.,'  January  and  Feb- 
ruary, 1862  ;  '  Coll.  Papers'  vol.  i. 
p.  492. 

-  Cf.  '  Coll.  Papers,'  vol.  i.  p.  r.OO  : 
"  The  velocity  of  transvense  undula- 
tion.s  in  our  hypothetical  medium, 
calculated  from  the  electro-magnetic 
experiments  of  MM.  Kohlrausch  and 


Weber,  agree.s  so  exactly  with  the 
velocity  of  light  calculated  from  the 
optical  experiment,s  of  M.  Fizeau, 
that  we  can  scarcely  avoid  the  in- 
ference that  light  consists  in  the 
transverse  undulation.s  of  the  .sjime 
medium  which  is  the  cause  of  electric 
and  magnetic  phenomena." 


86  SCIENTIFIC    THOUGHT. 

optical,  electrical,  and  magnetic  phenomena,  which  by 
carefully  devised  experiments  might  be  verified  and 
extended. 

Through  Maxwell,  following  on  Faraday  and  Thomson, 
the  treatment  of  electric  and  magnetic  phenomena  had 
thus  entered  on  a  similar  stage  to  that  which  the 
treatment  of  optical  phenomena  had  attained  lialf  a 
century  earlier  through  Young  and  Fresnel.  A  kinetic 
or  mechanical  view,  more  or  less  precise  and  definite,  had 
been  propounded ;  a  considerable  number  of  facts  had 
been  brought  into  connection,  into  line  and  order ;  the 
direction  which  experimental  research  must  take  had 
been  indicated  ;  and  finally  a  correspondence  had  been 
established  between  two  great  groups  of  phenomena,  those 
of  electricity  and  magnetism  on  the  one  side,  those  of 
light  on  the  other.  It  might  have  been  expected  that 
Maxwell  would  now  take  the  same  course  as  that  taken 
by  Fresnel  about  the  year  1820,  and  perfect  his  views 
by  giving  his  theory  of  molecular  vortices  greater  pre- 
cision and  definiteness — i.e.,  by  perfecting  the  electro- 
magnetic model,  as  Fresnel  and  others  perfected  in  their 
time  the  system  of  vibrations  by  which  they  visualised 
the  processes  of  light.  This  is  not  the  method  which 
Maxwell  adopted.^      In   his   later   and   more   important 

^  The  progress  of  Maxwell's  reason-    i   formulation    of    Faraday's  concep- 
ing  is  clearly  marked  in  the  three   |    tion,  much  in  the  spirit  of  Thorn 


memoirs,  belonging  respectively  to 
the  years  18.^5,  1861,  and  1864,  of 
which  the  last  appeared  in  the 
'  Transactions '  of  the  Royal  So- 
ciety, and  which  are  reprinted  in 
the  first  volume  of  the  '  Collected 
Scientific  Papers.'  The  first  memoir 
on  "  Faraday's  Lines  of  Force  "  ad- 
heres strictly  to  the  mathematical 


son's  many  expositions.  The  second, 
on  "Physical  Lines  of  Force,"  fol- 
lows Faraday  in  the  attempt  to  take 
the  original  symbol  in  real  earnest 
as  a  physical  arrangement,  and  de- 
vises, or  applies  for  that  purpose, 
the  theory  of  molecular  vortices. 
The  third  memoir,  which  is  by  far 
the  most  important   and  original, 


KINETIC    OR    MECHANICAL    VIEW    OF    NATURE.       87 


writings  he  adopted  a  different  and  more  general  process 
of  reasoning.  If  electrical  and  magnetic  as  well  as 
optical  phenomena  are  produced  by  the  motions  of  the 
parts  of  a  medium  possessed  of  certain  mechanical  pro- 
jjcrties,  this  medium  represents  a  mechanical  system,  and 
must  therefore  be  subject  to  the  general  laws  which 
regulate  all  mechanical  systems.  These  general  laws  are 
laid  down  in  dynamics,  where  it  is  shown  that  a  complete  'jucnces 

•^  '■  on  Uie  line* 

knowledge   of  the   behaviour   of   such   a  system  can   be  ^[g"^'"? 
reduced  to  the  knowledge  of  the  distribution  in  it  of  a 
quantity  called  Energy. 

I  intend  in  the  next  chapter  to  trace  historically  the 


ConM- 


drops  this  somewhat  crude  device, 
as  well  as  the  older  theory  of  par- 
ticles acting  at  a  distfince,  with 
forces  which,  according  to  Weber, 
depend  on  their  velocities,  and  starts 
from  "  the  conception  of  a  compli- 
cated mechanism  ca])able  of  a  vast 
variety  of  motion,  but  at  the  same 
time  so  connected  that  the  motion 
of  one  part  depends  ...  on 
the  motion  of  other  parts,  these 
motions  being  communicated  by 
forces  arising  from  the  relative  dis- 
placement of  the  connected  parts,  in 
virtue  of  their  elasticity  "  (Papers, 
vol.  i.  p.  533).  He  further  says  : 
"  I  have  on  a  former  occasion  at- 
tempted to  describe  a  particular 
kind  of  motion  and  a  particular 
kind  of  strain,  so  arranged  as  to 
account  for  the  j)henomena.  In 
the  pre.sent  paj)er  I  avoid  any  hy- 
pothesis of  thiii  kind  ;  and  in  using 
such  words  as  electric  momentum 
and  electric  elasticity  in  reference 
to  the  known  phenomena  of  the  in- 
duction of  currents  and  tiie  j)()lar- 
isation  of  dielectrics,  I  wish  merely 
to  direct  the  mind  of  the  reader  to 
mechanical  phenomena  which  will 
-assist  him    in    understanding  the 


electrical  ones.  All  such  phrases 
in  the  present  paper  are  to  hf.  con- 
sidered a-s  illustrative,  not  as  ex- 
planatory. In  speaking  of  the 
energy  of  the  field,  however,  I 
wish  to  be  understood  literally.  All 
energy  is  the  same  as  mechanical 
energy,  whether  it  exists  in  the 
form  of  motion  or  in  that  (jf  elas- 
ticitj%  or  in  any  other  form.  The 
energy  in  electromagnetic  phe- 
nomena is  mechanical  energy.  The 
only  question  is,  Where  does  it 
reside  ?  On  the  old  theories  it 
resides  in  the  electrified  bodies, 
conducting  circuits,  and  magnets, 
in  the  form  of  an  unknown  quality 
called  potential  energy,  or  the  power 
of  producing  certain  effects  at  a 
distance.  On  our  theory  it  resides 
in  the  electro-magnetic  field,  in  tlie 
space  surrounding  the  electrified 
and  magnetic  bodies,  as  well  as  in 
those  bodies  themselves,  and  is  in 
two  different  forms,  which  may  be 
described  without  liypothesis  as 
magnetic  polarisation  and  electric 
polarisation,  or,  according  to  a  very 
probable  hypothesis,  jis  tlie  motion 
and  tlie  strain  of  one  and  the  same 
medium  "  (p.  563). 


88  SCIENTIFIC    THOUGHT. 

growth  of  this  conception  as  apphed  not  only  to  the 
energy  of  visible  and  measurable  mechanical  motion,  but 
to  all  other  forces  of  nature  which  have  in  the  course  of 
the  century  not  only  been  measured  in  terms  of  this 
one  quantity,  but  also  represented  with  more  or  less 
success  as  dependent  on  the  energy  of  specific  forms  of 
motion,  be  this  rotatory  or  vibratory  or  translational 
motion,  regular  and  periodic  or  irregular  and  disorderly 
motion.  It  is  clear  that  such  a  general  abstract  view  as 
Maxwell  (first  among  natural  philosophers)  took  of  a 
special  problem  was  only  possible  after  it  had  been 
shown  how  all  physical  and  chemical  actions  and  effects 
can  be  reduced  to  a  common  measure.  The  influence  of 
the  development  of  these  views  on  the  kinetic  view  of 
nature  has  been  very  great.  The  first  and  most  natural 
effect  of  measuring  all  forces  of  nature  in  terms  of  the 
energy  of  motion  is  to  strengthen  the  kinetic  view  of 
natural  phenomena.  This,  however,  is  not  the  only  view 
which  is  possible,  or  which  has  been  taken,  as  I  shall 
endeavour  to  show  more  fully  hereafter. 

The  influence  of  Maxwell's  ideas  on  scientific — nay, 
even  on  popular — thought  has  been  very  considerable. 
The  main  conception  around  which  research,  both  mathe- 
matical and  experimental,  has  moved  during  the  last 
twenty  years  is  the  conception  of  light  as  an  electro- 
magnetic phenomenon.  This  view  has  been  much  sup- 
ported and  extended  by  the  experiments  of  Heinrich 
Hertz,  who  by  ingenious  contrivances  succeeded  in 
actually  exhibiting  electro  -  magnetic  waves,  and  in 
showing  how  they  differ  from  light  waves  merely  in 
length    and    period,    and    agree    with    them    so    far    as 


KINETIC    OK    MECHANICAL    VIKW    uK    NATURE.       89 

reflexion  and  refraction  and  other  properties  are  con- 
cerned. Luminous  waves  are  now  considered  !)>-  many 
physicists  to  be  merely  electro-magnetic  waves  of  short 
wave  length  and  great  frequency,  such  as  the  organ  of 
vision  is  capable  of  perceiving  in  the  form  of  light. 
The  electric  and  magnetic  medium  is  identical  with  the 
luminiferous  ether,  postulated  by  Young  and  Fresnel, 
and  rays  of  light  are  merely  an  electric  uiid  magnetic 
disturbance  propagated  as  a  periodic  or  wave  motion. 

These    discoveries    and    theories    have    gone    a    long        m. 

.  .  Destructive 

wav  to  destroy  the  older  astronomical  view  or  natural  .met  ut 

•'  ''  the  new 

phenomena,  which  explained  many  effects  by  the  action  [};^;"J^jJ^°" 
at  a  distance  of  particles  of  ponderable  or  imponderable  "lewT' 
matter.  The  firm  conviction  has  taken  hold  of  the 
modern  scientific  intellect  or  imagination  that  space  is  a 
plenum  tilled  with  a  continuous  medium,  and  that  the 
undoubted  atomic  nature  of  ponderable  matter  may  be 
owino-  merely  to  a  specific  and  unmoditiable  form  of 
motion  with  such  properties  as  Lord  Kelvin  has  shown 
to  belong  to  vortex  lilaments.  The  ditticulty  still  re- 
mains how  to  explain  the  phenomenon  of  gravitation  as 
well  as  the  increased  amount  of  inertia  or  mass  which 
belongs  to  all  ponderable  matter  as  compared  with  that 
material  substance  which  we  call  ether. 

The  reason  why  Maxwell  abandoned  his  earlier 
schemes,  in  which  he  tried  to  construct  a  mechanical 
model  of  the  electro-magnetic  field,  is  not  quite  clear.^ 
The  idea  has,  however,  been  taken  up  by  others,  and 
elaborate  descriptions  have  been  attempted,  by  whifh  the 

1  A  suggestion  regarding  this  is  given  by  Dr  J.  Laruior  in  '  .Etiier  and 
Matter,'  p.  28. 


90 


SCIENTIFIC    THOUGHT. 


processes  going  on  in  the  neighbourhood  of  electrically 
charged  bodies,  of  electric  currents,  of  magnets  and 
diamagnets,  can  be  visualised.^  For  didactic  purposes 
such  elaborate  models  may  prove  to  be  of  great  value, 
though  as  a  true  mechanical  basis  of  a  physical  theory  of 
natural  processes  they  have  to  be  received  with  caution. 
None  of  those  physicists  who  have  expended  their  ingen- 
uity in  devising  these  contrivances  seem  to  attach  more 
than  a  symbolic  or  ideal  value  to  them :  they  have,  how- 
ever, the  desired  effect  of  producing  on  the  mind  of  the 
learner,  of  the  practical  inventor,  or  of  a  popular 
audience  a  strong  conviction  that  all  physical  phenomena 
can  be  described  as  processes  of  motion,  and  that  the 
ultimate  solution  of  the  problem  of  natural  philosophy  is 
to  be  found  in  a  kinetic  or  mechanical  view  of  pheno- 
mena.     Physics   and   chemistry   are,   according   to    this 


^  Such  illustrations  may  be  found 
in  Dr  Oliver  Lodge's  'Modern 
Views  of  Electricity,'  a  book  which 
has  had  a  large  circulation  and  has 
helped  to  diffuse  correct  and  practi- 
cally useful  ideas  on  electric  and 
magnetic  problems  and  phenomena. 
There  is  a  danger  of  such  mechani- 
cal illustrations  becoming  too  rigid 
and  of  their  being  taken  too  literally ; 
still,  for  the  purposes  of  practical 
application  and  handling  it  is  indis- 
pensable to  possess  some  mechanical 
mode  of  representation  and  con- 
struction by  which  actual  problems 
can  be  readily  solved.  The  success 
of  Dr  Lodge's  attempt  both  in  this 
country  and  on  the  Continent, 
especially  in  Germany,  proves  suf- 
ficiently that  it  meets  a  much -felt 
want.  See  inter  alia  Prof.  Rosen - 
berger's  five  lectures,  '  Die  moderne 
Entwickelung  der  elektrischen  Prin- 
cipien,'    Leipzig,  1898,  p.    133.     A 


great  authority  abroad,  Prof.  Lud- 
wig  Boltzmann,  has  made  use  of  a 
peculiar  kind  of  mechanical  motion, 
investigated  by  Helmholtz,  to  il- 
lustrate electrical  phenomena.  The 
characteristic  of  such  motion  — 
which  is  termed  cyclic  —  is  this, 
"  that  in  the  place  of  every  particle 
which  changes  its  position,  an  equal 
and  equally  moving  particle  enters, 
so  that  the  condition  of  the  system 
during  the  motion  is  nowise  al- 
tered "  ( '  Vorlesungen  fiber  Max- 
well's Theorie,'  Leipzig,  1891  and 
1893,  vol.  i.  p.  14).  Cycles  can  be 
"  coupled,"  &c.  The  general  dyna- 
mical relations  of  such  cyclic 
systems  are  investigated,  and  by 
introducing  the  necessary  restric- 
tions, based  upon  experimental 
facts,  and  suitable  hypotheses  — 
facts  and  hypotheses  being  clearly 
distinguished  —  the  general  equa- 
tions of  Maxwell  are  arrived  at. 


KINETIC    OR    MECHANICAL    VIEW    OF    NATURK.       91 

view,  destined  to  become  idtiinately  merely  chaptei-s  in 
dynamics  as  the  doctrine  of  mechanical  motion. 

A  similar  reluctance  to  look  upon  the  vibrations  of  the 
luminiferous  ether  merely  as  a  convenient  symbolism,  as  a 
crude  method  of  visualising  molecular  processes,  which  in 
reality  we  cannot  picture  to  ourselves,  does  not  seem  to 
have  troubled  the  minds  of  the  great  propounders  of  the 
undulatory  theory  of  light  —  i.e.,  of  tlie  elastic  sohd 
theory,  as  it  is  now  termed  in  contradistinction  to  the 
electro-magnetic  theory  propounded  by  Maxwell.  The 
greatest  living  exponent  of  the  former  view.  Lord  Kelvin, 
who  in  his  Baltimore  Lectures  grappled  witli  tlie  dilli- 
culties  which  still  beset  that  view — falling  back  on  the 
principle  of  optical  consonance  and  resonance,  suggested 
by  Professor  Stokes  to  explain  some  of  the  interactions  of 
the  ether  and  ponderable  matter :  upon  the  theory  of  free 
and  forced  vibrations,  suggested  by  Bessel  and  Sellmeier ; 
and  on  liis  own  fruitful  suggestion  of  the  vortex  atom 
to  explain  some  of  the  properties  of  ponderable  atoms 
moving  in  the  continuum  which  fills  all  space — expresses        .'.r.. 

•      1  1   •  Lord  Kelvin 

himself  very  dehnitely   on  this  point.      "  We  must  not  <"'  *•"? 

•^  "^  ^  vibrations 

listen  to  any  suggestion  that  we  may  look  upon  the  "f  the  ether, 
luminiferous  ether  as  an  ideal  way  of  putting  the  thing. 
A  real  matter  between  us  and  the  remoter  stars  I  believe 
there  is,  and  that  light  consists  of  real  motions  of  that 
matter,  motions  just  such  as  are  described  by  Fresnel  and 
Young,  motions  in  the  way  of  transverse  vibrations.  If 
I  knew  what  the  magnetic  theory  of  light  is,  I  might  be 
able  to  think  of  it  in  relation  to  the  fundamental 
principles  of  the  wave  theory  of  light,  liut  it  seems  to 
me  rather  a  backward  step  from  an  absolutely  definite 


92  SCIENTIFIC    THOUGHT. 

mechanical  notion  that  is  put  before  us  by  Fresnel  and 
his  followers,  to  take  up  the  so-called  electro-magnetic 
theory  of  light  in  the  way  it  has  been  taken  up  by  several 
writers  of  late." 

But  whilst,  no  doubt,  the  train  of  reasoning  started  by 
Maxwell,  and  developed  by  his  followers,  has  somewhat 
destroyed  the  simplicity  and  directness  which  the  older 
vibratory  theory  of  light  and  the  kinetic  theory  of  gases 
had  brought  into  our  mechanical  views  of  natural 
phenomena,  the  subsequent  experimental  proof  of  the 
existence  of  electric  waves  by  Hertz  has  done  much 
popularly  to  strengthen  that  view.  The  discovery  of 
other  kinds  of  rays,  by  Lenard,  Eontgen,  and  others,  has 
likewise  tended  in  the  same  direction,  though  their  exact 
nature  is  still  a  subject  of  much  conjecture. 

Nor  can  it  be  denied  that  the  practical  usefulness 
also  of  these  lately  discovered  forms  of  radiation  has 
tended  in  the  same  direction ;  as  has,  all  through  the 
last  thirty  years,  the  enormous  development  of  electrical 
industry  in  its  many  branches.  Up  to  the  beginning 
of  the  nineteenth  century  the  principal  electric  and 
magnetic  phenomena  known  were  what  we  term  stat- 
ical ;  the  study  of  these  centred  in  the  conception  of 
electric  and  magnetic  charges  concentrated  on  or  in 
conductors  and  acting  at  a  distance.  The  practical 
interest  was  limited  to  mariners'  compasses  and  light- 
ning-conductors. The  discovery  of  the  galvanic  current, 
and  still  more  its  applications  by  Davy  to  the  decom- 
position of  the  most  refractory  chemical  compounds, 
introduced  an  entirely  new  class  of  phenomena.  Con- 
tinental science,  in  Coulomb,  Ampere,  and  Weber,  first 


KINETIC    OR    MECHANICAL    VIEW    OF    NATCKE.       93 

developed  the  line  of  reasoning  and  research  suggested 
Ijy  statical  phenomena  and  applied  this  to  dynamical 
phenomena.  Faraday,  folhjwing  Davy,  approached  the 
subject  from  the  point  of  view  of  the  chemist.  It  was 
soon  suspected,  and  latterly  proved  by  actual  measure- 
ments, that  the  quantities  whicli  come  into  play  in 
statical  charges,  and  even  in  a  violent  thunderstorm,  are 
small  compared  with  those  of  a  steady  electrical  current. 
The  phenomena  of  electricity  in  motion  became  of  in- 
finitely more  practical  importance  than  those  of  elec- 
trical equilibrium  or  of  static  tension.  The  views  of 
Faraday,  Thomson,  and  Maxwell,  which  Hehaholtz, 
educated  thoui^h  he  was  in  the  continental  methods, 
adopted  and  introduced  into  German  scientific  literature, 
lent  themselves,  as  he  recognised,  more  successfully  and 
directly  to  the  solution  of  the  problems  which  applied 
science  forced  upon  theorists. 

Something,  indeed,  has  been  lost  by  this  fundamental 
change  which  has  come  over  modern  reasoning  in 
electrical   matters.       This    has    been    most    clearly   and        56. 

Indefinite- 

pointedly  expressed  by  M.  Poincard,  the  eminent  French  nessorthe 
mathematician,  who  has  done  so  much  to  illumine  [Y"^'^!^'"^ 
physical  and  mechanical  problems  from  the  side  of  pure 
mathematics.  "  Maxwell,"  he  says,  "  does  not  give  a 
mechanical  explanation  of  electricity  and  magnetism ;  he 
confines  himself  to  the  proof  that  such  an  explanation  is 
possible."  Accordingly,  those  who  were  brought  up  in  the 
traditions  of  the  school  of  Laplace  and  Caucliy  feel  dis- 
mayed at  the  indetiniteness  whicli  adheres  to  the  exposi- 
tions of  Maxwell's  latest  and  greatest  work.  "A  groat 
French  philosopher,"  M.  Poincar^  proceeds,  "  one  of  those 


94  SCIENTIFIC    THOUGHT. 

who  have  most  completely  fathomed  Maxwell's  work, 
said  to  me  once,  '  I  understand  everything  in  the  book 
except  what  is  meant  by  an  electrically  charged  body.'  " 
Professor  Glazebrook  tells  us :  "  We  cannot  find  in  the 
'  Electricity '  an  answer  to  the  question,  What  is  an 
electric  charge  ?  Maxwell  did  not  pretend  to  know,  and 
the  attempt  to  give  too  great  definiteness  to  his  views 
on  this  point  is  apt  to  lead  to  a  misconception  of  what 
those  views  were.  .  .  .  Still,  in  order  to  grasp  Maxwell's 
theory,  this  knowledge  is  not  necessary." 

Nevertheless,  Maxwell's  followers  in  this  country  and 
abroad  are  not  satisfied  to  leave  those  points  which  are 
obscure  or  indefinite  in  his  theory  unilluminated.  I  have 
already  referred  to  the  valuable  practical  illustrations  of 
Lodge.  What  has  been  done  in  a  more  systematic 
manner  on  the  Continent  and  at  home  I  shall  briefly 
refer  to  at  the  end  of  the  next  chapter.  We  may  call  it 
a  revival  of  the  atomic  view  of  electricity. 


95 


CHAPTER    VII. 

ON    THE    PHYSICAL    VIEW    OF    NATURE. 

I  HAVE  already  remarked  that  none  of  the  three  great        i. 

T         •  1-1  p  ■  Rccapitula- 

generahsations  which  we  have  so  far  reviewed  have  been  t'on. 
creations  of  the  pliilosophers  of  the  nineteenth  century. 
Their  first  enunciation  belongs  to  antiquity,  though  they 
have  only  witliin  the  last  three  hundred  years  been  ex- 
pressed in  sufficiently  precise  terms  to  permit  of  practical 
measurements  and  mathematical  deductions.  The  first 
step  towards  a  scientifically  comprehensive  employment 
of  the  familiar  l)ut  vague  terms  of  attraction,  of  atoms, 
and  of  undulations  came,  as  we  have  seen,  in  each 
case  from  some  solitary  thinker  of  this  country :  from 
Newton,  from  Dalton,  from  Thomas  Young.  The  system- 
atic elaboration  belongs  to  the  combined  scientific  exer- 
tions of  all  the  civilised  nations  of  the  world.  In  books 
on  astronomy,  physics,  and  chemistry,  up  to  the  middle  of 
the  century,  we  can  hardly  find  any  theoretical  exposi- 
tions which  are  not  based  upon  one  or  more  of  these 
three  ideas.  Indeed  they  govern  the  entire  science  of 
inanimate  nature  during  the  first  half  of  the  century. 
None  of  these  three  principles,  however,  appeared  suf- 


96  ^  SCIENTIFIC    THOUGHT. 

ficient  to  cover  the  whole  field.  The  law  of  gravitation 
embraced  cosmical  and  some  molar  phenomena,  but  led  to 
vagueness  when  applied  to  molecular  actions.  The  atomic 
theory  led  to  a  complete  systematisation  of  chemical  com- 
pounds, but  afforded  no  clue  to  the  mysteries  of  chemical 
affinity.  And  the  kinetic  or  mechanical  theories  of  light, 
of  electricity,  and  magnetism,  led  rather  to  a  new  dualism, 
the  division  of  science  into  sciences  of  matter  and  of  the 

2.  ether.     The  unification  of  scientific  thought  which  was 

Insuffici- 
ency of  the    gained  by  any  of  these  three  views,  the  astronomical,  the 

astronoini-      o  ^  ./  ' 

and  kinetic    ^tomic,  and  the  mechanical,  was  thus  only  partial.     A 
views.  more   general   term   had    to  be  found  under  which  the 

different  terms  could  be  comprised,  which  would  give  a 
still  higher  generalisation,  a  more  complete  unification 
of  knowledge.  One  of  the  principal  performances  of 
the  second  half  of  the  nineteenth  century  has  been  to 
find  this  more  general  term,  and  to  trace  its  all-pervad- 
ing existence  on  a  cosmical,  a  molar,  and  a  molecular 
scale.  It  will  be  the  object  of  this  chapter  to  complete 
the  survey  of  those  sciences  which  deal  with  lifeless 
nature  by  tracing  the  growth  and  development  of  this 

3.  greatest  of  all  exact  generalisations — the  conception  of 

The  concep-    <=■  o 

tion  of         energy. 

energy.  °'' 

The  complex  of  ideas  and  the  manifold  courses  of 
reasoning  which  are  centred  in  this  conception  form 
such  an  intricate  network,  the  interests  involved  are  so 
great,  the  suggestions  which  led  up  to  it  so  numerous, 
the  consequences  which  resulted  for  science  and  practice 
so  far-reaching,  that  the  historian  has  no  little  difficulty 
in  laying  bare  the  many  lines  of  thought  which  appa- 
rently cross  and  re -cross  each  other.     Accordingly  the 


ON    THE    PHYSICAL    VIEW    OF    NATUKK. 


07 


history   of  this   sul»ject   has    been   written   from   various 
points  of  view/  and  angry  controversies^  as  to  priority 


■  Tlie  histories  are  mostly  in  Ger- 
man. I  give  the  titles  of  the  more 
inipurtiint.  Foremost  stiinil  the 
writings  of  Prof.  Ernst  Mach — viz., 
'  Die  Geschichte  uml  die  Wurzel 
(les  Satzes  von  der  Erhaltung  der 
Arbeit'  (Prag,  1872),  incorporated 
ill  the  author's  '  Poj)ular  Scientific 
Lectures,'  translate<l  l>y  Thomas 
J.  M'Cormack,  Chicago,  1894  ; 
and  the  same  authfir's  '  Die  Me- 
clianik  in  ilircr  Entwickelung,  his- 
torisch-kritisch  dargestellt '  (Leip- 
zig, 1883,  2nd  ed.,  1889,  also  trans- 
lated by  M'Cormack,  London  and 
Chicago,  1893).  The  philosoi)hical 
faculty  of  the  University  of  Got- 
tingen  has  twice  (in  1869  and  in  1884) 
made  the  principles  of  dynamics 
the  subject  of  a  prize  competition, 
presumably  both  times  at  the  in- 
stigation of  the  late  celebrated 
Professor  Wilhelm  Weber.  The 
first  competition  led  to  the  i)ublica- 
tion  of  E.  Duhring's  '  Kritische  Ge- 
schichte der  allgemeinen  Principien 
der  Mechanik  '  (Leipzig,  1872; 
re))ublished,  with  much  contro- 
versial matter,  in  1876  and  1887)  ; 
the  second  to  the  publication  of 
Prof.  Max  Planck's  '  Das  Piincip 
der  Erhaltung  der  Energie  '  (Leip- 
zig, 1887).  In  the  same  year  as 
the  last  book  there  appeared  '  Die 
Lehre  von  der  Energie,'  by  Dr  Georg 
Helm  (Leipzig,  1887),  and  lately 
his  very  complete  work,  '  Die 
Energetik,  nach  ihrer  geschicht- 
lichen  Entwickelung  '  (Leipzig, 
1898). 

-  The  controversy  turned  mainly 
on  the  question  of  the  claims  of 
Dr  Julius  Pobert  Mayer  of  Heil- 
bronn.  Tiie  experimental  work  of 
Joule  in  England  and  the  theoreti- 
cal work  of  Helmholtz  in  Germany 
were  published  in  ignorance  of  the 
writings  of  Mayer.  I']v('ii  tlie  earlier 
important  papers  of  William  Thom- 

VOL.  II. 


son  (Lord  Kelvin)  and  Rudolph 
Clausius  appeared  Ijefore  the  name 
of  Mayer  was  generally  known. 
The  question  then  arose  to  what 
extent  the  publications  of  Mayer 
really  anticipated  the  discoveries 
and  theories  of  Joule,  Helmholtz, 
Thomson,  and  Clausius.  It  can 
hardly  be  held  that  they  influenced 
them.  The  whole  of  the  evidence 
as  to  the  former  point  is  con- 
tained in  a  very  complete  publica- 
tion by  Prof.  Jacob  J.  Weyrauch, 
"  Kleinere  Schriften  und  Hriefe 
von  Robert  Mayer  "  (Stuttgart, 
1892),  which  forms  a  supplement 
to  the  edition  by  the  same  author 
of  Robert  Mayer's  '  Schriften,'  en- 
titled "Die  Mechanik  der Wiirme  " 
(Stuttgart,  3rd  ed.,  1893).  Both 
books  contain  very  careful  and  ex- 
haustive notes.  Whoever  desires 
to  settle  the  question  of  Mayer's 
claims,  which,  however,  will  always 
depend  much  on  individual  opinion, 
will  find  all  the  documentary  evi- 
dence collected  in  these  interesting 
volumes.  A  further  controversy 
arose  later  as  to  the  discovery  and 
enunciation  of  the  second  law  of 
thermodynamics,  the  great  doc- 
trine of  the  "Dissipation  of  En- 
ergy. "  This  controver.sy  arose  over 
the  publication  of  the  late  Prof. 
P.  G.  Tait's  'Sketch  of  Thermo- 
dynamics '  in  1868,  which  is  an 
amplification  of  two  articles  by 
the  same  author  in  the  '  North 
British  Review  '  of  1864.  The  con- 
troversy, which  referred  mainly  to 
R.  Clausius's  share  in  the  enuncia- 
tion of  the  second  law,  can  1)6 
studied  in  Tait's  little  volume  (1st 
ed.,  1868  ;  2nd  ed.,  1877),  in  vols. 
43  and  44  of  the  4th  scries  of 
the  '  Phil.  Mag.,'  in  his  '  Recent 
Advances  in  Physical  Science ' 
(esjjecially  the  pieface  to  the  3rd 
edition,    1885),    and    in     the    2nd 

G 


98  SCIENTIFIC    THOUGHT. 

of  discovery  and  as  to  the  real  points  at  issue  have' 
arisen.  The  history  of  thought  only  takes  note  of  these 
in  so  far  as  they  are  indications  of  what  was  of  real 
(not  of  personal)  interest  in  the  process,  and  are  thus 
a  measure  of  the  value  which  was  inherent  in  its 
development. 

None  of  the  different  views  or  theories  with  which  the 
earlier  generations  of  philosophers  during  the  century 
operated  seemed  sufficient  to  give  an  insight  into  the 
real  essence,  the  (pvaig,  of  natural  phenomena.  Neither 
the  astronomical  nor  the  atomic  nor  the  kinetic  view 
was  all-embracing.  On  the  Continent,  both  in  France 
and  in  Germany,  the  sciences  were  rigidly  marked  off 
from  one  another,  the  connecting  links  were  few  and 
ill  defined,  and  speculations  as  to  the  general  forces  and 
agencies  of  nature  were  left  to  metaphysicians  and  treated 
with  suspicion.  In  England  alone  the  name  of  natural 
philosophy  still  obtained,  and  in  the  absence  of  separate 
schools  of  science,  such  as  existed  abroad,  suggested,, 
at  least  to  the  self-taught  amateur  or  to  the  practical 
man,  the  existence  of  a  uniting  bond  between  all  natural 
studies.  It  is  significant  that  the  term  under  which  we 
now  comprise,  and  by  which  we  measure,  all  natural 
agencies,  the  term  Energy,  was  first  distinctly  used  in  this 
The  term  scusc  by  Dr  Thomas  Young  in  his  lectures  on  Natural 
Yoi^ng.        Philosophy,^  a  course  which,  be  it  noted,  also  embraced 

edition  of  the  2nd  vol.  of  Clausius,  Energy  may  be  applied,  with  great 

'  Die   mechanische  Wiirmetheorie '  ,    propriet}',  to    the   product    of   the 

(Braunschweig,    1879),  p.  324,  &c.  '    mass  or  weight  of  a  body  into  the 

In  the  labyrinth  of  these  eontro-  i    square   of   the    number  expressing 

versies   I   have  found   Helm  a  fair  its  velocity.  .  .   .  This  product  has 

and  conscientious  guide.  been  denominated  the  living  force 

^  Vol.  i.  p.  59  of  the  edition  of  i    (the  vis  viva),  .   .   .  and  some  have 

Kelland.    Young  says  :   "  The  term  I    considered  it  as  the  true  measure 


ON    THK    PHYSICAL    VIKW    OF    NATl'l'.K. 


99 


Chemical  Science,  tliough  for  merely  external  reasons 
this  was  summarily  handled.  iL  is  equally  significant 
that  the  first  valuable  suggestions  as  to  the  connection  of 
the  various  sciences,  and  the  practical  or  common  measure 
of  the  various  agencies,  came  from  practical  or  professional 
persons  who  took  an  outside  and  general  view  of  physical 
and  chemical  processes  and  their  application  in  arts  and 
medicine.  Young  himself  was  a  medical  man,  as  were 
liobert  Mayer  and  Hehuholtz  after  him.  Practical  men 
such  as  Watt  felt  the  necessity  of  measuring  not  so  much 
forces  (in  the  Newtonian  sense)  as  the  action  of  forces, 
and  introduced  the  term  power,  and  the  quantity  called        5. 

.  Watt  intro^ 

horse-power  ^  to  measure  the  capacity  of  an  engme  for  'luces  the 
doing  work.      Newton  had  already  measured  this  action"  "po**-"""" 


of  the  quantity  of  motion  ;  but 
although  this  opinion  has  been  very 
universally  rejected,  yet  the  force 
thus  estimated  well  deserves  a 
distinct  denomination."  See  also 
p.   172. 

'  The  cjuantity  called  horse- 
power was  introduced  by  Boulton 
and  Watt  to  measure  the  power  of 
the  engines  they  built  and  sold  at 
Soho  towards  the  end  of  the  eigh- 
teenth century.  They  caused  ex- 
periments to  be  made  with  thestrong 
liorses  used  in  the  breweries  in  Lon- 
don, and  from  the  result  of  these 
trials  they  assigned  33,000  lb.,  raised 
one  foot  per  minute,  as  the  value  of 
one  horse-power.  Dr  Young  in  his 
'  Lectures  '  has  the  following  state- 
ment :  "A  steam-engine  of  the 
best  construction,  with  a  30 -inch 
cylinder,  has  the  force  of  forty 
liorses  ;  and  since  it  acts  without 
intermission,  will  perform  the  work 
of  120  horses  or  of  600  men,  each 
square  inch  of  the  piston  being 
nearly  equivalent  to  a  laljourer" 
(vol.  i.  p.  103). 

-  See  the  Scholium  to  the  "■  Axio- 


mata  sive  Leges  Motus,"  p.  25  of 
the  first  edition  of  the  '  Princi[)ia,' 
in  which  the  "  Agentis  Actio  "  is 
measured  "  ex  ejus  vi  et  velocitJite 
conjunctim."  Thomson  and  Tait 
('  Natural  Philosopiiy,'  1886,  part  i. 
p.  250  S'lq.,  and  Tail,  'Dynamics,' 
1895,  p.  181)  have  drawn  attention 
to  tlie  fact  tiiat  this  passage  of  the 
'Principia'  contains  imjilicitly  the 
modern  notion  of  energy,  and  the 
principle  of  the  conservation  of 
energy.  The  continental  historians 
named  above  are  inclined  to  give 
Huygens  credit  for  having  first 
made  explicit  use  of  the  idea  of  tlie 
conservation  of  the  ([uautity  now 
termed  energy,  and  they  trace  the 
further  elucidation  of  it  to  the 
BernouUis,  es])ecially  John  Ber- 
noulli, who  repeatedly  speaks  of  the 
"  conservatio  virium  vivaruin,"  ami 
"urges  that  where  vis  viva  dis- 
appears, tlie  power  to  do  work 
{fucultas  agendi)  is  not  lost,  but  is 
oidy  changed  into  some  other 
form"  ('Opera,'  1742,  vol.  iii.  pp. 
239  and  243,  quoted  by  Planck,  /or. 
cit.,  p.  U»). 


100 


SCIENTIFIC    THOUGHT. 


of  a  force  by  the  product  of  the  force  (itself  measured  by 
the  velocity  of  a  moving  mass)  and  the  velocity  or  space 
per  unit  of  time  through  which  it  pushes  or  pulls  a 
moving  body,  and  Leibniz  ^  had  suggested  the  term  vis 
viva  to  distinguish  it  from  the  vis  mortua,  the  force 
or  pressure  itself.  But  the  first  clear  and  consistent 
fixing  of  the  terminology  which  has  since  been  universally 
adopted  is  to  be  found — not  in  the  '  Mecanique  analy- 
tique '  of  Lagrange  (that  classical  work  on  theoretical 
mechanics),  but  in  the  '  Mecanique  industrielle '  of 
Poncelet  (1829).^     He  introduced  the  term  "mechanical 


•"  Leibniz's  occupation  with  dyn- 
amics began  with  his  publication  of 
two  theses  in  1672,  which  he  dedi- 
cated respectively  to  the  Academy 
of  Sciences  in  Paris  and  to  the 
Royal  Society.  In  distinction  from 
the  writings  of  Huygens  and 
Newton,  where  precise  definitions 
take  the  place  of  metaphysical 
discussions,  Leibniz's  tracts  —  ex- 
cept in  the  comparatively  rare  cases 
where  he  confines  himself  to  mathe- 
matical formulae — are  vitiated,  like 
those  of  Descartes,  by  philosophical 
speculations.  Thus,  though  emi- 
nently suggestive,  they  contributed 
little  to  the  clearing  up  of  ideas. 
Influenced  by  Huygens  and  by 
Newton,  he  opposed  in  1686  the 
ideas  of  Descartes  on  the  measure 
of  force,  and  has  the  merit  of 
having  introduced  the  term  vis 
viva  in  1695,  and  of  having  started 
the  celebrated  discussion  on  the 
measure  of  force  which  was- carried 
on  during  fifty -seven  years  on  the 
Continent,  and  onlj-  settled  by 
D'Alembert  in  his  '  Traits  de  Dyn- 
amique'  (1743)  by  stricter  defini- 
tions. An  excellent  account  of  the 
questions  involved,  and  of  the 
gradual  clearing  up  of  ideas,  will 
be  found  in  Prof.  Mach's  historical 
treatise   on    dynamics    referred    to 


above.  See  the  English  translation 
by  M'Cormack,  p.  272,  &c.  It  is 
there  shown  that  one  of  the  great 
defects  of  Descartes'  and  Leibniz's 
dynamical  writings  was  the  want 
of  a  clear  definition  of  mass  or 
inertia  ;  also  that  this  conception 
follows  more  simply  from  Newton's 
definition  of  force  than  from  Huy- 
gens' conception  of  work  (ibid., 
p.  ^251). 

-  By  the  side  of,  and  sometimes 
in  opposition  to  the  purely  analytical 
school  headed  by  Lagrange,  Laplace, 
and  later  by  Cauchy,  there  grew 
up  in  Paris  the  school  of  practical 
mathematicians  which  taught  the 
application  of  theory  to  practice, 
to  problems  of  artillery,  engineer- 
ing, and  architecture.  They  created 
modern  geometrj",  and  to  a  great 
extent  modern  mechanics.  Monge, 
Coulomb,  the  elder  Carnot,  Pon- 
celet, Coriolis,  were  their  leaders  : 
Navier,  Lame,  Charles,  de  Saint 
Venant,  followed,  and  combined 
their  more  synthetic  methods  with 
the  analytical  methods  of  the 
former  school.  Through  Monge, 
Carnot,  Navier,  and  Poncelet, 
geometry  and  dynamics  were  led 
into  those  channels  which  have 
since  been  so  successfully  followed 
in    all   applied    work.      To    them 


ON    THE    PHYSICAL    VIEW    UF    NATLRK. 


lul 


work "  for  the  definite  quantity  which  liad  Ijefure  him 
been  variously  designated  as  power,  effect,  action,  &c., 
and  he  distinctly  states  that  the  inertia  of  matter  trans- 
forms work  into  vis  viva  and  vis  viva  into  work.  He 
also  measures  this  quantity  "  work  "  (luilc  in  the  luudcrn 
fashion — by  the  "  kilogrammetre,"  which  gives  the  same 
conception  as  the  foot-pound,  only  in  a  dillerent  measure. 
Long  before  the  terminology  thus  in\'ented  and  fixed 
by  Watt,  Young,  and  I'oncelet  had  been  accepted  by 
scientific  writers,  a  change  in  the  current  notions  on 
the  forces  of  nature  had  been  gradually  ljr(night  abinit 
from  quite  a  ditterent  quarter.  Uninfluenced  by  tiie 
theoretical  views  which  were  developed  and  firmly  held 


mathematics  was  not  merely  the 
science  of  magnitude,  but  quite  as 
much  that  of  position,  of  design 
and  perspective,  of  mechanical 
work  and  effect.  They  introduced 
a  whole  series  of  new  and  i)ractical 
ideas,  drawn  from  their  own  appli- 
cations, and  created  a  new  vocab- 
ulary. They  worked  hand  in  hand 
with  physicists  and  chemists,  some 
of  whom  had  little  taste  for  the 
extremely  abstract  and  analytical 
methods  of  the  school  of  Laplace 
and  Cauchy.  Poncelet's  original 
geometrical  work,  which  will  oc- 
cupy us  in  a  later  chapter,  led  him 
into  many  controversies.  It  was, 
however,  greatly  appreciated  in 
Germany  and  later  in  England. 
His  influence  on  German  applied 
mechanics  has  been  quite  as  great 
as  that  on  geometry  ;  and  the  great 
text-books  of  mechanics  by  Weiss- 
bach,  Redtenbacher,  Ruhlmanii.aiid 
others,  are  as  much  indebted  to 
Poncelet  and  other  French  models 
as  the  German  text-books  on  mathe- 
matics, physics,  antl  chemistry  were 
for  a  long  time  to  the  well-known 
works   of   Biot,    Pouillet,    Cauchy, 


Francccur,  Lame,  Regnault,  and 
others.  The  influence  of  Ponce- 
let on  practical  mechanics,  and 
especially  in  the  fixing  of  an  ade- 
(juate  terminology,  can  therefore 
be  studied  equally  well  in  French 
and  in  German  historical  writingB. 
Among  the  former  I  may  mention 
especially  the  '  lOxposd  de  la  .Situa- 
tion de  la  Mecanique  appliqu(5e 
par  Combes,  Phillips  et  Collignou,' 
Paris,  18ti7,  and  among  tiie  latter, 
notably  the  above-mentioned  writ- 
ings of  Helm,  who  traces  the 
growth  of  the  conception  of  me- 
chanical work  in  Freiicii  writings, 
and  its  influence  on  (ierman  thought 
(' Knergetik,'  j).  12,  &c.)  See  also 
Diihring,  loc.  cit.,  p.  471,  &c.  I  may 
also  refer  to  Heuu's  Report  ('Jaiires- 
bericht  der  deutscheu  Matheniat- 
iker-Vereinigung,'  vol.  ix.  part  2, 
1901),  where  the  sciences  comprised 
in  "Mechanics"  are  distinguished 
according  as  they  are  astronomical 
(Laplace,  Poincar^),  physical  (Eng- 
lish mathematical  jjiiysios,  Kirch- 
hoff,  Hclniholtz,  Hertz),  geometrical 
(Poinsot,  Charles,  Pall),  or  tet-hni- 
cal  (Watt,  Poncelet,  Rankine). 


102 


SCIENTIFIC    THOUGHT. 


by  the  school  of  which  Laplace  was  the  most  distin- 
guished representative,  natural  philosophers  like  Black,^ 
Eumford,  and  Davy  had  approached  the  study  of  those 
phenomena  where  heat  and  chendcal  change  are  the 
prominent  features.  The  phenomena  wdiich  they 
studied  experimentally  can  be  comprehended  under  the 
head  of  the  disappearance  and  appearance  of  heat  as 
measured  by  the  thermometer,  or  as  recognisable 
directly  by  our  sensation  of  heat.  Black  accounted 
for  the  disappearance  of  heat  by  the  doctrine  of  latent 
heat,  and  measured  this  by  the  capacity  ^  for  heat,  or 
the  specific  heat  of  different  substances.  Eumford 
made  exact  measurements  of  the  heat  generated  by 
friction,  and  showed  that  Black's  doctrine  of  latent 
heat  did  not  account  for  it.  Both  Black  and  Eum- 
ford were  led  to  science  from  the  side  of  practical  in- 
terests. Black,  like  Young  after  him,  was  a  physician. 
Eumford    was    all   through   his   life   occupied   with    the 

1  Joseph  Black  (1728-99),  one  of 
the  founders  of  chemistry,  and  a 
prominent  figure  in  that  illustrious 
circle  of  philosophers  who,  during 
the  second  half  of  the  eighteenth 
century,  made  the  literature  and 
science  of  Scotland  renowned  over 
the  whole  world,  published  very 
little,  being  mostly  known  througli 
his  teaching  and  his  pupils.  His 
name  is,  even  to  the  present  day, 
rarely  to  be  found  in  French  books ; 
whereas  in  Germany,  mainlj'  owing 
to  the  historical  writings  of  Herr- 
mann Kopp,  and  quite  recently  of 
Prof.  E.  Mach,  his  great  merit  and 
originality  have  been  fully  recog- 
nised. See  Kopp,  '  Geschichte  der 
Chemie,'  vol.  i.  p.  226,  &c.;  'Die  Ent- 
wickelungder  Chemie,'  1873, pp.  57, 
&c.,  88,  &c. ;  E.  Mach,  '  Die  Prin- 
cipien   der   Wiirmelehre,'  1896,  p. 


156,  &c.  Black,  who  as  early  as 
1755  had  shown  that  carbonic  acid 
gas  could  disappear  as  a  gas  and 
become  "fixed,"  showed  later 
that  heat  could  disappear  as  tem- 
perature and  become  "  latent." 
By  himself,  indeed,  the  former 
important  discovery  was  not  inter- 
preted against  the  then  i-eiguing 
phlogistic  theory,  nor  was  the  latter 
used  to  upset  the  material  theory 
of  heat.  Now,  however,  both  dis- 
coveries are  cornerstones  in  the 
history  of  science. 

^  According  to  Dr  Young  ('  Lec- 
tures,' new  ed.,  p.  499),  the  term 
"  capacity "  is  due  to  Dr  Irvine, 
who,  as  well  as  Dr  Crawford,  was 
much  influenced  by  Black's  lec- 
tures. These  were  first  published 
in  1802  by  Robison,  three  years 
after  the  author's  death. 


ON    THE    PHYSICAL    VIEW    OF    NATUKE.  103 

practical  application  of  scieutiHc  knowledge.  lilack's 
experiments  and  measurements  contributed  largely  to 
fix  the  difference  between  temperature  and  ([uantity 
tif  heat ;  he  demonstrated  clearly  that  heat  may 
disappear  in  the  form  of  temperature  and  exist 
as  latent  heat,  ihal  is,  licat  not  discoverable  by 
the  thermometer.  He,  however,  adhered  to  the  view 
that  heat  was  a  material  substance,  whicli,  tliough 
it  mi^ht  become  latent,  did  n(jt  disappear  as  such. 
Itumford^  was  the  first  who  definitely  went  a  step  further 
and  suggested  the  convertibility  of  heat  and  mechanical 
work.  It  was  not  the  disappearance  of  heat  but  its 
appearance  when  mechanical  work  was  performed  whicli 
attracted  his  attention.  After  eliminating  all  the 
sources  from  which  the  heat  produced  during  the  bor- 
ing of  cannon  could  have  been  derived,  he  comes  to  the 
conclusion  that  "  it  appears  to  be  extremely  ditticult, 
if  not  quite  impossible,  to  form  any  distinct  idea  of 
anything  capable  of  Ijeing  excited  and  communicated 
in  the  manner  the  heat  was  excited  and  communicated 
in  those  experiments,  except  it  be  motion."  Uavy, 
who,  like  lUack,  approached  science  in  tlie  interests  of 
the  medical  man,  comes  to  the  conclusion  in  his  firet 
published   papers,  from   experiments  on    the   generation 


^  Count  Rumford's  "Inquiiy  con- 
cerning  the   Source   of    the    Heat 


republislied  in  America  and  trans- 
lated    into     several     foreign     lan- 


which  is  excited  by  Friction"  was  |    guages.     See    Uuinford's    'Works,' 

published  in  a  later  edition  of  his  London,     1876,    vol.     i.     p.      48'2, 

'Ussays.'     The    experiments    with  and     vol.    ii.    p.    471.       In     1804 

the  boring  of  cannon  were  cairied  Count   Rumford   imblished,    in    lii.s 

on  at  Munich  in  1796  and  17f>7  ;  '  Meiuoires  sur  la  Clialcur '  [VuriA, 

the   substance    of    the    essay    was  an.    13),    a  "  Historical   Review  oi 

read  before  the  Roval  Society   in  j    the  Various  Experiments  on  Heat " 

Januarv  1798.     The*' Essays  '  were  |    (' Works,' vol.  iii.  pp.  138-240). 


104 


SCIENTIFIC    THOUGHT. 


of  heat  by  friction  and  percussion,  that  heat  is  not 
matter,  but  "  may  be  defined  a  peculiar  "  motion,  prob- 
ably a  vibration,^  of  the  corpuscles  of  bodies  tending 
to  separate  them,  Eumford's  and  Davy's  memoirs 
referred  to  belong  to  the  last  years  of  the  eighteenth 
century.  Dr  Young,  in  his  celebrated  lectures  on  natural 
philosophy,  discussing  the  experiments  of  Rumford  and 
Davy  came  to  the  conclusion  "  that  heat  is  a  quality, 
and  that  this  quality  can  only  be  motion."  He  refers 
to  Newton's  view  "  that  heat  consists  in  a  minute 
vibratory  motion  of  the  particles  of  bodies,"  and  to 
his  own  undulatory  theory  of  light.  This  analogy 
with  light  seems  to  have  for  a  long  time  served  to 
unify  the  speculations  -  of  those  who  were  inclined  to 


^  See  his  "  Essay  on  Heat,  Light, 
and  the  Combinations  of  Light," 
which  appeared  in  Beddoes'  '  Con- 
tributions to  Physical  and  Medical 
Knowledge,'  1799.  This  essay 
Davy  soon  after  condemned  as  "  in- 
fant chemical  speculations,"  from 
which  he  turned  away  to  ex- 
perimental work,  remarking  that 
chemical  knowledge  was  yet  too 
incomplete  to  allow  of  generalisa- 
tions, and  that  the  "fii'st  step 
will  be  the  decomposition  of  those 
bodies  which  are  at  present  un- 
decompounded."  This  was  written 
in  1799.  In  1800  (30th  March) 
Volta's  invention  of  the  "  pile " 
was  communicated  to  the  Royal 
Society,  and  on  the  30th  April  of 
that  year  the  first  pile  Was  con- 
structed in  this  country.  See  the 
first  and  second  volumes  of  Davy's 
'  Collected  AVorks,'  London,  1839. 
Davy's  first  publication  on  voltaic 
electricity  appeared  in  the  Septem- 
ber number  of 'Nicholson's  Journal.' 
Though  the  speculations  of  Davy 
on  heat  and  light,  in  which  heat 


is  conceived  to  be  motion  and  light 
(strangely)  to  be  material,  were  dis- 
carded by  him,  they  attracted  the 
attention  of  Franklin  and  of  Count 
Rumford.  Davy  states  that  his 
experiments  on  the  generation  of 
heat  "were  made  long  before  the 
publication  of  Count  Rumford's 
ingenious  paper  on  the  heat  pro- 
duced by  friction"  {loc.  cit.,  vol. 
ii.  p.  117).  In  spite  of  his  own 
refusal  to  follow  up  the  lines  of 
thought  suggested  by  them,  they 
were  probably  the  cause  of  Davy's 
appointment  as  lecturer  on  chem- 
istry at  the  Royal  Institution  :  see 
vol.  i.  p.  83  ;  also  Memoir  of  Count 
Rumford  ('AVorks,'  vol.  i.  p.  417), 
and  Paris's  'Life  of  Davy,'  vol.  i. 
p.  112,  &c.  Tait,  in  'Recent  Ad- 
vances,' gives  a  full  account  of 
Rumford's  and  of  Davy's  work. 

-'  See  'Young's  Lectures,'  51  and 
52.  In  the  second  edition,  pub- 
lished by  Kelland  forty  years  after 
the  Lectures  were  delivered,  the 
editor  makes  the  following  signifi- 
cant remark  :   "  The  theory  of  heat 


ON    THE    PHYSICAL    VIEW    (JF    NATIKK.  105 

embrace  a  mechanical  or  kinetic  view  of  the  nature 
of  heat.  Joule,  as  stated  above/  was  the  first  who 
emancipated  himself  from  it. 

But  whilst   these   suggestions    that   heat  may  te  re-        8. 

1  •   1  •  ComrUition 

garded  as  somehow  connected  witli  motion  remained  offoreai. 
mostly  vague  ami  undeveloped,  they  tended  to  impress 
upon  the  scientiiic  mind  the  interchangeability — or,  as 
it  was  called,  the  correlation  of  the  different  forces  of 
nature ;  and  the  idea  seems  to  have  forced  itself  in- 
dependently on  many  minds,  through  the  study  of  very 
different  groups  of  natural  phenomena.  In  Germany 
we    may    look    upon    Liebig    as    the   centre    of   a    great        9. 

Licbig. 

scientific  movement  which  tried  l)y  means  of  chemistry 
to  bring  the  realms  of  organic  and  animated  exist- 
ence under  the  treatment  of  exact  methods.  Xot 
(jiily  were  the  methods  of  organic  analysis  perfected 
l)y  him  and  his  school,  and  many  compounds  inves- 
tigated which  appeared  to  be  specially  the  bearera  of 
the  living  process  ;  but  he  was  also  among  the  first  to 
study  the  economy  of  li\ing  organisms,  the  circulation 
of  matter,  and  the  play  of  the  varied  processes  by 
which  life  is  maintained.  Among  these  processes,  the 
phenomenon  of  animal  heat,  its  origin,  and  the  part  it 
plays  in  the  living  organism  attracted  special  attention, 

may  be  said  to  rest  where  it  did  whiih  was  shown  to  have  the  same 

at   the  time   the.se   Lectures   were  properties  of  refle.\ion,  refraction, 

written.       The    facts    which    have  and  polarisation  as  Hght  possessetl. 

just  been  mentioned   clearly  point  The  analogy  of  this  form   of  heat 

out  its   undulatory  character"  (p.  with     liglit     threw    into    oblivion 

50(5).     Between  the  years  1835  and  the  beginnings  of  a   more  general 

184.')  theoretical  ideas  on  the  nature  mechanical   theory   of   heat,   which 

of    heat    were    entirely    dominated  i    — as  we  shall  see  further  on — had 

by   the   remarkable    discoveries   of  |   been     laid     by     Sadi     Carnot     iu 

Melloni,  Baden-Powell,  Forbes,  and  1824. 

others   referring   to   radiant    heat,  '        '  See  vol.  i.  of  this  work,  ji.  434. 


106  SCIENTIFIC    THOUGHT. 

By  his  work  on  organic  chemistry,  by  his  many  con- 
troversies, such  as  that  on  fermentation,  by  his  popular 
letters  on  chemistry,  and  especially  by  his  great  intlu- 
ence  as  a  teacher,  Liebig  himself  did  much  to  bring 
about  an  alliance  of  the  separate  sciences  and  a  connec- 
tion between  practical  pursuits  and  abstract  research,  and 
to  draw  attention  to  the  interdependence  of  the  various 
10.        forces  of  nature.     Only  second  in  influence  was  Johannes 

JohnMuller.  _  '' 

Mliller  of  Berlin.  Among  the  many  expressions  which 
took  their  origin  in  the  circle  of  studies  suggested 
by  these  influences,  we  may  select  three  as  giving 
increasingly  clear  emphasis  to  the  point  now  under 
consideration — viz.,  the  correlation  of  all  the  physical 
forces  of  nature.  These  expressions  are  those  of  the 
convertibility  of  forces,  of  the  existence  of  a  common 
measure  of  force,  and  of  the  conservation  implying 
the  perdurability  of  a  certain  quantity — now  termed 
Energy — of  which  all  phenomena  are  merely  a  partial 
exhibition.  They  are  connected  with  the  names  of 
Karl  Friedrich  Mohr,  Julius  Eobert  Mayer,  and  Her- 
mann Helmholtz. 

Were  it  my  object  merely  to  write  the  history  of 
science,  I  should  probably  follow  the  example  of  some 
historians  ^  and  omit  altogether  the  first  of  these  names 
in  the  present  connection.  But  as  my  object  is  to  write 
the  history  of  scientific  thought,  I  feel  bound  to  give  a 


^  Mach,  iu  his  recent  very  lucid 
and  valuable  work,  '  Die  Priiici- 
pien  der  Wiirmelehre,'  Leipzig, 
1896,  does  not  mention  Mohr.  On 
the  other  side,  Helm  ('  Die  Ener- 
getik,'  1898,  p.  9)  mentions  Mohr 
and  likewise  Planck  ('Das  Priucip 
der  Erhaltung  der  Energie,'  1887, 


p.  21).  Tait's  first  edition  of 
'Recent  Advances,'  1874,  does  not 
contain  Mohr's  name.  The  third 
edition  gives  a  full  account  of 
Mohr's  early  papers  (pp.  .51  and 
60,  &c.)  See  also  the  appreciative 
article  on  K.  F.  Mohr  in  the  '  Ency. 
Brit.' 


ON    THK    PHYSICAL    VIKW    OF    NATIIIK 


10' 


foremost  place  to  the  short  memoir  of  F.  ^lohr  entitled  n. 
"On  the  Nature  of  Heat,"  which  appeared  in  1<S:;7  in 
an  obscure  scientific  periodical  published  at  ^'ienna.  The 
publication  of  it  remained  unknown,  even  to  the  author 
himself,  and  was  certainly  unappreciated  by  the  scientific 
world  for  more  than  thirty  years.^ 


'  The  story  of  Mohr's  memoir  is 
curious,  not  to  say  romantic.  His 
original  paper,  '  Ueber  die  Natur 
<ler  Wiirme,'  was  offered  to  Pog- 
gendorf  and  refused,  as  were  the 
later  memoii'.s  of  Mayer  and  Hehn- 
holtz.  A  dread  of  inlroducing 
speculative  matter  into  the  '  An- 
naleu  '  prevented  likewi.-^e  —  as  I 
related  above  (p.  66,  note  2) — the 
appreciation  of  much  of  Faraday's 
later  work.  He  then  sent  the  ^lS. 
to  Baumgartner,  in  Vienna,  who — 
always  interested  in  theoretical 
jihysics — printed  it  in  a  periodical 
(' Zeitschrift  fiir  Physik ')  of  which 
he  and  von  Holger  were  joint- 
editors.  He  did  not  inform  the 
autliur  of  this.  Mohr  was  a  re- 
markably original  thinker,  in  whose 
mind  important  ideas  rose  at  times 
to  extraordinary  clearness,  but  who, 
like  many  original  thinkers,  did  not 
always  appreciate  his  own  itleas  at 
their  true  value,  and  accordingly 
treated  them  with  neglect,  and  did 
not  consistently  develop  them.  In 
the  present  instance  he  contented 
himself  with  inserting  an  abstract 
in  the  '  Annalen  der  Piiarmacie ' 
(vol.  xxiv.  p.  141),  of  which  he  was 
then  joint  -  editor,  together  with 
Liebig  and  Merck.  He  made  no 
further  inquiries  as  to  the  fate  of 
his  larger  memoir,  and,  in  con- 
versation with  friends  up  to  the 
j'ear  1860,  as  also  in  his  'Mechan- 
ische  Theorie  der  chemischen 
Aftinitat'  (Braunschweig,  1868,  p. 
4l>),  used  to  deplore  the  loss  of  a 
document  which,  more  fully  than 
the  short  paf>er  in  the  'Annalen  der 


Pharmacie,'  would  have  establislied 
his  priority  in  the  clear  enunciation 
of  a  remarkable  principle  wliich 
fifteen  years  later  received  general 
recognition.  The  matter  would 
probably  have  rested  there  had  it 
not  been  that  Tyudall,  in  the  year 
1862,  in  a  celebrated  lecture  before 
the  Royal  Institution,  commenced 
that  long  series  of  historical  and 
controversial  jtublications  in  which 
many  persons,  includhig  himself, 
Joule,  Tait,  d tiding,  Helmholtz, 
Akin,  Bohn,  Diihring,  Zollner, 
and  others  took  part,  and  in 
which,  among  several  claims  prior 
to  or  contemporary  with  Mayer's, 
those  also  of  Mohr  received  due 
recognition.  It  seems  to  have 
been  especially  l)r  Akin  who  drew 
attention  to  Mohr's  claims,  and 
searched  in  the  forgotten  volumes 
of  the  Austrian  periodical  for  the 
original  memoir,  which,  unknown  to 
the  author  himself,  had  been  in- 
scribed on  p.  419  of  the  fifth  volume. 
This  discovery  he  announced  to 
Mohr  himself  after  having  already, 
in  November  1864  ('Phil.  MagV 
4th  series,  vol.  xxviii.  p.  474 \ 
given  several  extracts,  among  which 
is  the  one  quoted  by  me  in  tlie 
text.  Mohr  published,  in  1869,  a 
sequel  to  the  above-mentioned  book, 
entitled  '  Allgemeine  Theorie  der 
Bewegung  und  Kraft,'  in  which  lie 
refers  to  Dr  Akins  discovery,  and 
reprints  the  original  menu>ir  in 
full.  Since  that  time  his  name  has 
figured  in  many  historical  uccount.s 
as  one  of  tlie  pioneers  in  the  de- 
velopment of   the  energy  -  coucep- 


108 


SCIENTIFIC    THOUGHT. 


12. 
Mayer. 


It  forms,  therefore,  no  link  in  the  actual  development 
of  the  energy-conception ;  but  it  is  a  significant  evidence  of 
the  direction  in  which  the  ideas  of  natural  philosophers 
were  then  moving,  and  of  the  high  degree  of  clearness 
to  which  they  rose  in  individual  instances.  When  we 
read  the  following  words :  "  Besides  the  known  fifty-four 
chemical  elements  there  exists  in  nature  only  one  agent 
more,  and  this  is  called  '  Kraft ' ;  it  can  under  suitable 
conditions  appear  as  motion,  cohesion,  electricity,  light, 
heat,  and  magnetism,"  it  seems  difficult,  even  after  the 
lapse  of  two  generations,  to  alter  anything  in  this  clear 
and  simple  enunciation  of  the  law  of  the  conservation 
of  energy.  It  has  indeed  been  stated  that  "  unless 
some  still  earlier  author  should  be  discovered,  there 
can  be  no  doubt  that  Mohr  is  to  be  recognised  as  the 
first  to  enunciate  in  its  generality  what  we  now  call 
'  conservation  of  energy.'  "  ^  At  the  same  time,  the 
case  shows  how  little,  at  the  beginning  of  a  scientific 
movement,  purely  abstract  statements  are  capable  of 
really  guiding  research  into  fruitful  channels.  There  is 
with  Mohr  no  attempt  to  establish  or  apply  an  actual 
measure  ^  of  the  amount  of  energy  appearing  in  the 
various  instances  which  he  mentioned.  This  further 
step  was  taken  five  years  later  by  J.  E.  Mayer,  who 
can    claim    to    be    the    first  ^   to    have    ventured   on    a 


tion  ;  his  merit  being  variously 
appraised  according  to  the  purely 
scientific,  the  philosophical,  or  the 
more  practical  standpoint  taken  up 
by  various  critics.  See,  inter  alia, 
P.  G.  Tait's  '  Recent  Advances,'  3rd 
ed.,  p.  60,  &c. ;  also  the  correspon- 
dence of  Mohr  and  Mayer  in  the 
latter's    '  Kleiners    Schrifteu    uud 


Briefe,'  ed.  Wayrauch,  p.  407, 
&c. 

1  See  the  article  on  K.  F.  Mohr 
in  the  '  Ency.  Brit.,'  9th  ed. 

-  See  on  this  point  Weyrauch,  in 
Mayer's '  Kleinere  Schriften,'  p.  408. 

^  Helm  ('  Energetik,'  p.  34)  begins 
the  list  of  undoubted  determina- 
tions of  the  heat-equivalent   with 


ON    THE    PHYSICAL    VIEW    OF    NATLKE. 


109 


numerical  estimate  as  between  mechanical  energj'  on 
the  one  side,  and  the  amount  of  one  of  the  imponder- 
ables— i.r.,  heat  as  measured  by  the  thermometer — (jn 
the  other.  Although  his  methods  were  not  free  from 
objection/   while   his   arguments    were   mixed    uj.    with 


Mayer,    1S42.      His    deteriuiiiaiiuii 
is  contained  in  his  first  paper,  pub- 
lished, a^  was  Mohrs,  in   Liebig's 
'Annalen'    (vol.    xlii..    May),    with 
the  title  "  Bemerkungen  iiber  die 
Krtif te  der  unbelebten  Natur."  The 
experiments  performed  by  Rumford 
in  179S  were  made  the  basis  of  a 
calculation  of  the  heat  equivalent, 
i.e.,  of   the   weight  which   can    be 
lifted  one  foot  if  the  heat  required 
to  raise  a  pound  of  water  1°  be  con- 
verted  into   work  against   gravita- 
tion,  and   the   figure   turns  out  to 
be  1034  lb.  its  compared  with  772 
lb.   given  by  Joule  himself  ('  Phil. 
Trans.,'  1850  ;  '  Joule's  Papers,'  vol. 
L  p.  299).    The  earlier  computations 
of  Seguin,  based  upon  the  work  done 
by  the   expansion  of   steam,   were 
referred  to  bv  Joule,  TvndaU,  and 
Tait  in  1862  and  1864  ('  PhiL  Mag.,' 
4th  series,  vols,  xsiv.aud  xxviii.),aud 
shown  to  lead  to  figures  further  off 
the  mark  than  those  of  Mayer.     In 
the  course  of  this  later  controversy 
it  became  for  the  first  time  gen- 
erally known  that  A.   Colding,  an 
engineer    in    Copenhagen,    had    a 
little  later  than  Mayer  (1843),  and 
almost  simultaneously  with  Joule, 
given  a  determination  of  the  equiva- 
lent based  upon  friction  of  metals, 
which  was  lower  than  Mayer's.     He 
accordingly  now  figures  as  second 
in    Helm's   list.       One   of   Joule's 
earliest     experiments    with    heat, 
"evolved  by  the  passage  of  water 
through   narrow  tubes,"  gave  the 
equivalent    as   770,  very    near    the 
figure,  viz.,  772,   finally  settled  on 
as  correct  in  18.50. 

'  The  reasoning  of  Mayer  is  not 
completely   contained   in    his    first 


paper,    which   subsetjuently,    on    a 
suggestion     of     Joule's,     appeared 
in  translation   in   the    '  Phil.  Mag.' 
(4th  series,  vol.  xxiv.  pp.  123,  and 
371  sqq.)     The  assumption  (calletl 
by     Thomson    in    1851     "  Mayer's 
hypothesis,"  see  '  Math,  and  Phys. 
Papers,'  vol.  i.   p.   213)  that  "the 
work  spent  in  the  compression  of 
a  gas  ...  is  exactly  the  mechani- 
cal equivalent  of    the    .    .    .    heat 
evolved,"  which  Joule  did  nut  think 
it  right  to  accept  without  satisfying 
himself  by  experiments  (see  '  Phil. 
Mag.,' 4th  series,  vol.  xxiv.  p.  122), 
was  based  by  Mayer  on  an  almost 
forgotten      experiment      of      Gay 
Lussac's  in  the  year  1807,  as  is  evi- 
dent  from   his   subsequent  pajjer, 
published     in     1845     (reprint     in 
'  Mechanik  der  War  me,'  ed.   Wey- 
rauch,  1893,  p.  53),  and  still  more 
from  his  correspondence  with  Baur 
previous    to    his    first    publication 
(ibid.,  p.  20,  and  '  Maver's  Briefe,' 
p.  130,  September  184 i).     The  sub- 
ject was  exhaustively   investigated 
by  Thomson  and  Joule  in  a  joint- 
memoir  on  "  the  thermal  effects  of 
fluids  in  motion,"  1852  (reprinted 
both  in  Joule's  and  Li>rd  Kelvin's 
Scientific     Papers),    when    it    was 
shown   that    for   air    Mayer's    hy- 
pothesis   was    approximately,    but 
not  absolutely,  correct.      So  long, 
therefore,  as  the  history  of  Mayer's 
rciisoning      was      not      conij'letely 
known,   it   appeared  as    if    he   bad 
by  a  kind  of  accident  hit  upon  an 
approximately  correct  figure.     See 
Tait,  'Recent  Advances'  (3rd  e<l., 
p.  53  ;  but  also  Helm,  '  Euergetik,' 
p.    24,    and    Mach,    '  Warmelehre,' 
p.  249). 


110 


SCIENTIFIC    THOUGHT. 


13. 


Joule. 


philosophical  speculations  which  tended  to  prevent 
their  ready  acceptance,  it  cannot  be  denied  that,  as 
a  first  approximation,  "  his  equivalent "  was  sufficiently 
near  the  truth   to  be  practically  useful. 

But  neither  the  happy  generalisation  of  Mohr,  which 
was  lost  or  forgotten,  nor  the  numerical  estimate  of 
Mayer,  which  remained  unnoticed,  succeeded  in  impress- 
ing contemporary  philosophers  with  the  importance  of 
the  subject.  This  was  done  almost  at  the  same  date, 
though  quite  independently,  by  the  persistent  and  per- 
severing experiments  and  measurements  of  James  Pres- 
cott  Joule,  who  laboured  unnoticed  and  practically 
without  support  from  1841  to  1847,  when  he  had 
the  good  fortune  of  gaining  the  attention  and  friend- 
ship  of  William  Thomson  (Lord   Kelvin).-^ 


^  Joule  not  only  defined  more 
clearly  the  different  data  and  con- 
ditions on  which  the  correctness  of 
the  result  must  depend,  but  had 
also  at  his  command  a  much  greater 
wealth  of  novel  experimental  facts, 
brought  together  by  his  own  re- 
sourceful mind.  Thus  from  1843 
to  1850  he  published  no  fewer  than 
ten  series  of  experiments,  approxi- 
mating from  widely  differing  results 
to  the  true  figure.  See  Helm's  list 
('  Energetik,'  p.  34).  After  he  had 
laboured  for  more  than  five  years 
his  work  was,  in  1847,  at  the  meeting 
of  the  British  Association  in  Oxford, 
still  almost  unknown.  He  himself 
reports  as  follows  in  1885  ('Joint 
Scientific  Papers,'  1887,  p.  215) : 
"  It  was  in  the  year  1843  that  I 
read  a  paper  '  On  the  Calorific 
Effects  of  Magneto- Electricity  and 
the  Mechanical  Value  of  Heat '  to 
the  Chemical  Section  of  the  British 
Association  at  Cork.  With  the  ex- 
ception of  some  eminent  men  .  .   . 


the  subject  did  not  excite  much 
general  attention  ;  so  that  when  I 
brought  it  forward  again  at  the 
meeting  in  1847  the  chairman  sug- 
gested that,  as  the  business  of  the 
section  pressed,  I  should  not  read 
any  paper,  but  confine  myself  to  a 
short  verbal  description  of  my  ex- 
periments. This  I  endeavoured  to 
do,  and  discussion  not  being  in- 
vited, the  communication  would 
have  passed  without  comment  if  a 
young  man  had  not  risen  in  the 
section,  and  by  his  intelligent  ob- 
servations created  a  lively  interest 
in  the  new  theory.  The  young  man 
was  William  Thomson,  who  had  two 
years  previously  passed  the  Univer- 
sity of  Cambridge  with  the  highest 
honour,  and  is  now  probably  the 
foremost  scientific  authority  of  the 
age."  See  also  Lord  Kelvin's  ac- 
count of  the  meeting  in  1847  in 
'  Popular  Lectures  and  Addresses  ' 
(London,  1894,  vol.  ii.  p.  556,  &c.) 


ON    THE    PHYSICAL    VIEW    OF    NATIKE.  Ill 

A  pupil  of  Daltou,  Joule  was  early  drawn  into  the 
circle  of  ideas  and  iii\estigations  winch  are  contained  in 
Faraday's  experimental  researches.  With  much  ampler 
means,  and  possibly  also  with  a  greater  hne  for  accurate 
quantitative  measurements,  than  P'araday  possessed,  he 
grasped  the  great  importance  of  the  law  of  electrolytic 
equivalence  as  affording  the  means  of  accurately  measur- 
ing chemical  processes,  and  of  giving  definite  expression 
to  the  vaguer  ideas  supported  by  Faraday  and  othei-s 
that  force  was  indestructible,  and  that  the  different 
forces  of  nature  w^ere  mutually  convertible.  These 
ideas  had  received  popular  circulation  and  current  ex- 
pression in  Grove's  celebrated  lectures  on  the  "  Corre- 
lation of  riiysieal  Forces"  in  1842  and  1843.  Joule, 
in  whose  mind  they  seem  to  liave  existed  as  axioms, 
set  himself  to  devise  accurate  instruments  and  methods 
by  which  the  convertibility  of  different  forces,  their 
"  mechanical  duty,"  could  be  measured,  and  their  equiv- 
alence put  into  figures.  The  first  numbers  which  Joule 
found  differed  considerably,-^  so  that  the  conclusion 
arrived  at  that  the  mechanical  duty  or  "  value "  of  a 
degree  of  heat  is  a  constant  quantity  could  only  have 
been   drawn   by  one   who   had   a   strong    a  priori^  con- 

^  For  details  see  Helm,  '  Ener-  A  predisposition  to  believe  that 
getik,'  p.  3-t  ;  also  vol.  i.  p.  265,  j  some  quantity  besides  matter  could 
note,  of  the  present  work.  Joule's  |  not  be  lost  or  created,  but  onlj* 
equivalent  varied  from  742  to  890 
fuot-pounds,  and  was  finally  fixed 
at  772  in  1850,  this  figure  being 
correct  to  h  per  cent  (Joule's 
'Scientific  Papers,'  p.   328). 

-  Philosophical  considerations  arc 
mixed  up  with  all  the  early  enun- 
ciations of  the  principle  of  the  in- 
destructibility of  force,  or  energy  as 
it  was   later   more  clearly  termed. 


preserved  and  transformed,  existed 
in  the  mitids  of  ^lohr,  iSeguin, 
Mayer,  Colding,  Joule,  Hirn,  antl 
has  been  traced  variously  back  to 
the  wiitings  of  earlier  thinkei-s, 
such  as  Montgolfier,  Faraday,  Davy, 
Oersted,  Leibniz,  &c.  Prof.  Mach 
('Wiirmelehre,'  p.  238,  &e.)  dis- 
cusses this  jioint  fully.  The  prin- 
ciple     gradually     became      firudy 


112 


SCIENTIFIC    THOUGHT. 


14. 

Helmholtz. 


viction  in  that  direction.  The  experimental  result  did 
not  satisfy  Helmholtz,  who,  about  the  same  time,  was 
led  to  consider  the  origin  of  animal  heat  in  living 
organisms,  a  problem  with  which  Liebig  ^  had  been 
greatly  occupied  for  several  years.  Without  himself 
devising  or  instituting  new  experiments,  or  attempting 
any  determination  of  the  equivalent  as  others — notably 
Colding  and  Holtzmann  —  were  doing,  Helmholtz,  in 
1847,  undertook  a  theoretical  investigation  which  has 
since  become  classical — a  corner-stone  in  the  philosophy 
of  the  subject.  He  first  of  all  gave  the  principle  in- 
volved a  correct  mathematical  expression,  showed  how  it 
could  be  considered  as  an  extension  of  the  theorem  known 
in  abstract  dynamics  as  the  conservation  of  the  vis  viva 
of  a  mechanical  system,  attempted  to  define  the  nature  of 
forces,  in  the  Newtonian  sense,  which  would  be  subject  to 
the  new  principle,  and  brought  it  into  logical  connection 
with  the  axiom  laid  down  and  used  by  French  philos- 
ophers, that  perpetual  motion  is  an  impossibility.  After 
clearing  the  ground  so  far  as  abstract  dynamics  is  con- 
cerned and  giving  the  necessary  definitions,  sharply  dis- 
tinguishing between  acting  (living)  forces  and  mere 
tensions  (dead  forces),  Helmholtz  proceeds   to  draw  all 


established  according  as  strict 
definitions,  experimental  proofs 
and  figures,  and  mathematical 
formulffi  took  the  place  'of  vague 
speculations.  Joule  did  the  experi- 
mental, Helmholtz  the  mathema- 
tical, part  of  the  work  ;  but  it  is 
interesting  to  see  how  little  the 
latter  without  the  former  was  able 
to  impress  contemporary  German 
writers  with  the  value  of  the  prin- 
ciple  which    he    established.      He 


himself  even  did  not  for  a  long 
time  develop  the  line  of  reasoning 
which  he  had  begun. 

^  See  Helmholtz,  '  Bericht  iiber 
die  Theorie  der  phj'siologischen 
Warmeerscheinungen,'  1845,  re- 
printed in  '  Wissenschaftliche  Ab- 
handlungen,'  vol.  i.  No.  1,  also 
on  Joule's  early  experiments  in 
'  Ueber  die  Erhaltung  der  Kraft,' 
ibid.,  vol.  i.  p.  33. 


ON    THK    PHYSICAL    VIEW    OF    NATURE.  113 

other  forces  of  nature  into  his  consideration,  showing,  in 
the  case  of  the  phenomena  of  heat,  electricity,  i^alvanism, 
and  magnetic  induction,  how  the  dillerent  agencies  can 
be  brought  into  comparison  with  mechanical  ones  by 
measuring  the  work  they  perform  ;  refers  to  tlie  attempts 
to  hx  the  mechanical  value  of  heat ;  concludes  in  each 
case  that  no  observed  phenomena — not  even  the  pro- 
cesses in  h\ing  organisms — stand  in  contradiction  with 
the  principle  announced,  and  ends  with  the  words :  "  I 
think  in  the  foregoing  I  have  proved  that  the  above- 
mentioned  law  does  not  go  against  any  hitherto  known 
facts  of  natural  science,  but  is  supported  by  a  large 
number  of  them  in  a  striking  manner.  I  liave  tried 
to  enumerate  as  completely  as  possible  what  con- 
sequences result  from  the  combination  of  other  known 
laws  of  nature,  and  how  they  require  to  be  con- 
firmed by  further  experiments.  The  aim  of  this 
investigation,  and  what  must  excuse  me  likewise  for 
its  liypothetical  sections,  was  to  ex[)lain  to  natural 
philosophers  the  theoretical,  practical,  and  heuristic  im- 
portance of  the  law,  the  complete  verification  of  which 
may  well  be  looked  upon  as  one  of  the  main  problems 
of  physical  science  in  the  near  future."  ^  The  reasons 
why  this  valuable  document  attracted  little  attention  at 
the  time  and  was  set  aside,  as  were  the  earlier  contribu- 
tions of  Mohr  and  ]\Iayer,  by  the  central  organ  of  ex- 
perimental physics  abroad,  are  interesting  from  a 
historical  point  of  view.  The  first  and  main  reason 
seems  to  have  been  that  none  of  the  three  original  and 
independent  expressions  contained  any  new  experimental 

^  'Gesammelte  Abhandlungen,'  vol.  i.  j).  (57. 
VOL.  J  J.  " 


114 


SCIENTIFIC    THOUGHT. 


facts,^  and  that  the  then  reigning  school  of  natural  philos- 
ophers in  Germany  discouraged  theoretical  deductions,  as 
possibly  leading  back  to  the  fatal  "  philosophy  of  nature," 
out  of  which  they  had  only  just  escaped.  Men  of  the 
intellectual  eminence  of  Liebig,  through  whose  labours  an 
enormous  mass  of  new  facts  had  been  accumulated,  and 
who  desired  to  see  the  more  hidden  processes  of  organic 
life  subjected  likewise  to  rigorous  measurements,  showed 
indeed  a  certain  appreciation  of  the  attempted  defini- 
tions of  Mohr  and  Mayer,  struggling  as  he  and 
they  alike  were  under  the  still  existing  confusion  in 
the    fundamental    conceptions.^       And    these   were    not 


1  See  Mohr,  '  Allgemeine  Theorie 
der  Bewegung  unci  der  Kraft,'  p. 
82,  kc.  Poggendorf  did  not  reply 
to  Mayer's  repeated  communica- 
tions and  did  not  return  the  MS. ; 
the  fact  that  he  received  it  was  first 
established  by  ZoUner,  who  in  1877 
recovered  the  MS.  from  Poggeu- 
dorf's  heirs  (Mayer's  '  Schrifteu  und 
Briefe,'  ed.  Weyrauch,  p.  100),  and 
gave  a  facsimile  of  it  in  his 
'  Wissenschaftliche  Abhandlungen ' 
(Leipzig,  vol.  iv.,  1881,  p.  672). 
Helmholtz,  who  in  1847  had  no 
knowledge  of  Mayer's  writings,  did 
full  justice  to  his  claims  in  his 
address,  '  Ueber  die  Wechselwirk- 
ung  der  Naturkrafte '  (1854),  and 
vindicated  them  against  Tait's 
criticisms  in  a  letter  published  by 
the  latter  in  his  '  Sketch  of  Ther- 
modj-namics'  (Edinburgh,  1868); 
see  Helmholtz,  '  Wissenschaftliche 
Abhandlungen,'  vol.  i.  p.  71,  &c. 
Helmholtz  closes  his  later  com- 
ments on  the  subject  ('  Yortriige 
und  Reden,'  vol.  i.,  3rd  ed.,  1884,  p. 
74)  with  the  following  significant 
remark  :  "  The  best  ideas  run  the 
risk  of  remaining  barren,  if  not 
accompanied  by  that  energy  which 
lasts  till  the   convincing   proof   of 


their  correctness  has  been  given." 
This  explains  the  neglect  of  Mohr 
and  Mayer,  and  why  in  England 
the  interest  in  the  energy  ideas 
only  became  general  after  Joule's, 
Thomson's,  and  Rankine's  labours, 
as  Helmholtz  himself  remarks  in 
1854  ('Vortrhge,'  &c.,   p.   39). 

^  Helmholtz  ("Ueber  Mayers 
Prioritiit,"  '  Yortriige,'  vol.  i.  p.  69) 
says:  "That  the  [i.e.  Mayers]  dis- 
sertation contained  really  important 
ideas,  that  it  did  not  belong  to  the 
wide  -  ranging  literature  of  vague 
suggestions,  such  as  are  annually 
served  up  by  badly  informed  ama- 
teurs, could  at  best  only  be  noticed 
by  a  reader  who  had  already  turned 
over  in  his  mind  similar  reflections, 
and  who  could  recognise  them 
under  the  somewhat  strange  vocabu- 
lary of  the  author.  Liebig,  who,  in 
the  same  year  in  which  Mayer's 
dissertation  appeared,  published  his 
book  on  animal  chemistry,  in  which 
he  fully  discussed  the  question  as  to 
the  origin  of  animal  heat,  was  per- 
haps such  a  reader,  and  was  there- 
fore willing  to  insert  the  article 
in  his  annals."  The  same  remark 
would  refer  equallj'  to  Mohr's 
earlier   essay.       It  is   now   known 


ON    THE    PHYSICAL    VIEW    OF    NATTKE. 


IL 


sutlicieully  cleared  up  in  ^luhr's  sliurt  aper^u,  which  dfyes 
not   attempt    to   distinguish    between    the  two  ditVerent 
meanings  of  tlie   word   force,  nor  in   the  earlier  papei-s 
of  Mayer,  wliu,  however,  in  later  writings  shows  a  clear 
appreciation  of   the  dilhculty.      In   Helmholtz's  menujii-s 
the  desired  clearness  was  only  attained  by  mathenuitical 
reasoning,  which  in  his  age  and  country  was  accessible 
to  but  few  naturalists.     The  second  and   probably  the 
fundamental    obstacle   in    the    way   of    a   just    recogni- 
tion of  the  new  truth  lu}'  in  the  fatal  use  of  the  term 
"  force  "  in  two  distinct  meanings.      Popularly  tlie  ditti- 
culty  has  only  been  removed  l>y  the  creation  of  a  new 
vocabulary,  and  dates  from  the  introduction  of  the  term 
"  work  "  by  Clausius  in  1850,  and  of  the  term  "  energy  " 
by  William  Thomson,  who  adopted  it  from  Young  in  the  ^^f '"'""" 
year  1852.      The  confusion  which  had  been  kept  up  by  '^'""'"''" 
employing  the  word  "  force  "  to  mean  not  only  pressure 
or  dead  force  (in  the  Newtonian  sense)  but  also  acting 
force  {vis  viva  in   the  Leibnizian  sense),  and  with  this 
confusion  the  whole  meaning  of  the  great  controversies 
which   raged    for   many   years    between    the    Cartesians 
and   Leibnizians    on    the   correct   measure  of  force,  was 
then   removed,  and   a    grammatical    and    logical   founda- 


15. 
Work"anil 
energy  " 
introluced 


from  Mayer's  published  correspond- 
ence that  some  remarks  of  Liel)ig 
himself,  which  appeared  early  in 
1842,  induced  him  to  send  him  his 
first  paper  in  order  "  not  to  lose  the 
right  of  j)riurity  "  (letter  to  Gries- 
inger,  fiili-Gth  December  184"2,  in 
'  Schriften  and  Briefe,'  ed.  Wey- 
rauch,  p.  190).  Mayer  there  says  : 
"  Liebig  wrote  to  me,  inter  alia: 
'  As  to  what  force,  cause,  and 
effect  are,    there    exist    in    general 


such  confused  notions  that  an 
easily  understood  explanation  must 
be  considered  to  V)e  of  real  value.' 
One  would  accordingly  tliink  tliat 
he  himself  considers  himself  quite 
above  this  general  confusion  ;  that 
this  is  ni>t  so,  1  could  see  surti- 
ciently  from  his  '  phenomena  of 
motion  in  the  animal  organism ' 
(Liebig,  'Die  organische  Chemie, 
&c.;  1842,   p.    183,  &c.)" 


116  SCIENTIFIC    THOUGHT. 

tion  secured  on  which  a  new  generation  could  enter 
at  once  into  the  possession  of  correcter  dynamical  and 
physical  views.  It  is  now  being  recognised  more  and 
more  that  the  word  "  force "  applies  only  to  a  mathe- 
matical abstraction,  whereas  the  word  "  energy "  or 
"  power  to  perform  work "  applies  to  a  real  quantity ; 
and  there  are  not  wanting  suggestions  that  the  former 
should  be  altogether  banished  from  scientific  text-books, 
and  that  the  latter  denotes  not  merely  a  property  of 
matter,  but  that  it  is  after  matter  the  only  real  thing 
or  substance  in  the  material  world.^ 

This  radical  change  in  the  fundamental  notions  which 
underlie  all  physical  reasoning  was  not  brought  about, 
however,  till  the  vaguer  views  expounded  by  Mayer  in 
Germany,  and  the  exact  measurements  of  Joule  in  England, 
had  been  united  by  the  independent  labours  of  Thomson 
and  Clausius,  whose  earliest  researches  (also  carried  on 
independently  of  each  other)  had  been  suggested  by  the 

^  The  late  Prof.  P.  G.  Tait  has  methods  and  systems  which  ia- 
on  various  occasions  expressed  volve  the  idea  of  force,  there  is  the 
himself  in  this  sense.  See  his  leaven  of  artificiality.  The  true 
lecture  on  "Force,"  delivered  be-  :  foundations  of  the  subject,  ba.sed 
fore  the  British  Association.  Glas-  <  entirely  on  experiments  of  the 
gow,  in  1876,  and  reprinted  in  most  extensive  kind,  are  to  be 
'Recent  Advances,'  3rd  ed.,  also  found  in  the  inertia  of  matter,  and 
the  closing  paragraphs  of  his  article  the  conservation  and  transfor- 
"  Mechanics,"  in  the  9th  ed.  of  the  ,  mation  of  energy.  With  the  help 
'Ency.  Brit.,'  reprinted  as  '  Dy-  of  kinematical  ideas,  it  is  easy  to 
namics,'  1895,  where  he  says  (p.  base  the  whole  science  of  dynamics 
356) :  "  The  only  other  known  I  on  these  principles  ;  and  there  is 
thing  in  the  physical  univer.se,  ;  no  necessity  for  the  introduction  of 
which  is  conserved  in  the  same  j  the  word  '  force,'  nor  of  the  sense- 
sense  as  matter  is  conserved,  is  j  suggested  ideas  on  which  it  was 
energy.  Hence  we  naturally  con-  '  originally  based."  We  must,  how- 
sider  energy  as  the  other  objective  ever,  in  that  ca.se  extend  the  con- 
reality  in  the  physical  universe,  ception  of  matter  to  embrace  also 
and  look  to  it  for  information  as  to  the  ether  (see  Tait,  '  Properties  of 
the  true  nature  of  what  we  call  Matter,'  p.  5,  2nd  ed.) 
force;"     and   (p.    361):     "In  all 


ON    THE    PHYSICAL    VIEW    UF    NATURE.  117 

still   earlier   writings   of   Sadi   Carnot  and  (Jlapevnjn   in        m. 

Sadi  C'arnot. 

France.  Thomson's  interest  in  the  8u]>ject  dates  from 
the  middle  of  the  'forties.  He  was  then  occupied  with 
finding  a  method  for  measuring  heat  on  the  ab.solute 
scale.  Mohr,  Mayer,  and  Helmholtz  all  approached  the 
thermo-dynamical  problem  in  the  medical  or  physiological 
interest.  Trained  in  the  school  of  Liebig  and  Johannes 
Midler,  they  were  led  to  study  the  economics  of  organic 
processes  and  the  mechanism  of  the  physiological  pheno- 
mena of  animal  heat,  of  motion,  and  of  nutrition.  Sadi 
Carnot,  as  after  him  Clapeyron  in  France  and  Joule  in 
^Manchester,  approached  the  thermo-dynamical  problem 
from  the  side  of  practical  interests,  created  by  the  intro- 
duction and  universal  application  of  steam  in  the  useful 
arts.  The  great  change  worked  by  the  steam-engine, 
especially  in  England,  the  utilisation  of  coal  and  iron- 
stone, the  foundation  of  England's  growing  industrial 
wealth,  seemed  to  Sadi  Carnot  to  be  concentrated  in  the 
problem  of  the  motive  power  of  heat ;  as  to  Liebig,  the 
key  which  would  unlock  the  mysteries  of  vegetable 
growth,  of  animal  nutrition,  and  of  human  labour,  with 
their  economic,  industrial,  and  political  aspects,  lay  in 
the  problem  of  combustion.  As  in  the  domain  of  electri- 
cal science,  so  in  that  of  thermotics,  the  first  thing  to 
do  was  to  arrive  at  a  correct  method  of  measuring  heat 
as  distinguished  from  temperature.  It  was  a  problem  of 
applied  mathematics.  About  the  same  time  Gauss  had 
established  the  system  of  absolute  measurement  from  a 
universal  point  of  view,  and  he  and  Weber  had  applied 
it  to  magnetic  and  electrical  plienomena.  Thomson 
set  himself   to   do    the   same    thing    in    thermotics,   and 


118 


SCIENTIFIC    THOUGHT. 


he  found  in  the  ideas  expounded  by  Poncelet,  Sadi 
Carnot,  and  Clapeyron,  the  means  of  accomplishing  the 
object.  We  now  see  how  there  lay,  in  the  fundamental 
problem  of  thermo-dynamics,  the  unifying  idea  of  sciences 
hitherto  far  apart  and  working  on  independent  lines  and 
with  independent  standards  of  measurement,  speaking,  as 
it  were,  separate  languages.  And  what  was  the  new  idea 
which  lay  concealed  in  Sadi  Carnot's  forgotten  pamphlet  ?  ^ 
In  Carnot's  original  memoir  it  appears  as  an  axiom  at 
the  beginning  of  his  reflections.  "  The  production  of 
motion,"  he  says,  "  in  steam-engines  is  always  accompanied 
by  a  circumstance  on  which  we  must  fix  our  attention. 
This  circumstance  is  the  re-establishment  of  equilibrium, 
or  level,  in  the  caloric — that  is  to  say,  its  passage  from 
one  body  where  the  temperature  is  more  or  less  elevated. 


^  The  story  of  Sadi  Carnot's 
memoir  is  not  less  curious  than  that 
of  Mohr's  first  paper.  It  was  first 
given  by  Lord  Kelvin  in  his  earliest 
article,  "On  an  Absolute  Thermo- 
metric  Scale"  (1848),  reprinted  in 
'  Math,  and  Phys.  Papers,'  vol.  i. 
p.  100),  and  "An  Account  of  Car- 
not's Theory"  (1849,  ibid.,  p.  113). 
He  had  in  1845  searched  in  vain  for 
the  '  Puissance  motrice  du  Feu  '  in 
all  the  bookshops  of  Paris.  In  1848 
he  obtained  a  copy  from  Levpis 
Gordon  in  Glasgow.  It  was  known 
to  him  before  through  Clapeyron 's 
memoir  in  the  14th  vol.  of  the 
'  Journal  de  I'Ecole  polytechnique  ' 
(1834).  Sadi  Carnot  published  his 
memoir  as  a  pamphlet  in  1824.  It 
has  since  been  republished  by  his 
brother,  Hippolyte  Carnot  ('  Reflex- 
ions sur  la  Puissance  motrice  du 
Feu  et  sur  les  Machines  propres  h, 
d^velopper  cette  Puissance,'  Paris, 
Gauthier- Villars,  1878),  with  im- 
portant posthumous  papers,  from 
which,  inter  alia,  it  is  evident  that 


Carnot,  before  he  died,  had  aban- 
doned the  material  theory  of  heat, 
and  actually,  by  an  unknown  pro- 
cess, calculated  the  mechanical 
equivalent  of  heat  as  360  kilogram- 
metres.  As  in  several  other  cases, 
so  also  in  that  of  Sadi  Carnot,  the 
line  of  reasoning  initiated  by  La- 
place, and  brilliantly  developed  by 
his  school,  militated  against  the 
acceptance  of  the  dynamical  as 
opposed  to  the  material  conception 
of  the  phenomena  of  heat ;  and 
M.  Bertin,  in  his  "Rapport  sur  le 
Progres  de  la  Thermodynamique  en 
France"  ('Recueil  de  Rapports,' 
&c.,  p.  5)  could  write  in  1867  :  "II 
faut  bien  I'avouer,  parceque  c'est  la 
v&-ite :  nous  sommes  restfe  long- 
temps,  je  ne  dis  pas  rebelles,  mais 
Strangers  aux  nouvelles  idees  :  elles 
nous  sont  restfes  trop  longtemps 
inconnues,  et  encore  aujourd'hui, 
on  peut  regretter  qu'elles  n'occupent 
pas  une  place  plus  considerable  dans 
notre  euseignement  scientifique." 


ON    THE   PHYSICAL    VIEW    OF    NATURE.  119 

to  another  where  it  is  lower,  .  .  .  The  production  of 
moving  force  is  therefore  due  in  steam-engines,  not  to  a 
real  consumption  of  caloric,  Ijut  to  a  transference  from  a 
hot  body  to  a  cold  body."  ^ 

If  it  is  the  object  of  physical  science  to  describe  the 
processes  of  nature  completely  and  in  the  simplest 
language,  we  have  here  an  instance  of  a  description  of 
a  very  general  property  in  very  simple  language,  and  in 
terms  which  reduce  it  to  a  measurable  quantity.  With- 
out this,  progress  is  impossible.  It  is  not  likely,  how- 
ever, that  Carnot  saw  the  full  significance  of  his  simple        i:. 

Camot 

statement,  how  in  it  he  had  introduced  into  physical  and  introduces 

'  ^    "^  the  idea  of 

mathematical  science  the  great  question  of  the  avail-  abjl'^y'.. 
ability  of  the  forces  of  nature,  as  Mohr  and  ]\Iayer  in 
(Germany,  and  Faraday  and  Grove  in  England,  somewhat 
later,  dwelt  on  the  correlation  or  interchangeability  of 
those  forces.  The  two  ideas  were  separately  developed. 
When  they  came  together  in  one  mind,  when  Thomson 
fully  realised  the  importance  and  meaning  of  Ijoth 
— as  he  undoubtedly  did  earlier  than  any  other 
natural  philosopher — he  at  once  established  the  great 
doctrine   of    the   dissipation,  also   called    degradation   or        is. 

.  Tliomson  iii- 

depreciation,  of   energy,      Jnit  it  required  some  modih- tr.Kiuctsihe 
cation  of  Carnot's  enunciation  of  this  general  property  '^'pation." 
before   it   could    be   put   into   its   modern    form.       This 
modification  was  preparing  itself  in  Carnot's  own  mind, 
as   his   papers,   posthumously   puljlished,   have    revealed 
to  US.2     What   required   to   be  modified  was   the  word 

1  Carnot,     '  Puissance     motrice,'  ed.    187S,     p.    <J0) :     "  Loi^iiu'une 

ed.  1878,  pp.  5  and  6.  liypothose  ne  suffit  plus  a  I'explica- 

*  His  notebook  contained  the  fol-  tion  des  phc^uom^ne8,  elle  doit  etre 

lowing  entry  {'Puissance  motrice,'  abandonnoe.      C'est   le   aw   oil    ee 


120 


SCIENTIFIC   THOUGHT. 


19. 
Fourier. 


caloric.  Carnot  was  brought  up  under  the  influence  of 
the  school  that  looked  upon  heat  as  an  imponderable 
substance  which  might  hide  itself — might  become  latent 
— but  could  not  be  created  or  destroyed.  This  was 
the  view  of  Black,  of  Laplace,  of  Fourier ;  it  was  not  the 
view  of  Cavendish,  of  Davy,  of  Eumford.  The  views 
of  the  former  were  embodied  in  great  treatises,  and  con- 
sistently worked  out  with  much  collateral  extension  of 
physical  and  mathematical  knowledge ;  the  views  of  the 
latter  were  expressed  in  detached  experiments  and  in 
casual  reflections.  Fourier^  had  just  (1822)  given  to 
the  world  his  epoch-making  work,  the  '  Th^orie  ana- 
lytique  de  la  Chaleur,'  in  which  he  had  stated  that  "  the 
properties  of  heat  form  a  special  order  of  phenomena 
which  are  not  to  be  explained  by  principles  of  motion 
and   equilibrium ; "  ^    and   again,   "  There   exists   a   very 


trouve  I'hypothese  par  laquelle  on 
considere  le  calorique  comme  une 
matiere,  comme  un  fluide  subtil." 
Again  (p.  92) :  "  La  chaleur  est  le  re- 
sultat  d'un  mouvement.  Alors  il  est 
tout  simple qu'elle  puisse  se  produire 
par  la  consommation  de  puissance 
motrice  et  qu'elle  puisse  produire 
cette  puissance.  Tous  les  autres 
ph^nomenes  .  .  .  pourraient  s'expli- 
quer  dans  cette  hypothese  :  mais  il 
serait  difficile  de  dire  pourquoi,  dans 
le  ddveloppement  de  la  puissance 
motrice  par  la  chaleur,  un  corps 
froid  est  necessaire,  pourquoi,  en 
consommant  la  chaleur  d'un 'corps 
^chauffe,  on  ne  pent  pas  produire 
du  mouvement."  And  (pp.  93  and 
94) :  "  Lorsque  Ton  fait  naitre  de  la 
puissance  motrice,  par  le  passage  de 
la  chaleur  du  corps  A  au  corps  B,  la 
quantite  de  cette  chaleur  qui  arrive 
k  B,  cette  quantite  est-elle  la 
meme,  quel  que  soit  le  corps  em- 


ploj-^  Ji  realiser  la  puissance  motrice  ? 
Y  aurait-il  moyen  de  consommer 
plus  de  chaleur  a  la  production  de 
la  puissance  motrice  et  d'en  faire 
arriver  moins  au  corps  B  ?  Pourrait- 
on  meme  la  consommer  tout  entiere 
sans  en  faire  arriver  au  corps  B  ? 
Si  cela  ^tait  possible,  on  pourrait 
creer  de  la  puissance  motrice  sans 
consommation  de  combustible  et 
par  simple  destruction  de  la  chaleur 
des  corps."  And  (p.  94):  "La 
chaleur  n'est  autre  chose  que  la 
puissance  motrice,  ou  plutot  que  le 
mouvement  qui  a  change  de  forme. 
C'est  un  movement  dans  les  par- 
ticules  des  corps." 

■'  On  the  tardy  reception  and 
recognition  of  Fourier's  work  see 
vol.  i.  p.  241,  note,  of  this  work. 

'^  '  Theorie  analytique  de  la 
Chaleur,'  1822:  '  Discours  prd- 
liminaire,'  p.  iii. 


ON    THE    PHYSICAL    VIKW    OF    NATL'KE.  1 1' 1 

extensive  class  of  phenomena  which  are  not  produced 
by  mechanical  forces,  but  which  result  solely  from  the 
presence  and  accumulation  of  heat.  This  part  of  natural 
philosophy  cannot  be  brought  under  dynamical  theories  ; 
it  has  principles  peculiar  to  itself,  and  is  based  ui^m 
a  method  similar  to  that  of  the  (^ther  exact  sciences.^ 
.  .  .  The  dilatations,  indeed,  caused  by  the  repulsive 
force  of  heat,  the  observation  of  which  dilatations  serves 
as  a  measure  of  temperature,  are  dynamical  effects ;  but 
it  is  not  these  dilatations  which  we  calculate  when  we 
investigate  the  laws  of  the  ])ropagation  of  heat." "  He 
proceeds  to  Imild  up  this  new  science  "upon  a  very 
small  nvmiber  of  simple  facts,  of  which  the  causes  are 
unknown,  but  which  are  gathered  by  observation  and 
confinned  by  experiments,"  ^  and  he  thus  arrives  at 
certain  general  relations,  expressed  in  the  form  of  equa- 
tions, which  are  different  from,  though  analogous  to,  and 
not  less  rigorous  than,  the  general  equations  of  dynamics. 
One  of  the  great  experimental  facts  upon  which  Fourier 
bases  his  theory  of  the  propagation  (i.e.,  the  conduction 
and  radiation)  of  heat  is  this,  that  all  motion  of  heat 
depends  on  differences  of  temperature.  He  examines 
how  differences  of  temperature  are  equalised  and  de- 
duces the  law  of  the  flow  of  heat."^     Although  he  does 


'Fourier,    '  Theorie    analytique,'   |    zig,    1896),    pp.    78,   &c'.,    116    sq/j. 
p.   13.  '^  Ibid.,  p.  14.         I    Every    studeut    of    pliy.sic.s   should 

•*  Ibid.,  pp.  xi,  18,  39.  read  the  chapters  referring  to  this 


*  I  cannot  here  omit  to  jxtint  out 
how  elegantly  Prof.  Mach  has  trans- 
lated into  the  language  of  common- 
sense  the  whole  process  of  Fourier 
for    establi.shing    the    fundamental 


subject.  The  mathematical  for- 
mulie  will  thus  l)ecome  living  to 
him ;  but  he  will  also  see  how 
necessary  the  abstract  mathematical 
expression    of    common-sen.se  cou- 


equation   of   the   theory.      See   his    '    ceptions  is  in  order  to  avoid   false 
'Priucipien  der  Warmelehre' (Leip-    |    reasoning. 


20. 
His  influ- 
ence on 
Carnot. 


122  SCIENTIFIC    THOUGHT. 

not  find  it  necessary  to  enter  npon  any  theory  of  the 
nature  of  heat,  the  analogy  with  the  flow  of  water  from 
higher  to  lower  levels  would  naturally  present  itself. 
For  his  purpose  this  analogy  had  no  importance.  For 
the  purposes  of  Sadi  Carnot,  who  noticed  that  upon 
the  difference  of  temperature  depended  not  only  the 
flow  of  heat,  but  also  the  work  it  might  eventually 
do,  the  same  analogy  seemed  all-important.  "  We  may," 
he  says,  "justly  compare  the  motive  power  of  heat  with 
that  of  a  fall  of  water :  both  have  a  maximum  which 
cannot  be  exceeded.  The  motive  power  of  a  fall  of 
water  depends  upon  its  height  and  the  quantity  of  the 
liquid ;  the  motive  power  of  heat  likewise  depends  on 
the  quantity  of  caloric  employed  and  on  what  we  will 
take  the  liberty  of  calling  the  height  of  its  drop — that 
is,  the  difference  of  temperature  of  the  bodies  between 
which  the  exchange  of  caloric  has  taken  place."  ^  In 
this  analogy  two  further  assumptions  seem  to  be  im- 
plied :  First,  that  the  work  capable  of  being  done  is  in 
direct  proportion  to  the  difference  of  levels  of  height 
or  of  temperature ;  secondly,  that  the  quantities  with 
which  we  operate,  of  water  or  of  caloric,  remain  the 
same,  before  and  after  the  fall.  Neither  of  these 
inferences  is  necessary ;  neither  is  permissible.  Carnot 
does  not  adopt  the  first  inference,^  but  he  does  adopt 
the  second,^   though  he   significantly   remarks   that  the 


^  '  Puissance  motrice  du  feu,' 
eel.  1878,  p.  15. 

"^  "  Dans  la  chute  d'eau,  la  puis- 
sance motrice  est  rigoureusement 
proportionelle  h,  la  difference  de 
niveau  entre  le  reservoir  supdrieur 
et  le  reservoir  inferieur.  Dans  la 
chute    du    calorique,   la   puissance 


motrice  augmente  sans  doute  avec 
la  dift'drence  de  temperature  entre 
le  corps  chaud  et  le  corps  froid  ; 
mais  nous  ignorons  si  elle  est 
proportionelle  k  cette  difference " 
(ibid.,  p.  15  ;  compare  also  pp. 
38,  39). 

^  "  La  production  de  la  puissance 


ON    THE    PHYSICAL    VIEW    OF    NATL'RE. 


l:i3 


foundations  on  which  the  theory  of  heat  rests  retiuire 
careful  examination.^  Further  thought  evidently  led 
him  to  douht  the  correctness  of  tlie  second  assumption. 
It  is  the  first  point  to  which  Thomson,  more  than 
twenty  years  after,  directs  his  attention.  He  conceives 
the  idea  of  measuring  temperature  hy  such  a  scale  that 
for  an  equal  drop  in  the  scale — i.e.,  Ijy  letting  down  heat 
by  an  equal  number  of  degrees  on  the  new  scale — equal 
amounts  of  work  shall  be  done.^  The  speculations  of  8adi 
Carnot  remained  unnoticed  for  a  long  time.  Ten  years  21. 
later  Clapeyron     reverted   to    the  subject,  and  itut  the  f.'rapiiicai 

■■^    *'  .  .  method. 

reflections  of  Carnot  into  graphical  form  and  into  mathe- 
matical language.  He  introduced  the  conception,  based 
on  Carnot's  theory,  of  the  ratio  of  heat  transferred  from 
a  higher  to  a  lower  level  of  temperature  to  the  maxi- 
mum of  work  obtainable, — a  quantity  independent  of 
the  substance  employed, — and  he  called  this  fixed  ratio 


Carnot's    function.       It    was 

motrice  est  .  .  .  due  .  .  .  uon  h 
uue  consommation  rdelle  du  cal- 
orique,  uiais  a  son  transport  d'un 
corps  chaud  h  un  corps  froid,  c'est- 
ii-dire  iV  son  retablissement  d'equi- 
libre  "  (ibid.,  p.  6). 

^  "  Au  reste,  pour  le  dire  en 
passant,  les  principaux  fondenients 
sur  lesquelles  repose  la  thot)rie  de 
la  chaleur  auraient  besoin  de  I'ex- 
anieu  le  j)lus  attentif.  Plusieurs 
faits  d'exporieuce  paraissent  ii  peu 
pr6s  inexplicables  dans  I'dtat  actuel 
de  cette  th^orie"  (ibid.,  p.  20, 
note).  "  La  loi  fondamentale  que 
nous  avions  en  vue  .  .  .  est  assise 
sur  la  thc'orie  de  la  chaleur  telle 
(ju'on  la  conc;oit  aujourd'hui,  et  il 
faut  I'avouer,  cette  base  ne  nous 
parait  pas  d'uue  solidite  indbran- 
lable"  (p.  50).  As  stated  above 
(p.  118,  note),  Carnot  emancipated 


through    his    paper    that 

himself  from  the  conventional  or 
material  view  of  the  nature  of 
heat.  See  the  appendix  to  the 
edition  of  1878. 

-  See  'Cambridge  Piiilosophical 
Society  Proceedings,'  June  1848  ; 
reprinted  in  Thomson's  (Lord  Kel- 
vin's) '  Matli.  and  Phvs.  Papers,' 
vol.  i.  p.   100. 

^  Beiioit  I'ierre  Emile  Clai>eyron 
was  an  engineer.  In  1834  he  puV)- 
lished,  in  tlie  fourteenth  cahier  of 
the  'Journal  de  I'Ecole  Poly  tech- 
nique,' his  "  Mcmoire  sur  la  Puis- 
sance motrice  de  la  Chaleur."  It 
was  througli  a  translation  of  tliis 
paper  in  'Taylor's  ScientiKc  Mem- 
oirs' that  Thomson  lieard  about 
Carnot's  earlier  work,  and  tlirough 
a  translation  in  Poggendorf's  'An- 
nalen'  (1843)  that  Helmlioltz  be- 
came acquainted  witli  the  subject. 


124 


SCIENTIFIC    THOUGHT. 


Helmholtz  in  Germany,  and  Thomson  in  England,  heard 
about  Sadi  Carnot  himself.  Sadi  Carnot,  so  much  earlier 
and  so  unlike  Mayer,  had  nevertheless  one  point  in 
common  with  him.  This  point  seems  to  have  given 
a  common  anchorage  to  all  those  thinkers  who,  in  the 
course  of  a  generation,  gradually  lifted  the  theory  of  heat 
and  energy  out  of  twilight  into  clear  thought.  Sadi 
Carnot,  Mayer,  Joule,  Helmholtz,  Thomson,  all  express 
or   imply   the   same   idea — viz.,  the  impossibility    of   a 

In   one  form  or   other  this  seems 


22. 
Perpetual 
motion  .        . 

impossible,    perpetual  motion.^ 


^  The  conception  of  a  "perpet- 
ual motion,"  or,  as  it  is  termed 
abroad,  of  a  "  perpetuum  mobile," 
and  that  of  its  impossibility, 
have  been  changed  and  more 
clearly  defined  in  the  course  of 
the  hundred  years  which  followed 
the  decision  of  the  Paris  Academy 
of  Sciences  in  1775  not  to  receive 
in  future  any  scheme  of  perpetual 
motion.  Into  the  same  class  of 
axiomatic  impossibilities  were  also 
thrown  the  "squaring  of  the 
circle"  and  the  "trisection  of  the 
angle."  Helmholtz  (appendix  to 
his  Lecture  on  '  Die  Wechselwirk- 
ung  der  Naturkraf te, '  1853,  dated 
1883)  remarks  that  the  proof  of 
the  impossibility  did  not  then 
exist,  and  that  the  resolution  was 
therefore  based  merely  on  the 
experience  of  past  failures.  The 
doctrine  of  Energy,  the  arithmet- 
ical discoveries  of  Gauss,  and  the 
elegant  researches  of  Hermite  and 
Lindemann,  have  thrown  much 
light  on  these  celebrated  prob- 
lems. In  the  last  chapter  of 
this  volume  I  shall  revert  to  the 
two  latter ;  as  to  the  first,  the 
"perpetual  motion,"  what  follows 
may  tend  to  clear  the  popular 
conceptions.  Tait  has  correctly 
remarked  that  "perpetual  motion 
is  simply  a  statement  of  Newton's 


first  law  of  Motion "  ( '  Recent 
Advances,'  3rd  ed.,  p.  74).  He 
might  have  added  that  it  took 
probably  as  much  ingenuity  on 
the  part  of  Galileo  to  arrive  at  the 
principle  of  inertia — viz.,  that  "all 
motion  is  perpetual  until  force  in- 
terferes to  alter  and  modify  it  " — as 
it  took  to  formulate  correctly  the 
other  principle  that  such  a  per- 
petual motion  is  of  no  use,  because 
you  cannot  do  any  work  with  it, 
except  by  using  it  up  or  anni- 
hilating it.  In  the  beginning  of 
the  nineteenth  century  the  im- 
possibility of  a  mechanical  device 
for  the  so-called  perpetual  motion 
was  universally  admitted,  though 
— as  Rosenberger  ('  Geschichte  der 
Physik,'  vol.  iii.  p.  229,  note) 
remarks  —  this  was  not  also  ex- 
tended to  physical  processes,  it 
being  taught  that  the  processes  of 
nature  represented  a  ' '  perpetual 
cycle  which  uninterruptedly  re- 
newed itself."  In  fact,  the  truth 
was  beginning  to  dawn  that  if 
motive  power  or  energy  could  not 
be  obtained  out  of  nothing  neither 
could  it  be  destroyed.  Carnot  in 
1824,  and  Mayer  in  1842,  both  take 
it  as  an  axiom  that  power  cannot 
be  created  ;  Mohr  in  1837,  and 
Joule  in  1843  and  1845,  are  equally 
convinced   that   power    cannot    be 


ON    THE    PHYSICAL    VIEW    OF    NATURE. 


125 


to  be  an  axiom  with  them,  but  even  this  apparently 
simple  article  of  faitli  in  natural  philosophy  meant 
somethini;  diflerent  to  different  thinkers  accordin<:  to 
the  greater  or  less  clearness  of  their  physical  concep- 
tions. Helmholtz,  in  his  celebrated  memoir  of  1847, 
conceives  all  natural  processes  to  be  ultimately  re- 
ducible to  purely  mechanical  processes,  and  in  doing 
so  he  sees  that  a  well-known  law  in  mechanics,  the 
conservation  of  the  vis  viva,  must  have  a  meaning  for 
all  natural  forces.  This  he  proceeds  to  develop.  Others, 
like  Faraday,  Mohr,  Grove,  have  a  silent  conviction  that 
besides  ponderable  matter  there  is  some  other  quantity 
in  nature  which  is  indestructible  and  cannot  be  created, 
but  only  changed  and  transferred ;  they  frequently  call  it 
force,  and  thus  entangle  themselves  or  their  readers  in 


destroyed.  Under  the  influence 
of  Oersted's  pliilosophy  Colding 
expresses  similar  ideas  in  1843 
(see  '  Phil.  Mag.,'  4th  series,  vol. 
xxvii.  p.  58).  In  fact,  during  the 
fifth  decade  of  the  century  the 
three  conceptions  of  the  impossi- 
bility of  creating  power,  its  inde- 
structibility, and  the  converti- 
bility of  its  different  forms,  were 
more  and  more  clearly  enunciated. 
They  were  at  last  expressed  in 
the  formula  of  the  "  conservation 
of  energy.''  It  was  Tiiomson  (Lord 
Kelvin)  who  then — in  1852 — first 
clearly  recognised  that  the  old  phan- 
tom of  a  perpetual  motion  was 
turning  up  again  in  a  new  form. 
(See  his  Essay  on  "  Dissijiation  of 
Energy  "  in  the  '  Fortnightly  Re- 
view,' March  1892,  reprinted  in 
'  Popular  Lectures  and  Addresses,' 
vol.  ii.  p.  452.)  Ever  since  Thom- 
son's essay  of  1852  naturalists 
and  philosophers  may  be  said  to 
be  tj-ying  to  formulate  in  the 
simplest  terms  the  great  [)i'inciple 


of  nature,  that  though  energy  is 
never  lost,  it  becomes  —  for  our 
practical  purposes  —  unavailable. 
Prof.  Ostwald  has  expressed  this 
by  reviving  the  terminology  of 
the  perpetual  motion.  "  It  is  not 
generally  recognised  that  the 
principle  of  perpetual  motion  has 
two  sides.  On  the  one  side  .  .  . 
perpetual  motion  could  be  realised 
if  one  could  create  energy.  .  .  . 
The  expression  of  the  impossi- 
bility of  doing  this  is  the  first  law 
of  Energetics.  ...  A  perpetual 
motion  could,  however,  on  the 
other  side  be  attained  if  it  were 
possible  to  induce  the  large  store 
of  energy  at  rest  to  enter  into 
transformations.  .  .  .  This  might 
be  termed  a  perpetual  motion  of 
the  second  kind."  The  impossi- 
bility of  this  Ostwald  terms  the 
second  princi|)le  of  Energetics 
('Allgemeine  Cliemie,'  vol.  ii. 
part  1,  p.  172  ;  cf.  Helm, 
'Energetik,'  p.  304). 


126 


SCIENTIFIC    THOUGHT. 


that  confusion  which  the  indefinite  use  of  the  word  had 
caused,  especially  among  Continental  writers.  One  of 
the  first  practical  applications  of  this  idea  as  referred 
to  the  motive  power  of  heat  in  Carnot's  sense  was  made 
23.        by  "William  and  James  Thomson  in    1849.     They  had 

Application 

by  William    both  fully  realised  that  lowering  of  temperature  might 

and  James  ''  r>  l  id 

Thomson,  ^q  accompanicd  by  the  doing  of  work  by  heat,  and 
that  elevation  of  heat  to  a  higher  temperature  meant 
expense  of  work.  If,  therefore,  work  could  be  done  by 
heat  without  lowering  the  temperature,  there  was  an 
apparent  gain  of  motive  power  without  corresponding 
expenditure.  It  was  known  that  water  at  freezing 
temperature  expanded  in  becoming  ice :  it  was  capable 
of  doing  work,  frequently  very  destructive  work,  with- 
out a  lowering  of  temperature.  In  order  to  convert 
water  into  ice  of  the  same  temperature,  heat  must  be 
abstracted.  Here,  then,  was  a  case  of  a  possible  trans- 
ference of  heat  without  fall  of  temperature,  and  the 
creation  or  gain  of  great  power  to  do  work ;  but,  ac- 
cording to  Carnot's  principle,  equality  of  temperature 
implied  an  absence  of  expenditure  of  work.  So  here 
was  a  case  of  gain  without  expenditure  of  power  sim- 
ply by  a  transference  of  heat  at  freezing-point.  James 
Thomson  ^  saw  the  solution  of  the  paradox.      If  water 


^  The  reasoning  of  James  Thom- 
son, based  again  upon  the  impossi- 
bihty  of  a  perpetual  motion,  is  given 
in  the  following  passage  of  his  com- 
munication to  the  Royal  Society  of 
Edinburgh,  dated  January  2,  1849 
(reprinted  in  his  brother.  Lord  Kel- 
vin's, '  Math,  and  Phys.  Papers,' 
vol.  i.  p.  156)  :  "  Some  time  ago  my 
brother.  Prof.  William  Thomson, 
pointed  out  to  me  a  curious  conclu- 


sion to  which  he  had  been  led  by 
reasoning  on  principles  similar  to 
those  developed  by  Carnot  with  ref- 
erence to  the  motive  power  of  heat. 
It  was  that  water  at  the  freezing- 
point  may  be  converted  into  ice  by 
a  process  solely  mechanical,  and  yet 
without  the  final  expenditure  of  any 
mechanical  work.  This  at  first  ap- 
peared to  me  to  involve  an  impossi- 
bility, because  water  expands  while 


ox    THE    PHYSICAL    VIKW    OF    XATURK. 


in  expanding  by  freezing  is  made  lu  du  wuik,  it  over- 
comes pressure ;  it  has  to  freeze  under  pressure.  The 
temperature  of  water  freezing  under  pressure  must  lie 
lower  than  that  of  water  freezing  under  ordinary  con- 
ditions.^ Knowing  the  mechanical  duty  of  a  degree  of 
temperature  and  the  work  of  the  expansion  of  ice,  he 
could  calculate  how  much  the  freezing-point  of  water 
must  be  lowered  by  pressure.  In  1850  his  brother 
William  Thomson  verified  this  theoretical  prediction  by 
actual  experiment."  It  is  well  known  how  Helmholtz 
in  1865  made  use  of  this  theoretically  predicted  and 
practically  verified  phenomenon  in  liis  celebrated  glacier 
theory.^  Both  James  and  AVilliam  Thomson,  when 
they  drew  the  conclusions  from  Carnot's  theory,  still 
adhered  to  the  doctrine  of  the  entire  conservation  of 
heat.^       But    William    Thomson,    who    was   equally   ac- 


freezing  ;  and  therefore  it  seemed 
to  follow  that  if  a  quantity  of  it 
were  merely  enclosed  in  a  vessel 
with  a  movable  piston  and  frozen, 
the  motion  of  the  piston  conse- 
quent on  the  expansion  being  re- 
sisted by  pressure,  mechanical  work 
would  be  given  out  without  any 
corresponding  expenditure  ;  or,  in 
other  words,  a  perpetual  source  of 
mechanical  work,  commonly  called 
a  perpetual  motion,  would  be  pos- 
sible. .  .  .  To  avoid  the  absurdity 
of  .supposing  that  mechanical  work 
could  be  got  out  of  nothing,  it 
occurred  to  me  that  it  is  necessary 
further  tocoiiclude  that  the  freezing- 
point  becomes  lower  as  the  pressure 
to  which  the  water  is  subjected  is 
increased." 

^  "  The  mechanical  pressure  pro- 
motes— as  is  generally  the  case  with 
the  alternate  action  of  different 
forces  in  nature — euch  a  change, 
viz.,  melting  of  ice,  as  is  favourable 


to  the  effect  of  its  own  action " 
(Helmholtz,  '  Vorthige  und  Reden,' 
vol.  i.  p.  217). 

-  '  Proceedings  of  the  Roy.  Soc. 
of  Edinburgh,'  January  1850,  re- 
printed in  'Math,  and  Phj's.  Papers,' 
vol.  i.  p.  165. 

■*  Helmholtz,  loc.  cit.,  p.  215  377., 
where  also  the  jdienomenon  dis- 
covered and  called  "  regelation  of 
ice,"  by  Faraday,  is  similarly  ex- 
plained. 

■*  It  is  important  to  notice  this, 
as  the  formula  with  which  we  are 
now  familiar,  that  the  mechanical 
work  gained  meant  consumption  of 
heat,  wiis  not  available  at  tiiat  time. 
This  is  significantly  pointed  out  by 
Helm  ('Energetik,'  p.  69).  The 
reasoning  was  accordingly  more 
difficult  and  refined.  James  Thom- 
son, however,  had  at  the  time  some 
misgivings  on  the  tlion  jirevalcnt 
view,  and  in  a  footnote  he  refers  to 
the  "  j)ossibility  of  the  absolute  for- 


128 


SCIENTIFIC    THOUGHT. 


24. 
The  two 
laws  of 
thermo- 
dynamics. 


quainted  with  Carnot's  ideas  and  with  Joule's  work, 
increasingly  felt  the  necessity  of  reconciling  both  views 
in  one  consistent  view.  So  did  Clansius  independently 
at  Ziirich.  The  result  was  the  doctrine  of  the  "  con- 
servation of  energy," — not  of  heat,  as  Carnot  had  it, — 
and  the  embodiment  of  the  two  correct  ideas  contained 
independently  in  Carnot's  and  Joule's  work  in  the  two 
well-known  laws  of  thermo-dynamics  ^  —  viz.,  the  con- 
servation, equivalence,  and  convertibihty   of  energy,  as 


mation  or  destruction  of  heat  as  an 
equivalent  for  the  destruction  or 
formation  of  other  agencies,  such  as 
mechanical  work  "  ( '  Math,  and 
Phys.  Papers,'  vol.  i.  p.  161,  note). 
The  acceptance  of  the  doctrine  of 
the  convertibility  of  heat  and 
mechanical  work  —  implying  the 
conservation  of  energy  in  place  of 
the  conservation  of  heat,  as  Carnot 
had  it — seems  to  have  taken  place 
in  Lord  Kelvin's  mind  immediately 
after  his  paper  referred  to  ahove  in 
consequence  of  a  paper  by  Rankine 
"  On  the  Mechanical  Action  of 
Heat  "  (Roy.  Soc.  Edinburgh,  Feb. 
1850),  as  is  shown  by  his  letter  to 
Joule,  dated  October  1850  {loc.  cit., 
vol.  i.  p.  170).  He  there  refers  also 
to  a  memoir  by  Clausius  in  Poggen- 
dorf's  '  Annalen  '  of  April  and  May 
of  the  same  year  as  adopting 
"  Joule's  axiom  instead  of  Carnot's  " 
(ibid.,  p.  173). 

^  The  reconciliation  of  Joule's 
dynamical  theorj'  of  heat  with  Car- 
not's doctrine,  and  the  necessary 
modification  of  the  latter,  is  con- 
tained in  Lord  Kelvin's  classical 
memoir,  "  On  the  Dynamical 
Theory  of  Heat,"  in  the  '  Trans,  of 
the  Roy.  Soc.  of  Edinburgh,'  March 
1851  ('Math,  and  Phys.  Papers,' 
vol.  i.  p.  173  sqq.)  In  the  intro- 
duction, Davy,  Mayer,  Joule,  and 
notably  Liebig,  are  mentioned  as 
earlier  supporters  of  the  doctrine  of 


the  convertibility  of  heat  into  me- 
chanical effect,  Rankine  and  Clau- 
sius as  the  latest  contributors  (p. 
176).  The  first  and  celebrated 
enunciation  of  the  second  law  by 
Thomson  is  given  at  the  very  be- 
ginning (p.  179),  and  in  the  sequel 
the  denial  of  it  is  shown  to  mean 
the  possibility  of  a  perpetual  mo- 
tion. A  little  farther  on  Thomson 
refers  to  Clausius  in  the  words : 
"  The  merit  of  first  establislung  the 
proposition  upon  correct  principles 
is  entirely  due  to  Clausius,  who 
published  his  demonstration  of  it 
in  the  month  of  May  last  year " 
(1850).  It  has  on  the  other  side 
been  admitted  by  Clausius  ('  Die 
mechanische  Wiirmetheorie,'  2te 
Aufl.,  1876,  vol.  i.  p.  358)  that 
Thomson's  independent  develop- 
ment of  the  second  law,  though 
published  later,  is  conducted  from 
a  more  general  point  of  view, 
whereas  his  own  treatment  was 
purely  mathematical  and  confined 
to  special  cases.  The  most  general 
and  philosophical  expression  of  the 
new  principle  was  given  by  Thom- 
son in  his  celebrated  communication 
to  the  Roval  Society  of  Edinburgh, 
April  19,"  1852,  "On  a  Universal 
Tendency  in  Nature  to  the  Dissipa- 
tion of  Mechanical  Energy "  (re- 
printed in  '  Math,  and  Phys. 
Papers,'  vol.   i.  p.   511). 


ON    THE    PHYSICAL    VIEW    OF    NATURE.  129 

expressed  in  the  first  law,  and  the  doctrine  of  the  avail- 
ability of  energy  as  expressed  in  ihe  second  law.  U  was 
Thomson  who  first  clearly  saw  that  the  axitjni  of  the 
impossibility  of  a  perpetual  motion  would  l)e  infringed  if 
the  first  law  of  thermo-dynamics — the  indestructibility  of 
energy — was  accepted  without  the  second.  P'or  practical 
use,  for  doing  work,  it  is  not  sufficient  that  energy  be  not 
lost ;  it  must  be  available — get-at-aljle.  Energy  may  Ije 
in  a  condition  in  w'hich  it  is  useless — hidden  away — and 
to  liring  it  forth  again  may  either  be  for  us  impossible 
(if  it  be  dissipated),  or  may  require  an  expenditure  of 
work — i.e.,  of  energy — to  do  so.  The  second  law  puts 
into  mathematical  language  another  very  inqxjrtant  and 
very  striking  property  of  the  processes  in  nature.  Let 
us  dwell  on  this  a  moment. 

The  doctrine  of  the  preservation  of  energy,  of  the 
equivalence  of  the  different  forms  of  energy,  tended  to 
put  all  the  forms  of  energy  on  the  same  level.  If  they 
be  convertible,  they  appear  to  be  of  the  same  value. 
If  in  doing  work,  energy  was  not  consumed  but  only 
changed,  it  stood  to  reason  that  it  might  be  changed 
back  again,  so  that  tlie  work  could  be  d(jne  over  again. 
In  other  words,  if  all  processes  are  purely  mechanical 
processes — modes  of  motion — a  supposition  which  very 
early  forced  itself  with  more  or  less  clearness  on  the 
pioneers  of  the  science  of  energy,  they  must  be  reversible  : 
it  must  1)0  possible  to  turn  them  round  again,  to  undo 
what  has  been  done,  or  to  do  what  has  been  undone. 
Now  the  common-sense  view  of  nature  tells  us  at  once 
that  this  is  impossible ;  but  it  does  not  seem  to  have 
struck  the   earlier   propounders   of   the  doctrine   of    the 

VOL.  IL  I 


130  SCIENTIFIC    THOUGHT. 

equivalence  and  correlation  of  forces,  such  as  Faraday,, 
Mohr,  Mayer,  Grove — not  even  Joule  and  Helmholtz — 
that  if  neither  matter  nor  power  is  lost,  the  phenomena 
of  loss  and  waste  in  nature  and  in  human  life  remain 
unexplained.  The  only  mind  to  whom  this  problem 
presented  itself  was  Sadi  Carnot,  and  it  presented  itself 
to  him  in  an  extreme  form ;  for  he  started  with  the 
idea  that  even  heat  itself  in  doing  work  was  not  lost 
or  destroyed,  but  handed  over  from  the  hotter  body 
(the  boiler  of  the  steam-engine)  to  the  colder  body  (the 
condenser  of  the  steam-engine).  We  now  know  that 
this  view  was  not  correct — that  the  whole  heat  is  not 
handed  over,  but  always  only  a  portion  of  the  heat.  But,, 
with  this  exaggerated  view  in  his  mind,  he  tried  to  explain 
the  phenomena  of  loss  and  waste,  and  he  conceived  that 
the  explanation  lay  in  the  lowering  of  the  temperature. 
"  It  would  be  difficult  to  say  why " — though  he  had 
assumed  it  as  an  axiom  that — "  in  the  development  of 
motive  power  by  heat,  a  cold  body  should  be  necessary, 
why  in  consuming  the  heat  of  a  heated  body  we  cannot 
produce  motion."  ^  Heat  at  high  temperature  is  of  more- 
value  for  doing  work  than  the  same  amount  of  heat  at 


^  The  words  quoted  are  taken 
from  cue  of  the  fragments  published 
in  the  year  1878  by  H.  Carnot  from 
the  posthumous  MSS.  of  his  brother, 
Sadi  Carnot.  In  this  fragment  he 
approaches  the  modern  conception 
that  heat  is  the  result  of  motion  : 
he  sees  that  all  other  phenomena 
can  be  explained  by  this  hypothesis ; 
but  he  pauses  after  having  stated 
the  difficulty  quoted  above  in  the 
text,  and  reverts,  after  some 
further  queries,  to  the  same  diffi- 


culty in  the  words,  ' '  Can  one  con- 
sume the  heat  entirely  without 
letting  any  arrive  at  the  body  B 
[viz.,  from  a  body  A]  ?  If  this  were 
possible,  one  could  create  motive 
power  without  consumption  of  fuel, 
and  simply  by  the  destruction  of 
the  heat  of  bodies"  ('Puissance 
motrice,  &c. ,'  ed.  1878,  pp.  92  and 
94).  It  is  interesting  to  see  how 
nearly  these  reflections  approach  to 
those  made  more  than  twenty  years 
later  by  Thomson. 


ON    THK    PHYSICAL    VIKW    UK    .NATCKK.  131 

low  temperature.  By  doing  work,  as  also  by  conduction, 
and  radiation  with  absorption,  this  inequality  of  tempera- 
ture is  spent,  i.e.,  lost.  Clausius  and  Thomson  alone 
seem  to  have  grasped  the  value  of  this  conception.  The 
difficulty  was  to  put  it  into  mathematical  language — 
into  calculable  terms.  Each  did  tiiis  independently. 
Thomson,  more  than  any  other  thinker,  put  the  problem 
into  common-sense  language,  brought  the  subject  home 
to  the  practical  reason ;  at  the  same  time  he  put  it  into 
mathematical  language,  allowing  the  conceptions  of  waste  ^ 
and  of  value  and  of  availability  (or  usefulness)  of  energy 
to  be  scientifically — that  is,  measurably — defined.  In 
1851  he  put  the  axiom  upon  which  Carnot's  reasoning 
is  based  (without  knowing  the  words  of  Carnot  quoted 
above)  into  the  following  words :  ^  "It  is  impossible  by 
means  of  inanimate  material  agency  to  derive  mechanical 
effect  from  any  portion  of  matter  by  cooling  it  below 
the  temperature  of  the  coldest  of  the  surrounding  objects." 
He  saw  at  once,  when  adopting  Joule's  doctrine  of  the 
convertibility  of  heat  and  mechanical  work,  that,  if  all 
processes  in  the  world  l)e  reduced  to  those  of  a  perfect 

'  The  term  "wasted,"  as  distiu- 
guished  from  "annihilated,"  is  first 
introduced  in  Part  1  of  the  "Dyn- 
amical Theory  of  Heat,"  18.51,  p. 
189  of  'Math,  and  Phys.  Papers,' 
vol.  i.  ;  and  in  the  following  year, 
in  a  paper  read  before  the  Royal 
Society  of  Edinburgh  on  the  19th  of 
April,  entitled,  "  On  a  Universal 
Tendency  in  Nature  to  the  Dissipa- 
tion of  Mechanical  Energy,"  the 
8uV)ject  is  brought  home  to  the 
general  understanding  by  a  succes- 
sioa    of   short   theses    referring    to 


the  dissipation  and  possible  limited    '    eternal  death. 


restoration  of  energy  ('  Papers,'  vol. 
i.  p.  511,  &c. ) 

■■^  'Math,  and  Phys.  Papers,'  vol. 
i.  pp.  179,  511.  Helndioltz  ('Vor- 
triige  und  Reden,'  vol.  i.  p.  43)  said 
in  1854  :  "  In  any  case  we  must 
admire  the  acumen  of  Thomson, 
who  could  read  between  the  letters 
of  a  mathematical  equation,  for 
some  time  known,  which  spoke 
only  of  heat,  volume,  and  press- 
ure of  bodies,  c<inclusi()iis  which 
tlireaten  the  universe,  thuugh  in- 
deed   only    in    infinite    time,    with 


132  SCIENTIFIC    THOUGHT. 

mechanism,  they  will   have   this   property  of   a   perfect 

machine,  namely,  that  it  can  work  backward  as  well  as 

25.        forward.       It   is   against   all   reason   and   common-sense 

Summary 

statement     to  carrv  out  this  idea  in  its  integrity  and  completeness. 

of  Thomson  "^  o       J  c      ^ 

KeTvIn)  "  "^^^  essence  of  Joule's  discovery  is  the  subjection  of 
physical  phenomena  to  dynamical  law.  If,  then,  the 
motion  of  every  particle  of  matter  in  the  universe  were 
precisely  reversed  at  any  instant,  the  course  of  nature 
would  be  simply  reversed  for  ever  after.  The  bursting 
bubble  of  foam  at  the  foot  of  a  waterfall  would  reunite 
and  descend  into  the  water ;  the  thermal  motions  would 
reconcentrate  their  energy  and  throw  the  mass  up  the 
fall  in  drops,  re-forming  into  a  close  column  of  ascending 
water.  Heat  which  had  been  generated  by  the  friction 
of  solids  and  dissipated  by  conduction  and  radiation  with 
absorption,  would  come  again  to  the  place  of  contact  and 
throw  the  moving  body  back  against  the  force  to  which 
it  had  previously  yielded.  Boulders  would  recover  from 
the  mud  the  materials  required  to  rebuild  them  into 
their  previous  jagged  forms,  and  would  become  re-united 
to  the  mountain  -  peak  from  which  they  had  formerly 
broken  away.  And  also,  if  the  materialistic  hypothesis 
of  life  were  true,  living  creatures  would  grow  backwards 
with  conscious  knowledge  of  the  future,  but  with  no 
memory  of  the  past,  and  would  become  again  unborn. 
But  the  real  phenomena  of  Hfe  infinitely  transcend 
human  science ;  and  speculation  regarding  consequences 
of  their  imagined  reversal  is  utterly  unprofitable.  Far 
otherwise,  however,  is  it  in  respect  to  the  reversal  of  the 
motions  of  matter  uninfluenced  by  life,  a  very  elementary 
consideration  of  which  leads  to  the  full  explanation  of 


ON    THE    PHYSICAL    VIEW    OF    NATURE. 


133 


the  theory  of  dissipation  of  energy."  ^  Whilst  Clausiius  in 
Germany  and  Thomson  in  England  were  busy  reconciling 
the  truths  contained  in  Carnot's  older  researches  with  the 
new  conceptions  firmly  established  by  Joule's  cla.ssical 
measurements,  putting  both  into  mathematical  and  into 
popular  language,  correcting  our  mathematical  fornmlie  as 
well  as  our  vocabulary,  other  applications  of  the  new 
ideas  assisted  in  procuring  for  them  general  recognition  Ranw^ine. 
and  acceptance.      Ifankine-  in  England,  Zeuner^  in  Cler-  uirn*''*" 


26. 


^  Lord  Kelvin,  in  a  paper  read 
before  the  Royal  Society  of  Edin- 
burgh, 2i)d  February  1874,  on  "The 
Kinetic  Theory  of  the  I)is.si])ation 
of  Energj' ""  ('  Proceedings,'  vol.  viii. 
p.  32.")  ii'i'i. )  See  ahso  hi.s  article  in 
the  '  Fortnightly  Review'  for  Mai'ch 
1892,  reprinted  in  '  Popular  Lec- 
tures and  Addresses,'  vol.  ii.  p. 
449  .S77. 

-  The  earliest  formal  treatise  on 
thermo  -  dynaniics  wa.s  Macquorn 
Rankine's  article  on  "  The  Mechani- 
cal Action  of  Heat"  in  Nichol'.s 
'Cyclopaedia'  for  the  year  18.')5. 
The  part  he  took  in  the  develop- 
ment of  the  new  science  was  prac- 
tical and  at  the  same  time  highly 
speculative.  His  papers  on  tem- 
perature and  elasticity  of  steam 
and  other  vapours,  on  the  expan- 
sion of  liquids  by  heat,  and  on 
the  mechanical  action  of  heat,  of 
dates  1849  and  1850  (see  '  Miscellan- 
eous Scientific  Papers,'  ed.  Millar, 
1881,  pp.  1,  16,  234),  entitle  him 
to  be  considered  as  one  of  the 
first — if  not  the  first  (see  his  claim 
to  priority  in  a  letter  in  Poggen- 
dorf's  'Annalen,'  p.  81,  IS.'JO)— to 
reconcile  Carnot's  di.scovery  with 
the  mechanical  view.  His  investi- 
gations were  peculiar,  combining 
practical  ai)[)lication8  of  great  value 
and  important  predictions  (see 
Tait's  memoir  prefaced  to  Ran- 
kine's '  Papers,'  p.  xxi.x)  with  daring 


speculation  ;  his  deduction.s  Inking 
founded  on  iiis  theory  of  molecular 
vortices.  Tiiough  he  exerted  in 
this  country  a  great  influence  on 
the  early  workers  in  thermo-dyn- 
amics,  his  theories  were  scarcely 
relished  in  (Jermany  (see  Helm- 
holtz's  criticism  of  Rankine's 
methods  in  1853,  quoted  by  Helm, 
'  Energetik,'  p.  114),  where  Claus- 
ius's  independent  and  simultaneous 
researches  on  the  same  subject  had 
meanwjiile  usurped  attention.  But 
Rankine's  '  Manual  of  Applied 
Mechanics'  (1857),  his  'Manual  of 
the  Steam-engine  and  other  Prime 
Motors'  (18.')9),  were  the  first  books 
of  practical  application  in  which, 
through  a  happy  nomenclature 
and  an  extensive  use  of  gra])iiical 
methods  (Watt's  indicator  diagram 
and  Carnot's  cycle),  the  new  ideas 
were  introduced  to  a  wider  circle. 
See  Helm's  estimate  of  Rankine's 
work  in   'Energetik,'  p.   116  .•(77. 

•*  Somewhat  later  than  Rankine 
in  this  country,  Zeuner  in  Switzer- 
land and  Germany,  following  upon 
Clausius's  theoretical  memoirs,  in- 
troduced the  mechanical  treatment 
of  practical  heat  -  problems.  His 
'  r.rund/.iige  dcr  mechanischen 
Warmetheorie '  (1860)  was  to  many 
a  revelation.  Aj)peuring  about  the 
time  when  the  German  meciianical 
and  chemical  industries  were  start- 
ing    upon     a     new     development. 


134 


SCIENTIFIC    THOUGHT. 


many,  and  Hirn^  in  France,  studied  the  most  important 
of  all  machines  then  in  use,  the  steam-engine,  in  the  light 
of  the  new  discoveries.  It  became  possible  to  define 
clearly  what  was  meant  by  the  efficiency  of  an  engine, 
and  to  distinguish  between  those  losses  of  the  energy  of 
heat  or  temperature  which  were  dependent  on  the  use  of 
steam  as  the  working  substance,  and  therefore  inherent 
and  unavoidable,  and  those  losses  which  depended  upon 
the  mechanism  and  upon  the  carrying  out  of  the  process 
employed.  The  older  teachings  contained  in  treatises 
written   before   a   knowledge,  or   even   an   idea,  of   the 


largely  based  upon  the  scientific 
training  afforded  in  the  excellent 
chemical  laboratories  and  poly- 
technic schools  of  Germany,  it 
assisted  in  giving  to  German  in- 
dustrial enterprise  that  scientific 
character  which  was  at  first  ridi- 
culed and  has  latterly  been  ex- 
tolled in  unbounded  measure,  and 
which — combined  with  the  organis- 
ing ability  inherited  from  English 
ancestry — seems  to  be  one  of  the 
distinctive  features  of  the  great 
industrial  progress  of  America. 
First  among  writers  on  the  Contin- 
ent Zeuner  gave  such  a  connected 
exposition  of  the  principles  de- 
veloped by  Clausius,  Thomson,  and 
Rankine  as  met  the  requirements 
of  practical  engineers  ;  attached  to 
them  applications  referring  to  the 
steam-engine  ;  criticised  the  views 
adopted  by  Watt  and  later  writers, 
notably  de  Pambour,  with  reference 
to  the  behaviour  of  saturated  va- 
pour in  the  steam-cylinder  during 
expansion  and  compression  ;  and 
largely  prepared  the  way  for  the 
great  improvements  in  steam,  air, 
and  refrigerating  engines  which 
have  been  brought  out  on  the  Con- 
tinent by  those  trained  in  his 
school.    Through  Clausius,  Zeuner, 


and  others,  Dingler's  *  Poly- 
technic Journal '  became  the 
organ  by  which  the  many  discus- 
sions on  the  new  mechanical  theory, 
and  notably  the  second  law  of  ther- 
mo  -  dynamics,  gradually  forced 
themselves  upon  the  attention  of 
practical  men. 

^  Equally  important  were  the 
labours  of  Adolph  Hiru  (1815-90). 
He  was  a  self-made  man  who  had 
grown  up  in  the  midst  of  the  im- 
portant textile  industry  of  Alsace. 
With  a  naturally  inquiring  dis- 
position he  combined  the  scientific 
and  artistic  accomplishments  for 
the  manifestation  of  which  the 
chemical  and  mechanical  products 
of  that  country  have  long  been 
renowned.  He  approached  some 
of  the  great  theoretical  problems 
connected  with  practical  engin- 
eering, such  as  those  of  heat, 
steam,  lubrication,  and  superheat- 
ing, by  a  long  series  of  carefully 
planned  experiments.  A  very  in- 
teresting account  by  several  authors 
is  given  in  a  publication  by  Faudel 
and  Schwoerer  ('  G.  A.  Hirn,  sa  Vie, 
sa  Famille,  ses  Travaux,'  Paris, 
1893).  Hirn,  like  Rankine,  was  not 
only  an  engineer,  but  also  an  artist 
and  a  philosopher. 


ox    THE    niYSICAL    VIKW    OF    NATrUK. 


135 


mechanical  value  and  the  availability  of  heat  ekist-ed, 
had  to  be  largely  altered,  and  corrected  notions  laid 
down,  fre(juently  as  a  result  of  prolonged  discussion.^ 
As  an  example,  I  may  refer  to  the  controversy  between 
Him  and  Zeuner  as  to  the  cause  of  the  grciit  discrepancy 
between  the  theoretical  and  practical  figures  referring  to 
the  work  in  the  steam-cylinder,  the  so-called  "  Water  or 
Iron  "  controversy.^ 

lint  whilst  it   must  be  admitted  that  the  corrected 
views  regarding  the  nature  of  heat  —  the  preservation 


'  The  best  account  of  the  prac- 
tical bearings  of  the  mechanical 
theories  of  Kankine  and  Clausius 
is  to  be  found  in  Prof.  Unwin's 
"  Forrest  Lecture,"  delivered  "ind 
May  189."),  before  the  Institute  of 
Civil  Engineers,  and  published  in 
the  '  Electrician,'  vol.  xxxv.  p.  46 
srjfj.  and  p.  77  S77.  He  there  refers 
to  the  great  discrepancy  between 
the  "rational"  and  the  "experi- 
mental "  theories,  and  to  Hirn's  ex- 
periments and  practical  results, 
notably  with  the  "  steam  -  jacket," 
and  his  introduction  of  "super- 
heating" in  1855.  "  Xo  doubt 
the  rational  theory  altogether 
underrated  the  enormous  facility 
of  heat-exchange,  which  arises  out 
of  the  contact  between  a  conduct- 
ing cylinder-wall  and  a  vapour  in  a 
condition  of  the  greatest  instability, 
and  liable  to  condense  or  evaporate 
on  the  slightest  change  of  thermal 
condition"  (p.  50).  The  several  con- 
troversies through  which  Clnusius 
ilefended  and  gradually  elucidated 
the  somewhat  obscure  statement 
which  he  gave  of  the  so-called 
second  law  of  thermo-dynamics  may 
be  studied  with  advantage  in  the 
"2nd  edition  of  his  collected  Memoirs 
('  Die  mechanische  Wiirmetheorie,' 
Braunschweig,  vol.  i.,  1876),  where 
his  replies   to  criticisms  of  Holtz- 


maim,  Decher,  Zeuner,  R<inkine, 
Wand,  and  Tait  are  most  instruc- 
tive. A  good  account  is  also  given 
in  Baynes's  '  Lessons  on  Thermo- 
dynamics,'   Oxford,    1878,    p.    103 

-  See  Prof.  Unwin,  loc.  cit.,  p. 
79.  "On  the  ajipearance  of  Isher- 
wood's  researches  in  1863,  the  dis- 
crepancy between  the  rational 
theory  and  the  results  of  experi- 
ment were  recognised  by  liankine 
and  others.  But  the  conditions  of 
the  steam  -  cylinder  conden.-^ation 
are  so  complex  that  for  a  long  time 
the  more  theoretical  writers  prac- 
tically ignored  both  Hirn's  and 
Isherwocxl's  results.  Zeuner  per- 
hajjs  had  jiushed  the  rational  theory 
to  the  furthest  limit  of  detail,  and 
with  the  greatest  insight  into  prac- 
tical conditions.  But  it  was  not 
till  1881  that  he  began  to  explicitly 
admit  the  largeness  and  importance 
of  the  condensing  action  of  the 
cylinder.  Zeuner  then  was  disposed 
to  attribute  initial  condeu.-iation  to 
the  presence  of  a  permanent  and 
not  inconsiderable  mass  of  water 
in  the  clearance  space  of  the  engine. 
...  In  o])oning  a  discu.s.sion  with 
Hirn  in  1881,  Zeuner  wrote  that  if 
the  presence  of  water  in  the  dejir- 
ance  space  waa  conceded,  the 
Alsiitian     calculations     would     be 


136  SCIENTIFIC   THOUGHT. 

and  waste  (degradation)  of  energy,  have  hardly  resulted 
in  those  practical  achievements  and  improvements  ^  which 
in  other  departments  of  applied  science,  notably  in 
chemistry  and  electricity,  have  followed  upon  new  dis- 
coveries, the  influence  of  these  new  conceptions  on 
scientific  thought  and  method  themselves  has  been 
enormous.  Next  to  the  conceptions  introduced  by 
Darwin  into  the  descriptive  sciences,  no  scientific  ideas 
have  reacted  so  powerfully  on  general  thought  as  the 
ideas  of  energy.  A  new  vocabulary  had  to  be  created ; 
the  older  text-books,  even  where  they  dealt  with  known 
subjects  in  perfectly  correct  ways,  had  to  be  rewritten ; 
well-known  and  approved  theories  had  to  be  revised  and 
restated  in  correcter  terms,  and  problems  which  had 
lain  dormant  for  ages  to  be  attacked  by  newly  in- 
vented methods.      I  propose  in  the  rest  of  this  chapter 

greatly  shaken.  .  .  .  There  thus  \  the  behaviour  of  steam  in  the 
arose  a  rather  angry  controversy  j  cylinder  at  all  calculable  were  so 
which  has  been  summed  up  in  the  far  wide  of  the  mark,  —  that  a 
question,  '  Is  it  water  or  iron  ? '  general  consensus  seems  to  prevail 
I  do  not  know  that  this  controversy  j  among  theoretical  engineers  that 
has  been  as  yet  completely  decided."  progress  depends  less  upon  an 
See  also  Peabodj-,  '  Thermo-  immediate  application  of  thermo- 
dynamics of  the  Steam  -  Engine,'  dynamic  principles,  than  upon  a 
4th  ed.,  New  York,  1900,  p.  301  careful  analysis — ^^guided  bj"  theory 
sqq.  — of  elaborate  tests  upon  the 
^  This  explains  how  it  comes  various  types  of  engines  now  in 
about  that  theoretical  thermo-  use.  Such  experiments  are  ac- 
dynamics  is  still  regarded  with  cordingly — following  the  example 
suspicion,  not  to  say  aversion,  by  of  Hirn  —  being  carried  out  in 
many  engineers  of  the  old  school,  i  many  scientific  establishments  in 
whose  knowledge  is  principally  this  country,  on  the  Continent 
baied  upon  experience  derived  from  of  Europe,  and  notably  in  the 
the  steam-engine.  The  first  theo-  :  United  States  of  America,  and  are 
retical  treatment  of  the  steam-  elaborately  recorded  in  many 
engine  by  Rankine  in  England,  [  modern  publications.  See  Pea- 
and  Zeuner  in  Germany,  exhib-  j  body,  '  Thermo  -  dynamics  of  the 
ited  such  enormous  discrepancies  '  Steam  -  engine,'  4th  ed.,  preface, 
between  theory  and  practice  ;  ;  and  chaps,  xiii.  and  xiv.  ;  Ewiug, 
the  simplifying  assumptions  which  '  'The  Steam-Engine,'  1894,  p.  31. 
were  introduced  in  order  to  make 


ox    THK    I'llVslCAI,    VIKW    OF    NATURE.  loT 

to  glance  suimmirily  at  these  revoliitiuns  in  ilif  duiuuin 
of  scientific  thought  which  the  physical  view,  Ijy  re- 
garding nature  as  the  playground  of  the  transformations 
of  energy,  has  brought  about.  What  I  have  just  in- 
dicated will  suffice  to  bring  some  order  into  the  account 
I  propose  to  give.  There  are  four  distinct  directiims  in  "^•^"^ 
which  we  have  to  look.  Firstly,  there  is  the  clearer 
definition  of  the  new  ideas  laid  down  in  the  new  vocab- 
ulary of  scientific  and  popular  language  during  the 
second  half  of  the  century.  Seamdly,  there  is  the 
revision  and  recasting  of  the  whole  body  of  ])hysical 
and  chemical  knowledge  in  the  light  of  the  new  insight 
which  had  been  attained.  Thirdly,  there  is  the  criticism 
of  existing  theories  from  the  new  points  of  view  ;  and 
lastly,  there  are  the  fresh  departures  which  these  novel 
ideas  have  suggested. 

The  first  definite  use  of  the  new  conceptions  of  power 
and  work,  and  of  a  scale  of  mechanical  value,  were  con- 
tained in  the  writings  of  Poncelet  and  Sadi  Carnot  in 
France  during  the  first  quarter  of  the  century.  The 
first  philosophical  generalisations  were  given  by  j\Iohr 
and  Mayer ;  the  first  mathematical  treatment  was  given 
by  Helmholtz  ;  the  first  satisfactory  experimental  verifica- 
tion by  Joule,  during  the  second  quarter  of  the  century. 
The  practical  elaboration  of  the  whole  system  following 
upon  Joule's  and  Kegnault's  experiments  belongs,  through 
Thomson  and  Eankine  in  this  country,  and  through 
Clausius  in  Germany,  to  the  third  quarter  of  the  century. 
Students  in  our  age  entering  on  the  study  of  mechanical, 
physical,  chemical,  and  even  physiological  processes,  reap 
the   benefit   of   these   labours   by  at  once   grasping   the 


138  SCIENTIFIC   THOUGHT. 

underlying  unity  and  correspondence  of  all  natural  phe- 
nomena, inasmuch  as  they  all  depend  on  the  trans- 
formation of  a  quantity,  termed  energy,  which  is  in 
many  cases  measurable  in  its  Lest-known  form — i.e.,  as 
energy  of  motion — and,  where  this  is  not  possible,  in 
the  form  of  heat. 

Helmholtz  had  already,  in  1847,  summarily  reviewed 
the  whole  field,  beginning  with  a  restatement  of  the 
fundamental  formula;  of  dynamics  in  the  light  of  the 
new  principle,  and  ending  with  a  reference  to  the  trans- 
formation of  energy  in  living  vegetable  and  animal 
organisms.  The  key  to  his  explanations  is  to  be  found 
in  the  introduction  of  a  term  to  denote  what  becomes 
of  energy  if  it  ceases  to  exist  as  energy  of  motion  or  as 
a  velocity,  when  it  is  changed  to  energy  of  mere  position. 
To  this  end  he  introduces  the  idea  of  stress  or  tension, 
h^olte'on  The  conception  is  already  contained  in  older  books  on 
mechanics  as  latent  force  (Carnot),^  and  the  purely 
mathematical  treatment  of  dynamics  by  Lagrange  and 
Hamilton  had  prepared  the  ground  by  showing  how  all 
dynamical  problems  could  be  reduced  to  the  knowledge 
of   two   quantities,  the  vis  viva  and  the   force    function. 

gether  with  Monge,  one  of  the 
founders  of  modern  geometry,  of 
which  more  in  a  subsequent  chapter. 
He  introduced  the  principle  of  the 


28. 
Helm- 


1  L.  N.  M.  Carnot  (1753-1823), 
usually  termed  the  great  Carnot, 
father  of  Sadi  Carnot,  member  of  the 
Directory,   War    Minister,  and  one 

of  the  most  celebrated  generals  of    i    '  Correlation   des   Figures   de   Geo- 
France,    has    a     name  •  in    science    !    m^trie'    (Paris,    1801).     His  books 


through  his  '  Essai  sur  les  Machines 
en  gdn^ral '  (Dijon,  1784),  his  '  Prin- 
cipes  fondamentaux  de  I'Equilibre 
et  du  Mouveraent'  (Paris,  1803),  as 
well  as  through  his  '  R(^flexions  sur 
la  Metaphysique  du  Calcul  infi- 
nitesimal'  (Paris,  1797)  and  his 
'  Th^orie  des  Transversales  '  (Paris, 
1806),   by    which    he   became,   to- 


were  translated  in  Germany,  where 
they  had  a  great  influence.  On  his 
connection  with  the  history  of  the 
conception  of  energy,  see  Bohn  in 
'Phil.  Mag.,'  iv.  300,  vol.  xxix.  ; 
also  Helm,  '  Euergetik,'  p.  13  ;  and 
the  Eloge  by  Arago  of  the  year 
1837. 


ON    THE    PHYSICAT.    VIEW    OF    NATURE. 


I.S9 


The  exposition  of  Helmhollz,  liDwever,  does  nol  seem  to 
have  been  understood  or  accepted.  The  general  recog- 
nition of  the  relation  of  active  and  latent  forces  dates 
rather  from  Thomson's  and  liankine's  writint's  in  18;")! 
and  the  following  years.  Thomson  uses  the  term 
"mechanical  energy"  (later,  from  1851,  intrinsic 
energy,  or  simply  energy),  and  considers  this  quantity 
to  be  a  measure  of  the  store  of  power  to  do  work 
which  a  material  system  possesses ;  ^  and  Itankine,' 
early  in  1858,  introduces  and  defines  the  terms  actual 
(or  sensible)  energy  and  potential  (or  latent)  energy,  29. 
which  are  at  once  adopted  by  Thomson^  in  the  place  tiai' and 

^  "^  '^  "actual' 

of  the  terms  dynamical  and  statical   energy,  which    he  t-nerKy. 


^  The  memoir  of  Thomson  in 
which  he  introduces  the  physical 
conception  of  the  quantity  "energy" 
in  the  place  of  a  merely  mathema- 
tical symbol  used  by  Clausius,  and 
inaugurates  the  terminology  of 
modern  physics,  is  contained  in 
the  '  Transactions  of  the  Royal 
Society  of  Edinburgh,'  vol.  xx.. 
Part  3  (read  December  15,  1851, 
and  reprinted  in  '  Math,  and  Phys. 
Papers,'  vol.  i.  p.  222),  as  an  ap- 
pendix to  the  great  paper  "On  the 
Dynamical  Theory  of  Heat,  with 
Numerical  Results  deduced  from 
Mr  Joule's  Equivalent  of  a  Thermal 
Unit,  and  M.  Regnault's  Observa- 
tions on  Steam"  (Trans.  Kdinb. 
Soc,  March  1851  :  reprinted  in 
'Phil.  Mag.,'  1852,  and  '.Math, 
and  Phy.s.  Pajiers,'  vol.  i.  p.  174 
tqq.  ;  see  especially  p.  186,  note). 
The  term  energy  had  indeed  been 
used  by  Thomson  already  in  1849 
as  a  synonym  for  mechanical  effect, 
but  he  had  not  then  accepted 
the  dynamical  theory.  He  merely 
puts  the  question  in  a  footnote  to 
his  exposition  of  Cariiot's  theory  : 
"  When    thermal    agency    is    .    .    . 


spent,  what  becomes  i>f  the 
meclianical  etiect  which  it  might 
produce  ?  Nothing  can  be  lost  in 
the  operations  of  nature — no  energy 
can  be  destroyed  "  ('  Papers,'  vol.  i. 
p.  118,  1849). 

•  In  a  paper  read  before  the 
Philosophiciil  Society  of  Gln-sgow, 
January  5,  1853,  reprinted  in 
'Miscellaneous  Scientific  Papers,' 
ed.  Millar,  p.  203  sf/r/.  See  also 
Rankine's  note,  dated  1864,  in  the 
28tii  vol.  of  the  4th  series  of  the 
'  Phil.  Mag.,'  p.  404. 

•*  See  the  Proceedings  of  the 
Glasgow  Philos.  Soc,  January 
1853,  reprinted  with  additions 
from  Nichol's  '  Cyclopa-dia  '  (1860) 
in  '  Math,  and  Phys.  Papers,'  vol. 
i.  p.  521.  In  this  j)a])er  Thomson 
also  introduces  the  term  '"  electrical 
capacity"  of  a  conductor.  Thom- 
son subsequently  introduced  the 
word  "  kinetic  "  in  place  of  "  actual  " 
energy.  See  also  Thomson's  Lec- 
ture before  the  Royal  Institution, 
February  '29,  1856,  rojirinted  in 
'  Math,  and  I'iiys.  PajK-r.t,'  vol.  ii.  p. 
182,  and  '  Pojiular  lectures,'  vol. 
ii.  p.  418,  especially  the  note  U)  p. 


140 


SCIENTIFIC    THOUGHT. 


had  employed  before.  How  little  these  ideas,  which 
have  now  been  introduced  into  elementary  text-books 
as  the  very  alphabet  of  physical  knowledge,  commended 
themselves  in  that  age,  except  to  a  few  intellects  that 
had  been  occupied  for  many  years  trying  to  fix  precise 
terms  which  should  be  capable  of  mathematical  defini- 
tion, and  at  the  same  time  correspond  to  common-sense 
experience,  is  evident,  inter  multa  alia,  from  the  criti- 
cism by  Sir  John  Herschel  in  1866,^  Here  it  is 
maintained  that  the  use  of  the  term  "  potential  energy  " 
"  is   unfortunate,   inasmuch   as   it   goes    to   substitute   a 


425.  A  very  complete  and  careful 
historical  account  of  the  gradual 
invention  and  crystallisation  of  the 
vocabulary  of  the  energy  concep- 
tion is  given  by  Helm,  '  Die  Lehre 
von  der  Energie,'  Leipzig,  1887,  p. 
36  sqq. 

^  The  passage  quoted  appears  in 
an  article  "  On  the  Origin  of  Force," 
by  Sir  John  Herschel,  in  the  first 
volume  of  the  '  F'ortnightly  Re- 
view,' 1865,  p.  439.  The  article  is 
well  worth  reading  for  those  who 
wish  to  realise  the  enormous  benefit 
which  has  been  rendered  to  science 
by  banishing  the  indefinite  use  of 
the  word  force  and  by  introducing 
the  term  energy,  restricting  the  use 
of  force  to  the  meaning  attached  to 
it  by  Newton.  Sir  John  Herschel 
still  speaks  of  the  ' '  conservation  of 
force  "  (as  did  likewise  Helmholtz, 
who,  however,  very  early  introduces 
the  term  Arbeitskraft,  power  to  do 
work,  thus  removing  all  ambiguity). 
Rankine  replied  to  Herschel's  criti- 
cism in  a  paper  read  before  the 
Glasgow  Philosophical  Societj^  23rd 
January  1867  (reprinted  in  'Mis- 
cell.  Scient.  Papers,'  p.  229  sqq.) 
He  there  states  that  the  quantity 
itself  occurs  as  a  mathematical  sj-m- 
bol  in  Newton's  '  Principia '  (prop. 
39),  but  till  recently  had  received 


no  appropriate  name.  He  closes  his 
remarks  by  the  still  more  import- 
ant reflection  :  "  One  of  the  chief 
objects  of  mathematical  physics  is 
to  ascertain,  by  the  help  of  experi- 
ment and  observation,  what  phy- 
sical quantities  or  functions  are 
'conserved.'"  As  such  he  enum- 
erates mass,  resultant  momentum, 
resultant  angular  momentum, 
total  energy,  thermo-dynamic  func- 
tion. Whilst  this  physical  problem 
was  being  defined  by  Rankine, 
Cayley,  Sylvester,  and  Hermite 
were  working  at  the  corresponding 
problem  in  pure  mathematics  to 
decide  what  properties  or  quanti- 
ties remain  unaltered  {i.e.,  in- 
variant), if  an  arrangement  of 
several  algebraical  symbols  is  sub- 
jected to  algebraical  operations. 
It  is  the  modern  doctrine  of  "  in- 
variants." This  doctrine  has  led  to 
an  enormous  extension  and  simpli- 
fication of  the  theory  of  mathema- 
tical forms  or  quantics.  It  is  the 
key  to  all  mathematical  tactics,  and 
prepares  a  useful  instrument  for 
the  application  of  mathematics  to 
physical  problems.  See  Major  Mac- 
Mahon's  Address  to  the  Mathema- 
tical Section  of  the  British  Associa- 
tion, Glasgow,  1891. 


ON    THE    PHYSICAL    VIKW    OF    NAT(-RK.  141 

truism  for  a  j^reat  tlyiuiiuical  fact  "  ;  an  admission 
which  would  mean  that  it  brings  common-sense  and 
precise  mathematical  expression  into  close  proximity 
and  harmony,  or  describes  a  very  general  jihenomenon 
completely  and   in   the  simplest  way. 

In  order  to  become  generally  recognised  as  the 
simple  alphabet  of  scientific  language,  the  new  ideas 
had  to  be  made  the  foundation  of  the  whole  structure 
of  physical  and  cliemical  knowledge,  theoretical  as  well 
as  experimental ;  the  elements  and  axioms  had  to  l>e 
restated  so  as  at  once  to  express  the  new  view  and  to 
open  out  the  enlarged  aspect  which  had  been  prepared. 
The  different  departments  of  mechanics,  pliysics,  and 
chemistry  had  to  l)e  elaborated  and  co-ordinated  ac- 
cording to  a  uniform  design.  Helmholtz  had  indeed, 
as  early  as  1847,  roughly  sketched  the  plan  of  the 
work,  but  occupied  as  he  was  during  the  twenty  fol- 
lowing years  mainly  with  another  much-neglected  field, 
the  analysis  of  the  phenomena  of  sensation,  he  did  not 
return  to  his  original  thesis  till  many  years  later,  when 
he  made  an  application  of  fundamental  importance. 

Meanwhile  the  important  task  of  rebuilding  the  edifice 
of  the  physical  sciences,  and  establishing  on  a  large  scale 
that  which  I  term  the  physical  view  of  nature,  fell 
almost  exclusively  into  the  hands  of  what  we  may  call 
the    Scotch    school    of    natural    philosophy — James    and        30. 

-,,       ,  .  T  «  '1      1     ^'"^  Scotch 

William    Thomson,    Macquorn    Kankme,    -James    LlerksciuHji. 
IMaxwell,  P.  G.  Tait,  and  Balfour  Stewart,  in  this  country  ; 
whilst  Clausius  abroad  worked  almost  alone.      IJankine 
and  James  Thomson  very  early    (1855)   conceived    the 
idea  of   a   general  science  called  "  Energetics "  or  "  the 


142  SCIENTIFIC    THOUGHT. 

abstract  theory  of  physical  phenomena  in  general."  ^ 
It  is  only  in  our  day,  after  the  lapse  of  a  quarter  of 
a  century,  that  these  ideas  have  been  taken  up  by 
others,  and  that  the  plan  begins  to  be  realised.  The 
reasons  why  at  the  time  it  was  abandoned  were 
manifold. 

To  begin  with,  it  was  soon  found,  notably  by  Joule, 
Helmholtz,  and  William  Thomson,  that  the  new  prin- 
ciple of  the  conservation  of  energy,  if  applied  to  various 
other  phenomena  outside  of  the  narrower  field  of  ther- 
motics,  led  to  a  co-ordination  and  comprehension  of 
them  which  was  then  quite  unexpected :  opening  out 
new  aspects,  disclosing  unknown  properties,  and  sug- 
gesting innumerable  experiments.  As  instances  I  may 
refer  to  the  thermo-elastic  and  thermo-electric  pheno- 
mena of  bodies,  which  very  early  occupied  the  atten- 
tion of  the  founders  of  the  theory  of  energy.  The 
discharge  of  the  Leyden-jar,  the  generation  of  electric 
currents  in  the  voltaic  cell,  the  heat  of  electrolysis, 
the  actions  of   permanent   magnets   and   those   between 

^  In  a  paper  read  before  the  to  find  a  general  rule  for  the  trans- 
Philosophical  Society  of  Glasgow,  ,  formation  of  energy  ('  Lehre  von 
May  1855,  entitled  "Outlines  of  ]  der  Energie,'  1887,  p.  63).  That 
the  Science  of  Energetics,"  and  re-  ]  such  a  general  rule  can  in  the 
printed  in  'Miscellaneous  Papers,'    ;    present    state    of    our    knowledge 

be  established  on  purely  energetic 
principles  is  upheld  by  some  (Ost- 
wald.     Helm)     and     disputed     by 


ed.  Millar,  p.  209  sqq.     See  for  the 

above    definition    p.    228.      James 

Thomson's   contribution    is    to    be 

found  in  a  paper  on  '*  Crystalliza-       others      (see      especiallj'      Planck, 

tion  and  Liquefaction,"  read  before       "  Thermodynamik,'      1897,     p.      71 

the    Royal    Society,    December    5,    |    sqq.),    who   state    their    conviction 


1861,  in  which  he  establishes  and 
gives  examples  of  the  application 
of  "a  general  physico-mechanical 
principle    or    axiom,"    which    indi- 


that  the  "  energj'-principle  clearly 
does  not  suiBce  for  the  definition 
of  natural  processes."  The  whole 
discussion    merges    into    a    philos- 


cates  when  a  "  substance  or  system    i    ophical    question,    of    which    more 
will  pass  into  the  changed  state."       later  on. 
As  Helm  says,  it  is  a  first  attempt 


ON    THE    PHYSICAL    VIEW    OF    NATIKE.  143 

electric  curreuls  and  nuignet.s,  tlie  pheiiomeiui  of  dia- 
magnetisia,  Ampere's  theory  ami  \Vel)er's  ImhIs  of 
electric  measurement,  Seebeck's  production  of  electric 
currents  by  heating  in  a  non-li(»mogeneous  conductor, 
the  remarkable  phenomena  known  by  the  name  of 
Peltier,  the  electro -dynamic  properties  of  metals,  the 
thermo- elastic  properties  of  matter,  were  all  studied 
in  the  light  of  the  new  principle,  the  conservation 
and  transformation  of  energy.  Another  very  import- 
ant problem  presented  itself,  vi/.,  the  introduction  of 
the  new  ideas  into  the  higher  educational  literature, 
the  re -writing  of  the  text -books  of  science  on  the 
basis  of  the  principle  of  energy,  and  especially  ihe 
development  of  the  fundamental  notions  in  mechanics 
in  conformity  with  the  more  modern  views.  Here, 
then,  it  became  evident  that  the  physical  view  of 
natural  phenomena,  according  to  which  they  are  all 
instances  of  the  transformation  of  energy,  could  l)e 
considered  and  expounded  as  a  further  development  of 
the  laws  of  motion  as  laid  down  in  Newton's  '  Prin- 
cipia.'  It  was  especially  the  third  law  of  motion,  in 
which  Newton  stated  the  equality  of  action  and  re- 
action, that  lent  itself  to  such  an  interpretation  a.s 
would  at  once  lead  to  the  wider  grasp  and  deeper 
insight  into  natural  processes  which  the  principle  of 
energy  afforded.  Accordingly  about  the  year  1860, 
when  the  new  ideas  on  energy  had,  in  the  nuntls  of 
the  great  pioneers,  acquired  that  importance  which 
has  enabled  them  to  become  the  basis  of  a  more 
and  more  comprehensive  view — the  physical  view — of 
natural    phenomena,   the   necessity    was   experienced    of 


144  SCIENTIFIC    THOUGHT. 

bringing  them  into  harmony  and  continuity  with  the 
older  Newtonian  ideas.  These  had  been  only  imper- 
fectly transmitted  by  the  many  commentaries  and  text- 
books of  the  Cambridge  school.  The  same  was  the 
case  in  the  system  of  Lagrange,  in  which  the  whole 
of  mechanics  had  been  reduced  to  a  mathematical  ex- 
pression, the  physical  and  experimental  foundations 
being  pushed  aside.  The  '  Principia '  of  Newton  was 
again  studied,  and  re -edited  in  the  unabridged  form, 
and  an  interpretation  and  amplification  of  the  third 
law  of  Motion— so  as  to  embrace  the  principle  of 
energy — was  made  the  key  to  the  science  of  dyn- 
amics. Dynamics  was  not  taught  after  but  before 
statics.  Statics  was  treated  as  a  special  case  of  the 
theory  of  motion.  To  make  the  new  position  still 
more  marked,  it  was  proposed  to  make  the  term 
dynamics  the  general  term  which  embraces  kinetics 
and  statics  as  subdivisions,  and  to  reserve  the  word 
"  mechanics  "  for  the  science  of  machines.  The  change 
which  then  took  place  in  the  didactic  methods  can 
be  seen  by  comparing  the  first  and  second  editions  of 
the  well-known  treatise  by  Tait  and  Steele  on  '  The 
Dynamics  of  a  Particle.'  The  real  compendium  of  the 
new  doctrine  is  the  treatise  on  Natural  Philosophy  by 
31.        Thomson  and  Tait,  which  has  probably  done  more  than 

Thomson 

and  Tait.  any  other  book  in  this  country  to  lead  the  mathe- 
matical studies  at  the  foremost  universities  and  colleges 
into  paths  more  useful  for  physical  and  experimental 
research.  The  greatest  exponent  of  the  new  ideas  was 
James  Clerk  Maxwell,  to  whom  is  also  due  the  merit 
of  having  applied  them  for  the  purpose  of  testing  and 


ON    THE    PHYSICAL    VIEW    OF    NATLUK.  l-4o 

conlinuinif  the  worth  ul'  the  tieiisure  which  lav  hidden 
in  the  experimental  researches  of  Faraday.  Next  to  the 
handbook  of  Thomson  and  Tait,  no  writings  prohahly 
have  done  mr)re — especiall}'  outside  of  England,  on  the 
Continent  and  in  America — than  those  of  Maxwell  to 
revolutionise  the  teaching  of  natural  philosophy. 

I  must  now  revert  to  what  I  said  in  the  last  chap- 
ter regarding   Maxwell's   attempt    to    ijut    the   ideas   of        32. 
Faraday  on  the  comnninication  of  electric  and  magnetic  Maxweii. 
phenomena  through  space  into  mathematical  language — 
i.e.,  into  measurable  terms.      T   there  related  how  Max- 
well's earliest  treatment  of  the  subject  was  an  attempt 
to  construct  a  mechanical  model   of  the   dielectric  that 
would  be  capable  of  exhibiting  and  transmitting  the  pro- 
perties  of   stress — i.e.,  of  tension  and   pressure — which 
the  experimental  researches  of  Faraday  had  partly  de- 
monstrated  and    partly   suggested.       In   the   sequel,  as 
was    said,    he    desisted    from    this    attempt,  which    lias 
since  been  taken  up  and  further  elaborated  by  others, 
and   resorted    to  a   different   train    of   reasoning.      This 
line    had    been    suggested    by    the    introduction   of    the 
doctrine   of  energy  into  all  phy.sieal  research.     As  the 
work    of    scientific   chemists   was   for   a   long   time   ex- 
clusively governed   by   the  application   of   the   principle 
of  the  constancy  of  weight  or  conservation    of   matter, 
so,    when    once     the    mathematical    expression    of    the 
various  forms  of  energy  had  been  correctly  established, 
it  became  possible  to  arrive  at  a  multitude  of  relations 
of  physical  quantities  merely  by  a})plying  the  ])riiu'ij.le 
of  the  constancy   of    the   quantity   of   energy.      In   this 
way    the   principle    of   energy    is   a    kind   of    regulative 
VOL.  IL  K 


14:6  SCIENTIFIC   THOUGHT. 

principle,  one  which  allows  us  to  deal  with  the  grand 
total  or  outcome — mathematically  called  the  integral — 
of  physical  processes  and  changes  without  necessarily 
possessing  a  detailed  knowledge  of  the  minute  elements 
or  factors — mathematically  called  differentials — out  of 
which  they  are  compounded.  Inasmuch  as  what  we 
actually  observe  are  always  integral  effects — -i.e.,  sum- 
mations or  aggregates  of  great  numbers  of  indi^ddual 
and  unobservable  processes — this  line  of  reasoning  is 
not  infrequently  very  useful,  and  has  been  in  many 
cases  applied  to  arrive  at  important  conclusions.  In 
fact,  it  is  the  analogue  in  science  of  the  method  accord- 
ing to  which  practical  men  very  often  succeed  in  carrying 
on  extensive  business  transactions,  of  which  they  possess 
a  merely  external  though  accurate  knowledge ;  or  of  the 
balance-sheet  of  an  industrial  undertaking  which  exhibits 
and  guarantees  the  correct  result,  though  only  the  profit 
and  loss  account  and  the  ledgers  would  show  how  this 
result  has  been  arrived  at. 
33.  Faraday  had  taught  us  how  to  look  upon  any  given 

Faraday.  .  .  .  ^  •    -i         t  ■  -i-i 

portion  or  space  m  which  electric,  magnetic,  chemical, 
and  thermal  changes  were  going  on  as  a  connected  system, 
which  he  termed  the  electro-magnetic  field.  He  and 
others — notably  Oersted,  Ohm,  Weber,  Lenz,  and  Joule 
— had  shown  how  the  different  occurrences  in  such  a 
system  could  be  reduced  to  a  common  measure,  and  how 
they  were  observably  connected.  Maxwell  brought  all 
these  phenomena  together  under  the  term  "  energy  of 
the  electro-magnetic  field,"  and  set  himself  to  study  the 
possible  forms  and  changes  of  this  quantity  under  the 
law  of  the  conservation  of  energy — i.e.,  as   the  preser- 


ON    THE    PHYSICAL    VIKW    OK    NATURK.  147 

vation  of  the  sum-total  of  the  energy.  TIiIh  energy 
could  exist  as  motion  (actual  or  kinetic  energy),  Ixiing 
either  motion  of  electricity  as  in  the  current  controlled 
by  the  law  of  Ohm,  or  motion  of  ponderable  masses,  such 
as  magnets  or  electric  conductors ;  or  it  might  be  dis- 
sipated energy — i.e.,  energy  apparently  lost  in  the  form 
of  heat — controlled  by  the  law  of  Joule,  or,  to  complete 
the  summation,  it  might  be  stored-up  energy — potential 
energy.  Faraday's  researches  had  suggested  where  this 
store  was :  it  was  in  the  surrounding  space,  which  must 
be  considered  as  capable  of  being  strained  or  put  int(j  a 
condition  of  stress,  as  elastic  bodies  are  capalile  of  being 
strained.  Thomson  and  Tait  had  shortly  before  shown 
how  to  submit  the  properties  of  elastic  systems  to  cal- 
culation in  the  most  general  manner,  by  studying  the 
modes  in  which  energy,  actual  and  potential,  was  dis- 
tributed in  them,  whether  at  rest  or  in  motion.  The 
way  seemed  then  paved  for  Maxwell  to  consider  with  the 
greatest  generality  the  properties  of  the  electro-magnetic 
field,  reducing  them  all  to  mechanical  measures.  This  he 
did  b}'  introducing  the  generalised  conception  of  a  dis- 
placement or  strain  wliich  exists  in  the  field,  and  which 
is  commimicated  as  a  periodic  or  vibratory  motion  with 
a  velocity  dependent  on  the  properties  or  so-called  con- 
stants of  the  medium.  It  is  known  how  he  succeeded  in 
identifying  very  completely  all  the  various  experimentally 
ascertained  electric  and  magnetic  phenomena,  fixing  their 
nature  and  quantities  in  conformity  with  experience, 
and  arriving  finally  at  the  suggestion  that  the  velocity  of 
tlie  transmission  of  the  electro-magnetic  displacement  in 
air  must  l)e  the  same  as  that  of  light,  the  latter   being. 


148  SCIENTIFIC    THOUGHT. 

in  fact,  an  electro-magnetic  disturbance  of  very  short 
wave  length.  I  also  mentioned  above  how  this  sug- 
gestion received  a  brilliant  confirmation  from  Hertz  when 
he  succeeded  in  exhibiting  electro-magnetic  waves,  which 
in  travelling  through  space,  though  not  luminous,  showed 
all  the  properties  peculiar  to  light  waves,  such  as  re- 
flexion, refraction,  polarisation,  &c. 

Whilst  in  this  country,  during  the  period  from  1850 
to  1870,  the  Scotch  school  of  natural  philosophy  was 
thus  occupied  in  rebuilding  the  whole  edifice  of  physical 
science  on  the  new  basis  afforded  by  the  energy  ideas, 
Clausius  in  Germany  worked  at  the  further  elaboration 
of  the  dynamical  theory  of  heat,  and,  as  I  stated  above, 
at  the  kinetic  theory  of  gases,  without  abandoning  the 
astronomical  view  of  natural  phenomena,  which,  with  its 
supposition  of  forces  acting  at  a  distance,  still  almost 
exclusively  governed  theoretical  physics  and  chemistry 
abroad.  No  one  did  more  to  emphasise  the  difference 
between  this  and  Faraday's  views  than  Clerk  Maxwell, 
who  had  welded  the  latter  into  a  consistent  scheme  by 
means  of  the  conception  of  energy.  About  the  year 
1870  Helmholtz  again  appeared  as  a  leader  of  scien- 
tific thought  in  this  domain,  and  placed  himself  at 
the  head  of  a  movement  which  by  degrees  almost 
completely  swept  away  the  older  ideas.  It  was  by  him 
or  at  his  suggestion  that  many  of  the  more  modern 
English   works   of   science   were   translated  ^    and  intro- 

1  Notably    Thomson    and    Tait's       natural    philosophers    of    eminent 
*  Natural  Philosophy, '  and    several    i    rank  abroad  who  broke  with    the 


of  Tyndall's  well  -  known  more 
popular  works  on  '  Sound,'  '  Heat,' 
and '  Fragments  of  Science.'    Helm- 


older  habit  of  exclusiveness  which 
clung  to  academic  teachers  in  Ger- 
many, and  who  followed  the  English 


holtz    was    also    one    of    the    first       example  set  by  the  "  Addresses "  of 


ON    THE    PHYSICAL    VIEW    OF    NATIKK. 


149 


duced  in  (Jermany,  and  that  especially  the  ideas  of 
Faraday  and  Maxwell  were  popularised,  expounded,  and 
submitted  to  elaborate  tests.  These  culminated  in  the 
brilliant  discoveries  of  Hertz  already  referred  to. 

As  in  his  earlier  researches  into  the  connection  of  the 
phenomena  of  heat  and  mechanical  work,  so  in  these 
later  ones  concerning  the  electro-dynamic  laws,  Helm- 
holtz  seems  to  have  approached  his  subject  primarily  in 
the   interest   of   physiological  ^  science.       At    that    time 


34. 

HelmholU 
on  electro- 
d/uimicii. 


tlie  British  Association  and  tlie  still 
older  "Lectures"  of  the  lloyal 
Institution.  Before  his  time  there 
were  only  rare  instimces  —  notably 
those  of  Bessel,  Liebig,  and  Hum- 
boldt— where  .scientific  thinkers  of 
the  tirst  rank  condescended  to  intiu- 
ence  general  opinion  and  polite 
literature  by  .stej)ping  down  from 
the  university  chair  into  the  arena 
of  a  popular  audience.  No  other 
German  scientific  thinker  has  left  a 
collection  ecjual  to  Hehnholtz's 
'  Vortriige  und  Reden,'  not  even 
Bessel,  whose  '  Popul;ire  Vorlesun- 
gen  liber  wissenschaftliche  Gegen- 
stiinde '  (ed.  Schumacher,  HamburL', 
1848)  are  too  little  known.  Du 
Bois-Reymond's  '  Reden  '  are  a  mine 
of  information  on  the  history  of 
science,  and  von  Baer's  '  Reden ' 
(Braunschweig,  1886)  cont^iin  some 
excellent  and  original  discourses. 

^  Emil  du  Bois  -  Reymond,  iu 
many  passages  of  his  reniarkaVde 
addresses,  an,d  latterly  in  his  ap- 
preciative Eloge  of  Helmlu)ltz 
(Leipzig,  1897),  has  preserved  the 
historical  data  for  a  genetic  history 
of  Hehnholtz's  electrical  researches, 
which,  beginning  in  1851,  and  cul- 
minating in  Hertz's  brilliant  ex- 
periments on  the  "  rays  of  electric 
energy  "  in  1888,  completely 
changed  the  aspect  of  electrical 
science  in  Germany  and  to  a  less 
degree  in  France.     The  older  view. 


based  upon  a  mathematical  develop- 
ment of  the  fundamentiil  concep- 
tion of  Ampere  and  mainly  asso- 
ciated with  the  brilliant  name  of 
Wilhelm  Weber,  whose  very  ex- 
tensive and  accurate  mea-sure- 
ments  largely  supplied  the  material 
for  the  modern  theory,  is  pnic- 
tically  unknown  to  electricians  in 
this  country.  No  English  text-book 
contains  even  a  reference  to  a  view 
which  was  once  dominant  abroad, 
and  which  for  this  reason  forms 
a  very  interesting  episode  in  tiie 
history  of  thought.  In  the  fourth 
chapter  I  have  referred  to  this 
view  as,  beside  the  theory  of  Bos- 
covicli,  presenting  one  of  the  moat 
remarkable  apj>lication8  of  the  as- 
tronomical view  of  nature,  which 
originated  in  this  country  but  was 
mainly  cultivated  by  the  French 
school.  I  must  now  briefly  refer 
to  the  counter-movement,  which 
in  Germany  is  mainly  identified 
with  the  name  of  Helinholtz.  He 
may  be  said  to  have  left  the  mark 
of  his  genius  on  the  scientific 
history  of  his  country  as  Lonl 
Kelvin  has  done  on  that  of  Eng- 
land. His  collected  pajiers  sliow  us 
— and  du  Bois-Reymond  tells  us — 
how  Hehnholtz's  interest  in  elect- 
rical problems  was  connected  with 
the  remarkalfle  jjlicnomena  of  ani- 
mal electricity,  to  the  exploration 
of   which   the    former  devoted    Ids 


150 


SCIENTIFIC    THOUGHT. 


there  existed  three  different  theories  which  aimed  at 
finding  a  general  formiila  or  law  that  should  embrace 
all  known  electro-dynamic  phenomena.  The  two  earlier 
ones  were  propounded  independently  and  about  the  same 


life.    Du  Bois-Reymond  was  a  pupil 
of  Johannes   MuUer.      One   of    the 
merits   of    Miiller's   school    was    to 
have  made  the  discoveries  of  phy- 
sics useful  for  physiology  and  medi- 
cine as  the  school  of  Liebig  made 
those    of    chemistry.       Helmholtz 
was  trained  in  the  school  of  Midler, 
but    he    also    came    largely    under 
the   influence   of    Franz    Neumann 
of  Konigsberg,  the  great  teacher  of 
mathematical  physics,  and  of  Gauss 
and  Weber,  the  originators  in  Ger- 
many   of   the    system    of    absolute 
measurements.     It  is  known   that 
the  interest  in  electrical  phenomena 
received  a  great  impetus   through 
Galvani's    and    Volta's    discoveries. 
But  as  du  Bois-Reymond  ('  Reden,' 
vol.  ii.  p.  389)  tells  us,  the  galvanic 
pile  constructed  by  Volta  withdrew 
attention   from  the   phenomena  of 
animal    electricity    to    the    much 
more  powerful  actions  of  artificial 
arrangements  of  metals  and   solu- 
tions.    The  study  of  animal  electric- 
ity was  for  a  time  continued  only  by 
Italian  professors,  and  beyond  the 
seas  by  Alexander  von   Humboldt 
in  his  observations  on  the  torpedo  ; 
and    had    to    wait    till    the    school 
of    Miiller,    and    notably   du    Bois- 
Reymond,  approached  the  subject 
methodically    with     the     methods 
and  ideas  of  modern  science.     This 
was   in    the    fifth    decade   of    the 
century.     Modern   science   in  Ger- 
many  had,    however,   studied    the 
properties  of  the  galvanic  current 
exhaustively    only   in    linear    (one 
dimensional)  and  in  closed  circuits 
or  conductors.     The  phenomena  of 
nervous  and  muscular  electric  cur- 
rents demanded  the  study  of  sud- 
den and  repeated  electrical  impulses, 
and  of  the  behaviour   of   currents 


in  two  and  three  dimensional  con- 
ductors, and  in  unclosed  conductors 
or  circuits.      Incited  by   du    Bois- 
Reymond,  Helmholtz  undertook  to 
deduce      from      the     formula;     of 
Ampere,  Neumann,  and  Weber  the 
action  of  electric  currents  in  these 
modified  conditions.     It   was   then 
found    that    these    formula;    gave 
indefinite   results  and    required  to 
be    modified    or    amplified.       After 
many  years  of  thought  and  research 
Helmholtz  arrived  at  a  generalisa- 
tion  which   comprehended  all    the 
different  existing  theories  as  special 
cases.      He  then — in  addition  to  a 
masterly    mathematical    discussion 
—  betook    himself    to    devise    spe- 
cial   experiments   to    decide  which 
of  the  three  possible  expressions  of 
the  general  formula  came  nearest 
the  truth.     A  perusal  of  the  me- 
moirs contained  in  the  first  volume 
of  his  '  Wissenschaftliche  Abhand- 
lungen '   (pp.   429-8-20)    shows   how 
by  gradual  and  strictly  logical  steps 
he    convinced    himself    of    the    in- 
trinsic correctness  of  Faraday's  con- 
ception, which,   in  addition  to  the 
phenomena  in  linear  conductors  or 
wires,  constaiatly  took  notice  also  of 
those  of  the  surrounding  medium 
or    space  —  i.e.,    of    the    electro- 
magnetic field.      Looking  back  from 
our  present  position  on  the  develop- 
ment of  the  ideas  concerning  elec- 
tricity in  motion,  we  can  say  that 
Continental  thinkers  tried  to  gain 
a  correcter  and  more  complete  un- 
derstanding   by    a    mathematical, 
English  science  by  a  phj'sical,  ex- 
tension of  the  then  existing  notions. 
Helmholtz  in  his  Faraday  Lecture 
(1881)   showed   how   both    courses, 
consistently  pursued,  lead   to   the 
same  result. 


ON    THE    PHYSICAL    VIKW    <>K    NATL'KK. 


151 


time  by  Franz  Xeuiuuun  and  Wilhehu  Weber;  the  later 
one  was  the  theory  of  Maxwell  Ijased  upon  the  totally 
different  view  which  was  maintained  and  gradually 
unfolded  in  the  experimental  researches  of  Faraday. 
The  two  former  looked  to  the  effects  *»f  tin;  action  of 
electricity  at  measurable  distances,  and  has  Ijeen  Ciilled 
the  telescopic  view ;  the  latter  reduced  these  to  the 
action  which  takes  place  in  contiguous  portions  of  matter 
or  of  space,  and  has  been  called  the  microscopic  view. 
Helmholtz  first  of  all,  by  an  independent  line  of  reason- 
ing, brought  the  tliree  mathematical  formulae  in  which 
these  different  views  found  expression  under  one  com- 
mon formula,  of  which  each  appears  as  a  special  case, 
and  then  proceeded  by  theory  and  experiment  to  decide 
which  of  the  three  possible  special  forms  is  to  be  adopted. 
As  a  theoretical  test  he  applied  the  j^rinciple  of  the 
conservation  of  energy  in  a  manner  in  wliicli  it  had 
at  that  time  hardly  been  used  by  ContiuenLal  thinkers. 
His  reasoning,  which  was  largely  discussed  and  criti- 
cised by  eminent  philosophers,  gave  to  this  principle 
the  prominence  and  im])ortance  wiiieh  it  has  ever 
since  maintained  in  all  Continental  treatises.  It 
meant  the  introduction  of  the  physical  view  of  natural 
})henomena.^ 


^  In  England  the  publiwition  of 
Thomson  and  Tait's  '  Natural  Phil- 
osophy '  formed,  as  stated  above 
(p.  144),  an  epoch  in  the  teaching 
of  the  physical  sciences,  notalily 
through  the  prominence  given  to 
tlie  piinciple  of  tlie  conservation 
of  energy.  A  similar  epoch  was 
created  in  Germany,  not  so  much 
by  Helmholtz's  enunciation  of  the 
principle  in  1847  as  by  tlie  use  he 


made  of  it,  in  one  remarkable  in- 
stance, in  reviewing  and  criticising 
the  existing  and  apparently  conflict- 
ing theories.  As  Lavoisier  intro- 
duced the  chemical  balance — baf.ed 
upon  the  conservation  of  matter — 
as  a  test  for  the  coriectness of  chem- 
ical statements,  so  Helndioltz  used 
the  princijjle  of  the  conservation  of 
energy  in  two  distinct  forms,  an  a 
test    of    the    validity    of    electrical 


152 


SCIENTIFIC    THOUGHT. 


In  the  mean  time  this  view  had  gained  great  support 
by  the  efforts  of  quite  a  different  section  of  scientific 
workers,  wliose  labours  had  opened  out  a  new  and 
promising  field  of  research.  The  new  field  for  a  con- 
siderable period  belonged  almost  as  exclusively  to  foreign 
science  as  the  energy- conception  had  for  twenty  years 
belonged  to  this  country.  Early  and  for  the  most 
part  isolated  labourers  were  Kopp  and  Hess  in  Germany, 
Eesnault  and  Berthelot  in  France,  Julius  Thomsen  in 
Copenhagen.^      They  (with  many  younger  men)  can  be 


statements.  These  two  forms  were 
the  impossibiHty  of  a  perpetual 
motion  and  the  equality  of  action 
and  reaction.  See  his  Faraday 
Lecture,  1881.  Both  in  the  posi- 
tions of  Thomson  and  Tait  and  of 
Helmholtz  the  principle  of  energy 
is,  however,  like  Lavoisier's  prin- 
ciple, purely  a  regulative,  not  a 
constructive,  principle  of  scientific 
research.  It  exerts  a  control  and 
enables  us  to  check  the  correctness 
of  results.  Both  in  chemistry  and 
physics  other  principles  or  methods 
are  required  for  extending  —  not 
merely  correcting — our  knowledge. 
Such  principles  are  in  the  abstract 
sciences  the  formula  of  gravitation, 
the  atomic  theory,  the  ether ;  in  the 
natural  sciences  the  morphological 
and  genetic  theories.  The  whole 
domain  of  physics  and  chemistry 
has  been  reviewed  for  teaching  pur- 
poses from  this  point  of  view  by 
Hans  Januschke,  '  Das  Princip  der 
Erhaltung  der  Energie,''  Leipzig, 
1897.     See  p.   14  sqq. 

^  Although  the  history  of  thought 
has  more  to  do  with  theories  than 
with  the  mere  discovery  of  facts, 
and  with  the  latter  mainly  when, 
as  in  exceptional  instances,  they 
change  the  scientific  aspect  of  phe- 
nomena, I  think  it  important  to 
mention  specially  the  great  merit 


of  Victor  Reguault's  experimental 
researches.  How  much  the  progress 
of  phj'sical  and  chemical  theory  is 
indebted  to  his  elaborate  and  ex- 
tremely accurate  measurements  of 
many  physical  constants  may  be 
seen  by  the  perusal  of  Lord  Kel- 
vin's earlj'  memoirs  on  the  dynami- 
cal theory  of  heat.  The  several 
(so-called)  laws  of  Boyle,  Dulong, 
and  others  were  subjected  by  Reg- 
uault  to  exhaustive  tests  ;  the  be- 
haviour of  steam  in  the  steam- 
engine  formed  a  subject  of 
elaborate  investigation  ;  the  proof 
that  chlorine  could  be  substituted 
for  hydrogen  in  hydrocarbons  sup- 
plied a  prominent  support  to  the 
chemical  theories  of  Laurent.  In 
general  Regnault's  work  is  a  model 
of  accuracy  supported  by  great  in- 
genuity in  the  construction  of 
apparatus  and  the  surmounting 
of  difficulties.  Like  Liebig,  he  was 
the  master  of  many  pupils  who  sub- 
sequently became  eminent.  Besides 
being  professor  of  chemistry  and 
physics  in  Paris,  Regnault  was 
actively  connected  with  the  cele- 
brated porcelain  works  of  Sevres. 
Similar  remarks  might  be  made 
with  reference  to  the  labours  of 
Hermann  Kopj),  who  v?as  for  many 
years  probably  the  only  professor 
of  physical  chemistry  in  Germany. 


ON    THE    PHYSICAI,    VIKW    OF    NATL'UK.  153 

considered  as  the  founders  of  the  modern  science  of 
physical  chemistry,  which  has  received  an  elaborate  ex- 
position in  the  great  work  of   Trofesscjr  Ostwald.      This  i  .     - 

cheiQiiitrjr. 

work  is  probably  quite  as  epoch-making  in  the  domain  of 
chemistry  as  Thomson  ami  Tait's  'Natural  riiilosophy  ' 
has    lieen    in    tliat   of  physics. 

1  liave  already  explained  how  in  the  development  of 
chemistry  the  attention  of  its  great  representatives  was 
almost  entirely  absorbed  in  gaining  a  knowledge  of  the 
different  substances  with  which  they  had  to  deal,  and 
how  through  preoccupation  with  the  natural  history  of 
matter,  its  decomposition,  analysis  and  synthesis,  and 
appropriate  classification,  the  other  more  scientific  ques- 
tions regarding  the  physical  agencies  which  were  at 
work  in  chemical  processes — constituting  the  doctrine 
of  chemical  affinity — were  almost  completely  neglected. 
This  I  traced  largely  to  the  influence  of  that  powerful 
instrument  of  exact  research,  the  atomic  view,  which 
had  been  introduced  into  chemical  science  through 
Lavoisier  autl  JJalton.^     The  pursuit  of  physical  chem- 

'  It  is  not  an  unusual  exjjerience  pened  when  the  older  ])hlogi.ston 
to  find  that  the  change  froui  one  ,  theory  was  disiielled  bj-  the  atomic 
theory   to  another,   though  an  ad-    '    theory  and  all   attention  was  oon- 


vance  from  disproved  to  more  cor- 
rect views,  is  also  accompanied  by 
some  loss  either  in  defiiiiteness  or 
in  actual  knowledge  of  facts.     The 


centrated  upon  change  of  weiglit. 
The  older  theory  maintained  that 
when  a  metal  is  calcined  it  loses 
something  —  viz.,    phlogiston  ;    tlie 


undulatory  theory  lo.st  the  definite  new  theory  had  proved  that  it  gains 

notion  of  a  rectilinear  ray  of  light,  something — i.e.,  weight  in  the  form 

which  was   only   regained    by  pro-  of  combined  oxygen.      More  recent 

longed  and   difficult  analysis ;    the  knowledge    has   shown    that    both 

electro-magnetic  theory  of  Maxwell  theories  are  right.     It  gains  weiglit 

has  not  as  yet  given  a  clear  repre-  and  loses  potential  energy,  or  power 

sentation  of  those  electrical  charges  to  do  work — i.e.,  to  coMil>ine,  giv- 

which  the  older  thcoiy  of  Coulomb  ing   rise    to    molecular    motion    or 

and  Weber  introduced  in  the  form  ,    heat.     The   phlogiston  theory  con- 

of  stationary  or   moving  electrical  I    tained  the  correct  idea  that  besides 

masses.       Something   similar   hap-  '    matter  there   is   sometijiiig   else — 


154 


SCIENTIFIC    THOUGHT. 


istry,  the  consideration  of  chemical  as  related  to  other 
physical  forces,  such  as  gravitation,  heat,  or  electricity, 
though  it  very  greatly  occupied  the  pioneers  of  chemical 
science  in  the  early  years  of  the  century, —  notably 
Berthollet  and  Gay-Lussac  in  France,  Dalton  and  Davy 
in  England,  Berzelius  in  Sweden, —  fell  gradually  into 
popular  disfavour;  so  much  so  that  even  Faraday's 
electrolytic  law  had  hardly  any  influence  on  the  de- 
velopment of  chemistry.-^  This  one-sided  direction  of 
chemical  reasoning  and  observation  was  still  further 
promoted  by  the  great  practical  and  technical  results 
which  followed  from  the  atomic  conception,  the  ease 
with  which  processes  worked  out  in  the  laboratory 
could  be  imitated  on  a  large  scale  in  the  factory  and 
the  workshop.  It  was  the  increased  power  over  matter 
and  its  manifold  transformations  which  followed  im- 
mediately in  the  wake  of  atomic  chemistry  that 
gave  it  its  interest,  notably  when  through  the  study 
of  the  carbon  compounds — incorrectly  termed  organic 
chemistry — new  industries  of  undreamt-of  magnitude 
and  importance  were  created,  and  when  through  chemical 
knowledge  the  older  methods  of  metallurgy  were  rapidly 
superseded.  To  the  popular  mind  the  result  is  always 
more  interesting  than  the  process  of  research  or  of 
reasoning  which  leads  up  to  it ;  the  possession  of  the 
product    than    the    knowledge    of    the    procedure.      The 


viz.,  energy.  That  the  correct  idea 
contained  in  the  phlogistic  concep- 
tion was  not  at  once  given  up,  but 
only  gradually  lost  sight  of,  is  seen 
from  the  fact  that  Lavoisier's  first 
table  of  elements  contained  'caloric ' 
as  one  of  the  simple  bodies.      See 


Kopp,  '  Entvrickelung  der  Chemie,' 
p.  209. 

^  On  the  causes  of  this  see  Helm- 
holtz's  Faraday  Lecture  ('  Wissen- 
schaftliche  Abhandlungen,'  vol.  iii.) 
and  Ostwald,  '  Allgemeine  Chemie,' 
2nd  ed.,  vol.  ii.  part  1,  p.  530. 


ON    THE    PHYSICAL    VIEW    OP    NATUHE.  I.'i5 

new  substance  witli  sUiiLling  properties — be   tliey  useful 
or    only    curious    and    rare — has   almost   innuediately    a 
value,  whereas   the   manifold    transformations  by   which 
it  was  discovered,  invented,  or  produced  escape  general 
notice,  and  are  accordingly  of  secondary  interest.     This 
interest  grows  in  proportion  as  another  factor  of  ec^ual 
commercial     importance     gradually    and    slowly    asserts 
itself,    namely,    the    factor   of    cost    of    ])roducti(jn,    the        3«. 
property    through    which    not    only    the    material    itself,  "e.«if  in 
but   also   the   labour   bestowed   upon    it,   and    the   most 
intricate   transmutations  and  secret  manipulations,  gain 
a    place    and     definite    figure     in    the    ledger     of     the 
accountant.       Those    of    us    who   entered   into   practical 
life  about  the  beginning  of   the  last   generation  of  the 
century  know  well  by  experience  how  then  for  the  first 
time  was  being  established  the  great  system  of  statistics, 
of  cost  of   production,  which   now  governs   every  well- 
conducted  industry  and  manufactory,  though  in  general 
this  department  is  still  but  little  understood.     Now,  in 
proportion  as  with  progressing  civilisation  we  come  more 
and  more   to   use  artificially   prepared   products   in   the 
place  of  natural  ones,  the  cost-figures  become  more  com- 
plex :  there  is  not  only  the  raw  material  and  the  labour 
of  getting  it,  not  only  the  general  economy  of  arrange- 
ment and  administration  by  which  we  save  labour  and 
avoid  waste — there   is   the   whole  aggregate  of  changes 
and  processes,  manual,  mechanical,  and  chemical,  through      . 
which   the  raw  material   has    to  pass.     These  must  all 
have  a  common  measure  1)y  which  they  possess  a  iigure 
of  value  in  the  ledger  of  the  book-keeper,  otherwise  the 
latter   r-nuld   not    ]>ro(luce    a   statement   of    cost.      Watt, 


156  SCIENTIFIC   THOUGHT. 

when  supplanting  manual  labour  on  a  large  scale  by  the 
introduction  of  his  perfected  steam-engine,  had  suggested 
the  term  "  horse-power  "  as  the  common  measure  of  both  ; 
and  the  French  mathematicians,  who  treated  mechanics 
with  a  view  to  practical  application,  had  introduced  the 
term  "  work,"     In  the  general  industries,  however, — out- 
side of  special  branches,  notably  marine  engineering, — 
these  measures  were  very  crudely  applied ;   they  became 
unintelligible  and   meaningless   where   other   agencies — 
notably  those  of   chemistry  and   electricity — had  to  be 
employed.      It   is   only  since   the    terms   "  power "   and 
"  work  "  have  been  enlarged  and  the  more  general  con- 
ception of  energy  introduced  that  it  has  become  possible 
to  measure  the  new  forces  or  agencies  in  terms  applic- 
able to  all   alike.     Practically  as   well   as    theoretically 
the  system  of  measurement  remained  imperfect  so  long 
as   the   energy    of    chemical   combination   could   not    be 
measured    in    the    same    way    as    Watt    measured     the 
energy    of    heat,   and   as    Joule   and    others    taught    us 
how  to  measure  the  energy  of  an  electric  current.     The 
term  "  energy "  has  thus   become   as   important   a   con- 
ception for  practical  as  it  has  been  long  recognised  to 
be   for   purely   scientific   purposes.      If    the   only  power 
we   use  is  manual  labour  or  steam  power,  there  exists 
a  crude  way  of  measuring  both  by  the  hands  employed 
and  the  weight  'of  coal  burnt ;    but  electrical  power  is 
not  so  exclusively  dependent  on  a  personal  or  material 
item,  and  thus  it  can  only  be  measured  by  a  system  in 
which  the  several  items  of  cost  are  reduced  to  a  common 
term.      It  is  through  the  wholesale  introduction  of  the 
electric  current  as  a  practical  agent  that  the  thing  called 


ON    THK    PHYSICAL    VIKW    OF    NAM  KK.  Ifj? 

"  energy  "  has  become  a  commercial  commodily  us  it   hud 
liefore  become  a  scientific  measure. 

That  chemical  reactions  are  connected  with  meciiun- 
ical,  gravitational,  optical,  caloric,  and  electric  phenomena 
has  been  known  for  a  long  time.  Each  of  these  mani- 
festations has  therefore  been  studied  as  attbrding  a 
measure  of  the  energy  of  chemical  reactions,  and  these 
have  in  turn  been  looked  upon  as  results  of  attrac- 
tions, or  of  mass  actions,  or  of  thermal  conditions,  or 
of  electrical  polarities.  We  have  thus  mechanical, 
I hermo- chemical,  electro -chemical  theories  of  atlinity. 
\'aluable  discoveries  and  important  suggestions  have 
also  been  arrived  at  by  these  special  researches :  we 
have  the  laws  of  mass-action  suggested  by  Berthollet 
and  revived  in  modern  times  by  Guldberg  and  Waage ; 
the  all-important  electrolytic  law  of  Faraday  and  the 
so-called    third    law  of    IJerthelot   in    therrao-chemistrv ;        37. 

Berthclot 

further,  the  important  researches  of  Kopp  and  Hess,  and  ost- 
Xone  of  these  discoveries,  however,  seemed  really  to 
grasp  the  whole  subject  of  chemical  reaction,  and  ac- 
cordingly they  remained  for  a  long  time  unknown,  or 
fell,  after  a  short  life,  into  oblivion  and  disrepute.  It 
has  been  one  of  the  greatest  performances  of  the  last 
twenty  years  of  the  century  to  have  approached  the 
all-important  question,  "  What  is  chemical  affinity,  and 
how  is  it  to  be  measured  ? "  in  a  comprehensive  spirit, 
and  to  have  brought  it  to  the  verge  of  solution.  The 
merit  of  having  done  this  belongs  the  more  incon- 
testably    to    l*rof.    Wilhelm    Ostwald,^    because    no    one 

'  Prof.  Ostwald's  principal   woik       Chemie,'  of  which  tlie  first  edition 
is  the   'Lehrbuch  der  allgemoiuen    '    appeared  in  two  volumes  (lAMi)zig, 


158 


SCIENTIFIC    THOUGHT. 


has  taken  such  pains  as  he  to  gauge  the  value  of 
many  single  and  isolated  steps  that  had  been  taken 
before  him,  and  to  combine  them  all  through  his  own 
researches  into  a  comprehensive  doctrine.  The  practi- 
cal importance  of  these  labours — so  long  insufficiently 
understood — will  doubtless  in  the  near  future  be  real- 
ised in  proportion  as  the  increasing  competition  of  in- 
dustry shall  emphasise  the  necessity  of  studying  the  eco- 
nomics of  production  :  this  economy  consisting  not  only 
in  the  absence  of  waste  of  matter,  but  likewise  in  the 
saving  of  work — i.e.,  in  the  absence  of  waste  of  energy.^ 


1885-87)  ;  the  second  edition,  of 
which  the  first  volume  appeared 
in  1891,  is  in  progress,  and  will 
comprise  three  volumes.  It  is 
divided  into  three  parts  :  Stochio- 
mctrie,  Chemische  Energic,  and  Vcr- 
ivandtschuftslchrc.  Nothing  can 
give  a  better  idea  of  the  enormous 
development  of  chemical  science 
in  the  nineteenth  century  than  a 
glance  at  those  two  monuments  of 
learning  and  research,  Beilstein's 
'  Organische  Chemie  '  (Leipzig, 
1893-1900,  5  vols.,  3rd  ed.)  and 
Ostwald's  '  AUgemeine  Chemie.' 
They  form  the  basis  for  future 
development,  as  did  Leopold 
Gmelin's  '  Handbuch  der  Chemie  ' 
for  the  greater  part  of  the  past 
century.  The  first  edition  of 
Gmelin  appeared  in  1817.  See 
Kopp's  '  Geschichte  der  Chemie  ' 
(vol.  ii.  p.  100).  Since  the  publi- 
cation of  his  great  text-book,  Prof. 
Ostwald  has  done  enormous  ser- 
vice to  science  by  the  foundation 
jointly  witli  Prof,  van't  HolF  of  the 
'  Journal  fur  physicalische  Chemie,' 
in  1889,  and  still  more  by  the  open- 
ing of  the  first  laboratory  specially 
designed  for  physical  chemistry,  in 
Leipzig,  in  the  year  1887.  But 
perhaps  the  most  original  and 
suggestive    work     of     Ostwald     is 


his  work  on  the  scientific  founda- 
tions of  Analytical  Chemistry 
(Leipzig,  3rd  ed.,  1901.  Transl. 
by  G.   M'Gowan). 

'  How  recent  is  the  systematic 
treatment  and  general  recognition 
of  physical,  theoretical,  or  general 
chemistry  can  be  seen  from  the 
historical  sketches  which  had  been 
published  prior  to  Ostwald's  great 
work.  Kopp,  in  his  excellent  ac- 
count of  the  development  of  chem- 
istry, published  in  the  Munich  col- 
lection, and  frequently  referred  to 
in  the  fifth  chapter  of  this  work 
(vol.  i.  pp.  382,  &c. ),  has  hardly  any 
occasion  to  refer  to  physical  chem- 
istry up  to  the  year  1870.  This 
is  the  more  remarkable  as  Kopp 
himself  was  a  solitary  ingenious 
worker  in  this  isolated  province. 
A  good  account  of  his  labours 
is  contained  in  Thorpe's  '  Essaj's 
in  Historical  Chemistry,'  1894, 
J).  299.  A  later  and  brilliant 
writer  on  the  historical  growth 
of  chemical  knowledge,  Dr  A. 
Ladenburg,  in  his  '  Vortriige  iiber 
die  Entwicklungsgeschiclite  der 
Chemie'  (2nd  ed.,  Braunschweig, 
1887),  condenses  all  he  has  to  sa^' 
regarding  this  subject  into  a  few 
pages  in  his  last  lecture.  If  Ger- 
man  science    is    destined    to    dis- 


ox    THK    I'llYSKJAL    VIEW    OF    NATrKK. 


15 'J 


Tlie  ideas  through  which  unity  and  L-(jhereiiee  have 
been  introduced  into  the  many  diil'ereut  trains  of  reason- 
ing whieli  were  henL  upon  unnivclhng  the  myHteries 
of  chemical  attinity  came  from  an  unexpected  quarter 
— from  the  country  whicli,  in  the  early  part  of  our 
century,  had  become,  through  Jierzelius,  the  centre  of 
a  great  school  of  chemical  research.  Vroi.  Ustwald, 
in  his  recent  historical  sketch  of  the  doctrines  of 
chemical  attinity,  dates  the  latest  ])eri(jd  frum  the  year 
188G,'  when  Svante  Arrhenius  j)ul)lislied  his  t]ie<»ry  as 
of  the  chemical  solutions  decomposeel  liy  the  galvanic 
current,  the  so-called  electrolytes.  That  the  reader 
may  understand  what  importance  belongs  to  this  latest 
development  of   physical  chemistry,  I   must  go  further 


Arrbeiiiuit. 


tinguish  hert^elf  in  the  wider 
spliere  of  general  or  physical 
chemistry  as  much  as  she  has 
done  in  the  past  l>y  the  extreme 
and  one-sided  culture  of  organic 
or  structural  chemistry,  it  will  be 
largely  owing  to  the  influence  of 
the  school  of  Ostwald  and  that 
of  tiie  industrial  factor  mentioned 
in  the  text,  which  nowadays  em- 
phasises as  nmch  the  economical 
control  of  chemical  reactions  as 
it  (lid  formerly  the  discovery  and 
preparati(jn  of  new  com|)ouuds. 
The  ultimate  success  in  the  in- 
dustrial preparation  of  artificial 
indigo,  which  was  theoretically 
l')ng  known,  is  an  example  well 
worth  careful  attention. 

'  Prof.  Ostwald  had  himself 
about  the  same  time  made  an 
attempt  in  the  second  volume  of 
the  first  edition  of  his  great  work 
to  unite  the  rlisjccta  mimbnt  of 
l>hysical  chemistry,  notably  of  the 
tlieory  of  affinity,  into  a  .system- 
atic whole.  This  first  attempt 
may    have    contributed    quite    a.s 


nmch  as  the  special  labours  of 
others,  among  whom  he  mentions 
specially  Helmholtz,  Van't  HoB', 
Duhem,  Planck,  and  Arrhenius,  ti> 
create  an  era  in  chemistry.  1 1 
may  also  be  noted  that,  like  every 
other  important  step  in  chem- 
istry, this  latest  theoretical  piia.se 
is  characterised  by  violent  contro- 
versies. The.se  became  more  pro- 
niiunced  as  Prof.  Ostwald  intro- 
duced into  the  second  eilition  of 
his  work  the  idea  of  "energetics" 
as  a  general  and  sufficient  basis 
for  the  whole  of  physics  and 
chemistry  ;  making  a  very  emphatic 
j)rotest  against  the  older  jihysical 
theories,  based  upon  attractions, 
atomism,  or  kinetics,  whidi  he 
stigmatises  as  mechanical.  On 
this  important  controver.sy  I  shall 
have  to  report  at  the  end  of  the 
])i'csent  chajiter,  where  I  shall  al.io 
give  the  full  literature  of  the  sub- 
ject. In  the  meantime,  see  also 
Ostwald,  '  Allgenieine  Cheniie,'  vol. 
ii.  part  1,  preface,  and  i>art  -,  p. 
182  .•«/<]. 


160  SCIENTIFIC    THOUGHT. 

back  in  the  history  of  the  subject  and  draw  attention 
to  the  gradual  change  which  the  nineteenth  century 
has  brought  about  in  our  ideas  regarding  the  different 
states  in  which  matter  is  supposed  to  exist,  be  it 
in  motion  or  in  rest :  the  solid,  the  liquid,  and  the 
gaseous  states. 

Not  very  long  ago  the  impressions  of  common-sense, 
according  to  which  a  fundamental  difference  separates 
solid  from  liquid  and  liquid  from  aeriform  bodies,  per- 
meated scientific  treatises  also.  Eigid  demarcations 
were  maintained  between  hydrostatics  and  pneumatics, 
and  likewise  between  the  doctrines  of  bodies  at  rest 
and  such  as  are  in  a  state  of  perceptible  motion. 
One  of  the  most  marked  changes  which  the  centmy 
has  witnessed,  has  been  the  breaking  down  of  these 
older  landmarks  of  science.  The  state  of  rest — once 
supposed  actually  to  exist — has  had  to  give  way  to  a 
state  of  concealed  yet  measurable  motion,  as  in  the 
case  of  the  kinetic  theory  of  gases,  which  explains  dead 
pressure  by  the  bombardment  of  innmnerable  particles 
darting  about.  The  idea  of  dynamical  equilibrium — 
i.e.,  the  maintenance  of  a  state  of  uniform  motion — has 
in  many  cases  taken  the  place  of  static  equilibrium  or 
rest,  as  in  the  doctrine  of  the  flow  of  heat,  the  theory 
of  exchanges  of  radiation,  and  the  conception  that  the 
rigidity  of  solids  depends  upon  a  peculiar  form  of  whirl- 
ing motion — the  vortex.  Similarly  the  intermediate  or 
transition  states  which  lie  between  the  solid  and  fluid, 
the  properties  of  viscosity  and  of  colloidal  substances, 
and  of  vapours  as  marking  the  transition  between 
liquids  and  gases,  have  attracted  more  attention  in  pro- 


ON    THK    PHYSICAL    VIKW    OF    NAILl;K. 


lol 


portion  as  experiiULUlul  science  has  tak(Mi  the  place  of 
that  purely  mathematical  treatment  wliich  ul)tained  at 
the  beginning  of  the  century,  notably  in  the  Continental 
schools,  and  whirh  thought  it  could  exhaust  the  infinite 
variety  of  natural  phenomena  by  a  few  easily  defined 
properties  measured  by  constants.  The  narrowness  of 
this  view  has  been  gradually  overcome  by  the  inlluenco 
of  the  great  experimental  philosophers  in  this  country, 
and  the  indepemlent  development  of  chemical  research 
abroad.  IJeside  Faraday  must  be  especially  named  Thomas 
Graham  ^    and   Thomas  Andrews,  whose  original  experi-        89, 

Gnham  and 

ments  did  so  much  to  extend  and  deepen  our  knowledge  Andrews, 
of  the  less  obvious  properties  of  matter.  Graham  car- 
ried on,  between  1825  and  1850,  extensive  experiments 
on  the  diffusion  of  liquids  and  gases,  on  absorption,  and 
on  the  phenomena  of  osmosis  or  gradual  filtering  of  sub- 
stances through  porous  partitions,  showing  how  in  liquids 
motion  and  pressure  exist  similar  to  that  which  is  now 


1  Thomas  Graham  (1804  -  69), 
for  many  years  professor  at  Uni- 
versity College,  London,  then 
Master  of  the  Mint,  cultivated  the 
unexplored  regions  of  physics  and 
chemistry  in  an  original  si)irit  and 
yet  with  very  himple  apparatus, 
some  of  which  is  still  used  under 
his  name.  His  ingenious  labours 
attracted  the  attention  of  Liebig, 
through  whose  intluence  was  brought 
about  the  translation  of  '  The  Ele- 
ments of  Chemistry '  into  Ger- 
man by  Otto.  This  work  in  its 
subsequent  enlarged  editions  has 
formed  for  sixty  years,  next  to 
Gmelin's  '  Handbook,'  a  corner- 
stone of  chemical  literature  in 
Germany,  where  Graham's  name 
ia  a  hou.sehold  word.  The  dia- 
coveries  of  Graham  on  the  move- 

VOL.  n. 


ment  and  "  miscibility "  of  gases 
led  to  the  well-known  law,  "  that 
the  diffusion  rate  of  gases  is  in- 
versely as  the  square  root  of  their 
density."  From  ga.ses  he  advanced 
to  the  more  comi)licated  study  of 
liquids,  divided  bodies  into  two 
classes,  "crystalloids"  and  "col- 
loids," studied  the  "  transpiration  " 
of  gases  tlirough  fine  tul>c.s,  and 
their  "osmosis"  or  gradual  filtering 
through  porous  (and  many  ap- 
parently noil  -  porous)  partitions. 
In  many  directions  he  anticipated 
later  discoveries  and  collecte«l  in- 
valuable materials  for  subsecjuent 
theories.  Inter  alia,  he  establislicd 
the  existence  of  '"  alcohoLites," 
compounds  analogous  to  "  iiydrates," 
and  niaiiiUiined  the  metallic  nature 
of  hydrogen. 


162  SCIENTIFIC    THOUGHT. 

generally  attributed  to  gases.  Andrews  ^  in  the  'sixties 
carried  on  his  important  experiments  on  the  transition  of 
bodies  from  the  Hquid  to  the  gaseous  state,  and  came  to 
the  conclusion  "  that  the  gaseous  and  liquid  states  are 
only  remote  stages  of  the  same  condition  of  matter,  and 
are  capable  of  passing  into  one  another  by  a  process 
of  continuous  change."  ^  He  also  referred  to  the  "  pos- 
sible continuity  of  the  liquid  and  solid  states  of  matter." 
Another  important  step  by  which  our  conceptions  of 
the  nature  of  the  liquid  condition  of  matter  were  con- 
siderably enlarged  and  altered — motion  being  introduced 
where  a  former  view  had  seen  only  rest — was  taken  by 
Clausius,  who,  following  Joule  and  Kronig,  had  about  the 
same  time  given  its  modern  form  to  the  kinetic  theory 
of  gases.  "What  suggested  this  step  was  the  pheno- 
menon of  electrolysis.  The  older  view  looked  upon  the 
action  of  the  electric  current,  which,  passing  through 
substances  in  a  state  of  fusion  or  solution,  liberated  the 
constituents  out  of  which  they  were  composed,  as  an 
exertion  of  a  force  contrary  to  the  forces  of  chemical 
affinity,  by  which  the  chemical  constituents  were  sup- 
posed to  be  held  together.  In  this  case  energy  would 
have  to  be  spent  in  doing  work  against  chemical  forces. 
It  was,  however,  very  soon  found  that  the  decomposi- 
tion, or — as  Sainte  Claire  Deville  first  called  it^ — the 


^  See  vol.  i.  p.  316,  note,  of  this 
History. 

"^  See  '  The  Scientific  Papers  of 
Thomas  Andrews,'  with  a  Memoir 


series  of  original  investigations,  first 
iu  organic  then  in  metallurgical 
chemistry,  entered  upon  his  re- 
markable work   in    thermal    chem- 


by  Tait  and  Crum  Brown,  London,       istry  at  the  time  when  Clausius  in 


1889,  p.  316. 

»  Sainte  Claire  Deville  (1818-81) 
approached  chemical  research  from 


Germany  was  being  led  from  an 
entirely  different  point  of  view  to 
the  same  subject.     He  introduced 


the  side  of  medicine,  and  after  a      the  term  dissociation  to  denote  the 


ON    THE    PHYSICAL    VI KW    oF    NAILKI-:. 


I  O.J 


dissociation  of  the  olectrolyte,  was  nut  tlie  conseniienee,  «o. 
but  the  Jicconipanyinji;  feature  or  condition,  of  the  exist-  '"-"^ 
ence  of  an  electric  current  in  a  sohition.  ("hiusiu.s  first 
expressed  tliis  distinctly  in  1857,  and  JiL*hnholt/.  re- 
peated it  in  1880.  The  conception  was  thus  intro- 
duced that  ill  certain  (not  in  all)  solutions  of  chenncal 
compounds  dissociation  nught  exist  independently  of  an 
electric  current,  and  that  the  latter,  if  introduced,  only 
directed  the  already  dissociated  and  wandering  molecules 
(ions),  freeing  them  at  the  same  time  of  their  electric 
charges.^       This    conception,    tliuugli    at    first    violently 


breaking-uj)  of  chemical  compounds 
not  so  much  through  the  presence  of 
other  chemical  agencies  as  through 
altered  physical  conditions,  such, 
notably,  as  heat,  evaporation,  and 
condensation.  "  Deville's  observa- 
tions on  dissociation  .  .  .  have  a 
very  direct  bearing  on  the  kinetic 
theory  of  gases,  and  it  is  a  fact  of 
interest  in  the  history  of  science 
that  Deville  did  not  recognise  the 
validity  of  that  theory.  Our  esti- 
mate of  the  ingenuity,  skill,  and 
patience  shown  in  his  experimental 
work,  and  of  the  genius  and  sound 
judgment  which  directed  his  theo- 
retical conclusions,  is  perhaps  raised 
when  we  recollect  that  he  was 
neither  led  in  the  first  nor  biassed 
in  the  second  by  ideas  derived 
from  the  kinetic  theory,  and  his 
hostile,  or  at  least  neutral,  attitude 
towards  it  gives  perhaps  greater 
value  to  the  evidence  that  his  work 
has  contributed  to  its  soundness  " 
(A.  Crum  Brown,  '  Ency.  Brit.,' 
9th  ed.,  article  "  Sainte  Claire 
Deville  "). 

'  I  have  already  mentioned  (vol. 
i.  p.  43.">,  note)  that  Clausius,  when 
introducing  his  kinetic  theory  and 
distinguishing  between  molecules 
and  atoms,  could  refer  to  several 
eminent  chemists   who   had    inde- 


pendently arrived  at  similar  ideas 
by  quite  different  ti-ains  of  reason- 
ing. Again,  when  introducing,  in 
18f)7,  his  theory  of  dis.sociation  by 
solution,  he  could  refer  to  similar 
anticipations.  Williamson  had  said 
already,  in  1850  (Liebig's  '  Annalen,' 
vol.  Ixxvii.  p.  .37),  at  the  meeting 
of  the  British  Association  in  Edin- 
burgh :  "  We  are  led  to  the  conclu- 
sion that  in  an  aggregate  of  mole- 
cules of  every  compound  there 
exists  a  continual  exchange  of  the 
elements  contained  in  it.  Suppose, 
for  instance,  that  a  ves.sel  with 
hydrochloric  acid  were  tilled  with 
a  great  number  of  molecules  of  the 
compound  CIH,  then  the  view  at 
which  we  have  arrived  would  lead 
us  to  the  supposition  that  everj' 
atom  of  hydrogen  does  not  re- 
main in  quiet  juxta])osition  with 
an  atom  of  chlorine,  with  which  it 
is  combined,  but  that  there  is  a  con- 
tinual exchange  of  places  with  other 
hydrogen  atoms  "  (Clausius,  '  Me- 
cliani.sche  Wiirnietheorie,'  vol.  ii.  p. 
167,  Braunschweig,  1879).  For  an 
illustration  of  the  theory  of  Ciau-iius 
modified  to  meet  more  recent  con- 
ceptions, see  ().  Lodge's  '  Mixleru 
Views  of  Electricity,'  1892,  y.  83, 
&c. 


164  SCIENTIFIC   THOUGHT. 

attacked  by  chemists,  became  gradually  better  under- 
stood and  gained  ground.  The  merit  of  having  finally 
introduced  into  our  modern  notions  the  idea  of  the  free 
mobility  of  the  constituents  of  electrolytic  compounds 
41.        belongs  to  W.  Hittorf  and  F.  Kohlrausch.     The  name 

Hittorfand  i    •         i         i  •  p         • 

Kohlrausch.  of  the  latter  will  be  connected  in  the  history  or  science 
with  the  phenomenon  of  the  "  migration  of  the  ions," 
which  he  has  expressed,  after  ten  years  of  research 
(1869-79),  in  his  well-known  law.  The  question  was 
put  and  answered,  "  What  becomes  of  the  energy  of  the 
electric  current  ?  "  It  was  found  that  electrolytic  conduc- 
tion increased  with  dilution  and  temperature — two  agents 
which  would  favour  dissociation.  The  phenomena  of 
dissociation  had,  moreover,  been  studied  independently  of 
the  galvanic  current.  Following  in  the  track  of  Graham 
and  Andrews,  a  number  of  physicists  abroad — notably 
van  der  Waals,  Eaoult,  and  Van't  Hoff — had  confirmed 
and  extended  the  view  that  bodies  in  solution  resembled 
gases,  that  the  osmotic  pressure  of  a  liquid  resembled 
ordinary  gas  pressure,  that  the  law  of  Avogadro  regard- 
ing the  number  of  molecules  in  a  gas  could  be  trans- 
ferred to  matter  in  a  state  of  solution,  and  that  the 
magnitude  of  the  osmotic  pressure  in  a  liquid  could  be 
used  as  a  measure  of  the  number  of  dissociated — wander- 
ing— molecules  which  are  contained  in  a  given  volume 
of  a  solution,  just  as  the  pressure  of  a  gas  would  increase 
if  the  number  of  molecules  in  a  given  space  were  in- 
creased through  the  splitting  up  of  compounds.  Apparent 
anomalies  in  the  behaviour  of  gases  approaching  conden- 
sation were  explained  by  the  aggregation,  and  similar 
ones  in  dilute  solutions  by  the  dissociation,  of  molecules. 


ON    THE    PHYSICAL    VIEW    OF    NATURE.  1G5 

Tho  decisive  step  was  taken  in  1887  by  Arrhenius/  whu 
has  the  merit  of  having  brought  together  the  two  inde- 
pendent courses  of  research  and  reasoning,  and  made 
them  fruitful  for  each  other.  He  shows  -  "  that  the  dif- 
ference between  active  and  inert  molecules  consists  in 
this,  that  the  former  are  split  into  tlieir  ions,  the  latter 
not.  Only  the  free  ions  take  part  in  tlie  conduction  of 
electricity  and  in  chemical  reactions :  this  is  the  rea.son 
for  the  proportionality  of  the  two  (Faraday's  law).  The 
ions  behave  in  solution  like  independent  molecules :  this 
is  the  reason  of  the  deviation  which  electrolytic  solutions 
show  from  the  extended  gaseous  laws  (Van't  Hott's  dis- 
covery)." "  What  a  change  has  come  over  our  concep- 
tions," exclaims  Victor  ]\Ieyer,^  "  if  we  have  to  accustom        a. 

.  ,  Victor 

ourselves  to  see  in  a  dilute  solution  ot  common  salt,  no  Meyor^.n 
longer  the  undecomposed  molecules  of  a  salt,  but  separate  ^^^'^^^ 
atoms  of  chlorine  and  sodium.  For  these  revolutionary 
innovations  we  are  indebted  to  the  labours  of  Van't 
Hoff,  Arrhenius,  Ostwald,  Planck,  Tfeffer,  de  Vries,  but, 
so  far  as  experiments  go,  notably  to  the  splendid  re- 
searches of  Kaoult,  wliich  for  years  have  been  prepar- 
ing the  way  for  this  miglity  theoretical  advance." 

The  year  1887,  which  brought  together  these  two 
fruitful  lines  of  reasoning  and  research,  can  also  be  con- 
sidered as  the  epocli  wlien  the  new  science  of  physical 
chemistry  was  fairly  laiiiiclied  into  existence.     The  year 

1  In    a    communication    to   the   I    Address    by  Victor    Meyer    before 
Academy  of  Stockholm  of  8th  June       the     German     "  Naturforscherver 


and  9th  November  1887. 

-  Quoted  from  Ostwald's  '  Allge- 
meine  Chemie,'  2nd  ed.,  vol.  ii. 
part  1,  p.   656. 

^  See     the     highly      interesting 


sammlung"  at  Heidelberg  in  1S89, 
entitled  "  Chemische  IVobleme 
der  Gegcnwart  "  (Heidelberg, 
1890),  p.   32. 


166  SCIENTIFIC    THOUGHT. 

1826   marks    the    revival    of    mathematical    studies    in 

Germany  through  the  appearance  of  Crelle's  journal ;  so 

43.        the  year   1887   saw   the   first  number   of  Ostwald  and 

Ostwald's 

journal.  Vau't  Hoff's  '  Zeitschrift  flir  physicalische  Chemie.'  From 
that  period  the  physical  properties  of  chemical  substances,, 
so  long  neglected,  or  only  studied  by  isolated  students, 
have  received  systematic,  mathematical,  and  exact 
treatment,  guaranteeing  something  like  continuity  and 
completeness,  and  leading  on  to  the  solution  of  the  great 
remaining  question.  What  is  chemical  affinity  ? 

The  eminent  natural  philosophers  to  whom  is  mainly 
due  the  foundation  of  this  modern  science,  claim  also  to 
be  gradually  realising  the  idea  which  was  suggested  ])y 
the  early  representatives  of  the  theory  of  energy — 
notably  by  Eankine  and  James  Thomson — ^that  of  a 
general  doctrine  of  energy,  termed  energetics ;  and  they 
hold  that  this  suggestion  is  only  realisable  by  breaking 
with  the  conventional  ideas  which  the  older  physical 
theories — the  astronomical,  atomistic,  and  kinetic  views — 
have  imposed  upon  our  reasoning.  They  further  hold 
that  the  gradual  development  of  chemistry  into  an  exact 
science  necessarily  requires  the  introduction  of  this 
broader  view  which  they  embrace,  and  that  the  older 
views — useful  in  their  way — only  suffice  to  comprehend 
certain  restricted  groups  of  natural  phenomena,  whereas 
in  chemical  changes,  where  all  imaginable  natural  pro- 
cesses seem  to  come  together,  a  laro-er  and  more  inde- 
pendent  theory  is  indispensable.  It  is  interesting  to 
note  how  very  generally  they  trace  this  larger  view  to 
the  long  unnoticed  labours  of  a  natural  philosopher  in 
the  New  World,  Professor  Willard  Gibbs  of  Yale. 


ON     I'UK    PFIYSICAL    VIKW    OF    NATl'RK.  1G7 

The   train    of    lliuugliL    nietliodiciilly    and    cuinpreheii-        «. 

*       1        i*    11  1  '/"I'll*  Wnl*rd 

sively  toiloweil  out  in  (fibbss  various  memoirs  had  it«  o ''»»»• 
origin  in  the  early  speculations  of  William  Thomson 
(Lord  Kelvin)  and  C'lausius,  to  which  1  ivfcrrt'd  above. 
Thomson  was  the  first  who,  in  adopting  (after  much 
hesitation)  the  mechanical  view  of  the  phenomena  of  heat, 
the  doctrine  of  the  convertibility  and  equivalence  of  the 
different  forms  of  energy,  recognised  that,  in  order  to 
describe  natural  phenomena  correctly,  this  view  required 
a  qualification.  Tiie  change  of  the  different  forms  of 
energy  into  each  other  can  for  the  most  part  take  place 
only  in  one  direction ;  there  is  a  general  tendency  in 
nature  towards  a  degradation  or  dissipation  of  energy. 
Energy,  though  not  lost,  becomes  less  useful,  less  avail- 
able. The  least  available  form  of  energy  is  heat ;  and 
it  is  in  that  form  that  in  all  natural  changes  a  por- 
tion of  energy  becomes  lost,  dissipated,  or  hidden  away. 
Thus  we  have  to  recognise  the  difference  between 
available  and  unavailable,  between  useful  and  useless, 
energy.  In  the  seqviel  Thomson  showed  in  definite 
instances  ^   how  to  calculate   the  availal)le  and   tlie  un- 

^  See  '  Math,  and  Phys.  Papers,'  in  this  connection,  is  applied  by  liiin 

vol.  i.  No.  LIX.,  18.02,  "  On  a  Uni-  to  the  negative  of  the  idea  we  most 

versal  Tendency  in  Nature  to  the  naturally  wish  to  express.    It  would 

Dissipation  of  Mechanical  Energy"  ;  only  confuse  the  student  if  we  were 

and    No.    LXIIL,    1853,    "On    the  to    endeavour    to    invent    another 

Restoration  of    Mechanical  Energy  term    for   our  purpose."     He  then 

from  an  unequally  heated  Space."  proceeds  to   use  the   term  entropy 

In  Tait's '  Sketch  of  Thermodynam-  in    an    altered    sense,    in   whicii    it 

ics'  (1868),  we  read  (p.  100):   "It  measures    the   available   instead  of 

is  very  desirable  to  have  a  word  to  the    unavailable    energy,    creating 

express  the  arai/aljilitij  for  work  of  for   some    time   a   great    confusion 

the    heat    in    a  given    magazine,    a  and    some    uiniccessarj'    irritJition. 

term  for  that  possession   the  waste  See  on    this    the   early  editic^ns  of 

of  which  is  called  Bisnipation.     Un-  Clerk  Maxwell's  excellent  '  Theory 

fortunately  the  excellent  word  civ-  of    Heat,'  and    the   footnote   to   p. 

<ro/)?/,  which  C'lausius  has  introduced  189,    8th   ed.,   and   Clausiua,    'Die 


168  SCIENTIFIC    THOUGHT. 

available  energy  :  he  introduced  the  word  "  motivity,"  the 
conception  of  a  quantity  of  a  "possession  the  waste  of 
which  is  calkd  dissipation."  Whilst  Thomson  was  thus 
putting  into  scientific  language  and  calculating  an  im- 
portant and  obvious  property  of  nature — namely  this,  that 
her  processes  mainly  proceed  in  a  certain  definable  direc- 
tion— Rankine  and  Clausius  were  labouring  independ- 
ently at  the  mathematical  wording,  the  analytical  expres- 
sion, of  this  remarkable  discovery.  Wherever  a  change  in 
a  system  of  various  elements,  factors,  or  quantities  takes 
place  mainly  in  a  definite  sense  or  direction,  it  is  presum- 
able that  there  exists  a  definite  quantity  which  is  always 
growing  or  always  decreasing.  This  quantity  may  not 
be  directly  observable  or  measurable,  as  in  mechanical 
motion  velocity  or  distance  is  directly  measurable ;  it 
may  be  hidden  —  we  may  have  no  special  sense  with 
which  we  can  perceive  it,  as  we  possess  a  pressure  sense, 
a  heat  sense,  a  sound  and  light  sense ;  nevertheless,  it 
may  be  indirectly  discoverable,  being  made  up  (a  func- 
tion) of  definite  observable  quantities  and  factors  (such 
as  heat,  temperature,  mass,  volume,  pressure,  &c.)  Now 
Rankine  and  Clausius  found  that  in  all  thermal  changes 


mechanische  Warmetheorie,'  vol.  i. 
p.  387,  and  vol.  ii.  p.  324  sqq.  A 
great  deal  of  this  confusion  would 
have  been  avoided  had  Tait  in  1868 
introduced  a  really  new  term — viz., 
that  suggested  later  (1876)  by 
Thomson  in  a  communication  to 
the  Royal  Society  of  Edinburgh, 
and  more  fully  explained  in  a 
paper  in  the  '  Phil.  Mag. ,'  May 
1879,  the  term  "  Thermo-dynamic 
Motivity."  W^e  should  then  have 
two  terms,  inasmuch  as  the  "con- 


sideration of  the  energy  and 
motivity,  as  two  functions  of  all 
the  independent  variables  specify- 
ing the  condition  of  a  body  com- 
pletely in  respect  to  tempera- 
ture, elasticity,  capillary  attraction, 
electricity,  and  magnetism,  leads 
in  the  simplest  and  most  direct 
way  to  demonstrations  of  the  theo- 
rems regarding  the  thermo-dynamic 
properties  of  matter"  {loc.  cit., 
'Papers,'  vol.  i.  p.  459). 


ON    THE    PHYSICAL    VIEW    OF    NATURE. 


169 


or  heat  processes  —  and  this  practically  means  in  all 
natural  processes — there  is  such  u  quantity  which  is 
always  on  the  increase,  and  which  thus  measures  in 
mathematical  language  the  growing  loss  of  available 
or  useful  energy  in  the  world.  Ifankine  simply  called  it 
the  "  thermo-dynamic  function " :  Clausius  thought  it 
important  to  give  it  a  name  which  would  co-ordinate  it 
with  energy,  and  he  called  it  entropy :  ^  energy  which 
is  turned  inside,  becomes  hidden  or  locked  up.  Clausius 
thus  gave  a  different  wording  of  Thomson's  doctrine  of 


Entropy. 


'  Clausius  had  already  in  1854 
(Pogg.  'Ann.,' vol.  xeiii.  p.  481)  ar- 
rived at  the  principal  consequences 
and  the  final  enunciation  of  what 
he  termed  "  the  second  law  of 
thermo  -  dynamics,"  a  law  which 
refers  to  the  transformation,  as  the 
first  refers  to  tlie  conservation,  of 
energy.  He  there  arrives  at  similar 
conclusions  to  those  put  forth  by 
Tliomson  two  years  earlier.  The 
word  entropy,  however,  wa.s  not  in- 
troduced by  him  till  186.5  (Fogg. 
'  Ann.,'  vol.  cx.w.  p.  390),  when  he 
introduced  it  with  the  following 
remarks :  "  I  have  intentionally 
formed  the  word  entropy  as  much 
as  possible  on  the  model  of  that 
of  energy,  for  the  two  cpiantities 
which  are  to  be  designated  by  these 
two  words  are  in  their  physical 
meaning  so  intimately  related  that 
a  similarity  in  the  terms  seemed  to 
me  to  be  justified."  As  stated 
above  (p.  167,  note),  Lord  Kelvin,  wlio 
worked  simultaneously  and  inde- 
pendently at  the  same  subject,  laid 
more  stress  upon  the  direct  state- 
ment, that  in  all  transformations 
of  energy  we  have  to  distinguish 
between  the  available  and  tlie  toUil 
intrinsic  energy,  and  inlroduccil 
the  terms  energy  and   motivity  as 


two  functions  of  all  the  variables 
specifying  the  conditions  of  a 
.system.  In  liis  article  on  Heat, 
contributed  to  the  '  Ency.  Brit.,' 
9th  ed.,  he  gives  the  mathematical 
relation  of  motivity  to  entropy 
('  Papers,'  vol.iii.  p.  167).  The  term 
motivity  has  not  become  current  in 
thermo  •  dynamical  treatises,  but 
the  need  has  been  very  generally 
felt  of  reserving  the  word  energy  in 
a  restricted  sense  for  available 
energy,  such  energy  as  can  be  put 
to  mechanical  use.  Wald,  in  a 
very  interesting  dis.sertiition,  '  Die 
Energie  und  ihre  Entwerthung ' 
(Leipzig,  1889),  deplores  (pp.  43 
and  44)  the  fact  that  the  word 
energy  has  not  been  re.served  to 
denote  useful,  available  energy. 
"  Had  the  word  energy,"  he  says, 
"  been  introduced  before  tl»e  dis- 
covery of  the  first  law  of  thermo- 
dynamics, then  certainly  only  me- 
chanical energy  wouhl  have  been 
termed  simply  energy."  In  the 
use  of  tlie  word  Knift  in  some 
writers,  such  as  Mayer,  there 
seems  occasionally  a  confusion  be- 
tween available  and  total  or  in- 
trinsic energy.  See  Le  Chatelier 
in  'Journal  de  Pliysique,"  1894. 


lYO  SCIENTIFIC    THOUGHT. 

the  universal  tendency  in  nature  towards  a  dissipation 
of  energy,  by  saying,  "  The  entropy  of  the  world  is 
always  on  the  increase." 

For  about  twenty  years  after  these  conceptions  had 
been  introduced  into  scientific  language  and  reasoning, 
mathematicians  and  physicists  were  mainly  occupied 
in  defining  more  clearly  this  hidden  quantity,  and  in 
defending  what  was  called  the  second  law  of  thermo- 
dynamics against  misconceptions  and  attacks.  In  1875 
Lord  Eayleigh  could  still  say}  "  The  second  law  of  thermo- 
dynamics and  the  theory  of  dissipation  founded  upon  it 
has  been  for  some  years  a  favourite  subject  with  mathe- 
matical physicists,  but  has  not  hitherto  received  full 
recognition  from  engineers  and  chemists,  nor  from  the 
scientific  public.  And  yet  the  question  under  what 
circumstances  it  is  possible  to  obtain  work  from  heat 
is  of  the  first  importance.  Merely  to  know  that  when 
work  is  done  by  means  of  heat,  a  so-called  equivalent  of 
heat  disappears,  is  a  very  small  part  of  what  it  concerns 
us  to  recognise." 

Whilst    these   words    correctly   describe    the    general 

attitude  of  the  scientific  public  towards  this  important 

discovery,    two  men   had   already  made  a  beginning  in 

Horstmann.  the  direction  indicated — Horstmann  ^  in  Germany,  and 


1  i 


Proceedings  of  the   Royal    In-    ]    which  began  in  the  year  1869  and 


stitution,'  vol.  vii.  p.  386. 

-  Prof.  Ostwald  in  the  historical 
section    of    his    '  Verwandtschafts- 


were  continued  in  Liebig's  '  An- 
nalen'  in  various  communications 
during    the    early    'seventies,    not 


lehre'    ('AUg.    Chemie,'    2nd    ed.,       without  undergoing  violent  attacks 


vol.  ii.  part  2,  p.  Ill,  &c.),  Helm 
in  'Energetik'  (p.  141,  &c.),  and 
Duhem  in  his  '  Traite  de  Mecanique 
chimique'  (1897,  vol.  i.  p.  84,  &c. ) 
all  do  full  justice  to  the  long-un- 
recognised  labours  of   Horstmann, 


from  representatives  of  the  older 
conceptions.  Ever  since  James 
Thomson's  celebrated  prediction 
(see  above,  p.  126),  physicists 
had  recognised  the  importance  of 
thermo  -  dynamical    considerations, 


ON    THE    PHYSICAL    VI KW    OF    NA'iTHE. 


171 


Willard  Gihlts  ^  in  America.  They  seem  to  have  l^een  the 
first  to  approach  the  question  of  chemical  equilihrium, 
the  result  of  llie  action  nf  various  conflicting  cliemical 
forces,  termeil  ailiiiities,  from  a  general  comjirehensive 
j)oint  of  view  ;  recognising  that  the  theory  then  com- 
monly adopted  on  the  Continent — the  thermo-chemical 
thenry  of  atlinity — was  incorrect  <ir  incom])lete.  This 
theory,  which  had  l)een  principally  ehil)orated  by  Julius 
Thomsen  in  Copenhagen  and  l)y  Berthelot  in  l-'iance, 
was  supi)orted  l>y  tlie  large  amount  of  valuable  ex- 
perimental research  for  whicli  we  are  indebted  t<^ 
these    two  eminent    men   and   their   numerous   follnwcrs. 


whilst  chemists  pemsted  in  the  ex- 
clusive use  of  atomistic  concej)tions, 
which,  as  Horstinann  pointed  out, 
are  of  no  avail  in  problems  of  that 
nature  (see  Helm,  'Energetik,'  p. 
143). 

^  More  fundamental  than  the 
labours  of  Hor.«tmann  were  those  of 
Gibbs,  which  began  with  the  year 
1874,  and  were  for  a  long  time 
buried  in  the  '  Transactions  of  the 
Connecticut  Academy."  They  were 
known  to  Maxwell,  but  remained 
generally  unknown,  partly  owing 
to  their  abstract  nature,  partly 
to  the  fact  that  the  majority  of 
Continental  chemists  wore  not 
prepared  to  appreciate  the  mathe- 
matical form  in  which  his  exposi- 
tions were  clothed.  Previous  to 
the  study  of  questions  of  chemical 
equilibrium,  Gibbs  had  successfully 
developed  an  idea  of  .lames  Thom- 
son's— viz.,  the  graphical  re])resen- 
tation  of  the  diti'erent  thermo- 
dynamic ([uantities  in  three  instead 
of  merely  in  two  dimensions.  Thom- 
son had  lepresented  the  projierties 
of  a  body  or  system  by  referring 
them  to  volume,  pressui-e,  and  tem- 
perature.      Gibbs    refers    them    to 


volume,  energy,  and  entropy,  tlie 
former  quantities  being  always  de- 
finable by  the  latter,  but  nut  vice 
rcrtsa.  The  advantages  of  this  rep- 
resentation were  demonstrated  to 
English  students  in  Maxweirs 
'  Theory  of  Heat."  In  Germany  it 
was  Prof.  Ostwald  who,  by  collect- 
ing and  translating  the  memoirs 
of  Gibbs,  first  made  them  accessible 
to  students  (' Thermodynamisciie 
Studien,"  von  Willard  tlibbs.  Leipzig, 
1892).  Subsequently  both  Ostwald 
and  Helm  have  done  much  to  pro- 
mote an  understanding  of  Gibbs's 
methods.  See  Ostwald,  'Allg. 
Chemie,"  vol.  ii.  part  2,  p.  114, 
&c.  ;  Helm,  '  Grundziige  der  niathe- 
matischen  Chemie"  (Leipzig,  1S94), 
and  'Energetik,'  passim.  Subse- 
quently Gibbs  also  introduced  the 
very  general  and  useful  term 
"phase"  to  denote  tiie  different 
states  in  which  a  substanc-e  can 
exist.  This  term  denotes  not  only 
such  difl'erences  as  were  formerly 
called  in  German  Af/i/rrt/atztutUindc, 
but  likewise  conditions  of  dis- 
sociation, allotropic  and  isomeric 
modifications. 


1V2  SCIENTIFIC    THOUGHT. 

It  measured  chemical  reactions  by  what  is  termed  their 
heat  -  toning,  i.e.,  by  the  amount  of  heat  developed, 
and  culminated  in  the  celebrated  third  law  of  thermo- 
chemistry— viz.,  that  such  reactions  take  place  as  are 
accompanied  by  the  greatest  amount  of  energy  liberated 
in  the  form  of  heat.  Now,  although  this  contains  an 
adequate  description  of  a  very  large  number  of  reactions 
that  take  place  at  the  temperatures  at  which  we  operate 
in  our  laboratories,  the  rule  is  by  no  means  universal, 
and  it  required  a  great  amount  of  ingenuity  to  ex- 
plain away  the  many  exceptions  which  presented  them- 
selves. The  rule  needed  to  be  modified  or  amplified. 
The  measurement  of  the  energy  of  a  chemical  process  by 
the  heat-toning  was  not  the  only  instance  in  which  the 
thermal  side  of  a  phenomenon  had  been  considered  a 
sufficient  means  of  measuring.  In  an  allied  department, 
that  of  electrolysis,  Helmholtz  had  suggested,  as  early 
as  1847,  that  the  electro-motive  force  of  a  galvanic  cell 
may  be  measured  by  the  heat-toning  of  the  chemical  pro- 
cesses which  produce  the  current,  and  for  a  long  time 
this  was  considered  to  be  a  correct  expression  of  facts. 
In  consequence,  however,  of  some  discrepancies  which 
had  presented  themselves,  Helmholtz  himself  was  induced, 
abovit  1881,  to  examine  the  subject  more  thoroughly. 
He  arrived  at  the  conclusion  that  the  heat-toning  is  not 
always  a  correct  measure  ;  and  at  the  same  time  he  intro- 
duced a  more  adequate  and  generally  applicable  method 
of  measurement.  In  fact,  he  arrived  at  the  conception 
of  available  or  useful  energy  for  processes  which  take 
place  at  constant  temperature.  To  this  quantity,  which 
decides  in  which  direction  a  reaction  takes  place  (tempera- 


ON    THK    PHYSICAL    VIEW    OF    NATl'ItE.  ITo 

ture  reinaiuing  constant),  lie  gave  the  name  of  free  energy.        «' 

Ilelmholu'* 

He  showed  that  in  a  state  of  equilibriiun  the  free  or  "'"* 
available  energy  must  he  a  minimum.  He  also  showed 
the  connection  in  which  the  available  or  free  energy 
stands  to  the  quantity  introduced  l)y  liankine  and 
Clausius,  the  entropy  wliich  measures  the  unavailable  or 
hidden  energy.  \'>y  making  chemical  changes  depend 
on  the  increase  or  decrease  of  a  definite  measurable 
quantity  a  parallel  was  established  between  chemical  and 
mechanical  processes,  the  latter  always  taking  place  in 
the  direction  of  a  decrease  of  potential  energy.  Free 
energy  has  thus  been  appropriately  termed  Ity  M.  Duhem 
the  thermo-dynamic  potential. 

Helmholtz  did  not  apply  this  fruitful  view  to  chemical 
processes  on  any  extensive  scale,  but  his  explanations 
have  done  much  to  establish  that  correcter  and  more 
comprehensive  way  of  treating  such  questions  which  has 
since  become  general,  llorstmann  had  indeed  leil  up 
to  this  view,  Willard  Gibbs  had  applied  it  before,  and 
Lord   liayleigh    had   suggested  it.^      The   conception  of 

^  The  general  use  of  the  concep-  and  11),  and  more  definitely  ex- 
tion  of  useful  or  free  energy  must  jilaincd  and  aijplied  to  the  phy.s- 
be  dated  from  the  remai'kably  lucid  ical  phenomena  of  dissociation  by 
expositions  of  Helmholtz,  though  Oibbs  (' Thermodynamisclie  Stud- 
it  is  now  recognised  by  all  who  ien,'  ed.  Ostwald,  p.  66,  kc.  ; 
have  studied  the  history  of  this  j  '  Amer.  Journ.  of  Sciences  and 
fertile  conception  that  the  physi-  t  Arts,'  1879) ;  and  that  it  is  ea- 
cal  notion  of  available  energy  goes  i)ecia!ly  owing  to  the  labours  of 
back  to  Thomson  (see  Tait,  '  Ther-  Duliem  that  the  subject  has 
modynamics,'  1868,  p.  100)  and  received  the  attention  of  oliemists. 
Maxwell  {'  Heat,'  p.  187,  8th  ed.  ;  M.  Duhem,  in  the  introduction  to 
Duhem,      '  Mdamique      chimi(|ue,'  the    work    of    1886,  gives   a    very 


vol.  i.  p.  92  ;  Le  Chatelier  in 
'Journal  de  Physique,'  1894,  p. 
291)  ;  that  the  mathematical 
formulic  were  given  by  Massieu 
(quoted  by  Duhem,  '  Le  Potential 


valuable  and  lucid  historical  ex- 
position, and  subsequently  in  liis 
large  work  in  four  volumes  ('M<5- 
canique  chin)i(|ue,'  1897-1900)  a 
vast  number  of  applications.     Kor 


Thermodynamique,'    1886,    pp.    v   I    the  history  of  thought  the  imiH.rt- 


174 


SCIENTIFIC    THOUGHT. 


48. 
Kelvin's 
available 

energy. 


available  energy  as  distinguished  from  total  energy  had 
been  introduced  by  Lord  Kelvin  and  by  Maxwell.  This 
free  energy  is  measured  not  only  by  the  heat  liberated, 
but  depends  on  all  the  other  factors,  such  as  volume  and 
pressure,  the  number  of  chemical  substances  engaged,  and 
their  physical  conditions.  The  doctrine  of  energy  and  the 
conception  of  free  energy  pointed  out  a  method  of  co- 
ordinatincr  all  these  different  factors  and  reducing  them 
to  a  common  measure.  As  Rankine,  by  the  introduction 
of  the  term  potential  energy,  did  much  to  clear  the  ideas 
and  guide  the  reasoning  in  dynamical  science,  so  Helni- 
holtz,  by  introducing  the  term  free  energy,  did  a  great 
deal  to  introduce  into  chemical  science  the  fruitful  con- 
ceptions which  had  been  elaborated  and  appHed  in  phys- 
ical research.  The  term  free  or  available  energy  seems 
to  describe  more  naturally  the  characteristic  property  of 
all  energy  which  is  useful  for  doing  w^ork,  whilst  the 
opposite  term  entropy — which  measures  the  unavailable 
or  hidden  energy — refers  to  a  quantity  for  which  we  have 
no  immediate  means  of  perception.^ 


auce  of  these  somewhat  abstruse 
expositions  lies  mainly  in  two 
directions :  First,  in  the  recog- 
nition of  the  fact  that  for  the  cor- 
rect description  of  natural  pheno- 
mena and  changes  the  knowledge 
of  the  total  energy  is  as  little  suf- 
ficient as  that  of  the  total  weight 
or  mass,  but  that  it  -is  necessary 
to  introduce  the  conception  of  use- 
ful energy,  of  energy  which  is  free 
or  available  for  doing  ■work  ; 
secondly,  in  the  recognition  that 
the  course  of  chemical  changes  or 
reactions  cannot  be  measured  by 
attending  to  one  special  property, 
such  as  weight,  or  temperature,  or 
«utropy,  but  that  it  requires  the 


measurement  of  a  quantity  which 
comprises  all  the  different  agencies 
in  nature,  this  quantity  being  the 
energy  of  the  system  or  substances 
in  question  and  its  availability.  A 
third  point,  which  is  of  more  or  less 
importance  according  to  the  general 
view  adopted,  is  this,  that  the  ma- 
thematical formula8  involved  have 
exhibited  the  analogy  between 
chemical  and  mechanical  processes, 
the  latter  being  those  which  were 
earliest  and  are  most  easily  grasped 
by  the  mind. 

^  As  Prof.  Ostwald  has  remarked, 
it  is  to  a  great  extent  a  matter  of 
taste  what  particular  form  one 
adopts  out  of  the  many  in  which  the 


ON    THE    I'HYSICAL    VIEW    iJi-'    NATL'KE. 


175 


It  was  about  this  time — after  experimental  research 
had  been  carried  on  for  many  years  by  Julius  Thomseu 
and  Berthelot,  after  Horstmann  had  made  a  lieginning  of 


second  law  of  therino-dynaiiiics  can 
be  expressed  ('  Allg.  Cheniie,'  vol.  ii. 
part  2,  p.  150).  In  every  case  it 
is  simjjly  a  question  how  most 
conveniently  to  express  and  apply 
the  general  jiriiiciplc  that  heiit 
cannot  of  itself  jiass  from  a  colder 
to  a  hotter  body,  the  principle  on 
which  Fourier  built  hi.s  "Theorie 
de  la  Chaleur,"  and  which  revealed 
itself  as  the  rationale  of  the  ex- 
positions of  Carnot  when  in  the 
middle  of  the  century  their  hidden 
truth  emerged  from  the  criticisms 
of  William  Thomson  (Lord  Kelvin) 
and  Clausius.  Thus  already  in  the 
dirt'erent  treatment  of  the  same 
subject  there  showed  itself  the 
twofold  tendency  which  reasoning 
on  physical  matters  so  frequently 
exhibits  —  viz.,  towards  physical 
directness  and  mathematical  ele- 
gance ;  the  former  leading  to  prac- 
tical a{)plication,  the  latter  to 
analytical  refinement.  Maxwell, 
in  a  review  of  Tait's  '  Ther- 
modynamics,' written  in  1877 
('  Scientific  Papers,'  vol.  ii.  p. 
666),  contrasts  the  methods  of 
Clausius  and  Thomson,  and  Prof. 
Mach  ('Warrnelehre,'  1896,  p.  300) 
has  made  similar  remarks.  Of 
Thomson  the  former  says,  "  that 
he  does  not  even  consecrate  a 
symbol  to  denote  the  entropy, 
but  he  was  the  first  to  clearly 
dehne  the  intrinsic  energy  of  a 
body,  and  to  him  alone  are  due 
the  ideas  and  the  definitions  of 
the  available  euergj-  and  the  dis- 
sipation of  energj'.  .  .  .  He  avoids 
the  introduction  of  quantities 
which  are  not  capable  of  ex- 
perimental measurement."  Since 
these  criticisms  a  great  deal  has 
been  written  to  make  the  second 
law   of  thermo-dynamics   and    the 


concepti(jn  of  entropy  more  intellig- 
ible. The  object  here  again  haii 
been  twofold :  first,  to  make  the 
cunceptions  useful  for  the  practical 
jiurpo.-e  of  perfecting  tlie  heat  en- 
gines (liiinkine,  Zeuaer  and  his 
school)  and  of  inve.-^tigating  the 
conditions  of  cheuiical  equilibrium 
(Gibhs,  Helmholtz,  Duhem)  ;  next, 
to  place  the  second  law,  which 
deals  with  the  transformation  of 
energy,  on  an  eijually  firm  foun<la- 
tion  with  the  first  law,  which 
deals  with  the  conservation  of  en- 
ergy. There  is  no  doubt  tiiat  the 
jirinciple  of  tlie  consenation  of 
energy  owes  a  very  lari;e  part  of 
its  inti-lligiliility  to  tlie  fact  that 
for  purely  mechanical  i-ystems 
it  follows  from  such  well-known 
dynamical  axioms  as  the  laws  of 
motion.  When  heat  was  con- 
ceived to  have  a  mechanical 
equivalent  in  mechanical  work, 
the  more  general  principle  of  the 
conservation  of  energy  seemed 
intelligible  bj-  mechanical  con- 
ceptions. The  second  law,  how- 
ever, introduced  a  property  of 
natural  processes  which  is  not  so 
easily  understood  n)echanically — 
viz.,  that  they  are  not  reversible 
— and  tliis  property  was  shown  to 
l)e  connected  witli  a  sjiecial  phys- 
ical quantity,  for  which  we  have 
a  sjjccial  sense — viz.,  temjierature. 
The  problem  of  making  the  second 
law  mechanically  intelligible  thus 
coincides  with  the  jiroblem  of 
giving  a  mechanical  definition  of 
temperature.  It  is  not  sufficient 
t<)  call  heat  a  mode  (or,  more  cor- 
rectly, the  energy)  of  motion  ;  we 
must  ex|iress  tcmi>erature,  on  the 
dill'erence  of  which  the  usefulneta 
of  heat  depends,  in  some  way  by 
motion,     we    must     nirivc     at     a 


176 


SCIENTIFIC    THOUGHT. 


introducing  thermo-dynamics  into  chemistry,  after  W. 
Gibbs  had  shown  how  to  look  at  chemical  energy  as  a 
sum  of  many  forms  of  energy,  and  after  Helmholtz  had 
more  clearly  defined  the  useful  conception  of  free  or 
available  energy  as  the  measure  of  chemical  reaction — 
49.        that  Prof.  Ostwald  at  length  ventured  after  the  lapse  of 

Ostwald's  .  •.        •  1  •  1  •  , 

'Aiigemeine  eighty  ycars  to  unite  m  a  comprehensive  doctrine  the 
scattered  fragments  of  our  existing  knowledge  regard- 
ing chemical  affinity.  This  he  did  as  a  restorer  of  the 
forgotten    labours    and    fame    of    Berthollet.^       By    the 


kinetic  definition  of  temperature. 
The  two  principal  founders  of 
thermo-dynamics,  Clausius  and 
Lord  Kelvin,  did  not  resort  to 
kinetic  conceptions  when  estab- 
lishing the  two  laws  which  deal 
with  the  conservation  and  trans- 
formation of  energy  :  Rankine, 
however,  connected  the  subject 
with  his  theory  of  molecular  vor- 
tices ;  and  Clausius,  who  was  one 
of  the  founders  of  the  kinetic 
theory  of  gases,  very  early  at- 
tempted to  interpret  the  laws  of 
the  transference  of  heat  by  the 
help  of  that  theory.  So  like- 
wise did  Maxwell,  Helmholtz, 
Boltzmann,  and  many  others. 
Mr  Bryan,  in  a  very  valuable 
report  on  the  "  Researches  relat- 
ing to  the  Connection  of  the 
Second  Law  with  Dynamical 
Principles,"  has  given  a  critical 
summary  of  these  various  at- 
tempts (see  Brit.  Assoc.  Reports, 
1891,  p.  85).  The  three  peculiar 
forms  of  motion  referred  to  in 
our  last  chapter  —  periodic,  rota- 
tional, and  rapid  translatioual  (dis- 
orderly) motion — have  been  used  to 
suggest  manifold  means  of  trans- 
lating thermo-dynamical  processes 
into  kinetic  models,  explaining, 
as  Mr  Bryan  says,  "  the  second 
law,  about  which  we  know  some- 


thing, by  means  of  molecules 
about  which  we  know  much  less  " 
(p.  121).  It  does  not  seem  that 
much  more  has  been  gained  than 
a  general  presumption  that  a 
mechanical  illustration  is  possible. 
To  the  statistical  ideas  elaborated 
mainly  by  Maxwell  and  Boltz- 
mann I  shall  revert  when  treat- 
ing generally  of  the  statistical  view 
of  nature. 

1  Prof.  Ostwald  has  himself,  in 
the  Inaugural  liecture  which  he 
delivered  on  the  occasion  of  his 
accession  to  the  chair  of  physical 
chemistry  at  Leipzig,  23rd  Nov- 
ember 1887,  given  a  very  lucid 
statement  of  the  principles  in- 
volved. He  goes  back  to  the  two 
theories  of  chemical  action  repre- 
sented at  the  beginning  of  the 
century  by  Bergmann  on  the  one 
side  and  I5ertliollet  on  the  other. 
In  place  of  the  conflict  of  chemical 
forces,  in  which  the  stronger  ob- 
tains a  complete  victory  (complete 
reactions) — the  view  of  Bergmann — 
Berthollet  introduces  the  "mani- 
fold play  of  forces  acting  to  and  fro, 
the  result  being  that  every  one  gets 
its  due.  The  more  powerful  sub- 
stance gets  more,  the  weaker  less. 
Only  in  cases  where  one  of  the 
possible  compounds  in  consequence 
of    its    properties    entirely    leaves 


ON    THE    PHYSICAL    VIKW    OF    NATriJE. 


17' 


publication  «>!'  the  second  vohnue  of  his  '  Lehrbuch  der 
allgenieinen  Chemie  '  a  great  impetus  was  given  to  phys- 
ical cheniistiy.  Ihe  large  addition  to  our  knowledge  in 
this  branch,  and  the  consolidation  and  criticism  of  re- 
seanh  wliich  it  brought  about,  and  to  which  the  second 
edition,  now  appearing,  gives  ample  testimony,  mark  this 
publication  as  an  epoch  in  modern  scientific  thouglit.  To 
tliis  development  is  attached  the  growth  oi  the  special 
view  of  natural  phenomena  which  Ostwald  and  some 
other  Continental  thinkers  embrace,  and  which  they  are 
inclined  to  place  in  opposition  to  tlie  older  views  as  a 
more  comprehensive  one.  The  older  views  they  some- 
what contemptuously  term  the  materialistic  views  of 
nature  —  the  views,  in  fact,  which  1  have  presented 
under  the  headings  astronomical,  atomic,  and  mechanical. 
As  this  most  recent  outcome  of  what  I  termed  the 
physical  view  of  nature  refers  to  fuiulamental  concep- 
tions   and    has    furnished    much    matter    for  discussion 


the  field  of  contest,  either  by  falling 
down  as  insoluble  or  escaijing  as 
gas,  can  that  complete  decomposi- 
tion take  place  which  Beigmaiin 
held  to  be  the  normal  result  " 
('Die  Energie  und  ihre  Waud- 
lungen,'  Leipzig,  1888,  p.  20).  That 
complete  reactions  were  for  a  long 
time  studied  with  predilection  was 
most  natural,  esj)ecially  as  they  are 
the  most  useful  for  practical  |)ur- 
j^oses  ;  but  the  study  of  moving 
cliemical  eciuilibrium,  depending  on 
what  is  now  termed  mass  action  and 
involving  the  question  of  the  velocity 
of  reactions,  has  in  recent  times 
again  asserted  itself.  Ostwald 
dates  the  revival  of  this  long- 
neglected  branch  of  research  from 
the  year  1867,  when  "two  Nor- 
wegian    chemists,    Guldberg     and 

VOL.  n. 


Waiige,  put  the  ideas  of  Berthollet 
into  precise  mathematical  form  and 
subjected  the  resulting  equations  to 
the  test  of  observation  and  verifica- 
tion "  (ibid.,  p.  21).  Ostwald  then 
shows  further  how  Bergmaun's 
theory  was  simultaneously  reviveil 
in  M.  Berthelot's  famous  third  law- 
derived  from  thermo  •  chemistry. 
This  in  turn  had  to  yield  to 
the  correcter  views  which  date 
from  Gibbs's  studies  "on  the 
equilibria  of  heterogeneous  sub- 
stances" (see  '  Tliermo<lynami.tche 
Studien,'  p.  66, 1875  ;  also  Ostwald, 
'  Allg.  Chemie,'  vol.  ii.  part  2,  p. 
163,  on  the  reconciliation  of  Berg- 
maun's and  BerthoUet'a  views  ;  ami 
further,  Berthelot  in  '  Conipte* 
Rendus,'  1894,  118). 


.M 


178  SCIENTIFIC    THOUGHT. 

abroad,  I  will  try  to  sum  up  finally  the  principal  points 
in  it  which  are  of  importance  for  the  history  of  con- 
temporary thought. 

Ever  since  the  conception  of  energy  as  a  quantity 
which,  like  matter,  is  preserved  in  all  natural  processes, 
forced  itself  with  more  or  less  clearness  upon  natural 
philosophers,  the  question  has  been  insistent  as  to  the 
number  of  different  forms  in  which  this  quantity  can 
manifest  itself ;  and  some  of  the  earliest  propounders  of 
the  doctrine  attempted  an  enumeration  of  the  different 
forms,  mechanical  energy  of  motion  and  of  attraction 
usually  heading  the  list.  When  that  form  of  energy 
which  we  call  heat  was  subjected  to  examination,  and  the 
remarkable  property  formerly  called  latent  heat  defined 
in  the  new  terminology,  the  want  arose  of  bringing  about 
some  kind  of  connection  between  our  ideas  of  motion  and 
those  of  heat,  which  were  shown  to  be  mutually  con- 
vertible quantities  in  nature.  Before  that  time  sound 
and  light  had  already  yielded  to  the  kinetic  view,  and  an 
enormous  increase  of  our  knowledge  in  acoustics  and 
optics  had  followed.  Thus  we  find  some  of  the  pioneers  of 
the  physical  or  energy  view  of  nature— notably  Rankine 
and  Joule  in  this  country,  Eedtenbacher  and  subsequently 
Clausius  abroad — engaged  in  translating  the  properties 
of  heat  into  mechanical  analogies.^      It  was  not  thought 

^  Rosenberger,  in  his  '  Geschichte      volumes     on      '  Die      mechanische 
der   Physik'   (vol.   iii.  p.  550,   &c.),    ,   Warmetheorie,' 2nd  ed.,  1876,  &c.). 


gives  a  number  of  references  to 
theories  mostly  forgotten  which 
were  published  before  and  after 
the  year  1850.  Clausius,  who 
keeps  his  mechanical  theory  of 
heat  quite  separate  from  his  kinetic 
theory    of     gases     (see    the    tln-ee 


admits,  nevertheless,  in  a  paper 
published  in  1857  (Pogg.  'Ann.,' 
vol.  c,  and  '  Mechan.  Wiirmetheor.,' 
vol.  iii.  p.  1,  &c. ),  that  "from  the 
beginning  of  his  researches  refer- 
ring to  heat  he  had  attempted  to 
account  to  himself  for  the  internal 


ON    THE    PHYSICAL    VIEW    OF    NATURE. 


179 


essential,  but  it  was  found  to  be  convenient — mainly  for 
didactic  purposes — to  elaborate  such  analogies,  explaining 
or  describing   the  less   known   by   that    which    is   more 
familiar,      liegarding   the  value  of  such  attempts  there 
have  always  existed  two  opinions.      I  have  had  occasion 
to  refer  to   them   when    explaining   the   atomic   theory. 
There  were  those  who  looked  upon  that  theory  merely 
as  a  convenient  symbolism,  and   there  were  those  who 
looked    upon    atoms    and    molecules    as    really   existing 
things.      The  latter  view  has  gained  force  and  importance 
through  the  necessity  of  more  and  more  elaborating  the 
atomic  hypothesis  in  order  to  represent  not  morely  the 
chemical  constitution  of  compounds,  Ijut   likewise  tiieir 
manifold   physical   differences,   some   of    which,   in    fact, 
could  only  be  described  by  geometrical  conceptions.      T 
need  only  refer  to  what    I  said   above   on   the   kinetic 
theory  of  gases,  and  on    the   property  termed  chirality 
manifested  by  some  chemical  substances  in  solution,  as 
well  as  on   tlie  phenomena  of  isomerism.      In    tlie  last 


state  of  motion  of  a  hot  body,  and 
that  he  haxl  arrived  at  a  conception 
which  he  had  already  before  his 
first  publication  (in  1850)  used  for 
various  investigations  and  calcu- 
lations." He  further  stiites  that 
hearing  through  William  Siemens 
that  Joule  had  expressed  a  similar 
idea  (Manchester  Phil.  Soc,  1848 
and  18.07),  and  more  especially  after 
the  publication  of  Kronig  (18,')6), 
he  resolved  to  puV)lish  his  views. 
It  is  interesting  for  our  present 
purpose  to  see  how  Clausius,  like 
Maxwell  in  a  different  domain  of 
re.search,  was  originally  guided  by 
definite  mechanical  representations. 
It  is  equally  noteworthy  that  Lord 
Kelvin's  original  researches  on  the 


subject  of  heat  were  quite  free 
from  this  element,  though  we 
owe  to  him  in  other  departments 
some  of  the  most  suggestive  kin- 
etic illustrations  ;  and  that  he  ha.s 
quite  recently  offered  valuable 
criticisms  on  the  attempted  me- 
chanical interpretation  of  the  second 
law  of  thermo-dynamics  (see  p.  112 
of  Bryan's  Report,  quoted  above,  p. 
176,  note).  Also  the  first  English 
treatise  on  thermodynamics  writ- 
ten for  didactic  jjurj" >ses  (Tail's 
Sketch,  1868)  contains  no  reference 
to  molecular  theory,  and  Hirn,  one 
of  the  most  active  workers  in  the 
region  of  experimental  proofs,  kept 
clear  of  it. 


180  SCIENTIFIC    THOUGHT. 

chapter,  while  dealing   specially  with   the  kinetic  view 
of  natural  phenomena,  I  had  again  occasion  to  refer  to 
the   opinion   which   has   latterly   crept   into   mechanical 
explanations — namely,  that  they  are  to  be  looked  upon 
merely  as  symbolical,  an  opinion  which  did  not  enter  the 
minds  of  the  original  propounders  of  the  vibratory  theory 
of   sound   and   light,  and   which   some  eminent  natural 
philosophers  to-day  strongly  oppose.     An  opposite  fate 
seems    to   have   befallen   the    mechanical    hypothesis   in 
chemistry  and  in  physics.      Whilst  Dalton's  atoms  were 
accepted  with  hesitation,  the  further  elaboration  of  the 
atomic  view  has  made  it  almost  impossible  to  resist  it 
as  a  physical  reahty ;    whereas  the  necessary  complica- 
tions   introduced    into    Young's    undulatory    theory    in 
order    to    make    it    cover   electro  -  magnetic   phenomena 
have  given  it  the  appearance  of  unnaturalness  and  arti- 
ficiality— so  much  so  that  Maxwell  himself  abandoned 
the  line  of   reasoning  which    led   him  originally  to  his 
fundamental  formulae,  and  contented  himself  with  more 
general  considerations   derived    from   the   conception   of 
energy. 
50.  The  conceptions  which  are  expressive  of  the  view  dealt 

"Kinetics"  .  .  -^  ^ 

and"ener.  with  in  this  chapter — the  energy  ideas — have  had  a 
similar  fate.  There  have  been  those  who  have  inter- 
preted this  view  to  mean  that  all  phenomena  in  nature 
can  be  translated  into  the  language  of  mechanics :  they 
have  accordingly  been  stimulated  to  invent  all  manner 
of  kinetic  contrivances  by  which  light,  heat,  electricity, 
and  chemical  action  can  be  represented.  Others  have 
interpreted  the  equivalence  of  all  forms  of  energy  to 
mean  that  kinetic  energy  is  only  one  of  the  forms  in 


getics." 


ON    THE    PHYSICAL    VIEW    OF    NATUUE.  181 

which  this  (quantity  can  appear :  they  have  thus  exerted 
themselves  to  lind  such  general  properties  as  Ijelong 
to  all  tlie  forms  in  which  energy  presents  itself  to  us. 
They  look  upon  energy  as  a  much  more  general  con- 
ception than  motion,  and  they  think  it  a  mistake  to 
try  to  narrow  the  conception  so  that  it  can  only  mean 
the  energy  of  attraction  and  repulsion  (tlie  astronomical 
view),  that  between  the  ultimate  particles  of  matter 
(the  atomic  view),  or  the  energy  of  various  forms  of 
motion  (the  kinetic  view). 

On  the  purely  scientific  side  the  mechanical  view  has 
much  to  say  for  itself,  and  can  point  to  achievements 
which  recommend  it  as  a  fruitful  method  of  progress  and 
research,  and  as  even  more  fruitful  for  the  purposes  of 
instruction.  It  can  claim  to  give  in  many  instances  an 
apparently  easy  account  of  the  common-sense  or  obvious 
properties  of  bodies,  and  it  gives  this  accomit  in  terms 
which  lend  themselves  to  strict  definition,  to  measure- 
ment, calculation,  and  prediction  of  phenomena ;  it 
destroys  all  \'agueness,  and  adopts,  as  it  also  stimulates, 
mathematical,  which  is  the  most  cogent  kind  of  reasoning. 
The  kinetic  theory  of  gases  and  the  vibratory  theory  of 
light  are  notable  examples.  The  ideas  of  energy  and  the 
remarkable  properties  of  the  lowest  form  of  energy — 
i.e.,  of  lieat  —  became  gradually  clearer  and  lost  their 
strangeness  as  potential  energy  came  to  be  defined  as 
energy  of  position,  aA'ailable  (or  free)  energy  as  the 
kinetic  energy  of  regular  or  orderly,  unavailal)le  (or 
bound)  energy  as  that  of  irregular  or  disorderly  motion, 
and  when  the  strange  quantity  termed  entropy,  which 
Clausius  and   IJankine  strove  in  vain  to  bring  home  to 


182 


SCIENTIFIC    THOUGHT. 


the  general  scientific  intelligence,  revealed  itself  as  the 
measure  of  the  disorder  which  prevails  in  the  motion  of 
the  ultimate  material  elements  of  a  system.^  Faraday's, 
lines  of  force  and  the  whole  elaborate  imagery  invented 
and  afterwards  discarded  by  Maxwell  to  describe  the 
interaction  of  magnets,  electric  currents,  and  charged 
bodies,  have  proved  to  be  most  valuable  instruments  of 
thought — a  useful  scientific  shorthand — in  the  hands  of 
the  teacher,  as  in  those  of  the  practical  electrician.  And 
although  the  illustrious  propounder  of  the  vortex-atom 
theory  of  matter  seems  latterly  to  have  discouraged  the- 
use  of  this  kinetic  contrivance  as  not  likely  to  lead 
to  any  great  revelations  regarding  the  ultimate  constitu- 
tion of  matter  or  the  nature  of  the  imponderal)les,^  the 


^  Helmholtz,  in  his  first  memoir 
on  the  thermo-dynamics  of  chemi- 
cal processes  (' Sitzungsberichte  der 
Akaderaie  zu  Beriin,'  2ud  February 
1882),  after  having  estabhshed  the 
formula;  for  the  free  energy  in  iso- 
thermal processes  without  reference 
to  kinetic  hypotheses,  concludes  his 
exposition  with  the  following  re- 
marks :  "  We  require,  finally,  an 
expression  in  order  to  be  able  to 
distinguish  clearly  what  in  theoreti- 
cal mechanics  is  termed  vis  viva  or 
actual  energj'  from  the  work  equiva- 
lents of  heat,  which  are  indeed 
mostly  to  be  regarded  likewise  as 
vis  viva  of  invisible  molecular  mo- 
tion. I  would  suggest  that  the 
former  should  be  called-  the  vis 
viva  of  orderly  motion.  I  call 
orderlj'  all  motion  in  which  the 
compounds  of  velocity  of  the 
moving  masses  are  difierentiable 
functions  of  the  space  co-ordinates. 
Disorderly  motion  would  then  mean 
all  motion  in  which  the  motion  of 
each  particle  has  no  similarity  to 
that  of  its  neighbours.     We  have 


every  reason  to  believe  that  heat- 
motion  is  of  the  latter  kind,  and  one 
might  in  this  sense  regard  entropy 
as  the  measure  of  disorder.  For 
our  means,  which  compared  with 
molecular  structure  are  coarse,  only 
orderly  motion  can  be  freely  con- 
verted again  into  other  forms  of 
mechanical  work"  (' Wissenschaftl. 
Abhandl.,'  vol.  ii.  p.  972). 

■•^  "  I  am  afraid  it  is  not  possible 
to  explain  all  the  properties  of 
matter  by  the  vortex-atom  theory 
alone  —  that  is  to  say,  merely  by 
motion  of  an  incompressible  fluid  ; 
and  I  have  not  found  it  helpful  in 
respect  to  crystalline  configurations, 
or  electrical,  chemical,  or  gravita- 
tional forces.  .  .  .  We  may  expect 
that  the  time  will  come  when  we 
shall  understand  the  nature  of  an 
atom.  With  great  regret  I  abandon 
the  idea  that  a  mere  configuration 
of  motion  suffices"  (Lord  Kelvin, 
quoted  by  Prof.  S.  W.  Holman  in 
'  Matter,  Energy,  Force,  and  Work,' 
New  York,  1898,  p.  226). 


ON    THE    PHYSICAL    VIEW    OF    NATUKl.. 


183 


foremost  intellects  are  still  busy  in  working  this  to 
them  promising  vein   of   reasoning.^ 

The  opponents  of  the  kinetic,  mechanical,  or  material 
views  of  natural  phenomena  have  always  existed  :  in  the 
early  yeare  of  the  century  they  described  their  view  by 
the  word  "  dynamic."  At  that  time  it  was  the  atomic 
theory  they  principally  objected  to.  But  their  criticisms, 
though  not  without  use  in  exposing  the  limited  nature 
of  all  mechanical  explanations,  failed  to  yield  any  fruits, 
inasmuch  as  they  moved  in  vague  expressions  and  did 
not  lend  themselves  to  that  powerful  method  by  which 
alone  the  conquest  of  nature  has  been  effected,  viz.,  mathe- 
matical reasoning,  combined  with  observation. 

The  more  recent  critics  of  the  mechanical  interpreta-        si. 

„        ,         .       ,        ,  T         Ml  1       Criticism  of 

tion   of   physical   phenomena,   among  whom    1  will   only  mechanical 

view. 

mention  Prof.  Ostwald  of  Leipzig,  Prof.  G.  Helm  of 
Dresden,  and   Prof.    Ernst   Mach   of  Vienna,"  are    fully 


^  "  With  reference  to  the  vortex- 
atom  tlieory,  I  do  not  know  of  any 
phenomenon  which  is  manifestly 
incapable  of  being  explained  by  it ; 
and  personally  I  generally  endeav- 
our (often  without  success)  to 
picture  to  myself  some  kind  of 
vortex-ring  mechanism  to  account 
for  the  phenomenon  with  which  I 
am  dealing.  ...  I  regard  the 
vortex-atom  explanation  as  tiie  goal 
at  which  to  aim,"  &c.  (Prof.  J.  J. 
Thomson,  quoted  ibid.) 

^  Prof.  Ernst  Mach  is  the  earliest 
of  these  writers  and  had  worked  on 
quite  independent  lines  before  the 
other  two  names  began  to  figure  in 
scientific  literature.  His  criticisms 
refer  both  to  metaphysical  and 
mechanical  theories.  His  position 
is  original  and  unique,  and  his 
writings,  which  are  a  splendid 
example    of  critical   and   liistorical 


analysis,  have  been  invaluable  to 
me.  His  earliest  important  es-says 
date  from  the  year  1872  ('  Die 
Geschichte  und  die  Wurzel  des 
Satzes  von  der  Erhaltung  der 
Arbeit,'  and  'Die  Ge.stalten  der 
Fliissigkeiten,'  Prag).  They  are 
now  generally  accessible,  having 
been  collected  and  translated 
(under  the  title  'Scientific  Lec- 
tures,' Chicago,  189.=i)  by  Prof. 
T.  J.  M'Cormack.  Hi.s  'Science  of 
Mechanics'  (translated  by  the  same 
author  from  the  second  German 
edition,  London  and  Chicago,  1893) 
has,  ever  since  its  first  ap|>oanince 
in  1883,  had  a  great  influence  in 
Germany  ;  and  latterly  also  in  this 
country,  as  may  be  seen  from  sucli 
works  as  Prof.  Karl  Pearsons 
'Grammar  of  Science'  (lat  ed., 
1892,  p.  387\  and  noUbly  from 
Prof.   Love's   'Dynamics'   (p.    85). 


184 


SCIENTIFIC    THOUGHT. 


aware  of  the  importance  of  mathematical  presentation  of 
their  doctrine,  and  the  two  former  have  in  fact  done 
more  than  any  one  else  to  introduce  mathematics  into 
chemistry.  But  they  maintain  that  their  exact  treatment 
is  not  arrived  at  by  introducing  hypothetical  quantities 
such  as  the  atomic  and  other  theories  are  founded  upon, 
but  by  contenting  themselves  with  measuring  such  quan- 
tities as  are  presented  directly  in  observation,  such  as 
energy,  mass,  pressure,  volume,  temperature,  heat,  elec- 
tric potential,  &c.,  without  reducing  them  to  imaginary 
mechanical  or  kinetic  quantities.^     To  what  extent  they 


A  great  many  aspects  of  physical 
science  which  have  been  more 
prominently  brought  forward  by 
the  modern  school  of  "  Ener- 
getics "  are  to  be  found  discussed 
in  Mach's  much  earlier  writings. 
To  his  valuable  'Principien  der 
Wiirmelehre '  (Leipzig,  1896)  I  have 
frequently  had  occasion  to  refer  in 
this  chapter. 

^  In  recent  discussions  and 
treatises  two  distinct  tendencies 
must  be  distinguished.  First  we 
have  tlie  very  useful  effort  to  bring 
about  a  correlation  of  the  differ- 
ent departments  of  physics  and 
chemistry,  including  their  applica- 
tions in  industry  and  in  physi- 
olog)',  by  the  introduction  of  the 
conception  of  energy  and  the 
principles  of  its  conservation  and 
transformation.  This  dates  prac- 
tically from  the  publication  of 
Thomson  and  Tait's  '  Natural 
Philosophy. '  The       theoretical 

foundations  of  this  undertaking 
have  been  very  fully  discussed, 
notably  in  Germany.  I  mention 
only  the  valuable  series  of  writ- 
ings of  Prof.  Max  Planck,  a  list 
of  which  is  contained  at  the  end 
of  his  '  Thermodynamik '  (Leipzig, 
1897).  They  begin  with  his  prize 
essay  ('  Das  Princip  der  Erhaltung 


der  Energie,'  1887)  and  his  earlier 
dissertation  (Munich,  1879)  "  On 
the  Second  Law."  Out  of  this  an- 
other endeavour  has  grown.  The 
aim  is  to  make  the  conception 
of  energy  the  fundamental  notion, 
and  by  following  its  physical  ap- 
pearance in  its  different  forms, 
to  arrive  at  certain  fundamental 
relations  expressed  in  equations, 
which  are  to  serve  as  the  basis 
for  calculation,  as  in  conventional 
physics  the  dynamical  equations 
formed  the  starting-point  for  the 
various  physical  theories.  In  this 
more  radical  scheme  the  quantity 
"  energy  "  was  to  play  a  part  similar 
to  that  which  the  quantity  "  force  " 
played  in  Newtonian  dynamics. 
This  method  was  probably  sug- 
gested by  the  novel  mode  of 
treatment  invented  originally  for 
heat  -  problems  by  Lord  Kelvin 
and  by  Clausius,  and  most  strictly 
adhered  to  by  the  former.  The 
isolated  character  of  this  classical 
thermo-dynamics  can  be  got  over 
either  by  introducing  a  kinetic 
hypothesis  on  the  nature  of  heat 
or  by  extending  the  method  of 
thermo-dynamics  to  other  physical 
provinces.  The  former  was  the 
most  plausible  view ;  it  has  its 
origin  in  the  writings  of  Rankine 


ON    THE    PHYSICAL    VIEW    OF    NA'l  I  l:E. 


18; 


!iiay  succeed  in  doing  this  consislenlly  seems  ul  juesenl 
uncertain.  It  has  been  maintained  that  the  very 
elements  of  all  physical  measurement,  the  independ- 
ence of  the  three  dimensions  in  space,  necessitates  us 
to  supplement  the  energy-conception — which  by  itself 
includes  no  more  reference  to  diroctinn  tlian  the  con- 
ception of  mass — by  an  assumption  of  ;i  purely  mecliani- 
cal  nature  such  as  the  numljer  of  degrees  of  freedom, 
and  that  the  much-discussed  correlation  of  all  forms  of 
energy,  as  it  is  suggested  by  W.  Gibbs's  formuhe,  cannot 
be  usefully  carried  farther.      This  correlation  ^  has  l^een 


and  Clausius.  The  latter  method 
grew  out  of  the  gradual  aj)|)lication 
of  thermo- dynamics  to  chemical 
phenomena,  where  the  mechanical 
treatment  had  turned  out  to  be 
powerless.  This  more 
scheme  of  remodelling 
of  j)hysics,  chemistry, 
ehanics  on  the 
classical     thermo 


ambitious 
the  whole 
and  me- 
model  of  the 
dynamics     dates 


from  the  year  1887,  when  Prof. 
Georg  Helm  published  his  first 
treatise  ('Die  Lehre  von  der  En- 
ergie,'  Leipzig)  and  revived  the 
word  "energetics"  invented  by 
Rankine.  Subsequently  he  pub- 
lished his  application  to  chemistry 
('Grundziige  der  mathematischen 
Chemie,'  Leipzig,  1894),  very 
much  under  the  influence  of 
Willard  (Jibbs's  studies  of  chem- 
ical equilibria  and  Duhem's  elab- 
oration of  Hehnholtz's  conception 
of  free  energy.  His  last  work 
('Die  Energetik,'  Leipzig,  1898) 
gives  a  history  of  the  gradual 
purification  of  the  energy  concep- 
tion from  mechanical  admixtures, 
into  which  all  earlier  writers  on 
the  subject  except  Lord  Kelvin 
are  shown  to  have  lapsed,  and 
attempts  a  reconstruction  of  me- 
chanics on  "energetic"  principles, 
<l€fending     the     author's    position 


against    various    criticisms    which 
had   meantime   been    made. 

^  The  great  generalisation  of  the 
science  of  energetics  referred  to  in 
the  text  was  first  explicitly  put 
forth  by  Helm  in  his  treatise  of 
1887.  He  himself  holds  that  he 
there  finally  brought  together  sug- 
gestions made  in  various  ways  by 
Zeuner  (1866),  Mach  (1871),  Oibbs 
(1875),  Maxwell  (187.'').  Von  Oettin- 
gen  (1885),  and  Popper  (1884),  and 
expressed  them  in  the  form  of  a 
general  i)rincii)le.  The  two  factors 
into  which  all  energy  can  be  sep- 
arated are  called  by  various  sub- 
sequent writers  intensity,  jiotentiai 
level  on  the  one  side  ;  extensity, 
capacity,  weight,  on  the  other. 
In  spite  of  further  expositions  of 
Helm  in  1890  the  subject  did  not 
attract  much  attention  till  Prof. 
Ostwald  introduced  it  in  a  slightly 
modified  form  in  the  second  edition 
of  his  great  work  on  physical  chem- 
istry (1893),  making  it  tiie  foun<la- 
tion  of  the  doctrine  of  affinity. 
He  had  evidently,  between  the 
first  and  second  editions,  given  up 
the  mechanical  for  tiie  "ener- 
getic "  treatment  of  the  subject 
(see,  inter  alia,  note  2,  p.  114, 
of  the  2nd  edition  ;  vol.  ii.  i>.  12). 
At   the    meeting    of    the    German 


186 


SCIENTIFIC    THOUGHT. 


placed  at  the  summit  of  the  modern  theory  of  energetics 
by  Helm  and  Ostwald,  after  earlier  writers,  such  as 
Zeuner  and  Mach,  had  already  used  it  or  drawn  atten- 


"Is'aturforscherversammlung,"  held 
at  Vienna  in  1894,  a  committee 
was  appointed  to  report  in  1895 
at  Liibeck  on  the  "  actual  position 
of  energetics,"  and  the  introduc- 
tion of  the  subject  was  put  into 
the  hands  of  Dr  Helm.  His  ad- 
dress and  the  discussion  which 
followed  have  been  given  in  extract 
in  the  published  '  Verhandlungen  ' 
(vol.  ii.  part  1,  p.  28.  &c.),  and 
since  continued  in  '  Wiedemann's 
Annalen,'  vols.  Ivii.  et  seqq.  Simul- 
taneously, however,  the  subject 
received  a  much  more  fundament- 
al or  philosophical  development 
through  Prof.  Ostwald's  general 
address  at  Liibeck  with  the  some- 
what polemical  title  "  Die  Ueber- 
windung  des  wissenschaftlichen 
Materialismus."  From  that  mo- 
ment the  mechanical  view  of 
nature  bore  the  stigma  of  ma- 
terialism, to  which  the  other 
side  replied  by  attaching  to  the 
new  or  energetic  view  the  stigma 
of  "  metaphysical "  (see  Planck, 
'Wied.  Ann.,'  vol.  Ivii.  p.  77)  as 
being  scientifically  vague  and 
useless.  It  cannot  be  said  that 
the  whole  matter  has  yet  been 
fully  discussed  or  fathomed.  Prof. 
Boltzmann,  Prof.  Carl  Neumann, 
and  Dr  Helm  have  treated  the 
questions  at  stake  with  much 
patience,  and  have  made  valuable 
approaches  to  a  mutual  under- 
standing. The  various  contrib- 
utions are  most  fully  discussed 
in  Helm's  latest  work,  '  Die  En- 
ergetik '  (Leipzig,  1898).  Some  of 
those  who  originally  assisted  in 
introducing  the  energetic  treat- 
ment have  since  refused  to  go  the 
length  of  Helm's  and  Ostwald's  final 
generalisations,  though  they  prefer 
— for  the  purpose  of  the  treatment 


of  thermo-dynamical  and  chemical 
problems  —  the  phenomenological 
method,  admitting  at  the  same 
time  the  usefulness  of  the  atomic 
and  mechanical  hypotheses,  though 
some  do  not  look  upon  them  as 
indispensable.  This  phenomeno- 
logical view,  which  deals  only 
with  observable  and  measurable 
quantities,  in  contradistinction  to 
the  atomic  and  kinetic  views, 
is  largely  represented  by  Prof, 
Xemgt  (see  his  '  Theoretical  Chem- 
istry,' translated  by  Palmer, 
London,  1895,  p.  22),  and  by 
Prof.  Planck  (see  his  'Thermo- 
dynamik,'  Leipzig,  1897),  though 
the  latter  considers  it  merely 
provisional,  a  stepping  -  stone  in 
the  direction  of  a  mechanical 
view  (p.  V,  preface).  Prof.  Boltz- 
mann has  summed  up  the  position 
from  a  general  point  of  view  in 
his  address  at  Munich  in  1899. 
He  there  very  lucidly  defines  the 
mechanical,  energetic,  and  pheno- 
menological positions,  admitting 
the  usefulness  of  all  three,  but  also 
points  out  the  fundamental  diffi- 
culties into  which  a  one-sided  and 
exclusive  development  of  any  of 
them  unavoidably  leads  us.  Hav- 
ing himself  done  so  much  in  ap- 
plj-ing  atomic  theories,  he  con- 
cludes by  saying  that  "  the 
I  numerous  conquests  of  the  atomic 
I  doctrine  cannot  be  won  by  pheno- 
I  menology  or  energetics,"  and  main- 
tains "  that  a  theoiy  which  yields 
something  that  is  independent 
and  not  to  be  got  in  any  other 
way,  for  which,  moreover,  so  many 
phy.sical,  chemical,  and  crystallo- 
graphic  facts  speak,  must  not  be 
combated  but  further  developed " 
('  Verhandlungen  der  Versamm- 
lung  zu  Miinchen,'  1899,  p.   121). 


ON    THE    PHYSICAL    VIKW    OF    NATrRE.  187 

tion  to  it.  It  can  be  set  out  in  tlie  sUitenient  that 
wherever  energy  shows  itself  it  appears  as  composed  of 
two  factors  —  the  intensity  and  the  capacity  factoi-s. 
These  terms,  borrowed  from  the  older  theories  of  heat 
and  electricity,  measure  the  quantity  of  energy  as  well  as 
the  direction  in  which  changes  of  energy  take  place:  the 
L^eneral  law  being  that  energy,  in  whatever  form  it 
may  appear,  tends  to  go  from  places  of  higher  to  places 
of  lower  potential  or  intensity. 

The  characteristic  feature  of  this  most  recent  outcome 
of  the  physical  view  uf  natural  phenomena  is  that  it  c™* 
takes  in  real  earnest  the  suggestion  at  which  many 
natural  philosophers  have  independently  arrived,  that 
energy  is  a  substance  quite  as  much  as  matter.  .This 
granted,  it  seems  at  least  reasonable  to  some  thinkers  to 
see  how  far  they  can  get  by  employing  the  two  con- 
ceptions of  matter  and  energy  alone  without  adopting 
a  third  something,  the  ether,  which  was  introduced  at 
a  time  when  the  idea  of  the  conservation  of  energy 
had  not  yet  been  formulated.^ 


The  oDt- 


'  For  an  indication  of  tlie  furtlier 
development  of  this  point  of  view  I 
must  refer  the  reader  to  tlie  chapter 
on  Photo -chemistry  in  Prof.  Ost- 
wald's  great  work  ('Allg.  Chemie,' 
2nd  ed.,  vol.  ii.  part  1,  p.  1014,  &c.) 
"  lu  the  interest,"  he  says,  "of  a 
conception  of  nature  which  is  free 
from  hypotheses,  we  must  ask 
whether  the  assumption  of  that 
medium,  the  ether,  is  unavoidable. 
To  me  it  does  not  .seem  to  be  so. 
If  we  a.sk  for  the  cause  of  all  dis- 


energy  to  be  a  real  thing,  indeed 
the  only  real  thing  in  the  so-called 
outer  world,  there  is  no  need  to 
inquire  for  a  carrier  of  it  when  we 
find  it  anywhere.  This  enables  us 
to  look  upon  radiant  energj'  as  in- 
dependently existing  in  sjiace.  A\'e 
have  found  in  the  gentral  law  of 
intensity  —  i.e.,  in  the  empirical 
fact  that  energy  tends  to  equalise 
forced  changes  of  its  den.sity  in 
space  —  the  principle  according  to 
which    transmission    of    energy    in 


placements     of     energy     in     s)>ace  space  necessarily  takes  place  when 

which    we    can    singly  observe,    we  tliere  appears  aiiywheic  an  excess." 

find  that  it  always  consists  in  differ-  From    this   and   other    passages  of 

ences  of  intensity.   .  .  .  The  main  Prof.    Ostwald's  writings   it  seems 

point    is    that,     having    conceived  ;    as  if  ma.s8  likewise  wad  to  lie  given- 


188 


SCIENTIFIC    THOUGHT. 


53.  But  whilst   the   question   as    to   the   true  method   of 

Recent 

triumphs  of  physical  research  is  still  being  ventilated  abroad,  as   it 

.atomic  view.  ^    ''  " 

has  recently  begun  to  be  in  this  country  also/  the 
mechanical  conceptions  of  atoms  and  ether  have  quietly 
gained  new  victories.  At  the  end  of  the  last  chapter 
I  related  how,  in  the  hands  of  Maxwell  and  his  fol- 
lowers, the  word  "  electricity "  gradually  lost  its  sub- 
stantial meaning,  so  that  there  remained  only  the  con- 
ception of  a  state  of  motion  or  stress  in  the  electro- 
magnetic field,  it  being  difficult  to  assign  a  definite 
sense  to  the  term,  an  electric  charge.  That  those  who 
were  brought  up  under  the  ideas  of  Coulomb  and  Weber 
would  naturally  regard  this  as  a  defect  has  also  been 
noted.  Still  more  had  the  substantial  nature  of  elec- 
tricity been  forced  upon  those  who  studied  the  electro- 
lytic action  of  solutions  and  currents,  the  wandering  of 


up  as  a  secondary  phenomenon  of 
£nerg}'.  See  Boltzmann,  loc.  eit., 
last  note,  p.  114,  &c.  ;  also,  inter 
alia,  Dr  R.  Pauli,  '  Der  erste  und 
zweite  Hauptsatz,'  Berlin,  1896, 
preface. 

^  The  discussions  which  began  in 
Germany  in  the  year  1895  at  the 
meeting  at  Liibeck,  and  have,  after 
being  continued  at  subsequent 
meetings,  and  in  the  volumes 
of  the  'Annalen  der  Physik  und 
Chemie,'  come  to  a  kind  of  stand- 
still by  the  exhaustive  treatise 
of  Helm  on  the  one  side  and 
by  Boltzmann's  summing  up  on 
the  other,  do  not  seem  to  have 
attracted  much  attention  in  this 
country.  Interest  in  the  subject 
was,  however,  latterly  aroused 
by  two  criticisms  of  the  princi- 
ples of  scientific  method  coming 
from  entirely  different  quarters. 
The  first,  which  was  of  a  purely 
philosophical    character,    was    con- 


tained in  Prof.  James  Ward's  '  Gif- 
ford  Lectures'  (1896-98),  published 
in  two  volumes  with  the  title 
'  Naturalism  and  Agnosticism.' 
The  other  was  an  Address  deliv- 
ered by  M.  Poincare  at  the 
Congress  of  Physicists  in  Paris  in 
1900.  In  consequence,  the  subject 
of  the  legitimacy  of  the  various 
physical  principles,  such  as  action 
at  a  distance,  atomism,  kinetic  and 
ether  theories,  the  use  of  meeliauical 
models,  and  many  kindred  ques- 
tions, have  been  discussed  in  the 
Addresses  of  Poynting  (1899),  Lar- 
mor  (1900),  and  Riicker  (1901), 
before  the  British  Association,  with 
a  very  emphatic  attestation  of  the 
usefulness  and  indispensableness  of 
the  atomistic  theory  regarding  the 
constitution  of  matter,  and  the 
view  that  a  continuous  ether  is 
the  carrier  of  all  physical  actions 
through  space. 


ON    THE    PHYSICAL    VIEW    oK    NATrRE.  189 

the  ions,  and  how,  during  Llie  process,  wandering  atoms 
gave  up  or  lost  a  definite  something — viz.,  their  electrical 
charges.  It  seemed  impossible  in  this  cose  to  do  without 
an  atomic  or  molecular  view  of  electricity.  Accordingly, 
Helmlioltz,  in  his  celebrated  Faraday  Lecture  (1881), 
after  Iiaving  traced  the  gradual  displacement  of  the 
Weberian  theory  of  electrical  particles  acting  at  a 
distance  by  that  of  Faraday,  feels  himself  constrained 
to  say:  "I  see  very  well  that  the  assumption  of  two 
imponderable  fluids  of  opposite  ([ualities  is  a  rather 
complicated  and  artificial  machinery,  and  that  the 
mathematical  language  of  Clerk  ^Maxwell's  theory  ex- 
presses the  laws  of  the  phenomena  very  simply  and 
very  truly ;  .  .  •  but  I  confess  I  should  really  ])e  at  a 
loss  to  explain  .  .  .  what  he  considers  as  a  quantity 
of  electricity,  and  why  such  a  quantity  is  constant,  like 
that  of  a  substance."  And  further  on  he  says :  "  If  we 
accept  the  hypothesis  that  the  elementary  substances 
are  composed  of  atoms,  we  cannot  avoid  concluding 
that  electricity  also  ...  is  divided  into  definite 
elementary  portions,  which  behave  like  atoms  of  elec- 
tricity." 

Besides    the    phenomena    of    chenucal    decomposition,       :>*■ 

^  '■  Modem 

there   was   another  very   large   and    important    class   of  f'cctncai 

•JO  I  researchcj. 

phenomena  which  gradually  led  up  to  the  conception 
of  the  substantial  and  atomic  nature  of  electricity. 
This  province  of  independent,  and  for  a  long  time 
isolated,  research  was  opened  out  by  the  coml)ined 
genius  of  PlUcker  and  Geissler.  It  was  in  tiic  year 
1857,  two  years  before  the  announcement  of  tlie  dis- 
covery   of    spectrum    analysis,    that    Pliicker,    with    the 


190 


SCIENTIFIC    THOUGHT. 


aid  of  the  now  well-known  vacuum  tubes  of  Geissler^ 
of  Bonn,  began  that  long  series  of  experiments  on  the 
discharge  of  electricity  in  rarefied  gases,  on  the  influence 
of  magnets  upon  the  course  of  the  luminous  rays,  and  on 
the  spectra  of  incandescent  gases,  which  subsequently, 
in  the  hands  of  Sir  WilHam  Crookes"  in  this  country, 
of  Hittorf,  Goldstein,  Elster  and  Geitel,  and  of  Giese  in 
Germany,  and  of  a  great  number  of  other  natural  phil- 


1  See  the  Memoir  of  Plticker  iu 
the  '  Anualen  der  Physik  und 
Chemie'  (1857);  "  Ueber  die  Ein- 
wirkung  des  Magneten  auf  die 
elektrischen  Entladungen  in  ver- 
diinnten  Gasen "  (reprinted  in 
'  Gesammelte  wissenschaftliche  Ab- 
handlungen,'  vol.  ii.  p.  475,  &c.) 
Before  Pliicker  took  up  the  investi- 
gation with  improved  means  of 
exhaustion  (later  perfected  by  the 
well-known  Sprengel  pump),  several 
French  experimentalists  —  notably 
Quet,  Gassiot,  and  Abria — had  in- 
dependently marked  the  difference 
of  the  light  near  the  positive  and 
negative  poles,  mostly  in  ignorance 
of  the  observations  recorded  by 
Faraday  in  his  early  "  Experi- 
mental Researches,"  as  far  back 
as  1838,  referring  to  the  "  dark 
discharge."  Lord  Kelvin,  in  his 
Presidential  Address  before  the 
Royal  Society  (November  1893),  re- 
fers to  the  researches  of  Faraday, 
and  to  a  long  list  of  contributions 
to  the  same  subject  contained  in  the 
Proceedings  and  Transactions  of 
the  Royal  Society.  Except  those 
of  Faraday,  they  are  all  later 
than  Pliicker's  earliest  papers. 
Lord  Kelvin  himself  saj's  :  "  Fifty 
years  ago  it  became  strongly  im- 
pressed on  my  mind  that  the  differ- 
ence of  quality  between  vitreous 
and  resinous  electricity,  ...  es- 
sentially ignored  as  it  is  in  the 
mathematical  theories  .  .  .  with 
which   I   was   then   much   occupied 


(and  in  the  whole  science  of  mag- 
netic waves  as  we  have  it  now), 
must  be  studied  if  we  are  to  learn 
anything  of  the  nature  of  electricity 
and  its  place  among  the  properties 
of  matter."  Cf.  the  words  of  Hit- 
torf (Pogg.  'Ann.,'  vol.  cxxxvi.  p.  1), 
quoted  by  Rosenberger,  '  Geschichte 
der  Physik,'  vol.  iii.  p.  778. 

-  The  experiments  and  discov- 
eries of  Sir  \V.  Crookes  on  "  Radiant 
Matter,"  beginning  with  his  paper 
in  the  '  Transactions  '  in  December 
1878,  and  continued  in  many  sub- 
sequent communications,  as  also  in 
his  Address  before  the  Brit.  Assoc. 
in  1879,  especially  his  theoretical 
explanations  based  upon  concep- 
tions taken  from  the  kinetic  theory 
of  gases,  made  a  great  sensation  and 
led  to  much  discus.sion  in  this  coun- 
try and  abroad.  The  term  Radiant 
Matter  was  adopted  from  Faraday 
(see  Rosenberger,  loc.  cit,  vol.  iii. 
p.  779).  The  corpuscular  theory 
of  light  was  not  indeed  revived  ; 
but  in  general,  after  much  criticism, 
Crookes's  views  have  to  a  large  ex- 
tent been  adopted  ;  and  if  not  the 
corpuscular  theory  of  light,  cer- 
tainly that  of  electricity  has  been 
greatly  supported  bj'  these  brilliant 
experiments.  See  J.  J.  Thomson  in 
the  Princeton  Lectures  (1898),  p. 
189  sqq.,  and  Prof.  Kaufmann's 
Address,  delivered  at  the  Hamburg 
meeting  in  September  1901  (trans- 
lated in  the  '  Electrician '  of  Nov- 
ember 8,  1901). 


ON    THE    PHYSICAL    VIKW    OF    NATUHK.  191 

osophers,  revealed  u  huge  unay  ul'  sliange  and  sUirtling 
phenomena,  whicli  have  latterly  been  brought  somewhat 
into  line  and  order  by  the  researches  of  Prof.  J.  J.  Tliom- 
son/  of  Cambridge.  A  great  many  half-forgotten  facts 
and  experiments,  wliich  did  not  fit  into  the  regular  pro- 
gramme of  electrical  science  or  practice  as  it  had  Ijeen 
elaborated  by  the  older  doctrine  of  Couloml)  and  Weber 
on  the  one  side,  or  by  the  more  modern  of  Faraday  and 
Maxwell  on  the  other,  were  collected  and  shown  to 
throw  (juite  a  new  light  on  the  processes  of  radiation 
and  electrification,  and  on  the  relations  of  the  atoms  of 
ponderable  matter  to  the  vacuum,  now  looked  upon  as 
filled  with  a  continuous  substance,  viz.,  the  ether.  The 
older  views  of  the  two  electricities,  brought  before 
the  eye  by  the  celebrated  figures  of  Lichtenberg ;  - 
many  isolated  facts  connected  with  the  electric  spark 
and  statical  electricity,  such  as  were  collected  by  Kiess 
seventy  years  ago,  or  demonstrated  in  the  hydro-electric 
machine  of  Armstrong ;   theories,  many  times  abandoned 

'   Impressed  with  tlie  importance  otiiers  as  well  as  of  their  own  by 

which  attaches  to  the  plienomena  in  Klster  and  (Jeitel,  will  be  found  in 

question  for  a  further  development  the   '  Annalen   der   Phj'sik'  (1889), 

of  tlie  theory  of  electricity  founded  i    vol.  xxxvii.  p.  315  sqq. 

by  Faraday  and  Maxwell,  Prof.  J.  J.  I        -  Whilst  the  diHerence.s  Vjetween 

Thomson,  in  his  '  Researches,'  jiub-  the  discharges  from  the  j)ositive  and 

lished  in   1893  as  a  sequel  to  Max-  negative     terminals,    after    having 

well's    great     treatise,    devoted     a  for  a  long  time  been   looked   ujion 

long   cha[)ter  to   "  The   Passage  of  ,    as   isolated  curiosities  of   electrical 

Electricity    through    Oases."       His  science,  were  being   taken   up  and 

own    celebrated     contributions     to  ;    studied     in     connection    with    the 

this    subject,    after    having    been  .   subject  here  referred  to  (see  J.  J. 

published     in     the    'Philosophical  Thomson,  '  Researches,' p.  172  577. ), 

Magazine,'  and  brought  before  the  Lord   Armstrong,  during    the   jwst 

Dover  meeting  of  tlie  British   As-  ten  years  of  his  long  and  eventful 

sociation  in  1899,  are  now  summar-  life,  carried   on  a  scries  of  e.\i>eri- 

ised   in   his  lectures  on   "The  Dis-  ;    ments  on   a   large  scjilc,  and    with 

chargeof  Electricity  through  Oases"  verj-    jjowerful    si>ccially    designed 

(1898).     A  very  interesting  earlier  apf)aratuH,  on  'Electrical  Discliarge 

summary     of     the     researches     of  in  Air  and  Water '  (ISS.'i). 


192 


SCIENTIFIC    THOUGHT. 


and  as  often  revived,  like  that  of  Prout/  on  the  con- 
stitution of  matter ;  the  fanciful  speculations  of  Zollner, 
based  upon  the  views  of  Wilhelm  Weber, —  all  these 
scattered  fragments  or  glimpses  of  knowledge  promise 
at  the  end  of  the  century  to  come  together  into  a  con- 
sistent theory  of  the  nature  of  electricity  as  an  atomi- 
cally  -  constituted  substance  which  is  associated  with 
particles  of  ponderable  matter,  or  may  even  be  the 
ultimate  constituent  of  such  matter  itself.  When  a 
large  mass  of  experimental  facts  and  many  lines  of 
special  reasoning  gradually  converge  towards  a  common 
view,  two  things  are  indispensable  in  order  to  weld  them 
into  a  consistent  whole,  viz.,  a  new  name  or  vocab- 
ulary and  an  hypothesis  as  to  the  elementary  processes 
which  will  allow  of  a  simple  construction  and  subsequent 
mathematical  calculation  of  the  more  complicated  phen- 
omena of  actual  experience.      In  the  case  before  us,  both 


^  See  the  concluding  chapter  of 
Prof.  J.  J.  Thomson's  '  Discharge  of 
Electricity  through  Gases '  (espe- 
cially p.  197,  &c.),  where,  after  dis- 
cussing Goldstein's  "ether"  theory 
and  Crookes's  "  corpuscular  "  theory 
of  the  nature  of  the  celebrated 
cathode  rays,  he,  mainly  on  the 
strength  of  his  own  and  Lenard's  ob- 
servations and  calculations,  inclines 
towards  the  latter  theory,  conclud- 
ing that  the  carriers  of  the  negative 
charges  of  electricity  "  are  small 
compared  with  ordinary  atoms  or 
molecules,  .  .  .  this  assumption 
being  consistent  with  all  we  know 
about  the  behaviour  of  these  rays." 
"It  may,"  he  continues,  "appear 
at  first  sight  a  somewhat  startling 
assumption  in  a  state  more  sub- 
divided than  the  ordinary  atom  ; 
but  a  hypothesis  which  would  in- 
volve somewhat  similar  assumptions 


— namely,  that  the  so-called  ele- 
ments are  compounds  of  some 
primordial  element — has  been  put 
forward  from  time  to  time  by" 
various  chemists.  Thus  Prout  be- 
lieved that  the  elements  were  all 
made  up  of  the  atoms  of  hydrogen, 
while  Sir  Norman  Lockyer  has  ad- 
vanced weighty  arguments  founded 
on  spectroscopic  considerations  in 
favour  of  the  composite  nature 
of  the  so-called  elements.  With 
reference  to  Front's  hypothesis, 
if  we  are  to  explain  the  cathode 
rays  as  due  to  the  motion  of  small 
bodies,  these  bodies  must  be  very 
small  compared  with  an  atom  of 
hydrogen,  so  that  on  this  view  the 
primordial  element  cannot  be  hydro- 
gen." See  also  Sir  \V.  Crookes's 
protyle  theory  referred  to,  vol.  i. 
p.  402,  note  2. 


ON    THE    PHYSICAL    VIKW    OK    NAJ  ll:i:. 


lO.i 


The  t«-nii 


requisites  were  supplied  before  the  close  of  the  ceuturv, 
Here  and  abroad,  the  term  electron,  introduced  l»y  l)r 
.Tohnstone  Stoney  ^  about  ten  years  ago,  has  been  gener-  "eieciruu. 
ally  accepted  to  denote  the  ultimate  particle  of  elec- 
tricity, tlie  atom  of  electricity — positive  or  negative — 
of  Helmholtz.  Mathematical  theories  have  been  Wfjrked 
out  independently  abroad  by  Prof.  H.  A.  Lorentz  -  of 
Leyden,  and  in  this  country  by  Dr  Joseph  Larmor"^  (;f 
Cambridge.'* 


^  See  'British  Association  Report.' 
1891,  p.  r.74,  "On  the  Cause  of 
Double  Lines  in  Spectra,"  by  G. 
Johnstone  Stone}' :  "  The  lines  of 
the  spectrum  of  a  gas  are  due  to 
some  events  which  occur  within 
the  molecules,  and  which  are  able 
to  affect  the  ether.  These  events 
may  be  Hertzian  discharges  be- 
tween molecules  that  are  differ- 
ently electrified,  or  they  may  be 
the  moving  about  of  those  irre- 
movable electric  charges,  the  sup- 
position of  which  offers  the  simplest 
explanation  of  Faraday's  law  of 
electrolysis.  .  .  .  Several  consider- 
ations suggest  that  the  source  of  the 
spectral  lines  is  to  be  sought  not 
in  the  Hertzian  discharges,  but 
in  the  carrying  about  of  the 
fixed  electric  clmrges,  which,  for 
convenience,  may  be  called  the 
electrons." 

-  Prof.  Lorentz's  principal  writ- 
ings are  the  two  memoirs,  ' '  La 
Theorie  dlectromaguetique  de 
Maxwell  et  son  Application  aux 
Corps  mouvants"  (Leyden,  1892), 
and  "  Versuch  einer  Theorie  der 
electrischen  und  optischen  Erschei- 
nungen  in  bewegten  Korpern " 
(Leyden,  189.o).  His  first  labours, 
indeed,  go  back  to  the  year  1880. 

•*  Dr  Larmor's  principal  publi- 
cations are,  "A  Dynamical  Theory  of 
the  Electric  and  Luminiferous  Med- 
ium" ('Philos.  Transactions,"  1894)  ; 

VOL.    II. 


Part  ii.,  "Theory  of  Electrons," 
1895;  Part  iii.,  "Relations  with 
Material  Media,"  1898  ;  and  his 
Adams  Prize  Essay,  "  .i-Ether  and 
Matter,  a  Development  of  the 
Dynamical  Relations  of  the  .lEther 
to  Material  Systems  on  the  Basis 
of  the  Atomic  Constitution  of 
Matter"  (Cambridge,  1900).  Dr 
Larmor's  several  shorter  pa])er8 
and  addresses,  to  which  I  shall 
refer,  are  very  hel[)ful  as  intro- 
ducing one  into  this  novel  domain 
of  science. 

■*  A  little  later  than  Lorentz  and 
Larmor,  Dr  Wiechert  of  Konigs- 
berg  began  (in  1896)  a  series  of 
publications  on  the  same  subject, 
with  the  aim  of  making  the  Max- 
welliaii  conceptions  more  definite. 
With  him,  also,  the  problem  narrows 
itself  down  to  a  reconciliation  of 
the  continuity  of  the  ether  with 
the  atomic  nature  of  ponderable 
matter,  and  of  the  electrical  charges 
attached  to  it.  His  views,  to- 
gether with  a  historicid  ana- 
lysis of  the  labours  of  his  great 
predecessors.  Coulomb,  Ampere, 
Biot  and  Savart,  Neumann,  Far- 
aday, Maxwell  (including  the 
formal  simplifications  introduced 
into  Maxwell's  scheme  by  0. 
Heaviside,  Hertz,  and  Poynting), 
Von  Helmh«)ltz,  and  H.  A.  Lorentz, 
are  very  concisely  set  out  in  a 
memorial   essay    entitled    '  Gruud- 

N 


194  SCIENTIFIC    THOUGHT. 

56.  The  theory  of  Maxwell  had  not  only  failed  to  give  a 

Difficulties  •  i>  ^  p       i 

of  Maxwell's  definite  meaning  to  the  conception  ot  a  charge  ot  eiec- 

theory.  °  .     „ 

tricity  ;  it  had  also,  in  the  general  term  "dielectric,  some- 
what obliterated  the  clear  distinction  between  empty 
space  and  space  filled  with  insulating  matter,  such  as 
air.  Empty  space,  i.e.,  space  devoid  of  matter,  was  sup- 
posed to  be  filled  with  some  continuous  substance,  the 
ether,  which  was  the  seat  or  bearer  of  electric  and  mag- 
netic actions,  the  electro-magnetic  field.  When  the  only 
clearly  known  property  of  this  ether,  the  fact  that  it 
was  the  carrier  of  radiation  or  the  luminiferous  medium, 
was  identified  with  its  electro-magnetic  nature — light 
being  conceived  to  be  an  electro-magnetic  disturbance — 
the  new  theory  had  to  attack  the  great  question  of  the 
relation  and  interaction  of  ether  and  matter,  in  which 
all  the  remaining  problems  of  physical  optics  seemed 
centred.-^     How  was  the  electro-magnetic  theory  of  light, 

lagen    der    Elektrodyiiamik,'    pub-  easily     explained      by      the      then 

lished  on   the   occasion  of  the  un-  I   current  projectile   theory  of   light 

veiling   at    Gcittingen,    in    1899,  of  '    (see  above,  chap.  vi.  p.  10,  note),  has 

the  monument  erected   in   honour  ■    cauised  great  difficulty   to  the  un- 

of  Gauss  and  Wilhelm  Weber.     It  dulatory    theory,     and     even    Sir 

is  interesting  to  see  how,  from  ap-  George  Stokes,  whose  ideas  on  the 

parently  quite  independent  begin-  subject   have    been  very  generally 

nings,  and  in  centres  far  removed  quoted  and  accepted,  would,  in  his 

from  each  other,  the  ideas  of  the  Burnett  Lectures  on  Light  (1883), 

atomic  nature   of   electricitj^    have  saj'  no  more  than  that  "  according 

almost  simultaneously  become  crys-  to  the  theory  of  undulations  .   .  . 

tallised,    and    have    united    them-  |    it  is  not  inexplicable "  (ed.  of  1887, 

selves  with  the  great  experimental  '    p.   25).     That  the  electro-dynamic 

labours    emanating    from    Pliicker  j    view  of  the  ether  should  take  up 

and  Crookes   to   give   rise,    at   the  '    the  problem  was  most  natural,  and 

end  of  the  century,  to  the  modern  !    the  discussion  of  it  is  accordingly 

theory  of  electrons.  placed  at  the  opening  of  Lorentz's 

^  One  of  the  most  important  of  memoir  of  1895  ;   the  effect  of  the 

these  problems  is  the  question    to  motion    of    the    earth    on    optical 

what  extent  the  ether  takes  part  phenomena    having    already    been 

in  the  motion  of  ponderable  matter  treated    by    him     in     1887.       Dr 

through    it.       Astronomical    aber-  Larmor    treats   very    fully   of   this 

ration,   discovered  by  Bradley,  and  subject  in   the  first  section  of  his 


ON    THE    PHYSICAL    VIEW    OF    NATURE.  195 

or  the  wave  theory  of  electricity,  to  deal  with  the  prob- 
lem  of  ether  and    matter  ?      In    this   combined   scheme       ". 
what  and  where  were  the  electric  charges  or  units  ?     'ic  ihc 

"^  charges  ? 

On  the  Continent  the  labours  of  Prof.  H.  A.  Lorentz 
of  I^yden,  and  the  almost  simultaneous  memoir  of  Von 
Hehnholtz,  approached  this  subject  from  the  side  of 
certain  optical  problems,  notably  the  vexed  question 
whether  the  luminiferous  ether  is  stagnant,  or  par- 
ticipates in  the  movements  of  ponderable  matter  through 
it,  and  the  phenomena  of  dispersion.  These  writings 
have  formed  the  beginning  of  a  long  series  of  theoretical 
and  experimental  researches,  which  are  by  no  means 
concluded.  In  this  country  we  must  chiefly  consult 
the  many  and  highly  interesting  writings  of  l)r  Larmor 
for  a  fundamental  discussion  of  the  numerous  problems 
involved.  At  the  same  time  we  find  there  a  very 
thorough  criticism,  appreciation,  and  embodiment  of  the 
many  scattered  suggestions  and  contributions  of  English 
and  Continental  thinkers.  Dr  Larmor  starts  from  a  ss. 
begnining  which  is  peculiar  to  him.  He  niids  among  iHJsiuon. 
the  older  theoretical  discussions  of  the  nature  of  the 
luminiferous  ether  one  ^   which  will  permit  of   such  an 

€6say    "  On    -Ether    and    Matter,"  etrate    a     little    deeper    into    the 

and    W.  Wien    has   quite    recently  nature    of    these    building    stones 

introduced     it    for     discussion     at  and  their  mutual  action "  {loc.  cit., 

the    "  Deutsche    Xaturforscherver-  p.  56). 

«ammlung"  (DiisseMorf,  1898,  Ber-  '  The  historical  traditions  of  Dr 

icht  i.  p.   49).     On  the  occasion  of  Larmor's    theory    seem    to    lie    in 

this  discussion,  Prof.  Lorentz  said  :  what   may   be   called    the    Dublin 

"  Ether,   ponderable   matter,    and,  school    of     mathematical     physics, 

we  may   say,    electricity,   are   the  with   the   great   names   of    Kownn 

building    stones    out    of    which   we  Hamilton    (vector    analysis),    Mac- 

•compound  the  material  woild,  and  Cullagh,  and,  in  recent  times,  the 

if  we  only   knew  whether   matter,  much   lamented   G.    F.    Fitzgerald, 

in    its    motion,    carries    the    ether  "The     form     under      which      tlie 

with  it  or  not,  a  way  would  have  atomic    electric    theory    is    intro- 

•opened   by    which    we   could    pen-  duced  in  Dr  I^armor'a  latest  es.say 


196 


SCIENTIFIC    THOUGHT. 


elaboration  as  admits  on  the  one  side  the  Maxwellian 
definitions  of  the  propagation  of  electro-magnetic  waves, 
and  on  the  other  the  definition  of  electrons  as  per- 
manent but  movable  states  of  twist  or  strain,  which 
form  the  atoms  of  electricity,  and  possibly,  in  their 
aggregate,  ponderable  matter  itself.  The  history  of 
thought  is  mainly  interested  in  this  latest  and  most 
comprehensive  "  theory  of  the  electric  and  luminiferous 
medium,"  because  it  is  almost  entirely  based  upon  that 
great  advance  in  physical  theory  which  we  owe  to 
Helmholtz  and  Lord  Kelvin,  "  the  discovery  of  the 
types  of  permanent  motion,  which  could  combine  and 
interact  with  each  other  without  losing  their  individu- 
ality, though  each  of  them  pervaded  the  whole  field." 
This  has  rendered  possible  an  entirely  new  mode  of 
treatment,^  and  at  least  made  thinkable  the  reconciliation 
of  the  two  apparently  contradictory  notions  of  modern 
physics,  the  continuity  and  uniformity  of  the  all- 
pervading  ether  and  the  discontinuity  of  the  embedded 
particles  of  matter  and  electricity.  The  history  of 
thought  also  takes  further  note  that  these  latest  and 
yet  unfinished  theories  revert,  after  the  interval  of  thirty 


originally  presented  itself  .  .  .  in  the 
course  of  an  inquiry  into  the 
competence  of  the  sether  devised 
by  MacCullagh  to  serve  for  elec- 
trical purposes  as  well  as  optical 
ones"  Cither  and  Matter,'  p.  vi.) 
"No  attempt  was  made  to  ascer- 
tain whether  MacCullagh's  plenum 
could,  in  addition  to  its  vibratory 
functions,  take  up  such  a  state  of 
permanent  strain  as  would  repre- 
sent the  electrostatic  actions  be- 
tween charged  conductors,  or  such 
state  of  motion  as  would  represent 


the  electro-dynamic  action  between 
currents.  The  first  hint  on  this 
side  of  the  matter  was  Fitzgerald's 
passing  remark  in  1880  ('  Phil. 
Trans.,'  "On  the  Electro-magnetic 
Theory  of  Light"),  that  Mac- 
Cullagh's optical  equations  '  are 
identical  with  those  of  the  elec- 
tro-dynamical theory  of  optics  de- 
veloped by  Maxwell '  "  (p.  78). 

^  See  Larmor's  Address  to  the 
British  Association  at  Bradford 
('Keport,'  p.  624). 


ON    THE    PHYSICAL    VIEW    OF    NATURE. 


10' 


years,  to  the  older  and  apparently  abandoned  views  con- 
tained in  the  writings  of  Wilhelni  Weber,  who  dealt 
with  electric  particles  and  tlieir  jictions  at  a  distance. 
The  chasm  has  been  bridged  over  by  such  theories  as 
those  of  Lorentz  and  Larmor,  and  tlie  missing  link  sup- 
plied which  prevented  Gauss  ^  from  accepting  that 
theory  when  it  was  first  comnninieated  to  him  by  its 
autlior." 


'  See  above,  p.  67,  note,  where 
Gauss's  letter  isquoted  ;  also  Laniior, 
loc.  cit.,  and  '.-Ether  and  Matter,'  pp. 
22,  72  ;  '  Philos.  Transactions,'  vol. 
clxxx\-i.  (1895),  p.  726  ;  H.  A.  Lor- 
entz, '  La  Theorie  ^lectromagndtique 
de  Maxwell,'  1892,  p.  71 :  "On  voit 
done   (^ue,  dans   la  nouvelle  forme, 
la  theorie  de  Maxwell  se  rapproche 
des    anciennes    idees.       On     pent 
meme,  apr^s   avoir   etabli  les   for- 
niules  assez  simples  .  .  .  regarder 
ces  formules  comme  exprimant  une 
loi     fondamentale     comparable      ii 
celles    de    Weber    et    de    Clausius. 
Cependant,    ces    equations    conser- 
vent     toujours     I'empreinte      des 
principes  de  Maxwell."     Further: 
Lorentz,    'Versuch  einer  Theorie,' 
&c.    (189.0),    p.    S :    "  In    general 
there  lies  in  the  assumptions  which 
1  make  in  a  certain  sense  a  return 
to  the  older  electric  theory.     The 
kernel  of  Maxwell's  vnews  is  hereby 
not   lost,   Vjut   it  cannot  be  denied 
that  with  the   assumption   of  ions 
we  are  not  very  far  removed  from 
the  electrical  particles  with  which 
one  operated  formerly."     W'iechert 
('  Orundlagen  der  Electrodynamik," 
p.  108)  expresses  himself  siniilarly. 
Lastly,  I  may  refer  to  Prof.  Kauff- 
mann's    very    interesting    Address 
delivered    at    Hamburg,     Septem- 
ber 1891,  translated  in  the  'Elec- 
trician'   (November    1901,    p.    95 
sqq.)     So  we  may  perhaps  say  that 
as  Larmor  attaclies  himself  to  the 
traditions    of    the    Dublin   school, 


Lorentz  and  other  continental 
representatives  of  the  atomic  view 
attach  themselves  to  the  school  of 
Gauss  and  Weber.  In  pro<jf  that 
Weber's  ideas  never  died  out  in  the 
Gottingen  .school,  see  Riecke's  Kloge 
of  Weber,  Gottingen,  1897,  p.  27, 
and  a  very  significant  remark  in  the 
verdict  of  the  philo30i)hical  faculty 
on  Planck's  Prize  Essay  ('Die  Erhal- 
tung  der  Energie,'  1887,  p.  10). 

"  It  would  be  unjust  to  dismiss 
this  subject,  the  overwhelming  im- 
portance of  which  becomes  evident 
if  we  glance  at  the  many  contri- 
butions which  fill  the  third  volume 
of  the  '  Rapports  presentcs  au  Con- 
grcs  International  de  Physique' 
(Paris,  1900),  without  stilting  that 
the  atomic  theory  of  electricity  nut 
only  furnishes  the  very  keystone 
which  Gauss  wa.s  looking  for  sev- 
enty years  ago,  but  that  it  has 
also  stood  the  test  of  experimental 
verification  in  the  observation  by 
Zeemann  of  the  effect  of  magnetism 
on  the  rays  of  light,  an  effect 
which  Faraday  souglit  for  in  vain 
about  the  time  when  Gauss  was  in 
search  of  the  keysUjne  of  electro- 
dynamics. A  very  concise  and 
interestitig  account  of  Zeonmnn's 
])hen(imenon  will  be  founil  in  M. 
A.  Cotton's  monograj)!!  "  Le  Phon- 
omcne  de  Zeemann"  ("' Scientia,'' 
Phys.  Mathem.,  Paris,  1899): 
"Comment  M.  Zeemann  a-t-il  eu 
I'iilde  d'etudier  avec  un  appareil 
de    polarisation    la    lumi{>re    t'misc 


198 


SCIENTIFIC    THOUGHT. 


59. 
Objections 
raised  by 
atomists. 


The  propounders  of  this  atomic  view  of  electricity 
very  naturally  look  with  little  favour  on  those  other 
theories  which,  under  the  name  of  energetics  or  pheno- 
menology, would  restrict  the  method  of  science  to  the  use 
of  only  such  quantities  and  data  as  can  he  actually  seen 
and  directly  measured,  and  which  condemn  the  introduc- 
tion of  such  useful  conceptions  as  the  atom,  the  electron, 
and  the  ether,  which  cannot  be  directly  seen  and  can 
only  be  measured  by  indirect  processes ;  and  there  is 
no  doubt  that  the  century  ends  with  a  very  emphatic 
assertion  of  the  rights  and  the  legitimacy  of  the  atomic 
and  mechanical  views  of  nature,  regarding  the  energy 
principle  as  a  regulative  but  not,  by  itself,  a  constructive 
method  of  research  and  progress ;  for,  as  Dr  Larmor  says, 
"If  a  molecular  constitution  of  matter  is  fundamental, 
energy  cannot  also  be  so."  ^  Nevertheless,  though  in 
many  ways  opposed,  the  two  views  of  nature  meet  at 
least  in  one  important  point.      Both  theories  have  been 


dans  le  champ  magu^tique  ?  Ici 
encore,  la  theorie  vint  aider  I'ex- 
perience  ;  cette  fois,  c'est  h  H.  A. 
Lorentz  que  Ton  est  redevable  du 
resultat  obtenu.  II  est  juste  de 
dire  que  d'autres  considerations, 
par  exemple  celle  de  Lord  Kelvin" 
(see  Tait,  Proc.  Royal  Soc,  Edin- 
burgh, 1875-76,  p.  118)  "auraient 
pu,  elles  aussi,  probablenaent  con- 
duire  k  cette  decouverte  de  la 
polarisation  des  raies.  Mais  en 
fait,  cette  decouverte  a  ete  faite 
grace  h,  I'intervention  de  la  theorie 
des  '  ions '  de  H.  A.  Lorentz.  Dans 
cette  theorie,  dit  M.  Zeemann,  on 
admet  qu'il  existe  dans  tons  les 
corps  de  petites  masses  electris^es, 
ou  '  ions,'  dont  les  mouvements 
constituent  tons  les  phenomenes 
electriques  ;  les  vibrations  lum- 
ineuses  seraient  des  vibrations  de 
ces   ions.      L'^tat    de    Father    est 


determine  entierement  par  la 
charge,  la  position  et  le  mouve- 
ment  de  ces  ions.  .  .  .  M.  Lorentz 
fit  remarquer  que  les  bords  des 
raies  elargies  devaient  etre  pol- 
arises. L'exp^rience  permit  a 
Zeemann  de  verifier  cette  conclu- 
sion de  Lorentz"  (p.   37). 

1  '  .Ether  and  Matter,'  p.  286  : 
"  One  efiect  of  admitting  a  mole- 
cular synthesis  of  dynamical  prin- 
ciples ...  is  to  depose  the  concep- 
tion of  energy  from  the  fundamental 
or  absolute  status  that  is  sometimes 
assigned  to  it.  .  .  .  We  can  know 
nothing  about  the  aggregate  or  total 
energy  of  the  molecules  of  a  ma- 
terial system,  except  that  its  numeri- 
cal value  is  diminished  in  a  definite 
manner  when  the  sj'stem  does  me- 
chanical work  or  loses  heat.  The 
definite  amount  of  energy  that  plays 
so  prominent  a  part  in  mechanical 


UN    THE    PHY.SH'AL    NIKW    i)l-    NATl'KK.  l'J9 

forced  to  consider  anew  tlie  ultimate  principles  of  all 
physical  reasoning,  notaljly  the  scope  and  validity  of  the 
Newtonian  laws  of  motion  and  of  the  conceptions  of 
force  and  action,  of  absolute  and  relative  motion,  as 
defined  or  implied  in  the  mechanical  scheme  which  is 
l)ased    upon    them.       Also    with    their   increasiui;   com-        «». 

"  Artllicul 

plexity     modern  dynamical  exidanations  have  undoubt-  e'^rarur  of 
edly,    to   every   impartial    observer,   acquired    a    certain  llxpuia"'' 
character  of  artificiality  which  su^^gests  the  question  to  """"■ 
what  extent  all  such  mechanical  schemes  are  an  expres- 
sion of  actual  truths  or  merely  useful  illustrations.      For 
the  pursuit  of  scientific  research  this  question  is  perhaps 
of   little    importance :   a   method    is  a  correct   one  if   it 
leads  to  correct  results  verified  by  oltservation.      Philo- 
sophically, as   bearing  upon    the   processes,  powers,  and 
limits  of  human  reasoning,  the  question  is  all-important. 
We  are  thus  led  beyond  the   province  of   scientific  into        m. 

''  ^  Tlie  philo- 

that  of  philosophic  thought.  In  future  chapters  we  shall  j^p'''^  p">*>- 
frequently  ha\e  occasion  to  note  this  tendency  of  the 
jiurely  scientific  thought  of  the  century  to  lead  uj*  to 
philosophical  problems.  Wherever  this  is  the  case  a 
history  of  scientific  thought  may  legitimately  close  one 
of  its  chapters. 

and   physical   theory  is   really  the      of   iitature   as   the   two    conditions 
mechanically  available  energy.   ...       whicli     make    generalisations     pos- 


This  energy  is  definite,  but  is  not, 
like  matter  itself,  an  entity  that  is 
conserved  in  unchanging  amount. 
...  It  may  and  usually  does  di- 
minish, in  the  course  of  gradual 
physical  changes." 

'  The  three  volumes  of  the 
'Rapports,'  ka.,  mentioned  above, 
have  been  significantly  prefaced  by 
a  discourse  of  M.  Poincard  on  the 
relations  of  exi>eriiiiental  and  ma- 
thematical physics,  in  wliiuh  he  in- 
sists ujion  tiic  unity  and  simplicity 


sible  and  useful.  With  special  ref- 
erence to  modern  electrical  theories, 
such  as  those  of  Lorentz  and  Ijarmor, 
which  he  had  aliejuly  criticised  in 
his  course  on  '  Electricit«5  ct  Op- 
tique'  (2nd  ed.,  1901,  p.  lul.  &c. ), 
he  discusses  the  i)i)ssibility  <»f  ulti- 
mate mechanical  explanations.  Of 
these,  according  to  his  view,  an 
"  infinity  "  is  always  possible.  He 
asks  what  is  the  aim  we  are  follow- 
ing— "  Ce  n'est  pas  le  mo<'anisme, 
le  vrai,  le  seul  but,  c'cit  lunito." 


200 


CHAPTER   VIIL 

ON    THE    MORPHOLOGICAL    VIEW    OF    NATURE. 

1.  The  different  aspects  of  nature  which  I  have  reviewed 
scilnces.""^  in  the  foregoing  chapters,  and  the  various  sciences  which 
have  been  elaborated  by  their  aid,  comprise  what  may 
appropriately  be  termed  the  abstract  study  of  natural 
objects  and  phenomena.  Though  all  the  methods  of 
reasoning  with  which  we  have  so  far  become  acquainted 
originated  primarily  through  observation  and  in  the  re- 
flection over  things  natural,  they  have  this  in  common, 
that  they — for  the  purpose  of  examination — remove 
their  objects  out  of  the  position  and  surroundings  which 
nature  has  assigned  to  them:  that  they  abstract  them. 
This  process  of  abstraction  is  either  literally  a  process  of 
removal  from  one  place  to  another,  from  the  great  work- 
and  store-house  of  -nature  herself,  to  the  small  workroom, 
the  laboratory  of  the  experimenter ;  or — where  such  re- 
moval is  not  possible — the  process  is  carried  on  merely  in 
the  realm  of  contemplation  :  one  or  two  special  properties 
are  noted  and  described,  whilst  a  number  of  collateral  data 
are  for  the  moment  disregarded.  In  the  former  case,  it 
is  by  a  process  of  actual  or  physical,  in  the  latter  by  one 


ON    THK    MOnPHOLOGICAL    VIEW    OF    NATURE.       201 

(if  purely  nu'iiial,  aUsLiuctitiu  lliat  (jur  .stiuly  l»cgins  aud 
is  prosecuted.  One  very  powerful  instrument  (jf  re- 
search, where  through  size  and  distance — be  they  very 
great  or  very  small — objects  of  nature  are  beyond  our 
actual  reach,  is  given  us  in  the  tliagram  and  the  model. 
There  we,  for  the  sake  of  study,  picture  or  imitate  on 
a  reduced  or  an  enlarged  scale  the  movements  of  the 
heavenly  bodies  which  are  too  large  or  of  the  atom.s 
which  are  too  small  for  our  actual  grip.  Now  and 
again  the  natural  philosopher  who  thus  uses  the 
abstract  methods  of  experiment,  registration,  and  cal- 
culation, is  forcibly  reminded  that  he  is  in  danger  of 
dealing  not  with  natural,  but  with  artificial,  things.  In- 
stances are  plentiful  where,  through  the  elal)oration  of 
fanciful  theories,  the  connection  with  the  real  world  has 
been  lost  and  scientific  reasoning  has  been  led  astray,  to 
be  recalled  to  a  more  fruitful  path  only  by  the  effort  of 
some  original  genius  living  in  immediate  connnunion 
with  the  actual  world. 

There  is,  moreover,  in  addition  to  the  aspect  of  con-        2. 

Convenience 

venience,  one  very    powerful    inducement   for    scientific  »»<!  useful- 

■^       '■  iies.s  of  the 

workers  to  persevere  in  their  process  of  abstraction,  in  ]^^^^"l„ 
the  study  of  such  things  and  phenomena  as  can  be 
handled  in  the  laboratory  and  the  workshop,  and  studied 
by  diagram  and  by  model.  This  is  the  practical  useful- 
ness of  such  researches  in  the  arts  and  industries.  In 
these  we  do  actually  abstract  the  possessions  of  nature 
from  their  proper  hiding-places ;  we  drag  the  minerals 
from  the  bowels  of  the  earth ;  we  cut  up  the  timber 
of  exotic  growth  into  artificial  fragments ;  we  break 
up    that    natural    eciuilibrium    in    which    eleclrieal    and 


202  SCIENTIFIC    THOUGHT. 

chemical  agencies  have,  for  thousands  of  years,  evaded 
our  discovery  and  our  regard.  Having  done  so,  we  create 
an  artificial  world  of  our  own  making  which  ministers 
to  our  wants,  comforts,  pleasures,  and  supplies  that 
most  inestimable  of  all  commodities  of  civilisation, 
varied  and  stimulating  work  for  ready  hands  and  active 
brains.  The  wants  and  creations  of  artificial  life  have 
thus  proved  the  greatest  incentives  to  that  abstract  and 
artificial  treatment  of  natural  objects  and  processes  for 
which  the  chemical  and  electrical  laboratories  with  the 
calculating  room  of  the  mathematician  on  the  one  side, 
and  the  workshop  and  factory  on  the  other,  have  in  the 
course  of  the  century  become  so  renowned.  All  this 
great  activity  is — as  I  have  abundantly  shown — more 
and  more  governed  by  the  scientific,  the  exact,  or  the 
mathematical  spirit. 
3.  There  is,  however,  in   the  human  mind  an  opposite 

Interest 

opposed  to    interest  which  fortunately  counteracts  to  a  considerable 

the  spirit  of 

abstraction,  extcut  the  onc-sidcd  working  of  the  spirit  of  abstraction 
in  science  and  the  growing  tendency  towards  artificial- 
ity in  our  practical  life.  This  is  the  genuine  love  of 
nature,  the  consciousness  that  we  lose  all  power  if,  to 
any  great  extent,  we  sever  or  weaken  that  connection 
which  ties  us  to  the  world  as  it  is — to  things  real  and 
natural :  it  finds-  its  expression  in  the  ancient  legend 
of  the  mighty  giant  who  derived  all  his  strength  from 
his  mother  earth  and  collapsed  if  severed  from  her.  In 
its  extreme  and  purest  form  this  interest  probably  lies 
at  the  root  of  all  poetry  and  all  art,  and  it  accordingly 
governs  a  great  part  of  the  literature  and  thought  of  the 
century.      It   will  occupy   us  later  on  in  our  historical 


ON    THE    MORPHOLOGICAL    VIKW    OV    NATUltE.      203 

survey.  At  present  it  interests  us  only  as  far  as  it 
asserts  itself  also  in  science.  In  the  study  of  natural 
objects  we  meet  with  a  class  of  students  who  are  at- 
tracted by  things  as  they  are :  not  so  much  by  those 
which  we  artificially  prepare  in  (jur  laboratories,  as  by 
the  infinite  variety  of  real  forms ;  not  so  much  ]jy  the 
geometrical  types  which  allow  us  to  bring  them  together 
under  some  abstract  formula,  as  Ijy  the  apparent  disorder 
;ind  di\-ine  confusion  in  which  real  things  are  scattered 
about  in  the  heavens  antl  on  our  globe.  It  is  not  the 
general  equation  which  in  its  complete  solution  contains 
all  real  and  many  unreal  instances  merely  as  special 
cases  that  interests  them,  Imt  the  individual  examples 
themselves.  The  general  laws  of  motion  admit  of  an 
infinity  of  special  cases  which  may  never  occur  in  nature  ; 
organic  chemistry  adds  daily  to  the  already  enormous 
array  of  compounds  which  do  not  present  themselves  in 
living  organisms.  Clearly,  besides  the  abstract  sciences, 
which  profess  t(^  introduce  us  to  the  general  relations 
or  laws  which  govern  everything  that  is  or  can  be  real, 
there  must  be  those  sciences  which  study  the  actually 
existing  forms  as  distinguished  from  the  possible  ones, 
the  "  here  "  and  "  there,"  the  "  where  "  and  "  how,"  of 
tilings  and  processes ;  which  look  upon  real  things  not 
as  examples  of  the  general  and  universal,  but  as  alone 
possessed  of  that  mysterious  something  which  dis- 
tinguishes the  real  and  actual  from  the  ]iossible  and 
artificial.       These    sciences     are     the    trul}-    descriptive         i. 

Tlic  dc«crip- 

sciences,  in  opposition   to  the  abstract  ones.     They  are  tivescieucos. 
indeed  older  than  the  abstract  sciences,  and  they  have, 
in  the  course  of  the  period  under  re\iow  in   this  work, 


204  SCIENTIFIC    THOUGHT. 

made  quite  as  much  progress  as  the  purely  abstract 
sciences.  In  a  manner,  though  perhaps  hardly  as 
powerful  in  their  influence  on  practical  pursuits,  they 
are  more  popular ;  they  occupy  a  larger  number  of  stu- 
dents ;  and  inasmuch  as  they  also  comprise  the  study  of 
man  himself,  they  have  a  very  profound  influence  on 
our  latent  opinions,  interests,  and  beliefs — i.e.,  on  our 
inner  life.  It  is  the  object  of  this  and  some  of  the 
following  chapters  to  trace  concisely  the  altered  ways 
and  means  by  which,  in  the  course  of  the  last  hundred 
years,  the  study  of  the  actual  things  and  events  of  nature 
has  been  prosecuted.  For  those  who  wrote  the  history 
of  the  descriptive  sciences  in  the  middle  of  our  century, 
the  arrangement  of  this  vast  subject  presented  little 
difficulty.  It  had  been  in  the  main  accomplished  by 
the  great  naturalists  who,  during  the  seventeenth  and 
eighteenth  centuries,  laboured  to  bring  the  large  and 
ever  increasing  number  of  natural  objects  into  some 
supposed  system  and  some  professed  order,  to  enumer- 
ate them  in  catalogues  or  marshal  them  in  museums. 
The  familiar  division  of  natural  things  into  animals, 
vegetables,  and  minerals  had  received  a  general  sanction. 
Separate  sciences,  with  separate  chairs  at  the  univer- 
sities, which  still  survive,  attended  to  the  separate 
treatment  of  these  subjects.  One  of  the  greatest 
changes  which  the  present  age  has  witnessed  has  been 
5.         the  breaking   down   of    the   old    landmarks  and   of   the 

The  break- 

ing  down  of  stereotyped  divisions  which  existed  in  the  beo-inning  and 

old  land-  "^  ^  o  o 

°^'^^-         all  throug;li  the  first  half  of  the  centurv.-^ 


^  This  change  has  also  very  much 
lessened  the  interest  with  which 
we  now  regard   the   solution   of   a 


times,  was  much  discussed— the 
classification  of  the  sciences.  It 
will  be  seen  that  of  the  many  prin- 


problem   which,    down    to    recent       ciples  of  division  which  have  been 


ON    THE    MORPHOLOGICAL    VIKW    OF    NATUKE.      205 


It'  we  try  to  specify  a  little  iiiuiv  closely  tiie  agencies 
iuul  interests  that  were  at  work  in  bringing  about  this 
\('ry  iiuirked  change,  which,  like  every  change  of  the 
kind,  has  been  retiected  1)\  the  altered  vocaVmlary  of 
our  languages,  we  come  upon   two  distinct  influences — 


adopted,  the  present  wurk  uiily  re- 
tains that  one  principle  which,  in 
>iime  form  or  other,  appears  in 
rvery  attempt  towards  classitica- 
lion — the  difference  between  the 
abstract  and  the  concrete  or  actual. 
The  two  original  philosophical  sys- 
tems which  France  and  England 
in  the  course  of  the  century 
have  produced,  the  positivist  phil- 
osophy of  Conite  and  the  j)hil- 
■  i-.)|ihy  of  evolution  of  Herbert 
Spencer,  have  both  dealt  elabor- 
ately with  the  problem  of  the 
1  l,i"iticatiou  of  the  sciences.  In 
ilii^  they  betray  their  descent  from 
the  philosophy  of  Bacon  and  their 
[Tactical  tendencies.  It  is  mainly 
in  the  interests  of  teaching  that 
the  division  of  the  sciences  is  of 
importance ;  and  so  here  it  has 
proved  to  be  indispenfcable,  but 
also,  not  unfrequently,  narrowing 
:uul  harmful.  German  philoso- 
phers, who  have  generally  been 
more  influenced  by  the  traditions 
ipf  Descartes,  Spinoza,  and  Leibniz, 
have  attached  less  importance  to 
the  rigid  divisions.  The  result 
has  been  that  in  Germany,  more 
tl\an  in  any  other  country,  those 
modern  sciences  have  grown  up 
which  cultivate  the  borderland 
tliat  separates  the  existing  well- 
niarkcd  jirovinces  whicii  arc;  aititi- 
ijally  kept  up  by  the  older  chairs 
at  the  universities.  Examples  of 
tliis  are  the  new  sciences  of  jdiysio- 
I'l'^'inal  psychology  and  of  physical 
rlicinistry,  both  brilliantly  and  for 
tlie  tirst  time  rejiresented  at  the 
university  of  Leipzig.  Tiie  two 
U'reat  conceptions,  however,  which 
have  ])robably  done  more  than  any 
'ithers  to  break  down  the  old  con- 
\entional     landmarks      that     kept 


the  .sciences  asunder,  the  concep- 
tion of  energj'  and  the  idea  of  de- 
scent, were  Hrst  prominently  )>ut 
forward  in  this  country.  The 
j  classical  treatise  on  the  division  of 
j  the  sciences  in  the  widest  sen.se  is 
'  the  '  De  Augmentis  Scientiarum  ' 
of  Lord  Bacon.  An  important  and 
original  work  on  the  subject  is 
Andre  Marie  Ampere's  '  Essai  sur  la 
Philosophie  des  Sciences,  ou  Ex- 
position analj'titjue  d'une  ChussiHca- 
tion  naturelle  de  toutes  les  Con- 
naissances  humaines'  (1834).  An 
analysis  of  the  book  is  given  in 
Whewell's  '  I'hilosophy  of  the  In- 
ductive Sciences,'  vol.  ii.,  Book  12. 
Ampere's  classification,  on  the 
model  of  that  in  bot;iny,  is  sym- 
metrical and  dichotomous.  Aug. 
Comte's  classification,  contained 
in  the  second  "  Leoon "  of  the 
'  Cours  de  Philosoj)hie  positive ' 
(1830,  vol.  i.),  is  termed  by  its 
author  "une  echelle  "  or"une  hier- 
archie  encyclop(5dique."  Mr  Her- 
bert Spencer,  in  an  essaj-  '  Ou  the 
Genesis  of  Science  '  (1854),  repub- 
lished with  additions  in  the  third 
volume  of  his  '  Essays  '  (1874),  criti- 
cised Comte's  attempt  to  classify  the 
sciences  "serially."'  He  more  than 
any  other  thinker  has  assisted  in 
breaking  down  the  older  idea,  which 
was  very  prominent  in  many  classi- 
fications of  the  great  French  natur- 
alists, the  idea  of  the  subordin- 
ation of  things  in  nature,  of  the 
"  (5chelle  des  otres,"  and  tiie  corres- 
ponding conception  of  an  hierarciiy 
of  the  sciences.  In  the  place  of 
this  serial  arrangement,  a  genea- 
logical arrangement,  uutler  the 
specific  term  of  evolution,  wiv*  in- 
troduced, and  the  sciences  were 
co-ordinated     according    to    their 


206  SCIENTIFIC    THOUGHT. 

one  of  which  has  tended  enormously  to  broaden  our 
view  of  natural  objects  and  events ;  the  other  to  narrow 
it  down  and  make  it  more  definite,  scientifically  ac- 
curate, and  precise.  The  former  has  tended  to  sweep 
away  the  older  landmarks  and  di\isions  as  inadequate 
to  afford  us  a  correct  \i.ew  of  nature ;  the  latter  has 
tended  to  create  new  di\'isions  and  definitions,  more  in 
harmony  with  the  lines  on  which  the  abstract  sciences 
of  physics  and  chemistry  have  been  developed,  and  has 
thus  brought  the  actual  objects  and  events  of  nature 
more  within  the  grasp  of  those  exact  and  mathematical 
6.        methods  which  those  sciences  have  perfected.    The  former 

The  spirit  of  .     ,  .         ,  i     i  ^  i_ 

exploration,  has  bccu  camcd  on  in  the  vast  workshop  or  nature  her- 
self by  those  daring  and  far-seeing  travellers  who,  with 
Alexander  von  Humboldt  at  theu-  head,  have  attempted 
to  gain  a  \iew  of  natui'e  on  an  extensive  scale.  For  the 
sake  of  the  increase  of  natural  knowledge  alone,  they 
visited  distant  countries  where  the  elemental  forces  of 
nature,  undisturbed  by  the  inroads  of  ci\'ilisation,  have 
battled  and  co-operated  to  produce  the  magnificent  floras 
and  faunas  of  the  tropics,  or  where,  as  in  Siberia,  the 
eternal  cold  has  preserved  intact  the  remains  of  bygone 
periods.  Equipped  with  the  instruments  and  methods  of 
modern  science,  they  recognised  the  necessity  of  studying 
the  actual  formation  and  stratification  of  rocks,  the  geo- 
graphical distribution  of  organic  life  on  the  siu'face  of  the 

genesis,   the  three   great   divisions  |    tinctions   which   I   have   adopted ; 

being   the    abstract,    abstract -con-  '    and  I  remind  them  again    that   I 

Crete,  and  concrete  sciences.      My  \    am  not  writing  a  history  of  Science 

readers      will      readily      see      the  j    but     of     Thought,     and    that    all 

similarities     and     the     differences  divisions  of  this  great  subject  are, 

which    exist    between    this    classi-  more  or  less,  arbitrary, 
fication  and  the  more  general  dis- 


ox    THE    MORPHOLOGICAL    VIEW    OF    NATrUE.      207 

globe,  i>v  in  tlie  depths  (if  the  ocean  ;  of  visiting  the  real 
dwelling-places,  the  habitat  of  living  beingH :  thus  coun- 
teracting and  enlarging  the  narrow  and  pedantic  views 
which  the  older,  purely  systematic,  and  lifeless  treatment 
of  natural  objects  was  in  danger  of  fostering.  We  know 
how  the  germs  of  two  of  the  greatest  generalisations  of 
science  were  laid  iu  llie  minds  of  Mayer  and  of  Darwin 
during  their  visits  to  distant  countries,  and  how  fertile 
in  natural  knowledge  of  all  kinds  have  been  the  voyage 
of  the  Challenger  and  many  other  similar  expeditions, 
and  with  what  interest  and  curiosity  scientific  and 
popular  audiences  listen  to  the  narrative  of  such  daring 
explorers  as  Fridjof  Nansen. 

The  other  and  much  more  concentrated  intluence, 
which  from  the  opposite  side  co-operated  with  the  labours 
of  the  great  explorers  in  remodelling  the  descriptive 
sciences  and  infusing  new  life  and  vigour  into  them, 
has  been  not  less  marked.  There  has  always  existed 
one  great  interest,  in  which  nearly  all  the  descriptive 
branches  of  natural  knowledge  have  found  a  common 
rallying   ground    and    a    uniting    purpose — namelv,    the        ". 

"  The  medical 

art  of  healing,  the  alleviation  of  human  suflering  and  i"ierest. 
the  curing  of  disease.  During  long  ages,  when  the  purely 
scientific  interest  was  almost  dead,  physical  and  chemical 
research  was  created  or  kept  alive  by  the  physician,  the 
alchemist,  and  the  apothecary ;  medical  works  like  those 
of  Celsus  and  Galenus  in  antiquity  ^  have  lieen  the  ency- 

'  It  may  also  be  pointed  out  l  the  medical  art  of  his  father 
that  Aristotle  was  descended  from  Nicomachus,  wlio  was  the  medical 
a  family  of  doctors,   that — accord-    1    adviser    and    friend    of    the    Mace- 


ing  to  Zeller  (' Philosophie  der 
Griechen,'  vol.  ii. ,  part  2)  —  the 
assumption     is    warranted     "  that 


donian  king,  Amyutais,  ha<l  a 
prominent  influence  on  tlie  mental 
development  of  his  son." 


208  SCIENTIFIC    THOUGHT. 

clopedias  of  the  existing  knowledge  of  nature,  and  celeb- 
rities like  Boerhaave,  Linneeus,  and  Haller  in  more  modern 
times  have  been  the  living  centres  of  all  the  natural 
sciences.  The  same  uniting  bond  has  not  been  want- 
ing in  our  century,  when  it  has  again,  as  many  times 
before,  manifested  its  powerful  influence,  has  brought 
together  researches  which  were  on  the  point  of  fall- 
ing asunder,  and  infused  new  life  and  interest  into  the 
driest  of  studies.  As  I  have  had  occasion  to  remark 
above,  the  modern  school  of  medicine  originated  in  the 
attempt — begun  by  Lavoisier  in  France,  but  carried  out 
on  the  largest  scale  in  the  chemical  and  physiological 
laboratories  of  Germany — of  making  the  new  discoveries 
8.  in  physical  science  and  chemistry  fruitful  for  medical 
science        purposcs  and  the  treatment  of  pathological  cases.     The 

applied  to 

medicine,  discovcry  of  galvauism  gave  probably  the  earliest  im- 
petus, and  was,  to  the  discredit  of  an  exacter  treatment, 
largely  misused  in  the  earlier  part  of  the  century,  till 
Du  Bois  Eeymond,  in  the  middle  of  the  period,  based  his 
elaborate  researches  on  more  correct  methods,  and  created 
nearly  all  the  knowledge  we  now  possess  of  the  electrical 
currents  in  the  nervous  system.  Somewhat  earlier,  Liebig 
led  the  study  of  the  phenomena  of  animal  heat  and  of 
the  food  relations  of  the  animal  and  vegetable  kingdom ; 
the  brothers  Weber  had  introduced  dynamics  into  the 
theory  of  the  motion  of  the  heart  and  the  limbs ;  whilst 
Johannes  Miiller  and  his  numerous  school  about  the  same 
time  laid  the  foundations  of  physiological  and  pathological 
acoustics  and  optics.  Quite  independently  of  these  appli- 
cations of  the  mechanical  and  physical  sciences,  which  led 
some  over-hastily  to  imagine  that  in  the  doctrine  of  the 


ON    THi:    MoltPHOLOGICAL    VIEW    OF    NATLKK.      209 

organism  as  a  pure  machine  lay  an  answer  to  the  great 
problems    of    life    and    consciousness,   Tlieodor    Schwann         9 

Schwanu. 

proclaimed  about  1840,  on  the  basis  of  minute  micro- 
scopic observation,  the  essential  identity  of  animal 
and  vegetable — i.e.,  of  all  living — structure,  thus  taking 
probably  the  greatest  ste])  in  uniting  researches  which 
had  so  far  been  carried  uu  in  a  tUsconnected  fashi(jn. 
Here  is  the  beginning  of  the  modern  theory  oi  the 
organic  cell — of  cellular  pathology,  antl  the  actual  in- 
auguration of  modern  biology.  Twenty  years  later,  the 
appearance  of  Darwin's  '  Origin  of  Species '  urged  still  10 
further  the  study  of  the  whole  of  organic  life  from  a 
comprehensive  point  of  view.  In  addition  it  led  to  a 
closer  union  with  the  sciences  of  inorganic  nature,  an 
appeal  being  now  made  to  palteontological  and  geological 
records  in  proof  of  the  gradual  development  of  all  forms 
of  living  as  well  as  of  inanimate  reality.  The  studies 
of  the  geologist,  which  up  to  then  had  l)een  prosecuted 
on  independent  lines,  joined  hands  not  only  with  those 
of  the  zoologist  and  botanist,  but  likewise  with  the 
theory  of  cosmological  genesis  of  the  planetary  system, 
as  proclaimed  at  the  end  of  the  former  century  by 
Laplace  in  his  '  Exposition  du  Systeme  du  Monde,'  and 
fifty  years  earlier  by  Kant  in  his  'Natural  History 
of  the  Heavens.'  If  in  the  course  of  our  century, 
through  the  combined  influence  of  travel  on  the  one  side 
and  medicine  on  the  other,  the  history  of  natural  objects 
has  been  united  in  the  larger  conception  of  bicjlogy,  this 
itself  at  the  close  of  the  century  promises  to  be  united 
with  geology  and  astro-physics  (a  science  almost  entirely 
founded  on  the  invention  and  on  the  nidations  of  the 

VOL.   II.  " 


210 


SCIENTIFIC    THOUGHT. 


11. 
Herbert 
Spencer. 


12. 

Whewell's 

divisions 

abandoned. 


spectroscope),  into  the  still  wider  conception  of  a  general 
science  of  evolution,  as  enunciated  already  forty  years 
ago  in  the  writings  of  Herbert  Spencer,  and  in  a  more 
shadowy  form  by  Herder  in  the  eighteenth  century,  and 
by  Leibniz  in  the  seventeenth. 

Seeing,  then,  that  the  treatment  of  the  descriptive 
sciences  of  nature  has  been  so  radically  changed  during 
the  course  of  the  century,  and  that  the  change  has  been 
accompanied  by  a  complete  revolution  in  our  modes  of 
thinking  and  reasoning  on  these  subjects,  the  historian  of 
Thought  cannot  be  content  with  merely  chronicling  the 
progress  of  the  methods  in  use  in  the  separate  sciences, 
such  as  mineralogy,  geology,  botany,  and  zoology,  even 
with  the  addition  of  the  more  recent  sciences  of  pale- 
ontology, physiology,  and  comparative  anatomy.  He 
might  in  doing  so  fairly  grasp  the  history  of  the  descrip- 
tive sciences  up  to  the  year  1850.  It  is  exactly  in  this 
manner  that  Whewell,  in  his  '  History  of  the  Inductive 
Sciences,'  treated  this  part  of  his  subject.  Beyond  that 
period  the  old  landmarks  designated  by  those  names 
have  disappeared  or  become  of  secondary  importance. 
On  the  other  side,  whilst  a  history  of  Evolution  in 
Science  might  seize  on  the  great  characteristic  feature 
of  the  more  modern  research  which  belongs  to  the 
second  half  of  the  century,  it  would  hardly  suffice  to 
sum  up  the  leading  ideas  of  the  descriptive  branches 
of  science  as  they  were  carried  on  on  independent 
lines  during  the  earlier  years  of  our  period.  Evolu- 
tion had  then  no  definite  meaning,  and  Biology  was 
a  disregarded  term.  We  must  thus  look  out  for  some 
more  general  aspects  which  belong  alike  to  the  earlier 


ON    THE    MORPHOLOGICAL    VIEW    OF    NATURE.      211 

and  later  perioils,  and  which   will   enable  us  to  see   how 
that  great  change  has  gradually  come  al)Out. 

All  studies  that  deal  witli  the  actual  things  and  events 
by  which,  on  a  large  and  on  a  minute  scale,  we  are  sur- 
rounded in  nature,  are  comprised  under  the  term  Natural 
History.  In  opposition  to  Natural  Philosophy,  which 
comprises  our  abstract  knowledge  of  the  possible  forms  of 
motion  and  the  possible  combinations  of  the  elements  into 
which  we  have  so  far  been  able  to  decompose  matter, 
Natural  History  deals  only  with  such  forms  and  combina- 
tions as  actually  exist  around  us,  only  with  such  processes 
of  change  as  actually  take  place  in  nature.  Some  of  these 
forms  and  changes  we  may  be  able  to  collect  in  our 
museums  or  imitate  in  our  laboratories,  but  the  forms  of 
nature  cannot  in  this  way  be  exhausted,  nor  her  pro- 
cesses understood.  Her  forms  or  things  do  not  exist  in 
isolation,  but  always  in  a  certain  environment,  having  a 
definite  plan,  a  position  in  time  and  space.  These  sur- 
rounding features  are  as  important  as  the  things  them- 
selves. Besides  this,  the  processes  of  nature  draw  on 
the  great  factor  of  time  with  a  much  more  liberal  hand 
than  we  can  permit  ourselves  to  do.      Nevertheless,  as  in        13. 

Divisions  of 

the  abstract  sciences  we  deal  with  things  at  rest  and  with  uatunu 

^  history. 

things  in  motion,  so  we  can  appropriately  divide  our 
study  of  the  real  and  the  actual  into  the  attempt  to 
give  some  accoimt  of  the  forms  and  things  which 
actually  exist  and  continually  recur,  and  the  study 
(jf  the  changes  which  things  undergo.  In  abstract 
science  the  terms  statics  and  dynamics,  the  doctrines 
of  rest  and  nf  uiotioii,  have  been  generally  introduced, 
to  distinguish   tiie  two   great  aims  of  study  ;   some  cor- 


212 


SCIENTIFIC    THOUGHT. 


responding  tenns  mar  appropriatelv  define  the  twofold 
interest  which  we  take  in  natural  objects.  The  term 
morphology^    was   introduced   early  in   the   century  by 


^  The  term  morphologr  was  in- 
troduced bv  Goethe  to  define  a  series 
of  researches  and  studies  to  which 
he  was  led  by  his  equal  interest  in 
art.  nature,  and  human  society. 
Returning  from  Italy,  which  he  de- 
scribes as  ■■'  rich  in  forms,"  to  Ger- 
many, which  he  tenns  in  contrast 
■•  gestaltlos,"  he  reports  that  three 
distinct  problems  had  presented 
themselvte.  "  Wie  die  b^iinstigte 
griechische  Nation  veriahren  um  die 
ht-ohste  Kunst  im  eigenen  National- 
kreise  zu  entwickeln.  .  .  .  THe  die 
Natur  gesetzlich  zu  Werke  gehe, 
um  lebendiges  Gebild,  als  Muster 
yiffi  kiinstlichen,  hervorzubringen. 
.  .  .  Wie  aus  dem  Zusammen- 
trefien  ron  Nothwendigkeit  und 
XNillktir,  von  Antrieb  und  Wollen, 
von  Bewegung  und  Widerstand  ein 
drittes  hervorgeht  .  .  .  die  mensch- 
liche  Gesellschaft."  For  the  pur- 
pose of  finding  an  answer  to  the 
second  of  thee  questions,  Goethe 
collected  and  observed,  read  and 
speculated,  and  formed  the  con- 
c-eprion  of  a  general  science  of  or- 
ganised beings,  termed  morpholt^y, 
which  was  not  to  treat  merely  of 
external  figure,  but  to  comprise  also 
physiology  and  the  study  of  develop- 
ment. It  is  the  first  great  attempt 
to  think  of  nature  as  a  whole,  and 
to  break  down  the  rigid  lines  which 
divided  the  several  natural  sciences. 
He  thus  inaugurated  the  modem 
view  of  nature  by  introducing  the 
general  science  of  morphology.  His 
first  literary  attempt  in  this  di- 
rection was  the  now  celebrated 
pamphlet  on  the  'Metamorphosis 
of  Plants,'  in  which  he  represents 
the  leaf  as  the  typical  formation 
from  which  the  other  parts  of  the 
plant  can  be  derived.  Whether 
this  derivation  is  a  real  proc-ess  in 


the  sense  of  modem  evolution,  or  a 
merely  ideal  one  in  the  sense  of  the 
earlier  archetypal  view,  Goethe  does 
not  clearly  say.  This  uncertainty 
Goethe  shares  with  the  whole  school 
of  the  •'Xatxirphilosophie, "  as  Julius 
Sachs  points  out  in  his  '  History  of 
Botsmy'  ^German  edition,  1S75, 
p.  170).  This  is  not  the  point  to 
which  I  want  to  draw  attention  at 
present.  More  important  is  the 
remark  which  Goethe  makes  in  the 
further  historical  accoiint  of  the 
gradual  development  of  his  morpho- 
logical ideas.  Wolf,  the  philol<^ist, 
pointed  out  to  him  that  his  own 
namesake.  Casp-ar  Friedrich  Wolf, 
had  anticipated  Goethe  in  the  at- 
tempt to  demonstrate  the  funda- 
mental identity  of  the  different 
parts  of  a  plant.  In  the  sequel  of 
his  most  appreciative  analysis  of 
Wolfs  expositions,  Goethe  charac- 
teristically notes  that  Wolf  does 
not  include  in  his  conception  the 
*'  metamorphosis  of  animals,"  or  in- 
troduces it  only  as  something  en- 
tirely difiierent.  That  Goethe's  idea 
of  morpholep  as  a  general  science 
of  the  forms  and  change  of  forms  in 
nature  is  applicable  likewise  to  in- 
animate forms — to  geological,  geo- 
grajdiical,  and  many  other  forma- 
tions, nay.  even  to  rigid  things  like 
crystals,  and  to  such  unstable  for- 
maticms  as  the  pa^ ts  of  speech  and 
language — has  in  the  course  of  the 
century  been  abundantly  recog- 
nised. It  is  known  how.  guided  by 
the  same  general  interest,  Goethe 
studied  the  formations  and  trans- 
formations of  animals,  rocks,  and 
clouds,  though,  according  to  Zittel 
( •  Gesch.  der  Geologie,'  1 599,  p.  275\ 
C.  F.  Xaumann  first  used  the  ex- 
pression, "  morphology  of  the  svu-- 
f ace  of  the  earth."  in  1 S50.  Goethe's 


ox  THE  MORPHOLOGICAL  VIEW  UF  NATURE.   213 


one  who  bjved  aliuve  all  things  to  watch  the  works  uf 
nature  in  their  proper  abodes — who  combined  the  poeti- 
cal with  the  scientific  interest, — by  Goethe.  The  ttirm 
genesis  ^  has  long  been  employed  to  describe  the  pro- 
cesses by  which  the  actual  world  has  come  to  l>e  wiiat 
it  is.  To  the  statical  and  dynamical  aspects  of  the 
abstract  sciences  correspond  accordingly  to  some  extent 
the  morphological  and  genetic  aspects  of  the  natural  u. 
sciences.  To  some  extent  only,  for  in  nature,  where  !i'"iKtnetic«. 
everything  is  subject  to  continual  liow,  we  ne\ev  come 
upon  a  realisation  of  absolute  rest,  a  pure  form,  a 
rigid  type.  Eather  would  I  put  it  in  this  way  :  In  tlie 
perpetual  variety  of  change  the  morphological  \'iew 
tries  to  define  those  recurring  forms  or  types  which 
present  themselves  again  and  again,  towards  which  all 
changes  seem  to  revert ;  thus  l)ringing  some  order  into 


morphological  writings  have  been 
for  the  first  time  completely  edited 
and  annotated  in  the  three  volumes 
(6  to  8)  of  the  second  division  of 
his  works  now  being  published  by 
the  Goethe-(!esellschaft  at  Weimar. 
The  authority  whom  I  approach 
nearest  in  the  use  I  make  of  the  term 
morphology  is  probably  Haeckel. 
See  the  first  book  of  his  '  Generelle 
Morphologieder  Organischen  Wesen ' 
(1866,  vol.  i.  pp.  1-108). 

'  Goethe's  morphological  studies 
were  equally  directed  towards  the 
formation  and  the  transformation 
of  living  things  :  morphology  was 
to  him  the  science  of  "  Bilduug 
uiid  Umbildung."  In  the  course  of 
the  century  the  terms  morphology 
and  morphological  school  have  come 
to  mean  more  and  more  that  com- 
plex of  comparative  researches 
which  historically  prepared  the 
genetic,  developmental,  or  evolu- 
tionist school  of  thought,  but  which 


were  mainly  dominated  by  the  con- 
ception of  fixed  types  and  forms, 
and,  though  searching  for  the  laws 
of  modification,  did  not  rise  to  a 
clear  enunciation  of  a  theory  of 
evolution  and  descent.  Goethe  him- 
self hovered  all  his  life  long  between 
an  artistic  predilection  for  the  per- 
fect form  or  model  and  a  deeper 
philosophical  conviction  of  the  con- 
tinual flow  of  things.  See  a  remark 
of  his  (' Werke,'  XL,  vol.  vi.  p.  304) 
in  an  aphorism  on  "  genetic  treat- 
ment "  :  "  Erst  bin  ich  geneigt 
mir  gewisse  Stufen  zu  denken  :  weil 
aber  die  Nalur  keinen  Sprung 
macht,  bin  ich  zuletztgenothigt  mir 
die  Folge  einer  ununterbrochenen 
Thiitigkeit  als  ein  Ganzes  anzu- 
schauen,  indem  ich  das  p]inzelne 
aufhebe,  ohne  deu  Eindruck  zu 
zerstoren."  See  also  a  remark  on 
Goethe's  undefined  position  in 
Cams,  '  Geschichte  der  Zoologie ' 
(1872),  p.  r,90. 


214 


SCIENTIFIC    THOUGHT. 


what  would  otherwise  be  disorder  and  confusion.  On 
the  other  side,  the  genetic  view  deals  with  the  tran- 
sition from  one  form  to  another  in  the  course  of  time ; 
takes  more  interest  in  movement  and  in  the  process 
and  function ;  and  seeks  for  their  probable  laws  and 
regularities.  Without  wishing  to  limit  these  remarks 
to  merely  organic  or  living  things,  the  difference  be- 
tween the  morphological  and  genetic  views  can  be 
brought  home  to  the  mind  by  referring  to  the  different 
objects  of  anatomy  and  physiology.^  This  twofold  and 
very  general  aim — the  desire  to  know  what  is,  and  how 
it  has  come  to  be — has  existed  at  all  times,  though  fre- 
quently obscured  by  artificial  and  temporary  restrictions. 
From  this  point  of  view  I  propose  to  survey  the  mental 
attitude  of  the  century  towards  the  real  things  and 
events  of  nature,  as  distinguished  from  the  artificial  or 
mathematical  forms  and  processes  of  our  studies  and  our 
laboratories,  our  calculating  and  measuring  rooms.     The 


^  Genetic  theories  have  every- 
where been  prepared  and  ushered 
in  by  morphological  studies.  So  in 
Goethe's  time ;  so  later  on,  after 
Darwin  had  given  a  definite  law 
of  descent,  and  Herbert  Spencer 
had  fixed  the  vocabulary  and  ideas 
of  evolution,  this  relation  is  mani- 
fested by  two  great  works,  the 
'  Generelle  Morphologie  der  Organ- 
ischen  Wesen,'  by  Ernst  Haeckel 
in  Germany  (1866),  and  Francis 
M.  Balfour's  '  Elements  of  Embry- 
ology '  (1874)  in  England.  It  is 
characteristic  that  Prof.  Haeckel, 
in  the  further  development  of  his 
literary  activity,  dropped  the  term 
morphology,  and  published  the  de- 
sired new  editions  of  his  great  work 
under  two  different  titles,  '  Natur- 
liche   Schopf ungsgeschichte '  (1868, 


2  vols.),  and  '  Systematische  Phylo- 
geuie'  (1896,  3  vols.)  The  division 
of  the  great  modern  biological  doc- 
trine into  morphology  and  genetics 
is  in  conformity  with  Mr  Herbert 
Spencer's  treatment  in  the  '  Prin- 
ciples of  Biology,'  vol.  ii.,  published 
in  1865,  and  with  the  two  divisions 
of  Haeckel's  '  Generelle  Morpho- 
logie,' which  treated  respectively  of 
the  "  science  of  developed  forms  "and 
the  "science  of  developing  forms" — 
i.e.,  of  structure  and  process.  I 
have  chosen  such  expressions  in  the 
text  as  will  permit  of  a  compre- 
hension of  inanimate  as  well  as  of 
animated  nature.  In  1875  there 
were  founded  simultaneously  in 
Germany  two  periodicals,  represent- 
ing respectively  the  morphological 
and  genetic  sides  of  animal  biology. 


ON  THE  MORPHOLOGICAL  VIKW  OF  NATURE.   215 

present  chapter  will   deal   with    the    innrphohjgical,  the 
following  with  the  genetic,  views  of  nature.^ 

Were  the  real  w<irM  unly  one  out  of  many  possible 
worlds  which  the  mathematical  iniiid  can  imagine,  though 
through  its  complication  and  intricacy  it  might  .still 
far  surpass  its  powers  of  analysis;  were  the  actual  forms 
of  nature  only  some  of  the  infinitely  possible  states  of 
equilibrium,  the  events  and  changes  surrounding  us  in 
space  and  time  only  a  few  of  the  countless  condjinations 
of  motion  taught  in  dynamics  ;  were  the  actual  course 
of  things — as  mathenuiticians  since  Laplace  have  fanci- 
fully put  it — only  one  particular  solution  of  the  general 
differential  equations  of  the  world -motion,  —  then  the 
two  great  domains  of  morphology  and  genesis  would 
exhaust  the  subject  and  satisfy  all  the  interests  by  which 
natural  historv  has  been  created.      Unfortunately  for  the        is. 

■^  other 

pure  mathematician,  but  fortunately  for  the  rest  of  man-  aspects, 
kind,  notably  the  poet  and  the  artist,  it  is  not  so.  An 
enormous  gulf  separates  the  creations  of  nature  from  the 
most  perfect  machine ;  and  the  fact  that,  with  all  the 
most  delicate  methods  at  her  command,  her  most  perfect 
machines,  like  the  human  eye,  do  not  come  up  to  the 
demands  of  the  optician,"'  shows  us  that  other  agencies 


'  As  in  abstract  mechanics,  the 
study  of  the  conditions  of  equili- 
brium, i.e.,  statics,  preceded  in  time 
the  study  of  the  phenomena  of 
motion,  i.e.,  dynamics,  so  in  tlie 
study  of  nature  the  apparently 
finished  or  developed  forms  at- 
tracted attention  before  their 
genesis  was  inquired  into  ;  and  as 
the  key  to  statics  has  in  the  course 
of  time  been  discovered  to  lie  in 
dynamics,  so  the  key  to  an  under' 


been  found  to  lie  in  the  dynamical 
theory  of  descent  or  evolution.  In 
animal  biology  a  separate  influence 
— the  medical  interest — led,  how- 
ever, very  early  to  a  studj'  of  func- 
tion and  of  the  processes  in  the 
living  organism. 

-  This  refers  to  a  well-known  re- 
mark of  Helmholtz  in  his  popular 
lectures  on  the  'Theory  of  Light' 
(1868),  where  he  enlarges  on  the 
remarkable  imperfections  of  the  eye 


standing  of  form  and  structure  has       as  an  optical  instrument.      His  real 


216  SCIENTIFIC    THOUGHT. 

and  other  interests  are  at  work  than  we  have  as  yet 
been  able  to  grasp.  So  long  as  astronomy  was  content 
to  observe  the  orbits  and  motions  of  the  heavenly  l)odies 
from  a  distance,  it  indeed  appeared  possible  to  define 
that  science  as  merely  "  une  question  d'analyse  "  ;  but  in 
astronomy  even,  spectroscopy  has  brought  distant  objects 
near  to  us  and  opened  out  endless  vistas  into  a  purely 
descriptive  branch  of  the  science,  a  natural  history  of 
the  heavens.  Still  more  so  is  this  the  case  when  we  fix 
our  gaze  on  the  world  immediately  surrounding  us — on 
the  things  and  events  in  which  we  ourselves  take  an 
active  part.  Here  two  phenomena  attract  our  attention 
16.  — the  problem  of  life,  and  the  problem  of  consciousness 
inind.  or  mind.      The  knowledge  which  we  possess,  or  imagine 

we  possess,  of  the  latter,  which  is  gained  from  a  purely 
introspective  point  of  view,  the  psychological  aspect,  I 
leave  at  present  quite  out  of  the  question.  As  external 
observation  through  our  senses  would  never  have  given 
it ;  as  in  the  map  of  reality  which  we  call  nature,  we 
have  not  even  succeeded  in  accurately  locating  conscious- 
ness,—I  relegate  this  large  department  of  Thought  to 
a  different  place  in  this  work.  At  present  we  have  to 
do  only  with  the  study  of  nature,  the  first  condition  of 


object  way  to  dispel  the  popular 
conception  that  the  accuracy  and 
variety  of  the  performances  of  the 
human  eye  could  be  explained  bj^ 
the  precision  and  complexity  of  its 
structure,  as  if  it  were  an  optical 
instrument  of  a  degree  of  perfection 
which  could  not  be  equalled  by  any 
optician.  In  the  sequel  Helmholtz 
shows  how  this  admiration  of  a 
wrongly  supposed  mechanical  per- 
fection must  make  room  for  an 
admiration  of  a  different  kind,  as 


"  every  work  of  the  organic  forma- 
tive power  of  nature  is  for  us 
inimitable  "  ;  a  remark  which  really 
supports  the  argument  in  the  text 
('Vortriige  und  Reden,'  3.  Aufl. 
1884,  vol.  i.  p.  240,  &c.)  It  is  also 
important  to  note  how  Helmholtz 
traces  the  imperfections  of  the  eye 
to  its  genesis — i.e.,  its  development 
in  the  embryo.  The  genetic  sup- 
plements the  purely  structural  ex- 
amination (ibid.,  p.   255). 


ON    THE    MORPHOLOGICAL    VIEW    OF    NATURE.      217 

which  is  that  her  phenomena  have,  or  have  at  some  time 
had,  a  definite  place  and  position  in  space.  Here,  then, 
the  phenomena  of  lower  and  higlier  life  and  tlie  new 
creations  of  human  culture,  art  and  industry,  open  out  a 
great  department  of  reality  which  is  accessible  to  external 
observation  and  study.  Without  committing  ourselves 
to  any  theory  on  the  subject,  we  have  in  this  department 
to  deal  with  the  phenomena  of  apparent  or  real  design 
and  purpose.  How  has  the  century  dealt  with  these 
phenomena  ?  The  answer  to  this  (question,  the  history 
of  nineteenth  century  thought  as  directed  towards  the 
phenomena  of  life  and  of  mind  as  natural  phenomena, 
will  be  dealt  with  in  two  further  chapters,  which  will 
respectively   deal   with    the    vitalistic^   and    the  psycho- 


^  It  would  have  been  in  some 
respects  preferable  to  use  the 
word  "  biological  "  instead  of  vital- 
istic.  In  fact,  in  the  original  draft 
of  this  passage  I  used  the  former 
term.  The  reasons  which  made  me 
alter  it  are  the  following :  The 
term  biology  was  first  used  in  1801 
by  Lamarck  in  his  '  Hydrogdologie.' 
"  About  the  same  time  it  occurred 
to  Treviranus  that  all  those  sciences 
which  deal  with  living  matter  are 
essentially  iind  fundamentally  one, 
and  ought  to  be  treated  as  a  whole  ; 
and  in  the  year  1802  he  published 
the  first  volume  of  what  he  also 
called  '  Biologic.'  Treviranus's  great 
merit  lies  in  this,  that  he  worked 
out  hi;-  idea,  and  wrote  the  very 
remarkable  book  to  which  I  refer. 
It  consists  of  six  volumes,  and  oc- 
cupied its  author  for  twenty  j'ears 
—from  1802  to  1822.  That  is  the 
origin  of  the  term  '  biologj' '  ;  and 
that  i.s  how  it  has  come  about  that 
all  clear  thinkers  and  lovers  of  con- 
sistent nomenclature  have  substi- 
tuted for  the  old  confusing  name  of 


'  natural  history,'  which  has  con- 
veyed so  many  meanings,  the  term 
'  biology,'  which  denotes  the  whole 
of  the  sciences  which  de<d  with 
living  things,  whether  they  be  ani- 
mals or  wiiether  they  be  plants." 
This  extract  from  Huxley's  "  Lecture 
on  the  Study  of  Biology "  (South 
Kensington,  Dec.  1876,  reprinted 
in  '  American  Addresses,' &c.,  1886, 
p.  129,  &c.),  has  induced  me  to 
adopt  the  term  "  vitalistic  "  to 
denote  those  doctrines  and  chapters 
in  biology  which  deal  specially  with 
the  principle  and  phenomena  of 
life.  A  very  large  portion  of  bi- 
ology deals  with  such  phenomena 
of  living  things  as  can  be  studied 
without  any  reference  to  a  doctrine 
or  theory  of  life  in  particular,  they 
being  either  mere  facts  of  distribu- 
tion or  that  very  large  and  increashig 
class  of  biological  processes  which 
admit  of  puiciy  mechanical,  ithysi- 
cal,  or  chemical  description  and 
explanation.  The  very  fact,  how- 
ever, tiiat  tlie  ijuestion  wiiether  the 
princijileof  life  is  purely  meclianical 


218 


SCIENTIFIC    THOUGHT. 


17. 
Vitalistic 
and  psycho- 
physical 
aspects. 


physical  views  of  nature.  Thus  four  distinct  chapters, 
dealing  severally  with  the  morphological,  the  genetic, 
the  vitalistic,  and  the  psycho-physical  aspects  of  nature, 
will  together  attempt  to  describe  the  manifold  and 
changing  methods  of  reasoning  by  which  our  century 
has  approached  the  actual  things  and  events  which 
surround   us. 


"  Nature  does  not  employ  all  figures,  but  only  certain 
ones  of  those  which  are  possible :  and  of  these,  the  deter- 
mination is  not  to  be  fetched  from  the  brain,  or  proved 
a  priori,  but  obtained  by  experiments  and  observations." 
These  words,  set  down  nearly  two  centuries  ago  by  a 
now  forgotten  natural  philosopher,-"^  express  clearly  the 
object  of  a  study  which,  towards  the  end  of  the  eigh- 
teenth century,  had  received  definite  expression  in  vari- 


or  not  is  not  yet  decided,  makes 
it  necessary  to  retain  in  a  history 
of  Thought  a  special  term  com- 
prising all  speculations  which  deal 
with  the  purely  scientific  solution 
of  that  problem.  In  fact,  the  ques- 
tion what  is  life  is  still  unanswered. 
A  fortiori,  these  remarks  refer 
also  to  the  question.  What  is  mind 
or  consciousness  ?  But  the  two 
chapters  referring  to  these  problems 
will  limit  themselves  to  an  historical 
exposition  of  what  has  been  done 
to  solve  them  by  purely  scientific, 
i.e.,  exact,  methods.  The  full  name 
of  the  author  of  the  '  Biologie ' 
was  Gottfried  Reinhold  Treviranus 
(1776-18.37)  of  Bremen.  Though 
introducing  the  larger  conception 
of  biology,  his  own  original  lab- 
ours were  mainly  in  the  domain 
of  zoology.  His  brother,  Ludolf 
Christian  Treviranus  (1779-1864), 
devoted  himself  mainly  to  botanical 


science,  and  was  largely  influenced 
by  the  doctrines  of  the  "  Natur- 
philosophie. "  On  the  former,  see 
Carus,  '  Geschichte  der  Zoologie  ' 
(Miinchen,  1872),  passim:  on  the 
latter,  Sachs,  '  Geschichte  der  Bo- 
tanik'  (ibid.,  1875,  p.  291). 

^  They  are  quoted  by  Whewell 
('Hist.  Indue.  Sciences,'  3rd  ed. , 
vol.  iii.  p.  165),  from  a  work  en- 
titled '  Dissertatio  de  Salibus ' 
(1707),  by  the  Italian  Professor  at 
Padua,  Dominico  Gulielmini  (1655- 
1710).  He  was  a  practical  physician 
as  well  as  a  natural  philosopher.  He 
was  the  forerunner  of  Rom^  de  Lisle 
and  Haiiy,  inasmuch  as  he  estab- 
lished the  principle,  not  then  suffi- 
ciently appreciated,  that  the  con- 
stancy of  the  angles  is  characteristic 
of  all  crystals.  See  Kopp's  '  Gesch- 
ichte der  Chemie,'  vol.  ii.  pp.  83- 
404. 


ON  THE  MORPHOLOGICAL  VIEW  OF  NATURE.   219 

ous   branches  of   natural  science,  and  which  can  be  best 
characterised  b}-  the  term  morphology.^      The  word  was        is. 

Morphology 

first  applied  only  to  plants,  then  also  to  animals,  and  <iciiued. 
later  still  to  crystals  and  minerals.  The  words  quoted 
above  refer  to  the  forms  of  inanimate  nature,  to  crystals. 
In  all  these  cases  we  have  to  do  with  definite  individual 
objects,  which  can  be  removed  from  their  surroundings 
and  examined  in  tlie  laboratory.  There  is,  however,  ncj 
reason  why  a  study  of  the  actual  forms  of  nature  on 
a  large  scale,  such  as  the  physiognomy  of  landscape,  the 
configuration  of  mountains  and  valleys,  the  shapes  (jf 
glaciei-s,  the  actual  distribution  of  land  and  water  on  our 
globe,  the  stratification  of  rocks,  the  formation  of  clouds, 
and  many  other  things,  should  not  all  be  comprised  under 
the  term,  the  morphological  view  of  nature.  And  con- 
ceived in  this  larger  sense,  the  study  of  nature  as  a  whole 
and  in  its  separate  parts  had  at  the  end  of  the  eighteenth 
century  already  made  very  important  progress.  In  fact, 
natural  history  had,  in  the  course  of  that  century,  gradu- 
ally emerged  from  the  previous  epoch,  that  of  the  purely 
systematic  and  classificatory  attempts,  which  aimed  at 
giving  inventories,  collecting  specimens,  and  classifying 
natural  objects,  naming,  describing,  and  identifying  them. 
The  interest  of  the  latter  was  a  practical  one,  frequently 


^  In  the  '  Lei;ons  sur  les  Phdno- 
mene.H  de  la  Vie  communs  aux 
Aniiuaux  et  aux  Vdg(5taux,'  a 
wijrk  whicli  did  so  much  to  break 
down  the  older  division  of  the 
sciences  which  deal  with  animals 
and  vegetables  separately,  Claude 
Bernard  says  (p.  333  of  vol.  i., 
1885) :  "  Dans  un  autre  equilibre 
cosmique,  la  morphologic  vitale 
serait  autre.      Je  pense,  en  un  mot. 


qu'il  existe  virtuellement  dans  la 
nature  un  nombre  infini  de  formes 
vivantes  que  nous  ne  connaissons 
pas.  Ces  formes  vivantes  seraicut 
en  ijuelque  sorte  dormantes  ou 
expectantes.  ...  II  en  est  ainsi 
des  corps  nouveaux  que  formeut 
les  chimistes  ;  ils  ne  les  crdeut  pas, 
ils  dtaient  virtuellement  possibles 
dans  les  lois  de  la  nature." 


220  SCIENTIFIC    THOUGHT. 

prompted  by  the  needs  of  the  medical  profession,  which 
studied  animals  as  affording  an  insight  into  the  analo- 
gous structure  and  functions  of  the  human  body ;  ^  and 
plants,  because  they  largely  furnished  the  materials  for 
the  preparation  of  medicines.  To  this  must  further 
be  added  the  practical  interests  of  agriculture,  of  garden- 
ing, and  of  the  artificial  culture  of  flowers  and  exotic 
plants,  and  the  breeding  of  domestic  animals.  All 
these  interests,  however  stimulating  they  may  have  been 
and  still  are,  introduce  an  element  of  artificiality  into 
the  study  of  nature.  They  have  all  a  greater  concern 
for  natural  objects,  be  they  beautiful  or  useful,  than 
they  have  for  nature  itself.  From  this  artificial  posi- 
tion the  true  sciences  of  nature  had  to  emancipate  them- 
selves by  slow  degrees  and  with  many  efforts.  Ever  since 
the  time  of  Linnaeus,  through  whose  labours  the  system- 
atic attempts  received  a  kind  of  finality,  and  even  in 
his  own  writings,  great  discussions  were  carried  on  as  to 
19.        the  difference  between  a  natural  and  an  artificial  order  of 


Artificial 


and  natural   plauts  and  animals.    "  The  natural  orders,"^  says  Linnseus, 

systems.  .       .    , 

"  teach  us  the  nature  of  plants,  the  artificial  orders  enable 
us  to  recognise  plants.  The  natural  orders,  without  a 
key,  do  not  constitute  a  method  ;  the  method  ought  to  be 
available  without  a  master.  .  .  .  The  habit  of  a  plant 
must  be   secretly  consulted.     A  practised  botanist  will 


^  Referring  to  Albrecht  von 
Haller,  Victor  Carus  ('  Gesch.  d. 
Zoologie,'  p.  567)  says,  "Through 
the  leap  which  physiology  took, 
thanks  to  his  labours,  zootomical 
researches  developed  in  a  direction 
which  brought  them  into  complete 
subjection  to  physiology,  with  a 
neglect  of  the  independent  import- 
ance which  belongs  to  them.   .   .   . 


It  diverted  attention  from  the  im- 
mediate object  of  zoology,  the  ex- 
planation of  animal  forms  and  their 
variety,  to  the  more  remote  problem 
— the  explanation  of  the  phenomena 
of  life." 

2  Quoted  by  Whewell  ('Hist.,' 
vol.  iii.  p.  268)  from  the  '  Genera 
Plantarum'  (1764). 


ON  THE  MORPHOLOGICAL  VIEW  OF  NATURE.   221 


cUstiiiguish  at  tlie  tiist  glance  tlie  plants  of  different 
([uarteis  of  the  globe,  and  yet  will  be  at  a  loss  to  tell  b}- 
what  mark  he  detects  them.  There  is,  I  know  not  what 
look — sinister,  obscure,  in  African  plants ;  superl>  and 
elevated  in  the  Asiatic  :  smootli  and  cheerful  in  the 
American  ;  stunted  and  indurated  in  the  Alpines."  ^  The 
inventor  of  the  sexual  system  of  plants,  which  proved  to 
be  such  a  good  "  finder  "  in  the  hands  of  the  botanist  and 
herbalist,  speaks  of  the  difficulty  of  the  task  of  discover- 
ing the  natural  orders.  "  Yet,"  he  says,  "  I,  too,  have 
laboured  at  this — have  done  something,  have  much  still 
to  do,  and  shall  labour  at  the  object  as  long  as  1  live." " 

Linn^eus's  artificial  system  met  with  little  acceptance 
in  France,  where,  under  the  opposite  infiuence  of  Buffbn,'^ 


20. 
Linnii'usand 
Buflon. 


1  Quoted  by  Whewell  ('  Hist.,'  vol. 
iii.  p.  268)  from  the  '  Philosophia 
Botaiiica'  (1751). 

-  Ibid.,  quoted  from  the  '  Chisses 
Plantarum  '  (1738).  Juliuw  Sachs, 
in  his  excellent  '  History  of  Botanj* ' 
(Munich,  1875,  transl.  from  the  Ger- 
man by  H.  E.  Garnsey,  1890),  .says 
of  Linnaeus,  that  in  his  morpho- 
logical as  well  as  in  his  systematic 
labours,  there  existed  two  unre- 
conciled conceptions  —  a  superhcial 
one,  meant  only  for  practical  use, 
which  found  expression  in  his  arti- 
ficial sexual  system,  and  a  deeper, 
scientifically  valuable  one.  "  For 
practical  jjurposes  of  description  he 
elaVjorated  his  nomenclature  of  the 
parts  which,  however  useful,  apjjears 
nevertheless  flat  and  superficial,  as 
any  deeper  foundation  through  a 
comparative  study  of  forms  is  want- 
ing. But  alongside  of  this,  there 
ai)i)ears  in  various  passages  of  his 
writings  the  desire  for  a  more  pro- 
found conception  of  plant-forms. 
What  he  had  to  say  on  this  subject 
he    brought    together     under    the 


term  '  metamorphosis  plantarum  '  " 
(p.  110  of  the  German  edition). 

^  Buffon's  great  name  has  a  place 
in  the  history  of  the  genetic  as  well 
as  of  the  morphological  view  of 
nature,  inasmuch  as  he  looked  at 
the  things  of  nature  as  much  from 
the  side  of  their  individual  speciality 
as  from  that  of  their  connection 
and  orderly  ariangement  in  time 
and  space.  And  inasmuch  as  he 
"  does  not  only  con.sider  the  form, 
but  tries  to  maintain  an  interest  in 
the  general  economj'  of  the  whole 
of  nature  by  picturing  to  us  the 
homes,  the  habits  and  customs,  the 
instincts,  &c.,  of  living  things,  so 
he  strove  in  general  to  represent 
the  single  phenomena  of  nature  as 
existing  in  intimate  connection " 
(Carus,  '  Gesch.  der  Zoologie,'  p. 
523).  "As  Buflon  opposed  the  ex- 
treme systemati.sers,  who  seeuicd  to 
think  it  the  end  of  science,  not  so 
much  to  know  about  an  object  as  to 
be  able  to  name  it,  and  fit  it  into 
their  system,  so  Daubenton  (the 
collaborator  of    Bufton    in    France) 


222 


SCIENTIFIC   THOUGHT. 


the  great  botanists,  from  Jussieu  to  De  Candolle,  and  the 
great  zoologists,  notably  Cuvier,  made  an  attempt  towards 
a  freer  and  more  generous  and  more  sympathetic  con- 
ception of  the  objects  as  well  as  the  totality  of  nature. 
These  attempts  were  continued  much  on  the  same  lines 
till  well  on  into  the  nineteenth  century.  Buffon's  com- 
prehensive scheme  was  premature,  but  it  had  a  very 
great  and  beneficial  influence  in  popularising  and  en- 
livening the  frequently  dry  and  uninteresting  pursuits 
of  the  collector  and  systematiser.  Cook's  voyages  during 
the  last  third  of  the  eighteenth,  and  Humboldt's  travels 
at  the  turn  of  the  two  centuries,  did  much  to  further  a 
comprehensive  view  ;  but  the  great  task  of  the  mor- 
phologist,  like  every  other  scientific  work,  had  to  be 
solved  by  special  studies  in  separate  departments.  It 
grew  from  small  beginnings  and  detached  contributions. 

One  of  the  most  notable  of  these,  and  one  also  which 
has  all  along  exerted  a  great  influence  on  all  morpho- 
logical studies,  is  the  theory  of  crystals,  both  natural  and 
artificial.  I  have  already  had  occasion  to  refer  to  the 
labours  of  Haiiy^  and  his  successors.  They  have  led  to 
a  complete  mastery  of  the  geometrical  forms  which 
minerals  occasionally  present  in  nature,  and  which  sub- 
stances assume  if  allowed  to  solidify  out  of  the  liquid 
21.  condition.  The  science  of  crystallography,  now  appro- 
of°c^sta°s.^   priately  termed  the  "  morphology  of  crystals," "  has  had 


insisted  on  the  study  of  each  animal 
as  an  individual  whole.  .  .  .  He  oc- 
cupied himself,  therefore,  with  the 
production  of  a  series  of  admir- 
able monographs  appended  to  the 
descriptions  of  Buffon  in  the  '  His- 
toire   Naturelle  '  "  (Huxley  in  the 


chapter  on  Owen's  position,  &c.,  in 
'Life  of  Richard  Owen,'  1894,  vol. 
ii.  p.  280). 

1  See  vol.  i.  p.  116,  &c.,  of  this 
history. 

-  See  '  The  Morphology  of  Crys- 
tals,' by  N.  Story  Maskelyne,  1895. 


ON  THE  MORPHOLOGICAL  VIEW  OF  NATURK.   223 

a  peculiar  fascination  as  forming  the  transition  from  the 
abstract  science  of  geometrical  forms  and  statical  equili- 
brium to  tlie  study  of  the  actual  forms  of  real  things. 
Here,  if  anywhere,  it  seemed  as  if  we  might  dis- 
cover the  link  that  connects  the  theoretically  calcul- 
able with  tlie  actually  existing,  the  possible  with  the 
real.  Accordingly,  we  find  a  very  general  and  recur- 
ring tendency  to  carry  over  the  notions  of  crystal- 
lography into  other  sciences  —  into  the  morphology 
of  plants  and  animals.  The  planes  and  axes  of 
geometry,  and  the  forces  of  attraction  between  particles 
of  matter,  have  formed  a  theme  which  has  been  end- 
lessly repeated  and  varied  in  explaining  the  elements 
and  the  forms  of  living  matter.  IJut  whilst  these 
fanciful  analogies^  of  organic  crystals,  of  polar  distribu- 
tion, and  the  network  of  tissues,  to  which  are  also  allied 
the  spiral  theories  of  leaves  and  branches  in  plants  and 
other  geometrical  arrangements,  have  at  times  attracted 
much  attention,-  and  have   served  to  give  at  least  the 

1  "  Ces    comparaisous    entre    les  for  analogies,  Jul.  Sachs,    '  Gesch. 

formes     minerales    et    les    formes  d.  Botanik,'  p.  173,  &c. 
vivantes    ne    constituent  certaine-  -  I  shall   revert  to  this  subject 

ment  que  des  analogies    fort  loin-  when    speaking    of    the   elder   De 

taines,   et   il   serait    imprudent   de  Candolle.     Here  only  a  passing  re- 

les  exagcrer.     II  suffit  de  le.s  signal-  mark  on^ the  "spiral  theory,"  which 

er.      Elles  doivent  simplement  nous  was    mainly    developed    by    K.    F. 

faire  mieux  coucevoir  la  separation  Schimper    and    Alexander    Braun, 

theorique  de  ces  deux  temps  de  la  after  the  regular  geometrical  ar- 
creation     vitale  :    la    creation    ou    !   rangement  of   leaves  around  their 


synthase  chiviiqxie,  la  creation  ou 
synthase  movphologiqiic,  qui  en  fait 
8ont    confondues    par    leur    simul 


stalks  had  already  been  nt)ticed  in 
the  eighteenth  century  by  Charles 
Bonnet,  following  Civsalpinus.     For 


tan^it^,    mais   qui    u'en    sont    pas  about  thirty  years,   from   1830  on- 

moins     essentiellement     distinctes  ward,   the   spiral   theory   was  very 

dans  leur  nature  "  (Claude  Bernard,  popular   in   Germany.     In    France, 

'Le(;on8  sur  les  Ph^nomfenes  de  l;i  tht>    sninewhat    related    theories  of 

Vie,' &c.,  vol.  i.  p.  296).    See  also  on  \  nuufiry  of  De  Candolle,  of  meta- 

the  extravagances   of   such   search  i    uiorphosis  of  Goethe,  and  of  spiral 


224 


SCIENTIFIC    THOUGHT. 


22. 
Morphology 
on  a  large 
scale. 


semblance  ^  of  an  explanation  of  organic  structures  and 
forms,  they  have  in  reality  done  as  little  as  Boscovich's 
centres  of  force  and  curves  of  attraction  and  repulsion 
in  mathematical  physics  to  establish  a  firm  basis  for 
actual  research;  for  nowhere  have  they  been  capable  of 
exact  determination  such  as  has  been  applied  to  the 
angles  and  figures  of  crystals. 

Simultaneously  with  the  science  of  crystallography 
there  came  into  being  the  science  of  minerals  on  a 
larger  scale  of  study,  through  actual  observation  in 
definite  localities  of  the  formation  and  stratification  of 
rocks ;    of    the    traces    of    the    influence    of    the 


great 


arrangements  of  Schimper,  became 
known  under  the  term  "Morph- 
ologie  v(^getale,"  through  Auguste 
de  Saint  Hilaire  in  his  '  Lemons  de 
Botanique'  (1840).  To  the  spiral 
theory,  although  strongly  opposed 
in  course  of  time  by  Wilhelm  Hof- 
meister,  one  of  the  founders  of  the 
genetic  conception  of  plant  life, 
Sachs,  the  historian  of  botany, 
nevertheless  assigns  an  important 
historical  influence,  "  as  through 
Schimper's  theory  the  morphologic- 
ally so  important  relative  position 
of  the  plant  organs  was  for  the  first 
time  placed  in  the  foreground  of 
morphology  "  {loc.  cit.,  p.  180).  See, 
however,  on  this  subject  the  paper 
by  A.  H.  Church  on  "  Phyllotaxis  " 
in  vol.  i.  p.  49  of  'The  New 
Phytologist,'  1902. 

^  The  early  propounders  of  the 
cellular  theory  of  organic  structures 
adopted  the  view  that  cells  were 
formed  in  a  surrounding  liquid  in 
the  manner  of  crystals  in  a  mother- 
liquor.  When  it  was  established 
that  organic  structures  grow  by 
intussusception,  not  by  juxtaposition 
and  accretion,  like  crystals,  and  that 
cells  multiply  by  division,  the  dis- 
coveries  of    Graham,    who   divided 


bodies  into  crystalloids  and  colloids, 
were  utilised  for  the  purpose  of 
explaining  or  illustrating  organic 
processes.  On  this  distinction  is 
based  the  celebrated  "  micellar 
theory"  of  Niigeli,  who,  in  his 
'  Mechanisch-physiologische  Theorie 
der  Abstammungslehre '  (Miinchen 
und  Leipzig,  1884),  works  out  a 
complete  mechanical  doctrine  of  the 
constitution  and  formation  of  or- 
ganic structures.  The  ideas  con- 
tained in  this  elaborate  treatise 
have  been  much  used  in  Germany 
by  various  writers,  but  mostly  only 
as  convenient  illustrations.  See 
0.  Hertwig,  '  The  Cell '  (transl.  by 
Campbell,  1895),  p.  58,  &c.  The 
micellar  theory  does  not  seem  to 
have  found  much  favour  in  France 
or  in  this  country,  where  a  general 
opinion  prevails  which  is  probably 
best  represented  in  the  words 
of  Claude  Bernard  :  "  Les  pheno- 
menes  physico-chimiques  des  etres 
vivauts,  quoique  soumis  aux  lois 
de  la  physique  et  de  la  chimie 
gdnerales,  ont  leurs  conditions  par- 
ticulieres  qui  ne  sont  realisdes  que  1^, 
et  dont  la  chimie  pure  ne  pent  ofifrir 
qu'une  image  plus  ou  moins  inexacte" 
('  Phen.  de  la  Vie,'  &c.,  vol.  ii.  p.  487). 


ON  THE  MOKPHOLOGICAL  VIEW  OF  NATURE.   225 


agencies  of  nature, — of  water,  atmosphere,  and  of  ice 
and  heat.  J^st  came  the  study  of  the  fossil  remains 
of  organic  life  as  the  means  of  fixing  the  age  and  the 
order  of  succession  of  various  geological  formations. 
Werner^  in  Germany,  Cuvier"  in  France,  Hutton  ^  in 
Scotland,  William  Smith  *  in  England,  led  the  way,  from 
different  points  of  view,  towards  an  actual  knowledge  and 
a  possible  theory  of  the  existing  forms  and  structures  in 
and  on  the  crust  of  our  globe.  The  study  of  these 
subjects,  morphology  on  the  largest  scale,  necessitated 
distant  travels,  the  examination  of  formations  in  situ 
and  under  diametrically  opposite  conditions.  Its  great- 
est and  unequalled  representative  was  Alexander  von 
Humboldt,^     who     also     brought     the     observations     of        23 

'  <-'  Huinbolat. 

geographical,  geological,  and  mineralogical  facts  and 
details  into  connection  with  the  study  of  climate,  of  the 
weather,   of    the    distribution    of    plants    and    animals." 


^  See  supra,  vol.  i.  p.  283. 
-  Ibid.,  p.  125. 

3  Ibid.,  p.  283. 

4  Ibid.,  p.  291. 

^  A  good  account  of  the  grad- 
ual development  of  the  plan  of 
"  Cosmos  "  will  be  found  in 
Bruhus's  '  Life  of  A.  von  Hum- 
boldt '  (transl.  by  Lassell,  1873), 
vol.  ii. ,  pas»irii.  It  is  clear  that 
two  great  intiuences  co  -  operated 
to  ripen  in  Humboldt's  mind  the 
conception  of  unrolling  a  great 
tableau  of  the  phj'sical  world  in  its 
purely  material  and  in  its  ideal  or 
jioetical  aspects  :  the  influence  of 
the  great  scientific  movement  then 
emanating  from  Paris,  and  the 
not  less  important  influence  of 
the  ideal  movement  rejiresented 
by  the  names  of  Herder,  Goethe, 
and  Schelling,  which  emanated 
from     the     centre     of     Germany. 

VOL.  II. 


"But,  however  gi-eatly  Humboldt 
may  be  indebted  to  the  inspiring 
influence  of  his  contemj)oraries,  the 
great  merit  of  the  work  lies  in 
what  he  alone  has  accomplished — 
the  attempt  by  means  of  a  com- 
prehensive collation  of  details,  and 
the  institution  of  the  most  search- 
ing comparisons,  to  give  a  scientitic 
foundation  to  the  ideal  cosmology 
of  Herder,  (Joethe,  Schelling,  and 
their  disciples  ...  In  him  may 
be  said  to  be  united  the  two 
schools  of  philosophy,  so  brilliantly 
represented  during  the  closing  years 
of  the  former  centurj'.  On  this 
iiccount  he  was  at  the  same  time 
exposed  to  the  censure  of  the 
representatives  of  either  system " 
(vol.  ii.  p.  312). 

®  The  third  volume  of  the  '  Life 
of  Humboldt,'  in  the  original 
German   edition,  gives  an  account 


226 


SCIENTIFIC    THOUGHT. 


He  may  be  called  the  morphologist  of  nature  on  the 
largest  scale :  the  representation  of  the  grand  aspect 
of  things  as  exhibited  in  his  '  Cosmos,'  and  in  his  earlier 
'  Ansichten  der  Natur,'  was  the  leading  idea  of  his  hfe 
and  work.  Through  him  and  his  friend  Karl  Eitter 
"  comparative  geography  received  a  treatment  worthy  of 
the  subject,  showing  its  connection  with  the  history 
of  the  human  race  and  the  advancement  of  civilisation, 
inasmuch  as  the  configviration  of  the  earth  is  proved  to 
have  been  an  important  element  in  the  dispersion  of 
nations."  ^ 

But  morphology,  or  the  study  of  forms  and  struc- 
tures, has  to  be  carried  on  not  only  on  the  large,  the 
gigantic  scale,  as  by  Humboldt ;  it  is  quite  as  im- 
portant, and  has  probably  been  even  more  influential, 
when  directed  towards  the  minute,  the  imperceptibly 
small,   which    ordinarily    quite    escapes    our   notice.      If 


by  various  specialists  of  Hum- 
boldt's labours  in  the  sciences  of 
astronomy,  geology,  geography,  the 
distribution  of  animal  and  plant  life, 
meteorology,  and  other  provinces  of 
research,  some  of  which  largely  owe 
their  existence  to  his  initiative.  The 
study  written  by  Ewald  on  his 
geological  work,  and  that  of 
Griesbach,  on  what  is  termed  in 
German  animal  and  plant  geo- 
graphy, are  specially  interesting. 
Unfortunately  this  most'  fascinat- 
ing volume  has  not  been  brought 
out  in  the  English  edition.  As  illus- 
trating the  comprehensiveness  of 
Humboldt's  view  it  is  well  to  note 
how,  before  beginning  to  put  to- 
gether his  materials  in  the  great 
tableau  which  the  '  Kosmos '  was 
intended  to  be,  he  drew  two 
entirely  different  pictures  of  nature 
on   our   globe ;    first   in   the  large 


work  on  the  New  Continent 
('Voyage  aux  Regions  equinoxiales 
du  Nouveau  Continent,'  in  six 
parts,  published  in  Paris,  1805  to 
1834)  and  then  from  an  entirely 
opposite  aspect  in  his  works  on 
Central  Asia  ( '  Asie  Centrale : 
Recherches  sur  les  Chaines  et 
Montagues  et  la  Climatologie  com- 
parde,'  3  vols.,  Paris,  1843).  "To 
Humboldt  the  importance  of  the 
Asiatic  expedition  consisted  in  its 
elevating  him  above  the  one-sided 
effect  of  having  contemplated 
nature  exclusively  in  the  New 
World,  and  leading  him,  so  to 
speak,  to  feel  experimentally  that 
the  earth,  in  common  with  every 
other  object,  is  possessed  of  op- 
posite sides"  ('Life  of  Humboldt,' 
vol.  ii.  p.  212). 

1  See    '  Kosmos,'    vol.    i.    p.     60 
(German  edition,  1845). 


UX  THE  MORPHOLOGICAL  VIEW  OF  NATURE.   227 

the    great    revolution    of    ideas    which    the   seventeenth 
century  witnessed  was  much  assisted  by  the  invention        24. 

Mori'hology 

of  the  telescope  and  founded  upon  its  revelations,  the  wi  a  miimu 
change  of  thought  during  the  nineteenth  century  has 
been  connected  more  with  the  revelations  <jf  the 
microscope.  The  great  movement  of  ideas  started  by 
Galileo,  and  continued  through  Kepler,  Newton,  and 
Laplace,  ^^•as  accompanied  l)y  the  jierfection  of  tlie 
telescope.  The  invention  of  the  microscope  enabled 
Nehemiah  Grew  and  Mal{)ighi  to  begin  half  a  century 
later  their  embryological  studies,  and  to  inaugurate  a 
line  of  research  which,  in  our  days,  through  a  long  series 
of  oljservations  ^  from  Amici  to  Strasburger  on  the  pro- 


'  These  observations  begin  with 
the  year  1830,  when  Amici,  to 
whom  great  improvements  in  the 
microscope  are  due,  "  traced  the 
pollen  grain  from  its  lighting  on 
the  carpel  tip  down  into  the 
recesses  of  the  ovule"  (Geddes  and 
Thomson,  '  The  Evolution  of  Sex,' 
p.  140),  and  removed  all  doubts 
and  uncertainty  by  his  observa- 
tions on  orchids  in  18-15  and  1846. 
^'  Here  he  demonstrated  the  whole 
series  of  processes,  from  the  pollen 
dust  on  the  stigma  to  the  for- 
mation of  the  embryo "  (Sachs, 
'Gesch.  d.  Botanik,'  p.  469). 
About  the  same  time  (184-3)  Martin 
Barry  "  observed  the  presence  of 
the  sperm  within  the  ovum  in  the 
rabbit  ovum"  (Geddes  and  Thom- 
son, loc.  cit.,  p.  142).  It  took,  how- 
ever, a  cjuarter  of  a  century,  from 
the  first  discovery  of  Amici,  before 
the  process  of  fertilisation  described 
by  him  was  accepted  by  embryo- 
logists  as  typical  for  both  plants 
and  animals.  Bischoff,  the  great 
authority  in  Germany,  after  con- 
firming the  entrance  of  the  sperm- 
cell  into  the  ovum,  maintained  by 


Barry  in  1843,  and  by  Newport 
(w'ith  frogs)  in  1851  and  1853,  ex- 
presses his  "infinite  astonishment," 
adding  that  "  Dr  Barry  is  certainly 
the  first  who  has  seen  a  sper- 
matozoon in  the  interior  of  any 
ovum,  and  notablj-  in  the  ovum  of 
a  mammal,  and  that  to  him  be- 
longs the  glory  of  this  discovery  " 
(Theod.  Bischort',  '  Bestiitigung  des 
von  Dr  Newport  bei  den 
Ijatrachiern  und  Dr  Barry  bei 
den  Kaninchen  behaupteten  Ein- 
dringens  der  Spermatozoiden  in 
das  Ei,'  1854,  p.  9).  For  the 
history  of  scientific  thought  it  is 
significant  to  see  how  little,  even 
in  the  middle  of  the  century,  dis- 
coveries referring  to  the  phenom- 
ena of  plant  life  or  structure  were 
known  or  utilised  by  students  of 
animal  life.  A  mutually  fructify- 
ing infiuence  seems  to  date  like 
so  many  other  advances  from  the 
publication,  in  1859,  of  the  '  Origin 
of  Species.'  "The  distinctively 
modern  era  in  the  history  of 
fertilisation  dates  from  about  1875, 
when  the  brilliant  researches  of 
Auerbach,  Van  Beneden,  Biitschli, 


228 


SCIENTIFIC    THOUGHT. 


25. 
The  Micro- 
scope. 


cess  of  fecundation  in  plants,  and  from  Martin  Barry  to 
Hertwig  and  Fol  on  that  in  animals,  has  been  brought 
to  a  temporary  climax.  The  combination  of  telescope 
and  microscope  in  the  spectroscope  has  opened  out  a 
field  of  research  in  astronomy  of  which  Laplace  had 
no  conception. 

So  much  has  depended,  during  our  century,  on  the 
unravelling  and  disentangling  of  the  imperceptibly  small 
(once  considered  an  unworthy  occupation),  that  a  short 
reference  to  the  history  of  that  optical  instrimient  to  which 
we  are  so  greatly  indebted  may  not  be  out  of  place. 

The  gradual  perfection  of  the  microscope  is  as  much 
indebted  to  the  problems  and  labours  of  anatomical 
workers  during  the  seventeenth  and  the  nineteenth  cen- 
turies, as  anatomy  itself  reciprocally  has  been  indebted 
to  the  microscope.  Eobert  Hooke,  in  1660,  first  gave  a 
useful  form  to  the  compound  instrument.  Leuwenhoek 
perfected  the  simple  microscope ;  and  during  the  earlier 
part  of  our  century  no  one  did  more  than  Amici  in 
Modena  and  Lister  in  England  ^  to  start  that  great  suc- 


Fol,  0.  Hertwig,  and  others, 
showed  that  one  of  the  essential 
phenomena  in  fertilisation  is  the 
intimate  and  orderly  association 
of  the  sperm-nucleus,  of  paternal 
origin,  with  the  ovum  -  nucleus, 
of  maternal  origin,  the  result 
being  the  cleavage  or  segmentation - 
nucleus.  The  researches  of  Stras- 
burger,  De  Bary,  and  others, 
established  the  same  result  in 
regard  to  plants "  (J.  A.  Thom- 
son, '  The  Science  of  Life,'  p. 
127,  1899). 

^  The  improvements  of  Amici 
seem  to  go  back  to  the  year  1812, 
those  of  Lister  to  1826.  The  for- 
mer is  usually  considered  the  in- 


ventor of  the  "  immersion  "  system, 
— that  of  placing  a  drop  of  water 
between  the  object  or  its  covering 
glass  and  the  objective  lens.  This 
system  has  lately  been  improved  by 
Abbe,  who  discovered  a  liquid  with 
the  same  refractive  index  as  the  glass 
of  the  objective  possesses.  Accord- 
ing to  Hogg  ('  The  Microscope,' 
15th  ed.,  1898,  p.  10),  the  immer- 
sion system  was  suggested  by  Prit- 
chard  in  London  before  Amici  hit 
upon  it.  The  necessary  modifica- 
tions required  where  the  immersion 
system  is  used,  seem,  however,  to 
have  been  first  worked  out  by 
the  celebrated  Paris  opticians,  MM. 
Hartnack  and  Nachet. 


ON  THE  MORPHOLOGICAL  VIEW  OF  XATURE.   229 

cession  of  iiuproveiuents  by  whicli  enois  due  to  colour 
and  indistinctness — the  chromatic  and  spherical  aberra- 
tions— were  removed.  In  the  middle  of  the  century 
the  influence  of  some  eminent  Ijotanists,  notably  of 
Hugo  von  Mohl  and  Nageli,  in  perfecting  micrometric 
processes  was  considerable ;  whilst  the  last  twenty 
years  have  witnessed  quite  a  new  departure  in  the 
theory  of  optical  images,  in  that  of  microscopic  vision, 
in  the  improvement  of  optical  glass,  and  in  the  in- 
vestigation of  the  possible  limit  of  the  magnifying 
powers.  The  most  eminent  physical  authorities — such 
as  Stokes  and  Lord  Rayleigh  in  England,  Helmholtz 
in  Germany  —  have  taken  up  one  or  more  of  these 
points ;  but  the  whole  subject  is  associated  with 
the  name  of  Prof.  Ernst  Abbe  ^  of  Jena,  who, 
through  his  connection  with  the  well-known  firm  of 
Carl  Zeiss,  has  been  able  to  put  into  actual  practice 
many  of  the  suggestions  which  resulted  from  his  the- 
oretical   investigations.      As    the    historians   of    zoology 


^  The  labours  of  Abbe  go  back  to 
the  year  1873.  Simultaneously  and 
independently,  Helmholtz  attacked 
the  theory  of  microscopical  vision 
and  the  question  of  "resolution  " — 
i.e.,  of  the  possible  limit  to  the  re- 
solving power  of  any  optical  arrange- 
ment. Airy  had  attacked  the  same 
subject  on  purely  dioptrical  lines. 
Helmholtz  and  Abbe  went  a  step 
farther,  taking  into  account  the 
physical  nature  of  light  as  a  wave- 
motion,  subject  to  interference 
phenomena,  notably  those  caused 
by  inflection,  where  objects  with 
very  fine  markings  are  concerned. 
Ablje's  methods  were  for  a  long 
time  only  imperfectly  known.  The 
publication,  however,  of  his  theories 


by  Czapski  ('Theorie  der  optischen 
Instrumente  nach  Abbe,'  Breslau, 
1893)  made  the  whole  subject  better 
known,  and  has  been  followed  by 
two  masterly  papers  by  Lord  Ray- 
leigh and  Prof.  Johnstone  Stoney  in 
the  42nd  vol.  of  the  '  Philos.  Mag.' 
(1896).  The  latter  paper  especially 
gives  several  interesting  examples 
of  the  use  of  recent  microscopic 
appliances  and  the  means  of  avoid- 
ing errors  in  handling  very  delicate 
and  minute  objects.  It  seems  that 
the  instrument  caimot  any  longer 
be  used  without  a  theoretical  know- 
ledge of  its  optical  construction, 
which  enables  the  observer  not  only 
to  see,  but  also  to  criticise  and  to 
interpret. 


230 


SCIENTIFIC    THOUGHT. 


and  botany  tell  us,  the  use  of  the  microscope  had 
made  little  or  no  progress  ^  during  the  eighteenth 
century :  the  study  of  structures  and  tissues  had  lost 
interest  in  comparison  with  the  study  of  the  physi- 
ological functions  of  the  parts  of  plants  and  the  organs 
of  animals,  which  had  been  respectively  furthered  by 
2R.        Hales   in   England   and    by    Haller   in  Germany."     Our 

Its  improve- 
ment, century    thus    found    the    morphological    studies    of    the 

imperceptibly  small  in  a  very  backward  state :  it  had 
to  improve  the  instrument  for  its  research  pari  passu 
with  this  research  itself.^  But  it  has  been  truly  re- 
marked that  the  increased  use  of  the  microscope 
necessitated  likewise  a  mental  training  in  the  inter- 
pretations and  delineations  of  what  was  observed 
through  it.      "  By   fortifying    the   eye   with    the   micro- 


^  "So  long  as,  in  consequence  of 
the  imperfections  of  optical  instru- 
ments, deceptive  images  existed, 
and,  for  instance,  all  microscopical 
structures  appeared  as  composed  of 
rows  of  beads,  the  explanation  of 
what  was  seen  stood  under  the  in- 
fluence of  deceptions,  which  were 
only  gradually  recognised  as  such  " 
(Carus,  'Gesch.  d.  Zool.,'  p.  629). 
Compare  also  what  Sachs  says 
(Gesch.  d.  Bot.,'  p.  241). 

^  "  The  characteristic  feature  of 
that  period  laj-  in  this,  that  the 
examination  of  the  finer  structure 
is  always  mixed  up  with  reflections 
on  the  functions  of  elementary 
organs,  so  that  anatomy  and  phy- 
siology always  support  each  other, 
but  also,  in  consequence  of  their 
imperfect  state,  do  each  other  in- 
jury "  (Sachs,  loc.  cit.,  p.  240). 
Similarly  Carus  {loc.  cit.,  p.  567), 
"  Through  the  progress  which  phy- 
siology made,  thanks  to  Haller's 
activity,   zootomical    investigations 


took  a  direction  which  brought 
them  into  complete  dependence  on 
physiology,  .  .  .  and  retarded  the 
progress  of  zoology  by  diverting  at- 
tention from  its  primary  object — 
the  exposition  of  animal  forms  and 
their  differences." 

'  As  late  as  1827  Aug.  Pyrame 
de  Candolle  could  still  write  ('Or- 
ganographie  v^gdtale,'  vol.  i.  p.  7), 
"  De  nos  jours,  MM.  Mirbel,  Link, 
Treviranus,  Spreugel,  Rudolphi, 
Kieser,  Dutrochet,  et  Amici  out 
public  des  recherches  tres  d^licates 
sur  le  tissu  vegdtal,  et  les  ont  ac- 
compagnees  de  figures  nombreuses 
et  soignees  ;  mais  la  necessite  d'em- 
ployer  continuellement  dans  ces 
recherches  un  instrument  aussi 
difiBcile  h,  bien  manier  que  Test  le 
microscope  compose,  fait  que  malgr^ 
I'habilet^  de  ces  observateurs,  I'anat- 
omie  delicate  des  veg^taux  est  encore 
.  .  .  d'une  incertitude  desesperante 
pour  les  amis  de  la  v^ritd. " 


ON  THE  MORPHOLOGICAL  VIEW  OF  NATURE.   231 

scope,  it  became  itself  a  scientific  instruiueut  wiiich 
no  longer  hurried  over  its  objects  in  tlighty  motion, 
but  is  disciplined  by  the  intellect  of  the  observer  and 
forced  into  methodical  work."  ^  Similarly,  no  doubt, 
the  increasing  devotion  to  the  pastime  of  sketching 
from  life  and  nature  in  our  days  must  have  the  effect 
of  obliging  the  eyes  of  many  persons  to  look  stedfastl>' 
and  carefully  at  the  forms  and  outlines  of  things,  and 
of  thus  training  the  artistic  faculty. 

It  is,  however,  a  remarkable  fact  that  one  of  the 
greatest  leaders  in  the  morphological  study  of  natural 
objects,  Bichat,  the  great  observer  of  membranes  and 
tissues,  despised  the  microscope,  the  instrument  by 
which  the  sciences  he  founded  were  to  benefit  so 
enormously. 

The  object  of  morphology,  as  distinct  from  that  of  27. 
classification,  can  be  defined  as  the  attempt  to  describe,  a"J.  ciassiti- 
and  if  possible  to  comprehend  and  explain,  the  relative 
similarity  as  well  as  the  graduated  differences  of  form 
and  structure  which  natural  objects  present  to  our  gaze. 
Although  the  study  can  be  conducted  on  a  large  as  well 
as  on  a  small  scale,  these  similarities  and  differences  sooner 
made  themselves  felt  in  the  comparatively  smaller  objects 
of  living  nature.  These  can,  without  apparent  loss  of 
their  characteristic  appearance  and  individuality,  be  col- 
lected and  brought  together,  whereas  a  collection  of 
minerals,  with  the  exception  of  crystals  and  gems,  always 
presents  only  fragments,  and  forces  upon  us  the  convic- 
tion that  they  can  really  be  studied  only  in  their  habita- 
tion, in  situ.      The  same  conviction  has  indeed  gradually 

1  Sachs,  loc.  cit.,  p.  237. 


232 


SCIENTIFIC    THOUGHT. 


made  its  way  into  botany ;  and  last  of  all  into  zoology. 
The  herbarium  or  collection  of  dead  plants  was  much 
sooner  superseded  by  the  "  jardin  des  plantes  "  than  the 
zoological  museimi  with  its  skeletons,  stuffed  animals,  and 
specimens  in  alcohol  has  been  supplanted  by  any  scientific 
collection  of  living  animals.  Marine  stations,  which  study 
plant  and  animal  life  m  situ,  are  quite  a  recent  invention.^ 
The  study  of  the  forms  of  nature  or  morphology  in  the 
earlier  or  more  limited  sense,  referred  thus  more  exclu- 


^  M.  Yves  Delage  distinguishes 
four  great  periods  in  the  study 
of  living  things.  The  first,  cul- 
minating in  Linnffius  and  Buffon, 
studies  living  objects  in  the  great 
outlines  of  their  external  forms,  of 
the  habits  of  plants  and  the  cus- 
toms of  animals.  Detailed  exam- 
ination by  dissection  is  resorted  to, 
but  only  as  a  secondary  method  and 
in  order  to  supplement  the  intuitive 
discovery  of  natural  affinities.  Then 
comes  the  second  period,  that  of 
Cuvier  and  his  followers,  relying 
mainly  on  anatomical  dissection. 
The  third  period  begins  with  the 
marine  stations.  "Je  ne  crains 
pas  de  dire  que  la  fondation  des 
laboratoires  maritimes  a  marque 
une  troisieme  p^riode  et  constitud 
une  nouvelle  m^thode  aussi  im- 
portante  que  les  pr&^dentes.  Si 
I'on  songe  que  plus  des  trois 
quarts  des  types  d'invertebrds 
appartiennent  au  monde  de  la 
mer,  que  le  plus  grand  nombre  ne 
pouvaient  parvenir  dans  les  cen- 
tres scientifiques  dans  un  ^tat 
convenable  pour  I'examen  micro- 
scopique,  si  Ton  songe  que  tout 
ce  qui  conceme  leurs  mccurs  et  leur 
embryogenie  ne  pent  s'  etudier  loin 
de  la  mer,  on  comprend  I'importance 
de  ces  creations.  Faut-il  rappeler 
que  I'introduction  de  cette  mc^thode 
est  due  u  H.  de  Lacaze-Duthiers  ? 
,    .   .   Aussi  la  fondation  du  laVjora- 


toire  de  Roscotf  a-t-elle  ete  le  signal 
de  la  creation  d'une  multitude 
d'dtablissements  plus  ou  moins 
similaires  sur  les  cotes  de  tons  les 
pays"  (' L'H(5redit<5  et  les  grands 
problemes  de  la  Biologic,'  p.  3). 
The  fourth  period  is  marked  by 
microscopic  anatomy,  and  this  — 
according  to  M.  Delage — has  its 
home  mainly  in  Germany.  "The 
study  of  marine  zoology  has,  since 
the  publication  of  the  '  Origin  of 
Species,'  been  found  to  require 
more  complete  arrangements  in  the 
form  of  laboratories  and  aquaria 
than  the  isolated  vacation  student 
could  bring  with  him  to  the  seaside. 
Seaside  laboratories  have  come  into 
existence :  the  first  was  founded  in 
France  by  Coste  (1859)  at  Concar- 
neau  (Brittany)  with  a  practical  end 
in  view — viz.,  the  study  of  food- 
fishes,  with  an  aim  to  pisciculture. 
.  .  .  The  largest  and  Vjest-supported 
]:>ecuniarily  is  that  founded  at  Naples 
by  Anton  Dohrn  in  1872;  others 
exist  at  Trieste,  Villefranche,  Cette, 
and  at  New  Haven  and  Beaufort  in 
the  United  States ;  wliilst  a  large 
laboratory,  on  a  scale  to  compare 
with  that  at  Naples,  has  been  (1888) 
opened  at  Plymouth  by  the  Marine 
Biological  Association  of  the  United 
Kingdom "  (Ray  Lankester,  art. 
"  Zoology  "  in  '  Encyclop.  Brit.,'  vol. 
xxiv.  p.  814). 


ON  THE  MORPHOLOGICAL  VIEW  OF  NATURE.   233 

sively  to  plants  and  animals,  and  here  the  term  was  first 
applied.  In  order  to  bring  some  kind  of  method  into 
the  perplexing  study  of  living  forms,  two  ways  presented 
themselves ;  and  they  were  consciously  or  unconsciously 
followed  by  morphologists  with  more  or  less  success.  As 
I  mentioned  above,  one  of  the  chief  interests  which 
led  to  zoological  and  also  to  botanical  studies  was  the 
medical  interest.  Animals  were  dissected  and  observed, 
as  affording  by  analogy  an  insight  into  the  structure  and 
processes  of  the  human  body.  Physiology,  the  science 
which  deals  with  the  actions  of  the  different  parts 
of  the  animal  or  human  frame,  termed  from  an  early 
period  the  functions  of  the  different  organs,  had  made 
considerable  progress  during  the  eighteenth  century.  It 
was  then  found  convenient  to  study  the  whole  organism 
as  an  assemblage  of  different  organs  or  machines,  each  of 
which  performs  a  certain  function.  Thus  we  have  the 
mechanism  on  which  voluntary  motion  depends,  the 
mechanism  of  respiration  and  of  the  circulation  of  the 
blood  through  the  body,  the  mechanism  of  digestion,  the 
mechanism  of  reproduction,  and  finally,  the  mechanism 
of  the  nervous  system  with  its  specified  and  localised 
optical,  auditory,  and  other  organs  of  sense.  All  these  ^  ^^^^2s 
parts  or  organs  could  to  a  great  extent  be  separately  H^Hf^ 
studied  and  described  in  their  mechanical,  chemical,  and 
electrical  actions.  These  studies  had,  since  the  time 
of  Harvey  in  England  and  Haller  in  Germany,  made 
great  progress.  The  application  of  chemistry  to  the 
processes  of  respiration  and  digestion,  and  finally,  the 
discovery  of  the  galvanic  current  by  Galvani,  had  given 
a  great  impetus  to  the  physiological  study  of  the  different 


234  SCIENTIFIC    THOUGHT. 

organs  in  living  beings,  and  their  functions.  In  plants, 
these  organs  and  functions  seemed  to  be  much  simpler 
and  more  easily  observed  than  in  animals,  and  Linnasus 
had  selected  the  sexual  organs,  since  they  were  the  most 
easily  distinguishable,  as  a  primary  character  for  his 
classification  of  the  vegetable  kingdom.  Somewhat 
later  ^  he  classifies  the  animal  kingdom  according  to  the 
internal  structure,  and  characterises  animals  for  the 
purpose  of  division  according  to  the  heart  and  the  blood. 
The  celebrated  dictum,  that  "  minerals  grow,  plants  grow 
and  live,  animals  grow,  live,  and  feel,"  which  appeared  in 
the  last  edition  of  the  '  Systema  Naturae,'  places  a  physio- 
lodcal  distinction  at  the  base  of  the  classification.  This 
conception,  which  has  been  somewhat  modified  since 
Linnseus's  time  to  meet  our  altered  views,  is  an  obvious 
first  step  towards  a  description  of  natural  objects.  Yet 
this  no  more  than  the  second  step,  which  fastens  upon 
the  organs  of  reproduction  in  plants,  on  the  heart  and 
blood  in  animals,  gives  any  clue  to  the  comprehension 
of  the  great  variety  and  apparent  fixity  of  forms  which 
the  living  world  presents  to  our  observation.  In  fact, 
purely  morphological  considerations  were  subordinated  to 
physiological  ones,  and  were  brought  in  only  to  assist 
in  the  further  subdivision  of  the  two  great  kingdoms. 
Linnaeus  felt  the  artificiality  of  his  classification — the 
arbitrariness  of  the  characters  he  selected  for  the  pur- 
29.  pose  of  division.  But  a  more  natural  system  could  only 
stodies.^  be  arrived  at  by  an  intimate  knowledge  of  and  intercourse 
with  living  nature,  as  well  as  by  a  careful  comparison  of 
its  hidden  forms  and  organisation — i.e.,  by  a  more  de- 

1  See  Carus,  '  Geschichte  der  Zoologie,'  p.  503,  &c. 


ON  THE  MORPHOLOGICAL  VIKW  OF  NATURE.   235 


tailed  extenial  and  internal  morphology.  Both  lines  of 
study,  with  their  respective  methods  of  observation,  re- 
search, and  reasoning,  were  ef[ually  wanted.  The  former 
was  more  easily  attained  with  plants,  the  latter  promised 
more  immediate  fruit  in  dealing  with  animals.  In  follow- 
ing the  former,  Bernard  de  Jussieu  became  the  founder 
of  modern  descriptive  botany  ;  in  taking  up  the  latter, 
in  founding  comparative  anatomy,  Georges  Cuvier  became 
for  a  long  time  the  leader  in  zoology. 

]>ernard  de  Jussieu  was  led  to  his  natural  system  of 
classification,  not  by  any  theoretical  considerations,  but  by 
the  practical  task  of  arranging  the  plants  in  the  garden 
of  Trianon,  confided  to  his  care  by  Louis  XV.,  who  was  a 
great  lover  of  botany.  He  had  with  him  as  assistant  his 
nephew,  Ant.  Laurent  de  Jussieu,  who  in  1789  published 
his  '  Genera  Plantarum,'  which  is,  so  far  as  method  goes, 
the  work  of  his  uncle.  "  This  work  produced  a  verit- 
able revolution  in  botany,  for  only  since  its  publica- 
tion have  plants  been  studied  according  to  the  relations 
which  they  exhibit  and  according  to  the  totality  of 
their  organisation."  ^  It  was  not  one  special  character 
or  side  of  their  existence,  arbitrarily  selected  by  a  first 
superficial  observation,  which  served  as  a  means  of  de- 
scription ;  tlieir  different  parts  or  organs  were  conceived 
to  be  correlated — i.e.,  dependent  on  each  other  and  united 
to  form  the  totality  of  their  organisation — their  various 
characters  were  all  taken  into  account,  and  looked  upon 
as  subordinated  one  to  the  other."     From  the  time  of 


30. 
Jussieu. 


'  See  '  Histoire  des  Sciences 
Naturelles,'  par  Geo.  Cuvier,  com- 
plot<;e  par  T.  M.  de  .Saint  Agy, 
Paris,  1845,  vol.  v.   p.  298. 


^  Aug.  Pyranie  de  Candolle 
( '  Tiieorie  (51dmentaire  de  la  Bo- 
tanique,'  Paris,  1819,  '2iid  ed.,  p. 
69)  gives  the  following  account  of 


236 


SCIENTIFIC    THOUGHT. 


31. 
Problem  of 
organisa- 
tion. 


Jussieu  we  find  introduced  into  natural  science,  mainly 
for  the  purposes  of  classification,  the  ideas  of  the  correla- 
tion of  the  different  parts  and  the  subordination  of  the 
various  characters  of  a  plant  or  an  animal.  Physiology 
and  anatomy,  hitherto  mainly  occupied  with  the  study  of 
the  different  organs,  were  henceforth  to  be  occupied  with 
the  problem  of  organisation,  the  problem  of  the  unity  of 
the  various  characters  and  organs.  Inspired  by  Jussieu, 
De  Blainville  looked  upon  the  whole  development  of  the 
natural  sciences  as  the  history  of  our  knowledge  of 
organisation,^  and  De  CandoUe,  Jussieu's  great  successor 
in  botany — the  name  that  in  systematic  botany  ruled 
the  nineteenth  century — wrote  an  '  Organographie  vege- 


tale,'  a   rational   description    of    the 


organs 


of    plants. 


the  method  of  the  two  Jussieus : 
"  Ce  qui  characterise  la  methode 
des  Jussieu,  c'est  qu'elle  est  fondee 
8ur  la  subordination  des  caracteres. 
Sentant  le  vague  des  simples 
methodes  de  tatonnement,  I'ex- 
ageration  du  principe  de  com- 
paraison  uniforme  et  g^nerale  des 
organes,  ils  ont  les  premiers  re- 
marque  avec  soin,  que  tons  les 
organes,  tous  les  points  de  vue 
sous  lesquels  on  pent  les  con- 
siderer,  n'ont  pas  un  egal  degrd 
d 'importance,  ni  de  permanence, 
que  quelques-uns  semblent,  pour 
ainsi  dire,  dominer  les  autres ;  de 
sorte  qu'en  ^tablissant  la  classifica- 
tion d'abord  sur  ces  organes  pr^- 
dominans,  puis  les  divisions 
secondaires  sur  ceux  qui  ont  un 
moindre  degre  d'interet,  on  est 
conduit  it  imiter  le  plus  possible 
I'ordre  de  la  nature  dans  celui  de 
la  classification.  Ce  principe  simple 
et  peu  contestable  a  ete  fecond  en 
consequences  importantes  ;  et  c'est 
sous  ce  point  de  vue,  que  I'un  des 
hommes   qui   a   le   plus   profoud^- 


ment  refldchi  sur  la  marche  des 
sciences  et  sur  le  plan  general  de 
la  nature,  a  proclam^,  dans  une 
occasion  solennelle,  le  livre  de  M. 
de  Jussieu,  'comme  un  ouvrage 
fondamental,  qui  fait,  dans  les 
sciences  d'observation,  une  epoque 
peut-etre  aussi  importante  que  la 
chimie  de  Lavoisier  dans  les  sciences 
d'experience. '  "  (See  Cuvier, '  Rap- 
port historique  sur  les  progres  des 
sciences  uaturelles,'  Paris,  1810, 
p.  305.) 

1  See  the  '  Etude  sur  la  vie  et 
les  travaux  de  M.  Ducrotay  de 
Blainville,'  par  Pol.  Nicard,  Paris, 
1890,  p.  157  sq. 

'  See  A.  Pyr.  de  CandoUe,  '  Or- 
ganographie vegetale  ou  Descrip- 
tion raisonnee  des  Organes  des 
Plantes,'  Paris,  1827,  2  vols., 
especially  vol.  ii.  p.  245,  &c. 
"  The  classifications  of  the  scientific 
taxonomist  are  of  two  kinds.  Those 
of  the  one  sort  are  merely  handy 
reference  catalogues.  Such  are  the 
'  artificial '  systems,  useful  in  their 
day  and  for  their  particular   pur- 


ON  THE  MORPHOLOGICAL  VIEW  OF  NATURE.   237 

The  problem  uf  organisuLion  was  imicli  easier  in  deal- 
ing with  plants  than  with  animals.  In  the  former  there 
seems  to  be  only  one  organ  or  system  of  organs  definitely 
developed  and  marked  off— namely,  the  organs  of  fructi- 
fication ;  and  these  had  accordingly  served  Linnteus  and 
his  successors  as  the  leading  character  for  their  de- 
scriptive classification.  In  animals  there  are,  or  seem  to 
be  at  least,  four  or  five  well-defined  and  separated  sys- 
tems of  organs.  The  selection,  for  the  purposes  of 
classification  and  morphology,  was  much  more  difficult. 
Accordingly   we    find    Cuvier,   who    between   the   years       32. 

.  Cuvier. 

1^95  and  1817  devoted  himself  to  the  morphological 
and  anatomical  study  of  the  animal  kingdom,  hesitating 
in  the  selection  of  the  leading  character  according  to 
which  he  should  classify  and  arrange  it.  As  I  have 
had  occasion  to  remark  above,^  he  finally  in  1812 
settled  on  the  nervous  system  as  the  leading  character 
governing   the   figure    of   an   animal  organism.^      Before 


pose,  but  of  no  other  value.  The 
others,  known  as  '  natural '  classi- 
fications, are  arrangements  of  ob- 
jects according  to  the  sum  of  their 
likenesses  and  unlikenesses,  in  re- 
spect of  certain  characters ;  in 
morphology,  therefore,  such  classi- 
fications must  have  regard  only  to 
matters  of  form,  external  and  in- 
ternal. And  natural  classification 
is  of  perennial  importance,  because 
the  construction  of  it  is  the  same 
thing  a,9  the  accurate  generalisation 
of  the  facts  of  form,  or  the  estab- 
lishment of  the  emjjirical  laws  of  the 
correlation  of  structure  "  (Huxley  in 
'Life  of  Owen,'  vol.  ii.  p.  28:3). 

*  See  vol.  i.  p.  130  of  this  history. 

"  On  the  gradual  development  of 
Cuvier's  classification  see  Carus, 
'  Geschichte  der  Zoologie,'  pp.  602, 


612,  614.  '^It  did  not  escape 
Cuvier  that  the  idea  of  subordina- 
tion is  artificial,  and  that  the  im- 
portance of  an  organ  can  only  be 
fixed  by  experience  —  namely, 
through  the  proof  of  its  constancy. 
Nevertheless  he  follows  this  prin- 
ciple, but  naturally  becomes  vacil- 
lating. Thus  in  1795  he  names 
the  organs  of  reproduction,  to  the 
action  of  which  the  animal  owes  its 
existence,  and  the  organs  of  cir- 
culation, on  which  depends  the 
individual  preservation  of  the 
animal,  as  the  most  important, 
whilst  in  1812,  following  the 
example  of  Virey,  he  declares  the 
nervous  system  to  be  that  system 
for  the  maintenance  of  which  the 
other  systems  solely  exist "  {loc. 
cit.,  p.  602). 


238  SCIENTIFIC    THOUGHT. 

that,  he  had  ah-eady  adopted  from  Lamarck/  whose 
many-sided  genius  has  made  a  lasting  impress  on  the 
history  of  natural  science  in  quite  a  different  direction, 
the  broad  morphological  division  of  the  animal  kingdom 
into  animals  with  or  without  backbone,  uniting  under 
the  former  designation  the  four  first  classes  of  Linnaeus. 
The  more  we  follow  Cuvier  in  the  development  of  his 
classifying  attempts,  the  more  we  find  the  form,  the 
figure,  the  external  and  internal  structure,  urged  as  the 
aspect  from  which  the  organisation  of  living  creatures  is 
to  be  considered.  To  him  fixity  of  form  is  the  ever- 
recurring  character  of  organised  beings  as  distinguished 
from  inorganic  structures  which  depend  on  fixity  of 
matter."  The  clearer  enunciation  of  this  fixity  of  form 
is  accompanied  in  Cuvier's  view  by  the  rejection  of  an 
idea  which,  before  him,  had  very  largely  governed  the 
speculations  of  naturalists.  This  idea,  by  which  Charles 
Bonnet  has  been  immortalised  in  natural  history,  is  the 
conception  of  a  graduated  scale  according  to  which  living 
creatures  can  be  arranged — viz.,  the  celebrated  Echelle  des 
Etres,  coupled  with  the  axiom,  "  Natura  non  facit  saltus." 
This  idea  Cuvier  rejects  as  untenable,  and  introduces  in 
the  place  of  it  the  conception  of  distinct  plans  called 
"Types."      later   "  types,"  ^   according    to    which    living   beings   are 


1  "  An  indirect  inducement  for  a 
more  pointed  enunciation  of  the 
types  of  the  various  classes  was 
given  by  Lamarck  in  1797  when 
he  placed  the  animals  with  white 
blood  as  '  invertebrates '  in  opposi- 
tion to  those  with  vertebrae,  which 
expressions  (k  vertebres  and  sans 
vertebres)  come  from  him  "  (ibid., 
p.  612). 


(El.  iii.  p.  156,  &c.)  and  the  extracts 
from  it  and  from  the  '  R^gne 
animal,'  given  in  the  first  volume 
of  this  History,  p.  129  and  notes 
passivi. 

'  According  to  Carus  ('  Gesch.  d. 
Zool.,'  p.  615),  the  term  "type," 
which  became  current  later,  was 
introduced  by  De  Blainville,  a  philo- 
sophical    naturalist    who     held    a 


"  See  Cuvier's  '  Eloge  of  Haiiy  '       kind    of    middle    position  between 


ON  THE  MORPHOLOGICAL  VIEW  OF  NATURE.   239 


modelled,  and  which  have  always  existed.  These  types 
or  archetectonic  models  are  capable  of  certain  modifica- 
tions, which,  however,  do  not  affect  the  main  features  of 
the  plan.  The  different  classes  of  these  main  types, 
called  "  embranchements,"  and  designated  as  l)ackljoned, 
molluscous,  articulate,  and  radiated  animals,  stand  near 
each  other  in  independence  and  form  no  scale.^ 

The  morphological  view  of  nature  took  a  somewhat 
different  turn  in  De  Candolle,  the  successor  of  Jussieu  in 
botany,  who,  while  greatly  indebted   to  Cuvier,  acknow- 


34. 
De  Candolle. 


Cuvier  and  hi.s  opponent,  GetjfFroy 
St  Hilaire.  In  ISltJ  Blainville  gave 
the  "  principles  of  a  new  classifica- 
tion of  the  animal  kingdom,  in 
which,  tor  the  first  time,  the  totality 
of  structure  of  animals  was  used  to 
characterise  larger  divisions."  He 
divides  animals  first  of  all  into 
three  sub-kingdoms— symmetrical, 
radiate,  and  those  without  regular 
form.  De  Blainville  seems  to  have 
been  an  inspiring  teacher,  whose 
ideas  became  suggestive  and  fruitful 
in  many  other  minds.  Nearly  the 
whole  of  the  third  volume  of 
Comte's  '  Philosophie  Positive  '  is 
written  under  a  sense  of  obligation 
to  De  Blainville,  whose  '  Cours  de 
physiologic  gL'nerale  et  comparee ' 
(1829-32)  Comte  considers  "  comme 
le  type  le  plus  parfait  de  I'etat  le 
plus  avancd  de  la  biologie  actuelle  " 
(vol.  iii.  p.  269,  Paris,  1838).  The 
'  Philosophie  Positive '  was  dedi- 
cated to  Fourier  and  De  Blain- 
ville. How  the  latter  also  antici- 
pated the  modern  conceptions  of 
"  Stoffwechsel "  and  "  Metabolism  " 
see  Claude  Bernard,  '  Phenom^nes 
de  la  vie  communs  aux  aniinaux 
et  aux  vegetaux '  (1885,  vol.  i. 
p.  36). 

'  It  is  historically  interesting  to 
note  that  about  the  time  when 
Cuvier  was  gradually  defining  more 


rigidly  his  four  classes,  Lamarck 
was  working  at  his  '  Histoire  natur- 
elle  des  Animaux  sans  vertebres,'  of 
which  the  'Systeme,'  &c.  (Paris, 
1801),  can  be  considered  the  first 
editif)n,  the  larger  work  appearing 
from  1816  to  1822.  With  him  there 
is  no  mention  of  a  plan  or  a  type. 
His  classes  form  a  progressive  series, 
and  he  was  the  first  to  follow  the 
path  from  the  simple  to  the  more 
complex.  In  opposition  to  Cuvier, 
he  thus  wrote  :  "  La  nature,  dans 
toutes  ses  operations,  ne  pouvant 
proceder  que  graduellement,  n'a 
pu  produire  tous  les  animaux  h,  la 
fois  :  elle  n'a  d'abord  forme  que  les 
plus  sinijiles,  et  passant  de  ccux-ci 
jusques  aux  plus  composes,  elle  a 
etabli  successivement  en  eux  dif- 
ferents  syst^mes  d'organes  par- 
ticuliers,  les  a  multiplies,  en  a 
augmente  de  plus  en  plus  IV'nergie, 
et  les  cumulant  dans  les  plus  par- 
faits,  elle  a  fait  exister  tous  les 
animaux  connus,  avec  Torgani-sation 
et  les  facultes  que  nous  leur  ob- 
servons.  Or,  elle  n'a  rien  fait 
absolument,  ou  elle  a  fait  ainsi." 
('Hist,  des  Animaux  sans  vertebres,' 
2nd  ed.,  par  Deshayes  et  Milue 
Edwards,  Bruxelles,  1837,  vol.  i. 
J).  42.  Cf.  also  Carus,  loc.  cii., 
p.  615.) 


240  SCIENTIFIC    THOUGHT. 

ledges  yet  another  prominent  influence  in  the  forma- 
tion of  his  ideas.  Cuvier,  the  zoologist,  contemplating 
the  existing  forms  of  nature  from  one  of  the  two  main 
points  of  view,  was  impressed  with  the  contrast  be- 
tween the  lifeless  and  the  living,  seeing  in  the  latter 
stability  of  form,  not  of  substance, — what  we  should 
now  term  dynamical  equilibrium.  To  him  the  vor- 
tex is  the  symbol  of  life.  De  Candolle  in  studying 
plants  is  struck  with  the  underlying  regularity  and 
symmetry  of  their  formation.  His  views  were  formed 
after  very  extensive  practical  occupation  with  descriptive 
botany,  which  was  followed  by  a  lengthy  residence  in 
Paris,  where,  next  to  Cuvier,  he  came  greatly  under 
the  influence  of  the  Abbe  Haiiy,  the  founder  of 
crystallography.^  From  the  Jussieus  he  learnt  the  im- 
portance of  looking  at  the  "  ensemble,"  the  "  port  et 
aspect "  (facies,  habitus) ; "  from  them  and  Cuvier  the 
value  of  the  principle  of  the  subordination  of  characters, 
and  the  correlation  of  parts  in  the  organisation  of  the 
whole.^     But    he   fastens   mostly   upon    the    underlying 

1  De  Candolle,  '  Th^orie  ^l^men-  j  conduit  h,  quelques-unes  des  id^es 

taire    de    la    Botanique,'  2nd   ed.,  j  que  j'exposerai   dans  le   livre  sui- 

Paris,  1819,  p.  72  :  "  Je  dois  encore  i  vant."     Cf.     also     '  Organographie 

compter,  au  nombre  des  causes  qui  vegetale,'    Paris,    1827,   vol.    ii.    p. 

ont    influe    sur    I'amelioration   des  !  237. 


m^thodes  botaniques,  d'un  cot^  les 
perfectionnemens  importans  que  la 
classification  zoologique  a  recus, 
principalement  par  les  travaux 
philosophiques  de  M.  Cuvier,  trav- 
aux qui  ont  reagi  sur  quelques 
parties  de  la  Botanique  elle-meme, 
et  dont  je  m'honore  d'avoir  profits  ; 
de  I'autre,  les  importans  travaux  de 
M.  Haiiy  sur  les  lois  de  la  crystallisa- 
tion, et  uotamment  sur  les  d&rois- 
semens  des  rangees  de  mol&ules  des 
cristaux,  lois  par  lesquelles  j'ai  et^ 


2'Theorie  ^lementaire, '  p.  89; 
also,  p.  216. 

^  This  principle  is  stated  very 
clearly  by  Cuvier  in  many  places — 
e.g.,  in  the  celebrated  "  Discours  " 
prefaced  to  the  '  Recherches  sur 
les  Ossemens  Fossiles '  (3rd  ed., 
4to,  1825,  vol.  i.  p.  47):  "Tout 
etre  organise  forme  un  ensemble, 
un  systeme  unique  et  clos,  dont  les 
parties  se  correspondent  mutuelle- 
ment,  et  concourent  ii  la  meme 
action  definitive  par  une  reaction 


ON    THE    MORPHOLOGICAL    VIKW    OF    NATL'IJK.      241 


regulurit}-  and  syiimietry,  and  studies  the  causes  which 
in  the  actual  visible  specimens  of  ])lant  life  veil  and 
cover  up  this  symmetry ;  as  Haiiy  '  had  taught  us  in 
crystallography  to  recognise  the  primitive  forms  which 
appear  changed  by  the  phenomena  of  decrescence."  De 
Candolle  accordingly  enters  very  fully  into  the  theory 
of  abortive,  degenerate,  and  -coalesced  forms,  recurring 
asain  and  again  to  the  statement  that  the  "  ciisemUe " 
of  nature  tends  to  make  one  think  "  that  all  organised        35. 

Regularity 

Ijeings  are  ret^ular  in  their  most  intimate  structure,  and  a"<i    ^ 

o  o  .symmetry. 

that  various  and  differently  combined  abortive  efforts 
produce  all  the  irregularities  which  strike  our  glance 
and   embarrass  our  combinations."  ^     And   the   morpho- 


rt5ciproque.  Aucuue  de  ces  parties 
ne  peut  changer  sans  que  les  autres 
changent  aussi  ;  et  par  const'quent 
chacune  d'elles,  prise  sdparement, 
iiidique  et  donne  toutes  les  autres." 

1  Cf.  '  Theor.  olem.,'  p.  116,  where 
he  draws  a  parallel  between  the  two 
methods  in  crystollography  repre- 
sented by  Rome  de  I'Lsle  and  Haiiy 
and  similar  methods  in  botany.  He 
reverts  to  this  freiiuently  —  e.<j., 
'  Organographie,'  vol.  ii.  p.  237, 
where  he  says  :  "  Le  premier  rai- 
sonnait  comme  ceux  des  botanistes 
qui  voyaient  une  feuille  ou  unc 
corolle  comme  un  tout  unique, 
entaillo  sur  ses  bords  par  une  cause 
incounue  ;  le  second  m'a  servi  de 
guide  lorsque  j'ai  tentc  de  montrer 
que  les  decoupures  diverses  des 
organes  veg(5taux  terraient  essenti- 
ellement  aux  modes  varies  et  aux 
degres  divers  de  leur  agregation." 

■^ 'Theorie  dlomentaire,'  p.  186: 
"  Les  avortemens,  les  soudures  des 
parties,  leurs  degen(5rescences,  ne 
sont  pas  plus  des  suppositions  de 
desordre  ou  d'imperfection  dans  les 
etres  organises,  que  les  docrois- 
semens  des  molecules  ne  sont  des 
desordres  dans  la  cristallisation." 

VOL.  II. 


^  '  Thdorie  elementiiire, '  p.  97, 
&c. ;  also  p.  236  :  "  La  vraie  science 
de  i'histoire  naturelle  g^ndrale  con- 
siste  dans  I't-tude  de  la  symctrie 
propre  u  chaque  famille,  et  des 
rapports  de  ces  families  entr'elles  ; 
toute  la  reste  n'est  qu'un  eehafaud- 
age  plus  ou  moins  industrieux  pour 
parvenir  h  ce  but. "  And  'Organo- 
graphie vogotale,  vol.  i.  p.  x.  : 
"  L'organographie  est  la  base  com- 
mune de  toutes  les  parties  de  la 
science  des  etres  organises ;  con- 
sideree  en  ce  qui  tient  Ji  la  symdtrie 
lies  I'tres,  elle  est  le  fou<lement  de 
toute  la  theorie  des  classification.s, 
&c."  And  again,  ibid.,  vol.  ii.  239: 
"  Plus  le  nombre  des  etres  connus 
a  augmente,  plus  on  les  a  etudies 
avec  soin,  plus  ou  s'est  convaincu 
de  ce  principe  que  j'ai  6t6  le  pre- 
mier, ou  I'un  des  premiers  Ji  dnoncer 
dans  sa  g^neralito,  qu'il  est  presque 
certain  cjue  les  etres  organises  sont 
symetriques  ou  reguliers  lors  qu'on 
les  considi^re  dans  leur  type,  et 
que  les  irregularitcs  apjiareutes 
des  vdgdtaux  tiennent  ii  des  pheno- 
m6nes  constans  entre  certaines 
limites,  et  susceptiblcs  d'exister, 
soit  separt^meut,   soit    rouuis,   tels 

Q 


242 


SCIENTIFIC    THOUGHT. 


logical  view  is  still  more  clearly  expressed  in  the 
further  analysis  of  their  regularity  and  symmetry.  The 
character  of  the  structure  is  to  be  found  in  the  ex- 
istence or  absence,  in  the  relative  or  absolute  position, 
number,  size,  and  shape  of  the  different  organs,^  whereas 
the  use  or  functions  of  the  organs,  as  well  as  their 
other  sensible  properties,^  are  considered  to  be,  not 
the  cause,  but  the  consequence,  of  their  structure,  and 
hence  of  little  importance  in  the  anatomy,  and  of 
none  in  the  classification,  of  plants,  whatever  may  be 
their  value  from  a  physiological  point  of  view.  "  But 
symmetry  supposes  a  primitive  plan  or  archetype,  and 
the  proofs  of  symmetry  are  those  of  a  general  order."  ^ 
"  The  natural  classification  of  organised  beings  consists 
in  appreciating  the  modifying  circumstances,  and  in  ab- 
stracting them  so  as  to  discover  the  real  symmetrical 
type  of  each  group."  *  Here  again  De  Candolle  refers  ^  to 
the  examples  of  the  crystallographer  and  the  astronomer, 
who  both  make  abstraction  of  the  disturbing  secondary 
influences  in   order  to  arrive  at  the  primitive  form  and 


que  I'avortement  ou  la  degener- 
escence  de  certains  organes,  leur 
soudures  entre  eux  ou  avec  d'autres, 
et  leur  multiplication  d'apres  des 
lois  regulieres." 

^  '  Theorie  elem.,'  p.  147  :  "  La 
sym^trie  organique  se  compose  d'un 
certain  nombre  d'^lemens  dont  les 
priucipaux  sont :  I'existeuce  ;  la 
position  relative  ou  absolue  ;  le 
nombre  relatif  ou  absolu  ;  la  gran- 
deur relative  ou  absolue  :  la  forme  ; 
I'usage  ;  la  duree  ;  ...  les  qualites 
sensibles,"  &c. 

-  Ibid.,  p.  170 :  "  L'usage  des 
organes  est  une  consequence  de 
leur  structure,  et  n'en  est  nulle- 
ment    la    cause,    comme    certains 


ecrivains  irr^fl^chis  semblent  I'in- 
diquer  ;  l'usage,  quelle  que  soit  son 
importance  dans  I'etude  j)bysiolo- 
gique  des  etres,  n'a  done  eu  lui- 
meme  qu'une  mediocre  importance 
dans  I'anatomie,  et  ne  peut  en 
avoir  aucune  dans  la  taxonomie." 
...  "Ce  que  je  viens  de  dire  de 
l'usage  des  organes,  s'applique  a 
bien  plus  forte  raison  encore  a  leurs 
qualites  sensibles,  qui  ne  sont  que 
des  consequences  plus  ou  moins 
directes  de  leur  structure,"  &c. 

3  Ibid.,  p.  185.       •*  Ibid.,  p.  188. 

^  See  especially  the  chapter  ' '  De 
la  Symetrie  vdgetale "  at  the  end 
of  the  '  Organographie, '  vol.  ii.  p. 
236  sqq. 


ox    THE    MORPHOLOGICAL    VIKW    OF    NATURE.      243 

the  true  orbit.  It  follows  that  "  we  must  study  tiiu 
different  species  as  constant  things,"  ^  and  that  this  is  a 
more  "  dignitied  "  occupation  for  a  "  naturalist  than  the 
accumulation  of  doubtful  cases  in  favour  of  the  non- 
permanence  of  species." "  He  agrees  with  Cuvier  in 
rejecting  the  older  idea  of  the  "  echelle  des  etres,"^  and 
ho  praises  the  sagacity  of  Linnaeus,  who  suggests  that 
the  vegetable  kingdom  resembles  a  geographical  chart,* 
— an  idea  which,  in  the  hands  of  several  French  and 
German  botanists,  has  become  a  fruitful  conception. 

In  De  Candolle  we  meet  with  a  repeated  accentuation 
of  the  recurring  symmetry  of  form,  of  the  existence  of 
definite  primitive  types,  in  the  vegetable  kingdom. 
Simultaneously  witli  him  there  was  labouring  another 
thinker  and  keen  observer  of  nature,  w^ho  was  primarily 
struck  by  the  resemblance  exhibited  in  the  different 
parts  or  organs  of  one  and  the  same  plant,  and  searched 
for  the  type  or  plan  on  which  they  were  modelled.  He 
introduced  into  the  vocabulary  of  scientific  language 
the  expression  "  metamorphosis  of  plants."  It  was  35. 
Goethe    the    poet  who,   in    1790,  published   under   this  metamor- 

pilosis. 

title  his  first  contribution  to  morphological  science.  In 
subsequent  publications  and  essays,  covering  the  last  forty 


1  "  Theorie  dlementaire,"  p.  195. 

2  Ibid.  Mbid.,  p.  230. 
■•  "  Linu^  a  le   premier,   avee   sa 


est  tellement  juste,  tellement 
fcconde  en  consequences  utiles, 
qu'il     est     pent  -  etre     convenable 


sagacit(5  ordinaire,  compard  le  r^gne  d'entrer     dans     quelques     ddtails 

vegdtiil  a  une  carte  geographique  ;  ultdrieurs.       Je    suppose    pour   un 

cette  inetaphore,  indiquee  dans  son  moment  cette  carte  executce  ;  les 

livre    i)ar    un    seul   mot,  a  etc  dd-  classes   r(5pondent    aux    parties    du 

veloppeeensuitepar  Giseke,  Batscli,  monde,  les  families  aux  royaumes, 

Bernardin  de  Saint-Pierre,  L'Hdr-  1   les  tribus  aux  provinces,  les  genres 

itier,      Petit  -  Tliouars,      &c.       Et  aux  cantons    et    les    espdces    aux 

quoi  qu'on  ne  doive  la  prendre  que  1    villes    ou     villages,"     &c.     (Thdor. 

pour  une  simple  image,  cette  image  |   diem.,  p.  231). 


244 


SCIENTIFIC   THOUGHT. 


years  of  his  extraordinary  life,  he  again  and  again  reverts 
to  the  subject,  which  with  him  is  only  one  chapter  in  the 
extensive  science  of  morphology,  of  which  he  was  indeed 
the  first  to  form  a  general  conception.  G-oethe's  ideas 
hardly  influenced  the  course  of  science,  but  in  the  history 
of  thought  they  form  a  remarkable  anticipation  of  later 
views,  and  have  accordingly  been  frequently  referred  to 
by  contemporary  writers,  notably  by  Haeckel  and  Huxley 
in  their  important  works  on  Morphology  and  Evolution. 
Of  the  foremost  scientific  writers,  De  Candolle  was  almost 
the  only  one  ^  who,  during  Goethe's  lifetime,  referred  to 
his  views  with  approbation ;  seeing  in  his  theory  of  the 
metamorphosis  of  the  leaf  a  truly  admirable  divination  "^ 
of  vegetable  organisation.  Saint  -  Hilaire's  honourable 
mention  of  Goethe's  morphological  contributions  to  zoology 
came  only  just  in  time  to  be  seen  by  Goethe  himself.^ 


^  See  '  Organograpliie, '  vol.  i.  p. 
551 :  "  Les  parties  de  chaque  rangee 
ou  de  chaque  verticille  sont  sus- 
eeptibles  de  se  transformer  dans  la 
nature  de  la  rangee  qui  la  touche 
immediatement.  Ainsi  Ton  trouve 
des  sepales  changes  en  nature 
petaloide  {Primula  calcycanthema), 
des  petales  changes  en  etamines 
{C'apsella  Bursa  -  jmstoris),  des 
Etamines  changees  en  carpel  les 
{Magnolia  fuscata),  ou  bien  I'in- 
verse,  savoir :  des  carpelles  changees 
en  etamines  (Euphorbia  ■palustris), 
des  (Etamines  changees  en  petales 
(toutes  les  fleurs  doubles),  ou  les 
petales  transformes  en  nature  de 
calice  {Ranunculus  abortivus).  M. 
Goethe  a  tres-heureusement  designe 
la  premiere  de  ces  series  de  trans- 
formations sous  le  nom  de  Metamor- 
phose aseendantc  ou  direete,  et  la 
seconde  sous  celle  de  Metamorphose 
descendante  ou  inverse.'^ 

2  Ibid.,   vol.    ii.     p.   243:  "  C'est 


ainsi  qu'en  voyant  la  maniere 
v($ritablement  admirable  dont  M. 
Goethe,  quoiqu'  habituellement 
occupe  d'id^es  si  ditferentes,  a 
comme  devine  1' organisation  vege- 
tale,  on  est  bien  tent^  de  croire 
qu'il  I'a  moins  invents  qu'il  n'a 
generalise  avec  genie  quelques  faits 
partiels  heureusement  choisis." 
This  was  written  in  1827. 

■^  See  Goethe's  '  Werke'  (W^eimar 
edition,  Abth.  II.  Bd.  vii.),  the 
review  of  "  Principes  de  Philosophic 
Zoologique.  Discutes  en  Mars 
1830  au  sein  de  I'academie  roj'ale 
des  sciences  par  M.  Geoffroy 
Saint-Hilaire,  Paris,  1830,"  especi- 
ally p.  181,  and  dated  Sept.  1830. 
In  1831  Geofifroy  says  of  the  unity 
of  organisation :  "  Elle  est  pre- 
sentement  acquise  au  domaiue  de 
I'esprit  humain  ;  et  I'honneur  d'un 
succes  aussi  memorable  appartieut 
b,  Goethe."  Quoted  by  Huxley  in 
'Life  of  Owen,'  vol.  ii.  p.  291. 


ON    THE    MOIIPIIOLOCKAL    VIEW    oF    NATCRE.      245 


What  did  great  haiiu  Lo  Goethe's  correct  anticipations 
was  the  fact  that  in  optics  he  had  unsuccessfully  com- 
bated the  generally  accepted  Newtonian  theory  of 
colours/  and  that  his  morphological  glimpses  were 
taken  up  by  Schelling  and  his  school  and  incorpor- 
ated in  the  fantastic  speculations  of  the  philosophy 
of  nature.  They  shared  the  fate  of  this  and  passed 
into  temporary  oblivion. 

Tlie  idea  of  the  fixity  of  certain  forms  in  nature,  of 
the  archetectonic  modelling  of  her  objects  according  to 
certain  archetypes,  which  Cuvier  had  put  forth  as  the 
result  of  extensive  observation  and  inductive  exam- 
ination of  living  and  fossil  forms,  which  in  Ue  CandoUe 
was  connected  with  the  conception  of  geometrical  order, 
regularity,  and   symmetry,  found   in   Goethe's   mind  an        37. 

The  ideal 

artistic   sanction.     "  It  is,"   as    the  historian  of  botany  type, 
lias  remarked,  "  the  idealistic  conception  of  nature  wliich 
looks   upon   the   organic   forms  as  continually  recurring 

^  A    full   discussion   of    Goethe's 


theory  of  colours  will  be  found  in 
two  addresses  of  Helmholtz :  the 
first,  from  the  year  1853,  was  re- 
printed in  the  first  volume  of 
his  often  -  quoted  '  Vortriige  und 
Keden '  ;  the  second  was  delivered 
nearly  forty  years  later  at  the 
meeting  of  the  Goethe  Society  at 
Weimar,  in  June  1892.  In  the 
latter  Helmholtz  :<ignificantly  re- 
fers to  the  great  revolution  which 
in  the  interval  hiul  come  over  scien- 
tific thought  through  the  general  re- 
cognition of  the  principles  of  energy 
and  of  evolution.  Bj-  the  light  of 
these  we  are  better  able  to  under- 
stand the  shadowy  but  nevertheless 
truthful  anticipati<jns  contained  in 
Goethe's  poetical  and  scientific 
writings.  Helmholtz  traces  the 
errors    of    Goethe's   colour  -  theory 


largely  to  the  fact  that  he  worked 
with  imperfect  apparatus  and  im- 
pure colours  ;  that  "  he  never  had 
before  his  eyes  perfectly  purified 
homogeneous  -  coloured  light,  and 
hence  W'Ould  not  believe  in  its 
existence.  On  this  difficulty," 
Helmholtz  continues,  "of  complete 
purification  of  the  simple  spectral 
colours,  a  man  like  Sir  D.  Brewster 
foundered,  who  was  much  more 
experienced  and  clever  in  optical 
experimenting  than  Goethe,  and 
was  equipped  with  the  best  in- 
struments" (Goethe's  '  Vorahnung 
kommender  naturwissensliaftlicher 
Ideen,'  by  H.  von  Helmholtz, 
Berlin,  1892,  p.  30).  Cf.  also 
Helmholtz's  Memoir  on  Brewster's 
Analysis  of  Sunlight,  1852.  Re- 
printed in  Wissenschaftl.  Abhandl., 
vol.  ii. 


246  SCIENTIFIC    THOUGHT. 

imitations  of  eternal  ideas  in  the  sense  of  Plato,  and 
which  confounds  these  abstractions  of  the  mind  with 
the  objective  nature  of  real  things."  ^  Nevertheless,  we 
must  recognise  that  through  the  vague  and  poetical  ex- 
positions of  Goethe's  writings  there  is  to  be  seen  the 
fruitful  idea  of  the  change,  the  instability,  of  forms,  as 
an  equally  important  side  of  reality.^  In  fact,  Goethe 
oscillates  in  his  half-formed  theories  between  the  ideal 
archetypes  of  Plato  and  the  more  recent  conceptions  of 
Darwin  and  Spencer,  as  is  proved  by  the  vivid,  even 
passionate,  interest  which  he  took  in  the  celebrated 
controversy  of  Cuvier  and  Saint-Hilaire  in  the  French 
Academy  of  Sciences  in  the  year  1830, — an  incident 
which  carries  us  into  the  midst  of  the  ideas  with  which 
the  following  chapter  will  be  occupied. 

Before  we  take  up  those  entirely  different  lines  of 
observation  and  reasoning,  we  must  note  a  great  ex- 
pansion and  development  of  the  study  of  the  form  of 
natural  objects — of  morphology — in  two  independent 
directions.  One  of  these  carried  the  study  of  forms 
into  the  larger  dimensions  of  time  and  space,  the  past 

■•  Sachs,  '  Geschichte  der  Botanik,'  apprehension    was   needed   to   give 

p.  181.  I    these  airy  nothings  a  local  habit- 

^  Of  Goethe  Huxley  says  ('Life  |   ation    and    a    name;     to    convert 

of    Owen,'   vol.    ii.    p.    290):    "On  '    vague     suppositions    into     definite 

the   face   of  the   matter  it    is  not  i   hypotheses.    And  I  apprehend  that 

obvious  that  the  brilliant  poet  had  it     was    just    this    service     which 

less  chance   of   doing  good  service  Goethe    rendered    by    writing    his 

in  natural  science  than  the  dullest  essays  on  the  intermaxillary  bone, 

of     dissectors    and    nomenclators.  on  osteologj'  generally,  and  on  the 

Indeed     there     was     considerable  ;    metamorphosis  of  plants."     A  very 


reason,  a  hundred  years  ago,  for 
thinking  that  an  infusion  of  the 
artistic   way    of   looking   at  things 


full  appreciation  of  Goethe's  merit 
will  be  found  in  all  the  principal 
writings  of  Ernst  Haeckel,  notably 


might  tend  to  revivify  the  some-  in  the  fourth  chapter  of  the  first 

what  mummified  body  of  technical  ;    volume  of  the  '  Natiirliche  Schbp- 

zoology  and  botany.      Great  ideas  i   fungsgeschichte,'    9th   ed.,    Berlin, 

were   floating  about ;    the    artistic  1898. 


ON    THE    MOKPHOLOGICAI.    \'IK\V    OF    NAirKK.       247 

of  history  and  the  morphological  changes  of  the  earth ; 
the  other  carried  it  into  those  small  dimensions  where 
the  unaided  eye  sees  only  sameness  and  repetition,  but 
where  the  microscope  reveals  the  liidden  structure,  the 
internal  and  minute  forms,  of  which  living  matter  is 
made  up. 

I  have  already  pointed  out  how  the  great  travellers 
of  the  second  half  of  the  eighteenth  century — Banks, 
Pallas,  and  Humboldt  —  carried  the  study  of  nature 
beyond  the  narrow  limits  of  the  museum  and  the  work- 
room into  the  larger  area  of  nature,  of  the  present  and 
the  past  world.  Camper  in  Holland,  Hunter  and  Monro 
in  this  country,  lUumenbach  and  Soemmering  in  (ier- 
many,  Saussure  in  Geneva,  towards  the  end  of  the  eigh- 
teenth and  the  beginning  of  the  nineteenth  century  had 
betfun  to  unite  these  scattered  discoveries  and  records 
into  something  like  order  and  system.  It  was  again  ss. 
the  great   merit  of    Cuvier     to   publish    a   monumental  toiogy. 


^  Of  the  labours  of  other  natural- 
ists who  preceded  Cuvier,  a  very 
full  account  will  be  found  in  a  post- 
humous work  of  Ducrotay  de  Blain- 
ville,  edited  by  M.  Pol  Nicard  and 
entitled  '  Cuvier  et  Geoffroy  Saint- 
Hilaire'  (1890).  The  author,  as  is 
well  known,  was  for  some  time  a 
colleague  and  collaborator  of  Cu- 
vier, with  whom  he  fell  out,  partly 
from  personal  reasons,  partly  owing 
to  the  whole  bent  of  his  scientific 
researches,  which  was  much  more 
philosophical  than  that  of  Cuvier. 
He  had  a  very  great  appreciation 
of  Lamarck  at  a  tune  when  that 
speculative  naturalist  was  unknown 
or  treated  with  neglect,  not  to  say 
with  ridicule.  The  criticisms  of  De 
Blainville  on  Cuvier  must  be  ttiken 
with     caution  :      nevertheless     his 


works  and  lectures  had  a  great 
influence  on  the  development  of 
the  more  philosophical  side  of  nat- 
ural science  in  France,  as  many  al- 
lusions of  Auguste  Comte,  Flourens, 
Claude  Bernard,  &c.,  sufficiently 
prove.  In  the  chapter  on  Palaeont- 
ology in  the  work  on  Cuvier  (p. 
380,  &c.),  De  Blainville  does  full 
justice  to  Camper,  Blumenbach, 
Soemmering,  and  other  Continental 
naturalists,  with  whose  laboui-s 
Cuvier,  through  his  German  educa- 
tion, was  better  acquainted  than 
his  French  colleagues.  There  is 
also  a  significant  remark  of  his 
on  the  fact  that  Cuvier  was  essen- 
tially a  collector  and  dissector, 
a  man  of  the  museum  and  the 
library,  not  an  outdoor  naturalist 
(!'.  241). 


248 


SCIENTIFIC    THOUGHT. 


work  on  the  subject  and  to  found  the  science  of 
palaeontology.  His  researches  in  this  subject  were 
based  upon  the  collection  of  fossil  remains  which  had 
been  begun  by  Daubenton  for  the  natural  history  of 
Buffon,  and  which  he  arranged  and  largely  increased ;  on 
the  collection  which  Camper  had  made  at  Amsterdam; 
on  descriptions  which  he  procured  from  all  the  collectors 
of  Europe,  notably  from  Blumenbach ;  on  his  excavations 
together  with  Brogniart  in  the  environs  of  Paris.  As 
early  as  1798  he  announced  his  intention  of  collecting 
everything  that  was  known  on  fossil  remains  in  a  great 
tableau — a  plan  which  was  not  realised  till  1812,  when 
his  many  separate  publications  were  united  in  the  great 
work  on  the  "  Ossements  fossiles,"  and  was  only  completed 
by  the  greatly  revised  and  augmented  edition  of  1821. 
This  work  is  important  in  morphological  science,  not 
only  because  it  contains  many  accurate  and  still  highly 
valued  descriptions  of  "  extinct  species,"  but  also  because, 
in  its  celebrated  introduction  ^  on  the  revolutions  on  the 
surface  of  our  globe,  it  takes  a  comprehensive  view  of  the 
changing  aspects  which  succeeding  ages,  divided  by  great 
catastrophes  characterised  by  distinct  geological  formations 


^  In  this  introduction  (p.  52  of 
vol.  i.)  there  is  also  to  be  found  the 
celebrated  passage  in  which  Cuvier 
says  that  by  the  application  of  his 
principle  of  the  "correlation  of 
parts  "  he  could,  if  he  only  pos- 
sessed one  well-preserved  fragment 
of  a  bone,  determine  everything  as 
certainly  as  if  he  possessed  the  whole 
animal — a  statement  on  which  De 
Blainville  [loc.  cit.,  p.  417)  has  some 
very  pertinent  remarks  :  "  Ce  ne 
sont  pas  des  anatomistes  vdritables 
comme  I'etaient    Hunter,   Camper, 


Pallas,  Vicq-d'Azyr,  Blumenbach, 
Soemmering  et  Meckel  qui  se 
seraient  aiusi  avances,  et  M.  G. 
Cuvier  aurait  et^  bien  embarasse 
lui-meme,  si  on  I'avait  pris  au  mot, 
et  cependant  c'est  cette  assertion 
qui  restera  formulee  dans  la  bouche 
des  ignorants,"'  &c.  Cuvier  by  this 
method  determined  and  classed 
more  than  150  mammals  (loc.  cit., 
p.  53).  A  more  favourable  view  of 
Cuvier's  work  on  fossil  remains  is 
taken  by  Huxley,  'Life  of  Owen,' 
vol.  ii.  p.  297. 


ON  THE  MORPHOLOGICAL  VIEW  OF  NATURE.   249 


ami  liy  the  I'ussil  iciuuius  ul'  exliiiel  (jigaiiic  creations,  pre- 
sented on  the  surface  of  our  earth.  "  What  is  certain," 
says  Cuvier  at  the  close ^  of  this  celebrated  discourse,  "is 
that  we  are  now  at  least  in  the  middle  of  a  fourth 
succession  of  terrestrial  animals,  and  that  after  the  age 
of  reptiles,  after  that  of  the  paheotheria,  after  tliat  of 
the  mastodons,  the  megatheria,  there  has  come  the  age 
when  the  human  race,  supported  by  some  domestic  animals, 
peaceably  rules  and  cultivates  the  earth,  and  that  it  is  only 
in  the  countries  formed  since  this  epoch  in  the  recent 
alluvial  deposits,  peat-bogs,  and  concretions,  that  we  find 
in  a  fossil  condition  those  bones  which  belong  to  animals 
known  and  now  living."  Such  is  the  r^nimd  of  the  ideas 
whicli  had  followed — nay,  even  tormented'- — (Juvier 
during  his  researches  into  fossil  remains,  and  which  led 
hiiu  to  the  conclusion  ^  "  that  it  required  great  events 
to  bring  about  the  important  differences  which  he  recog- 
nised " — differences  which  the  slow  "  inlluence  of  weather, 
or  of  climate,  or  of  domestication,"  could  not  explain, 
but  which  required  the  violent  action  of  sudden  "  catas- 
trophes," *  which  frequently  "  disturbed  the  life  on  this 
planet  by  frightful  events,"  ^  "  broke  off  the  thread  of 
operations,"  ^  "  none  of  the  present  agencies  of  nature 
sufficing   to   produce   her   bygone  works."  ^ 


'  "  Discours  sur  les  revolutions 
de  la  surface  du  globe  et  sur  les 
changemens  qu'elles  ont  produits 
dans  le  n'gne  animal,"  reprinted  in 
the  3rd  ed.  of  the  '  Recherches  sur 
les  osseniens  fossiles,'  182.5,  vol  i. 
p.  172. 

-  "  Ces  idues  m'ont  pouisuivi,  je 
dirai  presque  tourmento,  pendant 
que  j'ai  fait  les  recherches  sur  les  os 
fossiles,  dont  j'ai  donnd  depuis  peu 


au  ]iuhlic  la  collection,  recherches 
qui  u'embrassent  qu'une  si  petite 
partie  de  ces  phenomcne.s  de  I'avant- 
dernier  Age  de  la  terre,  et  qui 
ce]iendant  so  lieut  h  tous  les  autres 
d'une  maniOre  intiine"  (' Discours,' 
&c.,  p.  HO). 

='Ibid.,  p.  3.        •»  Ibid.,  p.  8. 

5  Ibid.,  p.  9.         "  Ibid.,  p.  14. 

^  "Ainsi,  nous  le  n'pi-tons,  e'est 
en  vain  <iue  Ton  cherchc,   dans  les 


250  SCIENTIFIC    THOUGHT. 

39.  These  words,  which  embody  a  conception  since  appro- 

Cuvier's  i   •    i 

catastro-      priatelv  termed  "  catastrophism,     and  which  picture  to 

phism.  r  J  jt 

the  mind's  eye  a  succession  of  morphological  changes  of 
the  entire  aspect  of  our  globe,  were  written  at  a  time 
when,  in  this  country  especially,  through  the  labours  of 
Hutton,  an  entirely  opposite  view  was  gradually  pre- 
paring. With  this  we  shall  deal  in  another  chapter. 
The  Cuvierian  conception  of  epochs  in  geology  harmon- 
ised with  that  of  distinct  types  of  organic  creation. 
These  exhibit  in  space,  as  those  do  in  time,  certain  definite 
and  distinct  morphological  characters— z.c,  certain  typical 
forms  and  structures  on  a  vast  or  a  small  scale,  around 
which  the  features  of  events  and  individuals  seem  to 
oscillate,  and  which  permit  us  scientifically  to  classify, 
describe,  and  comprehend  them.  This  conception  gave 
the  tone  to  a  long  line  of  researches  on  the  Continent 
and  in  this  country  in  geology  as  well  as  in  natural 
history. 

In  the  study  of  these  typical  forms  and  structures  in 
which  nature  repeats  herself,  reverting  again  and  again 
to  them,  but  in  every  single  case  departing  more  or  less 
from  them  ;  in  the  study  of  this  order  without  monotony, 
this  change  without  confusion,  this  variety  of  forms  in 

40.  which  leading  features  are  always  recognisable, — the  dis- 
anaio^es.      covcry    of    analogies    played    a    very    prominent    part. 

Goethe's  metamorphosis  of  plants  is  based  upon  the 
analogy  of   their  different  organs :  before  he  published 


forces  qui  agissent  maintenant  u  la 
surface  de  la  terre,  des  causes  suf- 
fisantes  pour  produire  les  revolu- 
tions et  les  catastrophes  dont  son 
enveloppe  nous  montre  les  traces  ; 


et  si  Ton  veut  recourir  aux  forces  ex- 
terieures  constautes  connues  jusqu'b, 
present,  Ton  n'y  trouve  pas  plus  de 
ressources"  (ibid.,  p.  20). 


ON    THE    MORPHOLOGICAL    VIEW    OF    NATURE.      251 


this  first  luorphulogical  fnigmeiit  he  had  already — led 
by  analogy — discovered  the  intermaxillary  bone  in  the 
upper  human  jaw.  Later  he  and  (Iken  independently 
traced  the  analogy  between  the  skull  and  the  vertebral 
column  in  vertebrate  animals,  a  view  which  was  taken 
up  by  eminent  anatomists,  such  as  Meckel,  Spix,  and 
Geoffroy  Saint-Hilaire.^  The  tendency  which  lay  in  these 
attempts,  of  which  the  metamorphosis  of  plants  and  the 
vertebral  theory  of  the  skull  are  only  prominent  examples, 
is  one  which  was  naturally  provoked  by  the  opposite 
tendency  which  anatomical  studies  had  received  through 
Linnaeus  and  Cuvier.  Goethe  himself  gives  a  clear  ex- 
planation of  its  origin.  In  a  remarkable  passage  in  the 
history "  of  his  botanical  studies,  he  mentions  Shake- 
speare, Spinoza,  and  Linnaeus  as  the  three  masters  who 
had  led  him  to  reflect  on  the  great  problems  of  art,  of  life, 
and  of  nature.  Now,  he  says,  the  intiuence  of  Linnaius 
lay    principally    in    the    opposition    which    he   provoked. 


^  A  good  account  of  the  part 
wliich  the  vertebral  theory  of  the 
skull  played  iu  com])arative  an- 
atomy will  be  found  in  Whewell's 
History,  vol.  iii.  p.  369,  Lc.  But 
see  against  this  Huxley  in  '  Life  of 
Owen'  (vol.  ii.  p.  304):  "The  hypo- 
thesis that  the  skull  consists  of 
modified  vertebra:',  advocated  by 
Goethe  and  Oken,  and  the  subject 
of  many  elaborate  works,  was  so 
little  reconcilable  with  the  mode  of 
its  development  that,  as  early  as 
1842,  Vogt  threw  well  -  founded 
doubts  upon  it.  'All  efforts  to  in- 
terpret the  skull  in  this  way,'  said 
he,  'are  vain.'  " 

'■^  See  the  \Veimar  edition  of  liis 
Scientific  Works,  vol.  ii.  The 
pa.ssage  given  in  the  text  is  from 
an  earlier  account  contained  in  two 
numljers    of    the    '  Morphologische 


Hefte'  (1817),  reprinted  loc.  cit.,  p. 
389,  &c.  How  Goethe  continually 
hovered  between  the  theory  of 
types  and  that  of  development  is 
seen  in  the  following  passage  (1831, 
W.  W.,  vol.  vi.  p.  120):  "Das 
Wechselhafte  der  Pflanzengestal- 
ten,  dem  ich  liingst  auf  .seinem 
eigenthiimlichen  Gauge  gefolgt, 
erweckte  nun  bei  mir  immermelu" 
die  Vorstellung :  die  uns  unige- 
benden  Ptlanzenformen  seien  nicht 
urspriinglich  determinirt  und  fest- 
gestellt,  ihnen  sei  viehmehr,  bei 
einer  eigensinnigen,  generischen 
und  specifischcu  Hartniickigkeit, 
eine  gliickliche  Mobilitiit  und 
Biegsamkeit  verliehen,  um  iu  so 
viele  Bedingungen,  die  iiber  dem 
Erdkreis  auf  sie  einwirken,  sich 
zu  fiigen  und  darnach  bildeu  und 
umbildeu  zu  kijnnen." 


252 


SCIENTIFIC   THOUGHT. 


"  For  as  I  tried  to  take  up  his  sharp  and  suggestive 
distinctions,  his  expressive,  useful,  but  frequently  arbi- 
trary laws,  there  arose  in  me  an  inner  confiiet :  what 
he  tried  forcibly  to  hold  asunder,  tended  according  to 
the  innermost  demands  of  my  nature  to  be  united."  And 
as  the  process  of  dividing,  classifying,  and  keeping  apart 
went  on  among  the  successors  of  Linnaeus,  so  it  must 
have  produced  in  many  genuine  observers  of  nature  a 
tendency  similar  to  that  which  Goethe  describes.  They 
would  emphasise  the  resemblances  and  analogies  of 
natural  objects  and  their  organs  in  proportion  as  the 
classijfiers  had  separated  and  distinguished  them.  And 
it  was  just  as  likely  that  the  artistic  mind  of  Goethe 
might  succeed  in  "  lifting  the  veil  of  nature,"  as  Hum- 
boldt ^  put  it,  when  he  transmitted  to  Goethe  his 
suggestive  work  on  the  geography  of  plants,  and  as 
Huxley"  repeated  in  1894.  Indeed  it  was  the  former 
who,  on  the  largest  scale,  Jiad  traced  those  analogies  and 
correspondences    in    nature    which   are    so   much   dearer 

-  See  quotation  su^wa,  p.  246 
note  ;  also  ( '  Life  of  Owen,  vol.  ii. 
p.  288)  :  "  The  cultivator  of  botany, 
who  went  bej'ond  the  classification 
of  '  hay,'  became  familiar  with  facts 
of  the  same  order.  Indeed,  flower- 
ing plants  fairly  thrust  morpho- 
logical ideas  upon  the  observer. 
Flowers  are  the  primers  of  the 
morphologist ;  those  who  run  may 
read  in  them  uniformity  of  type 
amidst  endless  diversity,  single- 
ness of  plan  with  complex  multi- 
plicity of  detail.  As  a  musician 
might  say,  every  natural  group  of 
flowering  plants  is  a  sort  of  visible 
fugue  wandering  about  a  central 
theme  which  is  never  forsaken, 
however  it  may,  momentarily, 
cease  to  be  apparent." 


^  See  Goethe's  own  account  (in 
Werke,  2  Abth.,  vol.  vi.  p.  163): 
"  Sollte  jedoch  meine  Eitelkeit 
einigermasseu  gekriinkt  sein,  dass 
man  weder  bei  Blumen,  Minern, 
noch  Knochelchen  meiner  weiter 
gedenken  mag,  so  kann  ich  mich 
an  der  wohlthatigeu  Theilnahme 
eines  hochst  geschiitzten  Freuudes 
genugsam  erholen.  Die  deutsche 
Uebersetzung  seiner  Ideen  zu  einer 
Geographie  der  Pflanzen  nebst 
einem  Naturgemiilde  der  Tropen- 
liinder  sendet  mir  Alexander  von 
Humboldt  mit  einem  schmeichel- 
haften  Bilde,  wodurch  er  andeutet, 
dass  es  der  Poesie  wohl  auch 
gelingen  konne  den  Schleier  der 
Natur  aufzuheben  ;  und  wenn  er 
es  zugesteht,  wer  wird  es  leugnen  ?" 


ON    THE    MOKPHOLOGICAL    VIEW    OF    NATURE.      253 

to  the  poetical  huirI  of  Goethe,  and  all  other  artists, 
thau  the  separations  and  chissitications  of  the  men  of 
science.  ''  It  is  one  of  Humboldt's  uncontested  merits 
that  he,  in  order  to  prove  the  unity  which  rules  in 
the  formation  of  the  earth,  searched  for  analogies  in 
the  geological  constitution  of  distant  countries.  As 
we  see  him  pointing  out  numerous  novel  coincidences 
between  the  formations  of  Mexico  and  Hungary,  so 
likewise  we  owe  to  him  suggestive  hints  for  other 
similar  comparisons."  ^  But  the  man  in  whose  labours 
the  tendency  of  thought  which  was  uncritically  followed 
by  Goethe,  and  magnificently  represented  in  Humboldt, 
found  the  clearest  scientific  expression,  so  far  as  animated 
nature  is  concerned,  was  liltienne  Geoffroy  Saint-Hilaire,        41. 

Geoffrey 

the    friend    and   colleague   and    then    the  great  rival  of  s»int- 

o  '^  Hilaire. 

Cuvier."  Xo  one  recognised  more  clearly  the  deeper 
significance  of  the  great  outburst  of  the  two  conflicting 
ways  of  viewing  nature  in  the  Paris  Academy  of  Sciences 
in  1 8 :» 0  than  Goethe  himself,  who  in  the  eighty-first  year 
of  his  life  was  deeply  stirred  by  seeing  his  favourite  ideas 
espoused    by   a   scientific    authority   of   the  first   order.^ 

'  See  Julius  Ewald  in  the  third  great  event  ?    The  volcano  has  come 

volume     of     the     '  Leben     Hum-  to   an    eruption,   everything   is   in 

boldt's '    Vjy  Bruhns   (German  edi-  flames,  and  it  is  no  longer  a  dis- 

tion),   p.   184.  cus.sion    with    closed    doors.'       'A 

-  See  Huxley  in  'Life  of  Owen.'  dreadful    affiiir,'    I    replied.      'But 

vol.   ii.   p.  293.  what   else  could   one  expect  undei- 

■*  Eckermann  in   the    '  L'onversa-  the  well-known    circumstances  and 

tions  with  Goethe '  gives  the  follow-  with  such  a  ministry,   but  that  it 

ing  remarkable  account,  under  date  would  end  with  the  expulsion  of  the 

2nd   August   1830:   "  The  new.s  of  Royal   Family.'"     '  We  do  not  seem 

the  outbi-eak  of  the  French  Revolu-  to     understand     each     other,    my 

tiim    arrived    to-day,    and    created  friend,'  retorted  Goethe.     '  I  am  in 

e.xcitement    everywhere.       In    the  iM'wi-c  speaking  of  tho.se  peojile  ;  I 

course  of  the  afternoon  I  went  to  am  iimcerued  with  quite  different 

Goethe.     'Well,'  he  called  out  to  iliiiiL,'s.     I  spe.ak  of  that  most  im- 

me,    '  wiiat    do   you    think  of    this  porlant    conflict    which    has    come 


254 


SCIENTIFIC    THOUGHT. 


Similarly  the  aged  Gauss,  twenty-four  years  later,  listened 
with  emotion  when  Eiemann,  in  his  celebrated  disserta- 
tion, touched  a  string  that  had  been  vibrating  in  the 
master's  soul  for  fifty  years,  unheard  or  unheeded  by 
any  other  thinker.^  We  can  best  understand  the  two 
ways  of  reasoning  in  natural  objects,  which  found  an 
expression  in  the  controversy  between  Cuvier  and  Saint- 
Hilaire,  if  we  read  the  account  which  Goethe  himself 
subsequently  pubHshed  in  a  Berlin  periodical :  "  Cuvier 
labours  untiringly  as  a  distinguisher,  describing  accur- 
ately what  lies  before  him,  and  thus  attains  a  command 
over  a  great  breadth  of  facts.  Geoffroy  Saint-Hilaire, 
on  the  contrary,  is  silently  exercised  about  the  analogies 
of  living  creatures  and  their  mysterious  relations." "  The 
two  men  had  worked  as  colleagues  for  thirty-eight  years, 
Cuvier  continuing  and  defining  more  clearly  the  classi- 
fying work  of  Linnseus,  who,  for  example,  had  thrown 
all  non-vertebrate  animals  into  one  class.      This  led  him 


to  pass  in  the  Academy  between 
Cuvier  and  Geoffroy  Saint-Hilaire, 
and  which  is  of  such  importance 
to  science.'  This  utterance  of 
Goethe  was  so  unexpected  to  me 
that  I  did  not  know  what  to  say, 
and  that  for  some  minutes  I  ex- 
perienced a  complete  cessation  of 
my  thoughts.  '  The  matter  is  of 
the  greatest  importance,'  continued 
Goethe,  '  and  you  have  no  idea 
what  I  feel  concerning  the  news 
of  the  19th  July.  We  now  have 
a  mighty  ally  permanently  in 
Geoffroy.  But  I  also  see  from  it 
how  great  is  the  interest  of  the 
scientific  world  in  France  in  this 
matter,  as,  in  spite  of  tlie  frightful 
political  excitement,  the  meeting 
took  place  in  a  crowded  house. 
What  is  best  is,  that  the  synthetic 
treatment  of  nature,  introduced  by 


GeofiFroy  in  France,  cannot  again 
go  back.  ...  I  have  for  fifty 
years  laboured  in  this  cause  ;  first 
alone,  then  supported,  and  at  last, 
to  my  great  delight,  excelled  by 
congenial  minds.  .  .  .  This  event 
is  for  me  of  incredible  value,  and 
I  rejoice  rightly  over  the  ultimate 
general  victory  of  the  cause  to 
which  I  have  dedicated  my  life, 
and  which  also  is  essentially  my 
own." 

^  On  this  incident  see  the  prefa- 
tory notice  in  Riemann's  '  Mathe- 
matische  Werke,'  ed.  Weber,  Leipzig, 
1875,  p.  517  ;  also  the  1.3th  chapter 
of  this  volume. 

^  Goethe  in  the  '  Berliner  Jahr- 
biicher  fiir  Wissenschaftliche  Kri- 
tik,'  vol.  ii.,  1830,  September,  re- 
printed in  Werke  II.  vol.  vii.  p.  167 
sqq. 


ON    THE    MORPHOLOGICAL    VIKW    UF    NATUKK.      255 

tinally  in  1817  to  establish  the  four  great  classes — the 
vertebrate,  the  molluscous,  the  articulate,  and  radiated 
types — in  the  animal  kingdom.  His  colleague  had  con- 
tributed much  to  Cuvier's  work,  but  had  been  increas- 
ingly struck  by  what  lie  termed  the  "  unity  of  organic 
composition,"  which  he  evermore  looked  upon  as  a  key  ^ 
to  the  comprehension  of  nature :  he  searched  for  one 
]ilan  or  type  where  Cuvier  saw  four  types.  In  1818 
lie  published  his  principle  in  a  celebrated  work  with 
the  title,  '  Theorie  des  Analogies,  ou  de  I'hilosophie 
Anatomique.' "  It  has  been  correctly  stated  that  he 
only  gives  more  precise  expression  to  a  truth  known 
to  Aristotle  and  proclaimed  by  Buffon,  that  the  mystery 
of  ort^anisation  consists  in  "  unity  of  plan  combined  with        42. 

'^  ^  iT  Cuvier  and 

variety  of  composition."  Cuvier  emphasised  and  studied  Geooroy. 
the  latter,  his  colleague  the  former.  For  an  intimate 
knowledge  and  description  of  natural  objects  the  work 
of  distinguishing  is  all  important;  for  a  comprehension 
of  nature  the  connection  of  things,  the  unity  of  plan, 
the  filiation  and  relations  of  beings,  the  mutability  of 
species,  will  ever  be  the  more  important  and  fascinating. 
The  former  was  a  purely  scientific,  the  latter  a  philo- 


'  See  Goethe's  detailed  Keport, 
loc.  cit.,  W^erke  IL  vol.  vii.  p.  173. 
A  very  full  account  of  this  cele- 
brated controversy  is  also  given  in 
the  i>osthumous  work  of  Ducrotay 
de  Blaiuville,  '  Cuvier  et  Geuffroy 
Saint-Hilaire,  Biographies  scientif- 
iques,'  ed.  Nicard,  Paris,  1890, 
pp.  3o7-378,  which  is  specially  in- 
teresting, because  Geotfroj''s  ideas 
were  there  traced  to  Lamarck  (p. 
351),  of  whom  Goethe  takes  no 
notice.  , 

2  See     the    "  Eloge    Historique 
d'Etienne    Geoffrey   vSaint-Hilaire," 


par  P.  Flourens,  in  the  third  volume 
of  his  '  Recueil  des  Eloges,'  &c., 
Paris,  1862,  pp.  229-281.  He  quotes, 
inter  alid,  a  passage  from  Vicq- 
d'Azyr  :  "  La  nature  seuible  operer 
toujours  d'aprcs  un  modele  primitif 
et  g^ndral  dont  elle  ne  s'ecarte  qu' 
b,  regret,  et  dont  on  rencontre  par- 
tout  des  traces.  ...  On  observe 
partout  ces  deu.x  charactores  (|ue  la 
nature  semble  avoir  imprimes  li  tous 
lea  etres,  celui  de  la  coustance  dans 
le  type  et  celui  de  la  variott^  dans 
les  modifications,"  &c.  (p.  276). 


256 


SCIENTIFIC    THOUGHT. 


sophical,  task.  Both  thinkers  were  right,  but  only  par- 
tially right,  as  Huxley  has  clearly  shown ;  ^  but  it  was 
natural  that  Cuvier's  position  should  for  a  long  time  be 
regarded  as  the  stronger ;  since  he  had  shown  how,  by 
detailed  research,  to  increase  enormously  the  stock  of 
actual  knowledge  about  the  things  of  nature ;  whereas 
the  uncritical  and  only  half  practical  suggestions  of 
Goethe  had  undergone  in  the  wild  speculations  of 
SchelHng,  Steffens,  and  Oken  a  development  that  fright- 
ened off  men  of  exact  thought.  Cuvier  saw  the  necessity 
of  crying  halt  to  these  vague  dreams  which  he  had  the 
merit  of  opposing,  for  the  lasting  benefit  of  true  science, 
with  the  full  force  of  his  great  authority.^ 

As  in  France  and  Germany  so  also  in  England,  the 
tendency  to  distinguish  minutely,  to  describe,  to  classify, 
and  in  doing  so  to  fill  the  museums  with  new  specimens. 


1  '  Life  of  Owen,'  vol.  ii.  p.  296  : 
"The  irony  of  history  is  nowhere 
more  apparent  than  in  science. 
Here  we  see  the  men  over  whose 
minds  the  coming  events  of  the 
world  of  biology  cast  their  shadows, 
doing  their  best  to  spoil  their  case 
in  stating  it ;  while  the  man  who 
represented  sound  scientific  method 
is  doing  his  best  to  stay  the  inevit- 
able progress  of  thought  and  bolster 
up  antiquated  traditions.  The  pro- 
gress of  knowledge  during  the  last 
seventy  years  enables  us  ,to  see  that 
neither  Geoffroy  nor  Cuvier  was 
altogether  right  nor  altogether 
wrong  ;  and  that  they  were  meant 
to  hunt  in  couples  instead  of  pull- 
ing against  one  another." 

2  As  to  Cuvier's  own  wavering  on 
the  great  question  of  the  fixity  of 
species,  see  Huxley,  loc.  cit.,  p.  294  : 
"  During  the  earlier  part  of  his 
career,  I  doubt  if  Cuvier  would 
have   categorically   denied    any    of 


GeofFroy's  fundamental  theses.  And 
even  in  his  later  years  Sir  Charles 
Lyell,  many  years  ago,  gave  me 
reasons  for  the  opinion  that  Cuvier 
was  by  no  means  confident  about 
the  fixity  of  species.  There  was 
never  any  lack  of  the  scientific  im- 
agination about  the  great  anato- 
mist ;  and  the  charge  of  indifference 
to  general  ideas,  sometimes  brought 
against  him,  is  stupidly  unjust." 
And  further,  p.  295  :  "  In  later  life, 
however,  Cuvier  seems  to  have  be- 
come so  much  disgusted  by  the 
vagaries  of  the  Naturphilosophie 
school,  and  to  have  been  so  strongly 
impressed  by  the  evil  which  was 
accruing  to  science  from  their  ex- 
ample, that  he  was  provoked  into 
forsaking  his  former  wise  and 
judicious  critical  attitude  ;  and  in 
his  turn  he  advocated  hypotheses 
which  were  none  the  better  than 
those  of  his  opponents." 


ON    THK    MUKI'HOLOGICAL    VIKW    OF    NATUKK.      257 


43. 
Richard 


and  Lo  discover  and  uiTunge  systeiiuitically  unknown 
and  extinct  species,  got  the  upper  hand  for  a  long 
time.  No  one  has  done  better  work  in  this  large 
field  than  Eichard  Owen,  who  has  been  termed  with 
some  propriety  the  British  Cnvier.  But  in  following  owcil 
the  lines  and  filling  up  the  schedules  which  Cuvier 
liad  prepared,  Owen  and  other  ^  contemporary  workers 
in  the  same  field  have  also  had  the  great  merit  of 
bringing  the  Cuvierian  view  to  the  point  where  it 
clearly  leads  on  to  another  and  more  comprehensive 
view  of  nature.  In  the  first  place,  it  happened  that 
in  finding  and  describing  the  remains  of  extinct  animals, 
increasing  difficulty  was  experienced^  in  deciding  to 
which  of  the  great  existing  groups  of  animals  they 
should  be  assigned.  There  arose  the  necessity  of  in- 
terpolating species  between  groups  which  we  now  look 
upon  as  widely  separated.  The  necessity  arose  of  form- 
ing the  conception  of  what  is  now  termed  the  "  inter- 


'  Huxley,  loc.  cit.,  p.  ;ilO  :  '•  Un- 
less it  be  in  the  '  Ossenients  fossiles,' 
I  do  not  know  where  one  is  to  look 
for  contributions  to  paUcontology 
more  varied,  more  numerous,  and, 
on  the  whole,  more  accurate,  than 
those  which  Owen  poured  forth  in 
rapid  succession  between  1837  and 
1888.  Yet  there  was  no  lack  of 
strong  contemporaries  at  work  in 
the  same  field.  De  Blainville's 
'  Ost^ographie  '  ;  Louis  Agassiz's 
monumental  work  on  fossil  fishes, 
achieved  under  the  ])ressure  nf 
great  obstacles  and  full  of  bi-illianl 
suggestions  ;  Von  Meyer's  long  series 
of  wondei-fully  accurate  memoirs, 
with  their  admirable  illustrations 
executed  by  his  own  hands,  all 
belong  to  Owen's  generation." 

-  See  on  this  Carus,  '  tleschichte 

VOL.  IL 


der  Zoologie,'  p.  648,  and  Huxley, 
loc.  cit.,  p.  309,  where  reference  is 
made  to  Owen's  memoir  "on  an  ex- 
tinct mammal  discovered  in  South 
America  by  Darwin  in  L833,  which 
Owen  named  Taxodon  Platensis.  It 
is  worthy  of  notice  that  in  the  title 
of  this  memoir  there  follow,  after 
the  name  of  the  species,  the  words 
'referal)Ie  by  its  dentition  to  the 
Rodentia,  but  with  affinities  to 
the  Pachydermata  and  the  herbi- 
vorous Cetacea '  ;  indicating  the 
imjiortance  in  the  mind  of  the 
writer  of  the  fact  that,  like  Cuvier's 
Anoplothcriurii  and  Palcvothcrium, 
Taxodon  occupied  a  position  be- 
tween groups  which,  in  existing 
nature,  are  now  widely  separated. 
The  existence  of  one  more  '  inter- 
calary '  type  was  establislied." 

B 


258 


SCIENTIFIC    THOUGHT. 


44. 
Study  of 
homology. 


calary  type."  Especially  through  palseontological  finds, 
the  landmarks  were  gradually  removed  which  separated 
the  distinct  species  and  groups  of  organised  beings. 
It  had  happened  to  Cuvier  only  in  single  instances 
that  he  had  to  record  resemblances  between  widely 
separated  groups.  Such  resemblances  became  more  and 
more  frequent  and  perplexing.  In  the  second  place, 
Owen  had  the  great  merit  of  giving  more  definite  ex- 
pression to  the  conception  of  analogies,  as  developed 
principally  by  the  school  which  Cuvier  opposed.  In 
fact,  he  revised  and  brought  into  general  use  the  term 
"  homology,"  which  had  already  been  used  by  French  and 
German    anatomists   before    him.^      This    term  signified 


^  Great  importance  has  been  at- 
tached to  the  term  "homology," 
which,  to  a  reader  uuiuitiated  iu 
the  complicated  and  changing  vo- 
cabulary of  the  natural  sciences, 
presents  not  a  little  difficulty. 
It  is  a  good  example  of  the 
classical  saying  of  Goethe,  "dass 
wo  Begriffe  fehlen,  da  stellt  ein 
Wort  zu  guter  Zeit  sich  ein."  In 
the  attempt  to  define  the  current 
term  "homology,"  in  seeking  for 
numerous  examples  of  homologies 
as  distinguished  from  analogies,  nat- 
uralists were  led  to  the  recognition 
of  i-eal,  not  only  of  verbal  or  logical 
distinctions.  In  this  respect  it  is 
most  instructive  to  read  Owen's 
treatise  '  On  the  Archetype  and 
Homologies  of  the  Vertebrate 
Skeleton'  (1848),  the  enlarged  re- 
print of  a  Report  to  the  British 
Association  in  1846.  In  it  he  gives 
a  pretty  full  history  of  the  term 
homology,  which  in  the  first  half  of 
the  nineteenth  century  became  cur- 
rent with  special  meanings  in  three 
independent  sciences.  With  the 
precision  of  the  usage,  both  in 
geometry  and  chemistry,  the  vague- 


ness of  the  term  as  used  by  nat- 
uralists stands  in  characteristic  con- 
trast. "  The  corresponding  parts," 
Sir  R.  Owen  there  says  (p.  5), 
"  in  different  animals  being  made 
namesakes,  are  called  technically 
'  homologues.'  The  term  is  used 
by  logicians  as  synonymous  with 
'homonyms,'  and  by  geometricians 
as  signifying  '  the  sides  of  similar 
figures  which  are  opposite  to  equal 
and  corresponding  angles,'  or  to 
parts  having  the  same  propor- 
tions :  it  appears  to  have  been 
first  applied  in  anatomy  by  the 
philosophical  cultivators  of  that 
science  in  Germany.  Geoffroy 
Saint  -  Hilaire  says,  '  Les  organes 
des  sens  sont  homologues,  comme 
s'exprimerait  la  philosophic  Al- 
lemande  ;  c'est-a-dire  qu'ils  sont 
analogues  dans  leur  mode  de 
develo2323ement,  s'il  existe  veritable- 
ment  en  eux  uu  meme  principe  de 
formation,  una  tendance  uniforme 
li  se  rep^ter,  h.  se  reproduire  de  la 
meme  fagon.'"  After  remarking 
on  the  looseness  of  this  definition, 
Owen  proceeds  to  give  his  own, 
taken    from    the    "  Glossary "    ap- 


ON    TUR    MORPHOLOGICAL    VIP:VV    OF    NATTRE, 


259 


correspondence  of  parts  or  organs  based  not  so  much  on 
external  likeness  as  on  similarity  of  origin.  Ly  admit- 
ting the  latter  conception,  the  idea  of  origin,  the  rigidity 
■of  the  purely  structural  classification  was  lost.  Morpho- 
logy became  the  science,  not  of  fixed,  but  of  flowing 
forms  and  structures.  It  is  remarkable  that  Owen,  in 
following  up  this  line  of  reasoning,  was  pre-eminently  at- 
tracted to  the  oracular  writings  of  Oken,  whose  influence 
his  great  forerunner  Cuvier  had  combated  with   all  his 


pended  to  tlie  first  volume  of  his 
'  Hunteriaii  Lecture.s,'  as  follows  : 
"  '  Analogue  ' — A  part  or  organ  in 
one  animal  which  has  the  same 
function  as  another  part  or  organ 
in  a  different  animal."  "  '  Hom- 
ologue'  —  The  same  organ  in  dif- 
■erent  animals  under  every  variety 
of  form  and  function."  He  then 
goes  on  to  distinguish  "  special," 
^'  general,"  and  "  serial "  homology. 
For  a  history  of  thought  the  imjwr- 
tant  point  in  all  these  discussions 
is  that,  besides  the  similarity  of 
sti'ucture  and  the  sameness  of 
function,  relations  and  jjoints  of 
comparison  of  a  different  kind 
were  introduc:ed  ;  tliat  these  were, 
with  more  or  less  clearness,  traced 
to  development ;  and  that  through 
this  the  genetic  view,  the  doctrine 
of  descent,  was  prepared  by  those 
who,  like  Owen,  were  least  ready 
to  accept  it  when  it  ap])eared  in  a  I 
■definite  form.  In  the  light  of  this  j 
new  view,  of  which  the  ne.\t 
chapter  will  treat,  the  whole  vocab- 
ulary of  the  older  morphologists  I 
required  recasting.  These  older 
views,  which  traced  homology  t<i 
the  existence  of  definite  types, 
models,  or  i)atterns  possessing  a 
purely  ideal  existence,  have  been 
termed  Platonic,  inasmuch  as  in 
the  philosophy  of  Plato  the  exist- 
•C'uce  of  a  world  of  ideal  forms  or 


archetypes  served  to  explain  what- 
ever of  order  is  found  in  the  real 
world  of  separate  things.  "  The 
term  'homology,'"  says  Prof.  Itay 
Lankester,  "  belongs  to  the  Platonic 
school,  but  is  nevertheless  used 
without  hesitation  by  those  who 
reject  the  views  of  that  school. 
Prof.  Owen  .  .  .  would  understand 
by  '  homologue '  the  same  firgan 
in  different  animals  under  every 
variety  of  form  and  function.  .  .  . 
But  how  can  the  sameness  of  an 
organ  under  every  variety  of  form 
and  function  be  established  or  in- 
vestigated r  This  is,  and  always 
has  been,  the  stumbling-block  in 
the  study  of  homologies  without 
tlie  light  of  Evolutionism  ;  for,  to 
settle  this  question  of  sameness, 
an  ideal  '  type '  of  a  group  of 
organisms  under  study  had  to  be 
evolved  from  the  human  mind, 
after  study  of  the  comj)onent 
members  of  the  group  ;  and  then 
it  could  be  assei-ted  that  organs 
might  be  said  to  be  the  '  same ' 
in  two  animals  which  had  a 
common  representation  in  the 
ideal  type"  {'Annals  and  Mag. 
of  Natural  History,'  4th  series, 
vol.  vi.,  1870.  p.  34,  &c.)  See  also 
Huxley  in  '  Life  of  Owen,'  vol.  ii. 
p.  303,  &c. ;  and  J.  Arthur  Thom- 
son, 'The  Science  of  Life,'  p.  32 
(1899). 


260  SCIENTIFIC    THOUGHT. 

might,  and  who  "  provided  him  with  the  subject-matter 
of  his  severest  as  well  as  of  his  most  justifiable 
sarcasms."  ^ 

The  great  extension  of  the  morphological  or  struc- 
tural view  of  nature  into  distant  time  and  space — into 
palaeontology  by  Cuvier  and  Owen,  into  geography  by 
Humboldt,  Eitter,  and  others — i.e.,  morphology  on  an 
extensive  scale — led  to  an  appreciation  of  the  labours 
of  a  different  class  of  students  of  nature,  namely,  those 
who — also  on  a  large  or  a  smaller  scale — investigated 
the  agencies  which  bring  about  and  the  laws  which 
CTovern  the  change  of  forms.  I  have  now  to  mention 
the  last  great  contribution  to  the  purely  morphological 
45.        view,  I  mean  the  cellular  theory,  which  tended  ultimately 

The  cellular    .  . 

theory.         m  a  Similar  direction. 

The  earlier  researches  into  the  minute  microscopic 
structure  of  organised  beings — such  as  those  of  Malpighi 
and  Grew  in  the  seventeenth  century— were  conducted 
by  persons  who  took  an  equal  interest  in  animal  and 
plant  life."  But  this  class  of  research  soon  fell  into 
the  hands  of  specialists,  with  the  result  that  anatomy, 
the  science  of  animal  structure,  and  phytotomy,  that 
of  vegetable  structure,  were  conducted  on  different  lines 

^  Huxley,  'Life  of  Owen,'  vol.  ii.  '    sequent  researches,  of  the  doctrine 

p.  315.  of  the  composition  of  all  organised 

-  Carus  ('Gesch.  der  Zoologie,'  p.  ]  bodies  out  of  cells,  which  has  given 
'  39.5)  mentions  especially  Malpighi  to  the  whole  conception  of  the  Hv- 
(1628-1694)  as  an  exception,  inas-  ing  creation  a  definite  starting- 
much  as  he  conducted  his  researches  !  point,  and  in  the  sequel  a  firm  basis 
from  a  purely  scientific  interest,  j  for  the  genetic  view."  See  also  on 
keeping  them  free  from  extraneous  '  the  same  subject,  and  on  the  rela- 
practical  considerations.  "  In  his  tion  of  structural  and  physiological 
anatomy  of  plants  there  are  laid,  researches  in  the  seventeenth  and 
moreover,  the  first  foundations,  eighteenth  centuries,  Sachs,  '  Gesch. 
more  firmly  established  by  all  sub-  d.  Botanik,'  p.  351,  &c. 


ON  THK  MORPHOLOGICAL  VIEW  oK  NATURE.   261 

ami  for  dill'ereiiL  purposes.  Thu  fuel  that  the  organisa- 
tion of  the  higher  animals,  which,  for  medical  reasons,  is 
more  interesting,  can  be  roughly  divided  into  a  variety 
of  separate  organs  or  systems  of  organs,  each  of  wliicli 
can  be,  to  some  extent,  studied  by  itself  as  we  study 
the  parts  and  workings  of  a  machine,  and  that  for  the 
physician  greater  interest  attaches  to  the  functions  of 
these  organs,  placed  anatomy  for  a  long  time  under  the 
influence  of  physiology,  which  is  the  science  of  the  per- 
formance, not  of  the  structure,  of  the  parts  of  living  crea- 
tures. Phytotomy,  on  the  other  side,  was  for  a  long  time 
neglected,  awaiting  the  greater  perfection  of  the  micro- 
scope. Thus  it  came  al)out  tliat  down  to  nearly  the 
middle  of  the  century  the  morphological  study  of  animals 
and  that  of  plants  were  pursued  without  much  mutual 
benefit  or  regard.  The  phytotomists  of  the  seventeenth 
century  had  established  the  fact  that  plants  are  built  up 
of  minute  parts  called  variously  utricles,  bladders,  vesicles, 
but  mostly  cells,  and  which  were  compared  with  tlie 
structure  of  the  foam  of  Ijeer  or  the  cells  of  a  honey- 
comb.^     Different  forms  were  assigned  to  these  cavities. 


'Aug.   Pyr.    de    Caiidolle    begins  isation  des  Plautes '  (Harlem,  1812) 

his    '  Organographie  '    (1827)    with  as  the  only  French  book  whicli  con- 

tlie  words:  "La  nature  iiitime  des  tains  an  account  of  the  phytotoniic 

vcgi'taux,  vue  aux  plus  forts  micro-  ,    reseaiclies  cai-ried   on  by  the   Ger- 

scopes,  offre  peu  de  diversitds.    Les  mans,  who,  after  the  lapse  of  a  cen- 

plantes  les  plus  disparates  par  leurs  tury,   were    the    first    to    take    uj) 

formes  extdrieures,  se  ressemblent  I    these  studies  again.     In  the  second 

;i   I'intc'rieur  a  un   degrd  viainieiit  chapter    l^e    Caiidolle    says;     "  Le 

extraordinaire,"    &c.  ;     and     after  ti-*su  cellulaiio,  considers  en  masse, 

going  back    to  the  observations  of  est  un  tissu  membraiieux  foi-mc  par 

Malpighi   and   Grew,  and   referring  '    un  grand  nombre  de  cellules  ou  de 

to  the  recent  ones  of  Mirbel,  Link,  i   cavites    closes    de    toutes    parts  ; 

Treviranus,      Sprengel,      Kudolphi  rccume    de  la   bicre   ou    un  rayon 

Kieser,  Dutrochet,  and  Amici,  men-  de  miel  en  donnent  unc  idee  gross- 

tions  Kieser's  '  Memoire  sur  I'Organ-  |   i6re  mai.s  assez  exacte  "  (j).  11). 


262 


SCIENTIFIC    THOUGHT. 


46. 

Hugo  von 
Mohl. 


and  it  was  also  recognised  that  they  were  frequently 
elongated  into  tubes  or  joined  so  as  to  form  larger 
vessels.  In  all  these  researches  and  descriptions  para- 
mount importance  was  attached  to  the  form  and  com- 
position of  the  framework  of  this  cellular  arrangement, 
and  only  little  to  its  contents.  In  fact,  the  historian 
of  botany^  characterises  the  period  from  1800  to  1840 
as  that  of  the  study  of  the  cellular  framework  of  plants. 
The  skeleton,  as  it  were,  of  plant  structure  received 
primarily  the  greater  attention.  In  the  course  of  these 
researches,  which,  with  a  few  important  exceptions,  were 
all  carried  out  in  Germany,  one  point  was  permanently 
settled,  namely,  that  "  the  cell  is  the  one  fundamental 
element  of  all  vegetable  structure."  ^  No  one  did  more 
to  establish  this  important  fact  than  Hugo  von  Mohl, 
whose  name  has  been  somewhat  cast  into  the  shade  by 
the  more  attractive  writings  of  Schleiden.  It  was 
Schleiden  who  first  brought  the  new  cellular  theory 
into  popular  recognition,  not  without  an  admixture  of 
errors,  which  had  to  be  gradually  eliminated  in  the 
various  controversies  with  which  his  name  is  connected. 


^  See  Sachs,  loc.  cit.,  p.  276,  &c. 
This  period  finds  its  consummation 
in  the  researches  of  Hugo  von  Mohl. 
It  begins  with  those  of  Brisseau 
Mirbel,  the  first  French  author  who 
took  up  this  line.  His  labours  were 
continued  and  criticised  by  a  long 
list  of  German  naturalists.  Sachs 
also  refers  to  the  erroneous  habit 
these  earlier  phytotomists  had  of 
getting  their  diagrams  of  what 
they  saw  by  the  microscope  made 
by  other  persons  who  were  sup- 
posed to  be  impartial  —  a  custom 
fortunately  abandoned  by  Mohl, 
who  in  his  drawings  did  not  give 


"  undigested  copies  of  the  objects 
but  his  own  impressions  of  them  " 
(p.^281). 

-  Sachs  assigns  the  final  estab- 
lishment of  this  principle  to  the 
year  1831,  and  considers  it  as  one 
of  Mohl's  achievements,  since, 
although  it  had  been  already 
announced  by  Sprengel  and  Mirbel, 
it  had  not  been  sufficiently  sup- 
ported by  observations.  Even  the 
curious  but  antiquated  idea,  accord- 
ing to  which  the  spiral  fibre  formed 
a  fundamental  part  of  plant  struc- 
ture, survived  up  to  1830  (p.  323). 


ON    THE    MORPHOLOGICAL    VIEW    OF    NATURE.      263 


Soliwanii. 


But  the  highest  value  for  a  history  of  Thought  attaches 
to  this  point  for  a  different  reason.  In  it  the  hjug- 
separutetl  Hues  ^  of  botanical  and  zoological  study  met 
again.      Immediately  after  the  appearance  of  Schleiden's        47. 

_  Sclilcideti 

epoch-making  publication — and  partly  in  consequence  of  and 
it — Theodor  Schwann  was  induced  to  collect,  in  1839, 
all  the  known  observations,  coming  principally  from 
the  scliool  of  Johannes  Miiller,  which  referred  to  the 
existence  and  formation  of  animal  cells,  and  to  utilise 
them  in  the  enunciation  of  liis  great  generalisation, 
"  that  there  is  one  universal  principle  of  development 
for  the  elementary  parts  of  organisms  however  different, 
and  that  this  principle  is  the  formation  of  cells."  ^ 


'  The  fourth  decade  of  the  cen- 
tury was  also  the  period  in  which 
pliysical  and  (.'lieiiiical  methods  and 
ideas  were — notably  in  France  and 
Germany  — made  useful  for  ana- 
tomical and  physiological  research 
in  zoology  and  botany.  Sachs, 
however,  significantly  warns  us 
against  the  view,  which  has  since 
been  frequently  put  forward  in  an 
exaggerated  form,  that  the  physi- 
ology of  jilants  consists  in  nothing 
but  a])i)lied  physics  and  chemistry 
{loc.  cit.,  p.  393,  &c. )  That  Schwann 
himself  attached  the  greatest  im- 
portance to  this  point  can  be  seen 
from  the  preface  to  his  jirincipal 
work.  This  appeared  in  1839,  and 
was  translated  into  English  by 
Henry  Smith,  and  published  l)y  the 
Sydenham  Society  in  1847  with  the 
signiticant  title,  '  Microscopical  Re- 
searches into  the  Accordance  in  the 
Structure  and  Growth  of  Animals 
and  Plants. '  The  translator  has  also 
attached  a  rendering  of  Schleiden's 
'  Contributions  t(j  Phylogenesis,' 
which  a[){)eared  Hrst  in  Part  IL  of 
Miiller's  '  Archiv  f  lir  Anatomie  und 
Physiologic'  in  1838,  and  was  also 


translated    in    '  Taylor's    Scientific 
Memoirs,'  vol.    ii.  part  6. 

-  Schwann,  loc.  cit.,  p.  165.  A 
little  farther  on  he  ;ulds  the  follow- 
ing generalisation,  which  it  is  well 
to  read  in  the  light  of  more  recent 
researches:  "A  structureless  sub- 
stance is  present  in  the  first  instance, 
which  lies  either  around  or  in  the 
interior  of  cells  already  existing ; 
and  cells  are  formed  in  it  in  accord- 
ance with  certain  laws,  which  cells 
become  developed  in  various  ways 
into  the  elementary  parts  of  organ- 
isms." It  is  clear  that  the  discovery 
of  what  may  be  called  the  morpho- 
logical clement  or  unit  of  organised 
structures  in  this  view  meant  the 
end  of  pure  morphology.  The 
problem  of  the  explanation  of  exist- 
ing forms  was  handed  over  to  the 
student  of  development,  to  the  gen- 
etic view  and  conceptinn  of  nature. 
The  cellular  theory,  thus  enunci- 
ated in  its  greatest  generality  by 
Scliwann,  has  formefl  a  kind  of 
provisional  resting  -  place  in  the 
study  of  the  forms  and  changes  of 
living  nature  ;  as  Newton's  gravita- 
tion formula  has  served  jvs  a  provi- 


264  SCIENTIFIC    THOUGHT. 

Morphologically  the  microscopic  examination  of  animal 
and  vegetable  tissues  had  thus  led  not  to  a  clearer  defini- 
tion of  the  great  differences  which  exist  in  the  forms  and 
structures  of  the  larger  and  the  full-grown  organisms,  but 
rather  to  a  conviction  of  their  intrinsic  and  essential 
sameness.  These  differences  could  not  be  explained  in 
the  purely  morphological  manner  in  which  Haiiy  had 
shown  how  to  trace  the  difference  of  crystalline  forms 
to  the  shapes  and  configuration  of  the  "  molecules  in- 
t^grautes."  The  diversity  of  forms  had  to  be  traced  to 
4S.        processes   of   growth   or   development  —  i.e.,   the   purely 

Transition  •  i     i  i  i  i  i 

to  the  study  morphological  examination  led  on  to  the  developmental 

of  develop-  ■"■  ^ 

ment.  qj.  genctic  study  of  organic  forms.      And  this  was  made 

still  more  evident  when  the  microscopic  examination 
revealed  yet  other  and  more  important  elements  in 
the  composition  of  organic  structures,  elements  which 
were  seemingly  quite  shapeless  or  amorphous.  The 
skeleton,  which  had  so  long  seemed  to  contain  the  key 
to  the  understanding  of  organic  forms,  the  framework  of 
the  plant  structure,  the  cell-walls  and  partitions,  with 
all  their  geometric  figures  and  arrangements,  turned  out 
to  be  of  quite  secondary  importance  compared  with  the 
cell  contents,  the  substance  called  in  animals  by  Dujardin 
sarcode,  and  in  vegetables  by  Von  Mohl  protoplasm,  and 
with  the  nucleus  or  cell-kernel,  which  had  been  discovered 
by  Eobert  Brown.^      Accordingly  great  interest  attached 

sioual  basis  for  physical  astronomy,    j    cell  contents  by  Dujardin  preceded 


Both  generalisations  involve  un- 
solved problems,  with  the  difference 
that  the  formulation  of  the  cellular 
theory  is  not  as  precise  as  that  of 
gravitation. 

^  Both  the  discovery  of  the  nucleus 
by  Robert  Brown  and  that  of  the 


the  enunciation  of  the  cellular 
theory.  Brown's  discovery  was  re- 
ferred to  both  by  Schleiden  and 
Schwann.  In  fact,  Brown's  re- 
searches were  much  better  known 
and  followed  up  in  Germany  than 
in  England.    His  papers  were  trans- 


ON  THE  MORPHOLOGICAL  VIEW  OF  NATUHE.   265 

tu  these  amorphous^  constituents,  and  chemical  investi- 
gations as  to  their  composition  were  added  to  the  previous 
microscopic  dissection.      The  purely  morphological  view 


lated  into  Uerniiin  \iy  a  number  of 
botanists,  and  edited  in  five  volumes 
between  1825  and  1834  by  Nees 
von  Essenbeck.  He  did  not  collect 
his  original  ideas  into  any  great 
work  or  propound  a  new  system  of 
classification  as  did  Jussieu  and  De 
Candolle,  whom  he  equals  in  scien- 
tific importance  ;  his  valuable  geu- 
eralisivtions  were  given  occasion- 
ally in  his  numerous  monographs, 
Sachs  considers  him  more  advanced 
than  the  two  great  rivals  just 
named,  inasmuch  as  he  had  an 
appreciation  of  questions  of  devel- 
opment which  they  lacked  ('  Gesch. 
d.  Botanik,'  p.  121).  Humboldt 
called  him  "'  botanicorum  facile 
princeps,"  and  succeeded  in  procur- 
ing for  him,  thruugli  his  influence 
with  Sir  Robert  Peel,  a  pension  of 
£200  per  annum. 

'  The  detinilion  of  a  cell — i.e.,  of 
the  morphological  or  form-element 
of  organised  matter,  as  consisting 
of  a  membrane,  a  cell  content,  a 
nucleus,  and  a  nucleolus — stood  in 
contrast  with  Felix  Dujardin's  de- 
scription, in  1835,  of  a  living  sub- 
stance which  he  met  with  in  his 
researches  in  lower  animal  life,  and 
which  he  had  called  "sarcode."  In 
the  place  of  this  name — the  observa- 
tion of  Dujardin  being  little  noticed 
— Von  Mold,  after  having  for  a  time 
accepted  the  erroneous  theory  of 
Schleiden  ami  Schwann  as  to  cell- 
formation,  introduced  the  term 
"  protoplasma,"  which  has  been  re- 
tained in  science  as  the  name  of  the 
elementary  constituent  of  all  living 
matter  with  very  varying  defini- 
tions, acc(jrding  to  the  ditterent 
observations  of  animal  or  vegetable 
organisms  and  the  increasing  powers 
of  the  microscope  ;  this  having  re- 
vealed structures  where  before  only 


formless,  amorphous  substance  had 
been  observed.  The  history  of 
these  fluctuations  of  ojnnions  and 
definitions  can  be  read  bcjth  in  the 
older  histories  (Sachs,  Cams)  and 
the  more  recent  accounts.  Among 
these  numerous  e.\|iositions,  see 
esi>ecially  Yves  Delage,  'L'HcSrcdite 
et  les  grands  jiroblemes  de  la  Bio- 
logie,'  1895,  p.  19,  &c.;  O.  Hertwig, 
'The  Cell,'  translated  from  the 
(ierman  by  H.  J.  Campbell,  1895  ; 
and  the  most  recent  work  by  Dr 
Val.  Hacker,  '  Praxis  und  Theorie 
der  Zellen  und  Befruchtungslehre, ' 
Jena,  1899,  p.  10,  &c.  The  cellular 
theory  has  gained  enormously  in 
importance  and  in  popular  esteem, 
as  has  also  the  study  of  all  micro- 
organisms, through  its  application 
to  medicine  and  hygiene.  In  1847 
Rudolph  Virchow  founded  his  cele- 
brated "cellular  jiatiiology,"  com- 
bining the  many  beginnings  of  the 
cellular  theory  which  had  been 
laid  by  others,  in  his  famous  axiom 
'■  omiiis  cellula  e  cellula. "  He  gave 
up  the  theory  of  the  free  forma- 
tion of  cells,  proclaimed  the  doctrine 
of  the  genesis  of  cells — even  patho- 
logical ones — by  cell-division,  and 
adopted  Goodsir's  theory  of  the 
uninterrupted  filiation  of  the  ele- 
ments of  all  living  matter,  of  tlie 
autonomous  cells.  As  in  general 
biologj',  so  al.so  in  cellular  path- 
ology, the  last  fifty  years  have 
witnessed  gi'cat  controversies  and 
many  special  theories,  one  of  the 
chief  difficulties  having  been  to  com- 
bine the  doctrine  of  the  autonomy 
or  individualitj'  of  the  cells  with  a 
correct  view  of  their  filiation  and 
connected  life.  In  sjiite  of  tiiese 
many  changes  and  modifications,  the 
name  of  Schwann  still  sti\nds  at  the 
opening  of  every  treatise  on  funda- 


266 


SCIENTIFIC    THOUGHT. 


had    exhausted    itself.     The    fundamental    unity  of  the 
organisation  of  living  beings  had  been  proved ;  how  was 
their  actual  diversity  to  be  explained  ?     This  evidently 
required  considerations  of  a  very  different  kind.     What 
they  were  we  shall  see  in  the  next  chapter.     The  posi- 
tion of  the  morphologist  in   the  middle  of  the  century 
had  thus  become  one  of  considerable  perplexity.^     It  may 
be  compared  to  that  of  the  organic  chemist  about  the 
same  time.     The   older   ideas,  around   which,  under  the 
great  influence  of  Cuvier   and   De  Candolle  in  zoology 
and  botany,   of  Werner  and  Humboldt  in  geology,  the 
morphological    classification    and   description   of   natural 
objects    had    clustered    on    the    Continent,   had   become 
obsolete.      The   doctrine   of  definite    types,   of   architec- 
tonic models,  or  of  distinct  ages  of   creation,  separated 
by  catastrophic  changes,  was  becoming  untenable ;  floras 
and   faunas   of   entirely   different   appearance   had   been 
revealed  in  other  countries  and  climates  in  the  distant 
past,^  or  in  the  great  newly-discovered  realm  of  living 


mental  biology,  and  that  of  Yirchovv 
at  the  origin  of  modern  pathology, 
as  the  greatest  practical  application 
of  the  cellular  theory.  An  exceed- 
ingly good  record  of  the  diffei-ent 
and  changing  views  referring  to 
the  cell  will  be  found  in  the  chapter 
on  "  Cell  and  Protoplasm  "  in  J. 
A.  Thomson's  'Science,  of  Life,' 
pp.   101-117. 

1  "  On  comprend  aisement  le 
d^couragement  de  Robin  renon9ant 
a  ^difier  son  '  Traite  d'Anatoniie 
generale,'  apres  avoir  teute  inutile- 
ment,  dans  sa  'Chimie  anatomique,' 
de  p^netrer  le  mecanisme  des 
phenomenes  moleculaires  s'accom- 
plissant  dans  les  corps  organises. 
La  morphologie,  pourtant,  n'avait 
pas    dit    son    dernier    mot,    et    la 


barriere  bio-chimique  ctait  nioins 
rapprochee  que  le  ne  croyaient  les 
disciples  de  Comte  et  de  De 
Blainville  "  (Herrmann,  article 
"Cellule"  in  'La  Grande  Ency- 
clo})^die,'  vol.  is.  p.  1060). 

■•*  Owen,  in  the  very  instructive 
"  General  Conclusions  "  to  the  third 
volume  of  the  '  Anatomy  of  Verte- 
brates '  (1868),  clearly  points  out 
how  the  position  of  Cuvier  has 
been  made  untenable  by  these 
discoveries  :  "  As  my  observations 
and  comparisons  accumulated,  with 
parijxtssu  tests  of  observed  phenom- 
ena of  osteogeny,  they  enforced  a 
reconsideration  of  Cuvier's  con- 
clusions to  which  I  had  previously 
yielded  assent"  (p.  188).  "Accord- 
ingly,  these   results   of   extensive, 


ON    THE    MOKPHULOGICAL    VIEW    OF    NATURE.      267 

forms  only  accessible  to  the  microscope.  The  metamor- 
phosis of  the  different  organs  in  the  plant  had  been  sug- 
gested by  Wolf,  and  more  fully  demonstrated  by  Goethe. 
Unity  of  organisation  had  Ijcen  proclaimed  by  Saint- 
Hilaire  and  De  lUaiuville,  and  the  ultimate  identity  of 
the  elementary  structure  of  animals  and  plants  had  been 
demonstrated  by  Schleiden  and  Schwann.  How  was  the 
evident  relationship  of  the  different  types  of  living  beings 
to  be  explained  ?  It  is  interesting  to  note  how  the  very 
terms  which  were  then  used  implied  the  explanation, 
though  this  was  only  apparent  to  one  or  two  natural 
philosophers  who  were  then  secretly  at  work.  The 
word  "  affinity,"  which  in  chemistry  has  for  ages  been        49. 

■^  ./  o  Affinity. 

used  to  denote,  without  explaining,  the  mystery  of  com- 
binations and  separations  of  different  substances,  had 
been  imported  into  philosophical  anatomy  to  denote  the 
deeper  structural  likeness  between  animals  which  at  the 
first  glance  appeared  to  belong  to  different  classes.  This 
word  ordinarily  implies  blood-relationship,  and  might  have 

patient,    and    unbiassed    inductive  i    which    tlicy     belonged,    I    was    at 

researcli— or,  if  there  were  a  bias,  length  led  to  recognise  one   cause 

it  was  toward  Cuvier — swayed  with  of  extinction  as  being  due  to  de- 

me    in    rejecting    the    principle   of  feat    '  in    the   contest    which,   as  a 

direct  or  miraculous  creation,  and  '    living    organised    whole,    the  indi- 

in    recognising   a    'natural    law    or  '    vidual     of     each     species    had    to 

secondary    cause     as    operative   in  maintain   against  the   surrounding 

the  j)ro(luction  of  species  in  orderly  agencies     which     might      militate 

succession  and  progression  '  (I'^^-iS) '■  against    its    existence'"    (p.    797). 

(p.  789).  ...  "Each  successive  parcel  .    Tlirough    this  passage,    quoted   by 

of  geological    trutli   has  tended  to  Owen   from   tlie  preface    (1866)  of 

di.ssipate    the    belief    in     the    un-  the  same  work,  a  controversy  arose, 

usually  sudden  and  violent  nature  it    being   taken    by   a    reviewer  to 

f  the  changes  recognisable  in  the  \    prove    the    admission    of  the   Dar- 


earth's  surface.  In  specially  direct- 
ing my  attention  to  tiiis  moot 
point,  whilst  engaged  in  investiga- 
tions of  fossil  remains,  and  in  the 
reconstruction    of    the    species   to 


winian  theory.  Tliere  followed  an 
e.xplanation  by  Owen,  rejecting 
natural  selection  and  the  admitted 
contest  as  explanations  of  the  origin 
of  species. 


268  SCIENTIFIC    THOUGHT. 

suggested  the  theory  of  descent :  it  was  used  by  those 
who  most  strongly  repudiated  such  a  doctrine.^ 

In  the  absence  of  any  satisfactory  explanation  of  the 
continual  recurrence  of  certain  definite  forms  in  nature, 
and  the  presence  of  an  evident  relationship  and  a  clear 
indication  of  metamorphosis  in  single  instances,  it  was 
natural  that  morphologists  of  the  first  order,  such  as 
Owen,  and  other  authorities  in  science,  such  as  Whewell 
in  England  and  Alexander  Braun  in  Germany,  should 
have  recourse  to  older  views  and  vague  philosophical 
theories.  Owen  in  1848  spoke  of  a  specific  organising 
principle  which  "  moulds  in  subserviency  to  the  exigencies 
of  the  resulting  specific  forms,"  argues  tliat  the  know- 
ledge of  such  a  being  as  man  must  "  have  existed  before 
man  appeared,  for  the  divine  mind  which  planned  the 
archetype  also  foreknew  all  its  modifications,"  and  con- 
cludes that  we  learn  from  the  past  history  of  our  globe 
that  "  nature  has  advanced  with  slow  and  stately  steps, 
guided  by  the  archetypal  light,  amidst  the  wreck  of 
worlds,  from  the  first  embodiment  of  the  vertebrate 
idea  under  its  old  ichthyic  vestment  until  it  became 
arrayed    in    the    glorious    garb    of    the    human   form.""^ 

1  Huxley   in   '  Life  of   11.  Owen,'  pertie.s    of    matter,    there    appears 

vol.  ii.   p.   302.  also    to    be    in    counter  -  operation 

-  See  Owen's  treatise  '  On  the  ■  during  the  building  up  of  such 
Nature  of  Limbs,'  1849,  pp  85,  bodies  the  polarising  force  pervad- 
86.  In  the  essay  '  On  the  Arche-  ing  all  space,  and  to  the  operation 
type  and  Homologies  of  the  Yerte-  of  which  force,  or  mode  of  force, 
brate  Skeleton,'  he  concludes  with  the  similarity  of  forms,  the  rep- 
tile following  remarks :  "  Now,  be-  etition  of  parts,  the  signs  of  the 
sides  the  iSe'a,  organising  ]irinciple,  unity  of  organisation  may  be 
vital  property,  or  force,  which  ]iro-  mainly  ascribed.  The  Platonic 
duces  the  diversity  of  form  belong-  iSia  or  specific  organising  principle 
ing  to  living  bodies  of  the  same  or  force  would  seem  to  be  in  an- 
materials,  which  diversity  cannot  tagonism  with  the  general  polar- 
be    explained    by    any  known    pro-  ising    force,    and    to    sul)due    and 


ON    THE    MOKPHOLOCilCAL    VIEW    OF    NATURE.      2G9 

Whewell,  in  various  passages  of  his  '  History  '  and  of  his 
•  I'hilosopliy  of  the  Inductive  Sciences,'  argues  that  the 
explanation  of  organic  forms  is  to  be  found  in  the  study 
of  the  functions  which  each  organ  is  destined  to  perform, 
and  brings  morphology  back  under  the  guidance  of  physi- 
ology, from  which  De  Candolle  and  others  had  only 
recently  liberated  it.^  Alexander  Braun,  the  great  German 
liotanist,  wrote  about  the  same  time :  "  Although  the 
organism  in  its  growth  is  subject  to  physical  conditions, 
the  real  causes  of  its  morphological  and  biological  speci- 
ality lie,  nevertheless,  not  in  these  conditions :  its  laws 
Ijelong  to  a  higher  grade  of  development  of  reality,  to  a 
sphere  in  which  the  capacity  for  spontaneous  self-deter- 
mination  becomes    evident."  '      Even   Johannes    ^liiller. 


mould  it  in  subserviency  to  the 
exigencies  of  the  resulting  specific 
form"  (p.  172).  Huxley  attributes 
these  theoretical  views  of  Owen  to 
the  influence  of  Lorenz  Oken,  the 
l)rincipal  scientific  representative 
of  the  school  of  the  "  Natur- 
philosophie.'"  In  this  respect  Owen 
left  the  direction  of  study  initiated 
and  so  successfully  followed  by 
Cuvier.  In  fact,  though  opposed 
to  Darwinism,  Owen  did  not,  like 
Cuvier,  believe  in  special  creation, 
as  is  clearly  shown  in  a  passage 
frequently  quoted,  taken  from  the 
conclusion  to  the  third  volume  of 
Owen's  great  work  '  On  the  An- 
atomy of  Vertebrates'  (1868),  p. 
807  :  "  Ho,  Vjeing  unable  to  accept 
the  volitional  hypothesis,  or  that 
of  impulse  from  within,  or  the 
.selective  force  exerted  by  outward 
circumstances,  I  deem  an  innate 
tendency  to  deviate  from  parental 
type,  operating  through  ])eriods  of 
adequate  dui-ation,  to  be  the  most 
{)ri)bable  nature,  or  way  of  opera- 
tion, of  the  .secondary  law,  whereby 


species  have  been  derived  one  from 
another." 

'  De  Candolle  is  very  clear  ou 
this  point  ;  he  says  ('  Theorie 
<51(5mentaire,'  p.  170) :  "  L'usage  des 
organes  est  une  con.sdquence  de  leur 
structure,  et  n'en  est  nullement  la 
cause,  comme  certains  ecrivains  irre- 
flechis  semblent  I'indiquer  ;  Tu-sage, 
quelque  soit  son  importance  dans 
I'dtude  physiologique  des  etres,  n'a 
done  en  lui-meme  qu'une  mi^diocre 
importance  dans  I'anatomie,  et  ne 
pent  en  avoir  aucune  dans  la  tax- 
onomie  ;  quelquefois  .seulement  on 
pent  s'en  servir  comme  d'un  indice 
de  certaines  structures  Ji  nous  en- 
core inconnues  ;  ainsi  lorsque  je  vois 
la  surface  unie  d'un  pctale  suinter 
une  liqueur,  j'en  conclus  que  cette 
partie  est  glandulaire,  et  je  I'assimile 
aux  nectaires  ;  mais  cette  assimila- 
tion, bien  que  reconnue  par  I'iden- 
titi5  de  l'usage,  est  rcellement 
otablie  sur  I'identitc  prusumee  de 
la  structure." 

-  Quoted  by  Sachs  ('  Gesch.  d. 
Botanik,'  p.  188). 


270 


SCIENTIFIC    THOUGHT. 


who  did  more  than  any  other  naturaUst  to  base  zoology, 
anatomy,  and  physiology  on  the  foundation  of  the  exact 
sciences,  physics  and  chemistry,  "  assumed  the  existence  of 
a  vital  force  which,  differing  from  physical  and  chemical 
forces,  enters  into  conflict  with  them,  and  which  in 
organisms  acts  the  part  of  a  supreme  regulator  of  all 
phenomena  according  to  a  definite  plan."  ^ 
50.  The  insufficiency  of  a  purely  morphological  description 

oftiiemor-'  of  living  bcins's,  the  unsuccessful  search  for  the  morpho- 

phological  &  o   ' 

view.  logical  elements  out  of  which  organisms  are  built  up,  as 

crystals  are  formed  out  of  the  moUculcs  inUgrantes  of 
Haiiy,  led  thinkers  (up  to  the  middle  of  the  century)  to 
have  recourse  to  older  and  vaguer  conceptions,  which, 
under  the  name  of  archetypes,  formative  influences,  vital 
forces,  &c.,  were  destined  to  help  where  the  purely 
mechanical  view  would  not  suffice.  This  dilemma  was 
appropriately  described  somewhat  later  by  one  who 
had— earlier,  perhaps,  than  any  other  thinker — eman- 
cipated himself  from  the  influence  of  these  fanciful 
conceptions.  Herbert  Spencer  in  his  '  Principles  of 
Biology,'  published  in  1863,  expresses  it  in  the  fol- 
lowing words : " — 

"  If   we   accept   the  word    '  polarity '   as   a   name  for 
the  force  by  which  inorganic  units  are  aggregated  into 


1  See  Du  Bois-Reymond,  "  Ge- 
iliichtuissrede  auf  Johanues  Miiller" 
('Reden,' vol.  ii.  p.  217). 

^  The  '  Principles  of  Biology,' 
from  which  this  extract  is  quoted, 
appeared  in  successive  instalments, 
beginning  in  January  1863.  It  is 
well  to  note  that  this  was  before  the 
appearance  of  Haeckel's  '  Generelle 
Morphologic,'  which  bears  the  date 
1866.       It   does    not    appear    tliat 


Spencer  lias  had  any  influence  on 
German  .science,  though  no  doubt 
many  of  the  conceptions  put 
forward  in  the  numerous  treatises 
of  German  biologists  are  anticipated 
in  Spencer's  'Biology,'  notably  in 
his  conception  of  the  physiological 
units  as  intermediate  between  com- 
pound chemical  molecules  and 
crystals  on  the  one  side,  and  cells 
on  the  other.      In  the  exhaustive 


ON    THE    MORPHOLOGICAL    VIEW    OF    NATURK.      271 

a  form  peculiar  to  them,  we  may  apply  this  word  to 
the  analogous  force  displayed  by  organic  units,  liut 
polarity  is  but  a  name  for  something  of  which  we  are 
ignorant.  Nevertheless,  in  default  of  another  word  we 
must  employ  this.  ...  It  will  be  well  to  ask  what 
these  units  are  wliich  possess  the  property  of  arranging 


review  of  these  theories,  given  by 
M.  Yves  Delage,  a  very  pi'ouiiiient 
position  is  accordingly  a-ssigned  to 
Herbert  Sjjencer's  biological  writ- 
ings. In  fact,  he  says  ('L'Herddite,' 
p.  424  note):  "Ici"— i.e.,  in  the 
'  Principles  of  Biology  '  —  "  est 
montrcSe,  pour  la  premiere  fois 
€t  avec  une  lucidito  parfaite, 
Tutilitc  de  coucevoir  des  particules 
sp^ciales,  elements  prirnitifs  de  la 
substance  vivaute,  intermediaries 
aux  molc'cules  et  aux  cellules.  Les 
tres  nombreux  auteurs  qui  ont 
utilise  la  mome  idi-e  n'eu  out 
cr66  que  des  variantes.  Spencer 
est  le  vrai  pere  de  la  conceiition 
initiale,  si  fecoude  comme  on  le 
verra."  And  again  (ibid.,  p.  836): 
"  Brusquement,  avec  H.  Spencer, 
on  tombe  en  plein  moderue.  lei 
plus  de  thiiories  vieillottes,  plus 
de  procedes  suranni's.  .  .  .  Les 
phenomenes  sont  decomposes  en 
leurs  elements  avec  une  puissance 
d'abstraction  qu'aucun  philosophe 
n'a  depassee,  des  }>rincipes  gener- 
aux  sont  dt'duits  qui  servent  a  leur 
tour  ;i  juger,  ii  interpreter  les 
phenomenes,  h.  les  ramener  a  leurs 
causes  vraies.  Comnie  resultat  de 
.-■■<  meditations,  Spencer  nous 
otl're  les  '  Unites  physiologiques,' 
particules  matcrielles  toutes  iden- 
ti'iues  dans  une  rneme  espcce 
d'etres  avec  lesquelles  il  croit 
que  I'organifime  doit  pouvoir  se 
construire  de  lui-meme,  par  le  seul 
jeu  de  leurs  forces  moli^culaires. 
.  .  .  11  a  .  .  .  ouvert  une  voie : 
sa  theorie  est  un  des  bras  prin- 
cipaux     du     Delta     de     ce    fleuve 


qui  nous  servait  de  terme  de  coni- 
paraison."  The  other  great  arm 
of  the  Delta  is  Darwin's  theory  of 
Pangenesis,  on  which  see  infru, 
chapter  xii.  of  this  volume.  Of 
others,  such  as  Erlsberg,  Haeckel, 
His,  Haacke,  M.  Delage  says  :  '"lis 
ont  reussi  seulenient  ii  montrer 
qu'en  substituant  aux  forces  polaires 
ties  '  Unites  physiologiques,'  des 
formes  de  mouvenient  ou  des 
proprietes  geometriques,  on  n 'arrive 
pas  a  un  meilleur  riSsultjit."  Prof. 
Haeckel  in  his  '  Generelle  Mor- 
phologie'  (1866)  has  interpolated 
a  special  investigation,  as  it  were, 
between  the  morphology  of  living 
tilings  and  the  corresponding 
science  of  inorganic  or  purely 
physical  (such  as  crystalline  and 
chemical)  sti-uctures  and  arrange- 
ment under  the  name  "  Pro- 
morphology,"  investigating  with 
mucli  ingenuity  all  manner  of 
symmetrical,  axial,  radial,  &e., 
configurations.  J.  Arthur  Thom- 
son ('Science  of  Life,'  p.  34)  re- 
marks that  little  attention  has 
been  paid  to  this  subject  since, 
but,  as  stated  above  (p.  223  note), 
the  systematic  treatment  of  crys- 
tallography has  all  through  the 
centur}'  ap[)eared  to  biologists  as 
an  enticing  and  seductive  model, 
and  M.  Yves  Delage's  great  work 
gives  many  examples  of  this  tend- 
ency— see,  c.y.,  his  remarks  on  the 
theories  of  Haacke,  Cope,  Niigeli, 
Erlsberg,  and  nianv  others,  pp. 
.304,  315,  424,  441,  451,  459,  475, 
495,  502,  593,  743,  &c. 


272  SCIENTIFIC    THOUGHT. 

themselves  into  the  special  structures  of  the  organism 
to  which  they  belong.  ...  On  the  one  hand,  it  cannot 
be  in  these  proximate  chemical  compounds  composing 
organic  bodies  that  this  specilic  polarity  dwells ;  .  .  . 
the  occurrence  of  such  endlessly  varied  forms  would  be 
inexplicable.  On  the  other  hand,  this  property  cannot 
reside  in  what  may  be  roughly  distinguished  as  the 
morpliological  units.  The  germ  of  every  organism  is 
a  microscopic  cell,  or  a  structureless  blastema  which 
nevertheless  exhibits  vital  activities.  ...  If,  then,  this 
organic  polarity  can  be  possessed  neither  by  the  chemical 
51.  units  nor  the  morphological  units,  we  must  conceive  it  as 
"^h"^sui-  possessed  by  certain  intermediate  units  which  we  may 
umts/'  term  ipliysiological.  .  .  .  We  must  conclude  that  in  each 
case  some  slight  difference  of  composition  in  these  units 
.  .  .  produces  a  difference  in  the  form  which  the  aggre- 
gate of  them  assumes." 

Now,  there  are  only  two  ways  open  to  the  purely 
scientific  thinker  by  which  he  can  reach  these  inter- 
mediate structures  lying  between  the  mathematical  forms 
of  crystals  or  the  molecular  arrangement  of  atoms,  and 
the  visible  but  apparently  structureless  forms  of  cells  and 
protoplasm.  One  of  these  is  the  still  more  advanced 
analysis  of  these  microscopic  structures  by  still  greater 
powers  of  magnifying  instruments ;  the  other  is  the 
mathematical  method  of  calculating  from  simple  begin- 
nings the  complex  forms  of  equilibrium  which  atoms  or 
molecules  are  capable  of  assuming  under  the  action  of 
known  forces.  It  appears  unlikely  that  the  powers  of 
the  microscope  can  be  much  further  extended ;  and  the 
mathematical  calculation  of  even  the  simplest  configur- 


ON  THE  MORPHOLOGICAL  VIEW  OF  NATURE.   273 

atioiis  of  attracting  and  repelling  centres,  or  of  linked 
vortex  rings,  is  already  so  formidable  that  much  cannot 
be  expected  in  that  direction.  Tliese  intermediate  units, 
vastly  more  complex  than  the  most  complex  chemical 
molecules,  and  vastly  more  minute  than  the  smallest 
\  isible  grain  of  protoplasm,  must  therefore  for  a  long 
time  to  come  lie  in  the  region  of  hypothesis,  unattainable 
for  the  eye  or  the  calculus;  an  indication  rather  than 
a  real  guide  for  our  scientific  researches.  Seeing,  then, 
that  the  study  of  forms  —  the  morphological  view  of 
natural  objects  in  the  case  of  organic  beings,  where  to 
the  naive  contemplation  of  things  these  forms  seemed  full 
of  so  much  significance,  indicative  of  so  much  meaning, 
])ossessed  of  so  much  beauty  and  striking  suggestiveness 
— has  led  to  no  comprehension  of  the  essence  of  vital 
phenomena,  and  hardly  even  afforded  a  safe  criterion  for 
classification,  it  is  intelligible  how  the  scientific  interest        52. 

®  Change  of 

has  moved  away  from  the  consideration  of  the  fixed  forms  scientific 

•'  interests. 

ami   structures    to    that  of  the  variation  and  continued 
change  of  these  forms.      This  alteration  in  tlie  scientific 
way  of  looking  at  the  actual  forms  of  nature,  goes  hand 
in    hantl   with   the   tendency  we   had   occasion   to   notice 
when  dealing  with  the  abstract  sciences.      Many  things 
which  once  seemed  at  rest,  or  possessed  of  very  simple 
rectilinear  motion,  have  revealed  themselves  to  the  mind's 
eye  as  complex  states  of  motion.     Colours  are  exceedingly 
minute  and  rapid  but  well  defined  vibrations ;  the  dead 
pressure  of  gases  is  the  impact  of  numberless  quickly- 
moving  particles ;    and   the  wonderful  properties  of  the 
whirling  vortex  ring  have  made  us  familiar  with  what 
has  been  termed  the  dynamical  or  moving  equilibrium,  the 

VOL.  IL  8 


274  SCIENTIFIC   THOUGHT. 

semblance  of  apparent  rest  produced  by  very  rapid  rotary 
motion.  Rest  and  fixity  of  form  seem  only  to  exist  j 
apparently  or  for  transient  moments  in  the  history  of 
natural  events  ;  and  even  the  finished  and  recurring  struc- 
tures of  living  beings,  which  appear  to  our  eyes  to  be 
possessed  of  so  much  finality  and  sometimes  of  so  much 
finish,  owe  these  qualities  only  to  the  comparatively  short 
space  of  time  during  which  we  are  permitted  to  gaze 
at  them,  and  to  our  ignorance  of  the  slow  but  endless 
changes  to  which  they  are  nevertheless  subject. 
53.  The  period  from   1800   to   1860   can  be  termed  the 

The  morpho- 
logical        morphological   period   of   natural   science.      It   succeeded 


period. 


the  period  of  the  simpler  natural  history,  which  had 
been  mainly  occupied  with  classification  and  description 
of  specimens.  During  the  morphological  period  the 
knowledge  of  the  existing  things  and  forms  of  nature 
was  not  only  largely  extended  by  excursions  into  distant 
lands  and  periods  of  history,  but  forms  were  also  studied 
in  situ,  and  the  living  things  visited  in  their  habitats. 
A  deeper  knowledge  of  the  connection  and  interdepend- 
ence of  natural  things  and  events  was  thus  gained,  and 
the  relations  and  resemblances,  the  analogies  and  homo- 
logies, of  the  various  forms  were  impressed  on  the  observer. 
Besides  all  this,  the  microscope  revealed  the  innermost 
composition  and  the  ultimate  structural  sameness  of  living 
matter,  adding  moreover  the  knowledge  of  an  enormous 
creation  which  remains  hidden  to  the  unarmed  eye  of 
the  ordinary  observer.  The  morphological  view  also  took 
note  of  the  relatedness  and  apparent  recurrence  of  definite 
forms  called  types,  of  the  so-called  fixity  of  species  and 
the   succeeding    characteristic    periods    of    creation,   and 


ON  THE  MORPHOLOGICAL  VIEW  OF  NATURE.   275 

sought  to  explain  these  morphologically :  i.e.,  it  sought 
in  the  abstract  study  of  forms — sometimes  geometrical, 
sometimes  artistic — the  key  to  an  understanding  of  the 
recurrence  as  well  as  the  continued  variation  of  definite 
types.  The  relationship  was  mostly  looked  upon  as  ideal, 
not  real.  How  a  gradual  change  came  over  this  view 
of  nature,  how  the  study  of  development  led  on  to  the 
modern  phase  of  natural  science  which  is  governed  by  the 
genetic  view,  I  shall  try  to  show  in  tlie  next  chapter. 


276 


CHAPTER  IX. 


ON  THE  GENETIC  VIEW  OF  NATURE. 


1. 
Statics 
and  dyna- 
mics of  liv- 
ing fonns. 


Whilst  the  great  influence  of  such  leaders  in  scientific 
thought  as  Cuvier,  De  Candolle,  and  Humboldt  on  the 
Continent,  and  of  Richard  Owen  in  this  country,  was 
mainly  exerted  in  spreading  the  morphological  view  of 
nature,  describing  on  a  large  scale  or  in  minuter  detail 
the  typical  recurring  forms  which  natural  objects  or 
natural  scenery  present  to  the  eye  of  the  unbiassed 
observer,  another  school  of  naturalists  was  secretly  busy 
in  following  up  the  changes  to  which  all  the  things  of 
nature  seem  continually  subjected.  They  were  as  much 
impressed  with  this  restless  movement  of  everything  as 
the  others  were  with  the  continual  recurrence  of  certain 
definite  forms — be  they  geometrical  or  artistic.  The 
general  ideas  which  underlay  their  researches  were  not 
new, — they  were  probably  older  and  more  familiar  ^  than 


^  Cosmogonies  of  all  sorts  abound 
in  almost  every  literature,  ancient  or 
modern,  whereas  Cosmograpliy,  ac- 
curate, painstaking,  and  reliable,  is 
of  comparatively  recent  date.  The 
first  attempt  to  give  a  purelj' 
descriptive  picture  of  nature  as  a 
whole,  beginning  with  the  larger 
features  of  the  universe  and  ascend- 


ing through  terrestrial,  inanimate 
and  animate,  phenomena  to  the 
central  and  crowning  phenomenon 
of  human  life,  was  A.  von  Hum- 
boldt's 'Kosmos';  and  it  is  interest- 
ing to  note  how  averse  the  author 
was  to  introduce  genetic  expositions. 
In  fact,  it  has  been  truly  remarked 
that  Humboldt's  influence  went  to 


ON  THE  GENETIC  VIEW  OF  NATURE. 


o  —  ■-' 


tlie  types  and  epochs  of  the  other  ami  <lominant  school ; 
liut  they  were  difficult  to  grasp,  being  not  unfrequently 
fantastic  compromises  between  Iho  legends  of  religious 
tradition  and  the  l)eginnings  of  scientific  thought.  For 
a  long  time  they  evaded  the  endeavour  to  put  them  into 


purely  lUDipliolugical 
and  to  discourage  genetic  con- 
siderations. Acconlingly  the  many 
beginnings  of  a  scientific  account 
of  the  origin  and  historical  develo|>- 
ment  of  the  things  around  us,  of 
whicli  Lyell  gave  the  first  fairlj- 
accuiate  summary  in  the  first 
volume  of  his  'Principles  of  Geol- 
ogy '  (1st  ed.,  1S30),  were  hardly 
noticed  in  the  'Kosmos'  (vol.  i., 
184.5,  vol.  ii.,  1847).  None  of  the 
celebrated  cosmogonical  hypotheses, 
which  we  shall  deal  with  in  this 
cliapter, — neither  tiie  'Protogica' 
of  Leibniz  nor  the  '  Epoques  de  la 
Nature'  of  Buffon,  neither  Kant's 
uor  Laplace's  nebular  theory,  nor 
even  tiie  brilliant  introduction  to 
the  '  Ossemens  fossiles '  of  Cuvier, 
though  the  latter,  and  still  more 
Laplace,  must  have  had  a  great 
personal  influence  on  him,  —  re- 
ceive any  adequate  attention  in 
the  pages  of  '  Kosmos. '  They  are 
rarely  referred  to,  and  then  only  as 
works  of  imaginative  value,  for 
which  the  true  .scientific  ground- 
work, extensive  observation,  and 
especially  the  experiences  and 
results  of  travel,  are  wanting. 
Humboldt,  whose  mind  was  stored 
with  these  rii'hes  in  an  abundance 
and  variety  unequalled  before  or 
since,  limited  himself  to  a  por- 
traiture, to  a  panoramic  and  mor- 
jiliological,  to  a  structural  and 
architectonic  view  of  things,  with 
which  he  combined  a  deep  sense  of 
the  reaction  which  the  ccntempla- 
tion  of  nature  must  have  on  the 
artistic  facultj'.  (See  the  Intro- 
<luction  to  the  second,  the  most 
brilliant,     volume     of     'Kosmos.') 


Genetic  theoi-ies  were  to  his  mind 
premature  and  foreign  to  his  pur- 
pose. "  The  mysterious  and  un- 
solved problems  of  development  <lo 
not  belong  to  the  empirical  region 
of  objective  observation,  to  the 
description  of  the  developed,  the 
actual  state  of  nur  planet.  The 
description  of  the  universe,  soberly 
contined  to  reality,  lemaius  averijc 
to  the  obscure  beginnings  of  a 
history  of  organic  life,  not  from 
modesty,  but  from  the  nature  of 
its  object  and  its  limits"  ('Kos- 
mos,' vol.  i.  p.  367).  "The  world 
of  forms,  I  repeat,  can  in  the  enum- 
eration of  space  relations  only  be 
pictured  as  something  actual,  as 
something  existing  in  nature  ;  not 
as  a  subject  of  an  intellectual  pi'ocess 
of  reasoning  on  already  known  causal 
connections.  .  .  .  They  are  facts  of 
nature,  resulting  from  the  conflict 
of  many,  to  us,  unknown  conditions 
of  active  push  -and  -  pull  forces. 
With  unsatisfied  curiosity  we  aj)- 
proach  here  the  dark  I'egion  of 
develojjment.  We  have  here  to  do, 
in  the  proper  sense  of  the  frequently 
misused  word,  with  world-events, 
with  cosmical  processes  of  im- 
measui'able  periods.  .  .  .  The 
present  form  of  things  and  the 
precise  numerical  determination  of 
relations  has  not  hitherto  succeeded 
in  leading  us  to  a  knowledge  of 
states  traversed,  to  a  clear  insight 
into  the  conditions  under  which 
they  originated.  These  comlitions 
are  not  therefore  to  be  termed 
accidental,  as  man  calls  everything 
that  he  cannot  explain  genetically  " 
(vol.  iii.  p.  431). 


278  SCIENTIFIC    THOUGHT. 

exact  language.  It  is  only  in  the  second  half  of  the 
nineteenth  century  that  the  many  independent  Hnes  of 
reasoning,  the  fragments  of  the  great  doctrine  of  develop- 
ment, have  been  united  together,  that  the  search  after  the 
principles  or  laws  which  govern  the  restless  change  has 
been  rewarded  by  a  certain  number  of  definite  results, 
and  that  what  was  once  vague,  fanciful,  and  legendary 
has  become  a  leading  idea  in  all  the  natural  sciences. 
As  in  other  instances  which  we  have  had  occasion  to 
notice,  so  also  in  this  case,  the  appearance  of  clearer  and 
more  definite  ideas  has  been  heralded  and  helped  by  a 
novel  mode  of  expression,  by  a  new  vocabulary.  The 
2.  word  "  evolution "  has  in  this  country  done  much  to 
tion."  popularise    this  way    of    regarding   natural   objects  and 

events :  abroad,  the  word  has  not  met  with  the  same 
popular  acceptance.  It  was  known  there  and  used  in 
science  and  literature  when  it  was  yet  unknown  in  this 
country,  and  has  in  consequence  not  been  monopolised  in 
the  same  way  as  in  the  English  language,  to  denote  the 
continuous  and  orderly  development  of  states  and  forms 
of  existence.^     Moreover,  it  has  been  identified  in  this 

^  On  the  older  and  iiKxlern  use  I  geneous  rudiment  (after-formation), 
of  the  word  "evolution"  in  the  Harvey,  the  expounder  of  the  latter 
English      language     see     Huxley's       theory  against  Malpighi,    who  em- 


article  in  the  9th  ed.  of  the 
'  Ency.  Brit.'  It  is  reprinted  in 
his  collected  essays  with  the  title 
"Evolution  in  Biologj-."  Accord- 
ing to  Huxley,  the  term  "evolu- 
tion "  was  introduced  in  the  former 
half  of  the  eighteenth  century  in 
opposition  to  "  epigenesis."  The  two 
terms  denoted  the  two  theories  of 
the  generation  of  living  things,  by 
development  of  pre-formed  germs 
(pre-formation)  or  by  successive 
differentiation  of  a  relatively  homo- 


braced  the  former,  calls  the  first 
"metamorphosis."  Leibniz,  Bon- 
net, and  latterly  Haller,  were  "evolu- 
tionists "  in  the  older  sense  of  the 
word ;  Harvey,  C.  F.  Wolf,  and 
the  modern  school  of  embryologists, 
with  von  Baer  as  its  most  eminent 
representative,  were  adherents  of 
the  originally  Aristotelian  theory 
of  "  epigenesis."  "  Nevertheless,"  as 
Huxley  says,  "  though  the  concep- 
tions origiuall}'  denoted  by  'evolu- 
tion '     and     '  development '     were 


ON    THE    GENETIC    VIEW    OF    NATURE. 


279 


country  with  a  special  philosophical  teaching,  that  of 
Mr  Herbert  Spencer,  which,  whilst  in  many  points 
coinciding  with  scientific  views  of  development,  has 
some  special  and  peculiar  features  which  will  occupy 
us  further  on  in  our  survey  of  thought.  Havuig  sought 
therefore  for  a  term  which  is  to  comprise  all  the  con- 
tributions to  scientific  thought  which  deal  with  the 
change  and  development  of  natural  objects  and  events, 
I  propose  to  use  the  older  word  "  genesis,"  and  to  call 
this  view  "  the  genetic  view  of  nature  "  :  it  is,  in  general, 
the    view   which   seeks   to  give  answer   to   the   (juestion, 


'Gi'iiesiH.' 


shown  to  be  untenable,  tlie  words 
retained  their  application  to  the 
process  by  which  the  embryos  of 
living  beings  gradually  make  their 
appearance  ;  and  the  terms  '  de- 
velopment,' '  Entwickelung,'  and 
'  evolutio  '  are  now  indiscriminately 
used  for  the  series  of  genetic  changes 
exhibited  by  living  beings,  by 
writers  wlio  would  emphatically 
deny  that  '  development '  or  '  Eut- 
wickelung'  or  'evolutio,'  in  the 
sense  in  which  these  words  were 
usually  employed  by  Bonnet  or  by 
Haller,  ever  occurs."  The  word 
evolution  has,  however,  acquired 
in  the  English  language,  mainly 
through  the  influence  of  Mr 
Spencer's  writings,  a  much  wider 
sense  than  evolution  in  biology 
implies  :  in  fact,  it  takes  the  place 
of  the  German  "  Werden,"  a  word 
much  used  in  the  philosophical 
writings  influenced  by  the  Hegelian 
doctrine,  which  indeed  taught  a  ■ 
logical  or  dialectic  devclo])ment  of 
tilings,  as  Herbert  Spencer  and  his 
school  teach  a  mechanical  develop-  i 
ment.  There  seem  to  be  given  to 
UH  by  observation  only  two  elemen- 
tary processes  of  change,  or  of 
"  Werden  "  (in  Greek  yiyi'fadat,  in 
French  "  devenir,"  in  English   "be- 


coming," in  Latin  "fieri,"  in  German 
also  the  synonym  "  gcschehen ",. 
These  are,  on  the  one  hand,  the 
process  of  mechanical  motion,  and 
on  the  other  hand  the  process 
of  logical  thought  :  the  one  being 
the  movement  of  external  things, 
ultimately  of  atoms,  the  other  the 
spontaneous  movement  of  what 
Hume  called  ideas.  When  the 
thinking  mind  fixes  its  attention  on 
the  "fieri"  rather  than  the  "esse" 
of  things  there  are  accordingly  two 
clues  available,  the  mental  or  the 
[)hysical,  the  logical  or  the  mechan- 
ical. Manj'  times  taken  uj)  in 
earlier  ages,  both  have  been  con- 
sistently applied  only  in  the  nine- 
teenth century,  the  latter  by  Her- 
bert Spencer,  the  former  fifty 
years  earlier  by  Hegel,  whose 
philosophy  is  fundamentally  as 
nmch  a  logical  as  the  former  is  a 
mechanical  system  of  evolution. 
The  narrower  meaning  of  evolution 
in  h'uAo^y  is  usually  given  in 
French  by  the  word  "transform- 
isme,"  in  German  by  "  Entwick- 
elungslehre"  or  "  Darwinismus." 
See  on  the  general  subject  Prof. 
James  Sully's  able  article  on 
"  Evolution  "  in  the  9th  ed.  of 
the  'Ency.   Brit." 


280 


SCIENTIFIC    THOUGHT. 


How  have  things  come  to  be  what  they  are  ?      What 
is   their  history  ^  in   time  ? 

The  first  great  philosopher  of  modern  times  who  seems 

to  have  approached  the  question  of  the  genesis   of  the 

objects   of    nature   in    the  modern   scientific   spirit  was 

4.        Leibniz,    who,   in    composing    his    local    history    of    the 

Leibniz's 

'Protogita.'  origin  of  the  Guelphs  and  the  antiquities  of  Brunswick, 
pushed  his  researches  into  prehistoric  times  and  made 
use  of  the  geological  and  mineralogical  data  supplied  in 
the  Harz  forest  and  mountains  to  arrive  at  conjectures 
as  to  the  past  history  of  the  earth.  His  ideas,  based 
upon  local  facts  and  observations  on  stratification 
and  fossil  remains,  were  collected  in  a  famous  tract 
entitled  '  Protogtea,'  which  during  his  lifetime  was  only 
known   in  abstract,^  and  was  published  in    1749,  many 


•*  Although  the  word  '"genesis," 
through  its  use  in  the  Scriptures, 
has  acquired  the  meaning  of  a  nar- 
rative of  the  origin  or  beginning  of 
things,  this  meaning  is  not  neces- 
sarily implied  in  the  wf)rd  yiyfea- 
dai,  and  the  genetic  view  of  nature, 
or  things  in  general,  may  limit  it- 
self to  the  study  of  observable, 
actual  change,  renouncing  alto- 
gether the  question  of  origins. 
The  German  words,  "werden"  and 
"  geschehen,"  are  in  this  respect  less 
ambiguous  and  less  ambitious,  and 
many  philosophers  may  accordingly 
prefer  "evolution"  to  "genesis." 

'^  On  the  connection  of  Leibniz's 
genetic  studies  with  his  History  of 
Brunswick,  which  expanded  under 
his  hands  into  the  '  Annales  im- 
perii occidentis  Brunsvicenses  ' 
(edited  by  Pertz  in  the  first  three 
volumes  of  '  Leibuizens  Gesam- 
melte  Werke,'  Hannover,  1843-47, 
4  vols.),  see  the  introduction  bj' 
Scheldt  to  his  complete  edition  of 
the   '  Protogsea,'    Gottingen,    1749 


(reprinted  in  the  second  volume  of 
Dutens'  '  Leibnitii  Opera  Omnia,' 
1768)  ;  the  words  of  Leibniz  him- 
self in  the  '  Plan '  of  his  History 
(quoted  by  Pertz,  vol.  i.  p.  xxiii)  : 
"  Prajmittetur  his  annalibus  qua3- 
dam  dissertatio  de  antiquissimo 
harum  regionum  statu  qui  ante 
historicos  ex  naturto  vestigiis  haberi 
potest  "  ;  the  address  of  Ehrenberg, 
'  Ueber  Leibnitzens  Methode '  (Ber- 
lin, 1845)  ;  the  account  in  Guhr- 
auer's  '  Life  of  Leibniz  '  (1846,  vol.  i. 
p.  205,  and  an  interesting  note  in  the 
apjaendix).  Fontenelle,who  knew  of 
the  'Protoga;a'  only  by  the  abstract 
(ed.  1693)  in  the  Leipsic  'Acta,' 
and  from  correspondence  with  Eck- 
hardt,  Leibniz's  executor,  says  in 
his  'Eloge  de  Leibniz':  "II  la 
[viz.,  the  History]  faisait  prec^der 
par  une  dissertation  sur  I'etat  de 
I'Allemagne,  tel  qu'il  dtait  avant 
toutes  les  histoires  et  qu'on  pouvait 
le  conjecturer  par  les  monuments 
naturels  qui  en  etaient  restes  ;  des 
coquillages  petrifies  dans  les  terres, 


ON    THE    GKNETIC    VIEW    oK    NATURE. 


281 


years  after  his  death.  He  conceived  that  lioth  tire  and 
water  ^  had  lieen  at  work  in  forming  the  surface  of  the 
earth,  ami  suggested  that  simihir  examinations  of  other 
localities '"  would  be  required  in  order  to  arrive  at  general 
conclusions.  Such  were  subsequently  supplied  by  Werner, 
de  Saussure,  Pallas,  Hutton,  Cuvier,  and  William  Smith, 
before  the  systematic  exploration  of  the  w'hole  globe  be- 
came in  the  nineteenth  century  one  of  the  tasks  of 
geological  science.  A  few  years  after  the  publication  of 
T.eibniz's  speculations,  which  pointed  to  an  accumulation 
of  local  observations  as  the  means  of  arriving  at  a  history 


des  pierres  oil  se  trouveiit  de.s  em- 
ineinles  de  poissons  ou  de  ])liuites 
<|ui  ne  sent  point  du  pays,  medailles 
iiicoutestables  du  deluge,'"  &c.,  &c. 
How  very  much  Leibniz  was — in 
this  as  in  niauy  other  ideas — in  ad- 
vance of  his  age  can  be  seen 
from  his  correspondence  with  the 
Ssviss  naturahst  Scheuchzer  of 
Ziirich  :  "  Mcrentur  Alpes  vestrtc, 
si  quis  ahus  Europic  locus,  banc  eru- 
diti  inquilini  curani  et  cieteros 
montes  utili  exemplo  pneibunt, 
queni  admodum  magnitudine  vinc- 
unt.  .  .  .  (Jerraanorum  nos- 
trorum  non  ea  est  diligentia  quam 
vellem  :  iUique  Historias  regionum 
naturales  habemus  nullas,  cum 
Angli  Scotique  nobis  egregiis  ex- 
etnj)lis  pnoiverint "  (quoted  by 
<:ulirauer  in  the  note  referred  to). 
An  interesting  reference  is  made  in 
*5  xvii.  of  the  "  Protogiea '  to  the 
use  of  the  microscope,  tlien  only 
recently  invented,  and  largely  used 
by  Leuwenhoek  in  connection  with 
the  examination  of  the  formation 
and  crystiils  of  the  celebrated 
"  Baumann  cave":  "  Et  velim 
microscopia  ad  inquisitionem  ad- 
hiberi,  (juibus  tautum  prxstitit 
s.igax  Leuwenhoekii  diligentia,  ut 
«;upe    iudigner     human;e    ignavite, 


quie  aperire  oculos,  et  in  paratam 
scientia  posse.~sionem  ingredi  non 
diguatur. "  A  very  fair  account  of 
the  contents  of  the  '  Protogiea ' 
is  given  in  W.  D.  Conybeare's  '  Re- 
port ou  the  Progress  ...  of  Geo- 
logical Science '  in  the  first  volume 
of  Brit.  Assoc.  Reports,  p.  366, 
&e. 

1  '  Protogiea,'  §  iv.  :  "  Donee 
quiescentibus  causis  atque  icquilib- 
ratis  consistentior  emergeret  sta- 
tus rerum.  I'lide  jam  duplex  origo 
intelligitur  firmorum  corporum  ; 
una,  cum  ab  ignis  fusione  refriges- 
cerent,  altera  cum  reconcrescerent 
ex  solutione  aquarum.  Neque  igitur 
putandum  est  lapides  ex  sola  esse 
fusione.  Id  enim  potissimum  de 
prima  tautum  massa  ac  terra;  basi 
accipio." 

-  Ibid,  g  V.  :  "  H;ec  vero  utcum- 
que  cum  plausu  forte  dici  possint  de 
incunabjlis  nostri  orbis,  seminaque 
contineant  scientiic  novic,  quam 
Geographiam  naturalem  appelles. 
.  .  .  Et  licet  conspirent  vestigia 
veteris  mundi  in  priesenti  facie 
rerum,  tamcn  rectius  omnia detinient 
postei'i,  ubi  curiosilas  mortalium  eo 
processerit,  ut  per  regiones  pro- 
curreutia  soli  genera  et  strata  des- 
cribunt. " 


282 


SCIENTIFIC   THOUGHT. 


5. 
Kant's 
nebular 
theory. 


of  the  earth,  another  philosopher  of  the  highest  rank 
took  an  important  step  in  the  direction  of  the  study  of 
the  genesis  of  things  natural,  on  the  largest  scale.  It 
was  Immanuel  Kant,  the  philosopher  of  Konigsberg,  who, 
stimulated  by  the  perusal  of  the  cosmical  theories  of 
Thomas  Wright  of  Durham,^  applied  the  principles  of 
the  Newtonian  philosophy  in  a  first  attempt  to  trace  out 
the  great  stages  in  the  formation  of  a  planetary  system. 


^  The  work  of  Wright  is  not  so 
rare  as  it  is  represented  to  be  by 
foreign  writers,  as  I  picked  up  two 
copies  from  a  second-hand  catalogue 
several  years  ago.  It  is  chiefly 
interesting  as  having  induced  Kant 
to  venture  on  his  genetic  specula- 
tions, which  appeared  anonymously 
at  Konigsberg  in  1855,  and  for  a  long 
time  remained  unknown.  About 
the  same  time  as  Kant,  the  cele- 
brated mathematician  J.  H.  Lam- 
bert published  his  '  Cosmological 
Letters  on  the  Structure  of  the 
Universe'  (Augsburg,  1761),  many 
ideas  in  which  coincide  with  the 
later  expositions  of  Herschel  and 
Laplace,  which  were  based  on  quite 
ditferent  considerations.  The  specu- 
lations of  WVight,  Lambert,  and 
Herschel  were  what  we  may  call 
morphological,  whereas  it  is  the 
merit  of  Kant  and  Laplace  to  have 
built  upon  the  ideas  as  to  the 
architecture  of  the  universe  a 
plausible  theory  of  its  genesis.  A 
full  account  of  Wright's  suggestions, 
which  were  accompanied  by  very 
beautiful  mezzotint  engravings  exe- 
cuted by  himself,  is  given  by  Prof. 
R.  A.  Sampson  of  Durham  in  the 
'  Proceedings  of  the  Society  of  Anti- 
quaries '  of  Newcastle-upon-Tyne, 
vol.  vii.  p.  99. 

Kant's  theory  has  been  dealt  with 
by  Helmholtz  in  his  Konigsberg  ad- 
dress (1854),  "Ueber  die  Wechsel- 
wirkung  der  Naturkriifte"  (' Vor- 
triige  und  Reden,'  vol.  i. ),  by  Faye 


('Sur   rOrigine   du   Monde,'  Paris, 

1885,  2nd  ed.),  by  C.   Wolf    (' Les 
Hypotheses  Cosmogoniques,'  Paris, 

1886,  which  contains  a  translation 
of  Kant's  work),  and  by  G.  F. 
Becker  (Amer.  Journal  of  Science, 
1898).  It  is,  however,  to  be  noted 
that  recent  writers  on  Astronomy 
are  inclined  to  speak  of  the  genetic 
theories  of  the  universe  very  mucli 
in  the  same  way  as  Humboldt 
treated  them  in  his  'Kosmos,' 
wliich  professedly  excluded  the 
historical  aspect  in  favour  of  a 
purely  descriptive  treatment,  recog- 
nising the  many  difficulties  which 
stand  in  the  way  of  a  consistent 
elaboration  of  the  "nebular  hypo- 
thesis." See  A.  Berry's  'History 
of  Astronomy'  (1898),  p.  409;  R. 
Wolf,  '  Handbucli  der  Astronomic  ' 
(vol.  i.,  1890),  p.  594  ;  G.  H. 
Darwin,  'The  Tides'  (1898),  p. 
302  ;  also  J.  Scheiner,  '  Der  Bau  de& 
Weltalls'  (Leipzig,  1901).  On  the 
additional  gi-eat  support  which 
has  been  given  to  a  genetic  con- 
ception in  general  in  the  second 
half  of  the  nineteenth  century  by 
Thermodynamics  and  Spectrum 
Analysis  I  shall  speak  later  on. 
The  writings  of  M.  Faye  in  France, 
and  of  Sir  Norman  Lockyer  in  this 
country,  utilise  to  the  fullest  extent 
the  arguments  derivable  from  these 
sources,  and  mark  a  great  con- 
trast to  the  manner  in  which  cos- 
mological questions  were  treated 
by  A.  von  Humboldt. 


ON    THE    GENETIC    VIEW    OF    NATURE. 


283 


Tlie  speculations  of  Wright  liad  been  purely  geometrical. 
Tfe  had  drawn  attention  to  the  apparent  unity  of  organ- 
isation ill  the  stellar  system,  as  established  by  the  ac- 
cumulation of  stars  in  a  certain  belt,  popularly  called 
"  the  milky  way."  He  also  suggested  that  the  whole 
system  was  moving  in  a  certain  direction.  Kant  pointed 
out  the  analogy  with  the  solar  system,  in  which,  viewed 
from  the  centre,  the  planetary  masses  would  likewise 
appear  situated  in  a  narrow  belt,  moving  all  iu  tlie  same 
direction.  From  these  data  he  proceeds  to  show  how, 
taking  for  granted  an  initial  movement  and  the  action  of 
sravitation,  the  formation  of  rint^s  like  those  of  Saturn^ 
can  be  explained  ;  further,  how  these  might  be  broken 
up  and  concentrated  in  satellites.  In  fact,  he  recognised 
how,  under  the  influence  of  gravitation,  the  solar  system 
miglit  liave  been  gradually  formed  out  of  matter  which 
was  previously  scattered  through  the  whole  of  that  space 
which  the  system  still  occupies.  Kant  also  descended 
somewhat  further  into  detail,  and  proceeded  to  discuss  the 
possible  retardation  of  the  earth's  rotation  through  tidal 
friction.^ 


'  The  tract  in  vvliicli  Kant  de- 
velops his  views  on  this  subject  was 
occasioned  by  a  prize  ottered  by  the 
Berlin  Academy  in  1754  for  an  answer 
to  the  question  whether  the  time  of 
revolution  of  the  earth  liad  suffered 
any  retardation,  and  if  so,  through 
what  causes?  Kant  did  not  com- 
pete for  the  prize,  deeming  his  re- 
flections not  capable  of  being  suffi- 
ciently perfected  to  deserve  to  be 
submitted.  So  he  simply  published 
them  in  a  local  Konigsberg  [laper, 
from  which  they  were  later  re- 
jirinted  in  the  collected  works, 
forming  one  of  the  first  "f  Kent's 


publications.  At  the  end  of  this 
tract  he  announces  his  "  Cosmo- 
gonie,'  which  appeared  the  follow- 
ing year  with  the  title  '  Natural 
History  of  the  Heavens,'  &c.  Kant 
had  the  satisfaction  of  seeing  many 
of  his  speculations  verified  by  the 
subsequent  discoveries  of  induc- 
tive research,  notabh-  through  Sir 
William  Herschel's  observations  of 
nebulie  ;  and  the  German  edition  of 
Herschel's  great  memoir  '  On  the 
Construction  of  the  Heavens'  ('  Phil. 
Trans.,'  1784),  which  appeared  in 
Konigsberg  in  1791,  by  Sommer, 
contains    an    extract    from    Kant's 


284  SCIENTIFIC    THOUGHT. 

The  two  lines  of  speculation,  originated  by  Leibniz 
and  Kant  as  to  the  genesis  of  things  on  this  earth  and 
in  the  universe,  mark  two  distinct  ways  of  approaching 
the  genetic  problem.  They  were  both  isolated,  and  it 
was  not  till  well  on  in  the  course  of  our  century  that 
they  were  again  taken  up  and  independently  developed 
— the  one  by  geologists,  the  other  by  physical  astronomers. 
They  remained  for  a  long  time  without  mutual  influence ; 
till,  within  the  last  generation,  they  were  brought  to- 
gether, their  different  results  deduced,  and  a  reconcilia- 
tion  attempted.  To  this  I  shall  revert  later  on.  Forty 
6.         vears    after    Kant,   Laplace   put   forward    his    so-called 

Laplace.  "^ 

nebular  hypothesis  at  the  end  of  the  popular  exposition 
which  he  gave  of  his  mechanical  theory  of  the  heavens. 
He  apparently  knew  nothing  of  Kant's  attempt,  and  his 
views  differ  materially  from  those  of  Kant,  in  so  much 
as  he  assumes  in  the  rotating  nebular  mass  an  attracting 
nucleus  from  which,  in  the  course  of  condensation  through 
attraction,  the  planetary  rings  and  bodies  were  thrown 
off  as  the  centrifugal  velocity  balanced  the  attracting 
forces.  For  a  long  time  this  sketch  of  a  possible 
genesis  of  the  planetary  system  was  paraded  in  popular 


work.  The  merits  of  Kant  have  only 
been  tardily  recognised  ;  they  were 
unknown  to  Laplace,  and  only 
imperfectly  known  to  more  recent 
authorities,  such  as  Helmholtz  and 
Lord  Kelvin,  who  were  fully  pre- 
pared to  do  him  justice.  Lord 
Kelvin,  in  his  Rede  Lecture  of 
1866,  refers  to  Kant  as  the  first 
to  publish  "  any  definite  estimate 
of  the  possible  amount  of  the 
diminution  of  rotatory  velocity 
experienced  by  the  earth  through 

tidal   friction"   ('Pop.    Lects.   and    j   Journal  of  Science,'  1898. 
Addr.,'  vol.   ii.    p.    65),  and  Jin   the    i 


controversj'  which  took  place  be- 
tween him  and  Huxley  on  "  Geo- 
logical time "  the  theories  of  Kant 
were  frequently  referred  to.  See 
his  lecture  on  "Geological  Time," 
1868  {loc.  cit.,  p.  10,  &c.) ;  Huxley 
on  "  Geological  Reform,"  1869  (re- 
printed in  '  Lay  Sermons,'  No.  XL) 
The  best  account  in  the  English 
language  of  Kant'.s  contributions 
to  cosmogony  will  be  found  in  an 
article  by  G.  F.  Becker  in  the  5  th 
vol.,  4th  series,  of  the   'American 


ON    THE    GENETIC    VIEW    OV    NATURE.  285 

works  on  astronomy  as  an  established  theory,  wliereas 
Laplace  himself  had  \n\t  it  forward  with  great  reserve, 
and  only  as  a  likely  suggestion.^  There  is,  however,  no 
(loiilit  that  it  powerfully  inlluenced  the  minds  of  many 
students  of  nature  in  the  direction  of  a  genetic  view  of 
phenomena. 

The  attempts  referred  to  so  far  can  ho  described  as 
belontrins  to  the  Komance  of  Science,  i  now  come  to 
the  more  solid  contril)utions — to  a  real  genetic  theory  of 
the  things  of  nature.  These  are  not  much  older  than 
our  century.  They  belong  to  two  entirely  independent 
lines  of  research  which  were  followed  up  hi  England  and 
on  the  Continent  respectively — the  former  in  palieon- 
tology,  the  latter  in  embryology.  Although  they  were 
carried  on  quite  independently  of  each  other,  they  had 
this  in  common,  that  they  both  resorted  to  a  study  of 
life — as  preserved  in  geological  strata  or  as  now  existing 
around  us — for  a  guide  in  comprehending  the  genesis  of 
Things  on  a  larger  scale. 

Tt  may  be  well  to  remark  here  that  the  contemplation 
of  the  phenomena,  the  forms  and  the  processes  exhibited 
in  the  living  portion  of  creation,  has  not  always,  and 
even  not  generally,  in  the  course  of  history  led  to  those 
theories  which  our  age  is  elaborating,  and  wliidi  will  in 
future  times  possibly  be  looked  upon  as  one  of  its  char- 

'   Laplace    himself     says  :     "  Je    I    '  Kosmos,'   vol.  vi.   p.    8).    gives   u.s 


pieseiite  cette  origine  du  syst^me 
planctaire  avec  la  defiance  que  doit 
inspirer  tout  ce  cjui  ii'est  point 
un  resultat  de  I'observation  et  du 
calcul."  The  elaborate  exposition 
of  the  architecture  and  system  of 
the  universe  contained  in  A.  von 
Humboldt's  'Kosmos,'  which  was 
professedly  inspired  by  Laplace  (see 


little,  if  anything,  about  the  history 
of  the  universe,  professing  to  be 
only  a  '' W'eltgemiildc  "  and  not  a 
"  Welterkliirung."  The  time  for 
genetic  theories  had  not  yet  come, 
and  both  Kant's  and  Laplace's  cos- 
mogonies are  only  casually  referred 
to. 


286 


SCIENTIFIC    THOUGHT. 


7. 
"  Cyclical ' 
▼iew. 


acteristic  achievements  —  the  genetic  view.  There  is 
another  view  which  a  superficial  glance  at  organic  life, 
with  its  well  known  phases  of  birth,  culmination,  and 
decay,  has  frequently  impressed  upon  the  observer ;  there 
seemed  another  lesson  to  learn  than  that  which  our  age 
is  trying  to  master. 

That  other  view  can  best  be  termed  the  "  cyclical " 
view  of  things,  the  doctrine  that  every  thing  runs  in  a 
cycle  ^  and  repeats  itself,  that  all  change  is  periodic  and 
recurrent,  that   there   is   nothing   new   under   the   sun.^ 


1  Mr  Thomas  Whittaker  has  given 
me  various  references  to  the  writ- 
ings of  ancient  philosophers  which 
bear  on  this  subject.  He  finds  the 
cyclical  or  recurrent  aspect  of  the 
world-process  prominently  put  for- 
ward by  the  Stoics.  Zeller  ('  Philo- 
sophie  der  Griechen,'  vol.  iii.  I.  p. 
136,  &c.,  2ud  ed.)  says  in  his 
account  of  the  stoical  philosophy  : 
"  Out  of  the  original  substance  the 
separate  things  are  developed  ac- 
cording to  an  inner  law.  For  in- 
asmuch as  the  first  principle,  accord- 
ing to  its  definition,  is  the  creative 
and  formative  power,  the  whole  uni- 
verse must  grow  out  of  it  with  the 
same  necessity  as  the  animal  or  the 
plant  from  the  seed.  The  original 
tire — according  to  the  Stoics  and 
Heraclitus — first  changes  to  '  air  '  or 
vapour,  then  to  water ;  out  of  this 
a  portion  is  precipitated  as  earth, 
another  remains  water,  a  third 
evaporates  as  atmospheric  air, 
which  again  kindles  the  fire,  and 
out  of  the  changing  mixture  of 
these  four  elements  there  is  formed 
— from  the  earth  as  centre — the 
world.  .  .  .  Through  this  separa- 
tion of  the  elements  there  arises 
the  contrast  of  the  active  and  the 
passive  principle  :  the  soul  of  the 
world  and  its  body.  .  .  .  But  as 
this  conti'ast  came  in  time,  so  it  is 
also  destined  to  cease  ;  the  original 
substance   gradually   consumes  the 


matter,  which  it  segregated  out  of 
itself  as  its  body,  till  at  the  end  of 
this  world-period  a  universal  world- 
conflagration  brings  everything  back 
again  to  the  primaeval  condition. 
.  .  .  But  when  everything  has  thus 
returned  to  the  original  unity,  and 
the  great  world-year  has  run  out, 
the  formation  of  a  new  world  begins 
again,  which  is  so  exactly  like  the 
former  one  that  in  it  all  single 
things,  persons,  and  phenomena 
return  exactly  as  before  ;  and  in 
this  wise  the  history  of  the  world 
and  the  deity  .  .  .  moves  in  an 
endless  cycle  through  the  same 
stages."  Zeller,  in  a  note  to  this 
passage,  remarks  that  "  the  con- 
ception of  changing  world-periods 
is  frequent  in  the  oldest  Greek 
philosophy  ;  the  Stoics  found  it 
first  in  Heraclitus.  The  further 
statement,"  however,  that  the  suc- 
ceeding worlds  resemble  one  another 
down  to  the  minutest  detail,  is  to 
be  found,  to  my  knowledge,  before 
Zeno  only  in  the  Pythagorean  school 
.  .  .  and  is  connected  with  the 
doctrine  of  metemp.sychosis  and 
the  world-year." 

^  Mr  Whittaker  quotes  a  pass- 
age from  Aristotle's  'Metaphysics,' 
towards  the  end  of  the  12th  book 
(Berlin  ed.,  p.  1074,  b.  10-12): 
"Kara  rh  fiKos  iroWaKis  evprifjL^vrjs 
el  rh  SvvaThv  l/catTTTjs  Kai  Tex^vs 
Kal  (pi\o<joc(>ias  Kai  TrdXiy  (pOfipofxevuiv. 


ON    THE    GENETIC    VIEW    OF    NATURE. 


287 


Poets  and  pliilosophers  have  repeated  this  theme  in  end- 
less variations,  probably  without  improving  upon  the 
classical  and  perfect  expression  which  it  has  found  in 
ancient  ^  poetry  and  in  the  sacred  writings.  History  has 
been  written  with  the  professed  object  of  gaining,  by 
analogy,  an  insight  into  the  drift  of  modern  or  future 
events,  and  economic  and  political  theories  have  been 
based  upon  the  likelihood  of  a  recurrence  of  what  has 
happened  before.  Especially  has  the  teaching  been 
impressed  upon  us  that  the  universal  fate  of  all  develop- 
ment is  to  lead  to  death  and  decay,  and  to  make  room 
for  the  endless  repetition  of  the  same  recurring  phases 


Every  art  and  every  kind  of  philo- 
sophy having  probably  been  found 
out  many  times  up  to  the  limits 
of  what  is  possible  and  again  de- 
stroyed ; "  and  remarks,  "  This 
notion  of  cycles  refers  to  human 
civilisation,  not  to  the  universe, 
which  is  one  eternal  system  with 
a  ti.xed  central  mass,  and  with  its 
outer  part  in  a  moving  equili- 
brium. Empedocles  undoubtedly 
had  a  theory  of  recurrent  cycles 
in  the  universe.  The  four  ele- 
ments,— which  he  first  brought  to- 
gether as  elements  of  tiie  whole, 
early  thinkers  having  tiiken  one  or 
other  of  them  as  a  first  principle 
from  which  the  rest  are  evolved, 
—  according  to  Empedocles,  are 
necessarily  aggregated  and  segre- 
gated by  the  predominance  of  prin- 
cii)les  which  he  calls  love  {(piKia) 
and  hate  {veiKos).  The  four  periods 
are:  1.  Predominant  love  (the 
ff<pa7pos),  a  state  of  complete  aggre- 
gation ;  2.  decreasing  love  and  in- 
creasing hate  or  strife ;  3.  pre- 
dominant strife  {a.Ku(T/xia,  complete 
separation  of  the  elements) ;  4.  de- 
creasing strife  and  increasing  love. 
These  are  cosmic  periods.  It  has 
been  supjjosed  —  Zeller  takes  this 
view — tliat   we  are   living   in   the 


fourth    cosmic    pei'iod,    the   period 
of  increasing  love." 

'  The  best  known  passage  is  that 
from  the  celebrated  fourth  eclogue 
of  Virgil,  where,  after  describing  the 
return  of  the  golden  Saturnian  age, 
the  poet  continues  (vv.  31-36): — 

"  Pauca  taiiieii   subenuit  j)riseai  vestigia 

fraudis, 
Qiue  tentare  Tlietini  ratibus,  quae  cingere 

imiris 
Oppida,    quii:   jubeaiit    telluri    iiifindere 

sulcos. 
Alter   eiit    tiun  Tipliys,  et   altera   qua; 

veliat  Argo 
Dt'lectos  licroas  :  erunt  etiam  altera  bella, 
Atqiie  ilfiuiii  ad  Trojam  nuignus  inittetur 

Achilles." 

Dugald  Stewart  ('  Philos.  Works,' 
vol.  iii.  p.  167)  refers  to  this 
with  the  following  quotation  from 
Clavius's  '  Commentary  on  the 
Treatise  on  the  Sphere,'  by  Joannes 
Sacro  Bosco  :  "  Hoc  intervallo,  qui- 
dam  volunt,  omnia  qmocunujue  in 
mundo  sunt,  eodem  ordine  esse 
reditura,  quo  nunc  cernuntur,"  and 
he  also  attriliutes  this  theory  of  re- 
currence to  an  extreme  application 
of  the  mathematical  spirit  (vol.  iv. 
p.  207).  How  tiiis  idea  of  recur- 
rent cycles  fascinated  and  haunted 
Fr.  Nietzsche  see  Seth's  article, 
'Contem.  Kev.,'  vol.  73,  p.  734. 


288 


SCIENTIFIC    THOUGHT. 


of  existence.^  This  view  was  considerably  strengthened 
by  the  popular  interpretation  of  the  teaching  of  modern 
astronomy,  which  laid  great  stress  on  the  periodicity  of 
the  planetary  movements,  and  the  stability  and  inherent 
readjustment  of  the  solar  system.  Also  the  insight 
gained  by  the  first  application  of  chemical  knowledge  to 


'  The  idea  of  recurrent,  periodic 
repetition    seems    opposed    to    the 
modern    idea    of    progress  and  de- 
velopment  as    taught    by    Leibniz 
and    Herder    abroad,    by    Spencer 
in    this    country  ;    still    it    seems 
almost     impossible     in    a     purely 
mechanical  system  to  avoid  intro- 
ducing the  conception   of  an  ulti- 
mate   recurrence,    so    long  as    one 
deals    with    finite    space,    time,    or 
number,  however  great   they   may 
be.     The  only  escape  seems  to  be  in 
assuming  an  infinite  process  or  an 
immaterial    principle  which   is  not 
subject  to  mathematical  treatment, 
the  latter  being  inherently  one  of 
repetition.     It  is  interesting  to  note 
how  Herbert  Spencer  at  the  end  of 
'  First  Principles  '  relapses  into  the 
cyclical  conception  :  "  Thus  we  are 
led    to    the    conclusion    that    the 
entire    process    of    things,    as    dis- 
played   in    the    aggregate    of    the 
visible  universe,  is  analogous  to  the 
entire  process  of  things  as  displayed 
in  the  smallest  aggregates.     Motion 
as    well   as    matter   being  fixed   in 
quantit}',    it  would  seem  that  the 
change     in     the      distribution     of 
matter  which  motion  effects,  item- 
ing to  a  limit  in  whichever  direc- 
tion it  is  carried,  the  indestructible 
motion    thereupon     necessitates    a 
reverse  distribution.      Apparently, 
the  universally  coexistent  forces  of 
attraction     and     repulsion,     which 
necessitate   rhythm    in    all    minor 
changes  throughout    the    universe, 
also     necessitate    rhythm     in    the 
totality  of  changes — alternate  eras 
of  evolution  and  dissolution.     And 


thus  there  is  suggested  the  concep- 
tion of  a  past  during  which  there 
have    been     successive     evolutions 
analogous   to    that    which    is    now 
going    on  ;    and    a    future    during 
which  successive  other  such  evolu- 
tions may  go  on — ever  the  same  in 
principle   but    never    the    same    in 
concrete      result "     ('  First      Prin- 
ciples,' 1st  ed.,  p.  536).     The  other 
great  system  of  modern  philosophy, 
which   aims   at  a  reconciliation    of 
the  mechanical  and  spiritual  aspects 
— the  philosophy  of  Lotze — though 
it  dwells  less  than  Spencer's  system 
on    the    genetic    problem,    gives    a 
different   view    of    cosmic  develop- 
ment.      "  The     series     of     cosmic 
periods    cannot    be    a    number   of 
phases,   in   each   of  which   the  one 
purpc-^e  of  the  universe  does  in  fact 
maintain  itself :  it  must  rather  be 
a  chain,  each  link  of  which  is  bound 
together  with  every    other    in    the 
unity   of    one   plan.     The  One  can 
manifest    itself    in    various    forms 
only  when    such  variety   of    forms 
is   necessary  for  the    expression  of 
its  meaning — in  a  definite  order  of 
succession    only    when    this    order 
corresponds  to  a  craving  for  develop- 
ment in  its  nature.     As  we  required 
that   each    section   of    the   worlds 
history  should  present  a  harmony 
of  the  elements  firmly  knit  through- 
out, so  we  must  now  require  that 
the  successive  order  of  these  sections 
shall   compoise  the  unity  of  an  on- 
ward advancing  melody  "  ('  Micro- 
cosmus,'  Eng.  transl.  by  Hamilton 
and  Jones,  Book  IV.  chap.  3). 


ON     rilK    GKNETIC    VIKW    OF    NATURE. 


289 


physiology  and  agriculture  in  the  school  of  I.iebig,  and 
the  first  chapters  of  meteorology,  seemetl  to  favour  the 
idea  that  the  elements  and  forces  of  nature  were  encracred 
in  cyclic  movements  wliich  return  again  and  again  in  the 
same  fashion.  To  the  same  cyclical  view  the  doctrine  of 
the  ti.xity  of  species,  as  well  as  that  of  the  repetition 
of  various  creations,  lent  further  support :  lunu-e  it  con- 
tinued  up    to    the    middle    of    our    century '    to    be    fre- 


'  In  Germany  Mijleschott's  'Kreis- 
lauf  des  Lcbens,'  a  jiopular  exposi- 
tion of  the  conceptions  developed 
in  the  second  quarter  of  the  century 
through  clieniistry  and  embryology, 
represented  adetpaately  the  cyclic 
conception  of  life  and  development 
in  a  catcliing  phrase.  Much  later 
we  find  —  inter  multa  aim  —  in 
Michael  Foster's  'Text-book  of 
Physiology '  a  concise  description 
of  the  process  in  nature  which  has 
always  served  as  a  type  for  the 
cyclic  conception  :  "  When  the 
animal  kingdom  is  surveyed  from  a 
broad  standpoint  it  becomes  obvious 
that  the  ovum,  or  its  correlative 
the  spermatozoon,  is  the  goal  of  an 
individual  existence  ;  that  life  is  a 
cycle  beginning  in  an  ovum  and 
coming  round  to  an  ovum  again. 
.  .  .  The  animal  body  is  in  reality  a 
vehicle  for  ova  ;  and  after  the  life 
of  the  parent  has  become  potentially 
renewed  in  the  offspring,  the  body 
remains  as  a  cast-off  envelope  whose 
future  is  but  to  die."  Another 
example  may  be  found  in  .Molir"s 
'  (ieschichte  der  Erde,'  where  the 
circulation  of  different  elements  in 
nature  is  considered.  The  concep- 
tion of  periodic  cycles  has  found 
poetical  expression  in  Riickert's 
beautiful  yujeni,  "Chidher,"  which 
is  evidently  the  poetical  render- 
ing of  an  Arabian  legend  quoted 
by  Lyell  ('  Principles,'  vol.  i.  p. 
31):- 

VOL.  II. 


"Chidlier,  the  ever  youtliful,  spake  : 
I  passed  a  city  on  my  way, 
A  man  in  a  garden  fiuit  did  break, 
I  asked  how  long  tlie  town  here  lay? 
He  spoke,  and  broke  on  as  before, 
'  The  town  sUinds  ever  on  this  shore. 
And  will  thns  stand  (or  evermore.' 

And  wlien  five  hundred  years  were  gone 

I  came  the  same  road  as  anon, 

Then  not  a  mark  of  the  lowii  I  met. 

A  shepherd  on  the  tlulc  did  play, 

The  ealtle  leaf  and  foliage  ate. 

I  asked  how  long  is  the  town  away? 

He  spake,  and  i)iped  on  as  before, 

'One  plant  is  green  when  Uie  other's  o'er. 

This  is  my  pasture  for  evermore.' 

And  when  five  hundred  years  were  gone 
I  can)e  the  same  road  as  anon. 
Then  did  I  lind  with  waves  a  lake, 
A  man  the  net  cast  in  the  bay, 
And  when  he  paused  from  his  heavy  take, 
I  asked  since  wlien  the  lake  here  lay"? 
He  spake,  and  laughed  my  question  o'er, 
'  As  long  as  the  waves  break  as  of  yore 
One  fishes  and  fishes  on  this  shore.' 

And  when  five  hundred  years  were  gone 
I  came  the  same  way  as  anon. 
A  wooded  place  I  then  did  see. 
And  a  hermit  in  a  cell  did  stay  ; 
He  felled  with  an  axe  a  mighty  tree. 
I  asked  since  when  the  wood  here  lay? 
He  spake  :  '  The  wood's  a  shelter  for  "ever- 
more, 
I  ever  lived  upon  this  lloor. 
And  the  trees  will  grow  on  as  before.' 

And  when  five  hundred  years  were  gone 

I  came  the  same  way  as  anon. 

Hut  then  I  found  a  city  filled 

With  markets'  clamour  shrill  and  gay. 

I  ask<'d  how  long  is  the  city  built, 

Where's  wood  and  sea  and  shei)herd'splay? 

They  pondered  not  my  question  o'er 

But  cried  :  '  So  was  it  long  before. 

And  will  go  on  for  evermore.' 

And  when  five  hundred  years  are  gone 

rU  go  the  same  way  as  anon." 


290 


SCIENTIFIC    THOUGHT. 


8. 

Supplanted 
by  genetic 
view. 


9. 

Geology. 


quently  put  forward  and  popularly  accepted.  It  is 
useful  then  to  note  that  in  the  course  of  the  second 
half  of  the  century  we  were  more  and  more  grow- 
ing out  of  the  cyclical  and  realising  the  meaning  of 
the  genetic  ^  view  of  things  natural.  We  have  been 
taught  in  astronomy  to  inquire  into  the  origin  of  our 
solar  or  any  similar  system  and  the  conditions  of  its 
duration,  to  ask  concerning  the  central  heat  of  the  sun 
whence  it  came  and  how  long  it  will  last — a  question 
unknown  to  Laplace, — to  consider  the  effects  of  tidal 
friction,  to  learn  that  all  the  movements  in  nature  are 
irreversible  as  distinguished  from  completely  reversible 
ones,  which  only  exist  in  abstraction ;  and,  finally,  we  are 
met  with  the  doctrine  of  the  immortality  of  the  germ- 
plasma,  an  idea,  the  meaning  and  significance  of  which  I 
shall  have  to  explain  later  on.  All  these  novel  theories 
and  views  combine  to  impress  upon  us  the  general 
significance  of  the  terms  "  genesis,  evolution,  develop- 
ment," the  fact  that  everything  in  and  around  us,  in 
spite  of  the  seeming  recurrence  of  smaller  movements  and 
phenomena,  and  of  the  periodicity  of  the  minuter  and 
elementary  changes,  is  slowly,  continuously,  and  inevit- 
ably tending  in  a  definite  direction,  which  is  certainly 
not  that  of  a  cyclical  recurrence. 

Leaving  aside  for  a  moment  these  more  general  views, 
which  have  been  clarified  in  the  course  of  our  century, 
it  is  interesting  to  note  how  they  gradually  emerged  in 


^  Perhaps  it  would  be  more 
correct  to  saj-  that  we  were  learning 
to  consider  the  changes  within  the 
larger  cycles,  confining  ourselves  to 
the  stud)'  of  one  brancli  only  of  the 


periodic  or  cyclical  movement  of 
things  around  us,  that  branch  which 
we  are  pleased  to  call  the  ascending 
or  progressive  branch. 


ON    THE    GExVETiC    VIEW    OF    NATURE.  291 

the  teachings  of  the  several  natural  pliilosophers  who 
initiated  the  genetic  conception  of  natural  phenomena. 
One  <if  llie  earliest  wIki  l»roke  with  the  older  and  intro- 
duced ihc  modern  metiiods  was  James  Hutton,  wlio  to- 
wards the  end  of  the  preceding  century  led  that  school  in 
geology  which  is  called  after  him,  and  wliicli  violently 
opposed  the  ideas  introduced  from  the  Continent.  The 
controversy  culminated  in  the  wrangle  of  the  Neptunists 
and  Vulcanists,  those  who  looked  to  the  agency  of  water 
and  those  who  upheld  that  of  lire  as  the  principal  cause 
of  geological  change.  This  difference,  which  at  the  time 
impressed  the  popular  mind,  is  hardly  thai  ]>y  whicli,  in 
ii  history  of  scientific  thought/  tliis  controversy  has 
become  important.  Hutton's  position  is  marked  rather 
hy  his  opposition  to  catastrophism,  and  by  his  doc- 
trine that  geological  changes,  such  as  the  decay  and 
reproduction  of  rocks,  were  going  on  with  the  utmost 
imiformity,  being  always  in  progress.  This  he  opposed 
to  the  Wernerian  view,  which  believed  in  the  existence 
of  certain  "  fundamental  rocks,"  which  were  "triuni])liantly 

'  The    great    merits    of     James   I    effect  in  circles  in  which  everything 
Hutton,  his  extensive  and  original       connected      with      the     revolution 


geological  .studies,  his  oi)position  to 
catastrophism,  were  overlooked 
through  the  theoretical  discussions 
and  the  unfortunate  title  of  his 
book.  Tlie  world  had  grown  tired 
of  '  Theories  of  the  Earth  '  and  the 
<h"scussi(m  of  fundamental  problems. 
A  spirit  of  observation  had  set  in  ; 
the  Geological  Society  was  formed, 


against  Church  and  State  was  dis- 
tasteful. As  Huxley  has  told  us, 
Hutton  came  before  his  time.  To 
him  belongs  the  merit  of  having 
initiated  the  line  of  research  and 
reasoning  wliich,  through  the 
brilliant  labours  of  Chailes  Lyell  a 
generation  later,  swept  away  the 
older  geology,  and  prepared  tlie  way 


and  theories  were  for  the  time  dis-   ;    for  the  genetic  study  of  nature  on  a 


countenanced.  (See  vol.  i.  p.  290, 
note  1 ,  of  this  '  History.' )  The  att.jicks 
a,lso  of  Kirwan  and  De  Luc,  which 
turned  upon  the  stale  argument 
that  Hutt'iii's  ideas  were  opposed  to 
the    scriptural    records,    had    tiieir 


large  scale.  (See  the  "Historical 
Sketch"  in  tlie  first  volume  of 
Lyell's  '  Princi|)les  of  (^leology,'  and 
Huxley's  address  on  "Geological 
Reform,"  ISey.) 


292 


SCIENTIFIC    THOUGHT. 


10. 
Htttton. 


appealed  to  if  anybody  ventured  to  doubt  the  possibility 
of  our  being  able  to  carry  back  our  researches  to  the 
creation  of  the  present  order  of  things."  ^  Hutton 
destroyed  these  characters,  which  were  considered  by 
many  as  sacred,  and  declared  that  in  the  economy  of  the 
world  he  could  find  "  no  traces  of  a  beginning  nor  signs 
of  an  end."  And  yet,  as  Lyell  has  shown,  his  principles 
were  only  imperfectly  carried  through,  for  though  he 
maintained  that  "  the  strata  which  now  compose  our 
continents  have  once  been  beneath  the  sea,  and  were 
formed  out  of  the  waste  of  pre-existing  continents,"  ^  he 
imagined  that  when  the  decay  of  old  continents  had 
furnished  the  material  for  new  ones  these  were  upheaved 
by  violent  and  paroxysmal  convulsions.  He  therefore 
required  "  alternate  periods  of  general  disturbance  and 
repose,  and  such  he  believed  had  been  and  would  for 
ever  be  the  courses  of  nature."  ^  A  strange  mixture  of 
the  genetic  and  cyclical  views  of  natural  phenomena ! 
Professor  Huxley  '^  has  explained  these  seeming  incon- 
sistencies in  the  theory  of  Hutton,  whom,  together  with 
Sir  Charles  Lyell,  he  has  described  as  having  founded 
the  "  uniformitarian  "  school  of  geology,  by  the  influence 
which  the  discoveries  of  physical  astronomy,  brought 
out  at  that  time  by  Laplace  and  his  contemporaries, 
had  upon  Hutton.  Thus  Hutton  writes  :  "  From  seeing 
revolutions  of  the  planets,  it  is  concluded  that  there 
is  a  system  by  which  they  are  intended  to  continue 
those    revolutions.       But    if    the    succession    of    worlds 


'•■  See  Lyell,  'Principles,'  Srd  ed., 
vol.  i.  pp.  90,  91. 

'  Ibid.,  p.  89.  3  Lyell,  p.  92. 

^  Huxley,    on    "  Geological    Re- 


form," quotes  largely  from  Hutton's 
'Theory  of  the  Earth'  f  1758)  and 
Playfair's  '  Ilustrations  of  the  Hut- 
tonian  Theory  '  (1802). 


Lyell. 


ON    THE    GENETIC    VIEW    OE    NATURE.  293 

is  established  in  tlie  system  cf  nature,  it  is  in  vain 
to  look  for  anything  higher  in  the  origin  of  the  earth. 
The  result,  therefore,  of  this  physical  inquiry  is,  that 
we  find  no  vestige  of  a  beginning,  no  prospect  of  an 
end."  The  lieginnings  of  the  genetic  view  of  geolog- 
ica]  phenomena,  which  in  Iluttun  were  still  mingled  with 
eatastrophism,  were  further  developed  ])y  Sir  Charles 
Lyell  in  his  celebrated  '  Principles  of  (xeology.'  When  u. 
lie  entered  upon  his  geological  researches,  which  were 
conducted  during  his  very  extensive  travels  all  over 
Europe,  a  new  element  had  already  been  introduced 
into  science,  of  which  neither  Hutton  nor  Werner  liad 
been  able  to  a\'ail  themselves  extensively.  This  was  the 
identification  of  geological  strata  according  to  the  fossil 
remains  which  were  contained  in  them, — a  realisation 
of  the  plan  of  work  already  dimly  foreshadowed  in 
Leibniz's  '  Protogica,'  but  nevertheless  accepted  even  by 
Humboldt  as  only  a  doubtful  indication.^  This  valuable 
brancli  of  geological  science  had  been  started  by  AA^illiam 
Smith  ill  his  'Tabular  View  of  the  British  Strata'  in 
1790,  and  further  elaborated  in  his  geological  map  of 
Kngland  (1815),  which  was  the  fruit  of  his  own  un- 
aided labours,  "  for  he  had  explored  the  whole  countrv 


'  'I'lu'  Wernerian  school  ;ire  gen- 
erally accused  of  having  neglected 
the  historical  record  afforded  by 
fossil  remains,  and  Humboldt,  in 
his  '  Essaj-  on  the  Superposition  of 
Rocks  in  both  Hemispheres'  (182-3), 
says  (Eng.  transl.,  j).  52):  "In 
the  present  age  naturalists  are  no 
longer  satisfied  with  vague  and 
uncertain  notions,  and  they  have 
sagaciously  observed  that  the  great- 
est number  of  those  fossils,  buried 
in    different    formations,    are    not 


specifically  the  same  ;  that  many 
species  wliich  they  have  been  enabled 
to  examine  with  precision  vary  with 
the  superposed  rocks.  .  .  .  Ought 
we  to  conclude  from  this  assem- 
blage of  facts  that  all  the  forma- 
tions are  cliaracteri.sed  by  particular 
species  ?  that  the  fossil  shells  nf  the 
chalk,  of  the  muschclkalk,  of  the 
Jura  limestone,  and  of  the  Alpine 
limestone,  all  differ  from  each  other  ? 
This  would  be,  in  my  opinion,  to 
carry  the  induction  much  too  far." 


294  SCIENTIFIC    THOUGHT. 

on  foot  without  the  guidance  of  previous  observers  or 
the  aid  of  fellow  -  labourers,"  ^  and  "had  thus  singly- 
effected  for  the  whole  of  England  what  many  celebrated 
mineralogists  had  only  accomplished  for  a  small  part  of 
Germany  in  the  course  of  half  a  century."  ^  Simultane- 
ously with  Smith  in  England,  Cuvier  and  Brongniart  were 
exploring  the  Paris  basin.  Thus  the  three  different 
nations  of  Europe  with  whom  I  am  mainly  concerned 
in  this  work  furthered  independently  the  main  divisions 
of  geological  inquiry.  "  The  systematic  study  of  what 
may  be  called  mineralogical  geology  had  its  origin  in 
Germany,  where  Werner  first  described  with  precision 
the  mineral  character  of  rocks ;  the  classification  of  the 
secondary  formations  belongs  to  England,  where  the 
labours  of  Smith  were  steadily  directed  to  these  ob- 
jects ;  the  foundation  of  the  third  branch,  that  relating 
to  the  tertiary  formation,  was  laid  in  France  by  the 
splendid  work  of  Cuvier  and  Brongniart."  ^  To  these 
words  of  Lyell  we  can  now  add  that  the  theoretical 
explanations  were  first  suggested,  and  the  correct  line 
of  reasoning  on  this  accumulated  evidence  initiated,  by 
Sir  Charles  Lyell  himself. 

The  key  to  the  doctrines  of  Lyell  was  the  study  of 
existing  causes  —  the  attempt  to  show  how  the  slow 
agencies  which  we  now  see  at  work  in  nature  around 
us    are    sufficient    to    explain    the    successive    changes  * 


^  Lyell,  '  Principles,'  vol.  i.  p. 
101. 

^  An  expression  of  cl'Aubuisson, 
quoted  by  Dr  Fitton,  '  Phil.  Mag.,' 
vols.  i.  and  ii.,  also  "  Edin.  Rev.,' 
Feb.  1818. 

^  See  Lyell,  loc.  cit.,  p.  100. 


only  by  carefully  considering  the 
combined  action  of  all  the  causes  of 
change  now  in  operation,  whether 
in  the  animate  or  inanimate  world, 
that  we  can  hope  to  explain  such 
complicated  ap]>earances  as  are  ex- 
hibited in  the  general  arrangement 


*  Id.  ibid.,  vol.  iii.  p.  273  :   "  It  is    •    of  mineral  masses." 


ON    THE    GENETIC    VIEW    OF    NATURE.  295 

which  the  recognisable  strata  of  the  earth's  crust 
with  their  fossil  remains  indicate  as  having  occurred 
in  former  ages.  It  was  an  attempt  to  "  reconcile  the 
former  and  the  present  state  of  nature."  ^  This  was 
to  break  with  the  idea  of  great  and  general  convulsions, 
to  which  the  Continental  school  resorted  in  their  ex- 
planations, and  it  also  meant  upsetting  the  vague  notions 
which  set  a  limit  to  the  time  '^  which  should  be  allowed 
for  the  operations  of  natural  causes.  It  is  possible  to 
admit  that  in  both  directions,  in  their  uniformitarian 
explanation  and  in  their  geological  time-reckoning,  the 
new  school  frequently  went  too  far,  the  indications 
of  actual  catastrophes  and  paroxysmal  convulsions  being 
to  many  observers  quite  unmistakable.  On  the  other 
side,  the  arguments  based  upon  physical  astronomy, 
mechanics,  and  thermodynamics,  which  aftbrd  an  inde- 
pendent basis  for  geological  time -reckoning,  were  not 
yet  elaborated,^  or  were  deemed  too  crude  *  to  be  of 
value ;    and  for  a  good  while  geologists  were  permitted 

^  Lyell,  vol.  i.  p.  114.  elementary    matter    of    the    earth 
-  Id.  ibid.,  p.  241:   "When  difR-  may  have  been  first   iu    a  gaseous 
culties    ari.se    in    interpreting   the  j   state,     resembling     those     nebula- 
monuments  of  the  past,  I  deem  it  j    which   we   behold   in    the   heavens, 
more  consistent  with  philo.^ophical  ,    and    which   are    of    dimension.-,    so 


caution  to  refer  them  to  our  present 
ignorance  of  all  the  existing  agents, 
or  all  their  possible  effects  in  an 
indefinite  lapse  of  time,  than  to 
causes  formerly  in  operation  but 
which  have  ceased  to  act." 

*  See  Lyell,   vol.  i.  p.   1.54,  &c., 


vast  tiiat  some  of  them  would  fill 
the  orbits  of  the  remotest  planets 
of  our  system.  .  .  .  Without 
dwelling  on  such  speculaiions 
which  can  never  have  any  direct 
bearing  on  geology,"  &c. 

*  See  Lyell,  vol.  i.  p.  206,  whei-e 


also  vol.  ii.  p.  274:    "It  has  long       he  refers  to  "astronomical  t•au^es 
been    a   favourite   conjecture    that       of  fluctuations  in  climate,"  and  to 


the  whole  of  our  planet  was  origin- 
ally in  a  state  of  igneous  fu.sion,  and 
that  the  central  parts  still  retain  a 


the  calculations  of  Sir  J.  Herschel 
and  the  fa<^t  that  "this  matter 
still    under   discussion,"    and    that 


great  portion  of  tiieir  primitive  |  "Mil.  Fourier  and  Herschel  iiave 
heat.  Some  have  imaginetl  witii  ,  arrived  at  very  different  opinions." 
the  late  Sir  W.  Herschel  that  the   i 


296 


SCIENTIFIC    THOUGHT. 


Embryol- 
ogy. 


to  draw  indefinitely  on  the  great  bank  of  time/  just  as  in 
former  ages  they  had  been  quickly  brought  to  book  by 
existing  prejudices.^ 

Wliilst  these  contributions  to  the  genetic  view  of 
nature  on  the  large  scale  were  being  independently 
worked  out,  the  sciences  which  deal  with  the  minute 
and  hidden  phenomena  of  organic  growth  had  made  great 
progress  in  the  same  direction.  Here  a  definite  scheme 
of  development  was  quite  evident  to  the  most  casual 
observer.  In  these  sciences  indeed  we  have  to  do  with 
what  is  called  in  the  German  language  "  the  history  of 
development  "  'par  excellence,  a  term  which  is  inadequately 
rendered  by  "  Embryology  "  in  French  and  English.  For 
it  is  an  error  which  has  frequently  and  for  long  periods 
obscured  the  correcter  view  to  assume  that  the  chang;es 
and  processes  which  characterise  the  development  of 
embryonic  or  germ  life  are  essentially  different  from 
those  which  exist  in  the  larger  and  more  complex  adult 
organism.  The  abohtion  of  the  fundamental  distinction 
between  the  processes  of  embryonic  and  of  adult  or  f ull- 


1  Lyell,  vol.  iii.  p.  358  :  "  Cou- 
fiiied  notions  in  regard  to  the 
quantitj'  of  past  time  have  tended 
more  than  any  other  prepossessions 
to  retard  the  progress  of  geology, 
.  .  .  and  until  we  habituate  our- 
selves to  contemplate  the  possibility 
of  an  indefinite  lapse  of  ages  having 
been  comprised  within  each  of  the 
more  modern  periods  of  the  earth's 
history,  we  shall  be  in  danger  of 
forming  most  erroneous  views  in 
geology." 

-  One  of  the  first  to  attack  the 
uniformitarian  doctrine  in  geology 
and  to  applj'  the  principles  of 
modern  physical  science  to  geolog- 


ical and  cosmical  questions  in  this 
country  was  Lord  Kelvin.  His 
influence  belongs,  however,  mainly 
to  the  post-Darwinian  period,  and 
begins  with  his  celebrated  memoir 
'  On  the  Secular  Cooling  of  the 
Earth'  (Edin.  Trans.,  1862,  re- 
printed in  the  3rd  vol.  of  '  Math, 
and  Phys.  Papers,'  p.  295).  See 
also  the  2nd  vol.  of  his  '  Popular 
Lectures  and  Addresses.'  Accord- 
ing to  the  introductory  statement 
in  the  former  paper  his  doubts 
regarding  the  uniformitarian  teach- 
ing began  as  early  as  1844.  I  shall 
refer  to  these  speculations  at  the 
end  of  this  chapter. 


ON    THK    (JENKTIC    VIKW    OF    XA'ICRE.  297 

giowu  life,  the  unification  of  thought  on  these  niattere,  is 
quite  as  important  in  the  history  of  science  as  tlie  abolition 
of  the  supposed  fundamental  difference  between  animal 
and  vegetable  growth  or  between  normal  and  abnormal  (or 
pathological)  development.  The  reduction  of  all  these 
seemingly  so  different  changes  to  the  one  great  problem 
of  cellular  structure,  cellular  growth,  and  cellular  division 
marks  one  of  the  greatest  achievements  of  our  century. 
"  Our  position  with  regard  to  the  cell  is  similar  to  that 
of  investigators  towards  the  whole  animal  or  vegetable 
body  a  hundred  years  ago,  before  the  discovery  of  the 
cell  theory."^ 

Anticipations  of  this  generalisation,  of  the  condensation 
of  the  whole  problem  of  animal  and  vegetable  embryology, 
of  generation,  growth,  and  organic  development  in  the 
formula,  "  omnis  cellula  ex  cellula,"  have  indeed  existed 
since  the  time  of  Harvey,  who,  in  addition  to  the  great 
discovery  of  the  circulation  of  the  blood,  laid  down  the 
thesis,   "  omnp    vivuni    ex    ovo." "      Th(>    further   correct 

'  See  O.    Hertwig,    "  Thy   Cell,  "  important   of    the    organs    of    the 

'  Outlines  of  General  Anatomy  and  i    adult,    nor    by    sudden    nietamor- 

Physiology.'     Transl.  by  Campbell,  phosis    of    a    formative    substance 

1895,  p.  11.  I    into    a    miniature    of    the    \vhole, 

-  One  of  the  best  expositions  of  '    which  subsequently  grows,  but  by 

Harvey's   idea.s  is   to    be   found   in  epigenesis,  or  successive  diffeientia- 

Huxley's  article  on  "  Evolution  in  tion    of   a    relatively    homogeneous 

Biologj'"    in    tlie    ninth  edition  of  rudiment  into  the  parts  and  struc- 


the  '  Encyclop;cdia  Britannica.'  He 
there  also  refers  to  Aristotle's 
opinions.  "  One  of  Harvey's  prime 
objects  is  to  defend  and  establish, 


tures  which  are  characteristic  of 
the  adult."  In  the  sequel  of  his 
exposition,  after  maintaining  epi- 
genesis  or  after-formation    against 


on  the  basis  of  direct  observation,  i    evolution  in  the  older  sense  or  pre- 

the  (jpinion  already  held   by  Aris-  ,    formation,  Huxley,  however,  makes 

totle,    that  in    the   higher   animals  [    a  passing  remark  that  "  though  the 

at  any   rate  the  formation   of   the  doctrine  of  epigenesis,  as  uiulerstood 

new   organism    by    the   process    of  I    by  Harvey,  has  definitely  triumphed 

generation    takes    place,    not    sud-  over  the  doctrine  of  evolution,  .   .   . 

denly  by  simultaneous  accretion  of  it  is  not  impossible  that,  when  the 

rudiments  of  all,    or  of    the    must  analysis  of  the  jirocess  of  develop- 


298 


SCIENTIFIC    THOUGHT. 


13. 

Epigenesis 
and  evolu- 
tion. 


14. 

C.  F.  Wolff. 


generalisation  which  he  ventured  to  put  forward,  that 
growth  and  development  of  the  germ  or  embryo  con- 
sisted in  the  addition  or  formation  of  new  parts  and 
structures  through  division  or  differentiation,  was,  how- 
ever, obscured  and  cast  into  the  shade  by  the  opposite 
doctrine,  termed  evolution,  according  to  which  every 
form  or  particle  of  organisation  was  minutely  pre-formed 
in  an  invisible  germ,  and  growth  consisted  merely  in  a 
process  of  enlargement,  as  a  particle  of  "  dry  gelatine 
may  be  swelled  up  by  the  intussusception  of  water." 
The  supporters  of  this  doctrine,  to  which  the  celebrated 
names  of  Leibniz,  Boerhaave,  Haller,  and  Bonnet  belonged, 
seemed  unable  to  conceive  of  any  force  in  nature  which 
was  capable  of  producing  organisation,  and  were  thus 
compelled  to  accept  in  some  form  or  other  the  doctrine 
of  the  pre-existence  of  germs,  a  theory  which  has  in 
modern  times  been  revived  under  an  altered  form. 

The  real  foundation  of  scientific  embryology,  of  the 
study  of  the  genesis  of  vegetable  and  animal  organisms, 
is  now  pretty  unanimously  ^  traced  to  Caspar  Friedrich 
Wolff,  whose  '  Theoria  generationis '  appeared  in  1759. 
His  observations  refer  alike  to  plant  and  to  animal  life, 
and  his  distinct  object  was  to  refute  the  theory  of  evolu- 


meut  is  carried  still  further,  and 
the  origin  of  the  molecular  com- 
ponents of  the  physically  gross, 
though  sensibly  minute,  bodies 
which  we  term  germs  is  traced, 
the  theory  of  development  will  ap- 
proach more  nearly  to  metamor- 
phosis than  to  epigenesis.  .  .  .  The 
process,  which  in  its  superficial 
aspect  is  epigenesis,  appears  in 
essence  to  be  evolution  in  the 
modified  sense  adopted  in  Bonnet's 


later  writings  ;  and  development  is 
merely  the  expansion  of  a  potential 
organism  or  original  pre-formation 
according  to  fixed  laws." 

^  See  J.  A.  Thomson,  loc.  cit. ,  p. 
121.  Yves  Delage,  '  L'H^rddit^,' 
p.  357,  note  ;  and  especiallly  O. 
Hertwig,  '  The  Biological  Problem 
of  To-day,'  transl.  by  P.  C.  Mitchell 
(Heinemann's  Scientific  Handbooks, 
1896),  p.  4,  &c. 


ON    THE    GENETIC    VIEW    OF    NATURE. 


299 


tion  and  replace  it  by  the  correcter  doctrine  of  epigenesis 
— i.e.,  of  repeated  or  after-formation.  I  Taller^  thought 
very  highly  of  this  attack  on  liis  own  view,  hut  was 
not  convinced  by  it :  and  although  in  botany  Wolfi's 
views  on  the  cellular  structure  of  plants  were  adopted 
in  France  by  Mirbel,  and  those  on  metamorphosis  were 
unknowingly  reproduced  ]»y  Goethe,  his  influence  on  em- 
bryology dates  actually  only  from  the  year  1812,  when 
Meckel  translated  one  of  his  treatises  and  thus  drew 
attention  to  his  great  merits.  Wolll"  tried  to  refute  the 
theory  of  evolution  or  pre-formation,  supplanting  it  by 
that  of  epigenesis  or  after -formation,  through  actual 
observations  of  the  development  of  germs  in  plants  and 
animals  in  definite  instances.  Tn  l)otany  his  views, 
after  lying  dormant  for  a  long  period,  led  ultimately  to 
the  famous  cellular  theory  of  Schleiden  and  IVlohl.  Tn 
zoology,  shortly  after  Meckel's  republication  of  his  treatise 
in  1812,  there  were  published  the  researches  of  Pander, 
who,  in  his  treatise  on  the  development  of  the  chick, 
"  gave  a  fuller  and  more  exact  view  of  the  phenomena 
less  clearly  indicated  by  Wolft*,  and  laid  the  foundation 
of  the  views  of  all  sul)sequent  embryologists."  ^ 

Pander  was  a  Eussian  by  l)irth,  anil  so  was  his  greater  pamierana 

n  K.  E.  von 

contemporary   and   friend,  Karl  Ernst   \-on  l5aer,    a  man  Baer. 


'  As  Prof.  J.  Ailhur  Thomson 
says  ('  Science  of  Life,'  p.  V2,Q),  "  A 
.single  sentence,  '  Es  gibt  kein 
Werden  —  there  is  no  IJecoming,' 
sufficiently  iiulicates  Haller's  posi- 
tion." 

-  .J.  A.  Thoin.^on  in  article  "  Em- 
bryolog\'"  (' Encv.  Brit.,'  9th  ed  , 
p.  16f.r 

='  The  work  of  von  Baer  (1792- 
1876)  remained  for  a  long  time  un- 


unrecognised  outside 


known     and 

of  Cerinany.  Huxley  made  him 
known  in  this  country  by  trans- 
lating extracts  from  his  principal 
writings  for  Taylor's  '  Scientific 
Memoirs'  in  18,o3,  nearly  thirty 
years  after  von  Baer  had  begun  the 
brilliant  .scries  of  his  researches.  It 
can  be  said  of  him  that  he,  even 
more  than  his  forermniers,  Pander 
and    Dijllinger,    withdrew    natural 


300 


SCIENTIFIC    THOUGHT. 


who  occupies  a  unique  position  in  the  history  of  natural 
science.  He  introduced  the  principle  and  aspect  of 
development  into  the  midst  of  those  studies  which,  under 
the  important  but  one-sided  influence  of  Cuvier  and  his 
school,  were  in  danger  of  being  confined  within  the 
limits  of  morphology  and  comparative  anatomy.  Through 
a  long  series  of  most  important  embryological  investiga- 
tions, conducted  during  the  years  181 9-1837,  he  demon- 


science  from  tlie  spell  under  which 
it  was  kept  for  a  long  time  in  the 
West  of  Europe  by  the  great 
authority  of  Cuvier.  Geograph- 
ically also,  von  Baer's  activity  was 
centered  in  Kiinigsberg  (where  he 
was  one  of  a  brilliant  company  who 
made  the  University  celebrated)  and 
St  Petersburg.  Though  a  great 
admirer  of  Cuvier,  whose  biography 
he  wrote,  and  an  adherent  of  the 
doctrine  of  animal  types,  which  he 
independently  arrived  at,  he  intro- 
duced three  distinct  lines  of  re- 
search into  his  scientific  labours,  to 
all  three  of  which  Cuvier  was  either 
foreign  or  distinctly  averse — viz., 
microscopic  research,  study  of  em- 
bryological development,  and  the 
philosophical  spirit  of  the  "  Natur- 
philosophie."  He  was  not  dazzled 
by  the  latter  ;  but  whilst  avoiding 
its  extravagances  and  premature 
generalisations  which  then  flooded 
Cerman  science,  he  always  appre- 
ciated the  search  for  the  connection 
and  unity  of  all  the  things  of  nature 
which  was  characteristic  of  that 
school.  Baer  stood,  historically  and 
philosophically,  in  the  middle  be- 
tween the  extreme  morphological 
and  genetic  views  rejiresented 
respectively  by  Cuvier  before  and 
by  Darwin  after  him.  Already  in 
1815,  when  studying  under  Dol- 
linger  at  Wiirzburg,  he  was  guided 
by  the  idea  that  "  nature  follows  in 
her  creations  certain  general  themes 
(types),  and  that  she  varies  these  in 
the  different   species."      Von    Baer 


also  combined  the  geographical  and 
anthropological  interest,  so  largely 
represented  by  Humboldt  and 
Ritter,  with  his  morphological 
and  genetic  studies.  In  fact,  it  is 
doubtful  whether  in  any  naturalist 
of  the  very  first  order  the  different 
interests  which  the  nineteenth 
century  inherited  and  created  were 
more  equally  and  impartially  bal- 
anced than  in  him.  The  embryo- 
logical  researches  of  von  Baer 
stimulated  many  ardent  students  in 
( Jermany,  such  as  Purkinje,  Rathtke, 
Bischoff,  and  it  is  mainly  through 
them  that  this  branch  of  science 
was  cultivated  and  made  generally 
known.  The  name  of  the  distant  or- 
iginator thus  became  .somewhat  for- 
gotten, so  that  in  French  science  we 
do  not  find  von  Baer  as  frequently 
and  appreciatively  mentioned  as  he 
deserves.  Ample  information  on  von 
Baer's  scientific  and  personal  char- 
acter can  be  found  in  later  publica- 
tions :  foremost  in  his  '  Auto- 
biography,' published  in  186.^)  ;  in 
his  'Life,'  by  Stieda  (1877)  ;  and  in 
an  elaborate  work  by  Professor  R. 
Stolzle,  entitled  '  K.  E.  von  Baer 
und  seine  Weltanschauung'  (Re- 
gensburg,  1897).  This  work  con- 
tains very  ample  and  useful  refer- 
ences and  extracts  from  Baer's 
writings  and  correspondence.  Very 
important  are  also  von  Baer's 
miscellaneous  writings  and  essays, 
which  were  published  by  Vieweg 
in  Brunswick,  in  three  parts  (2nd 
ed.,  1886). 


ON  THE  OKNKTIC  VIKW  OF  NATUKK.     301 

strated  in  the  completest  manner  the  truth  of  epigenesis. 
In  fact,  he  had  recognised  development  as  the  "  sole  basis 
of  zoological  classification ;  while  in  France  Cuvier  and 
Geoffrov  St  Hilaire  were  emljittering  each  other's  lives 
with  endless  merely  anatomical  discussions  and  replica- 
tions, and  while  in  Germany  the  cautious  study  of  nature 
was  given  up  for  the  spinning  of  Xatur-philosophies  and 
other  hypothetical  cobwebs."  ' 

The  position  which  Karl  Ernst  von  Baer  occupies  in 
the  liistory  of  science  and  thought  is  in  many  respects 
interesting  and  unique.  He  lived  early  enough  in  the 
century  to  experience  the  full  influence  of  Cuvier's 
authority,  and  lived  long  enough  to  witness  tlie  great 
change  which  Darwin's  writings  brought  on  in  all  the 
natural  sciences ;  whereas  his  great  contemporary, 
rlohannes  JMuller,  passed  away  before  the  name  of 
Darwin  was  known  outside  of  his  own  country.  In 
unison  with  Mliller,  and  yet  in  an  independent  manner, 
he  effectually  liberated  German  science  from  the  undue 
influence  of  the  speculative  school.  And  he  lias,  prob- 
ably more  than  any  other  great  naturalist,  recognised 
the  importance  of  the  three  aspects  which  a  contempla- 
tion of  natural  objects  forces  u]>()n  us:  the  apparent  or 
real  fixity  of  certain  forms  (the  morphological  view), 
the  continued  and  orderly  cliange "  of  these  forms  (the 
genetic  view),  and   the  apparent  or  real  existence  of  a 

•   Huxley   iu   Taylor's  'Scientific  far  as  observations  now  give  material 

Memoirs,'  New  Series,  p.  176.  for  inferences,  a  transformation  of 

'■^  Very  important  in  this  respect  certain  original  forms  of  animals  in 

is  a  lecture  delivered  by  von  Baer  the  succession  of  generations  is  very 

in   18-34,  with    the    title    'Das   all-  probable,  but  only  to  a  limited  ex- 

gemeinste  Gesetz  der  Natur  in  aller  tent"    (p.    60),    a    view    which   von 

Entwickelung'    (reprinted    in     the  Baer  maintained  to  the  cn<l  against 

Brunswick    edition,    vol.    i.    p.    ;j9  extreme  Darwinism  (see  p.  37). 
.^77.)     "  We  must  conclude  that,  so 


302  SCIENTIFIC    THOUGHT. 

design  in  this  process  of  change  (the  teleological  view). 
Though  his  own  researches  did  so  much  to  give  promi- 
nence to  the  genetic  view,  to  the  conception  of  develop- 
ment, he  retained  and  elaborated  the  doctrine  of  types ; 
and  though  he  effectually  handled  the  modern  methods 
of  the  mechanical  or  exact  sciences,  he  realised  the  full 
importance  of  studying  the  things  and  processes  of 
nature  in  their  actual  and  living  connection,^  and  not 
merely  in  the  artificial  isolation  of  the  laboratory  or 
the  dissecting-room.  And  he  never  became  an  adherent 
of  the  doctrine  so  prevalent  with  many  of  the  followers 
of  Darwin,  that  the  apparent  purpose  of  forms  and 
processes  in  organic  nature  could  be  mechanically  ex- 
plained. During  the  period  of  his  greatest  scientific 
activity  he  was  little  known  outside  of  Kussia  and 
Germany ;  in  England,  Carpenter  and  Huxley  alone 
drew  attention  to  his  embryological  and  genetic  studies; 
but  since  the  tide  of  Darwinism  has  somewhat  subsided, 
or  has  ceased  to  be  all-absorbing,  it  is  to  the  writings 
of  Baer  that  many  naturalists  revert.  In  fact  they 
belong  to  the  few  books  of  this  class  written  during 
the  pre-Darwinian  age  that  bear  to  be  read  and  re-read 
with  profit  by  those  who  take  a  philosophical  and  not 
merely  a  historical  interest  in  the  development  of 
16.        natural   science.     Perhaps  the  fact  that  von   Baer  was 

Von  Baer's 

comprehen-   as   great  in   relation    to   the   morphological    as    he   was 

sive  views.  "  jr  o 

in  relation  to  the  genetic  and  the  teleological  con- 
ceptions of  natural  phenomena  prevented  him  from 
producing  that  revolutionary  impression   on   the   minds 

^  See    the    introduction    to    the       geschichte  der  Thiere'  (Konigsbej-g 
second  part  of  his  '  Entwickelungs-    I    1837). 


ON    THE    GENKTIC    VIEW    OF    NATURE.  303 

of  his  contemporaries  which  Darwin  tlid,  and  for 
which  he  indeed  largely  ])repared  the  way.  Instead 
of  opposing  the  genetic  change  and  development  of 
the  forms  of  natural  objects  to  their  apparent  fixity, 
he  rather  reconciled  botli  views  with  each  other  by 
maintaining^  "that  in  order  to  (jbtain  a  just  insight 
into  the  mutual  affinities  of  animals  it  is  Ijefore  all 
things  necessary  to  distinguish  the  different  tyijes  of 
organisation  from  the  different  grades  of  development." 
He  considered  that "'  "  tlie  idea  of  animal  organisation 
does  not  vary  at  equal  intervals,  but  is  realised  in 
certain  principal  forms  which  again  break  up  into 
variations  of  a  lower  u;rade  "  :  and  he  ^  "  arrived  at  the 
four  principal  divisions  of  the  animal  kingdom  estab- 
lished by  Cuvier."  In  1828,  in  his  work  on  the  'De- 
velopment of  Animals,'  he  discusses  *  "  the  prevalent 
notion  that  the  embryo  of  higher  animals  passes  through 
the  permanent  forms  of  the  lower  animals  " — i.e.,  "  the 
doctrine  of  the  agreement  of  individual  metamorphosis 
with  the  ideal  metamorphosis  of  the  whole  animal 
kingdom."       Von   Eaer  had    himself    added  greatly  ^   to 

^  See    Huxley's    translation,    loc.  lesults :     "  It    was    von    Baer    who 

■c/t.,  p.  178.  first  clearly  discriminated  the  great 

-  Ibid.,  p.  182.  events    in    a    life-hi.^tory  ;    (a)    the 

•'  Ibid.,  p.  183.  primary    jjioeess    of    egg-cleavage, 

*  See   K.    E.   von   Baer's  '  Ueber  and     the     establishment     of     the 

Entwickelungsgeschichte  derThiere  germinal    layers;    {b)    the   gradual 

BeobaclitungundReflexi<jn,'Konigs-  differentiation   of  the   tissues   (hi.s- 

berg,    1828.       The    above    extracts  togenesis)  ;    and    (c)    the    blocking 

are  taken  from  the  fifth  scholion  :  out  of  the   organs  (organogenesis), 

"  Ueber  das  Verluiltnissder  Formen,    ,    and  the  shape-taking  of   the  entire 


die  das  Individuurii  in  den  versdiie- 
denen  Stufen  seiner  Entwickelung 
annimmt."  See  also  Huxley's 
Translation,  loc.  cit.,  pp.  186,  189. 
°  Prof.  J.  A.  Thomson  sum- 
marises as  follows  von    Baers  own 


organism  (morphogenesis)  ('  Science 
of  Life,'  p.  12'SJ.  The  classical 
work  of  von  Baer  is  dedicated  to 
his  friend  Pander,  from  whom  and 
DoUingcr  he  acknowledges  iiaving 
received  the  first  impulses  towards 


304  SCIENTIFIC    THOUGHT. 

the  existing  knowledge  of  the  early  development  of 
the  germs  of  animals  by  discovering  the  ovum  in  the 
body  of  the  mammalia  before  fructification,  and  by  this 
and  other  discoveries  secured  his  claim  to  be  considered 
the  greatest  embryologist  of  his  own  age,  and  perhaps 
of  all  time.  He  goes  on  to  examine  to  what  extent  the 
morphological  differences  which  the  animal  kingdom  ex- 
hibits in  its  various  members  can  be  taken  as  a  guide  to 
the  genetic  differences  in  the  growth  and  development  of 
the  higher  organisms.  He,  in  fact,  tried  to  ascertain 
how  far  the  facts  of  classification  throw  a  light  on  the 
facts  of  development,  how  far  the  changing  embryo  of 
the  higher  animal  gradually  passes  through  the  permanent 
forms  of  the  lower  animals.  He  combats  the  idea  that 
the  classification  or  morphological  arrangement  can  be 
uni-serial — i.e.,  brought  into  one  continuous  line  or  order. 


his   researches.      He  wishes  to  dis-  drew    from    all    this,    especially   in 

tinguish    carefully    between     facts  the  age  of  Schelling's 'Natur-phil- 

and   theory,    and  is   very  cautious  osophie,' the  conclusion  that  Cuvier 

as    to    the    latter,    a    trait    which  was  not  a  philosophical  mind.      To 

runs  through  all  his  writings.      It  me  it  seems  that  we  recognise  in  it 

is  also  very  interesting  to  see  how  Cuvier's  desire  for  clearness.      He 

iu  his  biography    of    Cuvier   (post-  dropped    the    higher    task    because 

humously  published  by  Stieda)  he  he  found  that    it   would    not   lead 

considers  it  a  merit  of  that  great  him    to    clear   views"    ('Lebensge- 

naturalist    not    to    have    indulged  schichte  Cuvier's  von  K.  E.  von  Baer,' 

in    genetic    theories.       "It    is    evi-  ed.   Stieda,   1897,  p.    72).      English 

dent  that  Cuvier  in  his  youth  had  readers,  to  whom  the  genetic  view 

als(}  a  genetic  system  in  view,  such  has     only    become    familiar     since 

as    Oken    afterwards    followed    up,  Darwin  or  perhaps  Lyell,  will  find 

but  that  he  must  soon  have  found  with    astonishment     how    in     the 

out  that  this  task  was  unattainable  writings  of  Baer,  before  Lyell  and 

for    him.       He    abandoned    it,  and  even    before     the     appearance     of 

sought   rather    to   draw   from    the  Cuvier's  final  system,  genetic  ideas 

mauifoldness    of    the    formed    pro-  were  thought  to  be  prevalent,  and 

duct  inferences  regarding  the  con-  were  criticised   elaborately  and  re- 

ditions    of    its    genesis.       Thus    he  ceived    with    the    utmost    caution 

arrived  at  the  teleological  concep-  even   by  the  great  pn^pounders  of 

tions  which  he  developed  on  vari-  the  doctrine  of  development, 
ous  occasions.     German  naturalists 


ON    THE    GENETIC    VIEW    OK    NATUKE.  ."05 

Animals  differ  according  to  the  type  of  organisation  tn 
which  they  belong.     Thus  the  "  embryo  of  the  vertebrate 
animal  is  from  the  very  first  a  vertebrate  animal,  and  at 
no  time  agrees  witli  an  invertebrate  animal."^     Having, 
however,   once    fixetl    the    existence    of    special    organic 
forms,  he  asks  whether  within   the  limits  of  such   form 
no  law  can  be  discovered  to  formulate  the  development  of 
the  individual.      He  believes  there  can,"  and  he  f>roceeds 
to  explain  it  in   terms  which   for  the  most  part  might 
appear  unaltered  in  the  most  modern  work  on  evolution. 
He  states  that  the  more  special  type  is  developed  from 
the    more   general,   "and    that   the   more   different    two 
animal  forms  are,  so  much  the  further  back  must  tlieir 
development  be  traced  to  find  them  similar."     Indeetl  he 
thinks  it  jirobable  that  "  in  tlie  condition  of   tlie  actual 
germ   all   embryos   which   are   developed   from   true  ova 
agree,"  and  he  anticipates  the  cellular  theory  of  Schwann, 
established  by  observation  ten  years  later,  by  suggesting 
that  the  simple  vesicle  is  the  common  fundamental  form 
"  from  which  all  animals  are  developed,  not  only  idcall}' 
but  actually  and   historically."  ^     In  further  examining 
the    process   of    development,    von    Baer   introduces    the 
N'ery  suggestive  term  "*  differentiation.      "  The  higher  and 
lower  development  of  the  animal  coincides  perfectly  with 
that  histological  and  morphological  differentiation  which 
gradually   arises   in    the   course   of    the    development   of 
the   individual." '"'      Development,   in   fact,  is   the   estab- 


'  Loc.  ciL,  p.  220;   tnuisl.,  p.  210. 

2  Ibid.,  p.  221. 

■>  Loc.  ciL,  p.  224  ;  tran.sl.,  p.  213. 
On  this  anticipation  see,   however, 
von    Baer's    later    explanation    in^ 
'  Heden,  &c.,'  vol.  ii.  p.  250. 


■*  The  (Jernian  term  is  "  Son- 
derung,"  which  Huxley  lenders  bv 
the  English  term  "  Ditlerentiation."' 

'^  Loc.  cit.,  p.  229,  230;  tran.sl., 
p.  219. 


VOL.   II.  U 


views  m 

modern 

terms. 


306  SCIENTIFIC    THOUGHT. 

lishing  of  differences,  and  in  reality  "  the  embryo  never 
passes  through  the  form  of  any  other  animal,  but  only 
through  the  condition  of  indifference  between  its  own 
form  and  others."  And  he  sums  up  his  reflections  by 
stating  that  the  "  development  of  an  individual  of  a 
certain  animal  form  is  determined  by  two  conditions : 
first,  by  a  progressive  development  of  the  animal  by 
increasing  histological  and  morphological  differentiation ; 
secondly,  by  the  metamorphosis  of  a  more  general  form 
into  a  more  special  one."  ^ 

In  order   better   to   understand   the   difference  which 

separates  these  various  reflections,  though  breathing  so 

17.        much  the  air  of  the  more  modern  theory  of  evolution. 

Von  Baer's  "^  ' 

from  later  views,  and  to  prepare  for  a  real  comprehension 
of  the  great  step  taken  by  Darwin,  it  will  be  helpful  to 
resort  to  modern  nomenclature.  None  of  the  terms  of 
that  vocabulary  which  was  invented  by  Darwin  and  his 
followers  to  bring  home  to  the  popular  mind  the  main 
points  of  his  revolutionary  doctrine  are  to  be  found  in 
the  earlier  writings  of  von  Baer.  Nevertheless  they 
are  useful  in  defining  the  views  of  the  great  naturalists 
who  preceded  Darwin.  Since  we  have  become  familiar 
with  the  idea  of  the  origin  and  the  transmutation  of  the 
different  animal  and  vegetable  species,  we  are  accustomed 
to  apply  the  genetic  view  not  only  to  the  growth  and 
development  of  individual  living  things  in  nature,  but  to 
everything  else.  When  von  Baer  speaks  of  development, 
when  he  tells  us  that  "  the  history  of  development  is  the 
true  source  of  light  for  the  investigation  of  organised 
bodies,"  he   means  development  in   the   narrower  sense, 

1  Loc.  cit,  p.  231  ,•*  transl.,  p.  220. 


ON    THE    GENETIC    VIEW    OF    NATURE. 


307 


that  which  Ilaeckcl  has  termed  "  Ontogenesis,"  the  genesis 
of  the  individual  being.  From  this  Haeckel  distinguishes 
"  Phylogenesis,"  the  genesis  of  the  phyla,  the  genera,  and 
species.  Xow,  in  discussing  the  relation  of  the  order 
which  prevails  in  the  natural  systems  of  animals  to 
the  stages  of  development  of  individual  embryos,  von 
]^>aer  does  not  seem  to  have  had  before  his  mind  the 
genesis  of  one  species  out  of  another,  a  view  which  he 
in  fact  ridicules  ^  after  a  verv  modern  fasliiou.     He  looked 


'  Lqc.  fit.,  p.  200;  transl.,  p.  187 
(1828) :  "  This  idea— viz.,  that  the 
higher  forms  of  animals  in  the  single 
stages  of  the  devehjpment  of  the  in- 
dividual, from  its  first  origin  to  its 
completed  development,  answer  to 
the  permanent  forms  of  the  animal 
series —  .  .  .  could  not  fail  to  be 
widely  accepted,  since  it  was  sup- 
ported by  a  multitude  of  special 
demonstrations.  Certain  of  its  ad- 
vocates were  so  zealous  that  they 
no  longer  spoke  of  similarity  but  of 
perfect  identity,  and  assumed  that 
the  correspondence  had  Vieen  de- 
monstrated in  all  cases  and  to  the 
minutest  details.  .  .  .  B\'  degrees 
it  became  the  custom  to  look  upon 
the  different  forms  of  animals  as 
developed  out  of  one  another,  and 
then  many  ajjpeared  to  forget  that 
this  metamorphosis  was  after  all 
only  a  mode  of  conceiving  the  facts. 
.  .  .  At  length,  in  sober  serious- 
ness, and  with  all  due  particularity, 
we  were  informed  exactly  how  they 
arose  from  one  another.  Nothing 
could  be  easier.  A  fisli,  swimming 
towards  the  shore,  desires  to  take 
a  walk,  but  finds  his  fins  useless. 
Tiiey  diminish  in  breadth  for  want 
of  use,  and  at  the  same  time  elon- 
gate. Tliis  goes  on  with  children 
and  grandchildren  for  a  few  myriads 
of  years,  and  at  last,  who  can  be 
astonished    that    the    tins    become 


feet  ?  It  is  still  more  natural  that 
the  fish  in  the  meadow,  finding  no 
water,  should  gape  after  air,  there- 
bj',  in  a  like  jteriod  of  time,  develop- 
ing lungs  ;  the  only  difficulty  being 
that  in  the  meanwhile  a  few  genera- 
tions must  manage  to  do  without 
breathing  at  all.  The  long  neck  of 
the  heron  arose  from  a  habit  its 
ancestors  ac(iuired  of  stretching  out 
their  necks  for  the  purpose  of  catch- 
ing fish.  .  .  .  An  immediate  conse- 
quence of  the  assumption  of  this 
idea  as  a  natural  law  was  that  a 
view  which  had  once  been  very 
general,  but  had  subsequently  been 
pretty  gcncially  given  up, — that  of 
the  universal  progression  of  the 
different  forms  of  animals, — gradu- 
ally got  footing  again.  ...  It 
must  be  confessed  that  the  natural 
law  being  assumed,  logical  conse- 
quence required  the  admission  of 
the  view  in  question.  There  was 
then  only  one  road  of  metamor- 
phosis, that  of  further  develop- 
ment, either  attained  in  one  in- 
dividual (inilivi<lual  metamor])li()sis) 
or  througli  the  different  animal 
forms  (the  metamorphosis  of  tlie 
animal  kingdom) ;  and  disea.se  was 
to  be  considered  as  a  retrogressive 
metamor[)hosis,  because  universal 
metamorjihosis,  like  a  raili-oad, 
allows  motion  backwards  oi-  for- 
wards, but  not  to  one  side.'' 


308  SCIENTIFIC    THOUGHT. 

upon  this  order  as  systematic  only,  and  ideal ;  ^  he  thinks 
merely  of  arrangement  or  "  taxonomy."  We  may  say 
that  he  deals  with  phylotaxy  (called  at  that  time  tax- 
onomy), not  with  phylogenesis.  He  conceives  that  onto- 
genesis, the  historical  development  of  the  individual 
thing,  throws  light  on  the  "  mutual  relations  of  organ- 
ised bodies  " ; "  he  wishes  to  make  ontogenesis  helpful 
in  taxonomy  or  in  phylotaxy.  This  term  did  not  then 
exist,  Ijut  it  is  useful  in  order  to  enable  us  to  under- 
stand the  change  which  came  over  natural  science  when 
18.        the  attempts  at  phylotaxy  were  succeeded  by  the  schemes 

Phylotaxy 

aiKi  phyio-  of  phylogenesis,  when  reasons  were  established  for  taking 
in  real  earnest  the  idea  then  fancifully  ^  put  forward  that 
the  natural  order  of  living  beings  represented  the  order 
in  which  they  had  developed  out  of  each  other  in  time. 
These  reasons  did  not  at  that  time  exist. 

A  suggestion  in  this  direction  had  indeed  been  thrown 
out,  and  an  elaborate  theory  had  been  published  about 


scem^sis. 


^  lu  his  later  writings  vou  Baer  that  of   the    "fieri"    (processes  of 

notes  especially   the  difference   be-  change  and  development).      See  the 

tween  a  purely  ideal  and  a  genetic  expositions  in   the  introduction    to 

or  genealogical    relationship.       See  the  article  on   Darwin.      He  there 

'  Reden,  &c.,' vol.  ii.  p.  386  (2nd  ed. )  ,    also  mentions  Meckel  and  Oken  as 

-'Entwickelungsgeschichte'  i    the  two  principal  exponents  of  the 

(1828),   p.   231;  transL,  p.   221.  |    extreme  view  then  put  forward  and 

'  In  a  later    publication   of   von  opposed  by  himself,  that  the  human 

Baer's  (see    '  Reden,   &c.,'  2  Theil,  being   in    its    development    passes 

No.  v.,   "Ueber  Dar\Vin's  Lehre")  through  the  different  higher  forms 

the  aged  author  trie.s  to  define  more  of    the    animal    creation,    and    he 

exactly    the    part   which  his   early  maintains    tiiat    Johannes    Miiller, 

writings     played    in     the    gradual  '    who  had  in  the  first  edition  of  his 

establishment  of  a  genetic  concep-  '    '  Physiology '    accejited    this    view, 

tion   of  natu7-e.     If   Haller  arrived  struck    it   out   in  the  second.      He 

ultimately  at  the  dictum  "  es  gibt  also  refers  to  a  passage  in  a  Memoir 

kein  Wei  den,"  we  may  say  that  von  of   1859,  published  just  before  the 

Baer  as  emphatically  asserted   the  appearance     of      the      '  Origin     of 

opposite,  that  "es  gibt  kein  Sein. "  Species,'  in  which  he  maintains  his 

In  Baer  we  have  progressed  from  the  belief  "  that  formerly  organic  forms 

study  of  the  "  esse '"  (fixed  forms)  to  i    were  less  rigid." 


ON    TJ[K    OENKTIC    VIKW    OF    NATURE. 


309 


ten  years  before  von  Baer  ^  took  up  "  the  subject,  which 
then  presented  itself  as  the  richest  which  an  anatomist 
could  take  up,  the  history  of  development,"  and  twenty 
years  before  his  first  larger  publication  on  this  subject. 
Lamarck's  "' Philosophic  Zoologique  '  appeared  in  1809. 
Though  known  to  von  IJaer,  it  does  not  seem  to  have 
ever  been  much  appreciated  by  liim,  but  it  was  the 
first  serious  attempt  to  deal  with  phylogenesis,  as  von 
Baer's  researches  were  the  first  consistent  studies  in 
ontogenesis. 

It  is  of  interest  to  inquire  into  the  reasons  which 
induced  Lamarck  to  form  opinions  so  entirely  different 
from  those  which,  through  the  influence  and  the  authoritv 
of  Cuvier,  were  then  prevalent  among  naturalists,  and  to 
oppose  the  idea  of  variability  and  of  descent  to  that  of 


19. 

I^iinarck. 


'  Von  Baer  himself  describes — 
usin<;  theae  words— how  in  the  year 
1819  the  play  of  accident  or  good 
fortune  "  threw  this  subject  into 
his  hands."     Stieda,  p.    67. 

*  Since  the  interest  in  the  specu- 
lations of  J.  Ba()tiste  de  Lamarck 
(1744  -  1829)  has  been  revived 
through  tlie  writings  of  Charles 
Darwin,  the  historical  antecedents 
of  his  ideas  have  also  been  studied, 
and  his  as  well  as  Geoff  roy's 
tiieories  have  Ijeen  brought  into 
connection  with  the  views  contained 
in  Butfon's  '  Epoques  de  la  Nature.' 
See  especially  the  interesting  an- 
alysis in  Edmond  Perier's  '  La 
Philosophie  Zoologique  avant  Dar- 
win,' 18S4.  "  Ainsi  surgissont, 
poses  par  Buffon,  ce  partisan  d'abord 
si  resolu  de  la  fixitc  des  esp^ces, 
tous  les  probl^mes  dont  la  solution 
aura  6t6  sans  aucun  doute  la  pensde 
dominante  de  la  seconde  nioitie  de 
ce  siccle.  .  .  .  Et  toutes  ces 
grandes  idees  que  Burton  dexine  en 


quelque  sorte,  vers  lesquelles  il  est 
invinciblement  entrainu  par  la  puis- 
sante  et  rigoureuse  logique  de  son 
genie,  sont  prdcisement  cellcs  qui 
coininencent  aujourd'hui,  appuyees 
sur  un  ensemble  imjiosant  de  re- 
cherehes,  h.  triompher  de  tous  les 
scrupules  "  (p  68).  "  Trois  gi-ands 
honimes  y  vont  poursuivre,  par  des 
voies  diverses,  ru?uvre  de  Buffon  : 
Lamarck,  Geoffroy  St  Hilaire,  et 
Cuvier  "  (p.  72).  For  the  histori- 
cal connections  of  Lamarck's  ideas 
see  also  Huxley's  article  in  the  0th 
ed.  of  the  '  Ency.  Brit.,'  in  which  he 
points  to  a  great  change  which  took 
place  in  Lamarck's  views  between 
1794  and  1809.  In  fact,  the  theories 
which  have  given  to  Lamarck  so 
distinguished  a  position  in  the  his- 
tory of  the  genetic  view  of  nature 
belong  to  the  latter  half  of  his  long 
life.  I  know  of  no  other  recent 
example  <>f  so  late  a  development  of 
(juile  original  ideas  except  ])erhaps 
the  critical  philosophy  of  Kant. 


810  SCIENTIFIC    THOUGHT. 

the  fixity  and  independence  of  species.  And  it  is  equally 
interesting  to  mark  the  causes  which  militated  against 
the  more  general  acceptance  of  his  views,  and  which 
cast  the  '  Philosophie  Zoologique '  into  oblivion.  To  the 
first  question  Lamarck  has  himself,  in  the  introduction  ^ 
to  his  great  work,  furnished  us  with  the  means  of  reply- 
ing. He  there  tells  us  that  when  the  real  study  of 
natural  history  began,  and  each  of  the  different  king- 
doms of  nature  received  the  due  attention  of  naturalists, 
animals  with  a  backbone — viz.,  mammalia,  birds,  reptiles, 
and  fishes — received  the  greater  attention.^  Being  in 
general  larger,  with  parts  more  developed  and  more 
easily  determinable,  they,  as  it  were,  obtruded  them- 
selves on  the  attention  of  man,  for  whom  they  are  both 
more  useful  and  more  formidable.  The  other  large  group 
of  animals,  classed  together  first  by  Lamarck  himself  as 
"  Invertebrates,"  are  mostly  very  small,  with  organs  and 
faculties  less  developed,  and  thus  much  further  removed 
from  man  and  his  interests.  Of  this  by  far  more  numer- 
ous class  of  beings,  those  called  insects  had  alone  at  the 
end  of  the  former  century  received  considerable  atten- 
tion, whereas  all  the  others,  classed  together  by  Linnaeus 
as  "  worms,"  formed  a  kind   of  chaos,  an  unknown   land. 

^  Lauiarck"s  later   genetic  views  taining    the    "  pieces    justificatives 

are  contained  in  the   '  Philosophie  de    ce    que    j'ai    publie    dans    ma 

Zoologique,'     which     appeared     in  Philosophie  Zoologique."   This  great 

1809,   and  was  republished   with  a  work   was  republished  in    1837   by 

biographical      notice     by      Charles  Deshayes  and  Milne  -  Edwards.     I 

Martin  in  1873.      I  quote  from  this  quote   from  this    edition,  which  is 

edition.     His  principal  ideas  are  also  in  three  volumes, 
summarised  in  the  introduction  to  -  See    'Philosophie    Zoologi(iue,' 

his     great      work,     '  Histoire     des  Discours  pr^liminaire,  vol.  i.  p.  29  ; 

Animaux   sans    Vertebres'     (1816),  also     '  Animaux     sans    VertSbres," 

which  in  fact  he  represents  as  cou-  Introduction,  vol.   i.  p.   11. 


ox     rHK    flKNKTIC    VIKW    DF    XATCRK. 


311 


It  was  to  some  extent  accidental '  that  Lamarck,  after 
having  devoted  himself  for  many  years  to  the  exclusive 
study  of  plants,  shouUl  on  the  occasion  of  the  foundation 
of  the  different  chairs  for  the  natural  sciences  at  the 
"Museum"  suggested  by  Lakaual,  have  allotted  to  him 
the  cultivation  of  this  department,  unknown  to  himself  as 
it  was  to  others,  and  where  even  the  systematising  genius 
of  Linnseus  had  abstained  from  trying  to  make  order. 
Thus  it  came  about  that  Lamarck  brought  to  the  study 
of  the  animal  world  a  mind  trained  in  a  very  different 
region   of  science,"   and   that  he   approached   this  study 


^  See  tlie  "  Introduction  Bio- 
graphique,"  Viy  Martins,  '  Philos. 
Zool. ,'  I.  xiii.  "La  Convention 
gouvernait  la  France,  Carnot  or- 
ganisait  la  victoire.  Lakanal  entre- 
prit  (I'organiser  les  sciences  Tiatur- 
elles  :  sur  sa  ])roposition,  le  ^luseum 
d'histoire  naturelle  fut  cri6.  On 
avait  pu  nommer  des  professeurs 
ii  toutes  les  chaires,  sauf  pour  la 
zoologie  ;  mais  dans  ces  temps 
d'enthousiasme  la  France  trouvait 
des  homnies  de  guerre  et  des 
hornmes  de  science, partout  oil  elle 
en  avait  besoin.  Etienne  Geoffroj' 
Saint-Hilaire  dtait  ag^  de  vingt-et- 
un  ans,  il  s'occupait  de  mineralogie 
sous  la  direction  d'Haliy.  Dauben- 
ton  lui  dit :  '  Je  prends  sur  moi  la 
responsabilitd  de  votre  inexpe- 
rience ;  j'ai  sur  vous  l'aut(>rit<^  d'un 
p6re ;  osez  entreprendre  d'en- 
seigner  la  zoologie,  et  un  jour  on 
l)uisse  dire  que  vous  en  avez  fait 
une  science  francaise.'  Geoffroy 
accepte,  et  se  charge  des  aniniaux 
supcrieurs.  Lakanal  avait  coiiipris 
qu'un  seul  professeur  ne  pouvait 
suffire  II  la  tilche  de  ranger  dans 
les  collections  le  r6gne  animal  tout 
entier.     Oeoffrov  devant  classer  les 


vertebres  seulement,  restaient  les 
invertdbrcs,  h,  savoir  les  insectes,  les 
moUusques,  les  vers,  les  zoophytes, 
c'est  -  <i  -  dire  le  chaos,  I'incounu. 
Lamarck,  dit  M.  Michelet,  accepta 
I'inconnu  ...  11  avait  tout  ^  ap- 
prendre,  tout  ii  crcer  dan.^  ce  mondo 
inexplorc,  ou  Linno  avait  pour  ainsi 
dire  renoncc  h,  introduire  I'ordre 
mdthodique  qu'il  avait  su  si  bien 
ctablir  parmi  les  animaux  supcr- 
ieurs."  Lamarck  was  accordingly 
about  fifty  when  he  undertook  this 
novel  study,  which,  as  Huxley 
pointed  out,  was  to  work  such  a 
change  in  his  views  {loc.  cit.) 

^  He  had  written  in  six  months 
his  '  Flore  franeaise,'  which  was 
prefaced  by  his  '  Cli5  dichotomique.' 
This  was  in  1778.  "Rousseau 
avait  mis  la  botanique  h,  la 
mode  ;  les  gens  du  monde,  les 
dames  s'en  occupaient.  Buifon 
fit  imprimer  les  trois  volumes  de 
la  'Flore  fran(,'aise '  h,  I'iiniiriiiierie 
royale  "  {loc.  c.lt.  p.  11).  Lamarck 
had  also  qualified  as  a  naturalist 
by  extensive  travels  in  many  Euro- 
pean countries  as  a  companion  to 
Buffon's  son. 


312 


SCIENTIFIC    THOUGHT. 


20. 
The  temi 
'•Biology.' 


from  that  side  which  at  the  time  was  the  least  known, 
and  probably  the  least  promising :  he  apjjroached  it, 
as  it  were,  from  below.  But  this  had  the  consequence 
of  giving  to  his  original  mind  in  two  ways  a  special 
direction.  First  of  all,  it  enabled  him  to  look  at  natural 
objects  from  a  more  general  point  of  view,  not  as  a 
zoologist  or  as  a  botanist,  but  as  a  naturalist  and  a 
biologist — i.e.,  from  the  more  general  view  of  the  pheno- 
mena of  Life.^  Indeed  he  himself  seems  to  have  been 
the  first,  if  not  to  use,  at  least  to  introduce  in  his 
published  writings,  the  term  "  biology."  ^     And  secondly, 


'   '  Philos.    Zool..'   Discours    pre- 
lim., p.    31:      "Le  vrai  moyeu  de 
])arvenir  a  bien  connaitre  un  objet, 
uieine  daus  se.?  plus  petits  details, 
c'est  de  comtnencer  par  I'envisager 
dans    son    entier  ;     par    examiner 
d'abord,     soit    sa    masse,    soit    son 
etendue,  soit  I'ensemble  des  parties 
qui  le  composent  ;    par  rechercher 
quelle  est  sa  nature  et  son  origine, 
quelles  sont  ses  rapports   aveo   les 
autres  objets  connus  ;  en  un  mot, 
par    le    considerer    sous    tous    les 
points    de    vue    qui    peuvent    nous 
eclairer  sur  toutes  les   g^neralit^s 
i|ui  le  concernent."      P.   32  :    "  La 
n^cessit^  reconnue  de  bien  observer 
les  objets  particuliers  a  fait  naitre 
riiabitude  de  se   boruer  a  la  con- 
sideration de  ces  objets  et  de  leurs 
plus    petits     details,    de     maniere 
qu'ils  sont   devenus,    pour  la  j)lu- 
part  des  naturalistes,  le  sujet  prin- 
cipal   de    I'etude.      Ce    ne    serait 
cependant  pas  une  cause  reelle  de 
retard  pour  les  sciences  naturelles, 
si  Ton  s'obstinait  k  ne  voir  dans  les 
objets    observes    que    leur    forme, 
leur    dimension,    leur    parties    bk- 
ternes,    memes    les    plus     petites, 
leur  couleur,   &c.,    et   si  ceux   qui 
se    livreut    k    une    pareille    etude 
dedaignaient  de  s'elever  h,  des  con- 
siderations sup^rieures,  comme  de 


chercher  quelle  est  la  nature  des 
objets  dout  ils  s'occupent  quelles 
sont  les  causes  des  modifications  ou 
des  variations  auxquelles  ces  objets 
sont  tous  assujettis,  quels  sont  les 
rapports  de  ces  memes  objets  entre 
eux,  et  avec  tous  les  autres  que 
Ton  connait,"  &c. 

'•^  Lamarck  in  his  '  Hydrog^o- 
logie,'  in  an  appendix  (p.  188) 
which  seems  to  be  a  rehear.sal  of 
his  opening  lecture  of  1801,  an- 
nounces a  work,  'Biologic,'  as  a 
sequel,  being  the  third  and  last 
part  of  the  Terrestrial  Physics. 
This  work  was  not  published,  but 
was  probably  comprised  in  his 
'  Philosophic  Zoologique.'  See  Prof. 
A.  S.  Packard's  excellent  work  on 
Lamarck,  '  The  Founder  of  Evolu- 
tion, his  Life  and  Work,'  London 
and  New  York,  1901.  As  La- 
marck's writings  are  very  scarce 
and  his  teaching  only  imperfectly 
understood,  frequently  misrepre- 
sented, even  bj'  competent  author- 
ities, and  in  popular  opinion  sur- 
rounded by  mystery  and  sometimes 
treated  with  ridicule,  the  work  of 
Prof.  Packard  is  most  welcome. 
It  contains  copious  extracts  —  un- 
fortunately all  translated  —  from 
the  earlier  biological  writings  and 
lectures,    which    are    otherwise    al- 


ON    THE    GENETIU    VIEW    OF    NATURE. 


8i::5 


it  intnjducetl  hiui  to  the  study  of  ;iiiiiiial  life  from  that 
side  where  organisation,  the  phenomena  and  the  organs 
of  life  were  the  simplest,  rudimentary  as  it  were,  an<I 
unformed.  Here  the  great  differences  of  form,  the 
morphological  differences  which  the  observation  of  the 
higher  and  more  developed  creatures  force  upon  our 
attention,  disappear ;  not  the  marked  differences,  but 
the  numerous  relations,  tlie  endless  varieties  and  re- 
semblances, seem  to  command  our  consideration.  These 
seem  to  be  much  more  likely  to  "  make  us  understand 
the  beginnings  of  all  organisation  as  well  as  the  cause 
of  its  complexity  and  of  its  development."  ^  Now  in 
descending  in  the  scale  of  the  living  objects  of  nature, 
Lamarck  was  struck  by  the  fact  that  many  of  the 
phenomena  of  life  which  in  the  higher  animals  seemed 
to  originate  within  were  in  tlie  lower  creatures  produced 


most  inaccessible.  According  to 
Huxley  (Lecture  "On  the  Studv 
of  Biology,"  1876,  and  "  Evolution 
iu  Biology,"  '  Kncy.  Brit.,'  9th  ed.), 
there  were  .simultaneously  three 
independent  attemjjts  to  treat  the 
phenomena  ot'  organic  life  as  a 
whole  and  in  connection,  emanat- 
ing from  Bichat  and  Lamarck  in 
France,  and  from  G.  R.  Treviranus 
in  Germany.  Tiie  great  but  un- 
finished work  of  the  latter,  witli 
the  title 
phie  der 
begun  in  1796,  when  the  author 
was  only  twenty,  but  the  finst 
volume  was  not  published  till  1802, 
one  year  after  Lamarck's  '  Hydro- 
gdologie.'  Haeckel  in  his  '  Natiir- 
liche  Schiipf ungs  geschichte '  gives 
some  account  of  Treviranus'  ideas 
(Band  L  Vorlesung  4).  Although 
so  much  has  been  written  aliout 
"Biology,"  the  deliiiition  of  the 
science   is   still    uncertain.      Prof. 


Biologic    oder    Philo.so- 
lebenden    Natur,'    was 


Goebel  says:  "The  word  Biology 
is  one  of  those  conceptions  of 
modei'n  times  which  have  not  yet 
arrived  at  a  generally  accepted 
limitation.  Some  understand  by 
it  the  whole  science  of  living 
things,  others  only  the  doctrine 
of  the  phenomena  of  life  iu  con- 
trast to  the  purely  de.scri])tive 
branches "'  ( '  Pflanzeubiologische 
Schilderuiigen,'  Marburg,  1889,  vol. 
i.  p.  1).  A\'ith  Lamarck  biology  was 
only  one  division  of  a  general 
science  of  nature,  for  he  says 
(' Hydrogdologie,'  p.  8):  "Toutes 
ces  considerations  partagent  natur- 
ellement  la  physique  terrestre  en 
trois  parties  essentielles,  dont  la 
premiere  doit  cotnpiendrc  la  thcorie 
de  ratmosphere,  la  Meteorolugie, 
la  seconde  celle  de  la  croute  externe 
du  globe,  I'Hydrogeologie  ;  la  troi- 
sieme  enfin,  celle  des  corps  vivants, 
la  Biologic." 

'   Philos.  Zool. ,  vol.  i.  I).  30. 


314  SCIENTIFIC    THOUGHT. 

or  excited  from  outside,  and  he  was  thus  led  to  the 
conception  that  nature  herself,  through  the  environment, 
did  a  great  deal  for  the  lower  creatures  which  in  the 
gradual  development  of  the  higher  ones  she  knew  how 
to  make  them  do  for  themselves.^  In  fact,  the  idea  is 
worked  out  in  the  '  Philosophic  Zoologique,'  that  if  we 
commence  the  study  of  living  creatures  from  below,  and 
from  the  side  of  vegetable  life,  we  are  inevitably  led 
to  the  conviction  that  the  surrounding  conditions  and 
21.        influences,   the   environment,   are   gradually   and   slowly 

"Environ-  .  i      i      i  • 

ment."  modifying  the  elementary  organisms,  and  through  habit 
and  inheritance  '^  developing  the  higher  ones,  endowing 
them  with  more  specialised  organs  and  more  complex 
powers  and  activities. 

Lamarck  is  aware  that  these  ideas  sound  strange  and 
novel,  and  he  is  quite  prepared  to  admit  in  the  reception 
of  them  by  his  readers  the  same  inevitable  force  of  habit 
which,  as  it  only  permits  gradual  modification  of  the  forms 

^  Philos.    Zool.,    '  Avertissement,'       un    grand    nombre   d'animaux    de- 

p.  13 :  "  Ayant  remarque  que  les  |  vaient  se  trouver  dans  le  meme 
mouvements   des  animaux  ne  sont       cas  ;  eb  comme  j'avais  eu  bien  des 

jamais    communiques,    mais    qu'ils  '    occasions  de  remarquer  que,   pour 

sont  toujours  excites,  je  reconnus  '   arriver   au    meme    but,    la   nature 
que  la  nature,  obligee  d'abord  d'em-       variait   ses    moyens,    lorsque    cela 
prunter  des    milieux   environnants       ^tait  n^cessaire,    je   n'eus   plus  de 
la  jDuissance  excitatrice  des  tnouve-       doute  a  cet  egard." 
ments    vitaux    et    des    actions    des  "Ibid.,   p.  13:  "  Je  ])us  saisir  le 

animaux  imparfaits,  sut,  en  com-  fil  qui  lie  entre  elles  les  causes 
posant  de  plus  en   plus  I'organisa-       nombreuses    des    phenomenes    que 

tion  animale,  transporter  cette  ;  nous  offre  I'orgauisation  animale 
puissance  dans  Tinterieur  meme  de  dans  ses  developpements  et  sa 
ces  etres  et  qu'^  la  fin  elle  parvint  diversite,  et  bientot  j'apergus  I'im- 
h,  mettre  cette  meme  puissance  h,  la       portance  de  ce  moyen  de  la  nature, 

disposition  de  I'individu."  P.  12  :  I  qui  consiste  h,  conserver  dans  les 
"Ayant  consid^r^  que  sans  les  nouveaux  individus  reproduits  tout 
excitations    de    I'int^rieur,    la    vie       ce  que  les  suites  de   la  vie  et  des 

n'existerait  point  et  ne  saurait  se  |    circonstances    influentes    avait   fait 

maintenir     en     activity    dans     les  \    acqu^rir  dans  I'organisation  de  ceux 

vdg(?taux,  je  reconnus  bientot  qu'  '    qui  leur  out  transmis  I'existence." 


ON    THK    OENKTIC    VIEW    OF    NATURE.  315 

of  nature,  so  also  opposes  a  great  resistance  to  any  sudden 
change  of  opinion.  "  I5ut  it  is  better,"  he  says,  "  that  a 
truth  once  perceived  sliould  struggle  a  long  time  to  obtain 
merited  attention  than  Lliut  everything  that  the  ardent 
imagination  of  man  produces  should  be  easily  accepted."  ^ 
Whereby  it  may  appear  to  us  worthy  of  note  that 
Lamarck  did  not  stop  to  reflect  on  the  existence  of  those 
sudden  changes  by  which  such  powers  as  the  "  ardent 
imagination  of  man "  are  continually  breaking  through 
the  slow  action  of  habit.  The  doctrine  of  the  mutability 
and  variability  of  species,  of  the  influence  of  the  environ- 
ment on  the  habits,  and  through  them  and  inheritance 
on  the  forms  of  living  creatures,  was  thus  opposed  to 
the  prevalent  doctrine  of  the  fixity  of  species  and  the 
permanence  and  recurrence  of  types.  Through  these 
generalisations,  and  through  the  larger  ^^ew  which 
Lamarck  took  of  the  phenomena  of  nature  and  of  life, 
he  stepped  outside  of  that  school  of  natural  studies 
which  was  then  dominant  in  his  country,  and  approached 
the  teaching;s  of  the  German  philosophers  of  nature,  such        22. 

'='  r  1  Tlie"Natur- 

as  Schelliny;,  Oken,  and  Steffens,  with  whom  Goethe   is  pj'i'oso- 

o'  '  '  pine. 

frequently  associated,  who,  rather  than  limit  themselves 
to  the  patient  study  of  detail,  indulged  in  fanciful 
theories  on  the  origin  of  life,  the  genesis  and  metamor- 
phosis of  forms,  and  the  ideal  significance  of  natural 
phenomena  and  processes.  A  wide  gap  separated  the 
speculations  of  the  author  of  the  '  Flore  fran^aise,'  the 
'Histoire  des  Animaux  sans  Vertfebres,'  and  the  'Memoires 
sur  les  Coquilles  fossiles  des  environs  de  Paris  '  from  those 
of   the  German   school,  yet  it   cannot  be  dcni(nl   tliat   in 

1  Philos.  Zoo).,  p.  15. 


316  SCIENTIFIC    THOUGHT. 

many  passages  of  the  '  Hydrogeologie,'  where  he  specu- 
lated on  matters  of  chemistry,  geology,  and  meteorology 
without  the  necessary  foundation  of  facts,  such  as  he 
possessed  in  botany  and  zoology,  he  laid  himself  open 
to  the  criticism  and  ridicule  ^  of  his  more  cautious 
opponents.  Thus  it  happened  that  the  most  original  con- 
tributions to  science  were  forgotten  or  disregarded  for 
more  than  half  a  century,  after  which  time  Lamarckism 
became  a  familiar  term  in  speculative  science,  denoting 
one  of  the  great  ideas  with  which  the  genetic  view  of 
nature  operates — viz.,  the  influence  of  environment, 
adaptation,  acquired  habits,  in  the  development  of  living 
organisms. 
23.  In    the   history   of   the   genetic   view   of   nature,    the 

Lamarck 

^nd  von  positiou  of  Lamarck  may  be  regarded  as,  in  a  certain 
sense,  complementary  to  that  of  von  Baer.  Both  brought 
the  study  of  living  forms  back  to  that  of  their  origins 
— Lamarck  to  the  study  of  the  lowest  forms  of  animal 
creation,  the  great  variety  and  abundance  of  which  he 
was  the  first  to  attempt  to  put  into  some  order ;  von 
Baer  to  the  study  of  the  embryonic  beginnings  of  the 
higher  organisms,  on  which  important  subject  he  was 
one  of  the  first   to   throw   some  light.      Though   widely 


^  See,  inter  alia,  what  Cuvier 
wrote  in  his  '  Eloge  de  Lamarck,' 
which    was    read    posthumously   in 


meme  paix  que  la  theorie  chim- 
ique  "  ;  and  farther  on  he  touches 
on  one  of  the  weakest  points  of  all 


the    Academy    by    Silvestre,    ■26th  ■,  genetic  speculations  (p.  sxii) :   "  Le 

November  1832  ('  Mem.  de  I'Acad.  i  temps   sans  borne  qui   joue   un   si 

des    Sciences,'    vol.    xiii.     p.     xx),  j  grand    role   dans    la    religion    des 

with   omissions    to    tone    down    its  I  mages,    n'en    joue    pas    un    moins 

severity  :   ' '  Quelque  int^ret  que  ces  |  grand   dans    toute   cette    physique 

ouvrages  excitassent  par  leurs  par-  \  de   M.  de   Lamarck,   et   c'etait  sur 

ties    po.sitives,    personne    ne    crut  lui  qu'il  se  reposait  pour  calmer  ses 

leur      partie     systematique     assez  '  propies   doutes    et    pour    repondre 

<langereuse     pour     meriter    d'etre  ]  a    toutes    les     objections     de     ses 

attaquee ;    on    la    laissa    dans    la  '  lecteurs." 


ON    TIIK    GENKTIC    VIKW    OF    NATURE. 


317 


different  in  their  mental  attitude,  the  two  men  agreed 
in  lookinii  for  tlie  advancement  of  natural  science  in 
an  understamling  ol'  the  simpler,  unspecified,  and  un- 
dittl'rentiateil  forms  or  stages  of  existence  out  of  which 
they  conceived  the  more  complex  to  have  grown  or  de- 
veloped by  a  process  of  specialisation  or  differentiation. 
Many  other  naturalists  and  philosophers  contributed, 
partly  independently,  partly  through  the  influence  of 
Lamarck's  systematic  and  von  Baer's  endiryological 
labours,  to  elaborate  the  same  ^•iew  and  strengthen  the 
same  tendency  of  thought  and  research.  Nor  were 
there  wanting  suggestions  as  to  the  ultimate  philo- 
sophical drift  of  the  line  of  reasoning.  It  is  doubtful 
whether  these  speculations,  like  those  of  Oken  in  his 
'  Physio-philosophy,'  did  not  retard  rather  than  promote 
the  acceptance  of  the  genetic  view  by  scientific  thinkers :  ^ 


'  On  tlie  position  of  Uoetlie  and 
Oken  in  the  history  of  the  genetic 
view,  see  Carus,  '  Geschichte  der 
Zoologie,'  p.  723  ;  von  Baer, 
'  Reden  und  wissenscliaftliche  Ab- 
handluiigen,'  Bd.  II.  p.  '2.')8,  «kc. 
Both  consider  Lamarck  as  the  real 
originator  of  a  scientific  theory  of 
Descent.  Von  Baer  gives  an  amus- 
ing account  of  the  extent  to  which, 
as  early  as  18-29,  actual  genealogical 
trees  were  given  in  Jacob  Kaup's 
'  Skizziitc  Kntwickelungsgeschichte 
und  naturliches  System  der  Eur- 
opaeischen  Thierwelt.'  Von  Baer 
sums  up  his  historical  account  in 
the  following  words  (p.  26-1):  "In 
general  1  believe  that  at  that  time, 
when  the  succession  of  different 
animals  and  plants  in  the  history  of 
the  earth — and  generally  from  im- 
perfect to  more  perfect  organisms 
— occupied  the  thoughts  of  natural- 
ists, and  when,  at  the  same  time, 
tlie  study  of  development  of  single 


I  organisms  had  taken  a  new  start, 
I  the  notion  of  their  'I'ransformation 
I  was  pretty  generally  accepted.'" 
The  view  expiessed  here  by  von 
Baer  would  probably  have  to 
be  limited  to  German  naturalists  at 
that  date.  It  must,  however,  bo  ad- 
mitted that  the  fairest  exposition 
and  criticism  of  the  arguments  of 
Lamarck  at  that  earlj*  date  is  prob- 
abh'  to  be  found  in  Lyell's  '  Prin- 
ciples of  Geology'  (vol.  ii.  Bk.  III. 
chap.  i.  to  iv. )  He  there  also  con- 
siders the  arguments  derived  from 
embryology  as  contained  in  the  re- 
searches of  Thiedemann,  confirmed 
by  Serres  ('Anatomic  Compareo  du 
Cerveau,'  1824),  and  comes  linally 
to  the  result  that— 1.  "There  is  a 
capacity  in  all  species  to  accommo- 
date them-selves."  2.  "  Tliat  the 
mutations  thus  superinduced  are 
governed  by  constant  laws."  3. 
That  "  some  acquired  jieculiarities 
of  form,  structure,  and  instinct  are 


318 


SCIENTIFIC    THOUGHT. 


24. 
Tlie 
'  Vestiges. ' 


they  belong,  therefore,  more  to  the  history  of  philo- 
sophical than  to  that  of  scientific  thought.  There  is, 
however,  one  instance  of  which  it  is  necessary  to  take 
a  passing  notice. 

In  the  year  1844  a  book  appeared  which  in  nine 
years,  up  to  1853,  ran  through  nine  large  editions.  It 
was    anonymous,^  and    bore 


trau.smissible  to  the  offspring."  i. 
That  "  indefinite  divergence  "  from 
the  original  type  is  "prevented." 
5.  That  "  tiie  intermixture  of  dis- 
tinct species  is  guarded  against  by 
the  aversion  of  the  individuals  com- 
posing them  to  sexual  union."  6. 
That  "it  appears  that  species  have 
a  real  existence  in  nature,  and  that 
each  was  endowed,  at  the  time  of 
its  creation,  with  the  attributes 
and  organisation  by  which  it  is 
now  distinguished."  Tlie  reviewers 
of  Lyell's  work — such  as  Whewell 
{'Quarterly,'  vol.  xlvii.  p.  113) — 
treat  Lamarck  with  much  less 
gravity  than  Lyell  himself,  who 
evidently  had  studied  the  '  Philoso- 
phic Zoologique  '  carefully  and  with 
much  interest ;  which,  I  am  afraid, 
was  not  the  case  with  many  others 
who  then  and  long  after  only  quoted 
certain  extreme  passages  and  ex- 
amples which  had  lieen  spread  in 
general  literature  in  a  garbled 
fashion.  Contrast  in  this  respect 
what  Lyell  wrote  to  G.  Mantell  in 
1827  ('  Life  of  Lyell,'  vol.  i.  p.  168), 
wliere  he  admits  having  "  devoured 
Lamarck  with  pleasure,"  and  though 
disagreeing  with  him,  admits  that 
it  is  impossible  to  say  "  what 
changes  species  may  really  under- 
go," with  the  remarks  of  Charles 
Darwin — otherwise  so  careful  and 
moderate — when  lie  talks  of  "  La- 
marck nonsense  "  ("  Darwin's  Life 
and  Letters,'  p.  23)  and  his  "  verit- 
able rubbish"  (p.  29),  and  attrib- 
utes to  him  statements  which  such 
a  careful  student  of  his  writings  as 


tlie   title  '  Vestiges   of   the 

Prof.  Packard  has  been  unable  to 
trace  (see  his  work  on  '  Lamarck,' 
1901,  p.  74).  One  would  be  in- 
clined to  agree  with  Darwin  that 
such  absurdities  have  done  the  sub- 
ject more  harm  than  gt)od,  but  to 
attribute  them  rather  to  garbled 
paraphrases  and  quotations  by  La- 
marck'scritics  (see  Darwin  to  Hooker, 
18.53, 'Life,' vol.  ii.  p.  39)  than  to 
Lamarck  himself.  More  than  thirty 
years  after  the  publication  of  the 
'  Principles,'  when,  in  consequence 
of  the  appearance  of  the  '  Origin  of 
Species,'  the  subject  of  Transmuta- 
tion was  much  discussed,  Lj'ell 
wrote  to  Darwin  that  he  had  re- 
read Lamarck,  and  admitted  that, 
"  remembering  when  his  book  was 
written,  he  felt  he  had  done  him 
[Lamarck]  injustice"  ('Life,  &c. , 
of  Sir  Charles  Lyell,'  1881,  vol.  ii. 
p.  365).  In  the  same  letter  Lyell 
states  that  forty  years  ago  (1823) 
Provost,  a  pupil  of  Cuvier's,  told 
him  his  conviction  "  that  Cuvier 
thought  species  not  real,  but  that 
science  could  not  advance  without 
assuming  that  thej^  were  so." 

^  Tlie  anonymity  of  the  work  was 
long  maintained,  and  though,  after 
various  guesses  as  to  the  author- 
ship— attributing  it,  e.g.,  to  Lyell  or 
Darwin— had  been  made,  it  was  gen- 
erally believed  that  Robert  Cham- 
bers (1802-1871)  was  the  author, 
this  was  not  jjublicly  admitted  till 
Alex.  Ireland — the  last  survivor  of 
the  few  friends  to  whom  the  secret 
was  committed  —  published  (1884) 
the    twelfth    edition    of   the   book, 


ON   'I'lIK  (jenktk;  vikw   of  natuke. 


.S 1 9 


Natural  History  of  Creation.'  This  book  cuuLaiiied  a  very 
clear  and  popularly  intelligible  statement  of  the  genetic 
or  development  hypothesis  as  applied  to  cosmic,  geolog- 
ical, and  organic  phenomena.  The  importance  of  the 
book  did  not  lie  in  its  own  original  L(intri])utions,  but  in 
the  great  controversy  Nvhich  it  occasioned.  In  this  con- 
troversy  most    of    the   arguments   for   and    against    the 


with  an  introduction,  in  wliieli  he 
"  tohl  for  the  first  time  "  the  "story 
of  the  authorship."  It  is  of  interest, 
after  the  hipse  of  liah"  a  century,  to 
read  the  various — mostly  liostile — 
criticisms  of  the  book  in  the  reviews 
and  magazines  of  the  day.  The 
attacks  came  from  two  distinct 
sides  :  from  scientific  authorities, 
who  —  each  in  his  own  specific 
branch — -challenged  the  correctness 
of  single  facts,  mostly  without  in- 
quiring whether,  in  spite  of  many 
misstatements,  sufficient  evidence 
was  not  after  all  adduced  to  prove 
the  main  thesis  ;  and,  secondly, 
from  both  scientific  and  jiopular 
writers,  who  used  the  well-known 
arguments,  that  the  teaching  of  the 
book  was  unorthodox,  both  in  a 
religious  and  scientific  sense.  In 
fact,  they  disjilayed  in  a  great 
degree  scientific  and  religious  dog- 
matism and  intolerance,  and  in  some 
cases  considerable  temper.  To  this 
larger  section  of  the  critical  attacks 
belonged  the  reviews  in  all  the 
leading  periodicals  of  the  day, 
headed  by  the  '  Edinburgh  Re- 
view '  (Adam  Sedgwick),  the  '  North 
British  '  (Sir  David  Brewster),  the 
'Eclectic,'  the  'North  American' 
(Boweu  and  Asa  Gray),  the  '  Brit- 
ish Quarterly.'  Tolerance  and  a[)- 
pieciation  were,  however,  shown 
by  some  of  those  more  recent  re- 
views which  were  professedly  the 
organs  of  freedom,  enlightenment, 
and  progress,  notably  the  '  Pros- 
pective'  (E.  W.  Newman)  and  the 
'  Westminster '   in   two   articles,   in 


the  first  of  which  the  genetic  view 
of  the  '  Vestiges '  is  suggestively 
contrasted  with  the  purely  descrip- 
tive of  the  '  Kosmos.'  Looking  at 
the  whole  controveisy,  the  '  West- 
minster Review  '  (.\liii.  130)  seems, 
in  the  light  of  history,  justified  iu 
maintaining  that,  after  "  having 
attentively  considered  the  objec- 
tions which  have  been  uiged  in 
numei'ous  able  criticisms  to  the 
theory  and  the  arguments  of  the 
author,"  after  noting  that  "  learned 
men  have  discovered  that  he  is  less 
familiar  than  they  with  the  pedantry 
of  science,"  tliat  "  they  have 
triumphed  in  the  detection  of  slips 
of  the  pen,  mistakes  in  technicali- 
ties, and  some  inaccuracies  of  fact," 
the  conclusion  is  nevertheless  justi- 
fied that  "  these  detract  but  little 
from  the  merit  of  a  work  which 
may  be  fairly  chaiacterised  as  the 
most  skilful  generalisation  ihat  has 
yet  (1848)  apj)eared  of  the  results  of 
geological,  astronomical,  aud  physi- 
ological researches  made  to  bear 
ujjon  the  history  of  the  first  and 
most  momentous  of  all  problems — 
the  order  and  plan  of  creation." 
It  is  known  that  some  scientific 
men  of  first  rank,  such  as  Baden 
Bowell  of  O.xford,  and  the  lihysi- 
ologist  W.  B.  Carpenter  (who, 
according  to  Huxlej',  was  the  only 
authoiity  in  this  ('nuiitry  ac(|uainted 
with  the  'Entwickelunnsgeschichte' 
of  von  Baer),  distinctly  supported 
the  doctrine  of  the  '  Vestiges  ' ;  and 
Darwin  himself,  who  had  studied 
the    '  Vestiges '    with   evident    cai-e 


influence. 


320  ~  SCIENTIFIC    THOUGHT. 

genetic  aspect,  which  have  since  become  familiar,  were 
very  ably  stated  by  scientific  as  well  as  by  popular 
writers.  Earlier  anticipations  of  the  genetic  view  were 
recalled,  the  historical  s^ketch  given  in  Lyell's  '  Prin- 
ciples '  was  supplemented  by  reference  to  many  great  and 
many  forgotten  authorities,  who  in  more  or  less  distinct 
terms  had  given  expression  to  their  belief  in  a  gradual 
development  of  the  existing  forms  and  phenomena  of 
nature  out  of  simpler  beginnings,  which  they  described 
with  more  or  less  precision.  It  cannot  be  denied  that 
the  enormous  literature  which  accumulated  during  the 
ten  years  following  the  publication  of  this  book  unsettled 
Po  uiar  ^^^®  popular  mind  in  this  country,  and  prepared  it  for  a 
really  able,  dispassionate,  and  exhaustive  exposition  of 
the  whole  subject,  and  especially  of  the  crucial  problem 
to  which  it  was  narrowed  down,  the  question  regard- 
ing the  fixity  or  variability,  the  historical  origin  and 
development  or  the  sudden  creation  and  persistence,  of 
animal  and  vegetable  species.  The  genesis  of  the  cosmos 
as  suggested  by  Laplace,  the  geological  history  of  our 
earth  as  worked  out  by  Lyell,  the  fact  of  organic  growth 
and  development  as  given  by  embryology,  seemed  clear 

(see  '  Life  of  Darwin,"  V(j1.  i.  p.  833),  :  in  tlius  preparing  the  ground  for 
gave  probably  the  fairest  verdict  on  j  the  reception  of  analogous  views  " 
tiie  book  in  the   historical    preface    i    ('Origin  of  Species,'  6th  ed.,  1872 


to  the  later  editions  of  his  own 
great  work,  where  he  saj's  :  "  The 
■work,  from  its  powerful  and  bril- 
liant style,  though  displaying  in  the 
earlier  editions  little  accurate  know- 
ledge and  a  great  want  of  scientific 
caution,  immediately  had  a  very 
wide  circulation.  In  my  opinion,  it 
has  done  excellent  service  in  this 
country  in  calling  attention  to  the 
subject,  in  removing  i^rejudice,  and 


p.  xvii).  In  a  history  of  European 
thought  it  is  well  to  mention  that 
the  '  Vestiges  '  had  no  influence  on 
the  Continent,  for  rea.sons  partially 
stated  in  the  text.  A  little  later, 
however,  a  similar  "  scandale  "  (as 
the  '  Grande  Encyclopedie  '  has  it- 
art.  "R.Chambers  and  L.  Biichner") 
arose  in  Germany  on  the  publication 
of  '  Kraft  und  Stofif.' 


ON    THK    GENKTIC    VIEW    oK    NATURE. 


321 


and  plausible  enough,  but  tliere  remained  the  last  strong- 
hold of  the  older  view,  the  existence  of  definite  forms  of 
animal  and  vegetable  life.  Were  these  to  be  merely  classi- 
tied  and  reduced  to  separate  types,  as  the  morphological 
view  was  contented  to  reduce  them,  or  was  the  growing 
evidence  of  variability  to  be  interpreted  in  favour  of  a 
gradual  development  of  the  higher  out  of  the  lower  and 
simpler  forms  of  life  ?  Above  all,  how  was  the  highest 
type  of  all,  man  himself,  to  be  regarded  in  such  a  com- 
prehensive scheme  of  development  ?      In  Germany  many        st;. 

'^  '^  .  Genetic  view 

great  naturalists^  were  quite  prepared  for  a  consistent '" 9';.""""^ 

^  x  r      r  and  trance. 

genetic  or  developmental  view  of  nature ;  in  France  at 
that  time  the  question  was  not  agitated  at  all,  the  sug- 
gestive writings  of  Lamarck  and  St  Hilaire  having  been 


^  This  does  not  refer  to  the 
earher  writings  of  Goethe,  Oken, 
Treviranus,  and  others,  whose 
merits,  since  the  appearance  of 
the  'Origin  of  Species,'  have  been 
variou.sly  estimated  by  Huxley  in 
England  and  by  Haeckel  in  Ger- 
many :  tlieir  speculations  had,  with 
the  generalisations  of  the  '  Natur- 
philosophie,'  been  swept  away  by 
the  inductive  school  represented  in 
botany  at  that  time  by  von  Mohl, 
Nageli,  and  Hofineister;  in  zoology 
by  the  einbryological  school  with 
von  Baer  at  its  head.  Of  W.  Hof- 
meister  (1824-1877),  whose  labours 
begin  about  ten  years  before  the 
appearance  of  Darwin's  great  work, 
Julius  Sachs  says  :  "  The  results  of 
his  '  Comparative  Researches'  (1849 
and  1851)  were  magnificent  beyond 
all  that  ha.s  been  achieved  before  or 
since  in  the  domain  of  descriptive 
botany,  .  .  .  the  conception  of  what 
was  meant  by  the  development  of 
a  plant  was  completely  changed, 
.   .  .   the  reader  was  presented  with 

VOL.  11. 


a  picture  of  the  genetic  connection 
between  cryptogams  and  phanero- 
gams which  could  not  be  reconciled 
with  the  then  reigning  belief  in  the 
constancy  of  species.  .  .  .  When, 
eight  years  after  Hofmeister's 
'Comparative  Researches,'  Dar- 
win's theory  of  descent  appeared, 
tiie  affinities  of  the  large  divisions 
of  the  plant-world  lay  so  openly,  so 
deeply  founded,  and  so  clearly  be- 
fore the  ej'es  of  students  of  nature, 
that  that  theory  had  only  to  recog- 
nise what  had  been  made  evident 
in  this  line  by  genetic  morph- 
ology "  ('  Ge.sch.  d.  Botanik,'  p.  '215, 
&c. )  In  another  direction  Nageli, 
by  his  mechanical  theory  of  "  the 
growth  and  internal  structure  of 
organisms,"  which  he  reduces  to 
"  physical,  chemical,  and  mechanical 
processes"  (1860),  fell  in  with  Dar- 
win's attempt  to  "  reduce  the  earlier 
purely  formal  consideration  of  or- 
ganic structures  to  a  causal  (genetic) 
view"  (ibid.,  p.  373). 


322 


SCIENTIFIC    THOUGHT. 


entirely  overruled  by  the  authority  of  Cuvier.^  In 
England,  where  geology  and  natural  history  were  always 
popular  pursuits,  the  question  was  one  of  more  than 
scientific  interest :  it  was  one  which  had  been  appropri- 
ated by  general  literature,''  and  the  larger  bearings   of 


^  Huxley  describes  the  position 
of  France  and  Germany  to  the  doc- 
trine  of    descent  as  follows:    "In 
France    the    influence    of    Elie   de 
Beaumont  and  of  Floureus,  to  say 
nothing    of    the    ill-will   of    other 
powerful  members  of  the  Institute, 
produced  for  a  long  time  the  effect 
of   a   conspiracy   of   silence.    .    .    . 
Germany    took    time    to    consider ; 
Bronn  produced  a  .  .  .  translation 
of  the  '  Origin '  .  .  . ;  but  I  do  not 
call   to    mind    that    any    scientific 
notability  declared  himself  publicly 
in  1860.     None  of  us  dreamed  that 
in   the   course  of  a  few  years  the 
strength  (and  perliaps,  I  may  add, 
the    weakness)    of    '  Darwiuismus ' 
would  have  its  most  extensive  and 
most  brilliant   illustrations  in   the 
land    of   learning.      If    a  foreigner 
may  presume  to  speculate  on  the 
cause    of    this   curious   interval    of 
silence,    I    fancy  it    was    that   one 
moiety    of    the    German    biologists 
were  orthodox  at  any  price  and  the 
other  moiety  as   distinctly  hetero- 
dox.    The  latter  were  evolutionists 
d  priori  alreadj',"  kc.  ('  Life  of  Dar- 
win,' vol.  ii.  p.  186).     The  two  men 
abroad    to    whose   opinion    English 
biologists  of  that  day  would  prob- 
ably attach  the  greatest  value  were 
Karl    Ernst   von    Baer  and   Milne- 
Edwards.     The  former   "  wrote  to 
Huxley  in  August  1860,  expressing 
his  general   assent  to  evolutionist 
views"  {loc.  cit.,  p.  186,  note).     It 
was  von  Baer  from  whom  Huxley 
admits  to  Leuckart  that  he  learnt 
the  "value  of  development  as  the 
criterion   of   morphological  views" 
('  Life  of  Huxley,'  vol.  i.  p.  163).  Von 
Baer  later  ou  qualified  his  adher- 


ence,  admitting  development   only 
within  the  regions  of  the  different 
types  which  he  had  established  (see 
the  second  volume  of  his  collected 
papers).     The  opinions  of  the  great 
contemporary      French      zoologist, 
Henri  Milne-Edwards  (1800-1SS5), 
are  fully  given  in  the  last  chapter  of 
his   very  interesting  '  Rapport  sur 
les    progres    recents    des    Sciences 
zoologiques     en     France'     (1867), 
where  he  also  refers  to  the  writings 
of    Isidore    Geoffroy   Saint-Hilaire, 
who  in  France  continued  to  some 
extent    the    line    of    research    and 
reasoning  which,  through  his  father, 
Etienne    Geoffroy,    and    Lamarck, 
dates  back  to  Buffon,  Bonnet,  and 
other   philosophical   naturalists,   of 
whom,  under  the  name  of  "  Trans- 
formistes,"  M.  Edmond  Perier  has 
given  a  connected    account    in  his 
very  valuable  historical  work,  '  La 
Philosophic   zoologique  avant  Dar- 
win "   (1884).      Milne -Edwards  re- 
mained to  the  end  unconvinced  by 
the  arguments  of  Darwin.      He  had 
already  in  1853  set  forth  his  ideas 
referring  to  the  general  problems  of 
zoology,  and  he  repeated  them  in 
1867   (loc.   cit.,  p.  432  sqq.)     It  is, 
however,    well   to   note    that    ever 
since  1827  [loc.  cit.,  p.  453,  note)  he 
had     contributed     largely    to     the 
furtherance  of  the  genetic  view  by 
his  principle  that  progress  in  nature 
depends  on  division  of  labour.      In 
his  subsequent  writings   he  dwells 
with  much  success  on  this  principle 
of   the    "  division    of   physiological 
labour."     (See  Spencer,  'Biology,' 
voh  i.  p.  160.) 

'■^  About  ten  years  after  the  con- 
troversy about  the  '  Vestiges  '  had 


ON    THE   GENETIC    VIEW    OF    NATURE. 


323 


which  liad  been  fullv  dcuionstiaLed  to  the  educated  and 
reading  public.  There  lias  always  existed  in  this  country 
a  class  of  literature  which  is  almost  entirely  wanting,  or 
has  died  out,  on  tlie  Coiitinenl.  The  value  of  this  class 
of  literature   has   been   difTerently  gauged,  but  it  never- 


tilled  the  columns  of  the  foremost 
British  periuilicivls,  we  lincl  in 
Germany  a  similar  agitation  origin- 
ating through  the  publication  of 
several  works  whicli  have  since 
been  generally  considered  as  the 
purest  expression  of  Materialism. 
The  controversy  begins  in  1852 
with  tlie  publication  of  Rudolf 
Wagner's  '  Physiological  Letters,' 
Moleschott's  '  Kreislauf  des  Le- 
bens,'  and  Carl  Vogt's  '  Bilder  aus 
dem  Thierleben  '  ;  it  came  to  its 
height,  after  the  appearance  (in 
18.5.5)  of  L.  Biichner's  'Kraft  und 
Stoff,'  and  occupied  the  meeting  of 
scientific  and  medical  men  which 
was  held  in  Giittingen  in  1854. 
The  subject  belongs  essentially  to 
the  history  of  philosophical  thought, 
and  can  be  studied  in  the  very  fair 
and  exhaustive  '  History  of  Materi- 
alism '  written  by  F.  A.  Lange,  with 
a  distinctly'  idealistic  tendency 
(English  translation,  three  vols.,  by 
Thomas,  1880).  I  mention  the  sub- 
ject in  this  connection,  because  in 
Germany  and  England  attempts 
were  made  about  the  same  time  to 
found  a  general  philosophy  of  life 
ui>nn  the  teachings  of  science.  This 
had  b<_'en  done  about  two  generations 
earlier  in  France  by  the  "  Sensu- 
alistes  "  and  the  "  Ideologues."  For 
a  French  public  neither  the  English 
nor  the  German  controver.sy  pre- 
sented any  essentially  new  feature, 
or  disclosed  any  novel  aigument. 
The  older  orthodox  conceptions  had 
been  abandoned  very  largely  in 
France  in  the  eighteenth  century, 
and  at  once  replaced  by  concep- 
tions derived  from  science.  In 
'Germany  a  similar  movement  took 


l>lace,  likewise  during  the  eight- 
eenth century  ;  but,  instead  of 
exact  science,  it  was  the  prevailing 
idealistic  philosophy  wiiich  was 
apjiealed  to  for  the  purpose  of 
gaining  new  foundations,  and 
science  only  came  in  when  the 
speculative  restoration  was  gener- 
ally considered  to  have  failed.  In 
England,  which  had  really  supplied 
the  beginnings  both  for  the  French 
sensualistic  philosophy  thiough 
Locke,  and  for  German  criticism 
through  Locke  and  Hume,  the 
older  orthodox  foundations  were 
not  materially  shaken  before  the 
middle  of  the  nineteenth  cen- 
tury. Tiie  author  of  the  '  Ve.s- 
tiges '  distinctly  ai)peals  to  science, 
though,  in  a  religious  spirit,  de- 
siring to  make  it  helpful  for  a 
general  philosophical,  and  not 
merely  an  industrial,  jiurjiose. 
Again,  the  English  movement, 
which  really  culminated  in  Herbert 
Spencer,  differs  from  the  German, 
being  more  influenced  by  biological 
conceptions,  whereas  in  Germany 
the  extreme  system  of  Biichner 
took  ])urely  mechanical,  though 
ill-defined,  ideas — force  and  matter 
— as  the  shibboleth.  It  is  signif- 
icant, as  showing  the  great  general 
importance  of  Darwinism,  that 
through  it  both  the  controversy 
over  the  '  Vestiges '  in  England 
and  that  over  '  Materialismus '  in 
Germany  were  soon  cast  into 
oblivion,  though  they  had  both  to 
some  extent  prepared  the  way  (see 
Lange,  '  Gesch.  des  Mat.,'  p.  570, 
Ausg.  1867;  and  Haeckel,  'Schop- 
fungsgeschichte,'  vol.  i.  p.  98,  9 
.\utl.) 


324  SCIENTIFIC    THOUGHT. 

theless  forms  an  important  feature  in  the  development  of 

English  thought,  if  not  also  of  English  science.      It  is 

27.        the   apologetic   literature,  those   works  which  deal  with 

Apologetic 

literature  in  what  liave  bccu  termed  the  "  Evidences."    In  the  absence 

England. 

of  any  scientific  theology  based  upon  accurate  historical 
research  and  philosophical  criticism,  such  as  has  existed 
with  many  good  and  some  evil  results  since  the  end  of 
the  eighteenth  century  in  Germany,  the  need  was  felt 
for  defending  or  interpreting  those  answers  to  the  great 
problems  of  Nature,  Man,  and  Life,  which  seemed  bound 
up  with  the  Christian  belief,  or  suggested  by  the  sacred 
writings.  The  teaching  of  science  had  not  become,  as  in 
France,  a  purely  secular  occupation ;  instruction  was  not 
separated  from  education ;  apologetics  had  not  become 
doubtful  through  the  bad  faith  and  duplicities  of  cynica 
like  Voltaire,  nor  ridiculous  through  the  puerilities  of 
shallow  writers  such  as  Campe  in  Germany.  Many 
serious  minds  were  occupied  with  the  growing  dis- 
crepancies between  scientific  and  popular  religious  teach- 
ing, and  believing  they  could  discern  the  drift  of  the 
former,  they  made  various  more  or  less  successful 
attempts  to  effect  a  reconciliation  between  the  moving 
and  developing  conceptions  of  scientific  thought  and  the 
fixed  and  unalterable  ideals  of  religious  belief.  Such 
attempts  must  be  doomed  to  failure,  or  at  best  they 
offer  an  individual  solution,  interesting  only  if  it 
happens  to  be  the  inspiration  of  a  poet  or  if  it  repre- 
sents the  creed  of  one  of  the  few  great  and  soaring 
intellects  which  appear  once  or  twice  in  a  century. 
The  conviction  is  gradually  gaining  ground  that  scientific 
and  religious  thought  emanate  from  two  separate  centres. 


ON    THE    GENETIC    VIEW    OF   NATURE. 


325 


that  although  they  ineviLably  come  into  frequent  con- 
tact, tlie  study  of  their  independent  origin  and  history 
and  their  different  psychological  method  is  more  valuable 
than  a  temporary  and  meiely  ephemeral  compromise  of 
their  respective  doctrines.  Happily  this  country  has 
produced  many  great  and  a  few  thinkers  of  the  first 
order,  in  whom  the  greatest  that  scientific  thought 
has  achieved  was  in  harmony  with  a  truly  religious 
spirit.  Tn  contemplating  these  illustrious  examples, 
and  bowing  before  their  greatness,  the  popular  mind 
will  probably  find  its  conviction  of  the  possibility  of 
an  ultimate  reconciliation  of  both  aspects  more  strength- 
ened than  by  leaning  on  the  doubtful  support  of  a 
voluminous  apologetic  literature,  which  proposes  to  give 
general  proofs  where  only  individual  faith  can  decide. 

I  deemed  it  appropriate  to  offer  these  few  remarks 
on  the  whole  of  the  voluminous  literature  ^  from  Butler 


^  The  largest  and  best  known 
type  of  publication  in  this  class  of 
literature,  which  is  jjractically  un- 
known on  the  Continent,  but  which 
belongs  to  our  jioriod,  is  found  in 
the  Bridgewater  Treatises  "  On  the 
Power,  Wisdom,  and  Goodness  of 
God,  as  manifested  in  the  Creation." 
The  circumstances  under  which 
this  series  was  published  are  .-^et 
forth  in  the  ])reliminai\v  notice  to 
the  first  treatise.  The  Earl  of 
Bridgewater,  heir  to  the  title  and 
fortune  of  Francis  Egerton,  thii'd 
Eai'l  of  Bridgewater,  who  con- 
.structed  from  the  plans  of  James 
Brindley,  and  in  accordance  with  the 
idea  of  liis  fatiior,  Lord  Chancelhir 
Egerton,  the  tirst  of  the  large  canals 
in  England,  from  his  coal  mines  at 
Worsley  to  Manchester  and  Liver- 
pool, left  in  his  will  to  the  Royal 
Society  tl»e  sum  of  £8000,  which. 


witli  its  accruing  interest,  was  to 
be  paid  to  the  person  or  persons 
selected  by  the  President  and  ap- 
pointed to  write  and  ])ublish  one 
thousand  copies  of  a  wurk  with  the 
above  title,  —  "  illustrating  sucli 
work  by  all  reasonable  arguments, 
as,  for  instance,  the  variety  and 
foi'ination  of  God's  creatures  iu 
the  animal,  vegetable,  and  mineral 
kingdoms  ;  the  effect  of  digestion, 
and  thereby  of  conversion ;  the 
construction  of  the  hand  of  man, 
and  an  infinite  variety  of  other 
arguments ;  as  also  by  discoveries, 
ancient  and  modern,  in  arts,  sciences, 
and  the  whole  extent  of  literature." 
The  series  contained  works  by  such 
foremost  men  of  science  as  Sir 
Charles  Bell,  AVilliam  Whewell, 
William  IVout.  and  William  Buck- 
land. 


o 


26  SCIENTIFIC    THOUGHT. 


to  Drummond  whilst  I  was  dealing  with  the  '  Vestiges,' 
because  the  latter  is  probably  the  last  example  of  that 
class  of  books  in  which  purely  scientific  thinkers  took 
any  great  interest.  Similar  publications  which  have 
since  appeared  have  made  no  impression  on  the  course 
of  scientific  thought,  though  they  may  have  won  a 
place  in  the  popular  literature  of  their  day.  To  bring 
about  that  complete  separation  and  independence  of 
the  scientific  and  the  religious  arguments  in  this  country 
which  has  been  recognised  during  the  whole  of  the 
nineteenth  century  on  the  Continent,  two  books  have 
probably  contributed  more  than  any  others :  Dean 
28.        Mansel's  Lectures,^  '  On  the  Limits  of  Eelis;ious  ThouQ-ht,' 

Manseland  ®  '^^ 

Darwin.  through  its  Unanswerable  logic :  and  Darwin's  '  Origin  of 
Species,'  through  treating  fearlessly  a  scientific  argu- 
ment which  was  based  upon  observation  and  expanded 
by  legitimate  inference  without  any  reference  to  the 
ulterior  consequences  which  might  be  drawn  from  it. 
It  required  some  courage  to  attack  a  problem  l)eset 
with  such  difficulties  and  which  had  become  hackneyed 


^  It  is  a  remarkable  coincidence, 
showing  the  general  tendencies  of 
English  thought  about  the  middle 


previously,  belong  to  a  different 
section  of  this  '  History.'  We  shall 
there  see  that  in  the  negative  por- 


of  the  century,  that  Dean  Mansel's    |    tion    of   this   analysis    lie   also    the 


"  Bampton  Lectures "  appeared 
just  a  year  before  the  '  Origin  of 
Species.'      The    argument    of    the 


germs  of  the  ideas  put  forward  by 
Herbert  Spencer  and  Huxley  under 
the     well  -  known     terms     of     the 


Lectures    "On   the   Limits    of    Re-    I    "  Unknowable"  and  "Agnosticism," 


ligious  Thought "  was  that  which 
was  elaborated  by  Sir  William 
Hamilton  on  the  lines  of  Kant's 
'  Critique  of  Pure  Reason '  in  his 
celebrated  article  in  the  '  Edinburgh 
Review  '  on  the  "  Philosophy  of  the 
Unconditioned."  A  further  ap- 
preciation of  this  line  of  reasoning, 
which  had  its  beginning  in  Hume's 
sceptical  writings  a  hundred  years 


and  there  is  no  doubt  that  both 
Hamilton  and  Mansel  had  a  con- 
siderable influence  in  forming 
Huxley's  attitude  in  this  respect. 
He  .says,  in  1863  ('Life,'  vol.  i.  p. 
242)  :  "  I  believe  in  Hamilton, 
Mansel,  and  Herbert  Spencer  so 
long  as  they  are  destructive,  and 
I  laugh  at  their  beards  as  soon  as 
they  try  to  spin  their  own  cobwebs.' 


ON    THK    (JENETKJ    VIKW    f»K    NATURE. 


327 


had   always 
which   iiiisht 


Ihrougli  periodical  and  popuhir  literature.  Others  who. 
Ijefore  Darwin,  treated  similar  controversial  subjects, 
such  us  Whewell,  liabbage,  Herschel,  Lyell,  Baden 
Powell,  and  the  author  of  the  '  Vestiges, 
taken  into  account  the  possible  inferences 
be  drawn  from  their  seientitic  statements,  and  had  often- 
times toned  thcni  down  sf)  as  not  to  offend  existing 
opinions.^  Darwin  thought  it  more  modest  and  more 
becoming  for  an  independent  scientific  thinker  to  state 
his  side  of  the  question  completely  and  simply,  without 
presuming  to  attack  or  to  support  a  view  of  things 
which  lay  outside  of  the  dominion  and  the  powers  of 
science.  And  this  is  not  the  least  of  the  many  reasons 
why   his   work    has   created   an   era,    especially    in    this 


^  The  position  adopted  by  several 
of  the  eminent  forerunners  of  Dar- 
win is  interestingly  analysed  by 
Huxley  in  the  chaj)ter  on  the  "  Re- 
ception of  the  '  OrigMi  of  Species  '  " 
contributed  to  the  .second  volume 
of  the  '  Tjife  and  Letters  of  Charles 
Darwin.'  Of  Lj^el!,  who  had  come 
nearest  to  the  doctrine  of  unbroken 
descent  of  species,  Huxley  sa3-s 
(vol.  ii.  p.  193):  "I  see  no  reason 
to  doubt  that  if  Sir  Charles  Lyell 
could  have  avoided  tlie  inevitable 
corollary  of  the  pithecoid  origin  of 
man — for  which  to  the  end  of  his 
life  he  entertained  a  profound 
antipatliy- — he  would  have  advo- 
cated the  efliciency  of  causes  now 
in  o])eratioii  to  bring  about  the 
condition  of  the  organic  world,  as 
stoutly  as  he  championed  that 
doctrine  in  reference  to  inorganic 
nature."  And  Lvell  himself  wrote 
to  Darwin  in  1S63  (' Life  of  Lyell,' 
vol.  ii.  p.  IBG.'J)  :  "I  rcmemlier  that 
it  wa.s  the  conclusion  lie  [Lamarck] 
came  to  about  man  tiiat  fortified 
me  thirty  years  ago  against  the 
great    impression    wliich    his  argu- 


ments at  first  made  on  my  mind." 
Treviranus,  the  author  of  the 
'  Biologie,'  the  contemporary  of 
Lamarck,  was  quite  conf.isteiit  in 
his  views  of  descent  and  mutabil- 
ity, for  he  declares  against  catas- 
trophism,  believes  in  the  evolution 
of  higher  .species  from  the  zoophytes, 
and  even  in  that  of  a  higher  species 
than  man  (see  '  Biologie,'  vol.  ii. 
p.  225,  kc.)  Neither  in  German}' 
nor  in  France,  at  the  beginning  of 
the  century,  did  those  prejudices 
exist  which  in  1S59  prevented  even 
Darwin  frcjm  developing  to  the  full 
the  consequences  of  his  main  thesis. 
This  was  done  in  his  later  works. 
See  his  letter  to  A.  R.  Wallace, 
22nd  Dec.  18.57  ('Life,'  vol.  ii.  p. 
109):  "You  ask  whether  I  shall 
discu.ss  'man.'  I  think  I  shall 
avoid  the  whole  subject,  as  so  sur- 
rounded witli  prejudices  ;  tliough  1 
fully  admit  that  it  is  the  higliest 
and  most  inteiesting  problem  for 
the  naturalist.  My  work,  on  which 
I  have  now  been  at  work  more  or 
less  for  twenty  j'ears,  will  not  fix 
or  settle  anything." 


view 


328  SCIENTIFIC    THOUGHT. 

country,  not  only  in  the  region  of  scientific,  but  quite 
as  much  in  that  of  philosophical,  thought. 
29.  So  far  as  the  purely  scientific  aspect  is  concerned,  the 

Truiiiii)h  of  r  J  £■  > 

^^p^^senetic  '  Origin  of  Species '  firmly  established  the  genetic  or 
developmental  in  the  place  of  the  morphological  view,  or 
the  earlier  purely  systematic  and  classificatory  treatment 
of  the  objects  and  processes  of  nature ;  and  it  is  interest- 
ing to  note  how  the  period  from  the  publication  of  the 
'  Vestiges '  to  that  of  the  '  Origin  of  Species,'  the  fifteen 
years  from  1844  to  1859,  was  also  the  period  during 
which  Humboldt  published  his  'Kosmos' — the  r6sum6 
of  the  labours  of  a  lifetime.  This  was  the  consumma- 
tion of  that  aspect  of  nature  which  I  have  termed  the 
purely  morphological  one,  and  which  in  his  mind  was 
expanded  to  the  panoramic  view :  the  attempt  to  unroll 
before  his  readers  a  picture  or  panorama  of  the  whole 
world  as  the  scientific  mind  was  then  able  to  see  it. 
Nature  appeared  mapped  out  in  bold  and  characteristic 
lines  and  colours,  without  allowing  the  questions  of  past 
history  or  future  development,  —  the  origin,  life,  and 
fate  of  the  cosmos, — to  present  itself  at  all.  The  fact 
that  this  latter  question  was  professedly  excluded  as 
foreign,  or  premature,  is  probably  the  reason  why  the 
book  attracted  so  little  attention  in  this  country,  where 
a  new  manner  of  treating  all  the  problems  of  natural 
science  was  being  inaugurated ;  but  it  is  interesting  to 
learn  from  Darwin  that  his  whole  life  was  influenced  ^ 

'  See  '  Life  and  Letters  of  Charles  I    duction    to    the  Study  of    Natui-al 

Darwin,' vol.  i.  p.  25  :   "  During  my  I    Philosophy,'    stirred    up    in    me    a 

last  year  at  Cambridge  I  read  with  burning  zeal  to  add  even  the  most 

care  and  profound    interest   Hum-  humble  contribution   to  the  noble 

bold t's  '  Personal  Narrative.'     This  structure   of  natural  science.      No 

work,  and  Sir  J.  Herschel's  'Intro-  !   one  or  a  dozen  other  books  influ- 


ON    THE    GENETIC    VIEW    OF    NATLKK. 


329 


and  his  studies  directed  by  reading  and  re  -  reading 
Humboldt's  '  Personal  Narrative.'  The  '  Kosmos '  of 
Humboldt  closed  the  older,  the  '  Origin  of  Species ' 
of  Darwin  opened  the  new,  epoch  of  natural  science : 
the  former  was  retrospective,  the  latter  prospective. 
Both  works  owe  their  origin  to  a  visit  to  the  same 
portion  of  the  globe,  to  a  study  of  the  subtropical  scenery 
and  life  of  South  America  —  Humboldt  having  visited 
the  inland,  Darwin  specially  the  maritime  and  island 
scenery.^       It   is    further   of   interest   to   note   how    the 


30. 
Huiiiboldt's 
'  Kiisrtios ' 
.iiid  the 
'  Origin  of 
Sjitcies.' 


enced  me  nearly  so  much  as  these 
two.  1  copied  out  from  Humboldt 
long  pas.sages  about  Tenerifie,"  &c. 
Also  vol.  i.  p.  337  :  "  I  never 
forget  that  my  whole  course  of  life 
is  due  to  having  read  and  re-read 
as  a  youth  Humboldt's  '  Personal 
Narrative.'" 

'  Besides  Darwin  and  Lyell,  to 
whom,  of  British  naturalists  as  rep- 
resenting the  genetic  view  in  the 
middle  of  the  century,  I  have  so  far 
confined  my  remarks,  there  were 
at  that  time  two  other  eminent  nicn 
working  in  the  same  direction.  The 
views  of  these  two  were  likewise 
much  influenced  by  travel  and  by 
the  study  of  plant  and  animal  life 
in  distant  countries.  I  refer  to  Sir 
J.  D.  Hooker  and  Mr  A.  Russel 
Wallace.  The  important  part  which 
these  men  played  in  the  gradual 
conception  and  birth  of  the  ideas 
which  were  for  the  first  time  com- 
prehensively set  forth  in  the  '  Origin 
of  Species '  is  lucidly  and  imparti- 
ally told  by  Hu.xley  in  the  well- 
known  chapter  which  he  con- 
tributed to  the  second  volume  of 
the  '  Life  and  Letters  of  Charles 
Darwin,' edited  by  his  son,  Professor 
Francis  Darwin,  in  1887.  Few 
episodes  in  the  history  of  thought 
have  been  treated  with  greater 
mastery.         Few     botanists     liave 


j)ossessed  a  greater  })ersonal  know- 
ledge of  different  and  gieatly  vary- 
ing floras  than  Sir  J.  D.  Hooker, 
who  succeeded  to  the  position  and 
labours  of  his  father.  Sir  W.  J. 
Hooker,  at  Kew.  After  having 
accompanied  Captain  Ross  on  his 
Antarctic  expedition  for  the  dis- 
covery of  the  South  magnetic  pole, 
he  became  best  known  by  his 
'Himalayan  Journal'  (1854).  It 
was  in  constant  correspondence  and 
intercourse  with  Hooker  that  Dar- 
win, from  1844  to  18.')9,  wrote  his 
first  great  work.  The  important 
original  contributions  of  Mr  Wal- 
lace are  well  known,  and  the  story 
how  his  paper,  "  On  the  Tendency 
of  Varieties  to  depait  indefinitely 
from  the  Original  Type,"  reached 
Darwin  when  he  had  got  half 
through  the  larger  work  which  he 
was  tiien  writing,  how  this  coinci- 
dence hastened  the  publication  of 
the  two  ])apers  by  Wallace  and 
Darwin,  which  "contained  exactly 
the  same  theory,"  in  the  'Journal 
of  the  Limiiuan  Society  '  (Zoology, 
vol.  iii.  p.  45),  has  been  told  by 
Lyell  and  Hooker  (ibid.,  letter  to 
the  secretary),  and  by  Darwin  him- 
self (Autobiography,  in  '  Life,'  &c. , 
vol.  i.  p.  84).  No  mystery  lies 
upon  the  history  of  the  first  enun- 
ciation  of  the  doctrine  of  natural 


330 


SCIENTIFIC    THOUGHT. 


same  year  which  witnessed  the  appearance  of  the  work 
of  Darwin  was  also  that  of  the  invention  of  Spectrum 
Analysis,  that  great  instrument  by  which  astronomy, 
doomed  by  the  purely  mathematical  treatment  to  be- 
come simply  "  une  question  d'analyse,"  was  once  more 
enrolled  among  the  natural  sciences ;  the  means  being 
supplied  for  that  natural  history  of  the  heavens  which  is 
now  one  of  the  most  progressive  and  fascinating  branches 
of  science.  The  reader  who  has  realised  from  the  fore- 
going exposition  how  the  genetic  view  of  nature  was 
anticipated  by  earlier  writers  on  cosmology,  such  as 
Leibniz  and  Laplace,  how  it  obtained  in  geology  through 
Hutton  and  Lyell,  how  it  became  dominant  in  embryo- 
logy through  von  Baer,  and  how  the  morphological 
treatment  broke  dow^n  through  the  recognition  of  the 
variability  of  species  and  the  impossibility  of  deiining 
clearly  the  landmarks  of  zoological  and  botanical  classi- 
fication, will  readily  understand  the  importance  and 
timeliness  ^    of    Darwin's   work,  which   proposed   to   deal 


selection,  no  national  or  personal 
jealousies  obscure  the  issues  which 
were  then  at  stake  ;  neither  of  the 
two  great  naturalists  has  ever  put 
forward  aiij'  complaint  that  the 
other  has  not  fairly  and  generously 
dealt  with  his  own  merit.  Since 
the  death  of  Darwin  Mr  Wallace 
has  written  the  well-known  book 
which,  under  the  title  of  '  Darwin- 
ism '  (London,  1889),  gave  to  many 
readers  the  first  comprehensive 
account  of  the  celebrated  theory 
which  is  generously  identified  with 
the  sole  name  of  only  one  of  its 
original  propounders. 

^  Both  propounders  of  the  theory 
of  natural  selection  have  in  their 
subsequent  writings  referred  to 
those  who   prepared    the    way  be- 


fore them,  and  Mr  Wallace  has 
taken  special  pains  to  explain  why 
a  doctrine  which  was  so  well  pre- 
pared, and  even  anticipated,  had 
not  been  more  distinctly  accepted 
before  the  ap[>earance  of  the  '  Origin 
of  Species'  (''  Darwinism,"  chap,  i.) : 
"  Notwithstanding  the  vast  know- 
ledge and  ingenious  reasoning  of 
Lamarck,  and  the  more  general 
exposition  of  the  subject  by  the 
author  of  the  '  Vestiges  of  Creation,' 
the  first  step  had  not  been  taken 
towards  a  satisfactory  explanation 
of  the  derivation  of  any  one  species 
from  any  other.  Such  eminent 
naturalists  as  Geoffroy  St  Hilaire, 
Dean  Herbert,  Professor  Grant, 
von  Buch,  and  some  others,  had 
expressed  their  belief  that  species 


ON    THK    GENETIC    VIKW    oK    NATL'HK.  331 

specially  with  the  actual  tact  and  the  luiictiuii  uf  vaiia-        3i. 

'■  ''  "Varia- 

tion   ill    the  domain   of    living   beings.      He   pushed   the  ^io"-" 

problem  of  variation  and  variability  into  llie  foreground, 

and  discussed  one  of  its  inaiii  features — \\z.,  its  possible 

etlect   and    results.       Since    his    time    the   eye   of   every 

botanist,    every    zoologist,   and    every   einl  )ryologist    has 

l)een    directed    towards    the   varialjility,   transition,   and 

genesis  of  forms,  to  their  history  rather  than   to  their 

portraiture,  whereas  before  him  it  was  mostly  attracted 

by  their  seeming  fixity  and  recurrence.    Variations  have 

been  studied  on  the  large  and  on   tlio  minute  scale  in 

geological    strata   at    home    ami    abroad,   and   the  vexed 

question  has  been  raised  as  to  their  causes  and  laws, — 

Darwin  having  been  mainly  occupied  with  their  existence 

and  operation,  the  results  which  they  brought  aV)0ut,  the 

gradual  alterations  of  the    forms  of  living  things.      On 

this  side  he   tells  us  that  he  found  an  important  clue 

through  reading  a  book  which  had  appeared  at  the  very 

end  of  the  eighteenth  century,  Alallhus's  '  Essay  on   the 

Principle  of   Population.'  ^ 

arose  as  .simple  varieties,  and  tliat  |  1798,  and  in  the  enlarged  and  much 

the  species  of  each  genus  were  all  |  improved  form  in  which  it  is  now 

descended  from  a  common  ancestor ;  I  known  in  1803.     Darwin  seems  to 

but  none  of  them  ><ave  a  clue  as  to  '  have  come  upon  it  accidentally.    In 


the  law  or  the  method  by  which 
the  change  had  been  effected.  This 
was  still  '  the  great  mystery '  "  (p. 
6).  "  Darwin,  by  his  discovery  of 
the  law  of  natural  selection  and  his 
demonstration  of  the  great  principle 
of  tlie  preservation  of  useful  varia- 
tions in  the  struggle  for  life,  lias 
not  only  thrown  a  Hood  of  light  on 
the  process  of  development  of  the 
whole  organic  world,  but  also  estab- 
lished a  firm  foundation  for  all 
futui-e  studj-  of  nature  "  (p.  9). 


his  Autobiography  ('  Life,'  vol.  i. 
p.  83)  he  writes  :  "  In  October  1  838 
—  that  is,  fifteen  months  after  I  had 
begun  my  systematic  iuquirj- — I 
happened  to  read  for  amusement 
'  Malthus  on  Population,'  and  being 
well  prepared  to  apjireciate  the 
struggle  for  existence  which  every- 
where goes  on,  from  lonij-continued 
observation  of  the  hat>its  of  animals 
and  plants,  it  at  once  struck  me 
that  under  these  circumstances 
favourable    variations    would    tend 


This    essay    apjieared    first    in    '    to  be  preserved,  and  unfavourable 


332  SCIENTIFIC    THOUGHT. 

32.  The  ideas  and  reflections  contained  in  this  celebrated 

Malthus. 

essay,  which  has  played  a  prominent  part  in  the  philo- 
sophical literature  of  economics,  could  not  have  occurred 
to  any  one  who  had  studied  human  society  or  nature 
merely  in  individual  specimens  or  isolated  cases ;  for 
they  referred  not  so  much  to  the  natural  history  of  a 
single  being,  as  to  the  peculiar  relations  and  complica- 
tions which  arise  in  a  community  or  society  of  beings, 
some  of  these  being  applicable  quite  as  much  to  animal 
and  plant  life  as  to  the  life  of  men.  In  fact,  it  was  a 
chapter  in  the  science  of  bionomics.  Malthus,  Darwin, 
and  Wallace  were  not  "  laboratory  naturalists,  to  whom 
the  peculiarities  and  distinction  of  species,  as  such,  their 
distribution  and  their  affinities,  have  little  interest  as 
compared  with  the  problems  of  histology  and  embryo- 
logy, of  physiology  and  morphology."  ^  The  problem  of 
population,  whether  it  refers  to  man  or  other  living 
creatures,  is  one  that  will  force  itself  upon  those  who 
study  nature  and  mankind  on  the  large,  on  the  outdoor, 
scale,  not  as  does  the  collector  or  dissector  of  specimens. 
How  has  the  face  of  the  earth  been  peopled  l)y  plants, 
animals,  and  human  beings  ?     What  are  the  forces  which 

ones  to  be  destroyed.     The  result  book  on    Population  came  into  his 

of  this  would  be  the  formation  of  hands,  the  idea  of  natural  selection 

new   species.      Here,    then,    I    had  j  came  into  his  mind  ('  Schopfungs- 

at  last  got  a  theory  by  which  to  ;  gesch.,'    chap.    vi. )       In    the    first 

work,"  &c.      Prof.   Haeckel,   in   his  j  paper  which   Darwin   published   in 

'History   of    Creation,'    has    dwelt  i  the     'Journal     of     the     Linnican 

e.xhaustively  on  this  connection  of  j  Society'    ("Letter   to   Asa    Gray," 

Darwin    with    Malthus,    quoting   a  vol.   iii.  p.   .51),    he   uses   the   term 

letter  of  Darwin's  to  him,  dated  8th  ■  "Natural  Selection,"  and  refers  in 

October  1864,  in  which  he  says  that  I  the  abstract  which  he   there  gives 


for  years  he  could  not  comprehend 
how  any  form  should  be  so  emi- 
nently adapted  to  its  special  con- 
ditions of  life,  but  that  when 
through    good     fortune    Malthus's 


to  Malthus;  whereas  Wallace  (ibid, 
p.  56)  introduces  the  term  "  Struggle 
for  Existence." 

^  Quoted    from    Wallace,    '  Dar- 
winism,' preface,  p.  vi. 


ON    THE    GKNETIC    VIEW    OF    NATURE.  333 

ensure  the  multiplicatiun,  what  are  those  which  clieck 
the  increase,  of  popuhition  ?  As  all  living  things  are 
dependent  on  each  other,  forming  tlie  great  household  or 
economy  of  nature  or  the  smaller  one  of  human  society, 
a  certain  adjustment  must  exist  hy  which  a  definite  place 
and  part  are  allotted  to  every  individual  and  to  every 
class  of  individuals.  Malthus  had  studied  the  problem 
from  a  political  point  of  view.  Here  it  was  felt  to  be 
of  human  and  social  importance,  but  his  principle  was 
applicable  to  all  living  creatures.  For  everywhere,  even 
in  the  remotest  and  only  recently  discovered  countries, 
we  see  at  work  the  luxuriant  and  productive  powers  of 
nature  on  the  one  side,  on  the  other  side  the  many 
difticulties  and  obstacles  by  which  they  are  forcibly  and 
automatically  kept  in  check,  resulting  in  the  ever-recur- 
ring spectacle  of  a  "  struggle  for  existence."     The  more        :«. 

"Struggle 

we  penetrate  into  the  hidden  and  remoter  provinces  of  for  exist- 
nature,  into  the  luxuriant  "  fauna  and  flora  "  of  tropical 
regions,  or  realise  the  enormous  population  among  the 
lower  forms  of  life,  the  more  the  conviction  forces  itself 
upon  us  that  the  apparent  equilibrium  is  only  maintained 
by  the  phenomenon  of  "  crowding  out "  on  a  scale  com- 
pared with  which  the  spectacle  unfolded  by  Malthus  in 
his  special  application  to  human  societies  is  quite  a  minia- 
ture display.  This  process  of  "  crowding  out  "  must  have 
been  at  work  during  the  untold  ages  which  modern 
geology  has  made  known  to  us,  and  the  effects  of  it 
must  indeed  have  been  extraordinary,  and  well  worthy 
of  study.  That  living  beings,  if  left  to  their  natural 
instincts,  multiply  at  an  enormous  rate,  and  would, 
except  for  certain  automatic  checks,  in  a  very  short  time 


euce. 


334 


SCIENTIFIC    THOUGHT. 


34. 
OuMoor 

shidies. 


people  the  whole  habitable  portion  of  the  globe,  is  a 
fact  which  has  only  been  realised  since  Malthus,  and, 
on  a  much  larger  and  more  general  scale,  Darwin  and 
Wallace  have  drawn  attention  to  it/  This  being 
generally  admitted,  the  questions  arise :  What  are  these 
automatic  checks,  and  what  results  do  they  produce  ? 
It  is  evidently  quite  a  new  line  of  reasoning,  unknown 
to  former  naturalists,  or  only  sporadically  and  fragment- 
arily  pursued  by  them ;  but  it  introduces  us  at  once 
into  nature  itself,  away  from  the  class-room  and  the 
museum,  where  we  hear  of  the  forces  and  laws  of  nature 
in  their  abstract  mathematical  development,  or  where  we 
behold  specimens  arranged  peacefully  and  lifelessly  side  by 
side.  We  are  face  to  face  with  the  fierce  and  continuous 
conflict  which  is  unceasingly  going  on  around  us,  and 
realise  the  endless  changes  which  it  must  be  producing. 

Among  the  many  influences  which  the  Darwinian 
view  has  had  in  opposite  directions  on  the  thought  of 
our  age,  none  is  greater  or  more  fundamental  than 
this,   that   whereas    before    Darwin    naturalists   stepped 


^  On  the  publication  of  the 
'  Origin  of  Species,'  Darwin  re- 
ceived many  letters  pointing  out 
earlier  anticipations  of  his  views. 
The  more  important  of  these — bear- 
ing upon  descent  and  change — have 
been  referred  to  in  tlie  present 
chapter.  The  special  principle  of 
natural  selection  seems  to  have 
been  already  foreseen  by  Dr  Wells 
in  1813,  and  published  in  his 
famous  '  Two  Essaj's  upon  Dew  and 
Single  Vision'  in  1818.  "In  this 
paper  he  distinctly  recognises  the 
principle  of  natural  selection,  and 
this  is  the  first  recognition  which 
has   been    indicated"    ('Origin    of 


Species,'  historical  sketch  to  later 
editions).  Another  anticipation  was 
that  of  Patrick  Matthew  in  1831,  in 
his  work  on  '  Naval  Timber  and 
Arboriculture.'  "  Unfortunately 
the  view  was  given  very  briefly  iu 
scattered  passages  in  an  appendix 
to  a  work  on  a  different  subject,  so 
that  it  remained  unnoticed  until 
Mr  Matthew  himself  drew  atten- 
tion to  it  in  the  '  Gardeners' 
Chronicle'  on  April  7,  1860.  ,  .  . 
He  clearly  saw  the  full  force  of  the 
principle  of  natural  selection " 
{loc.  cit.,  p.  xvi).  Neither  of 
these  writings  was  known  to 
Darwin  in  1859. 


ON    THE    GENETIC    VIKW    OF    NATUliK. 


!35 


out  of  doors  only  from  curiosity,  and  in  searcli  (jf  new 
specimens,  prompted  by  the  love  of  travel  and  adven- 
ture, or  as  companions  to  commercial  and  colonising  ex- 
peditions, they  are  now  forced  to  do  so,  because  one  of 
the  greatest  agencies  in  nature — "  the  struggle  for  ex- 
istence " — can  only  be  studied  in  nature  herself.  Before 
Darwin  the  study  of  nature  was  artificial ;  through  his 
influence  it  has  become  natural.  From  the  point  of 
view  of  the  history  of  thought,  this  is  surely  a  much 
greater  result  than  any  of  the  several  theories  or  special 
arguments  which  are  connected  \\ith  liis  name.  These 
are  indeed  numerous,  each  making,  as  it  were,  a  dis- 
tinctly new  departure  in  scientific  reasoning,  character- 
ised by  that  unmistakable  sign  '  of  all  that  is  really 
novel  in  the  realm  of  thought,  the  creation  of  a  new 
vocabulary  of  distinct  terms  and  phrases.  A'arieties 
were  known  to  liotanists  before  Dai'win,  but  whd  studied 
"  variation  "  and  "  variability  "  ?  or  who  spoke  of  the 
"  divergence  of  character  "  ?  Breeders  of  stock  and 
pigeon -fanciers  knew   what  "selection"  meant,  but  the 


'  The  late  Hewett  Cottrell 
Watson,  authur  of  the  '  Cj'bele 
Britannica" — one  of  a  most  valuable 
series  of  works  on  the  topography 
and  goograi)hical  distribution  of 
the  plants  of  the  British  Islands — 
wrote  to  Darwin  shortly  after  the 
publication  of  the  '  Origin  of 
Species,'  2l8t  November  1859  : 
"  1  am  tempted  to  write  you  the 
first  impressions,  not  doubting  that 
they  will,  in  the  main,  be  the 
permanent  impressions.  Your  lead- 
ing idea  will  assuredly  become 
recognised  as  an  established  truth 
in  science — i.e.,  'Natural  Selection.' 
It  has  the  characteristics  of  all 
great    natural     truths,     clarifying 


what  was  obscure,  simplifying  what 
was  intricate,  adding  greatly  to 
previous  knowledge.  You  arc  the 
gi-eatest  revolutionist  in  natural 
history  of  this  century,  if  not  of 
all  centuries.  .  .  .  Now  these 
novel  views  are  brought  fairly  be- 
fore the  scientific  public,  it  seems 
truly  remarkable  how  so  many  of 
them  could  have  failed  to  see  their 
right  road  sooner.  How  could  >Sir 
C.  Lyell,  for  instance,  for  thirty 
years  read,  write,  and  think  on  the 
subject  of  species  and  their  succes- 
sion, and  yet  constantly  look  down 
the  wrong  road?"  ('Life  of  Dar- 
win,' vol.  i.  p.  352,  and  vol.  ii.  p. 
226.) 


336  SCIENTIFIC    THOUGHT. 

35.  terms  "  natural   selection  "   and   "  sexual   selection  "  ap- 

"  Natural 

selection"     pearcd   for   the   first   time   in   Darwin's   writings.      The 

and  "sexual    -^  ° 

selection."  "  struggle  for  existence,"  and  the  resulting  "  survival  of 
the  fittest  "  individuals,  represent  definite  processes  always 
going  on  consciously  or  unconsciously  in  nature  and  in 
human  society ;  nor  is  it  less  significant  that  many  other 
phrases  have  been  coined,  by  which  the  same  idea  has  been 
made  useful  in  other  domains  of  research.  "  Hybrids," 
"  mongrels,"  "  rudimentary  organs,"  and  "  monstrous  " 
developments,  which  in  earlier  times  were  subjects  of 
mere  curiosity,  have  been  raised  to  scientific  importance 
as  indicative  of  the  concealed  and  mysterious  agencies 
by  which  natural  forms  are  altered  or  maintained,  and 
natural  processes  encouraged  or  checked.  "  Environ- 
ment "  and  "  adaptation "  open  out  great  vistas  of  in- 
quiry, whilst  nearly  all  those  different  lines  of  search 
and  of  reasoning  have  latterly  become  centred  in  the 
great  problem  of  "  heredity  " — the  central  question  of 
biological  science.  In  addition  to  these,  the  older 
terms  of  the  naturalists  and  anatomists  have  received 
new  interpretations.  It  has  been  shown  by  Darwin 
himself  how  the  vague  endeavours  of  system -makers, 
since  Linnaeus,  after  a  "  natural "  as  distinguished  from 

36.  a  merely   "  artificial  system  of   classification  "  of  living 

Meaning  of 

natural        bcings,   implied   "  something   more "   than   mere    resem- 
*'°°-  blance,  and  that  this   something  more   is  "  propinquity 

of  descent — the  only  known  cause  of  the  similarity 
of  organic  beings — it  being  the  bond,  hidden  by  various 
degrees  of  modification,  which  is  partially  revealed  to 
us   by   our   classifications."  ^       In  the  light  afforded  by 

^  '  Origin  of  Species,'  1st  ed.,  p.  413. 


ON  THM  GENETIC  VIEW  OF  NATURE. 


337 


this  idea,  the  whole  work  of  classiHcation  has  since 
Darwin's  time  heen  taken  up  anew ;  and  though  it  is 
prohably  premature  to  fix  upon  any  elaborate  scheme 
as  likely  to  aflbrd  a  correct  view  of  the  main  lines 
of  descent  in  the  two  great  realms  of  animal  and 
plant  life,  single  pedigrees,  such  as  those  of  the  rhino- 
ceros and  the  horse,  have,  with  the  assistance  of  the 
geological  record,  been  successfully  worked  out,  the 
missing  links  having  unexpectedly   turned  up.^ 

In  addition  to  this  great  service  of  directing  the 
glance  of  the  naturalist  outside,  and  of  helping  to  over- 
come the  bewildering  effects  which  the  aspect  of  nature 
must  produce  on  every  one  who  is  not  prepared  for 
research  by  some  definite  aim  and  a  distinct  habit  of 
reasoning,  the  Darwinian  spirit  has  further  proved  its 
usefulness  by  the  great  increase  of  our  knowledge  of 
the   things   and   phononicna  of  nature   which   has   taken 


'  "  It  is  certain  that,  before 
the  tlieory  of  descent  was  accepted 
or  even  discussed,  genealogical  trees 
were  used  to  represent  possible 
relationships  among  human  races, 
or  possible  affinities  among  animals. 
It  was  used  as  a  '  graphic '  way  of 
expressing  classification,  and  was 
true  just  in  jiroportion  as  the 
classification  was  true.  The  nat- 
uralist traveller,  Peter  Pallas,  was 
one  of  the  first  to  use  it  to  express 
affinities  among  animals,  though 
it  is  possible  he  .saw  a  deeper 
meaning  in  his  symbol.  But  when 
tiie  theory  of  descent  took  hold 
on  men's  minds,  the  genealogical 
tree  became  more  than  a  graphic 
register  of  affinities, — it  was  used 
to  express  the  suppijsed  facts  of 
descent.  To  Ernst  Haeckel  be- 
longs the  credit,  or,  as  some  critics 
would    say,    the    responsibility,    of 

VI  lb.  ir. 


introducing  the  use  of  genealogical 
trees  into  zoology  and  l)otany. 
In  his  '  Generelle  Morphologie 
(186(3)  and  in  his  '  .Sclii)i)fungs- 
geschichte'  (1868,  9th  ed.  1S97), 
he  displayed  numerous  genealogical 
trees  designed  to  show  the  descent 
of  various  stock.s  and  types  of  ani- 
mals and  plants.  There  can  be 
no  doubt  that  in  so  doing  he 
focu.ssed  the  idea  of  descent  into 
vividness,  and,  by  the  very  definite- 
ness  of  the  notation,  forced  natural- 
ists to  a  criticism  of  the  reality 
of  the  supposed  lines  of  descent. 
Prof.  Ij.  von  (Jraff.says  of  Haeckel's 
'  Stainmljilume,'  '  There  is  due  to 
them  the  immortal  credit  of  having 
given  the  first  impetus  to  the 
grand  revolution  in  the  animal 
morphology  of  the  last  decades '  " 
(J.  A.  Thomson,  '  The  Science  of 
Life,"  1899,  p.  15). 


338 


SCIENTIFIC    THOUGHT. 


place  since  the  publication  of  Darwin's  works,  by  the 
industry  of  friend  and  foe,  with  the  object  of  prov- 
ing or  of  disproving  and  modifying  Darwin's  theories. 
Whole  chapters,  such  as  those  referring  to  the  fer- 
37.        tilisation  of   plants   through  insects,   to   the  part   which 

Fertilisation  ^ 

of  plants  and  colour  plavs  in  the  world   of  Howers   or  in  the  plumage 

'Mimicry.  ±       ^  i  o 

of    birds    and    in    the    wings    of    butterflies    and   moths, 
have  been  added  to  our  handbooks  of  natural  history ;  ^ 


■*  Two  remarkable  instances  may 
be  aientioned.  It  was  known  to 
Christ.  Conrad  Sprengel  that  many 
tiowers  aie  "  dichogamous "  —  i.e., 
that  though  the  organs  for  self- 
fertilisation  exist  in  the  same  flower, 
nevertheless,  because  of  a  want  of 
timekeeping  or  for  other  reasons, 
polHnation  is  done  by  crossing, 
wherein  the  visits  of  insects  are  in- 
strumental through  elaborate  exist- 
ing arrangements.  "  Variously  col- 
oured spots  serve  as  honey-guides 
and  pathfinders  to  the  exploring 
insects,  hairs  protect  tlie  nectar 
from  rain  and  yet  offer  no  obstacle 
to  dc'iiirable  visitors,  other  arrange- 
ments secure  that  the  insects  are 
dusted  with  pollen "  (J.  A.  Thom- 
son, 'The  Science  of  Life,'  p.  192). 
Sprengel  published  his  observations 
in  a  remarkable  book  (1793)  with 
the  title  '  The  Secret  of  Nature 
discovered  in  the  Structure  and 
Fertilisation  of  Flowers. '  Such 
was  the  enthusiasm  of  this  true 
naturalist,  that  he,  "  after  being 
ejected  from  the  rectorate  of  Span- 
dau  for  neglecting  his  flock  in 
favour  of  Howers,  settled  down  to 
a  frugal  life  in  Berlin,  and  gave 
lessons  in  languages  and  botany. 
The  commonest  j)lant  became  new 
by  what  he  had  to  say  about  it ; 
a  hair,  a  spot,  gave  him  oppor- 
tunity for  questions,  ideas,  investi- 
gations" (ibid.,  p.  191).  Sachs 
('Gesch.,'  p.  449)  considers  Spren- 
gel's  little  work  to   contain    "the 


first  attempt  to  explain  the  genesis 
of  organic  forms  out  of  definite 
relations  to  their  environment."' 
For  sixty  years  this  biouomical 
classic  was  forgotten.  Darwin  in 
1841  heard  of  it  through  Robert 
Brown,  who,  according  to  Dr  Gray 
('Nature,'  1874,  p.  80),  "in  coni- 
mon  with  the  rest  of  the  world, 
looked  on  Sprengel's  ideas  as  fan- 
tastic." The  book  impressed  Dar- 
win, who  in  1837  had  written  in 
his  notebook  :  "  Do  not  plants 
which  have  male  and  female  organs 
together,  yet  receive  influence  from 
other  plants  J  "  as  being  "  full  of 
truth."  (See  '  Life  of  Darwin,'  vol. 
i.  p.  90  ;  vol.  iii.  p.  257.)  The  other 
important  research  which  has  been 
much  stimulated  by  the  two  great 
propounders  of  Darwinism,  is  the 
Btudy  of  tlie  meaning  of  colours 
in  plants  and  animals  and  the  allied 
subject  of  "Mimicry."  "It  is 
the  wonderful  individuality  of  the 
colours  of  animals  and  plants  that 
attracts  our  attention  —  the  fact 
that  the  colours  are  localised  in 
definite  patterns,  sometimes  in 
accordance  with  structural  char- 
acters, sometimes  altogether  in- 
dependent of  them,  while  often 
differing  in  the  most  striking 
and  fantastic  manner  in  allied 
species.  We  are  thus  compelled  to 
look  upon  colour  not  merely  as  a 
physical  but  also  as  a  biological 
characteristic,  which  has  been  dif- 
ferentiated     and      specialised     by 


ON    THE    OENETIC    VIEW    OF    NATURE.  339 

the  older  division  of  zoology  and  botany  having  to  a 
large  extent  been  removed  by  a  study  of  the  inter- 
dependence of  the  many  forms  of  living  things  and 
their  connection  with  peculiarities  of  climate  and  soil. 
The  Darwinian  attitude  to  the  study  of  natural  objects 
has  also  introduced  'into  the  natural  sciences  the  exact 
spirit  of  research, — accurate  measurements,  together  with 
elaborate  countings,  being  resorted  to  in  order  to  decide 
the  range  of  variability  of  species,  the  rate  of  increase 
in  numbers,  and  the  proportion  of  the  surviving  to  the 
lost  or  wasted  specimens.  A  large  amount  of  statistical 
information  ^  has  tlius  Ijeen  accumulated,  and  natural 
history  is  becoming  to  some  extent  an  exact  science. 
That  it  will  ever  Ije  so  to  a  very  large  extent  is  doubt- 
ful :  it  is  one  of  the  great  merits  of  Darwin  that  he  has 
introduced  a  special  method  into  the  sciences  of  nature — 
ihe  method  of  a  judicious  balancing  of  evidence.  He  ss. 
was  fully  "  aware  that  scarcely  a  single  point  was  dis-  method, 
cussed  in  his  works  on  which  facts  cannot  be  adduced, 
often  apparently  leading  to  conclusions  directly  opposite 
to  those  at  which  he  arrived,  and  that  a  fair  result  can  be 
obtained   only   by  fully  stating  and   l»alancing  the  facts 

natural  selection,  and  must,  there-  served  as  one  of  the  most  valuable 

fore,    find   its   explanation    in    tlie  illu.strations    and     proofs     of     the 
jjrinciple  uf  adaptation  or  utility "    '    theory   of  natural  selection.       The 

(Wallace,     'Darwinism,'     p.     189).  whole     matter    is     admirably    ex- 

Tlie    term     "Mimicry"    was    first  pounded    by    Mr    Wallace    in    his 

introduced  by  H.  \V.  Bates  in  his  long  article    in    the    '  Westminster 

paper   on    "  Mimetic    Butterflies,"  Review,'   July   1867,    reprinted    in 


road  befoie  the  Linnwan  Soc,  Nov. 
l>tjl,  and  hailed  by  Darwin  ('Life,' 


his   '  Contributions  to    the   Theory 
of  Natural  Selection  '  (1870,  pp.  45- 


vol.  ii.  p.  'i'j'2)  as  "one  of  the  most  ]  129),  and  again  in   'Darwinism, 

remarkable  and  admirable  pa])ers  "  j  ^  On  the  development   ><{  sUitis- 

he   ever  read.       Tiie    .'subject    had  |  tical  methods  in  the  service  of  the 

been  passed  over  in  the  first  editions  i  theory   of  evolution,   see  chap.  xii. 

of  the  '  Origin,'  but  was  introduced  below, 
in   later   edition-^,    and    has  always 


340  SCIENTIFIC    THOUGHT. 

and  arguments  on  both  sides  of  each  question."  ^  It  is 
quite  a  different  process  of  investigation  and  method  of 
thought  from  tliat  which  the  abstract  sciences  use,  where 
every  agency  is  first  considered  in  its  isolated  action  and 
mathematically  calculated,  and  a  complex  effect  is  rightly 
looked  upon  as  merely  the  resultant  of  specific,  well- 
defined  forces,  compounded  according  to  rigid  dynamical 
formulre.  That  the  whole  of  nature,  as  well  as  all 
observable  phenomena,  are  in  reality  only  the  result  of 
such  a  composition  of  definite  simple  actions,  and  can  be 
studied  as  such,  may  be  quite  correct ;  but  that  this 
method,  however  useful  in  isolated  cases,  and  especially 
however  fruitful  in  the  application  to  artificial  mechanisms, 
will  never  lead  to  a  just  comprehension  of  any  large 
cluster  of  phenomena,  or  to  an  appreciation  of  the  totality 
of  things  which  surround  us,  must  be  evident  to  any  one 
who  at  once  appreciates  the  rigidity  and  universality  of 
mathematical  calculations,  and  sees  how  soon  they  fail  to 
become  of  practical  use  when  we  attempt  to  attack  any 
complex  problem  through  them.  Now,  all  processes  in 
nature  herself,  as  distinguished  from  the  laboratory,  are 
eminently  complex,  and  far  transcend  the  powers  and 
grasp  of  the  mathematical  calculus,  so  far  as  the  human 
mind  is  able  to  employ  it.  In  fact,  the  outdoor 
naturalist  must  attack  the  problem  of  nature  and  life 
by  quite  a  different  method :  he  must,  like  a  judge,  con- 
front and  appreciate  the  evidence  of  many  witnesses 
who  are  speaking  on  all  sides  to  him,  and  he  must, 
with  an  open  and  unbiassed  mind,  judiciously  combine 
such  evidence  in  the  sentences  which  he  passes  or  the 

^  '  Origin  of  Species,'  1st  ed.,  p.  2. 


ON    THE    GENETIC    VIEW    OF    NATURE. 


341 


generalisations  which  he  attempts.  Absohite  mathe- 
matical certainty  is  almost  unknown  in  such  cases :  they 
can  only  Ite  made  out  willi  mnif!  or  less  clearness  and 
probability. 

It  seems  to  me  that  the  new  phase  into  which  scientific        39. 

•11  11-1  p  Darwin  aii<l 

thought  has  entered,  mainly  through  the  mnuence  of  xpw-ton 
Darwin,  has  not  been  sufficiently  appreciated  by  those  of 
his  critics  who  have  compared  his  methods  with  those  of 
earlier  philosophers  and  naturalists.  Darwin  has  l)een 
called  by  some  tlie  Xewton  of  tlie  natural  sciences,^  and 
again  by  others  his  method  has  l)een  unfavourably  con- 
trasted with  that  of  Xewton  and  C'uvier.^     Some  of  these 


*  It  is  in  many  instances  only 
a  fa^on  dc  parlcr.  Maxwell  simi- 
larly called  Ampl-re  the  Newton  of 
Electrodynamics  ;  and  Young  has 
been  called  the  Newton  of  Optics. 
Mr  Wallace  saj-s  ('Darwinism,'  p. 
9) :  "  We  claim  for  Darwin  that  he 
is  the  Newton  of  natural  hi.story, 
and  that,  just  so  surely  as  that  the 
discovery  and  demonstration  by 
Newton  of  the  law  of  gravitation 
established  order  in  place  of  chaos, 
and  laid  a  sure  foundation  for  all 
future  study  of  the  starry  heavens, 
80  surely  has  Darwin,  by  his  dis- 
covery of  tlie  law  of  natural  selec- 
tion and  his  demonstration  of  the 
great  ])rinciple  of  the  preservation 
of  useful  variations  in  the  struggle 
for  life,  not  only  thrown  a  flood  of 
light  on  the  process  of  development 
of  the  whole  organic  world,  but  also 
established  a  firm  foundation  for  all 
future  study  of  nature." 

'"  The  most  important  publica- 
tion of  this  kind  is  the  late  Pro- 
fessor Albert  Wigand's  %v(jrk,  in 
three  volumes,  '  Der  Darwinismus 
uiid  die  Naturforschung  Newton's 
und  Cuvier's  '  (Braunschweig,  1874- 
1877).  The  author  significantly 
classes  Humboldt  also  among  those 


who  belong  to  that  period  and 
school  of  research  which  has — un- 
fortunateh',  in  his  opinion — been 
superseded  bj'  the  modern  genetic 
treatment  (see  vol.  iii.  p.  14).  It  is 
not  likely  that  a  perusal  of  these 
volumes  will,  in  the  mind  of  the 
reader,  change  the  current  of 
thought  which  is  now,  even  more 
than  twenty-five  years  ago,  running 
in  genetic  lines,  nor  will  it  do  any- 
thing towards  diminishing  the  sense 
of  importance  which  attaches  to 
this  modern  movement.  Never- 
theless, the  book  is  valuable  as 
giving  a  very  complete  resume  of 
what  was  said  "  pro  and  con  "  Dar- 
winism during  the  first  tifteen  ye.ars 
of  its  existence.  It  is  interesting 
to  see  what  a  small  part  French 
scientific  opinion  jilayed  during  that 
period  as  to  the  tlieoi'ies  of  descent 
and  mutability  of  species,  which  had 
both  their  origin  and  their  first  gi'eat 
exponents  in  France.  The  book 
does  not  appear  to  have  had  much 
influence  in  its  time,  but  more 
recently  the  criticisms  of  Wigand, 
von  Baer,  and  other  writers  seem 
to  receive  greater  attention  since 
the  central  biological  jjroblems  have 
been  pushed  into  the  foreground.  Of 


342 


SCIENTIFIC    THOUGHT. 


comparisons  refer  to  the  law  of  "  natural  selection," 
which  is  placed  in  parallel  with  Newton's  law  of 
"  universal  gravity."  Now,  although  "  natural  selec- 
tion," the  automatic  process  which  ensures  the  survival 
of  the  fittest  and  the  extinction  of  the  less  adaptive 
members  in  a  crowd  of  living  beings,  is  a  definite 
formula  which  allows  us  to  understand  and  clearly 
define  one  of  the  nlany  factors  which  are  at  work  in 
the  development,  in  the  genesis  and  growth,  of  living 
beings,  it  is  only  one.  It  is  not  a  prime  mover  or  force, 
like  the  force  of  gravity ;  it  is  a  check  upon  the  over- 
luxuriance  of  other  existing  forces  of  production  and 
development.  These  are  only  very  imperfectly  known ; 
whereas  Newton  not  only  discovered  the  "  law  of  gravita- 
tion," but  also  the  correct  expression  for  the  general  and 
all-pervading  laws  of  motion  which  obtain,  even  where 
gravitation  or  any  similar  force  ceases  to  be  a  valid  con- 
ception. Again,  Newton's  greatness  does  not  rest  on 
the  "  law  of  gravitation  "  alone,  but  much  more  on  the 
general  foundations  of  dynamics  and  natural  philosophy 
which  he  has  laid.  So  also  Darwin's  greatness  is  not 
limited  to  the  formula  of  "  natural  selection,"  but 
depends  on  the  novel  conception  which  he  has  intro- 
duced into  the  study  of  nature  on  the  large  scale  and  as 
a  whole,  viewing  it  as  a  scene  of  conflict  and  ceaseless 
development.  From  this  time  dates  the  study  of  nature 
as    a   whole  ^    in    contradistinction    to    that   of    natural 


this  I  shall  treat  in  the  next  chap- 
ter. See  also  the  various  writings 
of  Hans  Driesch,  such  as  'Analyt- 
ische  Theorie  der  organischen  Ent- 
wicklung'  (Leipzig,  1894);  'Die 
Biologic    als    selbstiindige    Grund- 


wissenschaft  (1893),  especially  p.  7 
of  the  latter. 

'  Though  this  was  prepared,  as 
Darwin  himself  points  out,  by  A. 
von  Humboldt. 


UN     JHK    OKNKTIC    VIEW    OF    NATl^RE. 


34:^ 


"  1 


problems. 


objects  and  processes.  The  general  laws  which  obtain 
in  this  great  field,  and  wliit-h  would  correspond  to 
Xewton's  laws  of  motion — the  laws  of  variation  and  of 
heredity — have  not  yet  been  discovered ;  but  it  is  again 
Darwin  more  than  any  other  naturalist  wlio  has  called 
attention  to  these  prime  movers  in  the  living  universe. 
He  has  pushed  into  the  foreground  the  two  great  problems        *o. 

,  Unsolved 

of  "  variation  "  and  "  beriMlity 

'  Darwin  in  his  subsequent  writ- 
ings urged  another  important  prob-  | 
leui,  to  which  he  had  ah'eady  in  his 
first  and  greatest  work  drawn  pass- 
ing attention.  This  is  the  agency 
of  "sexual  selection."  It  occupies 
by  far  the  larger  portion  of  his 
third  great  work,  wliich  appeared 
in  1871  with  the  title  '  The  Descent 
of  Man  and  Selection  in  Relation  to 
Sex.'  In  the  introduction  he  says, 
"  During  many  years  it  lias  seemed 
to  me  highly  probable  that  sexual 
selection  has  played  an  important 
part  in  differentiating  the  races  of 
man  ;  but  in  my  '  Origin  of  Species  ' 
I  contented  myself  by  merely  allud- 
ing to  this  belief.  When  1  came 
to  apply  this  view  to  man,  I  found 
it  indispensable  to  treat  the  whole 
subject  in  full  detail.  Professor 
Haeckel  is  the  sole  autlior  who, 
since  the  publication  of  the  '  Origin,' 
has  discu.ssed  in  his  various  works, 
in  a  very  able  manner,  the  subject 
of  sexual  selection,  and  has  seen  its 
full  importance."  The  problem  of 
".sexual  selection"  is  introduced  in 
the  '  Origin '  (p.  87)  in  the  following 
words  :  "  Inasmucli  as  i)eculiaritips 
often  appear  under  domestication 
in  one  sex,  and  become  hereditarily 
attached  to  that  sex,  the  same  fact 
probably  occurs  under  nature  ;  and 
if  so,  natural  selection  will  be  able 
to  modify  one  sex  in  its  functional 
relations  to  the  otlier  sex,  or  in 
relation  to  wholly  different  iiabits 
of  life  in  the  two  sexes,  as  is  some- 


times the  case  with  insects.  And 
this  leads  me  to  say  a  few  words 
on  what  I  call  Sexual  Selection. 
This  depends  not  on  a  struggle  for 
existence,  but  on  a  struggle  be- 
tween the  males  for  possession  of 
the  females  :  the  result  is  not 
death  to  the  unsuccessful  com- 
petitor, but  few  or  no  offspring. 
Sexual  selection  is  thus  less  rigor- 
ous than  natural  selection."  A 
great  deal  has  been  written  about 
sexual  selection,  and  in  general  it 
maj'  be  said  that  the  question  be- 
longs to  quite  a  different  category 
from  that  of  natui-al  selection. 
Some  of  the  foremost  champions  of 
the  latter  doctrine,  notabl}'  Mr 
Wallace,  reject  sexual  selection  as 
unnecessary  in  tlie  whole  scheme. 
The  characteristic  feature  of  natural 
selection  is  this,  that  it  is  a  purely 
automatic  process,  dependent  on 
overcrowding,  whereas  in  sexual 
selection  it  becomes  much  more 
difficult  to  see  how  the  process 
works  automatically.  Nowadays 
the  question  of  natural  selection 
is  hardly  any  longer  doubtful  ;  it 
is  a  fact.  As  to  sexual  selec- 
tion, the  statistical  proofs  that 
there  is  a  superabundance  from 
which  to  choose  are  still  wanting. 
To  understand  sexual  selection, 
or  even  to  define  it,  we  need 
to  form  some  conception  of  the 
reason  and  origin  of  sexual  differ- 
entiation, and  this  cannot  be  ar- 
rived at  without  a  theory  of  life 


344 


SCIENTIFIC    THOUGHT. 


And,  besides  this,  it  is  well  to  remember  that  Newton 
was  condemned  by  some  of  his  contemporaries  on  the 
basis  of  the  philosophy  of  Bacon ;  Fresnel  and  Young 
were  condemned  on  the  ground  of  Bacon  and  Newton 
combined.  In  like  manner  the  novel  line  of  reasoning 
adopted  or  largely  cultivated  by  Darwin  has  been 
attacked  as  being  opposed  to  Bacon,  Newton,  and  other 
great  thinkers  before  him.  In  all  these  cases  it  is  the 
results,  and  not  the  theory,  of  the  process  of  reasoning 
which  have  justified  its  continued  employment.  Without 
attempting  to  elaborate  the  parallel  too  minutely,  we 
may  say  that  as  Newton  created  Natural  Philosophy 
and  took  one  Inilliant  step  in  fixing  for  all  time  one  of 
the  great  laws  of  the  material  universe,  so  Darwin  has 
founded  the  study  of  nature  as  distinguished  from  that 
of  the  objects  and  processes  of  nature,  and  has  enunciated 
one  of  the  great  factors  which  obtain  in  the  living 
portion  of  nature :  through  him  a  history  of  nature,  the 
genetic  view  of  nature  on  a  large  scale  as  distinguished 
from  the  older  natural  history,  has  for  the  first  time 
become  conceivable.  The  word  history  indeed  suggests 
other  analogies.  Political  history,  what  we  ordinarily 
term  history  proper,  has  in  the  course  of  our  century 
undergone  changes  and  developments  similar  to  those  in 
the  history  of  nature.  Confined  once  to  a  casual,  un- 
methodical, uncritical,  and  incomplete  record  of  isolated 


which  rests  ou  something  more 
than  the  two  purely  statistical  or 
numerical  facts  of  overcrowding 
and  of  variation — i.e.,  the  fact  that 
no  two  individuals  are  absolutely 
alike.  The  importance  of  the 
phenomenon  of  sex  in  the  economy 
of  living  nature  has  been  studied, 


and  given  rise  to  many  theories. 
A  very  good  account  of  these  will 
be  found  in  P.  Geddes  and  J.  A. 
Thomson,  'The  Evolution  of  Sex,' 
1889.  In  the  following  chapter, 
where  I  deal  with  the  various 
attempts  to  define  "  Life,"  I  shall 
revert  to  this  subject. 


ON    THE    GENETIC    VIEW    OF    NATURE. 


345 


events  or  biographies,  it  lias  Iteen  gradually  united  and 
organised  as  a  whole,  largely  through  the  same  judicial 
sifting  of  manifold  ovidenec  and  clalioration  of  critical 
methods  of  research.  Of  this  1  hope  to  treat  in  a 
different  portion  of  this  work :  here  1  only  wish  to 
diaw  attention  to  the  enlarged  aspect,  which  in  both 
instances  has,  through  the  same  process  of  development,  41. 
come  over  our  studies.      When  once  we  rise  from   the  on  a  large 

scale. 

contemplation  and  examination  of  details  and  single  facts, 
and  grasp  the  connection  and  economy  of  the  whole  as 
a  subject  worthy  of  special  attention,  we  involuntarily  in- 
troduce two  new  elements  into  our  research — the  element 
of  conjecture  and  the  element  of  speculation.  The  former 
is  needed  to  fill  up  the  many  gaps  which  we  find  in  the 
actual  records  when  we  wish  to  string  them  together  into 
a  united  and  intelligible  whole ;  the  latter  is  the  inquiry 
into  the  general  principles  which  underlie  any  and  every 
development  of  the  kind  we  have  in  view.  The  creation 
l)y  Darwin  of  the  science  and  history  of  nature,  as  dis- 
tinguished from  the  science  and  history  of  natural  ob- 
jects and  single  processes,  has  been  accompanied  and 
strengthened  by  the  appearance  of  conjectural  and  specu- 
lative attempts ;  just  as  the  cultivation  of  the  science 
of  general  history  has  gone  hand  in  hand  with,  and 
has  been  supported  by,  the  brilliant  results  of  philo- 
logical  conjecture  and  the    philosophy  of   history.^      Of 


'  In  an  el()i|Ueiit  passage  Professor 
Parker  coiiipaies  the  work  of  the 
naturalist  of  to-day  with  tliat  of 
the  pliih)logist.  This  passage  occurs 
in  his  Memoir  on  the  Fowl  (18ti8), 
and  is  (juoted  in  his  book  '  On  tlie 
Morphology  of  the  Skull '  (by  Parker 
and  Bettany,  London,  1877,  p.  362): 


"  Whilst  at  work  I  seemed  to  my- 
self to  iuive  been  endeavouring  to 
decipher  a  palimpsest,  and  one  not 
erased  and  written  upon  again  just 
once  but  five  or  six  times  over. 
Having  erased,  as  it  were,  the 
characters  of  the  culminating  type 
— those  of  the  gaudy  Indian  bird 


346 


SCIExNTIFIC    THOUGHT. 


these  I  shall  treat  elsewhere.  It  may  be  a  question 
capable  of  very  opposite  answers  whether  the  philosophy 
of  history,  such  as  it  has  been  offered  in  the  brilliant 

42.  generalisations  of  Kant,  Herder,  Hegel,  and  Buckle,  has 

Philosophi- 

caitheories.  really  aided  the  science  of  history  proper;  whereas  no 
question  can  arise  as  to  the  indispensable  service  that 
has  been  rendered  to  historians  by  the  criticism  and 
conjectural  emendation  of  texts  and  other  monuments 
of  antiquity.  With  Darwinism  the  matter  stands  dif- 
ferently :  no  person  who  peruses  the  great  and  increasing 
literature  of  the  subject  can  deny  the  enormous  assist- 
ance which  the  philosophical  ideas  of  evolution  have 
rendered  to  the  cause  of  Darwinism — how  the  latter, 
when  it  appeared,  found  ready  made,  though  then  only 
slightly  appreciated,  the  philosophical  canons  and  terms 
which  were  so  well  fitted  to  its  systematic  enunciation 

43.  and  literary  mise   en  scdne.     This  was  the  independent 
Spencer.       work  of  Mr  Herbert  Spencer.^     The  other  well-known 


— I  seemed  to  Vie  among  the  sombre 
grou.se  ;  and  then,  towards  incuba- 
tion, the  characters  of  the  sand- 
grouse  and  hemipod  stood  out  be- 
fore me.  Rubbing  these  away  in 
my  downward  work,  the  form  of 
the  tinamou  looked  me  in  tlie  face  ; 
then  the  aberrant  ostricli  seemed  to 
be  described  in  large  archaic  char- 
acters ;  a  little  while  and  these 
faded  into  what  could  just  be  read 
off  as  pertaining  to  the  sea-turtle  ; 
whilst  underlying  the  whole  the 
fish  in  its  simplest  myxinoid  form 
could  be  traced  in  morphological 
hieroglyphics. " 

'  The  part  and  position  which 
belongs  to  Mr  Herbert  Spencer  in 
the  history  of  evolution  as  a  scien- 
tific doctrine  has  not  yet  received 
due  attention  or  adequate  recogni- 


tion. There  is,  however,  no  doubt 
that  the  principal  features  of  the 
genetic  view  of  natural  phenomena 
were  clearly  before  his  mind  as 
early  as  1852,  when  he  wrote  his 
short  essay  on  "  The  Development 
Hypothesis  "  in  '  The  Leader,'  re- 
published in  the  first  volume  of  his 
'  Collected  Essays. '  It  has  been 
pointed  out  by  Romanes  ('  Darwin 
and  After  Darwin,'  vol.  i.  p.  257) 
that  though  the  attempts  towards 
a  genetic  conception  of  organic 
nature  were  numerous,  if  not 
abundant,  before  Darwin,  yet  this 
view  only  broke  through  and  be- 
came dominant  on  the  appearance 
of  the  theory  of  natural  selection. 
He  says  :  "  If  we  may  estimate  the 
importance  of  an  idea  by  the  change 
of    thought   which    it    eflfects,    this- 


ON    THE    GENETIC    VIEW    OF    NATURE. 


347 


name  which  is  so  frequently  associated  with  Darwin, 
especially  in  Germany,  is  that  of  Professor  Haeckel, 
whose  '  Generelle  Morphologic  '  and  '  History  of  Creation  ' 
have  done  much  to  introduce  the  spirit  of  Darwinism 
into  German  literature.      These  works  also  represent  the 


44. 

Haeckel. 


idea  of  natural  .selection  is  unques- 
tionably the  most  iinpoi-Uuit  idea 
that  has  ever  been  conceived  by  the 
niiud  of  man.  Yet  the  wonder  is 
that  it  should  not  have  been  hit 
upon  long  before  ;  "  and  after  re- 
ferring to  the  forgotten  antici- 
pations of  WelLs  and  Matthew, 
Romanes  proceeds :  "  Still  more 
remarkable  is  the  fact  that  Mr 
Herbert  Spencer  —  notwithstand- 
ing his  great  powers  of  abstract 
thought  and  his  great  devotion  of 
those  powers  to  the  theory  of  evo- 
lution, when  as  yet  this  theory  was 
scorned  by  science  —  should  have 
missed  what  now  appears  so  ob- 
vious an  idea."  In  this  connection 
it  is  interesting  to  note  how  those 
general  canons  of  evolutionary 
thought  which  were  established  by 
Spencer  before  the  publicjilion  of 
the  '  Origin '  were  brought  into 
general  recognition  by  scientific 
men  only  when  the  definite  mathe- 
matical or  statistical  formula  of 
natural  selection  was  announced, 
and  that,  after  the  lapse  of  a  whole 
generation,  it  is  not  this  precise 
formula  but  the  general  conception 
of  evolution  wdiich,  according  to 
many  of  the  foremost  naturalists, 
will  obtain  ;  the  part  which  natural 
selection  i>la}'s  being  uncertain  and 
variously  estimated  by  the  many 
adherents  of  the  theory  of  evolu- 
tion. See,  inter  alia,  the  article  on 
'•  Evolution  in  Biology  "  by  Huxley 
in  the  '  Ency.  Brit.,'  9th  ed.,  vol. 
viii.  p.  7.51:  "How  far  natural 
selection  suffices  for  the  production 
of  species  remains  to  be  seen.  Few 
can   doubt  that,  if  not  the  whole 


cause,  it  is  a  very  important  factor 
in  that  operation.  .  .  .  The  im- 
portance of  natural  selection  will 
not  be  impaired  even  if  further 
inquiries  should  prove  that  varia- 
bility is  definite  and  is  determined 
in  certain  directions  rather  than  in 
others  by  conditions  inherent  in 
that  which  varies."'  See  also  the 
Address  of  Lord  Salisbuiy  at  the 
meeting  of  the  Brit.  Assoc,  at  Ox- 
ford iu  1894,  and  the  subsequent 
remarks  of  Huxley  in  .seconding  the 
vote  of  thanks  ('Life  of  Huxley,'' 
vol.  ii.  p.  378) :  "  The  essence  of 
this  great  work  (the  '  Origin  of 
Species')  may  be  stated  summarily 
thus :  it  affirms  tlie  mutability  of 
species  and  the  descent  of  living, 
forms,  separated  liy  differences  of 
more  than  varietal  value,  from  one- 
stock.  .  .  .  And  yet  it  is  also  true 
that  if  all  the  conceptions  promul- 
gated in  the  'Origin  of  Species' 
which  are  peculiarly  Darwinian 
were  swept  away,  the  theory  of 
the  evolution  of  animals  and  plants 
would  not  be  in  the  slightest  degree 
shaken."  In  fact,  the  general  prin- 
ciples of  mechanical  evolution,  as 
first  systematised  by  Mr  Spencer, 
received  recognition  only  through  a 
definite  formula,  but  may,  after  all, 
survive  that  special  doctrine.  It 
is  further  very  evident  how  the 
parallel  with  Newton's  formula  of 
gravitation  entirely  breaks  down  if 
we  look  at  matters  in  this  light  : 
every  subsequent  discovery  having 
only  tended  to  confirm  that  special 
mathematical  relation,  and  proved 
the  all-important  part  it  plays  in 
nature. 


348 


SCIENTIFIC    THOUGHT. 


first  brilliant  attempt  to  fill  up  conjecturally  the  broken 
lines  of  development  and  descent  as  the  Darwinian  con- 
ception of  living  nature  postulates  them.^  As  a  first 
and  daring  approximation,  they  deserve  to  .have  assigned 
to  them  a  prominent  place  in  the  history  of  the  scien- 
tific thought  of  our  age.  In  elaborating  his  pedi- 
grees, Professor  Haeckel  has  taken  up  and  more  clearly 
defined  the  analogy  between  the  development  of  the 
■embryo  in  the  higher  organisms  and  the  supposed  transi- 
tion from  lower  to  higher  forms  which  is  found  in  the 
classification  of  the  genera  or  species  of  animals  and 
plants.  He  has  termed  this  analogy  the  great  law  of 
biogenesis,  of  the  development  of  life  in  the  individual 
(to  6v),  and  the  species  or  tribe  (to  cjjvXov),  expressed 
also  as  the  parallelism  of  ontogenesis  and  phylogenesis. 
Long  before  Darwin  and  the  appearance  of  the  theory  of 
descent  this  analogy  -   was  pointed  out  in  a  restricted 


^  The  later  editions  of  the  '  Origin 
of  Species '  contain  the  following 
reference  to  Haeckel  (6th  ed.,  p. 
381) :  "  Prof.  Haeckel,  in  his  '  Gen- 
erelle  Morphologic,'  and  in  other 
works,  has  brought  his  great  know- 
ledge and  abilities  to  bear  on  what 
he  calls  phylogeny,  or  the  lines  of 
descent  of  all  organic  beings.  In 
drawing  up  the  several  series  he 
trusts  chiefly  to  embryological  char- 
acters, but  receives  aid  from  homo- 
logous and  rudimentary  organs,  as 
well  as  from  the  successive  periods 
at  which  the  various  forms  of  life 
are  believed  to  have  first  appeared 
in  our  geological  formations.  He 
has  thus  boldly  made  a  great  be- 
ginning, and  shows  us  how  classi- 
fication will  in  the  future  •  be 
treated."  And  Huxley  (art.  "  Evo- 
lution," p.  752)  says:  "Whatever 
hesitation    may   not    unfrequently 


be  felt  by  less  daring  minds  in 
following  Haeckel  in  many  of  his 
.speculations,  liis  attempt  to  sys- 
tematise the  doctrine  of  evolution, 
and  to  exhibit  its  influence  as  the 
central  thought  of  modern  biology, 
cannot  fail  to  have  a  far-reaching 
influence  on  the  progress  of 
science." 

^  As  to  the  early  anticipations  of 
this  so-called  "law  of  biogenesis," 
they  are  given  with  more  or  less 
completeness  by  many  modern 
writers,  such  as  Huxley  in  his 
article  on  Evolution  (1878,  '  Ency. 
Brit.'),  P.  Geddes  (ibid.,  art.  "Re- 
production "),  Yves  Delage  ('  L'Her- 
ddite,'  &c.,  p.  159),  J.  A.  Thomson 
('The  Science  of  Life,'  p.  133,  &c.) 
The  most  important  earlier  state- 
ment is  that  quoted  by  Huxley 
from  Meckel's  '  Entwurf  einer  Dar- 
stellung  der  zwischen  dem  Embryo- 


ON    TIIK    fJENKTIC    VIEW    OF    NATURE. 


349 


sense  liy  Meckel,  mui  iUa-i,  jukI  Series.  It  h.as  some- 
times been  termed  von  liaer's  law,  tlmuiih  mui  IJaer 
very  carefully  guarded  himst'll'  against  many  ]»o])ular 
versions  of  the  analogy,  appl}  iug  it  only  wiihin  the 
limits  of  the  fonr  great  groups  or  plans  of  organisation 
into    which    he    divided    the    animal    kingdom.^      In    his 


zustande  der  hiilieren  Thioro  uud 
dem  permaneiiten  der  niederen 
stattfindenden  Parallele '  (1811): 
"There  i.-*  no  good  phyt^iologist  who 
has  not  been  struck  by  tlie  observa- 
tion that  the  original  form  of  all 
organisms  is  one  and  the  same,  and 
that  out  of  this  one  form  all,  the 
lowest  as  well  as  the  highest,  are 
developed  in  such  a  manner  that 
the  latter  pass  through  tlie  per- 
manent forms  of  the  formei-  as 
transitory  stages.  Aristotle,  Hal- 
ler,  Harvey,  Kielmeyer,  Autenrieth, 
and  many  others,  have  either  made 
this  observation  incidentally,  or, 
especially  the  latter,  have  drawn 
particular  attention  to  it,  and 
drawn  therefrom  results  of  per- 
manent importance  for  physiology'. '" 
Louis  Agassiz,  in  his  celebrated 
"Essay  on  Classification"  (1859), 
though  rejecting  the  doctrine  of 
descent,  "insisted,  nevertheless,  on 
the  correspondence  between  stages 
in  embryonic  development  and  the 
grades  of  differentiation  expressed 
in  the  classification  of  living  and 
extinct  animals  "  (Thomson,  '  The 
Science  of  Life,'  j).   134). 

^  "  A  careful  examination  of  von 
Baer's  '  laws '  shows  that  he  did 
not  accept  the  recapitulation  with- 
out many  saving  clauses.  He  be- 
lieved in  it  much  less  than  many 
a  modern  embryologist,  such  as  F. 
M.  Halfour  or  A.  Milnes  Marshall '" 
(Thomson,  j).  133).  Before  the 
puljlication  of  Haeckel's  '  Generelle 
Morphologic '  the  naturalist  who 
seems  to  have  most  clearly  ex- 
pressed   the    recapitulation    theory 


was  Fritz  Midler,  who  in  1864 
published  his  famous  tract  '  P'iir 
Darwin,'  which  appeared  in  1868 
in  an  English  translation  by  Dallas, 
with  the  title  'Facts  and  Argu- 
ments for  Darwin.'  The  work  of 
Fritz  Jlilller,  who  for  many  years 
lived  in  the  Brazils,  isolated  and 
secluded,  and  devoted  to  scientific 
observation,  was  welcomed  by  Dar- 
win as  one  of  the  first  and  greatest 
supports  to  his  doctrine :  the 
author  was  singled  out  by  him  as 
the  "prince  of  observers,"  and 
frequently  referred  to  in  the  latei- 
editions  of  the  'Origin  of  Species." 
Delage  considers  him  to  have  first 
expressed  the  fundamental  bio- 
genetic law  (' L'Heredite,'  pp.  ITjO, 
469),  and  this  is  in  agj-eement  with 
Haeckel's  own  declaration  in  the 
13tli  chapter  of  the  '  Historj'  of 
Cieation.'  It  is,  however,  well  to 
mention  that  the  recapitulation 
theory  has  found  little  favour  w  ith 
botanists  ;  that  Haeckel  himself 
admits  that  the  parallelism  be- 
tween ontogenesis  and  phylogenesis 
is  general  and  not  exact ;  that  there 
is  a  tendency  to  abbreviation  ;  that 
recent  adaptations  (called  by  him 
"  kainogenetic  ')  may  mask  more 
ancient  ("palingenetic '")  features, 
&c.  See  J.  A.  Thomson,  'The 
Science  of  Life,'  p.  13.').  Ziegler, 
in  his  recent  excellent  leview  of 
the  '  Present  Position  of  the  Doc- 
trine of  De.xcent '  (Jena,  1902,  p.  12), 
admits  that  the  theory  of  paral- 
lelism has  "  perhaps  not  realised 
all  the  expectations "  which  were 
cherished  thirty  years  ago. 


350  SCIENTIFIC    THOUGHT. 

time  also  no  attempt  was  made  to  bring  phytogenesis 
— the  genesis  of  plant-life  —  into  line  and  order  with 
zoogenesis,  the  genetic  arrangement  of  animals.  It  is 
Haeckel's  undoubted  merit  to  have  attempted  for  the 
first  time  to  carry  out  this  general  scheme  on  a  large 
scale,  and  by  means  of  detailed  pedigrees,  beginning 
with  the  undefined  organisms  in  which  as  yet  the 
peculiar  characters  of  animal-  and  plant -life  do  not 
appear  to  be  differentiated,  and  ascending  in  two  great 
trunks  into  the  vegetable  and  animal  kingdom,  and 
thence  through  many  ramifications  into  the  several 
classes,  families,  genera,  species,  and  varieties  of  living 
things,  to  construct  the  supposed  real  natural  system 
for  which  systematists  had  been  unconsciously  searching 
since  the  age  of  Eay  and  Linnaeus.  For  the  purpose  of 
elaborating  this  great  scheme  he  employs  not  only  the 
great  law  of  heredity,  according  to  which  ancestral 
characters  are  reproduced  in  development,  but  also  the 
older  law  of  adaptation  to  the  existing  environment,  as 
45.        pointed  out  by  Lamarck.      Haeckel,  in  fact,  combines  the 

Combines 

Darwin  and  vicws  of  Darwiu  and   Lamarck,  which  other  naturalists 

Lamarck. 

are  more  or  less  inclined  to  keep  apart,  whence  has 
arisen  the  well-known  division  into  the  two  great  schools 
of.  the  neo-Darwinians   and  neo-Lamarckians.^     Though 


^  Natural  selection  being  an  ad- 
mitted fact  among  living  things, 
like  gravitatiiin  in  the  physical 
universe,  three  distinct  f)roblems 
arise :  First,  how  far  does  it  reach  ? 
the  scope  of  the  principle.  The 
^^ubsequent  writings  of  Darwin  were 
mainly  occupied  with  this  question, 
though — as  we  shall  see  later — he 
also  ventured   upon    an    important 


suggestion  as  to  the  underlying 
problem  of  inheritance.  Secondly, 
the  fact  or  principle  itself  requires 
to  be  traced  to  deeper-lying  causes. 
We  may  say  natural  selection  is  a 
vera  causa,  but  not  a  pi-ima  cmisa  : 
it  is  a  true  but  not  a  prime  cause. 
The  investigations  regarding  "  varia- 
tion "  and  "  heredity  "  work  along 
this  line  of  research,   and  form  the 


ON    THK    fiKNKTKJ    VIKW    oK    NATTRE. 


351 


Haeckel's    work    is,  as    he    hiinsell'    admits,    highly    con- 
jectural,^ it  has  done  much  to  extend  and  po})ulahse  the 


whole  domain  of  moderu  post- 
Darwinian  biology.  The  {)roblem 
is  far  from  being  solved,  though  it 
is  perhaps  nearer  a  solution  than 
the  question  as  to  the  cause  of 
gravitation.  Thirdly,  there  is  the 
ambitious  attempt  to  construct  a 
general  philosophy  of  life  by  means 
of  the  new  principle,  or  some  modi- 
fication or  amplihcation  of  it.  After 
>.'ewt(jn  had  discovered  universal 
giaviuition,  the  attempt  was  made 
by  Boscovich  and  the  French  school 
of  mathematical  jihysics  to  use  the 
idea  of  attraction  at  a  distance  as  a 
general  [)hysical  theory.  Of  those 
who,  before  or  after  Darwin,  at- 
tempted the  more  ambitious  task, 
we  may  take  Herbert  Spencer,  Ernst 
Haeckel,  and  Niigeli  as  three  dis- 
tinct representatives.  They,  how- 
ever, agree  in  one  point — viz.,  in 
considering  natural  selection  to  be 
insufficient,  and  in  admitting  other 
agencies,  which  are  largely  drawn 
from  the  suggestive  writings  of 
Lamarck.  The  section  of  these 
philoso])hical  writers  who  consider 
Lamarck's  principles  to  be  more 
fundamental  than  Darwin's,  and 
who  are  laigely  repiesented  by 
American  naturalists  (notably  E. 
T>.  Cope  and  A.  Hyatt),  are  called 
111 '  i-Lamarckians.  The  best  account 
of  their  views  will  be  found  in  the 
last  chapter  of  Profes.sor  Packard's 
})ook,  '  Lamarck,  the  Founder  of 
Evolution'  (1901).  The  following 
passage  quoted  there  (p.  391)  from 
a  much  earlier  memoir  (1877)  gives 
a  very  clear  account  of  the  reason- 
ing of  this  school :  "  Darwin's 
phra.se,  '  natural  selection,'  or  Her- 
bert Sjiencer's  term,  '  survival  of 
the  fittest,'  expresses  simply  the 
final  result,  while  the  process  of 
the  origination  of    the    new    forms 


which  have  survived,  or  been 
selected  by  nature,  is  to  be  ex- 
plained by  the  action  of  the  physi- 
cal environments  of  the  animals, 
cou{)led  with  inheritance  -  force. 
The  |)hrase8  quoted  have  Vieen  mis- 
used to  sUite  the  cause,  when  they 
simply  express  the  result  of  the 
action  of  a  chain  of  causes  which 
we  may,  with  Herbert  Spencer, 
call  the  'environment'  of  the 
organism  undergoing  modification  : 
and  therefore  a  form  oi  Lamarck- 
ianism,  greatl}'  modified  by  recent 
scientific  discoveries,  seems  to  meet 
most  of  the  (lifiticulties  which  arise 
in  accounting  for  the  origination  of 
species  and  higher  groujis  of  organ- 
isms." It  is  also  well  to  note  that 
Mr  Wallace,  though  not  a  Lamarck- 
ian,  considers  the  principle  of  nat- 
ural selection  insufficient  especi- 
allj'  to  explain  the  higher  develop- 
ments of  mental  life.  (See  'Dar- 
winism,' p.  463,  &c.) 

'  "  It  is  evident  that  our  '  phyl- 
ogeny '  is  and  remains  an  edifice 
of  hypotheses  in  the  same  way  as 
her  sister,  historical  geology.  For 
she  tries  to  gain  a  connected  view 
of  the  course  and  causes  of  events 
long  past,  the  direct  invest igati<jn 
of  which  is  impossible.  Neither 
observation  nor  experiment  can 
give  us  direct  information  regard- 
ing the  endless  processes  of  change 
through  which  the  existing  animal- 
and  plant -forms  have  emerged  out 
of  lengthy  ancesti'al  stages.  .  .  . 
The  empirical  documents  of  our 
history  of  descent  will  always 
remain  lai-gely  incomplete,  however 
much  through  continued  discoveries 
our  region  of  knowledge  of  individ- 
ual things  may  increase."  (Haeckel, 
*  Systematische  Phylogenie,'  1894, 
vol.  i.  preface,  ]).  vi.) 


352 


SCIENTIFIC    THOUGHT. 


46. 
Philosoph- 
ical prob- 
lems. 


47. 
Problem  of 
life. 


genetic  view  of  nature,  drawing  likewise  into  this  circle 
of    ideas    the    great    departments    of    anthropology   and 
geography  ;  in  fact,  it  amounts  to  rewriting  the  '  Kosmos  ' 
of  Humboldt  on  genetic  instead  of  on  purely  descriptive 
lines.       But   in    perusing  these   and  similar  writings  of 
modern    times,    we   feel   on    the    one    side    that   we   are 
gradually  getting  out  of   the  depths  of  science,  not  only 
into   the  domain  of  conjecture,   without  which  a  know- 
ledge  of  the  past  cannot  be  gained,  but    also   into   the 
regions    of     philosophical    thought,    which    proceeds    on 
other  lines   than  those  prescribed  to  science,  and  which 
will  claim    our   attention    in    a    special    portion    of    this 
work.      On   the  other  side,  in  using  so  confidently  the 
ideas    of   descent   and  adaptation,   we    feel   that  we  are 
appealing    to    two    great    empirical    facts,    the    facts   of 
heredity  and  of  variation  of  living  things,  on  which  the 
genetic    view    of    nature,    when    applied    to    the    living 
portion  of  creation,  rests,  but  which  are    scarcely  even 
defined  in  clear  terms,  much    less  explained.      In  fact, 
we  are  face  to  face  with  the  problem  and  definition  of 
life   itself.      Neither  the  morphological  nor  the   genetic 
view  of  nature  is  limited  to  the  living  world,  although 
both  views  originated   there,  and  were  from  thence  ex- 
tended to  the  larger  domain  of  inorganic  and  cosmical 
phenomena.       Into    these    larger    views    which    try    to 
grasp  the  forms  of  nature  in  their  apparent  rest  or  in 
their    endless    change    and    history,    the   phenomena    of 
life  have  been  fitted  by  the  help  of  three  definite  con- 
ceptions—  the  conception    of    the   cell   as   the  morpho- 
logical  basis   or   unit   of   all   life,  and  the  two  concep- 
tions   of    inheritance    and    variation,    by    which    living 


ON    THK    GENETIC    VIEW    OF    NATUKE. 


353 


t'orias  are  partiall}'  nuiintained  and  cuiiLiuuou.sly  altered.^ 
These  three  conceptions  deserve  and  have  received  special 
attention  by  a  class  of  students  who,  since  the  begin- 
ning of  the  nineteenth  century,  have  termed  themselves 
biologists.  On  what  lines  of  reasoning  their  studies 
liave  been  conducted,  and  to  what  general  results  they 
iiave  led,  I  propose  to  discuss  in  the  following  chapter, 
which  might  be  appropriately  entitled  the  "  Biological 
view  of  Nature "  in  the  narrower  sense  of  the  term. 
In  order  to  distinguish  the  studies  which  I  shall  have 
to  deal  with  in  that  chapter  from  those  which  have 
occupied  us  in  this  and  the  last  chapter,  which  deal 
largely  but  not  exclusively  with  li\ing  things,  I  have 
preferred    to   give    to  it   the   title,  "  On   the  Vitalistic  - 


^  To  these  —  according  to  some 
naturalists  —  might  be  added  the 
factor  of  adaptation,  so  prominent- 
ly put  forward  by  Lamarck  and 
his  followers.  But  adaptation  is 
one  of  the  causes  of  variation,  as 
natural  selection  is  a  consequence. 
The  latter  is  a  physical  necessity 
wherever  overcrowding  exists  ; 
whereas  the  scope  of  adaptation, 
which  is  an  undeniable  fact  so  far 
as  individuals  are  concerned,  is, 
so  far  as  it  regards  inheritance — 
i.e.,  the  development  of  the  race — 
a  much  controverted  question.  It 
comes  under  the  larger  problem 
of  the  influence  of  enviionment, 
and  will  occupy  us  again  in  later 
chapters.  Among  the  most  valu- 
able contributions  to  this  subject 
are  Mr  Herbert  Spencer's  articles 
on  the  "  Factors  of  Organic  Evolu- 
tion," published  in  the  'Nineteenth 
Century  '  in  1886,  and  separately, 
with  additions,  in  1887.  In  these 
essays  he  also  shows  how  Darwin 
himself  in  his  later  writings  in- 
cludes the  influence  of  environ- 
ment   as    an    important   factor    in 

VOL.   11. 


development.      (See   p.   29  xqq.   of 
the  reprint.) 

-  As  the  two  terms  "  biological " 
and  "  vitalistic  "  might,  according 
to  their  etymology,  mean  the  same 
thing,  it  may  he  appropriate  to 
offer  some  explanation  of  the 
reasons  which  have  induced  me 
to  adopt  the  latter  term  for  the 
purpose  indicated  in  the  text. 
Biology  means  the  science  of  life. 
This  can  only  be  studied  in  living 
things.  Living  things,  however, 
are  formed  entirely  of  the  same 
elementary  substances  as  we  find  in 
inorganic  or  not  living  things,  and 
are  very  lai-gely  formed  through  the 
same  chemical  and  physical  pro- 
cesses as  we  tind  among  the  latter. 
And  as  our  scientific  —  i.e.,  exact, 
accurate,  and  useful  —  knowledge 
has  all  begun  with  the  study  of 
inorganic  phenomena,  it  is  natural 
that  biologi.sts  should  have  attacked 
the  problems  of  living  nature  from 
the  side  of  the  similarity  or  same- 
ness which  they  presented  when 
compared  with  lifeless  nature. 
The    main    progress    in    physiology 

Z 


354 


SCIENTIFIC    THOUGHT. 


view  of  Nature."  Clearly  both  the  morphological  and 
the  genetic  views  of  nature  remain  incomplete  unless 
they  embrace  the  forms  and  the  processes  of  life.  It 
is  the  problem  from  which  both  started  and  to  which 
both  lead.  They,  as  it  were,  presuppose  its  possible 
solution.  Let  us  see  what  has  been  done  in  the  course 
of  our  century  to  effect  it. 

Before  we  do  this  it  is  well  to  draw  attention  to 
the  great  strengthening  which  the  genetic  or  develop- 
mental view  of  natiu-e  has  received,  since  the  time  of 
Darwin,  from  other  quarters — notably  from  that  of 
general  physics  and  chemistry  in  their  application  to 
geology  and  astrophysics.-^ 


and  medicine  during  the  last  hun- 
dred years  has  come  from  that 
quarter.  This  large  class  of  studies 
can  be  carried  ou  without  facing 
the  problem  of  life  at  all  ;  and  thus 
it  happens  that  we  may  have  a  very 
large  biological  literature  in  which 
the  word  life  hardly  occurs,  and 
in  which  we  seek  in  vain  for  a 
definition  of  life.  "We  must,  there- 
fore, have  a  term  which  singles  out 
from  the  enormous  mass  of  bio- 
logical literature  that  smaller  por- 
tion which  professedly  deals  with 
those  properties  and  phenomena 
which  are  peculiar  to  the  living  as 
distinguished  from  the  lifeless  crea- 
tion. I  have  chosen  for  this  purpose 
the  term  vitalistic ;  but  I  may 
not«  that  in  using  it  I  do  not  limit 
myself  to  that  class  of  thinkers 
who  are  usually  termed  "  Vitalists," 
because  they  are  led  to,  or  start 
with  the  assumption  of,  a  special 
vital  principle.  Even  those  who, 
in  studying  the  phenomena  of  life, 
arrive  at  or  start  from  the  denial  of 
.such  a  principle  are  included  under 
the  vitalistic  view,  just  as  Kant  is 
rightly    termed     a     metaphysician 


although  the  outcome  of  his  phil- 
osophj'  may  be  considered  to  be 
the  destruction  of  metaphysics  in 
the  sense  which  was  current  in 
his  age. 

^  A  general  scheme  of  evolution, 
or  of  development  as  it  was  more 
frequently  termed,  which  would 
embrace  equally  cosmical  and  ter- 
restrial processes,  the  lifeless  and 
living  world,  was  clearly  before  the 
mind  of  Schelliug  and  his  followers, 
notably  Oken  and  Steffens.  The 
vagueness  and  extravagancies  of 
this  school  brought  the  idea  into 
discredit,  and  the  remedy  applied 
by  Hegel,  to  put  a  logical  process  in 
the  place  of  fantastic  suggestions, 
ruined  it  utterly  in  the  eyes  of  the 
cultivators  of  exact  research.  Only 
very  few  of  the  great  students  of 
organic  development,  but  among 
them  the  greatest,  von  Baer,  re- 
tained a  just  appreciation  of  the 
great  aims  of  Schelling.  The  study 
of  development  abroad  was  almost 
entirely  limited  to  embryology.  In 
other  sciences  the  "statical"  aspect 
ruled  supreme.  In  the  face  of  this 
somewhat     retrograde     movement 


ON    THE    GENETIC    VIEW    OF    NATURE. 


355 


In  the  second  chapter  ul'  this  vuhnue,  which  treated  of        48. 

Oi'iiftic  view 

the  ijhysical  view  of  nature,  and  developed  the  various  »tr.iiKih- 

i     ''  '  '^  fiail  by 

ideas  wliich  chister  arouiul  the  term  "  energy,"  I  sliowed  {.'J.'J^'l^t^'"' 
how,  in  the  middle  oi  the  century,  through  the  intro- 
duction of  these  ideas,  a  new  clue  w^as  gained  wherewith 
to  penetrate  the  connection  of  natural  phenomena  in 
time  and  space.  Before  that  time  the  conservation  of 
matter,  the  rule  that  matter  can  neither  be  lost  ncjr 
created,  guided  research  by  trying  to  account  for  the 
apparent  loss  or  gain  of  matter  whenever  and  wherever 
changes  take  yjlace  in  the  material  world.  The  science 
of  chemistry  with  its  instrument  the  balance  was  built 
on  the  foundation  of  this  axiom.  When,  through  the 
labom's  of  ]\Iayer,  Helmholtz,  and  Joule,  the  further 
axiom  became  established  that,  besides  matter,  there 
exists  in  the  material  universe  a  second  quantity  (or 
substance)  termed  "  energy,"  which,  like  matter,  can  Ijc 
changed,  but  which,  like  matter,  can  neither  be  created 
nor  annihilated,  the  questions  began  to  be  asked,  "  If  we 


abroad,  the  merit  of  Mr  Spencer 
in  urging  the  '"  dynamical "  aspect 
long  before  the  '  Origin  of  Species ' 
put  forward  a  delinite  niedianical 
agency  is  so  much  greater,  and  he 
himself  says  {'  Factors  of  Organic 
Evolution,'  p.  5) :  "  Of  the  few 
.  .  .  who,  espousing  the  belief  in 
a  continuous  evolution,  had  to  ac- 
count for  this  evolution,  it  must  be 
said  that  though  the  cause  assigned 
(viz.,  the  modification  of  structures 
resulting  from  modification  of  func- 
tions) was  a  true  cause,  ...  it 
left  unexplained  the  greater  i)art 
of  the  facts.  Having  been  myself 
one  of  these  few,  I  look  back  with 
surprise  at  the  way  in  which  the 
facts  which  were  congruous  with 
tlic  espoused  view  monopolised  con- 


sciousness and  kept  out  the  facts 
which  wei'c  incongruous  with  it — 
conspicuous  though  many  of  them 
were."  Mr  Spencer  was  also 
probably  the  first  who  defined  in 
mechanical  terms,  applicable  to 
cosmical,  lifeless,  and  living  pheno- 
mena alike,  the  process  of  develop- 
ment, adopting  the  term  evolution. 
This  fitting  of  the  process  of  or- 
ganic development  into  tlie  general 
formula  of  evolution,  and  the  sub- 
sequent announcement  by  Darwin 
of  the  mechanical  agency  of  over- 
crow<ling  and  selection,  has  had 
the  effect  of  strengthening  im- 
mensely the  genetic  view  of  nature, 
but  also  of  obscuring  and  pushing 
into  the  background  the  special 
prol)lcm  of  life. 


356  SCIENTIFIC    THOUGHT. 

receive  energy,  where  does  it  come  from  ?  if  we  lose 
energy,  where  does  it  go  to  ? "  It  was  recognised  that 
the  great  store  of  energy  on  which  we  at  present  depend 
is  the  heat  of  the  sun,  which  is  partly  used  or  wasted  by 
daily  radiation,  partly  stored  in  the  separated  energies 
of  chemical  substances,  such  as  were  produced  by  the 
agency  of  solar  heat  in  bygone  ages ;  the  deposits  of 
coal  in  the  bowels  of  the  earth  being  a  prominent 
and  important  example.  Where  does  the  heat  of  the 
sun  come  from,  and  how  is  it  maintained  ?  These  were 
some  of  the  questions  which  began  to  be  asked.  The 
genesis  of  the  cosmos,  as  suggested  by  Laplace  and  fanci- 
fully elaborated  by  popular  writers,  had  taken  note  only 
of  the  matter  in  the  sun  and  in  the  planetary  system, 
and  had  disregarded  the  heat  ^  or  energy  which  the  sun 
supplied,  and  on  which  the  historical  changes  on  the  sur- 
face of  our  globe  have  almost  entirely  depended.  "  But 
physical  laws  are  for  our  mental  vision,"  as  Helmholtz 
says,  "  like  telescopes  which  penetrate  into  the  farthest 
night  of  the  past  and  the  future."  ""  Shortly  before  the 
pioneers  of  the  mechanical  theory  of  heat  published  their 


1  "When  Playfair  (in  his  '  Illus- 
trations of  the  Huttonian  Theory') 
spoke  of  the  planetary  bodies  as 
being  perpetual  in  their  motion, 
did  it  not  occur  to  him  to  ask, 
What  about  the  sun's  heat  ?  Is 
the  sun  a  miraculous  body  ordered 
to  give  out  heat  and  to  shine  for 
ever  ?  "  (Lord  Kelvin  in  1868,  "  On 
Geological  Time,"  '  Popular  Lec- 
tures and  Addresses,'  vol.  ii.  p.  45.) 
"  The  old  nebular  hypothesis  sup- 
poses the  solar  system  and  other 
similar  systems  thi'ough  the  uni- 
verse which  we  see  at  a  distance  as 
stars  to  have  originated  in  the  con- 


densation of  fiery  nebulous  matter. 
This  hypothesis  was  invented  be- 
fore the  discovery  of  thermodyna- 
mics, or  the  nebulae  would  not  have 
been  supposed  to  be  fiery  ;  and  the 
idea  seems  never  to  have  occurred 
to  any  of  its  inventors  or  early 
supporters  that  the  matter,  the 
condensation  of  which  they  sup- 
posed to  constitute  the  sun  and 
stars,  could  have  been  other  than 
fiery  in  the  beginning"  (id.,  1871, 
ibid.,  vol.  i.  p.  184). 

''  See   '  Vortriige   und   lleden,'   3 
Aufl.,  vol.  i.  p.  57. 


ON    THE    GENETIC    VIEW    OF    NATURE.  357 

first  theoretical  and  experimental  essays,  experiments  had 
already  been  made  by  Sir  Joliii  Herschel  at  the  Cape, 
and  independently  by  PouilluL  in  France,  with  the  object 
of    incasurinL!;   the   annual   expenditure   of   heat   by   the        49. 

",„,.,  .1   Til.- heat  of 

sun.  They  had  found  it  to  be  an  enormous  quantity,  tii.hun. 
Tliey  represented  it  popularly  by  the  thickness  of  a  crust 
of  ice  on  the  surface  of  the  earth,  which  the  heat  radiated 
annually  by  the  sun  would  be  able  to  melt,  and  they 
frtund  this  to  be  about  -SO  metres  or  100  feet.  Mayer 
was  the  th'st  who  seems  to  have  put  the  question 
ilefinitely :  How  is  this  enormous  expenditure  of  heat 
defrayed,  which  would,  if  not  in  some  way  compensated, 
have  residted,  even  in  historical  times,  in  a  great  lower- 
ing of  the  temperature  of  the  sun,  and  hence  also  of  that 
on  the  surface  of  our  globe,  such  as  is  contradicted  by  all 
historical  evidence  ?  The  answer  which  j\Iayer  gave  to 
this  question  was  based  upon  an  application  of  his  con- 
ception of  the  equivalence  of  heat  and  the  energy  of 
mechanical  motion.  As  the  sun,  according  to  the  cos- 
nioLronic  liypothesis  "  of  Laplace,  was  originally  formed  by 

'  These  measurements  were  made  '    si(l(5raiit     le     grand     nombre    que 

in    1837,    and  very  nearly    agreed.  nous    voyons,    comme    bolides    ou 

The  resulting  figures  Ci\n,  of  course,  otoiles  tombantes,  uous  ne  pouvons 

only    be    considered    as    rough    ap-  pas  doubter  qu'a  tout  moment  des 

proximations  :  they  have  been  con-  myriades  d'astoroides  semblables  a 

siderably  increased  bj'  more  recent  une  grele  epaisse  se   jettent   dans 

observations.      See   A.    Berry,    '  A  j    tous    les    sens    sur  le   soleil    ou  ils 

Short   History    of  Astronomy,'   p.  perdent  la  force  vive  de  leur  mouve- 

397.  I    raent"    (Mayer's    '  Schriften     und 

-  It  does  not  appear  that  Mayer  I    Briefe,'  p.   264) ;  and  M.  Faye  re- 

brfiught  his  "  meteoric"  hypothesis  marks   that  the  fact  that  Mayer's 

of  the  generation  and  maintenance  ideas  are  opposed  to  Laplace's  theory 

of  the  heat  of  the  sun  into  conncc-  ]    of  the  origin   of  the  solar  system 

tion  with  the  nebular  hypothesis  of  j    explains  how  it    came   about   that 

Kant  and  Laplace.     In  fact,  in  hi.s  '    his  theories  were  never  reported  on 

first    mention    of    it    in    his    com-  or  explicitly  mentioned.      Leverrier 

munication  to  the   Paris  Academy  also    seems   to    have   ridiculed    the 

in  1810  he  says  simply:  "En  con-  '    meteoric   hypothesis,   according  to 


358 


SCIENTIFIC    THOUGHT. 


the  gathering  up  of  cosmical  matter  which,  under  the 
force  of  gravitation,  was  in  rapid  motion — so  the  heat  of 
the  sun  originated  through  the  conversion  of  the  energy 
of  this  arrested  motion  into  heat.  This  process  of  gather- 
ing up  of  cosmical  or  meteoric  matter  is  still  going  on, 
and  it  makes  up  for  the  loss  or  expenditure  of  solar  heat 
through  radiation.  Helmholtz,  in  the  sequel  of  his 
investigation  into  the  conservation  of  energy,  likewise 
takes  up  this  problem,  and  while  admitting  to  some 
extent  Mayer's  theory,^  shows  that  even  without  the 
accession  of  cosmical  matter,  the  mere  contraction  through 
gravitation  of  the  gaseous  substances  of  the  sun  would 
result  in  a  continual  production  of  heat.  His  calcula- 
tions show  that  the  amount  of  this  contraction,  resulting 
in  a  diminution  of  the  sun's  apparent  diameter,  would  not 
be  great  enough  to  be  perceptible  during  historic  ages. 
The  theory  of  Helmholtz  has  in  general  been  accepted  as 


which  the  sun's  heat  was  kept  up 
by  breakfasting  anil  dining  on 
meteorites.  (See  Wolf,  '  Handbuch 
der  Astronouiie,'  vol.  ii.  p.  433. )  It 
is  on  the  other  side  equally  interest- 
ing to  see  how  Herbert  Spencer,  for 
whom  the  nebular  hypothesis  was 
a  principal  example  of  cosmic 
evolution,  failed  to  avail  himself 
of  the  strengthening  support  it  re- 
ceived through  thermodynamics  (see 
'  Essays,'  vol.  i.,  "  On  the  Nebular 
Hypothesis,"  18.58).  Had  Mayer 
brought  his  ideas  into  connection 
with  I^aplace's  cosmogony,  he  prob- 
ably would  have  hit  upon  the 
correcter  version,  the  contraction 
theorj',  which  it  was  reserved  for 
Helmholtz  to  propound  in  18.'>4. 

^  The  subject  was  about  the  same 
time  taken  up  by  William  Thomson 
(Lord  Kelvin),  fii'st  in  a  paper  "  On 


the  Mechanical  Energies  of  the 
Solar  System  "  (Trans.  Edin.  Roy. 
Soc,  1854),  and  continued  in  a 
series  of  papers  and  addresses, 
reprinted  in  his  mathematical,  &c., 
papers  (vol.  ii. )  in  the  1st  volume 
of  his  '  Popular  Addresses,'  and  in 
an  appendix  to  Thomson  and  Tait's 
'Natural  Philosophy.'  He  shows 
that  the  form  of  the  meteoric  theory 
propounded  by  Mayer,  and  inde- 
pendently by  Waterston  (Brit. 
Assoc,  1853),  is  as  little  able  to 
explain  the  maintenance  of  the 
sun's  heat  through  known  historic 
ages  as  the  chemical  theory  of  com- 
bustion, which  was  alreadj-  aban- 
doned by  Mayer  in  1846,  and  finally 
adopts  Helmholtz's  foi  lu  of  the 
meteoric  theorj'  as  the  most  likely. 
('Pop.  Lect.,'  vol.  i.  p.  365,  &c. ;  p. 
373,  &c.) 


ON    THE   GENETIC    VIEW    OF    NATURE.  359 

a  valid  explanation  of  Lho  maintenance  of  solar  heat.  In 
fact,  "  as  to  the  sun,  we  can  now  go  both  l)ack wards  and 
forwards  in  his  liistory  upon  the  principles  of  Newton 
and  Joule."  ^ 

But  further  means  for  tcstin'T  the  correctness  of  these        so. 

Spectrum 

tlieories  were  afforded    by    the   invention,   in    1859,   of  AnaiybU 
Spectrum  Analysis.     It  was  found  that  the  composition 
of  the  light  of  luminous  bodies,  as  revealed  Ijy  prismatic 
scattering  in  the  spectrum,  enabled  us  to  tell  a  good  deal 
about  the  nature  of  the  body  itself  from  which  the  light 
emanated.      We  can   tell   whether  the    body   is  shining 
with  its  own  or  with  reflected  light,  what  are  the  con- 
stituents  of    the   incandescent   body,   whether  it   is    an 
incandescent  solid  or  an  incandescent  gas ;  also  whether 
tlie  body  is  in  motion  or  not.     The  nebular  hypothesis 
supposed  that   the  planetary  system  owed  its  origin  to 
incandescent,  perhaps  gaseous,  matter,  which,  through  the 
force  of  attraction,  was  collected  in  different  centres :  the 
tliscoveries  of  thermodynamics  and  of  spectroscopy  have 
enabled  us  to  expand  and  correct  some  of  the  assump- 
tions  of   this   theory,    and    to   add   new   features  to  its 
minuter  elaboration.      It  is  not  necessary  that  the  matter 
which   was  originally  scattered  through   space  and  was 
ofathered  into  attracting  centres  should  be  itself  incan- 
descent  or  gaseous  ;  it  may  have  been  cold  and  solid  like 
dust ;  rising  in  temperature  and  becoming  incandescent 
only  througli  the  conversion  of  arrested  motion  into  heat, 
which  again  was  maintained  for  some  time  through  acces- 
sion of  new  matter  or  progressive  shrinkage,  but  which 
must  in  a  calculable  time  be  radiated  away,  leaving  a 

1  Lonl  Kelvin,  loc.  cit.,  vol.  ii.  p.  131. 


360 


SCIENTIFIC    THOUGHT. 


51. 
Genesis  of 
the  cosmos 
-  Fays  and 
Lockyer. 


cold,  heavy,  lifeless,  and  lightless  body  behind.^  The 
action  of  attractive  power  would  sometimes  reveal  the 
existence  of  cold  bodies,  with  specific  gravity  much  in 
excess  of  our  earth,  as  in  the  case  of  the  satellite  of 
Sirius,  and  the  spectroscope  would  reveal  clusters  of 
stars  or  nebulte  in  the  various  stages  of  development, 
such  as  the  nebular  hypothesis  suggested  as  making  up 
the  genetic  process  of  our  planetary  system.  Much 
uncertainty  and  much  conjecture  must  of  course  exist 
in  these  chapters  of  science,  which  those  who  are  in 
full  possession  of  the  accumulated  and  yet  very  im- 
perfect facts  may  venture  to  elaborate  in  a  more  or 
less  plausible  or  fanciful  manner.  Such  attempts  to 
write  the  history  of  the  universe  have  been  made  in 
an  original  fashion  by  M.  Faye  in  France "  and  Sir 
Norman   Lockyer  ^   in   this    country.     They   have   tried 


'  See  Helmholtz,  '  Vortriige  und 
Reden,'  vol.  ii.,  3rd  ed.,  p.  88,  &c. 

-  '  Sur  rOrigine  du  Monde,'  2nd 
ed.,  Paris,  1S85.  The  author, 
finding  the  celebrated  cosmogonic 
hypothesis  of  Laplace  in  "full 
contradiction"  with  the  actual 
state  of  science,  takes  up  an  original 
theory  of  Descartes,  that  of  vortices, 
in  order  to  characterise  not  the 
actual,  but  the  initial,  stage  of  the 
solar  system  (see  Preface) :  "  Autre- 
fois, je  veux  dire  il  y  a  une  vingt- 
aiue  d'ann^es,  on  avait  les  coud^es 
franches  pour  imagiuer  un  sj'steme 
cosraogonique :  il  suffisait  de  I'ac- 
commoder  aux  notions  contem- 
poraiues  d'Astronomie  solaire  et 
de  m(5canique  celeste.  II  n'en  est 
plus  de  meme  aujourd'hui,  car  la 
thermodynamique  assigne  h,  notre 
Soleil  une  provision  limitee  de 
chaleur,  1' Analyse  spectrale  nous 
revile  la  constitution  intime  des 
astres  les  plus  ^loignes,  et  la  paM- 


ontologie  nous  fait  renionter  a  des 
epoques  oil  il  n'y  avait,  sur  notre 
globe,  ni  saisons,  ni  climats." 

*  Whereas  M.  Faye  has  ingen- 
iously modified  the  original  and 
older  nebular  hypothesis  so  as  to 
account  for  the  anomalies  in  the 
movement  of  some  of  the  members 
of  our  planetarj"^  system,  which 
were  unknown  or  unexplained  in 
Laplace's  time,  and  has  tried  to 
account  for  the  phenomena  of  loss 
and  supply  of  heat  which  thermody- 
namical  theory  and  palseontologieal 
records  reveal.  Sir  Norman  Lockyer 
has  during  more  than  thirty  years 
been  occupied  with  the  elaboration 
of  a  special  theory  which  tries  to 
harmonise  the  revelations  of  the 
spectroscope  as  to  the  chemical 
constitution  of  the  sun  and  other 
stars  with  the  more  recent  develop- 
ments of  the  atomic  theory  as 
suggested  by  chemical  and  electrical 
phenomena  observed  in  our  labora- 


ON    THE    GENETIC    VIEW    OF    NATURE. 


361 


to  do  what  Professor  Haeckel  has  done  in  the  more  re- 
stricted field  of  the  history  of  the  living  creation.  Whilst 
these   attempts   are   by  inany   scioiititif   authorities   con- 


tories.        His    speculations,    based 
upon  liis  own  oltservations  as  well 
as  those   of  many  other  Eurojiean 
and  American  authorities,  such   as 
Seec'hi,  Dumas,  Kayser  and  llunge, 
Kutherford,  Rowland,  Vouiig,   and, 
ahovo   all,  of    Sir   W.    Crookes  and 
the  late  Professor  Preston,— all  of 
which,  as  well  as  many  others,  he 
generously  quotes, — were  given   in 
three  works  'The  Chemistry  of  the 
Sun'   (1887),   'The  Meteoritic  Hy- 
jiothesis'   (1890),    and    'The    Suii's 
Place  in   Nature'  (1897).      He  has 
latterly  collected  the  whole  evidence 
in  a  brilliant  and  fascinating  volume 
entitled    '  Inorganic    Evolution    as 
studied     by     Spectrum     Analysis' 
(1900).     The  central  idea  contained 
in  these  books,  and  elaborated  with 
increasing  detail  and  clearness,  was 
suggested    as    eaily  as    1873,   when 
Sir  N.  Lockyer  pointed  out  "that 
many     of     the     difficulties    would 
vanish    it    it    were    conceded    that 
the    '  atoms '   of   the  chemist    were 
broken  up  or  dissociated  into  finer 
forms    by    the    high    temperatures 
emploj-ed    in    the   new    method   of 
investigation "    ('  Inorg.    Evol.,'    p. 
73).     This  "  dissociation  "  hypothe- 
sis has  been   much   criticised,    and 
can   only   be   firmly  established  by 
patient  and  prolonged   research   in 
that      borderland       which      unites 
chemistry  and  astronomy.     As  the 
author    says:     "The    chemist   has 
little    interest    in     an     appeal     to 
celestial    phenomena,   and    astrono- 
mers    do     not    generally     concern 
themselves   with   chemistry.      The 
region  investigated  by  the  chemist 
is     a     low     temperature     region, 
dominated  by  nionatomic  and  poly- 
atomic   molecules.       The    region    I 
have  chiefly  investigated  is  a  high 
temperature  region,  in  which  mer- 


cury gives  us  the  same  phenomena 
as     manganese.       In     short,     the 
'   changes  with  which  spectrum  analy- 
sis has  to  do  take   place  at  a  far 
higher  temperature  level  than  that 
employed      in     ordinary     chemical 
work."       It    is    well    to    note    that 
during   and    since    the    time   when 
the  dissociation  hyiiuthesis  was  first 
prominently  put  forward  researches 
conducted     on     entirely     different 
lines    have    led   to   similar   views — 
i.e.,    to   a    further    elaboration    of 
the  atomic  hypothesis.     M.  Berthe- 
Idt   wrote   in    1880:    "  L'etude   ap- 
profondie  des  propridtcs  physiques 
et   chimiques   des    masses   clcmen- 
taires,    qui    constituent    nos    corps 
simi)les   actuels,  tend   chaque    jour 
d'avantage  Ji    les   assimiler,    non    ;i 
des  atomes  indivisibles,  liomogenes 
et    susceptibles    d'eprcmver    scule- 
ment  des  mouvements  d'eusemble 
.    .    .   il  est  difficile  d'imaginer  un 
mot  et  une  notion   plus  contraires 
k  1 'observation  ;  mais  ii  des  edifices 
fort  comjilexes,  doues  d'une  archi- 
tecture   spociticiue    et    animcs    de 
mouvements  intestius  tres  varies " 
(quoted  in  'Inorg.    Evol.,'  p.    28). 
The   first  chemical  confirmation  of 
the    dissociation    hypothesis    came 
in     1883    through  'the    "beautiful 
researches  on  the  rare  earth  Yttria, 
contained    in    Sir    Wm.    Crookes's 
Bakerian    Lecture     to     the    Royal 
Society.      "  In  the  lectures  he  gave 
a  sketch  of  the  train  of  reasoning 
by   which   he  had  been  led   to  the 
oj)ini<)n  that  .   .    .   this  stable  mole- 
cular group  had  been  (by  a  process 
termed  '  fractionation  ')  split  up  into 
its  constituents"  (ibid.,  p.  llti) ;  and 
already,  in  1879.  Sir  Wna.   Crookes 
had      provisionally      accepted     the 
"dissociation"   hypothesis  (p.    74). 
Anomalies    also    in     the     periodic 


362 


SCIENTIFIC    THOUGHT. 


sidered  to  be  prematvire/  they  have  contributed  much  to 
impress  on  the  thought  of  our  age  the  genetic  or 
developmental  view  on  a  large  as  well  as  on  a  minute 
scale. 


law   of   Meudeleef  were   explained 
by  utilising  this  hypothesis  (p.  165\ 
and  in  the  sequel  other  authorities, 
such  as  Brodie   and    Rydberg,  ex- 
pressed   themselves    in    the    same 
sense  (p.    164).     These,   and  quite 
recently    the    electrical    researches 
of    Prof.    J.    J.  Thomson   (referred 
to  supra,  p.  192),  support  the  view, 
originally    suggested    in    a    cruder 
form  by  Prout,  that  what  we  call 
elements  are  really  compounds  or 
aggregations  or  complexes,  built  up 
"  from  similar   particles  associated 
with    the    presence  of   electricity " 
('Inorg.  Evol.,'  pp.  167,   190;  also 
J.  J.  Thomson,  '  Discharge  of  Elec- 
tricity through  Gases,'  p.  198  sqq.) 
^  It  would  be  unfair  not  to  state 
that  many  works  on  astronomy  are 
still  written    in   which  all    genetic 
hypotheses  are  left  out,  the  "  stat- 
ical "    view    being    still    the    pre- 
dominant one.     Especially  in  Ger- 
many,   it   seems    as    if    "  inorganic 
evolution"    is    not   very   popular; 
though  a  large  amount  of  the  best 
work   in  spectrum  analysis  of  the 
stars  has  been  done  there  by  H.  C. 
Vogel,  Kayser  and  Runge,  Scheiner, 
and  many  others.     Dr  Scheiner,  in 
his  valuable  work  (translated  with 
the    title    '  A   Treatise    on   Astro- 
nomical    Spectroscopy,'    by    Prof. 
Frost  of  Dartmouth  College,  U.S.A., 
1894),    has    some    important   criti- 
cisms    on     hypotheses     and    solar 
theories  (see  Preface,  and  the  dis- 
cussion of  the  Meteoritic  Hypothesis 
in    the    German    edition,    Part    II. 
chap.  i. )     In  his  '  Bau  des  Weltalls  ' 
(Leipzig,    1901)   genetic   views   are 
not    discussed.       The     older    very 
valuable  works  of  R.  Wolf  ('  Gesch. 
d.    Astronomic,'    1877,    'Handbuch 
der  Astrouomie,   2  vols.,   1890-92) 


give     only     slight     attention     to 
"  genetics,"  and  consider  even  the 
"statics"  of  the  universe  though  a 
possible  yet  a  difficult  problem  (see 
the  last-named  work,  §§  298,  299). 
The  latest  and  excellent  '  History 
of    Astronomy,'   by   Mr    A.    Berry 
(1898),    is    likewise   reticent   about 
the  evolution  of  the  universe,  ad- 
mitting only  a  general,  fairly  well- 
founded  presumption   in  favour  of 
a  modified   nebular  hypothesis  (p. 
409).       It     would,     therefore,     be 
doubtful     whether     a     history    of 
science  should,  at  the  end   of  the 
nineteenth  century,  give  much  room 
to  these  modern  genetic  theories  in 
astronomy.     It  is  different  with  a 
history  of  scientific  thought.     How- 
ever   premature    and   venturesome 
it  may  appear  to  purists  in  science 
to  elaborate  such  hypotheses,  there 
is  no  doubt  that  the  genetic  argu- 
ments and  lines  of  reasoning  have 
got    a    firm    hold    of    many    great 
thinkers    in    the    physics    of    the 
universe  as  well  as  in  biology,  and 
that    the    genetic   view    of    nature 
in  general  has  received  very  strong 
support    from    the    sevei-al    trains 
of   reasoning   and    the    rapidly    in- 
creasing   revelations    of    spectrum 
analysis  of  cosmical  and  terrestrial 
objects,   as    set    forth    in    Sir    N. 
Lockyer's       interesting      volumes. 
Already    thirty    years     ago     Lord 
Kelvin    said    of   the    spectroscope : 
"It  is   not  merely   the   chemistry 
of  sun  and  stars,  as  first  suggested, 
that  is  subjected  to  analysis  by  the 
spectroscope.     Their  whole  laws  of 
being   are   now   subjects   of   direct 
investigation  ;  and  already  we  have 
glimpses  of  their  evolutional  history 
through   the  stupendous   power  of 
this  most  subtle  and  delicate  test. 


ON    THE    GENETIC    VIEW    OF    NATURE. 


363 


It   is    intelligible    that   these   different    lines    in    the 
genetic  view  of  nature — the  different  trains  of  reason- 
ing which,  in    the  course  of   our   century,  have   started 
independently  in  astronomy,  in  geology,  and  in  natural        52. 
history — should,  as  they  develop  and  expand,  come  into  lofeT  and 

•'  'J  I  X  '  geophysics. 

contact,  and  in  the  event  either  support  or  invalidate 
each  other.  The  former  was  the  case  when  the  geological 
record,  the  discoveries  of  palaeontology,  were  brought  in 
to  throw  light  on  the  history  and  development  of  species ; 
the  stories  of  nature,  as  written  from  the  point  of  view 
of  the  embryologist,  the  systematic  zoologist  and  botanist, 
and  the  pakeontologist,  seemed  more  and  more  to  confirm 
and  support  each  other.  The  same  cannot  be  said  if  we 
write  the  history  of  our  earth  from  the  point  of  view  of 
the  geological  record  on  the  one  side  and  from  that  of 
the  purely  physical  data  afforded  by  thermodynamics 
on  the  other.      Lord  Kelvin  has  shown  ^  that  the  untold 


We  liarl  only  solar  and  stellar 
ciieiiiistry  ;  we  now  have  solar  and 
stellar  i)hysiology"  (Presid.  Address, 
Brit.  Assoc,  1871.  See  'Popular 
Lectures  and  Addresses,"  vol.  ii.  p. 
ISO). 

'  The  literature  of  the  subject 
begins  with  Lord  Kelvin's  Address 
to  the  Geological  Society  of  Glas- 
gow, February  27,  1868,  which  had 
been  preceded  by  a  paper  read  be- 
fore the  Royal  Society  of  Edinburgh 
in  1865,  briefly  refuting  the  "  Doc- 
trine of  Uniformity  in  Geology." 
The  address  began  with  the  words  ; 
"  A  great  reform  in  geological 
9[)eculation  seems  now  to  have  be-  ! 
come  neces.sary,"  and  in  the  sequel 
stated  :  "  It  is  quite  certain  that  a 
great  mistake  has  been  made — that 
British  popular  geology  at  the  pre-  ' 
sent  time  is  in  direct  opposition 
to  the  principles  of  natural  philo-    i 


sophy."  These  papers  are  reprinted 
in  the  2nd  vol.  of  '  Popular  Lec- 
tures and  Addresses'  (see  pp.  10 
and  44).  The  attack  was  taken 
up  by  Huxley  in  his  Address  to 
the  Geological  Society  for  1869, 
reprinted  in  'Lay  Sermons,'  &c., 
1891,  p.  198.  In  a  rejoinder  to 
this,  delivered  in  the  same  3-ear 
at  Glasgow  {Inc.  cit.,  p.  73),  Lord 
Kelvin  shows  how  the  current 
geology  was  in  the  habit  of  look- 
ing upon  geological  time  as  "  an 
element  to  which  we  can  set  no 
Ijounds  in  the  jiast  any  more  than 
we  know  of  its  limits  in  the  future" 
(quoted  from  Page's  '  Te.\t-book  '), 
that  Darwin's  arguments  themselves 
involve  an  almost  unlimited  dura- 
tion of  the  conditions  admitting  of 
the  operation  of  natural  selection, 
since,  in  his  view,  "  in  all  jirobability 
a  far  longer  period  than  300  million 


364 


SCIENTIFIC    THOUGHT. 


53. 
Dissipation 
of  energy. 


ages  with  which  geologists,  since  the  time  of  Lyell,  have 
been  accustomed  to  reckon,  are  not  supported  by  our 
present  knowledge  of  the  periods  during  which  the  so- 
called  secular  cooling  of  the  earth  has  been  going  for- 
ward— the  period  which  has  elapsed  since  the  "  consis- 
tentior  status "  of  Leibniz  set  in.  He  has  thus  put 
before  natural  philosophers  a  problem — the  reconcilia- 
tion of  the  geological  and  the  thermophysical  record — 
in  which  the  genetic  view  of  nature  must  be  greatly 
interested.  But  even  more  important  than  all  this  is 
the  doctrine  of  the  dissipation  of  energy,  referred  to  in 
the  second  chapter  of  this  volume — a  doctrine  of  which 


years  has  elapsed  since  the  latter 
part  of  the  secondary  period" 
('  Origin  of  Species,'  1st  ed.,  p.  287). 
He  shows  that  Button  and  the  uni- 
forniitarians  were  misled  l:>y  a  be- 
lief in  the  so-called  stability  of  the 
solar  system,  which  took  no  notice 
of  the  effect  of  tidal  friction,  nor 
of  the  phenomena  of  radiation  and 
cooling  in  the  past,  .still  less  of  the 
law  of  dissipation  of  energy,  and 
maintains  that  the  modern  ideas  of 
evolution  are  in  a  sense  a  return  to 
the  older  conceptions  of  Leibniz, 
Newton,  and  other  more  recent 
geologists  (loc.  cit,  p.  111).  Since 
the  subject  was  thus  brought 
prominently  forward,  astr(jnomers, 
physicists,  and  geologists  have  not 
only — as  Huxley  expected  them  to 
do  (see  '  American  Addresses,'  1886, 
p.  93) — adduced  arguments  in  order 
to  arrive  at  an  apjiroximate  idea 
how  long  the  earth  may  have  been 
able  to  maintain  organic  life,  but 
biologi.sts  have  been  induced  to  re- 
vise the  postulates  of  the  extreme 
— almost  infinite — slowness,  and  of 
the  uniform  continuitj'  of  organic 
changes,  originally  contained  in  the 
Darwinian  theory.  The  influence 
of  these  researches  upon  biological 


and  genetic  reasoning  has  been  to 
emphasise  the  sudden  changes,  the 
ruptures  in  the  continuity  of  de- 
velopment. In  England  the  great 
work  of  Mr  William  Bateson 
('  Materials  for  the  Study  of  Varia- 
tions,' 1894)  has  familiarised  us 
with  the  idea  of  "  Discontinuity  " 
in  the  origin  of  species.  On  the 
Continent  the  rapid  or  even  sud- 
den appearance  of  variations  is  not 
a  new  idea,  though  the  oiiginal 
suggestion  of  Maupertuis  (1748;, 
which  was  taken  up  and  elaborated 
by  Geoffrey  St  Hilaire  (see  Yves 
Delage,  '  L'Heredite,  p.  291),  was 
forgotten.  In  quite  recent  yeais 
the  reconciliation  of  the  "  persist- 
ence of  species  "  with  their  "  varia- 
bility," and  of  the  "geological" 
with  the  "  biological "  recoids.  has 
been  much  furthered  bj'  the  tiieory 
of  "  Mutation "  of  the  celebrated 
Dutch  botanist  de  Vries.  His  view 
is  that  "  every  species  has  its  be- 
ginning and  its  end  ;  it  behaves  in 
this  way  like  an  individual."  He  re- 
fers to  the  experiments  on  heredity 
and  crossing  of  butterflies  of  Stand- 
fuss,  who  has  been  led  to  maintain 
the  existence  of  sudden  or  ' '  ex- 
plosive "   transformations ;    and   he 


ON    THE    GENETIC    VIEW    OF    NATURE. 


3G5 


the  mechanical  and  cosmical  importance  was  clearly  fore- 
seen by  Lord  Kelvin  in  1852,  but  which  is  hardly 
assimilated  yet  by  scientific,  much  less  Ijy  popular, 
thought. 

The  two  doctrines  of  tlie  conservation  of  matter  and 
of  energy  would  lead  to  the  idea  that  nature  is  a  kind 
of  perpettitim  mobile,  nothing  in  the  way  of  matter  or 
energy  being  lost ;  and  that  such  a  reversal  of  her  pro- 
cesses is  possible  as  we  are  accustomed  to  deal  with  in 
purely  mechanical  contrivances.  But  a  closer  examina- 
tion of  the  processes  of  nature,  as  distinguished  from 
those    of    artificial    machines,    revealed    the    fact    that, 


speaks  of  "  periods  of  mutation  " — 
i.e.,  of  rapid  change  of  species,  of 
which  he  gives  various  instances. 
He  concludes  that  "  as  many  steps 
as  the  organisation  has  taken  since 
the  beginning,  so  many  periods  of 
'  inut<\tion '  must  have  existed." 
He  considers  the  vital  processes  to 
be  built  up  out  of  "units."  "Of 
such  units  there  are  probably  in 
the  higlier  plants  several  thousands, 
and  tiieir  ancestors  must  have  run 
through  as  many  periods  of  muta- 
tation."  He  concludes  with  the 
following  words:  "Although  such 
calculations  are  naturally  exposed 
to  much  criticism,  they  neverthe- 
less lead  on  very  different  roads  to 
identical  results.  Lord  Kelvin, 
who  a  few  years  ago  collected  and 
examined  criticiilly  the  various  data 
referring  to  this  subject,  arrives  at 
the  conclusion  that  provisionally, 
and  with  all  reservations,  the  dura- 
tion of  life  on  the  earth  can  be 
placed  at  '2-4  millions  of  years.  We 
accordingly  tiike  this  figure  for  our 
biochronic  equation.  And  as  we 
can  with  great  proy)ability  estimate 
the  number  of  elementary  pro- 
perties in  one  of  the  higher  plants 


at  some  thousands,  it  follows  tliat 
the  interval  of  time  between  two 
periods  of  mutation  must  have 
lasted  several  thousands  of  years." 
(See  de  Vries's  Address  to  the  (Ger- 
man Assoc,  of  Science  at  Hamburg 
in  1891,  '  Verhandelungen,'  &c-.,  ]>. 
202,  &c. ;  also  Lord  Kelvin  (Phil. 
Mag.  (5.)  47,  p.  66).  Mr  Wallace 
has,  from  an  entirely  diflerent  point 
of  view,  been  led  to  the  conclusion 
that  "  certiiin  detinite  portions  of 
man's  intellectual  and  moral  nature 
could  not  have  been  develo])ed  by 
variation  and  natural  selection  alone, 
and  that,  therefore,  some  other  in- 
fluence, law,  or  agency  is  required 
to  account  for  them."  This  would 
account  for  an  a{)parent,  though 
perhaps  not  an  actual,  bi'oak  in  the 
continuity  of  all  natural  processes, 
which,  in  the  dictum  nutura  non 
facit  saltum,  has  received  a  very 
general  expression  and  acceptance. 
This  dictum  —  supported  by  the 
authority  of  Leibniz — is,  however, 
by  some  modern  thinkers  de- 
nounced as  a  scholastic  and  anti- 
quated aphorism.  (See  Yves 
Delage,  '  L'Hert^dit^,'  &c.,  p.  266.) 


3H6  SCIENTIFIC    THOUGHT. 

though  matter  and  energy  be  mdestructible,  the  succes- 
sion of  phenomena,  the  changes  and  processes  which  we 
call  the  genesis  or  history  of  things,  are  dependent  on  the 
condition  in  which  energy  exists ;  it  being  a  general 
tendency  for  energy  not  to  be  lost,  but  to  become  un- 
available ;  change  and  action,  the  life  of  things  every- 
where, depending  on  an  equalisation  of  existing  differ- 
ences, say  of  level  or  temperature,  or  quicker  and 
slower  motions.  This  great  property  of  natural,  as  dis- 
tinguished from  purely  mechanical,  processes,  explains 
the  fact  that  the  processes  of  nature  are  irreversible, 
that  the  clock  cannot  be  turned  back,  that  everything 
moves  in  a  certain  direction.  Various  attempts  have 
been  made  to  explain  mechanically  this  remarkable 
property  of  all  natural  processes,  which  seems  to  lead 
us  to  the  conception  of  a  definite  beginning  and  to 
shadow  forth  a  possible  end — the  interval,  which  con- 
tains the  life  or  history  of  nature,  being  occupied  with 
the  slow  but  inevitable  running  down  or  degradation 
of  the  great  store  of  energy  from  an  active  to  an  in- 
active or  unavailable  condition. 
54.  This    doctrine    of    the    degradation   or  dissipation    of 

Mystery  of 

the  actual     energy  leads  us  one  step  farther  towards  an  understand- 

processes  of  ""^  ■•■ 

ing,  or  at  least  a  description,  of  the  processes  of  nature, 
but  also  of  their  mystery.  It  lias  been  urged  that,  as 
we  always  only  deal  with  a  small  portion  of  existing 
things,  we  have  no  right  to  apply  conceptions  which  are 
based  upon  a  restricted  observation  to  the  totality  of 
things  in  the  universe.  For  instance,  we  know  nothing 
of  what  becomes  of  the  energy  radiated  away  into  empty 
space.     This  is  a  reflection  we  should  always   bear   in 


nature. 


ON    THE    GENETIC    VIEW    UF    NATURE.  :^G7 

niind.  We  have  also  bcuii  iciuiiKlcd  that  the  theories  of 
ihe  so-called  stability  of  the  planetary  system  which 
were  propounded  in  the  earlier  years  of  our  century, 
and  which  have  found  their  way  into  popular  treatises 
on  astronomy,  are  only  approximations.  (Jn  the  other 
side,  we  have  daily  before  our  eyes  the  ever -recurring 
instances  of  the  building  up  and  running  down  of  natural 
forces  in  smaller  systems.  Tliese  we  term  organisms,  the 
living  things  of  nature.  It  is  from  and  through  them 
tiiat  we  first  learnt  to  iook  ui)ou  tlie  whole  of  nature 
as  having  a  history  and  a  life.  lmpercepti])ly  we  have 
been  led  to  study  life,  the  genesis  of  things,  on  the  large 
scale  and  in  the  abstract,  and  in  doing  so  have  lost  sight 
of  the  life  which  goes  on  around  and  near  us.  ImiUi  tlie 
morphological  and  genetic  views  of  nature  started  wilii  a 
liiological  interest,  but  have  gradually  lost  sight  of  it. 
It  is  time  to  come  back  to  it  and  to  see  what  real 
jirogress  has  been  made  during  our  century  in  the  study 
III  life  itself — the  truly  biological  view  of  nature.  This 
will  be  the  oliject  of  the  next  chapter. 


368 


CHAPTER    X. 

ON    THE    VITALISTIC    VIEW    OF    NATURE. 

In  the  foregoing  chapters,  where  I  have  treated  of  the 
several  distinct  aspects  of  nature  which  have  become 
helpful  in  science,  I  have  always  used  the  word  nature 
in  its  widest  sense  as  comprising  everything  which  is 
revealed  to  us  by  our  external  senses,  directly  or  in- 
directly. 

The  title  of  the  present  chapter  may  suggest  to  some 
of  my  readers  that  I  am  now  narrowing  down  the  mean- 
ing of  the  word, — the  vitalistic  view  of  nature  being 
possible  only  where  life  is  present.  The  astronomer 
might  say.  Life  is  only  known  to  exist  in  an  infini- 
tesimally  small  portion  of  the  universe,  on  the  surface 
of  our  planet.  This  infinitesimal  area  has  nevertheless 
for  us  the  greatest  importance,  inasmuch  as  all  that 
we  know  of  the  larger  outlying  world  is  only  won  by 
inference  from  observations  made  in  this  restricted  por- 
tion. Independently  of  this,  the  conception  of  life  itself 
has  always  fluctuated  between  the  two  extremes  of  con- 
sidering it  as  a  universal  property  of  all  matter,  or  on 
the  other  hand  as  quite  a  casual  and  accidental  occur- 
rence attached  to  conditions  which,  from  a  wider  point  of 


ON    THE    VITALISTIC    VIEW    OF    NATURE. 


369 


Between  these        i- 

The  cnsmi- 


view,  are  extremely  rare  unci  exceptional 

two  views,  the  cosmical  and  the  terrestrial,  the  wider '  ^"^ »'"/  Mj« 

'  t(!rreslnal 

and  the  narrower  views  of  life,  biological  theories  have  ^' 
tluctuated  even  in  our  century,  and  are  still  fluctuating. 


'  One  of  tlie  foremost  upliolders 
of  the  wider  coiic-ei>tion  of  anima- 
tion as  a  universal  property  of  all 
matter  is  the  celebrated  German 
naturalist,  Prof.  Ernst  Haeckel  of 
Jena.  See,  inter  alia,  his  Address 
"Uel)erdie  heutige  Eiitwickeluiigs- 
lehre  im  Verhiiltnis.se  zur  Gesanimt- 
wi.ssen.seiiaft,"  1876,  reprinted  in 
'  Gesammelte  popuUire  Vortriige,' 
&c.,  part  ii.,  Bonn,  1879,  p.  119  : 
"The  recent  controversies  regard- 
ing the  properties  of  the  Atoms, 
which  we  must  acce])!  in  some  form 
or  other  as  the  ultimate  elemen- 
tary factors  of  all  physical  and 
chemical  processes,  seem  to  be  most 
easily  settled  by  the  assumption 
that  these  smallest  particles  of  mass, 
as  centres  of  force,  possess  a  per- 
manent soul,  that  every  atom  is 
endowed  with  sensation  and  mo- 
tion," &c.,  p.  109  :  "  Arriving  at 
this  extreme  psychological  con- 
sequence of  our  monistic  doctrine 
of  development,  we  attach  ourselves 
to  tho.-e  ancient  conce[jtions  as  to 
the  animation  of  all  matter  which, 
in  the  philosophy  of  Democritus, 
Spinoza,  Bruno,  Leibniz,  Schopen- 
hauer, have  already  found  varied 
expression."  Tlie  cosmical  origin 
of  life  has  also  been  put  forward  by 
surh  authorities  as  Hclndioltz  and 
Lord  Kelvin,  as  long  ago  as  1871. 
(See  Helmholtz's  lecture  "  On  the 
Origin  of  the  Planetary  System," 
'  Popul.  Vortriige,'  &c. ,  vol.  ii.  p. 
91,  and  Lord  Kelvin's  celebrated 
addres.s  to  the  lirit.  Assoc,  at  Edin- 
burgh in  1871,  reprinted  in  '  Pt)p. 
Lects.,'  &c.,  vol.  ii.  p.  199,  &c.) 
This  theory  of  "Panspermia,"  of 
the  cosmical  or  ubiquitous  nature  of 
the  germs  of  life,  has  also  been  pro- 
po.sed  by  biologists  such  as   H.    E. 

vor,.   IL 


Kichter  (1865),  and  luis  been  more 
fully  elaborated  by  ]*rof.  W.  Preyer 
since  the  year  1880:  it  has  received 
further  support  in  the  genetic 
theories  of  the  chemical  elements 
and  compounds  put  forward  by 
him  in  1891  ('  Die  organischen 
Elemente  und  ihre  Stellung  im 
System,'  Wiesbaden),  and  in  1893 
('Das  genetische  System  der  cliem- 
ischeu  Elemente,'  Berlin).  Of  the 
fourteen  elements  which  are 
common  to  organic  substances,  he 
says  (p.  49)  "that  they  belong  to 
the  oldest  elements";  that  "they 
admit  of  more  varied  relations," 
and  "  agree  with  the  assumption 
that,  before  being  condensed  as  at 
present  on  the  surface  of  the  earth, 
they  formed  at  higher  tempera- 
tures more  stable  protoplasms 
which  might  be  in  other  places  the 
carriers  of  life "  ;  and  he  has  no 
doubt  "  that  there  existed  before 
the  present  terrestrial  phytoplasma 
and  zoojjlasma  another  plasma, 
which  ultimately  came  from  the 
sun  "  (p.  50).  In  fact,  Prof.  Preyer 
asks  whether,  instead  of  living 
being  evolved  from  dead  matter, 
the  latter  is  not  rather  a  product 
of  the  former.  See  also  the  refer- 
ence to  organic  evolution  as  a 
cosmical  process  in  Sii-  N.  Lockyer's 
'  Inorganic  Evolution  '  (1900,  p. 
168).  In  many  of  the  writings  of 
the  celebrated  German  physicist 
and  philosopher,  Gustav  Theod. 
Fechner,  the  fact  is  empliasi>ed 
that  we  never  see  the  organic  de- 
veloped out  of  the  inorganic,  but 
that  everywliere  the  living  gener- 
ates not  only  the  living  but  more 
frequently  the  inanimate.  See 
Lasswitz,  '  G.  T.  Fechner,'  Stutt- 
gart, 1896,  p.    130,  &c. 

2  A 


370 


SCIENTIFIC    THOUGHT. 


Vagaieness 

of  biological  mocleni 

theories. 

living 


No  theory  of  the  nature  and  origin  of  life  has  gained 
universal  acceptance :  the  very  alphabet  of  biology,  or 
the  science  of  life,  has  still  to  be  written.  We  fancy 
we  possess  some  knowledge  of  certain  forms  or  processes 
which  are  common  to  all  living  matter,  but  the  descrip- 
tion of  these  has  to  be  kept  in  the  most  general,  not  to 
say  the  vaguest,  terms :  quite  unlike  the  rudiments  of 
other  scientific  theories  which  deal  with  mathematically 
defined  conceptions  expressed  in  distinct  language  and 
formulae. 

For  instance,  if  we  take  one  of  the  best  founded  of 
biological  theories  —  the  cellular  theory  ^  of 
matter  —  we  notice  that  the  pretty  definite 
description  which  the  early  supporters  of  this  theory — 
Schleiden  and  Schwann — gave  of  this  morphological 
unit  of  vegetable  and  animal  structvire  has  been  dis- 
placed   by    much    vaguer    descriptions.      Schleiden    and 


^  The  history  of  tlie  cellular 
theory  has  been  written  from  vari- 
ous points  of  view  in  all  the  three 
languages.  I  give  the  titles  of  a 
few  out  of  the  great  abundance 
of  excellent  treatises.  Foremost 
stands  the  work  of  Prof.  Oscar 
Hertwig  of  Berlin,  '  The  Cell  : 
Outlines  of  General  Anatomy  and 
Physiology.'  English  transl.  by 
Campbell  (1895).  Then  there  is 
the  more  recent  book  by  Prof. 
Valentin  Hiicker  of  Freiburg, 
'  Praxis  und  Theorie  der  Zel- 
len-  und  Befruchtungslehre '  (Jena, 
1899).  In  the  French  language 
we  have  the  great  compendium  of 
biological  theories  by  M.  Yves 
Delage,  '  La  Structure  du  Proto- 
plasma  et  les  Theories  sur  I'Hdr- 
edite,'  &c.  (Paris,  1895).  In  English 
we  have  the  valuable  treatise  of 
Prof.    E.    B.    Wilson,    'The    Cell 


in  Development  and  Inheritance ' 
(1896),  and  the  excellent  little  work 
of  Pnif.  James  Arthur  Thomson, 
'The  Science  of  Life'  (1899).  Of 
high  importance  are  also  the  older 
works  of  the  great  master  and 
brilliant  expositor  in  biological 
science,  Claude  Bernard,  notably 
his  celebiated  lectures  entitled 
"  Lecons  sur  les  Phenomenes  de  la 
vie  communs  au.x  animaux  et  aux 
v(5g(5taux"  (1878  and  1879),  which 
every  j'^i'^^-'^ophical  student  of 
biology  should  read,  as  well  as  his 
excellent  posthumously  published 
little  work,  '  La  science  experi- 
mentale,'  1890.  Of  him  M.  Dumas 
says  that  he  has  "  epuisd  ses  forces  ii 
I'etude  du  grand  mystere  de  la  vie, 
sans  pretendre  a  pen^trer  toutefois 
sou  origine  et  son  essence"  ('Sci. 
Exper.,'  p.  6). 


ON    THE    VITALISTIC    VIEW    OF    NATURE. 


371 


Schwann  detined  the  cell  as  "  a  small  vesicle  with  a 
tirm  membrane  enclosing  Huid  content."  ^  i>ut  the 
cellular  theory  was  gradually  replaced  by  the  proto- 
plasmic theory  of  ]Max  Schultze,  the  distinct  membrane 
was  found  to  be  frequently  absent,  and  there  only 
remained  "  a  small  mass  of  protoplasm  endowed  with 
the  attributes  of  life."  The  cell,  which  had  once  been 
compared  to  a  crystal,  became  a  \ery  complicated  and 
indefinite  thing :  it  became,  in  the  conception  of 
biologists,  an  "  organism." ""  Further,  the  nucleus  or 
kernel  to  which  Schleiden  attached  great  importance 
in  his  cellular  theory  was,  for  a  while,  quite  lost  sight 
of — it  being  for  a  long  time  held  that  there  exist  non- 
nucleated  cells.  Elaborate  theories,  such  as  that  of 
Haeckel,^   were    founded   upon    this   view,   till   in    more 


'  O.  Hertwig,  '  Tlie  Cell,'  p.  5  n. 

-  Treatises  on  the  subject  uow 
usually  begin  with  an  apology,  the 
word  cell  being  considered  mislead- 
ing. Til  us  Hertwig  says  (foe.  cit., 
p.  8),  "It  is  evident  that  the  term 
'cell'  is  incorrect.  Thar,  it  has, 
nevertheless,  been  letained  may  be 
partly  ascribed  to  a  kind  of  loyalty 
to  the  vigorous  combatants  who 
conquered  the  whole  field  of  his- 
tology under  tlie  banner  of  the 
cell-theory,  and  partly  to  the  cir- 
cumstance that  the  discoveries 
which  brought  about  the  new 
reform  were  only  made  by  degrees, 
and  were  not  geuerally  accepted  at 
a  time  when,  in  consequence  of  its 
having  been  used  for  several  de- 
cades, the  woixl  cell  had  taken 
firm  root  in  the  literature  of  the 
subject." 

•'  "  Since,  in  consequence  of  the 
inadequacy  of  former  methods,  no 
nuclei  had  been  discovered  in  many 
of  the  lower  organisms,  the  exist- 
ence  of  two  kinds   of  elementary 


cells  was  assumed — ^  more  simple 
ones,  consisting  only  of  a  mass  of 
protoplasm,  and  more  complex  ones, 
which  had  developed  in  their  in- 
terior a  special  organ,  the  nucleus. 
The  former  were  called  cytodes  by 
Haeckel  (1866),  to  the  simplest 
solitary  forms  of  which  he  gave  the 
name  of  Monera ;  the  latter  he 
called  celluUe,  or  cytes.  But  since 
then  the  aspect  of  the  question 
has  been  considerably  changed. 
Thanks  to  the  improvements  in 
optical  instruments  and  in  staining 
methods,  the  existence  of  organisms 
without  nuclei  is  now  much  ques- 
tioned." (Hertwig,  'The  Cell,'  p. 
54.  See  also  Hacker,  p.  239.)  On 
the  other  side  ^l.  Delage  says 
(' L'Herodite,'  p.  37),  "  Apros  avoir 
decouvert  un  noyau  chez  la  plupart 
des  moneres  et  des  cytodes  et 
meme  chez  les  Bacteries,  on  a,  par 
une  induction  ii  mon  sens  un  peu 
hative,  nii;  I'existence  d'orgauismes 
sans  noyau." 


372 


SCIENTIFIC    THOUGHT. 


recent  times,  owing  to  improvements  in  the  microscope, 
the  existence  of  organisms  without  nuclei  has  become 
doubtful.  To  complicate  matters  still  more,  to  the 
nucleus  have  been  added  the  nucleolus,  the  vacuoles,  the 
central  or  pole  corpuscles  of  the  cell,  &c.  It  is  quite 
evident  from  this  short  reference  to  the  changes  which 
the  definition  of  the  morphological  unit  of  living  matter 
has  undergone,  that  no  complete  and  accurate  descrip- 
tion lending  itself  to  measurement  and  calculation  could 
be  based  upon  it.  The  conception,  useful  as  it  may 
l)e,  has  therefore  not  permitted  of  predictions,  such  as 
mechanical,  physical,  and  even  chemical  science,  abound 
in.  "  Has  one  ever,"  says  Delage,  "  in  a  single  instance 
biifty  of  pre-  clivined  in  advance  the  least  of  those  structures  which 

diction. 

the  microscope  has  unveiled  ?  Has  one  divined  the 
transverse  striation  of  muscles,  the  cilia  of  vibratile 
epithelia,  the  prolongations  of  nerve-cells,  the  action 
of  the  retina  or  the  arcades  of  Corti,  the  chromosomes 
of  the  nucleus,  the  centrosome  of  the  cytoplasma  ? "  ^ 
Or,  to  take  an  example  not  from  the  morphology  but 
from  the  physiology  of  organic  cellular  bodies.  It  is  a 
very  general  and  a  very  useful  property  of  cells  that 
they  readily  absorb  substances ;  in  fact,  this  property 
is  one  of  the  most  valuable  aids  in  microscopic  exam- 


3. 
Impossi 


1  '  L'Heredite,'  &c.,  p.  746. 
Prof.  Weismann,  in  his  celebrated 
'  Es:?ays  upon  Heredity  '  (Engl, 
tracsl.  by  Poulton,  &c.,  p.  2.55), 
claims  for  the  theory  of  descent 
that  "  it  has  rendered  possible  the 
prediction  of  facts,  not  indeed  with 
the  absolute  certainty  of  calcula- 
tion, but  still  with  a  high  degree  of 
probability.  It  has  been  predicted 
that  man,  who,  in  the  adult  state, 


only  possesses  twelve  pairs  of  ribs, 
would  be  found  to  have  thirteen  or 
fourteen  in  the  embryonic  state  ; 
it  has  been  predicted  tliat,  at  this 
early  period  of  his  existence,  he 
would  possess  the  insignificant 
remnant  of  a  very  small  bone  in 
the  wrist,  the  so-called  os  centralc, 
which  must  have  existed  in  the 
adult  condition  of  his  extremely 
remote  ancestors." 


ON    Till-:    VITALISTIC    VIEW    oF    NATURE. 


373 


ination,  insomuch  as  the  diHeieiit  behaviour  of  different 
parts  of  the  cellular  b(jdy  towards  organic  staining 
solutions  reveals  to  the  observer  dilTerences  of  structure 
otherwise  indistinguishable.  Yet  Professor  Pfeffer/  wIid 
has  studied  the  absorbing  powers  of  cellular  substances 
with  much  care,  states  that  these  cannot  in  the  least 
be  foretfjM,  but  can  only  be  determined  empirically; 
nor  is  the  fact  that  cells  require  some  substances 
fur  their  life,  while  others  are  harmful,  sufficient  to 
enable  us  to  predict  that  either  will  l)e  absorbed  or 
rejected.  Again,  hybridisation  has  Ijeen  much  studied 
by  gardeners  and  breeders,  and  also,  since  the  time 
of  Darwin,  by  naturalists ;  nevertheless,  the  result  of 
cross-fertilisation  of  individuals  l^elonging  "  to  different 
families  or  species,  or  even  only  to  different  varieties," 
cannot  be  theoretically  foretold,  but  "  can  only  be  dis- 
covered by  means  of  experiment." "' 

This  ignorance  in  which  we  are  still  placed  as  to  the 
forms  as  well  as  functions  of  living  matter,  has  been  a 
subject  of  much  comment  by  biologists  all   through   the 


1  See  W.  Pfeffer,  '  Ueber  Auf- 
nahiue  von  Anilinfarbeii  in  lebende 
Zellen.'  Unterriuchungon  aus  dem 
botaiiisclien  Institul  zu  Tiibingen. 
(juuted  by  Hertwig,  'The  Cell,'  p. 
136. 

-  Hertwig,  'The  Cell.'  p.  310. 
Annther  point,  .strongly  urged  by 
Claude  Hernard,  is,  that  a  knowledge 
of  structure  in  living  beings  —  i.e., 
anatomical  kno\vle<lge — in  no  wise 
sutfices  to  explain  the  functions, does 
not  lead  to  phj'siological  knowledge. 
See  '  La  Science  Expuriinentale,'  p. 
10.5,  "  L'impuissiince  de  I'anatoinie  a 
nous  apprendre  les  fonctions  organ- 
iques  devient  surtout  cvidente  <lans 
les    ca.s    particuliers    ou    elle    est 


roduite  a  elle  -  nieme.  Pour  le>: 
organes  sur  les  usage-s  desquels 
la  physiologic  exporinientale  n'a 
encore  rien  dit,  I'anatomie  reste 
absolument  uiuette.  Cest  ce  qui 
a  lieu  par  exeniple  jiour  la  rate, 
les  capsules  surrenales,  le  corps 
thyroide,  &c.,  tous  organes  dont 
nous  connaissons  parfuitement,  la 
te.xture  anatomique,  uiais  dont 
nous  ignorons  conipletement  les 
fonctions.  De  mcnie,  quaud  sur 
un  animal  on  dccouvre  un  tissu 
nouveiiu  et  sans  analogue  dans 
d'auti'es  organismes,  I'anatomie  est 
incapable  d'en  devoiler  les  pro- 
prictcs  vitales." 


374  SCIENTIFIC    THOUGHT. 

century,  nor  can  it  be  stated  that  uniformity  of  opinion 
exists  even  yet  as  to  the  cause  of  this  ignorance.  The 
enormous  progress  which  has  been  made  in  our  know- 
ledge of  the  different  properties  of  living  things  has 
had  an  effect  on  the  minds  of  those  searchers  to  whom 
we  are  mostly  indebted  for  it,  similar  to  that  produced 
on  a  wanderer  who  ascends  an  unexplored  and  distant 
peak.  Ever  and  anon,  after  scaling  the  eminence  just 
before  him,  he  beholds  a  new  and  greater  one  rising 
into  view,  which  he  contemplates  with  mixed  feelings 
of  discouragement  and  of  eager  desire  for  advance. 
But  whereas  our  wanderer  must  know  that  the  very 
greatest  height  or  distance  is  none  the  less  a  measurable 
and  attainable  quantity,  what  hope  has  the  biologist  to 
encourage  him  on  his  way  ?  No  other — as  it  appears  to 
some — than  the  assurance  that  he  is  all  the  time  ex- 
ploring an  unknown  country,  whereas  the  final  achieve- 
ment is  impossible  to  him  through  the  inaccessibiHty 
of  the  position  or  the  limitation  of  his  own  powers. 
Others,  indeed,  from  time  to  time  have  not  taken  this 
despondent  view,  but,  elated  by  the  triumphs  which 
every  new  step  has  afforded  them,  have  persistently 
maintained  that  some  day  the  last  step  will  be  taken 
and  the  central  peak  really  gained. 
4.  The    history    of   biological   thought,   as   distinguished 

Oscillation  "^  *=  o      '  o 

th'uiiT''^'  from  biological  knowledge,  presents  us  with  the  spec- 
tacle of  a  repeated  oscillation  between  these  two  ex- 
treme views :  on  the  one  side  the  continually  recurring 
conviction  that  the  problem  of  life  is  insoluble,  and, 
on  the   other,  the   assertion    that  it  is   soluble,  though 


ON    THK    VITALISTIC    VIEW    OF    NATURE.        375 

it  is  admittedly  as  yet  unsolved.  Biological  know- 
ledge itself  has  progressed  on  the  same  lines  as  chem- 
ical, physical,  and  mechanical  knowledge ;  it  registers 
the  progressive  conquest  of  new  regions  of  phenomena 
exhibited  by  living  matter  through  the  methods  which 
have  been  discovered  in  the  abstract  sciences :  but  it  has 
generally  been  felt  that  this  knowledge  does  not  ex- 
haust the  subject ;  that  there  is  some  principle  involved 
which  we  know  not ;  and  that  we  cannot  think  about 
the  living  portion  of  creation  without  consciously  or  un- 
consciously admitting  the  existence  of  this  principle. 
The  unknown — nay,  possiblv,  the  unknowable — element        5. 

■^     ^  "  .  .  The  un- 

or  factor  must  be  admitted  to  exist,  and  it  involuntarily  known 
governs  our  reflections  on  that  which  we  know.  To 
show  the  diflference  between  reflections  on  biological  and 
on  other  phenomena,  which,  though  equally  unknown, 
yet  do  not  contain  an  admittedly  unknown  factor,  it 
may  be  useful  to  refer  to  the  scientific  way  of  deal- 
ing with  meteorological  phenomena.  The  science  of 
meteorology  is  probably  as  young  as  that  of  biology, 
if  not  younger.  Prediction  of  the  weather  is  probably 
even  more  uncertain  than  the  prognosis  of  a  physician 
at  the  bedside  of  a  patient  suffering  from  a  malignant 
disease.  Yet  no  one  would  suggest  that  there  is  a 
special  meteorological  principle  involved,  as  in  the  case 
of  the  phenomena  of  life  and  death  there  is  a  special 
biological  principle.  We  are  quite  satisfied  that  purely 
mechanical  and  physical  and  possibly  chemical  pro- 
cesses make  up  the  whole  of  the  weather  problem, 
and    that    the   difficulty  of  the  latter  is  simply  one  of 


376 


SCIENTIFIC    THOUGHT. 


complexity  and  intricacy.  A  similar  -^  attitude  has  in 
the  course  of  our  century  frequently  been  taken  up 
with  regard  to  the  problem  of  life,  but  it  has  always 

We   are   still   told    that   "  in 


been   abandoned   again." 

^  See,  for  instaDce,  what  Huxley, 
who,  in  his  earlier  writings,  might 
be  termed  a  vitalist  (cf.  his  ad- 
dress "On  the  Educational  Value 
of  the  Natural  History  Sciences," 
1854,  and  his  own  criticism  thereof 
in  the  preface,  dd.  1870,  in  'Lay 
Sermons  and  Addresses'),  says  in 
his  article  "Biology,"  1875,  in  the 
'Ency.  Brit.,' vol.  iii.  p.  681:  "A 
mass  of  living  protoplasm  is  simply 
a  molecular  machine  of  great  com- 
plexity, the  total  results  of  the 
working  of  which,  or  its  vital 
phenomena,  depend — on  the  one 
hand,  upon  its  construction,  and 
on  the  other,  upon  the  energy 
supplied  to  it ;  and  to  speak  of 
'  vitality '  as  anything  but  the 
name  of  a  series  of  operations,  is 
as  if  one  should  talk  of  the  '  hor- 
ologity'  of  a  clock."  Similarly 
Claude  Bernard,  in  his  '  Lemons  sur 
les  ph(^nomenes  de  la  vie,'  &c.,  vol. 
i.  p.  379,  says:  "  Eu  un  mot,  le 
phenomene  vital  est  pre-^tabli 
dans  sa  forme,  non  dans  son  ap- 
parition. .  .  .  La  nature  est  in- 
tentionelle  dans  son  but,  mais 
aveugle  dans  I'execution."  Both 
Huxley's  comparison  of  an  organism 
with  a  clock  and  the  quotation 
from  Claude  Bernard  suggest  a 
parallel  between  the  dictum  of 
Archimedes  :  "  Sos  not  ttoC  (ttw  Kal 
Thy  K6(TfjLov  KivTjcrw,"  and  a  possible 
one  of  a  biologist:  "Give  me  an 
organism,  and  I  will  explain  its 
action  mechanically."  In  another 
place  Claude  Bernard  says  {loc.  cit., 
ii.  p.  524)  :  "  L'element  ultime  du 
phenomene  est  physique  ;  I'arrange- 
ment  est  vital." 

-  Examples  of  this  could  be 
multiplied  indefinitely.  I  take 
one    from     an     entirely    different 


field.  Prof.  Kerner  von  Marilaun, 
the  celebrated  botanist,  says  ('The 
Natural  History  of  Plants,'  transl. 
by  Dr  Oliver,  1894,  voL  i.  p.  52) : 
"  In  former  times  a  special  force 
was  assumed — the  force  of  life. 
More  recently,  when  many  i)hen- 
omeua  of  plant  life  had  been  suc- 
cessfully reduced  to  simple  chemical 
and  mechanical  processes,  this  vital 
force  was  derided  and  effaced  from 
the  list  of  natural  agencies.  But 
by  what  name  shall  we  now  desig- 
nate that  force  in  nature  which  is 
liable  to  perish  wliilst  the  proto- 
plasm suffers  no  physical  alteration, 
and  in  the  absence  of  any  extrinsic 
cause  ;  and  which  yet,  so  long  as 
it  is  not  extinct,  causes  the  proto- 
plasm to  move,  to  inclose  itself,  to 
assimilate  certain  kinds  of  fresh 
matter  coming  within  the  sphere 
of  its  activity  and  to  reject  others, 
and  which,  when  in  full  action, 
makes  the  protoplasm  adapt  its 
movements  under  external  stim- 
ulation to  existing  conditions  in 
the  manner  which  is  most  ex- 
pedient ?  This  force  in  nature  is 
not  electricity  nor  magnetism  ;  it 
is  not  identical  with  any  other 
natural  force,  for  it  manifests  a 
series  of  characteristic  effects  which 
differ  from  those  of  all  other  forms 
of  energy.  Therefore  I  do  not 
hesitate  again  to  designate  as  vital 
force  this  natural  agency,  not  to 
be  identified  with  any  other,  whose 
immediate  instrument  is  the  proto- 
plasm, and  whose  peculiar  effect 
we  call  life."  Another  example 
is  that  of  Prof.  Virchow,  to  whom 
we  are  indebted  for  the  great  rev- 
olution which  the  application  of 
the  novel  conceptions  of  the  cell- 
ular   theory    has    worked    in    the 


ON    THE    VITALISTIC    VIEW    OF    NATDRE.         377 


accepting  a  mechanical  conception,"  we  must  not  "  fall 
into  the  very  common  mistake  of  trying  to  explain  vital 
processes  as  being  duo  directly  {>>  mechanical  causes." 
It  has  Ijoeu  (piite  as  impossible  to  banish  the  word 
life  from  the  biological  vocabulary  as  it  has  been  to 
banish  the  word  "  ought "  from  the  ethical,  liiological 
knowledge  has  become  purely  chemical,  physical,  and 
mechanical,  but  not  so  biological  thought.  The  question 
"  What  is  life  ?  "  still  haunts  us.  Let  us  see  what  posi- 
tion the  foremost  representatives  of  modern  biological 
research  have  taken  up  to  this  question.  We  find  that 
they  can  be  <li\id('d  intd  Iwo  classes. 

First,  there  arc  those  who  have  studied  the  pheno-         «■ 

^  T}ie  purely 

mena  of  living  matter  solely  by  the  means  which  the  f^lf^J.^""^ 
advancing  sciences  of  dynamics,  physics,  and  chemistry 
have  placed  at  their  command.  To  them  liiology  is  an 
ai)plied  science.  The  question  "  AVhat  is  life  ? "  is,  ac- 
cording to  their  view  of  method,  only  to  be  solved  by 
degrees,  by  l)ringing  the  forms  and  processes  manifested 
in  the  living  world  more  and  more  under  the  sway 
of  observation,  measurement,  and  possibly  calculation. 
The  central  problem  as  to   the  essence  of  life  and  the 


aspect. 


field  of  pathology.  After  hiiviiig 
assisted  in  b.inishing  the  older 
vitalism,  he,  to  the  dismay  of 
many  of  his  own  school,  reintro- 
duced the  conceptiun  of  a  vital 
jjrinciple  in  a  well-known  review 
entitled  "  Old  and  New  Vital- 
ism," in  his  own  journal  (vol. 
ix.  {).  20).  "  Indeed,  the  living 
body  consists,  so  far  as  we  know, 
of  substances  of  the  same  kind 
as  we  find  in  'lifeless  nature,'  and 
these  substances  have  not  only 
no  other  properties  and  powers  in 


the  living  body,  but  they  do  not 
even  lose  any  of  them.  .  .  .  Never- 
theless, we  cannot  see  how  the 
phenomena  of  life  can  be  under- 
stood simply  as  an  assemblage  of 
the  natural  forces  inherent  in  those 
substances  :  rather  do  I  consider  it 
necessary  to  distinguish  as  an  es- 
sential factor  of  life  an  impressed 
derived  force  in  addition  to  the 
molecular  forces.  I  see  no  ob- 
jection to  designating  this  force  by 
the  old  name  of  vital  force." 


378 


SCIENTIFIC    THOUGHT. 


consensus  of  many  mechanical,  physical,  and  chemical 
processes  in  the  living  organism  does  exist,  but  it  can 
only  be  answered  by  attacking  it  from  all  sides  and 
reducing  it  to  ever  narrower  issues.  The  stronghold  in 
which  life  is  intrenched  is  to  be  conquered  by  surround- 
ing it  on  all  sides  by  the  attacking  forces  of  dynamics, 
physics,  and  chemistry.  It  will  have  to  yield  some  day, 
though  that  day  may  be  far  off.  The  number  of  those 
who  treat  biology  in  this  way  has  increased  very  much 
ever  since  Descartes,^  and  still  more  Lavoisier,  applied 


^  The  claims  of  Descartes  to  be 
considered  as  one  of  the  founders 
of  modern  physiology  are  put  for- 
ward by  Huxley  in  several  of  his 
addresses,  notably  in  that  of  '  On 
Descartes'  Discours,'  &c. ,  1870 
('Lay  Sermons,'  &c.,  p.  279);  and 
in  that  on  '  The  Connection  of  the 
Biological  Sciences  with  Medicine,' 
1881  ('Science  and  Culture,'  p. 
32.5).  In  the  latter  address  he  says  : 
"  Now  the  essence  of  modern,  as 
constrasted  with  ancient,  physio- 
logical science,  appears  to  me  to 
lie  in  its  antagonism  to  animistic 
hypotheses  and  animistic  phrase- 
ology. It  offers  physical  explana- 
tions of  vital  phenomena,  or  frankly 
confesses  that  it  has  none  to  offer. 
And,  so  far  as  I  know,  the  first 
person  who  gave  expression  to  this 
modern  view  of  physiology,  who 
was  bold  enough  to  enunciate  the 
proposition  that  vital  phenomena, 
like  all  the  other  phenomena  of  the 
physical  world,  are,  in  ultimate 
analysis,  resolvable  into  matter  and 
motion,  was  Ren^  Descartes.  .  .  . 
And  as  the  course  of  his  specula- 
tions led  him  to  establish  an 
absolute  distinction  of  nature  be- 
tween the  material  and  the  mental 
worlds,  he  was  logically  compelled 
to  seek  for  the  explanation  of  the 
phenomena  of  the   material  world 


within  itself"  (p.  335).  It  is  in- 
teresting to  contrast  with  this 
announcement  of  the  banishment 
of  the  animistic  aspect  from  modern 
physiology  what  Prof.  Bunge  says 
in  the  introductory  chapter  to  his 
well-known  '  Text-book  on  Physio- 
logical and  Pathological  Chemistry  ' 
(Engl,  transl.  by  Woolridge,  1890) : 
"The  mj'stery  of  life  lies  hidden  in 
activity.  But  the  idea  of  action 
has  come  to  us,  not  as  the  result  of 
sensory  perception,  but  from  self- 
observation,  from  the  observation 
of  the  will  as  it  occurs  in  our 
consciousness,  and  as  it  manifests 
itself  to  our  internal  sense  "  (p.  7). 
"  Physiological  inquiry  must  com- 
mence with  the  study  of  the  most 
complicated  organism,  that  of  man. 
Apart  from  the  requirements  of 
practical  medicine,  this  is  justified 
by  the  following  reason,  which  leads 
us  back  to  the  starting-point  of  our 
remarks  :  that  in  researches  upon 
the  human  organism  we  are  not 
limited  to  our  physical  senses,  but 
also  possess  the  advantage  afforded 
by  the  '  internal  sense '  or  self- 
observation"  (p.  11).  "  The  essence 
of  vitalism  does  not  lie  in  being 
content  with  a  term  and  abandon- 
ing reflection,  but  in  adopting  the 
only  right  path  of  obtaining  know- 
ledge, which  is  possible,  in  starting 


ON    THE    VITALISTIC    VIKW    OF    NATURE.         37l* 


tilt'  purely  scientific  or  exact  method    to  the   study  of 
the  organism. 

But  biology  is  not  only  a  subject  of  purely  scientific  7. 
interest.  There  is  a  second  and  larger  class  of  students  ""'''«''"=• 
— those  wlio  study  liiology  as  the  basis  of  the  art  of 
healing,  the  medical  profession.  To  them  the  question 
of  life  and  death,  of  the  normal  or  abnormal  co-opera- 
tion of  many  processes  in  tlie  preservation  of  liealth 
or  the  phenomena  of  disease,  is  of  prime  interest :  the 
knowledge  of  the  mechanical,  physical,  and  chemical 
properties  and  reactions  of  living  matter,  of  the  con- 
struction of  the  organs  and  their  functions,  is  only  the 
means  to  an  cml.  Before  the  time  of  Lavoisier,  with  the 
solitary  exception  of  Descartes,  biology  was  studied  only 
l)y  medical  men ;  indeed  to  them  both  the  existence  and 
the  progress  of  the  science  were  entirely  due.  For  them 
the  paramount  questions  must  always  be,  "  What  is  life  ? 
What  is  its  origin  ?  What  is  death  ?  What  are  its 
causes  ?  What  is  disease  ?  "  To  this  class  of  students  we 
are  indebted  for  again  and  again  l)ringing  forward  and  try- 
ing to  answer  these  fundamental,  these  central  questions.^ 

By  the  other,  the  smaller  yet  increasing  class  of  purely 
scientific  biologists,  we  are  being  continually  told  that 
these    questions    are    premature    or    metaphysical,"    and 


from  what  we  know,  tlie  internal 
world,  to  explain  wliat  we  do  not 
know,  the  external  world  "  (p.  12). 
'  See,  for  example,  the  two  very 
interesting  and  suggestive  addresses 
by  Prof.  Ed.  von  llindHeisch  of 
Wiirzburg,  '  Arztliche  Philoso- 
phie'  (Wiirzburg,  1888),  and  '  Neo- 
Vitalisinus '  (Verhandl.  d.  ,Ges. 
deutscher  Naturforscher  und  Arzte 
zu  Liibeck,  1895,  vol.  i.  \>.  111). 


-  See  Claude  Bernard, '  La  Science 
Expdriinentale,'  3""'  ed.,  p.  211  : 
"  La  vie  est  I'idce  directrice  ou  la 
force  evolutive  de  I'l'tre  ;  .  .  .  niais 
I'erreur  serait  de  croire  que  cette 
force  niotaphj'sique  est  active  h  la 
fa(;on  d'une  force  physique.  .  .  . 
La  force  mdtai)hysi(iue  evolutive  i)ar 
laquelle  nous  pouvons  caractt^riser 
la  vie  e.st  inutile  h.  la  science, 
parce  qu'<?tant  en  dehoi"3  des  forces 


380  SCIENTIFIC    THOUGHT. 

that  the  answer  which  we  may  give  to  them  is  of  no 
scientific  importance  and  of  no  scientific  value.  The 
question,  "  What  is  electricity  ?  What  is  the  ether  ?  " 
cannot  yet  be  answered ;  nevertheless  the  sciences  which 
deal  with  the  properties  of  the  ether  or  of  electrical 
bodies  are  advancing  daily.  So  also — we  are  told — 
does  the  science  of  biology  progress,  even  though  we 
leave  the  question  "  What  is  life  ?  "  unanswered.  This 
would  be  a  tenable  position  if  the  living  organism  were 
like  an  electrical  or  an  optical  apparatus,  constructed  by 
man  himself  with  the  modicum  of  knowledge  which  he 
possesses.  But  the  living  organism,  the  eye  that  can 
see  or  the  nervous  system  that  is  in  action,  or  even  the 
smallest  "  autonomous  "  cell,  visible  only  with  the  micro- 
scope, are  each  an  apparatus  constructed  by  nature  with 
the  employment  of  all  the  intricate  agencies  which  are 
at  her  command.  In  dealing  with  such  an  apparatus, 
we  are  again  and  again  tempted  to  ask,  "  What  is  life  ? 
On  what  does  the  normal  and  healthy  co-operation  of 
all  parts  in  the  living  organism  depend  ?  In  what  does 
it  consist  ? "  Fragmentary  knowledge  may  be  well 
enough  so  far  as  it  goes,  but  every  medical  practitioner 
must  painfully  feel  it  to  be  altogether  insufficient. 
Where  practical  interests  are  involved  we  cannot  in- 
definitely postpone  our  answers.      Science  can  wait  and 


physiques  elle  ne  peut  exercer 
aucune  iufluence  sur  elles.  II  faut 
done  ici  separer  le  monde  meta- 
physique  du  monde  physique  phe- 
nomenal qui  lui  sert  de  base,  mais 
qui  n'a  rien  h  lui  emprunter.  .  .  . 
En  rcsum^,  si  nous  pouvons  definir 
la   vie    ii    I'aide    d'une    conception 


pas  moins  vrai  que  les  forces  me- 
caniques,  physiques,  et  chimiques, 
sont  seules  les  agents  effectifs  de 
I'organisme  vivant,  et  que  la  physio- 
logiste  ne  peut  avoir  k  tenir  compte 
que  de  leur  action.  Nous  dirons 
avec  Descartes  :  on  pense  m^ta- 
physiquement,  mais    on    vit    et  on 


metaphysique  sp^ciale,  il  n'en  reste       agit  physiquement." 


ON    THE    VITALISTIC    VIEW    OF    NATURE. 


381 


content  itself  with  the  known  and  the  knowable.  Prac- 
tice is  placed  face  to  face  willi  tlio  unknown  and  tlie 
unknowable.^  Thus  the  question  will  auain  and  again 
be  asked,  "What  is  life?"  And  for  the  benefit  or 
injury  of  mankind  theories  will  exist  which  profess  to 
handle  this  delicate  problem  successfully,  even  as 
weather-prophets  will  always  exist  though  the  necessary 
knowledge  for  accurate  prediction  is  still  wanting. 

One  of  the  first  in  time  and  eminence  in  the  course  of 
the  nineteenth  century  to  whom  we  are  indebted,  not 


8. 
Practice 
ur^'cs  the 
quuKliun : 
Wlial  U 
Life? 


9. 
Bichat. 


'  See  what  Tlieod.  Bischoti',  one 
of  the  first  and  foremost  German 
anatomisttj  of  the  new  school,  says 
in  his  Eloge  of  Liebig  (Miinchen, 
1874),  p.  60.  "  Inorganic  science  is 
not  any  way  induced  and  is  nmch 
less  obliged  to  forsake  the  road 
from  the  known  to  the  unknown. 
But  what  would  have  been  the 
result,  what  would  still  be  the 
result,  if,  in  all  our  researches  into 
organised  nature,  and  yet  nioi-e  in 
all  our  actions  which  have  refer- 
ence to  our  state  of  health  or  ill- 
health,  we  had  proceeded,  or  were 
now  to  proceed,  only  from  data 
firmly  established  as  to  cause  and 
Connection  '(  Could  we  then  so  much 
a.s  take  a  morsel  into  our  mouths 
or  treat  a  cold  otlierwise  than  with 
fear  and  trembling  ?  Physiologists 
and  doctors  have  surcl^'  always  been 
ready  to  proceed  according  to  the 
methods  of  exact  science  so  far  as 
this  was  developed.  But  so  long  as 
this  gave  but  a  stone  instead  of 
bread,  acceptance  could  n(Jt  be 
thougiit  of  ;  necessity  compelled 
us  to  m.ake  some  attempt  towai-ds 
the  solution  of  questions,  to  invent 
some  language  in  order  to  gain  an 
understanding ;  and  through  this 
fi-e([uently  an  erroneous  ])ri>cedure 
has  arisen  which  outlives  the  means 
for  its  correction."     "Physiology," 


says  Du  Bois-Reymond  (Eloge  of 
Joh.  Miiller,  '  Reden,'  vol.  ii.  p. 
19!>),  "  is  the  only  science  in  which 
one  is  obliged  to  speak  about  things 
which  one  does  not  know.  Chem- 
istrv  need  not  treat  of  unknown 
compounds,  nor  physics  of  undis- 
covered forces  ;  botany  and  zoology 
do  not  miiid  what  kind  of  animals 
may  still  move  about  unknown 
among  unknown  vegetation  in  un- 
explored regions.  But  in  physi- 
ology, even  if  we  confine  ourselves 
to  man,  a  definite  number  of  things 
is  given  which  must  be  dealt  with. 
The  spleen,  the  thyroid  gland,  the 
thymus,  the  suprarenal  capsules  ; 
many  parts  of  the  brain,  ganglia, 
nerves,  the  labyrinth  of  the  ear — all 
these  are  there,  and  nmst,  accoidiiig 
to  the  customary  view,  be  there  for 
something.  Manifold  suppositions 
as  to  the  functions  of  these  parts, 
seemingly  supported  or  invalidated 
b}'  pathological  experience,  have 
put  in  the  place  of  absolute  dark- 
ness a  twilight  which  is  richer  in 
delusions  though  not  in  certainty. 
The  e.\  pounder  of  our  science  is 
obliged  to  lead  his  pupils  through 
this  twilight  on  an  anxious  ])ath, 
and  then  meet  in  return  with  that 
discouragement  which  really  is 
owing  to  the  suV)ject  itself." 


382  SCIENTIFIC    THOUGHT. 

indeed  for  the  name,  but  for  'the  modern  science  and 
direction  of  biology,  was  Xavier  Bichat,  who  during  the 
short  period  of  his  remarkable  career  (1771  to  1802) 
remodelled  biological  studies.  He  approached  the  sub- 
ject from  the  side  of  medicine  and  in  a  philosophical 
spirit.  In  1800  there  appeared  two  treatises,  one 
on  the  membranes  and  tissues,  and  another  entitled 
"  Eecherches  physiologiques  sur  la  vie  et  la  mort." 
These  by  their  titles  already  reveal  the  twofold  aspect 
of  biological  science  which  drew  the  attention  of  Bichat 
and  his  school.  First,  the  attempt  to  reform  biological 
and  medical  knowledge  by  a  close  anatomical  examination 
of  organic  tissues  in  their  normal  and  diseased  states,  for 
the  purpose  of  which  he,  within  a  very  short  time,  ex- 
amined six  hundred  corpses.  The  fuller  account  of  his 
researches  is  given  in  the  four  volumes  of  the  '  Anatomie 
Gen^rale '  (1801)  and  in  the  posthumous  five  volumes 
of  the  '  Anatomie  Descriptive,'  completed  by  some  of 
his  numerous  pupils  and  followers  after  his  death.  In 
these  works  Bichat  created  the  science  of  histology 
without  resorting  to  the  microscope,  which  was  to  do 
such  good  service  in  the  hands  of  those  who  came 
after  him,  and  without  that  application  of  physical  and 
chemical  principles  which  during  his  time  (notably 
by  Lavoisier  and  his  school)  had  been  applied  with 
much  success  in  the  theory  of  animal  combustion  and 
in  the  foundation  of  another  new  science — that  of 
organic  chemistry.  The  reasons  which  inclined  Bichat 
to  distrust  the  microscope  were  the  delusive  nature  of 
the  revelations  of  the  imperfect  instruments  then  in  use. 
They  disappeared  when,  in  the  course  of  the  next  thirty 


ON    THE    VITALISTIC    VIKVV    OF    NATUliE.         383 

years,  the  instrument  was  gradually  improved.  The 
reasons  which  prevented  Bichat  from  treating  biology 
as  an  application  of  pliysics  and  chemistry  lay  deeper, 
and  were  rooted  in  the  second  great  idea  which  governed 
him  and  his  school — his  "  Vitalism."  As  stated  above,  lo. 
those  who  have  studied  the  phenomena  of  life  can  be  vitalism, 
divided  into  two  classes.  There  are  those  who  have 
been  struck  by  the  resemblance  of  the  processes  and 
phenomena  in  living  matter  with  those  in  dead  or 
unorganised  matter :  their  attention  has  been  directed 
more  and  more  to  establishing  a  paralleHsm  between 
organic  and  inorganic  nature,  and  they  have  fre- 
quently ended  in  the  conviction  tliat  their  parallelism 
warrants  us  in  asserting  their  ultimate  identity.  There 
have  been  others  who  have  lieen  impressed  with  the 
essential  and  fundamental  difference  between  organic 
and  inorganic  processes  and  phenomena.  To  them,  all 
attempts  to  reduce  the  living  process  to  a  mechanism 
seem  to  have  failed,  and  however  much  they  have  ap- 
preciated the  insight  gained  Ijy  the  other  class  of 
students,  they  have  deemed  it  equally  important  to 
emphasise  the  essential  difference — the  independence, 
originality,  and  incommensurability  of  the  phenomena  of 
life.  The  latter  can  be  called  Vitalists  in  the  broadest 
sense  of  the  term.  Bichat  belonged  to  them.  As  the 
former  class  of  students  have  frequently  arrived  at  the 
thesis  that  organic  and  inorganic  processes  are  ulliin- 
ately  identical,  so  the  latter  have  frequently  arrived 
at  the  thesis  that  they  are  fundamentally  opposed  and 
antagonistic.      Bichat   gives  expression   to  this  view  in        n. 

°  O  1  Hisdctlni- 

his  celebrated  definition  of  life,  as  the  totality  of  those  ti'^""i'ife. 


384 


SCIENTIFIC    THOUGHT. 


functions  which  resist  death.  He  adopts,  on  the  one 
side,  the  method  of  looking  for  the  explanation  of  the 
phenomena  of  matter  in  the  properties  of  matter.  In 
the  introduction  to  the  '  Anatomie  Generale,'  he  says :  ^ 
"  The  connection  of  the  properties  as  causes  with  the 
phenomena  as  effects  is  an  axiom  which  has  become 
almost  tiresome  to  repeat  nowadays  in  physics  and 
chemistry :  if  my  book  establishes  an  analogous  axiom 
in  the  physiological  sciences,  it  will  have  fulfilled  its 
purpose."  But  being  convinced  of  the  essential  difference 
of  the  object  with  which  the  physiologist  is  concerned, 


1  Claude  Bernard  (1813-78),  from 
whose  various  writings  the  passages 
of  Bichat  are  mostly  taken,  has  very 
fully  analysed  the  theoretical  views 
of  his  eminent  predecessor.  The 
following  books  belong  to  the  best, 
in  substance  and  notably  in  style, 
that  have  been  written  on  the  sub- 
ject :  '  La  Science  Experimeutale,' 
3"'«  ed.,  1890  ;  especially  :  '  Defini- 
tion de  la  vie,'  p.  119,  kc.  ;  '  Lecons 
sur  les  Phenomenes  de  la  vie  com- 
muns  aux  animaux  et  aux  v^ge- 
taux,'  1878,  especiallj'  vol.  i.  p.  57, 
&c.  ;  '  Rapport  sur  les  progres  et 
la  raarche  de  la  Physiologie  gdnerale 
en  France,'  1867.  Inti-oduetion. 
Although-  Bichat  was  a  vitalist,  he 
took  a  tii'st  and  important  step  in 
the  direction  of  getting  out  of  the 
vitalistic  conceptions  which  he  in- 
herited from  Haller,  and  which  had 
assumed  a  special  form  in  the 
Montpellier  school.  Through  his 
foundation  of  physiological  research 
upon  an  anatomical  study  uf  tissues, 
he  localised  the  ])robleui  of  physi- 
ology. Had  he  proceeded  further 
on  the  lines  he  himself  started,  he 
would  have  thrown  off,  like  his 
successors,  notably  Magendie,  the 
hypothetical  distinction  between 
physical,  chemical,  and  vital  pro- 
perties,   and    become    a    pure   ex- 


perimentalist. The  founder  of  this 
purely  experimental  school  in 
France  was  Magendie  (1783-1855). 
It  is  interesting  to  note  that  prior 
to  Magendie  in  France,  Charles 
Bell  in  London  had  led  up  to 
experimental  physiology  in  Eng- 
land by  his  famous  distinction  be- 
tween sensory  and  motor  nerves 
(1811).  But,  according  to  Claude 
Bernard,  this  anatomical  distinction 
required  experimental  verification 
in  a  living  animal.  Magendie 
furnished  this  in  182"2,  and,  together 
with  this  corner-stone  of  modern 
physiologj',  laid  the  foundations  of 
the  art  of  vivisection,  with  all  its 
wonderful  discoveries  and  its  dis- 
favour in  certain  quarters.  There 
is  no  doubt  that  for  many  years 
Paris  became,  through  this  in- 
novation, the  centre  of  medical 
teaching  on  the  Continent.  As  to 
the  distinctive  merits  of  Bell  and 
Magendie,  see  Claude  Bernard's 
exhaustive  examination  ('  Physiol, 
gen.,'  p.  11,  &c. ),  but  also  Du  Bois- 
Keymoud's  Eloge  of  Johannes 
Miiller  ( '  Reden,'  vol.  ii.  p.  176, 
&c. )  According  to  him  the 
"Thesis  "  of  Bell  was  not  generally 
considered  to  be  proved  till  after 
Midler's  experiments  in  1831. 


ON    THE    VITALISTIC    VIEW    OF    NATURE. 


385 


he  does  not  advance  to  the  position  that  the  same 
method  will  lead  to  parallel  results.  "  There  are,"  he 
says,  "  in  nature  two  classes  of  things,  two  classes  of 
properties,  two  classes  of  sciences.  Beings  (things)  are 
organic  or  inorganic,  their  properties  are  vital  or  non- 
vital,  the  sciences  are  physical  or  physiological."  He 
did  not  anticipate  that  a  faithful  examination  of  the 
properties  of  organised  matter,  of  membranes  and  tissues 
— which  should  not  be  limited  to  lifeless  corpses — would 
more  and  more  reveal  that  their  properties,  the  forces 
acting  on  and  in  them,  could  be  analysed  into  the 
same   forces   as    those  we  find  in   the  inorganic  world.^ 


^  According  to  Claude  Bernard 
('Physiol,  gen.,'  p.  5,  &c.),  three 
things  were  wanting  at  the  be- 
ginning of  the  nineteenth  century 
to  place  physiology  on  a  sjitisfactory 
basis.  The  first — anatomical  know- 
ledge of  the  structure  of  living 
matter — \va.s  brilliantly  established 
by  Bichat.  But  Bichat  was  not  a 
physiologist  :  he  neglected  the 
second  requisite,  the  study  of  the 
continual  conflict  Vietween  the  liv- 
ing organism  and  the  mechanical 
influences  of  the  ''milieux,"  the 
environment.  "II  faudra" — says 
Bernard — "  tenir  compte  de  deux 
ordres  de  conditions  :  1°,  des  con- 
ditions anatomiques  de  la  matiore 
organisee  qui  domient  la  nature 
ou  la  forme  des  phcnomi^nes 
physiologiques  ;  2°,  des  conditions 
physico  ■  chimiques  ambiantes  qui 
ddterrainent  et  reglent  les  mani- 
festations vitales."  A  third  im- 
pulse was  wanted  in  phy .biology  : 
"  il  fallait  la  ramener  (lefinitive- 
ment  ^  la  mcthode  des  sciences 
expdrimentales  ;  il  fallait  la  jwusser 
avec  vigueur  dans  la  direction  des 
experiences  sur  les  organismes 
vivants,  afin  de  la  dctourner  de  la 

VOL.  II. 


voie  des  hypotheses  et  des  explica- 
tions prcmaturees  dans  laquelle 
elle  s'etait  si  souvent  egaree. 
Un  grand  physiologiste  francais, 
Magendie,  mon  maitre,  est  venu, 
au  commencement  de  ce  siecle, 
exercer  cette  action  gendrale  sur 
la  science  physiologique,  en  mcme 
temps  qu'il  I'enrichissait  par  ses 
propres  decouvertes.  Magendie  fut 
eleve  dans  I'ecole  anatomique  de 
Paris,  mais  il  n'otait  point  dispose 
a  suivre  les  successeurs  de  Bichat 
dans  leurs  explications  hypothe- 
tiques.  Doud  d'un  esprit  prt^cis 
et  penetrant,  sceptique  et  in- 
dependant,  il  fut  lie  de  bonne 
heure  avec  Laplace,  ([ui  le  patronna. 
Par  cette  influence  il  se  trouva 
encore  fortifid  dans  son  auti{)athie 
iunee  pour  les  explications  physi- 
ologiques dans  lesquelles  on  ne 
se  payait  que  de  mots.  Puis, 
par  une  tendance  spontande  de 
reaction  qui,  Ji  cette  dpoque,  fut 
trcs  utile  ii  la  physiologic,  il 
s'arreta  Ji  I'expcrimentation  em- 
pirique,  c'est-il-dire  au  rdsultat 
brut  de  I'expdrience  considdrde  en 
dehors  de  toute  interprdt;ition  et 
de  tout  raisonnement." 

2    B 


386  SCIENTIFIC    THOUGHT. 

Bichat,  as  Claude  Bernard  has  told  iis,^  thus  clearly  and 
eloquently  found  the  expression  or  "  formula  for  the 
fleeting  ideas  of  his  age.  All  the  ideas  of  his  con- 
temporaries regarding  life,  all  their  attempts  to  define 
it,  are,  in  a  way,  only  the  echo  and  paraphrase  of  his 
doctrine."  We  find  it  repeated  by  surgeons  like  Pelletan, 
who  practised  in  the  Hotel  Dieu,  and  by  great  naturalists 
like  Cuvier,  who  founded  comparative  anatomy.  To  both 
of  these  life  was  a  contest,  a  struggle,  as  it  is  at  the  end 
of  the  century  to  the  Darwinians ;  but  it  was  a  struggle 
of  the  living  forces  against  the  dead,  whereas  nowadays 
it  is  the  struggle  of  the  living  for  supremacy  amongst 
each  other  or  a  process  of  adaptation  to  external  condi- 
12.        tions.       Whilst  there  is    this    great   difference  between 

Vitalism  ami  _  _ 

Darwinism,  thcsc  two  views  characterising  respectively  the  begin- 
ning and  the  end  of  our  century,  they  have  one  point 
in  common — they  both  emphasise  the  unrest,  the  con- 
tinued change,  the  extreme  mobility  which  distinguishes 
Hving  matter.  But  even  this  distinction  has  ceased 
during  the  course  of  the  century  to  impress  us  so 
much  as  it  did  Bichat ;  since  the  stability  of  the  solar 
system  proclaimed  by  Laplace  has  ceased  to  charm 
astronomers,  and  the  dictum  of  ancient  science  has 
been  refuted  :  "  materiam  cceli  esse  inalterabilem."  ^ 


'  '  La  Science  Experimentale,' 
p.  164. 

-  Claude  Bernard  {loc.  cit.,  p. 
172,  &c.)  dwells  on  this  point  with 
great  eloquence.  "  Aujourd'hui 
I'esprit  des  astronomes  est  familiar- 
ise avec  I'idee  d'une  mobilite  et 
d'une  evolution  continuelle  du 
monde  sidoral.  Les  astres  n'ont 
pas  toujours  existe,  dit  M.  Faye ; 
ils    ont    eu    une    periode    de    for- 


mation ;  ils  auront  pareillement 
une  pi^riode  de  declin,  suivie  d'une 
extinction  finale.  .  .  .  Les  as- 
tronomes, avant  de  connaiti-e  les 
lois  des  mouvements  des  corps 
celestes,  avaient  imagine  de  i puis- 
sances, des  forces  siderales,  comma 
les  physiologistes  reconnaissaient 
des  forces  et  des  puissances  vitales. 
Kepler  lui  -  meme  admettait  un 
esprit  recteur  sideral  par  I'influence 


ON    THE    VITALISTIC    VIEW    OF    NATURE. 


387 


inorganic 
in    that 
century. 


After  the  age  of  IJichat,  and  largely  through  his 
influence, — i.e.,  through  the  cultivation  of  anatomical 
researches, — the  pendulum  swung  in  the  direction  of 
proving  more  and  more  the  parallelism  of  organic  and 
processes.  It  reached  its  maximum  swing 
direction  about  the  secon<l  third  of  the 
Since  then  it  appears  to  have  again  returned 
in  the  opposite  direction.  Let  us  follow  this  movement 
somewhat  more  closely,  and  see  liow  the  stronghold  in 
which  the  innermost  secret  of  life  is  intrenched  has 
been  attacked  from  all  sides  Ijy  all  the  processes  and 
methods  of  the  mechanical,  physical,  and  chemical 
sciences,  and  how  it  has  persistently  refused  to  sur- 
render.^      There   was    a    time   when   the  leading  repre- 


Uuquel  \es  plaiiotes  suiveut  dans 
I'espace  des  courbe.s  savantes  saus 
heurter  les  astres  qui  fournissent 
•d'autres  carricres,  sails  troubler 
rhannouie  reglee  par  le  diviii 
geoiiiotre."  Another  j)ri)pei-ty  which 
was  once  thouglit  pecuHar  to  and 
cliaracteristic  of  Hving  organisms, 
that  of  regeneration  after  mutila- 
tion, of  "redintegration,"  is  now 
known  to  exist  also  in  lifeless  struc- 
tures: "  M.  Pasteur  a  signalo  des  f aits 
<le  cicatrisation,  de  redintegration 
cristalline,  (\\ii  mdritent  toute  notre 
attention.  .  .  .  Ces  faits  .  .  .  se 
rapproclient  conipletement  de  ceu.K 
que  presentent  les  etres  vivants 
lorsqu'on  leur  fait  une  plaie  plus 
ou  moins  profonde"^(ibid.,  p.  173). 
^  Bischoff,  in  his  Eloge  of  Liebig, 
who  remained  all  his  life  a  vitalist, 
says  (p.  57) :  "We  must,  indeed,  as 
in  the  exact  sciences,  guard  against 
letting  a  mere  word  step  in  as  an 
explanation,  wherever  our  insight 
into  the  conditioning  causes  has 
been  insufficient,  as  was  indeed  re- 
peatedly dune  formerly,  when  a 
Word  was  considered  to  be  a  sufH- 


cient  reason.  We  must  consider  it 
to  be  the  continual  duty  of  organic 
science  to  wage,  as  it  were,  a  con- 
stant war  against  thi>  oi-ganic  force, 
and  to  dispute  its  territory  where- 
soever possible.  If,  for  example,  a 
talent  like  his  succeeds  in  deducing 
many  morphological  traits  of  the 
higher  animal  organisms  from  the 
mechanical  conditions  of  growth  in 
the  embryo,  &c.,  we  shall  grate- 
fully accejit  the  proof  ;  but  we 
must  all  the  while  not  forget  to 
ask  the  further  question,  by  whom 
these  mechanical  conditions  have 
been  brought  together.  If  it  be 
further  true  that  the  cells  of  the 
embryo  perform  the  most  extra- 
ordinary wanderings,  in  order  to 
arrange  tliemselves  into  the  various 
tissues  and  organs  of  the  animal 
body,  we  shall  welcome  this  as  a 
very  interesting  and  remaikalile 
phenomenon  in  the  obscure  region 
of  development  ;  but  we  have  re- 
ceived uo  light  on  the  question  who 
acts  as  guide  to  the  wandering  cells. 
Similarly,  if  chemistry  should  some 
day  succeed  in  forming  albumen  ar- 


388 


SCIENTIFIC    THOUGHT. 


13. 

The  extreme 
■vitalism. 


sentatives  of  the  medical  profession  considered  it 
unworthy  and  degrading  to  treat  the  human  frame 
as  a  mechanism,  and  to  approach  it  by  the  methods 
used  in  other  sciences.  "  For  the  vitalist  physician," 
says  Hehnholtz,^  "  the  essential  part  of  the  vital  pro- 
cesses did  not  depend  on  natural  forces  which  act 
according  to  fixed  laws.  What  these  could  do  ap- 
peared of  secondary  importance,  and  a  study  of  them 
hardly  worth  the  trouble.  He  thought  to  be  face  to 
face  with  something  soul-like," — the  anima  of  Stahl, 
the  vital  force  of  the  vitalists, — "  which  had  to  be  met 
by  a  thinker,  a  philosopher,  a  man  of  spirit.  .  .  .  Aus- 
cultation and  percussion  were  practised  in  the  hos- 
pitals," but  I   have  heard  it  said  that  these  were  crude 


tificially,  we  shall  probablj'  be  able 
to  date  from  that  day  an  entirely 
new  period  in  natural  science,  but 
this  artificial  production  of  albumen 
will  never  be  feasible  through  the 
simple  affinities  of  the  elements, 
but  only  by  producing  a  new 
arrangement  in  organic  substances 
already  formed  by  the  plant.  We 
shall  gratefully  receive  all  such 
increase  of  our  knowledge :  we  do 
not  require  wonders  and  belief  in 
miracles  for  the  vital  force,  but 
only  a  name  for  the  effects  of 
which  we  do  not  know  the 
causes.  .  .  .  Neither  the  ancient 
primpeval  ooze  nor  the  modern 
Bathybius,  neither  the  remote 
monads  nor  the  recent  monera, 
neither  protoplasm,  nor  nucleus 
and  cell  and  their  development, 
confessedly  so  simple  and  easily 
understood  up  to  self  -  conscious 
man,  give  us  the  smallest  clue 
to  the  forces  at  work  and  their 
origin.  This  induces  us  to  ascribe 
them  to  a  force,  regarding  the 
essence  of  which  we  indeed  know 


no  more  than  we  know  of  any 
cause  that  cannot  be  further  an- 
alysed. But  we  admit  in  doing 
so  the  imperfection  of  our  know- 
ledge, and  do  not  deceive  others 
by  suggesting  that  mechanical 
science  could  solve  the  secret  of 
organised  nature." 

^  'Vortriige  und  Reden,'  vol.  ii. 
p.  179. 

-  Chr.  Fried.  Nasse  (1778-1851), 
since  1822  professor  at  Bonn, 
where,  together  with  Walther, 
Joh.  Miiller,  and  others,  he  cul- 
tivated the  physiological  method 
in  medicine,  "  was,  as  it  seems, 
the  first  German  doctor  in  whose 
clinical  institute  physical  diagnosis 
was  introduced.  From  1820  on- 
ward percussion  was  practised  ; 
since  1821  the  stethoscope  was 
regarded  as  an  indispensable  in- 
strument "  (Haeser,  '  Geschichte 
der  Medizin,'  .3rd  ed.,  Jena,  1881, 
p.  912).  "The  thermometer  was 
first  used  extensively  at  the  bed- 
side by  James  Currie  (1756-1805). 
His  '  Medical  Reports  on  the  effect 


ox    THE    VITALISTIC    VIEW    OF    NATUKE. 


!89 


mechanical    devices    which    a    physician    witli     a    clear 
mental   vision   did   not    require :   moreover,   the   patient 
would   thereby  be  degraded  and  treated  as  a  machine. 
Feeling   of   the   pulse  was    the   most   direct  method  of 
ascertaining  tlie  reactive  power  of  the  vital  forces,  and 
was  delicately  practised  as  the  most  important  process. 
Elderly  practitioners  considered  counting  with  a  second- 
watch    as   hardly   good    taste :    taking   the    temperature 
was   not  thought  of.     As  to   the  eye-mirror,   a  highly 
celebrated   surgical   colleague   told   me   he  would  never 
use  the  instrument,  it  being  dangerous  to  throw  brilliant 
light   into   suffering  eyes :    another  declared  the  mirror 
might  do  well  for  oculists  with  poor  sight ;   he  himself 
possessed  very  good  eyes  and  did  not  need  it.  ...  A 
celebrated  professor  of  physiology  had  an  argument  with 
his   colleague   in   physics    regarding    tlie   images   in    the 
eye.     The  professor  of  physics  invited  him  of  physiology 
to  come  and  see  the  experiment.      This  was  indignantly 
refused :  a  physiologist  should  have  nothing  to  do  with 
experiments,  which  might  do  well  enough  for  a  physicist." 
The    first   great   attack    upon   the  organic  system   of        u. 

Attack  from 

forces,  upon  the  citadel  of  life,  was  made  by  chemistry,  ti'csideof 
and  was  led  by  Lavoisier  and  the  great  school  of  chemists 
which  continued  his  work.      It  consisted  in  the  applica- 
tion of  the  theory  of  combustion,  in  which  oxygen  played 
such  an  important  part,  to  the  processes  of  respiration, 


chemistry. 


of  water,  cold  and  warm,  as  a 
remedy  in  fever  and  otlier  disease.--,' 
Loudon,  1797,  "contains  observa- 
tions on  the  variations  of  the 
body-temjjerature.  .  .  .  But  these 
attempts  had  little  success.  Not 
till  the  middle  of  the  nineteenth 


century  was  the  importance  of 
medical  thermometry  recognised, 
first  through  the  classical  work 
of  von  Biirensprung  (1851),  tlien 
through  that  of  Trauhe,  but 
mainly  through  Wuuderlich " 
(ibid.,  p.  930). 


390  SCIENTIFIC    THOUGHT. 

nutrition,  and  the  generation  of  animal  heat.^  Already  in 
1783  Lavoisier  and  Laplace  had  presented  a  memoir  to 
the  Paris  Academy  of  Sciences,  in  which  they  attributed 
the  generation  of  animal  heat  mainly  to  a  process  of 
combustion  which  took  place  by  the  conversion  of  oxy- 
gen into  fixed  air  during  the  process  of  respiration. 
Lavoisier  continued  his  researches  on  these  and  other 
similar  physiological  processes,  such  as  perspiration, 
along  with  Seguin.  They  presented  a  joint  memoir 
on  the  subject  in  1790.  It  is  also  known,  through 
the  posthumous  publication  of  Lavoisier's  scientific 
papers  in  1862,  long  after  Liebig  had  brought  out  his 
series  of  researches  on  this  matter,  that  the  former  had 
entertained  very  correct  views  on  the  economy  of  organic 
life  as  it  exists  in  the  balance  of  the  animal  and  veo;e- 
table  creations.  After  Lavoisier,  the  application  of  the 
new  science  of  chemistry  to  questions  of  the  individual 
and  collective  life  of  organisms  was  extended  in  a  series 

^   The   two   great   discoveries    of  ]    de  riiomme '   (]798),  by  .1.    P.    T. 

oxygen    and    of    the    electric    cur-  !    Baumes     of     Montpellier,    against 

rent  at  the  close  of  the  eighteenth  which  Fourcroy  aimed  his  ciiticisnis 

century    were    not    long    in    being  in  a  letter  to  Humboldt.     On  these 

applied    to  the  reform  of  medical  extravagances     see     Haeser,     '  Ge- 

doctrine.     In  both  instances  exag-  j    schichte    der    Medicin,'    vol.    ii.    p. 

gerated  theories  were  not  wanting.  |    737,     &c.  ;      also     I)r     A.    Hirsch, 

Fourcroy,  himself  a  medical  student  I    '  Gesch.  d.  medicin.  Wissenschaften 


by  profession  and  one  of  the  most 
ardent  followers  and  promoters  of 
the  new  chemistiy,  who,  moreover, 
edited  a  journal  with  the  title  '  La 
medecine  eclairee   par  les   sciences 


in  Deutschland '  (Miinchen,  1893, 
p.  .567).  There  is  no  doubt  that 
opposition  to  this  one-sided  ap- 
plication of  some  chemical  or 
])hysical  theory,  or  of  some  special 


physiques'(1790-92), found  itnever-  [  therapeutic   method,    which    might 

theless   necessary  to  give   warning  '  be   valuable  to  a  limited    and    re- 

against  the  premature  introduction  ,  stricted    degree,    partly    accounted 

into  medical  teaching  of  the  new  !  for  the  fact  that  the  more  thinking 


ideas  of  chemistry.     Of  this  many 
instances   existed,   both   in    France 


members    of   the   pi-ofession    clung 
to   the  notion   of  a   vital  force  or 


and  Germany,  such   as  the  'Essai    \    principle,     as    yet    undefined    but 
d'un  systeme  chimique  de  la  science    1    nevertheless  existent. 


ON    THK    VITALISTIC    VIKW    UF    NATURK.         391 

of  very  valuable  but  unconnected  researches  in  all  the 
(litlerent  countries  where  chemistry  was  cultivated. 
Priestley,  in  England,  hiul  noticed  ilu'  purifying  effect 
of  plants  on  air ;  De  Saussure,  in  a  series  of  remarkable 
experiments,  carried  on  in  the  last  years  of  the  eighteenth 
century  at  Geneva,  established  the  fact  that  in  sunlight 
plants  increase  the  quantity  of  cailnm  and  other  con- 
stituents in  their  tissues.  Ingenhousz  in  Holland  and 
Senebier  in  France  had  shown  that  in  the  presence  of 
sunlight  bubbles  of  oxygen  gas  are  given  off  by  plants 
when  plunged  under  water,  and  had  traced  this  oxygen 
to  its  source,  the  carbonic  acid  in  the  atmosphere.  Sir 
Humphry  Davy  had  applied  chemistry  to  agriculture ; 
and,  much  later,  (Jerman  physiologists  like  Tiedemann 
and  Johannes  ^Midler  had  recognised  the  necessity  of 
explaining  the  processes  in  the  living  body  chemically. 
All  these  labours,  however,  were  detached,  and  their 
value  was  little  known.  It  was  therefore  a  very  timely 
proposal  which  issued  from  the  British  Association  in 
1839,  that  a  report  on  the  present  state  of  organic 
chemistry  should  1)6  drawn  up.  For  this  task  no  less 
a  person  than  Justus  Liebig  was  selected.^     The  event 


1  The  sources  of  information  on 
Liebig'.^  great  work  in  revolutionis- 
ing the  science  of  life  tViiough  his 
application  of  organic  chemistry  to 
agriculture  and  i>hysiology  are  nu- 
merous. In  particular  there  are 
two  aclilresses  by  Vogel  and  von 
Bischoff,  delivered  in  the  Munich 
Academy  in  1874,  Hof mann's  "  Fara- 
dav"  lecture,  delivered  in  the  Royal 


Liebig,  his  Life  and  Work."  Bis- 
ohofTs  address  contains  a  very  full 
discussion  of  Liebig's  vitalistic  sym- 
])athies.  His  great  influence  was 
established  as  much  by  his  sjjecial 
scientific  discoveries  as  by  his 
method  of  teaching, — by  his  early 
attempts  to  popularise  science  and 
make  it  an  educational  power 
through   his  well-known  '  Familiar 


Institution    in     187.'>,    and    a    very  j    Letters.'     He  was  in  this  respect  a 

able  sunnnary,  drawn  mainly  from  i    pioneer,  as  aftei- liiin  Hehuholtz  and 

these  sources  by  Mr  W.   A.   Shen-  [    Du  Bois-Reyniond  were  pioneers  in 

stone,  in  Cassell's 'Century  Science'  spreading  scientific  ideas  by  means 

Series  (189:")),  entitled  ".Justus  von  of  ]inpular  lectures  and  addresses. 


392 


SCIENTIFIC    THOUGHT. 


marks  an  epoch  equally  in  the  science  of  organic  chemistry 
proper  and  in  the  life-work  of  Liebig.  The  necessity 
of  collecting  and  systematising  the  scattered  labours 
of  chemists  and  physiologists  in  this  department  was 
simultaneously  felt  in  France,  where  Liebig's  friend  and 
rival,  Dumas,  published  his  '  Essai  de  Statique  chimique 
des  ^tres   organises '  as   a   conclusion   to   his  course  of 


Liebig  broke  through  the  barriers 
which  in  his  age  separated  science 
in  Germany  from  general  culture, 
and  the  university  professor  from 
the  man  of  the  world.  From  France 
he  learnt  the  merit  of  a  clear  style, 
and  from  England  the  higher  art  of 
popularisation.  His  fame  did  not 
grow  slowly  and  surely  like  that  of 
Helmholtz,  spreading  almost  imper- 
ceptibly from  narrower  into  ever 
wider  circles  :  he  took  the  world 
by  surprise,  and  stirred  up  every- 
where inquiry,  opposition,  and  con- 
troversy. He  ventured  on  great 
and  sweeping  generalisations  and  on 
daring  experiments  and  prophecies, 
with  the  result  that  in  the  final 
establishment  of  truth  his  oppon- 
ents had  frequently  as  great  a  share 
as  himself.  Notable  instances  are 
his  so  -  called  "  mineral  theory  " 
of  manuring  and  his  theory  of  fer- 
mentation. Through  the  former 
the  great  division  which  separated 
the  processes  in  the  living  from 
those  which  obtained  in  the  inani- 
mate (mineral)  world  was  broken 
down ;  and  through  the  latter  the 
modern  notions  of  the  ubiquity  and 
continuity  of  life  were  to  a  large 
extent  established,  as  will  be  seen 
in  the  sequel  of  this  chapter.  The 
correct  notions  which  he  enter- 
tained as  to  the  necessity  of  the 
mineral  ingredients  (phosphoric 
acid,  lime,  potash,  &c.)  in  plant- 
manures,  which  he  started  in  op- 
position to  the  older  "  humus  "  or 
"  vegetable  mould  "  theory,  was  on 
the  point  of  being  refuted  by  his 


insistence  on  making  his  chemical 
fertilisers  insoluble,  ignorant  as  he 
then  was  of  the  absorbing  and  re- 
taining function  of  mould  ;  but,  a 
generation  after,  the  prevailing  pre- 
dilection for  soluble  manures  was 
again  much  modified  by  the  intro- 
duction of  the  "  Thomas  slag,"  and 
the  enormous  improvements  in  the 
process  of  extreme  pulverisation. 
Prof.  Vogel  in  his  above-mentioned 
address  gives  many  extracts  from 
Liebig's  writings,  referring  to  the 
final  and  corrected  expression  of 
the  chemical  theory  of  fertilisation. 
These  are  so  characteristic  of 
Liebig's  habit  of  thought  and  his 
whole  mental  attitude,  that  I  tran- 
scribe them:  "When  I  knew  the 
reason  why  my  fertilisers  would  not 
act,  I  felt  like  a  man  who  had  re- 
ceived a  new  life,  for  through  this 
all  processes  of  agriculture  were 
explained,  and  now  that  the  law 
is  known  and  lies  clearly  before 
our  eyes,  there  remains  only  the 
wonder  that  we  did  not  see  it  long 
ago  :  but  the  human  mind  is  a 
queer  thing, — what  does  not  fit  into 
the  circle  of  ideas  once  given,  does 
not  exist  for  it.  ...  I  had  sinned 
against  the  wisdom  of  the  Creator, 
and  for  this  had  received  merited 
punishment.  I  wanted  to  improve 
His  work,  and  in  my  blindness  I 
thought  that  in  the  wonderful 
chain  of  laws  which  bind  life  to 
the  surface  of  the  earth,  one  link 
was  missing  which  I,  a  helpless 
worm,  could  supply"  {loc.  cit.,  p. 
34). 


ON    THE    VITALISTIC    VIEW    OF    NATURE. 


393 


chemistry  at  the  Medical  School  of  Paris  in  1841. 
AVilh  him  was  associated  Boussingault,  the  man  who, 
next  to  Liebig,  did  most  for  the  elaboration  of  the  true 
principles  of  agricultural  chemistry. 

To  Liebig,  organic  chemistry  did  not  mean  the  chemis- 
try of  the  carbon  compounds  as  it  is  defined  nowadays, 
and  has  largely  become  since  Dumas  himself  introduced 
into  science  the  fruitful  method  and  idea  of  substitution. 
This  idea  extended  the  facilities  of  the  laboratory  chemist 
enormously,^  but  also  marks  the  altered  view  which  has        15. 

Cliange  in 

since  taken  hold  of  organic  chemistry,  the  alliance  with  organic 

'='  •'  chemistry. 

arts  and  industries  rather  than  with  an  understanding 
of  the  economy  and  the  phenomena  of  living  organisms. 
From  the  moment  of  that  alliance  dates  the  division 
of  organic  chemistry  into  the  two  great  branches  of 
the  chemistry  of  carbon  compounds  and  the  chemistry 


'  It  is  well  known  that  organic 
cliemistry  during  Liebig'.s  lifetime 
outgrew  the  canons  and  tiie  circle  of 
ideas  in  which  he  moved,  and  that 
he  complained  of  not  being  able  to 
undeistand  the  pajjers  in  his  own 
]  periodical,  the  'Annalen,'  &c. 
Liebig  originally  opposed  Dumas' 
ideas  on  substitution,  but  in  the 
end  admitted  himself  defeated, 
wlien,  through  Hofmann,  he  became 
convinced  "  that  the  character  of  a 
chemical  substance  does  not  depend 
so  much  as  he  had  supposed  on  the 
nature  of  its  constituent  atoms, 
and  depends  very  largely  also  on 
the  manner  in  whicii  these  atoms  are 
arranged.  Some  years  afterwards, 
at  a  dinner  given  by  the  French 
chemists  to  chemical  visitors  to  the 
F-xliibition  of  18i)7,  LieV)ig  made  his 
defeat  on  tliis  occasion  tlie  source  of 
a  happy  retort  to  Dumas,  who  had 
asked  him  why  of  late  years  he  had 
devoted  himself  exclusively  to  agri- 


cultural chemistry.  "  I  have  with- 
drawn from  organic  chemistry,"  said 
Liebig,  "  for  with  the  theoi-y  of 
substitution  as  a  foundation,  the 
edifice  of  chemical  science  may  be 
built  up  by  workmen  :  masters  are 
no  longer  needed"  (Shenstone,  'J. 
von  Liebig,'  1895,  \i.  61).  Already, 
in  1838,  Liebig  and  Wohlei-,  in  their 
investigation  on  uric  acid  and  its 
derivatives,  prophetically  suggested 
the  twofold  development  which 
organic  chemistrj'  was  destined  to 
take :  "  From  these  researches  the 
philosophy  of  chemistry  must  draw 
the  conclusion  that  the  synthesis 
of  all  organic  compounds  wiiich 
are  not  orytinised  must  be  looked 
upon  not  merelj'  as  probable,  but  as 
certain  of  ultimate  achievement " 
('Annalen,'  &c.,  vol.  xxvi.  ]>.  'J4'J). 
In  fact,  we  have  now  a  chemistry 
of  organic  and  one  of  organised 
substances. 


394  SCIENTIFIC    THOUGHT. 

of  organised  nature.  From  this  organic  chemistry  of 
the  modern  school  Liebig  turned  away — continuing  to 
lead  research  in  the  older  and  less  fashionable  direc- 
tion. This  choice  is  explained  by  the  peculiarity  of 
his  great  mind,  which,  while  investigating  details,  never 
lost  sight  of  the  organic  whole  of  natural  processes, 
and  which  allowed  itself  many  a  flight  of  imagina- 
tion into  unexplored  regions.  In  fact,  if  we  review  the 
16.        work  of  Liebig  from  the  side  of  the  history  of  thought 

Influence  of 

Liebig.  rather  than  from  that  of  science,  we  must  assign  to 
it  a  very  great  and  lasting  influence.  He  was  prob- 
ably the  first  man  of  science  who  conceived  the  two- 
fold meaning  which  belongs  to  the  words,  life  and 
organism,  a  meaning  which  was  known  and  appreciated 
by  practical  men,  but  which  had,  at  that  time,  hardly 
received  scientific  recognition.^  Life  is  not  only  defined, 
as  Bichat  put  it,  by  the  contrast  with  death ;  it  is  just  as 
much  defined  by  the  idea  of  co-operation  or  solidarity : 
life  is  not  only  the  property  of  individual  beings,  but 
also  of  the  collection  or  society  of  several  individuals  in 
a  larger  organism.  As  such,  political  economy  had  con- 
ceived it  long  before  Liebig's  time,  but  Liebig  was  prob- 
ably the  first  scientific  thinker  who  studied  the  economy 
of  nature,  who  fully  realised  the  interdependence  of 
animal  and  plant  life,  and  tried  to  reduce  this  larger  life 
of  living  things  to  scientific  data  and  laws.  Through 
him  and  his  school  two  terms  have  become  current  in 
scientific  and  popular  literature  which,  especially  in  the 

1  The  idea  of  the  dependence  of  I  Lamarck  (see  p.  314  s«^ra) ;  but  the 

living  things  on  the  environment,  philosophical   ideas   of    that    great 

on  the   "  milieu,"  was  indeed  fully  j  thinker    were   then    unknown   and 

recognised      and      emphasised      by  i  disregarded. 


ON    THK    VTTALISTIC    VIKW    OF    NATUKK.         395 

(ieiiuaii  tongue,  have  cliaiacU'i-iscd  the  new  ideas  Llieii 
introduced  into  science,  and  have  brought  them  home 
to  the  intelligence  of  the  educated  classes.  These  two 
terms  have  only  heen  inadequately  rendered^  in  any 
other  modei-n  languaue  :  thev  are  the  words  "  Stoff-  n. 
wechsel "  and  "  Kreislauf  des  Lebens."  The  former  de-  Z'^^r^'^-^. 
notes  the  continual  change  of  matter  connected  with  u-bcnti- 
maintenance  of  form  in  all  living  things ;  the  latter 
denotes  the  continual  interchange  which  exists  between 
tlie  separate  members  and  the  different  provinces  of  the 
living  creation,  the  circulation  of  living  matter  and  living 
processes.  Liebig  looked  u})()u  nature  on  the  large  and 
on  the  small  scale  as  an  economy,  as  a  household,  and 
he  applied  himself  to  study  the  conditions  of  its  exist- 
ence, of  its  normal  and  abnormal  states.  Through 
Liebig  chemistry  entered  into  close  alliance  with  politi- 
cal economy,  or,  as  it  is  termed  abroad,  national  economics. 
We  shall  see  immediately  how  the  progress  of  science 
has,  in  the  further  course  of  the  century,  tended  to 
emphasise  this  twofold  aspect  and  define  it  more  clearly: 
how  the  individual  organism,  the  bearer  of  life,  lias  been 
traced  to  smaller  and  smaller  dimensions  and  units,  and 
how,  correspondingly,  life  as  we  see  it  on  the  larger  scale 
has  more  and  more  revealed  itself  as  consisting  in  co- 
operation, in  the  collective  action  of  societies  made  up 
of  individuals.  We  have  on  the  one  side  the  doctrine 
of  the  "  Autonomy  of  the  Cell,"  so  elociuentlv  proclaimed        is. 

■^  .  "Autonoiiiy 

by  ProfcssoT-  Yin'1u)w  :   nn  the  otiier  side  the  doctrine  of  oftueCeii." 


'  We  shall  see  farther  on  Ikjw 
the  word  "  Metabolism,"  with  its 
two    suborclinate    terms    "  A lui hol- 


ism"' and  *' Catabolism,"  is  eveu 
more  expressive  than  the  German 
term   "  Stotf wechsel." 


396 


SCIENTIFIC    THOUGHT, 


"  Division  of  the  "Physiological  Division  of  Labour,"  the  happy  ex- 

Physiologi-  ,  i       •    j.     tt 

cai  Labour."  pression  invented  by  the  great  trench  zoologist,  Menri 
Milne-Edwards, 

Whilst  Liebig  was  working  at  the  great  problems  of 
the  economy  of  life,  and  making  chemistry  subservient 
to  the  interests  of  agriculture,  physiology,  and  pathology, 
another  influence  was  exerted — mainly  in  Germany — on 
the  study  of  the  processes  which  take  place  in  the  living 
organism.  This  influence  had  its  source  in  an  application 
of  the  principles  of  dynamics  and  the  more  modern  teach- 
ings of  physics.-^  It  emanated  from  two  distinct  centres — 
from  Leipzig,  where  the  brothers  Weber  '^  taught  how  to 


^  In  many  passages  of  his  inter- 
esting and  brilliant  "Addresses" 
Du  Bois-Reymond  has  dwelt  on 
the  great  revolution  which  came 
over  physiological  studies  about  the 
middle  of  the  centurj-,  characteris- 
ing it  as  a  special  German  achieve- 
ment. Claude  Bernard  has  given 
us  an  interesting  account  of  a 
corresponding,  but  not  identical, 
change  of  ideas  in  the  great  medical 
schools  of  Paris.  Quite  recently  Sir 
Michael  Foster  has  created  in  this 
country  an  interest  in  the  history 
of  medicine,  notably  of  physiology, 
and  has  on  various  occasions  given 
us  masterly  summaries  of  the  results 
of  his  historical  research.  I  may 
refer  specially  to  his  very  lucid  and 
fascinating  monograph  on  Claude 
Bernard  (London,  1899,  in  Fisher 
Unwin's  '  Masters  of  Medicine ' 
Series).  Another  authority  in 
modern  physiology,  Prof.  M'Ken- 
drick  of  Glasgow,  has  treated  in  a 
companion  volume  of  Helmholtz, 
dwelling  mainly  on  his  physiological 
labours,  based  upon  his  brilliant 
application  of  physics  and  mathe- 
matics. The  two  monographs  ex- 
hibit very  clearly  two  distinct  in- 
fluences which  have  been  at  work 


in  remodelling  the  science  of  phy- 
siology and  the  conceptions  of  the 
phenomena  of  life. 

-  Regarding  the  position  and  in- 
fluence of  the  three  brothers  Weber, 
I  may  refer  to  former  passages  of  this 
history  (vol.  i.  p.  196;  vol.  ii.  chap.  vi. 
2xissim).  The  greatest  of  the  three 
—  Ernst  Heinrich  Weber  (1795-1878) 
— occupies  a  unique  position  in  the 
development  of  the  "  science  of  life  " 
in  Germany.  He  seems  never  to 
have  come  under  the  influence  of 
the  then  prevalent  "  jAilosophy  of 
nature,"  and  he  had  accordingly, 
unlike  Liebig  and  Johannes  Midler, 
nothing  to  unlearn.  See  on  this 
point  Du  Bois-Reymond's  Eloge  of 
Miiller  in  '  Reden '  (vol.  ii.  p.  216), 
also  Ludwig's  Eloge  of  Weber  (Leip- 
zig, 1878,  p.  10).  Weber  represents 
in  the  purest  form  the  influence 
which  physics,  based  upon  experi- 
ment and  measurement,  had  upon 
the  development  of  the  study  of 
organic  form  and  function,  as  Liebig 
represents  in  the  purest  form  the 
influence  of  chemical  research  and 
reasoning.  In  this  respect  Liebig 
was  more  nearly  related  to  the 
Paris  school,  Weber  to  the  Berlin 
school,  which  he  greatly  influenced. 


ON    THE    VITALISTIC    VIEW    OF    NATURE.        397 

apply  strict  experimental  research,  combined  with  actual 
measurements,  to  pliysical,  organic,  and  psychical  pheno- 
mena, which  had  so  far  escaped  all  exact  treatment ; 
and  from  Berlin,  where  in  the  person,  and  still  more  in 
the  school,  of  Johannes  iMiiller,  the  great  and  complex        i9. 

_  Johannes 

phenomenon  of  life  in  the  higher  organisms  was  analysed  muirt. 
into  various  mechanical  and  physical  processes,  each 
connected  with  some  well-defined  organ  which  was  more 
and  more  recognised  as  possessing  tlie  properties  of  a 
physical  apparatus.  A  great  deal  of  the  work  of  the 
numerous  members  of  this  school  consisted  in  unravel- 
ling with  the  microscope  the  structure  of  sucli  organic 
apparatus,  and  studying  its  action  by  physical  measure- 
ments and  experiments.  As  examples  and  models  of 
this  kind  of  work  we  have  Du  Bois-Reymond's  'Re- 
searches in  Animal  Electricity'  (1848),  and  Helmholtz's 
'Physiological  Optics '  (1867,  second  edition,  much  en- 
larged, 1896),  and  'Physiological  Acoustics'  (1862). 
In  the  course  of  these  labours  it  was  found  that  the 
older  ideas  of  "  Stoti'wechsel,"  and  the  conception  of 
the  circulation  of  matter  as  it  was  taught  in  the  school 
of  Liebig,  required  to  be  corrected  and  extended.  I  have 
referred  in  an  earlier  chapter  ^  to  the  interesting  circum- 
stances under  which  our  modern  notions  of  the  conserva- 
tion of  energy  first  dawned  independently  upon  Mayer 
and  Helmlioltz  whilst  studying  the  phenomena  of  heat 
in  the  animal  organism.  In  the  school  of  Liebig  we 
meet  with  an  occasional  attempt  to  extend  the  idea 
of  "  Stofiwechsel,"  the  exchange  of  material  or  of 
elementary  matter  in    the    living    body  of  animals  and 

'  See  supra,  ch.ip.  vii. 


398  SCIENTIFIC    THOUGHT. 

plants,  so  as  to  embrace  likewise  the  imponderables — 
heat,  light,  electricity,  &c.  We  find  Mohr  treating  of 
heat  and  animal  energy  as  substances  which  must  be 
counted  among  the  elements  or  prime  materials  known 
to  chemists — just  as  the  French  chemists  of  Lavoi- 
sier's school  enumerated  the  imponderable  along  with 
the  ponderable  elements  of  nature :  even  Liebig's  first 
edition  of  the  '  Chemical  Letters '  is  not  quite  averse  to 
such  an  interpretation.  The  ideas  on  this  matter  were, 
however,  vague,  and  needed  defining.  When  ]\Iayer 
.attempted  a  first  step  in  this  direction,  Liebig  did  not 
see  the  value  of  it.  The  subject  was  only  cleared  up 
when  Helmholtz,  in  1847,  showed  that  all  so-called 
living  forces  were  the  different  manifestations  of  a 
■certain  quantity  of  power  to  do  work — later  termed 
energy  —  and  that  this  power  could  show  itself  in 
actual  change  and  motion,  or  be  stored  up  in  tensions 
in  the  system,  later  called  "  potential  energy."  After 
this,  "  Stoffwechsel "  appeared  not  only  as  an  exchange 
of  material,  but  also  as  a  change  in  the  form  of  energy, 
whereby  potential  or  latent  energy  could  be  accumulated 
in  the  organism  and  let  loose,  as  the  latent  power  of 
an  explosive  substance  is  let  loose  by  the  pulling  of  a 
trigger. 

One  of  the  immediate  consequences  of  these  varied 
researches  —  all  tending  to  show  how  the  conception 
formerly  established  in  chemistry,  physics,  and  dynamics 
could  be  utilised  in  the  description  of  the  phenomena 
of  living  matter,  how  the  complex  phenomenon  of  life 
could  be  split  up  into  a  number  of  separate  chemical 
and    physical    processes,    which    could    be    imitated    in 


ON    THE    VITALISTIC    VIEW    OF    NATURE.         399 

tlic  laboratory,  and  how  tlie  living  organism  could 
be  analysed  into  a  complex  of  separate  apparatus  or 
machines,  acting  on  intelligible  mechanical  ami  i)hysical 
principles — was  a  radical  change  of  the  conception  of 
vital   force    and    tlic   vital    i)iinci])le.      It   ceased    in    the  .  „  ^o- 

'  '  Innueiicc  of 

opinion  of  many  to  be  opposed  to  other  non-living  forces,  g^r^"^"' 
as  it  was  with  Bichat ;  according  to  otlieis  it  was  non- 
existent, or  at  all  events  useless ;  others  again  reduced 
it  to  a  purely  regulative  function,  or  e\'en  a  meie 
idea.  A  popular  })hilosophy  founded  upon  the  unknown 
principle  of  matter,  and  tlic  c(|ually  unknown  and 
even  less  clear  princi])le  of  force,  pronmlgated  the 
notion  that  science  had  succeeded  in  banishing  all 
spiritual  entities,  and  was  able  to  explain  everything  on 
purely    mechanical    principles.      Vitalism    and    animism        21. 

^  •'  ^  ^  Mechanism. 

were  at  an  end ;  there  only  remained  mechanism  and 
materialism.  It  is  well  to  note  that  none  of  the  great 
men  to  whom  we  are  indebted  for  the  real  extension  of 
our  knowledge  of  Inological  phemonena  favo\ucd  or 
embraced  this  view.  The  reasons  which  ke^tt  tlunn 
from  drawing  what  seemed  to  some  the  inevitable  con- 
sequences of  their  discoveries  were  manifold. 

As  I  stated  before,  there  are  two  ways  of  approaching 
the  problems  of  nature,  and  two  interests  by  which  our 
researches  can  be  guided.  The  one  is  the  abstract 
mathematical  method,  which  begins  with  the  sunplest 
definable  and  measurable  elementary  processes,  and  tries 
to  i  nutate  the  complicated  phenomena  of  nature  by  more 
and  more  intricate  combinations  of  these  elemeiitaiv  pro- 
cesses. The  other  is  the  more  concrete  method  inspired 
by    practical   interests.       The  mechanical,  i)hysical,   and 


400  SCIENTIFIC    THOUGHT. 

chemical  methods  of  analysis  and  synthesis  follow  the 
former  way,  and  they  generally  arrive  at  satisfactory 
explanations  of  isolated  parts  of  the  actually  existing 
phenomena,  or  of  special  and  simple  cases.  Notably, 
they  create  the  artificial  world  of  manufactured  things, 
such  as  instruments,  machines,  chemical  and  mechanical 
compounds.  They  may  at  times  make  it  appear  as  if 
this  process  of  putting  together,  continued  indefinitely, 
would  ultimately  reach  the  real  things  which  we  behold 
in  inorganic,  organised,  and  even  in  animated  nature. 
At  all  events  no  other  way,  it  might  seem,  is  open  to 
science,  and  the  only  thing  that  delays  our  progress 
is  the  bewildering  intricacy  and  complexity  of  things 
natural.  At  the  beginning  of  our  century,  when, 
through  Laplace  and  his  school,  many  seemingly  com- 
plicated phenomena  of  nature,  notably  those  of  physical 
astronomy,  yielded  to  the  processes  of  analysis  just  de- 
scribed, there  seemed  for  the  moment  a  possibility  of 
building  up  a  complete  philosophy  of  nature  on  such 
a  groundwork.  Laplace  himself  indulged  in  a  fre- 
quently quoted  prophetic  vision  of  this  kind.  When,  in 
the  middle  of  the  century,  some  molecular  phenomena, 
notably  those  of  light,  had  likewise  yielded  to  the 
calculus,  and  when  correcter  views  as  to  the  nature  of 
forces  had  further  brought  another  and  different  world  of 
phenomena  into  a  calculable  form,  it  seemed  likely  that 
even  the  mysterious  processes  of  living  organisms  might 
be  subjected  to  similar  reasoning.  It  seemed  time  to 
abandon  the  familiar  conception  of  a  special  vital  force, 
and  to  hand  over  physiological  problems  likewise  to  the 
physicist,  the  chemist,  and  the  microscopist.     A  regular 


ON  THE  vitalistk;  view  of  nature. 


401 


crusade  was  accoidingly  started  in  Gerinany  by  philoso- 
phers, as  well  as  by  naturalists  and  biologists,  against  the 
vitalists — those  who  believed  in  a  special  principle  of  life  ; 
and  an  impression  was  createil  in  the  minds  of  thinking 
outsiders  that  a  purely  mechanical  explanation  of  life  and 
mind  was  finally  decided  on,  and  within  possible  reach. 
Among  those  who  assisted  in  bringing  about  this  im- 
pression, I  need  only  single  out  two  names — those  of  ^yfn*^ond 
Hermann  Lotze,^   the   philosopher  of  Gottingen,  and  of 


22. 
Lotze  and 
Vu  Bois- 


1  Tlie  position  wliich  Lotze  oc- 
cupies in  tiie  history  of  the  con- 
ceptions of  life  or  of  vitalism  is 
peculiar.  If  we  read  works  deal- 
ing specially  with  the  history  of 
medicine,  such  as  those  of  Haeser 
or  Hirscli,  we  do  not  come  across 
the  name  of  Lotze  at  all,  and  it  is 
only  in  quite  recent  times,  fifty 
years  after  the  appearance  of  Lotze's 
writings  dealing  with  vitalism,  that 
experts  in  physiology  have  re- 
verted to  his  discus.sion  of  the 
subject.  See  notably  the  follow- 
ing :  \.  Rauber,  "  Formbildung  und 
Formsttirung  in  der  Entwickelung 
von  Wirbelthieren  "  (' Morphol. 
Jahrbuch,'  Band  vi.),  1880.  2. 
Wilhelm  Roux,  "  Einleitung  zu  den 
Beitriigen  zur  Entwickelungsme- 
chanik  des  Embryo,"  188f)  (re- 
printed in  '  Gesammelte  Abhand- 
lungeu,'  vol.  ii.  p.  11,  Leipzig, 
1895).  3.  0.  Hertwig,  'Zeit  und 
Streitfragen  zur  Biologie'  (Heft  2, 
Jena,  1897),  pp.  2.3-29.  4.  Carl 
Hauptmann,  'Die  Metaphysik  in 
der  modenien  Physiologic '  (Jena, 
1894),  p.  3.  These  and  many  other 
recent  references  go  back  to  Lotze's 
article,  "  Leben  und  Lebenskraft," 
in  Rud.  Wagner's  '  Handworterbuch 
der  I'hysiologie,'  1842  ;  and  to  his 
larger  publications,  'Allgemeine 
Pathologic  undTherapie  als  median - 
ische  Naturwissenschaften  '  (Leip- 
zig, 1842),  an<l  'Allgemeine  Physi- 

VOL.  II. 


olugie  des  Kbrperlichen  Lebens ' 
(Leipzig,  18G7).  The  reasons  why 
Lotze's  expositions  were  so  little 
regarded  at  the  time  were  prob- 
ably twofold.  He  taught  that 
the  phenomena  of  life  consti- 
tuted a  mechanical  problem.  This 
was  enough  to  dismiss  in  the 
eyes  of  many  empirical  naturalists 
the  further,  but  not  easily  com- 
prehended, statement  of  Lotze  that 
life  was  not  merely  a  mechanical 
problem.  The  definition  and  solu- 
tion of  the  second  part  of  the 
problem  was  much  more  difiicult, 
and  Lotze  delayed  his  expositions 
on  this  side  of  the  question  for 
ten  years,  when  he  published  his 
'  Meclicinische  Psychologic  oder 
Physiologic  der  Seele '  (18r>2), 
which  contained  a  metaphysical 
introduction  apparently  little  in 
harmony  with  the  supposed  purely 
mechanical  or  even  materialistic 
standpoint  of  his  earlier  writ- 
ings. In  the  meantime  several 
important  works  had  appeared 
which  carried  out  in  wider  or 
narrower  regions  the  purely  me- 
chanical or  inductive  and  experi- 
mental treatment,  and  quite  revolu- 
tionised physiological  and  medical 
studies.  I  need  only  mention  such 
works  as  Jacob  Henle's  '  Allgemeine 
Anatomic'  (1840),  and  his  '  Hand- 
buch  der  rationellen  Pathologic ' 
(1846-53).     Henle,  as  von  Kulliker 

2   C 


402 


SCIENTIFIC    THOUGHT. 


Du  Bois-Eeymond,  the  eminent  physiologist  of  Berhn. 
The  former  owed  much  of  his  scientific  training  to  the 
school  of  Ernst  Heinrich  Weber  in  Leipzig,  the  latter 
to  that  of  Johannes  Mliller  in  Berlin.  Both  agreed 
in  denouncing  the  conception  of  a  vital  force  —  as  it 
was  then  called — as  illogical,  and  moreover  as  scienti- 
fically useless.  But  whilst  Lotze  distinctly  stated  that 
his  criticisms  on  this  subject  were  only  addressed  to 
scientific  thinkers,  and  promised  a  further  philosophical 


says,  "correctly  saw  that  the  work 
of  Bichat  had  to  be  remodelled  ou 
the  foundations  laid  by  Schleiden 
and  Schwann,"  an  undertaking  in 
which  von  KoUiker  himself  laboured 
with  the  greatest  success.  But 
above  all  must  be  mentioned  the 
appearance  of  Rud.  Virchow's 
'Cellular  Pathology'  (1858,  Engl, 
transl.  by  Chance,  1860),  "in  which 
he  himself  explains  that  he  does 
not  give  a  system  but  a  general 
biological  principle,"'  and  in  so 
doing  lays  the  foundation  for  the 
entire  exact  treatment  of  patho- 
logical cases.  It  is,  however,  well 
to  note  that  Yirchow  does  not 
regard  life  as  a  purely  mechanical 
problem.  The  works  of  such 
authorities  as  Henle  and  Virchow 
give  as  much  or  as  little  jihilosophy 
and  discussion  of  general  principles 
as  physiologists  of  the  exact  school 
required  for  about  thirty  years. 
Those  masters,  indeed,  had  them- 
selves grappled  with  the  philo- 
sophical problem,  and  had  arrived 
at  a  formulation  which  sufficed  to 
lead  research  into  fruitful  paths 
for  a  new  generation  of  experts 
who  themselves  were  not  philo- 
sophically educated.  The  term 
vital  force  disappeared,  and  in  the 
specialist  medical  literature  of  a 
lengthy  period  even  life  itself  was 
hardly  any  longer  discussed.  Thus 
a    firm   basis    was    laid    on    which 


mechanics,  physics,  and  chemistry 
could  be  usefully  applied.  A  similar 
silence  as  to  general  problems 
reigns  in  the  great  school  which 
for  two  centuries  built  on  the 
principles  laid  down  bj'  Newton 
in  natural  philosophy.  Similarly 
in  chemistry,  the  foundations  laid 
by  the  atomic  theory  sufficed  for 
the  greater  portion  of  the  century 
following  its  enunciation.  We 
have  seen  in  earlier  chapters  of 
this  work  how,  even  in  these 
much  more  firmly  established  me- 
chanical sciences,  our  century  has 
witnessed  before  its  end  discus- 
sions again  arising  as  to  funda- 
mental questions  and  leading  prin- 
ciples. A  similar  fate  has  come 
over  biological  science,  and  with 
it  a  renewed  interest  in  the  writ- 
ings which  stand  at  the  entrance  of 
that  epoch  which  was  so  rich  in 
the  unravelling  of  definite  and 
special  problems.  Authorities  like 
Prof.  0.  Hertwig  warn  us  now  of 
that  "  other  extreme  which  sees 
in  vital  processes  nothing  but 
chemico  -  physical  and  mechanical 
problems,  and  thinks  it  finds  the 
true  science  of  nature  only  in  so 
far  as  it  is  possible  to  reduce 
phenomena  to  the  motions  of 
attracting  and  repelling  atoms, 
and  to  submit  them  to  calculation  " 
('Die  Lehre  vom  Organismus, '  an 
Address,  Jena,  1899,  p.  8). 


ox    THE    VITALISTIC    VIEW    OF    NATURE. 


403 


investigation  of  the  question,  J  )ii   Jluis-Reyniuiul  ^  gave 
the    impression,  in    his    earliest    deliverance,  that    the 


'  Du  Bois-lleyiiiDiitl's  jjosilion  in 
the  vitiilistic  controversy  is  inter- 
esting and  instructive,  inasmuch 
jis  he  considerably  modified  his 
opinions  in  coui-se  of  time.  His 
first  dehverance  on  the  subject  is 
to  Ije  found  in  the  preface  to  his 
celebrated  '  Untei'suchungen  iiber 
Thierische  Elektrititiit '  (March 
1848).  This  discussion  of  the 
subject  followed  soon  after  the 
deliverances  of  men  like  Bcr/.elius 
(1839),  Schwami  (1839),  Schleideu 
(184'2),  Lotze  (1842),  on  the  same 
subject,  which  are  stated  to  have 
been  "  ineffectual. "  After  the 
lapse  of  twenty -four  years  Du 
Bois  -  Reymond  approached  the 
subject  again  in  his  celebrated 
address  at  the  German  Association 
of  Sciences  at  Leipzig,  1872,  en- 
titled "  Ueber  die  Grenzen  des 
Naturerkeunens."  This  deliverance 
created  a  great  sensation  :  the 
jiainjihlet  ajjjieared  in  many 
editions  and  translations,  and 
only  in  this  country  failed  to 
get  adequately  noticed.  A  further 
explanation  of  the  views  ex- 
])Ounded  in  it  was  given  by  the 
author  (1880)  in  an  oration  at 
the  meeting  held  annually  in 
honour  of  Ijcibniz  in  the  Berlin 
Academy  on  the  8th  of  July.  It 
bears  the  characteri.stic  title  "  Die 
sieben  Weltr;ithsel."  These  docu- 
ments together  contain  the  author's 
"  j)hilosophical  creed,"  which  ends 
ill  "Pyrrhonism,"  out  of  which 
there  seems  no  escape  exce))t 
through  "Supernaturalism,"  which, 
however,  begins  where  science 
ends.  (See  note  1  to  the  last- 
mentioned  address.)  All  three 
documents  are  reprinted  in  the 
two  volumes  of  '  ]{eden  '  (Leipsic, 
1886-87),  from  which  I  quote.  lu 
the  interval  of  a  quarter  of  a  cen- 
tury which  lay  between  the  first  and 


second  deliverance  great  changes 
had  come  ovei-  scientific  thought. 
The  mechanical  view,  which  had 
been  jiut  forward  in  an  extreme 
form  in  1S48,  when  it  was  projihe- 
sied  that  "  phy.-iology,  giving  up  its 
particularistic  interest,  would  dis- 
appear in  the  great  united  estate 
of  natural  pliilosophy,  would  be 
entirely  dissolved  in  organic 
physics  and  chemistry  "  (vol.  ii.  p. 
23),  had  had  time  and  opportunity 
to  show  its  power  and  its  limits. 
It  had  gained  through  gr(!ater 
facility  of  application  (such  as 
Ludwig's  automatic  curve  -  plot- 
ting), through  the  larger  con- 
cepti(Hi  of  "  StofFwechsel "  as 
denoting  "  metabolism  "  of  matter 
and  energy.  The  author  himself 
had  introduced  a  new  definition 
of  life  as  a  '•  dynamical  equi- 
libriuTU "  in  the  place  of  older 
descriptions  (vol.  ii.  p.  25) ;  and, 
above  all,  Darwin  had  shown  the 
possibility  of  a  mechanical  exjilan- 
ation  of  so-called  "final  causes" 
in  nature.  The  author  himself 
was  one  of  that  great  school, 
emanating  from  Johannes  Midler, 
but  now  represented  by  the  still 
greater  Helmholtz,  which  had 
pushed  the  mechanical  or  exact 
treatment  to  its  furthest  limits, 
to  the  analysis  of  the  phenomena 
of  the  nervous  system  in  its  high- 
est activity,  those  of  sensation 
and  perception.  It  is  therefore 
highly  significant  that,  instead  of 
confirming  the  earlier  dictum,  that 
the  exact  treatment  would  halt 
only  at  the  most  advanced  point — 
viz.,  the  manifestation  of  '"free 
will,"' — the  aulhoi-  is  now  forced  to 
admit  that  not  only  is  the  "  origin  " 
of  all  motion  quite  obscure,  but 
likewise  the  lowest  forms  of 
animation  or  con.sciousness  are 
not   to  be  exi)lained  mechanically, 


404  SCIENTIFIC    THOUGHT. 

question  was  definitely  settled  and  the  road  quite 
clear  for  research.  To  those — and  they  comprised  the 
second  class  of  thinkers  referred  to  above — who  were 
unwilling  or  unable  to  follow  Lotze  and  Du  Bois- 
Eeymond  into  the  details  of  their  criticism  of  the 
illogical  conception  of  force  as  employed  in  the  term 
"  vital  force,"  but  who  looked  at  the  great  facts  of 
economy,  design,  and  recurrent  order  which  are  exhibited 
in  the  living  creation,  these  criticisms  had  little  that 
was  convincing.  If  the  term  "  vital  force "  was  illogical, 
some  other  term  such  as  "  vital  principle "  might  be 
substituted.  The  enormous  difference  between  the 
phenomena  of  living  and  of  dead  matter  remained  and 
impressed  itself  on  them.  Liebig,  and  many  naturalists 
in  France  and  Germany,  had  approached  the  study  of 
nature  from  the  practical  side.  Their  methods  were  not 
mathematical  but  rather  experimental,  and  very  fre- 
quently not  limited  to  the  laboratory  and  dissecting-room, 
but  carried  out  in  the  workshop  of  nature  itself.  In 
spite  of  his  successful  attempts  to  establish  clearer  views 
regarding  the  economic  processes  of  living  nature  and 
the  application  of  chemical  analysis,  Liebig  ^  to  the  end 

the  mystery  which  attaches  to  i  be  studied  liy  every  one  who  desires 
all    beginnings    as   well   as    to    the       to  be  at  home  in  the  ancient  and 


great  transitions  in  the  ascending 
scale  of  natural  phenomena  being 
further  emphasised  and  forcibly 
driven    home    in    the    last  -  named 


modern  literature  of  the  f^ubject. 
The  position  of  the  author  has 
been  many  times  criticised.  See, 
inter  (dill,  Kaufmann,   '  Die  Meta- 


address,    which,    as  has  been   said,  |  physik  in   der   modernen  Biologic ' 

bears  the  title   "The  Seven  Enig-  !  (Jena,  lS9i],  passim. 

mas. "    The  three  deliverances  of  Du  i  ^  Lord  Kelvin  in  his  essay  "  On  the 

Bois-Reymond,   together    with    the  |  Dissipation  of  Energy "  (reprinted 


copious  notes  and  references  which 
he  gives  in  the  latest  reprint, 
serve  as  a  very  good  and  lucid 
exposition    of    the    inherent    diffi- 


in  '  Popular  Lectures,'  &c.,  vol.  iii. 
p.  464)  has  the  following  interesting 
note:  "The  influence  of  animal  or 
vegetable  life  on  matter  is  infinitely 


cuities  of  the  problem,  and  should   .   beyond  the  range  of  any  scientific 


ON    THE    VITALTSTIC    VIEW    UK    NATLKE.         405 
(if  his  life  never  satisfied  himself  that  the  phenomena  of  ,   ^.23. 

'■  I-icbigH 

life  can  he  mechanically  explained:  he  remained,  in  the  viuiiHin. 
face  of  much  criticism,  a  Vitalist.  So  did  WiJhler  in 
Germany — so  diil  most  of  the  eminent  physiologists  in 
France  and  in  England.  The  crusade  against  Vitalism, 
which  was  started  in  Germany,  seems  to  have  had  little 
influence  on  them.  In  1854,  six  years  after  Du  Bois- 
Eeymond's  essay  on  Vital  Force,  and  twelve  years  after 
that  of  Lotze,  Huxley  ^  couhl  still,  in  the  first  of  his 
'  Lay  Sermons '  "  On  the  educational  value  of  the  natural 
history  sciences,"  express  opinions  on  the  difference  be- 
tween living  and  not-living  bodies  which  were  distinctly 
vitalistic,  maintaining,  much  in  the  same  way  as  Liebig 
did  in  the  later  editions  of  his  chemical  letters,  that  "the 
phenomena  of  life  are  dependent  neither  on  physical  nor 
on  chemical,  but  on  vital  forces";  and  if,  in  1870,  he 
could  himself  state  that  he  had  long  since  grown  out 
of  this  view,  it  is  interesting  to  discover  what  were 
the  arguments  which  brought  about  this  remarkable 
change.  I  will  at  once  state  what  seems  to  me  to  be 
the  great  influence  which  combated  Vitalism  in  this 
country,  which  greatly  strengthened  the  anti-vitalistic  or 
mechanical  views  in  Germany,  but  which,  as  little  as  the 
mathematical  and  philosophical  criticism  of  Lotze  and 
Du  Bois-lieymond,  ever  took  real  hold  of  biological  thought 


iu(iuiry  hitherto  entered  ou.  About 
twenty  -  five  years  ago  I  asked 
Liebig  if  lie  believed  that  a  leaf  or 
■.i  Hower  could  be  formed  or  could 
grow  by  chemical  forcea.  He 
answered,  I  would  more  readily 
believe  that  a  book  on  chemistry 
or  on  botany  could  grow  out  of 
dead  matter  by  chemical  processes." 
'  The  address  referred  to  wa.-^  re- 


printed in  1870  in  the  well-known 
volume,  entitled  '  Lay  Sermons, 
Addresses,  and  Reviews,'  with  a 
"  prefatory  letter ""  to  Tyndall, 
in  wliich  the  following  passage 
occurs  :  "  The  oldest  essay  oi  the 
whole  contains  a  view  of  the  nature 
of  the  ditiereuees  between  living 
and  not-living  bodies,  out  of  which 
I  have  long  since  grown." 


406 


SCIENTIFIC    THOUGHT. 


24. 
Darwin. 


in  France,  where  a  modified  kind  of  vitalism  still  pre- 
vails.^ It  is  the  far-reachincj  influence  of  the  reasonine 
which  sprang  out  of  Darwin's  theory  of  descent. 


^  The  older  ideas  of  vital  forces 
have  in  all  the  three  countries  been 
combated  by  authorities  of  the  very 
first  order,  but,  characteristically, 
in  a  very  different  manner  — •  the 
phenomena  of  living  bodies  having 
been  attacked  from  different  sides. 
In  Germany  the  mechanico-physical 
school  was  for  a  time  the  dominant 
one.  In  France  the  dominant  school 
was  the  so-called  experimental,  also 
termed  the  vivisectional,  school, 
founded  by  Magendie.  Between 
these  two  extreme  positions,  both 
ecjually  opposed  to  the  older 
vitalism,  there  stood  in  the  middle, 
with  a  less  strongly  pronounced 
antagonism  to  earlier  conceptions, 
those  who,  like  Liebig  in  Germany, 
Dumas  and  Boussingault  in  France, 
approached  the  phenomena  of  life 
mainly  by  the  methods  and  reason- 
ing of  the  new  science  of  chemistry. 
This  school  had  a  profoundly  modify- 
ing influence  on  the  extreme  views  of 
the  experimental  school  in  France. 
It  made  itself  felt  mainlj'  tlirough 
Claude  Bernard.  In  Germany  this 
influence  was  felt  later,  after  that  of 
Darwinism  had  somewhat  subsided. 
In  England  it  was  the  doctrine  of 
descent  pure  and  simple  which  com- 
bated the  older  vitalism  :  the  ques- 
tion became  one  of  origins,  and  vital- 
ism, as  such,  could  be  temporarily 
ignored.  The  facts  of  variation, 
overcrowding,  natural  selection,  and 
inheritance,  presented  such  a  mass 
of  materia],  waiting  to  be  sifted  and 
arranged  by  exact  methods,  that 
the  problem  of  the  essence  of  life 
and  its  beginnings  was  set  aside. 
Accordingly,  the  attempts  both  of 
Darwin  and  Huxley  to  grapple  with 
the  central  and  final  problem  of 
vitalism  are  verj'  few  ;  the  latter 
only  repeating  what  had  been  said 


long  before  him   by  thinkers  of  a 
very  different  school.     The  question 
was  not  answered,  because,  for  the 
progress  of  the  sciences  and  for  their 
successful  application  in  medicine, 
it  did  not  require  to  be  answered. 
It   became    a   purely    philosophical 
question,    and    the    only    English 
writer  of  authority   who  seriously 
grappled   with  it    was  Mr  Herbert 
Spencer     in      his     '  Principles     of 
Biology.'     Darwin  in  1863  wrote  to 
Hooker  ('  Life,'  vol.  iii.  p.  18)  :  "  It 
is  mere  rubbish  thinking  at  present 
of  the  origin  of  life  ;  one  might  as 
well  think  of  the  origin  of  matter." 
Huxley,  in  a  letter  from  the  year 
1884  ('  Life,'  vol.  ii.  p.  67),  compares 
life  with    a  whirlpool,   a  favourite 
simile  of  Cuvier's  (see  supra,  vol.  i. 
p.  129),  but  is  doubtful  as  to  compar- 
ing it  with  a  machine.     M.  Delage 
names    Chevreul    ('Considerations 
gendrales  sur  I'analyse  organique  et 
ses  applications,'  1824):  "Ha  eu  le 
merite  d'ecrire  que  la  Force  vitale 
n'explique  rien,  qu'elle  aurait  besoin 
elle-meme  d'etre  expliquce  avant  de 
pretendre  expliquer  autre  chose,  et 
que   les  phenomfenes  de  la  vie  ont 
leur  cause  directe  dans  les  priucipes 
imra^diats  constitutifs  de  la  matiere 
organisce.     II   n'etablit    cependant 
sur  cette  donnde  une  theorie  de  la 
vie,    car    il   conclut,    au    contraire, 
que,  eut-on  ramene  les  phenomenes 
vitaux  II  leurs  causes  prochaines  et 
aux  forces  qui  rdgissent  la  matiere 
inorganique,  on  ne  serait  pas  encore 
en    etat   de   com  prendre    comment 
I'etre  organist  en    se    reproduisant 
repete    avec    une    Constance  si  re- 
marquable    les    caracteres    de    son 
espece."     Even  Francois  Magendie, 
the   great   founder   of   the    purely 
experimental  school  of  physiology, 
says  of  Bichat's  celebrated  '  Recher- 


1 


ON    THE    VITALISTIC    VIEW    OF    NATURE.         407 

In  order  to  enable  my  readers  to  comprehend  clearly 
the  great  change  which  has  come  over  biological  thought 
through  Darwin's  writings  and  reasonings,  I  must  now 
introduce  an  idea  which  I  have  so  far  intentionally 
avoided  in  discussing  the  various  scientific  views  of 
nature.  This  is  the  idea  of  final  causes,  the  apparent 
existence  of  a  purpose  (in  German  Zivcck),  or  an  end 
(in  German  Ziel)  in  all  processes  of  nature,  but  pre- 
eminently in  those  of  the  living  portion  of  creation.  In 
all  writings  prior  to  Darwin  a  great  deal  is  made  of 
final  causes  in  nature,  of  the  teleology  of  living  processes. 
The  phenomena  of  life  seemed  safely  intrenched  in  the 
citadel  of  final  causes :  no  mechanism  could  explain 
them  away.  The  very  fact  that  organisms  were  com- 
pared with  machines,  admitted  the  existence  of  a  definite 
end  and  purpose ;  for  it  is  the  peculiarity  of  every 
humanly  constructed  machine  or  instrument  that  it 
serves  a  definite  purpose  which,  in  the  mind  of  the 
inventor  or  maker,  suggested  the  peculiar  arrangement  or 
organisation  which  we  behold.     The  criticisms  of  Lotze  ^ 

ches,'  &c.  :  "  Les  esprits  sdvbres  et  say  tliat  Lotze,  though  ceasing  to 

amis  des  progrfes  des  sciences  ...  be  a  vitalist,  remained  an  animist. 

ont   regrettc   que  I'auteur  o))po.sat  Discarding  vital  force,  he  retained 

sans  cesse  la  vie  aux  lois  physiques,  the    couce|)tion     of    a    soul    in    a 

comme  si  les  etres  vivans  n'etaient  manner  which  drew  upon  him  the 

pas  de  corps,  avant  d'etre  des  vdgd-  ridicule  of  those  wIkjui,   like   Carl 

taux  ou  des  animaux  "  ("avertisse-  Vogt,   he   had   converted   to    pure 

ment "  to  the  4th  ed.   of    Bichat's  materialism.       This    has    had    the 

'  Recherches,' &c.,  1822).  consequence,   that  in    more   recent 

'  The  lengthy  discussions  of  Lotze  times    his    whole     philosophy    has 

contained    in    the    writings  quoted  been   stigmatised   as   dualistic,  and 

above  are  not  easy  to  understand,  that  he  has  been  accused  of  having 

and  it  is   not  surprising    that,   be-  halted  halfway.      His  real  meaning 

yond  the  elimination  of   the  con-  j   can  be  gathered  more  easily  from 

ception  of  vital  force  as  useless  to  '.    his   later   and    more  mature    writ- 

the    purely    scientific    student,    his  '    ings :    for    his    contcm)ioraries     it 

real  meaning  was  at  the  time  not  must   have    remained    to    a   great 

grasped  at  all.      In  fact,  we  may  extent     enigmatical.      See     Kauf- 


408 


SCIENTIFIC    THOUGHT. 


and  Du  Bois-Eeymond  ^  did  not  do  away  with  this  very 
evident  property  of  living  things,  but  only  maintained 


mann  {'  Die  Metaphysik  iu  der 
Physiologie,'  1894,  p.  7):  '^How- 
ever convincingly  Lotze  destroyed 
the  conception  of  a  vital  force,  he 
had  no  desire  to  criticise  in  a  sim- 
ilarly destructive  manner  the  prin- 
ciple of  a  soul,  though  both  have 
grown  up  in  the  same  climate,  in 
the  fertile  country  where  sub- 
stances blossom,  &c.  .  .  .  And 
although  he  emphatically,  and  in 
many  ways,  urged  that  all  organism 
is  a  definite  form  and  arrangement 
of  mechanism,  he  nevertheless 
accorded  to  the  principle  of  in- 
herent disturbances  (soul,  will)  a 
partial  control  over  the  functions 
of  the  animal  body,"  &c.  Accord- 
ingly this  view  set  only  the  physi- 
ology of  plant-life  quite  free  for  a 
purely  mechanical  treatment,  which 
it  received  —  after  the  suggestive 
beginnings  made  by  Schleiden — 
mainly  at  the  hands  of  Julius 
Sachs,  from  whose  '  Lectures  on 
Plant  Physiology'  (1887)  Kauf- 
mann  gives  the  following  very  char- 
acteristic extract :  "  The  organism 
is  only  a  machine  put  together 
out  of  different  parts  ;  ...  in  a 
machine,  even  if  only  made  by 
human  hands,  there  lies  the  result 
of  deepest  and  most  careful  thought, 
and  of  high  intelligence,  so  far  as 
its  structure  is  concerned,"  &c.  (p. 
623). 

^  The  two  great  facts  which  stare 
every  unbiassed  student  of  nature 
in  the  widest  sense  in  the  face, 
and  which  always  upset  a  purely 
mechanical  view,  are  Purpose  and 
"Will.  Lotze  recognises  both,  and 
in  all  his  writings  never  forgets  or 
ignores  them.  Naturalists,  who 
for  the  nonce  are  deeply  interested 
and  fully  absorbed  in  the  analysis 
of  some  definite  organ,  or  some 
special  chemical  power  in  the 
organism,      may     usefully     ignore 


these  two  facts,  of  which  the  first 
only  intrudes  itself  if  we  rise  to  a 
general,  a  comprehensive  aspect ; 
the  second  is  a  result  of  individual 
experience.  Nor  did  Du  Bois- 
Reymond  ignore  these  facts.  It 
is  interesting  to  see  how  he  deals 
with  them  in  his  earlier  and  later 
writings.  In  the  earlier  period 
he  eliminates  the  problem  of  free 
will  as  not  a  scientific  problem 
at  all,  and  gets  over  the  question 
of  purpose  bj'  a  reference  to  the 
evident  existence  of  purpose  in  in- 
animate nature  also, — an  idea  which 
really  comes  ultimately  back  to  an 
assumj)tion  of  a  general  animation 
of  the  whole  of  nature,  such  as 
has  been  maintained  by  many  phil- 
osophers and  naturalists  iu  very 
various  forms.  See,  for  instance, 
the  further  remarks  of  Julius  Sachs 
in  the  passage  quoted  above.  But 
there  is  no  doubt  that  this  method 
of  viewing  the  teleology  of  nature  did 
not  really  satisfy  Du  Bois-Reymond, 
for  in  the  reprint  of  his  paper  on  vital 
force  he  refers  to  it  as  superficial 
(' Reden,' vol.  ii.  p.  26),  having  in 
the  meantime  adopted  the  explana- 
tion of  Darwin,  whose  "  highest 
title  to  glory "  will,  "  so  long  as 
philosophy  of  nature  exists,"  be 
this,  that  he  to  "  some  extent 
allayed  the  agony  of  the  intellect 
that  ponders  over  the  problems  of 
existence"  ('Reden,'  vol.  i.  p.  216). 
In  1887  he  holds  that  what  he 
wrote  as  late  as  1859,  before  the 
appearance  of  the  '  Origin  of 
Species', —  for  instance  his  cele- 
brated Eloge  of  Johannes  Miiller — 
is  antiquated,  though  it  still  gives  a 
valuable  picture  of  the  "  tormenting 
confusion  of  those  who  could  not 
free  themselves  from  the  emban-ass- 
ing  fetters  of  the  fixity  of  species, 
the  incompleteness  of  the  paheonto- 
logical  records,  and,  more  than  all, 


ON    THK    VITALl.STIC    VIEW    UF    NATCRK. 


409 


lliat  this  end  or  purpose  was  attnined  ]>y  iiuroly 
luechuiiical  processes,  that  no  new  force,  called  vital 
force,  need  be  assumed  to  exist,  tliat  it  was  the  adequate 
and  sole  object  of  science  to  disclose  the  mechanism  by 
which  the  various  ends  of  life  were  attained.  The  very 
idea  of  life,  the  vitalistic  element  or  factor,  was  chased 
away  beyond  the  region  of  the  knowal>le,  and  remained 
merely  an  idea  in  the  realm  of  thought,  as  it  was  for 
Descartes  and  Leibniz,  and  as  it  has  remained,  up  to 
recent  times,  for  von  Baer  and  for  Claude  Bernard,  and 
for  all  those  who  do  not  accept  the  Darwinian  explana-  Lotzeand 
tion.     For  Lotze,  Du  Bois-Eeymoud,  and  Claude  Bernard  ^  uemard. 


of  fiual  causes ;  in  one  word,  of  all 
pre-Darwinian  Darwinians  "  (vol.  ii, 
p.  299). 

'  Du  Bois-Reymoncl  ('  Redeu,'  vol. 
ii.  p.  557)  claims  that  the  greater 
partof  the  progress  in  modern  phj'si- 
ology  belongs  to  Germany,  in  spite 
of  the  great  talent  and  originality 
of  Claude  Bernard.  He  thus  de- 
scribes the  different  position  of 
the  three  countries  :  "  One  branch 
of  physiology  especially  emanated 
from  Germany  —  general  physics 
of  muscle  and  nerves.  Whereas  in 
England  experimental  physiologj- 
lay  fallow,  while  it  moved  in  France 
in  vivisection  and  zoochemistry, 
being  held  down  in  both  countries 
by  vitalism,  German  science  was 
the  first  to  advance  to  the  in- 
vestigation of  the  surviving  organs, 
especially  of  the  frog,  looking 
upon  them  as  apparatus  built  up 
by  nature,  extremely  complicated, 
yet  conceivably  only  machines." 
This  was  spoken  in  1880.  Since 
that  time  a  certain  change  has 
come  over  physiological  reasoning, 
notably  even  in  the  very  centre  of 
the  physico  -  chemical  school  at 
Herlin.  In  1899  Prof.  0.  Hertwig 
warns   us   of    the   other   extreme. 


opposed  to  the  older  vitalism, 
"which  would  lead  us  to  a  one- 
sided and  equally  inadequate  con- 
ception of  the  vital  j)rocess  .  .  . 
which  would  see  in  it  merely  a 
chemico  -  physical  and  mechanical 
problem,  and  would  recognise  the 
genuine  science  of  nature  only  so 
far  as  it  is  possible  to  reduce 
phenomena  to  motions,  .  .  .  and 
to  subject  them  to  mathematical 
calculation  "  ( '  Die  Lehre  vom 
Oi'ganisnms,'  an  Address,  Jena, 
p.  8).  How  far  Du  Bois-Keymond 
in  later  j'ears  modified  his  earlier 
notions,  we  can  to  some  extent 
see  from  his  published  addresses. 
We  know  that  the  French  school, 
with  Claude  Bernard  as  its  most 
illustrious  represent<vtive,  never  fell 
into  the  mistake  of  looking  at  the 
living  organism  as  a  physico-chemi- 
cal machine,  and  we  may  be  inclined 
to  attribute  this  lo  a  large  extent 
to  those  experiments  on  the  living 
organism  which  were  first  institut- 
ed by  Magendie,  which,  under  the 
hands  of  Claude  Bernard,  led  to 
the  discovery  of  the  action  of  the 
pancreatic  juice,  of  the  glycogenic 
function  of  the  liver,  of  vaso- motor 
nerves,  and  of  the  etiects  of  poisons  : 


410 


SCIENTIFIC    THOUGHT. 


purpose  exists  in  nature,  notably  in  living  nature ;  it 
is  its  very  characteristic,  its  definition — the  very  "  quid 
proprium  "  of  life,^  but  it  is  useless  as  a  scientific  concep- 
tion.    It  remains  a  problem  for  the  philosopher,  but  the 


all  of  them  epoch  -  making  dis- 
coveries which  revolutionised 
physiological  science,  and  which  it 
is  difficult  to  conceive  of  as  having 
been  made  without  vivisectional 
methods.  We  have  also  a  remark 
from  the  pen  of  the  late  Prof.  Georg 
Wiedemann,  that  Helmholtz  him- 
self, that  greatest  master  in  the 
line  of  mechanico-physical  reason- 
ing on  the  processes  and  organs 
of  the  higher  senses  and  the  nerv- 
ous system,  foresaw  the  necessity 
of  resorting  for  further  progress 
to  vivisectional  research,  to  which 
he  had  a  personal  dislike.  (See 
Wiedemann's  Introduction  to  the 
third  volume  of  Helmholtz's 
'  Wissenschaf tliche  Abhandlungen, ' 
p.  xxiv.) 

1  In  many  passages  of  his  later 
writings  Claude  Bernard  has  dealt 
with  the  definition  of  life :  most 
fully  in  the  posthumously  pub- 
lished volume  entitled  '  La  Science 
Experimentale '  (3rd  ed.,  1890). 
He  there  arrives  at  the  final  state- 
ments (p.  207) :  "Je  pense,  quant 
h  moi  .  .  .  que  les  phenomenes 
chimiques  dans  I'organisme  sont 
executes  par  des  agents  ou  des 
precedes  speciaux  ;  mais  cela 
ne  change  rien  li  la  nature  pure- 
ment  chimique  des  phenomenes, 
&c.  .  .  .  Les  agents  des  phenom- 
enes chimiques  dans  les  corps 
vivants  ne  se  bornent  pas  ti  pro- 
duire  des  syntheses  chimiques,  .  .  . 
mais  ils  les  organisent.  .  .  .  Parmi 
ces  agents  .  .  .  le  plus  puissant  et 
le  plus  merveilleux  est  sans  con- 
tredit  I'ceuf,  la  cellule  primordiale 
qui  contient  le  germe,  principe 
organisateur  de  tout  le  corps. 
Nous  n'assistons  pas  h  la  creation 
de    I'ojuf   ex    nihilo,    il    vient   des 


parents,  et  I'origine  de  sa  virtualite 
Evolutive  nous  est  cachee.  ...  II 
y  a  comme  un  dessin  vital  qui  trace 
le  plan  de  chaque  etre  et  de  chaque 
organe  ;  ...  ils  semblent  dirigds 
par  quelque  condition  invisible  dans 
la  route  qu'ils  suivent,  dans  I'ordre 
qui  les  enchaine.  .  .  .  C'est  cette 
puissance  ou  propriete  evolutive  que 
nous  nous  bornons  h.  dnoncer  ici  qui 
seule  constituerait  le  quid  pi-oj)rium 
de  la  vie,  car  il  est  clair  que  cette 
propriety  evolutive  de  I'cEuf,  qui 
produira  un  mammif^re,  un  oiseau 
ou  un  poisson,  n'est  ni  de  la 
physique,  ni  de  la  chimie.  .  .  . 
En  disant  que  la  vie  est  I'idee 
directrice  ou  la  force  evolutive  dc 
Vetre,  nous  exprimons  simplement 
I'idee  d'une  unite  dans  la  succession 
de  tous  les  changements  morpholo- 
giques  et  chimiques  accomplis  par 
le  germe  depuis  I'origine  jusqu'a  la 
fin  de  la  vie.  ...  La  force 
metaphysique  Evolutive  par  laquelle 
nous  pouvons  caracteriser  la  vie  est 
inutile  h,  la  science,  parce  qu'etant 
en  dehors  des  forces  phj'siques  elle 
ne  pent  exercer  jaucune  influence 
sur  elles.  II  faut  done  ici  separer 
le  monde  m(^taphysique  du  monde 
phj'sique  phdnom(5nal  qui  lui  sert 
de  base  mais  qui  n'a  rien  Ji  lui 
emprunter.  Leibniz  a  exprime 
cette  delimitation  dans  les  paroles  : 
'  Le  corps  se  ddveloppe  mdcanique- 
ment,  et  les  lois  mecaniques  ne  sont 
jamais  violees  dans  les  mouvements 
naturels ;  tout  se  fait  dans  les  ames 
comme  s'il  n'y  avait  pas  de  corps, 
et  tout  se  fait  dans  le  corps,  comme 
s'il  n'y  avait  pas  d'ames. "...  Nous 
dirons  avec  Descartes :  on  pense 
metaphysiqtiement  mais  on  vit  et 
on  agit  physiquement." 


ON    TUK    VTTAT.TSTIC    VIKW    OF    NATURK.         411 

uaLuialist  may  neglect  it,  or  at  best  can  only  use  it  as  an 
"  heuristic  "  help,  as  an  indication  where  to  look  for  tlie 
special  mechanical  contrivances  ^Yhicll  he  is  trying  to 
unravel.  It  seems  to  me  that  the  position  which  such 
thinkers  take  up  towards  the  objects  or  individuals  of 
living  nature  is  similar  to  tliat  of  a  mathematical  student 
who  clearly  comprehends  the  solution  of  an  algebraical 
problem,  but  who  himself  would  be  unable  to  find  it. 
He  may  all  his  life  remain  in  this  attitude  without  being 
able  to  find  any  solution  himself :  he  has  got  complete 
hold  uf  the  mechanism,  but  not  of  the  idea,  of  mathe- 
matical reasoning.  The  student  of  nature  could  thus 
hope  eventually  to  understand  the  mechanism  of  life,  but 
the  idea  is  beyond  his  comprehension.  This  can  be  ex- 
pressed by  saying :  the  mechanism  of  life  is  ultimately 
comprehensible,  though  highly  intricate ;  the  idea  of  life 
is  transcendental,  incomprehensible.  Let  us  not  trouble 
ourselves  about  the  manner  in  which  life  first  originated, 
but  let  us  study  the  mechanical  processes  by  which  it  is 
maintained,  by  which  its  various  ends  are  accomplished. 
Let  us  study  the  mechanism  of  the  clock,  though  this 
may  not  tell  us  the  story  of  its  maker  nor  the  process 
of  its  manufacture.  Those  who  cling  to  the  conception 
of  a  vital  force  or  principle  would  probably  not  even 
admit  as  much  as  this.  It  is  doubtful  whether  Liebiu 
to  the  end,  whether  Huxley  in  his  earlier  period,  and 
l)u  Bois-Eeymond  in  his  later  writings,  would  have 
admitted  even  this  position. 

We  are  now  prepared  tu  understand  the  novel  position        26. 

.     .  Iiarwinism 

which    the   Darwinian   conception   of    natural    processes  "'"'  ''"ai 

^  causes. 

introduced  so  far  as  the  teleology  of  nature  is  concerned, 


412  SCIENTIFIC    THOUGHT. 

— how  it  dealt  with  final  causes,  with  the  apparent  exist- 
ence of  a  purpose,  an  end  in  the  processes  of  nature, 
notably  of  the  living  organism. 

It  must  here  be  remembered  that  the  question  how 
living  things  come  to  exhibit  traces  of  design  and  pur- 
pose has  really  nothing  to  do  with  the  nature  and  pro- 
cesses of  life :  it  is  not  necessarily  a  biological  question. 
Every  machine  show^s  the  same  marks  of  design,  but  is 
not  therefore  alive.  The  influence  of  Darwin's  principle 
of  natural  selection,  of  overcrowding  and  consequent 
struggle  for  existence  and  survival  of  the  fittest  speci- 
mens, has  therefore  not  been  in  the  direction  of  explain- 
ing any  of  the  vital  processes  which  are  at  work  in  the 
individual  organism.  It  is  at  best  merely  a  statistical 
relation,  a  peculiar  phenomenon  occurring  only  in  a  large 
or  congested  group  of  living  and  self-multiplying  beings : 
it  presupposes  the  facts  of  reproduction,  heredity,  and 
variation  ;  it  does  not  explain  them.  Hence  I  dealt 
with  Darwin's  ideas  in  the  last  chapter,  and  did  not 
introduce  them  under  the  present  heading  of  Biological 
Thought.  As  we  shall  see  later  on,  Darwin  did  re- 
cognise the  necessity  of  attempting  also  a  biological 
explanation. 

The  possibility  of  explaining  the  marks  of  design  as 
merely  apparent  depends  on  the  conception  of  the  genetic 
process  acting  on  a  large,  a  gigantic  scale  :  individual 
things  put  forth  ever  new  developments  by  which  they 
eventually  overtop  their  neighbours,  ultimately  advanc- 
ing to  such  a  degree  of  excellence  and  individual  per- 
fection that  to  an  outside  beholder  the  few  surviving 
specimens   give   the   impression   of   having   been  origin- 


0\    THE    VITALISTIC    VIEW    OF    NATrPJ-;.        413 

ally  designed.  In  fact,  they  (jnly  exist  because  those 
numberless  indiNiiluals  which  could  not  grow  in  a  suffi- 
cient degree  perished  in  the  struggle.  Onl\'  Ukjsc  in- 
dividual specimens  survived  in  whom,  in  one  or  a  few 
directions,  something  specially  excellent  was  produced 
at  the  expense  of  development  in  other  directions.  In 
the  mass,  the  crowd  are  sacrificed — i.e.,  automatically 
crushed,  in  favour  of  the  few :  in  the  individual,  one 
special  growth  is  automatically  pursued  at  the  expense 
of  a  general  l)ut  less  enduring — i.e.,  self-assertive — de- 
velopment. The  end  —  the  seeming  purpose — is  pro- 
duced in  the  process  of  production,  it  being  merely 
something  more  enduring — i.e.,  something  Ijetter.  It 
conveys  the  impression  to  an  outside  beholder  of  having 
been  consciously  set  at  the  term  of  the  process  of  devel- 
opment ;  in  reality  it  was  produced  simultaneously.  The 
mountain  peak  which  towers  above  its  neighbours,  and 
gives  a  distinctive  rounding  off  and  finish  to  a  landscape, 
may  be  conceived  as  having  been  Ijuilt  up  by  the  selective 
action  of  the  natural  artist  who  brought  together  the  best 
materials  and  placed  them  in  their  most  enduring  posi- 
tions :  in  reality  it  owes  its  existence  only  to  one  out  of 
the  numberless  throes  of  nature  which  happened  to  take 
place  with  stronger  materials  and  in  more  stable  forms 
of  arrangement  and  grouping,  or  it  is  due  to  the  denuda- 
tion of  the  strata  surrounding  it.      The  end  and  purpose        27. 

°  -^  "Natural 

of  any  natural  development  is  that  which  it  can  itself  Jf4",j^(_' 
automatically  produce  and   endow  with  most  distinctive  "P"'"Po«e-" 
and  enduring  characters,   for    this  only  survi\es  at   the 
expense  of  weaker  productions :   there  is  a  natural  result 
in  development,  but  there  need  not  be  a  purpose.      The 


414 


SCIENTIFIC    THOUGHT. 


contemplation  of  the  result  may  permit  us  to  trace 
backward  the  process  by  which  it  was  brought  about ; 
but  we  are  not  warranted  in  assuming  that  it  existed 
independently,  like  the  plan  of  a  building  or  the  purpose 
of  an  instrument.  In  the  place  of  a  growth  according  to 
a  prearranged  plan,  Darwin  put  the  conception  of  an 
automatic  adjustment  called  "  natural  selection  "  ;  in  the 
place  of  a  conscious  end  or  purpose  he  put  the  concep- 
tion of  a  mere  result,  a  product,  the  "  surviving  fittest."  ^ 
The  development  and  proof  of  Darwin's  ideas  gave  a 
new  impetus  to  biological  research,  as  it  did  also  to  the 
science  of  the  history  and  economy  of  nature.  The  fact 
that  the  phenomenon  of  selection,  or  rather  of  automatic 
crowding  out,  presupposes  intimate  relations  and  contact 
of  every  living  thing  with  numberless  other  similar  and 
dissimilar    beings,  led  naturalists  into   the   open  air,  to 


^  A  very  full  appreciation  of  the 
great  chanf^e  that  has  come  over 
the  sciences  of  nature  through  the 
influence  of  Darwin  will  be  found 
in  the  various  wiitings  and  ad- 
dresses of  Prof.  Haeckel,  ncjtablj' 
in  his  address  to  the  German  As- 
sociation in  1877  at  Munich,  "  Ueber 
Entwickelungslehre  "  (repj-inted  in 
'  Gesaminelte  popuUire  Vtjrtrage,' 
vol.  ii.  ]).  97).  A  more  critical  exam- 
ination, referring  specially  to  the 
central  biological  problems,  is  the 
address  by  Du  Bois-Reymond,  de- 
livered in  1876  in  the  Berlin  Acad- 
emy, and  reprinted  in  '  Heden,'  vol. 
i.  p.  21],  with  valuable  literary 
notes.  He  there  discusses  how  far 
the  principle  of  natural  selection, 
in  addition  to  the  general  doctrine 
of  descent,  has  been  adopted  or  op- 
posed, and  refers  to  the  outstand- 
ing difficulties.  "  One  of  the  great- 
est difficulties,"'  he  .says  (p.  226), 
"  presents  itself  in  phj'siology  in  the 


so-called  regenerative  power,  and — 
what  is  allied  to  it — the  natural 
power  of  healing  :  this  may  now  be 
seen  in  the  healing  of  wounds,  in 
tlie  delimitation  and  compensation 
of  morbid  processes,  or,  at  tlie 
farthest  end  of  the  series,  in  the 
re -formation  of  an  entire  fresh- 
water polyp  out  of  one  of  the  two 
halves  into  which  it  had  been 
divided.  This  artifice  could  surely 
not  have  been  learnt  by  natural 
selection,  and  here  it  ajjpeai's  im- 
possible to  avoid  the  assumption  of 
formative  laws  acting  for  a  pur- 
p<i.se.  The}'  do  not  become  moi-e 
intelligible  by  the  fact  that  the 
regeneration  of  mutilated  crystals, 
observed  by  Pasteur  and  others, 
points  to  similar  proce.sses  in  inani- 
mate nature.  Also  the  ability  of 
organisms  to  perfect  themselves  by 
exercise  has  not  found  sufficient 
appreciation  with  regard  to  natural 
selection." 


ON    THE    VITALLSTIC    VIEW    OF    NATURE.        415 

outdoor  research,  into  the  arena  of  real  life.  On  this 
I  dwelt  in  the  last  chapter.  Ideas  of  a  cognate  kind 
had  already  emanated  from  other  schools,  such  as  that 
of  Liebig, — the  circulation  of  life  in  the  different  pro- 
vinces of  nature,  the  interdependence  of  dillerent  species 
of  living  things.  Isolated  investigations,  like  those  of 
Gartner  and  Sprengel,  of  Iluber  and  Lubbock,  on  insect 
life,  or  of  bacteriologists  like  Pasteur  and  Boussingault 
on  fermentation  and  fertilisation,  received  a  fitting  place 
as  important  chapters  in  the  economics  of  nature.      The        ss. 

Oi'K'anisation 

problem  of  life  became  twofold — the  life  of  the  com- andiudivid- 

■^  nation. 

munity  and  the  life  of  the  individual :  organisation  and 
individuation.  Two  great  (juestions  presented  them- 
selves :  What  is  an  individual  ?  what  is  a  society  of 
individuals  1  Physiologists  were  from  of  old  accustomed 
to  ask  the  former ;  economists  like  Rousseau  and  Adam 
Smith  had  asked  the  latter  question.  Both  now  became 
questions  for  the  biologist.  Physiology  and  economics 
joined  hands.  In  isolated  instances,  as  in  those  of  Liebig 
and  von  Baer,  these  two  interests  had  already  been  united. 
The  real  meaning  and  reason  of  this  union  now  Ijecame 
clear  to  every  one :  it  revealed  itself  as  founded  on  the 
two  characteristic  features  of  life— individuality  and  co- 
operation.     With  the  exception  of  the  strong  emphasis        so. 

,  X  •    1  ■  •  1  Biology  and 

put  l)y  Liebig  on  tfie  latter  side  of  natural,  notably  loonomics. 
organic  processes,  biologists  before  Darwin  liad  mainly 
studied  the  phenomena  of  individual  life.  In  two  special 
directions — in  embryology  and  in  the  cellular  theory — 
they  had  made  great  progress.  1  have  already  treated 
of  these  advances  in  their  bearing  ujton  morphology,  the 
study  of  forms,  and  upon  genesis,  the  study  of  change 


416  SCIENTIFIC   THOUGHT. 

and  development.     Let  us  see  how  they  affected  biology 
proper — the  study  of  life. 

The  early  propounders  of  the  cellular  theory  were 
evidently  much  influenced  by  the  then  existing  theories 
which  explained  the  constitution  of  inorganic  chemical 
substances  by  atoms  and  by  the  processes  of  crystal- 
lisation. The  progress  of  science,  however,  was  in  the 
direction  of  showing  more  and  more  that  these  borrowed 
conceptions  are  quite  inadequate.  Eeasoning  or  thinking 
on  organised  matter  is  quite  different  from  that  which 
refers  to  unorganised  substance.  Chemists  and  physicists 
deal  with  atoms  as  imaginary  units,  which  form  the  ideal 
groundwork  for  constant  arithmetical  proportions  or  for 
the  action  of  calculable  mechanical  forces  measured 
by  observable  movements.  Biologists,  whether  dealing 
with  plants  or  animals,  approach  the  cells  which  they 
regard  as  the  units  of  living  matter  with  the  micro- 
scope— an  instrument  which,  till  quite  recently,  has  only 
been  sparingly  used  in  chemical  research.  The  units 
of  the  chemist  far  transcend  our  powers  of  vision ;  the 
units  of  the  biologist  are  to  some  extent  accessible  to 
our  senses.  All  organisms  have  been  found  to  be 
analysable  by  the  aid  of  the  microscope  into  similar 
morphological  constituents  called  cells,  which  present 
very  similar  forms  and  functions.  This  has  had  the 
advantage  of  permitting  the  phenomena  of  life  to  be 
analysed  into  a  few  fundamental  processes  common  to 
all  living  things ;  the  great  diversity  of  the  larger 
organisms,  and  the  more  conspicuous  phenomena  of  life, 
being  conceived  as  put  together  in  various  ways  out  of 
these  elementary  units,  which  exhibit  in  varying  degrees 


ON    TllK    VITALISTIC    VIKW    OF    NATIKb:.         417 

of  intensity  the  living  processes  common  to  all.  Just 
so  a  state  or  human  society  is  made  up  of  a  large 
numl)er  of  individuals,  all  having  the  same  human 
nature,  who  carry  on  the  different  functions  peculiar 
to  each  with  varying  degrees  of  efficiency.     The  concep-        3o. 

^.  .        ,  „  ,  .  -^  '-      The  cellular 

tion  or  the  cell  as  the  unit  or  type  of  all  living  H'wry. 
matter,  and  the  further  discovery  that  there  exist  uni- 
cellular beings  which  are  not  essentially  different  from 
the  constituent  living  elements  of  the  most  complicated 
organisms,  has  brought  physiological  research  to  a  focus. 
The  difficulties  in  the  study  of  biological  phenomena 
have  vanished  as  those  of  the  organic  chemist  did  on 
the  introduction  of  the  conception  of  valency,  of  the 
saturating  powers  of  chemical  substances.  Accordingly, 
if  we  compare  a  text-book  of  these  subjects  written  in 
the  middle  of  the  century  with  one  Ijelonging  to  the 
latter  part  of  it,  we  find  an  enormous  difference  of 
treatment.  It  is  instructive  to  contrast  the  introduction 
given  in  Johannes  ]\Iiiller's  '  Elements  of  Physiology ' 
and  that  of  Professor  Michael  Foster's  '  Text-book.'  The 
former  represents  the  most  advanced  knowledge  obtain- 
able at  the  end  of  the  thirties — the  latter  that  of  a 
generation  later.  The  former  contains  a  lengthy  intro- 
duction on  general  physiology — the  latter  a  short  one 
on   the  physiological  properties   of   a    living  amoeba,^  a 


'  Already,  in  1835,  K.  E.  vou 
Baer  pointed  out  how  tlie  study 
of  one  small  animal  can  revolution- 
ise our  entire  reasoning.  "  Ninety 
years  ago  a  naturalist  discovers 
the  hydropolyp,  an  insignificant 
slimy  animal,  not  larger  than  a 
peppercorn,  and  how,  without 
head,  sense-organs,  muscles,  nerves, 
blood,  and  sexual  organs  it  never- 


theless is  nourished,  grows,  feels, 
moves,  and  multiplies, — how  it  can 
even  be  divided,  each  part  form- 
ing a  whole  :  he  observes  it  with 
much  wonder  for  nine  years  with 
untiring  perseverance.  At  that 
time  many  would,  no  doubt,  con- 
sider such  an  occupation  childisii 
and  unworthy,  yet  these  diligent 
observations   have  slowlv   but   ma- 


VOL.  II.  2   D 


418  SCIENTIFIC    THOUGHT. 

unicellular  organism  which  is  taken  as  a  type,  a  model 
of  all  the  phenomena  of  life.  The  former  consists  of 
philosophical  and  abstract  generalisations,  gathered  from 
many  sources ;  it  treats  of  life  in  general,  of  the  vital 
force,  of  the  difference  between  animal  and  plant  life, 
&c. :  the  latter  sums  up  the  whole  matter  of  the  treatise 
under  a  few  heads,  taken  from  the  life  of  the  simplest 
liviuCT  thino;.  The  generalisation  has  become  an  actual 
observable  example.  This  transition  from  the  abstract 
to  the  concrete,  from  the  idea  to  the  thing  itself,  is  owing 
mainly  to  those  definite  conceptions  which  in  Mliller's 
time  were  being  slowly  elaborated  :  these  were  the  cellular 
theory,  the  larger  conception  of  "  Stoffwechsel "  as  con- 
tained in  the  term  "  metabolism,"  and  the  conception 
of  "  differentiation  of  tissue "  connected  with  division 
of  labour.  The  two  former  are  already  very  clearly 
foreshadowed  in  Theodor  Schwann's  microscopical  re- 
searches ;  the  latter  takes  us  back  to  K.  E.  von  Baer's 
embryological  researches,  to  which  the  Darwinian  idea 
of  a  struggle  for  existence,  and  the  consequent  tendency 
to  one-sided  development  of  form  and  function,  have 
given  an  additional  importance.  Of  the  first  and  third 
of  these  definite  modern  conceptions  I  have  treated 
above.  The  cell  is  the  morphological  unit  of  living 
matter.      The  process   of   differentiation  was  recognised 

terially  iuflueuced  phj'siology,   the  polyp  that  have  changed  the  former 

basis   of  medicine,  and   hence  also  aspect  of  things,  and  that  the  trans- 

the    latter  ;    and   it  is  incalculable  formation  of  the  general  views  of 

what  many  of   those  here   present  life  has  altered  the  theory  of  sensa- 

have  gained  through  such  influence  ,    tiou,  circulation,  &c.,  very  materi- 

in  days  of  sickness  or  may  still  gain.  ally,   and  is  still  active"  ("Blicke 

Whoever  carefully  studies  the   de-  ;    auf  die  Eutwickelung  der  Wissen- 

velopment   of    physiologj',    will    be  schaft,"    au    address,    reprinted   in 

convinced  that  it  is  mainly  Trem-  i    '  Reden,'  vol.  i.  p.  109). 

bly's    observations    of    the    hydro-  | 


ox    THE    VITAL18TIC    VIEW    OF    NATUKK. 


419 


ill  the  examination  of  dead  embryos  in  various  stages 
of  development,  and  the  idea  of  the  division  of  labour 
is  one  ilowing  from  the  premises  of  the  Darwinian 
theory — the  facts  of  variability  and  overcrowding.  The 
second  conception,  that  of  "  metabolism,"  touches  im- 
mediately upon  the  processes  of  life,  and  demands; 
special  treatment  in  the  present  chapter  which  deals 
with   biological  Thought. 

The  conception  of  a  continuous  exchange  or  circulation 
of  matter  and  of  energy  in  every  living  organism,  and 
the  study  of  this  elementary  i\pi(;d  form  of  the  living 
process  in  the  morphological  unit  of  all  living  or- 
ganisms, in  the  cell,  seems  to  have  originated  with 
Theodor    Schwann,^   and    is    laid    down    in   his  '  ]\Iicro-        3i. 

Scinvaun 

scopical  liesearches,'  published  in  18."! 9.  On  it  is  based 
the  whole  simplitication  and  unification  of  biological 
thought  which  distinguishes  the  second  from  the  first 
half    of    our    century.       The    study    of     the    cell  —  its 


'  On  the  change  whieli  came 
over  general  ]>hysiulogy  about  1S40, 
and  the  pai-t  he  himself  played, 
Theodor  Schwann  has  expressed 
himself  in  a  letter  addressed  to 
Du  Bois-lleymond,  which  is  given 
in  the  notes  to  the  latter's  Eloge 
of  Miiller,  reprinted  in  the  second 
volume  of  his  'Reden,'  pp.  143-334. 
It  forms  one  of  the  most  im- 
portant historical  documents.  The 
Eloge  itself  should  be  read  together 
with  Claude  Bernard's  'liapport,' 
&c.,  mentioned  above  (p.  3S4  n.), 
which  gives  the  historj-  of  the  great 
change  from  a  more  exclusively 
Frencli  point  of  view.  In  the 
letter  mentioned  above,  from  wliicli 
also  the  ([uotations  given  in  the 
text    arc    taken,    Schwann    claims 


that  the  first  instance  in  whicli 
an  "evidently  vital  phenomenon 
was  submitted  to  mathematical, 
numerical"  rule,  was  his  measure- 
ment of  the  carrying  power  of 
a  muscle  in  relation  to  its  con- 
traction in  1836.  The  purelj' 
physical  view  of  vital  phenomena 
exhibited  in  this  example  was  not 
adopted  by  Miiller.  nor  yet  the 
(juickly  following  general  principle 
of  the  cellular  theory.  Schwann 
refers  to  the  tliird  section  of  his 
'  Microscopical  Researches,'  in 
which  he  discards  "  vitalism,"  but 
ailinits  in  man  ("on  account  of 
his  freedom")  an  immaterial  prin- 
ciple, and  claims  that  this  assump- 
tion divides  him  distinctly  from  the 
materialists. 


420  SCIENTIFIC    THOUGHT. 

formation,  growth,  division,  and  maintenance  of  form 
amidst  change  of  matter  and  alternation  of  function — 
constitutes  the  "  prolegomena  "  of  physiology,  and  a  com- 
parison of  Prof.  0.  Hertwig's  recent  publication  on  the 
"  cell  "  with  the  introduction  to  Johannes  Mliller's  '  Phys- 
iology '  marks  well  the  change  of  ideas  which  half  a 
century  has  produced.  And  we  must  so  much  the  more 
admire  the  clear  anticipation  of  Schwann,  as  he  was  not 
in  possession  of  the  fvill  conception  of  energy  in  its 
two  interchangeable  forms  of  kinetic  and  potential 
energy,  which  was  developed  in  the  course  of  the  two 
decades  following  his  publication.  Schwann  not  only 
conceived  the  cell  to  be  the  morphological  unit  of  all 
living  matter,  but  he  also  saw  that  "  cell  formation 
must  be  the  general  principle  of  organic  development, 
and  that  there  can  be  only  one  such  principle."  In 
the  third  section  of  his  '  Microscopical  Eesearches '  he 
founds  on  this  "  his  theory  of  organisms,  and  rejects 
distinctly  therein  all  teleological  explanations  based  upon 
a  vital  force  acting  according  to  final  purposes."  He 
thus  showed  "  that  the  only  essential  property  of  all 
living  matter — viz.,  growth — is  not  inaccessible  to  a 
physical  explanation,"  and  he  did  this  at  a  time  "  when 
Liebig  had  not  yet  taught  physiologists  the  chemical 
changes  which  take  place  in  living  tissues."  These  ideas 
were  only  partially  adopted  by  Johannes  Miiller  and 
other  leading  physiologists  of  the  day.  Schwann's  view 
could  only  be  consistently  elaborated  in  proportion  as 
Circulation  to  the  older  conception  of  a  "  Stoffwechsel "  (a  chem- 
andmergy.   ic^l   proccss)  there   was   added    that   of    a  "  Kraft "-    or 


ON    THK    VITALISTIC    VIEW    OF    NATURE.         421 

"  Energie-wechsel  "  ^  (a  physical  process).  Bio-cheiuistiy 
had  to  be  supplemented  by  bio-physics.  With  a  clear 
anticipation  of  the  correcter  and  fuller  view,  Schwann 
introduced  the  Greek  term  "  metabole."  It  is  the  merit 
of  Prof.  ]\Iichael  Foster  to  have  domiciled  this  useful 
and  all-comprising  technical  term  in  English  physiological 


'  Du  Bois-Reymoiul  (' Reden,' 
vol.  ii.  J).  220)  mentions  this  as  tlie 
tliird  imjiortant  gain  which  phys- 
iological science  had  to  register 
since  the  appearance  of  Miiller's 
hook  ;  the  first  and  second  being 
tlie  cellular  theory  and  the  mech- 
aiiico-physical  method,  both  largely 
i)\ving  to  Schwann.  This  was 
written  just  before  the  great 
intluenee  of  Darwin  began  to  be 
felt.  In  the  ideas  introduced  by 
Helmholtz,  which  clarified  the  con- 
cejition  of  force,  he  sees  the  "key 
which  opens  a  comprehension  of 
the  '  Stotfweclisel '  in  plants  and 
animals."  The  term  "  Stott'- 
wechsel,"  also  "Stoffumsatz,"  or 
simply  "  Umsatz,"  has  been  quite 
familiar  in  German  physiological 
literature  during  the  whole  of  the 
century.  I  cannot  find  any  gener- 
ally accepted  term  in  English  liter- 
ature before  the  introduction  of 
Schwann's  term  "  metabolic  phen- 
omena,"' which,  I  believe,  was  first 
adopted  by  Sir  M.  Foster,  and 
is  now  cjuite  domiciled  in  English 
text-books  and  translations.  The 
passage  in  Schwann's  '  Microscop- 
ical Researches  '  is  as  follows 
('  Sydenham  Society's  Translation,' 
p.  193):  "The  phenomena  attend- 
ing the  formation  of  cells  may  be 
arranged  in  two  natural  groups : 
first,  those  which  relate  to  the 
combination  of  the  molecules  to 
form  a  cell,  and  which  may  be 
denominated  the  plantic  jjheiiom- 
ena   of  the    cells ;    secondly,   those 


which  result  from  chemical  changes, 
either  in  the  component  particles 
of  the  cell  itself  or  in  the  sur- 
rounding cytoblastema,  and  which 
may  be  called  lactabolic  phenomena 
(rh  ij.tTaQo\iK6v,  imjilyiug  that 
which  is  liable  to  occasion  or  to 
suffer  change)."  It  will  be  seen 
later  on  that  tiie  term  metabolism 
is  a  peculiarly  happy  one,  as  it 
lends  itself  by  a  slight  change  in 
the  prefix  to  denote  the  twofold 
process  of  building  up  and  of  run- 
ning or  falling  down,  which  con- 
stitutes the  changes  peculiar  to 
protoplasm  as  the  constituent 
element  of  all  organised  substance. 
It  is,  accordingly,  somewhat  sur- 
prising that  the  term  has  found 
so  little  favour  abroad.  In  France, 
where  this  twofold  movement  has 
long  ago  been  recognised  as  one 
of  the  characters  of  the  living 
process,  the  terms  "  composition 
et  decomposition "  (de  Blainville), 
"  organisation  et  desorgaiiisation  " 
(Claude  Bernard),  "assimilation  et 
desassimilation,"  have  been  variously 
adopted  (see  Claude  Bernard,  'Phon- 
omenes  de  la  vie,'  vol.  i.  p.  36, 
&c.)  M.  Yves  Delage  ('  L  'Herodito,' 
p.  53)  says  :  "  Les  Anglais  ont  sub- 
stitucS  it  ces  expressions  si  signi- 
ficatives  :  nutrition,  assijuilatidn, 
dSxassimilation,  une  terminologie 
qui  a  dil  leur  paraitre  bien  belle, 
car  ils  I'ont  tous  adopt(5e  avec 
un  empressement  remaniuable  ; 
c'est  celle  de  mctabolisme,"  &c. 


422  SCIENTIFIC    THOUGHT. 

literature,  to  have  placed  it  at  the  entrance  of  his  text- 
book of  physiology,  and  thus  to  have  given  the  student 
a  somewhat  more  detailed  description  of  the  elementary 
functions  of  living  matter  than  was  afforded  by  the  older 
term  "  vortex,"  employed  by  Cuvier. 
33.  These  merits  of  Schwann,  which  attach  more  to  the 

"Metabol- 
ism." conception  of  "  metabolism "   than   to   that    of    the    cell, 

are  not  reduced  by  our  having  to  state  that  the  latter 
conception  has  been  entirely  changed  since  his  time. 
The  cell  of  to-day  is  not  the  cell  as  Schwann  conceived 
it.  Of  the  pretty  clearly  defined  structure  or  organ- 
isation of  that  biologist,  with  its  wall  (membrane), 
its  kernel  (nucleus),  and  its  fluid  contents  (cell  sap), 
nothing;  has  remained  but  the  cell  contents,  termed 
protoplasm  by  von  Mohl ;  and  the  living  process  can  no 
longer  be  considered  as  the  function  of  a  well-defined 
organ  or  machine.  It  is  rather  the  fundamental  property 
of  an  almost  homogeneous  substance,  the  mass  of  proto- 
plasm, in  which  the  kernel  is  the  only  recognisable 
differentiated  portion.  The  immediate  eft'ect  of  this  de- 
structive analysis  of  the  early  conception  of  the  cell  was 
to  destroy  the  idea  that  the  living  processes  carried  on  in 
any  special  cell  or  organ  are  a  result  of  its  organisation, 
as  the  function  of  an  apparatus  is  dependent  upon  the 
arrangement  and  combination  of  its  parts.  It  has  pro- 
moted the  view  that — for  our  understanding  at  least — 
the  first  thing  to  learn  is  the  nature  of  the  processes 
themselves.  We  have  to  look  upon  the  visible  structure 
of  special  cells  and  organs  merely  as  "  mechanical  con- 
trivances, serving  only  to  modify  in  special  ways  the 
results  of   the  exercise  of   these  fundamental  activities. 


ON    THK    VITALISTIC    VIKW    OF    NATrilK. 


423 


ami     in    no    sense    determining    their    initial    develup- 
ment.    ^ 

It  seems,  iht-n,  that  we  can  date  back  to  Schwann's 
'  Kesearches  '  the  ori;_i;in  ni  two  distinct  courses  of  Thought 
which  in  tlie  second  half  of  our  century  obtain  in 
biological  science.  The  first  we  may  call  the  morpho- 
logical or  structural  school  of  biology.  It  is  based  on 
the  theory  of  the  cell  or  some  modified  conception,  ami  analysis  of 
attempts    to   explain    ihe    fundamental   processes   which  I,°|:',^^J,ts. 


34. 
StniPtural 


go    on    m 


liying   organisms    from    the    structure  of   the 


elementary   parts.       As    the    UKJst    minute    particles    of 


'  See  Sir  Michael  Foster's  excel- 
lent article  on  "  General  Physiologj- " 
in  the  19th  vol.  of  the  '  Eucy.  Brit.,' 
9th  ed.,  p.  ['2.  In  this  connection 
a  passage  from  an  early  review  of 
Hu.sley's,  "On  the  CeU  Tlieory," 
has  been  frequently  quoted,  ac- 
cording to  which  cells  maj'  be 
"  no  more  the  producers  of  the 
vital  phenomena  than  the  shells 
scattered  in  rjrderly  lines  along  tiie 
sea  beach  are  the  instruments  by 
which  the  gravitative  force  of  the 
moon  acts  upon  the  ocean.  Like 
these  the  cells  mark  only  where  the 
vital  tides  have  been  and  iiow  tliey 
have  acted"  (IS.'iS,  in  the  'Brit, 
and  Fit.  .Med.  Chirurg.  Review,' 
reprinted  in  the  first  volume  of 
'Scientific  Memoirs,' p.  277).  Ac- 
cording to  this  view,  which  has 
been  further  developed  in  more 
recent  times,  the  cells  would  be 
"  imlications,"  not  instruments,  of 
the  vital  phenomena,  which  "are  not 
necessarily  preceded  bj'  organisa- 
tion, nor  are  in  any  way  the  result 
or  efi'ect  of  formed  parts,  the 
faculty  of  manifesting  them  re- 
siding in  the  matter  of  which  living 
bodies  are  com|)osed,  as  such— or, 
to  use  the  language  of  tiie  day, 
the    '  vital    forces '    are    molecular 


forces."  It  is  interesting  to  quote 
together  witii  this  i)assage  fi'ora 
Huxley,  what  was  said  forty  years 
later  by  an  eminent  living  jihysio- 
logist.  Prof.  Max  \'erwoi-n  of  Jena  : 
'■  Tlie  fact  has  been  established  that 
a  fundamental  contrast  between 
living  organisms  and  inorganic 
bodies  does  not  exist.  In  contra- 
distinction to  all  inorganic  nature, 
however,  organ i.-^ms  are  character- 
ised solely  by  the  possession  of 
certain  highly  complex  chemical 
compounds,  especially  proteids " 
('  General  Phvsiologv,'  tran.-,!.  by 
F.  S.  Lee,  1899,  i."  li'ti).  "'We 
can  summarise  our  con.--i<lei'atii>ns 
and  give  simple  expression  to  the 
problem  of  all  physiology.  The  life- 
process  consints  in  the  metabolism 
of  proteids.  If  this  Ise  true,  all 
physiological  research  is  an  experi- 
ment in  this  field  :  it  consists  in 
following  the  metabolism  of  proteids 
into  its  details,  and  recognising  the 
various  vital  phenomena  as  an  ex- 
pression of  this  metabolism  which 
must  result  from  it  with  the  same 
inevitable  necessity  as  the  pheno- 
mena of  itioi'ganic  nature  result 
from  the  chemical  and  physical 
changes  of  inorganic  bodies"  (ibid., 
p.  136). 


424  SCIENTIFIC    THOUGHT. 

living  matter,  revealed  by  the  most  powerful  microscope 
aided  by  all  the  elaborate  processes  of  staining,  still 
appear  to  be  endowed  with  the  fundamental  properties 
of  life,  such  as  irritability,  contractility,  and  metabolism, 
i.e.,  change  in  form  and  chemical  constitution,  the 
object  of  this  line  of  research,  viz.,  the  investigation 
of  th-e  initial  structure  of  the  elements  of  living  matter, 
can  only  be  reached  by  indirect  means  or  by  conjecture. 
Structural  chemistry  and  stereo-chemistry  proceed  by 
similar  methods  of  investigation,  and  have  succeeded 
by  means  of  the  atomic,  molecular,  and  kinetic  theories 
of  matter  in  bringing  order  and  unity  into  a  very  large 
portion  of  our  knowledge  of  chemical  combinations.  The 
morphological  or  structural  biologist  pictures  to  himself 
very  much  more  complicated  arrangements  of  molecules 
than  the  carbon  tetrahedron  of  van  't  Hoff  or  the  benzine 
ring  of  Kekule,  yet  formed  on  similar  principles ;  and 
by  continuing  in  his  mind  these  combinations  which, 
as  they  become  more  complex,  also  become  more  \m- 
stable,  he  arrives  ultimately  at  a  very  complex  and 
continually  changing  chemical  structure,  which  he  imag- 
ines might  be  the  beginning  of  the  living  process,  the 
element  of  organisation.  This  conception,  so  far  as  I 
can  find,  was  first  introduced  into  biological  literature 
by  Herbert  Spencer.  He  has  termed  this  element 
of  living  matter  "  the  physiological  unit."  The  con- 
ception has  been  varied  in  endless  ways  by  many  sub- 
sequent biologists,  all  of  whom  have  invented  special 
names  for  these  elementary  units  of  life  out  of  which 
they  hope  to  put  together  the  many  observable  proto- 
plasmic and  cellular  tissues  of    the    plant  and    animal 


ON    THE    VITALISTIC    VIEW    OF    NATURE.         425 

organism  as  Haiiy  attempted  to  build  up  crystals  out 
of  his  "  jhuIccuIl's  inlegrantes."  The  most  elaborate  an- 
alysis of  this  conception  is  put  forward  in  the  '  ]\licellar 
Theory '  of  the  celebrated  botanist  Niigeli,  which  in 
Germany  has  found  favour  with  many  eminent  Ijio- 
logists  as  a  provisional  programme  of  the  various 
problems  involved.  It  is  clear  that  the  conception  of 
the  physiological  unit  opens  out  two  distinct  lines  of 
research.  We  can  approach  it  on  the  one  side  by 
artificially  producing  in  the  chemical  laboratory  more 
and  more  of  those  chemically  stable  compounds  which 
we    find   in    the    living    organism.      After   Wijhler    had        35. 

Synthesis  ol 

produced     urea     artificially    in     1828,    the    number    of  «""Kanic 

•^  "^  substances. 

these  artificial  .syntheses  greatly  increased,  and  we  are 
specially  indebted  to  M.  Berthelot  for  having  shown 
how  all  the  simpler  chemical  compounds  contained  in 
the  organism  can  be  put  together  by  inorganic  processes. 
Some  of  the  more  complex  substances  have  likewise 
subsequently  yielded  to  this  synthetic  method.  "  It  is 
possible,"  we  are  told,  "  that  after  a  time  our  know- 
ledge of  chemistry  may  have  advanced  sufficiently  to 
enable  us  to  produce  albuminous  bodies  artificially  by 
synthesis."  ^  "  We  are  already  able  artificially  to  build 
up,  atom  for  atom,  out  of  their  elements  a  series  of 
organic  compounds,  some  of  a  very  complicated  char- 
acter. We  no  longer  doubt  that  all  the  rest,  even 
the  most  complex,  will  be  thus  produced ;  it  is  only 
a   question    of   time." "       Jjut    the    ways    in    which    the 

'  See  0.  Hertwig,  'The  Cell,'  p.       Chemistry,'  trausl.  by  Wociki ridge, 
16.  p.  313. 


2 


See   G.    Bunge,    '  Physiological 


426 


SCIENTIFIC    THOUGHT. 


chemist  puts  together  these  substances  in  the  laboratory 
are  rarely  the  methods  adopted  by  nature  in  the 
living  organism,  and  in  many  cases  the  product  itself, 
though  apparently  the  same,  is  yet  essentially  different.^ 


^  This  touches  on  a  very  im- 
portant point,  which  is  much 
emphasised  in  all  the  best  modern 
treatises  on  the  subject.  Claude 
Bernard  in  all  his  writings  insisted 
on  the  fundamental  difference  be- 
tween the  processes  going  on  in  the 
organism  and  those  that  go  on  in 
the  laboratory  of  the  organic  chem- 
ist, though  the  two  produce  fre- 
quently the  same  apparent  result. 
"  Si  les  forces  que  I'ctre  vivaut  met 
en  jeu  dans  ses  manifestations  vitales 
ne  lui  appartiennent  pas  et  rentrent 
toutes  dans  les  lois  de  la  physico- 
chimie  generale,  les  instruments  et 
les  procedes  h  I'aide  desquels  il  les 
fait  apparaitre  lui  sont  certainement 
speciaux.  En  effet,  I'organisme 
manifeste  ses  phenomcnes  pliysico- 
chimiques  ou  mecaniques  a  I'aide 
des  elements  histologiques  cellu- 
laires,  epitheliaux,  musculaires,  ner- 
veux,  &c.  II  emploie  done  de  pro- 
c(5des,  c"est-k-dire  des  outils  organ- 
iques  qui  n'appartiennent  qu'a  lui. 
C'est  pourquoi  le  cliimiste,  qui  peut 
refaire,  dans  son  laboratoire,  les 
produits  de  la  nature  vivante,  ue 
saurait  jamais  imiter  ses  procedes, 
parce  qui  il  ne  peut  pas  creer  les  in- 
struments organiques  elementaires 
qui  les  executent.  Cela  revient  a 
dire  que  tons  les  appareils  des  etres 
organises  out  une  morphologie  qui 
leur  est  pro  pre "  ('Rapport,'  &c., 
1867,  p.  135).  Quite  recently 
Bunge  [loc.  cit.,  p.  313)  has  said, 
"  All  our  artificial  sj'ntheses  can 
only  be  achieved  by  the  application 
of  forces  and  agents  which  can  never 
play  a  part  in  vital  processes,  such 
as  extreme  pressure,  high  tempera- 
ture, concentrated  mineral  acids, 
free  chlorine  —  factors  which  are 
immediately    fatal    to    the    living 


cell.  ...  It  follows  that  the  animal 
body  has  command  of  ways  and 
means  of  a  totally  different  char- 
acter, by  which  the  same  object  is 
gained."  A  very  interesting  specu- 
lation, referring  specially  to  this 
point,  was  put  forward  by  the 
eminent  physiologist,  Prof.  E. 
Pfliiger  of  Bonn,  in  the  year  1875. 
It  is  fully  discussed  in  Verworn's 
frequently  quoted  work  on  General 
Physiology  (pp.  304,  311,  482). 
The  theory  is  based  upon  the  le- 
markable  part  which  the  compound 
radicle  cyanogen  seems  to  play  in 
the  organism.  Pfliiger  starts  from 
the  fundamental  characteristics  of 
the  substance  called  proteid,  with 
which  life  is  inseparably  con- 
nected. Proteid  is  known  to  exist 
in  a  stable  form  in  food-stuffs,  for 
instance  in  egg  albumen.  But  this 
is  not  the  same  as  the  proteid  con- 
tained in  living  matter.  In  the 
latter  it  is  not  stable,  but  is  being 
continually  decomposed.  The  de- 
composition was  found  to  be  due 
to  the  ox  J' gen  that  occurs  in  the 
living  proteid  molecule.  This  oxy- 
gen, which  is  intramolecular,  being 
continually  received  from  outside 
by  respiration,  transforms  the  more 
stable  molecule  into  an  unstable 
labile  molecule.  In  further  follow- 
ing the  clue  afforded  by  this  pro- 
perty, and  comparing  the  decom- 
position products  of  living  proteid 
with  those  obtained  by  artificial 
oxidation  of  dead  proteid,  Pfliiger 
is  led  to  the  conclusion  that  the 
presence  of  the  radicle  cyanogen  in 
the  living  proteid  will  explain  the 
difference.  "  In  the  formation  of 
cell-substance — i.e.,  of  living  proteid 
— out  of  food  proteid,  a  change  of 
the  latter  takes  place,  the  atoms  of 


ON    THE    VITALISTIC    VIEW    OF    XATCRK 


427 


AnoLliL'i-  way  of  iii([uii}'  is  b<  ;autl}'.^e  the  existing 
organic  tissues  still  further  by  microscopic  and  chemical 
methods,  in  order  to  tiud  out  how  they  are  built  up. 
As  the  result  of  such  inquiries  we  have  a  framework 
theory  of  protoplasm,  a  foam  theory,  a  filament  theory, 
a  granular  theory ;  antl  the  attempt  has  been  made  to 
define  liviiit;-  protoplasm  as  a  colony  of  still  smaller 
structural  units  termed  "  bioblasts."  By  this  twofold 
method — by  synthesis  and  by  analysis — the  biologist  may 
attempt  to  approach  the  physiological  unit,  the  seat  and 
stronghold  of  the  vital  process.^ 


nitrogen  entering  into  a  cyanogen- 
like relation  with  the  atoms  of 
carbon,  probaljly  with  the  absorp- 
tion of  considerable  lieat."  Cj'ano- 
gen  being  a  radicle  possessing  a 
great  quantity  of  internal  enei'gy, 
the  addition  of  it  to  the  living 
molecule  "  introduces  into  the  living 
matter  energetic  internal  motion." 
The  interest  which  attaches  to  the 
theory  lies  in  this,  that  it  allows  us 
to  form  some  conception  how  living 
matter  originated.  This  problem  is 
identified  with  the  problem.  How 
does  cyanogen  arise  ?  This  we 
know  is  formed  at  an  incandescent 
heat.  •'  Accordingly,  nothing  is 
clearer  than  the  possibility  of  the 
formation  of  cyanogen  compounds 
when  the  earth  was  wholly  or  par- 
tially in  a  tiery  or  heated  state.  .  .  . 
If,  now,  we  consider  the  inuneasur- 
ably  long  time  during  which  the 
cooling  of  the  earth's  surface 
dragged  slowly  along,  cyanogen, 
and  the  conijjounds  that  contain 
cyanogen  and  hydrocarbon  sub- 
stances, hail  time  and  o])portun- 
ity  to  indulge  extensively  tlieir 
great  tendency  towards  transfor- 
mation, .  .  .  and  to  pa.ss  over,  with 
the  aid  of  oxygen,  and  later  of 
water  aiid  salts,  into  that  self- 
destructive  proteid,  living   matter. 


.  .  .  The  first  proteid  to  arise  was 
living  matter,  endowed  in  all  its 
radicles  with  the  property  of 
vigorously  attracting  similar  con- 
stituents, adding  them  chemically 
to  its  molecule,  and  thus  growing 
ad  infinitum."  This  theory  is  in- 
teresting, as  it  is,  so  far  as  I  know, 
the  only  attempt  to  reconcile  the 
existence  of  living  matter  with  the 
fact  of  the  high  temperature  which 
once  existed  on  the  earth. 

1  A  description  of  these  several 
theories  on  the  structure  of  proto- 
plasm, among  which  the  mici'llar 
theory  of  Nageli,  the  foam  theory 
of  Biitschli,  and  the  *'  bioblasts " 
of  Altmann,  have  been  elaborately 
developed,  will  be  found  in  Prof. 
0.  Hertwig's  work  on  '  The  Cell ' 
(Engl,  transl.,  p.  19,  &c.),  as  also 
in  ^I.  Yves  Delage's  great  work, 
'L'Horcditc'  (pp.  299-310).  Ver- 
worn  (foe.  cit.,  \<.  87)  draws  special 
attention  to  the  "alveolar"  or 
' '  foam  "  theoiy,  which,  built  upon 
investigations  of  Prof.  (,>uincke, 
has  "comj)letely  claritied  our  ideas 
u[)on  the  real  nature  of  the  proto- 
plasmic structures  so  much  ob- 
serveil.  .  .  .  As  a  result  of  these 
recent  investigations  the  following 
picture  can  be  formed  of  the  tiner 
morphological    structure    of    proto- 


428 


SCIENTIFIC    THOUGHT. 


36. 
The 

"  physical ' 
method. 


There  is,  however,  a  second  way  open  to  the  student 
of  the  phenomena  of  hfe,  and  this  may  be  termed 
the  "  physical  method,"  as  opposed  to  the  "  structural." 
Thus  chemists  and  physicists  first  establish  the  general 
laws  of  motion  and  change  in  dynamics  and  energetics, 
and  subsequently  apply  them  to  special  problems,  such 
as  those  of  physical  astronomy  or  the  chemistry  of 
electrolysis  and  solution.  Similarly  the  physiologist 
may  study  the  processes  common  to  all  living  matter, 
and  look  upon  the  action  of  a  definite  cell,  tissue,  or 
organ  merely  as  an  application  of  these  general  processes. 
From  this  point  of  view  structural  biology,  like  struc- 
tural chemistry,  only  furnishes  illustrations,  not  an  ex- 
planation, of  the  vital  processes :  the  special  structure 
or  organ  is  a  result  of  the  process  or  function — 
not  its  cause.  As  Prof.  Michael  Foster  says,  "  We  may 
throw  overboard  altogether  all  conceptions  of  life  as 
the  outcome  of  organisation,  as  the  mechanical  result 
of  structural  conditions,  and  attempt  to  put  physi- 
ology on  the  same  footing  as  physics  and  chemistry, 
and  regard  all  vital  phenomena  as  the  complex  pro- 
ducts of  certain  fundamental  properties  exliibited  by 
matter,  which,  either  from  its  intrinsic  nature  or  from 


plasm.  Protoplasm  consists  of  a 
ground  mass  in  many  cases  com- 
pletely homogeneous,  in  most  cases 
very  finely  foam-like  or  honej'comb- 
like,  in  which  lies  embedded  a 
greater  or  less  quantity  of  very 
various  solid  elements  or  granules. 
In  the  foam -like  protoplasm  the 
granules  always  lie  at  the  corners 
and  angles  where  the  foam-vacuoles 
come  together,  never  in  the  liquid 
of  the  bubbles  themselves."  Some 
physiologists    think    that    none    of 


the  descriptions  of  protoplasmic 
architecture  help  us  much,  and 
"  hold  to  the  fundamental  principle 
that  living  matter  acts  by  virtue  of 
its  structure,  provided  the  term 
structure  be  used  in  a  sense  which 
carries  it  beyond  the  limits  of  ana- 
tomical investigation — i.e.,  beyond 
the  knowledge  which  can  be  at- 
tained either  by  the  scalpel  or  the 
microscope "  (Burdon  Sanderson, 
'Address,'  Brit.  Assoc,  1889,  p. 
607). 


ON    THE    VITALISTIC    VIEW    OF    NATURE. 


429 


37. 
Properties 


its  existing  in  peculiar  conditions,  is  known  as  living 
matter."  ^ 

Thus,  instead  of  trying  to  penetrate  to  the   physio- 

'  J       o  1  L     J  Properties 

logical   units  and   construct  them  through  a  process  of  oftheiiving 

o  o  i  iiUDstance. 

imagination,  this  latter  class  of  biological  thinkers  con- 
fine themselves  to  the  task  of  describing  in  the  simplest 
manner  and  as  completely  as  possible  the  various  proper- 
ties of   the   livincr  substance — i.e.,  its   functions."     And 


1  'Ency.  Brit.,'  article  "  Phy.si- 
ology,"  vol.  xix.  p.  12.  See  also  an 
address  delivered  by  Prof.  Burdon 
Sanderson  at  the  meeting  of  the  Brit. 
Assoc,  at  Newcastle  in  1889  ('Re- 
port,' p.  604)  :  "  During  the  last  ten 
or  fifteen  years  histology  has  carried 
her  methods  of  research  to  such  a 
degree  of  jierfection  that  further 
improvement  scarcely  seems  pos- 
sible. As  compared  with  these 
subtle  refinements,  the  '  minute 
anatomy  '  of  thirty  years  ago  seems 
coarse — the  skill  for  which  we  once 
took  credit  seems  but  clumsiness. 
Notwithstanding,  the  problems  of 
the  future  from  their  very  nature 
lie  as  completely  out  of  reach  of  the 
one  as  the  other.  It  is  by  different 
methods  of  investigation  that  our 
better -equipjied  successors  must 
gain  insight  of  those  vital  processes 
of  which  even  the  ultimate  results 
of  microscoi)ical  analj'sis  will  ever 
be  as  they  are  now,  only  the  out- 
ward and  visible  signs"  (p.  608). 

^  As  Prof.  Iiurdon  Sanderson  puts 
it  in  his  '  Address,'  it  is  a  reversion 
to  a  position  which  is  not  new  in 
the  history  of  physiology.  "  The 
departure  from  the  traditions  of 
our  science  which  this  change  of 
direction  seems  to  imi>Iy  is  indeed 
more  apparent  than  real.  In  tracing 
the  history  of  some  of  the  greatest 
advances,  we  find  that  the  recogni- 
tion of  function  has  preceded  the 
knowledge  of  structure.  Haller'.s 
discovery  of  irritability  was  known 


and  bore  fruit  long  before  anything 
was  known  of  the  structure  of 
muscle  "  (p.  607).  "  .  .  .In  nmch 
more  recent  times  the  investigation 
of  the  function  of  gland-cells,  which 
has  been  carried  on  with  such  re- 
markable results  by  Prof.  Heiden- 
hain  in  Germany,  and  with  equal 
success  by  Mr  Langley  in  this 
country,  has  led  to  the  discovery 
of  the  structural  changes  which 
they  undergo  in  passing  from  the 
state  of  repose  to  that  of  activit}'  ; 
nor  could  I  mention  a  better  ex- 
ample than  that  afforded  by  Dr 
Gaskell's  recent  and  very  important 
discover}-  of  the  anatomical  difier- 
ence  between  cerebro-spinal  nerves 
of  different  functions"  (ibid.)  What 
has  to  a  great  extent  worked  this  im- 
portant change  in  the  methods  and 
reasoning  in  ])hysiology  is  the  re- 
cognition of  "plurality  of  function 
with  unity  of  structure,"  a  princijile 
urged  strongly  bj-  the  experimental 
school  of  medicine,  with  Claude 
Bernard  as  its  greatest  representa- 
tive. Notably  this  was  tlie  effect  of 
his  "demonstration  that  the  liver 
had  other  things  to  do  in  the  animal 
economy  besides  secreting  bile. 
This,  at  one  blow,  destroyed  the 
then  dominant  conception  that  the 
animal  body  was  to  be  regarded  as 
a  bundle  of  organs,  each  with  its 
approjtriate  function — a  concejition 
which  did  much  to  narrow  inquiry, 
since  when  a  suitable  function  had 
once    been    assigned   to   au   organ 


430  SCIENTIFIC    THOUGHT. 

38        here  we  meet  first  of  all  with  the  great  fact  that  a  living 
ment.  thing  cannot  be  conceived  to  exist  alone :  it  is  dependent 

upon  its  environment,  and  upon  other  living  things  of 
similar,  never  quite  identical,  and  mostly  very  different 
nature.  As  a  consequence  of  the  conception  which 
guided  Lamarck  in  contemplating  the  living  world— 
especially  the  crowd  of  living  things  which  before 
him  had  remained  unobserved  —  the  influence  of  en- 
vironment plays  a  greater  and  greater  part  in  the 
study  of  every  form  of  life.  The  further  funda- 
mental property  of  all  living  matter — that  it  absorbs 
through  intussusception  other  matter  which  surrounds 
it,  that  it  grows  and  multiplies  by  division,  casting 
oh'  some  portions  of  its  own  substance  as  useful 
secretions  or  cumbrous  and  useless  excretions — has  the 
twofold  result  that  every  living  thing  modifies  its  own 
surroundings  and  that  it  creates  a  society  of  its  like  which, 
through  an  automatic  process  of  crowding-out,  exercises 
a  kind  of  selection  among  its  members,  they  being  forced 
to  accommodate  themselves  to  circumstances  and  to  each 
other.  ^    The  process  suggested  by  Darwin  as  the  rationale 

there  seemed  no  need  for  further  in-  of  the  experimental  as  distinguished 

vestigation.    Physiologj",  expounded  I    fromtheanatomical  method, namely, 

as  it  often  was  at  that  time  in  tlie  \    that    it   deals    with    the    organism 

light  of  such  a  conception,  was  apt  i    whilst  it  is  alive,  see  the  conclud- 

to  leave  in  the  mind  of  the  hearer  '    ing    remarks    in    Sir    M.    Foster's 


the  view  that  what  remained  to  be 
done  consisted  chiefly  in  determin 
ing  the  use  of  organs  such  as  the 
spleen,  to  which  as  j-et  uo  definite 


article  on  "  General  Physiology  "  in 
the  '  Ency.  Brit.,'  vol.  xix. 

^  The  relations  of   living  things 
to  each  other  and  to  their  environ- 


function   had   been  allotted.      The    |    ment  admit  of  being  contemplated 


discovery  of  the  glycogenic  function 
of  the  liver  struck  a  heavy  blow  at 
the  whole  theory  of  functions." 
(Sir  M.  Foster  in  '  Claude  Bernard,' 
p.  90.)     On  the  necessary  condition 


in  two  waj's,  which  may  be  best 
distinguished  by  a  reference  to 
human  society,  exhibiting  as  it  does 
the  two  phenomena  of  co-oi^eration 
and   of    competition.      The  former 


ON    THE    VITALISTIC    VIEW    UF    NATURE.         4ol 

of  variation  and  development  is  more  and  more  coming 
to  Le  recognised  as  an  inevitable  property  of  all  growing 

and  iiiultiplyinu;  living  things.  So  far  as  Uie  intluence  on 
the  envinninient,  the  medium  in  which  it  lives,  is  con- 
cerned, we  owe  to  the  great  French  biologist,  Claude 
Bernard,  the  helpful  conception  of  the  inner  medium,^  as 


is  based  upon  haniiony,  tlie  latter 
upon  conflict.  Tiie  former  aspect 
i.s  more  particularly  eiuphasi.sed  by 
the  French  school  of  Lamarck,  de 
Blaiiiville,  and  Claude  Bernard  ; 
the  latter  more  by  tlie  English 
.school  of  Malthus  and  Darwin  ; 
each  starting  ai)parentlj'  without 
any  reference  to  the  other.  Claude 
Bernard  in  particular  says  ('  Phuno- 
uione-s  de  la  vie,'  vol.  i.  p.  67) :  "  Pour 
nous  la  vie  resulte  d'un  conflit, 
d'une  relation  etroite  et  harmon- 
ique  entre  les  conditions  extcrieures 
et  la  constitution  pre-etablie  de 
I'organisme.  Ce  n'est  point  par 
une  lutte  contre  les  conditions 
cosmiques  que  I'organisme  se  dd- 
veloppe  et  se  maintient ;  c'est, 
tout  au  contraire,  par  une  adapta- 
tion, uu  accord  avec  celles-ci.  .  .  . 
L'otre  vivant  ne  constitue  pas  une 
exception  a  la  grande  harmonic 
naturelle  qui  fait  que  les  choses 
s'adaptent  les  unes  aux  autres  ;  il 
ne  rompt  aucuu  accord  ;  il  n'est  en 
contradiction  ni  en  lutte  avec  les 
forces  cosmiques  generales ;  bien 
loin  de  l:i,  il  fait  partie  du  concert 
universel  des  choses,  et  la  vie  de 
I'aninial,  par  exemple,  n'est  qu'un 
fragment  de  la  vie  totale  de  I'uni- 
vers." 

^  Although  the  biology  of  Claude 
Bernard  does  not  contain  the 
principle  of  descent  and  evolution 
which  so  powerfully  iniluenced  the 
contemporary  writings  of  Englisji 
and  German  naturalists,  one  is 
uevertheles.s  reminded  of  the  ideas 
of  Lamarck  in   reading  the  second 


of  his  lectures  on  the  '  Phenomena 
of  Life'  (vol.  i.  pp.  65-124). 
Lamarck  had  expressed  the  idea 
that  in  the  graduated  scale  of 
living  things  we  recognise  an  in- 
creasing inile]iendence  with  regard 
to  the  external  environment.  (See 
supra,  chap.  vii.  p.  315.)  Claude 
Bernard  says  (p.  67)  :  "  Le  mode 
des  relations  entre  I'ctre  vivant  et 
les  conditions  cosmiques  ambiantes 
nous  i)ermet  de  cunsidcier  trois 
formes  de  la  vie,  suivant  qu'elle  est 
dans  une  dependance  tout  ii  fait 
dtroite  des  conditimis  extcrieures, 
dans  une  dependance  moindre,  ou 
dans  une  indepeudance  relative.  Ces 
trois  formes  de  la  vie  sont  :  1°,  La 
vie  lattnte ;  vie  non  manifestce. 
2°,  La  vie  osrillitntc /  vie  a  manifes- 
tations vai'iables  et  dcpendantes  du 
milieu  extdrieur.  3°,  La  vie  coit- 
stantc ;  vie  K  manifestations  libres 
et  inddpendantes  du  milieu  ex- 
tdrieur."  Examples  of  the  "  vie 
latente "  are  to  be  found  in  the 
vegetable  and  animal  creation  alike. 
Grains  of  seed,  desiccated  animals, 
germs,  eggs,  fei-ment.s,  yeast,  &c., 
are  examples.  All  vegetables  Vjelong 
to  the  class  of  the  vie  oscillante,  also 
among  animals  all  inveitebrates, 
and  among  the  vertebiates  those 
with  cold  blood.  These  depend  on 
cosmic  conditions,  the  cold  of 
winter,  and  tlie  reviving  heat  of 
summer,  &c.  The  higher  animals 
with  warm  blood  whose  tempera- 
ture is  constant  are  not  in  the 
same  way  subject  to  the  influence 
of   the    external    medium.      They 


432 


SCIENTIFIC    THOUGHT. 


39. 
The 

"  internal 
medium." 


it  were  the  inner  atmosphere  which  any  large  assembly 
of  living  units  must  necessarily  create  for  itself.  All 
larger  organisms  are  complex  societies  of  living  units 
which  depend  not  only  on  the  external  but  also  on  the 
internal  medium  which  bathes  them.  It  was  one  of 
Claude  Bernard's  happiest  generalisations  to  look  upon 
the  blood,  not  as  a  living  tissue  but  as  a  means  of  com- 
munication of  the  living  tissues  of  the  organism,  as  an 
internal  medium  which  bears  the  same  relation  to  the 
constituent  tissues  that  the  external  medium,  the 
atmosphere,  does  to  the  whole  body. 

One  of  the  principal  functions  of  this  artificial  medium 
or  atmosphere  which  the  larger  organisms  possess,  create 
and  maintain  for  themselves  during  their  life,  is  to 
enable  a  particular  elementary  substance  to  get  access 
to  every  living  cell  or  tissue  of  the  organism.  This 
substance  is  oxygen,  without  which  the  continuance 
of  life  in  the  higher  organisms  seems  impossible. 
That  life  is   a   process   of   combustion   is  accordingly  a 


possess  "  un  milieu  intericur  per- 
fectionue  "  (p.  104).  But  they 
begin  their  existence  as  beings 
with  an  oscillating  life  when  they 
are  in  the  form  of  eggs.  Of  the  vie 
constante  ou  lihre  Claude  Bernard 
says  :  "  Je  crois  avoir  le  premier 
insiste  sur  cette  idee  qu'il  y  a  pour 
I'animal  reellement  deux  milieuxj; 
un  milieu  exterieiir  dans  lequel  est 
place  I'organisme,  et  un  milieu 
intcrieur  dans  lequel  vivent  les 
Elements  des  tissus.  L'existence 
de  I'etre  se  passe,  non  pas  dans  le 
milieu  exterieur,  air  atmospherique 
pour  I'etre  aerien,  eau  douce  ou 
sal^e  pour  le.s  animaux  aquatiques, 
mais  dans  le  milieu  liquidc  in- 
tcrieur    forme      par      le      liquide 


organique  circulant  qui  entoure  et 
baigne  tou.s  les  elements  auatom- 
iques  des  tissus  ;  c'est  la  lymphe 
ou  le  plasma,  la  partie  liquide  du 
sang  qui  chez  les  animaux  superieurs, 
penetre  les  tissus  et  constitue 
I'ensemble  de  tous  les  liquides  in- 
terstitials,  expression  de  toutes  les 
nutritions  locales,  source  et  con- 
fluent de  tous  les  echanges  ele- 
mentaires.  Un  organisme  complexe 
doit  etre  consider^  comme  une 
rdunion  d'etrcs  simples  qui  sont 
les  elements  anatomiques  et  qui 
vivent  dans  le  milieu  liquide  in- 
terieur.  La  fixitd  du  milieu  in- 
terieur  est  la  condition  de  la  vie 
libre  indepcndante "  (p.  113). 


ON    THE    VITALI8T1C    VIEW    UF    NATLKE.        433 

definition  which  has  been  put  forth  in  vari(ni.s  ways 
ever  since  Lavoisier's  time,  when  he  and  Laplace  tried 
to  explain  the  existence  of  animal  heat  in  this  manner. 
The  progress  of  science  in  the  course  of  the  century 
wliich  followed  Lavoisier  has  more  and  more  confirmed 
the  importance  of  the  role  which  oxygen  plays,  Init  lias 
also  shown  how  very  complex  are  the  products  of 
oxygenation  in  tlie  living  organism, — how  the  living 
processes  are  indeed  chemical  processes,  but  are  quite 
different  from  those  of  the  chemical  laboratory.  As 
Claude  Bernard  says,  "  The  chemistry  of  the  laljoratory 
is  carried  on  liy  means  of  reagents  and  apparatus 
which  the  chemist  has  prepared,  and  the  cliemistry 
of  the  li\ing  being  is  carried  on  by  means  of  reagents 
and  apparatus  which  the  organism  has  prepared."  ^ 
One  of  the  great  performances  of  living  matter  is 
the  production,  another  is  the  storing  up  and  distri- 
bution, of  oxygen.  But  though  we  know  that  the 
chlorophyll  -  containing  cells  of  green  plants,  under 
the  intiuence  of  sunlight,  are  able  to  decompose  that 
very  inert  body,  carbonic  acid,  breathed  out  by  both 
animals  and  plants,  into  free  oxygen  and  carljon,  allow- 
ing the  carbon  to  be  retained  or  utilised  in  the  form 
of    more    or    less    complex    carbohydrates,    and    though 


'  See  especially  the  extensive  ex- 
planations in  the  '  Itapport  sur  les 
progros  de  la  Physiul.  gen.'  (1867, 
p.  133  »qq.):  "Les  phenomenes 
physico-chiniiciues  qui  se  passent 
dans  les  corps  vivants  sent  exacte- 
ineut  les  monies,  ([uant  a  leur  nature, 
i|uant  aux  lois  qui  les  rogissent  et 
(|uant  a  leurs  produits,  (|ue  ceux 
(jui  so  passent  dans  les  corps  bruts  ; 
ce  qui  diffijre,  ce  sunt  seulenient  les   |   vivant"  (p.  2'22) 

VOL.  II.  1>   E 


procddes  et  les  ajipareils  h,  I'aide  des- 
(juels  ils  sont  manifestos.  ...  II 
est  doja  jjrouve  qu'un  gi-and  nombre 
de  phenomenes  qui  s'accomplissent 
dans  les  corps  vivants  peuvent  etre 
reproduits  artificiellement,  en  de- 
hors de  I'organisme,  dans  le  monde 
mineral.  Mais  ee  que  Ton  ne  j)eut 
jias  rej)roduire,  ce  sont  les  procodds 
et  les  outils  spociaux  de  I'organisme 


434  SCIENTIFIC    THOUGHT. 

we  also  know  that  the  red  blood  corpuscles  in  verte- 
brate animals  convey  oxygen  in  a  concentrated  form  ^ 
through  all  the  organs,  giving  it  up  wherever  it  may 
be  wanted,  the  real  chemical  process  concerned  in  the 
action  of  chlorophyll  is  not  cleared  up ;  ^  and  "  no  one 
has  been  able  hitherto  to  explain,  by  a  reference  to 
physical  laws,  the  active  functions  of  the  heart  and 
muscular  wall,"  by  which  the  circulation  of  the  blood 
is  effected.^ 

In  the  explanation  of  many  physiological  phenomena 
no  idea  has  proved  more  fruitful  than  the  con- 
ception of  natural  selection,  introduced  by  Darwin  to 
explain  the  growing  diversity  and  the  purposeful- 
ness  of  organisms.  Coupled  with  the  cellular  theory, 
which  looks  upon  every  living  organism  as  a  society 
of  self-accommodating  individual  units  or  cells,  forced 
by  circumstances  into  differentiation  of  form  and  into 
divided  labour  or  function,  it  relieved  biologists  of  that 
spectre  of  vitalism  which  still  survived  after  Lotze 
and  Du  Bois-Eeymond  had  placed  the  creative  and 
formative  influence  outside  of  the  mechanism — as  the 
watchmaker  lives  outside  of  the  watch,  which  exhibits 
only  mechanical  contrivances.  That  which  puzzles  the 
spectator  of  the  watch,  as  it  does  the  spectator  of  every 


1  See  Buuge,  '  Physiological 
Chemistry,'    p.    275. 

-  "  Iron  play.s  an  important  part  in 
vegetable  life  :  we  know  that  chlo- 
rophyll granules  cannot  be  formed 
without  it.  If  plants  are  allowed 
to  grow  in  nutritive  solutions  free 
from  iron,  the  leaves  are  colourless, 
but  become  green  as  soon  as  an 
iron  salt  is  added  to  the  fluid  in 
which  the  roots  are  immersed.     It 


is  even  sufficient  merely  to  brush 
the  suiface  of  the  colourless  leaf 
with  a  solution  of  an  iron  salt  to 
cause  the  ajjpearance  of  the  green 
colour  in  the  part  thus  i>ainted. 
Chlorophyll  itself  contains  no  iron, 
and  we  do  not  know  in  what  way 
the  iron  is  concerned  in  its  produc- 
tion "  (Bunge,  loc.  cit.,  p.  2.5).  See 
also  Hertwig,  'The  Cell,'  p.  1.53. 
•*  Bunge,  }).  7  ;  cf.  also  p.  275. 


ON    THE    VITALISTIC    VIEW    OF    NATLKE. 


435 


ort^^anism,  is  the  apparent  design  and  purpose,  without 
which  neither  could  be  conceived  to  have  been  formed.^ 
Here,  then,  tlie  idea  that  it  was  a  process  of  natural 
choice,  of  automatic  adjustment,  which  produced  the 
apparent  end  and  purpose  at  the  niDUient  when  the 
structure  itself  was  produced,  came  as  a  great  relief.^ 
It  explained  how  it  comes  about  that  nature,  even 
with  unloaded  dice,  so  often — yet  not  always — throws 
doublets.  It  permitted  naturalists  and  physiologists 
to  use  purpose  and  final  cause,  not  as  an  explana- 
tion, but  as  an  indication  where  to  look  for  causal — 
that  is,  for  mechanical — connections.  Accordingly  the 
first  systematic  attempt  to  use  natural  selectinu  in 
the  explanation  of  the  adjustment  of  the  internal 
parts   of  an   organism,  which   is   due   to   Prof.  A\"ilhelm 


1  "The  main  problem  which  the 
organic  world  offers  for  our  solu- 
tion i.s  the  purposefulness  seen  in 
organisms.  That  species  are  from 
time  to  time  transformed  into  new 
ones  might  perhayjs  be  understood 
by  means  of  an  internal  trans- 
forming force,  but  that  they  are 
so  changed  as  to  become  better 
adapted  to  the  new  conditions 
under  wliich  they  have  to  live  is 
left  entirely  unintelligible"  (Weis- 
mann  on  Niigeli's  "  Mechanisch- 
Physiologische  Theorie  der  Ab- 
staramungslehre  "  in  '  Essays  upon 
Heredity,'  Engl,  transl. ,  p.  257). 

-  See  Du  Bois-Reymond's  Ad- 
dress, "  Darwin  versus  Galiani " 
('Reden,'  vol.  i.  p.  211,  <fec.)  : 
"  Here  is  the  knot,  here  the  great 
difficulty  that  tortures  the  intellect 
which  would  understand  the  world. 
Whoever  does  not  i)lace  all  activity 
wholesale  under  the  sway  of  E\<i- 
curean  cliance,  whoever  gives  only 
hi.>  little  finger  to  teleology,  will 
inevitably    arrive    at    Paley's    dis- 


40. 
Xatiiral 
selection 
witliin  the 
organism. 


carded  '  Natural  Theology, '  and  so 
much  the  more  necessarily,  the  more 
clearly  he  thinks  and  the  more  in- 
dependent his  judgment.  .  .  .  The 
physiologist  may  define  his  science 
as  the  doctrine  of  the  ciianges 
which  take  ]ilace  in  organisms  from 
internal  causes.  .  .  .  No  sooner  has 
he,  so  to  speak,  turned  his  back  on 
himself  than  he  discovers  himself 
talking  again  of  functions,  ])er- 
formances,  actions,  and  i)urposes 
of  the  organs.  The  i)ossibility, 
ever  so  distant,  of  banishing  from 
nature  its  seeming  purpose,  and 
putting  a  blind  necessity  everywhere 
in  the  ])lace  of  final  causes,  ajijiears 
therefore  as  one  of  the  gi-eatest 
advances  in  the  world  of  thought, 
from  which  a  new  era  will  be  dated 
in  the  treatment  of  these  problems. 
To  have  somewhat  eased  the  torture 
of  the  intellect  which  ponders  over 
the  world-problem  will,  as  long  as 
j)hiloso))hical  naturalists  exist,  be 
Charles  Darwin's  greatest  title  to 
glory"  (p.  216). 


436 


SCIENTIFIC    THOUGHT. 


Eoux  in  his  work  on  tlie  '  Struggle  of  the  Parts  in 
the  Organism,'  was  hailed  by  Darwin  as  "  the  most 
important  book  on  development  that  has  appeared 
for  some  time."  ^  In  modern  books  on  physiology  the 
process  of  selection  is  a  familiar  conception ;  but  if  in 
natural  history,  in  the  life  of  plants  and  insects,  there 
still  remain  many  extraordinary   instances   of  selection 


1  The   work    appeared    in    1880, 
and    is   referred    to  by   Darwin  in 


letter  to  Romanes  ( '  Life  and 
Letters,'  vol.  iii.  p.  244  ;  16th 
April  1881),  where  he  suggests 
also  a  similar  consideration  of 
plant  life  and  structure.  It 
has  been  republished  in  Roux's 
'  Gesammelte  Abhandlungen  zur 
Entwickelungsmechanik  der  Organ- 
ismen  '  (Leipzig,  1895,  2  vols.),  with 
an  interesting  preface  (vol.  i.  p. 
139,  &c. ),  and  many  historical  and 
critical  digressions.  It  originally 
emanated  from  the  earliest  school 
of  Darwinism  in  Germany,  repre- 
sented by  Haeckel,  Gegenbaur,  and 
Preyer,  at  Jena.  It  has  been 
found  very  suggestive,  and  has 
been  the  beginning  of  a  very 
large  controversial  literature  in 
Germany,  in  which  the  funda- 
mental problems  of  biology  have 
been  discussed,  and  have  received 
new  formulations.  The  idea  of  the 
struggle  of  individuals  for  survival, 
suggested  by  Darwin,  is  applied  by 
Roux  to  the  different  parts  and 
organs  within  the  develoi^ing  or- 
ganism. Du  Bois-Reymond  almost 
contemporaneously  published  his 
brilliant  and  celebrated  address 
on  "Exercise"  ("Ueber  die 
Uebung,"  'Reden,'vol.  ii.  p.  404). 
In  England  Roux's  suggestive  treat- 
ise does  not  seem  to  have  been 
much  noticed,  and  Prof.  Roux 
himself  attributes  this  to  the  in- 
adequate notice  of  the  book  by 
Romanes  in  '  Nature '  (vol.  xxiv. 
p.     505),    in    which    his    doctrine 


was  erroneously'  compared  with 
Spencer's  ideas  of  "direct  equi- 
libration." Prof.  J.  A.  Thomson, 
in  'The  Science  of  Life,'  refers 
to  the  importance  of  Roux's  work 
(pp.  138,  229),  and  of  his  '  Archiv 
flir  Entwickelungsmechanik. '  Roux 
has  been  classed  by  some  of 
his  critics  among  the  "  organi- 
cists,"  a  school  represented  in 
France  chiefly  by  Claude  Bernard. 
The  main  the.sis  of  this  view 
seems  to  be  that  the  phenomena 
of  life  consist  in  the  play  of  two 
factors— the  organisation  and  the 
environment  of  the  living  thing. 
Roux  applies  the  process  of  natural 
selection  and  consequent  adapta- 
tion, which  Darwin  sees  at  work 
in  a  crowd  of  living  things,  to  the 
organisation  of  the  individuals 
themselves,  each  of  which  is  a 
microcosm,  a  society  of  auton- 
omous units,  say  of  cells.  He 
has  accordingly  gone  a  step 
farther  back  than  the  older 
"  organicists,"  studying  the  de- 
velopment, the  genesis  of  the 
organism  on  Darwinian  lines.  M. 
Delage  accordingly  dates  from  him 
a  new  school  of  "  organicism." 
"  L'organicisme  commence,  h,  mon 
sens,  avec  Descartes  (1642),  se 
continue  avec  Bichat,  Claude 
Bernard,  et  arrive  avec  Roux 
(1881)  11  une  theorie  si  profonde- 
ment  modifiee,  bien  qu'elle  derive 
du  meme  principe,  qu'elle  peut 
etre  consideree  comme  toute 
moderne"  (' L'Heredite,  p.  408). 


ox    THE    VlTALIisTlC    VIEW    Ub'    NATUKF:. 


437 


for  which  no  teleological  inechanisiu  hiis  been  invented, 
still  more  are  we  baiUed  by  the  apparent  "  autonomy 
of  th(.'  living  cell,"  in  consequence  of  which  it  is,  c.ff., 
"  able  to  select  its  food,  retaining  what  is  useful  and 
rejecting  what  is  harmful."  ^  And  what  shall  we  say 
of  the  so-called  "  w^andering  cells,  which  are  actually 
sent  out  by  the  organism  in  order  to  absorb  in  the 
alimentary  canal  food-stuffs,  notably  fat,  returning  with 
it  into  the  blood,  or  to  receive  into  themselves  malig- 
nant bacteria,  making  them  innocuous  by  a  process  of 
digestion  ?  "  ^  Xo  mechanical  physico-chemical  explana- 
tion of  this  process  is  imaginable,  and  the  word 
"  selection,"  with  which  Darwin  charmed  away  so  many 
mysteries,  has  revealed  new  ones  in  their  place.^ 


'  See  the  very  interesting  and 
frequently  quoted  address  by  Prof. 
G.  E.  Kiud%iscli  (Wiirzburg,  1888), 
entitled  '  Arztliche  Philusophie,' 
p.  13. 
-  Rindfleisch,  loc.  cit.,  p.  l.'n 
■'  Inthisconnectiou  it  is  interesting 
to  refer  to  a  discussion  which  was 
raised  by  the  suggestive  address  of 
Prof.  F.  R.  Japp,  entitled,  "Stereo- 
cheuiLstry  and  Vitalism"  ('Brit. 
Assoc.  Report,'  1898,  p.  813).  It 
refers  to  the  discovery  by  Pasteur 
of  "  chirality "  in  solutions  of 
certain  crystallised  organic  salts, 
on  which  I  reported  in  vol.  i. 
p.  450.  "Pasteur  regarded  the 
formation  of  asyumietric  organic 
compounds  as  the  special  pre- 
rogative of  the  living  organism. 
Most  of  the  substances  of  which 
the  animal  and  vegetable  tissues 
are  built  up  —  the  proteids,  cell- 
ulose—  are  asynnnetric  organic 
compounds."  Now,  in  his  ex- 
periments on  fermentation  Pasteur 
found  that  "  the  asymmetric  living 
organism    selected    for    its    nutri- 


ment that  particular  asymmetric 
form "  out  of  a  mixture  of  two 
euantiomorphous  compounds  held 
in  solution  — "  which  suited  its 
needs — and  left  the  opposite  form 
either  wholly  or,  for  the  most 
I)art,  untouched"  (p.  817).  Prof. 
Japp  proceeds  to  consider  the 
opinion  then  formed  by  Pasteur, 
"  that  compounds  exhibiting  optical 
activity  have  never  been  obtained 
without  the  intervention  of  life " 
(p.  818).  This  view,  to  which 
Pasteur  adhered,  and  which  he 
defended  against  eminent  op- 
ponents, has  been  frequently 
challenged,  and  seemed  definitely 
set  a.side  by  the  explanation  of 
Piof.  Emil  Fischer  of  Berlin,  and 
by  Jungfleisch's  synthesis  of  race- 
mic  acid  and  its  resolution  into 
dextro-  and  Itcvo  -  tartaric  acids. 
.  .  .  "Consecjuently,  the  overwhelm- 
ing majority  of  chemists  hold  that 
the  foregoing  synthesis  and  separ- 
ation of  optically  active  conqiounds 
have  been  effected  without  the 
intervention  of  life,  either  directly 


438 


SCIENTIFIC    THOUGHT. 


I 


41. 

Mobility  of 

living 

matter. 


Another  property  of  all  living  matter  which  has  been 
seized  upon  to  furnish  a  definition  of  life  is  its  extreme 
mobility.  It  has  been  stated  that  the  great  difference 
between  living  and  non-living  matter  is  this — that  the 
former  is  in  a  state  of  movable  or  dynamical  equilib- 
rium, whereas  the  latter  tends  always  to  a  condition 
of  rest  or  of  statical  equilibrium.  This  was  especially 
urged  by  the  late  celebrated  Du  Bois-Eeymond  of 
Berlin,  to  whom  we  owe  the  greater  part  of  our  know- 
ledge of  the  physical  and  chemical  changes  exhibited 
in  the  active  nervous  system.  In  comparison  with 
this  property  of  a  dynamical  equilibrium,  explained  by 
the  analogy  of  a  fountain  of  water  or  a  vortex  which 
change  their  substance  whilst  maintaining  their  form, 
other  older  distinctions  which  had  been  drawn  between 
organised  and  unorganised  bodies  sank  into  insignificance.^ 


or  indirect! J'."  (p.  824).  Prof. 
Jajip  and  Prof.  Crutn  Brown  of 
Edinburgh  are  of  the  opposite 
opinion,  inasmuch  as  in  the  view 
of  the  former  "  the  action  of  hfe, 
which  has  been  excluded  during 
the  previous  stages  of  the  pro- 
cess, is  introduced  the  moment 
the  operator  begins  to  pick  out 
the  two  enantiomorphs,"  as  was 
done  by  Jungfleisch. 

^  Among  the  okler  discussions 
of  the  best  way  of  defining  life 
which  belong  to  the  second 
third  of  the  century,  we  have 
in  Germany  the  various  writings 
of  Du  Bois  -  Reymond  ('Reden,' 
notably  vol.  ii.  p.  25)  ;  in  France 
those  of  Claude  Bernard  ('  Pheno- 
menes  de  la  vie,'  notably  vol.  i.  y>. 
21,  &c.)  ;  in  England  the  'Biology' 
of  Mr  Herbert  Spencer.  The  two 
last-named  authors  examine  with 
some  care  the  definitions  of  earlier 
writers.     All  three  should  be  read 


and  re-read  by  any  one  who  desires 
to  arrive  at  a  clear  understanding  of 
the  subject.  Du  Bois-Reymond's 
definition  shows  the  preponderat- 
ing influence  of  the  ideas  which 
governed  the  Berlin  school  of 
jihysiology,  and  which  centred  in 
Helmholtz's  tract  on  the  Conserva- 
tion of  Energy.  Claude  Bernard 
defines  life  by  the  words  "  La  vie, 
c'est  la  creation."  Organisation 
and  disorganisation  are  the  two 
sides  of  this  process,  organisation 
and  environment  the  two  factors. 
The  doctrine  of  evolution  goes  a 
step  farther  back,  and  attempts  to 
analyse  "organisation."  The  pro- 
cess of  creation  is  to  Mr  Herbert 
Spencer  a  process  of  development. 
The  word  creation  in  the  older  sense 
ceases  to  have  a  meaning.  Of  more 
recent  date  are  the  discussions  of 
the  subject  in  the  very  interesting 
work  of  Carl  Hauptmann,  'Die 
Metaphysik  in  der  modernen  Physio- 


ON    THK    VITALISTIC    VIKW    OF    NATUUK.         439 


orgiuusni 


are 


It  is  true  that  not  all  parts  of  a  higher 
subject  to  this  continued  change,  but  those  that  are  not 
— such  as  the  skeleton  of  an  animal  or  the  trunk  of  a 
tree — are  automatically  deposited  l)y  the  living  organism 
for  the  purpose  of  external  or  internal  support,  protection, 
or  communication.  They  are  the  permanent  mechanism 
by  which  the  economy  and  administration  of  the  society 
of  living  units  or  cells  are  kept  up.  These  it  has  been 
possible,  in  numy  instances,  to  analyse  into  stable 
chemical   compounds,   which    have    Ijeen    reproduced    in 


logie '  (Jena,  1894,  iieue  AuH.), 
esj)ecially  the  last  chapter.  Still 
more  recent  is  tiie  very  careful 
aualy.sis  contained  in  the  new 
edition  of  Mr  Spencer's  'Biologj',' 
notably  vol.  i.  p.  Ill  sqq.  The 
final  conclusion  arrived  at  by  these 
two  latest  philosophers  has  much 
in  common.  Both  strive  after  a 
dynamic  concejjtion  of  life  ;  both 
confess  that  such  is  at  present  un- 
attainable— a  desideratum,  not  an 
achievement.  Hauptmann  says  (p. 
386)  :  "  The  most  primitive  life, 
from  which  alone  the  living  world 
on  this  earth  can  have  sprung,  can 
only  be  assumed  to  be  a  species  the 
members  of  which  varied  in  manifold 
ways  and  propagated  themselves. 
Here  we  have  to  do  already  with 
an  eminently  complex  interaction  of 
elementary  processes.  .  .  .  We  still 
absolutely  lack  every  conception  of 
such  a  dynamical  system.  .  .  . 
Likewise  the  origin  of  the  simplest 
living  substance  is  mechanically 
quite  unknown  and  uncompre- 
hended.  .  .  .  The  individual  forms 
of  life  stand  in  the  midst  of  a 
yet  unintelligible  higher  order  of 
the  material  world."  Similarly 
Mr  Spencer  [loc.  cit.,  p.  120) : 
"  We  are  ol)liged  to  confess  that 
life  in  its  essence  cannot  be  con- 
ceived in  physico-chemical  terms. 
The  required  principle  of  activity. 


which  we  found  cannot  be  repre- 
sented as  an  independent  vital 
principle,  we  now  find  cannot  be 
represented  as  a  principle  iidierent 
in  living  matter.  If,  by  assuming 
its  inherence,  we  think  the  facts 
are  accounted  for,  we  do  but  cheat 
ourselves  with  pseudo-ideas.  .  .  . 
It  needs  but  to  observe  how  even 
simple  forms  of  existence  are  in 
their  ultimate  nature  incompre- 
hensible, to  see  that  this  most 
complex  form  of  existence  is  in  a 
sense  doubly  incomprehensible.  .  .  . 
While  the  phenomena  (of  life)  are 
accessible  to  thought,  the  implied 
noumenon  is  ina(;cessil)le,  .... 
only  the  manifestations  come  within 
the  range  of  our  intelligence,  while 
that  which  is  manifested  lies  be- 
yond it"  (p.  122).  There  seems 
ample  evidence  that  under  ditler- 
ent  forms  of  words  Claude  Bernard 
and  Du  Bois-Reymond,  in  his  later 
writings,  arrived  at  similar  con- 
clusions. See  '  La  Science  Ex- 
perimentale,'  j).  210,  and  "Die 
sieben  W'eltriithsel "'  ('Reden,'  vol. 
i.  p.  381).  "The  mystery  is  the 
more  profound  the  more  it  is 
brought  into  contrast  with  the 
exact  knowledge  we  possess  of  sur- 
rounding conditions"  (Prof.  Burdon 
Sanderson,  '  Brit.  Assoc.  Report,' 
1889,  p.  614). 


440  SCIENTIFIC    THOUGHT. 

the  cliemical  laboratory  by  processes  which  were  like 
or  unlike  those  going  on  in  the  organism  itself.  But 
such  stable  compounds  are  not  the  bearers,  they  are 
merely  the  collateral  j)roclucts,  the  accompaniments,  of 
the  living  process.  The  artificial  production  of  organic 
compounds,  beginning  with  Wohler's  production  of  urea, 
and  ending  with  the  production  of  albumen,  do  not 
approach  the  problem  of  the  production  of  living  matter. 
Could  the  chemist  produce  protoplasm,  it  would  not  be 
living ;  or  were  he  fortunate  enough  to  hit  upon  one  of 
its  many  metamorphoses,  it  would  die  the  next  moment, 
not  having  the  inner  structure  or  the  external  and 
internal  environment  necessary  for  its  self-conservation 
and  activity.  Nor  do  we  seem  to  get  any  nearer  the 
real  secret  by  analysing  more  closely  the  chemical  and 
physical  changes,  the  metabolism,  the  rhythmical  processes 
which  constitute  this  activity.  We  call  it  nutrition  or 
respiration,  assimilation  and  disassimilation,  oxidation  and 
reduction — storing  up  and  letting  loose  of  energy.  We 
picture  to  ourselves  the  building  up  of  more  and  more 
complicated  chemical  molecules,  containing  thousands  of 
atoms,  in  a  temporary  and  easily  disturbed  equilibrium, 
and  the  subsequent  breaking  down  again  of  these  complex 
structures  by  gradual  decomposition  or  by  sudden  explo- 
sions due  to  external  stimuli,  or  by  the  still  more  mysteri- 
ous directive  action  of  conscious  will :  we  liken  them  to 
the  pulling  of  a  trigger,  or  the  gathering  up  and  letting 
loose  of  a  destructive  avalanche  by  the  motion  of  a  flake  of 
snow  on  the  top  of  a  peak.  We  see  how  this  metabolism, 
this  "  Stoff-  und  Kraft-wechsel,"  goes  on  in  the  smallest 
amoeba  in   rhythmical   movements,  and   how,  in   higher 


Ox\    THE    VITALISTIC    VIEW    UF    NATURE. 


441 


organisms,  it  is  divided  into  many  stages,  allocated  to 
special  cells  or  to  (juite  distinct  classes  of  beings,  some 
of  which,  like  plants,  take  upon  tliemselves  the  first 
important  steps  of  the  anabolism,  so  that  others — the 
animals — may  carry  it  a  stage  higher,  preparing  a  dis- 
charge, or  catabolism,  which  becomes  more  and  more 
effective,  till  it  reaches  the  unique  nervous  function 
which  accompanies  the  highest  phenomenon  of  animal 
activity — the  mental  process.  Claude  Piernard  ^  has 
put  into  classical  words  the  rationale  of  this  i)rocess. 
"  If,  in  the  language  of  a  mechanic,  the  vital  phenomena 
— namely,  the  construction  and  destruction  of  organic 
substance — may  be  compared  to  the  rise  and  fall  of  a 
weight,  then  we  may  say  that  the  rise  and  fall  are 
accomplished  in  all  cells,  both  plant  and  animal,  but 
with  this  difference,  that  the  animal  element  finds  its 
weight "'  already  raised  up  to  a  certain  level,  and  that 
hence  it  has  to  be  raised  less  than  it  subsequently  falls. 


'  '  Ph(5noniene.s  de  la  vie,'  &c. , 
vol.  ii.  p.  513.  It  is  oue  of  Claude 
Bernard's  greatest  merits  to  have 
corrected  the  earlier  formula  in 
which  the  circulation  of  matter  had 
been  expressed.  Dumas  and  Bous- 
singault  had  said  :  '"  L'oxygene  en- 
leve  par  ies  auimaux  est  restitue 
par  Ies  vegotaux.  Les  premiers 
consomment  de  I'oxj'geue  ;  les 
seconds  produisent  de  l'oxygene. 
Les  premiers  brulent  du  carbone  ; 
les  seconds  produisent  du  carbone. 
Les  premiers  exhalent  de  I'acide 
carbonique  ;  les  seconds  fixent  de 
I'acide  carbonique."  On  this  pass- 
age Claude  Bernard  has  the  fol- 
lowing comment :  "  Cette  loi  qui 
sous  la  forme  j)rdcddente  ex  prime 
avec  v(5rit<5  le  mucanisme  d'une  des 
])lus  gnmdcs  harmonies  do  la  nature 
est  une  loi  cosmique  et  noii  une  loi 


physiologique.  Ajjplicjuc'e  ea  ph^'- 
siologie,  elle  n'explique  pas  les 
phdnomtnes  individuels :  elle  ex- 
prime  comment  I'ensemble  des 
animaux  et  I'ensemble  des  plantes 
se  comportent  en  definitive  par 
rapport  au  milieu  ambiant.  La  loi 
ctablit  la  balance  autre  la  sonnue 
de  tons  les  phenoniencs  de  la  vie 
animale  et  de  la  vie  vegetale  :  elle 
n'est  point  I'expression  de  ce  qui 
se  passe  en  p.articulier  dans  un 
animal  ou  une  plantc  donni's "  (p. 
512).  This  false  direction,  wiiich 
had  been  introduced  into  physio- 
logy a  generation  earlier,  Claude 
Bernard  corrected  by  the  view  that 
the  circulation  of  matter  takes 
place  not  only  between  the  two 
kingdoms  of  nature  but  in  every 
elementai-y  organism. 
'-  Or  its  potential. 


442 


SCIENTIFIC    THOUGHT. 


42. 
Anabolism 
and  Cata- 
bolisra. 


The  reverse  occurs  in  the  green  plant  cells.  In  a  word, 
of  the  two  movements,  that  of  descent  is  preponderant 
in  the  animal,  that  of  ascent  in  the  vegetable."  No  one 
has  done  greater  service  to  the  fixing  of  our  ideas  on 
this  subject  than  Dr  Gaskell  when  he  analysed  the 
whole  process,  called  "  Metabolism  "  by  Professor  Michael 
Foster  after  Schwann,  into  the  two  complementary  pro- 
cesses of  Anabolism  the  upward,  and  Catabolism  the 
downward,  movement  —  the  winding  up  and  running 
down  of  the  clock,  the  preparation  and  loading  of  the 
explosive  and  the  discharge  of  the  gun.-^ 


^  The  introduction  of  these  terms 
is,  however,  connected  with  a. 
special  view  —  differing  somewhat 
from  that  suggested  by  the  f(3rmula 
of  Claude  Bernard — which  is  now 
verj'  generally  adopted  in  text- 
books of  physiology.  Prof.  Burdon 
Sanderson  has  given  a  lucid  state- 
ment of  this  difference  in  his 
Address,  entitled  "  Elementary 
Problems  of  Physiology,"  before 
the  Brit.  Assoc,  in  1889  ('Report,' 
p.  613).  He  there  says:  "A  char- 
acteristic of  living  process  ...  is 
that  it  is  a  constantly  recurring 
alternation  of  opposite  and  comple- 
mentary states,  that  of  activity  or 
discharge,  that  of  rest  or  restitu- 
tion. Is  it  so  or  is  it  not  ?  In  the 
minds  of  most  physiologists  the 
distinction  between  the  phenomena 
of  discharge  and  the  phenomena 
of  restitution  (Erkolung)  is  funda- 
mental, but  beyond  this  unanimity 
ceases.  Two  distinguished  men — 
Prof.  Hering  and  Dr  Gaskell — 
have  taken,  upon  independent 
grounds,  a  different  view  to  the 
one  above  suggested,  according  to 
which  life  consists  not  of  alterna- 
tions between  rest  and  activity, 
charge  and  discharge,  loading  and 
exploding,  but  between  two  kinds 
of  activity,  two  kinds  of  explosion, 


which  differ  only  in  the  direction 
in  which  they  act,  in  tlie  circum- 
stance that  they  are  antagonistic  to 
each  other.  Now,  when  we  com- 
jjare  the  two  processes  of  rest  .  .  . 
and  discharge  .  .  .  with  each  other, 
they  may  further  be  distinguished 
in  this  respect,  that  whereas  resti- 
tution is  autonomic,  the  other  .is 
occasional — i.e.,  takes  place  onlj'  at 
the  suggestion  of  external  influ- 
ences. .  .  .  It  is  in  accordance  with 
the  analogy  between  the  alternation 
of  waking  and  sleeping  of  the  whole 
organism,  and  the  corresponding 
alternation  of  restitution  and  dis- 
charge, of  every  kind  of  living 
substance,  that  physiologists  by 
common  consent  use  the  word 
stimulus  [Reiz),  meaning  thereby 
nothing  more  than  that  it  is  by 
external  disturbing  or  interfering 
influence  of  some  kind  that  energies 
stored  in  living  material  are  dis- 
charged. Now,  if  I  were  to  main- 
tain that  restitution  is  not  auto- 
nomic, but  determined,  as  waking  is, 
by  an  external  stimulus,  that  it 
differed  from  waking  only  in  the 
direction  in  which  the  stimulus 
acts — i.e.,  in  the  tendency  towards 
construction  on  the  one  hand, 
towards  destruction  on  the  other — 
I    should  fairly  and    as    clearly   as- 


ON    THE    VITALISTIC    VIEW    OF    NATLllE.         443 

The  modern  theories  of  the  cell,  of  metabolism,  and 
selection,  have  also  greatly  influenced  and  modified  our 
conceptions  concerning  the  last  itnd  nmsl  imiHirlaiil  pro- 
perty of  all  living  matter — viz.,  that  it  is  self-reproductive. 
Older  text -books  on  i)liysiology  treated  of  the  great  -is- 
problem  of  generation — i.e.,  the  origin  of  a  new  individual  ^''"'- 
— as  a  phenomenon  of  organised  life  which  stood  quite 
isolated ;  and  although  the  sexual  difference  in  plants 
and  animals  had  early  led  to  certain  analogies,  to  similar 
terminology,  and  to  vague  inferences,  the  mysterious 
phenomena  of  generation,  and  especially  of  sexual  genera- 
tion, were  not  brought  into  line  with  the  general  pro- 
perties of  all  living  matter  till  about  fifty  jjears  ago. 
Even  Johannes  Miiller  in  his  great  text  -  book  on 
Physiology,  which  takes  a  much  wider  view  of  the  sub- 
ject than  any  work  before  it,  treats  of  the  reproduction 
of  tissues  and  of  generation  in  (juite  separate,  seem- 
ingly disconnected,  parts  of  his  work.  Into  this  un- 
certainty only  little  light  was  thrown  l)y  the  original 
prcjpounders  of  the  Cellular  theory,  who,  misled  by  the 
supposed  analogy  of  cells  and  crystals,  imagined  that 
cells  originated  out  of  the  surrounding  cell  sap,  as 
crystals  solidify  out  of  the  solution  or  mother  liquor. 
Correcter  views  were  gradually  elaborated  by  botanists. 
Mohl  emphasised  the  important  part  which  protoplasm 
plays  in  the  formation  of  cells.  Niigeli  established  the 
process  of  intussusception  as  against  external  accretion ; 
anatomists  like  Max  Schulze  and  Briicke  joined  hands, 


pos.sible  express  the  doctrine  wliicli 
Dr  Gaskell  and  Prof.  Hering  have 
embodied  in  word.s  which  have  now 
become  fainiliar  to  every  student. 
The  words  in  question — '  anabolism,' 


whiclr,  being  interpreted,  means 
winding-up,  and  'catabolism,'  run- 
ning down — are  the  creation  of  Dr 
Gaskell." 


444 


SCIENTIFIC    THOUGHT. 


44. 

Tlie  proto- 

lilasiiiic 

theory. 


and  the  year  1863  is  usually  given  as  that  in  which 
the  protoplasmic  theory  was  established.  According  to 
this  view  protoplasm  is  the  element  or  unit  of  all  living 
substance  :  it  grows  through  assimilation  (intussusception 
and  excretion),  and  multiplies  {i.e.,  gives  rise  to  other 
living  units)  by  subsequent  division.  This  process  was 
found  to  be  fundamental  :  it  describes  the  growth  of 
the  simplest  and  the  most  complicated  organisms  as 
beginning  alike  with  a  unit  cell,  which  may  or  may 
not  grow  by  division ;  it  is  the  formula  of  growth, 
restitution,  and  generation  (whether  sexual  or  asexual) ; 
and,  what  is  equally  important,  it  prevails  also  in  patho- 
logical cases — i.e.,  in  the  formation  of  diseased  tissues. 
In  fact,  the  great  generalisation  which  followed  Harvey's 
celebrated  dictum,  "  omne  vivum  ex  ovo,"  was  put  forth 
by  the  late  Professor  Eudolf  Virchow,  the  eminent 
founder  of  cellular  pathology,  in  his  formula,  "  omnis 
cellula  e  cellula."  The  formula  has  in  more  recent 
times  been  further  elaborated  on  the  same  lines  of 
thought  in  proportion  as  the  importance  of  the  nucleus 
or  cell  kernel  has  been  recognised,  or  as  the  granular 
structure  of  protoplasm  has  been  maintained ;  leading 
to  analogous  formulae,  such  as  "  omnis  nucleus  e  nucleo," 
"  onme  granulum  e  granule."     These  formulae  ^  are  the 


^  See  Roux  ('  Gesammelte  Ab- 
handlungen,'  vol.  i.  p.  393)  :  "  Un- 
interrupted durability  is  the  in- 
dispensable condition  of  all  that  is 
organic,  although  this  does  not 
involve  a  distinction  from  inorganic 
processes.  This  fact  is  expressed 
by  the  fundamental  theses  :  Omne 
vivum  ex  ovo  (Harvey),  Omnis 
cellula  e  cellula  (Virchow),  Omnis 
nucleus     e     nucleo    (Flemrning)." 


Hauptmann  ('  Die  Metaphysik,' 
&c.,  p.  334)  says:  "Altmann  for- 
nmlates  for  himself  in  analogy 
with  these  biological  princijiles  the 
further  princijale,  '  Omne  granulum 
e  granule.'  "  On  Altmann's  theory 
of  the  "bioblasts"  as  elementary 
organisms,  see  Yves  Delage, 
'  L'Hdredite,'  p.  498,  &c.,  Hertwig, 
'  The  Cell,'  p.  24. 


ON    THE    VITALLSTIC    VIEW    uF    NATCRE.         445 


expression  of  anatomical  observations  and  theories  repre- 
senting an  enormous  amount  of  research,  labour,  and  in- 
genuity, but  they  iuvohc  no  new  line  of  reasoning,  and 
they  belong,  accordingly,  more  to  the  history  of  Science 
than   to   that  of  Tliought. 

The  first  to  attempt  a  mechanical  explanation  of  the  .  *■'-., 
process  of  cellular  division  was  Mr  Herbert  Spencer,^  LTgrovrth.'^ 
who,  in  his  'Principles  of  Biology'  (I860),  pointed  out 
that  there  exists  a  limit  of  growth  through  assimilation 
or  intussusception,  inasmuch  as  volume  and  mass  increase 
at  a  greater  rate  than  the  surrounding  surface  through 
which  communication  with  the  environment  is  afforded. 
A  resultant  tension  brings  about  an  increase  of  surface 
through  rupture,  and  restores  the  balance  between  the 
contained  mass  and  the  surface.  In  his  analysis  of  this 
process  of  readjustment,  Spencer  has  given   mechanical 


^  The  principle  here  referred  to 
s-ometimes  goes  under  the  name  of 
the  Leuckart-Spencer  principle,  it 
having  heen  suggested  independ- 
ently by  Rudolf  Leuckart,  Herbert 
Spencer,  and  Alexander  James.  It 
requiret),  of  course,  a  great  many 
qualifii'ations.  See  the  '  Principles 
of  IJiology,'  vol.  i.  part  2,  chap.  i. 
But  "  it  follows  from  these  con- 
siderations tliat  the  cell  can  never 
surpass  a  certain  size  ;  for  if  the 
disturbance  of  metaVjolism  that 
arises  because  of  the  increasing 
disproportion  between  the  more 
superficial  and  the  deeper  layers 
has  reached  a  certain  extent,  the 
cell  can  no  longer  continue  living 
in  its  existing  form.  Thus  the 
remarkable  fact  is  exiilained  very 
simply,  tliat  no  cells  of  constant 
form  are  known  that  are  larger 
than  a  few  millimetres  in  diameter, 
and  thus  we  are  made  to  under- 
stand   why    the    development    of 


large 


organisms  is  only  possible 
by  the  arrangement  of  the  living 
substance  into  an  aggregate  of 
small  cells  instead  of  into  a  single 
cell,  for  example,  of  the  size  of  a 
man.  ...  If,  therefore,  the  living 
substance  of  such  a  cell  is  not  to 
perish  by  growth,  at  some  period  in 
its  growth  a  correction  of  this  dis- 
proportion between  mass  and  sur- 
face and  of  the  disturbance  of 
metabolism  conditioned  by  it  must 
come  in  :  such  a  correction  is  realised 
in  the  reproduction  of  the  cell  by 
division.  The  repnjduction  of  the 
cell  by  division  is  accordingly  to  be 
considered  merely  as  a  lesult  of 
growth,  and  the  morphologists  for 
a  long  time  have  rightly  termed 
i-epniduction  a  continuation  of 
growtli,  '  a  growth  beyond  the 
measure  of  the  individual '  "  (Ver- 
worn,  '  General  I'hysiology,'  Engl, 
transl.,  p.  530,  &c.) 


446  SCIENTIFIC    THOUGHT. 

biologists  a  formula  which,  like  his  physiological  units, 
has  helped  to  give  precision  and  direction  to  reasoning 
on  these  subjects.  But  as  growth  has  a  natural  limit 
and  leads  to  division,  so  reproduction  through  division 
appears  to  have  a  limit  also.  "  Only  the  very  lowest 
organisms,  such  as  fission  fungi,  appear  to  be  able  to 
multiply  indefinitely  by  repeated  divisions :  for  the 
greater  part  of  the  animal  and  vegetable  kingdoms  the 
general  law  may  be  laid  down  that,  after  a  period  of 
increase  of  mass  through  cell  division,  a  time  arrives 
45.  when  two  cells  of  different  origin  must  fuse  together, 
of  two         producing  by  their  coalescence  an  elementary  organism 

elements. 

which  affords  the  starting-point  for  a  new  series  of 
multiphcations  by  division."  ^  Fertilisation  is  now 
known  to  be  a  cellular  problem.  As  such  it  has  been 
studied  in  favourable  cases  which  permitted  of  direct  ob- 
servation, and  what  has  been  ascertained  in  those  cases 
— exhibiting  in  general  the  same  common  features  and 
phases  of  development — has  by  inference  under  the  great 
generalisations  of  the  cellular  theory  been  extended  to 
all  living  things  in  which  sexual  differentiation  exists, 
be  they  animals  or  plants.^      The  male  and  the  female 


1  Hertwig,  '  The  Cell,'  p.  2.r2. 
The  process  may  be  looked  at  as  an 
instance  of  tlie  cyclical  order  of 
change.  "  The  multiplication  of  the 
elementary  organism,  anil  with  it 
life  itself,  resolves  itself  into  a 
cyclic  process.  .  .  .  Such  cycles  are 
termed  generation  cycles.  They 
occur  in  the  whole  organic  king- 
dom in  the  most  various  forms." 
Similarly  Sir  M.  Foster  ('  Text-book 
of  Physiology,'  5th  ed.,  p.  l.^.")5),  as 
quoted,  supra,  p.  289.  We  may 
add  that  from  a  still  broader  stand- 
point, which  we  may  call  that  of 


bionomics  —  in  distinction  from 
biology  —  the  cycle  never  repeats 
itself,  but,  owing  to  overcrowding 
and  selection,  something  different, 
more  complex — i.e.,  externally  or 
internally  better  endowed — is  pro- 
duced. Philosophically  we  call  this 
progress. 

-  There  exists  no  more  remark- 
able instance  of  the  extension  of 
natural  knowledge  by  a  process  of 
very  incomplete  induction  than  the 
gradual  linn  establishment  of  the 
now  universally  adopted  doctrine  of 
fertilisation,  no  more  brilliant  refu- 


ox    THE    VITALISTIC    VIEW    UF    NATLKP:. 


447 


elements  concerned  have  both  been  recognised  to  be 
cells,  both  have  been  found  to  undergo,  before  what  is 
termed  the  stage  of  maturity,  similar  preparatory  changes. 
The  changes  represent,  as  it  were,  the  last  stages  of  their 
independent  existence  as  living  cells.  After  these 
changes  have  taken  place  they  can  only  enter  into  a 
new  cycle  of  existence,  exhibiting  new  powers  of  growth 
and  division  by  a  process  of  fusion  where  each  supjilies 
what  in  the  other  is  wanting  to  start  on  a  new  cycle  of 
life — i.e.,  of  difi'erentiation  and  development. 

Thus  the  vague  theories  of  former  times,  which  reach 
far  into  the  nineteenth  century,  the  speculations  of  the 
Spermatists  and  the  Ovists,  have  during  the  last  thirty 
years,  beginning  witli  Pringsheim's  observation  in  1869 
of    the    pairing    of    the    swarm-spores    of    certain   algse, 


tation  of  the  purely  enumerative, 
or  all-case  method.  The  number 
of  instances  in  which  the  process 
of  fertilisation,  with  its  various 
preparatory  stages  and  its  conse- 
(juences,  can  be  actually  observed 
is  infinitesimally  small  compared 
to  the  number  of  different  species 
and  varieties  in  which  it  is  end- 
lessly repeated  on  lines  which  no 
biologist  doubts  to  be  essentially 
the  same.  M.  Yves  Delage  says  : 
"C'est  une  chose  remarquable  com- 
bien  certains  etres,  par  des  particu- 
larites  en  apparence  sans  int<5ret 
ont  facilitc  la  solution  de  certains 
problemes  presque  insolubles  en 
dehors  d'eux.  L'Ascaris  ranjalocc- 
phula  [tiie  round  -  worm  of  the 
horse,  first  observed  by  van  Bcne- 
den  in  1883],  par  le  petit  nombre 
de  ses  chromosomes,  lea  Echino- 
dermes  [sea  urchins,  &c.]  par  la 
facilitc  avec  lafjuelle  ils  acceptent 
la  fecondation  artificielle,  out  fait 
faire,  en  di.\    ans,  plus  de   progres 


aux  questions  relatives  a  la  fdconda- 
tion  que  n'ont  fait  avant  ou  dcpuis 
tous  les  autres  animaux  rdunis. 
Dans  TAscaride,  le  tcsticule  foi-me 
un  long  tube  et  les  diverses  phases 
de  la  spermatogencse  s'acconqilis- 
sent  dans  les  rt%ions  diffcrentes  de 
I'organe  :  il  y  a  une  zone  il  sper- 
matogonies,  une  zone  a  si)ermato- 
cj'tes  en  voie  d'accroissement,  une 
zone  ou  se  font  les  divisions  r^- 
ductrices  et  une  enfin  oil  les  sper- 
matides  se  transforment  en  sper- 
matozoides"  {' L'Heredite,'  p.  133). 
See  on  the  variety  of  objects  which 
have  lent  themselves  to  the  gradual 
unravelling  of  the  processes  of  cell 
division,  nuclear  division,  fusion  of 
nuclei,  cleavage  and  embryonic  de- 
velopment, notalily  the  volume  of 
Prof.  Val.  Haeckcr,  '  Praxis  und 
Theorie  der  Zellen-  und  Befrucht- 
ungslehre'  (Jena,  189!>).  A  very 
lucid  summary  is  contained  in  J. 
A.  Thomson's  '  The  Science  of  Life ' 
(1899). 


448 


SCIENTIFIC    THOUGHT. 


47. 
New 
problems. 


and  centring  in  van  Beneden's  discovery/  been  replaced 
by  definite  conceptions  capable  of  typical  description. 
This  typical  process  consists  in  the  fusion  of  certain 
parts  of  the  male  and  female  cells, — the  nuclei  or 
kernels  playing  an  important  if  not  the  essential  part. 
Many  biologists  of  the  foremost  rank,  notably  in 
Germany  and  France,  have  contributed  to  make  clearer 
the  various  lines  in  this  typical  picture  of  the  most 
mysterious  process  in  the  physical  organism,  whilst 
every  new  discovery  has  brought  with  it  new  and 
unanswered  questions  or  given  a  novel  aspect  to  older 
problems. 

Of  these  problems,  those  of  heredity  and  variation 
are  at  present  by  far  the  most  important.  Both 
the  cellular  theory  of  living  matter  and  the  theory 
of  natural  selection,  including  the  principles  of 
differentiation  and  of  the  division  of  physiological 
labour,  converge  upon  these  two  great  facts  of 
modern   biology.     The  theory   of  natural  selection  pre- 


^  See  last  note.  "  Since  the 
researches  of  0.  Hertwig  and 
others  hi  1875,  it  had  been  clear 
that  each  parent  contributes  a 
single  germ -cell  to  the  foi-mation 
of  the  offspring  ;  but  the  masterly 
researches  of  E.  van  Beneden 
(1883)  showed  that  every  nucleus 
of  the  offspring  may  contain  nuc- 
lear substance  derived  from  each 
of  the  parents,  a  conclusion  which 
is  visibly  demonstrable  for  a  few 
of  the  first  steps  in  cleavage.  In 
fact,  van  Beneden  to  some  extent 
proved  what  Huxley  had  foreseen 
when  he  said,  in  1878,  'It  is 
conceivable,  and  indeed  probable, 
that  every  part  of  the  adult 
contains  molecules,  derived  both 
from     the     male     and    from     the 


female  jjarent  ;  and  that,  regarded 
as  a  mass  of  molecules,  the  entire 
organism  may  be  compared  to  a 
web,  of  which  the  warp  is  derived 
from  the  female,  and  the  woof 
from  the  male'"  (J.  Arth.  Thom- 
son, 'The  Science  of  Life,'  -p. 
129).  Another  theoretical  antic- 
ipation is,  according  to  Haecker 
(loc.  cit.,]}.  133),  the  "Idioplastna" 
of  Niigeli :  "  The  heritable  sub- 
stance, organised,  possessing  a  com- 
plex structure,  transmitted  from 
one  generation  to  another,"  which 
was  "  about  the  same  time  identi- 
fied by  Strassburger,  O.  Hertwig, 
von  Kolliker,  and  W'eismann,  with 
the  chromatin  substance  of  the 
nucleus." 


UN    THE    VITALISTIC    VIEW    UF    NATUIiE.         449 

supposes  the  fact  of  heredity — that  is,  the  transmission 
of  characters  peculiar  to  the  parents  (be  they  acquired 
by  them  or  not),  antl  llie  fact  of  variation,  1ml  it  does 
not  explain  them.  It  does  not  give  any  intelligil)le 
description  of  the  means  which  nature  uses  to  secure 
that  continuity  of  change  which  is  marked  on  the  one 
side  by  a  faithfulness  to  certain  typical  forms,  and  on 
the  otlier  by  a  gradual  development.  The  cellular 
theory  permits  us  to  comprise,  under  the  general 
categories  of  cell-growth,  cell-division,  and  cell-fusion, 
the  great  facts  of  the  history  of  all  living  matter,  but 
it  does  not  explain  hdw  tliat  apparent  sameness  of 
structure  which  the  ultimate  morphological  unit,  the 
cell,  presents  to  our  view,  develops  into  that  variety 
of  recurrent  forms  which  make  up  the  wealth  and 
the  order  in  the  world  of  natural  objects.  The  older 
naturalists  were  divided  into  two  distinct  schools :  one 
believed  in  pre-formation  with  development — the  older 
meaning  of  "  evolution  "  ;  tlie  other  in  after-formation, 
or  "  epigenesis."  The  former  foundered  on  the  difficulty 
of  explaining  or  making  plausible  how  all  the  germs 
of  hundreds  of  succeeding  generations  could  be  contained 
in  the  first  ancestor ;  the  latter  failed  to  explain  how 
nature  was  able  to  Imild  up  by  mechanical  forces  out 
of  unorganised  matter  a  structure  resembling  the  parent 
structures.  The  suggestion  of  a  "  nisus  formativus," 
which  we  owe  to  the  celebrated  Blumenbach,  is  only 
a  definition  of  tlie  ditliculty,  nut  an  explanation. 

The  three  distinct  ideas  represented  by  tliesi^  historic 
terms  occur  again  in  modern  biology,  though  altered  to 
suit  the  vast  extension  of  actual  knowledge  of  facts,  and 

VOL.  II.  2  F 


450  SCIENTIFIC    THOUGHT. 

the  three  great  generalisations  mentioned  above.  Out 
of  the  three  ideas  of  pre-formation,  after-formation,  and 
the  directive  principle,  the  three  generahsations,  namely, 
the  cellular  theory,  natural  selection,  and  metabolism, 
and  the  enormous  number  of  facts  collected  by  micro- 
scopists  and  naturalists  of  all  kinds,  many  more  or 
less  ingenious  theories  of  life  have  been  put  together. 
None  of  them  has  obtained,  though  some  have  had  a 
very  marked  influence  on  biological  science,  and  even 
48.        on  popular  thought.      Of  these  Prof.  Weismann's  theories 

Weismann  -^    ^  " 

on  heredity,  of  heredity  are  probably  the  best  known.  Without  en- 
tering upon  the  enormous  array  of  biological  facts  which 
have  been  marshalled  by  supporters  and  opponents  ahke, 
it  will  be  of  interest  to  point  out  the  novel  aspects 
and  lines  of  reasoning  which  have  come  into  prominence 
through  the  voluminous  discussion  belonging  to  this 
subject.  They  were  prepared  before  the  appearance  of 
Weismann's  writings  by  the  changed  and  enlarged  con- 
ceptions which  the  discoveries  of  the  middle  of  the 
century  introduced  concerning  the  general  phenomena 
of  Life,  Death,  and  Disease.  Three  distinct  convictions 
regarding  these  three  main  aspects  of  the  Hving  portion 
of  creation  have  been  forced  upon  the  scientific  and 
popular  mind.  First,  we  have  the  modern  doctrine  of 
the  ubiquity  of  organisms  and  germs,  at  least  so  far 
as  our  planet  is  concerned :  beyond  this  sphere  we 
can  say  that  we  know  no  more  of  the  existence 
of  living  matter  than  past  generations.  Secondly,  we 
have  the  generally  recognised  doctrine  that  spontan- 
eous generation  of  living  out  of  not-living  matter  is 
imknown   and  inconceivable   under   such    conditions    as 


ON    THE    VITALISTIC    VIEW    OF    NATURE.         451 

we  can  realise  or  imagine.  And  thirdly,  hand  in  hand 
with  the  conviction  of  this  unique  but  ubiquitous  character 
of  life,  the  impression  of  the  mutual  interdependence  of 
living  creatures  has  gained  ground,  and  has  especially  in- 
fluenced our  ideas  of  the  cause  and  treatment  of  disease. 

In    one   of    those    luminous    addresses    in    which    he        to. 

Biogenesis. 

has  rivalled  the  combination  of  literary  witli  scientific 
clearness  characteristic  of  the  French  genius,  the  late 
Prof.  Huxley  has  written  the  history  of  Biogenesis  ^ 
— i.e.,  of  the  theories  of  the  origin  of  life  from 
the  time  of  the  Italian  Eedi  down  to  Pasteur,  show- 
ing how  experiment  and  theory  alternately  supported 
and  contradicted  the  doctrine  that  living  matter  could 
be  formed  out  of  not -living  matter,  till  the  great 
French  biologist,  by  his  refined  experiments,  entirely 
banished  from  the  provinces  of  science  and  practice 
the  once  admitted  fact  that,  after  exclusion  or  destruc- 
tion of  all  living  germs,  phenomena  peculiar  to  life,  such 
as  fermentation  and  putrefaction,  could  be  generated. 
Those  great  departments  of  medical  practice,  the  anti- 
septic and  aseptic  treatment,  with  their  enormous  de- 
velopment of  prophylactic  and  antitoxic  methods,  form 
the  daily  and  ever-growing  argument  against  abiogenesis 


^  In  his  presidential  address  to 
the  British  Association  in  1870, 
reprinted  in  '  Critiques  and  Ad- 
dresses,' p.  218  s'lq.  A  very 
readable  and  much  earlier  deliver- 
ance on  "  The  Diffusion  of  Life " 
is  that  hy  K.  E.  von  Baer,  before 
the  Academy  of  St  Petersburg  in 
1838,  reprinted  in  the  first  volume 
of  his  'Reden,'  &c.,  p.  161  sqq. 
In  the  preface  of  1864  to  tliis 
reprint,  the  illustrious  author  tell.- 


there  were  probably  few  naturalists 
who  "did  not  consider  the  gener- 
ation without  parents  of  inferior 
organisms  as  proved,  or  at  least 
as  highly  jirobable,"  and  he  him- 
self would  not  at  that  time  (1838) 
"declare  it  to  be  non-existent" 
(p.  173).  In  1864  he  describes  the 
theory  as  having  almost  vanished, 
leaving  the  problem  of  the  first 
beginnings  of  life  in  the  number- 
less varieties,  even  after  Darwin's 


Ub    that    between    1810    ancl    1830    I    hypothesis,  unsolved  (p.   177) 


452  SCIENTIFIC    THOUGHT. 

— i.e.,  the  generation  of  living  out  of  dead  or  not-living 
matter. 

But    in    proportion    as    abiogenesis    or    spontaneous 
generation    has    disappeared    from    our    scientific     text- 
books, life  being  recognised  as  a  phenomenon   between 
which    and    dead    matter    there    exists    no    intelligible 
and  no  practical  transition  except  that   of  destruction, 
50.        the   ubiquity  of    life  has   forced  itself   more  and   more 
Theuiqmy^^  our  attention.      Not  long  ago,  as  Huxley^   tells   us, 
the   adherents   of   spontaneous   generation   urged   as   an 
argument    on    their    side    that    if     biogenesis    be    true, 
innumerable  facts  and  experiments  prove  "  that  the  air 
must  be  thick  with  germs ;  and  they  regarded  this  as 
the  height  of  absurdity.      But  nature,"  as  Huxley  con- 
tinues,  "  occasionally   is    exceedingly   unreasonable,    and 
Professor  Tyndall  has   proved   that   ordinary  air   is   no 
better    than  a  sort  of   stirabout  of    excessively   minute 
solid  particles."      It  is  now,  after  a  generation  has  passed, 
hardly  necessary  to  refer  to  any  special  experiments  of 
Tyndall  or  of   others,  when    the  daily  press   brings   us 
records  of  the  number  of  bilHons  of  germs  contained  in 
a  cubic  inch  of  the  atmosphere  of  large  cities,  precisely 
as    it   does  of  the  mortality  of  their  population.     The 
cellular  theory  of  disease  has  been  succeeded  and  ampli- 
fied by  the  bacillar  theory,  and  no  modern  scientific  fact 
has  fastened  on  the  popular  mind  with  a  stronger  hold 
than  the  ubiquity  of  the  micro-organisms,  which,  with 
beneficent  or  fatal  results,  assist  everywhere — chiefly  in 
the  larger  organisms — in  the  struggle  for  existence. 
It  is,  moreover,  only  a  logical  inference  that  if  living 

'  Critiques  aud  Addresses,'  p.  233. 


1  < 


ON    THE    VITALISTIC    VIEW    OF    NATURE. 


453 


matter  is  not  being  continually  formed  out  of  not-living 
matter,  while  it  is  an  undeniable  fact  that  livinir 
matter  is  continually  and  everywhere  passing  out  of 
existence,  the  preservation  of  life  is  dependent  upon 
an  enormous  self-overproduction  which,  combined  with 
the  process  of  natural  selection,  secures  its  permanence 
and  the  development  of  the  highest  forms  of  which  it  is 
capable.  The  continuity — i.e.,  the  interdependence — of  "^i- 
all  living  forms  in  time  and  space  guarantees  the  non-ex-  ,^'"."'^y  ^^ 

c  r  o  living  forms. 

tinction  of  this  phenomenon,  which,  for  all  that  we  know, 
is  of  a  unique  character.  The  modern  scientific  and  popular 
view  of  life  is  that  it  is  a  unique  phenomenon,  that  it  is 
a  ubiquitous  phenomenon,  at  least  within  the  area  of 
what  we  call  "  our  "  world,  and  that  it  is  a  continuous 
phenomenon.  The  unique  character  or  singularity  of 
life  has  been  directly  demonstrated  by  the  sameness  of 
the  ultimate  units  of  all  living  matter,  the  cells,  indirectly 
by  the  refutation  of  the  older  theory  of  spontaneous 
generation  ;  and  has  been  enormously  strengthened  by  the 
doctrine  of  descent,  the  phenomena  of  overcrowding,  and 
the  possibility  of  natural  selection.  The  ubiquity  of  life — 
within  certain  limits — has  been  revealed  directly  by  the 
microscope,  and  indirectly  by  the  modern  theories  of 
disease,  and  of  many  forms  of  growth.^     The  continuity  of 


1  There  is  a  striking  passage  in 
Nansen's  'Farthest  North,'  vol.  i. 
p.  445,  showing  the  ul)i(iuity  of 
organic  germs  :  "  When  the  sun's 
rays  had  gained  power  on  the  sur- 
face of  the  ice,  and  melted  the 
snow,  so  that  pools  were  formed, 
there  were  soon  to  be  seen  at  the 
bottom  of  these  pools  small  yellow- 
ish brown  spots,  so  small  that  at 
first  one  hardly  noticed  them.     J  )ay 


by  day  they  increased  in  size,  and 
absorbing,  like  all  dark  substances, 
the  heat  of  the  sun's  riiys,  they 
gradual! J'  melted  the  underlying 
ice  and  formed  round  cavities  often 
several  inches  deep.  These  brown 
spots  were  .  .  .  algto  and  diatoms. 
.  .  .  I  actually  found  bacteria,^ 
even  these  regions  are  not  free 
from  them." 


454 


SCIENTIFIC    THOUGHT. 


52. 
'Pan- 
genesis.' 


life  has — as  an  inevitable  corollary — come  more  and 
more  into  prominence.  It  has  been  the  subject  of 
much  discussion,  as  a  phenomenon  which  is  felt  to 
require  a  mechanical  explanation. 

The  problem  of  the  continuity  in  time  of  the  forms 
and  properties  of  living  matter  forced  itself  on  the  great 
propounder  of  the  modern  theory  of  Descent,  on  Darwin. 
He  looked  upon  the  principle  of  "Ee version^ — this  power 
of  calling  back  to  life  long-lost  characters — as  the  most 
wonderful  of  all  the  attributes  of  inheritance." 

At  the  end  of  his  second  great  work,  ten  years  after 
the  appearance  of  the  '  Origin  of  Species,'  he  ventured  on 
a  hypothetical  explanation,  his  theory  of  "  Pangenesis," 
"  which  implies  that  the  whole  organisation,  in  the  sense 
of  every  atom  or  unit,  reproduces  itself ;  hence  ovules  and 
pollen-grains,  the  fertilised  seed  or  egg,  as  well  as  birds, 
include  and  consist  of  a  multitude  of  germs  thrown  off 
from  each  separate  atom  of  the  organism,"  ^  This  idea, 
as  the  author  himself  admitted,  and  as  has  since  fre- 
quently been  pointed  out,  was  not  fmidamentally  new :  it 
had  been  anticipated  by  Buffon  in  his  celebrated  "organic 
molecules,"  and  since  Darwin  it  has  been  restated  and 
adapted  in  various  modified  forms.  It  is  hardly  an  ex- 
planation, but  it  is  a  statement  which  emphasises  the 
great  fact  of  modern  biology, — the  fact  Ijrought  out  by 
the  cellular  theory,  that  the  units  of  life  are  not  the  large 
visible  organisms  which  were  formerly  studied  by  prefer- 
ence,  but   the    innumerable,   infinitesimal   living   beings 


^  '  Animals     and     Plants     under 
Domestication,'  vol.  ii.  p.   372. 
^  'Animals     and     Plants     under 


Domestication,'  chap.  27,  vol.  ii.  p. 
358. 


ON    THE    VITALISTIC    VIEW    OF    NATURE. 


455 


called  cells  which,  through  growth  and  reproduction  by 
division  and  fusion,  maintain  life  as  a  continuous  unic^ue 
phenomenon. 

Into  this  view,  which  under  the  special  form  of 
pangenesis  has  not  found  much  favour,  hut  wiiich, 
nevertheless,  in  some  form  or  other,  forces  itself  more 
and  more  on  our  attention,  Professor  Weismann  has 
imported  a  further  distinctive  feature,  not  prominently 
brought  out  by  Darwin,  though  it  also  dates  farther 
back  ^   than   the  present  generation. 


^  The  history  of  tlie  knowledge 
and  theory  of  sex  and  heredity  has 
been  written  in  EngHsh  by  Profs. 
Patrick  (leddes  and  J.  Arthur 
Thomson,  in  a  book  entitled  '  The 
Evolution  of  Sex  '  (1st  ed.  1889)  ;  in 
French  by  M.  Yves  Delage,  in  his 
much-quoted  work,  '  La  Structure 
du  Protoplasma  et  les  Theories  sur 
rH(5redite  et  les  grands  problomes 
de  la  Biologie'  (1895).  The  latter 
work  contains  elaborate  criticisms, 
and  finally  inclines  towards  a  theory 
of  life  termed  in  France  "  Organi- 
cisme,"  the  main  idea  of  which  is 
the  assumption  of  two  distinctive 
factors  in  all  the  phenomena  of 
living  matter — viz.,  '"Organisation 
and  Environment."  This  view, 
according  to  the  author,  has  not 
yet  gained  sufficient  strength  to 
form  a  definite  current  of  thought 
like  the  three  earlier  views  de- 
fined by  the  terms  "  Animisme," 
"  Evolutionisme,"  "  Micronicrisme." 
The  first  of  these  centres  in  the  idea 
of  vital  force,  the  second  iu  the 
older  school  of  evolution  ;  the  last 
begins  with  Buffon,  and  comprises 
tiie  modern  theory  of  Evolution  with 
Spencer,  Darwin,  Haeckel,  Weis- 
mann. Of  the  last  M.  Dclage 
says :  "  Ce  dernier  est,  pour  le 
moment,  I'ouvrage  le  j)lus  jiarfait 
crec  pour   expliquer  rHcrddit^   et 


r  Evolution.     Nous     croj'ons    avoir 

montre  (ju'll   est  bati  d'hypoth^ses 

fragiles,   invraisemblables,   et,    tout 

en    rendant    justice    au    talent    de 

son  architecte,  nous  con.seillons  de 

I'admirer  de  loin  et  de  construire 

ailleurs"  (p.  837).     "  Organicisme  " 

is  represented  by  W.  Koux,  Uriesch, 

and  0.  Hertwig,  and  is  historically 

traced   back  to  Descartes   (p.  S'.jS), 

and  to  von  Baer  and  Claude  Bernard 

(p.  720).     To   the   theories  of  the 

others,   "les   Organicistes  opposent 

le    concours    d'une    determinatinn 

mod(5r^(5    et   des    forces    ambiantes 

toujours  agissantes,  toujours  n^ces- 

saires,  non  comnie  simple  condition 

d'activite,     mais     comme     element 

essentiel  de  la  determination  finale  " 

(p.    720).     As  iu  this  account  the 

names   of   Roux,    Driesch,   and    0. 

Hertwig  are  placed    together,   it  is 

well  to  remark  that  since  that  time 

the  two  last-named  authorities  have 

in    v.arious    polemical    publications 

signified    the    divergence    of    their 

fundamental  conclusions  from   the 

later    attitude    which    Prof.    Roux 

has   assumed.       For    those   of    my 

readers    who    desire    to    get    some 

insight  into  the  drift  of  this  most 

recent   and    advanced   controversy, 

in  which  questions  of  principle,  of 

scientific  and  philosojihical  method, 

I    alternate  with  discussions  of  minute 


456 


SCIENTIFIC    THOUGHT. 


Growth  by  intussusception  and  assimilation  has  long 
been   recognised   as    the    characteristic    property   of    all 
living  matter,  of  every  living  cell.     Mechanical  causes 
suffice  to   explain   the  further  process  of  division  as  a 
necessary  consequence   of  continued  growth,  the  forma- 
tion of  new  cells  out   of   existing  ones,  the  process  of 
reproduction.      Only  in   the   lower   organisms,   however, 
does    reproduction    exist    simply    as    multiplication    by 
division.      In  all  higher  organisms  at  least,  reproduction 
by    division    seems     connected    with    the     phenomenon 
of   death    of   a    portion    of   the   dividing   organisms :    a 
differentiation   seems    to   set  in   between  the  new  cells, 
some  gradually  losing  their  power  of  self-multiplication 
by   division,   and    thus    being    doomed    sooner   or   later 
to   arrive  at   the   end  of  their  organic  existence ;  while 
others  retain   this   power  or  regain  it  by  uniting  with 
others — the  process  of  fusion  of  male  and  female  elements 
— and  seem  thus  to  be  specially  endowed  with  the  work 
of  reproduction — i.e.,  the  preservation  of  the  continuity  of 
life.     The  great  morphologist  Eichard  Owen,  about  the 
middle  of   the   century,  in   a  tract  on  Parthenogenesis, 
remarked   that   "  not   all   the    progeny   of   the    primary 
impregnated  germ-cell  are  required  for  the  formation  of 
the  body  in  all  animals :  certain  of  the  derivative  germ- 
cells   may   remain   unchanged   and   become   included   in 


embryological  development,  assisted 
or  disturbed  by  experiments  carried 
on  in  microscopic  dimensions,  I 
recommend,  besides  the  larger  works 
of  Hertwig  and  Roux  already  re- 
ferred to,  the  highly  suggestive 
writings  of  Hans  Driesch,  notably 
his  'Analytische  Theorie  der  or- 
ganischen     Entwickelung '    (1894), 


and  '  Die  Biologic  als  selbstiindige 
Grundwissenschaft '  (1893).  As  a 
very  helpful  inti'oduction  to  the 
original  views  of  this  writer,  Eng- 
lish readers  will  welcome  the  con- 
cluding chapter  of  Prof.  E.  B. 
Wilson's  book, '  The  Cell  in  Develop- 
ment and  Inheritance'  (1896). 


ox    THE    VITALISTIC    VIEW    UF    NATL'UE.         457 

that  body,  ...  so  included,  any  derivative  germ-cell  or 
tlie  nucleus  of  such  may  commence  and  repeat  the  same 
processes  of  growth  by  imbibition,  and  of  propagation  l)y 
spontaneous  fission  as  those  to  which  itself  owed  its 
origin."  ^      We   have   here  the  first  enunciation  of  that  ,     ^3. 

"  Germ-sub- 

idea  of  a  differentiation  between  the  germ-substance  and  b^^y.gub-*^ 
the  body  -  substance,  between  that  portion  of  living  '"^*"*^- 
matter  which  is  destined  to  preserve  the  continuity  of 
life,  and  that  other  portion  which,  destined  to  differen- 
tiate more  and  more  into  the  aggregate  of  living  cells, 
each  bearing  a  special  form  and  carrying  out  a  special 
function  in  the  economv  of  the  higher  organisms,  is  at 
the  same  time  doomed  In  death,  gradually  losing,  as  it 
does,  its  power  of  assimilation,  growth,  and  division — i.e., 
of  self-preservation.  Prof.  Haeckel  in  186G,  and  Dr 
Jager  in  1877,  elaborated  the  idea  further,  pointing  out 
that  the  "  germinal "  element  or  substance  was  that 
portion  wliicli  in  the  ])rocess  of  division  is  reserved 
for  the  preservation  of  the  species  (the  ^uAor,  hence 
termed  the  phylogenetic  portion),  whereas  the  "  personal  " 
element  or  substance  goes  to  form  the  body  or  individual 
(tlie  ov,  hence  termed  the  ontogenetic  portion).^ 


'  Darwin  quotes  this  passage  in 
a  historical  note  to  his  theory  of 
"  Pangenesis "  in  the  concluding 
chapter  of  his  •  Animals  and  Plants 
under  Domestication'  (vol.  ii.  p. 
375).  He  adds  further,  "By  the 
agency  of  these  germ-cells  Prof. 
Owen  accounts  for  parthenogenesis, 
fur  propagation  by  self  -  division 
during  successive  generations,  and 
for  the  repairs  of  injuries.  His 
view  agrees  with  mine  in  the 
assumed  transmission  and  multi- 
|ilii:atioii  of  his  germ  -  cells,  but 
diU'ers  fundamentally  from  mine  in 


the  belief  that  the  primary  germ- 
cell  was  formed  within  the  ovarium 
of  the  female,  and  was  fertilised  by 
the  male.  My  gemmules  are  sup- 
posed to  be  formed,  quite  independ- 
ently of  sexual  concourse,  by  each 
separate  cell  or  unit  throughout  the 
body,  and  to  be  merely  aggregated 
within  the  reproductive  organs." 

'-'  Complete  references  to  the 
earlier  statements  of  this  theory, 
which,  tlirougli  tlic  various  writings 
of  Prof.  Weismann  (since  1881, 
when  he  read  a  paper,  "On  the 
Duration     of     Life,"     before     the 


458 


SCIENTIFIC    THOUGHT. 


This  provisional  statement,  which  emphasises  the  now 
generally  recognised  difference  between  the  germ-sub- 
stance and  the  body-substance,  requires,  however,  two 
further  quahfications  in  order  to  embrace  the  great 
characteristic  facts  of  life  and  death  as  modern  em- 
bryology and  the  phenomenon  of  descent  have  unfolded 
them. 

Only  in  rare  instances  can  we  observe  the  continuity 
of  cells — i.e.,  of  those  organisms  which,  so  far  as  our 
knowledge  goes,  form  the  ultimate  units  of  living  matter. 
Weismann  recognised,  as  did  the  great  botanist  Nageli, 
and  long  before  both  of  these  the  philosopher  Herbert 
Spencer,  that  though  in  the  cell,  with  its  nucleus  and 
protoplasm,  we  may  have  arrived  at  the  last  microscop- 
ically visible  independent  units  of  life,  we  must — with 
the  atomic  theory  in  chemistry — assume  the  existence 
of  much  smaller  units  in  all  living  matter,  compared  with 
which  even  the  nucleus  of  the  cell  is  a  very  complex 
aggregate.  If  the  continuity  of  life  is  dependent  upon 
that  of  an  underlying  living  substance,  this  substance 
must  be  only  an  infinitesimal  portion  of  any  visible  cell 
or  nucleus.  The  conception  of  a  continuous  germinal 
plasma  and    substaucc   lias  thus    taken   refuge   in    the   more   refined 

body-  *= 

plasma.  conception  of  a  germ-plasma,  as  distinguished  from  the 
body  or  somatic  plasma :  the  former  is  immortal  within 
the  limits  of  the  conditions  of  organic  life,  the  latter  is 


54. 


Germ- 


Naturforscher  -  versammlung  at 
Salzburg,  reprinted  in  '  Essaj's  upon 
Heredity,'  tran^^l.  by  Poulton  and 
others,  Oxford  1889  ;  see  also  the 
'  Studies  in  the  Theory  of  Descent,' 
transl.  by  Meldola,  2  vols.,  1882, 
and  the  earlier  essays  of  Weismann 
mentioned  in  the  preface,  p.  viii.). 


has  become  both  scientifically  and 
popularly  recognised  and  debated, 
are  given  in  Geddes  and  Thomson, 
'  The  Evolution  of  Sex,'  p.  93  ;  also 
in  M.  Delage's  great  woi-k,  p.  349, 
&c.,  and  in  Wilson,  'The  Cell,'  p. 
295,  &c. 


ON    THE    VITALISTIC    VIEW    OF    NATURE.         459 

perishable,  mortal,  doomed,  after  temporarily  serving  the 
purposes  of  individual  development,  to  disappear  from 
the  category  of  living  matter. 

And  secondly,  it  appears  that  the  germinal  substance  ^.^  55. 
or  germ  -  plasma,  when  once  differentiated  from  the  j',asni'''^""' 
personal  substance  or  body-plasma,  cannot,  as  a  ride, 
perform  unaided  the  function  of  continuous  preservation 
of  the  species  or  phylum.  In  all  the  higher  animals 
the  germ -substance  appears  in  two  distinct  seemingly 
complementary  forms,  and  only  by  the  fusion  of  these 
does  the  development  of  the  germ -substance  become 
possible. 

The  great  ditticulties  which  stand  in  the  way  of 
applying  these  conceptions  (which  have  found  an  ex- 
haustive exposition  in  Prof.  Weismann's  '  Essays  on 
Descent  and  Heredity ')  to  the  vegetable  kingdom  have 
been  pointed  out,  and  have  prevented  their  general 
adoption  by  biologists ;  ^  nor  have  the  elaborate  modifi- 
cations introduced  in  Prof.  Weismann's  later  writings 
tended  to  make  them  more  acceptable ;  the  idea,  never- 
theless, of  a  fundamental  differentiation  of  the  elements 
of  living  matter  into  germinal  and  personal  has  got  hold 
of  the  scientific  mind  at  the  present  day,  and  cannot  be 


'  On  the  objections  of  Prof.  Stras- 
burger,  wlio  pc.ints  to  the  fact  that 
in  the  Ciise  of  begonias  the  frag- 
ment of  a  leaf  jilanted  in  moist  sand 
can  rejiroduce  the  whole  plant ;  of 


Problem  of  To-dav,'  transl.  by  P. 
C.  Mitchell  (1896)'  p.  40,  &c.  On 
the  discovery  of  Weismann  "  that 
in  parthenogenetic  ova  only  one 
polar  globule  is  formed,  wliile  there 


Prof.  Vines,  wIkj  shows  that  whole    ;    are   always    two  in   ova   which   are 


groiq)s  of  champignons,  which  propa- 
gate annually,  are  nevertheless  rich 
in  genera  and  sjiecics,  which  have 
evidently  descended  from  one  an- 
other, see  Yves  Delage,  '  L'Heredito,' 
p.  L2^,  &c. ;  '  Nature,'  vol.  x.  ]).  02 1 ; 
also    O.    Hertwig,    '  The    Biological 


impregnated,"  and  the  "moment- 
ary "  prcsum])tion  in  favour  of  his 
theory  which  it  afforded,  see  '  Essays 
on  Heredity,'  i>.  333,  &c. ;  Geddes 
and  Thomson,  '  Evolution  of  Sex,' 
p.  180,  &c.  ;  and  Delage,  '  L'Hero- 
ditcV  p.  151. 


460  SCIENTIFIC    THOUGHT. 

passed  over  in  a  history  of  Thought.  Moreover,  it  has 
made  itself  felt  by  giving  rise  to  two  separate  views  of 
the  cause  of  variation — i.e.,  of  that  phenomenon  in  the 
living  creation  on  which  the  entire  modern  theory  of 
descent  is  founded. 

If  it  be  true  that  the  preservation  of  the  species,  the 
continuity  of  living  forms,  is  dependent  on  the  germ- 
plasma,  whereas  the  somatic  plasma,  from  this  point  of 
view,  only  serves  individual  ends  and  is  a  receptacle  or 
temporary  dwelling-place  for  the  germs  which  it  trans- 
mits but  does  not  create,  the  experiences  of  the  body,  its 
changes  and  development,  can  have  little  or  no  influence 
on  the  hidden  germs  and  their  further  history.  Thus 
56.        Weismann  is   led    to  a   denial   of   the   influence  of   en- 

Weismann  v. 

Lamarck,  viroumcut,  of  habit  and  acquired  characters,  except  in 
those  cases  where,  as  in  the  lower  organisms,  no  dif- 
ferentiation has  set  in  between  the  germinal  and  the 
personal  substance.  This  amounts  to  a  negation  of  those 
modifying  influences  which  Lamarck  emphasised,  and 
which  play  such  a  great  part  in  the  theories  elaborated 
by  Darwin,  Haeckel,  and  especially  by  Herbert  Spencer. 
On  the  other  side,  it  has  led  Weismann  to  lay  a  much 
greater  weight  upon  sexual  selection  and  the  effects 
of  crossing  in  the  process  of  descent  and  the  pheno- 
mena of  heredity.  But  for  sexual  selection,  and  the 
endless  combinations  of  different  germ  -  plasmas,  there 
would,  according  to  Weismann,  be  no  variation,  and 
hence  no  development  of  the  higher  forms  of  life.  The 
controversy  turns  mainly  upon  the  inheritance  of  acquired 
characters,   of  which  indeed  no   genuine   and   authenti- 


ON    THE    VITALLSTIC    VIEW    OF    XATUKE.         461 

cated  case  seems  to  have  been  established.^  On  the  other 
side  the  influence  of  crossing,  of  the  repeated  division 
and  fusion  of  different  germ-plasmas,  to  which  Darwin 
in  his  later  writings  attached  more  and  more  importance, 
and  on  which  Weismann  rehes  exclusively  for  an  ex- 
planation of  variation  and  natural  selection,  is  denied 
by  some  biologists  to  tend  in  the  direction  of  the 
gradual  growth  of  definite  characters :  they  point  rather 
to  the  obliterating  and  diluting  influence  of  such  pro- 
miscuous fusion,  and  they  maintain  that  the  presence  of 
an  environment  which  always  acts  in  a  constant  manner  ^ 
is  indispensable. 

If  we  now  look  back  for  a  moment  on  the  funda- 
mental change  of  ideas  which  the  century  has  brought 
about  in  the  biological  aspect  of  nature,  we  are  bound 
truly  to  halt  in  astonishment.  In  no  department  of 
thought  have  comparatively  small  beginnings  and  de- 
tailed discoveries,  referring  to  infinitesimally  small 
phenomena,  led  to  such  revolutionary  ideas  concerning 
those  phenomena  which  most  intimately  affect  our 
personal  interests — the  problems  of  life  and  death,  of 
conduct  and  of  health.  The  whole  of  this  change  has 
been  brought  about  by  introducing  and  extending  those 


^  It  i.s  needless  to  give  special 
references,  as  all  the  recent  works 
on    the    subject,   which    have    been 


hercditaires,  niais  il  parait  bien 
certain  qu'elles  le  sont  quekiuefois. 
Cela    dejiend    sans    doute    (le    leur 


largely  (juoted  in  this  chaj)ter,  deal    i    nature.     D'ailleurs  on   ne  sait   j)as 


with  this  point.  See,  however, 
Yves  Delage,  '  L'Hdrc^dito,'  p.  196, 
for  a  very  complete  bibliograjjhy. 
He  concludes  as  follows  :  "  II  n'est 
])a»s  deniontro  que  les  modifications 
acquises  sous  I'influence  des  con- 
ditions de  vie  soient  gtindralement 


quelle  est  dans  ce  rdsultat  la  part 
de  la  transmission  des  modifications 
somatiques  aux  cellules  gcrminales 
et  celle  de  Taction  directe  des  con- 
ditions ambiantes  sur  celles-ci "'  (p. 
221). 

-  Hertwig,  '  The  Cell,'  p.  319. 


462  SCIENTIFIC    THOUGHT. 

methods  of  investigation  and  reasoning  which  have 
been  learnt  in  the  mechanical,  physical,  and  chemical 
sciences :  the  processes  of  observation,  measurement, 
and  calculation.  And  yet  it  may  be  asked,  have  we 
come  nearer  an  answer  to  the  qviestion,  What  is  Life  ? 
At  one  time,  for  a  generation  which  is  passing  away, 
we  apparently  had.  But  a  closer  scrutiny  has  convinced 
most  of  us  that  we  have  not.  The  study  of  life  has 
indeed  been  transferred  from  the  higher  and  more  com- 
plex forms  to  the  lower,  the  minuter,  and  the  simpler ; 
and  now  lingers  by  preference  among  cells,  germs,  and 
primitive  organisms,  out  of  which  we  have  learnt  to 
consider  the  higher  ones  as  put  together  on  the  prin- 
ciples of  co-operation,  division  of  labour,  and  mutual 
57.        accommodation.       The    problem    "  What   is   Life  ? "   has 

Two  aspects 

of  the  in  all  this  sained  a  twofold  aspect.     Wherein  consists 

problem  ^  ^ 

of  life.  ^Yie  peculiarity  of  the  smallest  unit  of  living  as  com- 
pared with  not-living  matter  ?  In  organisation  we  are 
told,  in  growth  through  intussusception,  in  metabolism ; 
but  we  are  far  from  being  able  mechanically  to  describe 
these  phenomena  or  processes.  The  spectre  of  a  vital 
principle  still  lurks  behind  all  our  terms.^    On  the  other 


^  If  we  broadly  summarise  the 
properties  peculiar  to  living  things 
which  the  nineteenth  century  has 
dwelt  on  in  an  original  manner 
under  the  three  conceptions  of  adap- 
tation (fitness),  selection  (natural  or 
sexual),  and  organisation  (order  or 
harmony),  the  question  presents  it- 
self. Is  any  of  these  much-used  terms 
intelligible  or  definable  without 
reference  to  something  which  is  ex- 
traneous to  the  object  we  treat  of, 
this  reference  existing  in  our  own 
thinking  or  contemplating  mind, 
and,  if  actually  present  in  natural 


objects  themselves,  then  also  indi- 
cative of  the  existence  of  some  im- 
material principle  ?  Though  this  is 
manifested  in  mechanical  contriv- 
ances which  it  has  left  behind  with 
its  signature  upon  them,  it  is  never- 
theless vaguely  analogous  to  the 
selective,  purposeful,  or  orderly 
jjerformances  of  a  human  intellect 
The  exclusive  study  of  detail  on  the 
one  side,  the  aspect  of  the  whole  on 
the  other,  will  always  induce  opposite 
answers  to  this  question.  In  addi- 
tion to  the  literature  given  in  the 
notes  to  this  chapter,  I  may  refer 


ON    THE    VITALISTIC    VIEW    OF    NATURE.         463 

side,  the  union  ov  co-operation  of  many  essentially  similar 
units  in  a  complicated  organism  brings  out  more  and 
more,  as  we  ascend  in  the  scale  of  living  things,  a  new 
phenomenon,  a  new  kind  of  unity,  that  which  we  term 
"  individuality,"  the  wealth  of  an  inner  self-conscious  life, 
to  which  the  older  school  of  biologists  attached  primary 
importance.  Life  accordingly  has  now  for  us  two  sides 
— first,  the  life  of  the  smallest,  the  most  primitive  unit 
of  living  matter,  say  the  cell,  the  amoeba,  or,  if  you  will, 
the  idioblast,  the  gemmule,  the  germ-plasma,  the  physio- 
logical unit.  Secondly,  the  life  of  the  complex  society  of 
cells,  the  higher  organism  in  which  the  inner  world  with 
all  its  mental  phenomena  has  become  manifest.  How- 
ls the  unity  of  this  higher  complex  possible  ?  In  what 
does  it  consist  ?  What  can  we  know  of  it  ?  Neither 
the  physiological  nor  the  psychological  unity  is  in- 
telligible to  us.  An  eminent  biologist,  to  whom  we 
owe  the  creation  of  an  entire  new  science,  the  late 
Professor  Virchow,  the  founder  of  Cellular  Pathology, 
has  told  us  recently  ^  that  only  since  biologists  have 
ceased  to  try  to  understand  the  unity  of  life  in  the 
higher  organisms,  the  psychological  unity,  and  have 
realised  the  fact  that  the  unity  of  life  is  in  the 
autonomous  cell,  has  biology  in  theory  and  practice 
made  much  progress.  Be  it  so.  It  seems  likely  that 
the  progress  of  biology  depends  entirely  on  the  culti- 
vation of  the  mechanical  view ;    but  from  another  and 

to  the  following  tracts  which  deal  I    0.     Biitschli,     '  Meehaiiismus     unci 

specially     with     the     problems     of  I    Vitalismus '  (Leipzig,  1901) ;  Eugen 

mechanism    and     vitalism.       Hans  Albrecht,  "  Vorfragen  der  Biologic  " 

Driesch,'Die  mathematisch-mechau-  (Wiesbaden,  1899). 

ische  Betrachtung  morphologischer  ^  In  the  Hu.\ley  Lecture  of  1898. 
Problenie  der  Biologie' (Jena,  1891) ; 


464  SCIENTIFIC    THOUGHT. 

equally  legitimate  aspect,  the  unity  of  the  complex  as 
the  bearer  of  all  the  phenomena  of  higher  or  inner  life 
is  equally  important.  In  many  ways  it  is  a  counter- 
part of  the  other,  showing  a  peculiar  continuity  of  its 
own,  that  continuity  which  I  have  made  the  special 
subject  of  this  work.  In  proportion  as  the  biological 
view  of  nature  has  become  the  science  of  the  cell, 
another  science  has  grown  up  which  sets  itself  to  study 
this  higher  phenomenon  of  living  matter,  the  pheno- 
menon of  mind,  directly  by  the  methods  of  the  exact 
58.        sciences.      This  is  the  modern  Science  of  Psycho-physics. 

Transition  i       •  p       i 

to  psycho-     Even  the  microscopist  and  biologist  of  the  most  modern 

physics. 

type  are  occasionally  startled  by  phenomena  akin  to 
those  which  commonly  are  only  visible  in  the  highest 
organisms.  Psychical  existence,  an  inner  side  to  the 
external  phenomena  of  motion,  has  accordingly  been 
attributed  by  eminent  representatives  of  the  mechanical 
view  of  biological  phenomena  to  the  lowest,  the  most 
primitive,  unit  of  living  matter.  Another  school  of 
science  has  set  itself  to  study  this  inner  side  of  liv- 
ing organisms  in  its  more  perfect,  as  it  were  full- 
grown,  manifestations,  and  by  appealing  in  addition  to 
the  facts  only  known  by  introspection  or  self-conscious- 
ness. With  the  history  of  this  movement,  so  far  as  it 
belongs  to  exact  science,  I  propose  to  deal  in  the  next 
chapter  under  the  general  title  of  the  Psycho-physical 
View  of  Nature. 


465 


CHAPTER   XI. 

ON    THE    PSYCHO-PHYSICAL    VIEW    OF    NATURE. 

In  the  three  foregoing  chapters  I  have  attempted  to  trace  Abstr^t 
the  development  of  the  different  aspects  under  which  our  sciences, 
knowledge  of  the  real  things  which  surround  us,  and  of 
nature  as  a  whole,  has  been  extended  in  recent  times.  I 
have  brought  these  different  aspects  which  respectively 
consider  things  natural  according  to  their  forms,  their 
genesis,  or  their  life  and  purpose,  under  the  general  name 
of  the  biological  as  distinguished  from  the  abstract  view, 
with  which  I  dealt  in  the  four  previous  chapters.  The 
abstract  view  tries  to  arrive  at  the  general  properties  of 
all  things,  which  it  has  succeeded  in  our  times  in  sum- 
ming up  under  the  great  generalisations  of  Attraction, 
Atomism,  Kinetics,  and  the  doctrine  of  Energy.  The 
biological  view  is  interested  not  so  much  in  general 
properties  as  in  real  specimens — the  things,  beings,  and 
phenomena  in  which  we  see  the  general  properties  ex- 
emplified and  become  real  and  in  their  actual  union  or 
totality  which  we  call  nature.  The  abstract  sciences 
started  on  their  modern  career  with  mathematics,  and 
progressed  through  the  dcvelopmont  and  application  ^f 
VOL.  TI.  2  G 


Their 


466  SCIENTIFIC    THOUGHT. 

the  mathematical  methods  to  the  data  furnished  by 
observation  and  experiment ;  the  biological  or  concrete 
sciences  began  with  a  study  of  living  things,  and  have 
progressed  immensely  in  our  times  by  viewing  these  not 
in  isolation,  but  in  their  relations  to  each  other  and  to 
the  surrounding  lifeless  world — the  so-called  environ- 
ment. An  exact  treatment,  that  to  which  the  term 
"  scientific "  has  been  pre-eminently  applied,  seems  here 
also  to  depend  largely,  if  not  exclusively,  on  the  degree 
to  which  the  mathematical  processes  of  numbering  and 
measuring  can  be  applied,  and  on  the  utilisation  of  the 
general  results  arrived  at  in  the  abstract  sciences. 
2.  The  method  of  the  abstract  sciences  is  that  of  building 

different       up  from  Small  beginnings,  by  the  process  of  summation 

methods. 

or  integration,  intricate  complexes  which  not  infrequently 
are  found  to  correspond  to  phenomena  of  actual  experi- 
ence. It  has  at  its  command  the  unlimited  resolving 
powers  of  the  calculus,  and  the  well-established  assump- 
tion that  things  natural  are  made  up  of  numberless 
particles  entering  into  innumerable  combinations.  The 
wdiole  is  thus  for  the  mathematical  view  the  sum  of  its 
parts.  The  concrete  or  natural  sciences,  on  the  other 
hand,  start  with  the  ready-made  things  or  creatures  of 
nature,  or  on  a  larger  scale  with  the  great  order  and 
economy  of  our  world  or  the  universe,  and  only  descend 
into  the  minutiiK  of  the  observatory,  the  dissecting-room, 
or  the  laboratory,  with  the  hope  of  better  understanding 
the  great  and  complicated  objects  of  their  study.  The 
greatest  progress  in  the  abstract  sciences  has  been  made 
by  those  minds  that  could  concentrate  their  atten- 
tion  on   special   points,    not    infrequently   expressed   in 


ON    THE    PSVCHU-PHYSICAI.    VIEW    OF    NATURE.       467 

iiuithematical  formulae,  and  expand  their  view  through 
applications  :  the  greatest  progress  in  the  natural  sciences 
has  been  made  by  those  who  started  with  a  large  and 
comprehensive  view  of  things  natural,  and  gradually 
descended  into  detail.  Newton,  Lagrange,  Fresnel,  and 
Helmholtz  are  good  examples  of  the  former ;  Humljoldt, 
von  Baer,  Claude  Bernard,  and  Darwin  of  the  latter. 

Now,  it  is  a  frequent  experience  that  in  the  study 
of  things  natural,  through  the  unavoidable  process  of 
dissection  and  analysis,  the  subsequent  synthesis  or  sum- 
ming up  has  not  carried  the  student  back  to  the  real 
thing  from  which  he  started,  but  to  some  artificial  pro- 
duct differing  essentially  from  the  natural  object.  The 
real  essence  of  the  thing  seemed  lost  when  its  parts  were 
examined  by  themselves  or  in  their  apparent  aggrega- 
tion. A  prominent  example  of  this  kind  is  to  be  found 
in  the  living  organism.  Theories  have  accordingly  been 
formulated  which  looked  upon  life  as  a  special  prin- 
ciple to  be  superadded  to  any  conceivable  aggregation  of 
mechanical  processes,  in  order  to  raise  them  from  the 
lifeless  into  the  living  order  of  things.  The  last  chapter 
dealt  with  the  various  biological  hypotheses,  of  which 
three  are  conspicuous :  the  purely  mechanical,  according 
to  which  the  living  organism  is  merely  a  very  compli- 
cated chemical  molecule ;  the  vitalistic,  which  establishes 
an  essential  difference  between  the  action  and  constitu- 
tion of  a  living  and  a  lifeless  unit  of  matter ;  and  an 
intermediate  view,  which  looks  upon  organisms  as  manu- 
factured machines  built  up  according  to  some  plan,  de- 
sign, or  idea,  the  nature  of  which  can  be  further  inquired 
into,  but  which  does   not  try  to    throw  any  additional 


468  SCIENTIFIC    THOUGHT. 

light  on  the  mechanism  itself,  the  working  of  which, 
like  that  of  a  clock,  can  be  described  on  purely  mechani- 
cal lines  and  without  reference  to  the  idea  which  preceded 
its  construction. 

According  to  many  prominent  naturalists,  the  evident 
design  and  purpose  which  characterise  so  many  pheno- 
mena of  living  matter  are  explained  on  purely  mechan- 
ical lines  by  the  inherent  or  forced  teleology  of  living 
things,  which  through  over-production  have  to  submit  to 
an  automatic  process  of  selection  or  survival.  To  others 
this  automatic  process  does  not  seem  to  suffice,  and 
they  assume  a  principle  of  progress  which  acts  in  a 
regulative  manner.  This  vitalistic  view  is  further  sup- 
ported by  taking  into  account  an  extensive  class  of 
phenomena  which  I  have,  so  far,  hardly  noticed — 
the  marvellous  properties  of  the  higher  creations  of 
the  animal  world  which  exhibit  the  phenomena  of 
3.         consciousness   or  of   an   inner   experience.      That   these 

Inner  ^ 

experience,  phenomena  belong  to  the  realm  of  natural  science  as 
much  as  any  other  properties  of  living  things  cannot 
nowadays  be  doubted.  The  division  into  natural  and 
mental  science  can  no  longer  be  upheld,  or  only  with 
a  very  different  meaning  from  that  which  it  had  for  a 
bygone  age. 

It  will  be  my  object  in  this  chapter  to  give  an  account 
of  the  various  and  changing  aspects  which  this  great 
phenomenon  of  an  inner  or  conscious  life  has  presented 
to  naturalists — i.e.,  to  those  who  have  approached  the 
phenomena  of  Mind  from  the  side  of  nature,  and  of  the 
different  lines  of  research  and  reasoning  along  which 
they  have  dealt  with  it.      I  shall  comprise  the  whole  of 


ON    THE    PSYCHO-PHYSICAL    VIEW    OF    NATURE.       4G9 

this  section  of  scientific  thought  under  the  general   term 
of    Psycho  -  physics.^       It   refers    to    the    borderland    or        -i. 
common  ground  where  physical  and  mental  or  psychical  phys'C'*- 
phenomena  meet  or  interact. 

Although  the  term  psycho-physics  is  quite  modern,  the 
idea  of  a  special  science  dealing  with  the  relations  of 
mind  and  body,  or  of  the  physical  and  mental  life  of  the 
human  organism,  has  been  promiiR'utly  before  the  scien- 
tific world  ever  since  Cabanis  published  his  celebrated 
'  Eapports  du  Physique  et  du  JNIoral  de  I'Homme,'  in 
which  the  well-known  passage  occurs  which  has  been 
frequently  repeated,  modified,  and  quoted  with  varying 
approval  or  reproach  : ^  "In  order  to  arrive  at  a  correct 


^  The  term  was  first  u.sed  V)y 
G.  T.  Fechner  in  the  well-known 
work  bearing  this  title,  of  which  I 
shall  have  more  to  say  in  the  course 
of  the  ciiapter.  This  work,  deal- 
ing mainly  with  a  certain  numerical 
relation,  narrowed  the  term  down 
to  a  special  investigation,  whereas 
the  larger  problem,  the  study  of 
the  interaction  of  mind  and  body 
by  the  methods  of  the  exact 
sciences,  was  variously  designated 
as  physiological  psychology,  mental 
physiology,  psycho  -  physiology  or 
physiology  of  the  soul.  As  there 
is  a  tendency  to  regard  physiology 
more  and  more  as  the  physics  of 
the  living  organism,  it  is  evident 
that  physics  is  the  larger  term  ;  and 
in  dealing  with  the  relations  of  the 
j)hysical  and  the  psychical  in  the 
widest  sense,  the  term  psycho- 
physics  seems  the  more  appropriate. 

-  '  (JEuvres  completes  '  de  Cabanis 
(1834),  vol.  iii.  p.  159.  The  simile 
ha-s  attained  a  sort  of  historical 
celebrity  through  tlie  drastic  ver- 
sion which  was  given  to  it  by  Karl 
Vogt  in  his  '  Physiologische  Briefe ' 
(1847),     p.     206,     where,     with    a 


distinct  intention  of  rousing  an 
tosthetic  disapproval,  he  compares 
the  function  of  the  brain  with  the 
secretion  of  bile  by  the  liver  and 
of  urine  by  the  kidnej's.  ThLs 
dictum,  which  he  repeated  in  his 
controversy  with  lludolf  Wagner, 
led  in  the  middle  of  the  century, 
as  Du  Bois-lleymond  tells  us,  to  a 
kind  of  systematic  championshii)  of 
the  soul,  the  comparison  with  the 
kidneys  Ijeing  looked  on  as  a 
degrading  offence.  "  Physiology, 
however,  has  no  knowledge  of  such 
grades  of  dignity.  As  a  scientific 
problem  the  secretion  of  the 
kidneys  is  to  her  of  the  same 
dignity  as  the  investigation  of  the 
eye  or  the  heart  or  any  other  so- 
called  noble  (jrgan."  Vogt  used 
the  simile  as  an  illustration  of  his 
purely  materialistic  view.  Lange 
('  Hist,  of  Materialism,'  vol.  ii. 
p.  242)  shows  that  with  Cabanis 
the  dictum  is  by  no  means  bound 
up  with  such  a  view,  as  he  really 
was  a  pantheist.  The  mistake, 
says  Du  Bois-Reymond,  does  not 
lie  in  the  compari.son,  but  in  the 
implied  suggestion,   that  psychical 


470 


SCIENTIFIC    THOUGHT. 


Cabanis's 
simile. 


idea  of  those  operations  from  which  thought  arises,  we 
must  consider  the  brain  as  a  particular  organ,  destined 
specially  to  produce  it  in  the  same  way  as  the  stomach 
and  the  intestines  are  there  to  perform  digestion,  the 
liver  to  filter  the  bile,  the  parotid,  maxillary,  and  sub- 
lingual glands  to  prepare  the  salivary  juice." 

The  argument  which  led  Cabanis  to  draw  this  parallel 
between  the  functions  of  the  brain  and  those  of  other 
organs  of  the  human  body  was  based  upon  the  philo- 
sophy of  Locke,  which  had  been  domiciled  in  France  by 
Condillac  and  Helvetius.  This  philosophy,  in  its  popular 
version,  taught  that  all  our  thoughts  and  ideas  were 
ultimately  made  up  of  sensations.-^      On  the  other  side. 


activity  could  be  "  explained 
through  the  structure  of  the  brain, 
as  secretion  can  be  explained  from 
the  structure  of  a  gland  "  ( '  Reden,' 
vol.  i.  p.  129). 

^  Cabanis  (1757-1808),  in  the  pre- 
face to  the  'Rapports,'  &c.,  p.  11, 
gives  a  list  of  contemporary  French 
writers  who,  following  in  the  line 
of  Locke,  to  whom  "  philosophy  is 
indebted  for  the  greatest  and  the 
most  useful  impulse,"  have  taken 
up  different  sides  of  the  doctrine. 
Of  their  writings  a  very  clear  and 
exhaustive  analysis  will  be  found 
in  M.  Picavet's  '  Les  Ideologues, 
Essai  sur  I'histoire  des  iddes  et 
des  theories  scieutifiques,  philoso- 
phiques,  religieuses,  kc,  en  France 
depuis  1789'  (Paris,  1891).  Ca- 
banis's own  position  is  very  clearly 
defined  (p.  16)  when  he  says  that 
"  Les  operations  de  I'intelligence  et 
de  la  volonte  se  trouveraient  cou- 
fondues  h,  leur  origine  avec  les 
autres  mouvements  vitaux  :  le  prin- 
cipe  des  sciences  morales,  et  par 
consequence  ces  sciences  elles- 
memes  rentreraient  dans  le  domaine 
de  la  physique  ;    elles  ne  seraient 


plus  qu'une  branche  de  I'histoire 
naturelle  de  I'homme  :  I'art  d'y 
verifier  les  observations,  d'y  tenter 
les  experiences,  et  d'en  tirer  tous  les 
resultats  certains  qu'elles  peuvent 
fournir,  ne  dillereraient  en  rien 
des  moyens  qui  sont  journelle- 
ment  employes  avec  la  plus  entiere 
et  la  plus  juste  confiance  dans  les 
sciences  pratiques  dont  la  certitude 
est  le  moins  contestee."  This  was 
written  in  1802.  M.  Picavet  says 
of  Cabanis  with  much  truth : 
"  Le  continuateur  d'Hippocrate,  de 
Descartes  et  des  philosophes  du 
XVIII™*'  siecle,  a  ^t^  un  precurseur 
de  Lewes  et  de  Preyer,  de  Schopen- 
hauer et  de  Hartmaiin,  comme  de 
Lamarck,  de  Darwin  et  de  bien 
d'autres  peuseurs  qui  appartien- 
nent  aux  ecoles  les  plus  diflerentes, 
et  ne  soupwnnent  quelquefois 
meme  pas  que  les  idees  dont  ils 
sont  partis  leurs  sont  venues  in- 
directement,  mais  par  des  inter- 
mediaires  authentiques,  de  I'auteur 
des  '  Rapports  du  physique  et  du 
moral'"  ('Les  Ideologues,'  p.  264). 
M.  Picavet  also  gives  valuable  ex- 
planations how  it  came  about  that 


ON    THE    PSYCHO-PHYSICAL    VIEW    OF    NATURE.      471 

the  physiologists  of  the  eighteenth  century,  notably 
Hallcr,  had  demonstrated  that  tlie  properties  of  the  prej|,ej,  ^ 
physical  organism  culminated  in  those  of  the  nervous  li^l'Jr.*"'* 
system — irritability  and  sensibility.  The  phenomenon 
of  sensibility,  of  producing  and  combining — as  it  were 
digesting — sensations,  was  thus  the  function  of  the  brain, 
or  the  central  organ  of  the  nervous  system,  as  other  pro- 
cesses were  the  functions  of  other  organs  or  physiological 
apparatus.  Cabanis  was  led  on  from  medical  ^  studies, 
as  Locke  had  been  before  him,  to  the  study  of  mental 
and  moral  subjects,  and  he  formed  the  conception  of  a 
science  of  Man,  or  Anthropology,"  divided  into  Physio- 
logy, the  Analysis  of  Ideas,  and  JNIorals,  which  would 
ultimately  be  of  as  much  use  for  the  practical  purposes 
of  education  and  government  as  the  exact  study  of  other 
natural  phenomena  then  cultivated  in  France  for  the 
purposes  of  medicine,  industry,  and  material  civilisation. 
Although  it  may  be  admitted  that  Cabanis  created^ 
physiological  psychology,  and  that  he  cast  far-reaching 
glances   into   the   neighbouring  departments    of    animal, 


the  line  of  philosophical  thought 
so  clearly  indicated  by  Cabanis 
was  uot  more  systematically  de- 
veloped in  France  at  the  time, 
and,  like  many  other  lines  of  re- 
.search  which  originated  in  that 
country,  had  to  be  re-discovered 
fifty  years  later  in  other  countries. 
The  question  is  important,  and 
may  occupy  us  later  on.  See, 
however,  regarding  the  disfavour 
into  which  the  "  moral "  sciences 
fell  owing  to  political  reasons,  vol. 
i.  p.  149  of  this  work. 

'  Cabanis  blames  in  Condillac  and 
Helvetius  that  they  knew  noth- 
ing of  physiology.      "  S'ils  eusseut 


mieux  connu  I'economie  animale, 
le  premier  aurait-il  pu  soutenir  le 
systeme  de  regalitc  des  esprits  ?  le 
.second  n'aurait-il  pas  senti  que 
I'ame,  telle  qu'il  I'euvisage,  est  une 
faculty,  mais  non  pas  un  otre;  et 
que,  si  c'est  un  etre,  h  ce  titre  elle 
ne  saurait  avoir  plusieurs  des 
qualitos  (ju'il  lui  attribue "  (ibid., 
p.   66). 

-  "  C'est  ce  que  les  .\llemands 
appellent  I'anthropologie ;  et  sous 
ce  titre  ils  comprennent  en  efifet 
les  trois  objets  principaux  dont 
nous  parlous"  (Cabanis,  '  CEuvres,' 
vol.  iii.  p.  40). 

■'  Picavet,  loc.  cit.,  p.  292. 


472  SCIENTIFIC   THOUGHT. 

embryological,  and  morbid  psychology,  from  which  he 
expected  much  assistance,  his  ideas  remained  vague,  as 
did  those  of  the  contemporary  school  of  the  "  Ideologues," 
among  whom  Destutt  de  Tracy  ^  deserves  honourable 
mention  as  having  conceived  the  plan  of  a  psychological 
treatment  of  grammar.  Their  merit  lay  more  in  drawing 
the  plans  of  the  new  science  of  psychology  as  a  natural 
science  in  its  largest  sense,  and  of  urging  its  scientific 
and  exact  treatment,  than  in  making  a  real  and  fruitful 
beginning  on  special  lines. 

It  is  a  remarkable  fact  that  the  first  attempt  to 
analyse  in  detail  one  of  the  special  instances  of  psycho- 
physical interaction  came  about  a  hundred  years  earlier 
from  that  successor  of  Locke  who  has  always  been 
counted  as  the  extreme  idealistic  development  of  English 
7.         speculation.     Bishop  Berkeley's  '  Essay  towards  a  New 

Berkeley's         -^  r  J  J 

I^Theoryof  Thcory  of  A^isiou '  (1709)  has  been  called  "the  verit- 
able historical  starting-point  of  psycho-physical  investi- 
gation." ^  Although  averse  to  any  exact  theory  of  the 
universe,  deeming  it  "  beneath  the  dignity  of  the  mind 
to   affect   exactness,"  ^  and  at  war  with   the   mathema- 

1  Picavet  (p.  398)  says  of  Destutt  I  ^  Dr  Edmund  Montgomery,  iu 
de  Tracy  (1754-1836):  "Venu  par  his  very  interesting  and  valuable 
les  sciences  a  la  philosopbie,  D.  critical  analysis  of  '  Space  and 
de  Tracy  a  donne  h  I'id^ologie  un  Touch,'  three  memoirs  contained 
nom  et  un  caractere  positif.  S'il  |  in  the  tenth  volume  of  the  first 
a  CTU,  ^  tort,  qu'il  pouvait  la  series  of  'Mind'  (1885),  p.  385. 
constituer   de    toutes    pieces,    il    a  •'  See  '  A  Treatise  concerning  the 

fort  bien  vu  que,  pour  devenir  Principles  of  Human  Knowledge,' 
une  science  independante  et  com-  §  109 :  "  As  in  reading  other 
plete,  elle  devait  s'appuyer  sur  la       books,  a  wise  man   will   choose   to 

fix  his  thoughts  on  the  sense  and 
apply  it  to  use,  rather  than  lay 
them  out  in  grammatical  remarks 
on  the  language  ;  so  in  perusing 
the  volume  of  nature  it  seems 
beneath  the  dignity  of  the  mind 
to   afifect   an   exactness    in    reduc- 


Vision.' 


physiologie  et  la  pathologie,  sur 
I'etude  des  enfants,  sur  celle  des 
fous  et  sur  celle  des  animaux.  II 
I'a  unie  intimement  h,  la  grammaire 
et  k  la  logique,  a  la  morale  et  k 
I'economie  politique,  a  la  legislation 
et  a  la  politique." 


ON    THE    PSYCHO-PHYSICAL    VIEW    OF    NATURE.       473 


ticians/  as  Hobbes  had  been  before  him,  IJerkeley  hud  a 
clear  conception  of  the  following  definite  prol)lem :  By 
what  succession  of  physical  and  mental  experiences,  by 
what  "  organic  and  vital  data,"  do  we  become  aware  of 
space  and  of  body  or  matter  ?  His  answer,  which  makes 
tactile  sensations  the  base,  has  been  advocated  and  quoted 
by  English  psychologists  of  the  Association  school  up  to 
the  present  day,  and  forms  the  text  for  their  various 
explanations. 

The  genesis  of  space  perception  was  much  discussed 
in  the  circle  of  Locke's  friends,  Molyneux  proposing 
the  celebrated  query ""  named  after  him,  and  Cheselden 
describing  at  length,  in  the  Philosophical  Transactions, 
the  experiences  of  an  adult  blind  patient  who  had 
received  his  sight  l)y  couching.  The  eighteenth  century 
brought  other  isolated  researches  of  an  experimental  or 
mathematical  nature,  which  may  be  regarded  as  the 
beginnings  of  an  exact  treatment  of  the  relation  of  psy- 


ing  each  particular  phenomenon  to 
general  rules,  or  showing  how  it 
follows  from  them.  We  should 
propose  to  ourselves  nobler  views, 
such  as  to  recreate  and  exalt 
the  mind,"  &c.  In  the  following 
paragraph  Berkelej-  refers  to  the 
'  Principia  '  as  "  the  best  gj-ammar 
of  the  kind  "  lie  was  speaking  of. 

'  A  very  full  account  of  this  con- 
troversy will  be  found  in  a  paper 
by  Prof.  Geo.  A.  Gibson  in  the 
'  Proceedings  of  the  Edin.  Math. 
Soc.,'  vol.  .xvii. 

-  The  query  is  given  in  Locke's 
•  Essay,'  Book  II.  ch.  ix.  §  8,  as 
follows  :  "  Suppose  a  man  born 
blind,  and  now  adult,  and  taught 
by  his  touch  to  distinguish  be- 
tween a  cube  and  a  spheie  of  the 
.-^ame  metiil  and  nighly  of  the  same 
bigness,  so  as  ty  tell  when  he  felt 


one  and  the  other,  which  is  the 
cube  and  which  the  sphere.  Sup- 
pose, then,  the  cube  and  sphere 
placed  on  a  table,  and  the  blind 
man  made  to  see  :  Query,  whether 
b}-  his  sight,  before  he  touched 
them,  he  could  now  distinguish, 
and  tell,  which  is  the  globe,  whicii 
is  the  cube  ?  To  which  the  acute 
and  judicious  proposer  answers, 
No."  For  a  full  analysis  of  actual 
cases,  such  as  that  of  Cheselden, 
and  more  recent  ones,  see  Wundt, 
'  Physiologisehe  Psychologic,'  vol. 
ii.  p.  233.  That  Berkeley  was, 
however,  neither  a  psycho-physicist 
nor  a  physioloerical  psychologist  in 
the  modern  sense,  is  well  remarked 
by  Campbell  Frascr  in  his  essay 
on  Berkeley  (Blackwood's  "  Philos. 
Classics,"  '  Berkeley,'  p.  45,  &c.) 


474  SCIENTIFIC    THOUGHT. 

chical  with  physical  phenomena.  Fechner,  the  founder 
of  psycho-physics  as  an  independent  doctrine,  refers 
notably  to  two  ^  such  instances.  They  were  contributed 
8.  by  two  great  mathematicians,  Daniel  Bernoulli  and 
and  Buier.  Leouhard  Euler.  The  former  pointed  out  that  the  value 
which  we  attach  morally  to  the  addition  to  any  material 
possession  is  not  measured  by  the  actual  magnitude  of 
such  addition,  but  by  the  relation  it  bears  to  that  which 
we  already  possess.  The  first  sovereign  earned  by  a 
poor  and  starving  labourer  has  an  almost  infinite  value 
compared  with  what  it  has  for  a  person  already  possessed 
of  a  million.  Laplace  and  Poisson  referred  to  this  state- 
ment of  Bernoulli,  and  introduced  the  terms  "  fortune 
physique,"  "  fortune  morale,"  showing  that  they  stand 
in  a  simple  mathematical  relation.  The  same  relation 
was  shown  by  Euler  to  exist  between  our  estimate 
of  musical  intervals  in  the  harmonic  scale  and  the 
difference  of  the  number  of  vibrations  of  the  strings 
which  produce  the  two  notes.  It  was  above  a  cen- 
tury before  Fechner  correlated  these  isolated  remarks 
with  observations  of  modern  psycho  -  physics  in  his 
celebrated  law,  of  which  more  anon. 

On  the  whole,  little  progress  was  made  during  the 
eighteenth  century  in  the  department  of  research  I  am 
now  dealing  with ;  but  the  end  of  the  eighteenth  and 
the  beginning  of  the  following  century  brought  several 
important  discoveries,  some  of  which  were  at  the  time 
much  over-estimated,  whilst  others  were  for  a  long  time 
forgotten  or  overlooked. 

The  first   is  the   accidental  discovery  by  Galvani  in- 

1  'Psychophysik,'  1860,  vol.  ii.  p.  548,  &c. 


ON    THE    PSYCHO-PHYSICAL    VIEW    OF    NATURE.       475 

1786,  followed,  fifteen  years   after,  by    Vulta's   greater        9. 
invention.      The   late  eminent  I'rof.  Du  Bois-Keymond,  "Electricity, 
in  various  passages  ^  of  liis  scientific  and  literary  writ- 


ings, has  told  us  of  the  recurrent  fascination  which  the 
fata  morgana  of  Electricity  has  exercised  over  those 
interested  in  the  explanation  of  the  phenomena  of 
innervation ;  how  this  seductive   clue  has   been,  in  the 


'  See  vol.  ii.  i)p.  212,  386,  528  of 
Du  Boi-s-Rej-moud's  'Redeu,'  also 
his    '  Untersuchungen    iiber    thier- 
ische    Electricitiit '    (1848),    vol.    i. 
pp.  30-128.      One  of   the  first  to 
take  up  in  the  interests  of  nervous 
physiology  the  clue  which  Galvani's 
discovery     afforded     \va.s    A.     vou 
Humboldt,  who  i)ublished  in   1797. 
three  yeai-s  before  Volta's  discover}', 
his    valuable    "  Versuche    iiber   die 
gereizte  Muskel-  uud  Nervenfaser, 
nebst     Vermuthungen     iiber    den 
chemischen     Process     des     Lebens 
in    der  Thier-   und    Pflanzenwelt." 
A    lucid    account    of     Humboldt's 
work  is  given  by   Prof.    Wundt  in 
the  third  volume   of   the  German 
edition  of  Bruhns'  '  Life  of  Hum- 
boldt,"  p.    301    sqq.      "It   is   diffi- 
cult,"   he    says,     '"'to     picture    to 
oneself   nowadays    the    excitement 
which  the  observations  of  Galvani 
produced   in    the    scientific    world. 
.   .   .   Such  experiments  had  almost 
become  a  general  subject  of  enter- 
tainment in  cultured  circles.  .   .    . 
It    almost    ajjpeared    as     if    what 
at  that  time   was   looked   upon  as 
the  most  general  projjerty  of  living 
matter,    irritability,    were    by    the 
experiment   of   Galvani   to   be   for 
the  fir.st   time  unveiled  in  its  real 
essence.  ...    At   the   time    when 
Humboldt    m.ide    his    experiments 
the    contest    was    still     going     on 
between   the    followers  of    Galvani 
and    Volta."      This   referred    to    a 
physiological     or    purely    physical 
explanation    of    the    phenomenon. 


"  Barely    three     years     after     the 
publication     of    Humboldt's    work 
the   discovery   of    Volta's   pile    put 
an    abrupt    end     to     all     theories 
which  were  based  upon  the  phys- 
iological  origin   of    galvanic  phen- 
omena.    The  brilliant  development 
of    physical    galvanism    from    tliat 
moment    pushed    the    j)hysiological 
aspect    of    electricity    for    a    long 
time     into     the     background.  ,  .   . 
Humboldt's  work    was    forgotten " 
(p.  310).     In  the  meantime  Hum- 
boldt had  travelled  in  South  Amer- 
ica,   where    he    had  —  inter   alia  — 
observed      the     "  natural     electro- 
motors   which    stand    in    such    ex- 
traordinary   connection    with    the 
nervous  .system"    of  the  electrical 
eel  {(Jymiwtus  clcclricus),  giving  a 
thrilling    description    of    a    battle 
between   the   horses   and  the   eels 
which   he  witnessed  in    the  waters 
of     Calabozo.        (See     Humboldt's 
'  Personal  Nai-rative,'  vol.  iv.  p.  345 
sqq. ;  also   '  Ansichten  der  Natur,' 
vol.  i.  p.  33.)    Interest  in  the  subject 
of  animal  electricity  was  again  re- 
vived by  Italian  pliysiologists  about 
the  year  1835.     Nobili,  Marianini, 
Santi  -  Luiari,    Matt6uoci    repeated 
and   enlarged   the   expeiiments    of 
Galvani,  and  througli  the  influence 
of  Humboldt  and  Johannes  Miiller, 
the    study    of    the    whole    subject 
was  com))rehensivelj'   taken  uji    at 
Berlin  by  Du  Bois-Reymond  about 
1840,  and  exhaustivelj''  treated   in 
his  great  work  on  the  subject  (vol, 
i.  1848,  vol.  ii.  1860). 


476  SCIENTIFIC    THOUGHT. 

course  of  more  than  a  centurj,  alternately  taken  up 
with  enthusiasm,  and  abandoned  as  misleading.  At  the 
turn  of  the  centuries  the  mania  for  animal  electricity 
was  at  its  height.  Men  like  A.  von  Humboldt  took  up 
the  study  with  eagerness,  and  sovereigns  like  Napoleon 
offered  special  prizes,  in  the  hope  that  here  at  last  the 
secret  of  life  and  consciousness  would  be  revealed.  The 
school  of  the  "  Naturphilosophie  "  in  Germany  seized 
upon  the  suggestion  of  polarity  and  polar  forces  con- 
tained in  the  phenomena  of  galvanic  action,  and,  sup- 
ported by  the  still  more  mystical  processes  of  the 
so-called  animal  magnetism  which  had  been  exhibited 
by  Mesmer  twenty  years  earlier,  worked  up  these 
vague  indications  into  fanciful  theories  of  vitalism  and 
animism.  This  brought  the  whole  line  of  thought 
into  discredit,  drove  away  the  soberer,  more  scientific 
students  of  nature,  and  retarded  real  progress  in  the 
knowledge  of  the  electric  phenomena  of  the  muscular 
and  nervous  system  for  fully  a  generation.  At  length 
in  the  school  of  Johannes  Mliller  the  subject  was  again 
approached  and  was  put  on  a  firm  scientific  basis  by 
Helmholtz,  and  notably  by  Du  Bois  -  Eeymond.  It 
is  now  known  that,  as  in  inorganic,  so  also  in  organic 
systems,  the  energy  proper  to  them  can  appear  under 
the  different  forms  of  mechanical,  thermal,  electric  or 
chemical  energy,  but  also  that  in  none  of  these  can  be 
found  pre-eminently  the  principle  of  life,  still  less  that 
of  consciousness. 
10.  Another  important  line   of   research    which   has  had 

an    equally    fluctuating    development,    being    sometimes 
enormously  exaggerated,  to   the  damage  of   sound   pro- 


ON    THE    PSYCHO-PHYSICAL    VIEW    OF    NATURE. 


477 


gress,  sometimes  repudiated  and  treated  with  whole- 
sale contempt,  was  that  started  by  (Jail,  who  from  the 
year  1805  onward,  and  latterly  in  conjunction  with 
Spurzheim,^  started  on  an  anatomical  description  of  the 
brain    as    the  centre    of    nervous   and    conscious  mental 


'  Tlie  two  most  prouiineut 
teaoliers  of  phrenoloj^y  were  Franz 
Joseph  Call  (1758-1828)  of  Pforz- 
heim, and  Joli.  Christ.  Spurzheiiu 
(1776-1834)  of  Trier,  the  former 
an  excellent  doctor,  the  latter  a 
.skilled  anatomist.  Their  influence 
was  centred  in  Vienna  and  Paris. 
In  England  and  America  phren- 
ology dates  its  pojjularity  from 
George  Combe  (1788-1858).  The 
terra  phrenology  was  suggested  by 
George  Fonster  about  1815,  ten 
years  after  Gall  had  started  his 
'  Schiidellehre '  or  '  Craniology.' 
Of  eminent  medical  authorities, 
the  great  Broussais  in  France  (1772- 
1838)  and  C.  G.  Carus  (1789-1869) 
in  Germany  were  both  phren- 
ologists, the  latter  attempting  to 
^ve  the  doctrine  a  more  scientific 
foundation.  Though  ijhrciiology 
was  never  popular  in  l"'rance,  where 
the  Academy  of  Sciences  from  the 
beginning  assumed  a  very  sceptical 
attitude  (see  above,  vol.  i.  p.  136 
note),  the  opponents  of  Gall  have 
always  given  him  full  credit  for 
his  ability,  and  for  the  great  im- 
pulse he  gave  to  anatomical  science 
of  the  brain.  Flourens,  one  of  the 
most  formidable  critics  of  the  doc- 
trine of  the  special  faculties,  and 
consequently  of  the  separate  phren- 
ological organs  and  their  location, 
nevertlielcss  says:  "Gall  fut  un 
observateur  profond,  qui  nous  a 
ouvert,  avec  g^nie,  I'dtude  de 
I'anatomie  et  de  la  {)hysiologie  du 
cerveau.  .  .  .  Je  n'oublierai  jamais 
I'impression  que  j'eprouvai  la 
premiere  fois  que  je  vis  Gall  dissd- 
(juer  un  cerveau  ;  il  me  semblait 
que  je  n'avais  pas  encore  vu  cct  or- 


gane  "  (quot.  by  Langlois,  'Grande 
Encyclop.,'  vol.  xxvi.  j).  801).   Some- 
what earlier  than  phrenology    the 
science    or    art    of    phj-siognomics, 
which     was     known     already     and 
practised    by    the    ancients,    had    a 
representative    in    Caspar    Lavater 
of  Ziirich,  who,  from  1772  onward, 
published     his     '  Physiognoiaische 
Fragiuente,'  a  work  which,  accom- 
panied   by    engravings    by    Chodo- 
wiecki,   created   a  great    sensation 
in  philosophical,  literarj*,  and  artis- 
tic  circles,    the    whole    of    Europe 
being  divided    into    followers   and 
critics    uf    Lavater.       Among    the 
latter    was    the    celebrated     Lich- 
tenberg     of     Gottingen.       Among 
scientific    men    were    Camper    in 
Holland,  and  later  Charles  Bell   in 
England  ;  the  former  putting  for- 
ward   the    well  -  known    theory    of 
the   "facial   angle"   as  an  external 
measure  of  intelligence,  the  latter 
publishing  his  '  Essay  on  the  Ana- 
tomy   of   Expression'    (1806).      In 
more     recent     times     no     less     an 
authority     than     Charles     Darwin 
took   up   the   subject    in    his    work 
on    the   '  Expression    of   Emotions ' 
(1872).     Shortly  before  Ph.  Piderit 
published    his     '  Wissenschaftliches 
System    der    Mimik    und    Physiog- 
nomik  '  (1867)  ;  Duchesne  (lSb'2)  his 
'  Mecanisme  de  la  physionoinie  hu- 
maine  '  ;  and  more  recently  the  Ital- 
ian   Mantegazza    his    '  Physionomie 
et      I'expression    dcs     sentiments' 
(French    transl.,    1885).       A    very 
readable  essay  on  the  subject  will 
be    found    among    Prof.     Wundt's 
'Essays'      (1885).       See    also    his 
'  Physiologische  P.sychologie  '    (vol. 
ii.  p.  .598,  &c.,  4tli  ed.) 


478  SCIENTIFIC    THOUGHT. 

action.  The  scholastic  notion  of  the  older  psychol- 
ogists which  divided  the  mental  life  into  different  powers 
or  faculties  as  the  body  was  dissected  into  parts  and 
organs,  lent  itself  to  the  idea  of  a  localisation  of  these 
faculties  or  powers  in  different  spheres  of  the  brain, 
which  Gall  by  a  hasty  generalisation  maintained  to  be 
distinguishable  on  the  external  surface  of  the  skull. 
Though  these  popular  and  practical  applications,  which 
form  the  basis  of  phrenology,  were  speedily  and  easily 
refuted,  having  always  been  regarded  with  suspicion  by 
the  medical  profession,  the  anatomical  labours  of  Gall 
were  taken  up  and  continued  by  others.  Opinions 
fluctuated  between  the  different  views  of  Flourens,  who 
insisted  upon  the  unity  of  the  central  organ,  as  did 
Herbart  in  psychology  on  the  unity  of  the  mind ;  of 
G.  H.  Lewes,  who  assigns  to  the  spinal  cord  together 
with  the  brain  an  important  and  initiatory  role  in 
conscious  life ;  and  of  Hermann  Munk  and  Friedrich 
Goltz,  who  by  carefully  devised  experiments  on  living 
animals,  by  electrical  irritation,  and  by  systematic  re- 
moval of  parts  of  the  brain,  have  to  some  extent  suc- 
ceeded in  delimiting  the  special  "  spheres  in  which  the 
various  sensory  nerves  deliver  their  messages,  and  where 
the  latter  are  transformed  into  conceptions  and  mentally 
stored."  -^  Paul  Broca  had  already,  about  forty  years 
ago,  succeeded  in  localising  the  powers  of  speech. 


^  Du  Bois-Reymond,  '  Reden,'  vol. 
ii.  p.  558 :  "  Thougli  there  is,  in  prin- 
ciple, no  hoije  that  the  causal 
connection  between  material  pro- 
cesses in  the  brain  and  consciousness 
will  ever  become  clear  to  us,  this 
does  not  hinder  our  penetrating 
deeply  into   a  knowledge  of  those 


processes,  or  prevent  such  know- 
ledge being  of  the  greatest  import- 
ance and  of  fascinating  interest.  As 
a  first  step  in  this  direction  there 
presents  itself  naturally  to  our 
understanding  the  localisation  of 
the  different  faculties  into  which 
we    naturally    and    systematically 


ON    THE    PSYCHO-PHYSICAL    VIEW    OF    NATURE.       479 

Whilst  animal  electricity  and  the  examination  of  the 
brain  were  taken  np  with  ardour,  over-valued  by  popular- 
isers,  and  developed  into  fanciful  theories  which  postponed 
for  a  long  time  the  sober  inquiries  of  science,  another  very 
fruitful  vein  of  reasoning  and  research  was  struck  early 
in  the  century,  but  left  unexplored  for  fifty  years.  Since 
then  it  has  been  followed  with  success  and  profit. 


divide  nientiil  activity.  Out  of 
the  desire  for  such  localisation 
there  sprang  up  the  fundamental 
idea  of  the  phrenological  follies ; 
but,  as  so  often,  here  also  scien- 
titic  superstition  contained  a  kernel 
of  truth.  In  the  same  cortex 
of  the  brain  in  which  Gall  and 
Spurzheim  located  their  badly- 
chosen  thirty-five  mental  faculties, 
Munk  now  describes  the  spheres  in 
■wliich  the  various  sensory  nerves 
deliver  their  messages,  and  where 
the  latter  are  transformed  into  con- 
ceptions and  stored.  Thus,  for  the 
first  time  in  the  domain  of  sensa- 
tion and  intellection,  a  local  basis 
of  mental  activity  has  been  demon- 
strated, as  had  been  done  before 
by  Paul  Broca  in  the  domain  of 
volition,  in  the  localisation  of  the 
faculty  of  speech."  Most  modern 
jisycho-physicists  would  probably 
accept  this  statement  with  slight 
modifications ;  it  is  therefoie  well 
to  note  that  one  of  the  foremost 
and  most  original  workers  in  this 
field  of  research,  Prof.  Fr.  Goltz, 
takes  a  different  view  of  the  result 
of  the  experiments  of  himself  and 
others.  He  does  not  consider 
Munk's  teachings  as  the  foundation 
of  a  physiology  of  the  brain,  but 
looks  upon  them  as  a  system  of 
error,  and  "  hopes  to  see  the  day 
when  all  the  beautifully  elaborated 
modern  hypotheses  of  circumscribed 
centres  of  the  cortex  will  be  laid  in 
the  same  grave  in  which  Gall's 
phrenology    rests"    (quoted    from 


Goltz's  memoirs,  '  Uber  die  Verrich- 
tungen  des  Grosshirns,'  in  Pfliiger's 
Archiv,  bj'  Carl  Hauptmann,  '  Die 
Metaphysik  in  der  modernen  Bio- 
logie'  (1804),  p.  2-10).  Prof.  Fer- 
rier,  whose  '  Functions  of  the 
Brain'  (2nd  ed.)  is  a  standaid 
work  in  the  English  language,  takes 
up  a  less  negative  position  ;  yet  he 
says  (p.  23) :  "  We  are  still  on  the 
threshold  of  the  inquiry,  and  it 
may  be  questioned  whether  the 
time  has  even  yet  arrived  for  an 
attempt  to  explain  the  mechanism 
of  the  brain  and  its  functions.  To 
thoughtful  minds  the  time  may 
seem  as  far  off  as  ever."  Prof. 
William  James  of  Harvard,  in  his 
excellent  'Principles  of  Psychology' 
(2  vols.,  1891),  gives,  in  his  first 
chapter,  a  succinct  account  of  the 
"  localisation-question,"  which,  he 
thinks,  "  stands  firm  in  its  main  out- 
line "  (vol.  i.  p.  162).  The  standard 
work  in  tlie  German  language  is 
Prof.  Wundt's  '  Physiologische 
P.sychologie '  (2  vols.,  4th  ed., 
1893),  which  gives  in  the  first  divi- 
sion (chaps.  4,  5)  a  very  exhaustive 
account  of  the  experimental  and 
theoretical  work  on  localisation. 
Prof.  Wundt  himself  takes  up  a 
position  lying  between  the  doctrine 
of  sharp  delimitation  and  that  of  a 
denial  of  local  distinctions  (vol.  i.  p. 
159),  but  admits  that  the  whole 
question  is  still  highly  contro- 
versial, though  latterly  the  appar- 
ent diH'erences  of  opinion  have  been 
nuicii  toned  down  (vol.  i.  p.  240). 


480 


SCIENTIFIC    THOUGHT. 


11. 

Dr  Young's 

colour 

theory. 


The  beginnings  of  this  line  of  reasoning  are  to  be 
found  in  the  writings  of  Thomas  Young,  who  here,  as 
in  several  other  directions,  "  marched  far  in  advance  of 
his  age."  ^  During  the  last  decade  of  the  eighteenth 
century  Young  had  been  occupied  with  the  study  of 
the  phenomena  of  Light  and  Colours ;  and,  being  a 
student  of  medicine,  he  had  given  equal  attention  to 
the  physical  phenomena  and  the  physiological  sensations 
of  Light,  going  back  to  the  beginnings  laid  in  Newton's 
writings  on  these  two  important  branches  of  Optics."^ 
I  have  treated  of  his  epoch-making  discoveries  in 
physical  optics  in  an  earlier  chapter.  As  to  the  physi- 
ological problem  of  colour  sensations,  he  likewise  reviewed 
Newton's  work,  and  especially  took  up  the  remarkable 
fact  noted  by  Newton,  that  it  appears  possible  to  refer 
the  great  variety  of  colour  sensations  to  three  primary 
elements,  out  of  which  the  whole  wealth  of  the  colour 
scale — varying  in  intensity,  tint,  and  saturation — can 
be  made  up.      In  two  distinct  points  he  made  a  definite 


^  Note,  in  many  passages  of 
Helmholtz's  '  Physiologisohe  Optik  ' 
(2ud  ed.,  Braunschweig,  1896),  and 
his  often -quoted  '  Vortriige  und 
Reden,'  the  high  esteem  in  which 
he  held  the  work  of  Young. 

^  A  very  succinct  and  exhaust- 
ive account  of  how  Young  arrived 
at  his  colour  theorj'  is  given  in 
a  paper  by  A.  M.  5layer,  of  New 
Jersej',  in  the  '  Phil.  Magazine '  for 
1876  (5th  series,  vol.  i.  p.  111). 
Young  first  selected  red,  yellow,  and 
blue  as  the  three  simple  colour- 
sensations,  but  later  modified  his 
view  in  consequence  of  the  experi- 
ments of  Wollaston  between  the 
years  1802  and  1807.  How  little 
Young's  theory  was  thought  of  maj^ 
be  seen  from  the  words  of   Helni- 


holtz,  quoted  by  Mayer  (p.  114)  : 
"  The  theory  of  colour,  with  all 
these  marvellous  and  complicated 
relations,  was  a  riddle  which 
Goethe  in  vain  attempted  to  solve  ; 
nor  were  we  physicists  and  physiol- 
ogists more  successful.  I  include 
myself  in  the  number  ;  for  I  long 
toiled  at  the  task  without  getting 
any  nearer  mj'  object,  until  at  last 
I  found  that  a  wonderfully  simple 
solution  had  been  discovered  at  the 
beginning  of  this  century,  and  had 
been  in  print  ever  since  for  any  one 
to  read  who  chose.  This  solution 
was  found  out  and  published  by 
the  same  Thomas  Young  who  first 
showed  the  riglit  method  of  arriving 
at  the  interpretation  of  Egj'ptian 
hieroglyphics." 


ON    THE    PSYCHO-PHYSICAL    VIEW    OF    NATURE.       481 

advance  upon  Xewton.  For  the  three  primary  colours 
of  the  older  opticians  he  substituted  red,  <^reen,  and 
violet ;  and  for  the  remarkable  fact  that  the  simple 
colours  of  the  rainbow  can  be  compounded  out  of  these 
three,  he  suggested  a  physiological  reason — viz.,  that  the 
eye  possesses  three  distinct  colour -sensations  or  three 
distinct  senses  in  relation  to  light,  dependent  upon  some 
peculiarity  of  nervous  structure  or  function.  Young 
did  not  elaborate  his  ideas,  Ijut  it  is  clear  lliat  in  llic 
short  passages  in  his  '  Lectures  on  Natural  riiilusuphy' 
and  earlier  papers,  there  were  contained  a  ^•ariety  of 
definite  problems  and  hints  which  were  destined  to 
lead   research   for  a  long  time  after. 

The   next  great  stei)  in  advance,  which   has  revolu-        12. 

°  ^  Charles  Bell. 

tionised  and  permanently  fixed  our  ideas  on  the  action 
of  the  nervous  system,  was  taken  about  the  year  1810 
by  Charles  15ell,  who  discovered  the  anatomical  difference 
between  the  anterior  and  posterior  roots  of  the  nerves 
of  the  spine,  and  also  went  a  long  way  towards  show- 
ing their  different  functions.  The  point  as  regards 
functions  was  established  by  means  of  experiments  on 
living  animals  by  Magendie,  and  independently  Ijy 
Johannes  Miiller.^  Upon  the  comljined  labours  of  these 
three  masters  of  anatomy  and  experimental  physiology 
is  based  the  distinction  between  sensory  and  motor 
nerves — namely,  that  the  anterior  nerves  of  the  s[)ine 
are  employed  to  carry  the  nervous  stimulus  outward 
to  the  different  organs  (efferent  or  motor  nerves),  the 
posterior  and  better  protected   nerves  serving  to  carry 

'  Ou  the  respective  merits  of  Claude  Bernard  aud  Du  Bois-Rey- 
Charles  Bell,  Magendie,  and  Jo-  nioiul,  referred  to  supra,  p.  384  of 
hannes  Miiller,  see  tlie  writings  of      this  volume. 

VOL.  II.  2   U 


482 


SCIENTIFIC    THOUGHT. 


13. 

Jliiller's 
"  specific 
energies." 


the    peripheral    stimuli    of    the    senses    inward    to    the 
nervous  centres  (sensory  or  afferent  nerves). 

About  the  same  time  Johannes  Miiller,  under  the 
influence  of  Goethe's  observations  on  the  subjective 
colour -sensations  and  of  Kant's  doctrine  of  the  innate 
forms  of  perception/  introduced  another  important  dis- 
tinction into  the  theory  of  the  action  of  the  sensory 
nervous  apparatus.  This  doctrine  is  known  by  the 
name  of  the  "  specific  energies."  It  has  for  a  long  time 
governed  all  physiological  reasoning  on  the  subject  of 
our  sense  perceptions.  In  the  words  of  Helmholtz,  who 
more  than  any  other  has  lent  the  great  weight  of  his 
authority  to  an  elucidation  of  this  theory,  "  physiological 
experience  has  found  that  by  the  stimulus  of  any  single 
sensible   nerve -fibre,  only  such  sensations   can  be   pro- 


^  The  doctrine  of  the  "  specific 
energies  "  of  the  sensory  nerves,  one 
of  Joh.  Miiller's  earliest  speculations, 
which  has  governed  a  large  section 
of  psycho  -  phj'sical  research,  at 
least  in  Germany,  has  gi-own  out  of 
the  philosophical  discussions  in  the 
'  Kritik  der  reinen  Vernunft,'  and 
the  assthetic  treatment  in  Goethe's 
'  Farbenlehre,'  both  of  which  deal 
with  the  subjective  element  in  our 
sense-perceptions.  In  this  regard 
the  reform  of  physiology  in  Germany 
contrasts  with  the  contemporaneous 
reform  by  Mageudie  in  France, 
whose  extreme  experimentalism 
Miiller  even  ridiculed.  See  on  the 
historical  origin  of  Midler's  psycho- 
physics,  Du  Bois-Reymond's  excel- 
lent "Elogeof  MuUer"  ('Reden,'  vol. 
ii.  p.  159),  also  Helmholtz's  lecture  on 
"  Goethe's  Naturwissenschaftliche 
Arbeiten"  ('Vortrlige  und  Reden,' 
vol.  i.  No.  1,  1853),  and  his  address 
i)efoi-e  the  Goethe  Society  in  1892. 
Helmholtz   finds   the   cause   which 


misled  Goethe  in  his  optical  exi^eri- 
ments  to  be  the  same  which  misled 
Brewster — viz.,  the  difficulty  of  ob- 
taining really  pure  homogeneous 
light  of  any  special  tint.  He  woi-ked 
with  impure  light  and  dull  media. 
Helmholtz  experienced  great  diffi- 
culties in  obtaining  the  neces- 
sary purity  in  his  own  labours. 
Goethe,  however,  was  not  alone  in 
studying  with  predilection  the  sub- 
jective colour-sensations.  Du  Bois- 
Reymoud  mentions  Erasmus  and 
Robert  W.  Darwin  in  England,  and 
Purkinje  in  Germany,  as  working 
in  the  same  field  (loc.  cit.,  p.  160). 
Miiller's  work  is  contained  princip- 
ally in  the  treatise,  '  Zur  vergleich- 
enden  Physiologie  des  Gesicht- 
sinnes  des  Menschen  und  der  Thiere 
nebst  einem  Yersuche  liber  die 
Bewegungen  der  Augeu  und  iiber 
den  menschlicheu  Blick'  (1826),  and 
in  his  larger  work  on  Physiology. 
See  also  on  Goethe's  merits  Helm- 
holtz, '  Physiologische  Optik,'  p.  249. 


ON    THE    PSYCIIU-I'IIY.SICAL    VIKW    OF    NATURE.       483 

(lucecl  as  belong  to  the  (qualitative — or  order — region  of 
one  definite  sense,  and  that  every  stimulus  which  can  at 
all  atlect  this  nerve  fibre  produces  only  sensations  be- 
longing to  this  tletinite  order."  ^  This  means  that,  for 
instance,  any  effective  stimulus  of  the  optic  nerve 
apparatus  produces  only  and  always  the  sensation  of 
light,  whereas  the  same  stimulus  would  in  the  auditory 
nerve  apparatus,  if  effective,  produce  the  sensation  of 
sound.  "  The  same  vibrations  of  the  ether  wdiich  the 
eye  perceives  as  light,  the  nerves  of  the  skin  perceive  as 
heat.  The  same  vil^rations  of  air  which  the  latter  per- 
ceive as  a  tremor,  the  ear  perceives  as  a  musical  sound." " 
The  (j^uality  of  our  sensations  does  not  depend  on  the 
stimulus  but  on  the  ner\ous  apparatus. 

Helmholtz  has  said  ^  that  the  law  of  the  specific 
energies  forms  the  most  important  advance  which  the 
physiology  of  tlie  senses  has  made  in  recent  times,  and 
has  even  compared  it  with  the  discovery  of  the  law  of 
gravitation.'*     As  we  shall  see  immediately,  he  has  him- 

^  See  Helmholtz,  '  Handbucli  der  uiucli  limited  to  Germany,  and  there 

Physiologischen   Optik,'  2te   Aufl. ,  ,    also  almost  entirely  to  what  may 

1896,  p.  '2:313.  '    be  called  ]\Iiiller's  school,  in  which 

-  Helmholtz,  '  Vortriige  und  Re-  Helmholtz  is  the  central  figure.    In 

den,'  vol.  ii.  p.  224  ;  al^;o  '  Physiolo-  England  tiie  doctiine  was  subjected 

gische  Optik,'  p.  249  :  "  Miiller's  law  to  a  full  ciiticism  l>y  George  Henry 

of  the   specific   energies  marks  an  I    Lewes,  an  important  thinker,  whose 

advance  of  the  greatest  importance,  writings  contain  many  original  views, 

for  the  entire  doctrine  of  tlie  sense-  which  have  in  some  instances  since 

perceptions    has    since   become  the  been  inde])endently  put  forward  by 

scientific  foundation  of  this  doctrine,  other  authorities.     See  his  '  Physi- 

and  is,  in  a  certain  sense,  the  em-  ology  of  Common  Life "  (ISGO.chap. 

jjirical  e.xposition  of  the  theoretical  i    8)  ;  '  Problems  of  Life  and  Mind  ' 

discussion  of  Kant  on  the  nature  I    (vol.  i.  p.  135,  1874)  ;  '  Revue  Philo- 

of  the  intellectual  process   of  the  sophique'    (Paris,    1870,    No.    2); 

human  mind."     Of.  also  p.  584.  '  The  Physical  Basis  of  Mind'  (1877, 

•'  '  Vortriige  und  Reden,' vol.  i.  p.  j).  184).   Without  knowing  of  Lewes's 

;j78  ;  vol.  ii.  p.  181.  ^   criticisms,  Prof.  Wundt  was  led  to 

^  This  excessive  appreciation   of  j    a  criticism    of    the    doctrine   from 

^Midler's  theory  is,  however,    very  |    the  physiological  side  in  the  first 


484 


SCIENTIFIC    THOUGHT. 


self  made  a  very  important  application  of  it,  by  bringing 
it  into  connection  with  Young's  colour  theory.  But 
before  I  refer  to  this,  it  will  be  well  to  note  the  different 
lines  of  research  which  were  opened  out  by  Mliller's 
formula,  and  how  tliey  have  led  in  many  ways  to  very 
fruitful  expansion  of  natural  knowledge.  In  this  respect 
it  is  indeed  permissible  to  compare  Mliller's  formula  with 
that  of  gravitation,  which,  as  we  saw  above,  through 
the  different  ideas  which  it  introduced,  helped  to  guide 
research  for  fully  a  century.  Miiller  in  the  original 
statement  of  his  views  had  made  use  of  the  term  "  specific 
energy,"  and  had  applied  this  term  to  the  process  or 
sense  of  sight :  he  spoke  of  the  seeing  substance  or 
apparatus  of  sight.  Now  this  apparatus  is  a  complicated 
one,  consisting  mainly  of  three  parts — the  external  or 


edition  of  his  great  work  on  Physi- 
ological Psychology  in  1872.  See 
the  note  on  p.  332,  vol.  i.,  of  the 
4th  German  edition  (1893).  Wundt 
says  (p.  331):  "Historically,  the 
doctrine  ...  is  to  be  traced  to  the 
fact  that  the  philosophical  founda- 
tion of  modern  science,  and  especi- 
ally of  the  science  of  sensation,  rests 
on  Kant.  In  fact,  that  doctrine 
is  nothing  else  than  a  physiological 
reflexion  of  Kants  attempt  to  find 
the  conditions  of  knowledge  which 
are  given  a  priori,  or,  what  was 
mostly  considered  to  be  the  same, 
subjectively.  This  is  very  evident 
in  the  case  of  the  foremost  repre- 
sentative of  that  doctrine — viz., 
Johannes  Miiller."  In  opposition  to 
Miiller  and  his  school,  Lewes  and 
Wundt  put  forward  a  view  which 
has  been  termed  the  doctrine  of 
indifference  of  the  function  of  the 
nervous  elements.  The  difference 
between  the  two  views  is  very  clearly 
stated  in  an  excellent  paper  bj'  E. 


Montgomerj'  in  the  fifth  volume  of 
'Mind'  (1880):  "  According  to  the 
doctrine  of  functional  indifference, 
the  various  equalities — i.e.,  our  well- 
known  sensations — are  merely  due 
to  differences  in  the  stimulating 
rhythm,  to  differences,  therefore,  of 
motion  communicated  from  outside 
to  the  chemically  uniform  nerve - 
substance,  and  the  whole  complex 
make-up  of  our  consciousness  is, 
consequentlj',  thought  to  result 
from  the  coexistence  and  subse- 
quent combination  of  such  stim- 
ulated motions.  According  to  the 
doctrine  of  specific  energies,  the 
varieties  of  sensation  are  due  to  pre- 
existing differences  in  the  sub- 
stratum in  which  they  respectively 
arise,  and  all  their  manifold  combin- 
ations to  higher  products  are  be- 
lieved to  be  realised  in  materially 
higher  —  i.e.,  specifically  pre  -  en- 
dowed —  ranges  of  nervous  sub- 
stratum "  (p.   4). 


ON    THE    PSYCHO-PHYSICAL   VIEW    OF    NATURE.      485 

terminal  organ,  the  connecting  tibrc  or  nerve,  and  the 
central  or  percipient  organ  situated  somewhere  in  the 
brain.  How  are  these  different  parts  of  the  combined 
apparatus  anatomically  constituted,  and  what  are  their 
respective  physiological  functions — in  particular,  where 
does  the  specific  energy  reside  ?  The  answer  to  these 
c^uestions  as  regards  not  only  the  process  of  seeing,  but 
likewise  that  going  on  in  other  sense  organs,  involved 
an  enormous  amount  of  detailed  anatomical  and  physio- 
logical, analysing  and  experimenting  work.  With  this 
work  many  great  names  are  connected — first  of  all, 
Helmholtz,  who  in  liis  two  great  treatises  on  'Physio-        14. 

'  ^  "      _      Helmholtz. 

logical  Optics '  and  '  Thysiological  Acoustics,'  ^  has  laid 
the  foundation  of  those  two  psycho -physical  sciences 
which  bring  us  nearest  to  an  understanding  of  the  inter- 
action of  mind  and  body.  Like  Young  before  him,  for 
whom  he  expresses  the  greatest  admiration,  Helmholtz 
had  approached  the  study  of  nature  from  the  side  of 
medicine :  from  this  he  was,  l)y  the  peculiarity  of  his 
genius,  driven  to  mathematicu- physical  studies  on  the 
one  side,  to  psychological  on  the  other.  The  exact 
methods  of  the  mathematical,  the  experimental  methods 
of  the  medical  sciences ;  the  mental  analysis  of  Kant 
and  Fichte,  as  well  as  the  logical  methods  of  J.  S. 
Mill,  were  equally  familiar  to  him.  Inventions  of  his 
own,   like    that   of    the   eye -mirror,    or   of    others,   like 

^  '  iJic    Lchre   voii  den    Toneniii-  iiriucij>al   contents    of     tliose     two 

tindungen  ;    Physiologische  Urund-  great  treatises,  by  an  authority  in 

lage    fur   die   Theorie   der    Alusik,'  the  same  domain  of  science,  will  be 

1st    ed.,     1863.       '  Handbuch    der  '    found  in  chaps,   x.   to  xii.  of  Prof, 

yjhysiologischen    Optiii,'  18(57,    2nd  j   J.  G.  M'Kemhick's  volume  in  the 

ed.,    much    enlarged.       A    succinct  "  Mastei-s  of   Medicine"   Series    on 

and   very    lucid    exposition    of    tiic  H.  von  Helmlioltz,  1899. 


486  SCIENTIFIC   THOUGHT. 

the  stereoscope  of  Wlieatstone ;  pathological  cases,  like 
those  of  colour-blindness ;  a  host  of  ingeniously  de- 
vised experiments,  as  well  as  the  gift  of  an  exception- 
ally musical  ear, — all  these  factors,  and  innumerable 
others,  contributed  to  the  production  of  these  two 
monumental  works,  which  form  an  epoch  in  the  history 
of  science  as  well  as  of  philosophy  and  psychology. 
They  form  the  first  magnificent  examples  of  the  com- 
prehensive application  of  exact  methods  to  phenomena 
which  had  before  been  treated  only  fragmentarily,  and 
where  the  infiuences  of  taste,  fancy,  and  belief,  the 
vagueness  of  metaphysics  and  the  diificulties  of  nomen- 
clature, had  created  a  confusion  which  to  many  must 
have  appeared  hopeless.  This  confusion  of  language 
and  of  terms,  of  objective  observations  and  subjective 
fancies,  of  the  data  of  experience  and  the  prejudices  of 
theory,  Helmholtz  has  done  more  than  any  other  thinker 
to  unravel. 

In  his  two  great  treatises  on  the  psycho-physics  of  the 
Eye  and  the  Ear,  of  Vision  and  of  Music,  he  has  drawn 
two  elaborate  and  detailed  charts,  which  for  a  long  time 
to  come  will  have  to  be  consulted  by  those  who,  in  the 
interests  of  physics,  philosophy,  or  cesthetics,  enter  into 
these  mysterious  domains.  Many  celebrated  theories  or 
definite  aspects  and  lines  of  reasoning  invented  by  others, 
his  forerunners  or  contemporaries,  were  adopted,  but 
mostly  with  important  modifications.  It  may  be  of  use 
to  enumerate  briefly  the  principal  ones,  beginning  with 
the  most  mathematical  and  exact  and  ending  with  the 
more  general  and  metaphysical.  In  the  beginning  of  the 
century  Fourier  had  shown  how  any  forces  of  motion  in 


ON    THE    PSYCHO-PHYSICAL    YIE^Y    OF    NATURE.       487 

two  dimensions — however  coniplieuted  or  irregular  that 
motion  might  appear  to  be — could  be  mathematically 
represented  or  calculated  by  the  superposition  or  addition 
of  a  larger  or  smaller  number  of  simple  periodic  motions ; 
as  it  were  analysed  and  dissected  into  these  simple  move- 
ments, just  as  any  number  can  be  looked  upon  as  made 
up  by  the  addition  of  others — say  of  prime  numbers. 
Now,  it  was  also  known  that  sounds  were  produced  by 
wave-like  tremors  of  the  air  set  going  by  the  vibrations 
of  strings  or  other  sounding  musical  instruments  ;  further, 
that  definite  musical  notes  were  absorbed  or  transmitted 
by  neighbouring  sounding  bodies  according  as  these  were 
in  or  out  of  tune  with  the  vibrating  source  of  sound. 
This  is  the  well-known  phenomenon  of  resonance.  Ohm^ 
had  applied  Fourier's  mathematical  analysis  to  the  ex- 
planation of  the  partial  notes,  the  ground  tone  and  the 
harmonic  overtones  (or  upper  partial  tones),  of  which 
musical "  sounds  are   made  up.      Helmholtz  invented  a 

^  Ceo.    S.     Ohm,    the    same    to  See  the  introduction  to  his  treatise 

wh(jni    we    are    indebted     for    the  on     the    galvanic    current     ('Ges. 

well-known  law  which    obtains    in  I    Werke,'  p.  6'i). 

electric  currents,  published  in  1843  -  Cagniard  de  la  Tour  had  in- 
a  paper  in  Poggendorfs  '  Annalen '  }  vented  (1819)  and  Seebeck  the 
(reprinted  in  '  Gesammelte  Ab-  younger  had  improved  (1841)  the 
liandlungen,'  1892,  p.  575),  "On  first  mechanical  counter  for  the 
the  definition  of  a  tone  and  the  frequencies  of  musical  sounds,  the 
theory  of  the  sii-en,"  in  which  he  i  siren  ;  and  the  latter  as  well  as 
applied  the  mathematical  methods  Duhamel  had  studied  the  corn- 
introduced  by  Fourier  in  his  '  The-  position  of  such  sounds  out  of  their 
orie  analytique  de  la  Chaleur'  elements  or  simple  notes.  A  sug- 
(1822)  :  as  he  had  already  done  in  gestion  had  been  thrown  out  as  to 
liis    earlier   work    on    the    galvanic  ,    the     part     played     by    the    up])er 


current  (1827).     In  fact,  Ohm  was 
one  of   the   first   to   recognise   the 


partial    tones    which    accom])anied 
the  ground  tone.    Hehnholtz  treats 


value   of    Fourier's   conceptions   in  '    first  of  this    subject   in    a    lecture 

contradistinction    from     Laplace's,  '   (1857),  reprinted  in  'Vortriige  und 

which  were  bound  up  with  certain  Reden,'  vol.  i.   p.   79,  dealing  with 

hypothetical     notions    as     to     the  "the  psychological  causes  of  musi- 

niolecular    constitution    of    bodies.  I   cal  harmony." 


488 


SCIENTIFIC    THOUGHT. 


15. 
"Timbre" 
defined. 


series  of  simple  but  ingenious  apparatus  by  which  these 
partial  notes  could  be  analysed,  isolated,  and  made  speci- 
ally audible,  or  by  which  the  ground  tone  could  be 
purified,  and  thus  led  up  to  his  conception  of  the  human 
ear — the  different  parts  of  which  he  analysed  anatomic- 
ally and  acoustically — as  a  most  delicate  resonator  which 
separately  absorbed  the  different  elementary  periodic 
movements  that  constitute  musical  sounds,  the  different 
nerve-fibres  carrying  them  separately  to  the  central 
organ  of  perception.^  On  the  bases  of  these  distinc- 
tions, Helmholtz  succeeded  in  giving  an  accurate  defini- 
tion "  of  that  property  of  musical  notes  termed  "  timbre  " 
by  the  French,  "  Klangfarbe "  by  the  Germans  —  that 
peculiar  colouring  or  texture  which  characterises  the 
same  note^  if  produced  by  different  instruments.     He 


^  See  '  Die  Lehre  von  den 
Tonempfindungen,'  1st  ed.,  1863, 
pp.  92,  95,  97.  "The  main  result 
of  our  description  of  the  ear  can 
be  thus  stated,  that  we  have  found 
that  everywhere  tlie  ends  of  the 
auditory  nerve  are  connected  with 
special  auxiliarj'  apparatus,  jjartly 
elastic,  partly  solid,  which  under 
the  influence  of  external  vibrations 
are  made  to  vibrate  correspond- 
ingly and  then  probably  affect 
and  agitate  the  nerve-substance  " 
(p.   212). 

■■^  Helmholtz  was  the  first  to  give 
a  positive  definition  of  "timbre." 
As  he  himself  says  (p.  114),  before 
him  it  meant  all  the  peculiarities 
of  a  musical  sound  which  are  not 
defined  by  its  intensity  or  its  posi- 
tion in  the  scale— -i.e.,  its  "  pitch." 
Of  these  he  eliminates  all  such  as 
are  connected  with  the  beginning, 
rising,  and  dying  away  of  sounds, 
and  deals  only  with  sounds  which 
are  uniformly  maintained  (p.  116). 

^  The    terminology   of   acoustics 


and  of  music  has  been  considerably 
changed,  especially  in  this  country, 
through  scientific  literature,  in 
which  the  work  of  Helmholtz 
forms  a  kind  of  epoch.  Accord- 
ing to  Lord  Rayleigh  ('Sound,' 
vol.  i.  §  22,  1st  ed.),  the  word 
"  tone  "  in  the  English  language 
has  been  adopted  by  Tyudall  to 
denote  a  musical  sound  which 
cannot  be  further  resolved.  The 
word  was  used  before,  but  in  a 
general  sense,  not  limited  only  to 
sounds,  and  where  now  "  tone  "  is 
used  in  works  on  acoustics,  the 
word  "note"  was  more  usually 
employed.  Sir  John  Herschel 
(  '  Encyclop.  Metrop.,'  article 
"  Sound,"  1845)  does  not  con- 
sistently use  the  word  "  tone " 
as  an  equivalent  for  the  German 
"Ton,"  but  makes  use  of  "sound" 
or  "  note  "  or  "  tone  "  promiscu- 
ously. Still  more  uncertain  was 
the  terminology  by  which  to  ex- 
press the  quality  of  a  musical 
sound    other    than    loudness    and 


ON    THE    PSYCHO-PHYSICAL    VIEW    OF    NATURE.       489 

entered  into  an  analysis  of  the  processes  l»y  which  vocal 
sounds  and  notes  are  produced,  and  showed  their  im- 
portance in  musical  and  linguistic  theories.  Combined 
with  all  these  deductions  and  applications,  which  started 
from  Fourier's  mathematical  analysis  of  compound  move- 
ments, Helmholtz's  anatomical  dissection  of  the  organ  of 
hearing  leads  him  to  the  conclusiDU  that  there  "  must 
exist  in  the  ear  different  parts  which  are  set  in  \il)rati(in 
by  notes  of  different  pitch,  and  which  have  thus  a  sensa- 
tion of  these  notes."  ^  And  here  he  takes  up  a  different 
line  of  reasoning — that  suggested  by  Johannes  ]\Iiiller's 
theory  of  the  specific  sense  energies.  In  his  studies 
in  physiological  optics  he  had  already  accepted  Young's 
hypothesis  that  there  exist  in  the  eye  three  distinct 
kinds  of  nerve  -  fibres,  to  which  belong  distinct  modes 
of  colour -sensation.  Something  analogous  exists  in  the 
ear."     "  The   differences   in   notes  —  namely,   pitch   and        le. 

Analogy 

colour  [or  character] — are  reduced  to  differences  of  the  between 

-"  sound  and 

sensitive  nerve-fibres,  and  for  each  nerve-fibre  there  exists  *^°^°^''- 
only  the  difference  of  the  intensity  of  the  stimulus." 

This  brings  the  action  of  the  sensory  nerves  into  line 
with  that  of  motor  nerves  :  everywhere  the  nerve  itself  is 

pitch,  and,  to  the  present  clay.  Book  of  Physics,'  Sound,  p.  69)  we 
the  Euglisli  tongue  has  no  equiv-  read,  "  It  is  convenient  to  use  the 
alent  for  the  French  "  timbre  "  or       term    note    for    an    ordinary    coni- 


the  German  ''  Klangt'arlje."  Everett 

used    tiie    word    c:haracter,    and   so 

does    Lord    liayleigh.      Dr    Young, 

in    his  "Essay    on'   Music"    (1800, 

'  Miscell.    Works,'    vol.    i.    No.    5), 

speaks   of   the    tjuality   of    sound, 

sometimes  called  its   tone,  register, 

colour,  or  timbre  (p.  118).     In  the 

most     recent    scientific    work     on 

sound    in    the     English    language  "  Ibid.,  pp.  220,  2"21 

(Piiynting    and    Thomson's    'Text-    ' 


pound  sound  to  which  a  definite 
pitch  may  be  assigned,  and  the 
term  tone  for  each  sim})le  harmonic 
constituent  which  goes  to  form  it." 
There  is  an  important  note  on  the 
terminology  by  Alex.  T.  l->llis.  the 
learned  translator  of  Hehiiholt/.'s 
'Sensations  of  Tone  '  (187r>.  p.  36). 
'  '  Tonempfinduugen,"  p.  215. 


490 


SCIENTIFIC    THOUGHT. 


indifferent  to  the  stimulus,  which  it  carries  in  or  out  like 
a  telegraph  wire ;  which,  whilst  acting  in  every  case  in 
the  same  way,  may,  according  to  its  terminal  connection,^ 
"  deliver  messages,  ring  a  Ijell,  explode  a  mine,  decompose 
water,  create  or  move  magnets,  produce  light,  &c.  The 
same  with  the  nerves.  The  state  of  irritation  is,  so  far 
as  the  isolated  nerve-fibre  is  concerned,  everywhere  the 
same,  but  in  accordance  with  the  nature  of  different 
parts,  be  it  of  the  brain  or  of  the  external  portions 
of  the  body,  it  produces  motion,  secretion,  increase  or 
decrease  of  blood,  of  heat  in  different  organs,  or  lastly, 
sensations  of  light,  sound,"  &c. 

The  physiology  of  hearing  had  its  brilliant  application 
in  a  clearer  understanding  of  the  elements  of  language, 
of  the  formation  of  the  vowel  sounds,  and  in  the  study  of 
the  development  of  music — that  art  which,  more  than 
any  other,  seems  founded  on  definite  rules.^    In  analysing 


^ '  Tonempfindungen,'  p.  222. 

^  "  From  the  time  wlien  Pythag- 
oras is  said  to  have  discovered  the 
arrangement  of  tones  in  an  octave, 
by  observing  that  the  sounds  of  the 
blacksmith's  hammer  in  the  forge 
produce  a  fourth,  a  fifth,  and  an 
octave,  and  was  then  led  to  obtain 
harmonic  proportion  between  the 
strings  of  the  heptachord,  all  who 
investigate  musical  tones  know  that, 
although  these  are  fleeting  sensa- 
tions, they  depend  physically  on 
numerical  relations  between  various 
kinds  of  movements  ;  but  it  was 
Helmholtz,  more  than  any  other 
philosopher,  who  examined  the 
whole  range  of  the  phenomena, 
physical  as  well  as  physiological, 
and  whose  work  will  for  generations 
remain  an  enduring  monument  to 
his  genius"  (Prof.  M'Kendrick  in 
the     Helmholtz     volume     of     the 


"Masters   of  Medicine"  Series,  p. 
168). 

Since  the  appearance  of  the  last 
edition  of  Helmholtz's  great  work, 
of  which  there  exists  an  excellent 
English  edition  with  valuable  notes, 
many  of  the  points  first  investi- 
gated by  Helmholtz  have  been  taken 
up  by  other  experimentalists  as  well 
as  by  psychologists.  The  invention 
of  the  i)honograph  by  Edison  in 
1877  gave  a  great  impetus  to  exact 
research  in  the  problems  of  audi- 
tion, and  various  facts  and  theories 
have  been  advanced  confirming  or 
modifying  the  views  put  forward 
by  Helmholtz.  On  these  see  the 
last  chapter  of  Lord  Rayleigh's 
'  Treatise  on  Sound,'  2nd  ed.,  1894. 
On  the  psychological  side  see  the 
2nd  volume  of  Prof.  AVundt's 
'  Phvsiologische  Psychologie,'  pp. 
47-96. 


ON    THE    PSYCHO-PflYSICAL    VIEW    OF    XATFRE.       401 


these  Heliiilioltz  is  led  into  lesthetical  and  psycholofrical 
discussions,  clearly  distinguishing  between  such  principles 
as  are  inherent  in  natural,  physical,  and  physi(jlogical 
relations,  and  such  others  as  depend  on  the  inventions  of 
genius  and  the  gradual  changes  l)rought  aljout  by  exter- 
nal requirements  and  ingrained  by  habit  and  education.^ 
The  physiology  of  seeing  had  yet  more  remarkable 
consequences  for  the  history  of  Thought.  We  may  say 
that  through  Helmholtz's  analysis  of  the  formation  of 
our  space  perceptions  by  the  eye  in  connection  with  the 
tactile  and  muscular  senses,  psychology  and  metaphysics 
were  brought  into  immediate  contact  with  physics  and 
physiology.       It  is   here    that   Helniholtz    takes    up  an        ir. 

i.-iT/'P  ±^  1  •         1.1  1  Helmholtz 

entirely  ditJerent,  and,  previously,  isolated  line  of  reason-  a"d  Kant, 
ing,  which  centres  in  Kant's  theory  of  space  and  time  as 
innate  forms  of  perception — the  so-called  subjectivity  or 
ideality  of  time  and  space.  The  studies  of  this  subject" 
had  been  somewhat  prepared  by  the  writings  of  Herbart 
and  Lotze.  The  teachings  of  Kant  have  had  an  influence 
in  the  direction  indicated  through  two  distinct  channels, 
— through  Johannes  Midler's  rhvsiology  and  through 
Herbart's   Psychology  :    the   latter   seems    to    have    had 


^  See  the  closing  words  of  the 
13th  chapter  of  Helmholtz's  work  : 
"  As  the  fundaracntal  j)riiici|)le  for 
tlie  developeiiieiit  of  the  European 
tonal  system,  we  shall  assume  that 
tlie  whole  mass  of  tones  and  the 
connection  of  harmonics  must  stand 
in  a  close  and  always  distinctly 
perceptible  relationship  to  some 
arbitrarily  selected  tonic,  and  that 
the  mass  of  tone  which  forms  tlie 
whole  composition  must  be  de- 
veloped fi-om  this  tonic,  and  must 
finally  return  to  it.  The  ancient 
world   dcvelojicd    this   pirinciple   in 


homophonic  music,  the  modern 
world  in  harmonic  music.  But  it 
is  evident  that  this  is  merely  an 
icsthetical  princi])lc,  not  a  natural 
law.  The  correctness  of  this  juin- 
ciple  cannot  be  established  a  priori. 
It  must  be  tested  by  its  results. 
The  origin  of  such  wsthetical  i)rin- 
ciples  should  not  be  ascribed  to  a 
natural  necessity.  They  are  the 
inventions  of  genius,  as  we  pre- 
viously endeavoured  to  illustrate 
by  a  reference  to  the  principles  of 
arcliitectural  style." 


492  SCIENTIFIC    THOUGHT. 

little  influence  over  the  Berlin  school  of  physiology,  but 
it  has  had  a  considerable  influence  on  several  members  of 
the  Leipzig  school.      In  this  school  Lotze  was  educated. 

Locke  had  taught,  and  his  followers  had  accepted,  the 
doctrine  that  the  so-called  secondary  qualities  of  sensible 
things,  such  as  colour,  sound,  hardness,  &c.,  were  sub- 
jective. Speculative  physics  had  prepared  this  view  by 
translating  such  properties  into  special  forms  of  aggrega- 
tion or  periodic  motion,  leaving  only  extension  and  re- 
sistance as  the  primary  properties  inherent  in  things. 
Kant  had  gone  a  step  further,  and  maintained  that 
space  and  time  were  likewise  only  subjective  forms  of 
our  perceiving  sense  apparatus.  Two  problems  grew  out 
of  this  view,  which  are  not  clearly  stated  in  Kant's 
writings.  First,  How  does  the  perceiving  mind  arrive 
at  the  elaborate  and  systematic  space  conception  which 
is  peculiar  to  us  human  beings  ? — i.e.,  out  of  what  per- 
ceptive elements,  and  by  what  psychical  processes,  is  it 
gradually  built  up  ?  Secondly — What  is  it  that  locates 
our  sensations  at  definite  places  in  space  ?  There  is  a 
third  question  which  Kant  put  and  answered,  that  re- 
ferring to  the  nature  and  validity  of  the  geometrical 
axioms.  According  to  his  view  the  axioms  of  geometry 
are  innate,  expressive  of  the  inborn  nature  of  our  space 
conceptions ;  in  fact,  the  truths  of  geometry  formed  in 
his  view  the  only  instance  of  knowledge  gained  not  by 
experience  but  a  jpriori — before  or  outside  of  experience. 
18.  An  entirely  independent  series  of  psycho-physical  in- 

The  brothers  .  .  i      n  t    i 

Weber.  vcstigations  was  started  even  before  Johannes  Mliller, 
by  Ernst  Heinrich  Weber  of  Leipzig,  who,  with  his  two 
brothers,  Wilhelm  and   Eduard,  may   be   considered    as 


ON    THE    PSYCnO-PHYSK'AL    VIEW    OF    NATUIIE.       493 

the  ceiitie  uf  Lhc  Leipzig  schuul  ut'  Anatomy,  I'liysiology, 
and  riiysics.^  After  having  been  among  the  first  to 
import  the  exact  methods  of  research  into  physiology, 
and  having  carried  on  a  variety  of  investigations  refer- 
ring to  physiological  optics  and  acoustics,^  he  approached 
tlie  subjective  phenomena  of  sensation :  recording,  for 
cxani})le,  with  what  degree  of  accuracy  different  parts 
of  the  surface  of  the  skin  on  face,  arm,  leg,  &c.,  per- 
ceive the  distance  between  two  points  which  touch  the 
skin  —  say  the  two  points  of  a  pair  of  compasses ; 
recording  also  the  relation  of  the  smallest  increase 
of  any  given  sensation  to  the  corresponding  increase 
of  stimulus.  In  the  latter  series  of  experiments,  he 
arrived  at  what  has  been  termed''  "Weber's  I'sycho- 
physical  law.  He  did  not  call  it  so  himself ;  he  simply 
showed  by  experiment  that  in  a  variety  of  cases  the 
stimulus  had  to  increase  in  proportion  to  its  own  initial 
intensity  in  order  to  produce  a  just  perceptible  increase 
of  sensation.     These  experiments  did  not  attract  much        19. 

^  Fcchner's 

attention  till  Gustav  Theodor  Fechner  took  them  up,  Psycho- 
building  upon  them  his  celebrated  "  Principles  of  Psycho- 
physics."  Before  referring  more  in  detail  to  these,  I 
must  mention  a  third  line  of  reasoning  which,  as  stated 
above,  had  a  considerable  influence  on  the  Leipzig  school 
of    Psycho  -  physics,  though    probably    it   had    as    little 

1  On  the  labours  of  tlie  brothers  aiiatomicfc     et     physiologic^,'     in 

W'eber,   see    the    references    given  which,  in  1831,  tliere  appeared  his 

above,  vol.  i.  p.  196,  also  the  present  celebrated  treatise   ''Tastsinn   und 

volume,  p.  31,  note.  Oeincingefiilil."  Job.  Midler's 'Ver- 

-  E.  H.Weber  i)ublished  in  1817,  gleicliendc   Anatomic    des  Gesicht- 

'  Anatoinia    comparata    nervi   sym-  sinnes '  appeared  in  IS'Jti. 

pathici ; '    in    1820,    '  Ue    aure    et  ■*  By  Fechner   in  his  '  Elenieute 

auditu     hominis    et    animalium  ; '  der  Psychophysik  '  (2  vols.,  Leipzig, 

from    1827   onward,   '  Annotationes  1860). 


physics. 


494  SCIENTIFIC   THOUGHT. 

influence  on  E.  H.  Weber  as  the  earlier  philosophy  of 
nature,  to  which  it  formed  a  pronounced  opposition. 
20.  Herbart  was  not  an  experimental  philosopher ;  never- 

Influence  of  .  „  .  . 

Herbart.  thelcss  a  placc  in  a  history  of  scientific  Thought  lielongs 
to  him.  Indeed,  his  philosophy,  like  that  of  Kant,  and, 
in  quite  a  different  way,  of  Schelling,  has  had  a  marked 
influence  on  many  thinkers  and  men  of  science  who  have 
prepared  the  ground  for  an  exact  treatment  of  the  pheno- 
mena of  Life  and  ]\Iind.  Among  exact  psychologists  I 
need  only  name  Volkmann,  Drobisch,  Lotze,  and  in  our 
time  Professor  Wundt  ^  of  Leipzig.  It  is  therefore  of 
interest  to  mark  the  precise  point  where  Herljart's  in- 
fluence comes  in. 

Although  an  exact  school  of  psychology  might  aim  at 
studying  psychical  and  psycho-physical  phenomena  w^ith- 
out  reference  to  any  general  theory  of  the  soul  as  the 
supposed  centre  and  substance  of  these  phenomena, 
the  existing  ideas  and  theories  as  to  soul  and  mind 
have  nevertheless  always  played  a  great  part  in  these 
researches,  just  as  it  has  been  found  impossible  to  free 
biological  research  altogether  from  some  theory  of  life. 
Older  psychologists  were  consciously  or  unconsciously 
governed  by  the  conception  of  a  number  of  distinct 
mental  faculties.  Even  Kant's  philosophy  is  still 
embarrassed  by  this  view,  which  reigned  supreme  in 
the  teaching  of  his  predecessor  Wolf.     The  attempt  of 


'  This  is  not  the  place  to  speak 
about  the  Herbartian  school,  which 
is  almost  entirely  confined  to  Ger- 
many. I  have  referred  to  Prof. 
Wundt  because,  in  spite  of  a  run- 
ning criticism,  in  the  '  Physiologische 
Psychologie,'   of    Herbart's   special 


doctrines,  the  author  of  that  im- 
portant and  comprehensive  work 
himself  declares  (Preface  to  the  1st 
ed.,  1874)  that  for  the  formation 
of  his  own  views  he  is,  next  to 
Kant,  most  indebted  to  Herbart. 


ON    THE    rsYCHO-rHYSlCAL    VIEW    OF    NATURE.       495 
Heibait,  tlierefore,  to  overthrow  the  so-called    faculty-        21. 

His  attack 

psychoWv,  iind    to    insist    on    the    essential  iinilv  and  "","'« 
1  J  c^  >  J  "faculty- 

simplicity  of   the   inner  life,  must  have   made    a   great  J^gy*^'.'*"'' 

impression  on  all  who  came  uniler  the  intluence  of  his 

philosophy.       It   did    this    in    two    ways.^       It   first   of 


1  Besides  Herbart  (1776-1841), 
whose  psychological  writings  date 
from  1813  to  1825,  another  Oerman 
ps^'chologist  is  usually-  mentioned  as 
having  helped  to  overthrow  the  older 
l'acultj--i)sych()logy.  Beueke  (179S- 
1854),  a  younger  contemporary  of 
Herbart,  conceived  of  psychology 
as  a  natural  science.  His  principal 
work,  '  Lehrbuch  der  Psychologic 
als  Naturwissenschaft,'  appeared 
in  1833,  and  has  been  several  times 
republisiied,  the  fourth  edition  ap- 
pearing in  187 7.  Beneke  worked 
in  opposition  to  Hegel  at  Berlin, 
liis  historical  forerunners  being  the 
German  philosophers,  Jacobi,  Fries, 
and  Schleiermacher,  as  well  as  the 
English  philosophy  of  the  so-called 
Association  -  school.  An  account 
of  his  philosophy  does  not  belong 
to  a  chapter  on  psycho-physics  ex- 
cept in  as  much  as  he  introduced 
into  the  study  of  the  inner  life  not 
indeed  the  facts  and  data  of  jthysical 
—  i.e.,  physiological — science,  but 
the  i)hysical  method.  He  was  the 
purest  representative  of  the  psycho- 
logy of  the  "inner  sense."  Whilst 
Herbart  based  his  jjsychology  alike 
on  experience,  metaphj-sics,  and 
matiiematics,  Beneke  accejjted  only 
the  first,  and  discarded  the  latter. 
Standing  thus  outside  the  all- 
powerful  school  of  Hegel  and  the 
increasing  influence  of  Herbart, 
Beneke  had  during  his  lifetime 
only  a  limited  audience,  and  re- 
ceived due  attention  in  a  wider 
cii-cle,  fii'st  and  priucipally  through 
Ueberwcg,  who  was  gi-eatly  im- 
pressed by  him.  In  fact,  his 
influence    was     felt    in     Germany 


about  the  same  time  as  that  of 
the  English  and  Scottish  philo- 
sophers. Ueberweg,  in  his  well 
known  '  History  of  Philosuphy,' 
vol.  ii.  pp.  281-292  (Engl,  transl. 
by  Morris,  1874),  gives  a  full  ac- 
count of  Beneke.  Prof.  Erdmann 
gives  a  very  full  account  also  in 
his  excellent  '  Grundriss  der  Ge- 
schichte  der  Philosophic'  (3te  Aufl., 
1878,  vol.  ii.  pp.  628-641).  The  fact 
that  Beneke's  method  is  intro- 
spective, brings  him  not  only  into 
contact  with  the  English  school, 
but  also  with  French  thought, 
which  has  alwaj-s  been  character- 
ised by  subtle  psychological  aiial- 
j'sis.  This  explains  the  fact  that 
M.  Marion  (in  the  'Grande  Juicyclo- 
jjudie  ')  calls  Beneke  "  un  des  prin- 
cipaux  pliilosophes  Allemands  du 
siecle," — a  designation  which  would 
hardly  be  echoed  either  in  Germany 
or  in  England.  The  best  account 
of  Beneke's  position  in  the  de- 
velo])ment  of  psychology  extant  in 
the  Englisli  language  is  that  of  Dr 
G.  F.  Stout,  in  his  article 
"  Herbart  compared  with  English 
Psychologists  and  with  Beueke," 
in  the  14th  volume  of  the  1st 
series  of  '  Mind  '  (1889).  M.  Ribot, 
in  his  well-known  book  on  '  ^Modern 
German  Psychology  '  (Engl,  transl. 
by  Baldwin,  1899),  does  not  say 
much  about  Beneke,  but  his  ac- 
count of  Herbart  and  his  school, 
and  their  j)osition  in  psycho-physi- 
cal thought,  is  concise  and  nmch 
to  the  point.  Dr  Stout's  articles 
on  Herbart  in  'Mind'  (vols.  13,  14) 
are  also  much  to  be  reconmiended. 


496  SCIENTIFIC    THOUGHT. 

all  liberated  them  from  the  trammels  of  an  antiquated 
and  misleading  terminology ;  and  secondly,  it  impressed 
them  with  the  necessity  of  giving  an  answer  to  the 
question  how  the  multiplicity  of  sensations  or  the  flow 
of  ideas  was  held  together  in  the  unity  of  an  inner 
existence.  Thus  it  is  a  characteristic  of  all  psycho- 
physical writers  who  have  come  under  the  influence 
of  Herbart,  that  however  much  they  may  be  occupied 
with  detailed  description  of  physiological  processes,  with 
the  analysis  of  sensations  or  the  dissection  of  the  data 
of  experience,  they  never  lose  sight  of  the  underlying 
mental  unity  which  is  the  central  phenomenon  of  psy- 
chology and  of  psycho-physics,  just  as  it  must  be  the 
central  problem  of  biology  to  arrive  at  some  definition 
of  life.  Had  the  investigations  of  psycho-physical  pheno- 
mena remained  where  Weber  or  even  Helmholtz  left 
them,  we  should  have  brilliant  chapters  on  the  phenomena 
of  touch,  of  seeing,  hearing,  and  other  processes  where 
the  outer  and  inner  worlds  come  into  contact,  but  no 
attempt  to  sum  up  these  brilliant  contributions  in  a 
connected  view  of  the  inner  and  higher  life — the  most 
22.        remarkable  and  unique  phenomenon  in  nature.     It  seems 

Unity  of 

mental  life,  to  me  that,  in  Germany  at  least,  it  is  through  Herbart, 
more  than  through  any  other  thinker,  that  we  have 
been  preserved  from  a  threatening  disintegration  of 
psychological  research.  It  is  the  more  necessary  to 
recognise  this,  as  most  of  those  writers  who  at  one 
time  came  greatly  under  Herbart's  influence  have  found 
it  necessary,  after  having  become  thoroughly  saturated 
with  this  one  great  truth  in  his  philosophy,  to  abandon 
almost  the  whole  of  the  more  detailed  expositions  con- 


ON   THE    PSYCHO-PHYSICAL    VIEW    OF    NATURE.      49  7 


taiiied  in  his  woiks.^  Heibait  was  quite  as  correct 
in  his  ideal  of  what  psychology  should  l)e,  as  he  was 
unfortunate  in  the  particular  manner  in  which  he 
elaborated  it. 

Psychology  was  tu  be  fuuiided  on  experience,  meta- 
physics, and  mathematics.  Kant  had  studied  the  inner 
activity  of  the  mind  as  it  is  compounded  of  sensation, 
perception,  and  apperception  ;  of  understanding,  judgment, 
and  reasoning.  In  opposition  to  this  Herbart  went  back 
to  the  position  taken  up  by  Locke  and  Hume,  looking  at 
the  inner  life  of  a  conscious  mental  being  or  soul,  not  as 
a  complex  of  mental  faculties,  but  as  a  flow  of  ideas  or 
perceptions.  How  is  the  unity  and  simplicity  of  this 
mental  being  preserved  in  the  midst  of  this  continuous 
How  of  ideas  ?  how  is  it  regained  as  often  as  it  is  in 
danger  of  beimr  1(  )st  ?  His  investigations  start  at  the 
point  where  the  inquiries  of  the  association  school  of 
psychologists  started  in  England.  Having,  however,  the 
mechanics  and  dynamics  of  physical  forces  more  proniin- 


^  Dr  Stout  lias  fjiven  an  ac- 
count of  the  Herljartian  school 
in  the  14th  volume  of  'Mind,'  p. 
353  !i<iq.  He  confines  himself  to 
Drobisch,  Waitz,  and  Volkmann, 
the  psychologists  proper.  M. 
Uibot  {lac.  cit.)  has  dwelt  more 
on  the  develojjment  of  the  Herbart- 
ian  school  in  the  direction  of  an- 
thropology and  ethnology  ;  he 
mentions  specially  Waitz,  as  well 
as  Lazarus  and  Steinthal.  He 
contrasts  their  work  and  their 
positions  with  those  of  the  great 
anthropologists  of  the  English 
school,  such  as  Tylor,  Lubbock, 
and  Herbert  Spencer,  and  notes, 
in  the  German  school,  the  absence 
of  Darwinian  ideas.  It  is  import- 
ant to  observe  that  botli  in  the  case 

vor,.  II. 


of  Piof.  Wundt  of  Leipsic  and  of  Mr 
Spencer  in  luigland — that  is,  in  the 
case  (jf  the  latest  outcome  of  the 
Kant-Herbartian  philosophy  on  the 
one  side  and  of  the  Association  phil- 
osophy in  England  on  the  other — 
and  in  each  case  under  the  intiuence 
of  the  exact  and  biological  sciences, 
philosophy  ends  in  elaborate  treat- 
ises on  Anthropology,  which  with 
Spencer  is  conceived  under  the 
name  of  Sociology.  Similarly,  the 
school  of  Hegel  ended  in  elaborate 
historical  treatises.  Hume  turned 
fi-om  abstract  philosophy  to  politi- 
cal economy  and  history,  and 
Herder — as  we  shall  see  later  on 
—  anticipated  much  of  all  this 
movement  in  his  History  of 
Mankind. 

2  I 


498 


SCIENTIFIC    THOUGHT. 


23. 
Jlathe- 
niatical 
psychology. 


ently  before  his  mind  than  they  had,  he  was  tempted 
to  try  how  far  the  conceptions  of  equilibrium  of  motion 
and  of  the  composition  of  forces  could  l^e  applied  to  the 
inner  play  of  ideas  which  chase,  oppose,  and  displace 
each  other,  preserving  all  the  time  a  kind  of  dynamical 
equilibrium.  His  elaborate  mathematical  calculations  in 
the  first  part  of  his  greater  work  on  psychology  do  not 
specially  refer  to  the  purely  intellectual  process ;  ^  they 
refer  rather  to  all  inner  processes  which  oppose  each 
other,  which  come  into  conflict,  restraining  each  other  in 
proportion  to  their  contrast,  creating  a  tendency  towards 
reversion  to  former  conditions.  Such  a  play  of  oppos- 
ins;  forces  is  to  be  found  Hkewise  in  the  larger  field  of 
human  society ;  this  is  accordingly  quite  as  much  a  case 
for  the  application  of  those  psychical  mechanics  which 
Herbart  aimed  at  establishing. 

In  a  history  of  scientific  Thought,  which  aims  at 
showing  by  what  gradual  steps  the  various  provinces 
of  phenomena  have  been  brought  under  the  methods  of 
exact  treatment,  the  psychology  of  Herbart  has  an  im- 
portant as  well  as  a  unique  and  isolated  position.      It 


^  Herbart  himself  saj's  of  his 
mathematical  chapter,  that  the  re- 
.sults  thereiu  given  "  do  not  follow 
immediately  from  the  conception 
of  a  thinking  being ;  but  they  re- 
fer to  the  mutual  arrangements  of 
any  things,  in  so  far  as  they  are 
opposed  and  as  they  collide,  re- 
stricting each  other  in  proportion 
to  their  contrast,  tending  to  revert 
to  the  previous  condition,  the 
unrestricted  portions  being  fused 
into  complex  forces.  The  forces 
which  are  active  in  society  are 
doubtless  originally  psychological 
forces.    They  meet  in  so  far  as  they 


appear  in  language  and  in  actions 
in  a  common  sensual  world.  In 
the  latter  thej'  restrict  each  other  ; 
this  is  the  universal  spectacle  of 
conflicting  interests  and  social 
frictions.  Also  the  fusion  no  doubt 
exists.  .  .  .  We  therefore  assume 
that  among  men  living  together 
the  same  conditions  appear  which 

i    exist,  according  to  our  view,  among 

I  the  ideas  in  one  and  the  same  con- 
sciousness.     We   examine   the   re- 

I  suit  of  their  mutual  restrictive 
action"  ("  Psychologie  als  Wissen- 

:  schaft,"  'W^erke,'  ed.  Harteustein, 
vol.  vi.  Y>.  31,  &c.) 


ON    THE    PSYCHO-PHYSICAL    VIEW    OF    NATURE.       499 


led  psychologists  to  consider  more  closely  the  conditions 
under  which  a  mathematical  treatment  is  at  all  possible, 
and  to  recognise  that  exact  and  accurate  measurements 
must  precede  all  application  of  an  abstract  calculus. 
Herbart's  ideal  was  that  of  a  psychical  mechanics ;  he 
opposed  ^  the  idea  of  a  union  of  physiology  and 
psychology.      And   yet    this    was  just    the    direction    in 


'  In  a  very  interesting  note  <at 
the  end  of  tlie  introduction  to  tlie 
second  part  of  liis  larger  work  on 
psychology,  Herbart  explains  his 
position  with  regard  to  physiological 
psychology.  It  refers  to  certain 
extracts  which  he  makes  from 
Kudolph's  'Orundriss  der  Physiol- 
ogic,' in  which  that  eminent  physi- 
ologist referred  to  Herbart's  '  Lehr- 
buch  der  Psychologic.'  "It  is  not 
onlj-  a  metaphysical  but  also  a 
logical  en-or  to  confound  psycho- 
logical and  phj'siological  research. 
Psychological  phenomena  are  not 
in  space,  but  space  itself,  with  all 
that  appears  in  it,  is  a  psycholog- 
ical phenomenon,  and,  indeed,  one 
of  the  first  and  most  difficult  facts 
for  psychology,  which,  in  the  treat- 
ment of  it,  would  behave  very  im- 
])roperly  if  it  began  l)y  discussing 
the  forces  iu  the  nerves ;  for  the 
question  is  not,  where  sensations 
come  from,  but  how  sensations 
acquire  the  form  of  space.  Now,  I 
maintain  fuither,  tliat  tlie  ditl'er- 
ence  Vietwccn  lifeless  and  living 
matter — that  is,  between  physics 
and  physiology — cannot  be  under- 
stood until  we  know  mind  by  means 
of  p.sychologj',  for  in  all  the  count- 
less elements  of  the  organised  body 
— in  plants  as  well  as  in  animals — • 
there  is  an  analogue  of  mental  de- 
velopment which  cann(jt  po.ssibly 
be  found  on  the  surface  of  ])hen- 
omena.  We  observe  inteinally  a 
fragment  of  our  own  mental  exist- 
ence. This  fragment  is  developed 
into   scientific    knowledge    through 


speculative  psychology  based  on 
I  metaphysics.  This  knowledge 
I  meets  another  equally  metaphy- 
I  sical  science,  natural  philosophj', 
with  its  conception  of  matter — 
that  is,  of  such  inattei-  as  we  know 
througli  chemistry  and  dynamics. 
Then  onlj'  can  the  question  be  put, 
how  such  matter  must  be  con- 
stituted, so  that  its  separate  ele- 
ments are  determined,  not  only 
through  their  original  quality,  but 
also  through  a  development  analo- 
gous to  the  mental  one,"'  &c.  The 
section    closes   with   the   following 


characteristic       passage 


Those 


who  favour  empiricism  can  learu 
from  the  present  state  of  physi- 
ology how  much,  or  rather  how 
little,  mere  exjierience  can  do. 
Physiology,  as  an  empirical  doc- 
trine, has  attained  a  height  which 
nobody  can  despise.  ]\Ioreover,  it 
proceeds  in  the  light  of  modern 
physics.  Nevertheless,  it  has 
eagerly  sucked  up,  as  the  sponge 
sucks  u])  water,  that  philosophy 
of  nature  which  knows  nothing, 
because  it  began  by  construing  the 
universe  a  priori.  Towards  this 
error  no  science  has  proved  so 
weak,  so  little  capable  of  resist- 
ance, as  physiology.  The  talk 
about  life  ha^  liecome  tlie  Dead 
Sea  in  which  all  spirit  of  philo- 
sophical research  is  drowned,  so 
that,  if  a  resurrection  is  at  all  to 
be  hoped  for,  it  must  be  born  anew 
in  quite  unbiassed  minds"  (' Werke,' 
vol.  vi.  p.  05,  &c. ) 


500 


SCIEN'TIFIC    THOUGHT. 


24. 
Lotze's 
Physiology 
of  the  soul. 


which  an  exact  or  scientific  treatment  of  mental  phe- 
nomena could  meet  with  any  success  at  all.  It  was  in 
the  schools  of  physiology,  in  those  of  Johannes  Miiller 
and  of  Weber,  that  philosophers  had  to  learn  how  to 
attack  the  borderland  of  bodily  and  mental  phenomena. 
The  first  who  approached  the  subject  from  this  point 
of  view  was  Hermann  Lotze.  He  was  a  disciple  of 
E.  H.  Weber,  and  had  been  led  to  psychological  re- 
searches from  two  independent  starting-points  :  first  from 
the  study  of  the  medical  sciences  which,  under  the  hands 
of  his  great  master,  had  largely  benefited  by  the  ap- 
plication of  the  exact  methods  of  the  physical,  the 
measuring,  and  calculating  sciences,  but  also  from  an 
entirely  opposite  quarter.^  "  A  lively  interest  in  poetry 
and  art  had  led  him  to  philosophy."  He  was  attracted 
by  that  great  body  of  ideas  which,  through  the  systems 
of  Fichte,  Schelling,  and  Hegel,  had  become  permanently 
domiciled  in  German  culture.  In  this  great  realm  lie 
could  move  "  with  some  freedom,"  for  it  had  not  be- 
come crystallised  into  a  definite  system  of  doctrine ; 
exact  studies  had,  moreover,  easily  convinced  him  "  how 
absolutely  untenable  was  the  form  into  which  Hegel  had 
cast  that  valuable  possession." 


I 


^  The  quotations  in  the  text  are 
taken  from  Lotze's  polemical  pam- 
phlet, '  Streitschriften  '  (Leipzig, 
1857),  pp.  6,  7.  As  already  men- 
tioned (supra,  p.  407  note),  Lotze  had 
been  misunderstood  bj^  his  critics, 
of  whom  some  represented  him  as 
a  materialist,  others  as  a  follower  of 
Herbart.  In  refuting  the  latter 
charge  he  explains  his  position  to- 
wards the  idealistic  sj'stems  of  the 
first  half  of  tiie  nineteenth  century. 


He  acknowledges  two  great  personal 
influences,  that  of  C.  H.  Weisse, 
which,  as  it  were,  touches  the 
kernel  of  his  convictions,  and  that 
of  the  study  of  medicine,  which, 
in  his  case,  was  intimately  con- 
nected with  that  of  the  physical 
sciences.  He  admits,  as  did  Her- 
bart, having  passed  through  the 
magnificent  portal  of  Leibniz's 
Monadology  to  a  general  arrange- 
ment of  his  philosophical  opinions. 


ON    THE    PSYCHO-PHYSICAL    VIEW    OF    NATIKK.       501 

We  must  bear  in  mind  this  twofold  source  of  Lotze's 
reflections  if  we  want  to  estimate  correctly  the  value  of 
his  early  criticisms  regardin;^  the  llifii  juevalent  treat- 
ment of  such  questions  as  life  and  mind  in  the  medical 
sciences.  On  the  one  side  he  had  the  object  of  clear- 
ing the  way  for  purely  mechanical  explanations.  We 
learnt  in  an  earlier  chapter  how  he  was  one  of  those 
who  successfully  chased  out  of  biology  the  vague  idea  of 
a  vital  force.  And  when  lie  approached  the  problem 
of  mind  and  body,  we  liinl  hiiu  insisting  on  tlie  presence 
of  a  psycho-physical  mechanism  which  rules  ^  the  inter- 


'  The  opinion  of  Lotze  regarding 
the  relation  of  soul  and  body,  or 
rather  of  psychical  and  physical  i)he- 
noniena,  has  been  stated  by  him, 
variously,  as  parallelism,  occasional- 
ism, pre-established  harmony,  and 
was  ultimately  crystiillised  in  the 
term  psycho-physical  mechanism. 
The  question  is  fully  discussed  in 
the  articles,  "  Leben  und  Lebens- 
kraft,"  "Instinct,"  '' Seele  und 
Seelenleben."  which  he  contributed 
to  R.  Wagner's  '  Handworteibuch 
der  Physiologie.'  They  are  re- 
printed in  Lotze's  'KleineSchriften,' 
ed.  D.  Peipers,  4  vols.  (Leipzig, 
1885-91).  He  there  saj-s,  "The 
conception  of  a  psycho-physical 
mechanism  can  be  stated  as  fol- 
lows :  As  ideas,  volitions,  and  other 
mental  states  cannot  be  compared 
with  the  quantitative  and  special 
properties  of  matter,  but  as,  never- 
theless, the  latter  seem  to  follow 
upon  the  former,  it  is  evident  that 
two  essentially  different,  totally 
(lisj)arate,  series  of  processes,  one 
bodily  and  one  mental,  run  par- 
allel to  each  other.  In  the  intensive 
quality  of  a  mental  process,  the 
■extensivedefinitenessof  the  material 
jjrocess  can  never  be  found  ;  but  if 
the  one  is  to  call  forth  the  other, 


the  proportionality  between  them 
must  be  secured  through  a  connec- 
tion which  appears  to  be  extrinsic 
to  both.  There  must  exist  general 
laws,  which  ensure  that  with  a 
modification  (i  of  the  mental  sub- 
stance a  modification  b  of  the  bodily 
substance  shall  be  connected,  and  it 
is  only  in  consequence  of  this  inde- 
pendent rule,  and  not  through  its 
own  power  or  impulse,  that  a 
change  in  the  soul  produces  a 
corresponding  one  in  the  body " 
(vol.  i.  p.  193).  Lotze  destroyed 
the  idea  of  vital  force,  but  he 
oidy  chased  the  conception  of 
the  soul  bej'ond  the  limit  of  the 
psycho-physical  mechanism,  and  he 
maintains  that  natural  and  medical 
science  have  no  interest  in  pursuing 
the  question  lieyond  that  limit, 
"  however  interesting  the  further 
discussion  of  this  subject  may  be  to 
speculative  j>sychology"  (vol.  i.  p. 
197) — "  for  it  is  ((uite  indifferent  to 
medicine,  wherein  the  mysterious 
union  of  body  and  soul  consists,  as 
this  is  the  constant  event  which 
lies  equally  at  the  bottom  of  all 
phenomena.  But  it  is  of  the 
greatest  interest  to  medicine  to 
know  what  affections  of  the  soul 
are  connected  in    that   mysterious 


502  SCIENTIFIC    THOUGHT. 

action  of  external  and  internal  phenomena,  of  stimulus 
and  sensation. 
25.  There   existed   indeed   another   side — that   which   we 

Two  sides  of 

Lotze's  may  call  the  philosophical ;  it  does  not  at  present  enter 
into  the  course  of  our  narrative,  which  deals  only  with 
the  extension  of  scientific  or  exact  thought,  and  with 
mental  phenomena  and  the  inner  life  in  so  far  as  they 
form  a  province — perhaps  a  very  restricted  province — of 
the  whole  of  nature.  This  province  Lotze  was  among 
the  first  to  proclaim  distinctly  to  be  one  which  natural 
science  had  to  conquer  and  to  cultivate.  He  is  careful 
to  explain  that  it  does  not  cover  the  whole  ground  of 
psychology,  and  at  the  end  of  his  long  discourse  on  the 
"  soul  and  its  life,"  which  formed  an  important  con- 
tribution to  the  great  physiological  encyclopaedia  pub- 
lished in  the  middle  of  the  century,  he  clearly  marks 
out  "  physiology  of  the  soul  as  an  exposition  of  the 
physical  and  mechanical  conditions  to  which,  according 
to  our  observation,  the  life  of  the  soul  is  attached,"  ^  as 
one  of  the  several  problems  of  psychology.  It  formed  a 
counterpart  to  the  physiology  of  the  body,  of  the  physical 
side  of  our  existence,  and  was,  like  it,  to  become  a  natural 
— i.e.,  a  mechanical — science.  Subsequently  he  collected 
the  whole  of  his  reflections  belonging  to  these  two  de- 
partments in  two  treatises  on  the  '  General  Physiology 
of  Bodily  Life'  (1851),  and  on '  Medical  Psychology'  or 
'The  Physiology  of  the  Soul'  (1852). 

As  little   as   it   now   enters   into   our  programme    to 


manner  with  what  affections  of 
the  body.  Unfortunately,  medical 
science  has  only  too  often  lost  sight 


less  speculations  referring  to  that 
connection  itself  "  (p.  197).  Cf.  also 
'  Medicinische  Psychologic,'  p.  78. 


of  this  its  proper  pi'oblem  over  fruit-  ^  '  Kleine  Werke,'  vol.  ii.  p.  204. 


ON    THE    rSYCHO-PHYSICAL    VIEW    OF    NATUKE.       503 


folluw  ii[»  the  phil(js()i)hical  reasonings  of  Lotze  beyond 
the  limit  of  the  psycho-physical  mechanism,  so  little  were 
these  at  the  time  of  their  appearance  heeded  liy  many  of 
his  readers,  some  of  whom  he  seems  to  have  converted 
to  or  confirmed  in  a  purely  materialistic  conception  of 
the  phenomena  of  the  inner  or  mental  world.  Lotze  had 
banished  "  vital  forces "  from  Ijiology ;  why  not  follow 
him,  and  banish  all  other  higher  principles,  and  revive 
— as  Carl  Vogt  did  ^  —  the  dictum  of  Cabanis  about 
the  analogy  between  the  functions  of  the  brain  and 
the  kidneys  ?  AVhy  should  the  "  anima  "  of  Stahl  not 
have  the  same  fate  as  the  "  vital  force  "  of  Bordeu  and 
Bichat  ? 

This  was  a  misconception  of  what  Lotze  had  intended. 
He  had,  indeed,  banished"  the  principle  of  life  as  a 
factor  useless  in  physiological  explanations ;  but  not  the 
principle  of  organisation,  which  must  have  presided  over 
the  beginning  of  all  organic  forms.  This  might  he 
neglected  by  physiologists,  who  had  nothing  to  do  with 
origins  but  only  with  existing  relations.  It  was  (|uite 
different  with  mental  phenomena,  which,  manifesting 
themselves  alongside  of  physical  processes,  required  to  be 
dealt  with  and  recognised  as  actually  existing  and  con- 
current events.^     Herbart's  psychical  mechanism  might 


^  On  this,  see  the  account  given 
in  Lange's  '  History  of  Materialism  ' 
(Engl,  transl.,  vol.  ii.  p.  285)  and 
Lotze's  reference  to  it  in  '  Med. 
Psychol.,'  p.  43. 

-  "  There  is  no  doubt  that  a 
legitimate  attack  upon  '  vital  force  ' 
has  marked  in  our  days  that  line  of 
reasoning,  which  has  by  the  law  of 
inertia  carried  many  of  our  cou- 
temporaries  far  beyond  the  correct 


limit  on  to  a  negation  of  the  exist- 
ence of  a  soul"  (ibid.,  p.  41). 

•'  These  various  points  are  very 
fully  discussed  in  Lotze's  earliest 
philoso])hical  work,  '  Metaphysik  ' 
(Leipzig,  1841),  pp.  2.">1,  2.');'),  259  ; 
and  again  in  the  '  Med.  Psychologie  ' 
(1852),  p.  78.  Referring  to  tiie 
last  chapter,  in  which  I  dealt  with 
the  development  of  the  theories  of 
life   and    organisation,    two   points 


504  SCIENTIFIC   THOUGHT. 

be  an  unrealisable  ideal  in  that  it  dealt  with  inner 
phenomena  as  unconnected  with  outer  ones :  a  psycho- 
physical mechanism  was  a  nearer  approach  to  a  true 
description  of  reality,  and  could  not  be  narrowed  down 
to  a  purely  physical  occurrence ;  moreover,  the  unity 
of  mental  life  was  a  special  property  which  had  to 
be  recognised  and  defined. 
26.  Lotze  himself,  after  formulating  the  conception  of  a 

physucsof°'  psycho-physical  mechanism,  and  utilising   the   elaborate 

vision.  .  •  e 

and  fundamental  expermients  and  observations  of  Weber 
as  illustrations  of  what  was  meant,  made  an  important 
contribution  towards  an  analysis  of  a  compound  physico- 
psychical  process.  He  took  up  the  problem  which 
Berkeley  had  attacked,  of  the  formation  of  our  space 
perception.  It  had  been  introduced  into  German 
psychology  mainly  through  Herbart  with  reference  to 
the  Kantian  doctrine  that  space  is  a  subjective  form. 
Through  Lotze,  and  subsequently  through  Helmholtz,  it 
has  been  shown  to  have  not  only  a  psychological  but 
likewise  a  physiological  importance :  it  is  a  problem  of 
psycho-physics. 

There  exists  a  peculiar  difficulty  in  bringing  home  to 
the  popular  mind  the  fact  that  a  special  problem  is  in- 

maj'  be   noted.     First,    it  is   clear  i    in    the    ever  indistinct    manner  in 

that  Lotze  was  aia  "  organicist"  be-  which  language  operates  in  forming 

fore  Claude  Bernard  and  other  more  j    its  words,  it  may  form  the  correctest 

recent  thinkers    mentioned    above.  conceptions  in  just  as  incorrect  a 

Secondly,   it  is  very   evident  that  manner  as  the  most  erroneous  ones. 

Lotze  belongs  to  the  pre-  Darwinian  What  is  important  is  whether  the 

school  of  thought.     In  fact,  he  does  '    conception,    formed    anyhow,    can 

not  relish  the  genetic  aspect.     The  '   justify  itself  "(' Med.   Psychol.,' p. 

historical   beginnings   of  ideas  are  I    41).     I    shall   on   another  occasion 

for  him  no  indication  of  their  value  I    have    to  refer  more    fully  to   this 

and  correctness.     He  says  on  this  ,    marked   absence    of   the  historical 

point :  "  The  genesis   of  a  concep-  i    sense  in  Lotze. 
tion  is  no  argument  for  its  validity  ; 


ON    THE    PSYCHO-PHYSICAL    VIEW    OF    NATURE.      505 

volved  in  the  manner  in  which  (jur  senses  uf  sight  and 
touch  combine  and  arrange  simple  sensations  into  the 
whole  of  a  well-ordered  })erception  of  space ;  for  we  do 
not  become  able  to  appreciate  the  fact  of  the  slow 
and  gradual  growth  of  this  perception,  which  takes 
place  in  the  early  days  of  our  infancy,  till  long  after 
we  have  actually  gained  full  possession  of  it.  Some- 
thing similar  exists  wilii  regard  to  language  and 
thought :  we  only  hear  of  grammar  and  logic  long 
after  the  main  ditiiculties  of  speech  and  thinking  have 
been  unconsciously  mastered,  and  if  it  were  not  for 
the  existence  of  other  languages  than  our  own,  and 
of  an  erroneous  logic  as  exemplified  in  errors  of  cal- 
culation and  of  measurement,  it  is  doubtful  whether 
grammar  and  logic  would  have  Ijcen  so  early  developed. 
As  it  is,  the  physiological  problem  of  the  formation  of 
our  space  perception  was  actually  first  forced  upon 
naturalists  by  the  observation  of  pathological  cases,  such 
as  the  acquisition  of  sight  in  later  life  through  couching, 
the  existence  of  colour  blindness,  and  a  variety  of  optical 
delusions  which  still  serve  as  indispensable  test  cases  for 
the  various  theories  that  have  been  propoimded.  Only 
when  something  turns  out  to  be  palpably  wrong  do  we 
begin  to  inquire  what  constitutes  the  right  side  of  many 
things. 

Thus  the  cases  of  Cheselden  and  Wardrop  and  the 
colour  blindness  of  Dalton  set  physiologists  thinking 
about  the  genesis  of  our  space  and  colour  perceptions. 
A  very  great  impetus — perhaps  the  most  valuable  of  all        27. 

.  .  c       ^  Wlieat- 

— was  given   by  Wheatstone s  mvention  of  the  stereo-  stoiies 

_  _  _  _  stereoscope. 

scope  in  1838  ;  an  instrument  which,  as  it  were  through 


'06 


SCIENTIFIC    THOUGHT. 


a  kind  of  deception,  gave  to  perfectly  flat  surfaces  the 
vivid  appearance  of  depth  and  distance.  And  here  we 
may  note,  in  passing,  how  it  was  ahnost  entirely  left 
to  foreign  thinkers  to  utilise  this  remarkable  invention 
for  the  benefit  of  the  theory  of  vision  and  the  science 
of  psycho  -  physics  ;  ^  Whewell  having  characteristically 
omitted  this  epoch-making  fact,  as  in  his  well-known 
history  he  omitted  to  notice  many  other  contemporary 
British  contributions  to  science. 

Philosophers,  who  are  accustomed  to  find  hidden 
problems  where  ordinary  persons  only  see  common-sense, 
had  already  approached  the  question  of  the  genesis  of  our 
space  perception  from  two  definite  jDoints  of  view,  which 
we  may,  for  the  sake  of  convenience,  identify  with  the 
names  of  Kant  and  Herbart.  The  genetic  view  associ- 
ated by  the  physiologists  with  the  name  of  Kant,  and 
supposed  to  have  been  prepared  by  Locke,  Berkeley,  and 
Hume,  was  this,  that  what  we  know  of  external  things 
depends  upon   the   peculiarities   of  our  own   perceiving 


^  Sir  Charles  Wlieatstone  (1802- 
1875),  to  whom  several  inventions 
of  equal  scientific  and  practical 
interest  are  clue,  invented  the 
mirror  -  stereoscope  in  1833.  A 
notice  of  it  was  given  in  Mayo's 
'  Outlines  of  Human  Physiology,' 
but  neither  its  theoretical  nor  its 
practical  importance  was  recognised 
till  Wheatstone  published  his  paper 
in  the  'Phil.  Trans.' in  1838.  He 
there  refers  to  Leonardo  da  Vinci  as 
having  been  the  only  one  before  him 
to  notice  the  difference  of  binocular 
and  monocular  vision.  Since  Wheat- 
stone's  invention  became  known  and 
was  perfected  bj'  Brewster,  Moser, 
and  others,  and  especially  since 
Helmholtz  entered  the  field  with  his 
extensive  and  original  researches  in 


optics,  it  has  been  found  that 
ancient  as  well  as  more  recent 
philosophers  had  a^jproached  the 
subject  very  closely ;  and  many 
references  are  given  in  the  new 
edition  of  the  '  Physiologische 
Optik  '  (1896),  p.  840.  The  inven- 
tion of  photography  about  the  same 
time  (1835,  by  Daguerre,  after  ex- 
tensive and  i)rolonged  experiments 
by  himself  and  Niepce,  published  in 
1839  by  Arago),  which  was  of  great 
imjiortance  to  optical  theory,  was 
also  for  some  time  singularly  little 
appreciated  by  theorists.  See 
Rosenberger,  '  Gesch.  d.  Physik,' 
vol.  iii.  p.  316.  See  also  Helmholtz's 
lecture  "  Ueber  das  Sehen  des 
Menschen"  (1855). 


ON    THE    PSYCHO-PHVSrCAL    VIKW    OF    NATURE.       507 

and  tliinkiiig  self,  on  sensatiuns,  and  (jn  their  arrange- 
luent   or   orderly   presentation.      The    sensations    them-        29. 

LocalirtatioB 

selves  are  the  suhstance,  the  sijatial  arrangement  ".r»ensa. 
of  them  the  form,  of  owy  perception  of  external 
things.  The  question  was  gradually  put  more  and 
more  clearly,  H(jw  we  come  to  localise  certain  of  our 
sensations  at  definite  places  in  the  totality  of  a  spatial 
arrangement  ?  Herbart  added  another  important  refiec- 
tion,  which  really  dated  from  Leilmiz.  Impressed  with 
the  unity  of  all  mental  existence,  and  claiming  this  as 
the  characteristic  property  of  our  inner  life,  he  asked  the 
question.  How  can  the  oneness  or  simplicity  of  this  inner 
existence,  as  it  were,  expand  itself  without  losing  its 
unity,  into  the  orderly  variety  of  a  spatial  contemplation  ? 
For  the  purpose  of  an  answer  to  this  question  he  fixed 
on  the  phenomenon  of  motion.  The  conception  of  an 
orderly  arrangement  of  sensations  or  things  in  space  is 
gained  in  great  measure  by  the  aid  of  definite  move- 
ments of  the  sensitive  organs,  which  are  accompanied 
by  definite  sensations  of  motion  —  c.f/.,  1  )y  muscular 
sensations. 

The  first  of  these  two  questions  may  be  expressed  in 
the  words,  Given  the  subjective  form  of  a  space  percep- 
tion, either  complete  in  its  geometrical  arrangement  (the 
nativistic  hypothesis)  or  gradually  acquired  in  the  early 
moments  of  our  conscious  life  (the  empiric  hypothesis), 
who  do  we  make  ourselves  familiar  with,  and  at  home  in, 
this  form  of  perception  ?  And  secondly,  By  what  special 
properties  or  local  signs  do  we  localise  or  place  each 
single  sensation  in  its  right  and  orderly  position  ?  The 
first  is   the   prol)Iem  of  space  construction,  the  second 


508 


SCIENTIFIC    THOUGHT. 


29. 
Lotze's 
"local 
signs." 


30. 
Feclmer. 


that  of  localisation  of  things  in  space.  Lotze  was  one  of 
the  first  to  attempt  detailed  answers  to  these  questions. 
In  particular  he  propounded  the  theory  of  "  local  signs," 
which  with  certain  modifications  has  been  adopted  by- 
subsequent  writers  on  the  subject.  The  combination 
of  physiological,  optical,  and  psychological  investigations 
in  Helniholtz's  great  work  on  '  Physiological  Optics ' 
has  brought  deliniteness  and  mathematical  precision 
into  many  of  the  questions  suggested  by  philosophers 
and  naturalists  before  him.  Through  it  and  its  great 
companion,  the  '  Physiological  Acoustics,'  psycho-physics 
has  to  a  large  extent  become  an  exact  science. 

A  great  step  in  the  direction  of  drawing  psychical 
phenomena  into  the  circle  of  the  exact  sciences  was  taken 
independently  by  Gustav  Theodor  Fechner ;  ^  in  fact,  it  is 


1  G.  T.  Fechner  (1S01-1S87)  was 
a  unique  figure  in  German  liter- 
ature, science,  and  philosophy. 
Beyond  his  own  country  he  is  only 
very  imperfectly  known  and  appre- 
ciated. He  was  self-taught,  and 
living  all  his  life  somewliat  outside 
the  conventional  categories  of  Ger- 
man academic  activity,  he  made 
a  position  for  himself  which  has 
only  become  intelligible  to  a  larger 
public  through  the  issue  —  after 
liis  death — of  Prof.  Wundt's  ora- 
tion, Prof.  Kuntze's  (his  nephew's) 
charming  biography  (1892),  and 
Prof.  Lasswitz's  monograph  on 
Fechner  (Stuttgart,  1896),  in 
which  for  the  first  time  a  co- 
herent exposition  of  his  philo- 
sophical teaching 
Prof.  Wundt  has 
passages     of     his 

chology,  and  through  the  second 
edition  of  the  '  Psychophysik,'  con- 
tributed largely  to  a  better  under- 
standing of  Fechner's  views  and 
merits.       He    descended    on   both 


is  attempted, 
also,  in  many 
work     on     psy- 


sides  from  ancestors  whose  position 
was  that  of  highly  esteemed  Pro- 
testant pastors  ;  he  studied  medi- 
cine like  Lotze,  and  was  the  friend 
and  colleague  of  Lotze's  teachers, 
Weber  and  Weisse.  In  his  auto- 
biographical i-ecord,  communicated 
b}'  Kuntze,  he  confesses  having  be- 
come almost  an  atheist  under  the 
influence  of  his  medical  studies, 
until  he  became  acquainted  with 
the  jihilosophy  of  Schelling,  Oken, 
and  StefFens,  which  dazzled  him, 
touched  the  poetical  and  mystical 
side  of  his' nature,  and,  though  he 
hardly  understood  it,  had  a  lasting 
influence  on  him.  The  simultan- 
eous occupation  with  the  best 
scientific  literature  of  the  day  (he 
translated  French  text-books  such 
as  those  of  Biot  and  Thenard,  and 
verified  Ohm's  law  experimentally), 
however,  forced  upon  him  the  scep- 
tical reflection  whether,  "  of  all 
the  beautiful  orderlj'  connection 
of  optical  phenomena,  so  clearly 
expounded  by  Biot,  anything  could  1 


ON    THE    PSYCHO-PHYSICAL    VIEW    OF    NATURE.       509 

\n  him  that  we  are  indebted  for  the  term  Psycho-physics, 
wliich  in  the  present  cha})ter  ]  have  used  in  a  more 
general  sense.  Feclmer  Wdikcd  independently  of  Lotze 
and  Hehnholtz  on  th(>  lines  of  K.  H,  "Weber.  He  does 
not  seem  to  have  been  much  inlhienced  by  either  Kant 
(ir  Herbart.  In  ISGO  lie  ])ublished  his  '  Elemente  der 
Psychophysik,'  which  was  to  be  an  exact  treatise  on  the 
relations  of  "  mind  and  body,"  founded  upon  a  measure- 
ment of  psychical  quantities. 

Herbart's  attempt  to  submit  psychical  phenomena  to 
the  exact  methods  of  calculation  had  failed  through  the 
\vant  of  a  measure  for  psychical  ({uantities.  Lotze  had 
siiij:ested  the  idea  of  a  psycho-physical  mechanism — 
'.'.,  a  constant  and  definite  connection  between  inner 
and  outer  phenomena,  between  sensation  and  stimulus. 
Iv  IT.  AVeber  in  his  important  researches  on  "  Touch  and 
1  '>odily  Feeling  "  had  made  a  variety  of  measurements  of 
-ensations,  and  shown  that  in  many  cases  stimuli  must 
be  augmented  in  proportion  to  their  own  original  inten- 
sity in  order  to  produce  e([nal  increments  of  sensation. 
These  observations  lent  themselves  t(j  an  easy  mathe- 
matical generalisation.      Feehner  was  the  first  to  draw 


have    been    fouml    out    l>y    Okeii- 
Si-helling's    method'"'      This    mix- 
ture or  alternation  of  exact  science 
.mil  specuhition,  of  faithfuhiess  and 
loyalty  to  facts  as  well  as  to  theory, 
)uus    through    all    Foclmer's    life, 
Work,  and  writings.      Much   of   his 
)"ietry,    of    his   fanciful    and    para- 
il'xical  effusions,  is  meant  seriously, 
I  1  is  really  more  colierent  than  it 
.  p[>eared   to  his    readers,    some    of 
whom   knew    him    only    under    his 
'•udonym  of  Dr  Mi.>es.     He  lived, 
.ught,   and   worked  truly  on  the 
rderland  of  nature  and  mind,  of    I 


this  world  ami  another,  of  science 
and  poetry,  of  reality  and  fiction. 
Like  Lotze,  he  wanted  the  genuinely 
historical  sense.  Like  Lotze,  too, 
he  received  from  others  only  sug- 
gestions which  he  elaborated  in- 
dependently in  his  own  original 
fashion.  As  little  as  Lotze  does 
he  seem  ever  to  have  attempted 
to  realise  and  understand  any  other 
philosophical  system  than  his  own. 
To  both,  the  ultimate  problem  was 
capable  oidy  of  a  subjective  solu- 
tion.    Cf.  vol.  i.  p.  "200. 


510  SCIENTIFIC    THOUGHT.  | 

the  attention  of  philosophers  to  the  existence  of  this  re- 
lation in  a  variety  of  instances,  and  collected  a  large 
number  of  facts  to  prove  its  general  correctness.  He 
conceived  the  idea  of  measuring  sensations  by  their 
accompanying  stimuli,  a  mode  of  measurement  based 
upon  that  relation  which,  under  the  name  of  Weber's 
law  or  formula,  he  introduced  as  a  general  psycho- 
physical proposition.  The  intervals  in  the  numerical 
scale,  the  differences  in  the  magnitude  of  stars,  the 
facts  established  by  Weber  relating  to  our  estimate  of 
differences  of  touch,  of  weight,  and  of  temperature ; 
lastly,  the  relation  of  "  fortune  physique  "  and  "  fortune 
morale,"  known  to  Euler  and  Lagrange,  could  all  be 
utilised  towards  proving  the  general  accuracy,  within 
certain  limits,  of  the  psycho  -  physical  formula.  The 
work  gave  rise  to  many  discussions  ^  as  to  the  mean-  . 
ing  of  the  term  quantity  applied  to  psychical  pheno-  | 
niena,  as  to  methods  of  measurement,  and  as  to  the 
significance  to  be  attached  to  the  new  branch  of  research 

^  In   addition  to  the   '  Elemente  which   he   was    occupied   with  it." 

der  Psychophj'sik  '  (1860),  uf  which  i  (See  the  obituary  oration,  reprinted 

a  second  edition  appeared  in  1890,  {  in  Kuntze's   'Biography,'    p.  360.) 

the  author  enlarged,  discussed,  and  The  attacks  on  Fechner  came  from 

defended    his     special     ideas    and  j  many    quarters.       In    the    polemi- 

theories  in   three  further   pubHca-  '  cal    treatise    of    1877    he    notices 

tions.    The  year  1877  produced  '  In  '  iiow    the    views    of    his    critics  — 

Sachen  der  Psychophysik,' tlie  year  i  Hehnholtz,    Aubert,    Mach,    Bern- 


1882  the  'Revision  der  Hauptpunkte 
der  Psychophysik,'  and  shortly  be- 
fore   his    death    (1887)    there    ap- 


stein,  Plateau,  Delbreuf,  Bren- 
tano,  Hering,  Langer  —  agree  as 
little    among    themselves    as    with 


peared,     in     the     '  Philosophische  [    his   own.      He   sums  up   with  fine 

Studien  '  of  Prof.   Wundt,  his  last  |    humour:  "  The  tower  of  Babel  was 

contribution,    "  Ueber   die   psychi-  ,    not  finished,  because  the  builders 

schen     Maasprincipien      und      das  could  not  agree  how  to  build  it ; 

Webersche    Gesetz,"    which    Prof.  I    my  psycho-physical  structure  maj^ 

Wundt  declares  to  be  ''  the  clearest  i    remain  standing,  because  the  work- 

and   most   complete    exposition    of  I    men  cannot  agree  how    to  iiull  it 

the  problem  which  he  gave  in  the  down  "  ('In  Sachen,'  &c.,  p.  215). 

course  of   the  forty  years   during  I 


ON    THE    PSYCHO-PHYSICAL    VIEW    OF    NATUHE.       511 


as   well  as  to  the  interpretation  of  the  Weber- Feehner 
law  of  psycho-physical  dependence. 

We  are  indebted  to  Prof.  Wundt  of  Leipzig  for  a 
complete  and  exhaustive  exauiinatiiju  of  the  new 
jirovince  of  exact  science.^      He  enlarged  its  boundaries, 


31. 

WuiiUt. 


'  The  psycliulogical  t-clii)ol,  of 
which  Prof.  Wuudt  can  be  con- 
-iilered  the  head  or  centre,  has  been 
contrasted    by   M.    Kibot,    in    his 

■  I'sychologie  Allemande  Conlempo- 
i.tine'  (1st  ed.,  1879),  with  tlie 
llnglish  school,  and,  in  the  ex- 
position in  the  text,  I  have  taken 
a  simihir  view.  Ifc  would,  how- 
1  \er,  be  unjust  not  to  note  that  in 
Knglatid,  prior  to  the  publication  of 
I'rof.  Wundt's  princi[)al  writings,  a 
ii'velojiment  of  psychology  in  the 

-  tme  direction  had  already  begun. 
I'lie  principal  representative  of  this 

■  li'velopment  is  Prof.  Alexander 
Main  (born  1818),  whose  two  great 
v'.orks,  '  The  Senses  and  the  Intel- 
i.'ct'  (185.^)  and  'Tlie  Emotions 
and  the  Will '  (1859),  appeared  even 
I'cfore  Fechner's  '  Psychophj-sik,' 
and  were  characterised  by  J.  S. 
-Mill  as  "an  exposition  which  de- 
serves to  take  rank  as  the  foremost 
of  its  class,  and  as  mai-king  the 
most  advanced  jioint  which  the  a 
fistcriori  psychology  has  reached," 

I  eing  "  the  most  genuinely  scientific 
analytical  exposition  of  the  human 
mind  wliich  the  a  posteriori  psy- 
'  hology  has  up  till  this  time  pro- 

■  luced""  ('Edinb.  Rev.,'  October 
1  ^."^9,  reprinted  in  '  Di.ssertations 
and  Discussions,'  vol.  iii.  pp.  99, 
100).  Bain  carried  out  what  had 
been  called  by  Thomas  Hrown  "  the 
physical  investigation  of  the  mind," 
and  was  ])robably  the  first  ICnglish 
psychologist  who  enriched  the  older 
associational  jisychology  by  an  ex- 
tensive use  of  the  teachings  of  i)hj-si- 
ology  ;  the  germ  of  his  theory  being 
contained  in  a  passage  cited  by  him 
from  Johannes  Miiller  :  in  fact,  he 


apiircciated  the  well-known  dictum 
of  the   latter,    *'  psycholof/ux    nemo 
nisi  physiolo!/us.'"    Shortly  after  the 
appearance  of    Prof.  Bain's   works, 
the  overmastering  intiucnce  of  the 
evolutionist    school     in     England, 
headed   l>y   Mr   Spencer    and    sup- 
ported   by    Darwin,   and    the    jjro- 
nounced  opposition  with  which  the 
IJsycho-physical   school    started    in 
Germany,  cast  somewhat  into  the 
shade  the   steady  develoi)mont,  in 
this  country,  of  the  exact  science  of 
psychology  by  those  who  formed  the 
direct  succession  to  the  older,  purely 
introspective,    school    of     Scottish 
thinkers.     As  I  am  not,  in  the  ]ires- 
ent  chapter,  treating  of  iisych(jlogy 
and  philosophy,  but  of  the  attempt 
to  gain,    by    the    methods    of    the 
exact  sciences,  a  conception  of  the 
phenomena  of  animation  and  con- 
sciousness, I  leave  for  another  oc- 
casion    the    appreciation     of     the 
English  school  of  psychology-.     The 
members  of  this  scliool  considei-ed 
physiology  as  an  aid  to  psychological 
research,  whereas  most  of  the  rep- 
resentatives of  the  modern  German 
school  were,  to  begin  with,  physi- 
ologists   or    physicists,    and    only 
became  subseiiuently  psychologists 
or  philosophers.     Characteristic  of 
this   school   are    two    points :    the 
op])osition    they    made    from    the 
start  to  the  existing  methods,  and 
their  jiioniinent  use,  not  only  of  ob- 
servation, but  of  ex])eriment.     The 
less   ostentatious    development    of 
English  thought  would,  no  doubt, 
have  led  in  tiie  end,  but  for  the 
reasons  given  above,  to  like  results. 
An    ojiposition    similar   to    that  so 
marked  in  Geiniany  was,  howevei-, 


512  SCIENTIFIC    THOUGHT. 

taking  in  the  ground  covered  by  Lotze's  medical 
psychology  as  well  as  by  Helmholtz's  physiology  of 
hearing  and  seeing ;  added  a  large  number  of  measure- 
ments of  his  own,  some  of  them  quite  original,  such  as 
those  referring  to  the  time-sense,  many  of  them  in  con- 
firmation and  extension  of  Fechner's  collection  of  facts ; 
invented  new  methods  and  new  apparatus ;  brought  the 
whole  subject  into  connection  with  general  physiology,  as 
also  with  the  more  exclusively  introspective  psychology 
of  the  older,  notably  the  English  and  Scottish,  schools; 
and  pointed  to  the  necessary  completion  which  these  in- 
vestigations demand  from  the  several  neighbouring  fields 

32.        of  research.      Through  his  labours  "  physiological  psycho- 
physio- 
logical        logy "  as  an  independent  science  has  for  the  first  time 

psychology.        ""^  ^ 

become  possible.  The  influence  of  his  great  work  on 
this  subject,  as  also  of  his  teaching  and  demonstra- 
tions, has  been  very  stimulating.  With  its  place  in  the 
history  of  philosophical  thought  I  shall  have  to  deal  in  a 
later  portion  of  this  history.  At  present  I  will  merely 
refer  to  the  leading  ideas  and  contributions  it  contains  to 
our  scientific  reasoning  on  the  psycho-physical  problem. 

Wundt  approached   psychological    research   from   the 
side  of  physiology ;  -^  his  earlier  writings  referred  to  the 


taken  up  in  England  in  single  in- 
stances— e.g.,  by  G.  H.  Lewes  and 
Dr  H.  Maudsley,  the  former  in 
favour  of  Positivism,  the  latter  on 
the  foundation  of  his  '  Physiology 
and  Pathology  of  ]Mind  '  (1st  ed., 
1867). 

'  Tiie  researches  of  Wundt  and 
the  earlier  work  of  Fechner  re- 
mained practically  unknown  in 
this  country  up  to  the  time  of 
the  appearance  of  the  periodical 
'  Mind,'    edited    by    Prof.    Croom 


Robertson,  in  1876,  under  the 
generous  patronage  of  Prof.  Bain. 
Even  Lotze  and  Herbart  were 
hardly  known  in  this  country. 
A  similar  disregard  of  English 
psychology  existed  in  Germany. 
The  foremost  writers  on  the  his- 
tory of  modern  philosophy,  such  as 
Erdmann  and  Ueberweg,  wrote  as 
if  modern  philosophic  —  including 
psychological  —  thought  existed 
only  in  Germany.  Even  the 
singularly  imjjartial  and  unbiassed 


ON   THE    PSYCHO-PHYSICAL    VIEW   OF    NATURE.       513 


physiology  of  the  senses,  to  physiology  proper,  and  to 
such  phenomena  of  psychical  or  inner  life  as  can  he 
traced,  not  only  in  man,  l)ut  also  in  the  brute  creation. 
He  thus  seems  to  have  approached  psychology  with  the 
true  instinct  and  methods  of  an  exact  student  of  nature. 
In  the  course  of  years  his  psycho-physical  studies  took 
more  and  more  the  character  of  an  experimental  psycho- 
logy, and  in  the  latest  edition  of  his  great  work  he 
describes  it  as  such,  maintaining  that  the  designation  of 
physiological  psychology  has  rather  a  historical  meaning.^ 


author  of  the  '  History  of  Material- 
ism,' Albert  Lange,  does  only  scant 
justice  to  the  labours  of  the  Eng- 
lish school,  J.  S.  Mill  being,  in 
fact,  the  only  English  philosophical 
writer  of  the  middle  of  the 
century  who  was  appreciated  in 
Germany.  The  last  twenty -five 
years  have  entirely  altered  this 
state  of  things.  French  and 
American  writers,  such  as  M. 
Ribot,  Prof.  M'Cosh,  and  more 
recently  Prof.  James,  treat  im- 
partially of  the  rival  claims  of 
German  and  English  thinkers. 
'  Mind '  has  preserved  its  fairness 
in  admitting  contributions  from 
opposite  sides  ;  and  latterly  there 
has  been  started  bj'  the  publishing 
house  of  Froniniann  of  Stuttgart; 
under  the  editorship  of  Prof. 
Falckenberg,  a  series  of  very  use- 
ful monographs  on  recent  thinkers, 
whose  voluminous  or  scattered 
writings  make  it  difficult  to  arrive 
at  a  comprehehsive  and  just  ap- 
preciation of  the  main  diift  of 
their  doctrine.  Ever  since  some 
provinces  of  philosophy  were  con- 
quered by  exact  research,  unit}' 
of  plan  has  been  to  a  great  ex- 
tent sacrificed  ;  the  natural  science 
of  mind  is  becoming  split  up  into 
fragments  like  that  of  life.  Prof. 
Lasswitz  has  given  us  for  the 
first    time   a  coherent   account   of 

VOL.  II. 


Fechner's  philosophj',  and  although 
Prof.  Wundt  had  already  jiut  forth 
in  his  '  System  der  Philosophie ' 
(1st  ed.,  1890)  a  statement  of  his 
systematic  views,  the  monograph  by 
Edmund  KiJnig  (1901)  is  very  help- 
ful in  fixing  the  historical  position 
of  Wundt  and  the  genesis  of 
his  doctrine.  I  refer  to  these 
volumes  for  a  bibliography  of 
the  thinkers  discussed. 

^  In  the  introduction  to  the 
'  Physiologische  Psychologie'  (4te 
Aufl.,  vol.  i.  p.  9)  Prof.  Wundt 
saj's,  "  The  conception  of  experi- 
mental psychology  has  been  ex- 
panded beyond  its  original  limits, 
as  we  now  comprehend  under  it 
not  only  those  parts  of  psychologj' 
which  aie  directly  accessible  to 
experiment,  but  the  whole  of 
psychology  ;  as  it  makes  a  direct 
use  of  the  experimental  method 
wherever  this  is  possible,  and  an 
indirect  use  in  all  other  instances 
through  applying  the  results  gained 
in  the  former,  and  through  render- 
ing internal  observation  more  acute. 
.  .  .  The  designation  of  physio- 
logical psychology,  which  originated 
in  the  peculiar  historical  anteced- 
ents of  our  science,  is  one-sided. 
.  .  .  The  centre  of  gravity  of  the 
experimental  method  lies  in  this, 
that  it  alone  makes  reliable  inner 
observation  possible." 

2  K 


514  SCIENTIFIC    THOUGHT. 

WHiilsl  his  methods  are  exact  and  definite,  his  aim  is, 
nevertheless,  wide  and  compreliensive  ;  for  not  only  is  the 
animal  creation  studied  as  a  valuable  field  for  enlarged 
psycho -physical  research,  l)ut  also  the  psychology  of 
infancy  and  of  human  societies  (ethnical  psychology)  are 
drawn  into  the  circle  of  a  scientific  psychology.  At  the 
same  time  his  exposition  is  directed  towards  the  totality  ^ 
of  the  phenomena  of  life  and  mind,  it  being  his  ultimate 
object  to  arrive  at  some  appropriate  conception  of  the 
whole  of  human  existence.  In  this  respect  his  scientific 
labours  form  a  counterpart  to  those  of  naturalists  like 
Humboldt  and  Darwin,  who  did  so  much  to  direct  the 
attention  of  natural  science  to  the  whole  of  nature,  her 
history  and  economy.  It  seems  to  me  that  Prof.  Wundt 
has  similarly  introduced  into  the  psycho-physical  study 
of  nature  the  prominent  consideration  of  the  mental  side 
of  life  in  its  totality,  starting,  as  Darwin  and  Humboldt 
did,  from  a  large  accumulation  of  detailed  observations. 

This  regard  for  the  whole  problem  distinguishes 
Wundt's  waitings  from  those  of  other  eminent  psycho- 
physicists,  such  as  Hehnholtz,  who  deals  brilliantly  and 
exhaustively  with  certain  special  problems,  or  Fechner, 
who  relegated  the  discussion  of  the  fundamental  ques- 
tions to  a  series  of  half-poetical  treatises,  which  are  full  j 
of  suggestion  rather  than  close  scientific  reasoning.     But 

^  '  Physiologische      Psj-chologie  '  totality  of  the  phenomena  of  life, 

(4te  Aufl.,  vol.  i. p.  2) :  "Our  science  and,   if    possible,   to   gain   in    this 

has  accordinglj'  the    task,  first,   to  way  a  comprehensive  conception  of 

investigate  those  vital   phenomena  human    existence."      See   also    his 

which,  lying  in  the  middle  between  essay     "  Philosophic    und    Wissen- 

outer  and  inner  experience,  require  schaf  t "    in    a  volume  of  'Essays' 

the sinmltaneous application  of  both  ,    (Leipzig,    1885),    p.    1;    also    'Die 

methods  of  observation,  outer  and  '    Aufgaben       der      experimentellen 

inner;  and  secondly,  to  throw  light  Psychologie,'  ibid.,  p.  127,  &c. 
from  the  points  thus  gained  on  the 


ON    THE    PSYCHO-PHYSICAL    VIEW    OF    NATURE.       515 

Wuiult  differs  quite  as  much  from  Lotze,  who  also  strove        33. 

^  WulKlt, 

to  arrive  at  a  view  of  the  totaUty  of  liuman  life  and  its  Fecimer, 

''  and  Lotze 

significance.  Lotze  belonged,  in  spite  of  the  original  compared, 
and  independent  view  which  he  took  of  the  psycho- 
physical problem,  to  the  older  school  of  philosophers. 
AVundt  belongs  quite  to  the  modern  school.^  Fechner 
forms  the  transition.  Lotze  begins  his  psychology,  and 
even  his  physiology  of  the  soul,  with  a  lengthy  disserta- 
tion on  the  unity  of  the  soul  as  a  special  being,  just 
as  Herbart  begins  his  psychology  with  metaphysics. 
This  metaphysical  introduction,  these  definitions  relating 
to  the  essence  of  the  soul,  its  unity,  and  its  location,  are 
absent  in  the  modern  psychology.  Instead  of  founding 
psychology  on  experience,  metaphysics,  and  mathematics, 
AVundt  founds  it  on  experience  (including  experiment), 
physiology,  and  mathematics.  In  consequence  of  this 
altered  foundation  a  new  problem  has  arisen,  precisely 
as  a  new  problem  arose  for  biologists  when  they  dis- 
carded vital  force  as  a  meaningless  and  useless  encum- 
brance.     For  the  older  biologists  life  was  the  exhibition 


"O" 


^  See  the  preface   to  the  second    '    the  problems.     But  I  quite  well  uii- 


erlition  of  the  '  System  der  Fhilo- 
>ophie'  (Leipzig,  1897),  p.  ix  :  "I 
have  always  tried  to  co-operate  in 
the  endeavour  to  secure  for  psycho- 
logy an  independent  position  as 
an  empirical  science  outside  of 
philosophy,  and  to  see  that  she 
should  not  lack  the  support  of  the 
scientific  method  in  so  far  as  this 
could  be  transferred  to  her.  .  .  . 
As  I  started  from  natural  science 


understand  that  the  position  may 
be  different  for  him  who  begins  with 
philosophy  and  then  makes  occa- 
sional excursions  into  the  regions 
of  science  or|  psychologj'."  Com- 
pare with  this  what  Lotze  says  in 
the  Introduction  to  his  '  Streit- 
schriften  '  (1857),  or  the  following 
passage  from  one  of  his  last  essays 
('Contemp.  Rev.,'  January  1880), 
"  Except  in  rare  cases,  a  prolonged 


and     then     came      to     philosophy  1  philosophical  labour  is  nothing  else 

through  occupation  with  empirical  j  but  the  attempt  to  justify,  scientif- 

|)syc!iology,  it  would  have  appeared  ically,  a  fundamental  view  of  things 

to    me    impossible    to    philosophise  !  which   has   been   adc)pted    in    early 

in   any   other   way  than  in  corre-  j  life." 
spondence   with    this    sequence  of 


516  SCIENTIFIC    THOUGHT. 

of  vital  force.  This  having  been  dropped,  the  question 
arose  for  modern  biology,  What  is  life  ?  We  thus  find 
thinking  biologists  of  the  modern,  exact  school  aiming  at 
a  mechanical  definition  of  life.  Many  answers  have  been 
attempted,  such  as  that  it  is  the  action  of  a  very  com- 
plex chemical  molecule,  of  dynamical  equilibrium,  of  meta- 
bolism, of  a  special  form  or  organisation,  &c.  Similarly, 
when  the  word  soul  dropped  out  of  psychology  in  its 
older  metaphysical  meaning  as  a  separate  being  or  entity, 
when  it  was  used  to  mean  only  the  sum-total  of  the 
inner  ur  psychical  phenomena,  a  new  problem  arose  for 
the  psycho-physicist  or  experimental  psychologist.  The 
problem  now  was  to  give  some  definition  of  the  unity 
and  unified  totality  of  all  inner  or  mental  phenomena. 
The  older  metaphysical  psychology,  as  also  for  the  most 
part  the  so-called  empirical  psychology,  answered  this 
question  by  placing  the  conception  of  an  independent 
entity,  the  soul,  person,  or  self,  at  the  opening  of  their 
discussions.  Modern  exact  psychology  cannot  do  this. 
For  it  the  unity  of  the  inner  life  and  its  unified  totality 
has  become  a  problem.  This  problem  Prof.  Wundt  faces 
34.        fully  and  fairly.     He  asks  himself  the  ciuestion,  Wherein 

The  unity  of  . 

conscious-     consists  the  unity  of  consciousness,  wherein  the  totality 

ness.  ''  '  •' 

of  all  mental  life,  individual  and  collective  ?  Armed 
with  the  methods  of  exact  research,  he  tries  to  extract 
from  the  whole  array  of  mental  phenomena  an  idea  of 
their  essence  as  distinguished  from  external  or  natural 
phenomena,  and  of  their  collective  meaning  and  signif- 
icance. In  so  doing  he  enters  the  domain  of  philosophy, 
and  his  results  belong  to  the  realm  of  philosophical 
thought.     When  dealing  with  that  large  section  of  my 


ON    THE    PSYCHO-PHYSICAL    VIEW    OF    NATURE.      517 

subject  I  shall  have  to  take  up  Wundt's  theories  where 
I  now  leave  them. 

Through  the  efforts  and  widespread  influence  of  Prof. 
"Wundt,  the  inner  or  psychical  phenomena  have  been 
drawn  into  the  circle  of  exact  research ;  a  large  portion 
of  psychology  has  become  natural  science.  It  is  quite 
consistent  with  this  that  some  of  the  disciples  of  the 
modern  school  should  have  assumed  towards  the  new 
branch  of  natural  science  the  attitude  which  has  be- 
come habitual  among  those  who  cultivate  other  natural 
sciences.  All  these  sciences  are  based  upon  observation, 
aided  if  possible  by  experiment ;  none  of  them,  however, 
has  succeeded  in  rising  to  the  rank  of  an  exact  science 
without  the  aid  of  some  generalisation  which  admitted 
of  clear  expression  in  a  few  definite  conceptions,  being 
the  more  valuable  in  the  degree  that  it  lent  itself  to 
a  clothing  of  mathematical  language.  In  the  course  of 
the  last  centuries,  notably  the  nineteenth,  several  of 
these  fundamental  principles  —  such  as  the  laws  of 
motion,  gravitation,  atomism,  vibratory  motion,  the  con- 
ception of  energy,  natural  selection,  metabolism — have 
attained  in  various  degrees,  some  almost  perfectly,  to 
this  state  of  definiteness,  and  the  sciences  Ijuilt  up 
by  their  aid  have  accordingly  acquired  the  character 
of  certainty.  Psycho  -  physics  having  through  Weber, 
Lotze,  Fechner,  and  Wundt  gradually  evolved  the  notion 
of  a  partial  parallelism  of  physical  and  psychical  pheno- 
mena, the  conception  of  a  mathematical  dependence  or 
of  function  could  be  introduced  between  the  measur- 
aljle  external  processes  and  the  hidden  internal  events 
which  we  term  mental ;  the  whole  of  the  latter  being 


518  SCIENTIFIC    THOUGHT. 

looked  upon  as  concomitant  occurrences,  as  "  Begleit- 
erscheinungen "  or  "  Epi-phenomena "  of  the  more  ac- 
cessible though  very  complex  phenomena  of  the  nervous 
system  and  its  centres ;  whereby  it  had  to  be  noted, 
that  whilst  the  external  visible  processes  exhibit  that 
continuity  in  time  and  space  which  is  characteristic  of 
all  physical  phenomena,  the  epi-phenomena  were  subject 
to  discontinuous  appearance  and  disappearance,  to  sudden 
growth  and  collapse.  Having  got  hold  of  this  partial 
formula,  which  in  some  cases  admits  even  of  a  rigorous 
mathematical  expression,  psycho-physics  had  no  pressing 
need  of  investigating  its  meaning  any  further,  or  of  in- 
quiring into  the  supposed  independent  existence  or  signif- 
icance of  the  "  epi-phenomena  "  as  such  ;  similar  general 
inquiries  into  the  origin  of  gravitation,  of  atoms,  of  the 
essence  of  energy  or  inertia,  having  proved  to  be  of  little 
or  no  use  in  furthering  astronomy,  chemistry,  thermo- 
dynamics. It  cannot  be  denied  that  this  is  a  perfectly 
tenable  scientific  attitude.  Such  an  attitude  has  notably 
been  taken  up  by  Dr  Hugo  Munsterberg,  and  by  what 
we  may  term  the  Freiburg  school  of  psycho -physics. 
Also  there  is  no  doubt  that  throus-h  a  series  of  very 
cleverly  contrived  experiments — particularly  those  re- 
ferring to  the  muscular  sense  and  the  time  sense — a 
good  deal  of  light  has  been  thrown  upon  such  mental 
processes  as  association  of  ideas,  attention,  apperception, 
and  voluntary  effort,  which  have  thus  been  brought 
into  closer  correspondence  with  changes  taking  place  in 
35.        the  nervous  system.     In  fact,  a  parallelism  of  neurosis 

Doctrine  of 

parallelism,  and  of  psychosis  has  been  more  and  more  established. 
This    doctrine    of    psycho  -  physical    parallelism,    also 


ON    THE    PSYCHO-PHYSICAL    VIEW    OF    XATLKE. 


Id 


called  the  conscious  automaton  theory,  is  the  central 
conception  in  iisychology  as  a  natural  science,  or,  as 
I  have  termed  it,  of  the  psycho  -  physical  view  (tf 
nature.  It  was  ])repared  ^  by  earlier  thinkers,  such  as 
Descartes,  and,  in  a  different  form,  by  Spinoza,"  and  Ity 
Leibniz's  doctrine  of  pre-established  harmony.^  It  has 
been  strengthened  by  the  physiological  theory  of  reflex 
action,"*  and,  independently,  by  psycho -pliysics  in  the 
narrower  sense  of  the  word,  as  founded  by  AVeljer  and 
Fechner.  But  the  possibilities  of  the  automaton  theory 
were  not  scientifically  tested  till  towards  the  end  of 
the  nineteenth  century.      In  this  country,  two  thinkers 


'  The  doctrine  of  psycho-physical 
paralleHsiii  and  its  histoi-ical  genesis 
is  given  l)y  Huxley  in  his  address 
before  tlie  British  Association  Meet- 
ing at  Belfast  in  1874,  "On  the 
Hypothesis  that  Animals  are  Auto- 
mata, and  its  History,"  in  whicli  lie 
goes  back  to  Descartes  and  Charles 
Bonnet.  A  good  account  of  the 
theory  is  also  given  by  Prof.  Wra. 
James  in  the  .'Jth  chapter  of  his 
'  Principles  of  I'sychology  '  ;  and  it 
is  fully  discussed  by  Prof.  James 
AVard  in  his  Citibrd  lectures, 
'  Naturalism  and  Agnosticism,'  vol. 
ii.  pt.  iii. 

-  The  passage  from  Spinoza  which 
is  constantly  quoted,  and,  as  Prof. 
Ward  says,  usually  in  ignorance  of 
the  context,  is  in  '  Kthica,'  part  ii. 
prop.  7  :  "  Ordo  et  connexio  ide- 
arum  idem  est  ac  ordo  et  connexio 
rerum." 

'Leibniz,  as  Huxley  {loc.  cit.) 
tells  us,  also  invented  the  term 
"  automate  spirituel "  and  appplied 
it  to  man. 

*  Du  Bois  -  Reymond,  in  his 
"Kloge"  of  Johannes  Miillei",  iias 
shown  that  the  principle  of  reflex 
action  dates  back  to  Descartes, 
wlio  also  introduced  the  term  re- 


flex. Next  in  time  cauie  Willis 
('De  motu  muscular!,'  Amsterdam, 
1682).  The  subject  seems  to  have 
been  overlooked  to  such  an  extent, 
(1784)  got  for  a 
credit  of  having 
notion  of  reflex 
his  work   had    to 


that  Prochaska 
long  time  the 
established  the 
action,  and  even 


be  rediscovered  by  Eduard  Weber 
(1846),  after  the  principle  of  the 
transition  of  a  reaction  from  the 
afferent  to  the  efferent  nerves  in 
the  central  organs  had  been  prom- 
inently put  forward  bv  Legallois 
(1811),  Marshall  Hall  ('1835),  and 
Johannes  Miiller  (1835).  In  more 
recent  times,  Prof.  Pfliiger's  ''  Laws 
of  Keflex  Action,"  and  his  and  (i. 
H.  Lewes's  theory  of  the  jiresence 
of  consciousness  in  the  si)inal  cord, 
liave  formed  the  subject  of  much 
discussion  and  much  expeiimental 
work.  A  good  historical  account 
will  be  found  in  the  13th  Lei'on 
of  M.  Ch.  Hichets  '  Physiologie 
des  Muscles  et  dos  Nerfs '  (Paris, 
1882),  and  a  discussion  of  the  whole 
subject  in  Prof.  Wundt's  '  Physi- 
ologische  Psychologic,'  ch.  xxi., 
where  especially  the  difference  be- 
tween automatic  and  reflex  move- 
ment is  brought  out. 


520 


SCIENTIFIC    THOUGHT. 


of  eminence,  Huxley  and  Clifford/  have  made  the  theory 
accessible  to  the  popular  understanding,  without,  however, 
taking  a  comprehensive  view  of  the  study  of  mental 
phenomena,  inasmuch  as  they  approached  the  subject 
from  the  side  of  natural  science — the  former  more  from 
that  of  physiology,  the  latter  from  that  of  the  mechanical 
sciences.  Prof.  Wundt  treats  the  subject  exhaustively 
in  many  passages  of  his  works,  notably  in  the  last 
chapter  of  his  great  w^ork  on  '  Physiological  Psychology,' 
in  which  he  broadly  defines  "  the  psycho-physical  view 
as  that  view  which  starts  from  the  empirically  well- 
established  thesis,  that  nothing  takes  place  in  our  con- 
sciovisness  which  does  not  find  its  foundation  in  definite 
physical  processes.     The  simple  sensation,  the  connection 


^  Although  neither  Huxley  nor 
Clifford  added  anything  new  to  the 
conception  of  parallelism  as  con- 
tained in  the  writings  of  many  ear- 
lier Continental  philosophers,  the 
fact  that  they  were  driven  from 
their  purely  scientific  positions  to 
discuss  the  subject,  and  were  not 
psychologists  and  metaphysicians 
by  profession,  gave  their  exposi- 
tions, which  are  otherwise  as  fresh 
as  they  are  immature,  a  peculiar 
charm.  Being  both  masters  in 
style,  they  at  once  enriched  the 
vocabulary  with  new  terms  which 
have  since  become  classic.  The 
word  "epi-phenomenon,"  an  equiv- 
alent for  tlie  German  '  Begleit- 
erscheinung,'  which  is  of  independ- 
ent origin  but  expresses  Huxley's 
view,  is  a  real  enrichment  of 
thought.  It  is  also  the  direct 
way  to  bring  home  the  absurdity 
of  the  whole  theory.  The  things 
of  nature  being  first  considered 
as  "phenomena" — i.e.,  as  "ap- 
pearing" to  some  one, — the  some 
one  is  next  looked  upon  as  a 
secondary     phenomenon,    an     epi- 


phenomenon.  Clifford  actually  in 
liis  psychological  atomism  goes  the 
length  of  saying,  "  Reason,  in- 
telligence, and  volition  are  pro- 
l^erties  of  a  complex  which  is  made 
up  of  elements,  themselves  not 
rational,  not  intelligent,  not  con- 
scious "  fsee  '  Mind,'  vol.  iii.  p.  67). 
In  the  physical  theory  of  atoms  it 
has  been  truly  said  that  you  cannot 
get  anything  out  of  the  atoms  that 
you  have  not,  to  begin  witli,  put  into 
them.  Clifford's  dictum  reminds 
one  of  Carlyle's  definition  of  the 
object  of  political  economy,  which 
has  to  solve  the  problem,  "  Given 
a  community  consisting  of  fools  and 
knaves,  how  to  produce  efficiency 
and  honesty  by  their  comliined 
action  ?"  Clifford's  solution  of  the 
psychological  deadlock  is  the  "  Mind- 
stuff"  theory,  the  theory  that  all 
matter  is  the  phenomenal  correlate 
of  the  elements  of  mind.  Clif- 
ford's essay  "  On  the  Nature  of 
Things  in  themselves"  is  reprinted 
in  '  Lectures  and  Essays '  (1879), 
vol.   ii.   p.  71   sqq. 


ox    THE    PSYCHO-PHYSICAL    VIKW    OF    NATURE.       521 


of  sensations  and  peicepLions,  Liieir  associations,  linally, 
the  processes  of  apperception  and  volition,  are  acconi- 
])anied  by  physiological  nerve -processes.  Other  bodily 
processes,  such  as  the  simple  and  complex  reflex  actions, 
do  not  enter  directly  into  consciousness,  Itut  they 
form  important  auxiliary  processes  of  tlie  phenomena  of 
consciousness."^  It  is,  accordingly,  (|uite  consistent, 
from  a  purely  scientiiic  })oint  of  ^■ie^v,  to  test  this 
central  conception  of  exact  psychology,  and  to  refrain 
from  introducing  any  purely  psychical  conceptions  so 
long  as  the  possibilities  of  the  conception,  that  mental 
phenomena  are  only  concomitant  occurrences  of  changes 
which  take  place  in  the  nervous  system  and  centres, 
have  not  been  exhausted.  Investigations,  with  or 
without  this  definite  purpose,  have  been  very  largely 
prosecuted  in  the  course  of  the  nineteenth  century,  and 
have  been  in  part  purely  anatomical,  in  part  physio- 
logical, the  latter  again  either  referring  to  pathological 
or  to  normal  cases.  Systematic  courses  of  experiments 
have  been  begun  at  Leipzig  and  taken  up,  according  to 
a  well-defined  special  programme,  by  I)r  Miinsterberg  at        .%. 

Miinster- 

Freiburg,  wlio  in  the  researches  of  his  laboratory  has,  berg, 
more  distinctly  than  any  other  philosopher,  adopted  the 
theory  as  a  working  hypothesis.^ 


i  '  Physiologisclie  Psychologic '  (4 
Aufl.),  vol.  ii.  ]).  644. 

-  The  principal  writings  of  Dr 
MUn.sterberg,  in  which  his  psycho- 
jihy.sical  researclies  are  contained, 
are:  1,  'Die  Willenshandlung,' 
Freiburg,  1888;  2,  '  lieitnige  zur 
Experiinentellen  Ps}'chol()gie,'  4 
parts,  1889-92  ;  3, '  Ueber  Aufgaben 
und  Methodeii  der  P.-<yciiologie,' 
being  part  2  of  the  'Schriften  der 


Gesellschaft  fiir  Psychologi.sdie 
Forsehung,'  1891.  These  writings, 
altiiough  starting  from  the  position 
I)repared  by  the  Leijizig  school  of 
j)sycho-p!iysical  reseaicii,  are  largely 
]i()leniiial,  and  directed  against 
some  of  Prof.  Wundt's  principal 
theories.  They  have  received  a 
considerable  amount  of  attentinn 
in  Germany  and  America  and  in 
this  country,  and  also  a  good  clcal 


522 


SCIENTIFIC    THOUGHT. 


It  can  hardly  be  said  that  this  course  of  study  has 
done  more  than  make  a  start,  and  even  those  who  are 
incHned  to  consider  it  a  very  one-sided  attempt  are 
bound  to  admit  that  it  has  a  promising  future.  Thus 
Prof.  Wm.  James,  whose  '  Principles  of  Psychology  '  treat 
of  the  subject  from  many  and  very  different  points  of 
view,  refers  to  these  experiments  in  a  characteristic 
passage  as  follows  :  "  Within  a  few  years,  what  one 
may  call  a  microscopic  psychology  has  arisen  in  Germany, 
carried  on  by  experimental  methods,  asking  of  course 
every  moment  for  introspective  data,  but  eliminating 
their  uncertainty  l^y  operating  on  a  large  scale  and  taking 
statistical  means.  .  .  .  Their  success  has  brought  into 
the  field  an  array  of  experimental  psychologists,  bent  on 
studying  the  elements  of  mental  life,  dissecting  them 
out  from  the  gross  results  in  which  they  are  embedded, 
and,  as  far  as  possible,  reducing  them  to  quantitative 
scales.  .  .  .  The  mind  must  submit  to  a  regular  siege,  in 
which   minute   advantages,  gained  night  and  day  by  the 


of  opposition.  The  late  editor  of 
'  Mind,'  Prof.  Croom  Robertson, 
reported  pretty  fully  upon  Miinster- 
berg's  work  in  the  15th  volume 
of  the  fii-st  series  of  '  Mind,'  and 
drew  especial  attention  to  the 
confirmation  which  certain  views 
contained  in  the  writings  of  the 
British  Associationist  school  have 
received  through  Dr  Miinsterberg's 
expositions.  Prof.  E.  B.  Titchener 
criticised  Dr  Miinsterberg's  ex- 
periments and  theories  somewhat 
severely  in  the  16tli  volume  of  the 
first  series  of  'Mind,'  p.  521  sqq. 
As  the  subject  is  still  under  dis- 
cussion, and  as  in  more  recent  writ- 
ings of  Dr  Miinsterberg,  who  is  now 
professor  at  Harvard  University, 
his    studies?    have    shown   quite   a 


different  side  from  that  exhibited 
by  the  above-named  earlier  writ- 
ings, it  is  impossible  in  this  history 
to  do  more  than  refer  to  them 
as  marking  a  distinct  phase  in 
modern  psycho  -  physical  thought. 
It  does  not  appear  that  Prof. 
Wundt  agrees  with  much  of  the 
outcome  of  the  important  move- 
ment he  originated  ;  see  his  article 
in  '  Philosophische  Studien,'  vol.  vi. 
p.  382,  and  a  very  valuable  pajDer  by 
Prof.  J.  AVard  ('Mind,'  2nd  series, 
vol.  ii.  p.  54  aqq.),  entitled  "Modern 
Psychology  :  a  Reflexion. "  As  these 
discussions  refer  more  to  the  philo- 
sophical value  than  to  the  jaurely 
scientific  a.spect  of  psycho-physics, 
they  would  lead  us  beyond  the 
regions  of  purely  scientific  thought. 


ON    THE    PSYCHO-PHYSICAL    NIKW    OF    NATURE.       523 

forces  that  hem  her  in,  resolve  themselves  at  last  into 
lier  overthrow.  There  is  little  of  the  grand  style  about 
these  new  prism,  pendulum,  and  chronograph  philo- 
sophers. They  mean  Imsiness,  not  chivalry.  What 
generous  divination  and  that  superiority  in  virtue  which 
was  thousiht  bv  Cicero  to  irive  a  man  the  best  insight 
into  nature  have  failed  to  do,  their  spying  and  scraping, 
their  deadly  tenacity  and  almost  diabolical  cunning,  will 
doul)tless  some  day  bring  about.  ,  .  .  The  experimental 
method  has  quite  changed  the  face  of  the  science,  so  far 
as  the  latter  is  a  record  of  the  mere  work  done." 

Tt  is,  however,  only  fair  to  remark  that  it  has  never 
been  the  ol)ject  of  any  science,  and  can,  tlierefore,  no 
more  be  the  object  of  exact  psychology,  to  deal  with 
everything  at  once,  and  that  psycho-physical  science  has 
quite  as  much  right  to  postpone  the  question,  AVhat  is 
mind  ?  ^  as  Inological  science  has  had  to  postpone,  or 
even  to  eliminate,  the  question,  AVhat  is  life  ?  P.ut  tliis 
comparison  reveals  also  the  essential  difference  between 
the  exact  science  of  life  and  tlie  exact  science  of  mind. 
Of  life  we  know  only  througli  the  observation  of  living 
l)eings,  but  of  mind  we  have  not  only  the  apparent 
knowledge  of  its  unity,  which  introspection  forces  upon 


1"  Sensation,  Retentiveness,  As-    '   shocked  at  Lange's  9/io«  about  a  psy- 
sociation  by  Contit;uity,  —  these  are    j    clioh)gy    without   a    soul,    but    the 


to  bo  our  ultimate  and  sufficient 
psychological  conceptions  :  tiic 
facts  of  feeling  and  conation  are 
resolved  into    facts   of    sensation  ; 


'  modern  '  psychology  is  a  psychol- 
(jgy  without  even  consciousness. 
'  Content  of  consciousness'  as  much 
as  you  like,  but  consciousness  itself, 


and  all  mind-processes   held  to  lie  ci.nsciousness  as  activity,  is  not  our 

not    merely    conditioned,    but   ex-  affair  ;  we  leave  tliat  to  nietaphy- 

plaineil   by   brain-processes,    which  sics,  say   our    'modern'    teachers." 

they  accompany  as  epi-phenomena  (Pi-of.    J.   Ward,   on   "  Modern  P.sy- 

or  'Begleit-erscheinungen.'      It    is  chology,"  'Mind,' 2nd  series,  vol.  ii. 

not  80  long   since   the   world   was  p.  5.'j). 


tion 


524  SCIENTIFIC    THOUGHT. 

US,  but  we  have  also  a  large  array  of  external  facts  which 
have  been  appropriately  defined  by  the  term  "  the  ob- 
jective mind."  There  are,  in  fact,  two  properties  with 
which  we  are  familiar  through  common-sense  and  ordin- 
ary reflection  as  belonging  specially  to  the  phenomena 
of  our  inner  self-conscious  life,  to  the  so-called  "  epi- 
phenomena"  of  the  higher  organic  or  nervous  systems, 
and  these  properties  seem  to  lie  quite  beyond  the  sphere 
and  the  possibilities  of  the  ordinary  methods  of  exact 
37.        research.     The  first  of  these  properties  is  the  peculiar 

Phenomenon 

ofcentraiisa-  unity  exhibited  by  the  higher  forms  of  organic  existence, 
and  still  more  evident  in  the  phenomena  of  mental  or 
inner  life.  Instead  of  unity,  it  might  perhaps  be  better 
to  call  it  centralisation.  Now,  the  more  we  apply  mathe- 
matical methods,  the  more  we  become  aware  of  the  im- 
possibility of  ever  arriving  at  a  comprehensive  unity  by 
adding  units  or  elements  together.  The  sum  of  atoms  or 
molecules,  however  artfully  put  together,  never  exhibits 
to  our  reasoning  that  appearance  of  concentration  which 
the  higher  organisms  or  our  conscious  self  seem  to  exhibit. 
In  this  circumstance  lies  the  difficulty  of  ever  arriving  at 
any  really  satisfactory  definition  of  life — which  definition 
eminent  physiologists  have,  as  we  have  seen,  felt  com- 
pelled ultimately  to  relegate  to  the  realm  of  the  idea. 
In  the  last  chapter  I  showed  how  modern  research  into 
the  phenomena  of  life  has  impressed  upon  our  thoughts 
the  ubiquity,  the  continuity,  and  the  unique  character  or 
singularity  of  life,  without  being  able  to  fix  upon  any  one 
satisfactory  mechanical  definition  of  life.  But  as  we 
ascend  in  the  scale  of  living  things  we  become  aware  of 
another  property :  they  are  centred — i.e.,  they  exhibit  a 


ON    THE    PSYCHO-PHYSICAL    VIEW    OF    NATURE.       525 

si)eci;il  kind  of  unity  whicii  cannot  be  detined,  a  unity 
which,  even  when  apparently  lost  in  the  periods  of  nn- 
cunsciousness,  is  able  to  re-establish  itself  by  the  wonder- 
ful and  indefinable  property  called  "  memory  " — a  centre 
whicli  can  only  be  very  imperfectly  localised — a  together 
which  is  more  than  a  mathematical  sum ;  in  fact,  we  rise 
to  the  conception  of  individuality — that  which  cannot 
be  divided  and  put  together  again  out  of  its  parts. 

The  second  property  is  still  more  remarkable.  The 
world  of  the  "  epi-phenonicna,"  of  tlie  inner  processes 
which  accompany  the  highest  forms  of  nervous  develop- 
UKMits  in  human  beings,  is  capable  of  unlimited  growth; 
and  it  is  capable  of  this  by  a  process  of  becoming  ex- 
ternal :  it  becomes  external,  and,  as  it  were,  perpetuates        ss. 

ij..,  ,.  .  1  ,.,.  Extenialisa- 

itselr  in  language,  literature,  science  and  art,  legislation,  tionand 

°       °  '  '       °  '  growth  of 

society,  and  the  like.  We  have  no  analogue  of  this  in  "''"'^■ 
physical  nature,  where  matter  and  energy  are  constant 
quantities,  and  where  the  growth  and  multiplication  of 
living  matter  is  merely  a  conversion  of  existing  matter 
and  energy  into  special  altered  forms  without  increase  or 
decrease  in  quantity.  ]>ut  the  (iuantity  of  the  inner 
thing  is  continually  on  the  increase ;  in  fact,  this  increase 
is  tlie  only  thing  of  interest  in  the  whole  world. 

Now,  no  exact  scientific  treatment  of  the  phenomena 
of  mind  and  body,  no  psycho-physical  view  of  nature,  is 
complete  or  satisfactory  which  passes  by  and  leaves  un- 
defined these  two  remarkable  properties  of  the  inner  life, 
of  the  epi-phenomena  of  nervous  action,  of  consciousness. 
And  it  seems  to  me  that  Prof.  Wundt  is  the  only  psycho-        30. 

Wuiulf.s 

physicist  who,  starting  from  science  and  trying  to  pene-  treatment  or 
trate   Ijy   scientific   methods    into    the    inner  or  psychic  i"'"i''«"'- 


526 


SCIENTIFIC    THOUGHT. 


world,  has  treated  the  subject  comprehensively,  and  fairly 
and  fully  tried  to  grapple  with  these  two  facts  peculiar 
to  the  inner  world- — its  centralised  unity  and  its  capacity 
of  unlimited  growth  through  a  process  of  externalisation. 
He  has  done  so  by  his  philosophical  theory  of  "  ap- 
perception and  will,"  and  of  the  "  growth  of  mental 
values,"  two  conceptions  which  lead  us  into  the  realm 
of  philosophical  thought.-'^ 

But,  before  closing  this  chapter,  which  deals  with  the 
study  of  the  phenomena  of  an  inner  life  and  the  inter- 
action of  body  and  mind  by  the  methods  of  exact  research, 
it  is  well  to  note  that  long  before  psychology  existed  as 
a  natural  science,  a  large  amovmt  of  knowledge  had  been 
accumulated  by  a  different  method.  Especially  in  this 
country— ever  since  the  time  of  Locke — there  has  existed 
a  very  large  and  influential  school  of  thinkers  who  studied 
the  inner  phenomena  by  what  has  been  appropriately 
termed  the  inner  sense ;  every  observer  recording  his 
own  inner  experience  and  leaving  it  to  others,  by  doing 
the  same,  to  confirm  or  correct  his  statements.  Psy- 
chology, carried  on  through   self-observation  or  by  the 


^  It  would  serve  no  good  pur- 
pose to  string  together  a  list  of 
quotations  from  Prof.  Wundt's 
voluminous  writings  in  which  these 
two  central  ideas  of  his  ^jhilosophy 
find  expression,  especially  as  there 
is  no  one  passage  to  be  found  in 
which  his  highest  abstractions  and 
final  conclusions  find  an  adequate 
expression,  still  less  one  which  could 
be  conveniently  rendered  in  the 
English  language.  KiJnig  has,  it 
seems  to  me,  done  much  to  make 
Wundt's  view  more  easily  under- 
stood, and  I  must  content  myself 
at  present  with  referring  to  his  little 


volume,  notably  to  the  extracts 
given  on  pp.  134,  141,  and  167, 
which  explain  more  cle.arly  the 
theory  of  apperception  and  will. 
On  the  theory  of  the  "  growth 
of  mental  values,"  see  especially 
Wundt,  '  System  der  Philosophie  ' 
(2  Aufl.,  pp.  307,  596),  "Mental 
life  is,  extensively  and  intensively, 
governed  by  a  law  of  growth  of 
values :  extensively,  inasmuch  as  the 
multiplicity  of  mental  developments 
is  always  on  the  increase  ;  inten- 
sively, inasmuch  as  the  values 
which  appear  in  these  develop- 
ments increase  in  degree"  (p.  304). 


ON    THK    PSYCHO-PHYSICAL    VIKW    OF    NATCKE.       527 
introspective  method,  liad  grown  to  large  dimensions  in        40. 

Iiitros]<ec- 

Scotland  and  in  England,  long  Ijefore  Herbart  and  Beneke  t'^t  methou. 
in  Germany  gave  it  a  similar  direction.  In  fact,  most 
of  the  writings  of  the  introspective  school  in  Germany, 
which  dates  from  the  midille  of  the  centnry,  is  con- 
cerned with  the  material  accumnlated  by  Ikitish  psycho- 
logists. And  even  the  psycho -physical  method  itself 
would  carry  us  only  a  little  way  if  its  results  and  obser- 
vations could  not  continually  be  checked,  supplemented, 
antl  interpreted  l>y  what  we  already  know  by  introspec- 
tion. One  of  the  foremost  representatives  of  the  Eng- 
lish school  of  psychology  has  said,  and  many  will  agree 
with  him,^  "  In  our  desire  to  know  ourselves — to  frame 
some  conception  of  the  flow  of  our  feelings  and  thoughts 
— we  work  at  first  by  introspection  purely;  and  if  at  a 
later  stage  we  find  means  of  extending  and  improving 
our  knowledge,  introspection  is  still  our  main  resort — the 
Alpha  and  Omega  of  psychological  inquiry  :  it  is  alone 
supreme,  everything  else  sul)sidiar\'.  Its  compass  is  ten 
times  all  the  other  methods  put  together,  and  fifty  times 
the  utmost  range  of  psycho-physics  alone." 

A  history  of  Thought  must  accordingly  contain  some 
account  of  the  view  wdiieli  our  century  has  taken  of  the 
introspective  method  and  the  value  of  the  inner  sense  as 
a  means  of  enlarging  our  knowledge."     This  discussion 

'  See  Prof.  Bain's  e.s.^aj-  in  '  ^liml,'   ,   states,  has  been  not  onlj-  to  develop 


2n(l  series,  vol.  ii.  p.  42:  "The 
respective  Spheres  and  mutual 
Helps    of    Introspection    and     Psy- 


a  clearer  view  of  physiological  psy- 
chology, but  also  to  define  more 
cleaily    the    object   of    psychology 


cho-physical    E.xperimcnt    in    Psy-  |    proper  —  that    is,    of    the    science 

cliology."  I    which  deals  with  the  facts  revealed 

"  One  result  of  the  modern  psycho-  |   by   introspection.      When,    in    the 

l)hysiual  view,  or  of  the  doctrine  of  middle  of  the  century,  the  physiol- 

liarallelism  of  physical  and  mental  ogy   of   the   senses    attracted    the 


528 


SCIENTIFIC    THOUGHT. 


will,  in  a  future  volume,  form  one  of  the  appropriate 
links  which  join  science  to  philosophy — which  lead  us  on 
from  exact  to  speculative  thought.  At  present  I  have 
to  refer  to  another  and  very  extensive  field  of  research, 
into  which  the  natural  as  well  as  the  speculative 
philosopher  have  been  led  from  opposite  sides,  and  which 
especially  affords  a  hopeful  prospect  for  an  enlargement 
of  the  psycho-physical  view  of  nature.  If  the  natural 
philosopher  cannot  consistently  and  fairly  enter  into  the 
mysteries  of  an  inner  consciousness  from  which  his 
opponent — the  speculative  philosopher- — starts,  he  may 
perhaps  do  so  l^y  a  roundabout  way  or  a  side-door. 

As  I    stated   above,  the   inner  world,   the   psychosis, 
which  intermittently  accompanies  the  neurosis,  the  epi- 


attention  of  psychologists  in  all  the 
three  counti-ies,  it  became  custom- 
ary to  introduce  purely  psycholog- 
ical treatises  by  an  exiDosition  of 
the  psycho-physical  relations,  in- 
troducing into  psychology  chapters 
from  phj^siology.  The  consequence 
of  this  has  been  that  modern  works 
on  psychology  have  grown  to  in- 
ordinate length,  and  frequently  ex- 
hibit a  dual  aspect  and  method. 
Quite  recently  it  has  therefore  been 
insisted  on  that  psychology  can  be 
written  either  from  the  physio- 
logical or  from  the  purely  psycho- 
logical point  of  view.  A  good  ex- 
ample of  the  latter  is  Prof.  G.  F. 
Stout's  '  Analytic  Psychology '  (2 
vols.,  1896).  "Physiological  re- 
sults," he  says  (vol.  i.  p.  37),  "are 
likely  to  be  valuable  onlj'  in  pro- 
portion as  they  are  controlled  and 
criticised  by  psychological  analysis. 
This  holds  good  apart  from  con- 
sideration of  such  metaphysical 
questions  as  whether  the  brain- 
process  is  the  sole  real  agency,  and 
consciousness  a  mere  function,  or 
consequence,   or   epi  •  phenomenon  ; 


or  whether  consciousness  is  the 
reality  of  which  the  correlated 
brain-process  is  a  phenomenon,  or 
whether  they  are  two  asi>ects  of 
the  same  fact.  Whatever  may  be 
our  attitude  to  such  questions,  the 
psychologist  has  still  his  own  work 
to  do  on  his  own  lines ;  and  for  the 
sake  of  physiology  itself,  so  far  as 
it  entertains  the  hope  of  throwing 
light  on  the  mechanism  of  brain - 
processes,  he  must  attempt  to  do 
it.  It  is  idle  to  require  psj'chol- 
ogy  to  wait  for  the  progress  of 
physiology.  Such  a  demand  is 
logically  parallel  to  a  demand  that 
historj'  or  biography,  or  the  prac- 
tical estimate  of  character  and 
anticipation  of  men's  actions  in 
ordinary  life,  shall  come  to  a  stand- 
still until  they  have  a  sufficient 
physiological  basis.  On  this  view, 
Carlyle  should  have  abstained 
from  writing  his  '  French  Revol- 
ution,' because  he  did  not  know 
what  precise  configuration  and 
motion  of  brain  particles  deter- 
mined the  actions  of  the  mob  who 
stormed  the  Bastille." 


ON    THE    PSYCHO-PHYSICAL    VIEW    OF    NATURE.       529 

phenomenon  which  lies  on  tlie  other  side  of  Llie  phe- 
nomenon, is  not  only  characterised  by  a  peculiar  unity  or 
centred  connectedness  whifli  we  look  for  in  vain  in  the 
external  and  physical  world;   it  has  also  become  external        4i. 

^     "^  ,         The"objec- 

or  objective,  it  has  detached  itself  from  the  sul)jective  tivemind." 
and  hidden  source  from  w^hich  it  sprang,  and  can  be 
studied  as  such  in  the  great  creations  of  language,  litera- 
ture, society,  science,  art,  and  religion.  Why  not  study 
its  nature  and  its  life  in  these  great  and  undeniable 
manifestations,  and  instead  of  beginning  at  the  hidden 
source,  the  unknown  and  indefinable  centre,  try  to  reach 
this  by  beginning  at  the  periphery,  measuring  out  the 
great  circle  and  learning  what  it  contains  ? 

Ancient  philosophy,  which  found  its  consummation  in 
the  writings  of  Aristotle,  had  already  begun  this  work, 
and,  in  establishing  the  rules  of  grammar  and  logic,  had 
furnished  the  material  for  many  modern  speculations. 
"What  the  ancients  had  only  begun,  modern  thinkers  of 
the  most  opposite  schools  have  been  induced  to  continue 
on  more  methodical  lines,  and  with  the  more  or  less 
distinct  object  of  learning  something  definite  regarding 
that  mental  life  and  unity  whicli  they  have,  with  little 
success,  tried  long  enough  to  reach  by  various  direct 
roads,  such  as  introspection,  speculation,  physiological 
and  psycho-physical  experiment.  Accordingly  we  find 
springing  up  almost  simultaneously  in  the  three  coun- 
tries, ever  since  the  latter  part  of  the  eighteenth  century, 
the  study  of  mankind  or  of  human  culture  in  all  its 
historical  forms.  Hume  and  Adam  Smith,  Montesquieu, 
and  the  French  physiocrats,  studied  society  and  tlie  great 
falnif  of  industry  and  commerce;  Cabanis  and  the  "  Ideo- 

Vf)!,.    II.  1*    L 


530  SCIENTIFIC    THOUGHT. 

logiies  "  pointed  to  the  importance  of  the  philosophical 
study  of  language  and  grammar ;  the  idealistic  school  in 
Germany  ended  by  leading  to  the  study  of  the  objective 
mind  in  history,  art,  and  philosophy ;  the  school  of 
Herbart  in  Waitz,  Lazarus,  and  Steinthal  led  into 
"  Volkerpsychologie  "  and  "  Sprachwissenschaft "  ;  and  it 
is  well  known  how  in  our  days  the  synthetic  philosophy 
of  Mr  Herbert  Spencer  in  England  has  entered  on  the 
study  of  sociology  on  the  large  scale.  We  hear  on  all 
sides  of  natural  histories  of  mankind,  of  society,  of  re- 
ligion, &c.,  and  they  appear  either  in  the  modest  attire  of 
the  other  and  older  natural  histories  which  we  have  been 
accustomed  to,  preparing  the  ground  by  patient  and  un- 
biassed collection  of  facts,  or  they  attach  themselves  to 
certain  philosophical  theories,  such  as  are  furnished  by 
the  dialectics  of  Hegel,  or  by  the  evolutionary  doctrine  of 
Darwin  and  Spencer,  in  connection  with  which  we  shall 
meet  them  in  a  future  section  of  this  work.  For  it  has 
been  found  here,  as  it  had  been  in  the  older  natural 
histories,  that  the  accumulation  of  facts  and  materials 
was  of  little  use  unless  some  leading  idea  was  at  hand 
by  which  it  liecame  possilile  to  regulate  and  arrange 
them. 

Thus  we  see  how  the  psycho-physical  problem — the 
question  of  the  interaction  of  mind  and  body,  of  soul  and 
nature,  of  the  inner  and  the  outer  worlds — is  being 
attacked  from  two  entirely  different  sides, — from  the 
side  of  the  individual  and  from  that  of  the  collective 
life  of  the  human  being :  the  mental  principle  is  being 
studied  in  its  inner  and  hidden  existence  as  the  unifying 
and  centralising  factor  of  individual  life,  or  in  its  ex- 


ON    THE    PSYCHO-PHYSICAL    VIEW    OF    NATURE.       531 

teinul  numifestiitioiis  in  history,  society,  science,  art, 
industry,  and  religion, — in  fact,  in  the  history  of  culture 
and  civilisation.  If  Bishop  Berkeley  has,  with  some 
propriety,  been  called  "  the  historical  starting-point "  of 
psycho-physical  investigation  of  the  first  kind,  the  im- 
portance of  that  of  the  second  and  wider  kind  is 
nowhere  more  clearly  and  definitely  expressed  than — 
over  a  century  ago — in  the  writings  of  Johann  Gott-  its  study 
fried  Herder.^      His  influence  in  this  direction  was  very  uercier. 


*  The  influence  of  Herder  (17-14- 
1803)  on  German  literature  and 
tliought  was  fully  acknowledged  by 
his  contemjjoraries,  as  is  testified 
liy  the  frequent  references  to  him 
in  the  biographies  of  nearly  all  the 
eminent  men  who  lived  at  the  end 
of  the  eighteenth  and  the  beginning 
of  the  nineteenth  centuries,  as  also 
in  the  voluminous  correspondence 
which  he  carried  on  with  many 
eminent  contemporaries.  Had  it 
not  been  for  the  overjioweiing  and 
one-sided  influence  which  the  criti- 
cal, and,  later,  the  transcendental, 
schools  of  thought  gained,  not- 
ably at  the  German  universities, 
Herder's  ideas  would  have  been 
more  generally  acknowledged  as 
forming,  to  a  very  great  extent, 
the  starting-point  of  many  lines  of 
researcli  which  were  not  exclus- 
ively controlled  by  the  ruling 
philosophies,  and  which  gradually 
and  imperceptibly  united  at  a  later 
date  to  form  the  more  modern 
current  of  German  thought. 
Herder  was  much  more  allied 
with  the  historical  studies  refer- 
ring alike  to  nature,  literature, 
and  culture,  than  with  the  critical 
and  metaphysical  systems,  being 
also  well  acquainted  with  con- 
temporary English  thought,  as, 
inter  (tiki,  with  the  curious  writ- 
ings of  Lord  Monboddo.  Tln-ough 
Mfulame    de    Stai-1,    who    was    in- 


timate   with    Herder,   Ids   writings 
were     early     known     in     France, 
whereas      Carlyle's       studies       in 
German    literature,    though    most 
valuable     and     original     in     their 
way,  do  not  give  that  prominence 
to    Herder's    writings    which    they 
deserve.       In   more  recent  times, 
after    the    indefatigable    Diintzer, 
through     the    publication     of    his 
correspondence,    had     done    much 
to    revive    the    interest     in     Her- 
der,   full    justice    has    Ijeen    done 
to    his    great     merit     bj'     Rudolf 
Hayni,  whose  great  work,  '  Herder 
nach    seinem    Leben    und    seinen 
Werken'    (2    vols.,    Berlin,    1885), 
is    a    i)erfect    mine    of     informa- 
tion.    The  side  of  Herder's  influ- 
ence    which      is     not     suflicieutly 
dwelt  on  by  Haym,  but  which  in- 
terests us  most  at  present, — what 
we    may   call    his    anthropological 
view, — had   already  been   exhaust- 
ively  dealt  with    by    l)r    Heinrich 
IJoehmer      in      his      little  -  known 
'  Geschichte  der  Entwickelung  der 
Naturwissenschaftlichen       Weltan- 
schauung in   Deut-ichland  '  ((lotlia, 
187'i),    who    especially    draws    at- 
tention to  the  ])sycho-pliysical  ideas 
of  Herder.     It  has  been  truly  said 
that   there   is    hardly  any   modern 
idea   which  has  found   widespread 
application  that  cannot   be  traced 
in    the    writings   of    Heidor  ;    but 
Herder    liad    no    method,    having 


532 


SCIENTIFIC    THOUGHT. 


great,  and  would  have  been  greater  had  he  not  lived  at 
a  thne  when  the  study  of  the  human  mind  by  the  purely 
introspective  or  speculative  methods  had  absorbed  all 
philosophical  interest  in  England  and  Germany.  His 
opposition  to  the  (abstract)  subjective  philosophy  of 
Kant  and  Fichte  made  him  unpopular ;  he  was  only 
half  understood  at  the  time ;  and  only  towards  the  end 
of  our  century  have  his  ideas  been  recognised  as  con- 
taining the  clear  conception  of  psycho-physics  on  the 
large  scale — i.e.,  of  the  natural  history  of  humanity,  the 
genesis  and  evolution  of  the  objective  mind. 

Herder  was  a  pupil  of  Kant  during  his  pre-critical 
period.  He  was  still  more  influenced  by  great 
naturalists  like  Haller,  Buffon,  Camper,  Sommering, 
Forster,  and  Blumenbach,  wlio  through  physiology,  com- 
parative anatomy,  and  ethnology,  attempted  to  bring  the 
study  of  the  human  race  and  its  mental  development  into 
connection  with  that  of  the  brute  creation,  of  the 
surrounding  plant-life,  of  the  characteristics  of  climate 
and  soil,  and  of  the  great  natural  features  of  sky  and 
landscape.  He  did  not  believe  that  we  could  study 
the  great  forces  of  nature  and  mind  from  inside  or  in 
the  abstract — he  desired  to  follow  Haller's  physiology,  to 
complete  and  continue  it  into  psychology.      Irritability,-' 


characteristically  maintained  that 
method  is  frequently  only  a  con- 
vention, and  he  was  deficient  in 
critical  acumen.  The  German  mind 
had  to  go  through  the  severe  dis- 
cipline of  the  school  of  mathemati- 
cal and  critical  thought,  and  to 
amass  an  enormous  volume  of  ex- 
perimental and  historical  know- 
ledge, before  the  brilliant  concejition 
of  Herder  in  his  great  work  '  Ideen 


zur  Geschichte  der  Menschheit '  (4 
pts.,  1784-87)  could  be  partially  re- 
alised by  A.  von  Humboldt  in  his 
'Kosmos'  (1841-59),  and  by  Lotze 
in  his  '  Microcosmus '  (1856-64). 
See  especially  the  preface  to  the 
latter. 

*  See  above,  p.  471,  on  a  similar 
development  of  Haller's  teaching 
through  Cabanis  in  France  some- 
what later  in  time. 


ox    THE    PSYCHO-PHYSICAL    VIEW    OF    NATURE.      533 


tlie  higliest  pliysical  phenomenon  of  matter,  was  to  Ije 
the  starting-point  of  this  psychology.  In  an  early 
essay  on  understanding  and  sensation  (1778)  he  wrote: 
"  According  to  my  thinking  there  is  no  psychology 
possible  which  is  not  at  every  step  detinite  physiology. 
Haller's  physiological  work  once  raised  to  psychology, 
and,  like  Pygmalion's  statue,  enlivened  with  mind,  we 
shall  be  able  to  say  something  aliout  Thought  and 
Sensation."  ^ 

But  this  psycho-physiological  view  was  not  limited  to 
the  study  of  the  individual :  it  widened  out  and  em- 
Ijraced  the  whole  of  mankind ;  nature  on  a  large  scale 
had  to  be  observed ;  historical  records  had  to  be  collected 
on  all  sides  ;  origins  had  to  be  studied  and  the  elementary 
forces  followed  up  in  the  beginnings  of  poetry,  art,  and 
religion.  Materials  were  gathered  everywhere  from  his- 
torians, chroniclers,  travellers,  primitive  records,  and  the 
"  voices  of  the  peoples."  All  this  was  to  furnish  the 
materials    for    a    "  History    of    Mankind."      "  In    many 


'  "  Voin  Erkemion  uiid  Emp- 
tiiuleii  (ler  nien.schlichen  Seele " 
(1778),  in  the  9th  vol.  of  the 
Works  of  Herder  ('  Abtheilung 
y.ur  Philo.sophie  uiid  Geschichte,' 
1828).  To  give  an  idea  of  Herder's 
anticipation  of  modern  views,  see 
J).  10  :  •■  We  cannot  penetrate 
deeper  into  the  genesis  of  sensa- 
tion than  to  tlie  reinai-kablc  jihen- 
onienou  called  by  Haller  '  lleiz.' 
The  irritated  fibre  contracts  and 
expands  again  ;  periia])s  a  'stamen,' 
the  first  glowing  sparklet  of  sensa- 
tion, towards  which  dead  matter 
has  purified  itself  by  many  ste[)S 
and  stages  of  mechanism  and  or- 
ganisation."' Many  passages  could 
V)e  (juoted  from  Herder's  '  Idecn,' 
&c.,  and  other  writings,  anticijjating 


modern  Darwinian  ideas,  such  as 
those  of  the  struggle  for  existence, 
and  even  of  automatic  selection.  See 
Prof.  J.  Sully's  appreciative  article 
on  Herder  in  the  '  l-'ncyc.  Brit.' 
(0th  ed.),  and  notably  Fr.  von 
Biirenbach,  '  Herder  als  Vorgiinger 
Darwin's'  (Berlin,  1877).  Hayni 
('  Herder,'  vol.  ii.  p.  209)  object.s'  to 
this  extreme  view  of  Herder  as  a 
forerunner  of  Darwin  on  the  ground 
that,  according  to  the  former,  no 
animal  in  its  development  ever  for- 
sook that  adjustment  of  organic 
forces  peculiar  to  it,  nature  having 
kept  each  being  within  the  limits 
of  its  type.  Accordinglj',  Herder's 
evolutionism  would  be  moicakinto 
that  of  K.  E.  von  Baer  than  to 
that  of  Darwin  and   lliicckcl. 


534  SCIENTIFIC    THOUGHT. 

43.  parts,"   he   says/    "  my  book  shows  that  one  cannot  as 

His 'History  ^  '  -^    '  -^ 

ofMankind.'  yet  write  a  philosophy  of  human  history,  but  that  per- 
haps one  may  write  it  at  the  end  of  our  century  or 
of  our  chihad." 

And  indeed  the  whole  of  our  own  century  has  been 
busy  in  carrying  out  this  prophetic  programme  of 
Herder's,  consciously  as  planned  by  him  in  Germany — 
unconsciously  and  independently  in  other  countries.  As 
a  counterpart  to  the  introspective  labours  of  Kant  and 
their  followers,  a  large  array  of  naturalists,  historians, 
philologists,  and  ethnologists  have  in  the  spirit  of  Herder 
ransacked  every  corner  of  the  globe  and  every  monument 
of  history  with  the  distinct  object  of  tracing  there  the 
physical  basis  and  the  workings  of  that  inner  and  hidden 
principle  which  we  call  the  human  mind.  In  doing  this, 
they  or  their  numerous  followers,  who  belonged  to  a 
generation  which  knew  not  Herder,  have  strayed  far  away 
from  the  common  starting-point,  and  have  frequently  lost 
themselves  in  the  bewildering  details  of  special  research. 

44.  Above  all,  in  the  country  to  which  Herder  belonged,  a 

Separation  .  .  ,       .         , 

of  natural     Separation  set  m  early  m  the  century  between  what  ha^'e 

and  mental  i  xi 

sciences.  bccu  termed  the  natural  and  the  mental  sciences.  The 
former  came  more  and  more  under  the  sway  of  the 
mathematical  spirit,  which,  as  I  showed  in  an  earlier 
chapter,  turned  the  eyes  of  its  votaries  away  from  their 
own  national  scientific  literature  to  that  of  their  neigh- 
bours— first  to  France,  latterly  to  England.  The  mental 
sciences,  on  the  other  hand, — history,  philology,  the  social 
sciences, — came  under  the  influence  of  exactly  those  phil- 
osophical ideas  which  Herder  never  understood  nor  assimi- 

^  See  the  preface  to  the  first  part  of  the  'Ideen,'  1784. 


ON    THE    PSYCHO-PHYSICAL    VIEW    OF    NATURE.       535 


lated :  ^  the  critical  spirit  of  Kant,  and  the  constructive 
canons  of  his  successors,  each  of  these  distinct  and  separate 
movements,  supplied  exactly  what  was  wanting  in  the 
prophetic,  not  to  say  dithyrambic,  utterances  of  Herder ; 
they  supplied  coherence  and  method.  Earlier  chapters 
of  this  book  have  shown  how  the  mathematical  spirit 
has  permeated  and  revolutionised  the  natural  sciences, 
and  latterly  how  it  has,  in  the  science  of  psycho-physics, 
led  philosopliers  l)ack  to  the  problem  which  Herder  had 
adumbrated  at  the  end  of  the  previous  century.  A 
second  large  department  of  my  task  will  consist  in 
showing  how  what  in  Germany  are  called  the  mental 
sciences  have  been  developed  independently  of  the 
natural  sciences,  liow  the  studv  of  the  mind  as  such — 


'  During  the  latter  part  of  his 
life  Herder  was  occupied  to  a  great 
extent  witli  those  jiublications  in 
which  he  gave  expression  to  the 
opposition  which  he  consistently 
maintained  to  the  critical  writings 
of  his  master  Kant.  His  two  princi- 
l)al  works  referring  to  this  are  'Eine 
Metakritik  zur  Kritik  der  Heinen 
Vernunft'  (2  parts,  1799)  and  'Kal- 
ligone'  (1800).  Kant  had  reviewed 
the  first  volume  of  Herder's  greatest 
work,  tlie  '  Ideen,'  anonymously, 
criticising  the  absence  of  logical 
acumen  and  clear  definitions,  and 
also  the  attempt  towards  a  genetic 
as  opposed  to  a  critical  treatment 
of  the  intellect,  the  former  being 
an  enterprise  "which  transcends 
the  powers  of  human  reason,  whe- 
ther the  latter  gropes  with  physi- 
ology as  a  leader,  or  attempts  to 
soar  with  metaphysics."  In  the 
second  part  of  the  '  Ideen  '  If  erder 
had  taken  up  a  polemical  attitude 
to  Kant's  teacliings,  and  Kant  had 
.igain  reviewed  it,  dwelling  upon 
the  uncritical  maimer  in  which 
Herder  had  built  up  his  hypotheses 


on  unsifted  material  gatiiered  from 
all  sides.  In  the  '  Metakritik ' 
Herder,  irritated  by  what  he  con- 
sidered the  arrogance  of  the  Kant- 
ian school,  undertook  to  put  into 
systematic  form  his  criticism  of 
Kant's  principal  work,  following 
to  a  great  extent  the  suggestions 
thrown  out  l)y  a  mutual  friend  of 
himself  and  Kant,  .lohann  Georg 
Hamann  (1730-80),  and  falling  back 
upon  the  earlier  philosophies  of 
Spinoza  and  Leiljniz  on  the  one 
side,  and  upon  the  common-sense 
philosophy  of  the  Scottish  school  on 
the  other,  seeking  for  a  solution 
of  the  problems  i-aised  by  both, 
not  in  abstract  reasoning,  but  in 
the  realism  of  the  concrete  and  tlie 
historical  sciences.  In  tlie  '  Kal- 
ligone,'  Herder  similarly  attacks 
Kant's  rcsthetical  philosopliy  ('Kri- 
tik der  Urtheilskraft,'  1790),  which 
had  been  enthusiastically  received 
in  Herder's  immediate  neighbour- 
hood by  Scliiller.  A  full  account  of 
these  controversies  will  be  found  in 
the  2nd  vol.  of  Haym's  work. 


536 


SCIENTIFIC    THOUGHT. 


in  its  individual  and  collective  existence — has  proceeded 
when  separated  from  that  of  nature.  This  survey  will 
start  with  exactly  that  movement  of  thought  which  was 
so  distasteful  to  Herder,  the  critical  inquiry  of  Kant, 
and  it  will  follow  this  up  to  the  point  when  in  our  days 
a  junction  has  again  been  attempted,  not  unlike  in  spirit 
to  that  dreamt  of  by  Herder,  though  very  much  more 
accurate  and  precise  in  method.  There  is,  moreover,  one 
special  problem  where  this  has  been  markedly  the  case ; 
one  phenomenon  stands  out  pre-eminently ;  it  belongs 
equally  to  the  realm  of  nature  and  of  mind.  After 
being  independently  attacked  by  philosophers,  naturalists, 
travellers,  philologists,  and  latterly  by  physicists,  it  has 
revealed  itself  as  the  psycho-physical  problem  'par  ex- 
cellence ;  and  it  is  exactly  that  which  Herder  himself 
45.  treated  with  special  attention.  This  phenomenon  is  that 
of  language,  of  human  spccch — the  problem  of  language.-^ 


^  The  problem  of  language  and 
the  question  of  its  origin  inde- 
pendently occupied  thinkers  in  the 
three  countries  in  the  latter  half  of 
the  eighteenth  century.  In  France 
the  followers  of  Locke,  notablj- 
Condillac  ('  Essai  sur  I'origine  des 
connaissances  humaines,'  vol.  ii.), 
wrote  on  the  subject,  while  Rousseau 
opposed  them  ('Sur  I'inegalitd 
parnii  les  homines,'  1754).  In 
Germany  the  Pastor  Siissmilch,  of 
whom  I  shall  have  more  to  say  in 
the  next  chapter,  wrote  an  elab- 
orate work  to  prove  the  divine 
origin  of  language  ( '  Beweis  dass 
der  Ursprung  der  Menschlichen 
Sprache  Gottlich  sei,'  Berlin,  1776). 
In  order  to  settle  the  question  the 
Academy  of  Berlin  offered,  in  the 
year  1769,  a  prize  in  the  following 
terms  :  "  En  supposant  les  hommes 
abandonn(5s  a  leurs  facultes  natu- 


relles,  sont-ils  en  dtat  d'inventer 
le  langage  ?  et  par  quels  moj^ens 
parviendront-ilsd'eux-memesixcette 
invention  ?  "  a  problem  wliich  Her- 
der characterised  as  a  "  truly  philo- 
sophical one,  and  one  eminently 
suited  for  me."  He  had  already — 
following  Hamann — thought  much 
about  the  subject,  and  lie  proposes, 
in  his  prize  essaj-,  which  was  sub- 
sequently crowned  by  the  Academy, 
"  to  prove  the  necessary  genesis  of 
language  as  a  firm  philosophical 
truth."  A  short  time  after  Her- 
der had  written  his  essay  (1771), 
there  appeared  in  England,  by 
James  Burnett,  Lord  Monboddo,  a 
work  '  On  the  Origin  and  Progress 
of  Language'  (1773),  in  which  he 
refers  to  the  ideas  of  James  Harris 
in  his  work  '  Hermes  ;  or  a  Philo- 
sophical Enquiry  concerning  Lan- 
guage   and     Universal    Grammar' 


ON    THE    PSYCHO-PHYSICAL    VIEW    OF    NATURE.       537 


In  no  department  of  knowledge  has  the  scientific 
spirit  worked  a  greater  change  than  in  the  science  of 
hmguage.  "Witli  tlie  exception  of  suggestions  by  Leibniz, 
who  clearly  saw  the  necessity  of  founding  the  theory  of 
language  on  a  broader  basis  than  the  small  number  of 
classical  and  modern  tongues  then  current  attbrded, 
and  of  some  glimpses  of  a  corrector  view  such  as  those 
contained  in  the  much  ridiculed  writings  of  Lord  Mon- 
boddo,  we  find,  up  to  the  end  of  the  eighteenth  century, 
hardly  any  attempt  towards  a  metlKKlieal  treatment  of 
the  great  problem.  Philosophical  theories  and  vague 
etymologies,  amounting  frequently  to  little  more  than 
punning  with  words,  brought  the  subject  into  ridicule. 
Herder  has  the  great  merit  of  having  uryed  the  im- 
portance  of  the  study  of  language  and  literature  in 
primitive  forms  ^  as  the  great  gateway  into  anthropology 


(17r)l\  The  question  attracted  con- 
siderable attention,  partly  through 
the  eccentricities  of  Lord  Mon- 
boddo,  of  which  it  has  been  well 
said  that  they  appeared  more 
ridiculous  to  his  own  than  thej- 
would  to  the  present  age,  partly 
through  the  controversy  which 
arose  shortly  after  on  the  publi- 
cation of  Home  Tooke's  celebrated 
'"ETTfa  TTTtpoevTa,  oi-  the  Diversions 
of  Purley'  (1786).  Herder  was 
acquainted  with  Monboddo's  work, 
having  occasioned  a  translation  of 
it  to  be  made  and  written  a  i)reface 
(1787)  ;  but  he  does  not  seem  to 
have  taken  anv  notice  of  Home 
Tooke  (1736-1812),  who,  as  the 
historian  of  the  science  of  lang- 
uage (Theodor  Beufey,  'Geschichte 
<ler  Sprachwissenschaft,'  Miinchen, 
1869)  siiys,  would,  for  his  novel 
ideas  and  method,  deserve  to  be 
jjut  at  the  entrance  of  the  modern 
linguistic  epoch,  had  lie  been  able 


to  avail  himself  of  a  knowledge  of 
Sanskrit. 

'  This  refers  to  the  second  great- 
est work  of  Herder,  his  collec- 
tion of  popular  songs,  published 
under  the  significant  title  of 
"  Voices  of  the  Peoples  "  ('  Stimmen 
der  Volker  in  Liedeni,'  1778),  a 
work  which  had  the  greatest  in- 
fluence on  German  literature  as 
w^ell  as  on  modern  j^hilological 
studies.  See  Benfey,  loc.  cit.,  p. 
316,  &c.  That  the  publication  of 
the  '  Percy  Ballads  '  (1765),  of  Mac- 
pherson's  '  Ossian.'  and  of  Lowth's 
'  Lectures  on  Hebrew  Poetry ' 
(17.'J3),  formed  a  great  stimulus  to 
Herder  in  his  historical  and  poetical 
studies  is  shown  by  Haym  in  many 
extracts  and  passages,  also  in  the 
prefaces  of  Herder  him^^elf  and  of 
his  editor,  .Toil,  von  Midler  (Herder's 
■  Werkc'  1828,  •  Zur  .--choncn  Liter- 
atur  und  Kunst,'  vols.  vii.  and  viii.) 


538  SCIENTIFIC    THOUGHT. 

and  the  science  of  humanity.  Through  his  writings 
there  rose  two  distinct  views  both  fruitful  for  thought,  the 
philosophico- historical  and  the  strictly  scientific.  His 
immediate  successors,  or  rather  those  who  unconsciously 
imbibed  the  spirit  of  liis  writings,  took  up  the  former 
line.  The  great  development  of  classical  philology  in 
the  school  of  Wolf,  the  discovery  of  Sanskrit  and  the 
new  field  of  oriental  philology,  for  a  time  threw  the 
purely  scientific  aspect  into  the  backgrovmd.  Yet  at 
the  same  time  with  Wilhelm  von  Humboldt  and  his 
philosophical  interests  in  comparative  philology,  we  find 
his  brother  Alexander  giving  a  large  share  of  his 
attention  to  the  unknown  languages  of  the  New  World, 
of  which  he  has  been  called  "  the  scientific  discoverer." 
46.  But  the  real  beginnings  of  an  exact  treatment  of  the 

Its  exact 

treatment,  problem  of  spcech  were  laid  by  one  who  did  not  come 
under  the  conscious  influence  of  Herder,  though  he  came 
under  that  of  Goethe.  By  Johannes  Mliller  it  was 
carried  further,  and  it  was  completed  by  some  of  his 
most  illustrious  pupils  and  followers — Bonders,  Briicke, 
Helmholtz,  and  Czermak  of  Vienna.  Through  the 
anatomical  and  physiological  labours  of  these  and  other 
naturalists,  joined  to  the  physical  analysis  of  musical 
notes  and  sounds  contained  in  the  great  work  of 
Helmholtz  on  Acoustics,  aided  by  such  instnunents  as 
the  laryngoscope  or  throat-mirror,  and  the  wonderful 
inventions  of  the  phonograph  and  phonautograph,  the 
organ  of  speech  is  now  known  to  be  a  complicated  wind 
instrvmient  by  which  pure  notes  and  an  almost  infinite 
variety  of  nasal,  labial,  dental,  palatal,  guttural,  and  other 
sounds  can  be  produced  which  form   the   phonetic  ele- 


ox    THE    PSYCHO-PHYSICAL    VIKW    OF    NATURE. 


139 


iiients  of  s])eeeh.  Sinmllaneously  the  discovery  Ity  Broca, 
ill  ISGl,  (if  the  speech  centre  in  tlic  lirain  marked  an 
epoch  on  the  physiological  side.^  A  new  science,  called 
riionetics  or  Phonology,  has  sprung  up,  and  is  now 
universally  admitted  to  have  created  the  modern  science 
of  language."  In  addition  to  this  physiological  and 
physical    basis,    the    superstructure    of    the    science    of 


47. 
I'honetics. 


'  Thi.s  localisatiou  placeti  the 
speech  centre  in  "a  very  circum- 
scribed portion  of  the  cerebral 
h.emispheres,  and  more  especially 
of  the  left.  This  portion  is  situate 
on  the  upper  edge  of  the  Sylvian 
Fissure,  opposite  the  island  of 
Keil,  and  occupies  the  posterior 
half,  probably  only  the  posterior 
third,  of  the  third  frontal  convolu- 
tion "'  (Broca,  '  Bulletins  de  la 
Socicte  anatomique,'  ISGl).  The 
discovery  resulted  from  the  ex- 
amination of  the  brain  of  patients 
who  had  been  afflicted  with  '"aph- 
asia," which  is  accompanied  with 
'"a  lesion  of  the  posterior  half  of 
the  third,  left  or  right,  frontal  con- 
volution, nearly  always — nineteen 
times  out  of  twenty — of  the  left 
convolution."  The  phenomenon 
of  aphakia  has  ever  since  been 
one  of  the  great  psycho-physical 
problems  bringing  together  the 
most  refined  and  intricate  i>hysi- 
ological,  psychological,  and  linguis- 
tic analyses.  To  begin  with,  we 
have  to  distinguish  motor  aphasia 
and  sensory  aphasia.  "  Our  know- 
ledge of  this  disease  has  had  three 
stages  :  we  may  talk  of  the  period 
of  Broca,  the  period  of  Wernicke, 
and  the  period  of  Cliarcot.  Wer- 
nicke (1874)  was  the  first  to  dis- 
criminate those  cases  in  which  the 
patient  cannot  evfti  undcrKtand 
speech  from  those  in  wliich  he  can 
understand,  only  not  talk  ;  and  to 
ascribe  tlie  former  condition  to 
lesion    of  the  temporal  lobe.     The 


condiliou  in  question  is  ivord-diaf- 
ness,  and  the  disease  is  auditonj 
aphasia.  .  .  .  The  minuter  analy- 
sis of  the  facts  in  the  light  of 
individual  differences  constitutes 
Charcot's  contribution  toward?^ 
clearing  up  the  subject "  (James, 
'  Principles  of  Psychology,'  vol.  i. 
p.  54). 

-  In  the  modern  science  of  lan- 
guage we  have  one  among  the 
many  cases  where  a  historical  or 
philosophical  science  is  becoming 
an  exact  science  by  attaching  itself 
to  physics  and  physiology.  On 
the  other  side  we  have  the  great 
movement  initiated  by  Darwin  iu 
the  purely  natural  sciences,  which, 
as  was  shown  above,  relies  on  the 
historical  collection  of  facts  and 
the  judicious  critical  sifting  of  evi- 
dence. "  It  is  phonology,"  says 
Prof.  Sayce  ('  Introduction  to  the 
Science  of  Language,'  2  vols.,  ISSO, 
chap,  iv.),  "  which  has  created  the 
modern  science  of  language,  and 
phonology  may  therefore  be  forgiven 
if  it  has  claimed  more  than  right- 
fully belongs  to  it  or  forgotten  that 
it  is  but  one  side  and  one  branch 
of  the  master  science  itself.  .  .  . 
It  is  when  we  pass  from  the  out- 
ward vesture  of  speech  to  the 
meaning  which  it  clothes,  that  the 
.science  of  language  becomes  a  his- 
torical one.  The  inner  meaning 
of  speech  is  the  reflection  of  the 
human  mind,  and  the  devek)i>ment 
of  the  luniKui  mind  must  be  stud- 
ied historicallv." 


540 


SCIENTIFIC    THOUGHT. 


language  has  likewise  been  stated  to  be  no  longer  a 
historical  or  a  philosophical,  but  to  have  become  a 
physical,  science.  It  is  true  that,  as  with  other  natural 
sciences,  so  also  in  this  case,  the  morphological,  genetic, 
and  biological  aspects  can  be  specially  studied ;  also 
analogies  can  be  drawn  between  geology  and  glossology 
as  to  their  mode  of  inductive  reasoning.  The  great 
authority  who  first  took  up  this  novel  position  w^as  the 
late  Prof.  August  Schleicher  of  Jena,  and  the  same  has 
to  a  great  extent  been  simultaneously  adopted  by  Max 
]\Iuller  in  his  celebrated  '  Lectures  on  the  Science  of 
Language.'  It  is  interesting  to  note  that  Schleicher 
wrote  on  the  '  Morphology  of  Language '  in  the  same 
year  in  which  the  '  Origin  of  Species '  appeared,  and  that 
he  recognised  very  early  the  importance  of  Darwin's 
work  for  the  science  of  language.-^  This  became  still 
more  evident  on  the  publication,  twelve  years  later, 
of  the  '  Descent  of  Man,'  and  of  '  The  Expression  of  the 


1  On  August  Schleicher  (1821- 
68)  see  a  very  valuable  article  in 
the  'Allgemeine  Deutsche  Bio- 
graphic' (vol.  xxxi.  p.  402  sqq.)  by 
Johannes  Schmidt.  Very  different 
currents  of  modern  thought,  such 
as  we  shall  in  the  sequel  frequently 
have  to  represent  as  opposed  to 
■each  other,  the  study  of  the  classical 
and  of  the  modern  languages,  of 
critical  and  comparative  philology, 
the  historical  and  the  exact  spirit, 
Hegelianism  and  Darwinism — i.e., 
logical  and  mechanical  evolution 
— the  influence  of  Grimm,  Ritschl, 
and  Bopp,  of  botany  and  gram- 
mar, combined  to  generate  in  this 
remarkable  man  the  conception 
of  linguistic  as  a  natural  science 
in  contradistinction  from  phil- 
ology as  a  historical  science.     The 


principal  works  in  which  he  de- 
veloped his  original  view  were : 
'Die  deutsche  Sprache '  (1860); 
'  Compendium  der  vergleichenden 
Grammatik  der  indogermanischen 
Sprachen'  (1861);  'Die  Darwin'sche 
Theorie  und  dieSprachwissenschaft' 
(1863)  ;  and  '  Ueber  die  Bedeutung 
der  Sprache  fiir  die  Naturgeschichte 
des  Menschen  '  (1865).  Schleicher's 
ideas  have  been  taken  up  in  France, 
notably  by  Abel  Hovelacque  ('La 
Linguistique,'  4^'"^'  ed.,  1857),  who 
says  of  him  that  "he  had  com- 
pletely liberated  himself  from  meta- 
physical aspirations"  (p.  6).  On 
the  one  -  sidedness  of  the  purely 
jjhysical  theorj'  of  language  see 
Sayce,  '  Introd.  to  the  Science  of 
Language '  (1880),  vol.  i.  p.  76, 
&c. 


ON    THE    PSYCHO-PHYSICAL    VIEW    OF    NATURE.       541 


Emotions  in  Man  and  Animals '  a  year  after.  Tiiese 
\vritings  did  more  than  any  others  to  impress  upon 
jihilosophers  the  genetic  or  historical  view,  the  existence 
of  an  unln'oken  chain  or  transititjn  from  the  lower  to  the 
liigher  and  the  liigliest  forms  of  animal  structures,  and 
culminated  in  the  well-known  expression  of  Darwin,  that 
'  in  a  series  of  forms  graduating  insensibly  from  some 
ape-like  creature  to  man  as  he  now  exists,  it  would  he 
impossible  to  fix  at  any  definite  jjoint  when  the  term 
*  man '  ought  to  be  used."  ^  This  dictum  has  been  the 
theme  on  which  endless  variations  have  been  played 
down  to  the  present  day — Prof.  Ernest  Haeckel's  address 
to  tlie  Congress  of  Zoology  at  Cambridge  in  1898  being 
the  latest  summary  of  tlie  physical  aspect  of  the  proldem. 
But  the  problem  has  also  a  psycho-physical  side,  and  this 
aspect  is  concentrated  in  the  problem  of  language.  Even 
those  philologists  who,  like  August  Schleicher  and  I\lax 
Miiller,  look  upon  the  science  of  language  as  a  natural 
science,  bring  in  at  this  point  tlie  accumulated  and 
weighty  evidence  of  the  historical,  psychological,  ami 
})hilosophical  researches  into  the  growth  and  development 
of  human  speech  and  human  thought,  as  absolutely 
negativing  the  possibility  of  a  gradual  transition  from  the        4S. 

Tlie  dividing 

brute  to  the  Innnan  creation.     To   the  latter,  language,  Hne  between 

°       °       man  and 

which  he  considers  to  l^e  the  union  of  definite  concepts  '^™^'^- 
with  definite  names,  is    the    liubicon    which   cannot   be 
crossed,"  tlie  chasm    which    (li\i<les   that   ]K)rtion   of    the 


^  'Descent  of  Man,'  1st  ed.,  vol. 
i.  p.  23.'^. 

-  See  :^Iiix  Miiller,  '  The  Science 
of  Thouf^lit,'  piixxim,  notably  chap. 
iv.  p.  177,  where  he  (juotes  and 
maintains  his  dictum  of  1861  ( '  Lec- 


tures on  the  Science  of  Language,' 
vol.  i.  p.  403)  :  "  Language  is  our 
Rubicon,  and  no  biute  will  dare  to 
cross  it."  Referring  to  Schleicher, 
he  says  (p.  164) :  "  Professor 
Schleicher,  though  an  enthusiastic 


542  SCIENTIFIC    THOUGHT. 

living  creation  which  is  capable  of  an  unlimited  develop- 
ment and  an  external  realisation  of  its  inner  life  from 
that  which  has  no  mental  history  or  development :  it  is 
the  point  of  discontinuity  in  the  physical  development. 
The  study  of  language  in  its  physical  and  mental  aspects 
— i.e.,  in  phonetics  and  in  sematology — affords,  accord- 
ing to  this  view,  the  only  means  of  penetrating  from 
outside  into  the  inner  w^orld  of  thought :  it  is  the 
psycho-physical  problem  par  excellence- — ^the  "  Science  of 
Thought." 

Inasmuch  as  in  this  latest  development  of  psycho- 
physics  the  whole  of  the  accumulated  material  and 
most  of  the  arguments  have  been  drawn  from  the  his- 
torical and  philological  researches  of  such  thinkers  as 
Schlegel,  W.  von  Humboldt,  Bopp,  Grimm,  and  their 
followers,  who  were  without  exception  trained,  not  in 
the  mathematical  but  in  the  philosophical  schools  of 
Thought  which  ruled  in  the  earlier  part  of  our  century, 
the  further  consideration  of  their  ideas  belongs  properly 
to  that  portion  of  this  work  which  will  deal  specially 
with  philosophical  thought  and  its  application  in  such 
separate  branches  as  are  presented,  inter  alia,  by  the 
historical  sciences. 


admirer  of  Darwin,  observed  ouce  language  as   it   was   felt   by  Prof. 

jokingl}',  but  not   without  a  deep  Schleicher,    who,     though    a    Dar- 

irony,  '  If  a  pig  were  ever  to  say  to  winian,  was  also  one  of  our   best 

me,   "  I  am   a  pig,"   it  would  ipso  \    students  of  the  science  of  language, 

/acio  cease  to  be  a  pig.'     This  shows  |    But  those    who    know    best   what 

how  strongly  he  felt  that  language  j    language  is,   and  still   more,  what 

was  out  of  the  reach  of  any  animal,  it    presupposes,    cannot,    however 


I 


and   constituted    the  exclusive   or 


Darwinian  thev  mav  be   on   other 


specific  property  of  man.     I  do  not  !  points,   ignore   the    veto  which,   as 

wonder    that    Darwin    and    other  !  yet,  that  science  enters  against  the 

philosophers  belonging  to  his  school  last  step  in  Darwin's  philosophy." 

should  not  feel    the    difficulty   of  I 


ON    THE    PSYCHO-PHYSICAL    VIEW    OF    NATURE.       543 

It  now  only  remains  for  me  to  sum  up  in  a  few  words        49. 

Suiiiiiiary. 

the  leading  conceptions  which  the  psycho-physical  view  of 
nature  has  forced  upon  us.  In  the  last  chapter  I  showed 
how  the  study  of  life  has  in  the  course  of  our  century 
more  and  more  brought  out  the  conviction  that  life  is  a 
continuous,  a  ubiquitous,  and  a  unique  phenomenon ; 
an  exhaustive  or  even  a  working  definition  of  life  being 
so  far  hardly  possible.  In  this  chapter  we  have  learnt, 
by  following  the  psycho  -  i)hysical  lines  of  research,  to 
distinguish  another  and  peculiar  side  of  the  higher  forms 
of  living  matter,  that  which  is  coinuKmly  called  the 
mental,  inner,  or  self  -  conscious  side.  This  appeared, 
when  viewed  externally,  as  a  discontinuous  epi-pheno- 
menon — "  eine  Begleiterscheinung  " — of  some  very  com- 
plex physiological  processes  and  anatomical  arrangements 
of  living  matter,  and  as  such  it  exhiljits  a  property  with 
which  we  are  otherwise  not  familiar  in  the  visiltle  pheno- 
mena of  nature — namely,  discontinuity.  Viewed  exter- 
nally, the  inner  phenomena,  which  we  comprise  under 
the  term  "  mind,"  appear  and  disappear,  their  continuity 
being  preserved  in  association  with  the  permanence  of 
the  external  substratum  or  basis  to  which  they  are 
attached,  and  internally  regained  by  the  indefinable  pro- 
perty of  memory.  But  inasmuch  as  we  have  not  only  an 
external  but  also  an  internal  knowledge  of  at  least  some 
of  these  epi-phenomena,  we  have  had  forced  upon  us  an 
entirely  different  view  of  this  inner  life,  of  mind.  To 
the  inner  view  there  exists  in  self-conscious  l)eings  a 
centre  of  relatedness — a  special  kind  of  unity  which  we 
call  individuality  or  personality ;  and  this  inner  unity  is 
cai)able  of  being  externalised  or  made   objective   in  llie 


544 


SCIENTIFIC    THOUGHT. 


mental  life  of  mankind,  language  being  the  great  instru- 
ment by  which  this  is  accomplished.  In  this  external 
or  objective  existence — which,  however,  is  only  intel- 
ligible to  beings  which  form  a  part  of  it — that  con- 
tinuity is  regained  which  in  the  existence  of  every 
individual  is  continually  being  interrupted  and  in  danger 
of  being  lost.  Psycho-physical  research  reveals  to  us 
the  existence  of  a  unity  different  from  that  visible  in 
merely  external  or  physical  nature, — a  centred  unity 
which  is  something  else  than  the  sum  of  parts  in  a 
mathematical  whole.  Through  this  process  of  cen- 
tralisation and  externalisation  there  has  been  formed 
in  the  physical  world,  or  in  nature,  a  new  world — 
the  world  of  mind,  which  is  continually  growing  in 
contrast  to  the  former,  which  only  changes  without 
increasing  or  losing  its  two  constituents,  matter  and 
energy. 

This  new  world  within  the  old  one,  this  creation  of 
man,  forms  indeed  a  portion  of  nature — it  is  the  micro- 
cosm in  the  macrocosm.  It  might  be  investigated  by 
the  usual  methods  of  exact  research ;  and  the  science  of 
anthropology,  with  its  many  branches,  proposes  to  study 
it  in  the  same  way  as  natural  history  in  modern  times 
has  studied  the  social  life  of  certain  animals,  such  as 
bees,  ants,  and  beavers.  Inasmuch,  however,  as  the  exact 
methods  do  not  lead  very  far,  and  have  continually  to 
appeal  to  the  interpretations  of  psychology,  gained  by 
personal  experience  and  introspective  methods,-^  it  seems 


1  Prof.  E.  Hering  ('Ueber  das 
Gedjichtniss  als  eine  allgemeine 
Funktion  der  organischen  Materie,' 
Vienna,    1870)    says:    "So   long  as 


the  physiologist  is  only  a  physicist 
he  stands  in  a  one-sided  position 
to  the  organic  world.  This  one- 
sidedness    is    extreme    but    quite 


ON    THE    PSYCHO-PHYSICAL    VIEW    OF    NATURE.       545 

more  practical  to  range  tlie  whole  of  these  researches 
within  that  great  realm  of  thought  which  starts  with  a 
distinct  recognition  of  conscious  individual  life  as  its 
source  and  centre.  As  such,  in  fact,  these  researches 
have  l^een  till  quite  recently  carried  on,  and  the  main 
lines  of  their  recent  development  l)elong  accordingly  to 
philosophic  as  distinguished  from  scientific  or  exact 
thought. 

The  three  great  facts,  however,  which  even  the  exact  _    5o. 

o  '  Tlie  three 

treatment  of  mental  phenomena  has  impressed  upon  us  [fressed  by 
— namely,  the  existence  of  centralised  material  systems,  phys'cs. 
termed  "  individuals,"  the  discontinuity  of  their  inner 
life  as  viewed  from  outside,  and  the  phenomenon  of  its 
growing  external  manifestation  —  have  driven  natural 
philosophers  to  form  some  explanation,  or  at  least  to 
venture  upon  a  definition  of  this  hidden  principle, 
which  shows  itself  in  the  highest  forms  of  living  matter, 
and  which,  though  discontinuous  to  the  external  observer, 
acquires  in  the  aggregate  of  human  society  a  continuous 
and  ever  growing  reality  and  development.     Two   dis- 

legitimate.  As  the  crystal  to  complex  whose  external  aud  in- 
the  mineralogist,  the  vibrating  ternal  movements  are  causally  as 
string  to  the  student  of  acoustics,  rigidly  connected  amongst  each 
so  also  the  animal,  and  even  man,  other,  and  with  the  movements 
is  to  the  physicist  only  a  piece  of  of  the  environment,  as  the  work- 
matter.  That  the  animal  expcri-  ing  of  a  machine  is  with  the 
ences  pleasure  and  i)ain— that  with  revolution  of  its  wheels  (p.  4).  .  .  . 
the  material  life  of  the  human  Thus  the  i)hysiologist  as  physicist, 
frame  are  connected  the  joys  and  But  he  stands  behind  the  scene, 
sorrows  of  a  soul  and  the  vivid  and  while  he  painfull}'  examines 
intellectual  life  of  a  consciousness  ;  the  mechanism  and  the  busy  doings 
this  cannot  change  the  animal  and  of  the  actors  behind  the  drop- 
human  body  for  the  jihysical  scenes,  he  misses  the  sense  of  the 
student  into  anything  other  than  whole  which  the  spectator  easily 
it  is — a  material  conijilex  subject  recognises  from  the  front.  Could 
to  the  unalterable  laws  which  the  physiologist  not,  for  once, 
govern  also  the  stone  and  the  cliange  his  position?"  (p.  5.) 
substance  of  tiie  plant,  a  material 

VOL.  ir.  2  .M 


546  SCIENTIFIC   THOUGHT. 

tinct  views  have  been  evolved  by  modern  science  on 
this  matter. 

The  one  emphasises  the  fact  of  the  discontinuity  of 
mental — i.e.,  conscious — life,  regards  it  as  an  ultimate 
fact,  as  a  mystery  beyond  which  we  cannot  travel.  This 
idea  presents  itself  in  various  forms,  and  has  been 
notably  insisted  on — with  very  varying  philosophical 
inferences — by  Du  Bois-Eeymond  in  Germany,  by  Mr 
A.  E.  Wallace,  and  quite  recently  by  the  late  Prof,  St 
George  Mivart  in  England. 

The  other  takes  refuge  in  the  hypothesis  of  un- 
conscious or  subconscious  mental  life,  and  again  with 
very  different  philosophical  inferences  assumes  that  all 
physical  existence  has  an  inner  side  which  only  under 
certain  favourable  conditions  rises  into  the  light  of  self- 
knowledge  or  consciousness.  The  late  W.  K.  Clifford's 
"mind-stuff"  theory,  as  also  the  speculations  of  Fechner 
and  of  Prof.  Haeckel,  are  types  of  this  view,  which  has 
been  consistently  and  connectedly  elaborated  in  Hart- 
mann's  '  Philosophy  of  the  Unconscious.' 

These  speculations  can  be  summed  up  under  the  title 
"  The  Creed  of  Science,"  and  as  such  will  occupy  us  later 
on  in  one  of  the  chapters  on  the  Philosophical  Thought 
of  the  century. 

By  many  natural  philosophers  it  is  felt  that  the  tune 

has  not  yet  come  to  arrive  scientifically  at  any  definite 

51.        conclusions  on  these  last  questions.     Sufficient  facts  have 

Transition  ^ 

to  statistics,  not  been  collected ;  or  even  if  collected,  they  have  not 
yet  been  classified  and  tabulated.  This  is  especially  the 
case  with  the  vast  materials  referring  to  the  collective 
life  of  mankind,       Leibniz  had  in  his  time  foretold  the 


ON    THE    PSYCHO-PHYSICAL    VIEW    OF    NATURE.       547 

necessity  of  extensive  statistical  information  before  build- 
ing theories.  In  one  instance,  that  of  language,  his 
advice  was  followed  with  signal  success. 

But  even  some  of  the  purely  physical  sciences,  like 
meteorology,  are  still  almost  entirely  limited  to  statist- 
ical information. 

Statistics  have  thus  become  a  very  important  depart- 
ment of  knowledge,  and  before  taking  leave  of  the  exact 
lines  of  thought,  it  will  be  well  to  note  more  precisely 
the  part  which  these  have  played  in  our  age,  as  also  the 
methods  by  which  they  proceed.  This  will  be  the 
object  of  the  next  chapter,  which  will  accordingly  deal 
with  the  Statistical  View  of  Nature. 


548 


CHAPTER   XII. 

ON    THE    STATISTICAL    VIEW    OF    NATURE. 

I  HAVE  now  treated  of  the  several  grand  and  general 
aspects  under  which  the  objects  of  nature  can  be 
scientifically  regarded,  and  have  tried  to  show  how 
these  aspects,  not  unknown  to  former  ages,  have  never- 
theless, in  the  course  of  the  nineteenth  century,  become 
more  definite,  and  accordingly  more  useful,  as  means  for 
describing,  measuring,  and,  in  many  cases,  predicting 
phenomena.  It  is  true  that  the  two  last  chapters, 
which  dealt  with  the  phenomena  of  Life  and  Mind, 
had  to  take  notice  of  a  principle  or  of  principles  which 
have  hardly  yet  received  any  scientific  definition  at  all, 
and  which  in  the  progress  of  the  sciences  which  deal 
with  them  have  played  rather  a  negative  part.  It  has 
been  mainly  by  eliminating  the  conceptions  of  life  and 
1.         of  mind  as  special  agencies,  factors,  or  entities  that  the 

Life  and  _ 

Hnutin^  scientific  study  of  living  and  conscious  beings  has  pro- 
conceptions,  gressed ;  by  showing  more  and  more  how  an  accurate 
and  useful  knowledge  of  much  of  their  nature  and 
behaviour  can  be  gained  with  the  aid  of  the  methods 
adopted  in  other  scientific  inquiries,  which  we  may  call 
mechanical. 


ON    THE    STATISTICAL    VIEW    OF    NATURE, 


.49 


Scientific  iiUjuiiy  in  biology  and  p.sych(.-})liysics  has 
thus  advanced  on  the  lines  indicated  in  the  earlier 
chapters,  where  it  was  shown  how  several  positive 
scientific  conceptions  have  been  gained,  defined,  and  ap- 
plied. These  conceptions  are  all  generalisations  based 
upon  definite  observable  facts  of  nature,  such  as  attrac- 
tion, atomic  constitution,  motion  (rectilinear,  periodic, 
and  rotational),  energy,  form,  and  change  of  form,^  and 
they  have  given  rise  to  great  branches  of  science,  con- 
taining special  methods  of  thought  and  reasoning.  They 
have  all  shown  themselves  accessible,  in  a  greater  or 
less  degree,  to  mathematical  treatment,  and  have  con- 
sequently been  the  means  of  introducing  the  exact 
scientific   spirit   into  large  fields  of  research,  into   ever 


^  The  statement  in  the  text  is  not 
strictly  correct ;  for  of  the  six 
definite  conceptions  mentioned  we 
really,  even  in  single  cases,  only 
see  two  exemplified — viz.,  motion 
and  form.  Neither  attraction,  nor 
the  atom,  nor  energy,  nor  develop- 
ment is,  even  in  single  cases, 
observable,  though,  with  the  excep- 
tion of  energy,  they  are  very  early 
and  very  familiar  abstractions. 
This  remark  may  suggest  that 
motion  and  form  are,  at  least 
for  the  present,  the  simplest  and 
most  obvious  conceptions  into 
which  we  can  analyse  oi-  resolve 
all  external  observations,  and  that 
conseijuently  kinetics  and  mor- 
phology may  be  the  fundamental 
sciences,  the  first  in  natural  phil- 
osophy, the  latter  in  natural  his- 
tory or  biology  in  the  widest  sense. 
That  a  kinetic  view  will  gradually 
supervene  in  natural  phiUisoph\-  is, 
I  think,  generally  admitted.  It 
seems  less  generally  conceded  that 
morphology  will  supervene  in 
biology  ;  especially  as  all  the  rage 


is  just  now  for  evolution  and 
development.  But  as  development 
must  start  from  something,  it  is 
likely  that  it  will  lead  back  to 
morphology.  As  tending  in  this 
direction  I  read  the  expositions  of 
Lotze,  Claude  Bernard,  and  the 
"  Organicists."  Organisation  must 
mean  a  certain  arrangement,  and 
arrangement  is  ultimately  the  same 
as  order,  structure,  or  form.  It 
may  mean  something  more — viz., 
unity  or  centredness ;  but  this  is 
a  conception  not  capable  of  a  purely 
mechanical  or  geometrical  defini- 
tion ;  we  know  of  it  only  through 
introsj)ection.  A  great  deal  has 
been  written  on  Morphologj'  and 
Morphogenesis  by  that  very  sug- 
gestive author,  Hans  Driesch  ;  see 
a  list  of  his  writings,  stipra,  p.  4ft6 
note.  I  here  only  refei-  to  them  ; 
for,  being  myself  unable  clearly  to 
apprehend  his  main  drift,  I  hesitate 
to  quote  him  as  confirming  the 
argument  of  this  note.  The  reader 
must  judge  for  himself. 


550  SCIENTIFIC    THOUGHT. 

widening  circles  of  phenomena  and  events.  This  has 
been  most  decidedly  the  case  with  the  sciences  in  which 
the  law  or  formula  of  gravitation  has  become  the  lead- 
ing principle.  As  we  advanced  on  the  other  lines  of 
thought,  marked  by  the  conceptions  of  atomism,  of  the 
various  forms  of  motion  and  of  energy,  this  subjection 
to  precise  formulae  became  less  perfect,  more  com- 
plicated and  hypothetical,  whilst  the  study  of  the 
typical  forms  of  natural  objects,  and  even  more  of 
their  genesis  and  developments,  opened  out  a  field  for 
much  conjecture  and  fanciful  reasoning,  amid  which 
little  more  than  the  general  outlines  of  a  definite  theory 
could  be  established.  Lastly,  in  applying  these  various 
conceptions  to  the  phenomena  of  the  living  and  self- 
conscious  creation,  we  have  struck  upon  the  limiting 
ideas  of  life  and  mind,  of  which,  from  a  purely  external 
point  of  view,  little  more  can  be  said  than  that  they 
indicate  to  us  the  existence  among  natural  objects  of  a 
unity  of  a  different  kind  from  that  which  we  can  under- 
stand mechanically  as  the  sum  of  many  parts.  In  the 
higher  forms  this  unity  revealed  itself  to  us  through  the 
analogy  of  our  own  inner  life  as  a  peculiar  kind  of 
centralisation,  discontinuous  when  viewed  from  outside, 
but  possessing,  when  viewed  from  another  side,  a  con- 
tinuity, connectedness,  and  capacity  of  unlimited  growth 
of  its  own  which  is  the  special  object  of  the  psycho- 
logical and  historical  sciences.  These  characteristics  be- 
long to  the  great  realm  of  philosophical  as  distinguished 
from  exact  scientific  thought. 


"o' 


Results  of         Before   entering   on   this   other   great  branch   of   our 

a  V\  e  J"  f  o  f*  f" 

science.        subjcct,    wc   may   well    pause   for    a   moment   and   cast 


ox    THE    STATISTICAL    VIKW    OF    NATURE.       551 

a  general  and  unbiassed  glance  at  tlie  world  outside, 
leaving  our  study,  our  observatory,  our  laljoratory,  our 
dissecting-  or  our  nieasuring-rooni,  and  ask  ourselves 
the  simple  question,  By  the  work  carried  on  in  these 
various  secluded  places,  in  the  "  sapientum  templa 
Serena,"  hov^^  much  of  the  world  outside  have  we  really 
learnt  to  comprehend,  or  even  only  to  describe  and 
picture  to  ourselves  correctly  and  completely  ?  The 
answer  is  hardly  encouraging.  The  first  thing  we 
notice  in  stepping  out  of  our  door  is  a  phenomenon 
still  as  incalculable  as  it  has  ever  been,  and  yet  bound 
up  with  the  enjoyment  of  our  lives  and  the  success 
of  our  work  as  much  as  ever — the  weather.  What  do 
we  know  of  it  which  is  practically  reliable  and  useful  ? 
The  reply  must  be,  "  Next  to  nothing."  Some  general 
astronomical  and  some  more  detailed  physical  and 
chemical  relations  permit  us  to  describe  a  few  general 
meteorological  and  a  few  recurring  seasonable  events,  but 
scarcely  with  more  practical  detail  and  certainty  than  the 
unscientific  ancients  or  the  untaught  children  of  nature 
of  to-day.  We  know  in  general  the  cause  of  storms,  of 
changes  of  temperature,  of  the  seasons,  of  rain,  hail, 
drought,  and  cold,  but  we  do  not  know  much  more  of 
the  exact  when  and  where  of  these  various  changes 
than  did  our  forefathers.  The  natural  atmosphere  and 
climate  which  surround  us  are  still  elements  of  con- 
jecture and  uncertainty. 

Assume,  however,  that  we  go  a  step  further,  and 
having  accustomed  ourselves  to  take  the  weather,  good 
or  bad,  as  it  is,  enter  into  the  artificial  atmosphere  and 
surroundings  of    practical    life,   of  industry,   trade,    and 


552  SCIENTIFIC    THOUGHT. 

commerce,  of  politics  and  society,  in  which  most  of  us 
have  to  spend  the  larger  portion  of  the  working  hours  of 
our  existence.  We  can  again  put  the  question.  What  do 
we  know  with  certainty  of  the  changes  and  vicissitudes 
of  this  artificial  atmosphere  which  surrounds  us ;  what 
of  the  chances  of  a  fall  or  rise  in  prices,  of  increased 
or  lessened  demand,  of  impending  labour  troubles,  of  the 
risks  even  of  famine,  fire,  shipwreck,  disease,  or  war  ? 
Again  we  may  say  that  in  general  we  know  the  proxi- 
mate causes,  natural  or  artificial,  which  may  bring  them 
about,  but  the  exact  when  and  where  of  their  occurrence 
is  so  slightly  known  to  us  that  such  knowledge  is  of  little, 
if  of  any,  practical  value,  and  proceeds,  moreover,  where 
it  exists,  more  from  general  good  sense  and  practical 
experience  than  from  the  discoveries  of  science.  Indeed, 
the  latter  have,  through  the  wonderful  applications  in 
the  inventions  of  arts  and  crafts,  tended  to  make  our 
artificial  atmosphere  more  complex,  liable  to  more  rapid 
and  more  drastic  changes,  and  accordingly  its  features 
less  permanent  and  less  calculable  and  reliable. 
3.  Thus,  in  spite  of  the  wonderful  increase  of  scientific 

Uncertainty  ■>     ■,•  r'o      •  c        •         •  n        i 

in  the  con.  knowledge  and  the  general  diffusion  of  scientific  thought 
in  the  course  of  the  century,  uncertainty  is  still  the 
main  and  dominant  characteristic  of  our  life  in  nature 
and  society ;  the  atmosphere  and  climate  of  each  are  as 
fickle  and  changeable,  as  incalculable  and  unreliable,  as 
ever.  Neither  the  great  law  of  gravitation  nor  the 
fixed  proportions  of  chemistry,  neither  the  intricate 
doctrine  of  undulations  nor  the  conception  of  energy, 
neither  the  knowledge  of  typical  forms  of  nature  nor  that 
of  their  orderly  evolution,  has,  in  the  hands  of  those  who 


Crete. 


ON    THE    STATISTICAL    VIEW    OF    NATURE.       553 

fjovern,  regulate,  and  fashion  the  practical  work  of  life 
and  society,  become  an  instrument  of  personal  use  and 
daily  importance.  Statesmen,  legislators,  organisers  of 
men,  captains  of  industry,  contractors,  practical  engineers, 
colonisers,  pioneers,  and  leaders  of  all  kinds  are  still 
mostly  ignorant  of  these  scientific  ideas.  They  regard 
them  from  a  distance,  themselves  relying  mainly  on 
common -sense,  on  personal  experience,  or  on  the  innate 
but  indefinable  impulses  of  individual  genius ;  pro- 
fessional, scientific  knowledge  is  only  one,  and  hardly  the 
most  important,  of  the  many  agencies  with  which  they 
deal  and  which  they  have  to  take  into  account. 

And  yet,  in  spite  of  this  fact  that  the  ordinary  routine         4. 

r.     T  e       •  1  Scientific 

of   life   IS   a   very   different    process   from    the    ways  of  spirit  in 

"  ^  •'  business. 

science,  we  must  admit  that  the  scientific  spirit  very 
largely  pervades  the  business  of  to-day.  You  cannot 
enter  any  commercial,  shipping,  or  general  trading  office 
without  being  struck  with  the  number  of  carefully  pre- 
pared charts,  tables,  and  statistical  registers  of  all  kinds 
of  curves  showing  the  rise  and  fall  of  prices,  the  produc- 
tion and  consumption,  the  stocks  and  values  of  metals, 
coal,  grain,  chemicals,  cotton,  and  produce  of  every  kind ; 
and  in  quite  recent  years,  not  only  material  things  of  all 
sorts,  but  the  intangible  thing  called  energy  —  after 
supplanting  the  older  term  horse-power — has  become  the 
subject  of  elaborate  tabular  and  graphical  registration. 
The  streets  of  even  the  smaller  towns  in  every  civilised 
country  show,  besides  the  sign-boards  of  shops,  otiices, 
and  banks,  an  increasing  array  of  insurance  firms,  whose 
whole  business  depends  on  elaborate  calculations,  based 
on   long  tables  of  births,  deaths,  marriages,  shipwrecks, 


554  SCIENTIFIC    THOUGHT. 

and  other  casualties.  The  daily  newspapers  bring  us 
weather  charts  with  isothermic,  isobaric,  and  other  lines, 
on  which  they  found  weather  predictions  or  storm 
warnings.  vSurely,  if  counting,  measuring,  and  calculat- 
ing are  the  elementary  processes  of  the  scientific  method, 
it  must  be  admitted  that  the  latter  has  permeated  our 
practical  life  to  an  enormous  extent.  Thus  the  question 
can  be  asked,  If  the  calculating  spirit  is  so  general,  how 
does  it  come  about  that  in  its  application  to  life  and 
commerce  it  has  led  to  so  much  grasp  but  to  so  little 
certainty ;  whereas  in  science  itself  it  has  led  to  so  much 
actual  and  reliable  knowledge  ?  How  does  its  application 
in  practice  differ  from  that  in  theory  ?  The  answer  to 
this  question  is  not  far  to  seek,  and  it  will  introduce  us  to 
a  special  branch  of  science,  to  a  special  form  of  scientific 
thought  which  again  is,  if  not  a  creation  of  the  nineteenth 
century,  yet  one  of  its  characteristic  developments. 

That  which  everywhere  oppresses  the  practical  man 
is  the  great  number  of  things  and  events  which  pass 
ceaselessly  before  him,  and  the  flow  of  which  he  cannot 
arrest.  What  he  requires  is  the  grasp  of  large  numbers. 
The  successful  scientific  explorer  has  always  been  the  man 
who  could  single  out  some  special  thing  for  minute  and 
detailed  investigation,  who  could  retire  with  one  definite 
object,  with  one  fixed  problem  into  his  study  or  labor- 
atory and  there  fathom  and  unravel  its  intricacies,  rising 
by  induction  or  divination  to  some  rapid  generalisation 
which  allowed  him  to  establish  what  is  termed  a  law 
or  general  aspect  from  which  he  could  view  the  whole 
or  a  large  part  of  nature.  The  scientific  genius  can 
"  stay  the  moment  fleeting " ;  he  can  say  to  the  object 


ON    THE    STATISTICAL    VIKW    OF    NATURE. 


555 


of  his  choice,  "  Ah,  linger  still,  thou  art  so  fair " ;  he 
can  fix  and  keep  the  star  in  the  focus  of  his  telescope, 
or  protect  the  delicate  fibre  and  nerve  oi  a  decaying 
organism  from  succumbing  to  the  rapid  disintegration 
of  organic  change.  The  practical  man  cannot  do  this ; 
he  is  always  and  everywhere  met  by  the  crowd  of  facts, 
by  the  relentlessly  hurrying  stream  of  events.  What 
he   requires   is   grasp    of   numbers,   leaving  to  the  pro-        5. 

^  o        1  '  o  1  Tlie  science 

fessional  man  the  knowledge  of  detail.     Thus  has  arisen  of  large 

"  numbers. 

the  science  of  large  numbers  or  statistics,^  and  the  many 
methods  of  which  it  is  possessed.  It  will  form  the 
subject  of  the  present  chapter. 


1  Gottfried  Aclieinvall  (1719- 
1772)  is  commonl}'  tcnued  the 
"father"  of  statistics.  Tiiis,  how- 
ever, is  hardly  correct,  either  in 
relation  to  teaching  or  to  the 
practical  part  of  the  subject,  or  even 
so  far  as  the  name  is  concerned. 
In  connection  with  administration 
statistics  existed  in  anti([uity. 
They  were  taught  hy  the  celebrated 
professor,  Conring,  the  elder  con- 
temporary and  rival  of  LeiVjniz, 
and  the  name  occurs  in  the 
seventeenth  century  in  the  '  Micro- 
scopium  statisticum,  (juo  status 
imperii  Komano  -  (iermanici  rep- 
ricsentatur  auct.  Heleno  Politauo ' 
(1672).  By  Achenwall  and  his 
successor,  Ludwig  August  Schlozer 
(173.')-1809),  statistics  were  treated 
in  connection  with  liistory.  The 
latter  says,  "  Statistics  are  history 
standing  still,  and  history  is  sta- 
tistics put  in  motion."  See  on 
this  subject,  Wegele,  '  (Jeschichte 
der  deutschen  Hi^toriographie ' 
(MUnchen,  188.5),  ]>.  793  ;  also 
Iloscher,  '  Geschichte  der  Xational- 
Oekonomik  '  (ibid.,  1874),  p.  466. 
A  very  valuable  and  exhaustive 
account     of     the     etymology    and 


gradual  change  of  meaning  of  the 
words  "  statist "  and  statistics  will 
be  found  in  Dr  V.  John, 
'Geschichte  der  Statistik,'  1.  Theil. 
(Stuttgart,  1884),  pp.  3-14.  He 
divides  the  history  of  the  subject 
down  to  (^uetelet  into  that  of  the 
"  German  University  Statistics," 
following  in  the  lines  of  Conring, 
Achenwall,  and  Schliizer,  also  called 
the  "  Gottingen  School,"  and  that 
of  statistics  as  an  exact,  an 
enumerative  science,  which  he  calls 
the  modern  science  of  statistics.  It 
appears  that  in  English  also  the 
two  meanings  of  the  word  are  ex- 
em[)lified  in  the  older  use  of  the 
term  '"statist"  by  Shakespeare 
("  Handet,"  v.  '2.;  '' Cymbeline,"  ii. 
4.)  and  Webster,  in  which  sense  it 
meant  simply  "statesman";  and  the 
modern  title  'Statist,'  for  a  statis- 
tical and  financial  periodical.  Nor 
must  we  forget  that  England  has  in 
her  •  Liber  judiciarius  sen  censualis 
Willelmi  I.,  regis  Angli;e,'  called 
'  Domesday  -  book  •  (1083-86),  as 
David  Hume  says,  "  the  most 
valuable  piece  of  anticiuity  pos- 
sessed by  any  nation  "  ('  Hist,  of 
England,'  chai>.  iv.) 


556  SCIENTIFIC    THOUGHT. 

The  grasp  of  large  numbers,  the  methodical  array  of 
figures  and  the  registration  of  events,  would  in  itself  be 
of  little  use  were  it  not  for  a  fundamental  assumption 
which  appeals  to  common-sense  and  has  been  confirmed 
by  science,  though  it  is  hardly  anywhere  expressly  stated 
— namely,  the  belief  in  a  general  order,  in  a  recurrent 
regularity  or  a  slow  but  continuous  change  and  orderly 
development  of  the  things  and  events  of  the  world. 
Science,  in  the  different  aspects  which  we  have  so  far 
passed  in  review,  tries  to  give  a  definite  expression  to 
this  general  Order,  to  this  all-pervading  rule  and  regu- 
larity. Statistics  and  the  practical  use  of  them  limit 
themselves  to  the  bare  fact  that  such  order  and  regular- 
ity do  exist,  though  the  formula  or  reason  for  them 
may  be  unknown  or  unknowable.  It  may  also  be  well 
to  note  that  this  belief  in  a  general  order  is  common  to 
all  schools  of  thought,  be  they  ancient  or  modern,  pagan 
or  Christian,  religious  or  scientific,  optimist  or  pessimist. 
6.         The  dictum,  "  est  modus  in  rebus,"  is  the  fundamental 

Belief  in  in  •  ■>     ^  •      •      ^ 

general  axioiii  of  all  thought  and  all  practice ;  and  the  statistical 
view  of  nature,  which  merely  puts  into  form  and  figure 
this  general  axiom  or  truism,  has  accordingly  been  ap- 
pealed to  as  much  by  those  who  uphold  a  divine  order 
of  things  as  by  others  who  insist  on  a  natural  or 
mechanical  one.  In  the  school  of  Quetelet,  through 
whose  influence  statistical  knowledge  has  been  so 
greatly  furthered  in  the  course  of  our  century,  the 
regular  recurrence  of  events  and  the  stability  of  large 
numbers  has  been  sometimes  used  as  the  basis  for  a 
fatalistic  and  pessimistic  view,  whereas  nearly  a  hundred 
years  before  Quetelet,  statistics  had  been  elaborated  by 


order. 


ON   THE   STATISTICAL    VIEW    OF    NATURE.       557 


the  Pastor  Sussinilch  in  I'lussia,  in  a  celebrated  book 
bearing  the  title  '  On  the  Divine  Order,'  with  a  tendency 
towards  optimism,  and  as  a  proof  of  an  overruling 
Providence.^ 

Although  it  is  generally  admitted  by  writers  on  stat- 
istics that  in  the  narrower  sense  of  the  word  they  have 
existed  ever  since  the  existence  of  governments  which  re- 
quired to  know  the  number  of  their  population,  the  nat- 
ural resources  of  the  country,  and  its  means  of  subsist- 
ence or  defence,  there  is  a  general  opinion  current  that 
what  we  now  call  the  statistical  methods  in  science  and 
in  practice  were  introduced,  or  at  least  expressly  recom- 
mended, by  Lord  Bacon  under  the  name  of  the  "  Method 
of  Instances."  This  method,  which  consisted  in  a  kind 
of  tabulating  of  numbers  of  facts  referring  to  any 
special  sul)ject  under  investigation,    has  been  criticised 


7. 
Bacon's 
"Method  of 
Iiistances.  " 


^  The  difference  seems  to  narrow 
itself  down  to  thi.«,  th<at  one  class 
of  writers  refers  everything  to  a 
physical,  the  other  to  a  moral, 
order.  M.  Maurice  Block,  an 
eminent  writer  on  statistics,  dis- 
cusses this  question,  passing  a  num- 
ber of  modern  authors  under 
review  in  the  fifth  chapter,  §  3, 
of  his  excellent  'Traite  tht'oriciue 
et  pratique  de  Statistique,'  (2""^ 
ed.,  Paris,  1886).  Referring  to 
tlie  theological  statistician,  A.  von 
Oettingen,  and  comparing  him  with 
Quetelet,  he  says  (p.  146):  "Sous 
certains  rapports,  i'oj)inion  de  M. 
le  professeur  de  thcologie  Alex- 
andre d'QJttingen,  pouira  paraitre 
I'opposee  de  celle  de  (Quetelet, 
mais  elle  nous  semble  en  diHc'rer 
beaucoup  moins  que  le  savant  pro- 
fesseur ne  le  croit.  .  .  .  Nous 
pouvons  caractdriser  en  peu  de 
mots  ce  que  MM.  d'(Eltingen  et 
Quetelet  ont  de  commun  et  com- 


ment ils  different  :  ils  ont  de 
commun  le  fond  de  la  science  ;  ils 
constatent  I'un  et  I'autre  la  r6- 
gularite  du  mouvement  des  faits  ; 
ils  ne  different  que  par  linter- 
pretation  :  (Quetelet  voit  des  lois 
naturelles  l:i  oil  JI.  le  professeur 
d'Qilttingen  voit  des  lois  morales 
institutdes  par  Dieu.  Aussi  I'un 
uomme-t-il  son  Hvre  Physique 
sociale,  et  I'autre  Ethi(iue  sociale. 
M.  d'ffittiiigeu  est  uu  croyant  qui 
aime  h,  s'appuyer  sur  la  science. 
II  dit,  page  13  de  la  premiere 
edition  :  '  Dans  les  sciences  connne 
dans  la  religion,  ce  que  I'homme 
invente  ne  pent  etre  (jue  faux, 
tandis  que  les  verites  qu'il  de- 
couvre,  sont  uniquement  des  faits 
ou  des  lois  qui  rayonnent  du 
Createur.'"  The  reconciliation  of 
either  physical  or  moral  order  with 
the  existence  of  freewill  is  not 
a  statistical  but  a  philosophical 
problem. 


558  SCIENTIFIC   THOUGHT. 

by  writers  like  Whewell,  von  Liebig,  Stanley  Jevons, 
and  many  others,  and  shown  to  be  of  very  doubtful 
value ;  the  example  given  by  Bacon  himself — the  re- 
search into  the  nature  of  heat — being  especially  un- 
fortunate and  badly  chosen.  In  spite  of  this,  it 
is  noteworthy  that,  up  to  quite  recent  times,  the 
Baconian  method  is  continually  referred  to,  mainly  by 
writers  who  are  desirous  of  introducing  what  they  call 
the  exact  methods  of  research  into  other  sciences 
than  those  of  external  nature.  A  good  example  of  this 
kind  is  given  by  Walter  Bagehot,  and  as  it  serves  to 
make  an  important  point  more  intelligible  than  a  gen- 
eral statement  would,  I  will  here  give  it  in  full.  He 
speaks  of  the  Enumerative,  or,  as  he  calls  it,  the  "All- 
case  method,"  and  then  continues:  "A  very  able  Ger- 
man writer  ^  has  said  of  a  great  economical  topic — 
banking — '  I  venture  to  suggest  that  there  is  but  one 
way  of  arriving  at  such  knowledge  and  truth,  namely, 
a  thorough  investigation  of  the  facts  of  the  case :  by 
the  facts  I  mean  not  merely  such  facts  as  present 
themselves  to  so-called  practical  men  in  the  common 
routine  of  business,  but  the  facts  which  a  complete 
historical  and  statistical  inquiry  would  develop.  When 
such  a  work  shall  have  been  accomplished,  German 
economists  may  boast  of  having  restored  the  principle 
of  banking — that  is  to  say,  of  German  banking,  but 
not  even  then  of  banking  in  general.  To  set  forth 
principles  of  banking  in  general,  it  will  be  necessary 
to  master  in  the  same  way  the  facts  of  English,  Scottish, 
French,   and   American    banking  —  in    short,    of    every 

1  Prof.  Cohn  in  '  Fortnightly  Review,'  Sept.  1873. 


ON    THE    STATISTICAL    VIEW    OF    NATURF:.       559 

country  where  banking  exists.  .  .  .  The  only,  but  let  us 
add  also  the  safe,  ground  of  hope  for  political  economy, 
is  following  Bacon's  exhortation  to  recommence  afresh 
the  whole  work  of  economic  inquiry.  In  what  condi- 
tion would  chemistry,  physics,  geology,  zoology  Ije,  and 
other  branches  of  natural  science  which  have  yielded 
such  prodigious  results,  if  their  students  had  been  linked 
to  their  chains  of  deduction  from  the  assumptions  and 
speculations  of  the  last  century  ? ' "  To  this  Bagehot 
replies :  "  The  method  which  Mr  Colin  suggests  was 
tried  in  physical  science  ami  failed.  And  it  is  very 
remarkable  that  he  should  not  have  remembered  it  as 
he  speaks  of  Lord  Bacon,  for  the  method  which  he 
suggests  is  exactly  that  which  Lord  Bacon  himself 
followed,  and  owing  to  the  mistaken  nature  of  which 
he  discovered  nothing.  The  investigation  into  the 
nature  of  heat  in  the  '  Novum  Organum '  is  exactly  such 
a  collection  of  facts  as  Mr  Cohn  suggests,  but  nothing 
comes  of  it.  As  Mr  Jevons  well  says.  Lord  Bacon's 
notion  of  scientific  method  was  that  of  a  kind  of  scien- 
tific book-keeping.  Facts  were  to  1)0  indiscriminately 
gathered  from  every  source  and  posted  in  a  kind  of 
ledger,  from  which  would  emerge  in  time  a  clear  balance 
of  truth.  It  is  difficult  to  imagine  a  less  likely  way  of 
arriving  at  discoveries."  ^ 


1  '  The  Postulates  of  English 
Political  Economy  '  (1885),  p.  17, 
&c.  He  further  remarks  :  "  If  we 
wait  to  reason  till  the  '  facts '  are 
complete,  we  shall  wait  till  the 
human  race  has  ex])ired.  I  think 
that  Mr  Cohn,  and  tliose  who  think 
with  him,  are  too  'bookish  '  in  this 
matter.     They  mean  by  liaving  all 


tlie  'facts'  before  them,  liitving  all 
the  i>rinted  facts,  all  the  statistical 
tables.  But  what  has  been  said 
of  nature  is  true  of  commerce. 
'Nature,'  says  Sir  Charles  Lyell, 
'  has  made  it  no  part  of  her  con- 
cern to  provide  a  record  of  her 
operations  for  the  use  of  men  '  ; 
nor   does  trade  eitlier  —  tudy    the 


560 


SCIENTIFIC    THOUGHT. 


In  fact,  the  eight  chapters  of  this  work  which  have 
dealt  with  the  various  abstract  views  from  which  natural 
phenomena  have  been  considered  in  recent  times,  form 
an  elaborate  refutation  of  the  so-called  Baconian,  of  the 
enumerative  or  "  all  case,"  method.  It  was  the  light  of 
the  idea  which  brought  life  and  order  into  the  "  rudis 
indigestaque  moles "  of  badly  collected  facts,  and  in 
many  cases  even  led  for  the  first  time  to  their  useful 
and  intelligent  enmneration.  But  now  we  come  to  a 
further  important  question.  Allowing  that  in  certain 
large  but  nevertheless  secluded  spheres  of  science  a  few 
general  ideas  have  been  found  to  apply  and  work 
wonders  of  calculation,  prediction,  and  useful  applica- 
tion, how  about  those  complicated  phenomena  which 
form  our  natural  and  social  environment,  and  where  so 
far  no  scientific  formula  has  proved  powerful  or  com- 
prehensive enough  ?  Are  all  these  elaborate  enumer- 
ations and  graphical  representations  in  meteorology,  in 
sociology,  commerce,  industry,  and  finance,  to  which  we 
have  instinctively  and  increasingly  had  recourse  during 
the  whole   of  the  century,  of  no  value  ?      Is  no  useful 


smallest  of  fractions  of  actual 
transactions  is  set  down  so  that 
investigation  can  use  it.  Litera- 
ture has  been  called  the  '  fragment 
of  fragments,'  and  in  the  same  way 
statistics  are  the  '  scrap  of  scraps.' 
In  real  life  scarcely  any  one  knows 
more  than  a  small  part  of  what  his 
neighbour  is  doing,  and  he  scarcely 
makes  public  any  of  that  little,  or 
of  what  he  does  himself.  A  com- 
plete record  of  commercial  facts, 
or  even  of  one  kind  of  such  facts, 
is  the  completest  of  dreams.  You 
might  as  well  hope  for  an  entire 
record    of     human    conversation." 


Stanley  Jevous  ( '  Principles  of 
Science,'  Preface,  p.  vii),  says : 
"  Within  the  last  century  a  reaction 
has  been  setting  in  against  the 
purely  empirical  procedure  of 
Francis  Bacon,  and  physicists  have 
learnt  to  advocate  the  use  of 
hypotheses.  I  take  the  extreme 
view  of  holding  that  Francis 
Bacon,  although  he  correctlj-  in- 
sisted upon  constant  reference  to 
experience,  had  no  correct  notions 
as  to  the  logical  method  by  which, 
from  particular  facts,  we  educe 
laws  of  nature." 


ON    THE    STATISTICAL    VIEW    OF    NATURE.       oGl 


result  to  spring  from  them  ?  Had  they  been  conducted 
under  the  influence  of  no  useful  general  idea,  our  answer 
would   indeed  have   to   be   in  the  negative.      But  if,  as        8. 

General  idea 

practice  shows,  they  have  been  of  use,  if,  in   fact,  they  underlying 
prove  to  be  in  many  cases  quite  indispensable,  we  may  *''"»• 
ask.    What    is    the    idea,    the    abstract    thought,    which 
dominates  them  ?     I  will  give  the  answer  at  once  and 
then  fix  the  aspect  with  which  the  present  chapter  has 
to  deal.     It  is  the  conception  and  doctrine  of  averages.  o. 

Doctrine  of 

Although  to  the  general  reader  nothing  may  seem  to  averages, 
be  simpler  than  a  process  of  counting  and  of  registration, 
the  science  of  statistics,  the  systematic  collection  of  large 
numbers,  and  the  fixing  of  averages,  is  comparatively 
young :  it  dates  from  the  beginning  of  the  seventeenth 
century,  when  Sully  in  France,  followed  by  Eichelieu 
and  Colbert,  had  organised  what  may  be  called  the  first 
statistical  bureau.^  It  emanated  from  the  same  spirit 
which  called  into  existence  the  Paris  Academy  of 
Sciences.  Characteristically  for  the  two  other  nations 
with  which  we  are  mainly  concerned  in  this  history,  the 


'  M.  Bldck  (loc.  cit.,  p.  25)  says : 
"  En  France  Sully  avait  ddj^  or- 
ganise, vers  1602,  un  cabinet  com- 
plet  dc  politique  ct  de  finances,  qui 
peut  I'tre  considere  comme  le 
premier  bureau  de  statistique. 
Les  rapports  que  Sully  demandait 
einbrassaient  I'armee,  la  marine, 
les  finances  et  un  grand  nombre 
de  branches  de  I'adiuinistration, 
et  le  resultat  de  ses  investigations 
se  trouve  exj)ose  dans  I'ouvrage 
([ui  a  etd  souvent  reiniprinn'  sous 
le  titre  de  '  Memoires  de  Sully.' 
Kichelieu  et  Colbert  se  sent  (5gale- 
inent  fait  adresser  des  rapports, 
auxqut'ls    on     a    puise,    dans    ces 

VOL.  II. 


derniers  temps,  bien  des  dldments 
utiles  Ji  I'histoire  et  <\ue  la  statis- 
tique  pourrait  t?galemeiit  utiliser." 
The  Romans,  who  in  aiiticiuity  may 
l>e  regarded  as  the  forerunners  of 
the  French  in  administrative  ability 
and  business-like  conduct  of  State 
affairs,  seem  also  to  have  develojjed 
an  extensive  sj-stem  of  registration. 
Tiie  ([uestion  has  been  fully  treated 
by  the  late  Prof.  Hildebrand  of 
.lena  in  the  '  Jahrbuch  fiir  Nationale 
()konomie  und  Statistik  '  (186(5),  in 
an  article  entitled  '"  Die  Amtliche 
Hevolkerungs-statistik  iiu  alteu 
Rom." 

2  N 


562 


SCIENTIFIC    THOUGHT. 


10.        labour  of  statistics  was   taken  up  in  Germany  by  the 

statistics  in 

France,  Ger-  Universitics,  whcrcas  in  England  it  fell  to  the  lot  chiefly 

many,  and  '  "  •' 

Engiami.  ^f  .^  single  pcrson — the  celebrated  Sir  William  Petty, 
the  creator  of  the  term  "  Political  Arithmetic."  Thus,  as 
in  science  generally,  so  in  statistics,  Prance  marched 
ahead  with  her  systematic  and  administrative  genius ; 
Germany  followed  in  the  person  of  Professor  Conring,^ 
who  introduced  the  matter  as  a  subject  of  university 
teaching ;  whilst  Sir  William  Petty  ^  wrote  his  essay 
with  the  practical  object  of  disproving  an  opinion  then 
much  current  in  England,  and  which  has  periodically 
cropped  up  in  the  writings  of  journalists  at  home  and 
abroad — the   threatened  decline   of   the  English  nation. 


1  Hermann  Conring  (1606-81), 
Professor  of  lledicine  and  Phil- 
osophy at  Hehnstildt,  lectured  on 
"  Staatskunde,  Notitia  Rerum  Pub- 
licarum,"  from  about  1660. 

-  About  the  same  time  when 
lectures  on  '"  The  Science  of  the 
State  "  were  begun  in  Germany  bv 
Conring,  Sir  William  Petty  (162:3- 
87)  in  England,  one  of  the  founders 
of  the  Royal  Society,  occupied  him- 
self for  practical  reasons  with  similar 
subjects,  collecting  his  views  in  a 
tract  called  'Political  Arithmetic' 
about  the  j'ear  1677,  besides  con- 
tributing various  papers  to  the 
'  Philosophical  Transactions '  and 
publishing  several  'Essays'  (1681- 
86).  The  'Political  Arithmetic' 
would  have  been  printed,  but  for 
the  French  policy  of  Charles  II.,  to 
whom  it  was  presented  in  manu- 
script. It  was  not  published  till 
1690,  after  the  author's  death,  on  a 
permission  "given  at  the  Court 
of  Whitehall  on  the  seventh  day 
of  November,"  by  Lord  Shel- 
burne,  the  son  of  the  author. 
In   the   preface,   he  characteristic- 


ally saj's  :  "  I  have  thoui^ht  fit  to 
examine  the  following  Persuasions  ; 
which  I  find  too  current  in  the 
world,  and  too  much  to  have 
affected  the  minds  of  some,  to  the 
prejudice  of  all — viz.,  That  the 
rents  of  lands  are  generally  fallen  ; 
that  therefore,  and  for  many  other 
reasons,  the  whole  hingdom  grows 
every  day  poorer  and  poorer.  That 
formerlj'  it  abounded  with  gold  ; 
but  now,  there  is  a  great  scarcity, 
both  of  gold  and  silver.  That  there 
is  no  trade,  nor  employment  for  the 
people ;  and  yet  that  the  land  is 
under -peopled.  That  taxes  have 
been  many  and  great.  That  Ire- 
land and  the  Plantations  in 
America,  and  other  additions  to 
the  Crown,  are  a  burden  to  Eng- 
land. That  Scotland  is  of  no  ad- 
vantage. That  trade,  in  general, 
doth  lamentably  decay.  That  the 
Jlollanders  are  at  our  heels,  in  the 
race  for  naval  power  ;  the  French 
grow  too  fast  upon  both  ;  and  appear 
so  rich  and  potent,  that  it  is  but  their 
clemency  that  they  do  not  devour 
their  neighbours." 


ox    THE    STATISTICAL    VIEW    OF    NATURE. 


i63 


And  as  in  science,  so  also  in  statistics,  Germany  in  time 
followed  the  example  of  France  by  introducing  organis- 
ations similar  to  that  of  the  "  Cabinet  complet  de  poli- 
tique et  de  finances"  of  Sully.  It  was  notably  during 
the  reign  of  Frederick  the  Great  that  the  population 
statistics  were  regularly  and  systematically  collected  in 
Prussia,  this  enterprise  being  greatly  stimulated  by  the 
publication  of  J.  P.  Slissmilch's  ^  '  Treatise  on  the  Divine 
Order.'  In  England — with  a  notable  exception  to  Ije 
mentioned  immediately — the  line  of  research  opened  out 
by  Sir  William  Petty  was  not  followed  up,  and  Mac- 
CuUoch,  when  publishing,  at  the  beginning  of  our  cen- 


'  Johann  Peter  Siissmilch  (1707- 
67}  published,  in  the  year  1741,  a 
lx)ok  with  the  following  title  :  '  Die 
gottliche  Ordnung  in  den  Vehinder- 
ungen  des  menschlichen  Geschleclits, 
aus  der  Geburt,  dem  Tode  und  der 
Fortpflanzung  desselben  erwiesen 
von  Johann  Peter  Siissmilch,  Pre- 
diger  beym  hochloblichen  Kalck- 
sieinischen  Regiment.  Xebst  einer 
Vorrede  Herrn  Christian  Wolffens.' 
The  VxKjk,  as  well  as  the  author, 
was  for  a  long  time  but  little  ap- 
preciated ;  for  although  the  former 
was  dedicated  to  Frederick  the 
(jreat,  and  must  presumably,  to 
judge  from  the  several  editions 
which  appeared,  have  been  made 
use  of  in  the  statistical  labours  of  the 
Prussian  administration,  the  author. 
not  having  been  connected  with  any 
university,  had,  for  a  long  time, 
little  influence  on  the  so-called 
"university  school"  of  statistics. 
In  the  course  of  the  last  fifty  years, 
all  prominent  writers  on  statistics, 
such  as  Wappiius,  Roscher,  von 
Oettingen,  Knapp,  and  V.  John,  in 
Germany,  M.  Block  and  others  in 
France,  as  also  Italian  writers  on 
statistics,  have  taken  increased 
interest  in  the  book.     Dr  V.  John 


('Geschichte  der  Statistik,'  vol.  i. 
p.  241,  &c.)  gives  an  exhaustive 
analysis  of  the  work.  He  calls  the 
author  "the  first  statistician  in  the 
modem  sense,"  the  precursor  of 
Quetelet,  and  says,  moreover,  "It 
is  easily  explained  how  the  philos- 
opher .Siissmilch  would  vanish  into 
the  background  as  soon  as  the  con- 
ception of  the  encyclopfcdists,  that 
only  matter  in  motion  exists  and 
no  mind,  came  to  be  generally  ac- 
cepted, and  that  the  politician 
Siissmilch  should  utterly  disappear 
in  the  turmoil  of  the  French 
Revolution."  Von  Oettingen,  who, 
on  the  other  side,  agrees  in  accept- 
ing with  Siissmilch  the  existence 
<)f  a  Divine  or  moral  order,  says  of 
the  latter,  that  ' '  he  has  become, 
through  his  magnificent  labours, 
the  founder  of  the  science  which 
we  now  call  moral  statistics,"  inas- 
much as  he,  "for  the  first  time, 
recognised  the  intrinsic  regularity 
in  the  apparently  most  accidental 
human  phenomena  and  actions,  and 
trie<l  to  establish  it  by  inductive 
methotls "     ('Moralstatistik,'     3rd 


ed.,  18S2, 


21).     That    he   was 


known   to  Herder  and  appreciated 
by  him,  we  saw  tupra,  p.  5-36  note. 


564 


SCIENTIFIC    THOUGHT. 


tury,  his  '  Statistical  Account  of  the  British  Empire/ 
had  hardly  any  similar  work  to  refer  to  during  the 
whole  of  the  eighteenth  century. 

The  exception  just  referred  to  was  "  The   Tables  of 
Mortality,"  which  date  back  to  the  middle  of  the  six- 
teenth century,  and  in  a  more  regular  form  to   1603. 
11.        They  were  analysed  by  John  Graunt,  captain,  in  1661, 

JohnGraunt  •      ■,    r\-i 

and  Haiiey.  in  a  tract  with  the  title  '  iN  atural  and  Pohtical  Obser- 
vations upon  the  Bills  of  Mortality.'  ^  Of  Graunt's  " 
work,  M.  Maurice  Block  says  that  the  difficulties  of 
preparing  such  a  table  at  that  time  were  so  great 
that  it  might  wellnigh  be  considered  a  performance 
of    genius.       The    invention    once     made,    improvement 


^  The  tract  wa«  presented  to  the 
Royal  Society  in  1662,  and  printed 
by  order  of  the  lattei-  in  1665,  the 
author  becoming  a  fellow  at  the  re- 
quest of  the  king.  V.  John  gives 
a  full  account  of  the  book,  and  as 
much  of  the  author  as  he  could 
collect  from  the  scantj*  records 
of  him  which  exist  (loc.  cit.,  pp.  161- 
178).  He  was  born  in  1620,  was  a 
man  of  business,  and  latterly  became 
connected  with  the  Gresham  College 
and  with  sundry  matters  pertaining 
to  the  administration  of  the  City. 
He  died  in  1674.  In  1676  a  new, 
sixth,  edition  of  the  tract  was  pub- 
lished by  Sir  W.  Petty,  whom  both 
Halley  and  Evelyn  eiToneously 
referred  to  as  the  author. 

-  '  Statistique,'  p.  19-4.  Siissmilch, 
a  century  after  Graunt,  says  that 
the  material  for  the  determination 
of  the  '  Divine  Order '  existed  in 
the  parish  registers  since  the  time 
of  the  Reformation.  "  But  who,"  he 
exclaims,  "  made  use  of  it  for  this 
purpose  before  Graunt  ?  The  dis- 
covery was  just  as  easy  as  that  of 
America,    but    the   Columbus   was 


lacking"  (quoted  by  V.  John,  loc. 
cit,.,  p.  177).  The  author,  however, 
who  suggested  to  Siissmilch  the  re- 
searches which  led  to  the  celebrated 
'  Divine  Order,'  was  not  John 
Graunt,  but  Dr  William  Derham 
(1657-1735),  an  eminent  divine  and 
natural  philosopher,  who  published 
in  1713  his  '  Physico-Theology  ;  or 
a  Demonstration  of  the  Being  and 
Attributes  of  God  from  His  Works 
of  Creation,'  a  book  which  ran 
through  six  editions  in  ten  years, 
being  translated  into  French  and 
several  times  into  German.  This 
book  contained,  as  Siissmilch  him- 
self says,  besides  numerous  notes,  a 
collection  of  the  observations  of 
other  English  authors  on  the  lists 
of  births,  deaths,  and  marriages. 
On  following  up  the  clue  given  by 
it  he  arrived  ultimately  at  Graunt 
and  Petty,  of  whom  the  former 
had,  as  he  says,  broken  the  ice, 
whereas  Petty  had  mainly  dis- 
cussed the  influence  of  the  changes 
of  population  in  politics  (V.  John, 
'  Statistik,'  p.  243). 


ox    THE    STATISTICAL    VIEW    OF    NATURE.       565 

was  easy ;  the  invention  was  the  ditficulty.  The 
next  great  name  connected  witli  Uiis  subject  was 
the  astronomer  and  mathematician  Edmund  Halley,^ 
who  had  before  liim,  in  addition  to  John  Graunt's 
work,  the  figures  of  birth  and  mortality  during 
the  five  years  1686  to  1691  collected  by  Kaspar 
Neumann  for  the  city  of  Kreslau,  capital  of  the 
province  of  Silesia.  Tables  of  mortality,  based  upon 
several  thousands  of  life  annuities,  were  prepared  in 
Holland  by  order  of  the  Grand  Pensioner,  John  de 
Witt,  and  used  in  1671  as  the  basis  for  a  loan  in 
the  form  of  annuities."  The  growing  practice  of 
life  insurance,  as  is  well  known,  attaches  a  great 
interest  to  these  tables  of  mortality,  which  have  been 
slowly  perfected  in  the  course  of  the  last  hundred 
and  fifty  years ;  it  having  been  reserved  for  the  labours 


^  For  a  long  time  it  was  not 
known  how  Halley  came  into 
[I. Ksession  of  Ka.spar  Neumann's 
lii'.rtality  -  tables  ;  but,  in  recent 
times,  mainly  througli  examination 
of  the  local  records  of  the  city  of 
Breslau  by  Bergius  and  others,  and 
notably  by  the  aid  of  S.  Griitzer 
('  Edmund  Halley  und  Kaspar 
Neumann,'  Breslau,  1883),  it  has 
become  almost  certjiin  that  Neu- 
mann's registers  were  communi- 
cated to  the  Royal  Society  by  no 
less  a  person  than  Leibniz,  who 
corresponded  with  Neumann  on 
the  one  side  as  well  as  with  the 
secretaries  of  the  Royal  Society  on  I 
the  other.  Some  of  the  original 
documents  have  been  traced  in 
the  archives  of  the  Society  by  Dr 
Bond  and  Prof.  Burdon  Sanderson. 
It  is  well  kn(nvn  that  Leibniz  him- 
self attached  great  importance  to  j 
accurate    statistical    knowledge   of   \ 


all  kinds,  and  considered  the  collec- 
tion of  such  to  be  one  of  the  main 
duties  of  the  various  academies 
which  he  planned  or  founded. 

'•'  "  Le  grand  pensionnaire  de 
Hollande,  Jean  de  Witt,  se  fondant 
sur  les  calculs  de  probabilites  en- 
seignds  par  Chretien  Huygens,  se 
servit,  comme  elements  d'observa- 
tion,  des  n'sultats  constatds  sur 
quelques  milliers  de  rentiers  via- 
gers.  II  presenta  sa  table  aux 
<5tats  gdndraux  le  25  avril  1671, 
pour  servir  de  base  ii  un  emi)runt 
fait  sous  la  forme  d'annuites  via- 
gores.  Cette  table  citee  par  M.  de 
Baumhauer,  se  trouve  dans  les 
registres  des  dtats  de  Hollande, 
annc'e  1671 "  (Block,  loc.  cit.,  p. 
196).  A  translation  of  this  docu- 
ment ajijieared  in  'Contributions 
to  the  History  of  Insurance'  bv  F. 
Hendriks, '  Ass.  Mag.,'  vol.  ii.,  1852. 


566 


SCIENTIFIC   THOUGHT. 


of  quite  recent  writers  ^  to  place  the  whole  matter 
upon  a  thoroughly  scientific  basis.  But  it  is  not  these 
necessary  technical  refinements  that  interest  us  most 
at  present ;  rather  let  us  take  note  how  the  needs  of 
governments,  as  well  as  the  uncertainty  and  risks  of 
life,  have  automatically  led  to  the  definition  and  study 
of  three  distinct  statistical  conceptions,  which  in  our 
age  govern  a  very  large  part  of  all  our  practical 
12.       enterprises.      These    three    conceptions   are    the   proba- 

Probability,  ^  r  i. 

co-^opera-^^    bility  of  future  events  based  upon  long  series  of  past 
buuon!*'^'^'    experiences,   the    idea    of    reducing   or    averaging    risks 
by   "  amicable  "  co-operation,  and   the  "  equitable  "   dis- 
tribution of  the  burdens  of  such  co-operation  according 
to    the   individual    units   who   co-operate."^       It   will   at 


^  It  is  generally  admitted  that 
Prof.  G.  F.  Knapp  created  a  kind 
of  era  in  the  more  rigorous  mathe- 
matical treatment  of  the  subject 
by  his  various  publications,  dating 
from  the  year  1868  with  his  tract 
'  Ueber  die  Ermittelung  der  Sterb- 
lichkeit  aus  den  Aufzeichnungen 
der  Bevolkerungs -statistik.'  M. 
Block  {loc.cit.,  p.  232)  says:  "  Ce 
livre  a  fait  une  veritaVjle  sensation 
parmi  les  hommes  speciaux ;  noii 
que  I'auteur  ait  apporte  beaucoup 
de  uouvelles  pierres  a  I'edifice,  mais 
il  a  donn^  h,  ces  pierres  une  ordou- 
nance,  une  disposition  qui  les  con- 
stituent un  monument."  In  the 
year  1874  he  published  his  '  Theorie 
des  Bevolkerungswechsels. '  Manj- 
other  writers  have  followed  in  the 
new  track,  among  whom  I  will  only 
mention  Becker,  Zeuner,  and  Lexis. 
The  graphical  method  is  largely 
employed  by  these  authors,  amongst 
whom  Zeuner  resorts  to  a  repre- 
sentation in  three  dimensions  with 
some  very  elegant  results.  See  his 
'  Abhandlungen  zur  mathematischen 


Statistik'  (Leipzig,  1869).  A  his- 
torical and  critical  review  of  these 
and  older  writings  is  given  in  the 
last  -  named  woik  of  Knapp,  p. 
5'3,  &c.  See  also  Prof.  Lexis's 
'  Einleitung  in  die  Theorie  der 
Bevi ilkerungs-statistik '  (Strasburg, 
1875). 

^  This  is  not  the  place  to  dis- 
cuss the  social  and  moral  aspects 
of  co-operation,  which  by  future 
historians  will  possibly  be  looked 
upon  as  one  of  the  very  few  novel 
political  ideas  which  our  century 
lias  evolved  or  at  least  elaborated 
in  a  practical  form  ;  the  older  co- 
operative attempts,  such  as  were 
made  under  the  influence  of  the 
ideals  of  the  great  Revolution  by 
Fourier,  Saint  Simon,  and  Babeuf 
in  France,  and  by  Robert  Owen  in 
this  country,  not  having  contained 
the  elements  of  permanent  success. 
These  elements  seem  to  belong 
almost  exclusively  to  the  line  of 
development  started  by  the  "Roch- 
dale Pioneers." 


ON    THE    STATISTICAL    VIKW    OF    NATURK.        567 

once  be  seen  how  all  arrangements  which  are  based 
upon  these  three  conceptions  —  viz.,  probability,  co- 
operation, and  equitable  distribution  —  lead  us  away 
from  the  study  of  individual  cases  to  that  of  totals 
and  averages ;  how  they  merge  the  interests  of  single 
persons  and  the  peculiarities  of  single  cases  in  those 
of  the  aggregate  of  a  large  number  and  the  properties 
of  the  average  event  or  the  "  mean "  man.  Their 
value  and  success  depend  on  the  consideration  and 
participation  of  large  numbers,  and  they  have  accord- 
ingly only  arisen  during  the  latter  days  which  have 
witnessed  the  steady  growth  of  modern  populations 
and  the  bewildering  complication  of  modern  business. 
The  moral  or  social  aspect  which  has  simultaneously 
been  evolved  during  our  period  does  not  for  the 
moment  concern  us.  We  are  concerned  at  present 
only  with  the  fact  that  statistics  as  the  science  of 
large  numbers  and  of  averages  has  been  increasingly 
drawn  into  use.  In  fact,  we  might  call  our  century 
— in  distinction  from  former  centuries — the  statistical 
century. 

The  necessity  of  having  recourse  to  elaborate  countings, 
to  registrations  of  births,  deaths,  and  marriages,  to  lists 
of  exports  and  imports,  to  records  of  consumption  and  pro- 
duction of  food-stuffs  and  many  other  items,  forced  upon 
those  who  were  entrusted  with  the  gathering  and  using  of 
these  data  the  observation  that  all  such  knowledge  is  in- 
complete and  inaccurate.  Owing  to  the  variability,  within 
certain  limits,  of  recurring  events  and  the  errors  of  count- 
ing and  registration,  we  have  to  content  ourselves  always 
with   approximation  instead   of   certainty.      Error  bulks 


568 


SCIENTIFIC    THOUGHT. 


13. 

The  Science 
of  Chances. 


very  largely  in  all  statistics,  and  vitiates  them  ;  and  as 
regards  coming  events,  our  minds  are  in  a  state  of  ex- 
pectation rather  than  of  assurance.  But  events  can  be 
more  or  less  probable,  errors  can  be  greater  or  smaller, 
cumulative  or  compensatory,  and  our  expectations  may 
be  well-  or  ill-founded.  And  so  there  has  arisen  the 
science  of  Probabilities  and  of  Chances,  and  the  Theory 
of  Error,  two  subjects  intimately  interwoven.  The 
former  arose  in  the  seventeenth  century  out  of  the 
frivolous  or  vicious  practice  of  betting  and  gambling,^ 
whilst  the  latter  was  founded  when  astronomical  observa- 
tions accumulated,  and  the  question  presented  itself  how 
to  combine  them  so  as  to  arrive  at  the  most  reliable 
result.  The  greatest  mathematicians  and  philosophers, 
such  as  Pascal,  Huygens,  and  Leibniz,  the  BernouUis,  De 
Moivre,  Laplace,  Gauss  and  Poisson,  have  bestowed  much 
thought  on  the  subject,^  which  has  nevertheless  been  very 
differently  judged — praised  beyond  measure  by  some,  and 
ridiculed  by  others ;  sometimes  pronounced  to  be  merely 
common-sense  put  in  figures,  and  then  again  wrapped  up 


^  See  supra,  vol.  i.  p.  120  sqq. 

-  In  addition  to  tlie  references 
given  in  vol.  i.,  the  following  are  of 
importance.  The  history  of  the 
Theory  of  Probabilities,  as  stated 
above,  has  been  written  by  Isaac 
Todhunter.  This  history  brings 
the  subject  down  to  the  writings 
of  Laplace,  whose  two  works 
mentioned  in  the  text  still  re- 
main the  two  standard  works 
on  the  science.  In  quite  recent 
times  the  history  has  been  written 
and  brought  up  to  date  by  Prof. 
Emanuel  Czuber  in  his  '  Entwick- 
elung  der  Wahrscheinlichkeits- 
Theorie    und    ihre   Anwendungen,' 


contained  in  the  seventh  volume 
of  the  '  Jahresbericht  der  Deut- 
schen  Mathematiker  Vereinigung' 
(Leipzig,  1899).  The  latter  work  is 
written  on  a  different  principle  from 
that  of  Todhunter.  Whereas  Tod- 
hunter deals  in  separate  chapters 
with  the  work  of  the  foremost 
mathematicians  on  this  subject, 
Prof.  Czuber  gives  an  independent 
historical  and  critical  analysis  of  the 
different  developments  of  the 
theory  and  its  applications.  Quite 
recently  the  same  author  has  pub- 
lished an  independent  treatise  on 
the  subject  (Leipzig,  1902). 


ON    THE    STATISTICAL    VIEW    OF    NATURP:.        509 

in  appalling  niystei}.'  There  is,  however,  no  doubt  that 
the  Theory  of  Probability  increasingly  pervades  scientific 
as  well  as  statistical  work  in  our  age,  and  that  in  the 


'  In  spite  of  the  encomium  on 
the  theory  of  jtrobabilities  ((uoted 
in  vol.  i.  J),  l'2-i,  Sir  John  Herschel 
gave  onl}'  a  quahfied  adherence  to 
one  of  its  principal  applications 
(see  '  Brit.  Ah.soc.  Rep.,'  vol.  i.  p. 
16.")).  The  two  foremo.st  adverse 
critics  of  the  theory  were  Augu.ste 
Comte  in  France  and  John  Stuart 
Mill  in  England.  In  the  second 
volume  of  the  '  Philosophic  Posi- 
tive'  (Ist  ed.,  1835,  p.  371)  the 
former  explains  why  he  omitted 
to  deal  with  so  im])ortant  a  sub- 
ject in  his  mathematical  ])hiloso]ihy. 
"  Le  calcul  de.s  probabilit<Ss  ne  me 
.semble  avoir  6t6  rcellement,  pour 
ses  illustres  iuventeurs,  qu'un  te.\te 
commode  h,  d'ingunieux  et  difficiles 
problcmes  numeriques,  qui  n'en  con- 
servent  pas  moins  toute  leur  valeur 
abstraite,  comme  les  theories  ana- 
lytiques  dont  il  a  etc  ensuite  I'occa- 
sion,  ou,  si  Ton  veut,  I'origine. 
Quant  li  la  conception  philoso- 
jjhique  sur  laquelle  repose  une  telle 
doctrine,  je  la  crois  radicalement 
fausse  et  susceptible  de  conduire 
aux  plus  absurdes  consequences. 
Je  ne  parle  pas  seulement  de 
I'application  ovidemment  illusoire 
qu'on  a  souvent  tent<5  d'en  faire 
au  pretendu  perfectionnment  des 
.sciences  sociales  :  ces  essais,  neces- 
sairement  chimuriques,  seront  car- 
acteriscs  dans  la  dernicre  partie  de 
cet  ouvrage " :  and  in  the  fourth 
volume  (1839,  p.  512),  "La  seule 
aberration  de  ce  genre  .  .  .  c'est 
la  vaine  pretention  d'un  grand 
nomlire  de  gcomctres  a  rendre 
positives  les  etudes  sociales  d'aprcs 
une  subordination  chim(?rique  ^ 
I'illusoire  thdorie  mathematique 
des  chances.  .  .  .  (^uehiue  gros- 
siere  que  soit  dvidemment  une 
telle  illusion,  elle   etait  neanmoins 


essentiellement  excusable,  quand 
I'esprit  eminemment  philosojjhique 
de  I'illustre  Jaccjues  Bernoulli 
con(;ut,  le  premier,  cette  pensee 
g(5n(5rale,  dont  la  production,  h.  une 
telle  dpoque,  constituait  reellement 
le  prt-cieux  et  irrecusable  symptome 
du  besoin  premature  pour  ce  temps, 
mais  ()ui  n'y  pouvait  ctre  dprouvd 
nieme  ainsi  (jue  par  une  intelligence 
vraiment  sujidrieure. "  John  Stuart 
Mill,  in  the  .second  volume  of  his 
'  Logic,'  has  devoted  a  whole  chapter 
to  the  sul)ject,  in  which  he  corrects 
a  .statement  made  by  him  in  the 
first  edition  of  his  book,  attributing 
a  "  fundamental  fallacy  "  to  the 
arguments  of  Laplace  and  other 
mathematicians,  but  nevertheless 
takes  an  unfavourable  view  of  the 
usefulness  of  the  calculus.  In 
more  recent  times  the  subject  has 
been  exhaustively  treated  from  a 
logical  point  of  view  by  Mr  John 
Venn  in  his  work,  'The  Logic  of 
Chance'  (3rd  ed.,  London,  1888), 
and  by  Stanley  Jevons  in  '  The 
Principles  of  Science'  (vol.  i.  ch.  x.) 
The  doubts  with  which  Mill,  and 
still  more  Comte,  regarded  the 
subject,  .seem  to  have  been  dis- 
pelled in  works  on  Logic  ;  and  the 
increa.sing  use  to  which  the  methods 
for  the  correction  of  error  have 
been  put  in  manv'  branches  of 
science  have  convinced  mathema- 
ticians of  its  apjilicability.  The 
ninth  edition  of  the  '  Ency.  Brit.' 
contains  an  excellent  article  on 
"  Probabilities  "  by  M.  W.  Crofton. 
Among  the  clearest  and  .safest 
guides  in  this  intricate  subject 
must  be  counted  the  late  Prof. 
Augustus  de  Morgan,  whose  pro- 
found treatise  in  the  '  Ency. 
Metrop.'  (vol.  ii.),  as  well  as  his 
'  Essay  on  Probabilities  '  (London, 


570 


SCIENTIFIC    THOUGHT. 


course  of  the  last  hundred  years  much  has  been  done  to 
make  it  more  easily  understood. 

James  Bernoulli  had  already  in  his  celebrated  book 
which  bears  the  title,  '  De  arte  conjectandi,'  promised 
to  show  the  application  of  the  mathematical  doctrine 
of  probability  to  political,  moral,  and  economical  sub- 
jects,^ but  the  fourth  and  last  part  of  the  book  which 
was  to  give  this,  remained  unfinished.  It  was  left  to 
his  successors,  notably  to  Daniel  Bernoulli,  to  take  up 
this  side  of  the  question.  But  the  first  practical  states- 
condoixjet.    man    who — as    we   are   told    by  Condorcet  ^ — held   the 


1838),  still  rank  with  the  be.st 
that  has  been  written.  Stanley 
Jevons  sums  up  his  opinion  in  the 
words  :  "  This  theory  appears  to  me 
the  noblest  creation  of  the  human 
intellect,  and  it  passes  my  concep- 
tion how  two  men  possessing  such 
high  intelligence  as  Auguste  Comte 
and  J.  S.  Mill  could  have  been 
found  depreciating  it,  or  even 
vainly  attempting  to  question  its 
validity.  To  eulogise  the  theory 
is  as  needless  as  to  eulogise  reason 
itself  "  ('  Principles  of  Science,'  vol. 
i.  p.  227). 

^  James  Bernoulli  (1654-1705) 
was  the  eldest  of  the  celebrated 
family  of  mathematicians.  Daniel, 
his  nephew,  lived  half  a  century 
later  (1700-82).  The  'Ars  Con- 
jectandi '  was  published  posthum- 
ously in  1713  by  Nicholas,  another 
nephew  of  the  author.  In  a  letter 
to  Leibniz  the  author  says  :  "  Ab- 
solvi  jam  maximam  libri  jiartem, 
sed  deest  adhue  pnecipua,  qua 
artis  conjectandi  principia  etiam 
ad  civilia,  moral  ia,  et  ceconomica 
appHcare  doceo."  Daniel  Bernoulli, 
as  we  saw  above  (voL  i.,  chap.  v.  p. 
434),  was  the  father  of  the  kinetic 
theory  of  gases,  of  which  more 
hereafter.'  He  was  also  the  first 
to    make    a    distinction     between 


mathematical  and  moral  expecta- 
tion,—  a  difl'ereuce  which  led 
Laplace  to  distinguish  between 
"fortune  physique"  and  "fortune' 
morale,"  to  which  reference  was 
made  in  connection  with  Fechner's 
psycho-physical  measurements. 

-  '  Essai  sur  I'application  de 
r Analyse  h  la  Probabilite  des  D(5- 
cisions,  Rendues  a  la  plurality 
des  voix '  (Paris,  1785)  :  "  Uu 
grand  homme,  dont  je  regretterai 
toujours  les  le9ons,  les  exemples, 
et  surtout  I'amitie,  etait  persuade 
que  les  verites  des  sciences  morales 
et  politiques,  sont  suscejjtibles  de 
la  meme  certitude  que  celles  qui 
formeut  le  systeme  des  .sciences 
physiques,  et  meme  que  les 
branches  de  ces  sciences  qui,  comme 
I'astronomie,  paroissent  approcher 
de  la  certitude  mathematique. 
Cette  opinion  lui  dtait  chere,  parce 
qu'elle  conduit  h,  I'esperance  con- 
solante  que  I'espece  humaine  fera 
ndcessairement  des  progres  vers  le 
bonheur  et  la  perfection,  comme 
ell'i  en  a  fait  dans  la  connois- 
sance  de  la  vorite."  It  is  evident 
from  this  extract  that  Condorcet 
(1743-94)  thought  that  his  friend 
Turgot  shared  his  own  well-known 
opinions  as  to  the  unlimited  per- 
fectibility of  the  human  race. 


ON    THE    STATISTICAL    VIEW    OF    NATURE, 


571 


view  that  morals  and  politics  might  derive  the  same 
henefit  from  the  science  of  calculation  as  the  physical 
sciences  had  already  experienced,  seems  to  have  been 
Turgot.  To  show  the  importance  of  this  view,  Con- 
dorcet  wrote  his  much  quoted  hut  little  read  essay  on 
the  application  of  analysis  to  decisions  based  on  the 
plurality  of  votes.  Tn  his  fiitroductioii  tlie  author 
laments  that  his  friend,  on  whose  suggestions  he  had 
commenced  his  work,  did  not  live  to  see  it  finished/  It 
would  have  been  interesting  to  know  whether  so  emi- 
nent a  practical  philosopher  as  Turgot  is  considered  to 
have  been,  would  have  been  encouraged  by  his  friend's 
specimen  of  political  algebra,  or  whether  he  would  have 
held  the  opinion  of  Mill,  who  saw  in  tliese  "  appli- 
cations of  the  calculus  of  probabilities  .  .  .  the  real 
opprobrium  of  mathematics." " 


^  {Loc.  cit.,  p.  i.)  "Si  riiumanite 
n'eut  pas  eu  le  mallieur,  longtemps 
irreparable,  de  le  ])er<lre  trop  tot, 
cet  ouvrage  eut  etu  muiu-s  impar- 
fait:  cclairo  par  ses  conseils,  jaurois 
vu  mieux  ou  plus  loin,  et  j'aurois 
avauce  avec  plus  de  confiance  des 
principes  qui  auroieut  (5to  les  sieus. 
Prive  d'un  tel  guide,  il  ne  nie  reste 
qu'ii  fairo  h  sa  memoire  I'liommage 
de  mon  travail,  en  faisant  tous  rues 
efforts  ])our  le  rendre  moins  indigne 
de  I'amitid  dont  il  m'houoroit. " 

-  There  is  no  doubt  tliat  the 
writings  of  Condorcet,  through  the 
useless  accumulation  of  forniuUc 
with  very  little  substance  behind 
them,  contributed  to  bring  the 
whole  theory  into  discredit.  An- 
other still  moie  eminent  contem- 
porary mathematician,  D'Alembert, 
after  having  occupied  himself  at 
considerable  length  with  problems 
in  prtjbabilities,  formed  an  un- 
favourable opinion  of  the  usefulness 


of  the  calculus.  Gouraud  (quoted 
by  Todhunter,  p.  293)  says  :  '■  (^uaut 
au  reste  des  malhematiciens,  ce  ne 
fut  (jue  par  le  silence  ou  le  dedain 
qu'il  rcpondit  aux  doutes  que 
d'Alembert  s'ctait  permis  d'cmettre. 
Mi5pris  injuste  et  malhabile  oh  tout 
le  monde  avait  ii  perdre  et  qu'une 
posterite  moins  pr^venue  ne  devait 
point  sanctiouner."  It  is  interest- 
ing to  note  that  Laplace,  in  hi.s 
historical  account  at  the  end  of  his 
'  Essai  Philosophique,'  does  not 
refer  either  to  Condorcet  or  to 
D'Alembert.  J.  S.  Mill  ('Logic,' 
vol.  ii.  p.  66)  says  :  "  It  is  obvious, 
too,  that  even  when  the  proba- 
bilities are  derived  from  observation 
and  expei-iment,  a  very  slight 
improvement  in  the  data,  by  better 
observations,  or  by  taking  into 
fuller  consideration  the  s]>ecial 
circumstiinces  of  the  case,  is  of  more 
use  than  the  most  elaborate  appli- 
cation of  the  calculus  to  jjrobabil- 


»72 


SCIENTIFIC    THOUGHT. 


15. 

Laplace. 


So  far  as  the  formal  part  of  the  subject  was  con- 
cerned, it  was  left  to  Laplace  to  place  it  on  the  founda- 
tion upon  which  it  has  ever  since  rested.  He  brought 
together  the  ideas  of  his  predecessors,  notably  of 
De  Moivre,  the  two  Bernoullis,  Sterling,  Bayes,  and 
Lagrange,  as  well  as  his  own  extensive  researches,  in 
his  great  analytical  theory  of  Probability,  which  ap- 
peared in  1812,  and,  with  several  additions  and  an 
elaborate  introduction,  in  two  subsequent  editions  during 
his  lifetime.  This  work  has  been  justly  considered  a 
monument  of  human  genius,  and  stands  worthily  beside 
the    great    '  Mecanique    Celeste '    of    its    author.      The 


ities  founded  on  the  data  in  their 
previous  state  of  inferiority.  The 
neglect  of  this  obvious  reflection 
has  given  rise  to  misapplications  of 
the  calculus  of  probabilities  which 
have  made  it  the  real  opprobrium 
of  mathematics.  It  is  sufficient  to 
refer  to  the  applications  made  of  it 
to  the  credibility  of  witnesses,  and 
to  the  correctness  of  the  verdicts  of 
juries."  I  have  already  referred  to 
the  position  which  Comte  took  up. 
De  Morgan,  with  his  usual  clearness 
and  wisdom,  at  the  end  of  his 
"Theory  of  Probabilities"  ('Ency. 
Metrop.,'  vol.  ii.  p.  470),  whilst  re- 
ducing to  a  very  narrow  province 
these  applications  of  the  calculus  of 
probabilities,  says  :  "  There  are  cir- 
cumstances connected  with  the 
mathemathical  theory  of  independ- 
ent evidence  which  it  maj"  be  useful 
to  examine.  In  this,  as  in  several 
other  preceding  investigations,  it  is 
not  so  much  our  wish  to  deduce 
and  impose  results,  as  to  inquire 
whether  these  results  really  coincide 
with  the  methods  of  judging  which 
our  reason,  unassisted  by  exact 
comparison,  has  already  made  us 
adopt.  The  use  of  the  process  is, 
that  both  our  theory  and  our  pre- 


conceptions thus  either  assist  or 
destroy  each  other :  in  the  former 
case  we  feel  able  to  trust  this 
science  for  further  directions ;  in 
the  latter,  a  useful  new  inquiry  is 
opened.  For  when  we  consider  the 
very  imposing  character  of  the  first 
principles  of  the  science  of  proba- 
bilities, and  the  mathematical 
necessity  which  connects  those 
simple  first  principles  with  their 
results,  we  feel  convinced  that, 
even  on  the  supposition  that  the 
main  conclusions  of  the  present 
treatise  are  altogether  fallacious, 
there  must  arise  a  necessity  for 
investigating  the  reason  why  a 
methodical  treatment  of  certain 
notions  should  lead  to  results  in- 
consistent with  the  vuxjue  applica- 
tion of  them  on  which  we  are  ac- 
customed to  rely.  For  it  must  not 
be  imagined  that  opposition  to  the 
principles  laid  down  in  this  treatise 
is  always  conducted  on  other 
principles  :  on  the  contrary,  it 
frequently  happens  that  it  is  only 
a  result  of  themselves  obtained 
without  calculation,  which  is  ar- 
rayed against  arithmetical  deduc- 
tion." 


ON    THE    STATISTICAL    VIKW    OF    NATL'KK.       573 


labours  of  inatheinaticiau.s  since  Lapluix-  in  the  field  of 
probabilities  have  consisted  mainly  in  commentaries  on 
and  simplifications  of  his  expositions,  and  in  a  j^reat 
improvement  in  the  formal  methods,  due  mostly  to 
English  workers.^  At  present  we  are  not  interested 
in  the  purely  mathematical  side  of  the  subject,  which 
for  some  minds  has  a  great  fascination,  but  rather  in 
the  ([uesti<in  :  To  what  extent  have  the  anticipations  of 
yuch  men  as  Condorcet,  Turgot,  and  Laplace,  as  to  the 
practical  value  of  these  researches,  been  realised  ?  in  how 
far  hsixe  they  proved  to  be  "  the  happiest  supplement 
to  the  ignorance  and  weakness  of  the  human  mind  "  ?  ^ 
This  idea,  though  ridiculed  by  some,  has  as  often  cropped 


^  The  iirobleiiis  suErgested  by  the 
calculu.s  of  probabilities  gave  rise, 
collaterallj-,  to  several  important 
mathematical  (leveloj)inent.s,  not- 
ably the  oombinatorial  analysis, 
the  calculus  of  finite  differences, 
and,  in  tlie  hands  of  Laplace,  the 
theory  of  generating  function  and 
the  recurrent  series.  A  large  part 
of  Laplace's  great  work  is  taken 
up  with  this  purelj'  mathematical 
device.  It  has  in  more  recent 
times  been  supplanted,  especially 
under  the  hands  of  English  mathe- 
maticians, by  the  calculus  of  oper- 
ations, of  which  the  germ  is  to  be 
found,  according  to  Laplace,  in  a 
suggestion  of  Leibniz  (see  '  Essai 
Philusophique  sur  les  Probabili- 
tes,'  p.  65). 

-  "  La  theorie  des  probabilitus 
n'est,  au  fond,  ijue  le  bon  sens 
reduit  au  calcul :  elle  fait  apprdcier 
avec  exactitude  ce  ijue  les  esprits 
justes  sentent  par  une  sorte  d'in- 
stinct,  sans  (ju'ils  puissent  souvent 
s'en  rendre  c()mi)tc.  Elle  ne  laisse 
rien  d'arbitraire  dans  le  choix  des 
opinions  et  des  partis  a  prendre, 
toutes  les  fois  que  I'on  peut,  ii  son 


moyen,  di'terminer  le  choix  le  plus 
avantageux.  Par  la,  elle  devient 
le  supplement  le  plus  heureux  ii 
r  ignorance  et  ii  la  faiblesse  de 
I'esprit  humain.  Si  Ton  considere 
les  niethodes  analytiques  aux- 
quelles  cette  thcorie  a  doune 
naissance,  la  vc'ritd  des  principes 
qui  lui  servent  de  base,  la  logicjue 
tine  et  delicate  qu'exige  leur  emploi 
dans  la  solution  des  problcmes,  les 
dtablissemens  d'utiliti'  publicjue  qui 
s'appuient  sur  elle,  et  lextension 
qu'elle  a  revue  et  qu"elle  peut 
recevoir  encore,  par  son  application 
aux  questions  les  plus  importantes 
de  la  Philosophic  naturelle  et  des 
sciences  morales  ;  si  Ton  observe 
ensuite  que  dans  les  choses  memes 
qui  ne  j)euvent  elre  soumises  au 
calcul,  elle  donne  les  aper^us  les 
plus  surs  qui  puissent  nous  guider 
dans  nos  jugemens,  et  qu'elle  ap- 
preud  a  se  garantir  des  illusions 
qui  souvent  nous  egarent,  on  verra 
qu'il  n'est  point  de  science  plus 
digue  de  nos  mcilitations,  et  qu'il 
soit  plus  utile  de  faire  entrer 
dans  le  syatome  de  Tinstruction 
publique"  {foe.  cit.,  p.  273  ct  neq.) 


574 


SCIENTIFIC   THOUGHT. 


16. 
Four  ap- 
plications. 


17. 

Theory  of 
Error. 


up  again  in  the  course  of  the  century,  and  is  at  present 
occupying  the  attention  of  distinguished  thinkers.  It 
will  be  interesting  to  give  some  account  of  these  prac- 
tical applications. 

Of  these,  four  notably  attract  our  attention.  First, 
the  theory  of  error,  prominently  associated  with  the 
name  of  Gauss.  Secondly,  the  writings  of  Adolphe 
Quetelet,  and  the  great  impetus  given  by  him  to 
statistical  research.  Thirdly,  the  peculiar  development 
of  the  Atomic  theory  known  as  the  Kinetic  theory 
of  gases,  which  gave  to  many  scientific  investigations 
what  Clerk  -  Maxwell  termed  the  statistical,  in  oppo- 
sition to  the  historical  or  descriptive,  character.  Lastly, 
the  Darwinian  ideas  which  deal  with  the  great  and 
increasing  numbers  of  living  things,  and  the  changes 
inherent  in  their  growth  and  development.  These 
have  led  to  statistical  enumerations  and  registrations 
which,  beginning  with  ]\Ir  Francis  Galton's  researches 
into  the  phenomena  of  heredity,  are  at  the  present 
moment  being  continued  on  special  lines  by  Prof.  Karl 
Pearson. 

That  Error  is  subject  to  law,  or,  to  express  it  mathe- 
matically, to  regularity,  is  a  reflection  which  forced  itself 
upon  the  attention  of  thinkers  who  occupied  themselves 
with  the  doctrine  of  chances,  and  of  statisticians  who 
collected  registers  of  large  numbers  of  events.  Let 
special  known  sources  of  error  be  eliminated  or  allowed 
for  in  every  instance,  there  still  remains  a  very  large, 
practically  an  infinite,  number  of  unknown  sources  of 
error  which — where  we  have  to  do  with  simple  magni- 
tude— may  increase  or  reduce  our  result  by  mutually 


ON    THE    STATISTICAL    VIEW    OF    NATURE.       575 

destroying   or   augmenting    each    other.      Tlie   repeated 
measurement  of  a  physical  quantity,  of  the  position  of  a 
fixed  star ;   the  arrangement  of   the  bullet  marks  on  a 
target ;    the  grouping  of   the  impressions  made   on   the 
sand  by  a  stone  let  fall  vertically  from  the  same  point 
at  a  considerable  height ;  even  tlie  countings  by  a  large 
number  of  skilled  persons  of  the  same  number  or   the 
estimates  of  the  same  distance  or  height  of  an  object,  of 
the  weight  of  a  heap  of  materials :  all  these  statements 
will  show  a  certain  regularity  around  the  mean  number 
which  we  consider  to  be  the  most  probable  or  correct 
one.     Small  errors  will  be  more  frequent  than  large  ones  ; 
very  large  ones  will  be  practically  absent ;  and  the  mean 
will  be  the  result  of  a  mutual  destruction  or  compensa- 
tion of  many  small  sources  of  error  acting  both  ways. 
Mathematicians,     from     tlie     time     of     Lagrange     and 
Bernoidli,    have     tried    to    put    into    a    mathematical 
formula    this    regularity    in    the    distribution    of    error; 
and,  since  Laplace   and   Gauss   approached   the   subject 
from    different    points    of    view,  they   have    arrived    at 
a    definite    analytical    expression  ^    for    the    distribution 
of    errors   of    increasing   magnitude   around   a   fictitious 
centre  or  mean  which   is  considered  in  every  instance 
to    be    the    most    probable    quantity.       Practical    trials 
on    a    very    large    scale    have    been    made    by    Bessel, 
Encke,    Quetelet,  Faye,   and   others,  and    they  have   in 
every  case  yielded  a  satisfactory  approximation   to  the 
figure    given   1)y   the    theoretical    formula ;    so    tliat    at 
present   little   doubt   as    to  its  usefidness  exists  in  the 
minds   of    those   who    employ    it    for    the    purposes    of 

'  This  is  tlie  well-known  "curve  of  Error." 


576 


SCIENTIFIC    THOUGHT. 


18. 
Method  of 
Least 
Squares. 
Gauss. 


elaborate    calculations    in    astronomy,    geodesy,    and   in 
various  physical  and  statistical  researches. 

Bound  up  with  the  theory  of  Error  is  the  celebrated 
method  of  least  Squares,  first  used  by  Gauss  in  1795, 
published  by  Legendre  in  1805  in  his  memoir  '  On  a 
New  Method  of  Determining  the  Orbit  of  a  Comet,'  and 
elaborately  discussed  by  Laplace,  Gauss,  and  many  sub- 
sequent writers  to  this  day.^  It  may  be  looked  upon 
as  an  extension  or  generalisation  of  the  common-sense 


'  In  addition  to  the  references 
given  in  the  notes  to  pp.  120  and 
183  of  vol.  i.,  I  can  now  recommend 
two  excellent  summary  accounts 
of  the  history  and  theory  of  the 
method  of  least  squares — the  one 
in  Prof.  Czuber's  '  Bericht,'  quoted 
above  (pp.  150  to  224) ;  the  other 
in  Prof.  Edgeworth's  article  on 
"The  Law  of  Error"  in  the  Sup- 
plement to  the  last  edition  of 
the  '  Encj'.  Brit.'  (vol.  xxviii., 
1902,  p.  280,  &c.)  Prof.  Cleve- 
land Abbe,  in  a  "  historical  note 
on  the  method  of  least  squares " 
('American  Journal  of  Mathe- 
matics,' 1871),  has  drawn  attention 
to  the  fact,  that  already  in  1808 
Prof.  R.  Adrain  of  New  Brunswick 
had  arrived  at  an  expression  for  the 
law  of  error  identical  with  the 
formula  now  generally  accepted, 
without  knowing  of  Gauss's  and 
Legeudre's  researches.  See  a  paper 
by  Prof.  Glaisher  in  the  39th  vol., 
p.  75,  of  the  '  Transactions  of  the 
Royal  Astronomical  Society.'  The 
logical  and  mathematical  assump- 
tions upon  which  the  method  is 
based  have  been  submitted  to  re- 
peated and  very  searching  criti- 
cisms, many  rigid  proofs  having 
been  attempted,  and  every  sub- 
sequent writer  having,  seemingly, 
succeeded  in  discovering  flaws  in 
the  logic  of  his  predecessors.  In 
connection   with   another    subject, 


I  may  have  occasion  to  point 
out  how  nearly  all  complicated 
logical  arguments  have  shown 
similar  weakness,  and  how,  in  many 
cases,  the  conviction  of  the  correct- 
ness or  usefulness  of  the  argument 
comes  back  to  the  self-evidence  of 
some  common  -  sense  assumption, 
which  cannot  be  proved,  though  it 
may  be  universally  accepted.  Manj' 
analysts  have  tried  to  prove  the 
correctness  of  the  everyday  process 
of  taking  the  arithmetical  mean, 
but  have  failed.  Prof.  Czuber  says, 
inter  alia  (loc.  cit.,  p.  159):  "The 
fact  that  Gauss,  in  his  first  demon- 
stration of  the  method  of  least 
squares,  conceded  to  the  arithmeti- 
cal mean  a  definite  theoretical 
value,  has  been  the  occasion  for  a 
long  series  of  investigations  concern- 
ing the  subject,  which  frequently 
showed  the  great  acumen  of  their 
authors.  The  purpose  aimed  at — 
viz.,  to  show  that  the  arithmetical 
mean  is  the  only  result  which  ought 
to  be  selected  as  possessing  cogent 
necessity,  hereby  giving  a  firm 
support  to  the  intended  proofs,  has 
not  been  attained,  because  it  cannot 
be  attained.  Nevertheless,  these 
investigations  have  their  worth  be- 
cause they  aiford  clear  insight  into 
the  nature  of  all  average  values  and 
into  the  position  which  the  arith- 
metical average  occupies  among 
them." 


ON    THE    STATISTICAL    VIEW    OF    NATURE.       577 

method  of  taking  the  arithmetical  mean  in  determining 
what  figure  to  accept  in  a  number  of  slightly  differing 
computations.  Where  more  than  one  quantity  is  to  be 
determined — for  instance,  where  from  a  series  of  oljser- 
vations  dotted  on  a  chart  the  continuous  curve  which 
marks  the  course  of  a  planet  or  comet  is  to  be  deduced 
— the  simple  method  of  averaging  cannot  be  applied. 
Every  set  of  three  complete  observations  suffices,  as 
Gauss  has  shown,  to  determine  the  elements  or  con- 
stants of  an  elliptical  orbit.  IJut  astronomers  try  to 
get  as  many  observations  as  possible,  and  none  of  these 
is  a  repetition  of  the  same  observation — as,  for  in- 
stance, are  the  repeated  weighings  of  a  substance  in 
chemistry,  of  the  measurings  of  a  length  in  surveying, 
or  the  counting  of  a  number  in  statistics :  on  the  con- 
trary, each  is  the  independent  ascertainment  of  definite 
positions  in  a  moving  object.  It  is  clear  that  the 
method  of  averaging  must  be  more  general  than  the 
common-sense  method  of  taking  the  arithmetical  mean, 
but  must  —  where  the  latter  is  applicable  —  coincide 
with  it.  It  has  been  shown  that  the  following  rule 
answers  this  purpose.  Fix  the  average  constants  or 
elements  so  that  the  sum  of  the  squares  of  the  differ- 
ences between  the  observed  and  calculated  positions  is  a 
minimum.  In  mathematical  language  this  results  in  the 
algebraical  determination  of  the  constants  in  an  ec^uation. 

Whereas  the  labours  of  Gauss  and  the  school  of 
astronomers  which  he  headed  in  Germany  were  mostly 
occupied  in  the  mathematical  proof  of  this  rule,  and 
in  its  applications  in  astronomical  and  geodetic  com- 
putations, the  doctrine  of  probabilities  acquired  a  larger 

VOL.  II.  2  0 


578  SCIENTIFIC   THOUGHT. 

meaning  and  attracted  much  popular  attention  in  France 
19-        and  Belgium  through  the  dominating  influence  of  Lap- 

Laplace.  fe  o  o  r 

lace.  He  had  not  only  collected  in  his  abstract  and 
very  difficult  '  Analytical  Theory  of  Probabilities '  all 
that  himself  and  others  had  done  in  this  line  of  research, 
but  he  had  in  a  similar  manner  to  that  adopted  in  his 
'  Celestial  Mechanics '  tried  to  bring  the  substance  of 
the  theory  home  to  the  non-mathematical  student  in 
his   '  Essai  Philosophique  sur  les  Probabilites.' 

The  analytical  formulae  of  probabilities  can,  he  main- 
tained, "  be  regarded  as  the  necessary  complement  of  the 
sciences  which  are  founded  on  a  mass  of  observations 
which  are  subject  to  error.  They  are  indeed  indispens- 
able for  solving  a  large  number  of  questions  in  the 
natural  and  moral  sciences.  The  regular  causes  of 
events  are  mostly  either  unknown  or  too  complicated  to 
be  submitted  to  calculation :  frequently  also  their  effect 
is  disturbed  by  accidental  and  irregular  causes,  but  it 
always  remains  impressed  on  the  events  produced  by 
all  these  causes,  and  it  brings  about  changes  which 
a  long  series  of  observations  can  determine.  The 
analysis  of  probabilities  shows  these  modifications :  it 
assigns  the  probability  of  their  causes,  and  it  indicates 
the  means  of  increasing  their  probability  more  and 
more."  ^  Then,  referring  to  the  phenomena  of  the 
weather,  Laplace  proceeds :  "  Moreover,  the  succession 
of  historical  events  similarly  shows  us  the  constant 
action  of  the  great  moral  principles  in  the  midst  of 
the  diverse  passions  and  interests  which  agitate  society 
in    every    direction.       It   is   remarkable   how    a   science 

^  'Essai  Philosophique,'  p.  271. 


ON    THE    STATISTICAL    VIEW    OF    NATURE.       579 


wliicli   began   with    the  consideration  of   play  has  risen 
to  the  most  important  ol)jects  of  human  knowledge." 

In  1823,  soon  after  the  appearance  of  the  works  of 
Laplace  and  other  French  writers,  this  application  of 
the  theory  of  probabilities  was  taken  up  by  Adolphe 
Quetelet,  who  collected  his  researches  in  his  cele- 
brated work,  '  Sur  I'Homme  et  le  I)c\eloppement  de  ses 
Facultes,    ou    Essai    de    Physique    sociale.'  ^       Quetelet 


20. 
Quetelet. 


^  In  addition  to  this  work,  which 
was  published  at  Brussels  in  1836 
in  two  small  volumes,  and  which 
Quetelet  (1796-1874)  describes  as 
a  '  resume  de  tous  mes  travaux 
anterieurs  sur  la  stalistique,' 
he  published,  besides  a  great 
number  of  memoirs,  a  series 
of  '  Lettres  sur  la  Th(5orie  des 
Probabilites' (begun  in  1837,  pub. 
1845,  Eng.  trans,  by  O.  G.  Downes, 
1849),  and  as  a  continuation  of 
the  former  work  in  1848,  '  Du 
Systome  social  et  des  Lois  qui  le 
regissent.'  Less  known  than  those 
of  Quetelet,  but  about  the  same 
time,  and  independently,  there  ap- 
peared in  France  the  writings  of 
A.  M.  Guerry,  beginning  with  the 
publication  in  1829 — in  collabora- 
tion with  A.  Balbi — of  '  Statisticjue 
comparde,  et  I'dtat  de  I'instruc- 
tion  et  du  nombre  des  crimes,' 
and  in  1833,  'Essai  sur  la  sta- 
tistique  morale  de  la  France.' 
The  term  "'moral  statistics"  ap- 
pears here  for  the  first  time. 
Quetelet  was  the  inventor  of  the 
term  "  Social  Physics."  Guerry 
employed  graphical  methods,  and 
published  in  1864  '  Statistiijue 
morale  de  I'Angleterre  comparde 
avec  la  statistique  morale  de  la 
France.'  M.  Block  ('Statistique,' 
p.  43)  attributes  to  Guerry  and 
Charles  Dujiin  the  general  intro- 
duction of  the  gi-aphical  method 
in  statistics  ;  geometrical  represent- 
ations having  been  adopted  at  the 


end  of  the  eighteenth  century  by 
Wm.  Playfair  in  England,  and, 
before  him,  bj'  Crome,  professor 
at  Giessen,  in  1782,  and  tabular 
synoptical  statements  going  back 
to  the  Danish  writer  J.  P. 
Anchersen,  in  his  '  Descrijitio 
Statuum  Cultiorum  in  Tabulis ' 
(Cojjenhagen  and  Leipzig,  1741) ; 
see  V.  John,  '  Geschichte  der 
Statistik,'  p.  88.  Referring  to 
Guen-y,  V.  John  (p.  367)  says: 
"  (,!uetelet  is  incontestably  to  be 
regarded  as  the  founder  of  the 
new  science  (viz.,  moral  statistics), 
for  the  rival  works  of  the 
French  lawyer  Guerry  ajipeared 
only  partly  before  (,>uetelet's,  and 
are  excelled  by  the  latter  in  the 
use  made  of  the  material.  In- 
dependently of  this  formal  dif- 
ference, the  two  authors  have 
quite  different  conceptions  of  the 
new  science.  (Juerry  regards  its 
object  as  consisting  mainly  in  col- 
lecting data  in  order  to  gain  an 
opinion  of  the  moral  status  of  a 
country.  Thus  he  looked  upon 
moral  statistics  as  auxiliary  to  the 
history  of  civilisation.  <i>uetelet 
went  beyond  this,  inasmuch  as  he 
was  the  first  to  inquire  into  the 
cause  of  the  moral  level  of  a 
population,  and  in  as  much  as  in 
his  criminal  statistics  of  Belgium, 
1833,  he  had  already  given  ex- 
pression to  the  fundamentvl  idea, 
'  Society  bears  the  germs  of  crime 
in  itself.' "' 


580 


SCIENTIFIC    THOUGHT. 


21. 
The  "  mean 
man.' 


was  astronomer-royal  of  Belgium  and  the  founder  of 
the  Observatory  at  Brussels.  Having  opened  his  career 
by  some  memoirs  on  geometrical  subjects,  he  directed 
his  attention  to  questions  of  meteorology  and  statis- 
tics, which  he  was  probably  the  first  to  extend 
into  the  region  not  only  of  the  physical  but  also 
of  the  moral  attributes  of  man,  studying  the  phe- 
nomena of  crime,  suicide,  and  disease  as  revealed  by 
the  cruninal  courts  in  France,  the  Netherlands,  and 
other  covmtries. 

Subsequently  it  was  mainly  through  his  influence  that 
a  series  of  international  statistical  congresses  was  held 
in  the  principal  cities  of  Europe,  and  a  greater  uniformity 
in  the  methods  of  research  and  registration  attempted 
and  partially  attained. 

Quetelet's  statistical  inquiries  centre  in  the  conception 
of  the  average  or  mean  man  who,  in  a  very  geometrical 
fashion,  is  looked  upon  as  an  analogue  of  the  centre  of 
gravity^  of  a  body,  being  the  mean  around  which  the 
social  elements  oscillate.     "  If  one  tries,"  he  says,  "  to 


^  Quetelet  defines  the  object  of 
his  work  as  follows  ( '  Sur  1' Homme,' 
vol.  i.  p.  21):  "L'objet  de  cet 
ouvrage  est  d'etudier,  dans  leurs 
efifets,  les  causes,  soit  naturelles, 
soit  perturbatrices  qui  agissent  sur 
le  developpement  de  I'liomme  ;  de 
chercher  ii  mesurer  I'influence  de 
ces  causes,  et  le  mode  d'apres  lequel 
elles  se  modifient  mutuellement. 
Je  n'ai  point  en  vue  de  faire  une 
theorie  de  I'homme,  mais  seulement 
de  constater  les  faits  et  les  ph^nom- 
enes  qui  le  concernent,  et  d'essayer 
de  saisir,  par  I'observation,  les  lois 
qui  Kent  ces  phenomenes  ensemble. 
L'homme  que  je  considere  ici  est, 


dans  la  soci^td,  I'analogue  du  centre 
de  gi'avite  dans  les  corps  ;  il  est  la 
moyenne  autour  de  laquelle  oscillent 
les  elemens  sociaux  :  ce  sera,  si  Ton 
veut,  un  etre  fictif  pour  qui  toutes 
les  choses  se  passeront  conforme- 
ment  aux  resultats  moyens  obtenus 
pour  la  societe.  Si  I'on  cherche  ii 
etablir,  en  quelque  sorte,  les  bases 
d'une  physique  sociale,  c'est  lui 
qu'on  doit  eonsiderer,  sans  s'arreter 
aux  cas  particuliers  ni  aux  anom- 
alies, et  sans  rechercher  si  tel  in- 
dividu  peat  prendre  un  developpe- 
ment plus  ou  moins  grand  daus 
I'une  de  ses  facultes." 


ON    THE    STATISTICAL    VIEW    OF    NATURE.       581 

establish  in  some  way  the  foundation  of  Social  Thysics, 
it  is  the  mean  man  whom  one  must  consider  without 
stopping  at  particular  and  anomalous  cases  and  without 
investigating  whether  some  individual  can  take  a  de- 
velopment more  or  less  great  in  one  of  his  faculties.^ 
.  .  .  After  having  considered  man  at  different  epochs 
and  among  different  peoples,  after  having  successively 
determined  the  different  elements  of  his  physical  and 
moral  condition,  .  .  .  we  shall  be  able  to  fix  the  laws 
to  which  he  has  been  subjected  in  different  nations 
since  their  birth — that  is  to  say,  we  shall  be  able  to 
follow  the  course  of  the  centres  of  gravity  of  every  part 
of  the  system." "'  In  an  astronomical  fashion  Quetelet 
speaks  of  the  perturbing  forces  and  variations,  and  of 
the  "  stability  of  the  social  system,"  ^  and  compares  the 
new  science  of  society  to  the  mechanics  of  the  Heavens.* 
The  influence  of  Laplace  and  his  school  is  evident  in 
every  page  of  Quetelet's  work.  Whilst  speaking  of  the 
"  variability  of  tlie  human  type  and  the  mean  man 
among  different  peoples  and  in  different  centuries,"  he 


'  '  Sur  rHonujie,'  vol.  i.  p.  22. 

-  Ibid.,  p.  23. 

3  Ibid.,  p.  26. 

•*  Vol.  ii.  J).  338.  Quetelet  speaks  of 
the  annual  and  diurnal  j)eriods,  and 
continues  :  "  Les  causes  n-gulieres 
et  ptriodiqucs,  qui  dependent  ou  de 
la  pdriode  annuelle  ou  de  la  pcriode 
diurne,  exercent  sur  la  societe  des 
effets  plus  prononce.s  et  qui  varient 
dans  des  liinites  jilus  larges,  (jue 
les  effetH  combines  non  piriodiques, 
produits  annuellement  par  le  con- 
cours  de  toutes  les  autres  causes 
qui  agissent  sur  la  societe ;  en 
d'autres  ternies,  le  systi;me  social, 
dans  sa  maniere  d'etre,  parait  etre 


plus  dissemblable  a  lui  -  niOme 
pendant  le  cours  d'une  annee  ou 
nienie  pendant  resi)ace  d'un  jour, 
que  i)en<lant  deux  annees  con- 
secutives,  si  Ton  a  t'gard  ii  I'ac- 
croissenient  de  la  jiopulation.  La 
pdriode  diurne  semble  exercer  une 
influence  un  pen  plus  prononcee 
que  la  ])(iriode  animelle,  du  moins 
en  ce  ijui  concerne  les  naissauces. 
La  pdriode  annuelle  produit  des 
effets  j)lus  sensibles  dans  les 
campagncs  que  dans  les  vil!cs,  et 
il  parait  en  etre  de  meme  des 
causes  en  gentTal  qui  tendent 
Ji  modifier  les  faits  relatifs  Ji 
rhonmie." 


582 


SCIENTIFIC   THOUGHT. 


anticipates  discussions  which  came  fifty  years  later.^ 
His  aim  is  to  arrive  at  a  precise  knowledge  of  things 
hitherto  vaguely  known  and  merely  sketched  by  artists 
and  literary  persons ;  but  he  evidently  looks  beyond  the 
study  of  the  average  man  to  that  of  individual  departures, 
as  of  special  interest  to  the  physician,^  for  instance, 
in  the  case  of  disease,  and  he  significantly  recommends 
what  he  calls  the  "  study  of  maxima."  ^  He  regards  the 
"  mean  man  in  the  circumstances  in  which  he  is  placed 
as   the   type   of   all   that   is    beautiful   and   all    that   is 


1  Vol.  ii.  p.  270  :  "  Les  ancieiLs 
ont  represente  avec  un  art  iiifini 
I'homme  physique  et  moral,  tel 
qu'il  existaic  alors  ;  et  la  plupart 
des  niodernes,  frappes  de  la  perfec- 
tion de  leurs  ouvrages,  ont  cru 
qu'ils  n'avaient  rien  de  mieux  a 
faire  que  de  les  imiter  servilement ; 
ils  n'ont  pas  compris  que  le  type 
avait  chang^  ;  et  que,  tout  en  les 
iuaitant  pour  la  perfection  de  I'art, 
ils  avaient  une  autre  nature  a 
etudier.  De  la,  ce  cri  universel, 
'  Qui  nous  delivrera  de.s  Grecs  et  des 
Romains  ! '  De  Ik  cette  scission 
violente  entre  les  classiques  et  les 
romantiques  ;  de  la  enfin,  le  besoin 
d'avoir  une  litterature  qui  fut  verit- 
ablement  I'exprcssion  de  la  societe. 
Cette  grande  revolution  s'est  ac- 
coniplie,  et  elle  fournit  la  preuve  la 
plus  irrecusable  de  la  variabilite  du 
type  humain  ou  de  rhomme  moyen 
chez  les  difFerens  peuples  et  dans 
les  difFerens  siecles."  It  is  inter- 
esting to  see  from  this  quotation 
that  the  opposition  to  a  one-sided 
classical  education  emanated  at 
that  time  from  the  romantic  move- 
ment, whereas  in  our  days  it  is  the 
scientific  movement  which  forms  the 
opposition. 

^  Vol.  ii.  p.  281:  "Comme  dans 
le  plus  grand  nombre  de  cas,  le 
malade   ne  peut  presenter  aucune 


observation  satisfaisante  faite  sur 
sa  propre  personne,  ni  aucune  des 
elemens  qui  lui  sont  particuliers, 
le  medecin  se  trouve  force  de  la 
ramener  h,  I'echelle  commune,  et  de 
I'assimiler  h,  I'homme  moyeu  ;  ce 
qui  au  fond  semble  presenter  le 
moins  de  difEcultes  et  d'iucon- 
veniens  ;  mais  peut  causer  aussi  de 
graves  meprises  dans  quelques  cir- 
constances ;  car  c'est  encore  le  cas 
de  faire  observer  ici  que  les  lois 
gen^rales  relatives  aux  masses  sont 
essentiellement  fausses  etant  ap- 
pliquees  h  des  individus  :  ce  qui 
ne  veut  pas  dire  cependant  qu'on 
ne  peut  les  consulter  avec  fruit :  et 
les  ecarts  sont  toujours  consider- 
ables." 

3  Vol.  ii.  p.  284  :  "  II  ne  faut  pas 
confondre  les  lois  de  developpement 
de  I'homme  moyen  a  telle  ou  telle 
epoque,  avec  les  lois  de  developpe- 
ment de  I'humanite.  Elles  n'ont 
en  general  (jue  peu  de  rapjjort  entre 
elles  :  ainsi  je  serais  tres  dispose  a 
croire  que  les  lois  de  developpement 
de  I'homme  moyen  restent  a  peu 
pres  les  memes  aux  diffdrens  siecles, 
et  qu'elles  ne  varient  que  par  la 
grandeur  des  maxiriui.  Or,  ce  sont 
justement  ces  maxima,  relatifs  ii 
I'homme  develoj^pe,  qui  donnent, 
dans  chaque  siecle,  la  mesure  du 
developpement  de  Thumanite." 


ON    THE    STATISTICAL    VIEW    (»K    NATDRE.       583 


good."  ^  And  further,  "  one  of  the  principal  tilings 
accomplished  by  civilisation  is  to  draw  closer  and 
closer  the  limits  within  which  the  different  elements 
oscillate  which  are  characteristic  of  man."^ 

There  was,  however,  another  idea  besides  that  of 
the  mean  man  which  followed  in  the  course  of  this 
mathematical  or  astronomical  treatment  of  social 
statistics — namely,  the  seeming  negation  of  the  scope 
of  freewill  and  of  moral  responsibility,  which  seemed 
inconsistent  with  the  regularity  of  the  statistical  rec- 
ords. In  his  treatise,  '  Sur  I'Homme,'  Quetelet  had 
drawn  attention  to  the  regular  recurrence  of  crime 
— of  the  tendency  to  crime  —  as  one  of  the  most 
remarkable  features  in  society ;  which,  through  its 
physical  and  moral  constitution,  "  prepares  crime,  the 
guilty    being     only    the     instrument    which    carries     it 


'  Vol.  ii.  p.  287:  "J'ai  dit  prc- 
cedemment  que  I'houmie  inoyeii  de 
cha(jue  epoque  reprcsente  le  tj'pe  du 
developpeinent  de  rhumanite  pour 
cette  opoque ;  j'ai  dit  encore  que 
rhomme  iiioyen  utait  toujours  tel 
que  le  couiportaient  et  qu'exi- 
geaient  le.s  temps  et  le.s  lieux  ;  que 
ses  quaiito.s  se  developpaient  daus 
un  juste  equilibre,  dans  une  par- 
faite  harmonie,  egaleinent  eloiguee 
de.s  exci'.s  et  de.s  defectuosites  de 
toute  e.s{)oce ;  de  sorte  que,  dans 
le.-j  circonstances  oil  il  se  trouve,  on 
doit  le  considorer  coninie  le  type  de 
tout  ce  qui  est  beau,  dc  tout  ce  qui 
eat  bien."  P.  289  :  "  Uu  individu 
qui  n5sunierait  en  lui-merae,  ;i  une 
ejOTque  donnee,  toutes  les  qualites 
de  riiomine  moyen,  representerait 
Il  la  fois  tout  ce  tju'il  y  a  de  grand, 
de  beau  et  de  bien." 

-  Vol.  ii.  p.  342  :  "  Un  des  prin- 
cii)aux  faits  de  la  civili.-iation  est  de 
resserrer,  de  plus  en  jjIus,  les  liiaites 


22. 
Social  Htat- 
isticB  and 
freewill. 


dans  lesquelles  oscilleiit  les  ditferena 
elemens  relatifs  a  riioninie.  Plus 
les  luiuieres  se  rdpandent,  plus  les 
ecarts  de  la  moyeune  vout  en 
ditninuant ;  plus,  par  consequent, 
nous  tendons  a  nous  rapprocher  de 
ce  i[ui  est  beau  et  de  ce  qui  est 
bien.  La  perfectibilitc  de  I'espece 
humaiue  rosulte  comnie  une  conse- 
quence uecessaire  de  toutes  uos 
recherches.  Les  defectuosites,  les 
monstruositt5s  disparaissent  de  plus 
en  plus  au  physiijue  ;  la  frociuence 
et  la  graviti5  des  maladies  se 
trouvent  combattues  avec  plus 
d 'a vantage  par  les  progrts  des 
sciences  m«$dicales  ;  les  qualit(58 
morales  de  I'honime  n'eprouvent 
pas  de  perfeetionnemens  moiiis 
sensibles  ;  et  plus  nous  avancerons, 
moins  les  grands  bouleversemens 
politiques  et  les  guerrea,  ces  fleaux 
de  rhumanite,  seront  iv  craindre 
dana  leurs  effets  et  dans  leurs 
consequences." 


584 


SCIENTIFIC    THOUGHT. 


23. 
Buckle, 


out ';  society,  as  it  were,  exacting  a  certain  proportion 
of  crime,  as  it  does  of  suicide,  poverty,  physical  and 
mental  disease,  for  the  maintenance  of  its  equilibrium 
and  as  an  "  alarming " "  tribute  to  its  stability.  The 
extreme  consequences  which  seemed  to  flow  from  this 
doctrine  were  not  drawn  by  Quetelet,  who  believed  in  a 
gradual  though  slow  development  of  human  society,  and 
in  moral  as  well  as  physical  causes  and  influences.  They 
were  drawn,  however,  by  what  we  may  term  the  mathe- 
matical school  of  social  philosophers,  who  relied  greatly 
upon  the  figures  collected  by  Quetelet  and  confirmed  by 
others.  In  this  country  the  statistical  labours  of  Quetelet 
were  made  known  by  Sir  John  Herschel  in  a  brilliant 
article  ^  in  the  '  Edinburgh  Review  '  on  the  "  Translation 
of  Quetelet's  Letters  to  Prince  Albert  on  the  Theory  of 
Probabilities."  They  do  not  seem  to  have  been  regarded 
as  detrimental  to  the  moral  aspect  of  human  history  till 
Henry  Thomas  Buckle,  in  his  celebrated  '  History  of 
Civilisation,'  ^  made  use  of  Quetelet's  statistics  in  sup- 


^  '  Sur  I'Homme,'  vol.  ii.  p.  241. 

2  Cf.  vol.  ii.  p.  262  ;  also 
'Systeme  Social'  (1848),  p.  9.5, 
and  the  '  M^moire  sur  la  Statistique 
Morale'  (1848). 

3  Vol.  xcii.  p.  18. 

*  The  '  History  of  Civilisation,' 
vol.  i.,  appeared  in  1857,  and  was 
very  soon  translated  in  Germany, 
lunning  in  a  short  time  through 
five  editions.  There  the  statistical 
theories  of  Quetelet  had  not  made 
that  impression  which  they  made 
in  some  other  countries.  This  is 
explained  by  the  fact  that  the 
philosophy  of  Kant,  to  which 
Buckle  himself  referred  in  a  long 
passage  in  his  "Introduction,"  had 
long   before    Quetelet    accustomed 


thinkers  to  abandon  the  popular 
conception  of  freewill,  which  sees 
in  it  merely  the  absence  of  causal 
determinateness,  in  favour  of  the 
causal  connection  of  so-called  free 
actions  with  the  motives  and  the 
moral  character.  The  subject  has 
been  very  fully  discussed  by  F.  A. 
Lange  in  his  well-known  '  History 
of  Materialism '  (Eng.  trans,  by 
Thomas,  vol.  iii.  p.  196,  &c.) 
Lange  refers  to  a  remark  of  the 
well  -  known  political  economist, 
Prof.  Adolph  Wagner,  who,  in  his 
work  '  Die  Gesetzmiissigkeit  in  den 
scheinbar  willkiihrlichen  mensch- 
lichen  Handlungen  '  (Hamburg, 
1864,  p.  xiii,  &c. ),  mentions  the 
fact   that   Quetelet's  writings   had 


ON    THE    STATISTICAL    VIEW    OF    NATURE.       585 


port  of  one  of  his  favourite  theses  —  viz.,  that  the 
course  of  historical  progress  depends  on  the  combined 
action  of  the  external  physical  surroundings  and  of 
the  intellectual  side  of  liunian  nature.  Apart  from 
intellectual  modifications  the  moral  side  is  a  con- 
stant. In  the  course  of  the  discussions  following 
the  appearance  of  Buckle's  History,  especially  in  Ger- 
many, it  was  conclusively  shown  that  statistical 
figures  prove  neither  one  view  nor  the  other :  indeed, 
one  of  the  most  complete  and  exhaustive  treatises 
on  moral  statistics  comes  from  the  orthodox  pen  of 
Alexander  von  Oettingen,  a  Professor  of  Theology,  just 
as  we  saw  that  the  first  great  work  on  political  arith- 
metic in  Germany  came  from  the  pastor  Slissinilch 
a    century   earlier.      Philosophical   writers    like    Lotze  ^ 

facts  of  life,  while  the  German 
philosophy,  despite  its  clearness  as 
to  the  nullity  of  the  old  doctrine 
of  freewill,  still  always  prefers  to 
direct  its  view  inwards  upon  the 
facts  of  consciousness." 

^  Lotze's  deliverances  on  this 
subject  will  be  found  in  the  third 
chapter  of  the  seventh  book  of 
the  '  Microcosmus  '  (Eng.  trans,  by 
Hamilton  and  Jones,  vol.  ii.  p.  200, 
&c. ),  and  also  in  the  '  Logik '  of 
1874  (Book  II.  chap.  8).  In  the 
former  passage  he  says  :  "  The  dis- 
like with  which  we  hear  of  laws 
of  jisychic  life,  whilst  we  do  not 
hesitate  to  regard  bodily  life  as 
subordinate  to  its  own  laws,  arises 
partly  because  we  require  too 
much  from  our  own  freedom  of 
will,  partly  Ijecause  we  let  our- 
selves be  too  nmch  imposed  upon 
by  those  laws.  If  we  do  not  lind 
ourselves  involved  in  tlie  declared 
struggle  between  freedom  and 
necessity,  we  are  by  uo  means 
averse  to  regarding  the  actions  of 


not  received  the  attention  merited  : 
"This  reproach  does  not  quite 
hit  the  right  point.  .  .  .  Wagner 
might,  in  fact,  have  been  led  by 
Buckle  ...  to  see  that  German 
philosophy  in  the  doctrine  of  the 
freedom  of  the  will  has  for  once 
an  advantage  which  permits  it  to  re- 
gard these  new  studies  with  equan- 
imity ;  for  Buckle  supjiorts  himself 
above  all  upon  Kant,  adducing  his 
testimony  for  the  empirical  neces- 
sity of  human  actions,  and  leaving 
aside  the  transcendental  theory  of 
freedom.  Although  all  that  ma- 
terialism can  draw  from  moral 
statistics  .  .  .  for  the  practical 
value  of  a  materialistic  tendency 
of  the  age  as  against  idealism  has 
thus  been  conceded  by  Kant,  it 
is  by  no  means  indifferent  whether 
moral  statistics,  and,  as  we  may 
put  it,  the  wliole  of  statistics,  is 
placed  in  the  foreground  of  an- 
thropological study  or  not ;  for 
moral  statistics  direct  the  view 
outwards  upon  the  real  measurable 


586 


SCIENTIFIC    THOUGHT. 


24. 
Criticism  of 
pretension 
of  statistics. 


and  Drobisch^  have  long  ago  reduced  to  their  proper 
measure  the  pretensions  of  statistics,  and  it  is  now 
generally  admitted  that  in  the  sciences  dealing  with 
human  nature  and  society,  as  in  those  which  inves- 
tigate purely  physical  phenomena,  observations,  figures, 
and  measurements  rarely  if  ever  suffice  to  establish  a 
valid  generalisation ;  but  that,  if  such  be  suggested  by 
other  processes  of  thought,  notably  through  attentive  re- 
flection on,  and  analysis  of,  single  and  accessible  cases, 
statistics    supply    the    indispensable   material   by  which 


men  as  determined  by  circum- 
stances :  in  fact,  all  expectation  of 
good  from  education  and  all  the 
work  of  history  are  based  upon 
the  conviction  that  the  will  may 
be  influenced  by  growth  of  insight, 
by  ennoblement  of  feeling,  and  by 
improvement  of  the  external  con- 
ditions of  life.  On  the  other  side, 
a  consideration  of  freedom  itself 
would  teach  us  that  the  very 
notion  is  repugnant  to  common- 
sense  if  it  does  not  include  sus- 
ceptibility to  the  worth  of  motives, 
and  that  the  freedom  of  willing 
can  by  no  means  signify  absolute 
capacity  of  carrying  out  what  is 
willed."  And,  further,  he  remarks 
on  "  the  extreme  overhastiness 
with  which  the  statistical  myth 
has  been  built  up  from  deductions 
which  cannot  be  relied  upon.  We 
have  yet  to  obtain  from  exacter 
investigations  the  true  material 
for  more  trustworthy  conclusions 
— material  whicli  should  take  the 
place  of  the  statistical  myth  above 
referred  to." 

^  Before  Lotze,  and  as  early  as 
1849,  M.  W.  Drobisch,  the  Her- 
bartian,  had  reviewed  Quetelet's 
Memoir,  'Sur  la  Statistique  morale,' 
&c.  ;  and  later  (1867),  after  the 
publication  of  A.  Wagner's  work,  he 
came  back  to  the  subject  in  an  im- 


portant tract,  '  Die  moralische  Stat- 
istik  und  die  menschliche  Willens- 
freiheit,'  which  should  be  read  by 
every  one  who  desires  to  form  just 
views  on  the  subject.  "  In  all 
such  facts,"  says  Drobisch,  "there 
are  reflected  not  natural  laws  pure 
and  simple,  to  which  man  must 
submit  as  to  destiny,  but  at  the 
same  time  the  moral  conditions  of 
society,  which  are  determined  by 
the  mighty  influences  of  family 
life,  of  the  school,  the  Church, 
of  legislation,  and  are,  therefore, 
quite  capable  of  improvement  by 
the  will  of  man "  (Zeitsch.  fiir 
exacte  Philos.,'  vol.  iv.  p.  329). 
After  all  that  has  been  said  by 
Quetelet,  Buckle,  and  others,  the 
words  of  Schiller  (' Wallenstein's 
Tod,'  ii.  3)  still  remain  the  best 
statement  of  the  problem  : — 

"  Des  Mensclieu  Thaten  uml  Gedankeii, 

wisst ! 
Sind    uiclit  wie    Meeres    blind    bewegte 

Wellen. 
Die  inure  Welt,  sein  Microcosmus,  ist 
Der   tiefe    Schacht,  aus    deni   sie   ewig 

quellen. 
Sie   sind   notliwendig,  wie   des   Baumes 

Fniclit ; 
Sie    kann    der    Zufall   gaukelnd    nicht 

verwandeln, 
Habicli  des  Mensclien  Kern  erst  unter- 

sucht, 
So  weiss  ich  audi  sein  WoUen  und  seiu 

Handeln." 


ON    THE   STATISTICAL    VIEW    OF    NATURE.       587 

these  generalisations  can  be  tested,  elevated  to  the  rank 
of  leading  canons  of  thought  and  research,  and  in  rare 
cases  to  that  of  the  expression  of  a  law  of  nature.  So 
far,  therefore,  as  the  complicated  phenomena  presented 
in  meteorology,  agriculture,  and  economics  are  concerned, 
.  the  suggestions  leading  to  so-called  laws  have  in  every 
case  been  got  elsewhere — from  astronomy,  chemistry, 
psychology,  history,  &c. ;  and  the  work  of  science  has 
subsequently  consisted  largely  in  gathering  the  necessary 
statistical  materials  by  which  to  prove,  amplify,  curtail, 
or  refute  them.  In  many  cases  it  has  been  found  that 
even  elaborate  series  of  observations  had  not  been  per- 
formed in  such  a  manner  ^  as  would  permit  of  the 
necessary  inferences  being  drawn  from  them.  Similarly 
biologists  after  Darwin  have  had  to  rearrange  the  collec- 
tions made  by  those  who  came  before  the  epoch  marked 
by  that  great  name. 


^  This  refers  as  much  to  statist- 
ical figures  as  to  the  knowledge 
accumulated  in  many  of  the  natural 
sciences.  Especially  it  refers  to  the 
statistical  material  upon  which 
Quetelet  based  his  st;irtling  and 
epix-h-making  assertions :  theearlier 
critics  had,  as  V.  John  observes 
('  Geschichte  der  St;itistik,'  p.  364), 
dealt  with  the  deductions  whicii 
(Quetelet  had  drawn,  without  deal- 
ing witii  the  empirical  material 
itself.  It  was  therefore  of  great 
importance  that  Prof.  Kchnisch  of 
Gottingen  for  the  first  time  sub- 
mitted the  figui'es  themselves  to  a 
searching  analysis.  He  did  this 
in  the  years  1875-76,  in  his  articles 
in  the  '  Zeitschrift  fiir  I'hilosophie 
und  Philosophische  Kritik,'  through 
which  it  became  evident  that  the 
inferences  were,  as  Lotze  had 
already  suggested,  to  sny  the  least. 


premature.  "  In  the  memoir  '  Sur 
le  Penchant  au  Crime'  (1831),  only 
four  years,  and  in  the  work  '  Sur 
THomme,'  only  six  years  (1826-31) 
of  the  'compte  general,' furnished 
the  data  upon  which  the  astound- 
ing regularity  with  which  crime 
repeats  itself  was  maintained  "  (V. 
John,  p.  365).  Rehnisch  adds  many 
other  examples  of  the  extreme  in- 
completeness of  the  recoids  upon 
which  the  theory  of  (Quetelet  is 
built  up.  More  recent  labours 
have  therefore  been  to  a  large 
extent  directed  towards  gathering 
inoie  complete  statistical  data,  as 
well  as  towards  improving  the 
mathematical  methods  themselves 
to  which  not  only  these  but  also 
the  population  and  mortality 
statistics  have  been  submitted,  for 
the  purpose  of  arriving  at  average 
figures. 


588  SCIENTIFIC    THOUGHT. 

With  the  scientific  treatment  of  the  phenomena  of 
human  society,  the  name  of  Adolphe  Quetelet  will 
always  be  associated ;  yet  the  mathematical  or  exact 
school  was  not  the  only  one  which  in  the  course  of 
the  first  half  of  the  century  had  approached  the  subject. 
25.        Notably    in    Germany,    under    the    ruling    influence    of 

Historical  ''  ''  *^ 

criticism,  philosophical,  historical,  and  critical  studies,  a  school 
of  research  had  grown  up  calling  itself  the  his- 
torical. If  the  centre  of  gravity  of  the  mathematical 
view  lies  in  the  conception  of  a  certain  uniformity 
and  stability  of  social  phenomena,  the  other  school 
looked  more  to  historical  changes  and  developments, 
opposing  the  doctrine  of  the  movement  or  of  the 
dynamics  to  that  of  the  statics  of  society.  Its  in- 
spiration came  from  a  different  quarter,  and  will 
occupy  us  in  a  later  portion  of  this  work.  For  the 
moment  it  suffices  to  remark  how  here  also,  in  the 
study  of  economics  and  social  phenomena,  the  develop- 
mental or  genetic  view  has  gradually  dispelled  the 
earlier  search  for  recurrent  forms  and  regularities, 
which  we  may  term  the  morphological  aspect :  the 
physiology  has  succeeded  the  anatomy  of  society. 

But  statistical  methods,  with  the  accompanying  doc- 
trines of  probability  and  averages  and  the  theory  of 
error,  have  not  only  been  extensively  and  usefully 
employed  where  large  numbers  of  similar  facts  and 
events  crowd  in  upon  our  observation,  and,  as  it  were, 
overwhelm  us  by  their  multitudes,  as  in  astronomy, 
meteorology,  economics,  and  political  arithmetic :  they 
have  also  shown  themselves  applicable  by  what  we 
may  term   the   inverse   method.     Quetelet,   when   deal- 


ON   THE    STATISTICAL    VIEW    OF    NATCRE.       589 

iug  with  lonj;-  columns  of  Imiuaii  statistics,  felt  a 
relief  in  studying  the  average  or  mean  man.  Is  it 
not  possible  that  in  many  instances  what  nature  and 
experience  show  us  is  only  the  average  itself — our 
senses  and  our  intellect  being  too  coarse  to  penetrate 
to  the  numberless  individual  cases  out  of  which  the 
sum  or  the  average  is  made  up  ?  May  not  even  the 
simplest    phenomenon    or    thing   in   nature    be   in   fact        20. 

Application 

an  aggregate,  a  total,  and  its  apparent  behaviour  and  'i  pi'y^'cs. 
properties  merely  a  collective  effect  ?  Both  the  kinetic 
and  the  atomic  view  of  natural  objects  and  phenomena 
seem  to  favour  this  way  of  regarding  things, — the 
former  showing  us  in  many  cases  motion  and  unrest 
where  at  the  first  glance  we  saw  only  rest,  and  the 
latter  dissolving  apparently  continuous  and  homogene- 
ous structures  into  crowds  or  assemblages  of  many 
particles. 

Thus  the  apparently  steady  pressure  of  gases  is  now 
known  to  be  in  reality  the  violent  bombardment  of 
the  wall  of  the  containing  vessel  by  their  mole- 
cules ;  and  the  most  homogeneous  and  transparent 
crystal  is  revealed,  by  its  optical  properties,  as  an 
assemblage  of  very  minute  particles,  held  together  by 
forces  which  may  be  overcome  by  mechanical  or 
chemical  agencies.  Regarded  from  this  point  of  view, 
our  knowledge  of  natural  objects  is  merely  statistical : 
it  deals  with  aggregates ;  it  is  a  collective  knowledge. 
And  if  we  further  consider  that  the  sameness  of  the 
numberless  constituent  particles  is  by  no  means  proved, 
this  collective  knowledge  turns  out  to  be  merely  con- 
cerned  witli   averages  :    it  is  statistical,   not  individual, 


590  SCIENTIFIC    THOUGHT. 

information  that  we  seem  to  possess ;  it  resembles  the 
knowledge  which  an  economist  may  possess  of  the 
statistics  of  a  society  or  of  the  properties  of  the 
"  mean "  man.  If  such  be  the  case,  the  theory  of 
large  numbers  and  the  calculus  of  probabilities  must 
be  applicable  and  useful  in  dealing  with  those 
phenomena  which,  through  their  minuteness  and  great 
nimiber,  elude  our  detailed  examination. 

The  first  to  introduce  this  conception  of  treat- 
ing a  very  large  assemblage  of  moving  things  by  the 
method  of  averages  was  Joule,^  who,  adopting  Daniel 
Bernoulli's  conception,  calculated  the  average  velocity 
which  a  particle  of  hydrogen  gas  must  possess  in 
order  to  explain  the  total  effect  which  shows  itself 
as  a  definite  gas  pressure  at  a  definite  temperature. 
His  result  was  that  this  average  speed  must  be  6055 
feet  per  second  in  order  to  be  equal  to  the  pressure 
of  one  atmosphere  at  the  zero  temperature  of  the 
Centigrade  scale.  The  speed  of  the  particles,  however, 
cannot  be  assumed  to  be  equal,  owing  to  continual 
encounters ;  and  we  are  indebted  to  Clausius  and 
27.        Clerk-Maxwell  for  introducing  the  more  refined  statis- 

Clausius 

and  Clerk  tical  mctliods  of  the  theory  of  probabilities.  They 
calculated  the  mean  free  path,  and  showed  that 
former  calculations  of  the  average  speed  were  in  the 
main  correct.  The  kinetic  theory  of  gases  afforded  an 
opportimity  of  brilliantly  applying  the  conceptions  of 
averages  or  means  and  of  the  differences  of  frequencies 
as  the  measure  of  the  probability  of  certain  occurrences. 
In  this  case — as  was  first  shown  by  Joule's  figures — we 

^  See  stipra,  vol.  i.  p.  434,  and  vol.  ii.  p.  110. 


ON    THE    STATISTICAL    VIEW    OF    NATURE.        591 

have  to  do  with  billions  and  trillions  of  particles,  moving 
with  velocities  varying  from  zero  to  many  thousands 
of  miles  per  second :  we  have  therefore  to  do  with 
numbers  which  practically  mean  infinity — that  is  to 
say,  we  have  to  do  with  that  condition  of  things 
where  alone  the  laws  of  probability  become  strictly 
correct.^ 

In  this  case,  any  deductions  which  can  be  made  as  to 
the  average  condition  or  collective  behaviour  of  an  in- 
finitely large  assemblage  of  particles,  whose  individual 
members  move  about  with  infinitely  varying  velocities 
at  infinitely  varying  speeds  in  infinitely  varying  direc- 
tions, must  be  realised  in  the  well  -  known  laws  of 
gaseous  bodies  referring  to  pressure,  volume,  expansion, 
molecular  structure,  and  heat,  assuming  the  latter  to  be 
merely  the  sensible  effect  on  our  nerves  of  very  numer- 
ous impingements  of  infinitesimally  small  particles.  It 
is  one  of  the  greatest  triumphs  of  the  mathematical 
methods  applied  in  one  of  the  most  difficult  instances, 
that  the  average  behaviour  and   collective  properties  of 


J  P.  G.  Tait  ('Heat,'  1884,  p.  has  its  course  changed.  He  thus 
•355)  says  :  "  It  is  to  Clausius  that  explains  also  the  slowness  of  diffu- 
we  are  indebted  for  the  earliest  i  sion  of  ga.ses,  and  their  very  small 
approach  to  an  adequate  treatment  '  conductivity  of  heat.  Clerk-Max- 
of  this  question.  He  was  the  first  well  shortly  afterwards  improved 
to  take  into  account  the  collisions  the  theory  by  introducing,  also  from 
between  the  particles,  and  to  show  the  statistical  point  of  view,  the 
that  these  did  not  alter  the  pre-  consideration  of  the  variety  of 
viously  obtained  results.  He  has  speed  at  which  the  different  par- 
also  the  great  credit  of  introducing  tides  are  moving  ;  Clausius  having 
the  statistical  methods  of  the  expressly  limited  his  investigations 
theory  of  probabilities,  and  of  thus  by  assuming  for  simplicity  that  all 
giving  at  least  approximate  ideas  as  move  with  equal  speed.  Clerk- 
to  the  probable  length  of  the  nwin  Maxwell  explained  gaseous  friction, 
free  path — i.e.,  the  average  distance  and  gave  a  more  definite  determina- 
travelled  over  by  a  i)article  before  tion  of  the  length  of  the  mean  free 
it  imjjinges  on  another,  and  thus  path." 


592 


SCIENTIFIC    THOUGHT. 


28. 

Mathe- 
matical rep- 
resentation 
of  experi- 
mental laws, 


such  moving  crowds  turn  out  to  be  exactly  those  laws 
which  Boyle,  Charles,  Gay-Lussac,  Dalton,  and  Avogadro 
had  found  out  by  direct  experiments  with  gaseous  bodies. 
James  Clerk  -  Max  well  was  the  first  to  recognise  the 
great  importance  of  the  statistical  methods,  and  to 
apply  them  in  an  exhaustive  manner.^  And  we  witness 
here  the  same  spectacle  which  presented  itself  in  the 
history  of  the  theory  of  probabilities.  Problems  which 
are  to  be  solved  by  the  mere  application  of  a  few  rules 
dictated  by  common-sense  and  an  exercise  of  common 
logic,  present  in  their  complexity  such  a  multitude 
of  traps,  snares,  and  pitfalls,  that  it  required  the  suc- 
cessive application  of  the  highest  intellects  to  free  the 
reasoning  from  insidious  errors,  and  put  the  results  on 


\/ 


^  The  mauner  in  which  Joule 
dealt  with  the  problem  of  a  large 
crowd  of  moving  particles  in  his 
memoir  of  1851  was  not  strictly 
statistical,  inasmuch  as  he  dealt 
with  an  average  velocitj'  of  the 
molecules,  and  assumed  that  all  the 
molecules  of  a  gas  moved  with  the 
same  velocity.  Clausius,  in  his 
memoir  of  1857,  made  use  of  as- 
sumptions which  were  more  in 
conformity  with  nature :  he  had. 
accordingly,  to  employ  the  calculus 
of  probabilities.  Clerk  -  Maxwell's 
occupation  with  the  subject  dates 
from  the  year  1859,  when  he  read 
his  paper,  "  Illustrations  of  the 
Dynamic  Theory  of  Gases,"  Part  I. 
(published  in  the  '  Phil.  Mag.,'  4th 
series,  vol.  xix.  p.  19,  reprinted  in 
'Scientific  Papers,'  vol.  i.)  He 
showed  that  "  the  velocities  are 
distributed  among  the  particles 
according  to  the  same  law  as  errors 
are  distributed  among  the  observa- 
tions in  the  theory  of  the  method 
of  least  squares.  The  velocities 
range  from  0  to  <x,  but  the  number 


of  those  having  great  velocities  is 
comparatively  small."  If  we  leave 
out  Joule's  imperfect  attempt  to 
employ  the  statistical  method,  one 
of  the  first  applications  of  the 
method  of  averages  to  a  physi- 
cal problem  is  to  be  found  in 
Sir  G.  G.  Stokes's  paper  "On 
the  Composition  of  Streams  of 
Polarised  Light  from  different 
Sources"  ('Camb.  Phil.  Trans.,' 
1853),  where  he  shows  "what 
will  be  the  average  effect  of  a  very 
great  number  of  special  sources 
of  light :  thus  giving  one  of  the 
earliest  illustrations  of  the  use, 
in  physics,  of  the  statistical  methods 
of  probabilities.  .  .  .  From  this 
point  of  view  the  uniformity  of 
optical  phenomena  becomes  quite 
analogous  to  the  statistical  species 
of  uniformity,  which  is  now  found 
to  account  for  the  behaviour  of  the 
practically  infinite  group  of  particles 
forming  a  cubic  inch  of  gas  "  (P.  G. 
Tait,  'Light,'  2nd  ed.,  1889,  p. 
237). 


ON   THE    STATISTICAL    VIEW    OF    NATURE.       593 

undisputed  and  indisputable  bases.^  In  proportion  a8 
this  has  been  done  the  calculated  results  have  proved 
to  be  in  closer  and  closer  accord  with  observed  facts.  1 
will  here  mention  only  one  of  the  latest  achievements 
in  this  line  of  research  and  reasoning.  Assuming — as 
the  atomic  and  kinetic  theories  do — that  all  external 
phenomena  of  bodies  can  be  reduced  to  the  collective 
or  mean  effect  of  a  practically  infinite  variety  of  tur- 
bulent movements  of  a  very  large  number  of  particles,  it 
must  be  possible  to  give  a  mechanical  explanation  of 
that  remarkable   property  of  all  phenomena  of  nature,        29. 

■^  Irreversi- 

tirst  noticed  by  Lord  Kelvin,  that  they  are  essentially  |^^'|*yj|'' 
irreversible — i.e.,  that,  with  very  rare  exceptions,  they  i"'"<=e-''«es. 
take  place  in  a  certain  direction  which  we  may  define  as 
an  equalisation  of  existing  diflterences  of  level,  tempera- 
ture, electric  pressure,  and  similar  inequalities.     In  order 
to  fix  this  remarkable  property  of  all  natural  phenomena, 
physicists  found  themselves  obliged  to  introduce,  along-    • 
side  of  energy  and   mass  (which    are   both   assumed  to 
conserve  or  maintain  their  total  quantity),  a  third  some- 
thing which  is  the  measure  of  the  degree  in  which  an 
existing  distribution  of  mass  and  energy  can  be  con- 
sidered to  be  capable  of  external,  visible,  finite  activity 

^  Those   who   are    interested    in  'Mathematical  Appendix,'    ]>.    17  ; 

seeing   how   difficult   it  is  to  link  and  the  great  number  of  memoirs 

together   the   common-sense    argu-  ,    referred  to  on  p.  60  of  that  book, 

ments  of  the  theory  of  probabilities  ,    Nevertheless  Tait  speaks  of  the  still 


in  a  consistent  chain  of  unimpeach- 
able logic,  should  read  the  report 
on  the  various   attempts   to  prove 


remaining  difficulties  in  the  kinetic 

theory    of    gases    as    having    been 

'  greatly  enhanced  by  an  apparently 


Clerk-Maxwell's  law  (mentioned  in  ;  unwarranted     application     of     the 

the    foregoing    note)    contained    in  I  theory    of    probabilities    on    whicli 

Prof.    0.    E.    Meyer's    '  Kinetische  I  the   stiitistical    method    is   based." 

Thoorie  der  Gase' (2nd  ed.,  Breslau,  ('Properties   of   Matter,'   •2nd   ed., 

1899),   esiiecially   p.    46,    ic,    and  1  1890,  p.  291.) 

VOL.  II.  2   P 


594 


SCIENTIFIC    THOUGHT. 


30. 
Lord 
Kelvin. 


— i.e.,  of  its  availability  to  do  work.-^  The  infinitesimally 
small  motions  of  an  immense  crowd  may  be  exerted  in 
such  a  way  as  to  total  up  to  a  finite  movement  per- 
ceptible to  our  senses  and  accessible  to  our  handling,  or 
they  may  so  mutually  annul  each  other  as  to  present  in 
their  finite  sum  and  aggregate  the  appearance  of  rest  and 
inaction,  however  turbulent  their  behaviour  might  appear 
to  an  observer  gifted  with  powers  of  perception  millions 
of  times  more  delicate  than  ours.  Lord  Kelvin  intro- 
duced the  conception  of  the  availability  of  energy,^ 
Clausius  that  of  entropy  (or  energy  which  is  hidden 
away),  to  measure  this  condition  of  any  natural  system. 
Has  the  statistical  view  any  conception  to  put  at  the 
base  of  this  remarkable  property  of  natural  phenomena  ? 
It   has,   and    we   must   assign    to    Clerk  -  Maxwell  ^   the 


\/ 


^  See  supra,  chap.  vii.  p.  128, 
&c. 

-  Or  of  "  motivity  "  {i.e., 
"  energy  for  motive  power  "), 
this  being  "the  possession,  the 
waste  of  which  is  called  dissi- 
pation." See  supra,  chap,  vii., 
p.  168  ;  also  Thomson  (Lord 
Kelvin),  'Popular  Addresses,'  vol. 
i.  p.   141. 

■*  The  contributions  of  Clerk- 
Maxwell  to  this  topic  are  notably 
two,  independently  of  the  larger 
view  which  he  took  of  statistical, 
as  compared  with  historical,  know- 
ledge, of  which  I  treat  farther  on 
in  this  chapter.  First,  in  the  con- 
cluding remarks  of  his  treatise  on 
the  'Theory  of  Heat'  ("On  the 
Limitation  of  the  Second  Law  of 
Thermodynamics")  he  introduced 
his  famous  conception  of  a  "  sort- 
ing demon,"  the  meaning  of  which 
fanciful  device  was,  to  impress  upon 
the  student  of  the  dynamical  theory 
of    heat,    first    the   fact   that   the 


loss  of  availability  of  the  energy  of 
molecular  motion  is  owing  to  the 
coarseness  of  our  senses  ;  and  second, 
that  the  restoration  of  differences 
of  temperature,  or  of  availability 
of  energy,  is  simply  a  matter  of 
arrangement  or  order,  not  of  an 
increase  of  the  intrinsic  energy 
of  the  system.  The  subject  has 
been  frequently  referred  to,  notably 
by  Lord  Kelvin,  who  says  ("  On  the 
Sorting  Demon  of  Clerk-Maxwell," 
Royal  Institution,  February  1879. 
Reprinted  in  '  Popular  Lectures 
and  Addresses,'  vol.  i.  p.  1.37,  &c. ) : 
"  Dissipation  of  energy  follows  in 
nature  from  the  fortuitous  con- 
course of  atoms.  The  lost  motivity 
is  essentially  not  restorable  other- 
wise than  by  an  agency  dealing 
with  individual  atoms  ;  and  the 
mode  of  dealing  with  the  atoms 
to  restore  motivity  is  essentially  a 
process  of  assortment,  sending  this 
way  all  of  one  kind  or  class,  that 
way  all  of  another  kind  or  class  " 


ON    THE    STATISTICAL    VIEW    OF    NATURE. 


i95 


credit  of  having  first  indicated,  and  lo  I'rof.  Boltzniann  ^ 
— aided  by  many  otlier  eminent  natural  pliilosopliers 
— that  of  having  definitely  established,  this  higlily 
suggestive  explanation  or  illustration.  The  doctrine 
of    chances,   to    which    artifice    the    statistical    view    of 


(p.  139).     "The  conception  of  the 
'  sorting  demon  '  is  merely  mechan- 
ical, and  is  of  great  value  in  purely 
physical   science.      It   was  not  in- 
vented   to    help   us    to    deal    with 
questions    regarding  the   influence 
of   life  and   mind  on   the  motions 
of  matter,  questions  essentially  be- 
yond the  range  of  mere  dynauiics" 
(p.    1-41).     The    other   contribution 
througli     which     Clerk  -  Maxwell's 
name  has  become  celebrated  in  this 
connection   is  to  be  ftjund  in  the 
so-called    Maxwell -15oltzmann   law 
of  the  distribution  of  kinetic  energy 
in    a    mass    of    moving    particles. 
The     discussion     of     the     subject 
dates    from    the    first    memoir    of 
Clerk-Maxwell,  quoted  above  ;  and, 
after  Prof.  Boltzmann  had  tre;ited 
of     the     siime     subject     in     1868, 
and    Mr    Watson    in    1876,    Clerk- 
Maxwell  returned  to  it  in  a  paper 
' '  On     Energy     in     a     System     of 
Material    Points"    ('Camb.    Phil. 
Soc.,'  vol.   xii.)     In  the  year  1894 
Prof.     Bryan    presented    the    2nd 
part     of      his     Report     on     "  Our 
Knowledge    of    Thermodynamics " 
('Brit.    Assoc.   Rep.,'    1894,    p.    64, 
&c. ),  in  which  he  gives  an  account 
of   all    the    different   investigations 
referring    to    this    subject,    up    to 
that  date.      This  was  followed   by 
a    long    discussion    of    the    subject 
in  the  pages  of   '  Nature '  (vol.  li. ), 
in  which  Messrs  Bryan,  Boltzmann, 
Burbury,  Culverwell,  Larmor,  and 
H.     W.    Watson    took    part,    and 
which    gave    Prof.    P.olt/mann    the 
opportunity   of  giving  a  hnal   ex- 
pression of  his  opinion  (p.  415). 

'  Prof.     Bolizmann's     investiga- 
tions  connected   witli   tlie    second 


law    of    thermodynamics    and    the 
kinetic   theoi-y   of  gases  cover  the 
last    thirty  -  five    years.       He    has 
succeeded    in    putting    the    whole 
problem    more    and    more    into    a 
strictly    accurate,    <i.s    also    into    a 
popularly    intelligible,  form.      Un- 
fortunately his  vciy  numerous  con- 
tributions lire  scattered  in  various 
periodical    jiublications,    and    have 
not    yet    appeared    in    a  collected 
edition.     Most  of  them  apjieared  in 
the    Proceedings  and  Transactions 
of    the    Vienna    Academy,    among 
which    the    Atklress    delivered    on 
the      29  th      May     1886     can      be 
specially      recommended.         Since 
then,  and  after  the  correspondence 
in    '  Nature '    referred    to    in    the 
last    note,    he    has    jjublished    his 
lectures    '  Vorlesuugen    iiber    Gas- 
Theorie'  (2  vols.,  Leipzig,  1896-98). 
He    there    (vol.    ii.    p.    260,    note) 
gives  a  list  of  the  most  important 
literature  on  the  subject,  and  also 
a   general  summary  regarding  the 
application  of  the  theory  of  prob- 
abilities to  the  distribution  of  the 
kinetic     energy     of     a     crowd     of 
moving    particles.       In    this    con- 
nection   he    also    deals    with    the 
consequences    of    the    atomic    hy- 
pothesis, the   irreversibility    of   all 
natural  pnjcesses,  and  the  applica- 
tion   of    tiie    second    law    to    the 
history  of  the  universe.     He  there 
says    (p.    253)  :     "  The    fact    that 
the     closed     system     of     a     finite 
number    of    molecules,    if    it    had 
originally  an  orderly  condition,  and 
has   then   la])sed   into  a   disorderly 
one,   must  finally,  after  the  lapse 
of    an    inconceivably   long    i)eriod, 
assume  again  orderly  conditions,  is 


596 


SCIENTIFIC    THOUGHT, 


phenomena  reduces  us,  distinguishes  between  probable 
and  improbable  events  or  arrangements  of  a  crowd 
of  elements — i.e.,  between  such  as  are  of  an  average 
and  such  as  are  of  an  exceptional  character.  Any 
highly  improbable  arrangement — though  possible — will 
be  followed  by  a  gradual  settling  down  to  more  prob- 
able or  average  arrangements.  And  as  in  nature  you 
are  forced  to  introduce  the  conception  of  availability,  so 
in  the  calculus  of  chances  you  can  introduce  a  certain 
mathematical  quantity  which  is  the  measure  of  the  proba- 
bility.    The  more  improbable,  i.e.,  exceptional,  the  begin- 


not  a  refutation,  but  a  confirmation, 
of  our  theory.  But  one  must  not 
consider  the  matter  thus :  as  if 
two  gases  .  .  .  which  were  initially 
unmixed,  then  became  mixed,  after 
a  few  days  again  unmixed,  then 
again  mixed,  &c.  We  find,  rather, 
that  .  .  .  only  after  a  period 
which,  even  compared  with  10  10  ^" 
years,  is  enormously  great,  a  per- 
ceptible unmixing  would  take  place. 
That  this  is  practically  equivalent 
to  never,  we  see,  if  we  consider 
that  in  this  period  there  would 
be,  according  to  the  laws  of  prob- 
ability, many  years  in  which,  by 
mere  chance,  all  the  inhabitants  of 
a  large  city  would,  on  the  same 
day,  commit  suicide,  or  fire  break 
out  in  all  its  buildings  ;  whereas 
the  insurance  companies  are  in  so 
good  an  agreement  with  facts  that 
they  do  not  consider  such  cases  at 
all.  If  even  a  much  smaller  im- 
probability were  not  practically 
identical  with  imi)ossibility,  nobody 
could  rely  upon  tlie  present  daj' 
being  followed  by  night  and  the 
latter  again  by  day. "  And  further 
(p.  255)  :  "  If  we,  therefore,  repre- 
sent the  world  under  the  figure  of 
an  enormously  large  mechanical 
system,    composed    of   enormously 


numerous  atoms,  which  started 
from  a  very  perfectly  ordered 
condition,  and  exist  still  mainly 
in  an  orderly  condition,  we  arrive 
at  consequences  which  actually 
stand  in  perfect  harmony  with 
observed  facts";  and  (p.  258), 
"  That  in  nature  the  transition 
from  a  probable  to  an  improbable 
condition  does  not  happen  as  fre- 
quently as  the  reverse,  can  be  ex- 
plained by  the  assumption  of  a 
very  improbable  initial  state  of  the 
whole  surrounding  universe,  in 
consequence  of  which  any  arbitrary 
system  of  interacting  bodies  is,  in 
general,  in  an  improbable  condition 
to  begin  with.  But  one  might 
say,  that  here  and  there  the 
transition  from  probable  to  im- 
probable conditions  must,  after 
all,  be  observable.  .  .  .  From  the 
numbers  regarding  the  inconceiv- 
ably great  rarity  of  a  transition 
from  probable  to  improbable  con- 
ditions, happening  in  observable 
dimensions  and  during  an  ob- 
servable period,  it  is  explained 
how  such  a  process  within  what 
we,  cosmologically,  call  a  single 
world,  or,  specially,  our  world,  is 
so  extremely  rare  that  any  exjjeri- 
ence  of  it  is  excluded." 


ON    THE    STATISTICAL    VIEW    OF    NATURE.       5  97 

ning  yoii  choose,  the  greater  your  distance  from  the 
average  or  most  probable  condition  into  wliich,  in  the 
long-run,  things  must  settle  down ;  the  more  play  for 
the  equalising  and  levelling  down  of  coming  events. 
The  world — or  at  least  that  part  of  the  world  accessible 
to  our  observation,  and  the  playground  of  our  activity — 
shows  a  large  amount  of  available  energy,  or,  expressed 
in  a  purely  statistical  manner,  it  started  from  a  highly 
improbable  condition,  and  it  is  descending  or  running 
down  into  a  more  probable  or  average  condition.     The        si. 

^  ^  "Avail- 

doctrine  of  availability  or  of  its  reverse,  of  entropy  ^^'^^^.y^j^  f^ 
— i.e.,  of  the  loss  of  availability — turns  out  to  be  a  Probability, 
theorem  of  probabilities ;  and  the  refined  mathematical 
researches  of  Prof.  Boltzmann  and  others  show  that 
these  two  conceptions  can  be  made  to  cover  each  other. 
Moreover,  we  can  bring  home  to  the  popular  under- 
standing the  difference  between  the  exceptional  con- 
dition, with  its  large  amount  of  available  energy,  and 
the  average  condition,  with  its  large  amount  of  self- 
destructive  and  wasted  energy  (or  entropy),  by  the 
simile  of  order  and  disorder.  For  every  arrangement  of 
a  crowd  of  things  or  beings  which  is  orderly,  there  are 
innumerable  arrangements  which  are  disorderly ;  every 
one  knows  how  easily  the  orderly  arrangement  lapses 
into  disorder,  and  nobody  expects  by  mere  haphazard 
or  chance  movements  to  produce  order  out  of  disorder. 
There  are  thousands  of  ways  by  which  a  stone  can  fall 
from  the  peak  of  a  mountain  to  the  lower  levels,  but 
only  one  direction  which  would  take  it  up  again  to  the 
top.  A  tree  has  been  suggested  as  the  picture  of  the 
course  that  natural  movements  take  :  for  the  one  position 


598  SCIENTIFIC    THOUGHT. 

in  the  trunk,  where  all  branches  and  all  roots  meet, 
there  are  in  both  directions  numberless  ways  of  rami- 
fication or  dissipation  into  the  twigs  or  the  root-fibres. 
The  statistical  view  measures  the  chances  of  an  orderly 
arrangement  compared  with  disorder,  of  a  commanding 
unique  position  compared  with  the  average  or  mean 
position,  by  saying  the  odds  are  infinity  to  one  against 
it.  The  orderly  exceptional  position  and  arrangement 
of  a  crowd  does  not  possess  more  actual  energy,  but  its 
energy  is  directed,  arranged,  it  has  become  available — 
get-at-able. 
32.  And  what  is  it  that  changes  disorder  into  order  ?      It 

"Selection" 

as  conceived  ig  a  proccss  of  sclection.      Maxwell  imagined  a  sorting 

by  Maxwell.  ^  o  & 

demon  endowed  with  powers  of  perceiving  and  dividing 
the  immeasurably  small  movements  of  a  gaseous  body — 
i.e.,  of  a  crowd  of  particles  in  turbulent  to  and  fro  move- 
ment. Such  a  being  could,  by  mere  selection  and 
separation  of  the  slow  and  fast  moving  particles,  bring 
order  into  disorder,  converting  the  unavailable  energy 
into  available  energy.  It  would  be  a  process  of  mere 
sifting  and  arranging,  such  as  is  apparently  carried  out 
in  the  living  creation  and  by  organic  structures.-^  And 
Maxwell  went  a   step   further,  and   conceived  the  idea 

^  See  supra,  chap.  x.  p.  4-37,  note,       The  mflueuce  of  animal  or  vegetable 

life  on  matter  is  infinitely  beyond 
the  range  of  anj'  scientific  inquiry 
hitherto  entered  on.  Its  power  of 
directing  the  motions  of  moving 
particles,  in  the  demonstrated  daily 
miracle  of  our  human  free-will,  and 
in  the  growth  of  generation  after 
generation  of  plants  from  a  single 
seed,  are  infinitely  different  from 
anj'  possible  result  of  the  fortuitous 
concourse  of  atoms." 


where  the  selective  action  of  certain 
organisms  is  referred  to  in  connec- 
tion with  Prof.  Japp's  Address  to 
the  Brit.  Assoc,  in  1898.  Lord  Kel- 
vin says  ("On  the  Dissipation  of 
Energy,"  1892,  'Popular  Lectures 
and  Addresses,'  vol.  ii.  p.  463,  &c. ) : 
"  It  is  conceivable  that  animal  life 
might  have  the  attribute  of  using 
the  heat  of  surrounding  matter,  at 
its  natural  temperature,  as  a  source 
of  energy  for  mechanical  effect.  .  .  . 


ON    THE    STATISTICAL    VIEW    OE    NATURE.       599 

that,  after  all,  the  whole  of  our  knowledge  of  natural 
phenomena  and  natural  things  may  be  only  statistical, 
not  historical  or  individual.  "  In  dealing,"  he  says,^ 
"with  masses  of  matter,  while  we  do  not  perceive  the 
individual  molecules,  we  are  compelled  to  adopt  the 
statistical  method  of  calculation,  and  to  abandon  the 
strict  dynamical  method  in  which  we  follow  every 
motion  by  the  calculus.  It  would  be  interesting  to 
inquire  how  far  those  ideas  about  the  nature  and  the 
methods  of  science  wdiich  have  l)een  derived  from 
examples  of  scientific  investigation  in  which  the 
dynamical  method  is  followed,  are  applicable  to  our 
actual  knowledge  of  concrete  things,  which,  as  we  have 
seen,  is  of  an  essentially  statistical  nature,  l)ecause  no 
one  has  yet  discovered  any  practical  method  of  tracing 
the  path  of  a  molecule,  or  of  identifying  it  at  different 
times."  And  elsewhere  ^  he  says :  "  The  statistical 
method  of  investigating  social  questions  has  Laplace 
for  its  most  scientific  and  Buckle  for  its  most  popular 

^   'Theory  of  Heat,'  8th  ed.,   p.  I    rather   that   of    a   steersman   of  a 

329.  vessel  —  not    to    produce,    but    to 

-  '  Life    of    Clerk  -  Maxwell     by  regulate    and    direct,   the     animal 

Campbell  and  Garnett.'     Chap.  xiv.  powers."     He    then    speaks  of  the 

contains    a    paper   with    the    title,  I    '•  powerful  effect   on   the   world  of 


Does  the  progress  of  Physical 
Science  tend  to  give  any  advantage 
to  the  opinion  of  Necessity  (or 
Determinism)    over    that    of     the 


thought"  which  the  developments 
of  molecular  science  are  likely  to 
have,  considering  the  "most  im- 
portiint  effect  on  our  way  of  think- 


Contiiigency    of    Events    and    the   '    ing    to    be    that    it    forces    on    our 


Freedom  of  the  Will?"  In  it  (p. 
435)  there  occurs  the  following 
passage  :  '"  The  doctrine  of  the 
conservation  of  energy,  when  ap- 
plied to  living  beings,  leads  to  the 


attention  the  distinction  between 
two  kinds  of  knowledge,  which 
we  may  call  for  ctmvenience  the 
Dynamical  and  Sbitistical."  The 
paper  from  which   the  extracts  in 


conclusion    that    the    soul    of    an       the   text  are   taken  is  dated  1873. 


animal  is  not,  like  the  mainspring 
of  a  watch,  the  motive  power  of 
the  body,  but  that  its  function  is 


Clerk-Maxwell  was  then  forty-one 
years  of  age. 


600  SCIENTIFIC    THOUGHT. 

expounder.  Persons  are  grouped  according  to  some 
characteristic,  and  the  number  of  persons  forming  the 
group  is  set  down  under  that  characteristic.  This  is 
the  raw  material  from  which  the  statist  endeavours 
to  deduce  general  theorems  in  sociology.  Other 
students  of  human  nature  proceed  on  a  different 
plan.  They  observe  individual  men,  ascertain  their 
history,  analyse  their  motives,  and  compare  their  ex- 
pectation of  what  they  will  do  with  their  actual  con- 
duct. .  .  .  However  imperfect  this  study  of  man  may 
be  in  practice,  it  is  evidently  the  only  perfect  method  in 
principle.  ...  If  we  betake  ourselves  to  the  statistical 
method,  we  do  so  confessing  that  we  are  unable  to 
follow  the  details  of  each  individual  case,  and  expecting 
that  the  effects  of  widespread  causes,  though  very  differ- 
ent in  each  individual,  will  produce  an  average  result  on 
the  whole  nation,  from  the  study  of  which  we  may 
estimate  the  character  and  propensities  of  an  imaginary 
being  called  the  Mean  Man.  Now,  if  the  molecular 
theory  of  the  constitution  of  bodies  is  true,  all  our 
33.        knowledge  of  matter  is  of   a  statistical  kind.     A  con- 

Statistieal  .  i         i         /.  i      i      i  •  i-  m 

knowledge  stitucut  molcculc  01  a  body  has  properties  very  different 
from  those  of  the  body  to  which  it  belongs.  The 
smallest  portion  of  a  body  which  we  can  discern  con- 
sists of  a  vast  number  of  molecules,  and  all  we  can 
learn  about  the  group  of  molecules  is  statistical  in- 
formation. .  .  .  Hence  those  uniformities  which  we  ob- 
serve in  our  experiments  with  quantities  of  matter  con- 
taining millions  of  millions  of  molecules  are  uniformities 
of  the  same  kind  as  those  explained  by  Laplace  and 
wondered  at   by  Buckle,  arising  from  the  slumping  to- 


of  nature. 


ON    THE    STATISTICAL    VIEW    OF    NATURE.       COl 

gether  of  multitudes  of  cases,  eacli  of  whicli  is  by  no 
means  uniform  with  the  others.  .  .  .  Much  liglit  may 
be  thrown  on  some  of  these  questions  by  the  consider- 
ation of  stabihty  and  instabihty.  When  the  state  of 
things  is  such  that  an  infinitely  small  variation  of  the 
present  state  will  alter  only  by  an  infinitely  small 
quantity  the  state  at  some  future  time,  the  condition 
of  the  system,  whether  at  rest  or  in  motion,  is  said  to  be 
stable ;  but  when  an  infinitely  small  variation  in  the 
present  state  may  bring  about  a  finite  difference  in  the 
state  of  the  system  in  a  finite  time,  the  condition  of  the 
system  is  said  to  be  unstable.  It  is  manifest  that  the 
existence  of  unstable  conditions  renders  impossible  the 
prediction  of  future  events,  if  our  knowledge  of  the 
present*state  is  only  approximate  and  not  accurate.  It 
has  been  well  pointed  out  by  Prof.  Balfour  Stewart  that 
physical  stability  is  the  characteristic  of  those  systems 
from  the  contemplation  of  which  determinists  draw  their 
arguments,  and  physical  instability  that  of  those  living 
bodies,  and  moral  instability  ^  that  of  those  developable 
souls  which  furnish  to  consciousness  the  conviction  of 
free-will." " 


'  There  is  an  awkward  misprint 
in  the  first  edition  of  'The  Life,' 
which  i.-i  corrected  in  the  second 
edition. 

-  Clerk  -  Maxwell  frequently  re- 
verts to  this  subject.  In  an  article 
on  "  Molecules,"  contributed  to  the 
ninth  edition  of  the  '  Ency.  Brit.' 
(reprinted  in  '  Scientific  Pajters,' 
vol.  ii.),  he  contrasts  historical  and 
statistical  knowledge  as  follows  (p. 
373) :  "  The  modern  atoinists  have 
ado[)ted  a  method  which  is,  I 
believe,  new  in  the  department  of 


mathematical  physics,  though  it 
has  long  been  in  use  in  the  section 
of  statistics.  When  the  working 
members  of  Section  F  (of  the  Brit. 
Assoc.)  get  hold  of  a  report  of  the 
census,  or  any  other  document  con- 
taining the  numerical  data  of 
economic  and  social  science,  they 
begin  by  distributing  the  whole 
population  into  groujis  according  to 
age,  income-tax,  education,  religious 
belief,  or  criminal  convictions.  The 
number  of  individuals  is  far  too 
great  to  allow  of  their  tracing  the 


602 


SCIENTIFIC    THOQGHT. 


The  conceptions  involved  in  the  atomic  and  kinetic 
views  of  natural  processes,  and  the  statistical  manner  of 
dealing  with  these  crowds  of  moving  particles,  have  thus 
introduced  into  natural  philosophy  two  distinct  and  novel 
considerations  not  known  to  former  ages :  first,  the  con- 
sideration that  our  knowledge  of  things  and  phenomena 
in  nature  is  not  historical,  but  that  it  is  that  of  the 
mean  or  average  and  of  the  total  effects  produced  by  an 
immensely  large  number  of  singly  imperceptible  events 
upon  our  senses  which  are  too  coarse  to  receive  or  deal 
with  individual  occurrences ;  secondly,  the  consideration 
that  our  knowledge  is  not  purely  mechanical,  inasmuch 


history  of  each  separately,  so  that, 
in  order  to  reduce  their  labour 
within  human  limits,  they  concen- 
trate their  attention  on  a  small 
number  of  artificial  groups.  The 
varying  number  of  individuals  in 
each  group,  and  not  the  varying 
state  of  each  individual,  is  the 
primary  datum  from  which  they 
work.  This,  of  course,  is  not  the 
only  method  of  studying  human 
nature.  We  may  observe  the  eon- 
duct  of  individual  men  and  compare 
it  with  that  conduct  which  their 
previous  character  and  their  present 
circumstances,  according  to  the  best 
existing  theory,  would  lead  us  to 
expect.  Those  who  practise  this 
method  endeavour  to  improve  their 
knowledge  of  the  elements  of 
human  nature  in  much  the  same 
way  as  an  astronomer  corrects  the 
elements  of  a  planet  by  comparing 
its  actual  position  with  that  de- 
duced from  the  received  elements. 
The  study  of  human  nature  by 
parents  and  schoolmasters,  by  his- 
torians and  statesmen,  is,  there- 
fore, to  be  distinguished  from  that 
carried  on  by  registrars  and  tabu- 
lators, and  by  those  statesmen  who 
put  their  faith  in  figures.     The  one 


may  be  called  the  historical  and 
the  other  the  statistical  method. 
The  equations  of  dj-namics  com- 
pletely express  the  laws  of  the 
historical  method  as  applied  to 
matter,  but  the  application  of  these 
equations  implies  a  perfect  know- 
ledge of  all  the  data.  But  the 
smallest  portion  of  matter  which 
we  can  subject  to  experiment  con- 
sists of  millions  of  molecules,  not 
one  of  which  ever  becomes  sensible 
to  us.  We  cannot,  therefore,  ascer- 
tain the  actual  motion  of  any  one 
of  these  molecules  ;  so  that  we  are 
obliged  to  abandon  the  strict  his- 
torical method  of  dealing  with  large 
groups  of  molecules.  The  data  of 
the  statistical  method,  as  applied  to 
molecular  science,  are  the  sums  of 
large  numbers  of  molecular  quan- 
tities. In  studying  the  relations 
between  quantities  of  this  kind,  we 
meet  with  a  new  kind  of  regularity, 
the  regularity  of  averages,  which 
we  can  depend  upon  quite  suffi- 
ciently for  all  practical  purposes, 
but  which  can  make  no  claim  to 
that  character  of  absolute  precision 
which  belongs  to  the  laws  of 
abstract  dynamics." 


ox    THE    STATISTICAL    VIEW    OF    NATUKE.        GO.i 

as  l)esides  the  i>urt'l}'  luecluiuical  luoveiuents  uud  their 
summation,  it  must  contain  a  reference  to  the  nature  of 
our  own  faculties — a  principle  which  indicates  to  what 
extent  the  elementary  movements  come  under  our  control 
or  escape  it.  There  must  be  a  principle  which  measures 
the  availability  and  usefulness — for  our  powers — of  natural 
processes,  marking  of!"  what  is  orderly  for  our  senses  and 
accessible  to  our  powers,  from  what  is  disorderly  and  in- 
accessible. This  principle  the  founders  of  the  science  of 
Thermodynamics — liankine,  Clausius,  and  Thomson — had 
empirically  established :  Thomson  haA'ing  foreseen  its 
far-reaching  importance  in  the  economy  of  nature  and 
the   applications   of  industry.      The   statistical   view   of        34. 

As  opposed 

natural    phenomena    forced    upon    us    by    atomism    and  to  historical 

*-  L  */  ana  laeciian- 

kinetics    has    shown    us   that   it   is    not    a    purely    me-  ledge."""'' 
chanical^  principle.      It  is  one  belonging  to  the  theory 
of    averages    and    probability.       The    scientific    view   of 
nature  is    thus,  as   Clerk-Maxwell   says,  neither  purel}' 
historical  nor  purely  mechanical — it  is  statistical." 

To   this  view  of  the   scientific   treatment   of   natural 
phenomena  Clerk-Maxwell  has  attached  a  further  con- 

^  Clerk-Maxwell,  m   a  review  of  commercial      and      the      technical 

Tait's  "Thermodynamics"  (' Scien-  chiefs.      As    regularity  is    in  many 

tific  Papers,'  vol.  ii.  p.  670)  :   "The  i    instances  the  condition  of  success, 

truth  of  the  second  law  is  therefore  '    any   Ijreak   of    its   routine    is   care- 

a   statistical,   not  a    mathematical,  fully  examined  and  criticised.     In 

truth,  fur  it  depends   on   the  fact  such  cases  the  technical    man  will 

tbit  the  bodies  we  deiil  with  consist  i    look  to  the  proximate  mechanical 


of  millions  of  molecules,  and  that 
we  never  can  get  hold  of  single 
molecules." 

"  Any  one  who  has  had  occasion 


causes  for  an  e.Kplanation,  whereas 
the  commercial  man,  unable  to 
reflect  on  the  technical  and  mechani- 
cal  conditions  of   tlie  special   case. 


to  observe  the  internal  work  of  any    ,  will  always  refer  to  his  statistics  of 

large    industrial   or    manufacturing  the  past  as  a  guide  in  judging  the 

organisation,  will  have  noticed  the  immediate  difficulty  that  is  before 

twofold    way    in    which    important   I  him. 
occurrences   are  looked  at    bv   the   ' 


604  SCIENTIFIC    THOUGHT. 

sideration,  which  is  interesting  inasmuch  as  it  shows 
that  that  which  I  called  above  the  inverse  method  of 
statistics  does  not  involve  ideas  identical  with  those 
which  the  direct  method  —  as  applied  in  ordinary 
economic  and  social  statistics — involves.  In  the  direct 
processes  of  statistics,  which  we  may  class  under  the 
all-case  or  enumerative  method,  we  rise,  from  a  large 
number  of  individual  facts  and  data  which  are  all 
different,  to  the  conception  of  certain  uniform  averages, 
to  recurring,  or  continuously  and  slowly  changing,  totals, 
such  as  we  handle  daily  in  sciences  like  meteorology, 
in  moral,  economic,  and  industrial  statistics.  The 
averages  are  nowhere  represented  by  the  individuals, 
and  the  regularity  of  the  totals  does  not  appear  in 
dealing  with  single  instances,  or  with  such  restricted 
numbers  as  come  under  the  personal  control  of  any 
of  us ;  hence  the  general  uselessness  of  statistics  in 
handling  individual  cases  or  predicting  special  occur- 
rences. But  the  statistical  view  of  natural  phenomena, 
as  applied  to  the  atomic  constitution  of  bodies,  leads 
us  ultimately  to  the  conception  that  the  smallest  con- 
stituents of  matter,  the  atoms,  exhibit  a  regularity  and 
recurrent  uniformity  of  structure  which  reminded  Sir 
John  Herschel  of  manufactured  articles.  The  attempt 
to  reduce  the  somewhat  numerous  types  of  these  ulti- 
mate elements  to  purely  geometrical  configurations  of 
the  homogeneous  elements  of  one  substance  has  indeed 
failed,  though  it  is  being  continually  revived.  But 
allowing  that  there  exist  some  sixty  or  seventy  distinct 
forms  of  matter  or  atomic  structures,  these  structures 
seem  to   be   alike  and   stable  wherever  we    meet  with 


ON    THE    STATISTICAL    VIEW    OF    NATUKK.        605 

them ;  our  observations  ranging  over  very  large  distances 
ill  space  and  time,  from  the  particles  immediately  before 
u.s  in  artificial  flames  to  the  vibrations  of  atoms  of  distant 
stars,  which  must  have  taken  millions  of  years  to  reach 
us.  "  I  do  not  think,"  says  Clerk-Maxwell,^  "  that  the 
perfect  identity  which  we  observe  between  dilierent  por- 
tions of  the  same  kind  of  matter  can  be  explained  on  the 
statistical  principle  of  the  stability  of  the  averages  of 
large  numbers  of  quantities,  each  of  which  may  differ 
from  the  mean.  .  .  .  For  if  the  molecules  of  some  sub- 
stance, such  as  hydrogen,  were  of  sensibly  greater  mass 
than  others,  we  have  the  means  of  producing  a  separation 
between  molecules  of  different  masses,  and  in  this  way 
we  should  be  able  to  produce  two  kinds  of  hydrogen, 
one  of  which  would  be  somewhat  denser  than  the  other. 
As  this  cannot  be  done,  we  must  admit  that  the  equality 
which  we  assert  to  exist  between  the  molecules  of  hydro- 

'   '  Theory  of   Heat,'  p.   329,  &c.        rlesign,  it  is  replied  that  those  varia- 
Cf.     also    many    passages    in     the    i    tions   which  are    not  conducive  to 


articles  on  "Atom,"  "Molecule," 
"Constitution  of  Bodies,"  &c.,  re- 
printed in  the  second  volume  of 
'  .Scientific   Papers  '  ;   inter  alia,    p 


the  growth  and  multiplication  of 
living  beings  tend  to  their  destiuc- 
tion,  and  to  the  removal  thereby  of 
the  evidence  of  any  adjustment  not 


483  :    "  ]5ut    the    equalitj'    of    the    i    beneficial.     The  constitution  of  an 
constants  of  the  molecules  is  a  fact    i    atom,  however,  is  such  as  to  render 


of  a  very  difi'erent  order.     It  arises 
from    a    particular    distribution    of 


it,  so  far  as  we  can  judge,  independ- 
ent of  all  the  dangers  arising  from 


matter,  a  cuUocution,  to  use  the  ex-  I  the  struggle  for  existence.  Plaus- 
])ression  of  Dr  Chalmers,  of  things  \  ible  reasons  may,  no  doubt,  be  as- 
which  we  have  no  difficulty  in  signed  for  l)elieving  that  if  the 
imagining  to  have  been  arianged  constants  had  varied  from  atom  to 
otherwise.  But  man}'  of  the  atom  through  any  sensible  range, 
ordinary  instances  of  collocation  are  the  bodies  formed  by  aggregates  of 
adjustments  of  constants,  which  are  ■  such  atoms  would  not  have  been  so 
not  only  arbitrary  in  their  own  well  fitted  for  the  construction  of 
nature,  l)ut  in  which  variations  the  world  as  the  bodies  which 
actually  occur  ;  and  when  it  is  ,  actually  exist.  But  us  we  have 
pointed  out  that  these  adjustments  I  no  experience  of  bodies  formeil  of 
are  beneficial  to  living  beings,  and  |  such  variable  atoms,  this  must  re- 
are  therefore  instances  of  benevolent  '    main  a  bare  conjecture." 


606 


SCIENTIFIC    THOUGHT. 


gen  applies  to  each  individual  molecule,  and  not  merely 
to  the  average  of  groups  of  millions  of  molecules." 
And  Clerk-Maxwell  goes  on  to  show  how  the  fact  that 
the  molecules  ^  "  all  fall  into  a  limited  number  of  classes 
or  species  with  no  intermediate  links  ...  to  connect 
one  species  with  another  by  miiform  gradation,  produces 
that  kind  of  speculation  with  which  we  have  become  so 
familiar  under  the  name  of  theories  of  evolution,  it  being 
quite  inapplicable  to  the  case  of  the  molecules.  The 
individuals  of  each  species "  of  molecules  are  like  tuning- 
forks  all  tuned  to  concert  pitch,  or  like  watches  regulated 
to  solar  time."  ^ 


1  'Theory  of  Heat,' p.  330. 

2  Ibid.,  p.  331. 

^  The  passages  quoted  from  Clerk- 
Maxwell's  writings,  and  the  infer- 
ences drawn  by  liim.  were  criticised 
by  Clifford  in  a  lecture  delivered 
in  1874  with  the  title,  "The 
First  and  the  Last  Catastrophe. 
A  Criticism  of  some  recent  Specula- 
tions about  the  Duration  of  the 
Universe"  (reprinted  in  'Lectures 
and  Essays,'  vol.  i.  p.  191  sqq.)  ;  and, 
quite  recently.  Prof.  Ward  has,  in 
his  Gifford  lectures,  reviewed  both 
Maxwell's  and  Clifford's  arguments 
('Naturalism  and  Agnosticism,'  vol. 
i.  p.  99,  &c. )  As  Prof.  Ward  says, 
the  ideas  of  Herschel  and  Clerk- 
Maxwell  "  are  far  more  due  to  theo- 
logical zeal  than  to  the  bare  logic  of 
the  facts."  It  is,  therefore,  out  of 
place  to  discuss  here  the  philosophi- 
cal consequences  of  the  ideas  of  the 
immutability  or  of  the  gradual 
evolution  of  the  ultimate  elements 
of  matter.  In  a  former  chapter 
(see  pp.  360  sqq.  and  369,  note,  of 
this  volume)  I  referred  to  the 
theories  of  the  evolution  of  the 
different  chemical  elements  as 
they  have  been  put  forward  by 
various  scientific  authorities.     The 


intei-est  which  attaches  to  the  pas- 
sages quoted  from  Clerk-Maxwell 
is,  that  in  them,  for  the  first  time, 
an  instance  was  given  of  the 
application  of  statistical  methods 
in  the  domain  of  abstract  science. 
The  reader  may  gather  from  a 
perusal  of  the  writings  mentioned 
above,  as  also  of  the  present 
and  foregoing  chapters  of  this 
history,  that  there  is  an  inherent 
contradiction  (or  as  Kant  would 
say,  antinomy)  between  the  logi- 
cal methods  and  the  highest  ob- 
jects of  scientific  reasoning.  The 
methods  all  tend  in  the  direction 
of  reducing  existing  differences  in 
the  things  and  phenomena  of  natui'e 
to  a  small  number  of  data  which 
are  easily  grasped  and  calculated, 
whereas  the  observation  of  things 
natural  forces  increasingly  upon  us 
the  existence  of  ever  greater  differ- 
ences, changes,  and  varieties.  The 
question  presents  itself,  Is  it  likely 
that  a  process  the  principle  of  which 
is  unification  and  simplification,  will 
ever  lead  to  a  comprehension  of 
that  which  increasingly  reveals 
itself  to  be  infinitely  complex  and 
varying  ?  Dr  Larmor  has  some 
remarks  which  bear  on  this  subject 


ON    THE    STATISTICAL    VIEW    OF    NATURE.       607 

The   progress   of  modern   science  has,  however,  given        35. 

SariieneBii 

a  great  impetus  to  the  development  of  statistical  or  ""J  vari- 
enumerative  methods,  and  notably  to  the  graphical 
registration  of  these  results,  through  the  importance 
whicli  the  phenomena  of  variation  attained  in  all  theories 
of  evolution,  and  chiefly  in  those  based  upon  natural 
selection.  Quetelet  had  already  pointed  to  the  study  of 
the  maxima  of  the  possible  deviations  from  the  mean  and 
average,  as  of  special  interest  and  value.  Xevertheless, 
the  centre  of  gravity  of  the  aspect  unfolded  in  the 
writings  of  Quetelet  and  his  followers  was  the  idea  of 
miiformity  and  average  sameness.  The  conception  of 
change  and  development  did  not  fit  naturally  and  logi- 
cally   into    their  scheme.^       It    was   not   till   after   the 


C-Etlier  and  Matter,'  j).  288): 
"  Tlie  processes  by  which  our  con- 
ception of  the  uniformity  of  Nat- 
ure is  obtained  essentially  involve 
averaging  of  effects,  and  lose  their 
eflScacy  long  before  the  individual 
molecule  is  reached.  Mechanical 
deterniinateness  thus  need  not  in- 
volve molecular  determinateness  ; 
then  why  should  either  of  them 
involve  determination  in  the  en- 
tirely distinct  province  of  vital 
activity  .•  .  .  .  Every  vital  process 
may  conceivably  be  correlated  with 
a  mechanical  process,  as  to  its  pro- 
gress, just  to  that  extent  to  which 
it  is  possible  experimentally  to 
follow  it,  without  lending  any 
countenance  to  a  theory  that  would 
place  its  initiation  under  the  control 
of  any  such  system  of  mechanical 
relations.  In  other  terms,  there  is 
room  for  com])lete  mechanical  co- 
ordination of  all  the  functions  of  an 
organism,  treated  as  an  existing 
material  system,  without  requiring 
any  admission  that  similar  prin- 
ciples  are   supreme    in    the    more 


remote  and  infinitely  couiidex 
phenomena  concerned  in  giowth 
and  decay  of  structure." 

^  A  fate  overtook  the  theories  and 
writings  of  Quetelet  and  Buckle 
similar  to  that  which  I  had  occasion 
to  notice  above  in  referring  to  the 
great  work  of  A.  von  Humboldt. 
Through  the  influence  of  the  evolu- 
tionist movement,  prepared  by 
Lamarck,  von  Baer,  Spencer,  and 
others,  centring  in  Darwin,  the 
statical  or  morphological  view  had 
in  every  department  of  science  to 
give  way  to  the  kinetic  or  genetic 
view.  This  explains  why  some 
names,  once  celebrated,  like  Hum- 
boldt and  Buckle,  sank  rajiidly 
into  oblivion.  Grant  Allen,  in 
his  somewhat  one-sided  but  spirited 
monograph  on  Darwin  ('  English 
Worthies,'  1888),  ha.s  drawn  atten- 
tion to  this.  I  give  here  the 
striking  ))assage,  reserving  for  the 
sequel  of  this  work  the  liberty  to 
differ  in  detail  from  much  in  it 
that  is  too  drastically  expressed  : 
"There  is  no  dej)artment  of  human 


608 


SCIENTIFIC   THOUGHT. 


36. 
Darwin. 


publication  of  the  '  Origin  of  Species  '  that  the  phenomena 
of  variation — i.e.,  of  deviation  from  the  existing  type 
or  average — forced  themselves  upon  naturalists  and 
statisticians  as  requiring  to  be  specially  observed,  de- 
scribed, and  accounted  for.  Since  that  time  a  new 
branch  of  science  has  sprung  up,  unknown  before  even 
by  name — the  study  of  variation  in  nature.  This,  as  we 
have  seen  in  a  former  chapter,  is  one  of  the  great  and 
important  aspects  of  nature  brought  prominently  before 
the  thinking  naturalist  by  Darwin's  and  Wallace's  dis- 
coveries, and  strongly  urged  forward  by  the  independent 
arguments  of  Mr  Herbert  Spencer.  It  involves  the 
great  problems  of  Inheritance  and  Adaptation.  What 
are  the  facts,  and  what  the  causes  of  variation,  of  the 
moving  and  propelling  principle  in  natural  selection  and 
evolution  ?  The  latter  is  a  physiological  problem — the 
former  is  one  of  statistics. 


thought  or  human  action  which 
evolutionism  leaves  exactly  where 
it  stood  before  the  advent  of  the 
Darwinian  conception.  In  nothing 
is  this  fact  more  conspicuously  seen 
than  in  the  immediate  obsolescence 
(so  to  speak)  of  all  the  statical 
pre-Darwinian  philosophies  which 
ignored  development,  as  soon  as 
ever  the  new  progressive  evolu- 
tionary theories  had  fairly  burst 
upon  an  astonished  world.  Dog- 
matic Comte  was  left  forthwith  to 
his  little  band  of  devoted  adherents  ; 
shadowy  Hegel  was  relegated  with 
a  bow  to  the  cool  shades  of  the 
common-rooms  of  Oxford  ;  Buckle 
was  exploded  like  an  inflated  wind- 
bag ;  even  Mill  himself, — magnum 
et  venerabile  nomen, — with  all  his 
mighty  steam  -  hammer  force  of 
logical  directness,  was  felt  instinct- 
ively to  be  lacking  in  full  appreci- 


ation of  the  dynamic  and  kinetic 
element  in  universal  nature. 
Spencer  and  Hartmann,  Haeckel 
and  Clifford,  had  the  field  to  them- 
selves for  the  establishment  of  their 
essentially  evolutionary  systems. 
Great  thinkers  of  the  elder  genera- 
tion, like  Bain  and  Lyell,  felt  bound 
to  remodel  their  earlier  conceptions 
by  the  light  of  the  new  Darwinian 
hypotheses.  Those  who  failed  by 
congenital  constitution  to  do  so, 
like  Carlyle  and  Carpenter,  were, 
philosophically  speaking,  left  hope- 
lessly behind  and  utterly  extin- 
guished. Those  who  only  half 
succeeded  in  thus  reading  them- 
selves into  the  new  ideas,  like 
Lewes  and  Max  Muller,  lost  gi-ound 
immediately  before  the  eager  on- 
slaught of  their  younger  com- 
petitors"  {loc.  cit.,  p.   197). 


ON    THE    STATISTICAL    VIKW    OF    XATURp].       609 

The  first  who  seems  to  have  fully  grasped  the  Dar- 
winian problem  from  this  point  of  view  is  Mr  Francis 
Galton/  who  in  a  series  of  papers,  and  notably  in  his  37. 
well-known  works  on  'Hereditary  Genius '  (1869)  and 
on  '  Inheritance'  (1889),  made  a  beginning  in  the  statis- 
tical treatment  of  the  phenomena  of  Variation.  The 
novel  point  of  view  which  was  thus  introduced  into 
natural  science  was  perhaps  somewhat  obscured  by  its 
immediate  application  to  a  most  ditticult  and  unic^ue 
problem,  which  can  hardly  be  discussed  without  im- 
porting what  may  be  called  a  sentimental  bias.  This 
was  the  question  of  the  connection  through  descent 
of  those  rare  occurrences  in  human  nature  which  we 
term  genius.  Mental  phenomena  had  been  almost 
entirely  passed  over^  by  Darwin.  The  residts  which 
Mr  Galton  arrives  at,  so  far  as  the  phenomena  of  genius 
are  concerned,  are  of  minor  importance  compared  with 
the  general  methods  which  he  introduced  or  suggested 
for  dealing  with  statistics  of  heredity.  In  these  he 
combined    the   ideas    of    Quetelet  with    that   remarkable 


^  Mr  Francis  Galton  (born  1822,  genius,"       which       was      "usually 

a    grandson    of    Erasmus    Darwin)  scouted."     He  rightly    claims   "to 

had,     like    his    celebrated    cousin,  be  the  first  to  treat  the  subject  in 
begun     his     career    as    a    medical    |    a  statistical    manner,   to   arrive    at 

student,  and   then  become  a   well-  numerical  results,  and  to  introduce 

known      traveller      and      explorer.  the    'law    of    deviation    from     an 

Subsecjuently    he    devoted    himself  average  '       into      discussions       on 
to    meteorology,    where    he    drew 
attention     to    the    e.Kistence     and 
theory  of  anticyclones.      His  first 


heredity"  (Preface  to  'Hereditary 
Genius,'  published  one  j-ear  after 
Darwin's  great  work  in  which  was 

publication,  referring  not  to  physi-       jiut    forward    the     hypothesis     of 

eal    Vjut    to    human    statistics,    ap-    •    Pangenesis). 

peared   in    '  Macmillan's  Magazine  '  -  As  stated  by   Darwin   himself. 

in    186.'),     in     the    shape     of    two       See    'Animals    and    Plants    under 

articles     on     "Hereditary     Talent       Domestication'    (1868),    vol.    ii.    p. 

and    Character."      Here    he  intro-       353. 

duced    the    "  theory    of    hereditary 

VOL.   II.  2   Q 


610 


SCIENTIFIC    THOUGHT. 


38. 
"Pan- 
genesiB.' 


speculation  of  Darwin's  which  he  put  forward  at  the 
end  of  his  work  on  '  The  Variation  of  Animals  and 
Plants  under  Domestication'  (1868) — the  theory  of 
"  Pangenesis."  "  This  hypothesis  implies  that  the  whole 
organisation,  in  the  sense  of  every  separate  atom  or  unit, 
reproduces  itself.  Hence  ovules  and  pollen  grains,  the 
fertilised  seed  or  egg  as  well  as  buds,  include  and  consist 
of  a  multitude  of  germs  thrown  off  from  each  separate 
atom  of  the  organism."  ^  These  germs  he  calls  gem- 
mules,  and  admits  that  they  agree  to  some  extent  with 
Buffon's  organic  molecules,  only  that  neither  in  these  nor 
in  Spencer's  physiological  units  does  it  seem  clear  that 
each  "  independent  or  autonomous "  organic  unit,  say 
each  cell,  throws  off  or  contributes  its  free  gemmule  (or 
gemmules),  which  is  capable  of  reproducing  a  similar 
cell.2 

The  theory  of  Pangenesis  has  not  found  much  favour 
with  biologists.^      Por  their  purposes  it  would  be  neces- 


^  Loc.  cit.,  vol.  ii.  p.  358. 

-  "  Physiologists  agree  that  the 
whole  organism  consists  of  a  multi- 
tude of  elemental  parts,  which  are 
to  a  great  extent  independent  of 
each  other"  {loc.  cit.,  vol.  ii.  p. 
368).  Darwin  then  quotes  Claude 
Bernard  (1866)  and  Virchow  (1860) 
on  the  doctrine  of  the  "  autonomy'  " 
of  cells  :  "  I  assume  that  the  gem- 
mules  in  their  dormant  state  have 
a  mutual  affinity  for  each  other, 
leading  to  their  aggregation  either 
into  buds  or  into  the  sexual  ele- 
ments" (p.  374).  "Physiologists 
maintain,  as  we  have  seen,  that 
each  cell,  though  to  a  large  extent 
dependent  on  others,  is  likewise,  to 
a  certain  extent,  independent  or 
autonomous.  I  go  one  small  step 
farther,  and  assume  that  each  cell 


casts  off  a  free  gemmule,  which  is 
capable  of  reproducing  a  similar 
cell''  (p.  377).  "As  each  unit,  or 
group  of  similar  units  throughout 
the  bodj',  casts  off  its  gemmules, 
and  as  all  are  contained  within  the 
smallest  egg  or  seed,  and  within 
each  spermatozoon  or  pollen-grain, 
their  number  and  minuteness 
must  be  something  inconceivable  " 
(p.  378). 

^  Grant  Allen  dismisses  the 
whole  speculation  in  the  fol- 
lowing words  :  "  The  volume  on 
the  variation  of  animals  and 
plants  contained  also  Darwin's  one 
solitary  contribution  to  the  pure 
speculative  philosophy  of  life — his 
'  Provisional  Hypothesis  of  Pan- 
genesis,' by  which  he  strove  to 
account,  on  philosophical  principles, 


ON    THE    STATISTICAL    VIEW    ()F    NATURE.       611 

saiy  to  define  soinewluil  more  clearly  what  those  units 
or  gemmules  are.  This  has  accordingly  been  attempted 
in  several  other  hypotheses  put  forward  about  tlie 
same  time  or  somewhat  later;  each  thinker  having 
elaborated,  when  so  inclined,  his  own  fanciful  picture, 
following  consciously  or  unconsciously  in  the  line  of 
Spencer's  physiological  units.  We  have  in  Germany 
Niigeli's  micellar  theory,  Haeckel's  kinetic  hypothesis, 
Prof.  Weismann's  idioplasma  theory,  and  Prof.  Ptiiiger's 
theory  of  the  compound  organic  molecule.  All  these 
theories  attempt  to  bring  biological  phenomena  into 
closer  connection  with  the  firmly  established  concep- 
tions current  in  physics  and  chemistry,  where  atomism 
and  kinetics  have  been  so  successfully  used  in  analysing 
and,  to  a  smaller  extent,  in  putting  together  the  com- 
plex processes  of  nature.      Of  this  I  treated  in  former        39. 

Lends  itself 

chapters.     But  the  hypothesis  of  Darwin  is  capable  of  ^  statistical 

■■■  -^  ^  A  treatment. 

another  treatment.  Wherever  we  have  to  deal  with  a 
large,  an  immense  number  of  single  elements  or  units, 
which  in  their  totality  form  certain  phenomena,  there 

for   the   general   facts   of   physical  put   forth   expressly   to   meet  the 

and    mental    iieredity.         Not    to  self -same    difficulty.       But    while 

mince     matters,    it    was    his    one  Darwin's      hypotliesis      is      rudelj' 

conspicuous    failure,    and    is    now  materialistic,     Herbert     Sjieucer's 

pretty  universally  admitted  as  is  built  up  by  an  acute  and 
such.      Let    not   the   love   of    the    ,   subtle  analytical  perception  of  all 

biographer    deceive     us ;     Darwin  the    analogous  facts    in    universal 

was  liere  attempting  a  task  ultra  nature.      It  is  a  singular  instjince 

vires.       As    already    observed,    his  of     a    crude    and    essentially    uu- 

mind,  vast  as  it  was,  leaned  rather  pliilosophic   conception    endeavour 

to     the     concrete     than     to     the  ing    to     replace     a    finished     and 

abstract     side  :      he      lacked     the  delicate    philosophical    idea "    {loc. 

distinctively       metaphysical       and  cit.,    p.    12G).        See     also     many 

sjjeculative  twist.     Strange  to  say,  references      to     the     unfavourable 

too.   liis   abortive   theory  appeared  criticisms     of    Pangenesis    in    the 

some     years     later    than     Herbert  tliird     volume     of     the     '  Life     of 

Spencer's  magnificent  all-sided  con-  Charles  Darwin.' 
-cejition    of    '  Phymological    Units,' 


612  SCIENTIFIC   THOUGHT. 

is  room  for  the  statistical  treatment.  This  treatment 
entirely  ignores  the  definite  nature  of  the  component 
units,  and  merely  investigates  those  properties  which 
depend  upon  aggregation  in  large  numbers,  the  average 
or  mean  results,  and  the  chances  of  deviations  or  vari- 
ations. Now,  if  organic  beings  are  supposed  to  be  made 
up  of  immeasurably  large  numbers  of  units  transmitted 
to  them  by  inheritance,  and  capable  of  self -multiplication, 
they  must  be  subject  to  certain  regularities,  to  regular 
deviations  or  recurrent  changes ;  and,  under  the  influ- 
ence of  selection,  be  it  artificial  or  automatic,  to 
certain  developments  which  can  be  studied  without  a 
precise  knowledge  of  the  biological,  chemical,  or  physi- 
cal nature  of  these  units  themselves,  or  of  the  mechan- 
ism of  their  movements.  Economics,  meteorology,  the 
kinetic  theory  of  gases,  deal  in  this  way  with  complex 
phenomena,  the  exact  individual  history  of  which  they 
are  quite  incapable  of  narrating.  As  in  the  case  of  the 
kinetic  theory  of  gases  we  had  to  translate  into  statis- 
tical language  the  phenomena  of  pressure,  temperature, 
volume,  available  or  hidden  energy,  &c.,  so  in  dealing 
statistically  with  biological  phenomena,  such  as  inherit- 
ance, on  the  basis  of  the  theory  of  Pangenesis,  we  have 
to  translate  into  statistical  language  such  phenomena  as 
"  types,  sports  of  nature,  stability,  variation  and  in- 
dividuality." "  The  word  man,"  as  ]\Ir  Galton  says,^ 
"  when  rightly  understood,  becomes  a  noun  of  multitude, 
because  he  is  composed  of  millions,  perhaps  billions,  of 
cells,  each  of  which  possesses  in  some  sort  an  independ- 
ent life,  and  is  parent  of  other  cells.      He  is  a  conscious 

1  'Hereditary  Genius'  (1892),  pp.  349,  350. 


ON    THE    STATISTICAL    VIEW    OF    NATURE.       613 

whole,  formed  by  the  joint  agencies  of  ;i  host  of  what 
appear  to  us  to  be  unconscious  or  barely  conscious 
elements.  .  .  .  The  doctrine  of  Pangenesis  gives  excellent 
materials  for  mathematical  formulas,  the  constants  of 
which  might  be  supplied  through  averages  of  facts."  ^ 
Mr  Galton  does  "  not  see  any  serious  difficulty  in  the 
way  of  mathematicians  in  framing  a  compact  formula, 
based  on  the  theory  of  Pangenesis,  to  express  the  com- 
position of  organic  beings  in  terms  of  their  inherited 
and  individual  peculiarities,  and  to  give  us,  after  certain 
constants  had  been  determined,  the  means  of  foretell- 
ing the  average  distribution  of  characteristics  among  a 
large  multitude  of  offspring  whose  parentage  was 
known."  ...  In  short,  the  theory  of  Pangenesis  brings 
all  the  influences  that  bear  on  heredity  into  a  form  that 
is  appropriate  for  the  grasp  of  mathematical  analysis." 

Evidently  in  the  mind  of  Mr  Galton  the  problem  of        40. 

Problem  of 

heredity  divides  itself  into  two  distinct  problems ;  and  Heredity. 
he  has  himself  laboured  at  the  solution  of  both.  We 
may  call  the  one  the  "  historical  "  or  the  "  mechanical  " 
problem,  the  other  the  "  statistical "  problem,  following 
the  distinction  which  Maxwell  drew  when  dealing;  with 
the  kinetics  of  gases.  The  historical  problem  would 
involve  a  more  detailed  account  of  the  nature  of  those 
organic  units  which  the  theory  of  Pangenesis,  in  common 
with  other  similar  theories,  like  those  of  Buffbn  and 
Niigeli,  assumes,  and  of  the  mechanism  by  which  they 
unite  and  are  transmitted.  If  this  is  impossible,  or  at 
all  events  highly  hypothetical,  the  actual  following  up — 
by  observation    and   experiment — of   the   phenomena  of 

'  ^Hereditary  Genius'  (1892),  p.  .356.  -'  Ibia..  p.  358. 


614 


SCIENTIFIC    THOUGHT. 


variation  in  special  instances  would  at  least  allow  us  to 
accumulate  many  interesting  life-histories  of  families  of 
living  creatures,  and  might  some  day  lead  to  important 
generalisations.  Mr  Galton  has  himself  made  an 
attempt  to  modify  and  further  elaborate  the  hypothesis 
of  Pangenesis ;  ^  and  Mr  William  Bateson  has  given  us. 


^  Mr  Galton  in  1871  advanced 
certain  objections  to  the  theory 
of  Pangenesis,  based  upon  experi- 
ments made  with  the  transfusion 
of  blood,  and  tending  to  show  that 
blood  cannot  be  the  carrier  of  the 
germs  or  gemmules.  See  a  paper 
read  before  the  Royal  Society, 
March  30,  1871.  Darwin  did  not 
think  Pangenesis  had  "received  its 
deathblow,  though  from  presenting 
so  many  vulnerable  points,  its  life 
is  always  in  jeopardy "  ('  Life  of 
Darwin,' vol.  iii.  p.  195).  In  1875  Mr 
Galton  published  an  article  in  the 
'  Contemporary  Review,'  vol.  xxvii. 
p.  80,  entitled  "  A  Theory  of  Hered- 
ity," in  which  he  put  what  may  be 
termed  the  atomic  theorj^  of  life 
and  its  propagation  into  a  form  in 
which  it  might  serve  as  a  working 
formula  for  statistical  research. 
It  is  a  mistake  to  look  upon  any 
such  theory  as  a  biological, 
mechanical,  or  historical  explana- 
tion. For  statistical  purposes  only 
the  scantiest  data  need  be  borrowed 
from  biology.  There  is,  however, 
one  very  important  biological  con- 
ception which  Galton  introduced, 
which  is  not  contained  in  Darwin's 
"provisional  hypothesis, "and  which 
somewhat  later  became  celebrated 
mainly  through  the  writings  of 
Prof.  Weismann.  This  is  the  dis- 
tinction between  the  germ-plasma 
and  the  body- plasma,  the  former 
preserving  the  continuity  of  life 
and  inheritance,  whereas  the  latter 
forms  the  character  of  the  indi- 
vidual, and  is  probably  sterile.  In 
fact,  Galton,  from  a  purely  statis- 


tical point  of  view,  anticipated — as 
several  other  naturalists  did,  from 
various  other  aspects — the  theory 
of  the  differentiation  of  the  ger- 
minal from  the  personal  portions 
or  aggregates  of  life  units  in  the 
■'  stirp  "  or  sum  -  total  of  organic 
units  of  some  kind  which  are  to  be 
found  in  the  newly  fertilised  ovum. 
Prof.  J.  A.  Thomson  ('The  Science 
of  Life,'  p.  147)  gives  the  following 
succinct  statement  of  the  concep- 
tion of  "stirps":  "  Fir.st.  Only 
some  of  the  germs  within  the  stirp 
attain  development  in  the  cells  of 
the  'body.'  It  is  the  dominant 
germs  which  so  develop.  Second. 
The  residual  germs  and  their  pro- 
geny form  the  sexual  elements  or 
buds.  The  part  of  the  stirp 
developed  into  the  '  body  '  is  almost 
sterile.  .  .  .  The  continuity  is  kejit 
up  by  the  undeveloped  residual 
portion.  Third.  The  direct  descent 
is  not  between  body  and  body,  but 
between  stirp  and  stirp.  The  stirp 
of  the  child  may  be  considered  to 
have  descended  directly  from  a 
part  of  the  stirps  uf  each  of  its 
parents  ;  but  then  the  personal 
structure  of  the  child  is  no  more 
than  an  imperfect  representation  of 
his  own  stirp,  and  the  personal 
structure  of  each  of  the  parents  is 
no  more  than  an  imperfect  repre- 
sentation of  each  of  their  own 
stirps.  This  is  a  definite  expression 
of  the  notion  that  the  germinal  cells 
of  the  offspring  are  in  direct  contin- 
uity with  those  of  the  parents.  The 
antithesis  between  the  '  soma '  and 
the  chain  of  sex-cells  is  emphasised." 


ON    THE    STATISTICAL    VIEW    OF    NATURE.       G15 

in  iiis  '  Muteiiiils  for  the  Study  of  Variation,'  a  remark-        41. 

MrBateson'i 

able  specimen  of  tlie  historical  treatment  of  the  proljlem.  i''storicai 

*^  *■  treatment. 

But  the  aspect  we  are  at  present  specially  interested  in 
is  the  other  one  which,  in  the  course  of  Mr  Galton's 
studies,  has  presented  itself  to  him  with  increasing  clear- 
ness, namely,  the  bearing  which  the  general  laws  of 
averages  and  statistics  have  on  the  facts  of  inheritance. 
Thus,  in  his  second  main  contribution  to  the  suljject, 
which  appeared  in  1889,  twenty  years  after  the  earlier 
work,  the  statistical  problem  comes  out  much  more 
clearly,  and  quite  separated  from  the  mechanical  or  the 
historical  one.  The  hypothesis  of  Pangenesis  is  retained 
only  as  a  general  scheme  which  suggested  "  the  idea 
though  not  the  phrase  of  particulate  inheritance."  It 
was  felt  to  be  no  longer  necessary,  for  the  purpose  of 
the  problem,  "  to  embarrass  ourselves  with  any  details  of 
theories  of  heredity  beyond  the  fact  that  descent  either        42. 

,  1  •  I.    •  )>  1  .       1        1  "Particul- 

was  particulate  or  acted  as  11  it  were  so.  And  what  ate" descent, 
is  meant  by  "  particulate  "  {i.e.,  "  bit  by  bit ")  is  illus- 
trated in  the  following  expressive  manner : "  "  Many  of 
the  modern  buildings  in  Italy  are  historically  known  to 
have  been  built  out  of  the  pillaged  structures  of  older 
days.  Here  we  may  observe  a  column  or  a  lintel  serving 
the  same  purpose  for  a  second  time,  and  perhaps  liearing 
an  inscription  that  testifies  to  its  origin ;  while  as  to  the 
other  stones,  though  the  mason  may  have  chipped  them 
here  and  there  and  altered  their  shape  a  little,  few  if 
any  came  direct  from  the  quarry."  "  This  simile  gives  a 
rude  though  true  idea  of  the  exact  meaning  of  Particulate 
Inlicritance— namely,  that  each  piece  of  the  new  structure 

^  'Natural  Inheritance,'  p.  193.  -  Iliiil.,  p.  8. 


616  SCIENTIFIC    THOUGHT. 

is  derived  from  a  corresponding  piece  of  some  older  one, 
as  a  lintel  was  derived  from  a  lintel,  a  column  from  a 
column,  a  piece  of  wall  from  a  piece  of  wall.  .  .  .  We 
appear  to  be  severally  built  up  out  of  a  host  of  minute 
particles  of  whose  nature  we  know  nothing,  any  one  of 
which  may  be  derived  from  any  one  progenitor,  but  which 
are  usually  transmitted  in  aggregates,  considerable  groups 
being  derived  from  the  same  progenitor.  It  would  seem 
that  while  the  embryo  is  developing  itself,  the  particles 
more  or  less  qualified  for  each  new  post  wait,  as  it  were, 
in  competition  to  obtain  it.  Also  that  the  particle  that 
succeeds  must  owe  its  success  partly  to  accident  of  posi- 
tion and  partly  to  being  better  qualified  than  any  equally 
well-placed  competitor  to  gain  a  lodgment.  Thus  the 
step-by-step  development  of  the  embryo  cannot  fail  to  be 
influenced  by  an  incalculable  number  of  small  and  mostly 
unknown  circumstances."  ^ 

Now,  wherever  we  have  to  do  with  a  very  large 
number  of  unknown  elements  which  combine  to  produce 
a  result,  we  are  introduced  to  those  conditions  with 
which  the  theory  of  averages  and  probability  deals.  The 
curve  of  error  discovered  by  Laplace  and  Gauss  to 
picture  the  distribution  of  a  large  number  of  observations 
around  the  average  or  mean  position,  which  is  taken  as 
the  most  probable  or  correct  one,  conies  in  as  a  valuable 
aid,  not  in  studying  the  errors  of  natural  growth,  but  as 
the  graphical  illustration  of  the  deviations  or  variations 
which  cluster  around  what  we  call  the  normal,  or  with 
Quetelet  the  mean,  figure.  Only  the  interest  is  now 
attached  not  so   much    to   specifying   and   defining   the 

^  '  Natural  Inheritance,'  p.  9. 


ON    THE    STATISTICAL    VIEW    (JF    NATURE.        Gl7 

hommc  'n\oyen  as  to  studying  the  deviations  from  this 
ideal  standard.  "  How  little,"  says  Mr  Galton/  "  is  con- 
veyed by  the  bald  statement  that  the  average  income  of 
English  families  is  £100  a-year,  compared  with  what  we 
should  learn  if  we  were  told  how  P^nglish  incomes  were 
distributed."  A  crowd  of  data  furnish  for  the  astronomer 
the  material  out  of  which  he  has  to  choose  the  most 
probable,  the  correct  figure ;  a  crowd  of  observations 
furnish  for  the  naturalist  the  material  from  which  he 
has  to  learn  how  nature  deviates  from  her  types  and 
exhibits  variations  which  are  the  factors  of  change  and 
development.  Thus,  under  the  hands  of  Mr  Galton,  the 
Law  of  Error  becomes  a  Law  of  Distribution,  and  the 
whole  machinery  of  the  doctrine  of  probabilities,  "  excogi- 
tated for  the  use  of  astronomers  and  others  who  are 
concerned  with  extreme  accuracy  of  measurement,  and 
without  the  slightest  idea,  until  the  time  of  Quetelet,  that 
they  might  be  applicable  to  human  measures,"  become 
the  only  tools  1)y  which  an  opening  can  be  cut  through 
the  formidable  thicket  of  difficulties  that  bars  the  path  of 
those  who  pursue  '  the  science  of  man.' " 

Hence  while  most  people  regard  statistics  as  dull, 
they  become  for  the  naturalist  and  student  of  human 
nature  "  full  of  beauty  and  interest "  ;  ^  there  is  scarcely 
anything  so  apt  to  impress  the  imagination  as  the 
wonderful  form  of  cosmic  order  expressed  by  the  "  law 
of  frequency  of  error."  "It  would  have  been  per- 
sonified by  the  Greeks,  and  deified  if  they  had  known 
of  it."* 


'  'Natural  InheriUnce,'  p.  35.         :        ^  Ibid.,  p.  62. 
-  Ibid.,  pp.  55,  62.  |       *  Ibid.,  p.  66. 


618 


SCIENTIFIC    THOUGHT. 


43.  Every  mathematical   instrument,  when   applied   to   a 

Application 

of  theory  of  novel  purpose  for  which  it  was  not  originally  in- 
vented, "  derives  as  much  benefit  in  its  development 
as  it  confers  through  being  made  use  of."  Thus  Mr 
Galton's  application  of  the  theory  of  error  to  the 
facts  of  distribution  and  variation  not  only  enabled 
him  to  bring  method  and  order  into  such  questions 
raised  by  the   Darwinian    theory  ^  as  natural   selection, 


1  It  is  perhaps  premature  to 
speak  with  great  confideuce  of  the 
actual  results  which  have  been 
gained  by  this  novel  branch  of 
scientific  inquiry,  or  of  the  practical 
importance  which  these  results  may 
have  in  the  future  with  regard  to 
some  of  the  great  social  questions. 
Still,  in  a  history  of  thought  it  is 
of  importance  to  note  how,  through 
Mr  Galton's  writings,  the  problem 
of  Inheritance  has  acquired  quite 
a  new  aspect.  This  finds  expres- 
sion in  his  famous  so-called  "  law 
of  filial  regression,"  which  goes 
against  "  the  current  belief  that 
the  child  tends  to  resemble  its 
parents  "  (p.  104).  In  fact,  all 
opinions  and  theories  which  had 
been  propounded  before  Galton, 
either  popularly  or  scientifically, 
were  based  upon  a  one-sided  re- 
gard to  the  more  visible  portion  of 
the  ancestry  —  viz.,  the  parents  ; 
whereas,  if  any  general  theory  like 
that  of  "  pangenesis,"  or  of  "  stirps," 
or  of  the  "  differentiation  of  the 
germ-plasma  and  the  body-plasma" 
be  made  the  basis  of  discussion,  the 
whole  ancestral  tree  must  be  con- 
sidered to  contribute  to  the  for- 
mation of  the  characters  of  any 
individual.  In  fact,  we  have  be- 
fore us  not  one  pair,  but  an  endless 
line  of  pairs  which  are,  as  the 
terms  of  a  series,  connected  by  the 
powers  of  the  number  two  ;  and 
it    is    then    easily    seen,    without 


going  into  refinements  (which,  how- 
ever, in  the  further  elaboration  of 
the  problem,  may  become  very 
important),  that  the  first  term  of 
the  series,  which  represents  the 
parents,  contributes  only  one-half 
of  the  whole,  that  is,  each  parent 
one  quarter.  It  is  also  evident,  if 
each  parent  only  contributes  on 
the  average  one  quarter,  that  an 
exceptional  bias  in  any  direction 
communicated  by  them  would  be 
balanced  in  the  long-run  by  tlie 
opposite  action  of  the  remaining 
ancestry,  and  that,  contrary  to 
ordinary  belief,  inheritance  would 
operate  in  the  direction  of  bring- 
ing each  individual  back  to  the 
average  of  the  whole  lineage.  Mr 
Galton  first  observed  this  law  of 
regression  to  the  average  by  definite 
countings  with  seeds  and  "  a  com- 
paratively small  number  of  ob- 
servations of  human  .stature"  ;  and 
he  remarks  that  if  it  was  only  by 
these  experiments  and  observa- 
tions that  the  law  of  regression  had 
been  established,  it  could  not  have 
been  expected  that  the  truth  of 
the  apparent  paradox  would  be 
recognised.  When,  however,  tlie 
rule  was  once  expressed,  it  was 
"  easily  shown  that  we  ought  to 
expect  filial  regression,  .  .  .  two 
different  reasons  for  its  occurrence  " 
existing — "  the  one  connected  with 
our  notions  of  stability  of  type,  the 
other  as  follows  :  the  child  inherits 


ON    THE    STATISTICAL    VIEW    OF    NATURE. 


61D 


regression,  reversion  to  ancestral  types,  extinction  of 
families,  effect  of  bias  in  marriage,  mixtm-e  of  in- 
heritance, latent  elements,  and  generally  to  prepare 
the  ground  for  the  combined  labours  of  the  naturalist 
and  tlie  statistician ;  he  was  also  able  to  put  novel 
problems   to   the   mathenuitician. 

To  miderstand  this  latter  point  we  must  realise  the 


partly  from  his  parents,  partly 
from  his  ancestry.  In  every  pop- 
ulation that  intermarries  freely, 
when  the  genealogy  of  any  man  is 
traced  far  backwards,  his  ancestry 
will  be  found  to  consist  of  sucli 
varied  elements  that  they  are 
indistinguishable  from  a  sample 
taken  at  haphazard  from  the 
general  i)opulation."  As  to  the 
mathematical  problem  referred  to, 
it  was  submitted  by  Mr  Galton  in 
a  definite  form  to  Mr  J.  D.  H. 
Dickson,  whose  solution  is  given 
in  the  appendix  to  '  Natural  In- 
lieritance.'  On  this  solution  Mr 
Galton  lemarks  :  "  The  problem 
may  not  be  difficult  to  an  ac- 
complished mathematician,  but  I 
certainly  never  felt  such  a  glow 
of  loyalty  and  respect  towards  the 
sovereignty  and  v^'ide  sway  of 
mathematical  analysis  as  when  his 
answer  arrived,  conlirming,  by  i)ure 
mathematical  reasoning,  my  vari- 
ous and  laborious  statistical  con- 
clusions with  far  more  miimteness 
than  I  had  dared  to  hope,  because 
tiie  data  ran  somewhat  roughly, 
and  I  hail  to  smooth  them  with 
tender  caution.  ...  It  is  obvious 
from  this  close  accord  of  calcula- 
tion with  oVjservation,  that  the  law 
of  Error  holds  throughout  with 
sufficient  precision  to  be  of  real 
service,  and  that  the  various  results 
nf  my  statistics  are  not  casual  and 
disconnected  determinations,  but 
strictly  interdependent"  (p.  202). 
Another  passage  indicating  how 
nmch  the  inferences  from  the  law 


of  regression  run  contrary  to 
popular  opinions  on  inheritance  is 
the  following:  "The  law  of  Re- 
gression tells  heavily  against  tlie 
full  hereditary  transmission  of  any 
gift.  Only  a  few  out  of  many 
children  would  be  likely  to  differ 
from  mediocrit}'  so  widely  as  their 
mid-parent,  and  still  fewer  would 
differ  as  widely  a.s  the  more  excep- 
tional of  the  two  j)arents.  The 
more  bountifully  the  parent  is 
gifted  by  nature,  the  more  rare 
will  be  his  good  fortune  if  he  be- 
gets a  son  who  is  as  richly  endowed 
as  himself,  and  still  more  so  if  he 
has  a  son  who  is  endowed  yet  more 
largely.  But  the  law  is  even- 
handed  ;  it  levies  an  equal  succes- 
sion -  tax  on  the  transmission  of 
badness  as  of  goodness.  If  it  dis- 
courages the  extravagant  hopes  of 
a  gifted  parent  that  his  children 
will  inherit  all  his  powers,  it  no 
less  discountenances  extravagant 
fears  that  they  will  inherit  all  iiis 
weakness  and  di.sease "  (p.  106). 
Prof.  Karl  Peaison  ( '  The  Grammar 
of  Science,'  '2nd  ed.,  p.  479)  says 
of  the  law  of  ancestral  inheritance  : 
"  If  Darwinism  be  the  true  view 
of  evolution  —  i.e.,  if  we  are  to 
describe  evolution  bj'  natural  selec- 
tion coml)ined  with  heredity — then 
the  law  which  gives  us  definitely 
and  concisely  the  type  of  the  i>ff- 
spring  in  terms  of  the  ancestial 
peculiarities,  is  at  once  the  founda- 
tion-stone of  biology  and  the  basis 
upon  which  heredity  becomes  an 
exact  branch  of  .science." 


620  SCIENTIFIC    THOUGHT. 

44.        great   difference   which   exists    between    dealing   with   a 

Difference  in  «      t     •  •  mi 

application    yast    number    of    lifeless    and    of    living    units.       This 

to  living  and 

unllr^  difference  becomes  evident  if  we  consider  that  in  the 
former  case  the  number  of  units  is  unalterable  and 
the  units  are  indestructible ;  in  the  latter  the  elements 
or  units  are  subject  to  enormous  increase  and  corre- 
sponding destruction,  generally  with  a  preponderance  of 
the  first.  In  the  kinetic  theory  of  gases  we  have  to 
consider,  in  every  finite  system,  the  conservation  or 
persistence  of  mass  and  motion,  the  two  units  we 
deal  with.  To  these  two  properties  of  an  immensely 
large  crowd  we  have  to  reduce  the  various  phenomena 
of  pressure,  temperature,  volume,  available  or  unavail- 
able energy.  In  the  vast  crowTl  of  gemmules  which 
build  up  a  new  organism  or  regenerate  an  existing 
one,  we  have  to  deal  with  a  continual  influx  or 
creation  of  new  units  and  a  continual  extinction  and 
ejection  of  old  or  dead  ones.  Without  venturing  on 
any  theory  as  to  how  this  state  of  things  has  come 
about,  we  may  see  that  the  mathematics  and  statistics 
of  such  crowds  must  be  different  from  those  referrino- 
to  stable,  lifeless  assemblages.  The  twofold  task 
arises  of  formulating  the  new  problems  and  solving 
them.  To  the  extent  that  this  is  possible  we  shall 
be  able  to  deal  mathematically  with  the  great  prob- 
lem of  variability ;  and  for  the  practical  application  of 
these  mathematical  formuhe  we  shall  have  to  collect 
long  series  of  facts  and  data  of  measurements — the 
material  which  has  to  be  statistically  arranged  and 
sifted,  and  which  is  to  confirm  the  conclusions  and 
test    the    results    which    calculation    has    brought    out. 


ON    THE    STATISTICAL    VIEW    OF    NATURE. 


G21 


Mr  Galton  found  ready,  or  instituted  himself,  vari- 
ous countings  of  large  numbers,  which  formed  valuable 
material  for  his  mathematical  schemes,  and  wliich 
confirmed  them  in  a  surprising  degree.  Some  very 
elaborate  series  (if  measurements  of  the  varying  dimen- 
sions of  individual  members  in  large  crowds  of  animals 
were  published  by  Prof.  Weldon,  whose  monograph  on 
Crabs  will  always  remain  an  historical  document.^  It 
was  noticed  about  the  same  time  that  the  attempt  to 
bring  the  measured  deviations  from  the  average  into 
a  symmetrical  arrangement  on  the  sides  of  more  or 
less  was  impossible,  and  the  fact  had  to  be  realised 
and  mathematically  expressed  that  special  influences 
tending  towards  change  on  the  intermixing  of  different 
varieties  produced  an  asymmetrical  distribution  or  fre- 
quency : "  in  fact,  nature  works  with  loaded  dice,  pro- 
ducing a  bias  in  certain  directions;  this  is  the  favour 
which,  according  to  Darwin,  Wallace,  and  Lamarck's 
ideas,  must  meet  the  better  fitted  individuals  and 
exact  from  them  a  smaller  tribute  in  the  inevitable 
process  of  destruction  and  removal. 

We  owe  it  to  f'rof.  Karl  Pearson  to  have  first  grasped        45. 

Prof.  Pe.ir- 

clearly  and   comprehensively   the  mathematical  problem  son.   The 
involved,  and   to  have  solved  it  in  a  manner  useful  for  ^^^  problem. 


^  See  the  '  Proceedings  of  the 
Royal  Society  '  since  1890,  notably 
vol.  Ivii.,  1895,  p.  360  sr/r^. 

•  "  An  a.syrametrical  frequency 
curve  may  arise  from  two  (|uite 
distinct  cla.sses  of  causes.  In  the 
fir.st  place  the  material  mea.sured 
may  be  heterogeneous,  and  may 
consist  of  a  mi.xturc  of  two  or 
more  homogeneous  materials.  .  .  . 


The  second  class  of  frequency 
curves  arises  in  the  case  of  homo- 
geneous material  when  the  tend- 
ency to  deviation  t)n  one  side  of 
the  mean  is  unequal  to  the  tend- 
ency to  deviation  on  the  other 
side"'  (Karl  Pearson,  "On  tlie  Ma- 
tlieuiatical  Theory  of  Evolution," 
'Trans.  Hoy.  Soc.,'  1895,  p.  344). 


622 


SCIENTIFIC   THOUGHT. 


biological  research.^  He  has  thus  put  into  the  hands  of 
naturalists  an  instrument  wherewith  to  describe  graphi- 
cally  the  observed   facts   of   variation  and  other  allied 


^  A  considerable  literature  has 
already  accumulated  iu  this  novel 
branch  of  exact  inquiry.  The 
complete  list  of  it  is  given  in  a 
pamphlet  by  Georg  Duncker,  en- 
titled 'Die  Methode  der  Variations- 
statistik'  (Leipzig,  1899).  From 
this  list  (p.  60)  it  will  be  seen  that 
one  of  the  earliest  workers  in  the 
field  of  biological  statistics  was 
the  botanist  F.  Ludwig,  whose 
'  Abschnitte  der  Mathematischen 
Botanik '  have  appeared  in  various 
periodicals  abroad  since  the  year 
1883.  The  philosopher,  however, 
to  whom  we  are  most  indebted  for 
the  mathematical  foundations  of  the 
whole  theory,  is,  as  noted  above. 
Prof.  Karl  Pearson,  whose  "  Con- 
tributions to  the  Mathematical 
Theory  of  Evolution "  have  been 
appearing  since  the  year  1893  in 
the  Trans,  of  the  Royal  Society. 
Very  helpful  abstracts  of  these 
contributions,  covering  a  large 
field  of  mathematical  theory,  and 
containing  elaborate  discussions  of 
many  of  the  terms  recently  in- 
troduced into  biological  science, 
such  as  regression,  reversion,  in- 
heritance, panmixia,  selection,  &c. , 
will  be  found  in  the  Proceedings  of 
the  Royal  Society  (1893,  onwards). 
Also  in  his  collected  essays,  'The 
Chances  of  Death  and  other  Studies 
in  Evolution  '  (2  vols.,  1897);  and, 
lastly,  iu  the  later  chapters  of  the 
second  edition  of  his  '  Grammar  of 
Science'  (1890).  From  the  latter  it 
will  be  seen  what  far-reaching  infer- 
ences may  eventually  be  drawn 
from  the  quantitative  treatment 
and  mathematical  discussion  of 
biological  data  ;  notably  the  results 
so  far  gained  "lead  us  to  consider 
variation  as  a  permanent  attribute 
of  living  forms,  which  can  hardly 


have  been  substantially  modified 
since  the  beginnings  of  life.  In  the 
same  manner  we  find  heredity  in- 
timately associated  with  variation 
in  the  individual,  and  not  differing 
very  substantially  as  we  pass  from 
one  character  to  a  second,  or  from 
one  to  another  form  of  life.  We 
conclude  that  variation  and  inherit- 
ance rather  precede  than  follow 
evolution  ;  they  are,  at  present,  one 
fundamental  mystery  of  the  vital 
unit"  (p.  502).  Prof.  Pearson, 
whose  training  was  that  of  a 
mathematician  and  a  lawyer,  ap- 
proached the  problems  of  Ijiology 
from  the  exact  point  of  view,  and 
it  is  interesting  to  see  how,  in  many 
ways,  he  comes  to  results  similar  to 
those  arrived  at  by  one  of  the  other 
great  representatives  of  modern 
biological  research,  Mr  Wm.  Bate- 
son.  See  his  '  Materials  for  the 
Study  of  Variation,  treated  with 
especial  regard  to  the  discontinuity 
in  the  Origin  of  Species  '  (1894).  If 
I  understand  him  rightly,  his  re- 
searches have  led  him  to  the  con- 
clusion that  variation  cannot  be 
the  work  of  natural  selection,  since 
he  lias  given  "  such  evidence  as  to 
certain  selected  forms  of  varia- 
tions "  as  to  afford  "  a  presumption 
that  the  discontinuity  of  which 
species  is  an  expression  has  its 
origin,  not  in  the  environment,  nor 
in  any  phenomenon  of  adaptation, 
but  in  the  intrinsic  nature  of 
organisms  themselves,  manifested 
in  the  original  discontinuity  of 
variations"  (p.  567).  This  "dis- 
poses, once  and  for  all,  of  the 
attempt  to  interpret  all  perfection 
and  definiteness  of  form  as  the 
work  of  selection.  ...  It  suggests, 
in  brief,  that  the  discontinuity  of 
species  results  from  the  discontinu- 


ON    THE    STATISTICAL    VIEW    OF    NATURE, 


G23 


phenomena,  such  as  correlation,  heredity,  regression  and 
panmixia,  and  he  has  shown  how  to  analyse  tliese  graphi- 
cal tracings  so  as  to  indicate  the  several  possible  elements 
out  of  which  they  are  compounded,  representing  separate 
agencies  which  are  at  work  in  nature.  The  mathemati- 
cal inventions  of  Fourier  had  similarly  enabled  physicists 
to  analyse  the  complicated  periodicity  of  tidal  curves 
into  their  elements,  and,  under  the  hands  of  Ohm  and 
Helmholtz,  to  resolve  the  harmonies  of  music. 

We  have  here  arrived  at  the  last  stage  of  the  devel- 
opment of  tlie  statistical  view  of  nature.  It  has  been 
variously  judged  l)y  biologists  according  to  the  special 
views  they  take  of   their  problems,  and  also  according 


ity  of  variation  "  (p.  568).  Mr  Bate- 
son  expects  great  assistance  from 
the  statistical  methods.  '"There 
is,"  lie  says,  "no  common  shell  or 
butterfly  of  whose  variations  some- 
thing would  not  be  learnt,  were 
some  hundreds  of  the  same  species 
collected  from  a  few  places  and 
statistically  examined  in  respect  of 
some  varying  character.  Any  one 
can  take  part  in  this  class  of  work, 
though  few  do"  (p.  574).  Not- 
withstanding the  general  resem- 
blance noted  above  between  the 
ideas  of  ^Ir  Bateson  and  of  Prof. 
Pearson,  they  differ  so  much  in 
detail  as  to  be  led  to  confess 
that  they  do  not  understand  one 
another's  languages.  Cf.  W.  Bate- 
son, "  Heredity,  Differentiation,  and 
other  Concei)tions  of  Biology," 
'Roy.  Soc.  Proc.,'  vol.  Ixix.  pp. 
193-205;  K.  Pearson,  "On  the 
Fundamental  Conceptions  of  Biol- 
ogy," '  Biometrika,'  vol.  i.  pp.  320- 
344.  Prof.  Pearson's  view  is  that, 
for  the  working  out  of  the  theoiy 
of  evolution,  "  biological  conceptions 
can  be  accurately  dethied,  and  so 
defined    measured    with    quantita- 


tive exactness"  {loc.  cit.,  p.  324). 
Mr  Bateson,  on  the  other  hand, 
regards  them  as  to  some  extent 
out  of  the  reach  of  mathematical 
definition  and  measurement.  "Dis- 
continuous variation"  in  Mr  Bate- 
son's  special  sense — by  which  we 
niaj-  perhaps  understand  great  as 
distinguished  from  small  but  num- 
erous deviations  from  the  average 
— Prof.  Pearson  regards  as  "statis- 
tically negligible  for  the  purpose 
of  vital  statistics"  (pp.  33-3,  334). 
He,  in  fact,  holds  closer  to  Dar- 
winism as  understood  by  Darwin, 
who  never  looked  with  much 
favour  on  Huxle\'"s  view,  for  ex- 
ample, that  "sports,"  as  distin- 
guished from  the  sum  of  small 
differences  in  individuals,  might 
furnish  an  ap[)reciable  part  of  the 
materials  for  natural  selection. 
Mr  Bateson's  view  found  favour 
with  Huxley,  as  may  be  observett 
in  the  '  Life  and  Letters.'  On  the 
novelty  and  value  of  Prof.  Pearson's 
methods,  see  ealso  the  Address  by 
Prof.  Weldon  to  the  Zoological 
Section  of  tiie  British  A.s.sociation 
in  1898. 


624  SCIENTIFIC    THOUGHT. 

to  the  degree  in  which  they  appreciate  and  are  able  to 
grasp  mathematical  methods.  The  subject  is  still  under 
discussion,  and  will  belong  to  the  History  of  Thought  of 
a  coming  age.  It  is  enough  to  have  indicated  the  latest 
lines  of  reasoning  which  our  century  has  marked  out, 
and  to  notice  how  they  form  a  new  and  remarkable 
instance  of  the  growth  and  diffusion  of  the  exact  or 
mathematical  spirit  in  a  department  of  research  hitherto 
almost  untouched  by  it,  prepared  though  it  has  been  for 
such  treatment  by  one  among  whose  great  endowments 
a  grasp  of  mathematical  reasoning  hardly  formed  a  dis- 
tinctive feature.  In  former  chapters  I  have  had  occasion 
to  show  how  Charles  Darwin  introduced  into  the  science 
of  nature  two  novel  points  of  view — the  genetic  view 
and  the  process  of  judicial  sifting  of  evidence.  We  may 
now  add  that  he  has  indirectly,  more  than  directly, 
furthered  quite  as  much  the  statistical  view  of  natural 
phenomena  through  which  we  have  learned  to  find  and 
trace  law  and  order  in  great  realms  of  phenomena  and 
events  usually  supposed  to  be  governed  by  what  is 
termed  blind  chance.  The  study  of  this  blind  chance 
in  theory  and  practice  is  one  of  the  greatest  scientific 
performances  of  the  nineteenth  century. 
46.  But  whilst  acknowledging  the  great  importance  which 

statistical  ...  p       ^  •       i     • 

knowledge     tlic  Statistical  treatment  of  phenomena  has  acquired  in 

one-sided. 

our  age,  and  the  value  of  the  statistical  view  of  many 
large  departments  of  natural  processes  which  escape 
almost  every  other  mode  of  dealing  with  them,  we 
must  not  forget  that  it  is  essentially  one-sided. 

Clerk-Maxwell  has  suggestively  opposed  it  alike  to  the 
mechanical  and  the  historical  views,  of  which  the  former 


ON    THE    STATISTICAL    VIEW    OF    NATURE.       025 

tries  to  describe  the  general  mechanism  u/uler  which, 
the  hitter  the  indiviihuil  steps  and  incidents  hj/  whicli, 
special  events  or  phenomena  proceed  and  are  character- 
ised. Pearlier  chapters  of  this  narrative  attempted  to 
give  an  account  of  the  former,  whilst  the  essentially 
historical  treatment  belongs  to  another  portion  of  the 
work.  The  word  history  has  generally  been  reserved  for 
records  which  deal  with  those  events  in  which  human 
consciousness  has  played  a  large,  if  not  an  overwhelming, 
part,  and  has  been  able  to  assist  the  observer  by  its  own 
accounts  and  representations.  What  should  we  know  of 
Iniman  life  and  himian  interests  without  them,  and  how 
helpless— in  spite  of  minutest  observation — do  we  still 
appear  to  be  in  understanding  the  life  of  the  brute 
and  mute  creation,  even  of  the  domestic  animals,  our 
daily  friends  and  companions  ?  But  if  history,  as  opposed 
to  statistics,  really  seems  only  possible  where  the  living 
voice  or  the  surviving  narrative  of  those  who  have  de- 
parted helps  us  to  a  true  understanding  of  its  incidents 
and  its  meaning,  it  also  imposes  upon  us  the  task  of  sift- 
ing its  value  and  trustworthiness  critically.  Mathe- 
matics, logic,  and  statistics  may  do  something  to  exclude 
the  actually  impossible  or  the  highly  improbable  from 
a  vast  mass  of  material;  but  more  delicate  criteria  are 
requireil  in  dealing  with  the  accumulated  testimony  of 
bygone  ages.  With  an  unerring  instinct  of  what,  in 
addition  to  mathematical  measurements,  may  be  required 
in  order  to  accomplish  this  task,  the  nineteenth  century 
has  not  only  nursed  the  scientific  spirit  and  cultivated 
its  methods,  but  with  equal  diligence  and  originality 
those  other  methods  which  lie  at  the  foundation  of 
VOL.  II.  1'  i: 


626 


SCIENTIFIC   THOUGHT. 


47. 
Critical 
methods. 


philosophical 


thought 


the    methods     of 


48. 
The  instru- 
ment of 
exact  re- 
search. 


all    recent 
criticism. 

And  yet,  before  taking  leave  of  science  and  entering 
on  a  comprehensive  appreciation  of  the  workings  of 
the  Critical  Spirit  with  which  all  our  thought  seems 
to  be  permeated,  I  owe  to  my  readers  the  attempt 
to  answer  one  remaining  question.  If  it  be  true, 
as  the  foregoing  narrative  has  abundantly  insisted, 
that  through  the  increasing  application  of  mathematical 
methods  of  measuring  and  calculating,  our  thought  has 
become  truly  scientific  and  our  knowledge  accurate  and 
useful  for  describing  and  predicting  phenomena,  as  also 
for  manifold  practical  applications,  we  may  be  curious  to 
know  whether  the  refined  instrument,  mathematical 
thought  itself,  has  been  subject  to  such  change  and 
development  as  has  been  undergone  by  the  various 
branches  of  science  to  which  it  has  been  applied.  In 
fact,  we  have  to  ask  the  question,  How  has  mathe- 
matical thought  itself  fared  in  the  course  of  the  nine- 
teenth century  ?  The  concluding  chapter  of  the  present 
volume  will  try  to  give  a  reply  to  this  question. 


62' 


CHAPTER    XIII. 

ON  THE  DEVELOPMENT   OF    MATHEMATICAL   THOUGHT  DURING 
THE  NINETEENTH   CENTURY. 

In  venturino;  upon  the  last  and  most  abstract  portion  of        i. 

^      ^  ^  History  of 

the  great  domain  of  Scientific  Thought  of  the  century,  it  thought. 
may  be  well  to  remind  the  reader  that  it  is  not  a  history 
of  science  but  a  history  of  tliought  that  I  am  writing. 
When  dealing  in  the  foregoing  chapters  with  mani- 
fold discoveries,  drawn  promiscuously  from  the  various 
natural  sciences,  I  have  done  so  only  to  show  how  the 
scientific  mind  has,  in  the  course  of  the  period,  come 
to  regard  the  things  of  nature  from  dillerent  points  of 
view,  and  to  think  and  reason  on  them  differently. 
Such  changes  have  frequently  been  l)roug]it  about  by 
the  discovery  of  novel  facts,  but  this  alone  has  not 
generally  sufficed  to  mark  also  a  cliange  in  the  manner 
of  reasoning  on  and  thinking  about  them.  The  increase 
in  the  number  of  natural  species,  of  the  chemical  ele- 
ments or  of  the  smaller  planets,  luis  not  necessarily 
made  us  think  differently  about  tliese  things  in  them- 
selves :  tlie  theory  and  point  of  view  may  change  without 
any  change  in  the  oliject  towards  which  they  are  directed, 


628 


SCIENTIFIC    THOUGHT. 


for  they  mark  more  the  attitude  of  the  beholder  than 
the  things  which  he  regards.  It  is  true  that  a  very 
small  addition  to  our  actual  knowledge  of  facts,  like  the 
sudden  appearance  of  some  characteristic  feature  in  a 
landscape,  may  sometimes  entirely  alter  the  whole  aspect, 
induce  us  to  abandon  our  accustomed  views,  and  call  up 
suddenly  an  unforeseen  train  of  ideas ;  in  such  a  case, 
perhaps,  this  insignificant  discovery  becomes  historically 
interesting,  although  it  is  mainly  by  the  altered  trains 
of  thought  which  it  has  evoked  that  it  has  become 
important  to  us. 
2.  The   difference  of   scientific   knowledge  and  scientific 

Difference 

between       thought  is   thus   owiug   to   the   two   factors   which   are 

thought  and  »  O 

knowledge,  involvcd— the  facts  of  science  or  nature  on  the  one  side 
and  the  scientifically  thinking  mind  on  the  other.  Xow 
it  might  appear  as  if  this  difference  vanished  when  we 
approach  the  abstract  science  of  mathematics,  or  at  least 
that  of  number ;  for  in  numbering  and  counting  we 
have  really  only  to  do  with  a  process  of  thought,  and  it 
would  seem  as  if  the  science  of  number  were  itself  the 
science  of  thought,  or  at  least  a  portion  of  it.  In  fact, 
the  question  arises,  Is  there  any  difference  between 
mathematical  science  and  mathematical  thought  ?  Some 
considerations  might  induce  us  to  think  that  there  is 
not.  On  the  other  side,  I  shall  try  to  show  in  this 
chapter  that  there  is,  and  that  the  development  of 
mathematics  during  our  period  has  brought  this  out 
very  clearly  and  prominently. 
Popular  There   is   an    opinion  current  among  many  thinking 

re^rding*     pcrsous  who  have  not  occupied  themselves  with  mathe- 

mathe-  ^    . 

matics.        matical  science,  though   they  may   be  very  efficient  in 


DEVELOPMENT    OF    MATHEMATICAL    THOUGHT.        629 

calculating  and  measuring,  that  tlieie  is  really  nothing 
new  in  niatheniatics,  that  two  and  two  always  make 
four,  that  the  sum  of  the  angles  in  a  triangle  always 
make  two  right  angles,  and  that  all  progress  in  mathe- 
matics is  merely  a  question  of  intricacy,  a  never-ending 
process  of  increased  complication  liy  whicli  you  can 
puzzle  even  the  cleverest  calculator.  To  them  the  his- 
tory of  mathematics  would  Ije  something  analogous  to 
the  history  of  games  like  whist  or  chess,  the  resources  and 
complications  of  which  seem  to  be  inexhaustible.  So  they 
think  ^  that  the  intricacies  and  refinements  of  elementary 
and  higher  mathematics  will  supply  endless  material  for 
training  the  minds  of  schoolboys  or  trying  the  ingenuity 


'  "Some  people  have  been  found 
to  regard  all  niatheniatics,  after  the 
47th  proposition  of  Euclid,  as  a 
sort  of  morbid  secretion,  to  be 
compared  only  with  the  pearl  said 
to  be  generated  in  the  diseased 
oj'sler,  or,  as  I  ha%'e  heard  it  de- 
scribed, '  une  excroissance  maladive 
de  I'esprit  humain.'  Others  find 
its  justification,  its  raison  d'etre,  in 
its  being  either  the  torch-bearer 
leading  the  way,  or  the  handmaiden 
liolding  up  the  train  of  Physical 
Science  ;  and  a  very  clever  writer 
in  a  recent  magazine  article  ex- 
presses his  doubts  whether  it  is,  in 
itself,  a  more  serious  i)ursuit,  or 
more  worthy  of  interesting  an  in- 
tellectual human  being,  than  the 
study  of  chess  problems  or  Chinese 
puzzles.  What  is  it  to  us,  they 
say,  if  the  three  angles  of  a  triangle 
are  equal  to  two  right  angles,  or  if 
every  even  number  is,  or  may  be, 
the  sum  of  two  i)rimes,  or  if  every 
equation  of  an  odd  degree  nmst 
have  a  real  root  ?  How  dull,  stale, 
Hat,  and  unprotitable  are  such  and 
such  like  announcements  !  Much 
more  interesting  to  read  an  account 


of  a  marriage  in  high  life,  or  the 
details  of  an  international  boat- 
race.  But  this  is  like  judging  of 
architecture  from  being  shown  some 
bricks  and  mortar,  or  even  a  quar- 
ried stone  of  a  public  building,  or  of 
painting  from  the  colours  mixed  on 
the  palette,  or  of  music  by  listening 
to  tl.e  thin  and  screech  sounds  pro- 
duced by  a  bow  passed  haphazard 
over  the  strings  of  a  violin.  The 
world  of  ideas  which  it  discloses  or 
illuminates,  the  contemplation  of 
divine  beauty  and  order  which  it 
induces,  the  harmonious  connexion 
of  its  j)arts,  the  infinite  hierarchy 
and  absolute  evi<lence  of  the  truths 
with  which  it  is  concerned,  these, 
and  such  like,  are  the  surest  grounds 
of  the  title  of  mathematics  to 
human  regard,  and  would  remain 
unimpeached  and  unimpaired  wore 
the  plan  of  the  universe  unrolled 
like  a  map  at  our  feet,  and  the 
mind  of  man  qualified  to  take  in 
the  whole  scheme  of  creation  at  a 
glance"  (Prof.  J.  J.  Sylvester, 
Add  less  before  Brit.  Assoc,  see 
'Report,'  1869,  p.  7). 


630 


SCIENTIFIC   THOUGHT. 


4. 
Use  of 
mathe- 
matics. 


of  senate-house  examiners  and  examinees,  without  for  a 
moment  considering  the  question  whether  mathematical 
thought  as  distinguished  from  mathematical  problems  is 
capable  of  and  has  undergone  any  radical  and  funda- 
mental change  or  development. 

Closely  aUied  with  this  is  the  further  question  as  to 
the  use  of  mathematics.  Two  extreme  views  have  always 
existed  on  this  point.^  To  some,  mathematics  is  only  a 
measuring  and  calculating  instrument,^  and  their  interest 


^  Of  the  two  greatest  mathemati- 
ciaus  of  modern  times,  Newton  and 
Gauss,  the  former  can  be  considered 
as  a  representative  of  the  first,  the 
latter  of  the  second  class ;  neither  of 
them  was  exclusively  so,  and  New- 
ton's inventions  in  the  pure  science 
of  mathematics  were  probably  equal 
to  Gauss's  work  in  applied  mathe- 
matics. Newton's  reluctance  to 
publish  the  method  of  fluxions  in- 
vented and  used  by  him  may  per- 
haps be  attributed  to  the  fact  that 
he  was  not  satisfied  with  the  logical 
foundations  of  the  calculus ;  and 
Gauss  is  known  to  have  abandoned 
his  electro-dynamic  speculations,  as 
he  could  not  find  a  satisfactory 
physical  basis  (see  stipra,  p.  67). 
Others  who  were  not  troubled  by 
similar  logical  or  practical  scruples 
stepped  in  and  did  the  work,  to  the 
great  benefit  of  scientific  progress. 
Newton's  greatest  work,  the  '  Prin- 
cipia,'  laid  the  foundation  of  mathe- 
matical physics  ;  Gauss's  greatest 
work,  the  '  Disquisitiones  Arith- 
meticfo,'  that  of  higher  arithmetic 
as  distinguished  from  algebra. 
Both  works,  written  in  the  syn- 
thetic style  of  the  ancients,  are 
difficult,  if  not  deterrent,  in  their 
form,  neither  of  them  leading  the 
reader  by  easy  steps  to  the 
results.  It  took  twenty  or  more 
years  before  either  of  these  works 
received  due  recognition  ;    neither 


found  favour  at  once  before  that 
great  tribunal  of  mathematical 
thought,  the  Paris  Academj-  of 
Sciences.  Newton's  early  reputa- 
tion was  established  by  other 
researches  and  inventions,  notably 
in  optics  ;  Gauss  became  known 
through  his  theoretical  rediscovery 
of  Ceres,  the  first  of  the  minor 
planets  (see  above,  vol.  i.  p.  182). 
The  country  of  Newton  is  still  pre- 
eminent for  its  culture  of  mathe- 
matical physics,  that  of  Gauss  for 
the  most  abstract  work  in  mathe- 
matics. Not  to  speak  of  living 
authorities,  I  need  only  mention 
Stokes  and  Clerk-Maxwell  on  the 
one  side,  Grassmann,  Weierstrass, 
and  Georg  Cantor  on  the  other. 

^  Huxley  said  :  "  Mathematics 
may  be  compared  to  a  mill  of 
exquisite  workmanship  which  grinds 
you  stuff  of  any  degree  of  fineness  : 
but,  nevertheless,  what  you  get  out 
depends  on  what  you  put  in  ;  and 
as  the  grandest  mill  in  the  world 
will  not  extract  wheat-flour  from 
peas-cods,  so  pages  of  formulaj  will 
not  get  a  definite  result  out  of 
loose  data  "  ;  and  on  another  occa- 
sion he  said  that  mathematics  "is 
that  study  which  knows  nothing  of 
observation,  nothing  of  induction, 
nothing  of  expeiiment,  nothing  of 
causation."  The  former  statement 
was  endorsed  by  Lord  Kelvin 
('Pop.    Lectures,'    &c.,    vol.    ii.     p. 


DKVELOPMENT    OF    MATHEMATICAL    THOUGHT.       631 


ceases  as  soon  as  discussions  arise  which  cannot  benefit 
those  who  use  the  instrument  for  the  purposes  of 
application  in  mechanics,  astronomy,  physics,  statistics, 
and  other  sciences.  At  the  other  extreme  we  have 
those  who  are  animated  exclusively  by  the  love  of  pure 
science.  To  them  pure  mathematics,  with  the  theory  of 
numbers  ^  at  the  head,  is  the  one  real  and  genuine 
science,  and  the  applications  have  only  an  interest  in 
so  far  as  they  contain  or  suggest  problems  in  pure 
mathematics.  They  are  mainly  occupied  wiLli  examin- 
ing and  strengthening  the  foimdations  of  mathematical 
reasoning  and  purifying  its  methods,  inventing  rigorous 
proofs,  and  testing  the  validity  and  range  of  applicability 
of  current  conceptions.  We  may  say  that  the  former 
are  led  by  practical,  the  latter  by  philosophical,  interests, 
and  these  latter  may  be  either  logical    or  ontological," 


102)  ;  the  latter  was  energetically- 
repudiated  by  Sylvester  in  his 
famous  Address  to  tiie  first  section 
of  the  British  Assoc,  at  Exeter 
(1869,  '  Report,'  &c.,  p.  1,  &c.) 

^  Gauss  considered  mathematics 
to  be  "  the  (^ueen  of  the  Sciences, 
and  arithmetic  the  (^ueen  of  Mathe- 
matics. She  frequently  conde- 
scends to  do  service  for  astronomy 
and  other  natural  sciences,  but  to 
her  belongs,  under  all  circum- 
stances, the  foremost  place"  (see 
'  Gauss  zum  (lediichtniss,'  by  Sar- 
torius  von  Waltershausen,  Leipzig, 
1856,  p.  79).  Cayley's  presidential 
Address  to  the  Britisli  Association, 
1883,  has  been  frequently  quoted  : 
"Mathematics  connect  themselves 
on  one  side  with  common  life  and 
the  physical  sciences  ;  on  the  otiier 
side  with  philosophy  in  regard  to 
our  notions  of  space  and  time  and 
the  questions  which  have  arisen  as 
to  the  universality  and  necessity  of 


the  truths  of  mathematics,  and  the 
foundation  of  our  knowledge  of 
them.  I  would  remark  liere  that 
the  connection  (if  it  exists)  of 
arithmetic  and  algebra  with  tlie 
notion  of  time  is  far  less  obviou.s 
than  that  of  geometry  with  the 
notion  of  space"  ('Mathematical 
Papers,'  vol.  xi.  j).  130).  In  addi- 
tion to  founding  higher  arith- 
metic. Gauss  occupied  himself  with 
the  foundations  of  geometry,  and, 
as  he  expected  much  from  the 
development  of  the  theory  of  num- 
bers, so  he  placed  "  great  hopes  on 
the  cultivation  of  the  f/roinefriit 
sitim,  in  which  he  saw  large  unde- 
veloped trivcts  which  could  not  be 
concjuered  by  the  existing  calculus  " 
(Sartorius,  loc.  cit.,  p.  88). 

'  To  this  mitrht  be  added  the 
psychological  interest  wliich  at- 
taches to  matliematical  concep- 
tions. The  late  Prof.  Paul  Du 
Bois  -  Reymond    occupied    liimself 


632 


SCIENTIFIC    THOUGHT. 


Twofold 
interest 
in  mathe- 
matics. 


inasmuch  as  number  and  form  are  considered  to  be 
the  highest  categories  of  human  thought,  or  likewise  as 
the  ultimate  elements  of  all  reality.  These  two  interests 
existed  already  in  antiquity,^  as  the  word  "  geometry  " 


much  with  the  question.  See  the 
following  works  :  '  Die  AUgeraeine 
Functionentheorie,'  part  i.,  Tiib- 
ingen,  1882;  '  Ueber  die  Gruud- 
lagen  der  Erkenntniss  in  den  ex- 
acten  "Wissenschaften,'  Tubingen, 
1890;  and  his  paper  "Ueber  die 
Paradoxien  des  Infiuitiircalciils " 
('Mathematische  Annalen,'  vol.  ix. 
p.  149).  In  addition  to  the  two 
main  interests  which  attach  to 
mathematical  research,  and  which 
I  distinguish  as  the  practical  and 
the  philosophical,  a  third  point  of 
view  has  sprung  up  iu  modern 
times  which  can  be  called  the 
purely  logical.  It  proposes  to 
treat  any  special  development  of 
mathematical  research  with  the 
aid  of  a  definite,  logically  con- 
nected complex  of  ideas,  and  not 
to  be  satisfied  to  solve  definite 
problems  with  the  help  of  any 
methods  which  may  casually  pre- 
sent themselves,  however  ingenious 
they  may  be.  In  this  way  the 
gi-eat  geometrician,  Jacob  Steiner, 
e.g.,  refused  the  assistance  of  ana- 
lysis in  the  solution  of  geometrical 
problems,  conceiving  geometry  as 
a  complete  organism  which  should 
Solve  its  problems  by  its  own 
means.  This  view  has  been  much 
.strengthened  by  the  development 
in  modern  times  of  the  theory  of 
Groups  ;  a  group  of  operations 
being  ^defined  as  a  sequence  of  such 
operations  as  alwaj^s  lead  back 
again  to  operations  of  the  same 
kind.  Mathematical  rigorists  in 
this  sense  would  look  upon  the 
use  of  mixed  methods  or  opera- 
tions not  belonging  to  the  same 
group  with  that  kind  of  disfavour 
with   which   we  should    regard    an 


essaj'ist  who  could  not  express  his 
ideas  in  pure  English,  but  was 
obliged  to  import  foreign  words 
and  expressions.  It  is  interesting 
to  see  that  the  country  which  has 
offended  most  by  the  importation 
of  foreign  words  —  namely,  Ger- 
many— is  that  in  which  this  purism 
in  mathematical  taste  has  found 
the  most  definite  expression.  (See, 
inter  alia,  Prof.  Friedrich  Engel's 
Inaugural  Lecture,  "  Der  Gesch- 
mack  ill  der  neueren  Mathematik," 
Leipzig,  1890,  as  also  Prof.  F. 
Klein's  suggestive  tract,  '  Ver- 
gleichende  Betrachtungen  iiber 
neuere  Geometrische  Forschungen,' 
Erlangen,  1872.) 

■*  The  literature  of  this  subject 
is  considerable.  I  confine  myself 
to  two  works.  The  late  eminent 
mathematician,  Hermann  Hankel, 
of  whom  more  in  the  sequel  of 
this  chapter,  besides  showing  much 
originalitj'  in  the  higher  branches 
of  the  science,  took  great  interest 
in  its  philosophical  foundations 
and  historical  beginnings.  In  1870 
he  published  a  small  but  highly 
interesting  volume,  '  Zur  Ge- 
schichte  der  Mathematik  in  Alter- 
thum  und  Mittelalter'  (Leipzig, 
Teubner).  We  have,  besides,  the 
great  work  of  Prof.  Moritz  Cantor, 
'  Vorlesungen  iiber  Geschichte  der 
Mathematik,'  in  three  large  volumes 
(Leipzig,  Teubner).  It  brings  the 
history  down  to  1758.  Referring 
to  the  two  interests  which  led  to 
mathematical  investigations,  Hankel 
says  (p.  88)  :  "  From  the  moment 
that  Greek  philosophers  begin  to 
attract  our  attention  through  their 
mathematical  researches,  the  as- 
pect   which    mathematics    present 


DEVELOPMENT  OF  MATHEMATICAL  THOUGHT.   G38 

and  the  well-known  references  to  mathematical  ideas 
in  the  schools  of  Pythagoras  and  Plato  indicate.  An 
ancient  fragment  ^  which  enumerates  briefly  the  Grecian 
mathematicians,  says  of  Pythagoras,  "  He  changed  the  oc- 
cupation with  this  branch  of  knowledge  into  a  real  science, 
inasmuch  as  he  contemplated  its  foundation  from  a 
higher  point  of  view,  and  investigated  the  theorems 
less  materially  and  more  intellectually  ;  "  -  and  of  Plato 
it  says  that  "  He  filled  his  writings  with  mathematical 
discussions,  showing  everywhere  how  much  of  geometry 
attaches  itself  to  philosophy."  ^ 

This  twofold  connection  of  mathematical  with  other 
pursuits  has,  after  the  lapse  of  many  centuries,  come 
prominently  forward  again  in  the  nineteenth  century. 
We  have  already  had  to  record  a  powerful  stimulus  to 
mathematical  thought  in  almost  every  chapter  in  which 
we  dealt  with  the  fruitful  ideas  which  governed  scientific 
work,  and  we  have  now  no  less  to  draw  attention  to  the 
philosophical  treatment  which  has  been  bestowed  upon 
the  foundations  of  science  and  the  inroad  of  niatheraati- 


chaiiges  radically.  Whilst  among 
the  earlier  civilised  nations  we  only 
meet  with  routine  and  practice, 
with  empirical  rules  which  served 
practical  purposes  in  an  isolated 
manner,  tlie  Grecian  mind  on  the 
other  side  recognised,  from  the 
first  moment  when  it  became 
acquainted  with  this  matter,  that 
it  contained  something  which  tran- 
scended all  those  practical  ends, 
but  which  was  worthy  of  special 
attention,  and  which  could  be  ex- 
pressed in  a  general  form,  be- 
ing, in  fact,  an  object  of  science. 
This  is  the  high  merit  of  the  Greek 
mathematicians  ;  nor  need  one  fear 


that  this  merit  should  be  dimin- 
ished by  admitting  tiiat  they  bor- 
rowed the  new  material  from  the 
ancient  Egyptian  civilisation." 

'  The  fragment  referred  to  is 
preserved  by  Proclus,  and  is  given 
in  full  in  Cantor's  work  (vol.  i.  p. 
124  s<iq.)  He  calls  it  an  ancient 
catalogue  of  mathematicians.  It 
is  generally  attiibuted  to  Eudemus 
of  Rliodes,  who  belonged  to  the 
peripatetic  school  of  philosophy, 
and  was  the  author  of  seveial  his- 
torical treatises  on  geometry  and 
astronomy  (Cantor,  vol.  i.  p.  108). 

-  I'antor,  vol.  i.  p.  137. 

^  Ibid.,  p.  213. 


634 


SCIENTIFIC    THOUGHT. 


6. 

Origin  of 
mathe- 
matics. 


cal  into  philosophical  thought ;  ^  so  much  so  that  this 
closing  chapter  on  the  development  of  mathematical 
thought  forms  a  fitting  link  with  the  next  great  depart- 
ment of  our  subject — the  Philosophy  of  the  Century. 

We  are  told  that  mathematics  among  the  Greeks  had 
its  origin  in  the  Geometry  invented  by  the  ancient 
Egyptians  for  practical  surveying  purposes.  The  first 
mathematical  problems  arose  in  the  practice  of  men- 
suration. Modern  mathematical  thought  received  in 
an  analogous  manner  its  greatest  stimulus  through  the 
Uranometry  of  Kepler,  Newton,  and  Laplace :  through 
the  mechanics  and  the  survey  of  the  heavens  new 
methods  for  solving  astronomical  problems  were  in- 
vented in  the  seventeenth  and  eighteenth  centuries, 
and  the  nineteenth  century  can  be  said  to  have  at- 
tempted to  perform  towards  this  new  body  of  doctrine 
the  same  task  that  Euclid,  three  hundred  years  before 
the  Christian  era,  performed  towards  the  then  existing 
mathematics.  As  Proclus  tells  us,  "  putting  together 
the  elements,  arranging  much  from  Eudoxus,  furnishing 
much  from  Thesetetus,  he,  moreover,  subjected  to  rigorous 
proofs  what  had  been  negligently  demonstrated  by  his 
predecessors." "  What  one  man,  so  far  as  we  know,  did 
for  the  Grecian  science,  a  number   of  great   thinkers  in 


^  Thus,  for  instance,  the  recent 
investigations  and  theories  of  the 
"  manifold,"  as  they  have  been 
set  forth  by  Prof.  Georg  Cantor 
of  Halle,  constitute,  as  it  were, 
a  new  chapter  in  mathematical 
science,  whereas  they  were  for- 
merly a  subject  merely  of  philoso- 
phical interest.  See  a  remark  to 
this  effect  by  B.  Kerry  at  the  end 
of  his    very    interesting  article  on 


Cantor's  doctrine  in  the  9th 
vol.  of  Avenarius's  '  Zeitschrift 
f iir  wissenschaftliche  Philosophic ' 
(1885),  p.  231,  where  he  refers  to 
Kant's  comparison  of  philosophy 
to  a  Hecuba  "  tot  generis  natisque 
potens." 

'^  Quoted  by  Cantor,  vol.  i.  p. 
247.  See  also  Hankel,  loc.  cit., 
p.   381  sqq. 


DEVELOPMENT    OF    MATHEMATICAL    THOUGHT.       635 

our  century,  among  whom  I  only  mention  Gauss,  Cauchy, 
and  Weieistrass,  attempted  to  do  for  the  new  science 
which  was  created  during  the  two  preceding  centuries. 
As  Prof,  Klein  says,  "  We  are  living  in  a  critical  period, 
similar  to  that  of  Euclid."  ^ 


^  See  '  The  Evanston  Colloquium, 
Lectures  on  Mathematics  delivered 
in  August  and  September  1893,'  by 
Felix  Klein,  notably  Lecture  vi. 
In  this  lecture  Prof.  Klein  ex]>lains 
his  view  (to  which  he  had  given 
utterance  in  his  address  before  the 
Congress  of  Mathematics  at  Chicago: 
'  Papers  published  by  the  American 
Mathematical  Society.'  vol.  i.  p. 
133.  New  York,  1896)  on  the 
relation  of  pure  mathematics  to 
applied  science.  This  view  is  based 
upon  the  distinction  between  what 
he  calls  the  "  naive  and  the  refined 
intuition."'  .  .  .  "  It  is  the  latter 
that  we  find  in  Euclid  ;  he  carefully 
develops  his  system  on  the  basis  of 
well  -  formulated  axioms,  is  fully 
conscious  of  the  necessity  of  exact 
proofs,  clearly  distinguishes  be- 
tween the  commensurable  and  the 
incommensurable,  and  so  forth.  .  .  . 
The  naive  intuition,  on  the  other 
hand,  was  especially  active  during 
the  period  of  the  genesis  of  the 
differential  and  integral  calculus. 
Thus  we  see  that  Newton  assumes 
without  hesitation  the  existence,  in 
everj-  ca.se,  of  a  velocity  in  a  mov- 
ing point,  without  troubling  himself 
with  the  inquiry  whether  there 
might  not  be  continuous  functions 
having  no  derivative." 

In  the  opinion  of  Prof.  Klein 
'■  the  root  of  the  matter  lies  in  the 
fact  that  the  naive  intuition  is  not 
exact,  while  the  refined  intuition  is 
not  properly  intuition  at  all,  but 
arises  through  the  logical  develop- 
ment from  axioms  considered  as 
perfectly  exact." 

In  the  sequel  Prof.  Klein  shows 
that  the   naive   intuition    imports 


into  the  elementary  conceptions 
elements  which  are  left  out  in  the 
purely  logical  development,  and  that 
this  again  leads  to  conclusions  which 
are  nut  capable  of  being  verified  by 
intuition,  no  mental  image  being 
possible.  Thus,  for  instance,  the 
abstract  geometry  of  Lobatchev.sky 
and  Kiemann  led  Beltrami  to  the 
logical  conception  of  the  pseudo- 
sjdiere  of  which  we  cannot  form 
any  mental  image.  Similar  views 
to  those  of  Prof.  Klein  have  been 
latterly  expressed  by  H.  Poincar^ 
in  his  suggestive  volume  '  La 
Science  et  I'Hypoth^se '  (Paris, 
1893).  He  there  says  (p.  90) : 
"...  L'exp(5rience  joue  un  role 
indispensable  dans  la  gencse  de  la 
geometric ;  mais  ce  serait  une 
erreur  d'en  conclure  que  la  geo- 
metric est  une  science  experi- 
mentale,  meme  en  partie.  .  .  .  La 
g(5ometrie  ue  serait  que  I'etude  de.* 
mouvements  des  solides ;  mais  elle 
ne  s'occupe  pas  en  realite  des  solides 
naturels,  elle  a  pour  objet  certains 
solides  ideaux,  absolument  invari- 
ables,  qui  n'en  sont  qu'une  image 
simplifiee  et  bien  lointaine.  .  .  .  Ce 
qui  est  I'objet  de  la  gcomclrie  c'est 
I'etude  d'un  '  groupe  '  particulier  ; 
mais  le  concept  gdndral  de  groupe 
preexiste  dans  notre  esprit  au 
moins  en  puissance.  .  .  .  Seule- 
ment,  parmi  tons  les  groupes 
jiossibles,  il  faut  choisir  celui  qui 
sera  pour  ain.^i  dire  I'dtalon  autiuel 
nous  rapporterons  les  phenomenes 
naturels."  This  distinction  be- 
tween tiie  matliematics  of  intuition 
and  the  mathematics  of  logic  has 
also  been  forced  upon  us  from  quite 
a  different  quarter.     The  complica- 


636 


SCIENTIFIC   THOUGHT. 


Gauss. 


8. 
Cauchy. 


It  is  right  to  place  the  name  of  Gauss  at  the  head,  for 
his   investigations    regarding    several    fundamental    and 
critical  questions  in  arithmetic  and  geometry  date  from 
the   last  years   of   the   eighteenth   century,  long   before 
Cauchy's  influence  made  itself  felt.     This  is  now  abund- 
antly clear  through  the  publication  of  Gauss's  works,  and 
from  much  of  his  correspondence  with  personal  friends, 
notably    with    the    astronomer    Bessel.      We    can    now 
understand  how  those  who  knew  him  regarded  him  as 
a   kind   of   mathematical   oracle   to    whom  "  nothing  in 
theory  existed  that  he  had  not  looked  at  from  all  sides,"  ^ 
and  who  anticipated  in  his  own  mind  the  development 
which   mathematical    thought   was    to    take   for   a  long 
time  after  him.     And  yet  it  was  not  to  him  primarily 
that  the  great  change  was  due  which  came  over  mathe- 
matical reasoning  during  the  first  half  of  the  century. 
Gauss  was  not  a  great  teacher.      In  fact,  there  existed 
in  the  first  quarter  of  the  period  only  one  great  training 
school   in    advanced   mathematics,  and    that  was   Paris. 
There   it  was  that  Augustin  Cauchy — first  as  lecturer. 


tiou  of  modern  mathematics  and 
the  refinement  of  the  modern 
theories  have  brought  about  the 
desire  "to  create  an  abridged 
system  of  mathematics  adapted  to 
the  needs  of  the  apphed  sciences, 
without  passing  through  the  whole 
realm  of  abstract  mathematics" 
(Klein,  loc.  cit.,  p.  48).  In  this 
country  Prof.  Perry  has  made  a 
beginning  by  publishing  his  well- 
known  work,  '  Calculus  for  En- 
gineers,' which  has  been  welcomed 
by  Prof.  Klein  in  Germany,  and 
which  has  led  to  an  extensive 
correspondence  in  the  pages  of 
'  Nature ' ;  it  being  recognised  by 
many  that  a  quicker  road  must  be 


made  from  the  elements  to  the 
higher  applications  of  mathematics 
in  the  natural  sciences  than  the 
present  school  sj'stem,  beginning 
with  Euclid,  admits  of.  The 
separation  of  the  logical  and  prac- 
tical treatment  of  any  science,  as 
likewise  the  independent  develop- 
ment in  Germany  of  the  poly- 
technic school  alongside  of  the  uni- 
versitj",  has,  however,  its  dangers, 
as  is  recognised  by  Prof.  Klein 
('  Chicago  Mathematical  Papers,'  p. 
136). 

^  See  Bessel's  letter  to  Gauss, 
27th  December  1810,  in  '  Brief- 
wechsel  zvvischen  G.  and  B.,  Leipzig, 
1880,  p.  132. 


DEVELOPMENT    OF    MATHEMATICAL    THOUGHT.       637 

then  as  professor — exerted  his  great  influence  in  the 
famous  lilcole  Polytechnique,  in  the  Sorbonne,  in  the 
ColleKe  de  France.^  In  contrast  with  Gauss — who  was 
self-contained,  proud,  and  unapproachable,  whose  finished 
and  perfect  mathematical  tracts  were,  even  to  those  who 
worshipped  him,  an  abomination,"  owing  to  their  unin- 
telligible and  novel  enunciation,  who  hated  lecturing 
— Cauchy  possessed  the  enthusiasm  and  patience  of 
the  teacher,^  spent  hours  with  liis  pupils,  and  pub- 
lished his  lectures  on  the  foundations  of  the  Calculus 
for  the  benefit  of  the  rising  mathematical  generation. 
Thus  lie  has  the  merit  of  having  created  a  new  school 
of  mathematical  thought — not  only  in  France  but  also 
al)road,  where  the  greatest  intellects,  such  as  that  of 
Abel,*  expressed  themselves  indebted  to  him  for  hav- 
ing ])ointed  out  the  only  right  road  of  progress.  Tt 
will  he  useful  to  define  somewhat  more  closely  wherein 
this  new  school  differed  from  that  preceding  it,  which 
culminated  in  the  great  names  of  Euler,  Lagrange,  and 
Laplace. 

The  great  development  of  modern  as  compared  with 
ancient  mathematics  may  be  stated  as  consisting  in  the  in- 

^  See    Valson,    '  La   Vie    et    les  genie  des  Euler,  des  Lagrange,  des 

Travaux  du  Baron  Cauchy,'  Paris,  Laplace,    des    Gauss,    des    Jacobi, 

1868,  vol.  i.  p.  60  sqq.  I'aniour    de    I'enseignement    portd 

^  "  On    disait    que     sa    manicre  jusqu'Ji    I'enthousinsnie,    une    rare 

d'exposer  etait  niauvaise,  ou  encoie  bonte,  une   siniplicite,  une  chaleur 

qu'il   faisait  comuie  le  renard,  qui  de  c(Kur  qu'il  a  conservees  jusqu'h 

efface  avec  sa  ([ueue  les  traces  de  ses  la  fin  de  sa  vie  "  (Combes,  quoted 

pas  sur  le  sable.     Crelle  dit,  selon  by  Valson,  vol.  i.  p.  63). 
Al)el,    ([ue   tout  ce  qu'ecrit  Gauss  *  See  Bjerknes,  'N.-H.  Abel,' p. 

n'est  qu'abomination  (Griiuel),  car    j    48  sqt). ;  p.  300.     Cauehy's  '  Cours 

c'est   si   obscur    qu'il    est    pres(iue  d'Aiialyse'  ajipcared  in  1821  :   the 

impossible    d'y    rien    comprendre "  '  Kdsume  des    lei;ons   sur  le    caitul 

(Bjerknes,     '  Niels     Henrik     Abe!,'  infinitesimal,'  to  which  .\bel  refers 

Trad,  fram/aise,  Paris,  188."),  p.  92).  in  a  letter  to  Holmboe,  dated  1826, 

■*  "  C'est  que   Cauchy  alliait   au  appeared  in  1823. 


638  SCIENTIFIC    THOUGHT. 

troduction  of  algebra  or  general  arithmetic,  in  the  applica- 
tion of  this  to  geometry  and  dynamics,  and  in  the  invention 
of  the  infinitesimal  methods,  through  which  the  rigorous 
theorems  of  the  older  geometricians  which  referred  to  the 
simpler  figures — such  as  straight  lines,  circles,  spheres, 
cones,  &c. — became  applicable  to  the  infinite  variety  of 
curves  and  surfaces  in  which  the  objects  and  phenomena 
of  .nature  present  themselves  to  our  observation.  Logic- 
ally speaking,  it  was  a  grand  process  of  generalisation, 
based  mostly  on  inference  and  induction,  sometimes 
9.         merely  on  intuition.^      Such  a  rirocess  of  generalisation 

Processor  ''  i  o 

generaiisa-     j^as  a  twofold  cffect  on  tlic  progrcss  of  science. 

The  first  and  more  prominent  result  was  the  greatly 
increased  power  of  dealing  with  special  problems  which 
the  generalised  method  affords,  and  the  largely  increased 
field  of  research  which  it  opened  out.  We  may  say  that 
the  century  which  followed  the  inventions  of  Descartes, 
Newton,  and  Leibniz,  was  mainly  occupied  in  exploring 
the  new  field  which  had  been  disclosed,  in  formulating 
and  solving  the  numberless  problems  which  presented 
themselves  on  all  sides ;  also,  where  complete  and 
rigorous  solutions  seemed  unattainable,  in  inventing 
methods  of  approximation  which  were  useful  for  prac- 
tical purposes.  In  this  direction  so  much  had  to  be  done, 
so  much  work  lay  ready  to  hand,  that  the  second  and 
apparently  less  practical  effect  of  the  new  generalisations 
receded  for  a  time  into  the  background.      We  may  term 

^  "  On  se   reportait   incousciem-  ;  claire  et  rigoureuse,  mais  par  une 

nient    au    niodele    qui     nous     est  I  sorte    d'intuition    et   d'obscur    in- 

fourni  par  les  fonctions  considerees  stinct"  (Pnincarc,  "  L'ujuvre  math, 

en    mecanique   et   on   rejetait  tout  |  de  Weierstrass,"    '  Acta  Mathema- 

ce  qui  s'ecartait  de  ce  modele  ;  on  !  tica,'  vol.  xxii.  p.  4). 

u'otait  pas  guide  par  une  d(5finition  • 


DEVELOPMENT    OF    MATHEMATICAL    THOUGHT. 


639 


this  second  and  more  hidden  line  of  research  the  logical 
side  of  the  new  development.  It  corresponds  to  the  work 
which  Euclid  performed  in  ancient  geometry,  the  framing 
of  clear  dehnitions  and  of  unambiguous  axioms ;  pro- 
ceeding from  these  by  rigorous  reasoning  to  the  theorems 
of  the  new  science.^  But  the  translation  of  geometrical 
and  mechanical  conceptions  into  those  of  generalised 
arithmetic  or  algebra  brought  with  it  a  logical  problem 
of  quite  a  novel  kind  which  has  given  to  modern  mathe- 
matics quite  a  new  aspect.  This  new  problem  is  the  re- 
translation  of  algebraical — i.e.,  of  general — formuhe  into 
geometrical  conceptions — the  geometrical  construction  of 
algebraical  expressions.  It  is  the  inverse  operation  of 
the  former.  Tu  tliis  inversion  of  any  given  operation  operations, 
lies  the  soul  and  principle  of  all  mathematical  progress, 
both   in   theory  and   in  application."     The  invention  of 


10. 
Inverse 


'  lleferring  sixjcially  to  the 
defiDition  of  a  "  function "  or 
mathematical  dependence,  a  con- 
ception introduced  l»y  Kuler,  but 
not  rigorou.sly  defined  by  him, 
M.  Poincare  sayw,  loc.  cit.  :  "  Au 
cr)mmenceraent  du  sifecle,  I'idde 
de  fonction  etait  une  notion  Ji 
la  fois  trop  restreinte  et  trop 
vague.  .  .  .  Cette  definition,  il 
fallait  la  donner  :  car  I'analyse  ne 
jjouvait  qu'ii  ce  prix  actjuerir  la 
parfaite  rigueur. "  In  its  generality 
tliid  task  wa«  performed  in  the 
last  third  of  the  century  by 
Weierstrass,  but  tlie  necessity  of 
this  criticism  of  the  formulic  in- 
vented by  modern  mathematics 
dates  from  the  api)earance  of 
Cauchy's  '  Momoire  sur  la  thdorie 
dcs  intcgiales  ddfinies'  of  1814, 
which  Legcndre  reported  on  in  this 
sense,  but  which  wxh  not  published 
till  182f). 


-  The  operations  referred  to  are 
generally  of  two  kinds  :  first,  there 
is  the  operation  of  translating 
geometrical  relations,  intuitively 
given,  int<5  algebraical  relations; 
and,  secondly,  the  operation  of 
extending  algebraical  relations  by 
going  forward  or  backward  in  the 
order  of  numbers,  usually  given 
by  indices.  In  each  ca.se  the 
new  relations  arrived  at  reijuire 
to  be  interpreted,  and  thi.s  inter- 
pretation leads  nearly  always  to 
an  extension  of  knowledge  or  to 
novel  conceptions.  A  simjde  ex- 
ample of  the  first  kind  presents 
itself  in  the  geometrical  construc- 
tion of  the  higher  powers  of 
quantity.  Having  agreed  to  ilefine 
by  a  tiie  length  of  a  line,  by  a^ 
an  area,  what  is  the  meaning  of 
n^  n*  .  .  .  a"  ?  Can  any  geomet- 
rical meaning  be  attaoiied  to  these 
symbols  ?       An    example    of     the 


640 


SCIENTIFIC    THOUGHT. 


the  seventeenth  century  afforded  two  grand  occasions 
for  such  progress,  and  the  creation  through  it  of  novel 
mathematical  ideas.     The  translation  of  geometrical  con- 


second     class     i.s     the    following : 
having  defined  the  symbols 
dy     d-y  d"y 

dx     dx^  '   '  '    rfa;"' 
an  operation  suggests  itself  in  the 
inverse  order,  the  indices  or  their 
reciprocals  (inversions)  being  taken 
negatively.      Can  any  meaning  be 
attached  to  these  latter  symbols  ? 
Further,  if  the  operation  denoted 
by    going   on    from    one    of    these 
symbols  to  the  next  is  known  and 
feasible,  how  can  the  inverse  oper- 
ation be  carried  out  ?     In  the  first 
class  of  problems  we  proceed  from 
an    intuitively   given    order    to    a 
purely   hjgical   order,   and   have   in 
the    sequel    to   go    back    from    the 
purely  logical  order  to  an  intuitive 
order    of    ideas.       In    the    second 
case,    having    followed     a    certain 
logical    order,    we   desire    to    know 
what  the  inversion  of  this  order  will 
produce  and  how  it  can  be  carried 
out.     The  view  that  the  direct  and 
indirect  processes  of  thought  form 
the     basis     of     all     mathematical 
reasoning,  and    an    alternation    of 
the  two  the  principle  of  progress, 
has    been   for   the    first    time    con- 
sistently  expounded    by   Hermann 
Hankel   in   his  '  Theorie  der  Com- 
plexen    Zahlen  -  Systeme,'    Leipzig, 
1867.       But    it   had   already    been 
insisted   on   by  George   Peacock  in 
his    "  Report,"    &c.,    contained    in 
the    3rd    vol.    of    the    '  Reports   of 
the  Brit.    Assoc.,'  183.3,   where   he 
says    (p.    223)  :    "  There    are    two 
distinct   processes  in   Algebra,   the 
direct  and  the  inverse,  presenting 
geneially  very  different  degrees  of 
difficulty.       In    the    first   case,    we 
proceed    from    defined    operations, 
and    by    various   processes   of    de- 
monstrative   reasoning    we    arrive 
at    results    which    are    general    in 


form  though  particular  in  value, 
and  which  are  subsequently  gen- 
eralised in  value  likewise  ;  in  the 
second,  we  commence  fi-om  the 
general  result,  and  we  are  either 
required  to  discover  from  its  form 
and  composition  some  equivalent 
result,  or,  if  defined  operations 
have  produced  it,  to  discover  the 
primitive  quantity  from  which  those 
operations  have  commenced.  Of 
all  these  processes  we  have  alreadj- 
given  examples,  and  nearly  the 
whole  business  of  analysis  will 
consist  in  their  discussion  and 
development,  under  the  infinitely 
varied  forms  in  which  they  will 
present  themselves." 

It  is  extraordinary  how  little  in- 
fluence this  verj'  interesting,  com- 
prehensive, and  up-to-date  re- 
port on  Continental  mathematics, 
including  the  works  of  Gauss, 
Cauchy,  and  Abel,  seems  to  have 
had  on  the  development  of  English 
mathematics.  But  the  latter  have 
through  an  independent  movement 
— viz.,  the  invention  of  the 
Calculus  of  Operations  —  led  on 
to  the  radical  change  which  has 
taken  place  in  recent  mathematical 
thought.  This  change,  which  can 
be  explained  by  saying  that  the 
science  of  Magnitude  must  be 
preceded  by  the  doctrine  of  Forms 
or  Relations,  and  that  the  science 
of  Magnitude  is  only  a  special 
application  of  the  science  of  Forms, 
was  independently  prepared  by 
Hermann  Grassmann,  of  whom 
Hankel  says  {loc.  cit.,  p.  16)  :  "The 
idea  of  a  doctrine  of  Forms  which 
should  precede  a  doctrine  of  Mag- 
nitude, and  of  considering  the 
latter  from  the  point  of  view 
of  the  former,  .  .  .  remained  of 
little    value    for   the    development 


DEVELOPMENT    OF    MATHEMATICAL    THOUGHT.       G41 

ceptions  into  algebraical  language  suggested  the  inverse 
operation  of  interpreting  algebraical  terms  by  geometrical 
conceptions,  and  led  to  an  enormous  extension  of  geo- 
metrical knowledge.^  Further,  the  infinitesimal  methods 
through  which  curves  and  curved  surfaces  were  conceived 
as  being  made  up  of  an  infinite  number  of  infinitesimally 
small,  straight — i.e.,  measurable — lines,  led  to  the  in- 
verse problem;  given  any  algebraical  operations  which 
obtain  only  in  infinitesimally  small  dimensions — i.e.,  at 
the  limit — lutw   do   they  sum  iip  to  finite  quantities  and 


of  mathematics,  so  long  as  it 
was  only  used  to  prove  tlieorems 
which  besides  being  already  known, 
were  sufficiently  though  merely 
empirically  proved.  It  was  H. 
Grassmann  who  took  up  this  idea 
for  the  first  time  in  a  truly 
philosophical  spirit  and  treated 
it  from  a  comprehensive  point 
of  view."  Hankel  also  refers 
to  Peacock  as  well  as  to  De 
Morgan,  whose  writings,  however, 
he  was  insufficiently  accjuainted 
with  (ibid.,  p.  15).  In  quite 
recent  times  Mr  A.  N.  Whitehead 
has  conceived  "  mathematics  in 
the  widest  signification  to  be  the 
development  of  all  tj'pes  of  formal, 
necessary,  deductive  reasoning," 
and  has  given  a  first  instalment 
of  this  development  in  his  '  Treatise 
on  Universal  Algebra'  (vol.  i., 
Cambridge,  1898).  See  the  preface 
to  this  work  (pp.  6,  7). 

^  A  good  example  of  the  use  of 
the  alternating  employment  of  the 
intuitive  (inductive)  and  the  log- 
ical (deductive)  methods  is  to  be 
found  in  the  modern  doctrine  of 
curves.  The  invention  of  Descartes, 
by  which  a  curve  was  represented 
by  an  equation,  led  to  the  intro- 
duction of  the  conception  of  the 
"  degree  "  or  "  order  "  of  a  curve 
and    its    geometrical    equivalent ; 

VOL.  n. 


whereas  the  geometrical  concep- 
tion of  the  tangent  to  a  curve  led 
to  tiie  distinction  of  curves  ac- 
cording to  their  "class,"  which 
was  not  immediately  evident  from 
the  equation  of  the  curve  but 
which  led  to  other  analytical 
methods  of  representation  where 
the  tangential  properties  of  curves 
became  more  evident.  A  third 
method  of  studying  curves  was 
introduced  by  Pliicker  (1832),  who 
started  from  "the  singularities" 
which  curves  present,  defined 
them,  and  established  his  well- 
known  ecjuations.  A  further  study 
of  these  "  singularities  "  led  to  the 
notion  of  the  "genus"'  or  "de- 
ficiency "  (Cayley)  of  a  curve.  The 
gradual  development  of  these  and 
further  ideas  relating  to  curves  is 
concisely  given  in  <an  article  by 
Cayley  on  "  Curve  "  in  the  6th  vol. 
of  the  '  Kncyclopicdia  Britannica,' 
reprinted  in  Cayley's  collected 
papers,  vol.  xi.  This  article  fur- 
nishes also  a  good  example  of  the 
historical  treatment  of  a  ])urely 
mathematit-al  subject  by  showing, 
not  so  much  the  ])rogress  of  mathe- 
matical knowledge  of  special  things, 
as  the  development  of  the  manner 
in  which  such  things  are  looked  at 
— i.e.,  of  malheinatical  thought. 

2  s 


642 


SCIENTIFIC    THOUGHT. 


figures  ?  What  are  the  properties  of  these  finite  figures 
as  inferred  from  the  properties  of  their  infinitesimally 
small  parts  ?  The  infinitesimal  methods  evidently  corre- 
sponded with  the  atomistic  view  of  natural  objects, 
according  to  which  the  great  variety  of  observable 
phenomena,  the  endlessly  complicated  properties  of 
natural  objects,  could  be  reduced  to  a  small  number 
of  conceivable  properties  and  relations  of  their  smallest 
parts,  and  could  then  be  made  intelUgible  and  calculable. 
The  general  reader  who  is  unacquainted  with  the 
numberless  problems  and  intricate  operations  of  higher 
mathematics  can  scarcely  realise  how  in  these  few  words 
lie  really  hidden  the  great  questions  of  all  the  modern 
sciences  of  number  and  measurement ;  the  trained  mathe- 
matical student  will  recognise  in  a  process  of  inversion 
not  only  the  rationale  of  such  extensive  doctrines  as  the 
integral  calculus,  the  calculus  of  variations,  the  doctrine 
of  series,  the  methods  of  approximation  and  interpolation, 
but  also  the  application  of  analysis  to  geometry,  the 
theory  of  curves  of  higher  order,  the  solution  of  equations, 
&c.  All  these  various  branches  were  diligently  cultivated 
by  the  great  mathematicians  of  the  eighteenth  century, 
mostly,  however,  with  the  object  of  solving  definite 
problems  which  were  suggested  by  the  applied  sciences,^ 


1  In  general  it  can  be  stated  that 
the  impetus  given  to  mathematical 
research  by  the  problems  set  by 
the  applied  sciences  has  been  im- 
measurably greater  than  that  which 
can  be  traced  to  the  abstract  treat- 
ment of  any  purely  mathematical 
subject.  We  have  a  good  example 
of  this  at  the  beginning  of  the 
nineteenth  century  in  the  gi'eat 
work    of   Laplace  as   summed    up, 


for  the  most  j)art,  in  the  'Me- 
canique  Celeste  '  and  the  '  Theorie 
des  Probabilites,'  which  contain 
the  beginnings  and  the  develop- 
ment of  a  great  number  of  purely 
mathematical  theories  suggested 
by  problems  in  astronomy,  physics, 
aud  statistics.  On  the  other  side 
we  have  at  the  same  time  the  so- 
called  "Combinational  School "  in 
Germanj',     whose     members    and 


DEVELOPMENT  OF  MATHEMATICAL  THOUGHT. 


043 


notably  astronomy — not  infrequently  also  as  objects  of 
mere  curiosity  without  any  practical  purpose  whatever. 
In  the  latter  part  of  the  eighteenth  century  the  need 
was  felt  of  putting  the  new  science  into  a  compre- 
hensive system.  The  attempts  to  do  this — notably  the 
great  text-books  of  Leonhard  Euler  in  Germany  and  of 
Lacroix  in  France — revealed  how  uncertain  were  the 
foundations  and  how  paradoxical  some  of  the  apparent 
conclusions  of  the  reasoning  which,  in  the  hands  of  the 
great  inventors  and  masters,  had  led  to  such  remarkable 
results. 

As  in  other  cases  which  we  dealt  with  in  former 
chapters  of  this  work,  so  also  in  the  present  instance  we 
may  find  a  guide  through  the  labyrinth  of  modern  mathe- 
matical thought  in  the  terms  of  language  around  which 
cluster  the  more  recent  doctrines.      Two   terms  present        n- 

Modem 

themselves  which  were  rare  or  altogether  absent  in  older  Jj^^j'ly'g'^jf 
treatises :  these  terms  are  the  "  complex  quantity  "  and  [uougTi. 
the  "  continuous."  To  these  we  can  add  a  third  term 
which  we  meet  with  (m  every  page  of  the  writings  of 
mathematicians  since  Newton  and  Leibniz,  but  which  has 
only  very  recently  been  subjected  to  careful  analysis  and 
rigorous  definition, — the  term  "  infinite."  Accordingly  we 
may  say  that  the  range  of  mathematical  thought  during 


their  labours  are  almost  forgotten, 
although  in  their  elaborate  treat- 
ises there  are  to  be  found  many 
formul;!.'  which  had  to  be  redis- 
covered when,  fifty  years  later, 
the  general  theory  of  forms  and 
substitutions  began  to  be  sye- 
teinatically  developed,  and  proved 
to  be  an  indispensable  instrument 
in  dealing  with  many  advanced 
mathematical    i)roblems.       See    on 


the  latter  subject  an  article  by 
Major  MacMahon  on  "  Combin- 
ational Analysis"  ('Proc,  London 
Math.  Soc. .'  vol.  xxviii.  p.  5,  &c. ), 
as  also  the  chapters  on  this  subject 
and  on  "Determinants"  in  tlie 
first  vol.  of  the  '  Encyclopiidie  der 
Mathematischeu  W'issenschaften ' 
(Leipzig,  1898).  Also, /»i<'.'r  a/i«,  a 
note  by  J.  Muii'  in  'Nature,'  vol. 
Ixvii.,  1903,  11.  .")l-2. 


644 


SCIENTIFIC    THOUGHT. 


12. 

Complex 
quantities. 


13. 
The  con- 
tinuous. 


14. 

The  infinite. 


the  last  hundred  years  has  grown  in  proportion  to  the 
methodical  study  and  stricter  definition  of  the  notions  of 
the  complex  quantity,  of  the  continuous,  and  of  the  infinite. 
And  these  conceptions  indicate  three  important  logical 
developments  which  characterise  modern  mathematical 
reasoning.  The  conception  of  the  complex  quantity  or 
the  complex  unit  introduces  us  to  the  possible  extension 
of  our  system  of  counting  and  measuring,  retaining  or 
modifying,  the  fundamental  rules  on  which  it  is  based. 
The  conception  of  the  continuous  and  its  opposite,  the 
discontinuous,  introduces  us  to  the  difference  of  numbers 
and  quantity,  numbers  forming  a  discontinuous  series, 
whilst  we  conceive  all  natural  changes  to  be  made  up  of 
gradual — i.e.,  of  imperceptibly  small — changes,  called  by 
Newton  fluxions.  The  discussion,  therefore,  of  the  con- 
tinuous leads  us  ultimately  to  the  question  how  our 
system  of  counting  can  be  made  useful  for  dealing  with 
continuously  variable  quantities — the  processes  of  nature. 
The  conception  of  the  infinite  underlies  not  only  the 
infinitesimal  methods  properly  so  called,  but  also  all  the 
methods  of  approximation  by  which — in  the  absence  of 
rigorous  methods — mathematical,  notably  astronomical, 
calculations  are  carried  out. 

Problems  involving  one  or  more  of  these  concep- 
tions presented  themselves  in  large  number  to  the 
analysts  of  the  eighteenth  century :  there  were  notably 
two  great  doctrines  in  which  they  continually  occur — 
the  general   solution    of    equations,^   and  the   theory  of 


^  A.S  it  may  not  be  immediately 
evident  how  the  ideas  of  continuity 
have  to  do  with  the  general  solution 
of  equations,  I   refer  to   the   first 


publication  by  Gauss,  in  1799,  con- 
taining a  proof  of  the  fundamental 
theorem  of  algebra,  and  its  republi- 
cation fifty  years  later  (see  Gauss, 


DEVELOPMENT  OF  MATHEMATICAL  THOUGHT.   G4  5 

infinite  series.  The  solution  of  an  equation  being  called 
finding  its  roots,  it  was  for  a  long  time  assumed  that 
every  equal  icui  has  as  many  roots  as  are  indicated  by 
its  degree.  A  proof  of  this  fundamental  theorem  of 
algebra  was  repeatedly  attempted,  Ijut  was  only  com- 
pleted by  Gauss  in  three  remarkable  memoirs,  which 
prove  to  us  how  much  importance  he  attached  to  rigorous 
proofs  and  to  solid  groundwork  of  science.  The  second 
great  doctrine  in  which  the  conceptions  of  the  continuous 
and  the  infinite  presented  themselves  was  the  expansion 
of  mathenuitical  expressions  into  series.      In  arithmetic,        15. 

.  Doctrine 

decimal  fractions     taken  to  any  number  of  terms  were  of  series. 

"^  Gauss. 

quite  familiar ;  the  infinite  series  presented  itself  as  a 
generalisation   of  this  device.      A  very   general   formula 


'  Werke,'  vol.  iii.  pj).  1  aiul  71).  .\ 
very  good  suiiiiiuiry  of  this  proof 
is  given  liy  Hankel  ( '  Couiplexe 
Zahlen-Systenie,'  p.  87).  A  purely 
algebraical  deuion.stration  of  the 
same  theorem,  not  involving  con- 
sidt-rations  of  continuity  and  ap- 
pruximatifjn.s,  was  also  given  by 
Gauss  in  the  year  1816,  and  re- 
produced by  others,  including 
George  Peacock,  in  his  '  Report,' 
(juoted  above,  p.  297.  Hankel 
{loc.  cit.,  p.  97)  shows  to  what 
extent  Gauss's  proof  supplemented 
the  siniiiar  proofs  given  by  othei-s 
before  and  after. 

^  Decimal  fractions  seem  to  have 
been  introduced  in  the  sixteenth 
century.  Series  of  other  numbers, 
formed  not  according  to  the  decimal 
but  to  the  dyadic,  duodecimal,  or 
other  sj'stems,  were  known  to  the 
ancients,  and  continued  in  use  to 
the  middle  ages.  The  dyadic  sys- 
tem wa.s  much  favoured  by  Leibniz. 
It  was  also  known  that  every 
rational  fraction  could  be  de- 
veloped into   a   periodical   decimal 


fraction.  l*i-ominent  in  the  re- 
commendation of  the  use  of  deci- 
mal fractions  was  the  celebrated 
Simon  Stevin,  who,  in  a  tract 
entitled  '  La  Disme '  attached  to 
his  '  Arithmetique '  (1590,  trans- 
lated into  English,  1608),  described 
the  decimal  system  as  "  enseignant 
facilement  expodier  par  nombres 
entiei's  sans  rompus  tons  comptes 
se  rencontrans  aux  affaires  des 
hommes."  Prof.  Cantor  ( '  Gesch. 
der  Math.,'  vol.  ii.  p.  616)  says, 
"  We  know  to-day  that  this  pre- 
diction could  really  be  ventured 
on — that  indeed  decimal  fractions 
perform  what  Stevin  promised." 
At  the  end  of  his  tract  he  doubts 
the  sj)eedy  adoption  of  this  device, 
connecting  with  it  the  suggestion 
of  the  universal  adoption  of  the 
decimal  system.  The  best  account 
of  the  grail ual  introduction  of  deci- 
mal fractions  is  still  to  be  found  iii 
George  Peacock's  '  History  of  Aiilh- 
metic'  ( '  Ency.  ^tetrop.,'  vol.  i.  p. 
439,  &c.) 


646 


SCIENTIFIC    THOUGHT. 


of  this  kind  was  given  by  Brook  Taylor,  and  somewhat 
modified  by  Maclaurin.  It  embraced  all  then  known  and 
many  new  series,  and  was  employed  without  hesitation 
by  Euler  and  other  great  analysts.  In  the  beginning  of 
the  centur}",  Poisson,  Gauss,  and  Abel  drew  attention  to 
the  necessity  of  investigating  systematically  what  is 
termed  the  convergency  ^  of  a  series.  As  a  specimen 
of  this  kind  of  research,  Gauss  published,  in  1812,  an 
investigation  of  a  series  of  very  great  generality  and 
importance."  We  can  say  that  through  these  two  isolated 
memoirs  of  Gauss,  the  first  of  the  three  on  equations, 
published  in  1799,  and  the  memoir  on  the  series  of 
1812,  a  new  and  more  rigorous  treatment  of  the  in- 
finite and  the  continuous  as  mathematical  conceptions 
was  introduced  into  analysis,  and  that  in  both  he  showed 
the  necessity  of  extending  the  system  of  numbering  and 
measviriug  by  the  conception  of  the  complex  quantity. 
But  it  cannot  be  maintained  that  Gauss  succeeded  in 
impressing  the  new  line  of  thought  upon  the  science  of 


^  A  very  good  account  ot  the 
gradual  evolution  of  the  idea  of 
the  convergency  of  a  series  will  be 
found  in  Dr  R.  Reiff's  '  Geschichte 
der  unendlichen  Reihen"  (Tiibin- 
gen,  1899,  p.  118,  &c.)  Also  in 
the  preface  to  Joseph  Bertrand's 
'Traite  de  Calcul  Differeutiel' 
(Paris,  1864,  p.  xxix,  &c.)  Accord- 
ing to  the  latter  Leibniz  seems  to 
have  been  the  first  to  demand 
definite  rules  for  the  convergency 
of  Infinite  Series,  for  he  wrote  to 
Hermann  in  1705  as  follows: 
"  Je  ne  demande  pas  que  Ton 
trouve  la  valeur  d"uue  serie  quel- 
conque  sous  forme  finie ;  un  tel 
probleme  surpasserait  les  forces 
des  geometres.  Je  voudrais  seule- 
ment  que  Ton  trouvat  moyen   de 


decider  si  la  valeur  exprimee  par 
une  serie  est  possible,  c'est-a-dire 
convergente,  et  cela  sans  connaitre 
I'origiue  de  la  serie.  II  est  neces- 
saire,  pour  qu'une  serie  indefinie 
represente  une  quantite  finie,  que 
Ton  puisse  demontrer  sa  converg- 
ence, et  que  Ton  s'assure  qu'en  la 
prolongeant  suflfisamment  Terreur 
devient  aussi  petite  que  I'on  veut.'' 
In  spite  of  this,  Leibniz,  through 
his  treatment  of  the  series  of 
Grandi,  l-l  +  l-l,&c.,  the  sum 
of  which  he  declared  to  be  |,  seems 
to  have  exerted  a  baneful  influence 
on  his  successors,  including  Euler 
(See  Reiff,  loc.  cit.,  pp.  118,  158). 

-  The  memoir  on  the  Hypergeo- 
metrical  series. 


DEVELOPMENT    OF    MATHEMATICAL    THOUGHT.       G47 

mathenuitics  in  j^eneral.  This  was  done  about  fifteen  or 
twenty  years  after  Gauss  had  begun  to  puljlish  his 
isolated  memoirs,  in  a  comprehensive  treatment  of  the 
subject  by  Cauchy,  who,  before  1820,  delivered  lectures 
on    Analysis   at  the  J^cole    Polytechnique   and   in   (jther        lo. 

Caucliy's 

colleges,  and  commenced  their  puldication  in  1821.  In  Anaiy>.is. 
this  course  of  lectures  the  discussion  of  the  notions  of  the 
infinite,  of  the  continuous,  of  the  convergence  of  series, 
and  of  the  extension  of  our  conception  of  quantity 
beyond  the  ordinary  or  real  quantities  of  algebra,  is 
put  in  the  foreground,  and  the  illicit  habit  of  using  the 
generalisations  of  algebra  without  defining  the  conditions 
of  their  validity  severely  criticised.^  It  is  also  evident, 
from  the  extensive  notes  which  Cauchy  added  to  the 
"cours"  of  1821,  that  he  felt  the  necessity  of  a  revision 
of  the  fundamental  notions  of  algebra.  The  publication 
of  1821  was  followed  by  others  on  the  Calculus,  and  it 
is  through  these  treatises  mainly  that  a  new  spirit  was 
infused   into    general    mathematical    literature,    first    in 

'  The  earliest  labours  of  Cauchy  cotnme    des    inductions    projires    h. 

were  geonietrical,  and  he  evidently  faire    pre.-*.sentir    quelque     fois     la 

ac([uired  through  them  an  insight  verite,    mais    t[ui    s'accordent   peu 

into     the    contrast     between     the  avec     I'exautitude    si     vantee    des 

rigour    of    the    older    geonietrical  sciences  niath(5matiques.       On  doit 

and  the   looseness   of  the    modern  meme  observer  qu'elles  tendent  a 

algebraical   methods.       In   tliis  re-  faire    attribuer    aux     fcjrmules   al- 

gard  he  says  :   "J'ai  cherchc  a  leur  '    gcljriques    une    i^tendue     indctinie, 

donner     toute    la    rigueur     (|u'on  tandis  ([ue,  dans  la  rcalitt-,  la  plu- 

exige    en  goonietrie,   de  manifcre  a  part    de   ces    fornmles     subsistent 

ue   jamais     recourir    aux     raisons  uniquenient  sous    certaines   condi- 

tirees  de  la  goneralite  de  I'algcbre.  titms,  et  pour  certaines  valeurs  des 

Les  raisons  de  cette  espece,  quoitjue  ((uantiti's  (ju'elles  renferment.      Kti 

assez  communement  admises,  sur-  doteriainant  ces  conditions  et   ces 

tout  dans  le  passage  des  series  con-  valeurs,  et  en  iixant  dune  maniore 

vergenles    aux    series    divergentes,  precise  le  sens  des  notations  dont 

et   des    (luautitos    reelles   aux    ex-  '    je  me  sers,  je  fais  disparaitre  toute 

presbions  iniaginaires   ne    peuvent  1    incertitude"    ('Coura    d'Analyse,' 

etre  consider($s,  ce  nie  senible,  que  I    1821,  Introd.,  p.  ii). 


648 


SCIENTIFIC   THOUGHT. 


France,  somewhat  later  also  in  England  and  Germany. 
In  the  latter  country,  the  highly  original  writings  of 
Abel,  and  the  independent  labours  of  Jacobi,  opened  out 
an  entirely  new  branch  of  higher  mathematics,  beginning 
with  the  discovery  of  the  property  of  double  periodicity  of 
certain  functions.^  This  extensive  and  fruitful  province  of 
analysis  for  a  time  retarded  the  revision  and  extension  of 
the  groundwork  of  mathematical  reasoning  which  Cauchy 
had  begun,  and  upon  which  Gauss  evidently  desired  to 
make  the  extension  of  higher  mathematics  proceed." 


^  Before    the    discovery    of    the 
functions    with    a    double    period, 
functions    with    one    period    were 
known  :    the    circular    and    expon- 
ential  functions  —  the  former  pos- 
sessing a  real,  the  latter  an  imagin- 
ary, period.     The  elliptic  functions 
turned  out  to  ''share  simultaneously 
the  properties  of  the  circular  func- 
tions and  exponential  functions,  and 
whilst  the   former  were  periodical 
only    for    real,  the    latter  only  for 
imaginary,  values  of  the  argument, 
the  elliptic  functions  possessed  both 
kinds  of  [jeriodicity. "      This  great 
step  became  clear  when  it  occurred 
to   Abel  and  Jacobi  independently 
to  form  functions  by  inversion    of 
Legendre's  elliptic  integral  of   the 
first  kind.     The   two   fundamental 
principles    involved    in    this     new 
departure  were  thus  the  process  of 
inversion  and  the  use  of  the  imagin- 
ary, as  a  necessary  complement  to 
the    real,   scale    of   numbers.      The 
share  which  belongs  independently 
to  Abel  and  Jacobi  has  been  clearlj^ 
determined  since  the  publication  of 
the  correspondence  of  Jacobi  with 
Legendre  during  the  years  1827-32 
(reprinted  in  Jacobi's  '  Gesammelte 
Werke,'     ed.    Borchardt,     vol.     i., 
Berlin,  1881),  and  of  the  complete 
documents  referring  to  Abel,  which 
are  now  accessible  in  the  memorial 


volume  published  in  1902.  A  very 
lucid  account  is  contained  in  a 
pamphlet  by  Prof.  Klinigsberger, 
entitled  'Zur  Geschichte  der  Theorie 
der  Elliptischen  Transeendenten 
in  den  Jahren  1826-29'  (Leipzig, 
1879). 

-  Of   the    four   great    mathema- 
ticians who  for  sixty  years  did  the 
principal  work  in    connection  with 
elliptic    functions  —  viz.,    Legendre 
(1752-1833),    Gauss    (1777-1855), 
Abel   (1802-29),  and  Jacobi  (1804- 
51),  each  occupied  an  independent 
position  with  regard  to  the  subject, 
— suggested  originally  bj^  Euler,  and 
important  for  the  practical  applica- 
tions which  it  promised.     Legendre 
during  fortj'  years,  from  1786  on- 
ward,   worked    almost    alone :     he 
brought  the  theory  of    elliptic   in- 
tegrals, whicli  had  occurred  origin- 
ally in  connection  with  the  compu- 
tation of  an  arc  of  the  ellipse,  into 
a    system,  and  to  a  point   bej'ond 
which   the   then    existing   methods 
seemed  to  promise  no    further  ad- 
vance.    This  advance  was,  however, 
secured    by  the   labours  of   Jacobi 
through    the    introduction    of    the 
novel  principles  referred  to  in  the 
last  note.    Two  years  before  Jacobi's 
publication   commenced,   Abel    had 
already  approached  the  subject  from 
an  entirely  different  and  much  more 


DEVELOPxMENT    OF    MATHEMATICAL    THOUGHT.        049 


That  such  a  revision  had  become  necessary  was  seen,        17. 

1         1       •  i>    •  1  •        1  •  1  U'-vision 

slowly  if  lu  many  quarters,  l)ut  it  tlid  not  become  gener-  'jffu"<ia- 
ally  recognised  till  lute  in  the  century,  when  thinkers  of 


iiientalfi. 


general  point  of  view.  "  Abel,"  as 
Monsieur  L.  Sylow  says  ( '  Memorial 
des  dtudes  d'Abel,'  j).  14),  "otait 
avant  tout  algebriste.  II  a  dit  lui- 
mcuie  (jue  la  theorie  des  equations 
(jtaitson  sujet  favori,cequid'ailleui-s 
apparait  claireinent  dans  ses  omvre.s. 
Dans  ses  travaux  sur  les  fonctious 
elliptiques,  le  traitenient  des  di- 
verses  Equations  algdbriques  dont 
cette  theorie  abonde  est  mis  forte- 
meiit  en  ovidouce,  et  dans  le  premier 
de  ces  travaux,  la  resolution  de  ces 
equations  est  meme  indiquee  comme 
etant  le  sujet  principal.  Qui  plus 
est,  la  theorie  des  wiuations  etait 
entre  ses  mains  I'instrument  le  plus 
dfficace.  Ce  fut  ainsi  sans  aucun 
doute  la  resolution  de  IV'quation  de 
division  des  fonctions  elliptiques  qui 
tout  d'abord  le  couduisit  a  la  theorie 
de  la  transformation.  Elle  joue 
encore  un  role  capitale  dans  sa  de- 
monstration du  thcoreme  dit  theo- 
rcme  d'Abel,  et  dans  les  recherehes 
gendrales  surles  integrates  des  diffcr- 
entielles  alg(5briques  qui  se  trouvent 
dans  son  dernier  memoire  le  '  Prdcis 
d'une  Theorie  des  fonctions  ellip- 
tiques.' "  But  whilst  Abel  certainly 
took  a  much  more  general  view 
than  either  Legendre  or  Jacobi,  both 
of  whom  came  to  a  kind  of  dead- 
lock on  the  roads  they  had  chosen 
(Jacobi,  when  he  attempted  to  ex- 
tend the  theory  of  the  periodicity 
of  functions),  it  is  now  quite  clear 
that  Gauss  viewed  the  whole  sub- 
ject almost  thirty  ye.ars  before  Abel 
and  Jacobi  entered  the  field  from  a 
still  more  general  jMjint  of  view. 
Already,  in  1798,  when  he  was  only 
twenty-one,  he  must  have  recognised 
the  necessity  of  eidarging  and  defin- 
ing the  fundamental  concej)tions  of 
algebra  and  of  functionality  or  math- 
ematical dependence  ;  and  it  is  very 
likely  that  the   magnitude   of   the 


uudeitaking,  fur  which  his  astron- 
omical labours  left  him  no  time, 
debarred  him  from  publishing  the 
important  results  wliich  he  had 
already  attained,  and  which  covered 
to  a  great  extent  the  field  cultivated 
in    the    meantime     by    Abel    and 

'  Jacobi,  leaving  only  the  celebrated 
theorem  of  the  former  (referring  to 
the  algebraical  comparison  of  the 
higher  non  -  algebraical  functions) 
and  the  discovery  of  a  new 
function  on  the  part  of  Jacobi 
(his  Theta  function)  as  the  two 
great  additions  which  we  owe  to 
them  in  this  line  of  re.search  (see 
Kiiuigsberger,  loc.  cit.,  p.  104). 
In   this   recognition  of   the  funda- 

!  mental  change  which  mathematical 
science  demanded,  and  its  bearing 
upon  these  special  problems  here 
referred  to.  Gauss  must  have  for  a 
long  time  stood  alone  ;  for  his  great 
rival  (.'aucliy,  to  whom  we  are 
mainly  indebted  for  taking  the  first 
steps  in  this  direction,  did  not  for 
many  years  apply  his  fundamental 
and  novel  ideas  to  the  theory  of 
elliptic  functions,  which  up  to  the 
year  1844,  when  Hermite  entered 
the  field,  were  almost  exclusively 
cultivated  by  German  and  Scandi- 
navian writers  (see  R.  L.  Ellis, 
"  Report  on  the  recent  Progress  of 
Analysis,"  Brit.  Assoc,  1846  ;  re- 
printed in  '  Mathematical  and  other 
Writings,'  p.  311).  Nor  could  it 
otherwise  be  exidained  how  Cauchy 
could  keep  the  manuscript  of  Abel's 
great  memoir  without  ever  occupy- 
ing himself  with  it.  and  thus  delay 
its  publication  for  fifteen  years  after 
it  held  been  presented  to  the  .\cad- 
emy.  (See  the  above  -  mentioned 
corrcs])ondence  Ijctween  Legendre 
and  Jacobi,  1829  ;  also  Sylow,  p. 
31). 


650  SCIENTIFIC    THOUGHT. 

the  highest  rank,  who  for  some  time  had  lived  apart 
in  the  sechided  regions  of  sublime  analysis,  descended 
again  into  the  region  of  elementary  science,  both  pure 
and  applied,  where  they  speedily  remodelled  the  entire 
mode  of  teaching.  England  possessed  very  early  a  writer 
of  great  eminence  who  represented  this  tendency,  and 
whose  merits  were  only  partially  recognised  in  his  day — 
Augustus  de  Morgan. 
18.  It  will  now  be  necessary  to  explain  more  definitely 

Extension  of  ^  r  j 

otnumbe"  wliat  is  meant  by  the  extension  of  our  conception  of 
number  and  quantity  through  the  introduction  of  com- 
plex numbers  or  complex  quantities.  This  extension 
first  forced  itself  on  analysts  in  the  theory  of  equations, 
then  in  the  algebraical  treatment  of  trigonometrical 
quantities  —  i.e.,  in  the  measurement  of  angles,  or,  as 
it  is  now  called,  of  direction  in  geometry.  The  first 
extension  of  the  conception  of  number  lay  in  the  intro- 
duction of  negative  numbers.  These  admitted  of  com- 
paratively easy  representation  arithmetically  by  counting 
backward  as  well  as  forward  from  a  given  datum ; 
practically  in  the  conception  of  negative  possessions, 
such  as  debts,  geometrically  by  the  two  opposite  direc- 
tions of  any  line  in  space.  In  algebra,  where  the  simple 
operations  on  quantities  are  usually  preserved  in  the 
result  and  not  lost  in  the  simple  numerical  value  of 
the  result  as  in  arithmetic,  compound  quantities  were 
looked  upon  as  generated  by  the  processes  of  addition, 
resulting  in  the  binomial  (of  which  the  polynomial  was 
an  easy  extension),  and  further  by  the  multiplication 
with  each  other  of  different  binomials  or  polynomials, 
through   which   process   expressions   of   higher  order  or 


DEVELOPMENT  OF  MATHEMATICAL  THOUGHT.   651 

degi'ee  were  arrived  at.  The  forward  or  direct  process 
was  easy  enough,  though  even  here  assumptions  or  arbit- 
rary rules  were  included  which  escaped  notice  for  a  long 
time;  l)ut  the  real  labour  of  the  analysts  only  began 
with  the  inverse  problem — viz.,  given  any  compound 
(juantity,  similar  in  structure  to  those  directly  produced 
by  multiplication  of  binomials,  to  find  the  factors  or 
binomials  out  of  which  it  can  be  compounded.  Now 
it  was  found  that  as  in  the  arithmetical  process  of 
division,  the  invention  of  fractional  quantities ;  as  in 
that  of  extraction  of  roots,  the  irrational  quantities 
had  to  be  introduced :  so  in  the  analysis  of  compound 
algebraical  expressions  into  binomial  factors,  a  new 
(quantity  or  algebraical  conception  presented  itself.  It 
was  easily  seen  that  this  analysis  could  be  carried  out 
in  every  case  only  by  the  introduction  of  a  new  unit, 
algebraically  expressed  by  the  square  root  of  the  nega- 
tive unity.  There  was  no  difficulty  in  algebraically 
indicating  the  new  quantity  as  we  indicate  fractions 
and  irrational  quantities ;  the  difficulty  lay  in  its  inter- 
pretation as  a  number.  Since  the  time  of  Descartes 
geometrical  representations  of  algebraical  formulic  had 
become  the  custom,  and  it  was  therefore  natural  when 
once  the  new,  or  so-called  imaginary,  unit  was  formally 
admitted,  that  a  geometrical  meaning  should  be  attached 
to  it. 

Out  of   the  scattered  beginnings  of  these  researches        i9 
two   definite   problems  gradually   crystallised:  the   one,  ""'*!"'*"''' ^'"i 
a    purely    formal    or    mechanical    one  —  ^■i/.,    the    geo-  i"""*^'*^'"'*- 
metrical   representation   of    the   extended   conception   of 
quantity,  of  the  complex  quantity ;   the  other,  a  logical 


652 


SCIENTIFIC    THOUGHT. 


or  philosophical  one — viz.,  the  clearer  definition  of  the 
assumptions  or  principles  which  underlie  arithmetical 
and  algebraical  reasoning.  And  if  algebraical,  then  also 
geometrical  reasoning.  Both  problems  seem  to  have 
presented  themselves  to  the  youthful  mind  of  Gauss, 
as  is  evident  from  his  correspondence  with  Bessel  ^  and 
Schumacher,  and  from  his  direct  influence  on  Bolyai,^ 
Mobius,  and  Von  Staudt,  perhaps  also  indirectly  on 
Lobatchevsky.'^     It  does  not,  however,  appear  as  if  he 


'  See  especially  the  letters  of 
Gauss  to  Bessel,  dated  November 
and  December  ISll  and  May  1812 
( '  Brief  wechsel,'  Leipzig,  1880,  p. 
151  sqq.) 

2  Bolyai,  the  elder  (1775-1856), 
was  a  student  friend  of  Gauss  in 
the) years  1797  to  1799,  and  kept 
up  a  correspondence  with  him  dur- 
ing half  a  century.  Th  is  correspon  - 
dence  has  now  been  published  by 
F.  Schmidt  and  P.  Stackel,  Leipzig, 
1899,  with  a  supplement  containing 
some  information  about  this  extra- 
ordinary man.  His  son,  Johann 
Bolyai  (1802-60),  is  the  author  of 
the  celebrated  "  Appendix,  scien- 
tiam  spatii  absolute  veram  ex- 
hibens,"  which  was  attached  to 
his  father's  '  Tentamen,  juven- 
tutem  ...  in  elementa  matheseos 
pura;  .  .  .  introducendi,'  1832. 
The  tract  seems  to  have  been 
written  in  1823.  A  translation, 
with  introduction,  has  been  pub- 
lished by  Dr  G.  Bruce  Halsted 
('Neomonic  Series,'  vol.  iii.  4th  ed., 
Austin,  Texas,  1896).  When  the 
elder  Bolyai  sent  to  Gauss  in  the 
year  1831  to  1832  a  copy  of  his 
son's  tract  and  of  his  own  work  on 
Geometrj-,  Gauss  expressed  great 
surprise  at  the  contents  of  the 
former.  (See  his  letter  of  March 
6,  1832.)  His  remarks  that  the 
younger  Bolyai  had  anticipated 
some   of    his    own    ideas    on    the 


subject,  remind  one  of  a  similar 
remark  which  he  made,  Maj'  30, 
1828,  to  Schumacher  with  refer- 
ence to  Abel's  "  Memoir  on  Elliptic 
Functions  "  in  vol.  ii.  of  Crelle's 
'  Journal '  (see  Gauss,  '  Werke, '  vol. 
iii.  p.  495).  In  both  cases  he  felt 
himself  relieved  from  the  necessity 
of  publishing  his  own  results, 
though,  so  far  as  those  referring 
to  the  foundations  of  geometry  are 
concerned,  it  does  not  appear  that 
his  ideas  had  arrived  at  that  state 
of  maturity  which  the  publication 
of  his  posthumous  papers  has 
proved  to  have  been  attained  in 
his  treatment  of  the  higher  func- 
tions. Indeed  little  or  nothing  of 
prime  importance  has  been  found 
among  his  papers  referring  to  the 
principles  of  geometry ;  and  he 
stated  to  Bolyai  that  though  he 
had  intended  to  commit  his  views 
to  paper,  so  that  they  should  not 
be  lost,  he  had  not  intended  to 
publish  anything  during  his  life- 
time. 

■*  It  is  doubtful  whether  Gauss's 
speculations  had  any  influence  on 
the  younger  Bolyai's  theory,  and 
still  more  so  as  regards  Lobat- 
chevsky,  whose  first  tract  ap- 
peared in  the  '  Kazan  Messenger,' 
1829  to  1830,  but  dates  back 
probably  to  1826.  Inasmuch, 
however,  as  the  younger  Bolyai 
must     have     become     acquainted 


DEVELOPMENT    OF    MATHEMATICAL    THOUGHT.        G53 


had  airived  at  any  finality  in  his  .speculations,  and, 
beyond  occasional  hints  which  have  only  subsequently 
become  intelligilile,  the  love  of  finish  exhibited  in  all  his 
published  writings  prevented  liini  from  giving  to  tiic 
world  the  suggestive  ideas  which  evidently  formed  the 
groundwork  of  his  mathematical  labours.  There  is  no 
doubt  that — like  Goethe  in  a  very  different  sphere — 
Gauss  anticipated  individually  the  developments  in  the 
sphere  of  mathematical  thought  down  to  the  end  of  the 
century.  The  interpretation  of  the  complex  quantity 
had  been  given  by  Wessel,  Buee,  and  Argand  ^  in  the 
early  years  of  the  century ;  but  it  remained  unnoticed 
till  it  received  the  sanction  of  Gauss  in  a  celebrated 
memoir  referring  to  the  theory  of  numbers,  and  iniiil  in 


through  his  father  with  the 
speculations  of  the  j'outliful  Gauss, 
and  as  Lobatchevsky  was  a  pupil 
of  another  student  friend  of  Oauss 
in  the  person  of  Prof.  Bartels,  it  is 
not  unlikely  that  the  interest  which 
these  thinkers  took  in  the  subject 
can  be  originally  traced  to  the  same 
source.  (See  Dr  Halsted's  ad- 
dress on  Lobatchevsky,  '  Neomonic 
Series,'  voh  i.,  1894).  A  complete 
bibliography  of  the  earlier  papers, 
referring  to  the  so-called  "non- 
Euclidean"  literature  down  to 
1878,  is  given  by  Dr  Halstcd  in 
the  first  two  vols,  of  the  '  Ameri- 
can Journal  of  Mathematics  ' :  the 
most  recent  publications  are  those 
of  the  Hon.  B.  A.  W.  Russell  in 
his  work,  'The  Foundations  of 
Geometry'  (1897)  and  his  ex- 
cellent article  on  "  Non-Euclidean 
Geometry  "  in  the  28th  vol.  of  the 
'  Ency.  Brit.'  See  also  Klein's  litho- 
graphed lectures  on  '  Nicht-Euk- 
lidische  Geometrie,'  Gottingen, 
189.3. 

'  The  first  somewhat  exhaustive 
historical    statement     as     to     the 


geometrical  representation  of  the 
complex  or  imaginary  quantity  wa.s^ 
given  bj'  Hankel  in  the  above- 
mentioned  work  (see  above,  note, 
p.  645),  p.  82.  He  there  says,  after 
discussing  the  claims  of  others, — 
notably  of  Gauss, — that  Argand  in 
his  'Essai'  of  the  j-ear  1806  (re- 
edited  by  Hoiiel,  1874)  "had  so 
fully  treated  of  the  whole  theory 
that  later  nothing  essentially  new 
was  added,  and  that,  except  a 
publication  of  still  earlier  date 
were  found,  Argand  must  be  con- 
sidered the  true  founder  of  the 
representation  of  complex  (juan- 
tities  in  the  plane."  Such  an 
earlier  publication  has  indeed  been 
met  with  in  a  tract  by  Caspar 
Wessel,  which  was  presented  to 
the  Danish  Academy  in  1797,  and 
puljlished  in  1799.  Having  been 
overlooked,  like  Argand's  'Essai,' 
it  has  now  been  republished  at 
Copenhagen,  1897,  with  the  title 
'  Essai  sur  la  representation  de  la 
direction '  (see  '  Eucyk.  Math. 
Wissenschaften,'  vol.  i.  p.   155). 


654 


SCIENTIFIC   THOUGHT. 


20. 
Quater- 
nions. 


this  country  the  labours  of  De  Morgan  and  of  Sir  William 
Eowan  Hamilton  gave  the  matter  a  further  and  very- 
important  extension.^  It  was  also  in  this  country  that 
the  second  problem,  tlie  critical  examination  of  the 
principles  which  underlie  the  process  of  legitimate 
generalisation  of  algebra,  received  distinct  attention.  To 
George  Peacock,  and  to  the  school  of  algebraists  which 
followed  him,  is  due  the  merit  of  having  brought  out 
clearly  the  three  fundamental  laws  of  symbolical  reason- 
ing now  generally  admitted  in  text-books  on  the  subject — 
the  associative,  distributive,  and  commutative  principles. 
That  these  principles  were  to  a  great  extent  conventional, 
or  empirically  adopted  from  ordinary  arithmetic,  and  in 
consequence  not  necessarily  indispensable  for  a  consistent 
system  of  symbolical  reasoning,  has  been  generally  ad- 
mitted ever  since  Sir  William  Eowan  Hamilton,  after 
ten  years  of  labour,  succeeded  in  establishing  a  new 
calculus — the  method  of  quaternions,  in  which  the  com- 
mutative principle   of  multiplication  is   dropped.     This 


^  Far  more  important  than 
the  suggestions  or  artifices  men- 
tioned in  the  foregoing  note,  and 
which  since  the  time  of  Argand 
and  Gauss  have  been  variously 
modified,  is  the  conception  that 
our  common  numbers  do  not  form 
a  complete  system  without  the 
addition  of  the  imaginary  unit, 
but  that  with  the  introduction 
of  a  second  unit  "  uumbei's  form 
a  universe  complete  in  itself,  such 
that,  starting  in  it,  we  are  never 
led  out  of  it.  There  may  very  well 
be,  and  perhaps  are,  numbers  in  a 
more  general  sense  of  the  term  ; 
but  in  order  to  have  to  do  with 
such  numbers  (if  any)  we  must 
.start  with  them"'  (Cajdey  in  art. 
"Equation,"    '  Ency.  Brit.';    'Coll. 


Works,'  vol.  xi.  p.  50.3).  There 
seems  little  doubt  that  this  con- 
ception was  first  clearly  established 
in  the  mind  of  Gauss,  and  that 
none  of  the  contemporary  writers 
can  be  shown  to  have  had  a 
similarly  clear  insight.  Since  this 
has  become  generallj'  recognised — 
and  we  owe  this  recognition 
probably  to  the  independent 
labours  of  Gra'^smann  and  Rie- 
mann — the  discussion  of  the  whole 
subject  has  been  raised  to  a  much 
higher  level,  as  may  be  seen  by 
comparing  the  Report  of  Peacock, 
quoted  above,  with  the  discussion 
of  Hankel  [loc.  cit.),  and  still  more 
with  the  exhaustive  article  by  Prof. 
E.  Study  in  vol.  i.,  'Encyk.  Math. 
AViss.,'  pp.  147-184. 


DEVELOPMENT  OF  MATHEMATICAL  THOUGH'l'.   (".55 


calculus  was  shown  to  l)e  of  special  use  in  expressing 
the  relations  of  spherical  trigonometry.  Two  terms 
expressing  definite  notions  special  to  geometry,  by  which 
science  has  been  enriched  and  practical  application  greatly 
simplified,  are  an  outcome  of  this  line  of  research.  These 
are  the  terms  "vector,"  to  express  the  iidtion  of  directed 
magnitude — i.e.,  of  direction  and  magnitude  combined  as 
distinguished  from  magnitude  and  position  alone ;  and 
the  notion  of  an  "  operator  "  which  changes  direction  and 
magnitude  as  an  ordinary  multiplier  changes  magnitude 
only.^      It   was  shown    by   Argand   and  others  that  the 


^  ThetiC  two  notions,  wliich  have 
their  origin  in  the  writings  of 
Hamilton  on  the  one  side  and  the 
Calculus  of  Operations  on  tiie 
other,  belong  to  this  country  and  to 
a  period  during  which  mathematical 
researches  were  carried  on  in  a  frag- 
mentary manner,  and  much  out  of 
cont;ict  with  the  contemporary 
mathematics  of  the  Continent. 
Both  the  Calculus  of  Quaternions 
of  Hamilton  and  the  Calculus  of 
Operations  were  looked  upon  for  a 
long  time  as  curiosities  (as  was  also 
the  Barycentric  Calculus  of  Mobius 
in  Germany).  Gradually,  however, 
the  valuaVjle  ideas  which  were  con- 
tained  in  them  became  recognised 
as  much  from  the  practical  as  from 
the  theoretical  jjoint  of  view.  Jn 
the  former  interest  the  application 
of  Vector  Analysis  or  the  Algebra 
of  Directed  Quantities  received  a 
great  impetus  when  the  need  was 
felt  of  having'  an  'algebra  of  "  i)hy- 
sical  quantities."  This  found  e.x- 
jiression  in  the  writings  of  Clerk- 
Maxwell.  (See  his  '  Treati.se  on 
Electricity  and  Magnetism,'  vol.  i. 
J).  8,  2nd  ed.,  as  also  his  paper  on 
"  The  Mathematical  Classification  of 
Physical  Quantities,"  1871.  'Coll. 
I'aiiers,'  vol.  ii.  p.  2.'>7.)  In  the  prac- 
tical ajjplication  of  electrical  tiieories 


these  notions  have  since  become  in- 
disi)ensable,  and  the  subject  lia,s  re- 
ceived increjvsing  attenti(jn,  notably 
in  America,  which  holds  a  foremost 
place  in  the  development  of  electrical 
-science  and  its  application.  Mathe- 
maticians of  the  first  order,  such 
as  J.  Willard  Gibbs,  have  pub- 
lisheil  te.xt-books  on  the  subject, 
whilst  other  electricians  of  emin- 
ence, such  as  Mr  Oliver  Heaviside, 
have  elaborated  sjiecial  forms  of  the 
Directional  Calculus  to  serve  their 
purpose.s.  In  Dynamics  the  Dublin 
School,  represented  after  the  death 
of  Hamilton  by  Sir  Robert  S.  Ball 
(in  his  '  Theory  of  Screws,'  1876), 
has  had  an  imjjortant  influence  in 
tlie  introduction  of  novel  and  more 
a])propriate  methods  whicii  have 
gradually  permeated  the  general 
treatment  of  the  subject.  Whilst 
there  is  no  doubt  that  for  a  long 
time  the  Calculus  of  Quaternions 
was  the  oidy  methodical  elaboration 
of  these  novel  and  useful  ideas,  it 
was  overlooked  that  simultaneously 
and  quite  independently  H.  Grass- 
mann  of  Stettin  (see  above,  vol.  i. 
p.  213)  had  worked  out  a  much  more 
com])rehensive  and  fundamental 
calculus,  of  which  the  method  of 
quaternions  and  all  the  dili'erent 
forms  of   Vector   Analysis   can   l>e 


656  SCIENTIFIC    THOUGHT. 

arithmetic  based  upon  two  units  instead  of  one — i.e.,  the 
arithmetic  of  couples  or  complex  quantities — could  be 
completely  and  consistently  represented  by  choosing  as 
axes  whereon  the  separate  units  were  counted,  the  two 
perpendicular  axes  of  Cartesian  geometry.  An  attempt 
to  extend  this  geometrical  representation  into  space  led 
Hamilton  to  the  invention  of  his  method,  Gauss  having 
very  early  satisfied  himself  that  within  the  limits  of 
ordinary  algebra  no  further  extension  was  necessary  or 
possible. 

The  examination  into  fundamental  principles  was  not 

limited  in  the  mind  of  Gauss  to   those  of  algebra :  he 

early  applied  himself  likewise  to  those  of  geometry  and 

of   dynamics.     The   great  French  mathematicians,  such 

21.        as  Legendre  and  Lagrange,  were  also  occupied  with  such 

Foundations  ®    _  o         o    '  r 

of  geometry,  speculations.  They  have  been  carried  on  all  through 
the  century,  but  have  only  towards  the  end  of  the 
period  been  brought  into  connection  and  shown  to  be 
of  importance  for  the  general  progress  of  mathematics. 
The  secluded,  and  for  a  long  time  unappreciated,  labours 
of  isolated  but  highly  original  thinkers  have  accordingly 

considered  as  merely  special  in-  '  Grassmann's  works  is  being  pub- 
stances.     This  has  now  been  abund-    '    lished  by  Teubner.     Those  who  are 


antly  proved  through  the  writings 
of  mathematicians  in  all  countries, 
among  whom  I  will  only  mention 
Hankel  and  Dr  V.  Schlegel  in  Ger- 
many, Clifford,  Prof.  Henrici,  and 
latterly  Mr  Whitehead  in  England, 
Prof.  Peano  in  Italy,  and  M.  Burali 
Forti  in  France.  See  on  the  whole 
subject,  on  the  fate  of  Grassmann 
and  of  his  great  work,  V.  Schlegel, 
'  Die  Grassmann'sche  Ausdehnungs- 
lehre,'  Leipzig,  1896  ;  also,  by  the 
same  author,  a  short  biography  of 
Grassmann  (Leipzig,  Brockhaus, 
1878).       A     complete    edition     of 


interested  in  seeing  how  the  notions 
underlying  the  directional  calculus 
are  gradually  becoming  clarified,  and 
the  terminology  and  notation  settled, 
may  read  with  profit  the  controversy 
carried  on  in  the  pages  of  '  Nature,' 
vols,  xlvii.  and  xlviii.,  between  Pi'of. 
Macfarlane,  Willard  Gibbs,  Mr  0. 
Heaviside,  Mr  A.  M'Aulay,  and  Dr 
Knott ;  also  Dr  Larmor's  review  of 
Hay  ward's  '  Algebra  of  Coplanar 
Vectors'  (vol.  xlvii.  p.  266),  and 
Sir  R.  S.  Ball's  reference  to  the 
'  Ausdehnungslehre '  of  Grassmana 
(vol.  xlviii.  p.  391,  1893). 


DEVELOPMENT  OF  MATHEMATICAL  THOUGHT.   657 

received  tardy  recognition.  Such  speculations  can  hi 
carried  on  either  as  fascinating  exercises  of  mere 
ingenuity,  or  for  practical  purposes  to  improve  the 
refined  instruments  of  mathematical  calculation,  or  in 
the  philosophical  interest  of  arriving  at  the  fundamental 
processes  of  human  thought  .ind  intuition.^  Many 
persons   think   tliat    only    the   second   of  these   three   in- 


'  Already  Euler  had  remarked  on 
the  different  interests  that  prompted 
mathematical  research.  Referring 
to  tiie  wTitings  of  Count  Fagnano, 
he  says  in  the  introduction  to 
the  tirst  of  his  memoirs  on  Elliptic 
Integrals  (1761,  ([Uoted  by  Brill  & 
Nuther  in  '  BerichL  der  Deutschen 
Matheniatiker-Vereinigung,'  vol.  iii. 
p.  206)  :  "  If  one  looks  at  mathe- 
matical speculations  from  the  point 
of  view  of  utility,  they  can  be  divided 
into  two  classes  :  first,  those  which 
are  of  advantage  to  ordinary  life 
and  other  sciences,  and  tiie  value 
of  which  is  accordingly  measured  by 
the  amount  of  that  advantage.  The 
other  class  comprises  speculations 
which,  without  any  direct  advant- 
age, are  nevertheless  valuable  be- 
cause they  tend  to  enlarge  the 
boundaries  of  analysis  and  to  exer- 
cise the  powers  of  the  mind.  Inas- 
much as  many  researches  which 
promise  to  be  of  great  use  have  to 
be  given  up  owing  to  the  inade- 
(juacy  of  analysis,  those  speculations 
are  of  no  little  value  which  i)romise 
to  extend  the  province  of  analysis. 
Such  seems  to  be  the  nature  of 
observations  which  are  usually  made 
or  found  a  posteriori,  but  which 
have  little  or  no  chance  of  being 
discovered  a  priori.  Having  once 
been  established  as  correct,  methods 
more  easily  present  themselves 
which  lead  up  to  them,  and  there 
is  no  doubt  that  thrcjugh  the  search 
for  such  methods  the  domain  of 
analysis  may    be   considerably    ex- 

VOL.  II. 


tended."  The  school  of  mathema- 
ticians headed  by  Abel  and  Jacobi 
pursued  mathematics  from  purely 
scientific  interest,  and  was  criti- 
cised on  this  ground  bj-  eminent 
contemporary  mathematicians  in 
France  :  see  a  letter  of  Jacobi  to 
Legendre,  dated  July  2,  1830,  in 
which  he  refers  to  a  Report  of 
Poisson  on  his  great  work,  but 
adds  :  "  M.  Poisson  n'aurait  pas 
du  reproduire  dans  son  rapport 
une  phrase  pcu  adroite  de  feu  M. 
Fourier  oii  ce  dernier  nous  fait 
des  rej)roches,  a  Abel  et  h,  moi,  de 
ne  pas  nous  etre  occupes  de  pre- 
fdrence  du  mouvement  de  la  chaleur. 
II  est  vrai  que  M.  Fourier  avait 
I'opinion  ijue  le  but  principal  des 
mathcmatiques  ot^iit  I'utilite  pub- 
lique  et  lexplication  des  i)hcno- 
menes  naturels ;  mais  un  philosophe 
comme  lui  aurait  du  savoir  que  le 
but  uni<iue  de  la  science,  c'est 
I'honneur  de  I'esprit  Immain  et  que 
sous  ce  titre,  une  question  de 
nombres  vaut  autant  ([u'une  (jues- 
tion  du  systemedu  monde."  In  the 
sequel  he  adds  :  "  Je  crois  entrevoir 
que  toutes  ces  transcendantes "  (i.e., 
the  elliptic  and  Abelian  functions) 
"jouissent  des  jiroprictcs  admir- 
ables  et  inattendues  auxquclles  on 
l)eut  etre  conduit  par  le  theorfcme 
d'Abel.  .  .  .  J'ai  retlcchi  aussi  de 
temps  en  temps  sur  une  methode 
nouvelle  de  traiter  les  perturbations 
celestas,  methode  dans  laciuelle 
doivent  entrer  les  theories  nou- 
velles  des  fonctions  elliptiques." 

2   T 


658 


SCIENTIFIC    THOUGHT. 


22. 
Descriptive 

Geometry. 


ducements  is  likely  to  prove  fruitful  for  the  progress  of 
science ;  they  look  upon  the  first  as  an  amusing  pastime, 
and  upon  the  third  as  empty  and  not  devoid  of  danger. 
In  recognition  of  the  partial  correctness  of  this  view,  I 
will  follow  up  the  practical  stimulus  in  its  fruitful  in- 
fluence upon  the  development  of  the  lines  of  mathe- 
matical research. 

This  stimulus  came  in  the  closing  years  of  the  pre- 
ceding century  through  the  lectures  of  Gaspard  Monge 
at  the  I^cole  Normale,  and  has  become  popularly  known 
through  his  invention  of  Descriptive  Geometry,  the  first 
modern  systematic  application  of  purely  graphical  methods 
in  the  solution  of  mathematical  problems.  As  Cauchy 
was  the  founder  of  the  modern  school  of  analysts,  so 
Monge,  together  with  Carnot,  founded  the  modern  school 
of  geometricians ;  Dupin,  Poncelet,  and  Chasles  being 
among  his  most  illustrious  pupils.  The  aim  of  this 
school  was  to  give  to  geometrical  methods,  such  as 
had  been  practised  by  the  ancients,^  the  same  generality 
and  systematic  unity  which  characterised  the  analytical 
methods  introduced  by  Descartes. 

Not  long  after  the  introduction  of  the  latter,  Leibniz 


^  These  methods  had  been 
largely  used  in  this  country  by 
Newton,  Robert  Simson,  and 
Stewart.  They  were  systematised 
by  L.  N.  M.  Cai-not.  Chasles 
("  Discours  d'inauguration,  &c.," 
1846,  'G(?om^trie  Superieure,'  p. 
Ixxvii)  says  :  "  Dans  le  siecle 
dernier,  R.  Simson  et  Stewart 
donnaient,  li  I'instar  des  Anciens, 
autant  de  demonstrations  d'une 
proposition,  que  la  figure  h.  laquelle 
elle  se  rapportait  presentait  de 
formes  differentes,  h,  raison  des 
positions  relatives  de  ses   diverses 


parties.  Carnot  s'attacha  a  prouver 
qu'une  seule  demonstration  ap- 
pliquee  h.  un  ^tat  as.sez  general 
de  la  figure  devait  suftire  pour 
tous  les  autres  cas  ;  et  il  montre 
comment,  par  des  changements 
de  signes  de  ternies,  dans  les 
formules  d^montrees  par  une 
figure,  ces  foruiules  s'appliquaient 
il  une  autre  figure  ne  ditteraut  de 
la  premiere,  commes  nous  I'avons 
dit,  que  par  les  positions  relatives 
de  certaines  parties.  C'est  ce  qu'il 
a()pela  le  '  Principe  de  correlation 
des  figures.' " 


DEVELOPMENT  OF  MATHEMATICAL  THOUGHT.   659 

had  foretold  ^  the  possibility  and  necessity  of  such  an 
independent  development  of  pure  geometry,  in  which  the 
relations  of  position  in  space,  as  opposed  to  those  of 
measure,  magnitude,  or  quantity,  would  be  placed  in  the 
foreground.  Projection,  as  practised  in  the  drawing  of 
maps,  and  perspective,  as  practised  in  the  fine  a.nd 
descriptive  arts,  had  already  re^'ealed  a  number  of 
remarkable  properties  of  figures  in  the  plane  and  in 
space.  By  continuous  motion  of  points  or  lines,  by 
artifices  like  throwing  of  shadows,  by  sections  of  solids 
with  lines  and  surfaces,  a  vast  number  of  problems  had 
been  solved  and  isolated  theorems  established.  The 
method  here  practised  was  that  of  construction,  as  in 
analysis  the  method  was  that  of  calculation  with  sub- 
sequent interpretation.  All  this  purely  constructive 
work  was  to  be  brought  together  and  systematically 
combined  in  a  whole.  It  was  evidently  a  distinct  line 
of  research,  based  upon  intellectual  processes  other 
than  the  purely  analytical  method  —  a  line  which, 
as  it  seemed  to  its  followers,  had  been  unduly  neglected 
and  pushed  into  the  background.  Although  Monge 
became  the  founder  of  this  purely  descriptive  or  con- 
structive branch  of  geometry,  he  was  himself  equally 
great  as  an  analyst ;  in  fact,  the  fusion  in  his  mind 
of  the  two  methods  was  the  origin  of  much  of  his 
greatest  work.  In  attempting  to  carry  out  more 
thoroughly  the  separation  or  independent  development 
of  the  constructive  or  descriptive  method,  his  great  pupil, 

23. 

J.  V.  Poncelet — whilst  deprived  of  all  literary  resources  Poneeiet. 

^  See  the  quotations  fi-oni  his  letters  to  Huygens  and  others  given 
above,  vol.  i.  p.  103  note. 


660  SCIENTIFIC    THOUGHT. 

in  the  prisons  of  Kussia — meditated  on  the  real  cause  of 
the  power  which  algebraical  analysis  possessed,  on  the 
reason  why  geometry  proper  was  deprived  of  it,  and 
what  might  be  done  to  give  it  a  similar  generality.  In 
pursuing  this  line  of  thought  he  was  led  to  discover  the 
cause  of  the  existing  limitation  of  purely  geometrical 
reasoning  in  its  rigidity,  inasmuch  as  it  was  arrested  as 
soon  as  its  objects  ceased  to  have  a  positive  or  absolute, 
that  is  a  physical,  existence.-^  Opposed  to  this  limitation 
was  the  freedom  of  the  analytical  method,  which,  operating 
with  indeterminate  symbols,  could,  by  letting  them  change 
gradually,  include  not  only  what  was  explicitly  given, 
but  also  that  which  was  merely  implied ;  not  only  the 
finite,  but  likewise  the  infinite ;  not  only  the  real,  but 
likewise  the  fictitious  or  imaginary.  In  order  to  gain  a 
similar  generality  in  purely  geometrical  or  descriptive 
science,  a  similar  fiexibility  would  have  to  be  introduced. 
Poncelet  was  thus  led  to  the  enunciation  of  his  celebrated 
and  much  -  criticised  "  principle  or  law  of  continuity."  ^ 

1  See  the  "  Introduction "  to  the  '  122,  &c.  :  "Originally  the  ex- 
ist volume  of  the  '  Traite  des  Pro-  |  positions  referring  to  the  prin- 
ciple of  continuity  were  intended 
to  occupy  much  greater  space.  .  .  . 
In  consequence  of  correspondence 
with  Terquem,  Servois,  and  Brian- 
chon,  Poncelet  desisted  from  the 
publication  of  it.  .  .  .  However 
cautiously   Poncelet   advanced   his 


pridtes  projectives  des  figures,'  pp. 
xi,  xii.  I  quote  from  the  2nd  edi- 
tion of  1865.  The  1st  was  published 
in  1822.  The  researches  date  from 
1813,  the  year  of  Poncelet's  im- 
prisonment. See  "  Preface  de  la 
premiere  edition." 

^  Ibid.,  Introduction,  p.  xiv.  ;  principle  " — in  the  '  Essai  sur  les 
On  the  principle  of  continuity  \  proprietes  projectives  des  sections 
in  geometry,  see  an  article  in  coniques  '  (presented  to  the 
vol.  xxviii.  '  Ency.  Brit.'  by  the  i  Academy  in  1820)  — "  it  never- 
Rev.  Charles  Taylor,  and  the  re-  |  theless  aroused  the  doubts  of 
ferences  given  therein ;  also  Prof.  ]  Cauchj^,  who  in  his  report  on 
E.  Kotter's  Report  on  the  i  Poncelet's  paper  warns  against  the 
"  Development  of  Synthetic  Ge-  too  hasty  application  of  the 
ometry "  in  vol.  v.  of  the  i  principle.  Gergonne  accompanied 
'  Jahresbericht  der  Deutschen  '  the  reprint  of  this  report  with 
Mathematiker      Vereinigung,'      p.    I    notes,    in   which    he   characterised 


DEVELOPMENT    OF    MATHEMATICAL    THOUGHT.       661 

Analytical  geometry,  Ijy  substituting  an  algebraical  ex- 
pression for  a  geometrical  figure — say  a  curve, — could 
apply  to  it  all  the  artifices  of  abstract  analysis.  By 
varying  the  co-ordinates  you  can  proceed  along  the  whole 
extent  of  the  curve  and  examine  its  behaviour  as  it 
vanishes  into  infinity,  or  discover  its  singular  points  at 
which  there  occurs  a  break  of  continuity :  you  can  vary 
its  constants  or  parameters,  and  gradually  proceed  from 
one  curve  to  another  belonging  to  the  same  family,  as  is 
done  in  grouping  together  all  curves  of  the  second  order, 
or — as  was  done  in  the  calculus  of  variation,  invented 
by  Euler  and  Lagrange — you  can  vary  the  form  of  the 
equation,  proceeding  from  one  class  of  curve  to  another. 
Now  clearly  all  this  operating  on  equations  and  sym- 
bolic expressions  was  originally  abstracted  from  geom- 
etry, including  the  mechanical  conception  of  motion ;  in 
particular  the  ideas  which  underlie  the  method  of 
fluxions  were  suggested  by  the  motion  of  a  point  in 
space.      The  conception  of  continuous  motion  in  space- — 

the    principle    as    a    valuable    in-  j  the  habit  of   considering  real  and 

.strument    for     the     discovery     of  !  imaginary     quantities     as    equally 

new  truths,  whicii  nevertheless  did  '  legitimate    led    to    that    principle 

not  make   stringent  proofs  super-  ,  which,  without  analytical  geometry, 

fluous."     Cauchy's  report  seems  to  |  could  never  have  been  discovered, 

have  aroused  Poncelet's  indignation,  j  Thus  pure  geometry  was  compen- 

Hankel  ('Elemente  der  Projectiv-  !  sated   for    the   fact   that    analysis 


ischeu  Geometrie,'  187.5,  p.  9) 
says:  "This  principle,  which  was 
termed  by  Poncelet  the  '  Prin- 
ciple   of    Continuity,'  inasmuch   as 


had  for  a  long  time  absorbed  the 
exclusive  interest  of  mathemati- 
cians ;  indeed  it  was  perhaps  an 
advantage    that    geometry,    for    a 


it     brings     the    various     concrete    i    time,  had   to  lie  fallow."      Kotter 


cases  into  connection,  could  not 
be  geometrically  proved,  because 
the  imaginary  could  not  be 
represented.  It  was  rather  a 
present  which  pure  geometry  re- 
ceived from  analysis,  where  im- 
aginary quantities  behave  in  all 
calculations  like   real   ones.     Only 


continues :  "  Von  Staudt  was  the 
first  who  succeeded  in  subjecting 
the  imaginary  elements  to  the 
fundamental  theorem  of  projective 
geometry,  thus  returning  to  analyt- 
ical geometry  the  present  which, 
in  the  hands  of  geometricians,  had 
led  to  the  most  beautiful  results." 


662  SCIENTIFIC    THOUGHT. 

of  motion  of  points,  lines,  planes — corresponded  accord- 
ingly to  the  notion  of  vai-iability  in  analysis.  The  intro- 
duction of  motion,  gradual  and  continuous,  would  give 
to  purely  geometrical  or  descriptive  reasoning  the  same 
flexibility  which  analysis  had  acquired  in  the  calculus  of 
fluxions  and  of  variations.  Figures  would  lose  their 
rigidity  and  isolation  and  limited  nature  and  become 
movable,  related  to  each  other,  filling  the  whole  of  space 
24.        instead  of  a  restricted  and  confined  area  or  region.      It 

Character 

of  modem     is  the  peculiarity  of  the  modern  as  opposed  to  the  older 

geometry.  j.  ^  x  x 

geometry,  never  to  let  figures  become  motionless  or 
rigid,^  never  to  consider  them  in  their  isolation,  but 
always  in  their  mutual  relations ;  never  to  have  regard 
only  to  a  finite  portion  of  a  line  or  surface,  but  to 
conceive  of  it  in  its  infinite  extension.  By  a  reaction 
of  analysis  and  geometry  on  each  other,  freedom  and 
generality  have  been  gradually  acquired. 

But  this  moving  about  of  figures  in  space  in  order 
to  learn  their  properties  and  mutual  relations  must  b& 
according  to  some  method ;  otherwise  it  will  not  lead  to 
scientific  and  exact  knowledge.  Poncelet,  in  considering 
how  the  two  successful  methods  in  geometry  —  the 
Cartesian  and  the  Descriptive — had  attained  to  their 
perfection,  discovers  a  general  principle  which  underlies 
their  proceedings,  and  which  is  capable  of  great  extension: 
this  is  the  principle  of  projection." 


^  See,  inter  ulia,  what  Geiser 
says  of  Jacob  Steiner's  method  in 
his  pamphlet  '  Zur  Erinnerung  an 
Jacob  Steiner,'  Schaffhausen,  1874, 
p.  27. 

^  'Traite  des  Proprietes  pro- 
jectives,'  voh  i.  p.  xviii :  "  En 
reflechissant    attentivement    Ji    ce 


qui  fait  le  principal  avantage  de 
la  Geometric  descriptive  et  de  la 
mdthode  des  coordonnees,  h  ce  qui 
fait  que  ces  branches  des  Mathe- 
matiques  offrent  le  caractere  d'une 
veritable  doctrine,  dont  les  prin- 
cipes,  peu  nombreux,  sont  li^s  et 
enchaiiies  d'une  maniere  necessaire 


DEVELOPMENT    OF    MATHEMATICAL    THOUGHT. 


663 


Of  this  principle  of  projection,  which  Poncelet  at  once  25- 
introduces  in  the  more  general  form  as  conical  or  central  projection, 
projection,  two  signal  applications  existed  in  the  treatises 
on  Conic  Sections  handed  down  from  antiquity,  and  in 
the  practical  methods  and  Eules  of  Perspective  invented 
by  Lionardo  da  Vinci  and  further  developed  by  various 
geometricians.  The  results,  which  lay  scattered  in  many 
books  and  memoirs,  Poncelet  collected  in  a  systematic 
form,  bringing  them,  by  the  application  of  the  law  of 
continuity,  under  a  few  general  and  eminently  useful 
points  of  view  or  principles.  By  the  method  of  projec- 
tion or  perspective  he  "  transformed  figures  which  are 
very  general  into  others  which  are  particular,  and  vice 
versa."  He  established  the  principle  of  "  homology  "  in 
figures,  and  by  showing  how  figures  apparently  very 
different  could  be  described  by  the  process  of  projection 
from  the  same  original  figure,  he  showed  that  there 
existed  a  peculiar  relation  among  figures — viz.,  their 
"  reciprocity."  ^ 


et  par  uiie  uiarche  uniforme,  on 
ne  tarde  pas  h  reconnaitre  que  cela 
tient  uuiquement  ii  I'usage  qu'elles 
font  cle  la  projection." 

'  The  properties  of  figures,  called 
by  Poncelet  "  liomology  "  and  "I'e- 
ciprocity,"  refer  to  the  correspond- 
ence of  certain  elements  of  one 
figure  to  those  of  another  figure. 
In  the  case  of  "  homology,"  we 
have  to  do  with  corresponding 
points  or  corresponding  lines— ix., 
with  the  correspondence  of  the 
same  elements.  In  the  case  of 
"reciprocity,"  we  have  to  do  with 
correspondence  of  points  or  lines 
in  the  one  figure,  with  lines  or 
points  in  the  other — i.e.,  with 
the  correspondence  of  different 
elements.      The    idea     of     placing 


figures  in  an  homologous  rela- 
tion was  got  by  the  device  of 
making  two  planes,  which  con- 
tained figures  in  perspective,  fall 
together  into  one  plane  ;  upon 
which  the  section  of  the  two  orig- 
inal jilanes  became  the  "  axis," 
and  the  ej-e-point  the  "  centre " 
of  homology — all  situated  in  one 
and  the  same  plane.  Poncelet  had 
already  conceived  of  the  possibil- 
ity of  reducing  the  two  planes  in 
Monge's  '  Descriptive  Geometry,' 
which  represent  the  plan  and  ele- 
vation of  a  figure  in  one  plane, 
on  which  the  elevations  were 
marked  by  what  are  now  called 
"  contour  lines."  The  idea  of  the 
correspondence  of  figures  by  what 
is    called    "  reciprocity "    was    sug- 


664  SCIENTIFIC   THOUGHT. 

26.  By  the  law  of  continuity  he  showed  how  in  pure 
continuity,  geometry  it  became  necessary  to  introduce  the  considera- 
tion of  points  and  lines  which  vanish  into  infinity  or 
which  become  imaginary,  establishing  by  their  invisible 
elements  the  continuous  transition  from  one  geometric 
form  to  another ;  just  as  in  algebra  these  conceptions 
had  forced  themselves  on  the  attention  of  analysts. 
Ideal  elements  were  thus  made  use  of  to  lead  to  the  dis- 
covery of  real  properties. 

The  consideration  of  lines  and  points  which  vanish 
or  lie  at  infinity  was  familiar  to  students  of  perspective 
from  the  conception  of  the  "  vanishing  line  " ;  but  the 
inclusion  of  ideal  points  and  lines  was,  as  Hankel  says, 
a  gift  which  pure  geometry  received  from  analysis, 
where  imaginary  (i.e.,  ideal  or  complex)  quantities  behave 

27.  in  the  same  way  as  real  ones.     "Without  the  inclusion  of 

Ideal  _  "^ 

elements,  tlicsc  ideal  or  invisible  elements  the  generality  or  con- 
tinuity of  purely  geometrical  reasoning  was  impossible. 
The  geometrical  reasoning  of  Monge,  Carnot,  and 
Poncelet  was  thus  largely  admixed  with  algebraical  or 
analytic  elements.  It  is  true  that  Monge's  descriptive 
geometry    was    a    purely    graphical    method,    and    that 


gested  to  Poncelet  by  the  prop- 
erty, known  already  to  De  la 
Hire  ("Sectiones  ConicEc,"  1685), 
that  in  the  plane  of  a  conic 
section  every  point  corresponds 
to  a  straight  line  called  its 
"polar,"  that  to  everj^  straight 
line  corresponds  a  point  called 
its  "  pole,"  that  the  "  polars " 
corresponding  to  all  the  points  of 
a  straight  line  meet  in  one  and 
the  same  point,  and  vice  versa 
that  the  "poles"  corresponding  to 
all  lines  going  through  one  and 
the   same   point  lie   on  a  straight 


line  ;  the  line  and  point  in  ques- 
tion standing  in  both  cases  in  the 
relation  of  pole  and  polar  to  each 
other.  Poncelet  uses  "this  trans- 
formation of  one  figure  into  its 
reciprocal  polar  systematicallj'  as  a 
method  for  finding  new  theorems : 
to  every  theorem  of  geometry 
there  corresponds  in  this  way 
another  one  which  is  its  '  polar,' 
and  the  whole  of  geometry  was 
thus  split  up  into  a  series  of 
truths  which  run  parallel  and 
frequently  overlap  each  other " 
(Hankel,  loc.  cit.,  p.  20). 


DEVELOPMENT    OF    MATHEMATICAL    THOUGHT.        665 

Poncelet's  method  of  central  projection  attacked  geometri- 
cal problems  from  a  purely  constructive  point  of  view. 
Nevertheless  the  frequently  expressed  oljject  of  the  later 
writings  of  Monge,  as  well  as  those  of  Carnot  and 
Poncelet,  was  to  introduce  into  geometrical  reasoning 
the  generality  and  continuity  which  analysis  possessed, 
and  this  was  largely  attained  by  the  interpretation  of 
notions  taken  over  from  analysis.  Their  endeavours 
were,  however,  in  the  sequel  crowned  by  the  discovery 
of  a  purely  geometrical  property,  the  understanding  of 
which  has  ever  since  formed  the  basis  of  what  may  be 
termed  modern  geometry. 

This  remarkable  property,  which  may  be  regarded 
as  revealing  the  very  essence  of  extension  in  space  or 
of  the  "  space -manifold," — inasmuch  as  it  brings  the 
different  elements  of  space  into  mutual  relation, — is  the 
go-called  principle  of  "  duality  "  or  of  "  reciprocity."     The        ss. 

.  ,  I  J  Principle  ol 

principle  of  duality  is  now  usually  defined  to  mean  that  duality. 
in  geometry  on  the  plane  or  in  space,  "  figures  coexist  in 
pairs,  two  such  coexisting  figures  having  the  same  genesis 
and  only  differing  from  one  another  in  the  nature  of  the 
generating  element."  ^     The  elements  of  plane  geometry 
are  the  point  and  the  line  ;  the  elements  of  solid  geometry 
i  are  the  point  and  the  plane.      By  interchanging   these 
I  correlative  terms,  correlative  propositions  may  be  written 
down  referring  to  plane  and  to  space  geometry.      In  pro- 
jective geometry  there  are  two  processes  which  are  cor- 
;  i  relative  or  complementary  to  each  other — the  process  of 
;i  projection  and  the  process  of  section.      We  can  project 

^  Cremona,  '  Elements  of  Projective  Geometry,'  transl.  by  Leudesdorf. 
Oxford,  1885,  p.  26. 


666 


SCIENTIFIC    THOUGHT. 


29. 
Keciprocity, 


from  a  point  drawing  lines  or  rays  on  the  plane  and  in 
space,  and  we  can  cut  these  by  lines  in  a  plane  or  by 
planes  in  space.  And  it  can  be  shown  that  "  if  one 
geometric  form  has  been  derived  from  another  by  means 
of  one  of  these  operations,  we  can  conversely,  by  means 
of  the  complementary  operation,  derive  the  second  from 
the  first."  ^ 

The  projective  geometry  of  Poncelet  contains  the  two- 
fold origin  of  the  principle  of  duality  in  his  method  of 
projection  and  section,  and  in  his  theory  of  the  reciprocity 
of  certain  points  and  lines  in  the  doctrine  of  conic  sections, 
called  the  theory  of  reciprocal  polars.  But  the  mathe- 
matician who  first  expressed  the  principle  of  duality  in  a 
general — though  not  in  the  most  general  —  form  was 
Gergonne,  who  also  recognised  that  it  was  not  a  mere 
geometrical  device  but  a  general  philosophical  principle, 
destined  to  impart  to  geometrical  reasoning  a  great 
simplification.  He  sees  in  its  enunication  the  dawn  of 
a  new  era  in  geometry.^ 


1  Cremona,  loc.  cit.,  p.  33. 

-  The  priuciple  of  Duality  seeiu.s 
to  have  been  first  put  forward  in  its 
full  generalit}'  by  Gergonne,  in- 
spired probably  by  the  theory  of 
Reciprocal  Polars  (see  note,  p.  663) 
enunciated  by  Poncelet,  who  many 
j'ears  afterwards  carried  on  a  vol- 
uminous polemic  as  to  the  priority 
of  the  discovery.  "  Gergonne  saw 
that  the  ])arallelisni  (referred  to 
above)  is  not  an  accidental  conse- 
quence of  the  property  of  conic 
sections,  but  that  it  constitutes  a 
fundamental  principle  which  he 
termed  the  'principle  of  duality.' 
The  geometry  which  is  usually 
taught,  and  in  which  a  line  is  con- 
sidered to  be  generated  by  the 
motion  of   a    point,  is    opposed   by 


another-    geometry    equallj'    legiti- 
mate   in    which  a  point  is  gener- 
ated   by   the    rotation    of    a    line. 
Whereas  in  the  first  case  the  line  is 
the  locus   of  the   moving  point,  in 
the    latter    case   the   point   is    the 
geometrical      intersection     of     the 
rotating  line.       In    this   generality 
the  principle  of  duality  has  been  in- 
corporated into  modern  geometry  " 
(Hankel,  loc.  cil.,  p.  21).     Gergonne 
says  of  the  new  principle  (1827,  see 
Supplement  to  vol.    ii.    2nd  ed.  of; 
Poncelet's  '  Traite,'  p.  890) :   "  II  ne 
s'agit  pas  moins  que  de  commencer 
pour     la     geometric,    mal    connucii 
depuis  pros  de  deux  mille  ans  qu'oni 
s'en    occupe,    une   ere   tou  t  -  h  -  f aiti 
nouvelle  ;  il  s'agit  d'en  mettre  tousH 
les  anciens   traites    ii   pen   pres  auj 


DEVELOPMENT  OF  MATHEMATICAL  THOUGHT.   667 

It  must,  however,  in  all  fairness  be  stated  that  about 
the  period  from  1822  to  18.")0  this  great  simplification 
and  unification  of  geometric  science  was  as  it  were  in  the 
air — that  it  had  presented  itself  to  various  great  thinkers 
independently,  being  suggested  from  different  points  of 
view.  The  beginnings  can  no  doubt  be  traced  in  the 
beautiful  theorems  of  older  French  mathematicians,  such 
as  Pascal  and  De  la  Hire,  and  more  generally  in  the 
suggestive  methods  of  i\Ionge  and  Poncelet ;  its  first 
formal  enunciation  is  in  the  memoirs  of  Gergonne :  but 
the  comprehensive  use  of  it — -the  rewriting  of  geometry 
from  this  point  of  view — was  the  idea  of  Jacob  Steiner,        3o. 

Steiner- 

who,  in  his  great  but  unfinished  work  on  the  "  Systematic 
Development  of  the  Dependence  of  Geometric  Forms  " 
(ISoO),  set  himself  the  great  task  "of  uncovering  the 
organism  by  which  the  most  different  forms  in  the  world 
of  space  are  connected  with  each  other."  "  There  are," 
he  says,  "  a  small  number  of  very  simple  fundamental 
relations  in  which  the  scheme  reveals  itself,  by  which 
the  whole  body  of  theorems  can  be  logically  and  easily 
developed."  "  Through  it  we  come,  as  it  were,  into  pos- 
session of  the  elements  which  Nature  einploys  with  the 
1  greatest  economy  and  in  the  simplest  manner  in  order  to 
invest  figures  with  an  infinite  array  of  properties."^ 

rebut,  de  leur  substituer  des  traites       tion    aussi    iuiperieusement   u^ces- 
Vune  forme  tout  a  fait  ditfurente,       saire    qu'elle    a    ete   jusqu'ici    peu 


kles  traites  vraiment  philosophiques  prevue. 

'qui  nous  montreut  eutin  cette  eten-  ^  See    the  Preface   to   the   '  Sj's- 

Idue,  receptacle  universel  de  tout  ce  tematische       Entwickelung,      &c.,' 

qui  existe,  sous  sa  veritable  physi-  i    in    Jacob    Steiner's    '  Gesammelte 


nnomie,  que  la  mauvaise  inethode 
•d'enseignement  adoptee  jusqu'ii  ce 
ijour  ne   nous  avait  pas  permis  de 


Werke '  (ed.  Weierstrass),  vol.  i. 
p.  229.  "  In  the  beautiful  theorem 
that  a  conic  section  can  be  gener- 


ii-eniarquer ;    il   s'agit,   en    un    mot,    '    ated    by    the    intersection    of    two 
I'operer  dans  la  science  une  revolu-       projective  pencils  (and  the  dually 


668 


SCIENTIFIC    THOUGHT. 


The  labours  of  Poncelet  and  Steiner  introduced  into 
geometry  a  twofold  aspect,  and  accordingly,  about  the 
middle  of  the  century,  we  read  a  good  deal  of  the 
two  kinds  of  geometry  which  for  some  time  seemed  to 
develop  independently  of  each  other.  The  difference 
has  been  defined  by  the  terms  "  analytic  or  synthetic," 
"  calculative  or  constructive,"  "  metrical  or  projective." 
The  one  operated  with  formulae,  the  other  with  figures ; 
the  one  studied  the  properties  of  quantity  (size,  magni- 
tude), distances,  and  angles,  the  other  those  of  position. 

The  projective  method  seemed  to  alter  the  magnitude 
of  lines  and  angles  and  retain  only  some  of  those  of 
position  and  mutual  relation,  such  as  contact  and  inter- 
section. The  calculating  or  algeliraical  method  seemed 
to  isolate  figures  and  hide  their  properties  of  mutual 
interdependence  and  relation. 
31.  These    apparent    defects    stimulated    the    representa- 

Mutual  in-         •  n        i 

fluence  of     tivcs    of    the    two    mctliods    to    investigate    more   min- 

metrical  and  ° 

projective     utcly   their   hidden   causes   and   to    perfect    both.     The 

geometry.  ^  ^ 

algebraical  formula  had  to  be  made  more  pliable,  to: 
express  more  naturally  and  easily  geometrical  relations ; 
the  geometrical  method  had  to  show  itself  capable  of' 
dealing  with  quantitative  problems  and  of  interpreting 
geometrically  those  modern  notions  of  the  infinite  and 
the  complex  which  the  analytic  aspect  had  put  promi- 


correlated  theorem  referring  to 
projected  ranges),  Steinei-  recog- 
nised the  fundamental  principle 
out  of  which  the  innumerable 
properties  of  these  remarkable 
curves  follow,  as  it  were,  automat- 
ically with  playful  ea.se.  Nothing 
is  wanted  but  the  combination  of 
the  simplest  theorems  and  a  vivid 


geometrical  imagination  capable  oi 
looking  at  the  same  figure  from 
the  mo.st  different  sides  in  orderi, 
to  multiply  the  number  of  pro-l 
perties  of  these  curves  indefl 
initely "  (Hankel,  loc.  cit.,  p.j 
26  ;  see  also  Cremona,  '  Projectivfjj 
Geometry,'  p.  119). 


DEVELOPMENT    OF    MATHEMATICAL    THOUGHT. 


669 


nently  into  the  foreground.  The  latter  was  done  by 
the  geometric  genius  of  Von  Staudt,  who  succeeded  in 
giving  a  purely  geometrical  interpretation  of  the  imagin- 
ary or  invisible  elements  ^  which  algebra  had  introduced, 
whilst  Steiner  astonished  the  mathematical  world  by  the 
fertility  of  the  methods  by  which  he  solved  the  so- 
called  isoperimetrical  problems — i.e.,  problems  referring 
to  largest  or  smallest  contents  contained  in  a  given 
perimeter  or  vice  versd,  problems  for  which  Euler  and 
Lagrange  had  invented  a  special  calculus.^     In  spite  of 


'  The  geometrical  interpretation 
of  tlie  imaginary  elements  is  given 
by  Von  Staudt  in  a  sequel  to  his 
'Geometrie  der  Lage'  (1847),  en- 
titled '  Beitriige  zur  Geometrie  der 
Lage'  (1856-60);  and  after  hav- 
ing been  looked  upon  for  a  long 
time  as  a  curiosity  or  a  "  hair- 
splitting abstraction,"  it  has 
latterly,  through  the  labours  of 
Prof.  Reye  ( '  Geometrie  der  Lage,' 
1866-68)  and  Prof.  Liiroth  ( '  Math. 
Annalen,'  vol.  xiii.  p.  145),  become 
more  accessible,  and  is  systematic- 
ally introduced  into  many  excel- 
lent text-books  published  abroad. 
The  simplest  exposition  I  am  ac- 
quainted with  is  to  be  found  in 
the  later  editions  of  Dr  Fiedler's 
German  edition  of  Salmon's  '  Conic 
Sections  '  (6th  Aufl.,  vol.  i.  p.  23,  &c., 
and  p.  176,  &c. )  In  1875,  before 
the  great  c'nange  which  has  brought 
unity  and  connection  into  many 
isolated  and  fragmentary  contribu- 
tions had  been  recognised,  Hankel 
wrote  with  regard  to  Von  Staudt's 
work,  and  in  comparison  with  that 
of  Chasles,  as  follows:  "The  work 
of  Von  Staudt,  classical  in  its 
originality,  is  one  of  those  attempts 
;  to  force  the  manifoldness  of  nature 
I  with  its  thousand  threads  running 
!  hither  and  thither  into  an  abstract 
scheme  and  an  artificial  system  :  an 
attempt  such  as  is  only  possible  in 


our  Fatherland,  a  country  of  strict 
scholastic  method,  and,  we  may  add, 
of  scientific  pedantry.  The  French 
certainly  do  as  much  in  the  exact 
sciences  as  the  Germans,  but  they 
take  the  instruments  wherever 
they  find  them,  do  not  sacrifice 
intuitive  evidence  to  a  love  of 
system  nor  the  facility  of  method 
to  its  purity.  In  the  quiet  town 
of  Erlangen,  Von  Staudt  might  well 
develop  for  himself  in  seclusion 
his  scientific  system,  which  he 
would  only  now  and  then  explain 
at  his  desk  to  one  or  two  i^upils. 
In  Paris,  in  vivid  intercourse  with 
colleagues  and  numerous  jjupils, 
the  elaboration  of  the  system 
would  have  been  impossible  "  {loc. 
cit,  p.   30). 

'^  See  the  lecture  delivered  by 
Steiner  in  the  Berlin  Academy, 
December  1,  1836,  and  the  two 
memoirs  on  '  Maximum  and  Min- 
imum '  (1841),  reprinted  in  '  Ge- 
sammelte  Werke,'  vol.  ii.  p.  75 
nqq.,  and  177  sqq.,  especially  the 
interesting  Introductions  to  both, 
in  which  he  refers  to  his  fore- 
runner Lhuilier  (1782),  deploring 
that  others  had  needlessly  forsaken 
the  simple  synthetical  methods 
adopted  by  him.  Some  of 
Steiner's  expositions  in  these 
matters  were  apparently  so  easy 
that    non  -  mathematical    listeners 


670 


SCIENTIFIC   THOUGHT. 


these  marvellous  works  of  genius,  science  is  probably 
indebted  for  its  greatest  advances  to  those  mathema- 
ticians who,  like  Pllicker  in  Germany,  Chasles  in  France, 
and  Cayley  in  England,  employed  the  analytic  and  con- 
structive methods  alternately  and  with  equal  mastery. 

It  is  impossible — and  it  is  not  my  object — to  allot  to 
each  of  these  original  thinkers  the  special  ideas  intro- 
duced by  him  into  modern  science ;  but  for  the  purpose 


like  Johannes  Miiller  could  not 
understand  how  such  simple  things 
could  be  brought  before  the 
Academy  of  Sciences,  whereas  the 
great  mathematician  Diiichlet  was 
full  of  praise  of  the  ingenuity  of 
the  method  by  which  problems 
were  solved  which  the  Calculus 
of  Variations  attacked  long  after 
Steiner,  and  then  only  in  ways 
which  the  synthetical  method  had 
indicated  (see  Geiser,  '  Zur  Erin- 
nerung  an  Jacob  Steiner,'  p.  28). 
It  must  not  be  supposed,  however, 
that  Steiner  was  an  extreme  purist 
so  far  as  geometrical  methods  were 
concerned,  for  he  says  himself 
"  that  of  the  two  methods  neither 
is  entitled  to  exclude  the  other  ; 
rather  both  of  them  will,  for  a  long 
time,  have  plenty  to  do  in  order  to 
master  the  subject  to  some  extent, 
and  then  only  can  an  opinion  as  to 
their  respective  merits  be  formed  " 
('Ges.  Werke,'  vol.  ii.  p.  180). 
An  instance  of  a  celebrated  prob- 
lem being  treated  alternately  by 
synthetic  and  analj'tic  methods 
is  that  of  the  Attraction  of 
Ellipsoids,  in  which  the  Theorem 
of  Maclaurin  had  created  quite  a 
sensation.  In  spite  of  the  ad- 
miration which  it  evoked,  both 
Legendre  and  Poisson  expressed 
the  opinion  that  the  resources  of 
the  synthetic  method  are  easily 
exhausted.  The  latter,  whilst  ad- 
mitting "que  la  synthese  ait 
d'abord  devance  I'analyse,"  never- 


theless concludes  that  "la  question 
n'a  ete  enfin  rdsolue  completement 
que  par  des  transformations  ana- 
lytiques  .  .  .  auxquelles  la  syn- 
thase n'aurait  pu  suppleer."  This 
expression  of  opinion  was  falsified 
when  Chasles  presented  to  the 
Academy,  in  the  year  1837,  a 
memoir  in  which,  through  the 
study  of  confocal  surfaces,  the 
Theory  of  Maclaurin  was  synthet- 
ically proved  in  its  full  generality. 
Poinsot,  who  reported  on  this 
memoir,  attached  the  following  re- 
marks :  "  Ce  m^moire  remarquable 
nous  offre  un  nouvel  exemple  de 
r^legauce  et  de  la  clarte  que  la 
geometrie  pent  repandre  sur  les 
questions  les  plus  obscures  et  les 
jjIus  difficiles.  ...  II  est  certain 
qu'on  ne  doit  ndgliger  ni  I'une  ni 
I'autre  ;  elles  sont  au  fond  presque 
toujours  uuies  dans  nos  ouvrages, 
et  forment  ensemble  comme  I'in- 
strument  le  plus  complet  de  I'esprit 
humain.  Car  notre  esprit  ne 
marche  guere  qu'h,  I'aide  des  signes 
et  des  images;  et  quand  il  cherche 
h,  pendtrer  pour  la  premiere  fois 
dans  les  questions  difficiles,  il  n'a 
pas  trop  de  ces  deux  moyens  et 
de  cette  force  particuliere  qu'il  ne 
tire  souveut  que  de  leur  concoura. 
C'est  ce  que  tout  le  monde  peut 
sentir,  et  ce  qu'on  peut  recon- 
naitre  dans  le  Memoire  meme." 
(Chasles,  '  Rapport  sur  les  progr^ 
de  la  geometric,'  1870,  p.  105,  &c.) 


DEVELOPMENT    OF    MATHEMATICAL    THOUGHT.        671 

of  bringing  some  order  into  the  tangled  web  of  mathe- 
matical speculation,  mainly  represented  by  these,  I  shall 
identify  the   name  of  Pliicker  with  the   great   advance        32. 

''  °  Pliicker, 

which  has  taken  place  in  geometry  through  the  change  ^l^f^^' 
in  our  ideas  as  to  the  elements  of  space  construction  and 
the  generalisation  of  our  ideas  of  co-ordinates :  with 
Chasles  I  shall  specially  connect  the  modern  habit  in 
geometry  of  combining  figures  in  finite  space  with  their 
infinitely  distant  elements,  and  with  Cay  ley  the  application 
to  geometrical  science  of  the  novel  and  comprehensive 
methods  of  modern  algebra.  Let  us  dwell  for  a  moment 
on  each  of  these  three  great  departures. 

The  elements  of  any  science  are  a  very  different  thing 
from  the  elements  of  the  special  object  with  which  that 
science  is  concerned.  The  elements  of  chemistry  are  not 
the    chemical    elements.      The    latter    are,   we    suppose,        33. 

Historical 

somethino;  existing  in  nature,  something  fixed  and  un-  aud  logical 

t'  "  ^  foundations 

alterable,  which  science  aims  at  finding  out ;  the  former 
are  certain  conceptions  from  which  we  find  it  convenient 
to  start  in  teaching,  expounding,  and  building  up  the 
science  of  chemistry.  The  latter  are  artificial,  the  former 
iare  natural.  The  same  remark  obtains  in  geometrical 
science.  The  elements  of  geometry  have  an  historical, 
a  practical  beginning :  the  elements  of  space  form  a  con- 

eption  which  gradually  emerges  in  the  progress  of  geo- 
oaetrical  science.  In  every  science  there  is  a  tendency 
bo    replace    the    casual   and   artificial   elements    by    tlie 

latural  or  real  elements,  and  to  build  up  the  historical 
traditional  body  of  doctrine  anew,  using  the  very 
'dements  which  Nature  herself,  as  it  were,  employs  in 

•reducing  her  actual  forms  and  objects.      As  the  pass- 


672  SCIENTIFIC    THOUGHT. 

age  quoted  above  shows,  such  an  idea  must  have  been 
before  the  mind  of  Jacob  Steiner  when  he  wrote  the 
'  Systematische  Entwickelung.'  Through  Euclid  geo- 
metricians had  learnt  to  begin  with  the  straight  line  of 
definite — not  indefinite — length,  the  triangle,  the  circle, 
advancing  to  more  complicated  figures ;  practice  had 
made  geometry  a  science  of  mensuration,  involving 
number ;  the  convenience  of  practice  in  astronomy, 
geodesy,  and  geography  had  introduced  the  artifice  of 
referring  points  and  figures  in  space  to  certain  arbi- 
trarily chosen  data — points  and  lines.  The  terms  "  right 
ascension  "  and  "  dechnation,"  "  altitude  "  and  "  azi- 
muth," "  latitude "  and  "  longitude,"  led  to  the  co- 
ordinates of  Descartes  and  to  analytical  geometry.  In 
this  older  and  modern  geometry,  the  beginnings  were 
arbitrary,  and  many  conceptions  were  introduced  which 
were  foreign  to  the  object  of  research.  It  was  through 
a  slow  process  that  in  quite  recent  times — notably  dur- 
ing the  nineteenth  century  —  mathematicians  became 
aware  how  artificial  were  their  methods,  and  with  how 
many  foreign  elements  they  had  encumbered  the  objects 
of  their  study.  To  replace  the  artificial  by  natural  con- 
ceptions, and  to  open  the  eyes  of  geometricians  to  the 
advantage  of  not  confining  themselves  to  the  point  (its. 
motion  and  distances)  as  the  element  in  their  space 
construction,  no  one  did  more  than  Julius  Pliicker  of 
Bonn.  We  have  now  not  only  a  point  -  geometry,] 
but  likewise  a  line-geometry  —  i.e.,  we  have  a  geom- 
etry in  which  the  line  is  the  primary  element,  the 
point  being  the  secondary  element,  defined  by  the 
intersection     of     two     lines.       This     conception,    whichP 


DEVELOPMENT    OF    MATHEMATICAL    THOUGHT. 


673 


can  be  applied  also  to  geometry  in  space,  the  point 
being  conceived  as  generating  a  plane  by  its  motion,  or 
three  planes  defining  a  point  by  their  intersection,  leads 
us  to  the  same  idea  of  dual  correspondence  or  reciprocity 
which  Poncelet  and  Gergonne  had  arrived  at  by  entirely 
different  considerations.  Pliicker's  was  an  analytical 
mind,  and  with  him  the  principle  of  duality  at  once 
assumes  an  analytical  form.  He  saw  that  the  same 
equation  lent  itself  to  a  twofold  interpretation,  accord- 
ingly, as  we  adopt  point  co-ordinates  or  line  co-ordinates 
— i.e.,  according  as  we  refer  our  geometrical  figure  to  the 
point  or  the  line  as  the  moving  and  generating  space 
element.     Through    this   step    the    idea   of    co-ordinates        34. 

°  Generalised 

was  generalised,  and  the  dualistic  conception  of  figures  ates"''" 
in    space    received    an    analytical    expression.       It    was 
the  junction  of  analytical  and  descriptive  methods  on  a 
higher  level,  from  which  an  entirely  novel  and  fertile 
development  of  geometry  became  possible. 

Whilst  the  labours  of  Pliicker  lay  in  the  direction  of 
making  analytical  formulae  more  natural,  better  adapted 
to  the  expression  of  geometrical  forms  and  relations,  and 
of  reading  out  of  these  remodelled  formula?  novel  geometri- 
cal properties,  the  French  school,  with  Michel  Chasles  ^ 


^  In  addition  to  numerous  valu- 
able memoirs,  Chasles  published, 
among  others,  two  works  of  para- 
mount importance,  inasmuch  as 
they  for  a  long  time  dominated 
purely  geometrical  research,  not 
only  in  France  but  also  in  Ger- 
many and  England, — the  'Aper(;u 
historique  sur  I'origine  et  le 
ddveloppement  des  methodes  en 
gfometrie'  (1837),  and  the  'Traite 
de  geometi'ie  superieure '  (1852). 
These    works,    through    their    bril- 

VOL.  II, 


liant  style,  not  only  threw  into  the 
shade  for  a  time  the  labours  of 
contemporary  German  mathema- 
ticians, such  as  Mobius,  Steiuer, 
Pliicker,  and  Von  Staudt,  but  also 
obscured  some  of  the  single  dis- 
coveries of  the  author  himself. 
The  '  Aper(;u '  was  early  trans- 
lated into  German  ;  whereas  in 
this  country  it  was  the  Dublin 
school,  notably  Townsend  and  Dr 
Salmon,  who  spread  a  knowledge 
of  Chasles's  work. 

2  u 


674  SCIENTIFIC   THOUGHT. 

as  its  leader  and  centre,  laboured  at  the  introduc- 
tion into  pure  geometry  of  those  ideas  which  were 
peculiar  to  the  analytical  method,  and  which  gave  to 
that  method  its  unity,  generality,  and  comprehensiveness. 
Two  ideas  presented  themselves  as  requiring  to  be  geo- 
metrically dealt  with :  the  infinite  and  the  imaginary — 
i.e.,  the  elements  of  a  figure  which  lie  at  infinity  and  those 
which  are  ideal  or  invisible,  which  cannot  be  construed. 
It  is  usually  supposed  that  the  consideration  in  geometry 
of  imaginary  or  invisible  elements  in  connection  with  real 
figures  in  space  or  on  the  plane  has  been  imported  from 
algebra;  but  the  necessity  of  dealing  with  tbem  must 
have  presented  itself  when  constructive  geometry  ceased 
to  consider  isolated  figures  rigidly  fixed,  when  it  adopted 
the  method  of  referring  figures  to  each  other,  of  looking 
at  systems  of  lines  and  surfaces,  and  of  moving  figures 
about  or  changing  them  by  the  processes  of  projection 
and  perspective.  The  analytical  manipulations  applied 
to  an  equation,  which  according  to  some  system  or  other 
expressed  a  geometrical  figure,  found  its  counterpart 
in  projective  geometry,  where,  by  perspective  methods, — 
changing  the  centre  or  plane  of  projection, — certain 
elements  were  made  to  move  away  into  infinity,  or  when 
a  line  that  cut  a  circle  moved  away  outside  of  it,  seem- 
ingly losing  its  connection  with  it.  By  such  devices, 
implying  continuous  motion  in  space,  Poncelet  introduced 
and  defined  points,  lines,  and  other  space  elements  at 
35.        infinity,  and  brought   in  the  geometrical   conception  of 

Ideal  .  . 

elements,  ideal  and  imaginary  elements.  "  Such  definitions,"  he 
says,  "  have  the  advantage  of  applying  themselves  at 
once  to  all  points,  lines,  and  surfaces  whatsoever ;  they 


DEVELOPMENT  OF  MATHEMATICAL  THOOGHT.   675 

are,  besides,  neither  indifferent  nor  useless,  they  help  to 
shorten  the  text  and  to  extend  the  object  of  geometrical 
conceptions ;  lastly,  they  establish  a  point  of  contact,  if 
not  always  real,  at  least  imaginary,  between  figures  which 
appear — prima  vista — to  haAe  no  mutual  relation,  and 
enable  us  to  discover  without  trouble  relations  and 
properties  which  are  common  to  them."  ^  It  was  the 
principle  of  geometrical  continuity  which  led  Poncelet 
to  the  consideration  of  infinite  and  imaginary  elements. 

As  we  saw  above,  the  projective  methods  of  Poncelet 
had  introduced  into  geometrical  reasoning  a  remark- 
able distinction  among  the  properties  of  figures.  In 
general  it  was  recognised  that,  in  the  methods  of 
central  and  parallel  projection  ur  in  drawing  in  per- 
spective, certain  properties  or  relations  of  the  parts  of 
a  figure  remain  unaltered,  whereas  others  change,  be- 
come contorted  or  out  of  shape.  Poncelet  called  the 
former  projective  or  descriptive,  the  latter  metrical, 
properties.  This  distinction  introduced  into  all  geom- 
etry since  his  time  several  most  important  and  funda- 
mental points  of  view ;  it  divided  geometrical  research 
into  two  branches,  which  we  may  term  positional 
and  metrical  geometry — the  geometry  of  position  and 
that  of  measurement.  We  know  that  ancient  geometry 
started  from  problems  of  mensuration :  modern  geometry 
started,  with  Monge,  from  problems  of  representation  or 
graphical  description.  It  has  thus  become  a  habit  to 
call  ancient  geometry  metrical,  modern  geometry  pro- 
jective. This  habit  has  led  to  an  unnecessary  separation 
of  views,  but  in  the  further  course  of  development  also 

^  '  Traite  des  Propriet^s  projectives,'  vol.  i.  p.  28. 


676 


SCIENTIFIC    THOUGHT. 


36. 
Invariants. 


to  a  unification  on  a  higher  level.  But  the  distinc- 
tion mentioned  above  led  to  another  most  remarkable 
line  of  thought  and  research  which  tends  more  and 
more  to  govern  mathematical  doctrine.  The  methods 
of  projection  are  based  upon  the  motion  or  upon  the 
transformation  of  figures.  Under  such  a  process  some 
relations  remain  unaltered  or  invariant,  others  change. 
As  analytical  methods  in  the  hands  of  Pllicker  and 
others  began  to  accommodate  themselves  more  closely  to 
geometrical  forms,  as  an  intimate  correspondence  was 
introduced  between  the  figure  and  the  formula,  it  became 
natural  to  study  the  unalterable  properties  of  the  figure 
in  the  invariant  elements  of  the  formula.  This  is  the 
origin  and  meaning  of  the  doctrine  of  Invariants.^  It 
is  the  great  merit  of  the  English  school  of  mathe- 
maticians, headed  by  Boole,  Cayley,  and  Sylvester,  both 
to  have  first  conceived  the  idea  of  a  doctrine  of  invariant 


1  '•  In  anj  subject  of  inquiry 
there  are  certain  entities,  the 
mutual  relations  of  which,  under 
various  conditions,  it  is  desirable  to 
ascertain.  A  certain  combination 
of  these  entities  may  be  found 
to  have  an  unalterable  value  when 
the  entities  are  submitted  to  cer- 
tain processes  or  are  made  the 
subjects  of  certain  operations. 
The  theory  of  invariants  in  its 
widest  scientific  meaning  deter- 
mines these  combinations,  eluci- 
dates their  properties,  and  expresses 
results  when  possible  in  terms  of 
them.  Many  of  the  general  prin- 
ciples of  political  science  and 
economics  can  be  expressed  by 
means  of  invariantive  relations 
connecting  the  factors  which 
enter  as  entities  into  the  special 
problems.  The  great  principle  of 
chemical  science  which  asserts  that 


when  elementary  or  compound 
bodies  combine  with  one  another 
the  total  weight  of  the  materials 
is  unchanged,  is  another  case  in 
point.  Again,  in  physics,  a  given 
mass  of  gas  under  the  operation 
of  varying  pressure  and  tempera- 
ture has  the  well-known  invariant, 
pressure  multiplied  by  volume  and 
divided  by  absolute  temperature. 
Examples  might  be  multiplied.  In 
mathematics  the  entities  under  ex- 
amination may  be  arithmetical, 
algebraical,  or  geometrical ;  the 
processes  to  which  they  are  sub- 
jected may  be  any  of  those  which 
are  met  with  in  mathematical 
work.  It  is  the  principle  which 
is  valuable.  It  is  the  idea  of  in- 
variance  that  pervades  to-day  all 
branches  of  mathematics."  (Major 
P.  A.  MacMahon,  Address,  Brit, 
Assoc,  1901,  p.  526.) 


DEVELOPMENT    OF    MATHEMATICAL    THOUGHT.        677 


forms,  and  to  have  foreseen  its  importance  and  corre- 
sponding significance  when  applied  to  a  great  variety  of 
scientific  problems,  notably  to  the  projective  processes 
in  geometry.  These  were  known  to  them  mainly 
through  the  classical  treatises  of  Poncelet  and  Chasles, 
the  leading  ideas  of  which  had  Ijeen  introduced  to 
British  students  by  the  labours  of  the  Dublin  school.^ 
The  investigations  referred  to  mark  the  junction  of 
two  important  lines  of  mathematical  research,  which 
had  been  carried  on  independently  in  earlier  times,  or 
only  united  for  special  purposes  or  for  the  solution 
of  special  problems.  The  history  of  the  progress  of 
geometry  during  the  nineteenth  century  has  already 
shown  us  the  use  and  interest  which  belong  to  two 
different  aspects  of  tlie  common  object,  of  which  the 
one  relies  mainly  on  processes  of  measurement,  including 
number,  the  other  mainly  on  processes  of  description,  in- 


^  The  history  of  the  doctrine  of 
invariants  has  been  written  by  Dr 
Franz  Meyer,  and  is  pubhshed  in  the 
first  volume  of  the  '  Jahresbericht 
der  Deutschen  Matheuiatiker  Ver- 
eiuigung'  (p.  79  sqq.)  The  fact  that 
this  formed  the  first  of  the  several 
Reports  which  the  German  Mathe- 
matical Society  has  undertaken  to 
publish,  testifies  to  the  great  im- 
portance which  belongs  to  this 
doctrine  in  the  history  of  recent 
mathematics.  A  concise  summary 
with  copious  references  is  given  by 
the  same  author  in  the  first  volume 
of  the  '  Encyklopiidie  der  Math. 
Wissenschaften,'  p.  320  sqq.  How 
necessary  the  form  and  perfection 
of  algebraic  operations  was  for  the 
development  of  the  geometrical 
conceptions  which  are  laid  down, 
e.g.,  in  the  works  of  Pliicker, 
can  be  seen  in  the  work  of 
Otto   Hesse,    who    introduced    ele- 


gance and  conciseness  into  many 
of  the  expositions  which,  for  want 
of  this  formal  development,  ap- 
pear cumbrous  in  the  writings  of 
Pliicker.  "The  analytical  form  in 
which  Pliicker's  Researches  present 
themselves  is  frequently  wanting 
in  that  elegant  form  to  which  we 
have  become  accustomed,  sjaecially 
through  Hesse.  Pliicker's  calcula- 
tions frequently  bear  the  stamp  of 
mere  aids  for  representing  geo- 
metrical relations.  That  algebraical 
connections  possess  an  interest  in 
themselves,  and  require  an  ade- 
quate representation,  was  realised 
only  by  a  generation  which  habitu- 
ally emjiloyed  methods  that  had 
been  largely  devised  by  Pliicker 
himself"  (A.  Clebsch,  '  Zum  Ge- 
dachtniss  an  Julius  Pliicker,'  1872, 
p.  8.  See  also  Gustav  Bauer, 
'  Gediichtnissrede  auf  Otto  Hesse,' 
Muucheu,  1882). 


678  SCIENTIFIC    THOUGHT. 

eluding  arrangement.  The  same  difference  of  views  can 
be  established  with  regard  to  many  other  things  which 
form  the  objects  of  other  sciences.  In  geometry  this 
difference  obtrudes  itself,  as  it  were,  in  its  naked  form. 
Thus  in  all  the  natural,  and  even  the  social,  sciences  we 
have  become  accustomed  to  look  first  at  the  constituent 
elements  or  parts  of  things,  to  count  and  measure  them, 
then  afterwards  to  look  at  their  possible  arrangement, 
or  existence  together  in  the  actual  world  of  nature  or 
society.  Astronomy,  crystallography,  chemistry,  geology, 
the  natural  history  sciences,  economics  and  statistics,  the 
doctrine  of  chances, — all  furnish,  especially  in  their  sys- 
tematic development  during  the  last  hundred  or  hundred 
and  fifty  years,  examples  of  the  twofold  aspect  just  re- 
ferred to.  The  progress  of  these  sciences,  as  we  have 
abimdantly  seen,  has  depended  largely  upon  the  application 
of  mathematical  methods.  As  the  analysis  into  elements 
or  parts,  and  the  possible  synthesis  of  such  elements  in 
complicated  structures,  has  become  everywhere  the  order  of 
study,  so  there  must  exist  in  the  abstract  science  of  mathe- 
matics— i.e.,  in  the  framework  of  our  scientific  reasoning 
— not  only  the  theory  of  measurement  and  number,  but 
also  that  of  combination,  form  or  arrangement,  and  order. 
37.  The    doctrine    of    forms    in    the    well  -  known    prob- 

Theory  of  .  ...  ,         . 

forms.  lems  of  permutations  and  combmations  begms  with 
modern  mathematics  in  the  seventeenth  century,  and 
received  scientific  recognition  mainly  in  connection 
with  the  doctrine  of  chances  at  the  hands  of  James 
Bernoulli  abroad,  and  of  De  Moivre  in  this  country. 
The  process  of  multiplication  of  binomials  and  poly- 
nomials   leads    to    the  formation    of    combinations,  and 


DEVELOPMENT    OF   MATHEMATICAL   THOUGHT.       679 


where  the  factors  are  the  same,  as  in  Newton's  Iji- 
noniial  theorem,  to  combinations  with  permutation ;  and 
consequently  the  doctrine  of  chances  and  of  arrange- 
ments in  triangular,  pyramidal,  or  other  figures  is  closely 
connected  with  the  doctrine  of  series  and  algebraical 
expressions.  In  this  country  the  interest  in  the  subject 
has  been  stimulated  and  kept  alive  by  isolated  problems 
and  puzzles  in  older  popular  periodicals,  such  as  the 
'  Gentleman's  Magazine  '  and  the  '  Ladies'  Diary  ' ;  in  Ger- 
many— as  we  noticed  before — a  school  of  mathematicians 
arose  who  attempted  a  systematic  treatment  of  the  whole 
subject,  which,  owing  to  its  barrenness  in  practical  re- 
sults, brought  this  line  of  research  somewhat  into  dis- 
repute. What  was  wanted  was  a  problem  of  real 
scientific  interest  and  a  method  of  abbreviation  and 
condensation.      Both    were    supplied    from    unexpected  ^ 


^  The  theory  of  arrangement  or 
of  order,  also  called  the  "  Ars  Com- 
binatoria,"  has  exerted  a  great 
fascination  on  some  master  minds, 
as  it  has  also  given  endless  opi)or- 
tunities  for  the  practical  ingenuity 
of  smaller  talents ;  among  the 
former  we  must  count  in  the  first 
place  Leibniz,  and  in  recent  times 
J.  J.  Sylvester,  who  conceived  the 
"  sole  proper  business  of  mathe- 
matics to  be  the  development  of 
the  three  germinal  ideas — of  which 
continuity  is  one,  and  order  and 
number  the  other  two"  ('Philo- 
soi)hical  Transactions,'  vol.  clix.  p. 
61.3).  This  idea  has  been  dwelt  on 
by  Major  MacMahon  in  his  address 
(I5rit.  Assoc,  1901, p.  526),  whosays  : 
"The  combinatorial  analysis  may 
be  described  as  occupying  an  ex- 
tensive region  between  the  algebras 
of  discontinuous  and  continuous 
quantity.  It  is  to  a  certain  extent 
a  science  of  enumeration,  of  mea- 


surement by  means  of  integers  as 
opposed  to  measurement  of  quan- 
tities which  vary  by  infinitesimal 
increments.  It  is  also  concerned 
with  arrangements  in  which  differ- 
ences of  quality  and  relative  position 
in  one,  two,  or  three  dimensions  are 
factors.  Its  chief  problem  is  the 
formation  of  connecting  roads  be- 
tween the  sciences  of  discontinu- 
ous and  continuous  quantity.  To 
enable,  on  the  one  hand,  the 
treatment  of  quantities  which  vary 
per  salturii,  either  in  magnitude 
or  position,  by  the  methods  of  the 
science  of  continuously  varying 
quantity  and  position,  and,  on  the 
other  hand,  to  reduce  problems  of 
continuity  to  the  resources  avail- 
able for  the  management  of  dis- 
continuity. These  two  roads  of 
research  should  be  regarded  as  pene- 
trating deeply  into  the  domains 
which  they  connect." 


680 


SCIENTIFIC    THOUGHT. 


38. 
Tlieory  of 
numbers. 


quarters — the  one  purely  theoretical,  the  other  practical. 
Accordingly  the  doctrine  of  forms  and  arrangements  has 
during  the  last  century  been  developed  by  mathematicians 
in  two  distinct  interests,  which  only  quite  lately  seem  to 
approach  and  assist  each  other. 

The  purely  abstract  or  theoretical  interest  came  from 
the  side  of  the  theory  of  numbers,  a  branch  of  research 
which  was  revived  by  Legendre  in  France  and  by  the 
youthful  genius  of  Gauss  in  Germany ;  the  more  practical 
one  came  from  the  theory  of  equations,  notably  in  its 
application  to  problems  of  geometry.  The  methods  by 
which  these  subjects  were  treated  had  in  the  early  part 
of  the  nineteenth  century  undergone  a  great  change. 
The  older  inductive  method  in  both  branches — namely, 
in  the  solution  of  equations  and  in  the  investigation  of 
the  properties  of  numbers — relied  mainly  on  ingenious 
devices  which  were  mostly  of  special,  not  of  general, 
vakie.  Theorems  were  found  by  induction,  and  had 
afterwards  to  be  proved  by  rigorous  logical  deduction. 
Success  depended  on  the  degree  of  care  with  which  the 
mind  operated  with  mathematical  symbols,  and  rested 
frequently  on  the  intuition,  if  not  the  inspiration,  of 
genius.       Two   of   the    greatest    mathematical   minds — 

stood 


greatest 
Fermat  ^   in   France   and  Newton  ^  in  England 


1  Pierre  Fermat  (1601-65)  pre- 
pared au  edition  of  the  Treatise  of 
Diophantus,  and  his  marginal  notes 
contain  many  theorems  referring 
to  the  properties  of  numbers  which 
have  been  the  subject  of  much 
comment  and  examination  by 
mathematicians  of  the  first  rank 
down  to  the  present  day.  In 
letters  to  contemporaries  he  re- 
ferred to  many  of  these  dis- 
coveries, and  to  liis  proofs,  which 
he   did   not    communicate.     Some 


of  these  proofs  seem  not  to  have 
satisfied  him,  being  deficient  in 
rigour.  In  spite  of  the  labours  of 
Euler,  Lagrange,  Cauchy,  Dirich- 
let,  Kummer,  and  others,  one  of 
these  theorems  still  awaits  proof. 
A  full  account  of  Fermat's  theorems 
is  given  in  Cantor's  '  Geschichte  der 
Mathematik,'  vol.  ii.  2nd  ed.,  p. 
773  sqq.  Also  in  W.  Rouse 
Ball's  'History  of  Mathematics,' 
p.   260  sqq. 

-  Newton,     in     his     '  Universal 


DEVELOPMENT    OF    MATHEMATICAL    THOUGHT.       681 


foremost  in  having  with  unrivalled  fertility  propounded 
theorems  which  were  as  difficult  to  prove  as  the 
manner  in  which  they  had  been  arrived  at  was  mysteri- 
ous. The  great  analytical  genius  of  Euler,  who  possessed 
unequalled  resources  in  the  solution  of  single  problems, 
spent  much  time  and  power  in  unravelling  the  riddles 
of  Fermat.  In  the  theory  of  equations  the  general 
solution  beyond  the  fourth  degree  battled  the  greatest 
thinkers.  The  time  had  come  when  in  both  branches 
a  systematic  study  of  the  properties  had  to  be  at- 
tempted. This  was  done  for  the  theory  of  numbers  by 
Gauss,  for  that  of  equations  by  Abel.  Every  great 
step  in  advance  of  this  kind  in  mathematics  is  accom- 
panied by,  and  dependent  on,  skilful  abbreviations,  and 
an  easy  algorithm  or  mathematical  language.  An  as- 
semblage of  elements  held  together  by  the  simplest 
operations  or  signs  of  arithmetic — namely,  those  of 
addition  and  multiplication — is  much  easier  to  deal 
with  if  it  can  be  arranged  with  some  regularity,  and 
accordingly  methods  were  invented  by  which  algebraical 
[expressions  or  forms  were  made  symmetrical  and  homo- 
geneous ;  ^  the  latter  property  signifying  that  each  term 


39. 
Symmetry. 


Arithmetic,'  gave  an  interesting 
[theorem  by  wliich  the  number  of 
imaginary  roots  of  an  equation  can 
be  determined  ;  he  left  no  proof, 
and  the  theorem  was  discussed  by 
jEuler  and  many  other  writers,  till 
at  last  Sylvester  in  1866  found  the 
broof  of  it  in  a  more  general 
theorem.  In  more  recent  times 
Jacob  Steiner  published  a  great 
lumber  of  theorems  referring  to 
dgebraical  curves  (see  Crelle's 
;  Journal,'  vol.  xlvii. )  which  have 
been  compared  by  Hesse  with  the 
I' riddles  of  Fermat."  Luigi  Cre- 
nona  succeeded  at  last  in  proving 


them    by    a     general     sj^nthetical 
method. 

1  The  introduction  of  homogene- 
ous expressions  marks  a  great 
formal  advance  in  algebra  and 
analj'tical  geometry.  The  first  in- 
stance of  homogeneous  co-ordinates 
is  to  be  found  in  Mobius's  "Bary- 
centric  Calculus"  (1826),  in  which 
he  defined  the  position  of  any  point 
in  a  plane  by  reference  to  three 
fundamental  points,  considering 
each  point  as  the  centre  of  gravity 
of  those  points  when  weighted. 
"  The  idea  of  co-ordinates  appears 
here  for  the  first  time  in   a  new 


682 


SCIENTIFIC    THOUGHT. 


40. 
Determin- 
ants. 


contained  the  same  number  of  factors.  Such  forms 
could  be  written  down  on  the  pattern  or  model  of 
one  of  their  terms  by  simple  methods  of  exchange  or 
permutation  of  the  elements.  It  would  then  not  be 
necessary  to  write  down  all  the  terms  but  only  to  indicate 
them  by  their  elements,  these  also  being  abbreviated  by 
the  use  of  indices.  Eows  and  columns  or  arrangements 
in  squares  suggested  themselves  as  easy  and  otherwise 
well-known  artifices  by  which  great  masses  of  statistics 
and  figures  are  marshalled  and  controlled.  Out  of  these 
manifold  but  simple  devices  there  grew  an  algebra  of 
algebra,  a  symbol  for  denoting  in  a  very  general  way 
symmetrical  and  homogeneous  algebraical  expressions.^ 
Gauss  termed  such  expressions  Determinants  :  they 
turned  up  in  his  '  Disquisitiones  Arithmeticae  '  as  they  had 
done  half  a  century  before  in  Cramer's  '  Analyse  des  lignes 
courbes  alg^briques.'     Just  as  common  fractions  can  be 


garb,  which  soon  led  to  a  more 
general  conception.  The  Bary- 
centric  co-ordinates  were  the  first 
instance  of  homogeneous  co-ordin- 
ates, .  .  .  and  already  with  Mobius 
the  advantages  become  evident 
through  the  symmetry  and  ele- 
gance of  his  formulaj"  (Hankel, 
'Project.  Geom.,'  p.  22). 

^  Determinants  were  first  used 
by  Leibniz  for  the  purpose  of 
elimination,  and  described  by  him 
in  a  letter  to  the  Marquis  de 
I'Hospital  (1693).  The  importance 
of  his  remarks  was  not  recognised 
and  the  matter  was  forgotten,  to 
be  rediscovered  by  Cramer  in  the 
above  -  named  work  (1750,  p. 
657).  It  is  interesting  to  note 
that  the  same  difficulty  of  the 
process  of  elimination  induced 
PHicker   to   resort   to   geometrical 


interpretation  of  analytical  ex- 
pressions, and  that  whilst  he  "saw 
the  main  advantage  of  his  method 
in  avoiding  algebraical  elimination 
through  a  geometrical  considera- 
tion, Hesse  showed  how,  through 
the  use  of  Determinants,  algebraical 
operations  could  receive  that  pliabil- 
ity the  absence  of  which  was  the 
reason  for  Pliicker  to  discai'd  it." 
(See  the  account  of  Clebsch's  work 
in  'Math.  Ann.,'  vol.  vii.  p.  13.) 
Through  this  invention  the  com- 
binatorial analysis,  which,  in  the 
hands  of  the  school  in  Germany, 
had  led  into  a  desert,  was  raised 
again  into  importance.  It  has  be- 
come still  more  important  since  the  | 
general  theory  of  forms  and  of 
groups  began  to  play  an  increasing 
jiart  in  modern  analysis. 


DEVELOPMENT    OF    MATHEMATICAL    THOUGHT.        683 

dealt  with  as  if  they  were  special  things  having  special 
properties,  though  the  latter  depend  only  on  the  pro- 
perties of  the  numbers  they  are  made  up  of  and  their 
mode  of  connection ;  as  powers  and  siirds  are  separately 
examined ;  so  the  arrangements  called  determinants  can 
be  subjected  to  a  special  treatment,  their  properties 
ascertained,  and  themselves  subjected  to  the  ordinary 
operations  of  arithmetic.  This  doctrine,  which  con- 
stitutes the  beginning  and  centre  of  the  theory  of 
algebraical  forms  or  "  quantics "  and  of  algebraical 
operations  or  "  tactics,"  was  pretty  fully  worked  out 
and  first  introduced  into  the  course  of  teaching  by 
Cauchy  in  France ;  then  largely  adopted  by  Jacobi  in 
Germany,  where  Otto  Hesse,  trained  in  the  ideas  of 
Pllicker,  first  showed  its  usefulness  in  his  elegant 
applications  to  geometry.  In  France  it  was  further 
developed  by  Hermite,  who,  together  with  Cayley  and 
Sylvester  in  England,  proclaimed  the  great  importance 
of  it  as  an  instrument  and  as  a  line  of  mathematical 
jthought.^  In  the  latter  countrv  the  idea  of  abbrevi- 
ating  and  summarising  algebraical  operations  had  become 
jquite  familiar  through  another  device  which  has  not 
found   equal   favour   abroad  —  namely,  the   Calculus  of 


'    ^  "For    what    is    the    theory    of  ,  p,     301)    refers    to    Otto    Hesse's 

jdeterminants  ;      It   is    an    algebra  '  "  problem     of    reducing     a     cubic 

upon    algebra  ;    a    calculus    which  function  of  three  letters  to  another 

enables  us  to  combine  and  foretell  |  consisting   only   of   four    terms   by 

the    results    of    algebraical    opera-  j  linear    substitutions  —  a    problem 

jbions,  in  the  same  way  as  algebra  I  which  appears  to  set  at  defiance  all 


enables  us  to  dispense  with  the 
performance  of  the  special  opera- 
tions of  arithmetic.  All  analysis 
nust  ultimately  clothe  itself  under 
:his  form."  In  this  connection 
Sylvester  ('Phil.  Mag.,'  1851,  ApL, 


the  processes  and  artifices  of  com- 
mon algebra,"  as  "perhaps  the 
most  remarkable  indirect  question 
to  which  the  method  of  determin- 
ants has  been  hitherto  applied." 


684 


SCIEiNTIFlC    THOUGHT. 


41.        Operations,  the  idea  of   treating   algebraical   operations 

Calculus  of         "^  '  o         o  r 

Operations.  ai^(j  their  symbols  as  quantities,  and  of  subjecting  them 
to  arithmetical  treatment  separately  from  the  mate- 
rial operated  on.  The  genius  of  Arthur  Cayley  was 
specially  fertile  in  this  direction,  as  was  that  of 
Sylvester  in  the  nomenclature  or  language  of  the 
doctrine  of  forms.^  The  merit,  however,  of  having 
brought  together  the  new  ideas  which  emanated  from 
the  schools  of  Poncelet  and  Chasles  in  France,  of  Cayley 
and  Sylvester  in  England,  into  a  connected  doctrine,  and 
of   having   given    the    impetus    to    the  fundamental   re- 


^  The  theory  of  invariants  was 
gradually  evolved  from  many  inde- 
pendent beginnings.  In  1864  Syl- 
vester wrote  ('Phil.  Trans.,'  p. 
579),  "As  all  roads  are  said  to  lead 
to  Rome,  so  I  find,  in  my  own  case 
at  least,  that  all  algebraical  in- 
quiries, sooner  or  later,  end  at  the 
Capitol  of  Modern  Algebra,  over 
whose  shining  portal  is  inscribed 
the  Theory  of  Invariants."  About 
the  same  time  (1863)  Aronhold  de- 
veloped the  principal  ideas  which 
lay  at  the  foundation  of  the  theory 
in  organic  connection  and  in  com- 
plete generality,  hereby  domiciling 
in  Germany  the  doctrine  which  had 
previous!}'  owed  its  development 
mainly  to  English,  French,  and 
Italian  mathematicians  (see  Meyer, 
'Bericht,'  &c.,  p.  95).  The  differ- 
ent roads  which  Sylvester  refers  to 
can  be  traced,  first,  in  the  love  of 
symbolic  reasoning  of  Boole,  who 
was  "  one  of  the  most  eminent  of 
those  who  perceived  that  the  sj'm- 
bols  of  operation  could  be  separated 
from  those  of  quantity  and  treated 
as  distinct  objects  of  calculation, 
his  principal  characteristic  being 
perfect  confidence  in  any  result 
obtained  by  the  treatment  of  sym- 
bols    in     accordance     with     their 


primary  laws  and  conditions,  and 
an  almost  unrivalled  skill  and 
power  in  tracing  out  these  results  " 
(Stanley  Jevons  in  article  "  Boole," 
'Ency.  Brit.');  secondly,  in  the 
independent  geometrical  labours  of 
Hesse  in  Germany  (whose  mathe- 
matical training  combined  Pliicker's 
and  Jacobi's  teaching)  and  Dr 
Salmon  in  Dublin  (who,  after 
having  transplanted  Poncelet  and 
Chasles  to  British  soil,  recog- 
nised the  importance  of  Cayley 's 
and  Sylvester's  work,  and  in- 
troduced in  the  later  editions  of 
his  text  -  book  modern  algebraical 
methods)  ;  thirdly,  in  the  independ- 
ent investigations  belonging  to  the 
theory  of  numbers  of  Eisenstein  in 
Germany  and  Hermite  in  France. 
In  full  generality  the  subject  was 
taken  up  and  worked  out  by  Syl- 
vester in  the  '  Cambridge  and 
Dublin  Mathematical  Journal ' 
(1851  -  54),  and  by  Cayley  in  the 
first  seven  memoirs  upon  Quantics 
(1854-61),  which  "in  their  many- 
sidedness,  together  with  the  ex- 
haustive treatment  of  single  cases, 
remain  to  the  present  day,  for  the 
algebraist  as  well  as  for  the  geo- 
metrician, a  rich  source  of  dis- 
covery"   (Meyer,  loc,  cit.,  p.  90). 


I 


DEVELOPMENT    OF    MATHEMATICAL    THOUGHT. 


685 


modelling  of  the  text-books  and  school-books  of  algebra 
and  geometry  in  this  country  and  in  Germany,  belongs 
undeniably  to  Dr  Salmon  of  Dublin.^  The  conception  of 
a  form — be  this  geometrical  or  algebraic — suggests  the 
investigation  of  the  change,  the  recurrence  of  forms. 
How  do  forms  under  the  process  of  geometrical  or 
algebraical  manipulation  alter  or  preserve  their  various 
properties  ?  The  processes  of  projection  practised  by 
Monge,  Poncelet,  and  Chasles  in  France  had  already 
led  to  a  distinction  between  descriptive  and  metrical 
properties  of  geometrical  figures.  A  corresponding  ex- 
amination of  algebraical  forms,  which  are  all  capable  of 
geometrical  representation  or  interpretation,  would  lead 
to  the  extensive  and  fundamental  doctrine  of  the  in- 
variants of  these  forms — i.e.,  of  such  arrangements  of 
the  elements  as  remain  absolutely  or  proportionally  un- 
altered during  the  processes  of  change  and  combination, 
Notably  instead  of  the  geometrical  process  of  projection 
by  central  perspective  we  may  employ  in  our  algebraic 
jformulai  a  corresponding  process,  that  which  is  known  as 
jlinear  substitution.  And  at  the  time  when  it  was 
that     geometrical     transformation     had     its 


Irecognised 


'   Of    Dr    Salmon,    whose    '  Les- 
ions introductory   to   the    Modern 
Higher  Algebra '  appeared  in  1859 
,4th  ed.,  1855  ;  1st  German  ed.  by 
Fiedler,  1863),   Meyer  says:   "  Re- 
,;oguising  how   the    special  results 
n  this  domain  gradual!}'  acquired 
I  considerable  bulk,  we   must  the 
nore   gratefully    acknowledge    the 
vork  of  Salmon — who  had  already, 
n  the  direction  of  algebra  as  well  as 
I'f  geometry,  furnished  valuable  con- 
ributions    of  his    own — in    under- 
aking  the  labour  of  collecting  the 


widely -scattered  material  in  a  con- 
cise monograph.  For  the  promulga- 
tion in  Germany  we  have  to  thank 
Fiedler  both  for  his  edition  of 
Salmon,  and  for  having  already 
given  an  independent  introduction 
to  the  subject,  in  which  especially  lie 
made  Cayley's  applications  to  pro- 
jective geometry  generally  access- 
ible. About  the  same  time  (1862) 
there  appeared  likewise  an  edition 
by  Brioschi,  which  gained  many  ad- 
herents for  the  theory  of  Invariants 
in  Italy." 


686 


SCIENTIFIC    THOUGHT. 


42. 
Principle  of 
substitu- 
tion. 


counterpart  in  the  transformation  of  algebraical  forms 
by  the  processes  of  substitution,  these  latter  had 
already  been  extensively  studied  for  their  own  sakes  in 
the  theory  of  algebraical  equations,  which  in  the  first 
quarter  of  the  century  had  undergone  a  great  develop- 
ment under  the  hands  of  two  brilliant  mathematical 
talents  both  lost  to  science  at  an  early  age  —  the 
Norwegian  Abel  and  the  Frenchman  I^variste  Galois.^ 
Like  all  algebraical  expressions,  those  termed  equa- 
tions were  originally  invented  and  commanded  attention 


^  Evariste  Galois  is  held  to  have 
been  one  of  the  greatest  mathema- 
tical geniuses  of  modern  times,  who, 
if  he  had  lived,  might  have  been  a 
rival  of  Abel:  he  was  born  in  1811, 
and  died  before  he  was  twenty-one, 
in  consequence  of  a  duel.  For  a 
long  time  his  writings  remained  un- 
published and  unknown,  till  Liou- 
ville  published  them  in  the  11th  vol. 
of  his  'Journal'  (1846).  Liouville 
was  also  the  first  to  recognise  the 
importance  and  absolute  correctness 
of  Galois's  method,  which,  when  sub- 
mitted to  the  Academy  in  the  year 
1831,  and  reported  on  bj'  Lacroix 
and  Poisson,  had  appeared  almost 
unintelligible.  On  the  eve  of  his 
death  Galois  addressed  a  letter  to 
his  friend  Auguste  Chevalier,  which 
is  a  unique  document  in  mathema- 
tical literature,  forming  a  kind  of 
mathematical  testament.  He  de- 
sires this  letter  to  be  published 
in  the  'Revue  Encyclop^dique,' 
referring  publicly  the  "import- 
ance," not  the  "  correctness,"  of  his 
discoveries  to  the  judgment  of 
Jacobi  and  Gauss,  and  expressing 
the  hope  that  some  persons  would 
be  found  who  would  take  the 
trouble  to  unravel  his  hieroglyphics. 
The  first  attempt  to  make  Galois's 
ideas  generally  accessible  is  to  be 
found  in  Serret's  '  Algebre  Superi- 
eure'  (3rd  ed.,   1866),   but  it    was 


not   till   after   the    publication    of  i 
Camille      Jordan's      '  Theorie     des 
Substitutions'     (1870)    that     the 
short  papers  of  Galois  were  recog- 
nised as  containing  the  germs  and  i 
beginnings  of  an  entirely  novel  and 
comprehensive  mathematical  theory, 
— viz.,    the    "  Theory   of    Groups." 
The  relation  between  the  writings, 
of  Abel  and   Galois  is  exhaustively', 
treated  in  Prof.   Sylow's   Paper  on^ 
Abel's  work,  contained  in  the  '  Me- 
morial Volume,'    1892,  p.   24.     Hei 
there  .says:  "  Le  merite  de  Galois 
ne  consiste  pas  essentiellement  dans 
ses  propositions,  mais  dans  la  gener- 
alite  de  la  methode  qu'il  appliquaj 
C'est  son  admirable  theoreme  fondan 
mental    qui  a   donne    a   la   theorie 
des  Equations  sa  forme   definitive, 
et  d'oii  est  sortie,  en  outre,  la  theorie 
des    groupes    generalisee,   qui    est 
d'une  si  grande  importance,  on  peut 
le  dire,  pour  toutes  les  branches  dee 
mathematiques,  et  qui  deja,  entre 
les  mains  de  Jordan,  de  Klein,  de 
Lie,  de  Poincaro  et  d'autres,  a  eun 
richi  la  science  d'une  longue  suitt 
de  decouvertes  importantes."     Th( 
memoirs   of    Abel    and    Galois  reP 
ferring  to  the  Theory  of  Equations 
have  been  conveniently  edited,  iu  if 
German  translation,  by  H.   Maserl 
1889.     See  also  Cayley's  article  oil 
"  Equation  "  in  the  '  Ency.  Brit., I 
§  32. 


DEVELOPMENT    OF    MATHEMATICAL    THOUGHT.        687 

as  instruments  or  devices  for  the  solution  of  definite 
problems  in  arithmetic,  geometry,  and  mechanics.  The 
solution  of  the  equation — i.e.,  the  expression  of  the  un- 
known quantity  in  terms  of  the  known  quantities — 
served  a  practical  end.  Gradually  as  such  solutions  be- 
came more  and  more  difficult,  owing  to  the  complexity  of 
the  formuke,  the  doctrine  divided  itself  into  two  distinct 
branches,  serving  two  distinct  interests.  The  first,  and 
practically  the  more  important  one,  was  to  devise  methods 
by  which  in  every  single  case  the  equations  which 
presented  themselves  could  be  solved  with  sulficient 
accuracy  or  approximation ;  this  is  the  doctrine  of  the 
numerical  solution  of  equations.  The  other  more  scien- 
tific branch  looked  upon  equations  as  algebraical  ar- 
rangements of  quantities  and  operations  which  possessed 
definite  properties,  and  proposed  to  investigate  these 
properties  for  their  own  sake.  The  question  arose, 
How  many  solutions  or  roots  an  equation  would  admit  of, 
and  whether  the  expression  of  the  unknown  quantity  in 
terms  of  the  known  quantities  was  or  was  not  possible 
lij  using  merely  such  operations  as  were  indicated  by 
the  equation  itself — i.e.,  the  common  operations  and  the 
ordinary  numbers  of  arithmetic  ?  This  doctrine  of  the 
general  properties  of  equations  received  increasing  atten- 
'tion    as    it    became   empirically   known    that   equations        43. 

-*•  "^  ^  General 

beyond  the    fourth    degree   could  not  Ije  solved  in  the  'solution  of 
most   general   form.^      Why  could   they  not  be  solved, 

^  Since    the    researches    regard-    ,    toward    the    development    of    the 
ing    the    solubility     of    Equations    |    theory  of  groups  —  the  history  of 


have  led  on,  through  Galois  and 
the  French  analysts,  to  the  same 
line  of  reasoning  as  other  re- 
searches  mentioned   before  —  viz. , 


the  whole  subject  has  aroused 
special  interest.  The  earlier  be- 
ginnings and  the  labours  of  for- 
gotten   analysts    have     been    un- 


688 


SCIENTIFIC    THOUGHT. 


aud  what  were  the  conditions — i.e.,  the  special  proper- 
ties— of  an  equation  which  rendered  it  soluble  ^  These 
were  some  of  the  questions  which  the  great  mathe- 
maticians, such  as  Gauss,  Abel,  and  Galois,  placed  before 
themselves  during  the  earlier  part  of  the  century.  There 
are  other  unsolved  problems  which  the  nineteenth  cen- 
tury inherited  from  preceding  ones,  where  the  same  line 
of  reasoning  was  adopted — i.e.,  where  the  question  was 
similarly  reversed.  Instead  of  trying  to  solve  problems 
as  yet  unsolved,  it  was  proposed  to  prove  their  general 
insolubility,  and  to  show  the  reason  of  this ;  also  to 
define   the  conditions  which  make    a   solution   possible. 


earthed  and  placed  in  their  cor- 
rect historical  perspective.  Prof. 
Burkhardt  of  GottiDgen,  to  whom 
we  also  owe  the  chapter  on  this 
subject  in  the  first  volume  of  the 
'Encvklopadie,'  &c.,  contributed  iu 
the  year  1892  a  most  interesting 
historical  paper,  "  Die  Anfange  der 
Gruppentheorie  und  Paolo  Ruffini  " 
{'Abhandl.  zur  Gesch.  der  Math.,' 
6  Heft).  In  this  paper  he  also 
goes  back  to  other  earlier  analysts, 
among  them  Prof.  Waring  of  Cam- 
bridge, who  during  his  lifetime  used 
to  complain  that  he  knew  of  no  one 
who  read  his  mathematical  tracts. 
It  appears  that  during  nearly  the 
last  thirty  years  of  the  eighteenth 
century  nothing  had  been  added  re- 
garding the  general  theory  of  equa- 
tions, and  that  Ruffini  was  the  first 
to  begin  a  new  epoch  in  the  year 
1799,  with  the  distinct  assertion  that 
a  general  solution  of  algebraic  equa- 
tions beyond  the  fourth  degree,  by 
means  of  radicals,  was  impossible, 
and  with  an  attempt  to  prove  this. 
His  researches  were  therefore  con- 
temporaneous with  those  of  Gauss, 
who  published  his  '  Dissertation ' 
(see  note  p.  644)  in  the  same  year, 
and   his   great    arithmetical   work 


in  1801.  Although  Gauss  seems  i 
to  have  arrived  at  the  same  con- 
clusion, and  perhaps  even  to  have  i 
anticipated  much  later  attempts  to 
solve  the  general  equation  of  the  fifth 
degree  by  other  than  algebraical 
operations  (see  Sylow,  loc.  cit.. 
16),  his  published  researches  rathe 
took  the  hne  of  the  study  of  a| 
definite  class  of  soluble  equations^ 
which  were  connected  with  the 
celebrated  problem  of  the  divisioa 
of  the  circle  ;  a  satisfactory  proof  of 
Ruffini's  statement  being  withheld 
till  Abel  published  his  c-elebrated 
memoir  in  the  year  1825  in  the  firet 
volume  of  CVelle's' Journal.'  With 
this  memoir  the  theory  of  equations 
entered  a  new  phase,  towards 
which  the  labours  of  Ruffini  we 
preparatory.  As  in  so  many  othe 
cases,  so  also  in  this,  the  sola-l 
tion  of  the  problem  depended  up(n| 
stricter  definitions  of  what 
meant  by  the  solution  of  an  eqna-l 
tion,  and  by  "algebraical"  and! 
other  ("  transcendental  ")  functiong| 
and  operations.  We  know  tl 
both  Abel  and  Galois  began  the 
research  by  futile  attempts  to  fine 
a  solution  of  the  general  equatiocj 
of  the  fifth  degree. 


DEVELOPMENT    OF    MATHEMATICAL    THOUGHT.       689 

In  following  this  altered  course  of  investigation,  an 
enormous  amount  of  mathematical  knowledge  was  gained, 
and  problems  were  solved  which  had  previously  never 
been  thought  of.  Especially  through  the  theory  of  equa- 
tions the  abstract  doctrine  of  algebraical  forms  was 
created  and  greatly  advanced  long  before  it  was  gener- 
ally recognised  that  it  had  peculiar  importance  through 
the  correspondence  or  parallelism  which  existed  be- 
tween algebraical  expressions  and  geometrical  con- 
figurations. 

Out  of  these  earlier  algebraical  and  later  combined  al-        44. 

,  Theory  of 

gebraical  and  geometrical  investigations,  a  novel  and  very  groups, 
useful  point  of  view  has  been  gradually  gained  which 
represents  the  most  general  conception  of  mathematical 
tactics.  This  centres  in  the  notion  of  a  group  of  ele- 
ments. These  elements  may  be  quantities  or  opera- 
tions, so  that  the  theory  of  Groups  embraces  not  only 
the  doctrines  which  deal  with  quantities  but  also  those 
which  deal  with  arrangements  and  their  possible  changes. 
The  older  combinatorial  analysis  dealt  mainly  with 
assemblages  of  a  quantity  of  separate  elements,  their 
number,  their  variety :  the  modern  theory  of  groups 
deals  rather  with  the  processes  and  operations  by  which 
different  arrangements  can  be  transformed  one  into  the 
other.  It  is  an  algebra  of  operations.  The  methods 
of  transformation  which  presented  themselves  first  of 
all  were  the  methods  known  in  algebra  as  substitution. 
Accordingly  the  first  comprehensive  treatise  on  the 
theory  was  the  '  Treatise  on  Substitutions,'  published  in 
1870  by  M.  Camille  Jordan.  This  book  forms  a  land- 
mark in  modern  mathematics ;  it  brought  into  a  system 
VOL.  n.  2  X 


690 


SCIENTIFIC    THOUGHT. 


the  beginnings  of  the  new  and  comprehensive  calculus 
of  operations  which  were  contained  in  the  writings  of 
Lagrange,  Abel,  Cauchy,  and  Galois,  and  established  the 
terminology  and  the  algorithm.  A  group  of  substitu- 
tions is  defined  as  having  the  property  that  each  two  or 
more  operations  belonging  to  it  and  successively  applied 
can  be  replaced  by  another  single  operation  contained  in 
the  same  group.  Succeeding  operations  are  symbolically 
represented  by  the  product  of  two  or  more  letters.  This 
product  has  certain  algebraical  properties,  and  in  analogy 
with  common  products  it  has  factors,  a  degree,  an  index ; 
the  substitution  may  be  cyclical  and  symmetric,  and  may 
have  many  other  remarkable  properties  which  the  theory  ^ 


1  The  "Theory  of  Groups"  has 
now  grown  into  a  very  extensive 
doctrine  which,  according  to  the  late 
Prof.  Marius  Sophus  Lie  (1842-99), 
is  destined  to  occupy  a  leading  and 
central  position  in  the  mathemati- 
cal science  of  the  future.  "  The 
concej^tion  of  Group  and  Invariant 
was  for  him  not  only  a  methodical 
aspect  from  which  he  intended  to 
review  the  entire  older  region  of 
mathematics,  but  also  the  element 
which  was  destined  to  permeate 
and  unify  the  whole  of  mathemati- 
cal science  "  (M.  Nother,  '  Math. 
Ann.,'  voh  liii.  p.  39).  But  though  it 
is  an  undoubted  fact  that  the  largest 
systematic  works  on  the  subject 
emanate  from  that  great  Norwegian 
mathematician,  and  that  his  ideas 
have  won  gradual  recognition, 
especially  on  the  part  of  prominent 
French  mathematicians,  notably 
M.  Picard  ('Traite  d' Analyse,' 
1896,  vol.  iii.)  and  M.  Poincare, 
the  epoch  -  making  tract  which 
pushed  the  novel  conception  into 
the  foreground  was  Prof.  F. 
Klein's  '  Erlangen  Programme ' 
(1872),     entitled      "  Vergleichende   I 


Betrachtungen    iiber    neuere    geo- 
metrische  Forschungen. "     To  those 
who  read   and    re-read    this    short 
but  weighty  treatise,  it  must  in- 
deed  have  been  like  a  revelation, 
opening   out  entirely  new  avenues 
of  thought  into  which  mathematical 
research  has  been   more  and  more 
guided  during  the  last  generation. 
The    tract,    which    has    now    been 
translated   into  all    the  important 
modern   languages,  remained  for  a 
long  time  comparatively  unnoticed, 
and,  twenty  years  after  its  publica- 
tion, was  reprinted  by  the  author 
in  the  4'3rd  volume  of  the  '  Math. 
Annalen,'   with  some   introductory 
remarks  which  indicate  the  changes 
that    had    taken    place   in    the    in- 
terval as  regards  the  scope  of  the 
idea.     The  main  result  of  the  dis- 
sertation  is  this  :  That,  primarily, 
for  all   geometrical    investigations, 
the  characteristic  properties  of  any 
manifold    (or  arrangement)    is  not 
the  element  out  of  which  it  is  com- 
posed, but  the  group,  the  transfor- 
mations of  which  reveal  its  invarian- 
tive  properties.     There  are,  accord- 
ingly, as  many  different   ways   of 


DEVELOPMENT  OF  MATHEMATICAL  THOUGHT.   691 

of  groups  investigates.  Its  immediate  application,  and 
the  purpose  for  which  it  was  elaborated,  was  the  theory 
of  Equations.  Every  equation  constitutes  an  arrange- 
ment in  which  a  finite  number  of  independent  elements, 
called  constants  or  coefficients,  is  presented  under  a 
certain  algebraical  form.  The  solution  of  the  equation 
means  the  finding  of  sucli  an  arrangement  as  when 
substituted  in  the  equation  for  the  unknown  quantity, 
will  satisfy  the  equation. 

The  conception  of  a  group  of  operations  standing  in 
the  defined  relations  is,  however,  capable  of  a  great 
and  fundamental  extension  into  that  region  of  mathe- 
matics which  deals,  not  with  fixed  or  constant,  but  with 
variable  or  flowing  quantities ;  not  with  elements  which        45. 

Continuous 

are  disconnected  or  discontinuous,  but  with  such  as  are  and  dis- 

'  continuous 

continuous.     To  understand  the  development  of  modern  '^^°^vs. 
mathematical  thought,  it  is  accordingly  necessary  to  go 
back    somewhat    and    review    the    progress    which    the 


studying  any  manifold  (e.g.,  such  as 
projective  geometry,  line  geometry, 
geometry  of  reciprocal  radii,  Lie's 
sphere  geometry,  analysis  situs, 
&c.)  as  there  are  continuous  groups 
of  transformations  that  can  be 
established  ;  and  there  are  as  many 
invariant  theories  (see  '  Ency.  Math. 
"\Viss.,' vol.ii.  p.  402 ;  Nother,  loc.  cit., 
p.  22).  From  that  date  onward  the 
different  kinds  of  groups  have  been 
defined  and  systematically  studied, 
notably  by  Klein  and  Lie  and  their 
pupils.  In  this  country,  although 
many  of  the  relevant  ideas  were 
contained  in  the  writings  notably 
of  Cayley  and  of  Sylvester,  the 
systematic  treatment  of  the  subject 
was  little  attended  to  before  the 
publication  (1897)  of   Prof.  Burn- 


side's  '  Theory  of  Groups  of  Finite 
Order,'  and  latterly  of  his  article 
on  the  whole  Theory  of  Groups  in 
the  29th  volume  of  the  '  Ency.  Brit.' 
It  has  been  remarked  by  those  who 
have  studied  most  profoundly  the 
development  of  the  two  great 
branches  of  mathematical  tactics 
— viz.,  "  The  Theory  of  Invariants  " 
and  the  "  Theory  of  Groups  " — that 
the  progress  of  science  would  have 
been  more  rapid  if  the  English 
school  had  taken  more  notice  of  the 
general  comprehensive  treatment 
by  Lie,  and  if  Lie  himself  had  not 
refrained  from  entering  more  fully 
into  the  special  theories  of  that 
school  (see  Dr  F.  Meyer,  '  Bericht,' 
&c.,  p.  231). 


692 


SCIENTIFIC    THOUGHT. 


conception  of  the  variable  ^  has  nndergone  in  the  course 
of  the  last  hundred  years.  Here  we  come  upon  a 
term  which  was  introduced  into  mathematical  language 
mainly  through  the  writings  of  Euler  —  the  term 
function.  It  is  used  to  denote  the  mathematical 
dependence  of  two  or  more  variable  quantities  on  each 


1  To  the  theory  of  equations  in 
algebra  there  corresponds  the 
theory  of  differential  equations  in 
analysis ;  and  as  the  theory  of 
algebraical  equations  had  gradually 
emerged  in  a  complete  form  out  of 
investigations  of  special  equations, 
or  sets  of  equations,  so  likewise  in 
analysis  a  general  theory  of  differ- 
ential equations  is  gradually  being 
evolved  out  of  the  scattere'd  and 
very  extensive  investigations  of 
special  differential  equations  which 
presented  themselves  notably  in 
the  apijlication  of  analysis  to  astro- 
nomical and  physical  problems.  It 
is  claimed  by  those  who  have 
grasped  the  abstract  ideas  of 
Sophus  Lie,  that  he  has  taken  a 
great  step  forward  in  the  direction 
of  a  general  theory  of  differential 
equations,  by  apjjlying  methods 
which  suggested  themselves  to  him 
through  the  general  theory  of  alge- 
braic forms  and  its  C(jnnection  with 
geometry.  Accordingly,  the  the- 
ories of  Lie  can  be  termed  an 
algebraical  theory  of  differential 
equations,  depending  upon  trans- 
formations analogous  to  those 
which  had  been  established  in  the 
general  theory  of  forms  or  quantities 
of  which  I  treated  above.  Prof. 
Engel,  in  his  obituarj'  notice  of 
Sophus  Lie  ('Deutsche  Math.  Ver.,' 
vol.  viii.  p.  35),  tells  us  that  in  the 
year  1869-70,  when  Lie  met  Prof. 
Klein  in  Berlin,  the  former  was 
occupied  with  certain  partial  differ- 
ential equations  which  exhibited, 
under  certain  transformations,  in- 
variantive  properties,  and  that  Klein 


then  pointed  out  "  that  his  pro- 
cedure had  a  certain  analogy  with 
the  methods  of  Abel.  The  sug- 
gestion of  this  analogy  became  im- 
portant for  Lie,  as  he  was  generally 
intent  upon  following  up  more 
clo.^ely  the  analogies  with  the 
theory  of  algebraical  equations." 
Dr  H.  F.  Bakei-,  in  his  recent  article 
on  Differential  Equations  in  the 
'Ency.  Brit.'  (vol.  xxvii.  p.  448), 
roughly  distinguishes  two  methods 
of  studying  differential  equations, 
which  he  names  respectively 
"  transformation  theories "  and 
"function  theories,"  "the  former 
concerned  to  reduce  the  algebraical 
relation  to  the  fewest  and  simjjlest 
forms,  eventually  with  the  hope  of 
obtaining  explicit  expressions  of 
the  dependent  in  terms  of  the 
independent  variables  ;  the  latter 
concerned  to  determine  what  gen- 
eral descriptive  relations  among 
the  quantities  are  involved  by  the 
differential  equations,  with  as  little 
use  of  algebraical  calculations  as 
may  be  possible."  For  the  historj' 
of  thought  and  connection  of  ideas, 
it  is  interesting  to  learn,  through 
Prof.  Engel,  that  it  was  not  purely 
algebraical  work, — such  as  is  rep- 
resented by  Galois  and  Jordan, 
to  which  Lie  was  early  intro- 
duced by  Pi'of.  Sylow, — but  the 
study  of  Poncelet's  and  Pliicker's 
methods  which  led  Lie  to  his 
original  conceptions,  and  that  he 
was  fond  of  calling  himself  a  pupil 
of  Pliicker,  whom  he  had  never 
seen  (Engel,  loc.  cit.,  p  34). 


I 


DEVELOPMENT  OF  MATHEMATICAL  THOUGHT.   693 

other.  The  question  arises,  What  are  we  to  under- 
stand under  this  term  ?  What  is  a  mathematical 
function  or  dependence  ?  The  question  was  approached 
by  the  great  analysts  of  the  second  half  of  the 
eighteenth  century.  A  preliminary  answer  which  served 
the  requirements  of  a  very  wide  field  of  practical 
application  was  given  by  Fourier  at  the  beginning  of 
the  nineteenth  century.  Since  that  time  the  question 
has  been  independently  treated  by  two  schools  of 
Continental  mathematicians.  Of  these  the  first  was 
founded  by  Cauchy  in  France,  and  is  mainly  represented 
by  Bernhard  Eiemann  and  his  numerous  pupils  in 
Germany ;  the  other  centres  in  the  Berlin  school, 
headed  by  Weierstrass,  and  goes  back  to  the  work 
of  Lagrange. 

The  interests  which  have  led  to  this  modern  branch        46. 

Theory  of 

of    mathematical    research  ^    are    various,    but    we    can  Functions. 


^  The  literature  suitable  for  intro- 
ducing the  student  of  mathematics 
to  the  modern  theory  of  functions 
— which  plays  in  analysis,  i.e.,  the 
doctrine  of  variable  quantity,  a 
part  of  similar  importance  to  that 
which  the  theory  of  forms  plays  in 
algebra — is  so  enormous,  the  sub- 
ject being  approached  from  so 
many  sides  by  different  writers, 
that  it  seems  worth  while  to  refer 
to  two  expositions  which  may  be 
read  with  profit,  and  which  do  not 
require  extensive  mathematical 
knowledge.  First  and  foremost  I 
would  recommend  Cayley's  article 
on  "  Functions "  in  vol.  ix.  of  the 
'Ency.  Brit.'  Then  there  is  the 
chapter  on  "  Foundations  of  the 
General  Theory  of  Functions,"  con- 
tained in  the  2nd  volume  of  the 
German  '  Mathematical  Encyclo- 
pedia,'  written    by    Prof.    Prings- 


heim.  Cayley's  article  intro- 
duces the  general  theory  after 
giving  a  short  summary  of  tlie 
more  important  "  known "  func- 
tions, including  those  which  pre- 
sented themselves  in  the  first  half 
of  the  nineteenth  century,  and 
whicli  I  referred  to  in  dealing  with 
the  work  of  Abel  and  Gauss  (see 
note,  p.  648).  The  treatment  of 
these  latter  functions,  which  had 
been  brought  to  a  certain  degree  of 
perfection  by  Jacobi,  had  made  it 
evident  that  more  general  aspects 
had  to  be  gained  and  broader 
foundations  laid.  But  ever  since 
the  middle  of  the  eighteenth 
century  another  development  of 
mathematical  ideas  had  been  going 
on  which  started  from  the  solution 
of  a  problem  in  mathematical 
physics — -namely,  that  of  vibrating 
strings,  which  led  in  the  sequel  to 


694  SCIENTIFIC    THOUGHT. 

distinguish  two  which  are  very  prominent,  and  are 
roughly  represented  by  the  two  schools  just  referred 
to.  In  the  first  place,  a  function  can  be  formally 
defined  as  an  assemblage  of  mathematical  symbols, 
each  of  which  denotes  a  definite  operation  on  one 
or  more  quantities.  These  operations  are  partly 
direct,  like  addition,  multiplication,  &c. ;  partly  indirect 
or  inverse,  like  subtraction,  division,  &c.  Now,  so  far 
as  the  latter  are  concerned,  they  are  not  generally 
and  necessarily  practicable,  and  the  question  arises. 
When  are  they  practicable,  and  if  they  are  not,  what 
meaning  can  we  connect  with  the  mathematical  symbol  ? 
In  this  way  we  arrive  at  definitions  for  mathematical 
functions  which  cannot  immediately  be  reduced  to  the 
primary  operations  of  arithmetic,  but  which  form  special 
expressions  that  become  objects  of  research  as  to  their 
properties  and  as  to  the  relation  they  bear  to  those 
fundamental  operations  upon  which  all  our  methods  of 
calculation  depend.  The  inverse  operations,  represented 
by  negative,  irrational,  and  imaginary  quantities  ;  further, 
the  operations  of  integration  in  its  definition  as  the  in- 

a    certain    finality    when    Fourier  Euler,    Daniel    Bernoulli,    d'Alem- 

introduced   his    well-known    series  bert,   and    Lagrange.      The    above- 

and  integrals,   by  which  any   kind  named   chapter,    written    by  Prof, 

of    functionality    or    mathematical  Pringsheim,  gives  an  introduction 

dependence,  such  as  physical  pro-    I  to  the  subject  showing  the  historical 

cesses   seem  to   indicate,  could  be  genesis  of  the  conception  of  function 

expressed.     The   work  of  Fourier,    \  and  the  various  changes  it  was  sub- 

which  thus  gave,  as  it  were,  a  sort   i  jected    to,    and   then    proceeds    to 

of  preliminary  specification   under  expositions  and  definitions  mostly 

which  a  large  number  of  problems  taken  from  the  lectures  of  Weier- 

in  physical  mathematics   could  be  strass  (see  p.  8),  whereas  Cay  ley's 

attacked    and     practically    solved,    ,  article  introduces  us  to  the  elements 

together   with   the    stricter  defini-    '  of  the  general  theory  of  functions 

tions  introduced  by  Lejeune   Dir-    j  as  they  were  first  laid  down  by  Rie- 

ichlet,  settled  for  a   time  and  for   i  mann  in  the  manner  now  commonly 

practical  purposes  the  lengthy  dis-   !  accepted, 
cussions    which    had    begun    with 


DEVELOPMENT  OF  MATHEMATICAL  THOUGHT.   695 

verse  of  differentiation, — led  early  to  investigations  of 
the  kind  just  mentioned.     The  experience  that  ordinary 
fractions  might  be  expressed  by  decimal  fractions — i.e., 
by  finite  or  infinite  series — led  to  the  inverse  problem 
of  finding  the  smn  of  such  series  and  many  other  an- 
swerable  and   apparently  unanswerable  problems.     The 
older   method   of    research   consisted  in    treating    these 
problems  when  and  as  they  arose :   new  chapters  were 
accordingly    added    to    the    existing    chapters    of    the 
text -books,   dealing   with    special   functions    or    mathe- 
matical expressions.      It  was   only   towards  the  end  of 
the   eighteenth   century,  and   at   the   beginning  of    the 
nineteenth,  that  Lagrange,  Gauss,  and  Cauchy  felt  and 
proclaimed  the  necessity  of  attacking  the  question  gener- 
ally  and   systematically ;    the   labours   of   Euler   having 
accumulated  an  enormous  mass  of  analytical  knowledge, 
a  great  array  of  useful  formulte,  and  amongst  them  not 
a  few  paradoxes  which   demanded  special  attention.      I 
have  already  had  occasion   to  refer   to   the  problem  of 
the  general  solution  of  equations  as  an  instance  where, 
in  the  hands  of  Abel,  the  tentative  and  highly  ingenious 
attempts  of  earlier  analysts  were  replaced  by  a  method- 
ical and  general  treatment  of  the  whole  question.     An- 
other chapter  of  higher  mathematics,  the  investigation  of 
expressions  which  presented  themselves  in  the  problems 
of  finding  the  length  of  the  arc  of  an  ellipse,  and  which 
opened  the  view  into  the  large  province  of  the  so-called 
higher  transcendents,  gave  Abel  further  occasion  of  lay- 
ing new  foundations  and  of  creating  a  general  theory  of 
equations  or  of  forms. 

But  yet  another  interest  operated  powerfully  in  the 


696 


SCIENTIFIC    THOUGHT. 


47. 
Physical 
analogies. 


direction  of  promoting  these  seemingly  abstract  re- 
searches. Nature  herself  exhibits  to  us  measurable 
and  observable  quantities  in  definite  mathematical  de- 
pendence ;  ^  the  conception  of  a  function  is  suggested  by- 
all  the  processes  of  nature  where  we  observe  natural 
phenomena  varying    according  to    distance  or   to   time. 


1  Nearly  all  the  "known"  func- 
tions have  presented  themselves  in 
the  attempt  to  solve  geometrical, 
mechanical,  or  physical  problems, 
such  as  finding  the  length  of  the 
arc  of  the  ellipse  (elliptic  func- 
tions) ;  or  answering  questions  in 
the  theory  of  attraction  (the  poten- 
tial function  and  other  functions, 
such  as  the  functions  of  Legendre, 
Laplace,  and  Bessel,  all  comprised 
under  the  general  term  of  "har- 
monic functions ").  These  func- 
tions, being  of  special  import- 
ance in  mathematical  physics,  were 
treated  independently  before  a 
general  theory  of  functions  was 
thought  of.  Many  important  pro- 
perties were  established,  and 
methods  for  the  numerical  evalu- 
ation were  devised.  In  the  course 
of  these  researches  other  functions 
occurred,  such  as  Euler's  "Gam- 
ma" function  and  Jacobi's  "Theta" 
function,  which  possessed  interest- 
ing analytical  properties.  These 
functions,  suggested  directly  or 
indirectly  by  applications  of  analy- 
sis, did  not  always  present  them- 
selves in  a  form  which  indicated 
definite  analytical  processes,  such 
as  processes  of  integration  or  the 
summation  of  series.  Very  fre- 
quently thej'  presented  themselves, 
not  in  an  "  explicit "  but  in  an 
"implicit"  form;  their  properties 
being  expressed  by  certain  con- 
ditions which  they  had  to  fulfil. 
It  then  remained  a  question 
whether  a  definite  symbol,  indi- 
cating a  set  of  analytical  operations, 
could  be  found.     This  arises  from 


the  fact  that  the  solution  of  most 
problems  in  mechanics  and  physics 
starts  from  the  assumption  that, 
though  the  finite  observable  pheno- 
mena of  nature  are  extremely 
intricate,  they  are,  nevertheless, 
compounded  out  of  comparatively 
simple  elementary  processes,  which 
take  place  between  the  discrete 
atoms,  or  the  elementary  but  con- 
tinuous portions  of  matter.  M  athe- 
matically  expi-essed,  this  means  that 
the  relations  in  question  present 
themselves  in  the  form  of  differen- 
tial equations,  and  that  the  solution 
of  them  consists  in  finding  func- 
tions of  finite  (observable)  quanti- 
ties which  satisfy  the  special  con- 
ditions. A  comparatively  small 
number  of  differential  equations 
has  thus  been  found  empirically 
to  embrace  very  large  and  appar- 
ently widely  separated  classes  of 
physical  phenomena,  suggesting 
physical  relations  between  those 
phenomena  which  might  otherwise 
have  remained  unnoticed.  The 
physicist  or  astronomer  thus  hands 
over  his  problems  to  the  mathe- 
matician, who  has  either  to  in- 
tegrate the  differential  equations, 
or,  where  this  is  not  possible,  at 
least  to  infer  the  properties  of  the 
functions  which  would  satisfy  them 
— in  fact,  the  differential  equation 
becomes  a  definition  of  the  function 
or  mathematical  relation.  In  con- 
sequence of  this  the  theory  of 
differential  equations  is,  as  Sophus 
Lie  has  said,  by  far  the  most  im- 
portant branch  of  mathematics. 


DEVELOPMENT  OF  MATHEMATICAL  THOUGHT.   697 

The  attraction  of  the  heavenly  bodies  varies  with  the 
distance,  the  velocity  of  a  falling  stone  or  the  cooling 
of  a  hot  body  varies  with  the  interval  of  time  which 
has  lapsed  or  flown.  We  are  now  so  much  accus- 
tomed to  represent  such  dependence  by  curves  drawn  on 
paper,  that  we  hardly  realise  the  great  step  in  advance 
towards  definiteness  and  intelligibility  that  this  device 
marks  in  all  natural  sciences  and  in  many  practical 
pursuits.  But  the  representation  of  the  natural  con- 
nections of  varying  quantities  by  curves  also  forms  the 
connecting  link  with  the  other  class  of  researches  just 
mentioned.  Descartes  had  shown  how  to  represent 
algebraical  formula?  by  curves  in  the  plane  and  in  space ; 
and  at  the  beginning  of  the  nineteenth  century  this 
method  was  modified  by  Gauss  and  Cauchy  so  as  to 
deal  also  with  the  extended  conception  of  number 
which  embraced  the  imaginary  unit.  Two  questions 
arise,  Is  it  possible  to  represent  every  arbitrary  de- 
pendence such  as  we  meet  with  in  the  graphical  descrip- 
tion of  natural  phenomena  by  a  mathematical  formula — 
i.e.,  by  a  formula  denoting  several  specified  mathematical 
operations  in  well-defined  connections  ?  and  the  inverse 
question,  Is  it  possible  to  represent  every  well-defined 
arrangement  of  symbols  denoting  special  mathematical 
operations  graphically  by  curves  in  the  plane  or  in 
space  ?  The  former  question  is  one  of  vital  importance 
in  the  progress  of  astronomy,  physics,  chemistry,  and 
many  other  sciences,  and  has  accordingly  occupied  many 
eminent  analysts  ever  since  Fourier  gave  the  first  ap- 
proximative answer  in  his  well-known  series :  the  latter 
question  can  only  be  answered  by  much  stricter  defini- 


698  SCIENTIFIC    THOUGHT. 

tions  of  all  the  more  advanced  and  of  some  even  of  the 
elementary  operations  which  analysts  had  become  accus- 
tomed to  use  without  a  previous  knowledge  of  the  range 
of  their  validity.  AH  applications  of  mathematics  con- 
sist in  extending  the  empirical  knowledge  which  we 
possess  of  a  limited  number  or  region  of  accessible 
phenomena  into  the  region  of  the  unknown  and  inac- 
cessible ;  and  much  of  the  progress  of  pure  analysis  con- 
sists in  inventing  definite  conceptions,  marked  by  symbols, 
of  complicated  operations ;  in  ascertaining  their  proper- 
ties as  independent  objects  of  research  ;  and  in  extending 
their  meaning  beyond  the  limits  they  were  originally 
invented  for, — thus  opening  out  new  and  larger  regions 
of  thought. 
48.  A  brilliant  and  most  suggestive  example  of  this  kind  of 

The 

potential,  reasoning  was  afforded  by  a  novel  mode  of  treating  a  large 
class  of  physical  problems  by  means  of  the  introduction  of 
a  special  mathematical  function,  termed  by  George  Green, 
and  later  by  Gauss,  the  "  Potential  "  or  "  Potential  func- 
tion." ^  All  the  problems  of  Newtonian  attraction  were 
concentrated  in  the  study  of  this  formula :  and  when  the 
experiments  of  Coulomb  and  Ampere  showed  the  analogy 
that  existed  between  electric  and  magnetic  forces  on  the 


"o' 


^  See  vol.  i.  p.  231  of  this  work.       algebraischen  Functionen' (Leipzig, 


The  history  of  the  subject  has  been 
written  by  Todhunter  ('  History  of 
the  Theories  of  Attraction  and  the 
Figure  of  the  Earth,'  2  vols.,  1873) 


1882,     trans,    by    F.     Hardcastle, 

Cambridge,  1893) ;  Prof.  Carl  Neu 

mann's  '  Untersuchungen  tiber  das 

Logarithmische    uud    Newtouische 


;l 


for  the  earlier  period  down  to  1832.  Potential'     (Leipzig,     1877);      Dr 

For  the  later  period  see  Bacharach's  '    Burkhardt's  '  Memorial  Lecture  on 

'Abriss  der  Geschichte  der  Poten-  Riemann '  (Gottingen,   1892);   and 

tialtheorie,'   Gottingen,   1883  ;    for  i   jointly  with  Dr  F'ranz  Meyer,  the 

the  connection  of  the  theory  with  !    same  author's  chapter  on  "  Poten- 

Riemann's   mathematical   methods,  tialtheorie "    in    the    2nd    volume 

especially    Prof.    F.    Klein's   tract,  i    (p.  464)  of  the  '  Encyclopildie  der 

'  Ueber     Riemann's     Theorie     der  Math.  Wiss.,'  1900. 


DEVELOPMENT    OF    MATHEMATICAL    THOUGHT.        699 


one  side,  and  Newtonian  forces  on  the  other ;  still  more 
when  Fourier,  Lame,  and  Thomson  (Lord  Kelvin)  pointed 
to  the  further  analogy  which  existed  between  the  distri- 
bution of  temperature  in  the  stationary  tiow  of  heat 
and  that  of  statical  electricity  on  a  conductor,  and  ex- 
tended the  analogy  to  hydrostatics  and  hydrodynamics, 
— it  became  evident  that  nature  herself  pointed  here 
to  a  mathematical  dependence  of  the  highest  interest 
and  value.  Many  eminent  thinkers  devoted  themselves 
to  the  study  of  this  subject,  but  it  was  reserved  for 
Bernhard  lliemann  to  generalise  the  mode  of  reasoning 
peculiar  to  these  researches  into  a  fundamentally  novel 
method  for  the  explanation  and  definition  of  mathe- 
matical function  or  dependence.^ 


'  Althougli  Riemanii's  original 
method  of  dealing  in  a  general  way 
with  algebraical  functions  is  here 
introduced  as  a  generalisation  of 
certain  ideas  suggested  by  mathe- 
matical physics,  it  was  not  in  this 
way  tliat  they  were  intioduced  to 
the  mathematical  world.  This  was 
done  in  his  very  abstract  and  difficult 
memoir,  '  Theorie  der  Abel'schen 
Functionen  '  (published  in  1857 
in  vol.  liv.  of  Crelle's  'Journal'). 
In  this  memoir  the  connection 
which  existed  with  mathematical 
physics  was  not  patent,  and  it 
took  a  long  time  before  his 
methods,  which  seemed  to  be  a 
development  of  Cauchy's  earlier 
researches,  were  understood  and 
fully  appreciated.  It  was  only 
after  he  had  lectured  repeatedly  on 
the  subject,  and  initiated  a  num- 
ber of  younger  mathematicians, 
who  now  occupy  many  of  the  chairs 
at  the  German  universities,  tliat 
the  discoveries  and  inventions  of 
Riemann  received  their  deserved 
appreciation.  Even  in  his  own 
lectures  on  matliematical  physics — 


notably  on  partial  differential 
equations  (including  harmonics) 
and  the  theory  of  the  potential  — 
he  did  not  lead  up  to  the  funda- 
mental ideas  which  he  developed 
in  his  lectures  on  the  theory  of 
the  Abelian  functions.  Some  light 
is  thrown  on  tlie  subject  of  the 
genesis  of  Riemann's  ideas  by  his 
dissertation  written  in  the  year 
1851,  though  even  the  biographical 
notice  attached  to  the  1st  edition 
of  his  works  (1876)  did  not  deal 
with  the  origins  of  his  theory. 
It  seems,  therefore,  correct  tO' 
date  the  adequate  recognition  of 
Riemann's  work  in  wider  circles  from 
the  publication  in  1882  of  Prof. 
F.  Klein's  tract  mentioned  above. 
Like  seveial  other  short  treatises 
of  this  eminent  living  mathema- 
tician, it  must  have  thrown  quite 
a  new  light  upon  the  subject  ; 
and,  like  several  of  his  other  wiit- 
ings,  it  revealed  connections  be- 
tween regions  of  thought  which  to 
many  students  must  have  appeared 
isolated.  "Through  the  treatment 
initiated   by   Klein,  the  theory  of 


700 


SCIENTIFIC    THOUGHT. 


49. 
Biemann. 


The  peculiarity  of  such  dependence,  as  exemplified  in 
the  phenomena  of  the  steady  How  of  heat  or  of  electric 
distribution,  consisted  in  this,  that  if  at  certain  points 
or  in  certain  regions  of  space  the  thermal  or  electrical 
conditions  were  defined  and  known  by  actual  observation, 
then  the  whole  distribution  in  other  points  and  regions 
was  completely  determined.  Those  boundary  conditions 
could  therefore  be  regarded  as  the  necessary  and  sufficient 
definition  of  the  whole  existing  distribution.  Translated 
into  mathematical  language,  this  means  that  functions 
exist  which  are  completely  defined  l^y  boundary  values 
and  singularities — i.e.,  values  at  single  points.  Nature 
herself  had  shown  the  way  to  define  and  calculate 
measured  relations  when  through  their  intricacy  they 
evaded  the  grasp  of  the  ordinary  operations  of  algebra.-^ 
Pliicker  had  already  in  geometry  (following  in  the  lines 
of  Xewton),  wiien  attacking  the  problem  of  the  infinite 
variety  of  higher  curves,  suggested  the  method  of  classi- 
fying them  according  to  their  characteristic  properties 
or  singularities.  What  had  been  done  by  geometers 
and  physicists  in  isolated  cases  with  the  expenditure 
of  much  ingenuity  and  skill,  Kiemann  and  his  school 
elevated  to  the  rank  of  a  general  method  and  doctrine. 


functions  acquires  a  great  degree 
of  clearness  and  connectedness, 
which  is  mainly  gained  by  concep- 
tions derived  from  the  (physical) 
theory  of  the  potential,  and  thus 
exhibits  the  intimate  relationship 
of  these  theories"  (Bacharach, 
'  Geschichte  der  Potentialtheorie,' 
Gottingen,  1883,  p.  71). 

^  On  this  subject  see  Burkhardt's 
'  Memorial  Lecture  on  Riemann  ' 
(Gottingen,  1892),  p.  5,  &c.;  Bach- 
arach {loc.  cit.),  p.  30,  &c.  The 
latter  especially  with  reference  to 


the  theorem  called  by  Clerk-Maxwell 
"  Thomson's  theorem  "  ('Cambridge 
and  Dublin  Mathematical  Journal,' 
1848,  or  '  Reprint  of  Papers  on 
Electro  -  statics,'  &c.,  p.  139);  and 
abroad  'Dirichlet's  Principle,'  after 
Riemann  (1857).  Further,  Brill 
and  Nother's  "Bericht"  ('Math. 
Ver.,'  vol.  iii.  p.  247) ;  and  lastly, 
a  very  suggestive  address  by  Prof. 
Klein  ("  On  Riemann's  Influence  on 
Modern  Mathematics")  to  the  meet- 
ing of  the  German  Association  in 
Vienna  in  1894  ('Report,'  p.  61). 


DEVELOPMENT    OF    MATHEMATICAL    THOUGHT.       701 

It  is  a  process  of  generalisation  and  simplification. 
Moreover,  Riemann's  manner  of  proceeding  brought 
with  it  the  gain  that  he  could  at  once  make  the 
various  theorems  of  the  doctrine  of  the  potential  useful 
for  purely  mathematical  purposes :  the  equation  which 
defined  the  potential  in  physics  became  the  definition 
of  a  function   in   mathematics/ 


^  "One  may  define  Riemann's 
developments  briefly  thus  :  that, 
beginning  with  certain  differential 
equations  which  the  functions  of 
the  complex  variable  satisfy,  he  is 
enabled  to  ajjply  the  principles  of 
the  potential  theory.  His  start- 
ing-point, accordingly,  lies  in  the 
province  of  mathematical  physics  " 
(Klein,  'Vienna  Report,'  loc.  cit., 
p.  60).  By  starting  with  physical 
analogies  Prof.  Klein  evades  certain 
difficulties  which  the  purely  mathe- 
matical treatment  had  to  encounter. 
In  the  preface  to  his  tract  of  the 
year  1882,  quoted  above, — in  intro- 
ducing his  method  of  explaining 
Riemann's  theory, — he  says:  "I 
have  not  liesitated  to  make  exactly 
these  physical  conceptions  the  stai't- 
ing-point  of  my  exposition.  In- 
stead of  them,  Riemann,  as  is  well 
known,  makes  use  in  his  writ- 
ings of  Dirichlet's  principle.  But 
I  cannot  doubt  that  he  started 
from  those  physical  pi'oblems,  and 
only  afterwards  substituted  Dirich- 
let's jjrinciple  in  order  to  support 
the  physical  evidence  by  mathe- 
matical reast)ning.  Whoever  under- 
stands clearly  the  surroundings 
among  which  Riemann  worked  at 
Gottingen,  whoever  follows  up  Rie- 
mann's speculations  as  they  have 
been  handed  down  to  us,  partly 
in  fragments,  will,  I  think,  share 
my  opinion."  And  elsewhere 
he  says  :  "  We  regard  as  a  specific 
performance  of  Riemann  in  this 
connection  the  tendency  to  give 
to  the  theory  of  the  potential  a 
fundamental    importance    for    the 


whole  of  mathematics,  and  further 
a  series  of  geometrical  construc- 
tions or,  as  I  would  rather  say,  of 
geometrical  inventions"  ('Vienna 
Report,'  p.  61).  Klein  then  refers 
to  the  representation  on  the  so- 
called  "  Riemann  surface,"  which 
is  historically  connected,  as  Rie- 
mann himself  points  out,  with  the 
problem  which  Gauss  first  attacked 
in  a  general  way — viz.,  the  repre- 
sentation of  one  surface  on  another 
in  such  a  manner  that  the  smallest 
portions  of  the  one  surface  are 
similar  to  those  of  the  other :  a 
problem  which  is  of  importance  in 
the  drawing  of  maps,  and  of  which 
we  possess  two  well-known  examples 
in  the  stereographic  projection  of 
Ptolemy  and  the  projection  of 
Mercator.  This  method  of  repre- 
sentation was  called  by  Gauss  the 
"  Conformal  Image  or  Representa- 
tion." His  investigations  on  this 
matter  were  suggested  by  the 
Geodetic  Survey  of  the  kingdom  of 
Hanover,  with  which  he  was  occu- 
pied during  the  years  1818  to  1830. 
(See  Gauss,  'Werke,'  vol.  iv.,  also 
his  corresp<nidence  with  Schum- 
acher and  Bessel. )  A  very  complete 
treatise  on  this  aspect  of  Riemann's 
inventions  is  that  by  Dr  J.  Holtz- 
miiller,  '  Theorie  der  Isogonalen 
Verwandschaften '  (Leipzig,  1882). 
On  the  historical  antecedents  of 
Riemann's  conception,  which  for 
a  long  time  appeared  somewhat 
strange,  not  to  say  artificial,  see 
Brill  and  Nother's  frequently 
quoted  "  Report  "  ('  Bericht  der 
Math.  Verein.,'  vol.  iii.),  p.  256  sqq. 


V02  SCIENTIFIC    THOUGHT. 

In  the  investigation  of  those  higher  functions  which 
the  purely  analytical  methods  of  Abel  and  his  followers 
had  forced  upon  the  attention  of  mathematicians,  the 
methods  of  Eiemann  proved  to  be  eminently  useful  and 
suggestive.  But  these  novel  methods  themselves  had 
been  imported  into  the  pure  science  from  the  side  of  its 
application  in  physics.  The  value  of  such  ideas  has 
always  been  questioned  by  another  class  of  thinkers  who 
aim  at  building  up  the  edifice  of  the  science  by  rigorous 
logic,  without  making  use  of  practical  devices  which  could 
only  be  legitimately  employed  when  once  their  validity 
had  been  thoroughly  proved  and  its  limits  defined.  The 
merit  of  having  done  this  in  the  whole  domain  of  those 
conceptions  which,  since  the  age  of  Descartes,  ISTewton, 
and  Leibniz,  had  been  introduced  as  it  were  from  the 
outside  into  analysis,  belongs  to  the  school  of  mathe- 
maticians headed  in  Germany  by  Karl  Weierstrass. 
50.  Eiemann  had  grown  up  in  the  traditions  of  the  school 

Weierstrass.       ^  . 

of  mathematical  thought  which  was  inspired  by  Gauss 
and  Weber  in  Gottingen.  Geometrical  representation 
and  physical  application,  including  the  immediate  evi- 
dence of  the  senses,  formed  a  large  and  important  factor 
in  the  body  of  arguments  by  which  scientific  discovery 
and  invention  was  carried  on  in  that  school ;  though 
Gauss  himself  made  logical  rigour  the  final  test  of 
maturity  in  all  his  published  writings,  abstaining  in 
many  cases  from  communicating  his  results  when  they 
had  not  satisfactorily  passed  that  test  in  his  own  mind. 
Through  this  self-imposed  restriction  he  had  permitted 
important  discoveries,  which  led  to  large  increase  of 
mathematical   knowledge,   to    be   anticipated   by   others. 


! 


DEVELOPMENT  OF  MATHEMATICAL  THOUGHT.   703 

The  cases  of  Cauchy,  Abel,  and  Jacobi  are  the  best- 
known  instances.  Through  their  labours  an  entirely 
new  field  had  been  prospected  and  partially  cultivated. 
It  was  to  this  that  Weierstrass,  the  other  great  leader 
in  modern  theory,  was  attracted.  He  made  the  clear 
definition  and  logical  coherence  of  the  novel  concep- 
tions which  it  involved  his  principal  ahn.  Gauss 
had  laboured  without  assistance  at  similar  problems, 
making  many  beginnings  which  even  his  colossal  intellect 
could  not  adequately  develop.  Weierstrass  early  gathered 
around  him  a  circle  of  ardent  and  receptive  pupils  and 
admirers,^    to    whose    care   and   detailed   elaboration   he 


^  The  researches  of  Weierstrass 
(1815  to  1897)  began  somewhat 
earlier  than  those  of  liiemann,  but 
only  became  generally  known  and 
appreciated  in  their  fundamental 
originality  through  his  pupils — his 
academic  influence  dating  from 
the  year  1861.  Some  account  of 
Weierstrass's  activity  is  given  bj^ 
Emil  Lampe  in  the  6th  volume 
(1899)  of  the  '  Bericht  der  Math. 
Verein.,'  p.  27,  &c.  The  genesis 
of  his  ideas  is  traced  by  Brill 
and  Neither  in  the  Report  quoted 
in  the  last  note,  and  by  M. 
Poincar^  in  '  Acta  Math.,'  vol.  xxii. 
The  former  divides  his  Researches 
roughly  into  two  periods,  during 
the  first  of  which  (1848-56)  he 
dealt  with  what  Cayley  would 
call  "  known  "  functions  ;  progress 
during  this  period  depending  not 
so  much  upon  fundamentally  new 
ideas  as  upon  an  investigation  of 
special  problems  and  great  analyti- 
cal skill.  The  second  period  begins 
in  the  year  1869,  and  is  devoted  to 
nothing  less  than  the  building  up 
of  the  entire  structure  of  mathe- 
matical thought  from  the  very 
beginning  upon  altered  definitions, 
through  which  the  dilemmas  and 


paradoxes  would  be  obviated  that 
had  shown  themselves  ever  since 
the  middle  of  the  eighteenth  cen- 
tury in  consequence  of  a  too 
confident  application  and  extension 
of  conventional  ideas  suggested 
mainl}^  by  practical  problems.  The 
elements  of  this  grand  edifice  are 
now  largely  accepted,  not  only  in 
Germany,  Ijut  also  in  France,  Italy, 
and  England.  In  Germany  Prof. 
0.  Stolz,  through  his  works  on 
General  Arithmetic,  2  vols.  (1885 
and  1886),  and  the  Calculus,  3  vols. 
(1893  to  1899),  has  probably  done 
more  than  any  other  academic 
teacher  to  utilise  the  new  sj'stem 
of  mathematical  thought  for  the 
elementary  course  of  teaching.  It 
seems  of  importance  to  state,  how- 
ever, that  outside  of  the  circle  of 
Weierstrass's  influence,  and  quite 
within  the  precincts  of  Riemann's 
school,  the  necessity  was  felt  of 
strengthening  the  foundations  on 
which  research  in  higher  mathe- 
matics was  carried  on,  by  going 
back  to  the  fundamental  ideas  of 
arithmetic.  The  principal  repre- 
sentative of  this  line  of  research 
was  Hermann  Hankel  (1839-73),  a 
pupil   of   Riemann's,   who,    in   the 


704 


SCIENTIFIC    THOUGHT. 


confided  many  separate  and  lengthy  investigations.  It 
was  through  one  of  these  that  a  test-case,  in  which  exist- 
ing mathematical  definitions  broke  down,  was  published 
in    1872.     It    forms   a   kind  of   era  in   the  history  of 


middle  of  the  sixties,  delivered 
lectures  at  the  University  of 
Leipsic  upon  "  Complex  numbers 
and  their  functions,"  starting  in  a 
characteristic  manner  with  that  ex- 
tended algebra  which  Cauchy  and 
Riemann  had  used  to  such  good 
purpose.  The  first  part  of  these 
lectures  was  published  in  1867. 
In  the  preface  Hankel  says  :  "  In 
the  natural  sciences  we  witness  in 
recent  times  the  distinct  tendency 
to  ascend  from  the  world  of  em- 
pirical detail  to  the  great  principles 
which  govern  everything  special  and 
connect  it  into  a  whole — i.e.,  the 
desire  for  a  philosophy  of  nature, 
not  forced  upon  us  from  outside, 
but  naturally  evolved  out  of  the 
subject  itself.  Also  in  the  domain 
of  mathematics  a  similar  want 
seems  to  make  itself  generally  felt 
— a  want  which  has  always  been 
alive  in  England."  Had  the  author 
not  been  prematurely  taken  away, 
there  is  no  doubt  that  he  would 
have  still  more  largely  contributed 
to  the  revolution  of  mathematical 
ideas  now  in  progress.  As  it 
is,  he  made  one  further  import- 
ant contribution,  of  which  more 
hereafter.  In  Italy  Prof.  Ulisse 
Dini  began  to  lecture  in  the  year 
1871  to  1872  on  the  theory  of 
functions,  and  published  his  lec- 
tures in  1878.  A  translation  was 
brought  out  in  German  (1892)  by 
Prof.  Liiroth  and  Mr  A.  Schepp, 
in  which  many  of  the  modern 
developments  aie  utilised.  In 
France  we  owe  to  M.  Jules  Tannery 
a  valuable  introduction  to  the 
theory  of  functions  of  one  variable, 
based  upon  a  series  of  lectures 
delivered  in  the  Ecole  Normale 
in    1883,    in    which,    as    he    says 


(Preface,  p.  vii),  he  collected 
the  labours  of  Cauchy,  Abel,  Le- 
jeune  Dirichlet,  Riemann,  Ossian 
Bonnet,  Heine,  Weierstrass,  and 
others ;  after  which  he  considers 
that  nothing  essential  need  be 
added  in  the  way  of  elucidation  of 
the  , foundations  of  the  theory. 
M.  Emil  Borel  published  in  1898 
'  Lectures  on  the  Theory  of  Func- 
tions,' the  first  of  a  series  of 
text  -  books  dealing  with  various 
aspects  of  the  theory  of  functions, 
in  which  he  largely  refers  to  the 
labours  of  Weierstrass.  Before 
Weierstrass's  theory  had  become 
known,  however,  j\l.  Meray  had  al- 
ready entered  upon  an  exposition 
of  the  foundations  of  analysis  on 
lines  which  had  much  analogy  with 
those  adopted  by  Weierstrass.  In 
England  the  late  Prof.  Clifford  had 
occupied  himself  in  various  memoirs 
with  the  theories  of  Riemann  ;  but 
we  owe  the  first  comprehensive 
treatise,  embracing  the  work  of 
Riemann  as  well  as  that  of  Weier- 
strass, to  Prof.  Forsyth  ('  Theory 
of  Functions  of  a  Complex  Vari- 
able,' Cambridge,  1893).  Almost 
simultaneously  Professors  Harkness 
and  Morley  published  a  '  Treatise  on 
the  Theory  of  Functions,'  and  in 
1898  an  '  Introduction  to  the 
Theory  of  Analytic  Functions,'  in 
which  they  in  the  main  adopted  the 
point  of  view  of  Weierstrass.  A 
very  original  thinker,  whose  in- 
dependent researches  reach  back  to 
the  year  1872,  and  who  played  an 
important  part  in  the  investigation 
of  many  obscure  points,  was  the 
late  Prof.  Paul  Du  Bois-Reymond, 
who  published  in  1882  the  first 
part  of  his  '  Allgemeine  Func- 
tionentheorie,'       containing       the 


DEVELOPMENT    OF    MATHEMATICAL    THOUGHT.       705 

mathematical  thought.  Up  to  that  time  "  one  would 
have  said  that  a  continuous  function  is  essentially  cap- 
able of  being  represented  by  a  curve,  and  that  a  curve 
has  always  a  tangent.  Such  reasoning  has  no  mathe- 
matical value  whatever ;  it  is  founded  on  intuition,  or 
rather  on  a  visible  representation.  But  such  representa- 
tion is  crude  and  misleading.  We  think  we  can  figure 
to  ourselves  a  curve  without  thickness ;  but  we  only 
figure  a  stroke  of  small  thickness.  In  like  manner  we 
see  the  tangent  as  a  straight  band  of  small  thickness, 
and  when  we  say  that  it  touches  the  curve,  we  wish 
merely  to  say  that  these  two  bands  coincide  without 
crossing.  If  that  is  what  we  call  a  curve  and  a  tangent, 
it  is  clear  that  every  curve  has  a  tangent ;  but  this  has 
nothing  to  do  with  the  theory  of  functions.  We  see  to 
what  error  we  are  led  by  a  foolish  confidence  in  what 
we  take  to  be  visual  evidence.  By  the  discovery  of  this 
striking  example  Weierstrass  has  accordingly  given  us  a 
useful  reminder,  and  has  taught  us  better  to  appreciate 
the  faultless  and  purely  arithmetical  methods  with  which 
he  more  than  any  one  has  enriched  our  science."  ^ 


"metaphysics  and  theory  of  the 
fundamental  conceptions  in  mathe- 
matics :  quantity,  limit,  argument, 
and  function "  (Tubingen).  This 
work  touches  the  borderland  of 
mathematics  and  philosophy,  as 
does  the  same  author's  posthumous 
work  '  Uber  die  Grundlagen  der 
Erkenntniss  in  den  exacten  Wissen- 
schaften'  (Tiibingen,  1890),  and  will 
occupy  us  in  another  place. 

1  M.  Poincare  in  the  '  Acta 
Mathematica,' vol.  xxii.,  "L'ceuvre 
mathematique  de  Weierstrass,"  p. 
5.  The  "test-case"  referred  to  in 
the  text  consisted  in  the  publica- 

VOL.  II. 


tion  by  Weierstrass  (in  the  year 
1872,  'Trans.  Berlin  Academy,'  re- 
printed in  Weierstrass's  '  Math. 
Werke,'  vol.  ii.  p.  71)  of  the  proof 
of  the  existence  of  a  continuous 
function  which  nowhere  possessed 
a  definite  (finite  or  infinite)  differ- 
ential coefficient.  This  example 
cleared  up  a  point  brought  into 
prominence  by  Riemann  in  his 
posthumously  (1867)  published 
Inaugural  Dissertation  of  1854 
('Werke,'  p.  '213).  The  question 
had  already,  following  on  Rie- 
mann's  suggestions,  been  dis- 
cussed  by  Hermann  Hankel   in   a 

2  Y 


706 


SCIENTIFIC   THOUGHT. 


Before  Weierstrass,  Caiichy  and  Eiemann  had  at- 
tempted to  define  the  vague  term  "  function "  or 
mathematical  dependence.  Both  clung  to  the  graphical 
representation  so  common  and  so  helpful  in  analysis 
since  Descartes  invented  it.  We  have,  of  course,  in 
abstract  science,  a  right  to  begin  with  any  definition 
we  choose.      Only   the  definition  must  be  such  that  it 


remarkable  tract  on  "Oscillating 
functions,"  in  which  he  drew 
attention  to  the  existence  of  func- 
tions which  admit  of  an  integral, 
but  where  the  existence  of  a  differ- 
ential coefficient  remains  doubtful. 
In  fact,  it  appears  that  the  question 
as  to  the  latter  had  never  been 
raised  ;  the  only  attempt  in  this 
direction  being  that  of  Ampere  in 
1806,  which  failed  (Hankel,  p.  7). 
Hankel  in  his  original  investigation 
showed  that  a  continuous  curve 
might  be  supposed  to  be  generated 
by  the  motion  of  a  point  which 
oscillated  to  and  fro,  these  oscilla- 
tions at  the  limit  becoming  in- 
finitely numerous  and  infinitely 
small :  a  curve  thus  generated 
would  present  what  he  called  "a 
condensation  of  singularities  "  at 
every  point,  but  would  possess  no 
definite  direction,  hence  also  no 
differential  coefficient.  The  argu- 
ments and  illustrations  of  Hankel 
have  been  criticised  and  found  fault 
with.  He  nevertheless  deserves  the 
credit  of  having  among  the  first 
attempted  "to  gain  a  firm  footing 
on  a  slippery  road  which  had  only 
been  rarely  trodden"  (p.  8).  In 
this  tract  (which  is  reprinted  in 
'Math.  Ann.,'  vol.  xx.),  as  well  as 
in  his  valuable  article  on  "  Limit " 
(Ersch  und  Grubei-,  '  Encyk.,'  vol. 
xc.  p.  185,  art.  "Greuze"),  Hankel 
did  much  to  establish  clearly  the 
essential  point  on  which  depends 
the  entire  modern  revolution  in 
our  ideas  regarding  the  foundations 


of  the  so-called  infinitesimal  cal- 
culus ;  reverting  to  the  idea  of  a 
"  limit,"  both  in  the  definition  of 
the  derived  function  (limit  of  a 
ratio)  and  of  the  integral  (limit  of 
a  sum)  as  contained  in  the  writings 
both  of  Newton  and  Leibniz, 
but  obscured  by  the  method  of 
"  Fluxions  "  of  the  former  and  the 
method  of  "  Infinitesimals  "  of  the 
latter.  Lagrange  and  Cauchy  had 
begun  this  revolution,  but  it  was 
not  consistently  and  generally 
carried  through  till  the  researches 
of  Riemann,  Hankel,  Weierstrass, 
and  others  made  rigorous  defini- 
tions necessary  and  generallj'  ac- 
cejited.  It  is,  however,  well  to 
note  that  in  this  country  A.  de 
Morgan  very  early  expressed  clear 
views  on  this  subject.  Prof.  Voss, 
in  his  excellent  chapter  on  the 
Differential  and  Integral  Calculus 
('  Encyk.  Math.  Wiss.,'  vol.  ii.  i.  p. 
54,  &c.),  calls  the  later  period  the 
period  of  the  purely  arithmetical 
examination  of  infinitesimal  con- 
ceptions, and  says  (p.  60),  "  The 
purely  arithmetical  definition  of 
the  infinitesimal  operations  which 
is  characteristic  of  the  present 
critical  period  of  mathematics  has 
shown  that  most  of  the  theorems 
established  by  older  researches, 
which  aimed  at  a  formal  extension 
of  method,  only  possess  a  validity 
limited  by  very  definite  assump- 
tions." Such  assumptions  were 
tacitly  made  by  earlier  writers,  but 
not  explicitly  stated. 


DEVELOPMENT    OF    MATHEMATICAL   THOUGHT.       707 

-corresponds  with  conditions  which  we  meet  with  in 
reahty,  say  in  geometry  and  physics,  otherwise  onr 
science  becomes  useless :  further,  our  definitions  must  be 
•consistent,  and  follow  logically  from  the  fundamental 
principles  of  arithmetic,  otherwise  we  run  the  risk  of 
sooner  or  later  committing  mistakes  and  encountering 
paradoxes.  We  have  two  interests  to  serve :  the  ex- 
tension of  our  knowledge  of  functions  and  the  rigorous 
proof  of  our  theorems.      The  methods  of  Eiemann  and        51. 

Riemann 

'01  Weierstrass  are  complementary.      "  By  the  instrument  a>"i 

•^  J  J  Weierstrass 

•of  Eiemann  we  see  at  a  glance  the  general  aspect  of  compared, 
things — like  a  traveller  who  is  examining  from  the  peak 
of  a  mountain  the  topography  of  the  plain  which  he  is 
going  to  visit,  and  is  finding  his  bearings.  By  the  in- 
struments of  Weierstrass  analysis  will,  in  due  course, 
throw  light  into  every  corner,  and  make  absolute  clear- 
ness shine   forth."  ^-     The    complementary    character    of 


'  Poiucare,  loc.  cit.,  p.  7.  Simi- 
larly Prof.  Klein  {loc.  cit.,  'Vienna 
Report,'  p.  60):  "The  founder 
■of  the  theory  [viz.,  of  functions] 
is  the  great  French  mathema- 
tician Cauchy,  but  only  in  Ger- 
many has  it  received  that  mod- 
ern stamp  through  which  it  has, 
so  to  speak,  been  pushed  into  the 
centre  of  our  mathematical  con- 
victions. This  is  the  result  of  the 
simultaneous  exertions  of  two 
workers — Riemann  on  the  one  side 
and  Weierstrass  on  the  other. 
Although  directed  to  the  same  end, 
the  methods  of  these  two  mathe- 
maticians are  in  detail  as  different 
as  possible  :  they  almost  seem  to 
contradict  each  other,  which  contra- 
diction, viewed  from  a  higher  aspect, 
naturally  leads  to  this — that  they 
mutually  supplement  each  other. 
Weierstrass    defines   the   functions 


of  a  complex  variable  analytically 
by  a  common  formula  —  viz.,  the 
'  Infinite  Power  Series '  ;  in  the 
sequel  he  avoids  geometrical  means 
as  much  as  possible,  and  sees  his 
specific  aim  in  the  rigour  of 
proof.  Riemann,  on  the  other 
side,  begins  with  certain  differential 
equations.  The  subject  then  im- 
mediately acquires  a  physical  as- 
pect. .  .  .  His  starting-point  lies 
in  the  region  of  mathematical 
physics."  We  now  know  from  the 
biographical  notice  of  Riemann, 
attached  to  his  collected  works 
(1st  ed.,  p.  520),  that  he  was 
pressed  (in  1856)  by  his  mathe- 
matical friends  to  publish  a  resume 
of  his  Researches  on  Abelian  func- 
tions— " be  it  ever  so  crude."  The 
reason  was  that  Weierstrass  was 
already  at  work  on  the  same  sub- 
ject.    In  consequence  of  Riemann's 


708 


SCIENTIFIC    THOUGHT. 


the  labours  of  the  two  great  analysts  is  nowhere  better 
shown  than  in  the  special  manner  in  which  Weierstrass 
succeeded  in  strengthening  the  foundations^  on  which 
much  of  Eiemann's  work  rests. 

The   labours   of    the  great   analysts — Gauss,  Cauchy, 
Eiemann,  and  Weierstrass — all  tended  to   increase   our 


publication  Weierstrass  withdrew 
from  the  press  an  extensive  memoir 
which  he  had  presented  in  the  year 
1857  to  the  BerUn  Academy,  be- 
cause, as  he  himself  says  (Weier- 
strass, 'Math.  Werke,'  vol.  iv.  p.  10) : 
"Riemann  published  a  memoir  on 
the  same  problem  which  rested  on 
entirely  different  foundations  from 
mine,  and  did  not  immediately 
reveal  that  in  its  results  it  agreed 
completely  with  my  own.  The 
proof  of  this  required  investigations 
which  were  not  quite  easy,  and  took 
much  time  ;  after  this  difficulty 
had  been  removed  a  radical  remod- 
elling of  my  dissertation  seemed 
necessary,"  &c.,  &c.  The  mutual 
influence  of  Riemann's  and  W^eier- 
strass's  work  is  also  referred  to  by 
Weierstrass  in  a  letter  to  Prof. 
Schwarz,  dated  1875,  in  which 
he  utters  what  he  calls  his  con- 
fession of  faith:  "The  more 
I  ponder  over  the  principles  of 
the  theory  of  functions  —  and  I 
do  this  incessantly  —  the  stronger 
grows  my  conviction  that  it  must 
be  built  up  on  the  foundation  of 
algebraical  truths,  and  that,  there- 
fore, to  employ  for  the  proof  of 
simple  and  fundamental  algebraical 
theorems  the  '  transcendental,'  if  I 
may  say  so,  is  not  the  correct  way, 
however  enticing  privia  vista  the 
considerations  may  be  by  which 
Riemann  has  discovered  many  of 
the  most  important  properties  of 
algebraical  functions.  It  is  a  mat- 
ter of  course  that  every  road  must 
be  open  to  the  searcher  as  long  as 
he  seeks ;  it  is  only  a  question  of 


the  systematic  demonstration " 
(Weierstrass,  'Werke,'  vol.  ii.  p, 
235). 

^  This  refers  mainly  to  Weier- 
strass's  investigation  of  the  principle 
called  by  Riemann  "Dirichlet'& 
principle,"  but  which  had  been 
stated  already  with  great  generality 
by  Thomson  (Lord  Kelvin)  in  the 
year  1847.  The  validity  of  this 
method  depended  on  a  certain 
minimum  theorem.  Weierstra.ss- 
has  shown  that  the  existence  of 
such  a  minimum  is  not  evident,  and 
that  the  argument  used  is  not  con- 
clusive. He  laid  before  the  Berlin 
Academy  in  the  year  1870,  a  com- 
munication giving  a  test  -  case  tO' 
prove  that  Dirichlet's  method  was 
not  generally  valid  ('W^erke,'  vol. 
ii.  p.  49).  "Through  this,"  Prof. 
KJein  says  (loc.  cit.,  p.  67),  "a 
great  part  of  Riemann's  develop- 
ments become  invalidated.  Never- 
theless the  far  -  reaching  results 
which  Riemann  bases  upon  the 
prineiple  are  all  correct,  as  was 
shown  later  on  exhaustively  and 
with  all  rigour  by  Carl  Neumann 
and  H.  A.  Schwarz.  Indeed  we- 
must  come  to  the  conclusion  that 
Riemann  himself  arrived  at  these 
theorems  by  a  phj-sical  intuition, 
and  only  afterwards  resorted  to  the 
principle  referred  to  in  order  to 
have  a  consistent  mathematical  line 
of  reasoning  "  {loc.  cit.,  p.  67).  See 
on  this  also  Poincar^  (loc.  cit., 
pp.  10  and  15),  who  gives  other 
instances  where  the  work  of  Weier- 
strass supported  that  of  Riemann. 


DEVELOPMENT  OF  MATHEMATICAL  THOUGHT.   709 


knowledge  of  the  higher  mathematical  relations,  but 
also  to  reveal  the  uncertainty  and  absence  of  rigorous 
definition  of  the  foundations  of  arithmetic  and  of  geo- 
metry. Accordingly  we  find  these  great  thinkers  con- 
tinvially  interrupting  their  more  advanced  researches  by 
examinations    of    the    principles.       This   feeling   of   un-        52. 

^  ^  °  Bxamiua- 

certainty  had  led,  ever  since  the  end  of  the  eighteenth  fg^Jj^ations 
century,  to  many  isolated  attacks  and  half-philosophical 
discussions  by  various  writers  in  this  country  and 
abroad.  Many  of  them  remained  long  unrecognised ; 
such  were  the  suggestive  writings  of  Hamilton,  De 
Morgan,    Peacock    in    England,    Bolzano  ^    in    Bohemia, 


^  The  merits  of  Bernhard  Bolzano 
(1781-1848)  as  oue  of  the  earliest 
representatives  of  the  critical  period 
of  mathematics  were  recognised 
after  a  long  interval  of  neglect  by 
Hankel  in  his  article  on  "  Limit " 
mentioned  above.  This  philosophi- 
cal mathematician  published  many 
years  before  Caucliy  a  tract  on  the 
Binomial  Theorem  (Prague,  1816), 
iu  which  he  gives,  in  Hankel's 
opinion,  the  first  rigid  deduction  of 
various  algebraical  series.  "  Bol- 
zano's notions  as  to  convergency  of 
series  are  eminently  clear  and 
correct,  and  no  fault  can  be  found 
with  his  development  of  those  series 
for  a  real  argument  (which  he 
everywhere  presupposes)  ;  in  the 
preface  he  gives  a  pertinent  criti- 
cism of  earlier  developments  of  the 
Binomial  Theorem,  and  of  the  un- 
restricted use  of  infinite  series, 
which  was  then  common.  In  fact, 
he  has  everything  that  can  place 
him  in  this  respect  on  the  same  level 
with  Cauchy,  only  not  the  art  pecu- 
liar to  the  French  of  refining  their 
ideasandcommunicatingthemin  the 
most  appropriate  and  taking  man- 
ner. So  it  came  about  that  Bolzano 
remained   unknown  and  was  soon 


forgotten  ;  Cauchy  was  the  happy 
one  who  was  praised  as  a  reformer  of 
the  science,  and  whose  elegant  writ- 
ings were  soon  widely  circulated." 
(Hankel,  luc.  cit.,  p.  210.)  Follow- 
ing on  this  statement  of  Hankel 
and  a  remark  of  Prof.  H.  A. 
Schwarz,  who  looks  upon  Bolzano 
as  the  inventor  of  a  line  of  reason- 
ing further  developed  by  Weier- 
strass  ('Journal  fiir  Mathematik,' 
vol.  Ixxiv.  p.  22,  1872),  Prof.  0. 
Stolz  published  in  1881  ('Math. 
Ann.,'  vol.  xviii.  p.  255)  an  account 
of  the  several  writings  of  Bolzano, 
beginning  in  the  year  1810,  in  so  far 
as  they  referred  to  the  principles  of 
the  Calculus.  "  All  these  writings 
are  remarkable  inasmuch  as  they 
start  with  an  unbiassed  and  acute 
criticism  of  the  contributions  of  the 
older  literature"  {toe.  cit.,  p.  257). 
A  posthumous  tract  by  Bolzano, 
'  Paradoxieen  des  Unendlichen,' 
was  republished  in  1889  in  '  Wis- 
senschaftliche  Classiker,'  vol.  ii., 
Berlin  (Meyer  and  Miiller).  As 
stated  above,  Hankel  was  also  one 
of  the  first  to  draw  attention  to 
the  originality  and  importance  of 
Hermann  Grassmanu's  work. 


710 


SCIENTIFIC   THOUGHT. 


Bolyai  in  Hungary,  Lobatchevski  in  Kasan,  Grassmann 
in  Stettin.  Most  of  these  were  unknown  to  each 
other.  However,  near  the  beginning  of  the  last  third 
of  the  century  three  distinct  publications  created  a 
great  stir  in  the  mathematical  world,  brought  many 
scattered  but  cognate  lines  of  reasoning  together,  and 
made  them  mutually  fertile  and  suggestive.  These 
three  were — first,  the  publication  in  1860  of  Gauss's 
correspondence  with  Schumacher,  in  which  two  letters 
of  the  former,  dated  May  and  July  1831,^  became 
known,  where  he  referred  to  his  extensive  but  un- 
written and  unfinished  speculations  on  the  foundations 
of  geometry  and  the  theorem  which  refers  to  the 
sum  of  the  angles  in  a  triangle.  The  second  was  the 
publication  in  1867  of  the  first  and  only  part  of  Her- 
mann Hankel's  "  Lectures  on  the  Complex  Numbers 
and  their  Functions."  '^  The  third  was  the  posthumous 
publication  in  the  same  year  of  Eiemann's  paper,  dated 
1854,^  "  On  the  Hypotheses  which  lie  at  the  Foundation 
of  Geometry."  Almost  simultaneously  there  appeared 
the  first  of  Helmholtz's  two  important  papers  ^  on  the 


^  See  '  Briefwechsel  zwischen 
Gauss  und  Schumacher,'  ed.  Peters, 
1860,  vol.  ii.  pp.  260,  268. 

^  The  small  volume  contains  so 
much  original  and  historical  matter 
that  I  have  on  several  occasions 
refened  to  it.  See  above,  pp.  645, 
653. 

^  Riemann,  'Math.  Werke,'  1st 
ed.,  p.  254  sqq. 

*  The  first  publication  of  Helm- 
holtz  was  a  lecture  on  "  the  actual 
foundations  of  geometry,"  which 
he  delivered  on  the  22nd  May  1868 
to  the  Medical  Society  at  Heidel- 
berg.    This  communication,  which 


referred  to  investigations  carried  on 
for  many  years, — notably  in  con- 
nection with  the  theory  of  the 
colour -manifold,  —  was  occasioned 
by  the  publication  of  Riemann 's 
paper  in  the  '  Transactions '  of  the 
Gottingen  Society.  He  had  heard 
of  this  through  Schering,  to  whom 
he  wrote  on  the  21st  April  1868 
before  having  seen  Riemann's 
paper :  "  I  have  myself  been  oc- 
cupied with  the  same  subject  dur- 
ing the  last  two  years,  in  connection 
with  my  researches  in  physiological 
optics.  ...  I  now  see,  from  the 
few  hints  which  you  give  as  to  the 


DEVELOPMENT    OF    MATHEMATICAL    THOUGHT.       711 

same  subject,  through  which  it  became  more  widely 
known  and  attracted  the  attention  of  other  than 
purely  mathematical  writers.  The  small  but  eminently 
suggestive  volume  of  Hankel  showed  the  necessity  of 
a  revision  and  extension  of  the  fundamental  principles 
and   definitions  ^    of  general   arithmetic   and  algebra  as 


result  of  the  investigation,  that 
Riemanu  has  arrived  at  exactly 
the  same  results.  My  starting- 
point  was  the  question,  How  must 
a  magnitude  of  several  dimensions 
be  constituted,  if  solid  bodies  are 
to  move  in  it  everywhere  continu- 
ously, monodromically,  and  as  freely 
as  bodies  move  in  real  space?"  On 
receiving  from  Schering  a  reply 
with  a  copy  of  Riemann's  paper, 
Helmholtz  wrote  (18th  May),  "I 
enclose  a  short  exposition  of  that 
which  in  my  researches  on  the  same 
subject  is  not  covered  by  Riemann's 
work."  A  fuller  paper,  with  the 
title  "  On  the  Facts  which  lie  at  the 
foundation  of  Geometry,"  appeared 
in  the  '  Gottinger  Nachrichten,' 
June  3,  1868.  See  Helmholtz, 
'  Wiss.  Abhandl.,'  vol.  ii.  pp.  610 
and  618,  &c.  ;  also  '  H.  von  Helm- 
holtz,' by  Leo  Koenigsberger  (1903), 
vol.  ii.  p.  138,  &c.  Li  another 
lecture,  "  On  the  origin  and  mean- 
ing of  the  .\xioms  of  Geometry " 
(1870,  reprinted  in  abstract  in 
'  The  Academy,'  vol.  i. ),  as  well  as 
in  an  article  in  vol.  i.  of  '  Mind ' 
(p.  301),  he  discussed  "the  philo- 
sophical bearing  of  recent  in- 
quiries concerning  geometrical 
axioms  and  the  possibility  of 
working  out  analytically  other 
systems  of  geometry  with  other 
axioms  than  Euclid's  "  (reprinted  in 
vol.  ii.  of  '  Vortriige  und  Reden '). 

^  In  this  treatise  Hankel  intro- 
duced into  German  literature  the 
three  terms  "distributive,"  "asso- 
ciative," and  "commutative"  to 
define  the  three   principles  which 


govern  the  elementary  operations 
of  arithmetic,  and  introduced  fur- 
ther what  he  calls  the  principle  of 
the  permanence  of  formal  rules 
in  the  following  statement :  "  If  two 
forms,  expressed  in  the  general 
terms  of  universal  arithmetic,  are 
equal  to  each  other,  they  are  to 
remain  equal  if  the  symbols  cease 
to  denote  simple  quantities  ;  hence 
also  if  the  operations  receive  a 
different  meaning."  Hankel  seems 
to  have  been  led  to  his  definitions 
by  a  study  of  French  and  English 
writers,  among  wliom  he  mentions 
Servois  ('  Gergonne's  Ann.,'  v.  p.  93, 
1814)  as  having  introduced  the 
terms  "distributive"  and  "com- 
mutative," and  SirW.  R.  Hamilton 
as  having  introduced  the  term 
"  associative."  He  further  says 
(p.  15):  "In  England,  where 
investigations  into  the  funda- 
mental principles  of  mathematics 
have  always  been  treated  with 
favour,  and  where  even  the  great- 
est mathematicians  have  not 
shunned  the  treatment  of  them 
in  learned  dissertations,  we  must 
name  George  Peacock  of  Cambridge 
as  the  one  who  first  recognised 
emphatically  the  need  of  formal 
mathematics.  In  his  interesting 
report  on  certain  branches  of 
analysis,  the  principle  of  perma- 
nence is  laid  down,  though  too 
narrowly,  and  also  without  the 
necessary  foundation."  Other 
writings,  of  what  he  terms  Pea- 
cock's Cambridge  school,  such  as 
those  of  De  Morgan,  Hankel  states 
that  he  had  not  inspected  ;  mention- 


712 


SCIENTIFIC    THOUGHT. 


53. 
Non- 
Euclidean 
geometry. 


an  introduction  to  the  advanced  theories  of  Gauss  and 
Kiemann ;  and  for  this  purpose  he  went  back  to  the 
unnoticed  labours  of  Grassmann  in  Germany,  to  the 
writings  of  Peacock  and  De  Morgan  in  England,  and 
incidentally  introduced  into  Germany  the  elaborate 
algebra  of  quaternions,  invented  and  practised  by 
Hamilton  twenty  years  before  that  time.  The  papers 
of  Eiemann  and  Helmholtz  similarly  showed  the  neces- 
sity of  a  thorough  investigation  of  the  principles  and 
foundations  of  ordinary  or  Euclidean  geometry,  and 
showed  how  consistent  systems  of  geometry  could  be 
elaborated  on  other  than  Euclidean  axioms.  Only 
from  that  moment,  in  fact,  did  it  become  generally 
recognised  that  already,  a  generation  before,  two  in- 
dependent treatises  on  elementary  geometry  had  been 
published  in  which  the  axiom  of  parallel  lines  was 
dispensed  with  and  consistent  geometrical  systems 
developed.  These  were  contained  —  as  already  stated 
—  in    the   '  Kasan    Messenger,'    under    date    1829   and 


ing  ouly  a  short  paper  by  Dr  F. 
Gregorj'  on  Symbolical  Algebra 
in  the  Edinburgh  '  Transactions.' 
Whilst  Hankel  was  delivering 
lectures  on  these  fundamentals, 
Weierstrass  in  Berlin  was  likewise 
in  the  habit  of  introducing  his 
lectures  on  the  Theory  of  Analytic 
Functions  by  a  discussion  of  the 
theory  of  Complex  Numbers.  This 
introduction  was  published,  with 
Weierstrass's  permission,  in  the  year 
1872  by  Dr  E.  Kossak  (in  a  pro- 
gramme of  the  Friedrichs-Werder 
Gymnasium),  after  lectures  de- 
livered by  Weierstrass  in  1865-66. 
To  what  extent  Hankel  may  have 
been  influenced  by  Weierstrass's 
lectures,  which  he  seems  to  have 
attended  after  leaving   Gottingen, 


is  uncertain,  for  in  spite  of  his  very 
extensive  references  he  does  not 
mention  Weierstrass.  In  Kossak's 
'  Elemente  der  Arithmetik '  the 
term  "  permanence  of  formal  rules  " 
is  not  used,  but  the  treatment  of 
the  extended  arithmetic  is  carried 
on  along  the  same  lines — i.e.,  not 
by  an  attempt  to  represent  the 
complex  quantities,  but  on  the 
ground  of  maintaining  the  rules 
which  govern  the  arithmetic  of 
ordinary  numbers.  Great  im- 
portance is  also  attached  to  the 
principle  of  inversion  as  having 
shown  itself  of  value  in  the  theory 
of  elliptic  functions,  and  being  not 
less  valuable  in  arithmetic.  As 
stated  above  (p.  640,  note),  this  prin- 
ciple is  also  insisted  on  by  Peacock. 


DEVELOPMENT    OF    MATHEMATICAL    THOUGHT.        713 

I80O,  the  author  being  Lobatchevski ;  and  in  the 
appendix  to  an  Introduction  to  Geometry,  published 
by  Wolfgang  Bolyai  at  Maros  Vasarheli,  a  town  of 
Transylvania,  the  appendix  being  by  the  author's  son, 
Johann  Bolyai.  The  elder  Bolyai  having  been  a 
friend  and  correspondent  of  Gauss,  and  his  speculations 
evidently  of  the  same  nature  as  those  indicated  by  the 
latter  in  the  above-mentioned  correspondence,  conjectures 
have  been  made  as  to  which  of  the  two  originated  the 
whole  train  of  thought.^  The  independent  investiga- 
tions of  Eiemann  and  Helmholtz  started  from  a  differ- 


^  See  above,  p.  652,  note.  What 
is  important  from  our  point  of 
view  in  the  investigations  of  both 
Riemann  and  Helmholtz  lies  in  the 
following  points :  First,  Neither 
Riemann  nor  Helmholtz  refers  to 
the  non  -  Euclidean  geometry  of 
Lobatchevski  or  Bolyai.  This  is 
not  surprising  in  the  case  of 
Helmholtz,  whose  interest  was 
originally  not  purely  mathematical  ; 
in  fact,  we  may  incidentally  re- 
mark how,  in  spite  of  his  profound 
mathematical  ability,  he  on  various 
occasions  came  into  close  contact 
with  mathematical  researches  of 
great  originality  and  importance 
without  recognising  them  —  e.g., 
the  researches  of  Grassmaun  and 
Pliicker.  As  regards  Riemann,  his 
paper  was  read  before  Gauss,  who 
certainly  knew  all  about  Bolyai,  and 
latterly  also  about  Lobatchevski,  of 
whom  he  thought  so  highlj^  that  he 
proposed  him  as  a  foreign  member 
of  the  Gbttingen  Societj*.  Gauss 
could  therefore  easily  have  pointed 
out  to  Riemann  the  relations  of 
his  speculations  with  his  own  and 
those  of  the  other  mathematicians 
named.  Since  the  publication  of 
the  latest  volume  of  Gauss's  works, 
it  has  become  evident  that  Gauss 


con-esponded  a  good  deal,  and 
more  than  one  would  have  sup- 
posed from  reading  Sartorius's 
obituary  memoir,  on  the  subject 
of  non-Euclidean  (astral  or  imag- 
inary) geometry,  notably  with 
Gerling ;  and  that  several  con- 
temporary mathematicians,  such  as 
Schweikart,  came  very  near  to 
Gauss's  own  position.  Second,  al- 
though Riemann,  and  subsequently 
also  Helmholtz,  made  use  of  the 
term  "  manifold  "  {3fannigfaltig- 
keit),  it  does  not  appear  in  the 
course  of  their  discussion  that  they 
considered  the  space-manifold  from 
any  other  than  a  metrical  point 
of  view.  In  fact,  the  manifold  be- 
comes in  their  treatment  a  magni- 
tude {Grossc).  It  is  true  that 
Riemann  does  refer  to  certain 
geometrical  relations  not  con- 
nected with  magnitude  but  only 
with  position,  as  being  of  great 
importance.  These  two  points 
through  which  the  researches  of 
Riemann  and  Helmholtz  stand  in 
relation  to  other,  and  at  the 
time  isolated,  researches,  were 
dwelt  on,  the  first  by  Beltrami, 
and  the  second  by  Cajdey  and 
Prof.   Klein. 


714  SCIENTIFIC    THOUGHT. 

ent  origin :  both  made  use  of  tlie  more  general  con- 
ception of  an  extended  magnitude,  introduced  the 
notion  of  the  curvature  of  space  by  analogy  with 
Gauss's  measure  of  curvature  of  a  surface,  and  tried 
to  express  in  algebraical  formulae  the  general  and 
necessary  properties  of  a  magnitude  which  should  form 
the  foundation  of  a  geometry.  The  relation  of  these 
algebraical  results  to  those  arrived  at  by  the  critical 
and  purely  geometrical  methods  of  Lobatchevski  and 
Bolyai  were  set  out  by  Beltrami,  who  showed  clearly 
that  three  geometries  of  two  dimensions  are  possible — 
the  Euclidean,  that  of  Lobatchevski,  where  the  three 
angles  of  a  triangle  are  less  than  two  right  angles, 
and  a  third  where  they  are  more.  He  showed  the 
analogy  of  the  third  with  geometry  on  the  sphere, 
and  suggested  the  pseudo-sphere  as  a  surface  on  which 
the  second  could  be  similarly  represented.  At  the 
same  time  he  indicated  the  generalisation  through  the 
algebraical  formula  of  the  conception  of  dimensions,  and 
introduced  the  symbolical  term  geometry  of  four  or 
more  dimensions,  as  Grassmann  and  Cayley  had  done 
before  him.^     Through  all  these  investigations  a  habit 


^  The  geometry  of  non-Euclidean 
space,  as  well  as  the  geometry 
of  four  or  more  dimensions  (both 
usually  comprised  under  the  term 
"  non  -  Euclidean  geometry  "),  can 
now  boast  of  an  enormous 
literature,  the  enumeration  of 
which  alone  would  fill  many 
pages.  A  complete  bibliography 
up  to  the  year  1878  is  given  in 
vols.  i.  and  ii.  of  the  American 
'  Journal  of  Mathematics '  bj-  Prof. 
Bruce  Halsted,  who  has  done 
much  to  make  known  to  English 
readers    the    original    writings    of 


the  pioneers  in  this  subject. 
Later  publications  are  referred  to 
in  Dr  Victor  Schlegel's  papers 
('Leopoldina,'  xxii. ,  1886,  Nos. 
9-18):  "Ueber  Entwickelung  und 
Stand  der  n-dimensionalen  Ge- 
ometric,"  &c.,  &c.  In  France 
Houel  published  (beginning  with  the 
year  1866)  translations  of  memoii-s 
referring  to  this  subject  ;  in  fact, 
he  was  almost  the  first  to  draw 
attention  to  this  important  modem 
departure.  But  it  is  almost  ex- 
clusively owing  to  the  various 
writings  of  Prof.  Felix  Klein  that 


DEVELOPMENT    OF    MATHEMATICAL    THOUGHT.        715 

has  been  introduced  into  mathematical  writings  which 
has  not  a  little  puzzled  outsiders,  and  even  exposed 
the  logically  rigorous  deductions  of  mathematicians  to 
the  ridicule — not  to  say  the  contempt — of  eminent 
philosophical  authorities.  The  complete  parallelism  or 
correspondence  of  geometrical  with  algebraical  notions 
— the  possibility  of  expressing  the  former  with  perfect 
accuracy  by  the  latter,  and  of  retranslating  the  latter 
into  the  former,  and  this  in  more  than  one  way,  accord- 
ing to  the  choice  of  the  space  element  (point,  line, 
sphere),  led  to  the  habit  of  using  purely  geometrical  pre- 
sentable ideas  as  names  for  algebraical  relations  which 
had  been  generalised  by  the  addition  of  more  than 
a  limited  number  of  variables.  Thus  the  conception 
of    curvature,    easily    defined    for    a    plane    curve,    and        54. 

"^  ^  ^         Curvature 

extended  by  Gauss  to  surfaces,  was,  by  adding  a  third  cf  space, 
variable  in  the  algeljraic  formula,  applied  to  space. 
We  are  then  told  that  it  is  necessary  to  understand 
what  is  meant  by  the  curvature  of  space,  this  being  a 
purely  algebraical  relation,  not  really  presentable,  but 
only  formed  by  analogy  from  the  geometrically  present- 
able relations  of  geometrv  on  a  surface.      In  a  similar 


the  different  points  of  origin  of  this 
most  recent  mathematical  specula- 
tion, which  are  to  be  found  in 
the  mathematical  literature  of  all 
the  principal  nations,  have  been 
put  in  the  true  light  and  brought 
into  connection.  In  fact,  here, 
as  in  sevei-al  other  subjects,  his 
publications,  including  his  litho- 
graphed lectures  on  non-Euclidean 
geometry  (delivered  at  Guttingen, 
1893-94),  serve  as  the  best  guide 
through  the  labyrinth  and  contro- 
versies of  this  intricate  subject. 
See  especially  his   article   "Ueber 


die  so-genannte  nicht-Euclidische 
Geometrie"  in  vol.  iv.,  "Math.  Ann.,' 
1871.  In  this  paper  he  connects  the 
independent  researches  of  Cayley 
(following  Laguerre,  '  Nouv.  Ann. 
de  Math.,'  1853),  who  in  his  sixth 
memoir  on  Quantics  showed  how 
metrical  geometry  can  be  included 
in  projective  geometry  by  refer- 
ring figures  to  a  fundamental  fixed 
figure  in  space  called  by  him  the 
"Absolute,"  with  the  independent 
researches  of  Lobatchevski,  Bolyai, 
Riemann,  and  Beltrami. 


716 


SCIENTIFIC    THOUGHT. 


way  the  idea  of  the  dimensions  of  space  was  extended, 
and  four  and  more  dimensions  freely  spoken  of  when 
really  only  a  limited  number  is  geometrically  pres- 
entable. In  the  hands  of  mathematicians  these  terms 
are  useful,  and  we  may  discard  the  criticism  of  philo- 
sophers and  laymen  as  based  on  misunderstanding.^ 
The  introduction,  however,  into  geometrical  work  of  con- 
ceptions such  as  the  infinite,  the  imaginary,  and  the 
relations  of  hyperspace,  none  of  which  can  be  directly 
imaged,  has  a  psychological  significance  well  worthy 
of  examination."^  It  gives  a  deep  insight  into  the 
resources  and  working  of  the  mind.  We  arrive  at 
the  borderland  of  mathematics  and  philosophy. 


^  The  most  important  philosophi- 
cal criticism  of  the  iiou-Euclidean 
geometry  is  that  of  Lotze,  con- 
tained in  the  second  book,  chap, 
ii.,  of  the  '  Metaphysik '  (1879,  p. 
249,  &c. )  It  must  not  be  forgotten 
that  Lotze  wrote  at  a  time  when 
tlie  novel  and  startling  conceptions 
put  forward  by  popular  writers  on 
the  subject  had  been  employed  in 
the  interest  of  a  spiritualistic  philo- 
sophy, to  the  delusions  of  which 
some  even  of  Lotze's  friends  had 
fallen  a  prey.  This  explains  the 
severity  of  Lotze's  criticisms,  which 
are  of  the  very  same  nature  as  those 
he  pronounced  many  years  earlier 
on  similar  aberrations  (see  '  Kleine 
Schriften,'  vol.  iii.  p.  329).  Those 
who  are  interested  in  following  up 
the  subject  should  refer  to]  the 
writings  of  Friedr.  Ztillner  as  col- 
lected in  the  four  vols,  of  his 
'  Wissenschaftliche  Abhandlungen  ' 
(Leipzig,  1878-81).  They  belong 
to  the  curiosities  of  the  philosophi- 
cal and  scientific  literature  of  that 
age,  but  can  hardly  claim  a  place  in 
the  history  of  thought. 

"^  See  the  remark  of  Cayley  in  his 
Presidential  Address  ('  Coll.  Works,' 


vol.  xi.  p.  434)  :  "  The  notion, 
which  is  really  the  fundamental 
one  (and  I  cannot  too  strongly 
emphasise  the  assertion),  under- 
lying and  pervading  the  whole  of 
modern  analysis  and  geometry,  is 
that  of  imaginary  magnitude  in 
analysis  and  of  imaginary  space  (or 
space  as  a  locvs  in  quo  of  imaginary 
points  and  figures)  in  geometry.  I 
use  in  each  case  the  word  imaginary 
as  including  real.  This  has  not 
been,  so  far  as  I  am  aware,  a  subject 
of  philosophical  discussion  or  in- 
quiry. As  regards  the  older  meta- 
physical writers,  this  would  be  quite 
accounted  for  by  saying  that  they 
knew  nothing,  and  were  not  bound 
to  know  anything,  about  it ;  but  at 
present,  and  considering  the  prom- 
inent position  which  the  notion 
occupies — say  even  that  the  conclu- 
sion were  that  the  notion  belongs 
to  mere  technical  mathematics  or 
has  reference  to  nonentities,  in 
regard  to  which  no  science  is  pos- 
sible— still  it  seems  to  me  that  (as 
a  subject  of  philosophical  discussion) 
the  notion  ought  not  to  be  thus 
ignored  ;  it  should  at  least  be  shown 
that  there  is  a  right  to  ignore  it. " 


DEVELOPMENT    OF    MATHEMATICAL    THOUGHT.        7 17 

There  exists,  moreover,  an  analogy  between  the 
manner  in  which  these  novel  and  extended  ideas  have 
been  historically  introduced  and  the  mode  of  reasoning 
which  led  Sir  W.  E.  Hamilton  to  the  invention  of  a  new 
and  extended  algebra — the  algebra  of  quaternions.  This 
analogy  becomes  evident  if  we  study  the  small  volume  of 
Hermann  Hankel,  which  appeared  about  the  same  time 
as  Riemann's  and  Beltrami's  fundamental  geometrical 
dissertations. 

The  extension  of  Hamilton  was  only  possible  by  drop- 
ping  one  of  the  fundamental  principles  of  general  arith-  conceptions, 
nietic,  the  commutative  principle  of  multiplication,  which 
is  symbolically  expressed  by  saying  that  a  x  &  is  equal  to 
h  y.a.  By  assuming  that  «  x  &  is  equal  to  —  &  x  a,  Hamil- 
ton founded  a  new  general  arithmetic  on  an  apparently 
paradoxical  principle.  Similarly  Lobatchevski  and  Bolyai 
constructed  new  geometries  by  dropping  the  axiom  of 
parallel  lines.  Hankel  made  clear  the  significance  of  the 
new  algebra,  Riemann  and  Beltrami  that  of  the  new  geom- 
etry. The  practical  performance  anticij)ated  and  led  up 
to  the  theoretical  or  philosophical  exposition  of  the  under- 
lying principles.  But  there  was  a  third  instance  in 
which  a  new  science  had  been  created  by  abandoning  the 
conventional  way  of  looking  at  things.  This  was  the 
formation  of  a  consistent  body  of  geometrical  teaching 
by  disregarding  the  metrical  properties  and  studying 
only  the  positional  or  projective  properties,  following 
Monge  and  Poncelet.  The  two  great  minds  who  worked 
out  this  geometry  independently  of  the  conception  of 
number  or  measurement,  giving  a  purely  geometrical 
definition  of  distance  and  number,  were  Cayley  in  Eng- 


718 


SCIENTIFIC   THOUGHT. 


56. 

Klein's 
exposition. 


land  and  Von  Staudt  in  Germany.  It  was  reserved  for 
Prof.  Felix  Klein  of  Gottingen  to  show  how  the  gener- 
alised notions  of  distance  introduced  into  geometry  by 
Cay  ley  and  Von  Staudt  opened  out  an  understanding  of 
the  three  geometries  of  Euclid,  of  Lobatchevski,  and  of 
Eiemann.^  We  have  to  go  back  to  the  purely  projective 
properties  of  space  to  understand  these  different  possi- 
bilities. Lobatchevski  attacked  the  problem  practically, 
Eiemann  analytically,  Klein  geometrically.  Through  the 
labours  of  Klein  the  subject  has  arrived  at  a  certain 
finality.  And  what  was  still  wanting  after  he  had 
written  his  celebrated  memoir  (which  was  approved  and 


^  See  the  note  ou  p.  714,  above  ; 
also  '  Math.  Ann.,'  vol.  iv.  p.  573, 
and  vol.  vi.  p.  112.  Prof.  Klein 
— following  a  usage  iu  mathe- 
matical language  —  distinguishes 
three  different  geometries,  the 
hyperbolic,  the  elliptic,  and  the 
parabolic  geometry,  corresponding 
to  the  possession  by  the  straight 
line  at  infinity  of  two  real  or  two 
imaginary  (that  is,  none)  or  two 
coincident  points.  The  whole 
matter  turns  upon  the  fact  that, 
although  metrical  relations  of 
figures  are  in  general  changed 
by  projection,  there  is  one  metri- 
cal relation — known  in  geometry 
as  the  "  anharaionic  ratio"  (in 
German  Doppdve7-hdltniss)— which 
in  all  projective  transformations 
remains  unchanged.  As  this  an- 
harmonic  ratio  of  points  or  lines 
can  be  geometrically  constructed 
without  reference  to  measure- 
ment (Von  Staudt,  'Geometrie 
der  Lage,'  1847  and  1857),  a 
method  is  thus  found  by  which, 
starting  from  a  purely  descriptive 
property  or  relation,  distance  and 
angles — i.e.,  metrical  quantities — 
can  be  defined.     Some  doubts  have 


j  been  expressed  whether,  starting 
from  the  purely  projective  pro- 
perties of  space  and  building  up 
geometry  in  this  way  (arriving  at 
the  metrical  properties  by  the 
construction  suggested  by  Von 
Staudt),  the  ordinary  idea  of 
distance  and  number  is  not  tacitly 
introduced  from  the  beginning. 
This  may  be  of  philosophical, 
but  is  not  of  mathematical, 
importance,  as  the  main  object 
in  the  mathematical  treatment  is 
to  gain  a  starting  -  point  from 
which  the  several  possible  con- 
sistent systems  of  geometry  can 
be  deduced  and  taken  into  view 
together.  See  on  this  point, 
inter  alia,  Cayley's  remarks  in 
the  appendix  to  vol.  ii.  of  '  Col- 
lected Works '  (p.  604  sqq),  also 
Sir  R.  S.  Ball's  paper  (quoted 
there),  and  more  recently  the  dis- 
cussion on  the  subject  in  Mr 
Bertrand  Russell's  '  Essay  on  the 
Foundations  of  Geometry'  (1897, 
p.  31,  &c.  ;  p.  117,  &c.)  See 
also  the  same  author's  article  on 
non-Euclidean  Geometry  in  the 
supplement  of  the  '  Ency.  Brit.,' 
vol.  xxviii. 


DEVELOPJMENT    OF    MATHEMATICAL    THOUGHT.       719 

commented  on  by  Cayley)  was  later  on  supplied  in  con- 
sequence of  a  suggestion  of  his.  The  researches  of 
Eiemann,  and  still  more  those  of  Helmholtz,  had  not 
merely  a  mathematical,  they  had  also  a  logical  and  a 
psychological,  meaning.  Space  was  conceived  to  he  a 
threefold  -  extended  manifold.  There  are  other  mani- 
folds besides  space — such,  for  instance,  as  the  threefold- 
extended  manifold  of  colours.  Helmholtz  came  from  the 
study  of  this  manifold  to  that  of  space.  Now  the 
question  arises  as  to  the  conditions  or  data  which  are 
necessary  and  sufficient  for  the  foundations  of  a  science 
like  geometry.  We  have  seen  that  the  axiom  of  parallel 
lines  is  not  required ;  we  have  also  seen  that  the  notion 
of  distance  and  number  can  be  generalised.  What  other 
data  remain  which  cannot  be  dispensed  with  ?  Helm- 
holtz had  attempted  to  answer  this  question.  But 
neither  he  nor  Eiemann  had  considered  the  possibility 
of  a  purely  projective  geometry.  Now  it  is  the  merit  of 
Prof.  Klein  to  have  seen  that  there  exists  a  purely  alge- 
braical method  by  which  this  problem  can  be  attacked. 
This   is    the   method   of  groups  referred   to  above,  and        57. 

Sophus  Lie. 

applied  by  Sophus  Lie  to  assemblages  of  continuously 
variable  quantities.  Klein  was  one  of  the  first  to  recog- 
nise the  power  of  this  new  instrument.  He  saw  that 
the  space  problem  was  a  problem  of  transformations,  the 
possible  motions  in  space  forming  a  group  with  definite 
elements  (t]ie  different  freedoms  of  motion)  which  were 
continuously  variable — i.e.,  in  infinitesimal  quantities — 
and  which  returned  into  themselves  under  certain  well- 
defined  conditions.  They  possessed,  moreover,  in  the 
maintenance  of   distance  the   algebraic   property  of  in- 


720 


SCIENTIFIC    THOUGHT. 


variance.  He  also  expressed  some  doubt  regarding  the 
logical  consistency  of  the  assumptions  of  Helmholtz. 
Sophus  Lie  undertook  this  investigation,  and  thus 
brousht  the  log-ical  side  of  the  labours  of  Eiemann 
and  Helmholtz  to  a  final  conclusion.^  This  is  one  of 
the  celebrated  instances  where  the  rigorous  algebraical 
methods  have  detected  flaws  in  the  more  intuitional  or 
purely  geometrical  process,  and  extended  our  knowledge 
of  hidden  possibilities. 

But  there  is  yet  another  branch  of  the  great  science 
of  number,  form,  and  interdependence,  the  principles 
and  foundations  of  which  had  been  handed  down  from 
earlier  ages,  where  the  critical  and  sifting  process  of  the 
nineteenth  century  has  led  to  an  expansion  and  revolu- 
tion of  our  fundamental  ideas.  Here  also,  as  in  so 
many  other  directions,  the  movement  begins  with  Gauss. 
Hitherto  I  have  spoken  mainly  of  algebra  or  general 
arithmetic,  of  geometry,  of  the  connections  of  both  in  the 


^  "  Lie  was  early  made  aware  by 
Klein  and  his  "program  "  that  the 
space  problem  belonged  to  the 
theory  of  groups.  .  .  .  Ever  since 
1880  he  had  been  pondering  over 
these  questions  ;  he  published  his 
views  first  in  1886  on  the  occasion 
of  the  Berlin  meeting  of  natural 
philosophers.  Helmholtz's  concep- 
tion was  itself  unconsciously  (but 
remarkably  so,  inasmuch  as  it 
dates  from  1868)  one  belonging  to 
the  theory  of  groups,  trying,  as  it 
did,  to  characterise  the  groups  of 
the  sixfold  infinite  motions  in 
space,  which  led  to  the  three 
geometries,  in  comparison  with  all 
other  groups.  He  did  this  by 
fixing  on  the  free  mobility  of  rigid 
bodies — i.e.,  on  the  existence  of  an 
invariant  between   two   points    as 


the  only  essential  invariant.  When 
Lie  took  up  this  problem  in  prin- 
ciple, as  one  belonging  to  the  theory 
of  groups,  he  recognised  that  for 
our  space  that  part  of  the  axiom  of 
monodromy  was  unnecessary  which 
added  periodicity  to  the  free  mo- 
bility round  a  fixed  axis.  .  .  . 
The  value  of  these  investigations 
lies  mainly  in  this,  that  they  permit 
of  our  fixing  for  every  kind  of  geo- 
metry the  most  appropriate  system 
of  axioms.  .  .  .  And  they  justly 
received  in  the  year  1897  the  first 
Lobatchevski  prize  awarded  by  the 
Society  of  Kasan"  (M.  Nother, 
'Math.  Ann.,'  vol.  liii.  p.  38).  A 
lucid  exposition  of  Lie's  work  will 
be  found  in  Mr  B.  Russell's  '  Essay,' 
&c.,  p.  47  sqq. 


DEVELOPMENT    OF    MATHEMATICAL    THOUGHT.       721 

theory  of  forms  and  functions  :  there  remains  the  science 

of  numbers — of  number  in  the  abstract  and  also  of  the        ss. 

Theory  of 

named  numbers  of  ordinary  arithmetic.  Gauss's  earliest  numbers. 
labours  were  connected  with  this  branch.  Superseding 
the  work  of  Fermat,  Euler,  and  Legendre,  he  produced 
that  great  book  with  seven  seals,  the  '  Disquisitiones 
Arithmetica?.'  The  seals  were  only  gradually  broken. 
Lejeune  Dirichlet  did  much  in  this  way  :  others  followed, 
notably  Prof.  Dedekind,  who  published  the  lectures  of 
Dirichlet  and  added  much  of  his  own.  The  question 
may  be  asked,  Have  we  gained  any  new  ideas  about 
numbers  ? 

In  this  abstract  inquiry  we  can  again  facilitate  our 
survey  by  distinguishing  between  the  practical  and  the 
purely  theoretical  interests  which  stimulated  it.  Look- 
ing at  the  matter  as  well  as  the  formal  treatment  by 
which  it  was  rendered  accessible,  we  may  say  Gauss  not 
only  taught  us  some  very  remarkable  new  properties  of 
numbers^he  also  invented  a  new  instrument  or  calculus 
for  their  investigation.  Let  us  consider  his  work  and 
that  of  his  followers  from  these  different  points  of  view. 

First,  then,  there  were  certain  definite  problems  con- 
nected with  the  properties  of  numbers  which  had  been 
handed  down  from  antiquity.  Such  were  the  division  of 
the  circle  into  equal  parts  by  a  ready  geometrical  con- 
struction, the  duplication  of  the  cube,  and  the  quad- 
rature  of  the  circle  or  the  geometrical  construction 
of  the  number  it}       To  the  latter  may  be  attached  the 


^  See  above,  vol.  i.  p.  181,  note. 
The  student  will  find  much  in- 
teresting matter  referring  to  these 
problems    in    Prof.    Klein's    little 


volume  entitled  '  Famous  Problems 
in  Elementary  Geometry,'  transl. 
by  Beman  and  Smith,  Boston  and 
London,  1879.     In  it  is  also  given 


VOL.  II.  2  Z 


722  SCIENTIFIC    THOUGHT. 

properties  of  the  number  c,  the  basis  of  the  Napierian  or 
natural  logarithms,  this  number  having  been  shown  by 
Euler  to  stand  in  a  remarkable  arithmetical  relation  to 
the  number  tt — a  relation  which  could  be  very  simply 
expressed  if  one  had  the  courage  to  make  use  of   the 
imaginary  unit.     As  in   the  instance  referred  to  above, 
when  I  dealt  with   the   problem  of  the  solution  of  the 
higher  order  of  equations,  so  also  in  the  case  of  the  three 
celebrated  problems  now  under  review,  the  reasoning  of 
the  mathematicians  of  the  nineteenth  century  lay  largely 
in   proving   why   these   problems    were   insoluble   or  in 
defining  those  special  cases  in  which  they  were  soluble. 
Moreover,  the  labours  of  Gauss  and  the  class  of  mathe- 
maticians   who    followed    or    read    him    were    dii'ected 
towards  the  defining  and  fixing  of  general  conceptions, 
the  study  and  elaboration  of  which  embraced  these  single 
problems  as  special  cases.     Prime  numbers  had  always 
been  the  object  of  special  attention.     Division  and  par- 

an  account   of   several   mechanical  the  true  septisection  of  the  circle 

contrivances    for    the    solution    of  \    was   so    close    that    he    could    not 

transcendental  problems,  or  of  those  discover,    up    to    the    7th  decimal, 

where  the  use  of  the   compass  and  whether  the  error  was  in  the  direc- 

ihe  ruler  do  not  suffice.     Although  ,    tion  of  more  or  less.      On  carrj-ing 

accurate  constructions  with  a  ruler  ,    the  calculation  further,  he  found  the 


and  compass,  or  with  either  alone, 
were  known  to  the  ancients  only  in 


approximation   to  be  such  that  a 
heptagon   stepped   round    a   circle 


comparatively  small  numbers,  ap-  i  equal  in  size  to  the  equator  would 
jiroximations,  and  sometimes  very  |  reach  the  starting-point  within  50 
close  ones,  seem  to  have  been  |  feet.  The  inventor  or  discoverer 
known.  A  very  interesting  exam-  of  this  method  —  Rober,  an  archi- 
ple  is  Rober's  construction  of  the  tect  of  Dresden — supposed  that  it 
regular  heptagon,  of  which  we  read  ,  was  known  to  the  ancient  Egj'ptians, 
in  the  correspondence  of  Sir  W.  R.  and  in  some  form  or  other  con- 
Hamilton  with  De  Morgan  (Life  of  I  nected  with  the  plans  of  the  temple 
Hamilton,  by  Graves,  vol.  iii.  pp.  at  Edfu,  but  on  this  point  I  have 
141,  5.34).  and  which  was  described  \  obtained  no  information.  The  ques- 
by  him  in  the  'Phil.  Mag.,'  Feb-  I  tion  is  not  referred  to  in  Prof. 
ruary  1864.  The  approximation  to  {  Cantor's  '  History  of  Mathematics.' 
the   correctly   calculated    figure   of 


DEVELOPxMENT    OF    MATHEMATICAL    THOUGHT.       723 

tition  of  numbers  had  been  studied,  and  many  interesting 
formulce  had  been  found  by  induction,  and  subsequently 
proved — or  not  proved — by  a  multitude  of  ingenious 
devices.  As  in  so  many  other  directions  of  research 
so  also  here,  the  genius  of  Gauss  gave  a  great  impetus  to        59. 

'  ®  001  Gauss's 

progress  by  the  invention  of  a  definite  calculus  and  an  *^^"^°' 
algorithm.  This  invention  referred  to  the  solution  of  ™*^^^- 
what  used  to  be  known  as  indeterminate  equations :  to 
find  two  or  more  numbers — notably  integers,  which  obey 
a  certain  algebraical  relation.  For  one  large  class  of 
these  problems  (which  already  occupied  the  ancient 
geometers),  viz.,  those  of  the  divisibility  of  one  number 
by  another  (called  the  modulus)  with  or  without  residue. 
Gauss  invented  the  conception  and  notation  of  a  con- 
gruence. Two  numbers  are  congruent  if  when  divided 
by  a  certain  number  they  leave  the  same  remainder.  "  It 
will  be  seen,"  says  Henry  Smith,  "  that  the  definition  of 
a  congruence  involves  only  one  of  the  most  elementary 
arithmetical  conceptions— that  of  the  divisibility  of  one 
number  by  another.  But  it  expresses  that  conception 
in  a  form  so  suggestive  of  analysis,  so  easily  available  in 
calculation  and  so  fertile  in  new  results,  that  its  introduc- 
tion into  arithmetic  has  proved  a  most  important  contri- 
bution to  the  progress  of  the  science."^  Notably  the 
analogy  with  ordinary  algebraic  equations  and  the  possi- 
bility of  transferring  the  properties  and  treatment  of 
these  was   at   once   evident.     It    became    a    subject    of 

^  See  Henry  J.  S.  Smith  in  his  :  pp.  38-364).     It  gives  a  very  lucid 
most    valuable     '  Report    on     the  ;  account  of  the  history  of  this  de- 
Theory  of  Numbers'  (Brit.  Assoc. ,  |  partment  of   mathematical  science 
1859-65,   six  parts.      Reprinted  in  ]  up  to  the  year  1863. 
'  Collected   Math.    Papers,'    vol.    i.  j 


724  SCIENTIFIC    THOUGHT. 

interest  to  determine  the  residues  of  the  powers  of 
numbers.  A  number  is  said  to  be  a  quadratic,  cubic, 
or  biquadratic  residue  of  another  (prime)  numljer  (the 
modulus)  if  it  is  possible  to  find  a  square,  cube,  or  bi- 
quadratic number  which  is  congruent  with  the  first 
number.  The  theory  of  congruences  was  a  new  calculus : 
as  such  it  was,  like  the  theory  of  determinants  or  of  in- 
variants or  the  general  theory  of  forms,  a  tactical  device 
for  bringing  order  and  simplicity  into  a  vast  region  of 
very  complicated  relations.  Gauss  himself  wrote  about  it 
late  in  life  to  Schumacher.^  "  In  general  the  position  as 
regards  all  such  new  calculi  is  this — that  one  cannot 
attain  by  them  anything  that  could  not  be  done  without 
them  :  the  advantage,  however,  is,  that  if  such  a  cal- 
culus corresponds  to  the  innermost  nature  of  frequent 
wants,  every  one  who  assimilates  it  thoroughly  is  able — 
without  the  unconscious  inspiration  of  genius  which  no 
one  can  command — to  solve  the  respective  problems, 
yes,  even  to  solve  them  mechanically  in  complicated 
cases  where  genius  itself  becomes  impotent.  So  it  is 
with  the  invention  of  algebra  generally,  so  with  the 
differential  calculus,  so  also — though  in  more  restricted 
regions — with  Lagrange's  calculus  of  variations,  with 
my  calculus  of  congruences,  and  with  Mobius's  calculus. 
Through  such  conceptions  countless  problems  which 
otherwise  would  remain  isolated  and  require  every  time 
(larger  or  smaller)  efforts  of  inventive  genius,  are,  as  it 
were,  united  into  an  organic  whole."  But  a  new  calculus 
frequently  does  more  than   this.      In  the  course  of  its 

^  See  '  Briefwechsel,'  &c.,  vol.  iv.  p.  147  ;  also  Gauss's  '  Werke,'  vol.  viii. 
p.  298. 


DEVELOPMENT  OF  MATHEMATICAL  THOUGHT.   725 

application  it  may  lead  to  a  widening  of  ideas,  to  an 
enlargement  of  views,  to  a  removing  of  artificial  and  con- 
ventional barriers  of  thought.  As  I  stated  early  in  this 
chapter,  the  attempts  of  Gauss  to  prove  the  fundamental 
theorem  of  algebra,  that  every  equation  has  a  root, 
suggested  to  him  the  necessity  of  introducing  complex 
numbers ;  the  development  of  the  theory  of  congruences 
and  of  residues — notably  of  the  higher  residues — con- 
firmed this  necessity.  In  the  year  1831,  in  his  memoir 
on  biquadratic  residues,  he  annovmces  it  as  a  matter  of 
fundamental  importance.  In  the  earlier  memoir  he  had 
treated  this  extension  of  the  field  of  higher  arithmetic 
.as  possible,  but  had  reserved  the  full  exposition.  And 
before  he  redeemed  this  promise  the  necessity  of  doing 
so  had  been  proved  by  Abel  and  Jacobi,  who  had  created 
the  theory  of  elliptic  functions,  showing  that  the  concep- 
tion of  a  periodic  function  (such  as  the  circular  or  har- 
monic function)  could  be  usefully  extended  into  that 
theory,  if  a  double  period— a  real  and  an  imaginary 
■one — were  introduced.  A  simplification  similar  to  that 
which  this  bold  step  led  to  in  the  symbolic  represen- 
tation of  those  higher  transcendents,  had  been  discovered 
by  Gauss  to  exist  in  the  symbolical  representation  of 
the  theory  of  biquadratic  residues  which  only  by  the 
simultaneous  use  of  the  imaginary  and  the  real  unit 
'"  presented  itself  in  its  true  simplicity  and  beauty."  In 
this  theory  it  was  necessary  to  introduce  not  only  a  posi- 
tive and  negative,  but  likewise  a  lateral  system  of  count- 
ing— i.e.,  to  count  not  only  in  a  line  backwards  and  for- 
wards, but  also  sideways  in  two  directions,  as  Gauss 
showed  very  plainly  in  the  now  familiar  manner.     At  the 


726 


SCIENTIFIC    THOUGHT. 


60. 
Generalised 
conception 
of  number. 


same  time  a  metaphysical  question  presented  itself — viz.. 
Can  such  an  extension  into  more  than  two  dimensions  be 
consistently  and  profitably  carried  out  ?  Gauss  had  satis- 
fied himself  that  it  could  not ;  ^  but  the  proof  of  this 
was  only  given  in  more  recent  times  by  Weierstrass,  who 
definitely  founded  the  whole  discussion  of  the  subject  on 
the  logical  principle  "  that  the  legitimacy  of  introducing 
a  number  into  arithmetic  depends  solely  on  the  definition 
of  such  number."  And  this  leads  me  to  another  ex- 
tension in  the  region  of  number  suggested  by  Gauss's 
treatment,  which  has  also  become  fundamental,  and,  in 
the  hands  of  Dirichlet,  Kummer,  Liouville,  Dedekind, 
and  others,  has  remodelled  the  entire  science  of  higher 
arithmetic.     It  is  based  on  the  logical  process   of   the 


^  A  concise  history  of  this  sub- 
ject is  given  by  Kossak  in  the 
Program  referred  to  above,  p. 
712,  note.  Gauss  had  promised 
to  answer  the  question,  "  Why 
the  relations  between  things  whicli 
have  a  manifoldness  of  more  than 
two  dimensions  would  not  admit 
of  other  "  (than  the  ordinary  com- 
plex numbers  introduced  by  him) 
"fundamental  quantities  being  in- 
troduced into  general  arithmetic  ?  " 
He  never  redeemed  his  promise. 
In  consequence  of  this,  several 
eminent  mathematicians,  notably 
Hankel,  Weierstrass,  and  Prof. 
Dedekind,  have  attempted  to  reply 
to  this  question,  and  to  estab- 
lish the  correctness  of  the  im- 
plied thesis  according  to  which 
any  system  of  higher  complex 
numbers  becomes  superfluous  and 
useless.  Prof.  Stolz,  in  the  first 
chapter  of  the  second  volume  of  his 
'Allgemeine  Arithmetik,'  gives  an 
account  of  these  several  views, 
which  do  not  exactly  coincide. 
In  general,  however,  the  proof 
given    by    Weierstrass,    and    first 


published  by  Kossak,  has  been 
adopted.  This  proof  is  based  upon 
the  condition  that  the  product  of 
several  factors  cannot  disappear 
excejit  one  of  its  factors  is  equal  to 
zero.  "We  must,  therefore,  ex- 
elude  from  general  arithmetic  com- 
plex numbers  consisting  of  three 
fundamental  elements.  This  is,, 
however,  not  necessary  if  the  use  of 
them  be  limited  "  by  some  special 
conditions  (Kossak,  loc.  cit.,  p.  27). 
In  the  course  of  the  further  de- 
velopment of  this  matter  Weier- 
strass arrives  at  the  fundamental 
thesis  "  that  the  domain  of  the- 
elementary  operations  in  arithmetic 
is  exhausted  by  addition  and  multi- 
plication, including  the  inverse- 
operations  of  subtraction  and 
division."  "There  are,"  says 
Weierstrass,  "no  other  funda- 
mental operations  —  at  least  it  is 
certain  that  no  example  is  known 
in  analysis  where,  if  an  analytical 
connection  exists  at  all,  this  cannot 
be  analysed  into  and  reduced  to 
those  elementary  operations"  (p.. 
29). 


DEVELOPMENT  OF  MATHEMATICAL  THOUGHT.   727 

inversion  of  operations  in  the  most  general  manner.  In 
the  direct  process  we  build  up  algebraical  formula} — 
called  equations  or  forms — by  a  combination  of  addition 
and  multiplication.  We  can  omit  subtraction  and 
division,  as  through  the  use  of  negative  quantities  and 
fractions  these  are  reduced  to  the  former.  Now,  given 
the  most  general  algebraical  equation  or  form,  we  can 
search  out  and  define  the  simple  factors  or  forms  into 
which  it  can  be  split  up,  and  these  factors  and  their  pro- 
ducts we  can  take  to  serve  as  the  definition  of  numbers. 
The  question    then   arises.  What   are  the   properties  of        ei. 

Process  of 

numbers  thus  mversely  defined  ?  and,  secondly,  Do  these  '"version. 
numbers  exhaust  or  cover  the  whole  extent  of  number  as 
it  is  defined  by  the  uses  of  practical  life  ?  The  answer 
to  the  former  question  led  to  the  introduction  of  complex 
and  subsequently  of  ideal  numbers ;  the  discovery  by 
Liouville  that  the  latter  is  not  the  case  has  led  to 
the  conception  of  transcendental,  i.e.,  non  -  algebraic, 
numbers. 

The  idea  of  generalising  the  conception  of  number,  by 
arguing  backward  from  the  most  general  forms  into 
which  ordinary  numbers  can  be  cast  by  the  processes  of 
addition  and  multiplication,  has  led  to  a  generalised 
theory  of  numbers.  Here,  again,  the  principal  object  is 
the  question  of  the  divisibility  of  such  generalised 
algebraical  numbers  and  the  generalised  notion  of 
prime  numbers — i.e.,  of  prime  factors  into  which  such 
numbers  can  be  divided.  Before  the  general  theory 
was  attempted  by  Prof.  Dedekind,  Kronecker,  and  others, 
the  necessity  of  some  extension  in  this  direction  had 
already  been  discovered  by  the  late  Prof.  Kummer  of 


728 


SCIENTIFIC   THOUGHT. 


62. 
Kummer's 
ideal 
numbers. 


Berlin  when  dealing  with  a  special  problem.  This  was 
no  other  than  the  celebrated  problem  of  the  division  of 
the  circle  into  equal  parts,  which  had  been  reduced  by- 
Gauss  to  an  arithmetical  question.  Gauss  had  shown 
that  the  accurate  geometrical  solution  of  this  problem 
depended  on  the  solution  of  certain  simple  binomial 
forms  or  equations.  The  study  of  such  forms  accord- 
ingly became  of  special  interest :  it  necessitated  the 
employment  of  the  extended  notion  of  number  called  by 
Gauss  that  of  complex  numbers.  Now  it  is  one  of  the 
fundamental  laws  in  the  theory  of  ordinary  numbers  that 
every  integer  can  be  divided  only  in  one  way  into  prime 
numbers.  This  law  was  found  to  break  down  at  a 
certain  point  if  complex  numbers  were  admitted.  Rum- 
mer, however,  suggested  that  the  anomaly  disappeared  if 
we  introduced  along  with  the  numbers  he  was  dealing 
with  other  numbers,  which  he  termed  ideal  numbers — 
i.e.,  if  we  considered  these  complex  factors  to  be  divisible 
into  other  prime  factors.  The  law  of  divisibility  was 
thus  again  restored  to  its  supreme  position.  These 
abstract  researches  led  to  the  introduction  of  a  very 
useful  conception — the  conception  not  only  of  generalised 
numbers,  but  also  of  a  system  (body,  corpus,  or  region) 
of    nimibers ;  ^   comprising   all   numbers   which,   by   the 


^  The  idea  of  a  clo.sed  system  or 
domain  of  generalised  numbers  has 
revolutionised  the  theory  of  num- 
bers. Originally  the  theory  of 
numbers  meant  only  the  theory 
of  the  common  integers,  excluding 
complex  numbers.  Gauss,  in  the 
introduction  to  the  '  Disquisitiones,' 
limits  the  doctrine  in  this  way. 
He  excludes  also  the  arithmetical 
theories    which     are     implied     in 


cyclotomy — i.e.,  the  theorj'  of  the 
division  of  the  circle ;  stating  at 
the  .same  time  that  the  principles 
of  the  latter  depend  on  theories 
of  higher  arithmetic.  This  con- 
nection of  algebraical  problems 
with  the  theory  of  numbers  be- 
came still  more  evident  in  the 
labours  of  Gauss's  successors — 
Jacobi  and  Lejeune  Dirichlet,  and 
was    surprising    to   them.      "The 


DEVELOPMENT    OF    MATHEMATICAL    THOUGHT. 


V29 


ordinary  operations  of  arithmetic,  can  be  formed  out  of 
the  units  or  elements  we  start  with.  Thus  all  rational 
integers  form  a  system ;  we  can  compound  them,  but 
also  resolve  them  into  their  elements.  Where  we  intro- 
duce new  elements  or  units  we  only  arrive  at  cor- 
rect laws  if  we  are  careful  to  cover  the  whole  field  or 
system  which  is  measured  by  the  application  of  the 
fundamental  operations  of  arithmetic.  Throughout  all 
our  abstract  reasoning  it  is  the  fundamental  operations 
which  remain   permanent  and  unaltered, — a  rule  which, 


reason  for  this  connection  is  now 
completely  cleared  up.  The  theory 
of  algebraical  numbers  and  Galois's 
'  theory  of  equations '  have  their 
common  root  in  the  general  theory 
of  algebraical  systems  ;  especi- 
ally the  theory  of  the  system  of 
algebraical  numbers  has  become 
at  the  same  time  the  most  im- 
portant province  of  the  theory  of 
numbers.  The  merit  of  having  laid 
down  the  first  beginnings  of  this 
theory  belongs  again  to  Gauss. 
He  introduced  complex  numbers, 
he  formulated  and  solved  the 
problem  of  transferring  the 
theorems  of  the  ordinarj'  theory 
of  numbers,  above  all,  the  pro- 
perties of  divisibility  and  the  re- 
lation of  congruence,  to  these 
complex  numbers.  Through  the 
systematic  and  general  develop- 
ment of  this  idea,- — based  upon  the 
far  -  reaching  ideas  of  Kummer,- — 
Dedekind  and  Kronecker  suc- 
ceeded in  establishing  the  modern 
theory  of  the  system  of  algebraical 
numbers "  (Prof.  Hilbert  in  the 
preface  to  his  "  Theorie  der  Alge- 
braischen  Zahlkorper, "  '  Bericht  der 
Math.  Ver.,'  vol.  iv.  p.  3).  In  the 
further  course  of  his  remarks  Prof. 
Hilbert  refers  to  the  intimate  con- 
nection in  which  this  general  or 
analytical  theory  of  numbers 
stands     with    other     regions      of 


modern  mathematical  science,  not- 
ably the  theory  of  functions.  "  We 
thus  see,"  he  says,  "how  arith- 
metic, the  queen  of  mathematical 
science,  has  conquered  large  do- 
mains and  has  assumed  the  leader- 
ship. That  this  was  not  done 
earlier  and  more  completely,  seems 
to  me  to  depend  on  the  fact 
that  the  theory  of  numbei's  has 
only  in  quite  recent  times  arrived 
at  maturity."  He  mentions  the 
spasmodic  character  which  even 
under  the  hands  of  Gauss  the 
progress  of  the  science  exhibited, 
and  says  that  this  was  characteristic 
of  the  infancy  of  the  science,  which 
has  only  in  recent  times  entered 
on  a  certain  and  continuous  de- 
velopment through  the  systematic 
construction  of  the  theory  in  ques- 
tion. This  systematic  treatment 
was  given  for  the  first  time  in  the 
last  supplement  to  Dedekind's  edi- 
tion of  Dirichlet's  lectures  (1894, 
4th  ed.,  p.  134).  A  very  clear 
account  will  also  be  found  in  Prof. 
H.  Weber's  '  Lehrbuch  der  Algebra  ' 
(vol.  ii.,  1896,  p.  487,  &c.)  He 
refers  (p.  494)  to  the  different 
treatment  which  the  subject  has 
received  at  the  hands  of  its  two 
principal  representatives  —  Prof. 
Dedekind  (1871  onwards)  and  Kron- 
ecker (1882)  —  and  tries  to  show 
the  connection  of  the  two  metliods. 


'30 


SCIENTIFIC    THOUGHT. 


63. 
Modern 
algebra. 


64. 
Algebraical 
and  trans- 
cendental 
numbers. 


as  we  saw  above,  was  vaguely  foreshadowed  by  Peacock, 
and  expressly  placed  at  the  head  of  all  mathematical 
reasoning  by  Hermann  Hankel.  In  passing  it  may  also 
be  observed  how  the  notion  of  a  system  of  algebraical 
numbers,  which  l^elong  together  as  generated  in  certain 
defined  ways,  prepares  us  for  the  introduction  of  that 
general  theory  of  groups  which  is  destined  to  bring  order 
and  unity  into  a  very  large  section  of  scattered  mathe- 
matical reasoning.  The  great  importance  of  this  aspect 
is  clearly  and  comprehensively  brought  out  in  Prof.  H. 
Weber's  Algebra.  Nothing  could  better  convince  us  of 
the  great  change  which  has  come  over  mathematical 
thought  in  the  latter  half  of  the  nineteenth  century 
than  a  comparison  of  Prof.  Weber's  Algebra  with  stand- 
ard works  on  this  subject  published  a  generation  earlier. 

I  have  shown  how  the  definition  of  alg-ebraical 
nvmibers  has  led  to  an  extension  and  generalisation  of 
the  conception  of  number.  Another  question  simultane- 
ously presented  itself,  Does  this  extension  cover  the 
whole  field  of  numbers  as  we  practically  use  them  In 
ordinary  life  ?  The  reply  is  in  the  negative.  Practice 
is  richer  than  theory.  Nor  is  it  difficult  to  assign 
the  reason  of  this.  Numbering  is  a  process  carried  on 
in  practical  life  for  two  distinct  purposes,  which  we 
distinguish  by  the  terms  counting  and  measuring.  Num- 
bering must  be  made  subservient  to  the  purpose  of 
measuring.  Thus  difficulties  arising  out  of  this  use  of 
numbers  for  measuring  purposes  presented  themselves 
early  in  the  development  of  geometry  in  what  are  called 
the  incommensurable  quantities :  taking  the  side  of  a 
square  as  ten,  what  is   the  number  which  measures  the 


DEVELOPMENT    OF    MATHEMATICAL    THOUGHT.        731 

diagonal  ?  Assume  that  we  prolong  the  side  of  the  square 
indefinitely,  we  have  a  clear  conception  of  the  position 
of  the  numbers  15,  20,  30,  &c. ;  but  what  is  the  exact 
number  corresponding  to  the  length  of  the  diagonal  ? 
This  led  to  the  invention  of  irrational  numbers :  it 
became  evident  that  by  introducing  the  square  root  of 
the  number  2  we  could  accurately  express  the  desired 
number  by  an  algebraical  operation.  But  there  are 
other  definite  measurements  in  practical  geometry  which 
do  not  present  themselves  in  the  form  of  straight  lines, 
such  as  the  circumference  of  a  circle  with  a  given  radius. 
Can  they,  like  irrational  quantities,  be  expressed  by 
definite  algebraical  operations  ?  Practice  had  early  in- 
vented methods  for  finding  such  numbers  by  enclosing 
them  within  narrower  and  narrower  limits ;  and  an 
arithmetical  algorithm,  the  decimal  fraction,  was  in- 
vented which  expressed  the  process  in  a  compact  and 
easily  intelligible  form.  Among  these  decimal  fractions 
there  were  those  which  were  infinite — the  first  instances 
of  infinite  series — progressing  by  a  clearly  defined  rule 
of  succession  of  terms ;  others  there  were  which  did  not 
show  a  rule  of  succession  that  could  be  easily  grasped. 
Much  time  was  spent  in  devising  methods  for  calculat- 
ing and  writing  down,  e.g.,  the  decimals  of  the  numbers 
TT  and  c} 

It  will  be  seen  from  this  very  cursory  reference  to 
the  practical  elements  of  mathematical  thought  how 
the  ideas   or   mental   factors  which   we   deal   with   and 


'  The  transcendent  nature  of  the 
numbers  e  and  it  was  first  proved 
by  Hermite  and  Prof.  Lindemann. 
The    proofs    have    been    gradually 


simplified.  A  lucid  statement  will 
be  found  in  Klein's  '  Famous 
Problems,'  p.  49  sqq. 


nieasurins. 


732  SCIENTIFIC    THOUGHT. 

string  together  in  mathematical  reasoning  are  derived 
from  various  and  heterogeneous  sources.  We  begin 
65.  with  counting,  then  we  introduce  measuring;  in  both 
and  "  cases  we  have  definite  elements  or  units  which  may 
serve  to  express  order  or  quantity  or  both,  and  we 
have  definite  conventional  operations ;  then  we  have 
symbols  which  may  denote  order  or  quantity  or  oper- 
ation. With  these  devices  we  perform  on  paper 
certain  changes,  and  we  get  accustomed  to  use  in- 
discriminately these  heterogeneous  conceptions,  arith- 
metical, geometrical,  algebraical — nay,  even  dynamical,  as 
when  Newton  introduced  the  conception  of  a  fiow  or 
fluxion.  As  mathematics  is  an  instrument  for  the 
purpose  of  solving  practical  problems,  skill  in  al- 
ternately and  promiscuously  using  these  incongruous 
methods  goes  a  very  long  way.  Geometrical,  mechan- 
ical evidence  helps  frequently  where  pure  logic  comes 
to  a  standstill,  and  pure  logic  must  help  and  correct 
where  apparent  evidence  might  deceive  us.  Mathe- 
matics and  science  generally  have  always  progressed 
by  this  alternate  use  of  heterogeneous  devices,  and 
will  probably  always  do  so.  The  straight  line  of  pure 
logic  has  but  very  meagre  resources,  and  resourcefulness 
is  the  soul  of  all  progress.  But  though  this  may  be 
so  in  practice,  there  are  two  other  interests  which  govern 
scientific  reasoning.  There  is  the  love  of  consistency  and 
accuracy,  and  of  clean  and  transparent,  as  distinguished 
from  muddled  and  scamped,  work.  The  latter  leads 
inevitably  into  serious  errors  and  paradoxes,  as  the 
great  mathematicians,  Gauss,  Cauchy,  Abel,  pointed  out 
early    in    the    century.       Mathematics   then   frequently 


DEVELOPMENT  OF  MATHEMATICAL  THOUGHT. 


733 


exhibited  the  slovenliness  of  a  man  who  talks  at  the 
same  time  in  more  than  one  language,  because  he  is 
too  negligent  to  arrange  his  thoughts  clearly.  Then 
there  come  in  the  demands  of  the  teacher  who  has 
to  introduce  abstract  and  difficult  subjects  in  a  clear, 
consistent,  and  simple  manner,  taking  heed  that  with 
the  elements  he  does  not  introduce  the  sources  of 
future  error.  The  same  interest  that  led  in  ancient 
times  to  the  composition  of  the  Elements  of  Euclid  has 
led,  in  the  higher  education  of  the  nineteenth  century, 
beginning  with  the  Ecole  Poly  technique  and  ending  with 
Weierstrass's  famous  courses  of  lectures  at  Berlin,  to 
a  revision  and  recasting  of  the  whole  elementary  frame- 
work of  mathematics.  In  the  mean  time  the  resource- 
fulness in  applied  mathematical  thought  which  ever 
since  the  age  of  Newton  has  characterised  the  in- 
dividual research  of  this  country,  has  opened  out  new 
vistas  and  afforded  much  material  for  critical  siftings 
and  strict  definitions.  Both  qualities  were  united  in 
the  great  mind  of  Gauss  with  a  regrettable  absence  of 
the  love  of  teaching  and  the  communicative  faculty. 
Like  Newton's  '  Principia,'  his  greatest  works  will 
always  remain  great  storehouses  of  thought ;  while  his 
unpublished  remains  might  be  compared  to  the  Queries 
appended  to  the  '  Opticks '  and  to  the  '  Portsmouth 
Papers.' 

Several  eminent  mathematicians  in  France,  Germany, 
and  Italy  have  been   for  many  years  ^  working   at  the 


'  The  literature  of  this  sub- 
ject has  been  rapidly  increasing 
since  the  year  1872,  —  the  ap- 
proximate date    of    the   following 


publications,  which  created  an 
epoch :  R.  Dedekind,  '  Stetigkeit 
und  irrationale  Zahleu  '  (Braunsch- 
weig,    1872)  ;     E.     Heine,     "  Die 


I 


V34 


SCIENTIFIC   THOUGHT. 


clearer  enunciation  of  the  fundamental  conceptions  of 
the  science,  and  though  the  ways  in  which  they 
approach  the  subject  are  different,  a  general  consensus 
seems  to  be  within  view  as  to  the  elementary  definitions. 
The  main  difficulty  lies  in  the  introduction  into  pure 
arithmetic  of  the  ideas  which  are  forced  upon  us  when 


Elemente  der  Functionenlehre " 
{'  Journal  fiir  Mathematik,'  vol. 
Ixxiv.  p.  172,  1872).  This  paper 
refers  both  to  Weierstrass's  and 
Cantor's  theories ;  H.  Kossak,  in 
the  pamphlet  referred  to  above 
(p.  7i2,  note).  This  contains  the 
principles  of  Weierstrass's  theory  ; 
C.  H.  Meray,  '  Nouveau  Precis 
d' Analyse  infinitesimale '  (Paris, 
1872).  The  first  comprehensive 
publication  of  Georg  Cantor  be- 
longs to  the  year  1883,  '  Grund- 
la^en  eiiier  allgemeinen  Mannig- 
faltigkeitslehre  '  (Leipzig,  Teub- 
ner).  It  was  preceded  by  various 
articles  in  the  '  Journal  fiir  Mathe- 
matik,' vol.  Ixxvii.  p.  257,  vol. 
Ixxxiv.  p.  82,  aud|  '  Math.  Ann.,' 
vol.  XV.  p.  1,  in  which  he  had  in- 
troduced and  defined  several  of  the 
terms  and  conceptions  that  have 
since  become  generally  accepted  in 
writings  on  this  subject.  These 
earlier  publications,  by  —  or  refer- 
ring to — the  pioneers  in  this  new 
province  of  mathematical  thought, 
were  followed  by  a  number  of 
further  expositions  by  Cantor, 
Dedekind,  and  Weierstrass.  The 
principal  writings  of  Cantor  have 
been  republished  in  the  '  Acta 
Mathematica,'  vol.  ii.  Prof.  Dede- 
kind published  in  the  year  1888  an 
important  pamphlet,  '  Was  sind 
und  was  sollen  die  Zahlen,'  and  has 
incorporated  many  of  the  results  of 
his  researches  in  his  later  editions 
of  Dirichlet's  'Lectures  ' ;  whilst  the 
lines  of  reasoning  peculiar  to  Weier- 


strass have  become  better  known 
through  the  writings  of  his  pupils 
and  the  collected  edition  of  his 
mathematical  works  which  is  now 
in  progress.  A  complete  biblio- 
graphy is  given  in  three  important 
articles  in  vol.  i.  of  the  German 
'Math.  Encyc'  by  Profs.  Schu- 
bert (p.  1,  &c.),  Pringsheim  (p. 
48,  &c.),  and  Schonflies  (p.  184, 
&c.)  Important  works,  giving  a 
summary  and  analysis  of  these 
various  researches,  now  exist  in 
the  mathematical  and  philosophical 
literature  of  France,  Germanj-, 
Italy,  and  England.  Like  the  non- 
Euclidean  geometry,  the  subject 
has  attracted  considerable  atten- 
tion also  outside  purely  mathe- 
matical circles.  Notably  Cantor's 
writings  have  been  exhaustively 
dealt  with  from  a  philosophical 
point  of  view  —  in  Germany  by 
Walter  Brix  (Wundt's  '  Philoso- 
phische  Studien,'  vol.  v.  p.  632, 
vol.  vi.  p.  104  and  261),  and  by 
B.  Kerry,  '  System  einer  Theorie 
der  Grenz-begriffe '  (Leipzig  und 
Wien,  1890)  ;  in  France  by  M. 
Louis  Couturat,  '  De  I'lnfini  ma- 
thematique'  (Paris,  1896);  and 
latterly  in  this  country  by  Mr 
Bertrand  Kussell,  '  The  Principles 
of  Mathematics,'  vol.  i.  (Cambridge, 
1903).  Italian  mathematicians  have 
also  dealt  largely  with  the  subject, 
notably  G.  Peano,  who  published 
an  important  work,  '  Arithmetices 
principia  nova  methodo  exposita ' 
(Turin,  1889). 


DEVELOPMENT    OF    MATHEMATICAL    THOUGHT.       735 

we  apply  the  counting  process  to  the  needs  of  geometry 
and  physics.  We  are  here  confronted  with  notions 
which  require  to  be  arithmetically  defined  —  the  in- 
finite and  the  continuous.  The  same  notions  at  the 
beginning  of  the  century  attracted  the  attention  of 
eminent  analysts  like  Cauchy.  It  is  now  clear,  thanks 
to    the   labours   of   Prof.    Georar   Cantor   of   Halle,   that        66. 

'^  Geor-Can- 

for  mathematical  purposes  we  must  distinguish  between  Qf''yjg*''*'°''y 
the  indefinitely  great  and  the  actually  infinite  in  the  ^'■'^'^'^""'te- 
sense  of  the  transfinite.  To  deal  with  the  actually 
infinite,  as  distinguished  from  the  immeasurably  or 
indefinitely  great,  we  have  to  introduce  new  notions  and 
a  new  vocabulary.  For  instance,  in  dealing  with  infinite 
aggregates,  the  proposition  that  the  part  is  always  less 
than  the  whole  is  not  true.  Infinities,  indeed,  differ, 
but  not  according  to  the  idea  of  greater  and  smaller,  of 
more  or  less,  but  according  to  their  order,  grade,  or 
power  (in  German  Mdchtigkeit).  Two  infinities  are 
equal,  or  of  the  same  power,  if  we  can  bring  them  into 
a  one-to-one  correspondence.  Prof.  Cantor  has  shown 
that  the  extended  range  of  numbers  termed  algebraic 
have  tlie  same  power  as  the  series  of  ordinary  integers — 
one,  two,  three,  &c. — because  we  can  establish  a  one-to- 
one  correspondence  between  the  two  series — i.e.,  we  can 
count  them.  He  has  further  shown  that  if  we  suppose 
all  numbers  arranged  in  a  straight  line,  then  in  any 
portion  of  this  line,  however  small,  there  is  an  infinite 
number  of  points  which  do  not  belong  to  a  countable  or 
enumerable  multitude.  Thus  the  continuum  of  numeri- 
cal values  is  not  countable — it  belongs    to   a   different 


736  SCIENTIFIC    THOUGHT. 

grade  of  infinity ;  it  has  a  higher,  perhaps  the  second, 
power/ 

In  all  these,  and  in  many  similar  investigations,  a 
conception  has  gradually  emerged  which  was  foreign  to 
older  mathematics,  but  which  plays  a  great  and  useful 
part  in  modern  mathematical  thought.  Older  mathe- 
matics, ever  since  the  introduction  of  general  arithmetic 
or  algebra,  centred  in  the  conception  of  equality  and  in 
the  solution  of  equations.  Everything  was  reduced  to 
magnitude.  But  there  are  other  relations  besides  those 
of  magnitude,  of  more  or  less.  Often  in  practical  pur- 
suits, if  we  cannot  find  k  counterpart  or  write  down 
an  exact  numerical  equation,  we  can  gain  information 
67.        by  a  correspondence.     This  conception  of  correspondence 

Correspond-  .  . 

ence.  plays  a  great  part  m  modern  mathematics.      It  is  the 

fundamental  notion  in  the  science  of  order  as  dis- 
tinguished from  the  science  of  magnitude.  If  older 
mathematics  were  mostly  dominated  by  the  needs  of 
mensuration,  modern  mathematics  are  dominated  by  the 
conception  of  order  and  arrangement.  It  may  be  that 
this  tendency  of  thought  or  direction  of  reasoning  goes 
hand  in  hand  with  the  modern  discovery  in  physics, 
that  the  changes  in  nature  depend  not  only  or  not  so 
much  on  the  quantity  of  mass  and  energy  as  on  their 
distribution  or  arrangement. 

With  these  reflections  w^e  touch  the  limits  of  mathe- 

^  A  summary  of   Prof.  Cantor's   i   the    different    recent    theories   set 


work  is  given  by  Prof.  Schonflies 
in  the  '  Eneyklop.  Math.  Wiss.,' 
vol.  i.  p.  184  sqq.  The  importance 
of  accurate  definitions  and  distinc- 
tions regarding  the  infinite  and 
the  continuous    is    dwelt   on   and 


forth  in  a  very  lucid  address  to  the 
London  Math.  Society  by  Prof. 
Hobson,  "  On  the  Infinite  and  In- 
finitesimal in  Mathematical  Analy- 
sis," November  1902. 


DEVELOPMENT    OF    MATHEMATICAL    THOUGHT.       737 

matical  thought  and  enter  the  region  of  metaphysics. 
Like  other  lines  of  reasoning  which  have  occupied  us 
in  former  chapters,  the  exact  and  rigid  definitions  and 
deductions  of  arithmetic  and  geometry  lead  us  up  to 
that  other  large  department  of  our  subject — philosophic 
thought.  Many  eminent  mathematicians  of  recent  years 
have  noticed  this  tendency,  and  have  urged  the  mutual 
help  which  arithmetic  and  geometry  on  this  side,  logic 
and  psychology  on  that,  may  derive  from  each  other. 
The  names  of  Helmholtz,  Georg  Cantor,  and  Dede- 
kind  in  Germany ;  of  M.  Tannery  and  M.  Poincare  in 
France ;  of  Peano  and  Veronese  in  Italy,  stand  prom- 
inently forward  abroad  ;  while  England  can  boast  of  hav- 
ing cultivated,  much  earlier,  by  the  hands  of  De  Morgan 
and  Boole,  a  portion  at  least  of  this  borderland,  and  of 
having  in  recent  years  taken  up  the  subject  again  in 
an  original  and  independent  manner.^  Cayley,  in  his 
address  to  the  British  Association  in  1883,  has  said  : 
"  Mathematics  connect  themselves  on  the  one  side  with 
common  life   and    the  physical   sciences ;  on    the   other 


^  I  refer  to  the  imjjortant  but 
unfinished  works  of  Mr  Wliitehead 
on  '  Universal  Algebra '  (vol.  i., 
1898),  and  of  Mr  Bertrand  Russell 
on  '  The  Principles  of  Mathematics ' 
(vol.  i.,  1903).  I  must  defer  a 
more  detailed  appreciation  of  these 
and  other  writings  of  this  class, 
such  as  those  of  the  late  Prof. 
Ernst  Schroder  ('  Algebra  der 
Logik,'  3  vols.,  1890-95)  and  of 
Prof.  Gottlob  Frege  (see  an 
account  of  his  writings  in  the 
appendix  to  Mr  Russell's  '  Prin- 
ciples ').  They  belong  largely  to 
a  department  of  philosophical 
thought    which    may    be    termed 

VOL.  XL 


"  the  Philosophy  of  the  Exact 
Sciences."  This  deals  with  two 
great  questions — the  logical  found- 
ations of  scientific  reasonmg,  and 
the  general  outcome  and  import- 
ance of  scientific  thought,  not  for 
technical  purposes,  but  in  the 
great  edifice  of  human  thought 
which  we  may  term  Philosophy. 
It  deals  with  what  has  been 
called  "  the  Creed  of  Science " 
and  its  value.  Stanley  Jevons 
and  Prof.  Karl  Pearson  in  this 
country,  Prof.  Mach  in  Germany, 
and  M.  Poincare  in  France,  have 
treated  the  philosophy  of  science 
in  one  or  both  of  these  aspects. 

3  A 


738  SCIENTIFIC   THOUGHT. 

side  with  philosophy  in  regard  to  our  notions  of  space 
and  time,  and  in  the  questions  which  have  arisen  as 
to  the  universality  and  necessity  of  the  truths  of 
mathematics  and  the  foundation  of  our  knowledge  of 
them";  and  he  subsequently  refers  specially  to  the 
"  notion  which  is  really  the  fundamental  one  under- 
lying and  pervading  the  whole  of  modern  analysis  and 
geometry,"  meaning  the  complex  magnitude,  as  deserv- 
ing to  be  specially  discussed  by  philosophers.  Be- 
ginnings of  the  philosophical  treatment  of  this  and 
other  questions  indeed  exist.  The  questions  are  still 
suh  judice,  and  the  historian  can  merely  refer  to  their 
existence  and  importance. 

There  is,  however,  one  controversy  which  has  arisen 
out  of  these  and  similar  speculations,  and  out  of  the 
desire  to  bring  unity  and  consistency  into  the  funda- 
mental notions  of  elementary  as  well  as  higher  mathe- 
matics, which  deserves  to  be  specially  mentioned,  because 
it  occupies  a  prominent  place  in  foreign  literature,  hav- 
ing given  rise  to  a  special  term,  and  thus  commanding 
more  general  attention.  Prof.  Klein  of  Gottingen,  under 
whose  master-hand  many  abstract  and  obscure  subjects 
have  become  plain  and  transparent,  has  prominently 
brought  the  subject  before  the  scientific  public  in  a 
68.        recent  address.^      I   refer    to  the   tendency  represented 

Arithmetis- 

ing  tendency  in   its   extreme   form    by   the   late   Prof.    Kronecker  or 

in  niathe-  "^ 

matics.  Berlin,  to  reduce  all  mathematical  conceptions  to  the 
fundamental  arithmetical  operations  with  integral  num- 
bers, banishing  not  only  all  geometrical  and  dynamical 
conceptions,  such  as   those   of  continuity  and  flow,  but 

^  '  Ueber  Arithmetisirung  der  Mathematik '  (Gbttingen,  1895). 


DEVELOPMENT  OF  MATHEMATICAL  THOUGHT.   739 


also  siich  apparently  algebraical  notions  as  those  of 
irrational  and  complex  quantities.  This  attempt  is  an 
outcome  of  the  school  of  Weierstrass,  which  has  done 
so  much  to  banish  vagueness  and  introduce  precision 
into  modern   text-books. 

Opposed  to  this  so-called  arithmetising  ^  tendency  is 
the  equally  emphatic  view,  strongly  urged  by  the  late 
Prof.  Paul  Du  Bois-Eeymond  in  his  general  theory  of 
Functions,  that  the  separation  of  the  operations  of 
counting  and  measuring  is  impossible,  and,  if  it  were 
possible  (as,  since  the  publication  of  his  work,  the  fuller 
expositions  of  Kronecker  and  his  followers  have  tried  to 
show  that  it  is),  would  degrade  mathematics  to  a  mere 
play  with  symbols.'^  He  tries  to  show  that  such  is  philo- 
sophically impossible,  and  finds  a  support  for  his  view  in 
the  historical  genesis  of  the  idea  of  irrational  numbers  in 
the  incommensurable  magnitudes  of  Euclid  and  ancient 
geometry.  Prof.  Klein  in  his  address  favours  the 
arithmetical  tendency   as  destined   to    introduce   logical 


^  The  term  seems  to  have  been 
coined  by  Ki-onecker.  See  Prof. 
Pringsheira  in  the  '  Encyklop. 
Math.  Wiss.,'  vol.  i.  p.  58,  note  40. 
Kronecker' s  position  is  set  forth 
in  Journal  fiir  Math.,  vol.  ci.  pp. 
337-355,  1887. 

^  "The  separation  of  the  con- 
ception of  number  and  of  the 
analytical  symbols  from  the  con- 
ception of  magnitude  would  reduce 
analysis  to  a  mere  formal  and 
literal  skeleton.  It  would  degrade 
this  science,  which  in  truth  is  a 
natural  science,  although  it  only 
admits  the  most  general  properties 
of  what  we  perceive  into  the  domain 
of  its  researches  ultimately  to  the 
rank  of  a  mere  play  with  symbols, 
wherein  arbitrary  meanings  would 


be  attached  to  the  signs  as  if  they 
were  the  figures  on  the  chessboard 
or  on  playing-cards.  However  amus- 
ing such  a  play  might  be,  nay, 
however  useful  for  analytical  pur- 
poses the  solution  would  be  of  the 
jjroblem, — to  follow  up  the  rules  of 
the  signs  which  emanated  from  the 
conception  of  magnitude  into  their 
last  formal  consequences, — such  a 
literal  mathematics  would  soon 
exhaust  itself  in  fruitless  efforts  ; 
whereas  the  science  which  Gauss 
called  with  so  much  truth  the 
science  of  magnitude  possesses  an 
inexhaustible  source  of  new  ma- 
terial in  the  ever-increasing  field 
of  actual  perceptions,"  &c.,  &c. 
('  Allgemeine  Functionen-Theorie,' 
1882,  p.  54.) 


740 


SCIENTIFIC    THOUGHT. 


precision  and  consistency  into  the  foundations  of  mathe- 
matics, and  everywhere  to  further  the  very  necessary 
process  of  critical  sifting;  but  he  denies  that  pure 
logic  can  do  all,  and  points  to  the  valuable  assistance 
and  suggestive  power  of  geometrical  construction  and 
representation.^  Most  of  my  readers  will  no  doubt 
agree  with  this  view.  Indeed  the  perusal  of  the  fore- 
going chapters  must  have  produced  on  their  minds  the 
conviction  that,  so  far  as  the  advance  of  science  and  also 
of  mathematics  is  concerned,  it  largely  depends  upon 
the  introduction  of  different  aspects  leading  to  different 
courses  of  reasoning.  The  unification  of  all  of  these 
into  one  consistent  and  uncontradictory  scheme,  though 
it  remains  a  pious  hope  and  far-off  ideal,  has  not  been 
the  prominent  work  of  the  nineteenth  century.  Eather, 
wherever  it  has  been  attempted  it  has  had  a  narrowing 
effect,  and  has  resulted  in  a  distinct  curtailment  of  the 
great  and  increasing  resources  of  Scientific  Thought. 


^  Prof.  Klein  summarises  the 
opinion  which  he  holds  as  to  the 
present  task  of  mathematical 
science  as  follows :  "  Whilst  I 
everywhere  demand  the  fullest 
logical  elaboration,  I  at  the  same 
time  emphasise  that  pari  passti 
with  it  the  intuitive  representation 
of  the  subject  should  be  furthered 
in  every  possible  manner.  Mathe- 
matical developments  which  have 
their  origin  in  intuition  cannot 
count  as  a  firm  possession  of  science 
unless  they  have  been  reduced  to  a 
strict  logical  form.  On  the  other 
side,  the  abstract  statement  of 
logical  relations  cannot  satisfy  us 
until   their   importance   for   every 


form  of  representation  has  been 
clearly  demonstrated,  so  that  we 
recognise  the  manifold  connections 
in  which  the  logical  scheme  stands 
to  other  departments  of  knowledge 
according  to  the  field  of  application 
which  we  select.  I  compare  mathe- 
matical science  to  a  tree  which 
stretches  its  roots  ever  deeper  into 
the  soil,  and  at  the  same  time 
expands  its  branches  freely  up- 
wards. Are  we  to  consider  the 
root  or  the  branches  as  the  more 
important  part  ?  The  botanist  will 
tell  us  that  the  question  is  wrongly 
put,  and  that  the  life  of  an  organ- 
ism consists  in  the  interaction  of 
its  various  parts"  {loc.  cit.,  p.  91). 


EETROSPECT  AND  PROSPECT. 

In  the  foregoing  chapters  I  have  attempted  to  set  forth 
the  chief  conceptions  which  are  contained  in  the  scien- 
tific literature  of  the  nineteenth  century.  Upon  these 
the  scientific  work  of  that  period  has  been  founded  or 
they  are  the  results  to  which  its  scientific  reasoning 
has  led.  The  most  important  outcome  of  the  scientific 
work  of  the  century  does  not  lie  in  the  region  of 
thought,  but  rather  in  that  of  practical  application ; 
and  this  I  have  only  incidentally  referred  to.  Only 
in  so  far  as  it  has  reacted  upon  scientific  thought,  sug- 
gesting or  modifying  scientific  ideas,  has  it  been  necessary 
to  allude  to  it. 

My  readers  who  have  so  far  accompanied  me  may  be 
struck  by  one  feature  which  indeed  is  characteristic  of 
scientific  thought.  Our  survey  has  presented  such 
thought  as  broken  up  into  a  series  of  different  aspects ; 
and  although  certain  connections  between  these  aspects 
have  been  occasionally  pointed  out,  no  attempt  has  been 
made  to  combine  them  into  one  comprehensive  or  united 
view.  The  reason  for  this  is  to  be  found  in  the  nature 
of  scientific  thought  itself,  which,  proceeding  by  a  def- 
inite method,  starts  from  the  great  variety  of  phenomena 
which  surround  us  in  time  and  space ;  the  only  assump- 


742  SCIENTIFIC    THOUGHT. 

tion  which  science  is  obliged  to  make  being  the  inevitable 

one  that  Nature  is  intelligible  to  the  human  mind,  which 

1.        is  the  same  as  saying  that  we  must  assume  the  existence 

Order  and  "^      ° 

Unity.         of  some  kind  of  Order. 

There  exists,  indeed,  in  the  human  mind  a  further 
demand,  which  may  l^e  defined  by  saying  that  the  con- 
ception of  order  in  Nature  or  of  its  intelligibility  should 
not  be  held  merely  as  a  formal  iteration,  but  should  be 
expressed  as  a  highest  Unity  by  some  term  which  conveys 
to  our  minds  something  more  than  the  idea  of  an  empty 
form.  From  this  demand  there  have  further  arisen  at 
all  times  various  attempts  to  give  expression  to  the 
ideas  of  unity,  of  simplicity,  and  of  the  significance  of 
the  whole  scheme  of  existence  which  we  call  Nature. 
Such  attempts  do  not  form  part  of  purely  scientific 
thought.  They  are  speculations  for  which  those  prin- 
ciples of  science  that  are  capable  of  exact  enunciation 
do  not  suffice.  They  have,  indeed,  frequently  appeared  in 
the  literature  of  the  nineteenth  century.  But  although 
there  are  isolated  cases  where  scientific  authorities  of  the 
first  order  have  indulged  in  them,  such  authorities  have, 
as  a  rule,  shown  an  increasing  reluctance  to  deal  with 
fundamental  questions  or  with  principles  which  extend 
beyond  the  limits  of  scientific  thought.  We  have  no 
examples  in  the  nineteenth  century  of  such  intellects  as 
those  of  Leibniz  or  Newton.  However  different  these 
two  great  thinkers  of  an  earlier  age  may  have  been,  they 
had  this  in  common,  that  for  them  the  scientific  and  the 
religious  aspects  were  not  only  equally  important,  but 
equally  occupied  their  attention.  The  characteristic 
difference   was   that  Leibniz    apparently    strove  after  a 


RETROSPECT  AND  PROSPECT.         743 

unification  of  scientific  and  religious  reasoning,  frequently 
to  the  disadvantage  of  both,  whereas  Newton  kept  them 
so  distinctly  apart  that  his  immortal  scientific  works 
can  be  studied  without  any  reference  wliatever  to  his 
theological  writings. 

The  two  positions  represented  by  these  two  great 
men  —  namely,  the  attempt  on  the  one  side  to  unify 
or  combine  the  scientific  and  the  religious  aspects,  and 
on  the  other  to  keep  them  apart  or  contrast  them — 
have,  indeed,  been  adopted  by  many  thinkers  in  the 
course  of  our  period ;  but  an  attempt  to  do  justice  to 
such  problems  has  been  more  usually  considered  the 
duty  of  philosophy  par  excellence.  In  the  rare  instances 
in  which  scientific  authorities  of  the  first  order  have 
ventured  upon  a  solution  of  these  problems,  they  have 
stepped  outside  of  the  limits  of  scientific  reasoning ; 
having,  as  it  were,  attempted  to  occupy  the  more  im- 
partial if  not  more  elevated  position  of  judges  who  as- 
sign to  scientific  reasoning  its  position  and  its  value  in 
the  connected  whole  of  human  thought  and  interests.^ 

Consistently  with  the  division  of  thought  which 
underlies  the  present  history,  and  which  has  been 
explained  in  the  third  part  of  the  Introduction,  I 
relegate   the   exposition  of  such  theories  to  the  second        2. 

°  ^  Philosophi- 

part    of     this    work,    which    deals    with    philosophical  cai  prob- 
thought.     The  fact  that  in  the  course  of  the  nineteenth 
century  there  have  still  appeared  scientific  thinkers  who 
have  not  only  attacked  special  scientific  problems,  but 
also  the   great   universal    world -problem,   may   well   be 

1  Examples  of  this  will  be  found       mond,    and     of     Gustav    Theodor 
in   the   writings    of    Andre    Marie       Fechner. 
Ampere,    of    Emil    Du   Bois-Rey- 


744  SCIENTIFIC   THOUGHT. 

noted  as  a  connection,  a  bond  of  union,  between  those 
two  great  realms  of  systematic  thought  which,  for  the 
sake  of  convenience,  I  have  kept  apart  in  this  historical 
survey. 

There  are  other  features  in  the  scientific  thought 
of  the  period,  as  it  has  become  known  to  us,  which 
naturally  lead  up  to  a  different  treatment  from  that 
which  is  peculiar  to  science.  In  almost  every  instance, 
in  following  up  the  various  aspects  of  scientific  thought, 
I  have  had  to  show  how  they  have  brought  us  to 
problems  which  cannot  be  solved  by  the  means  which 
we  call  scientific  or  exact;  and  in  many  instances  I 
have  shown  how  the  foremost  scientific  thinkers  them- 
selves have  been  led  up  to  inquiries  which  they  have 
variously  termed  philosophical,  metaphysical,  logical,  or 
psychological.  Such  has  notably  been  the  case  with 
the  ultimate  conceptions  of  the  atomic  theory,  of  the 
doctrine  of  energy,  and,  still  more,  with  the  concep- 
tions which  underlie  the  scientific  treatment  of  the 
phenomena  of  life  and  consciousness.  The  further  we 
have  advanced  from  the  simple  mechanical  conceptions 
of  motion  and  inertia  or  mass,  into  the  phenomena 
of  the  actual  world  of  natural  objects  which  exhibit 
order,  development,  purpose,  and  consciousness,  the  more 
we  have  been  obliged  to  make  use  of  terms  not 
capable  of  being  defined  by  the  simple  categories  of 
exact  or  mathematical  thought ;  and  with  whatever 
zeal  some  of  the  foremost  thinkers  have  in  the  course 
of  the  century  attempted  to  express  these  more  indefinite 
conceptions  in  terms  of  mechanical  science,  they  have 
only  partially  succeeded,  and   have   certainly  failed   in 


RETEOSPECT  AND  PROSPECT.        745 

banishing  them  from  the  scientific  vocabulary.  Such 
conceptions  have  always  crept  in  again,  proving  that 
they  are  indispensable  even  to  the  purely  scientific 
comprehension  or  description  of  natural  objects,  or  of 
nature  as  a  whole. 

It  is  not  surprising,  therefore,  that  an  independent 
examination  of  the  ultimate  conceptions  which  science 
makes  use  of,  or  which  it  evolves,  should  have  been  a 
task  which  has  occupied  some  of  the  greatest  intellects 
of  our  period,  and  that  the  problem  arising  from  this 
should  form  a  fitting  transition  from  the  purely  scientific 
to  the  philosophical  portion  of  this  history. 

Now,  if  we  try  to  characterise  in  the  briefest  possible 
manner  the  general  problems  which  scientific  thought  as 
a  whole  has  definitely  formulated  and  placed  before  the 
philosophical  thinker,  there  are  two  words  which  stand 
out  prominently  as  indicating  the  two  grand  and  com- 
plementary conceptions  which  either  underlie  all  scien- 
tific inquiry  or  result  from  it.  The  first  of  these  has 
already  been  stated.  We  saw  that  exact  or  scientific 
thought  assumes  that  there  exists  in  Nature  an  in- 
telligible Order.  The  closer  definition  of  this  order  in 
the  so-called  laws  of  the  cosmos  has  to  be  ascertained 
by  experience,  and  has  been  the  subject  of  the  fore- 
going narrative.  The  subject  which  remains  for  phil- 
osophical discussion  is  not  any  special  form  of  order, 
but  the  fact  that  any  kind  of  order  exists  at  all,  and 
that  it  is  accessible  to  the  human  intellect.  Clearly 
this  is  a  question  which  affects  Nature,  the  object,  as 
much  as  the  human  Intellect,  the  subject. 

But  if  the  idea  of  Order  underlies  all  scientific  thought, 


^- 


46  SCIENTIFIC    THOUGHT. 


standing  as  it  were  at  the  entrance  of  scientific  reason- 
ing, there  is  another  idea  which  stands  at  the  end  of  all 
3.  scientific  thought.  This  is  the  idea  of  Unity  in  its 
luty!"^"'  most  impressive  form  as  Individuality.  It  remains  over 
as  an  ultimate  empirical  fact  to  which  scientific  reason- 
ing advances,  of  equal  importance  with  order. 

These  two  conceptions  of  Order  and  Individuality 
likewise  govern  the  two  great  divisions  under  which 
scientific  thought  has  been  studied  by  us — Physics  and 
Biology.  After  reviewing  in  the  first  three  chapters 
the  characteristic  attitudes  taken  up  by  the  three  lead- 
ing nations  in  scientific  thought,  I  entered  upon  the 
four  abstract  conceptions  —  namely,  Attraction,  Atom- 
ism, Kinetics,  and  Energy — which  are  capable  of  strict 
mathematical  definition,  and  which  form  the  skeleton 
or  framework  around  or  in  which  the  sciences  of 
Astronomy,  Dynamics,  Physics,  and  Chemistry  have 
arranged  their  various  doctrines.  They  serve  together 
to  define  more  precisely  the  conception  of  the  general 
order  of  things,  appropriately  termed  the  Cosmos.  In 
the  four  chapters  following  upon  these  I  dealt  with 
the  different  conceptions  under  which  a  comprehension, 
not  so  much  of  the  general  order  as  of  the  special  events 
and  things  of  our  world,  has  been  gained.  These  con- 
ceptions, referring  to  the  actual  forms,  the  history,  the 
life  and  soul  of  things  natural,  have  been  likewise 
dealt  with  in  four  chapters.  On  them  the  physics 
of  the  universe  and  of  our  earth,  the  sciences  dealing 
with  the  organised  and  animated  creations,  have  been 
built  up.  Beginning  with  a  special  kind  of  order — 
namely,  that  indicated  by  external  figure — these  sciences 


RETROSPECT  AND  PROSPECT.         747 

have  advanced  through  the  study  of  the  changes  of  figure 
to  an  increasing  appreciation  of  an  underlying  unity. 
In  many  of  the  organs  of  living  creatures  the  unity 
seems  to  lie  outside  the  organs  themselves,  as  the  unity 
of  a  machine  which  exists  in  the  design  of  the  maker 
adapting  it  to  a  certain  purpose ;  whereas  in  the  ani- 
mated world  it  seems  to  be  inside  the  objects  of  Nature. 
The  sciences  of  life  have  accordingly  forced  upon  us 
more  and  more  the  conception  not  only  of  orderly 
arrangement,  but  also  of  a  unifying  principle  —  that 
is.  Individuality. 

These  two  conceptions  of  Order  and  Individuality  are 
as  little  new  as  are  the  various  conceptions  of  purely 
scientific  thought,  most  of  which,  as  has  been  shown, 
have  been  handed  down  to  us  from  earlier  times.  They 
have  accordingly  been  defined  and  studied  by  phil- 
osophers from  antiquity.  The  various  positions  which 
thinkers  have  taken  up  with  regard  to  them  during  the 
nineteenth  century  have,  however,  been  characteristic 
of  the  age,  and  have  been  very  largely  influenced 
by  the  conceptions  of  Order  and  Unity  which  science 
itself  has  elaborated.  In  this  connection  it  is  of 
importance  to  note  that  the  idea  of  Order  or 
arrangement  has  only  within  the  nineteenth  century 
met  with  a  comprehensive  mathematical  treatment ;  and, 
so  far  as  that  of  Unity  is  concerned,  it  can  also  be 
said  that  the  mathematical  sciences  have  in  the  course 
of  the  nineteenth  century  for  the  first  time  approached 
the  analysis  of  the  allied  idea  of  Continuity,  which 
indeed  plays  an  increasingly  important  part  in  many 
scientific    theories.       It    may    even    be    held    that    the 


748  SCIENTIFIC    THOUGHT. 

scientific  mind  advances  from  the  idea  of  Order  or 
arrangement  to  that  of  Unity  through  the  idea  of 
Continuity. 

If,  however,  these  highest  conceptions  had  been  intro- 
duced to  us  by  scientific  thought  in  the  form  only 
of  hmiting  ideas  or  highest  abstractions,  it  is  doubt- 
ful whether  the  special  discussion  of  them  would  have 
attracted  so  much  attention  or  occupied  so  many 
minds  as  has  actually  been  the  case.  In  many  in- 
stances we  found  it  to  be  quite  sufficient  for  the  pur- 
poses of  science  that  fundamental  principles  should 
be  dogmatically  asserted,  and  that  their  usefulness 
should  be  the  only  proof  of  their  correctness.  If 
no  other  interest  attached  to  the  conceptions  of  order 
and  unity  than  attaches,  for  instance,  to  the  ultimate 
principles  of  dynamics,  to  atomism,  or  to  the  axioms 
of  geometry,  the  number  of  persons  who  take  up 
these  refined  studies  would  probably  be  exceedingly 
small.  The  reason  why  the  conceptions  of  order,  unity, 
and  individuality  have  received  so  much  attention  lies 
in  this,  that  they  have  not  only  a  logical  meaning  as 
instruments  of  thought,  but  also,  as  the  words  them- 
Practfcki  ^^^^^^  indicate,  a  practical  meaning,  being  bound  up 
IStechiugto  ^^^^^  ^^^®  highest  ethical  and  sesthetical,  as  well  as  with 
uLlty.''"'^  01^1'  social  and  religious,  interests.  The  word  order  means 
something  more  than  arrangement  when  we  speak  of  the 
social  or  moral  order ;  the  word  unity  is  more  than  an 
arithmetical  conception  when  we  speak  of  the  unity  of 
action  or  of  purpose,  or  the  unity  of  design  in  art ;  the 
word  individuality  acquires  a  higher  meaning  in  the 
term    personality.       Those    thinkers   who   in   the   nine- 


RETROSPECT  AND  PROSPECT.         749 

teenth  century,  as  well  as  in  former  ages,  have  dealt 
exhaustively  with  these  the  most  abstract  and  highest 
conceptions  of  which  human  thought  is  capable,  have 
not  been,  or  have  only  very  rarely  been,  led  to  their  in- 
quiries from  the  side  of  purely  scientific  interests ;  they 
have  approached  them  with  a  full  appreciation  of  the 
great  moral  and  religious  interests  which  lie  hidden  in 
the  deeper  significance  which  we  attach  to  the  words. 
In  starting,  therefore,  on  the  survey  of  philosophical 
thought,  it  would  be  quite  inadequate  to  take  scientific 
ideas  as  a  suitable  introduction.  Whatever  future  ages 
may  bring,  the  philosophy  of  the  nineteenth  century  has 
certainly  not  been  exclusively,  or  even  pre-eminently, 
scientific  or  exact.  If  philosophy  has  assumed  the  name 
of  a  science,  it  has  done  so  in  that  larger  sense  of  the 
word  which,  as  we  have  seen,  is  peculiar  to  the  Ger- 
man language.  In  this  connection  scientific  treatment 
means  simply  methodical  treatment,  whereas  there  is  an 
increasing  tendency  in  many  circles  to  identify  the  word 
science  with  exact  mathematical  or  positive  treatment. 
The  exact  treatment  of  philosophical  problems,  such  as 
has  been  attempted  but  only  very  partially  carried  out 
in  the  systems  of  Auguste  Comte  in  France  and  of 
Herbert  Spencer  in  England,  belongs  almost  entirely  to 
a  later  part  of  that  century,  and  forms,  even  then,  only 
one  side  of  its  large  philosophical  literature.  Philo- 
sophical thought  had  a  brilliant  history  in  the  earlier 
part  of  the  century  before  the  ideas  of  Positivism  or 
of  modern  Evolution  were  much  thought  of.  It  will 
therefore  be  necessary  in  any  account  of  philosophical 
thought   to   ascertain   and   clearly   define    the    positions 


750  SCIENTIFIC    THOUGHT. 

occupied  by  the  great  thinkers  who  governed  and 
revolutionised  the  thought  of  earlier  generations  before 
the  great  generalisations  of  science,  notably  those  con- 
nected with  the  ideas  of  energy  and  the  theory  of  descent, 
could  have  had  any  influence  whatever.  Though  the 
latter  have  acquired  in  recent  times  a  great,  perhaps 
an  undue,  importance,  it  will  only  be  after  becoming 
acquainted  with  an  earlier  and  different  phase  of  philo- 
sophic thought  that  we  shall  have  once  more  to  return 
to  those  conceptions  and  trains  of  reasoning  which  must 
be  uppermost  in  the  mind  of  the  writer  as  well  as  of  the 
reader  of  the  foregoing  chapters. 
5.  But  in  starting  on  the  historical  account  of  an  en- 

Tlie  geo- 
graphical     tirely  different  realm   of  thought,  I  shall  not  only  have 

centre  of  °  "^ 

thouTt'"'^  to  ask  my  readers  to  enter  into  a  new  circle  of  ideas, 
which  for  a  long  time  during  the  course  of  the  nineteenth 
century  lay  entirely  outside  of  that  circle  of  ideas  with 
which  we  have  become  acquainted  so  far;  we  shall  be 
assisted  also  by  finding  an  entirely  different  geographical 
centre  from  which  these  ideas  emanated.  It  has  been 
repeatedly  pointed  out  that  the  great  volume  of  scientific 
thought  with  which  we  have  hitherto  been  occupied, 
emanated  in  the  latter  part  of  the  eighteenth  century 
from  the  French  capital ;  and  in  the  course  of  narration 
I  have  had  to  go  back  almost  in  every  single  instance 
to  the  foundations  laid  in  French  scientific  literature. 
I  shall  now  have  to  invite  my  readers  to  give  their 
attention  to  the  peculiar  features  which  were  charac- 
teristic not  of  French  but  of  German  literature  at 
the  end  of  the  eighteenth  and  the  beginning  of  the 
nineteenth  century. 


RETROSPECT  AND  PROSPECT.         751 

The  centre  of  philosophical  thought  during  the  first 
half  of  the  nineteenth  century  lay  as  much  in  Germany 
as  the  centre  of  scientific  thought  lay,  somewhat  earlier, 
in  France.  It  is  true  that  in  both  cases,  if  we  trace 
the  movement  a  little  further  back,  we  come  upon  the 
powerful  influences  of  English  thought.  Newton  can 
be  considered  as  marking  the  beginning  of  the  modern 
era  of  scientific  thought;  Locke  can  be  looked  upon 
as  having  infused  into  philosophic  thought  much  of 
its  modern  spirit.  But  though  this  must  be  conceded 
to  a  large  extent,  it  must  also  be  admitted  that 
the  scientific  thought  of  the  nineteenth  century  for 
a  long  time  received  its  special  colouring  through 
the  influence  of  the  French  mathematicians  and 
naturalists,  with  Laplace  and  Cuvier  as  their  most 
illustrious  representatives  ;  while  philosophical  thought 
for  a  long  time  received  its  specific  colouring  from 
the  idealistic  movement  which  began  with  Kant  and 
culminated  in  Hegel.  And  although  it  was  again 
the  specific  influence  of  English  thought  which  in 
the  latter  part  of  the  nineteenth  century  diverted 
alike  scientific  and  philosophical  thought  from  the 
channels  in  which  they  ran  during  the  first  half 
of  the  century,  we  have  only  very  partially  emanci- 
pated ourselves  from  the  overwhelming  influence  which 
the  conceptions  of  the  idealistic  school  of  German 
philosophy  have  had  upon  the  deeper  philosophical 
thought  of  all  three  nations  alike.  The  features 
peculiar  to  that  period  are  still  strongly  marked  on 
the  philosophical  countenance  of  the  age :  neither  the 
lights   nor   the   shadows    thrown    by    the   great   lumin- 


752  SCIENTIFIC   THOUGHT. 

aries   which  appeared   on   the   philosophical   horizon   of 
Germany  a  century  ago  have  as  yet  died  away. 

It  will  be  the  object  of  the  second  part  of  this  work 
to  trace  in  more  detail  this  powerful  influence,  to  define 
more  clearly  wherein  it  consisted,  and  to  discover  to 
what  extent  it  still  survives  or  is  mingled  with  other 
influences,  among  which  that  which  we  have  studied 
exclusively  in  the  first  part  of  this  history  will  prove 
to  have  been  one  of  the  most  important. 


INDEX. 


Abbe,  Ernst,  improvements  in  the 
microscope,  ii.  228,  229. 

Abbe,  Prof.  Cleveland,  method  of  least 
squares,  ii.  576. 

Abel  N.  H.,  memoir  by  Bjerknes  cited, 
i.  184 ;  investigations  of,  185 ;  and 
Crelle,  186 ;  on  Gaii.ss,  ii.  637 ;  his 
'  Life '  by  Bjerknes,  ib. ;  on  Cauchy, 
637  ;  ou  convergency,  646  ;  his  jjion- 
eering  work,  648 ;  his  relation  to 
Jacobi  and  Legeudre,  ib. ;  Sylow's 
memorial  of,  649  ;  his  addition  the- 
orem, 649  ;  657  ;  theory  of  equations, 
681,  686,  690,  692,  693,  695,  704,  732. 

Abelard,  i.  74. 

Abraham,  M.,  '  Geometrische  Grund- 
begriffe,'  ii.  73. 

Abria,  experiments  with  vacuum  tubes, 
ii.  190. 

Absolute,  the,  Cayley  on,  ii.  715. 

Abstraction,  process  of,  ii.  201. 

Academic  culture  in  France,  i.  134. 

Academie  de  Chirurgie,  i.  107. 

Academic  des  Sciences,  i.  107. 

Academie  des  Sciences  morales  et  pol- 
itiques,  i.  145, 

Academies,  provincial,  in  France,  i. 
107. 

Academy  of  Saxony  founded,  i.  100. 

Academy  of  St  Petersburg  founded, 
i.  100. 

Academy  of  Vienna  founded,  i.  100. 

Academy,  Paris,  organisation  and  co- 
operation of  members  of,  i.  99. 

Achenbach,  i.  165. 

Achenwall,  Gottfried,  the  "  father "  of 
statistics,  ii.  555. 

Acland,  Sir  Thomas  Dyke,  '  Chemistry 
of  Farming, '  i.  284. 

Acoustics,  ii.  12,  485. 

VOL.  II. 


Adams  discovers  Neptune,  i.  277 ; 
lunar  theory,  329. 

Adare,  Count,  i.  106. 

Adrain,  law  of  error,  ii.  576. 

^Etiology,  Huxley's  definition  of,  i.  194. 

Affinity,  chemical,  neglect  of  the  study 
of,  i.  420 ;  chemical,  ii.  157,  267. 

Agassiz  on  fossil  fishes,  ii.  257  ;  "Essay 
on  Classification,"  349. 

Agnosticism,  ii.  326. 

Airy  and  Herschel,  article  in  '  En- 
cyclopsedia  Metropolitana,'  i.  236. 

Airy,  Sir  George  Biddell,  worked  in  har- 
mony with  the  Analytical  Society, 
i.  271  ;  the  discovery  of  Neptune, 
277  ;  measurement  of  an  arc  of 
loarallel,  322  ;  calculus  of  probabili- 
ties, 325  ;  Tides,  330. 

Akin,  ii.  107. 

Albrecht,  Eugen,  '  Vorfragen  der  Bio- 
logic,' ii.  463. 

Alexander  the  Great,  Napoleon  com- 
pared with,  i.  153. 

Alexander  VI.,  Pope,  and  the  Univer- 
sity of  Aberdeen,  i.  268. 

Alison,  W.  P.,  i.  272. 

Allen,  Grant,  monograph  on  Darwin 
quoted,  ii.  607;  on  "pangenesis," 
610. 

Altmann,  theory  of  "  bioblasts,"  ii.  427, 

444. 
America,    influence    of,    only    touched 
upon,  i.  14;  declaration  of  Independ- 
ence, 79. 
Amici,  embryological  studies,  ii.  227 ; 
improvements    in    microscope,    228 ; 
230,  261. 
Ampere,  A.  M.,  on  electro-magnetism, 
i.  92  ;  "mechanical  theory  of  gases," 
310  ;  313  ;  electric  currents,  347,  367  ; 

3   B 


754 


INDEX. 


develops  astronomical  view  of  na- 
ture, 366  ;  368,  370,  371  ;  import- 
ance of  his  discoveries,  372 ;  chem- 
ical discovery  of,  408 ;  Avogadro's 
hypothesis,  427  ;  '  Essai  siir  la  Phil- 
osophic des  Sciences,'  ii.  5,  205 ; 
requested  Fresnel  to  write  his 
'  Mi-moire  sur  la  Diffraction,'  25  ;  sug- 
gested transverse  vibrations  to  explain 
polarisation  of  light,  26  ;  equation  of 
wave  surface,  42 ;  Lord  Kelvin  on 
electro-magnetic  theory  of,  73 ;  re- 
ferred to,  78  ;  electrical  formulse  of, 
79  ;  researches  of,  92  ;  theory  of,  143  ; 
193,  698  ;  on  oscillating  functions, 
706,  742. 
Amyntas,  King  of  Macedonia,  ii.  207. 
Anabolism,  ii.  395,  442. 
Analogies,  studies  of,  ii.  250  ;  physical, 

Klein  on,  701. 
Analytical  Society  of  Cambridge,  i.  271. 
Auchersen,  J.  P.,  statistics,  ii.  579. 
Andrews,   Thomas,    "critical  tempera- 
ture "  of  gases,  i.  316  ;  experimental 
work  of,  ii.  161  ;  'Scientific  Papers' 
of,  162  ;  164. 
Angle,  trisection  of  the,  ii.  124. 
Angstrom,  spectrum  analysis,  ii.  278. 
Anhalt  -  Dessau,     Princess    of,    letters 

from  Euler  to,  ii.  7. 
Anharmonic  ratio,  ii.  718. 
Anilin  colours,  discovery  of,  i.  92. 
'Annales  de  Chimie  et   de   Physique,' 

i.  236,  ii.  25,  54. 
Anthropology,  ii.  497. 
Apologetic    literature    in   England,   ii. 

324. 
Appelt,  i.  209. 

Arago,  letter  from  Young  to,  i.  230  ; 
'  Annales  de  Chimie  et  de  Physique,' 
236 ;  and  Fresnel,  241  ;  eloges  of, 
279  ;  his  appreciation  of  the  labours 
of  Fresnel,  ii.  21  ;  views  on  "  sided- 
ness"  of  rays  of  light,  24  ;  requested 
Fresnel  to  write  his  '  Memoire  sur  la 
Diffraction,'  25  ;  never  accepted  theory 
of  transverse  vibrations,  26  ;  visit  to 
England,  27, ;  property  of  polarised 
light,  28  ;  Eloge  on  Carnot  the  elder, 
138  ;  506. 
"  Arbeitskraft, "   term   used   by   Helm- 

holtz,  ii.  140. 
Archimedes  quoted,  ii.  376. 
Arfvedson,  chemist,  i.  188. 
Argand,  geometrical  representation   of 
imaginary  quantities,  i.  184  ;  on  im- 
aginaries,  ii.  653. 
Argon  discovered,  i.  423. 
Aristotle,  constructive  system  of,  i.  75  ; 


his  works  models  of  scientific  re- 
search, 95 ;  120 ;  philosophy  in 
English  universities  represented  by, 
254  ;  views  of  Heraclitus,  ii.  3  ;  4, 
207  ;  analogies  of  nature,  255,  349  ; 
grammar  and  logic,  629. 
Arithmetic,   fundamental    laws    of,    ii. 

654  ;  703. 
Arithmetising  tendency,   Klein  and  P. 
Du  Bois-Reymond  on,  ii.  738  et  seq. 
Armstrong,    Lord,   hydro  -  electric   ma- 
chine :  electrical  discharge,  ii.  191. 
Arnold,  Matthew,  introduced  new  words 
into  English,  i.  22  ;  on  German   cul- 
ture, 225  ;  '  Literary  Influence  of  Aca- 
demies,' 298. 
AronTiold  on  invariants,  ii.  684. 
Arrhenius,    Svante,   theory   of  electro- 
lytes, ii.  159,  165. 
Art,  German,  not  patronised  by  royalty, 

i.  157. 
Arundel  collection  of  antiquities,  i.  295. 
Ascherson, '  Deutscher  Universitats-Kal- 

ender,  i.  161. 
Association,  British,  founded,  i.  42. 
Astronomical  view  of  nature  :  cosmical, 
molar,    and    molecular    phenomena, 
i.    348 ;   developed    by   Ampere    and 
Weber,  366  ;  opposition  to,  381  ;  in- 
sufficiency of,  ii.  96. 
'  Athenffium  '  of  Schlegel,  i.  84. 
Athens     under    Pericles,    i.     67 ;    the 

schools  of,  74. 
Atom   and  molecule,    i.    432 ;    size   of, 

437. 
Atomic  theory  (see  Dalton),  i.  385  ;  two 
aspects  of,  415  ;  development  of,  431 ; 
accepted,  437  ;  crystallographic  laws, 
analogy  between,   444  ;  linkage,  449  ; 
defects  and  insufficiency  of,  461  ;  ii. 
574. 
Atomic   view   of  nature,   i.  382  ;  criti- 
cisms  of,    455 ;    insufficiency   of,    ii. 
96  ;  recent  triumphs  of,  188. 
Atomism,  ii.  465. 
Atoms,  geometrical  arrangement  of,  i. 

441. 
Attraction,  ii.  465. 
Attraction  and  repulsion,  i.  342. 
Attraction  of  ellipsoids,  ii.  670. 
Aubuisson,  d',  ii.  294. 
Aucoc,  Leon,  'L'Institut  de  France,'  i. 

90,  127,  148,  149. 
Auerbach,    modern    era    in    history   of 

fertilisation,  ii.  227. 
Autenrieth,  ii.  349. 

"Availability,"  idea  of,  introduced  by 
Carnot,  ii.  119  ;  597.  See  also  Kelvin, 
Lord. 


INDEX. 


755 


Averages,  doctrine  of,  i.  440  ;  ii.  561. 
Avogadro,      "mechanical      theory     of 

gases,"  i.  310 ;  313 ;  law  of,  4i5,  ii. 

165,  592 ;  hypothesis  of,  i.  427  ;  428  ; 

hypothesis    of,    revived    by    Cauuiz- 

zaro,  445. 

Babbage,  Charles,  i.  18  ;  '  Decline  of 
Science  in  England,'  127  ;  history  of 
his  calculating  engine,  248  ;  educa- 
tional movement  begun  by,  261  ; 
formed  the  Analytical  Society,  271  : 
criticisms  of  science  in  Britain,  233  ; 
236  ;  Prof.  Moll's  reply  to,  ib.  ; 
English  replies  to,  238  ;  not  a  univer- 
sity man,  '^39  ;  ii.  2,17. 
Babeuf,  co-operation,  ii.  566. 

Baeharach,  14istoryof  Potential  Theory, 
ii.  698  ;  on  Klein's  Tract,  699. 

Bacon,  Lord,  his  influence  on  the 
Encyclopedists,  i.  34  ;  his  interpre- 
tation of  the  word  "science,"  90; 
unscientific,  93 ;  his  philosophical 
status,  94,  311  ;  and  Newton  com- 
pared, 96  ;  influence  in  new  Univer- 
sity of  Halle,  160 ;  215 ;  schemes  ol',  re- 
alised by  the  'Encyclopedie,'&c.,  250; 
appreciated  educational  work  of  the 
"  Order  of  Jesus,"  256  ;  Harvey,  and 
Napier,  282  ;  on  the  study  of  natural 
phenomena,  285  ;  311  ;  his  philos- 
ophy, 385  ;  system  of  philosophy,  ii. 
205,  344;  "  method  of  instances," 
557. 

Bacon,  Roger,  i.  249,  403. 

Baconian  philosophy,  decay  of,  i.  306. 

Badeu-Powell,  radiant  heat,  ii.  105  ; 
apologetic  writings,  327. 

Baer,  Karl  Ernst  von,  his  opinion  on 
the  Naturphilosophie,  i.  207  ;  em- 
bryologist,  ii.  278  ;  his  labours,  299  ; 
quoted,  307,  417  ;  Lamarck  and,  316  et 
seq. ;  Huxley  on,  322 ;  genetic  view 
in  embryology,  330 ;  341  ;  law  of 
biogenesis,  349  ;  and  Schelling,  354  ; 
idea  of  life,  409  ;  embryological  re- 
searches, 418;  on  "diffusion  of  life," 
451;  "  organicism,"  455;  467,  533, 
607.    ■ 

Bagehot,  Walter,  quoted,  ii.  558. 

Bailie,  Matthew,  English  medical 
science,  i.  208. 

Bailly  guillotined,  i.  147. 

Baily  on  Greenwich  Observatory  and 
the  Rev.  J.  Flamsteed,  i.  98. 

Bain,  'The  Senses  and  the  Intellect,'  ii. 
511;  512:  on  psychology,  527  ;  608. 

Baker,  H.  F.,  on  differential  equations, 
ii.  692. 


Balbi,  ii.  579. 

Balfour,  Francis  M.,  organic  mor- 
phology, ii.  214  ;  349. 

Ball,  Sir  R.  S.,  'Gravitation,'  i,  320; 
memoir  of  Helmholtz,  ii.  63 ;  geo- 
metrical mechanics,  10 1;  his  theory 
of  screws,  655 ;  on  Grassmann, 
656 ;  on  generalised  notion  of  dis- 
tance, 718. 

Ball,  W.  Rouse,  'A  History  of  the 
Study  of  Mathematics  at  Cambridge,' 
i.  275,  321  ;  history  of  mathematics, 
ii.  680. 

Banks,  Sir  Joseph,  i.  83,  155  ;  travels 
of,  ii.  247. 

Barenbach,  '  Herder  als  Vorganger  Dar- 
wins,'  ii.  533. 

Biirenspruug,  von,  medical  thermom- 
etry, ii.  389. 

Bariire,  foundation  of  Ecoles  normales 
proposed,  &c.,  i.  112. 

Barlow,  not  member  of  any  university, 
i.  239. 

Barry,  Martin,  embryological  observa- 
tions, ii.  227,  228. 

Bartels,  friend  of  Gauss,  ii.  653. 

Barthez,  vitalist,  i.  r26. 

Barycentric  Calculus  of  Mtibius,  ii. 
655,  681. 

Basedow,  "  philanthropinism,"  i.  166; 
educational  work  of,  256  ;  257  ;  was 
inspired  by  Rousseau,  259. 

Bates,  H.  W.,  "mimicry,"  ii.  339. 

Bateson,  William,  'Materials  for  the 
Study  of  Variations,'  ii.  364;  study 
of  variation,  614  ;  622 ;  and  Karl 
Pearson,  6i!3  ;  agrees  with  Huxley 
against  Darwin,  623. 

Bathybius,  ii.  3S8. 

Bauer,  G.,  on  Otto  Hesse,  Ii.  677. 

Baumes,  J.  P.  T.,  '  Essai  d'uu  systeme 
chimique  de  la  science  de  I'homme,' 
ii.  390. 

Baumgartner,  i.  44 ;  printed  Mohr's 
'  Ueber  die  Natur  der  Warme,'  ii.  107. 

Baumhauer,  ii.  565. 

Baur,  ii.  109. 

Bavaria,  Elector  of,  and  Count  Rum- 
ford,  i.  248. 

Bayes,  ii.  572. 

Bayle,  value  of  work  of,  i.  93  ;  followed 
Newton,  96  ;  French  medical  science, 
208. 

Bayne,  Peter,  '  Life  and  Letters  of  Hugh 
Miller,'  i.  2^8. 

Beaumont,  Elie  de,  doctrine  of  descent, 
ii.  322. 

Becker,  G.  F.,  on  Kant's  theory,  ii. 
282  ;  284. 


756 


INDEX. 


Becker  on  mortality  statistics,  ii.  566. 

Becqiierel,  E.,  phenomenon  of  fluor- 
escence, ii.  52. 

Bedson,  Prof.,  '  Memorial  Lecture '  on 
Lothar  Meyer,  i.  427. 

Beer,  physics,  i.  44 ;  '  Einleitung  in 
die  Elektrostatik,'  ii.  76. 

Bell,  Henry,  built  the  "Comet,"  i.  303. 

Bell,  John,  i.  293. 

Bell,  Sir  Charles,  discovery  of  the  two 
kinds  of  nerves,  i.  193,  292,  293  ;  ii. 
481  ;  physiological  discovery  of,  230  ; 
and  German  universities,  i.  251  ;  of 
Edinburgh  University,  272  ;  Bridge- 
water  Treatise,  ii.  325 ;  experimental 
physiology,  384  ;  '  Anatomy  of  Ex- 
j>ression,'  477. 

Bell,  Sir  Lowthian,  phosphorus  as  fer- 
tiliser, i.  93. 

Beltrami,  the  pseudosphere,  ii.  635  ; 
supplements   Riemann's   work,    713  ; 

717. 

Bence  Jones,  'Life  and  Letters  of  Fara- 
day,' i.  246  ;  Royal  Institution,  246, 
248. 

Beneden,  Van,  on  fertilisation,  ii.  227  ; 
discovery  of,  448. 

Beneke,  psychologist,  influenced  by 
school  of  Fries,  i.  209;  "faculty- 
psychology,"  ii.  495  ;  introspective 
method,  527. 

Benfey,  Theodor,  '  Geschichte  der 
Sprachwissenschaft,'  ii.  245,  537. 

Beutham,  Jeremy,  school  of,  i.  84. 

Beutley,  Richard,  i.  169 ;  influence  of, 
on  German  thought  and  literature, 
212  ;  services  to  classical  learning 
and  criticism,  222  ;  his  theories,  251 ; 
Newton's  philosophy  and  atheism, 
337  ;  Newton's  letter  to,  340. 

Bergmaun,  i.  117  ;  forerunner  of  Ber- 
zelius,  391  ;  doctrine  of  chemical 
affinities,  392 ;  theory  of  chemical 
affinity,  452 ;  chemical  theory  of,  ii. 
176. 

Berkeley,  and  Hume,  i.  47 ;  '  Theory  of 
Vision,'  ii.  472;  space  perception, 
504 ;  genetic  view,  506 ;  psycho- 
physical view,  531. 

Berlin  Academy,  language,  ii.  536, 

Berlin,  foundation  of  University  of,  i. 
38. 

Berlin  school  of  mathematicians,  ii.  693. 

Bernard,  Claude,  "Association  Fran- 
9aise,"  i.  298;  on  identity  of  Animal 
and  Vegetable  Morphology,  ii.  219  ; 
quoted,  223,  410  ;  '  Phenomenes  de  la 
Vie '  quoted,  224,  239,  370,  438 ;  De 
Blainville,  247  ;  '  La  Science  Experi- 


mentale '  quoted,  373,  376,  379,  384, 
385,  386  ;  change  of  ideas  in  medical 
schools  of  Paris,  396 ;  406,  409 ; 
'Rapport,'  419;  "organisation  et 
desorganisation,"  421;  'Rapport' 
quoted,  426 ;  429 ;  school  of,  431  ; 
the  "internal  medium,"  432;  chem- 
istry of  the  living  being,  433  ;  school 
of  "  organicists,"  436;  rationale  of 
the  mental  process,  441;  442;  "or- 
ganicisme,"  455,  467,  481,  504,  549  ; 
quoted  by  Darwin,  610. 
Bernard,  Thomas,  associated  with  Rum- 
ford's  philanthropic  schemes,  i.  249. 
Bernoulli,  Daniel,  the  theory  of  prob- 
abilities, i.  120,  ii.  570  ;  i.  135  ;  hypo- 
thesis of,  314  ;  on  gravitation,  quoted, 
351;  '  Hydrodynamica '  (the  kinetic 
theory  of  gases),  433  ;  motion  of  par- 
ticles of  gaseous  matter,  434 ;  on 
Euler's  theory  of  the  continuity  of  the 
ether,  ii.  8  ;  psychophysics,  474  ; 
572,  590,  694. 
Bernoulli,  James,  took  wp  the  calculus, 
i.  101  ;  the  theory  of  probabilities, 
120  ;  ii.  569  ;  '  De  Arte  conjectandi,' 
570  ;  572  ;  theory  of  error,  575  ;  doc- 
trine of  chances,  678. 
Bernoulli,  John,  took  up  the  calculus, 
i.  101  ;  the  conservation  of  energy, 
ii.  99. 
Bernstorif,  Minister  von,  i.  158. 
Berry,  A.,  '  History  of  Astronomy,'  ii. 

282,  357,  362. 
Berthelot  quoted  on  crystallography,  1. 
117;  'La  Synthese  chimique,'  418; 
'  Chimie  organique  fondee  sur  la  Syn- 
these,' 454  ;  '  La  Synthese  chimique  ' 
quoted,  455,  457  ;  a  founder  of  physi- 
cal chemistry,  ii.  152;  third  law  in 
thermo  -  chemistry,  157  ;  chemical 
affinity,  171,  177 ;  quoted,  361  ; 
chemistry  of  organic  compounds,  425. 
Berthollet  issued  '  Annales  de  Chimie,' 
i.  41  ;  '  Essai  de  Statique  chimique,' 
83,  116  ;  chemistry  at  the  Ecole  nor- 
male,  112 ;  practical  discoveries  of, 
147  ;  gunpowder,  iron,  steel,  148  ; 
152,  200  ;  chemical  saturation,  347  ; 
influenced  by  Laplace,  380 ;  chem- 
ical equilibrium,  392  ;  quoted,  416  ; 
heat  a  material  substance,  433 ; 
theory  of  chemical  affinity,  452 ;  ii. 
154 ;  law  of  mass-action,  157  ;  (see 
Ostwald),  176. 
Bertholon  quoted,  i.  327. 
Bertin,  M.,  '  Rapport  sur  le  Progres 
de  la  Thermodynamique  en  France,' 


INDEX. 


757 


Bertrand,  Joseph,  quoted,  i.  121,  134; 
'  Calcul  des  Probabilites,'  324  ;  his 
'  Calcul  difl'erentiel '  referred  to,  ii. 
646. 

Berzelius,  Rej^orts,  i.  42  ;  chemistry,  44  ; 
discoveries  published,  83  ;  services  to 
chemistry  of,  188  ;  biographical,  189  ; 
'  Jahresbericht,'  190;  organic  analy- 
sis, 190  ;  191  ;  influence  on  German 
science,  208  ;  mechanical  view  in  bi- 
ology, 219  ;  220,  238  ;  experimentally 
proved  Dalton's  atomic  theory,  245; 
and  Faraday,  365  ;  electrical  action 
in  chemical  processes,  366  ;  chemical 
combinations,  396 ;  elaborated  Dal- 
ton's theory,  399 ;  400 ;  disproves 
Prout's  hypothesis,  402  ;  403  ;  electro- 
chemical theory,  404 ;  organic  chem- 
istry, 4(17;  409;  "  radicle  "  theory, 
411  ;  death  of  the  binary  theory,  412  ; 
413,  414  ;  atomic  theory,  416,  417  ; 
426 ;  characteristic  of  hydrogen 
atoms,  430 ;  theories  of  chemical 
affinity,  452  ;  ii.  154 ;  chemical  re- 
search, 159,  403. 

Bessel,  Friedr.  vVilh.,  services  to  as- 
tronomy of,  i.  177 ;  corresjiondence 
with  Gauss,  185,  ii.  6.52 ;  i.  199  ; 
measurements  of,  322  ;  taught  at 
Kcinigsberg,  with  Neumann  and  Eich- 
elot,  ii.  54  ;  popular  work  of,  149  ; 
on  Gauss,  636  ;  functions  of,  696. 

Bessel-Sellmeier  hypothesis,  ii.  54. 

Beuth  founded  industrial  schools  in 
Prussia,  i.  166. 

Beverwijck,  i.  282. 

Bewick,  wood  engraver,  '  British  Birds, ' 
i.  289. 

Bichat,  works  of,  i.  83 :  not  amoug  the 
academicians,  126  ;  biological  labours 
of,  194,  ii.  313  ;  i.  195,  2U0  ;  morpho- 
logical study  of  natural  objects,  ii. 
231  ;  the  science  of  biology,  381  ; 
"Vitalism,"  383,  384;  386,  387;  on 
life,  394 ;  doctrine  of  energy,  399  ; 
402  ;  quoted,  406  ;  school  of  "  orgaui- 
cism,"  436  ;  vital  force,  503. 

Billroth,  Prof.,  '  Lehren  und  Lernen  der 
medicinischeu  Wissenschaften,'  i.  197; 
198  ;  influence  of  English  science  on 
medical  studies  in  Germany,  208  ; 
quoted  on  services  of  Kant  to  Ger- 
man science,  219. 

Biogenesis,  ii.  451. 

Biology  a  German  science,  i.  193  ;  grew 
out  of  science  and  philosophy  com- 
bined, 216  ;  essential  unity  of  sciences 
of,  not  yet  recognised  in  Germany, 
220  ;  British  contributions  to,  232  ;  ii. 


208,  312 ;  vagueness  of  theories  of, 
370 ;  oscillation  of  thought,  374  ; 
415. 
Biot,  experimental  physics,  1.  44,  200 ; 
fall  of  stones  at  I'Aigle,  328  ;  his  dis- 
covery, 431  ;  opposed  to  undulatory 
theory  of  light,  ii.  16,  21  ;  member 
of  Commission  of  Paris  Academy  of 
Sciences  competition,  1819,  25  ; 
"laterality,"  27  ;  influenced  German 
thought,  101  ;  193,  508. 

Biran,  Maine  de,  '  Menioire  sur  I'habi- 
tude,'  i.  83. 

Bischoft',  Theod.,  embryology,  ii.  227  ; 
300  ;  quoted,  381,  387  ;  address  on 
Liebig,  391. 

Bjerknes,  A.,  on  Abel,  i.  184, 185,  ii.  637. 

Black,  Joseph,  discovered  carbonic  acid, 
i.  115  ;  on  latent  heat,  229,  399,  ii, 
102  ;  Scottish  university  professor,  i. 
272;  and  Lavoisier,  386,  387;  391, 
400  ;  formula!  of,  4.36  ;  biographical, 
ii.  102  ;  attitude  to  science  that  of  a 
medical  man,  ln3. 

'  Blackwood's  Edinburgh  Magazine  ' 
published,  i.  273. 

Blair,  Hugh,  i.  273. 

Blennerhasset,  Lady,  on  De  Stael,  i.  17. 

Block,  statistics,  ii.  557,  563  ;  quoted, 
561,  566  ;   '  Statistique  morale,'  579. 

Blomstrand,  'Die  Chemieder  Jetztzeit,' 
i.  430. 

Blumenbach  of  Gottingen  University, 
i.  165,  194,  ii.  247;  fossil  collec- 
tions, 248  ;  influences  Herder,  532. 

Bcickh,  science  for  its  own  sake,  i.  211  ; 
212 ;  classical  learning  of,  222 ; 
'  Logos  epitaphios '  on  Wilhelm  von 
Humboldt  quoted,  263. 

Bode's  law,  i.  422. 

Bodenhausen,  i.  104. 

Bodenstedt,  '  Mirza  Schafty,'  i.  213. 

Boehmer,  Dr  Heinrich,  '  Gesch.  d. 
Entwick.  d.  Naturwissenschaftlichen 
Weltanschauung  in  Deutschland,'  ii. 
531. 

Boerhaave,  i.  144,  175  ;  and  the  medi- 
cal schools  of  Germany,  208  ;  268 ; 
atoms  and  viassulce,  398 ;  epigenesis, 
ii.  298. 

Bohmer,  "libertas  docendi,"  i.  164. 

Bohn,  ii.  107. 

Bohnenberger's  gyroscopic  instrument, 
ii.  61. 

Boileau  referred  to  by  Voltaire,  i.  105. 

Boltzmann,  Ludwig,  lectures  on  Max- 
well's theories,  i.  251  ;  quoted,  ii.  90  ; 
176,  186,  188,  595;  "availability," 
597. 


758 


INDEX. 


Bolyai,  i.  161 ;  a  pupil  of  Gauss,  181  ; 
father  and  son,  and  Gauss,  ii.  652  ; 
710,  713. 

Bolzano,  Bernhard,  on  undulatory 
theory  of  light,  ii.  10  ;  on  the  infinite 
and  couvergency,  709  ;  and  Cauchy 
compared,  ib.;  Stol.^  on,  ih. 

Boniare,  Valmont  de,  tirst  course  of 
natural  history  at  Paris,  i.  106. 

Bonald,  De,  on  origin  of  language,  i.  23. 

Bond,  Dr,  ii.  565. 

Bonnet,  Charles,  regular  a,rrangement 
of  leaves,  ii.  223 ;  '  Echelle  des 
etres,'  238;  "evolutionist,"  278; 
279  ;  epigenesis,  298  ;  322,  519. 

Bonnet,  Ossian,  ii.  704. 

Boole,  George,  neglect  of,  in  England, 
i,  247  ;  272 ;  and  modern  school  of 
mathematics,  ii.  676  ;  Stanley  Jevous 
on,  68-4. 

Bopp,  language,  ii.  540,  542. 

Borda,  i.  113,  148. 

Bordeu,  vitalist,  i.  126  ;  vital  force,  ii. 
503.    , 

Borel,  Emil,  his  lectures,  ii.  704. 

Borelli,  medicine  in  alliance  with 
physics,  i.  126. 

Boscovich,  Roger,  theories  of  molecular 
attraction  and  repulsion,  i.  357 ; 
metaphysical  theorist,  371  ;  416  ;  on 
the  nature  of  matter,  419  ;  applica- 
tion of  theory  of  gravitation  to  mole- 
cular physics,  ii.  28  ;  gravitation  as  a 
general  physical  theory,  351. 

Bossut,  i.  107. 

Bougainville,  pupil  of  the  Ecole  nor- 
male,i.  112;  113. 

Boiiillier,  M.,  quoted,  i.  107,  108 ; 
'Eloges  de  Fontenelle,'  135. 

Boulton,  use  of  the  term  "horse- 
power," ii.  99. 

Boussinesq  quoted  on  transmission  of 
vibrations  of  ether  to  ponderable 
bodies,  ii.  54. 

Boussingault,  agricultural  chemistry, 
ii.  393  ;  406 ;  bacteriological  work, 
415  ;  quoted,  441. 

Bowen,  criticism  of  '  Vestiges,'  ii.  319. 

Boyle  Lectures,  Bentley's,  i.  169. 

Boyle,  Hon.  Robert,  Newton  to,  i.  342  ; 
and  Lavoisier,  386  ;  atoms  and  mass- 
idce,  398 ;  law  of  pressures,  425  ; 
427  ;  law  of,  429 ;  ii.  592. 

Boys,  Prof.,  determination  of  force  of 
gravitation,  i.  320. 

Bradley,  i.  158 ;  observations  of,  utilised 
by  Bessel,  177  ;  238  ;  aberration  of 
light,  ii.  10  ;  astronomical  aberration, 
194. 


Brandt,  Sebastian,  i.  163. 

Braun,  Alex.,  sjjiral  theory,  ii.  223 ;  268 ; 

quoted,  269. 
Bravais,    'Etudes   crystallographiques,' 

i.  443. 
Breal,   educationalist,  ou  Rousseau,   i. 

259  ;  260. 
Brewster,    Sir   D.,    'Life    of    Newton,' 

i.  98,  321,  342  ;  experiments  of,  230  ; 

quoted    on   foundation   of  suggested 

"British    Association,"    238;    never 

adopted    theories     of    Young,    244 ; 

Scottish    university    professor,    272 ; 

opposed    to    undulatory    theory    of 

light,  ii.  16  ;  letter  from  Young,  27  ; 

theory   of   undulations,    37 ;    experi- 
mental work  of,    45 ;    adherence   to 

projectile  theory,   46 ;    observed   the 

phenomenon  of  fluorescence,  52  ;  245  ; 

criticism    of    '  Vestiges,'    319  ;    482 ; 

stereoscope,  506. 
Brianchon,  ii.  660. 
Bridgewater  Treatises,  ii.  324. 
Briggs,  Henry,  '  Logarithmorum  Chilias 

prima,'  i.  269. 
Bright,  i.  272. 
Brill  and  Nother, '  Theory  of  Functions,' 

i.    308  :    '  Bericht '   quoted,   ii.    657  ; 

700,  701. 
Brioschi  and  invariants,  ii.  685. 
Brisseau,    a    pioneer    of    the    cellular 

theory,  ii.  262. 
British  Association,  i.  42,  236  ;  founded, 

89,  238  ;  suggested  by  Brewster,  ib.  ; 

successful  work  of,  239  ;  Sir  Charles 

Lyell  on,  240  ;  reports,  ii.  54  ;  55,  58, 

73  ;  meeting,  163. 
'  British  Quarterly  Review  '  quoted  on 

the  two  older  universities,  i.  254. 
Brix,  Walter,  ii.  734. 
Broca,  .speech,  ii.  478,  479,  .539. 
Brockhaus,   'Conversations-Lexicon,'  i. 

273. 
Brodie,  ii.  362. 
Brongniart  (see  Cuvier),  associated  with 

Cuvier  in    palajontological   work,    i. 

139  ;  excavations,  ii.  248  ;  exploration 

of  Paris  basin,  294. 
Bronn,     translation     of      '  Origin      of 

Species,'  ii.  322. 
Brougham,    Lord,   unfair    criticism    of 

Young,  i.   244;  '  Edinburgh  Review,' 

273;  on  Dr  Young,  ii.  9,  19. 
Broussais,    French   medical   science,    i. 

208  ;  phrenology,  ii.  477. 
Brown,    Crum,    and    Tait,    Memoir    of 

Thomas  Andrews,  ii.  162 ;  on  Sainte 

Claire    Deville    and    "dissociation," 

163 ;  438. 


INDEX. 


759 


Brown,  John,  i.  126. 

Browu,  Robert,  used  the  term  "cell,"  i. 
195 ;  scientific  publications  of,  230  ; 
not  member  of  any  university,  238 ; 
discovery  of  the  cell  nucleus,  ii.  264 ; 
338. 

Brown,  Thomas,  '  Cause  and  Effect,'  i. 
84  ;  ii.  511. 

Browning,  maturer  thought  of,  i.  76. 

Briiclce,  i.  198  ;  protoplasmic  theory,  ii. 
443  ;  language,  538. 

Bruhns,  'Life  of  A.  von  Humboldt,' 
i.  238,  ii.  225,  253,  475. 

Bruno,  animation  of  all  matter,  ii. 
369. 

Brunswick,  history  of,  ii.  280. 

Bryan,  Prof.,  second  law  of  thermo- 
dynamics, ii.  176 ;  595. 

Bryce,  James,  quoted  on  German  uni- 
versities, i.  159. 

Buache,  geography  at  the  Ecole  uor- 
male,  i.  112  ;  113. 

Buch,  von,  on  descent,  ii.  330. 

BUchner,  L.,  materialism,  i.  60  ;  'Kraft 
uud  Stoff,'  ii.  320  ;  323. 

Buckland,  Wm.,  i.  106;  palseontologi- 
cal  work  of,  139  ;  ii.  325. 

Buckle  quoted,  i.  114 ;  statistical 
method,  124  ;  philosophy  of,  ii.  346  ; 
statistics,  584,  599  ;  607,  608. 

Buee  on  imaginaries,  ii.  653. 

Buffon,  importance  in  French  literature 
of,  i.  105  ;  283  ;  intiuence  of,  on  the 
study  of  nature,  106 ;  at  the  Jaidin 
des  Plantes,  107  ;  philosoiihical  in- 
fluence of,  111  ;  113  ;  discouraged 
views  of  Linuaius  in  France,  117; 
119,  131  ;  natural  history  of,  126  ; 
137,  142;  'Tlieorie  de  la  Terre,' 
144  ;  288  ;  against  Clairault's  attempt 
to  correct  gravitation  formula,  334; 
classification  of  natural  objects,  ii. 
22,1  ;  232  ;  analogies  of  nature,  255  ; 
'Epoques  de  la  Nature,'  277,  309; 
322;  "organic  molecules,'  454,  610; 
455  ;  influences  Herder,  532  ;  613. 

Bunge,  '  Physiological  Chemistry ' 
quoted,  ii.  378,  425,  426,  434. 

Bunsen,  Baron  von,  relative  merits  of 
Young  and  Cliamx)ollion,  i.  244 ; 
'  Egypit's  Place  in  Universal  History,' 
245. 

Bunsen,  R.  W.  von,  i.  412 ;  ciesium 
and  rubidium,  ii.  49  ;  spectrum 
analysis,  57. 

Burali  Forti,  ii.  656. 

Burbury,  ii.  595. 

Burckhardt,  J.  K.,  calculates  orbit  of 
Ceres,  i.  182  ;  lunar  theory,  329. 


Burkhardt,  H.,  on  Ruftini,  ii.  688  ;  on 

Riemann,  698,  700. 
Burnet,  Thomas,  i.  283. 
Burnett,  James.     See  Lord  Monboddo. 
Burns,   healthy   spirit   of,    i.   78  ;   212, 

285. 
Burnside,   his   '  Theory  of  Groups,'  ii. 

691. 
Butler,  philosophy  in  English  universi- 
ties represented  by,  i.  254  ;  apologetic 

writings  of,  ii.  325. 
Blitschli,  on  fertilisation,  ii.  227  ;  foam 

theory,    427  ;     '  Mechanismus    und 

Vitalismus,'  463. 
Buys   Ballot    and    Boscovich's   theory, 

i.  359  ;  Doppler's  principle  proved  in 

acoustics,  ii.  49. 
Byron,  revolutionary  spirit  of,  i.  78. 

Cabanis,  alliance  with  medicine,  i.  126  ; 
127  ;  '  Revolutions  de  la  Medecine,' 
135  ;  152  ;  '  Rapports  du  Physique 
et  du  Moral  de  I'Homme,'  ii.  469; 
his  simile,  470,  503  ;  science  of  man, 
471 ;  language  and  grammar,  530 ; 
532. 

CiBsalpinus,  arrangement  of  leaves  of 
plants,  ii.  223. 

Cffisar,  Napoleon  compared  with,  i.  153. 

Ctesium  found  by  Kirchhoff  and  Bun- 
sen, ii.  49. 

Cailletet,  condensation  of  piermanent 
gases,  i.  316. 

Caloric,  ii.  154. 

Calvin,  direct  influence  of,  on  Scotland, 
i.  253  ;  educational  work  of,  255. 

'Cambridge  Mathematical  Journal,'  i. 
41. 

Campbell  and  Garnett,  '  Life  of  Clerk- 
Maxwell,'  ii.  599. 

Campbell,  H.  .J.,  translation  of  Hert- 
wig's  'The  Cell,' ii.  265. 

Campe,  edition  of  'Robinson  Crusoe,' 
i.  256  ;  ii.  324. 

Camper,  ii.  247  ;  collection  of  fossils, 
248  ;  physiognomy,  477  ;  influences 
Herder,  532. 

Cannizzaro  showed  the  value  of  Avo- 
gadro's  hypothesis,  i.  427,  445. 

Canton,  M.,  history  of  mathematics,  ii. 
632  ;  quoted,  633  ;  631,  680. 

Cantor,  G.,  on  theory  of  probabilities, 
i.  122 ;  ii.  630 ;  a  new  chapter  in 
mathematics,  634  ;  734  ;  on  the  trans- 
finite,  735,  737. 

Capillary  action,  i.  356. 

Carbon  tetrahedron,  the,  i.  450. 

Carlyle,  influence  of,  on  English  style 
and    language,   i.    22 ;    first  to   give 


760 


INDEX. 


specific  meaning  to  the  word  Thouglit, 
26;  'Life  of  Schiller,'  134;  171; 
quoted,  ii.  520  ;  528,  531,  608. 

Carnot,  Hippolyte,  Sadi  Carnot's  '  Puiss- 
ance Motrice,'  ii.  118;  referred  to, 
130. 

Carnot,  L.  N.  M.,  on  correlation,  ii. 
100,  138,  658  ;  Chasles  on,  ib. 

Carnot,  Sadi,  valuable  researches  utilised 
by  Helmholtz,  Thomson,  and  Joule, 
i.  201 ;  absolute  scale  of  temperature, 
315  ;  the  steam-engine,  331  ;  mech- 
anical theory  of  heat,  ii.  105  ;  prac- 
tical character  of  his  labours,  117  ; 
'  Puissance  Motrice  '  quoted,  118, 
122 ;  analogy  between  flow  of  water 
and  of  heat,  122 ;  heat  theories, 
123 ;  perpetual  motion,  124,  126 ; 
and  Joule,  128  ;  dissipation  of  energy, 
130 ;  first  definite  use  of  new  con- 
ceptions of  power  and  work,  137 ; 
his  theory  refeiTed  to,  139  ;  second 
law  of  thermo-dynamics,  175. 

Carocher,  i.  113. 

Carpenter,  labours  of  von  Baer,  ii.  302  ; 
6U8. 

Carruthers  quoted  on  Hugh  Miller, 
i.  288. 

Cartesian  physical  jjhilosophy,  i.  433. 

Carus,  C.  J.,  phrenology,  ii.  477. 

Cams,  Victor,  '  Geschichte  der  Zoologie,' 
i.  130,  ii.  213  ;  comparative  anatom- 
ist, and  the  Naturphilosophie,  i.  207  ; 
'  Geschichte  der  Zoologie  '  quoted,  ii. 
220,  221,  230,  234,  237,  239,  260, 
265 ;  Goethe,  Oken,  and  the  genetic 
view,  317. 

Cassini,  i.  107,  113;  astronomical  con- 
stants, 322 ;  the  motion  of  light,  ii. 
10. 

Catabolism,  ii.  395,  442. 

Cauchy,  Augustin,  mathematics  and 
physics,  i.  45 ;  188 ;  theories  of  elastic 
forces  in  solid  bodies,  360 ;  properties 
of  ether,  ii.  31,  33  ;  theory  of  elasticity, 
31,  41  ;  molecular  researches  of,  43  ; 
analytical  method  of,  45  ;  referred  to, 
54  ;  school  of,  referred  to,  93,  1 00  ; 
influenced  German  thought,  101  ;  his 
reforming  influence,  &c.,  636 ;  and 
Gauss,  637  ;  Abel  on,  ib.;  Combes  on, 
ih.;  his  memoir  on  definite  integrals, 
639 ;  Legendre  on,  ib.  ;  640  ;  his 
'  Cours  d'Analyse  '  quoted,  647  ;  on 
Poncelet's  principle,  660;  680,  683, 
690;  and  Eiemann,  693,  695,  697, 
704,  706  ;  707,  732. 

Cavendish,  discovered  hydrogen,  i.  115  ; 
155 ;   scientific    discoveries    of,   229 ; 


not  member  of  any  university,  238 
important     papers      of,     lost,     277 
measurement     of    gravitation,    320 
measurements  of,  343  ;  founded  exact 
science  of  electricity,  347 ;  discoveries 
of,    354 ;    researches    of,    363 ;    and 
Lavoisier,     386,     387;     391,      393; 
chemical  equivalents,  418  ;  ii.  70. 

Cavendish  Society,  1.  43. 

Cayley,  Arthur,  and  PlUcker,  1.  242  ; 
developed  theories  of  Boole,  247 ; 
doctrine  of  "invariants,"  ii.  140; 
on  mathematics,  631;  on  "Curve," 
'  Encyclopffidia  Britannica,'  641  ;  on 
"deficiency,"  ih.;  on  extended  sys- 
tem of  numbers,  654  ;  670  ;  geometry 
and  modern  algebra,  671  ;  676,  684  ; 
his  great  memoirs  on  Quantics,  684, 
686,  691  ;  on  functions,  693  ;  on 
non-metrical  relations,  713  ;  on  the 
"Absolute,"  715;  on  the  "Imagin- 
ary," 716. 

Cell,  autonomy  of,  ii.  395. 

Cellular  theory,  i.  194 ;  ii.  260,  417  ; 
pathology,  i.  195. 

Celsus,  medical  works  of,  ii.  207. 

Centralisation,  ii.  524. 

Century  does  not  inherit  all  of  the 
past,  i.  56  ;  nineteenth,  the  scientific 
century,  89. 

Ceres,  discovery  and  rediscovery  of,  i. 
54,  82  ;  discovery  of,  423. 

Challis  and  the  discovery  of  Neptune, 
i.  277. 

Chambers,  Robert,  authorship  of  'Ves- 
tiges,'ii.  318;  320. 

Chambers,  Robert  and  William,  publish 
their  Journal,  i.  273. 

Chambers's  Encyclopedia,  "  Educa- 
tion," i.  257  ;  first  published,  273. 

Champollion,  "hieroglyphics,"  i.  244. 

Chances,  science  of,  ii.  668. 

Chaptal,  practical  discoveries  of,  i.  147. 

Charcot,  language,  ii.  539. 

Charles,  and  Gay  -  Lussac's  law  of 
temperatures,  i.  425,  429. 

Charles,  Duke  of  Wiirtemberg,  i.  133. 

Charles  II.  built  Greenwich  Observa- 
tory, i.  98  ;  ii.  562. 

Chasles,  Michel,  quoted  on  Monge,  i. 
114  ;  synthetic  method  of,  ii.  100 ; 
geometrical  mechanics,  101 ;  his  'Geo- 
metric supevieure'  quoted,  592,  658; 
670  ;  infinitely  distant  elements,  671 ; 
brilliant  writings  of,  673 ;  eclipses 
German  mathematicians,  673 ;  684, 
685. 

Chatelet,  du,  Madame,  explained  New- 
ton to  Voltaire,  i.  106. 


INDEX. 


761 


Chemical     laboratories    established,    i. 

188. 
Chemical  symbolism,  i.  417  ;  affinity, 
neglect  of  the  study  of,  420  ;  theory, 
Kopp  on,  421  ;  and  physical  reason- 
ing contrasted,  424  ;  affinity,  theories 
of,  452 ;  affinity,  ii.  157. 
'  Chemie,  Gehlen's  Allgemeines  Journal 

fiir,'  i.  41. 
'  Chemische  Annalen,'  Crell's,  i.  41. 

Chemistry,  a  French  science,  i.  114 ; 
equivalents,  399  ;  organic,  407  ;  Lie- 
big's  definition  of,  409  ;  substitution, 
ib.  ;  "type"  theory,  411  ;  uncertainty 
about  theory  in  middle  of  century, 
413 ;  periodic  law,  422  ;  structural 
and  stereo-chemistry,  447  ;  change  in 
definition  of,  454  ;  ii.  389  ;  change  in 
organic,  393. 

Chenier,  Marie  -  Joseph,  Report  on 
French  literature,  i.  149. 

Cherbuliez,  E.,  '  Ueber  einige  physik- 
alische  Arbeiten  Eulers,'  ii.  8  ; 
quoted,  46. 

Cheselden,  space -perception,  ii.  473; 
505. 

Chesterfield's,  Lord,  Letters,  quoted 
from,  i.   105. 

Chevalier,  Aug.,  Galois's  letter  to,  ii. 
686. 

Chevenix,  not  member  of  any  university, 
i.  238. 

Chevreul,  '  Recherches  sur  les  Corps 
gras  d'origine  aniniale,'  i.  454  ;  ii.  406. 

'Chimie,  Annales  de,'  issued  by  Ber- 
thollet,  i.  41. 

"Chirality"  discovered  by  Pasteur,  i. 
431 ;  origin  and  meaning  of  the  word, 
ii.  22  ;  437. 

Chladni,  '  Akustik,'  i.  83;  theory  of 
elasticity,  ii.  31. 

Chloral  discovered  by  Liebig,  i.  93. 

Chloroform  discovered  by  Liebig,  i.  93. 

Christiansen  and  Kundt,  discovery  of 
anomalous  dispersion  of  wave -motion, 
ii.  53,  54. 

Christie,  not  member  of  any  imiversity, 
i.  239. 

Christison  of  Edinburgh  University,  i. 
272. 

Chronometers,  i.  329. 

Chrystal,  G.,  PlLicker,  and  Faraday,  i. 
242;  "John  Napier,  Baron  of  Mer- 
chiston,'  quoted,  269;  on  David 
Gregory,  270;   "  Magnetism,"  ii.  75. 

Church  on  the  sjairal  theory,  ii.  224. 

Cicero,  ii.  523. 

"Cinematique,"  the  word  introduced 
by  Ampere,  ii.  5. 


Circle,  squaring  of  the,  ii.  124  ;  division 
of  the,  728. 

Clairault  followed  Newton,  i.  96  ;  his 
'  Theorie  de  la  Figure  de  la  Terre,' 
99  ;  referred  to  by  Voltaire,  106,  107  ; 
mathematics  made  fashionable  in 
France,  237 ;  Laplace  and,  319 ; 
lunar  theory,  329  ;  attempt  to  cor- 
rect Newton's  law,  334 ;  capillary 
attraction,  356,  378. 

Clapeyron,  i.  379  ;  suggested  earlier  re- 
searches of  Clausius  and  Thomson,  ii. 

117  ;    Caruot's    '  Puissance    Motrice,' 

118  ;  lieat  and  work,  123  ;  biographi- 
cal, ih. 

Clark,  J.  W.,  and  T.  M'K.  Hughes, 
'  Life  and  Letters  of  Adam  Sedgwick,' 
i.  267. 

Clark,  Latimer,  "  Weber  "  unit,  i.  369. 

Clarke,  Newton's  "descriptive  and 
calculating"  philosophy,  i.  337;  let- 
ter to  Leibniz  on  gravitation  quoted, 
340. 

Classics,  foreign,  superiority  in  nundjer 
and  quality  of  German  translations 
of,  i.  213. 

Classification,  ii.  231. 

Clausius,  Rudolf,  on  atoms,  i.  313 ; 
"Entropy,"  316,  ii.  169,  181,  184, 
594 ;  the  kinetic  theory  of  gases,  i. 
433,  ii.  34,  162  ;  '  Die  niechanische 
Warmetheorie,'  i.  434,  ii.  163,  167  ; 
"  on  the  average  mean  path  of  a  par- 
ticle," i.  438  ;  theoretical  thermo- 
dynamics, ii.  62  ;  independence  of 
Mayer's  writings,  97;  "work"  and 
"energy,"  115  ;  unifies  the  views  of 
Mayer  and  the  measurements  of 
Joule,  116;  "conservation  of  en- 
ergy," 128  ;  "dissipation  of  energy," 
131  ;  labours  of,  133,  173  ;  researches 
of,  133 ;  Prof.  Uuwin's  account  of 
theories  of,  135  ;  elaboration  of  Joule's 
and  Regnault's  experiments,  137  ; 
physical  view  of  nature,  141  ;  dyna- 
mical theory  of  heat,  148 ;  dissoci- 
ation, 163;  "free  energy,"  175  ; 
heat,  178  ;  theory  of  probabilities, 
590 ;  thermo-dynamics,  603. 

Clavius  quoted,  ii.  287. 

Clebsch,  A.,  on  Julius  PlUcker,  i.  242, 
ii.  75,  76,  677. 

Clifford,  W.  K.,  "axioms  of  geometry," 
i.  352  ;  refiex  action,  ii.  520  ;  "  mind- 
stutt""  theory,  546;  criticism  of  Clerk- 
Maxwell,  606,  608,  656  ;  on  Riemann, 
704. 

Cohu,  quoted,  ii.  559. 

Colbert  recognised  the  practical  value 


762 


INDEX. 


of  science,  i.  98  ;  134  ;  first  statisti- 
cal bureau,  ii.  5t)l. 

Coldiiig,  ii.  107,  lu9  ;  indestructibility 
of  force.  111,  125  ;  heat,  112. 

Coleridge  imports  philosophy  of  Kant 
and  Schelling  into  England,  i.  17  ; 
healthy   spirit   of,   78;    '  Christabel,' 

84  ;  influence  on  metaphysical  studies 
of,  91  ;  lectured  at  Royal  Institution, 
249,  264. 

College  de  France,  i.  107. 

Colh'ge  et  iScole  de  Chirurgie,  i.  107. 

CoUignon  (see  Combes),  ii.  101. 

Collins,  invention  of  the  calculus  by 
Leibniz  communicated  to,  i.  101. 

Colour,  ii.  484  et  seq. 

Combe,  Geo.,  phrenology,  ii.  477. 

Combes,  Phillips  et  Collignon,  '  Expose 
de  la  Situation  de  la  M^canique  ap- 
pliquee,'  ii.  101 ;  quoted  by  Valson  on 
Cauchy,  637. 

Combinatorial  school  in  Germany,  ii. 
642 ;  analysis,  Leibniz,  679 ;  Mac- 
Mahon  on,  ib. 

Combustion,  theory  of,  i.  389. 

Commutative  principle,  ii.  717. 

Compayre,  educationalist,  on  Rousseau, 
i.  259,  260. 

Complex  quantity,  ii.  643  ;  interpreta- 
tion of,  653. 

Comte,  Auguste,  philosophy  of,  i.  18, 
61,  ii.  105 ;  his  three  stages  of 
thought,  i.  73  ;  positivist  theory  of, 

85  ;  306  ;  '  Philosophie  Positive,'  307, 
308,  ii.  37,  239  ;  scientific  errors  of, 
i.  310  ;  opposed  to  undulatory  theory 
of  light,  ii.  37  ;  and  De  Blainville, 
247,  266  ;  theory  of  probabilities,  569, 
608 ;  749. 

Comtism,  failure  of,  i.  72. 

Condamine,  La,  astronomical  constants, 
i.  322. 

Condillac,  'Essai  sur  les  Origines  des 
Counaissances  humaines,'i.  144;  ne- 
glect of,  by  Napoleon,  149 ;  his 
ignorance  of  physiology,  ii.  471 ; 
language,  536. 

Condorcet,  importance  in  French  litera- 
ture of,  i.  105  ;  quoted,  110 ;  educa- 
tional work  of,  112 ;  the  theory  of 
lirobabilities,  120  ;  alliance  with  medi- 
cine, 126 ;  Academie  des  Sciences 
morales  et  politiques,  145  ;  suicide  of, 
147  ;  neglect  of,  by  Napoleon,  149  ; 
distinguishes  education  and  instruc- 
tion, 259,  260  ;  statistics,  ii.  570,  573. 

Conflict  between  the  scientific  and  the 
philosophical  views,  i.  205. 

Conformal    representation,   Gauss    and 


Riemann    on,    ii.    700 ;    Holtzmiiller 

on,  701. 
Congruences,  theory  of,  ii.  723  ;  calculus 

of,  724. 
Conrad,  Prof.,  'The  German  Universi- 
ties for  the  last  Fifty  Years,'  i.  159  ; 

quoted  on  German  universities,  160  ; 

'Die  Deutschen  Universitaten,'  197, 

198. 
Conring,  Hermann,  statistics,  1.  121,  ii. 

555  ;  political  statistics,  562. 
Consciousness,  ii.  516. 
Conservation  of  force,  i.  218. 
Constable,  his  influence  on  painting  in 

France,  i.  19. 
Constant,   Benj.,  visits  Germany  with 

Mme.  de  Stael,  i.  17. 
Continuity,  of  living  forms,  ii.  453 ;  in 

geometry,  660. 
Contifiuous,  the,  ii.  643. 
Convention,  decree  on  Academy  of,  i. 

148. 
Convergency  of  series,  ii.  646. 
Conybeare,  W.  D.,  report  on  the  jjro- 

gress  of  geological  science,  ii.  281. 
Cook,  Captain,  i.  52,  179 ;  voyages,  ii. 

222  ;  Von  Baer  on,  304. 
Cooper,  Astley,  English  medical  science, 

i.  2("i8  ;  no  connection  with  the  English 

universities,  272. 
Co-operation,  ii.  566. 
Cope,  E.  D.,  ii.  271  ;  neo-Lamarckian, 

351. 
Copernicus,  i.  118  ;  precursor  of  Kepler, 

317  ;    stimulated    star  -  gazing,    327  ; 

astronomical  theory  of,  ii.  13. 
Coriolis,  St  Veuant  quoted  on,  i.  369 ; 

practical  school  of,  ii.  100. 
Cornu,  "Association  Frau9aise,"  i.  298. 
Correspondence     in     mathematics,     ii. 

736. 
'  Correspondenz,  Monatliche,'  Zach's,  i. 

41. 
Corti,  arcades  of,  ii.  372. 
Cosmical  view,  ii.  369. 
Cosmos,  genesis  of  the,  ii.  360. 
Cossar  Ewart  on  Jameson,  i.  283. 
"Cost"  as  factor  in  industry,  ii.  155. 
Coste,  study  of  food  fishes,  ii.  232. 
Cotes,   Roger,    '  Aestimatio  errorum  in 

mixta  mathesi,' i.  324;  "description 

and  e-xplanation  of  phenomena,"  337  ; 

second   edition   of    'Principia,'   351; 

preface    to    '  Principia '    misleading, 

355. 
Cotton,    M.    A.,    "  Le    Phenomene    de 

Zeemann,"  ii.  197. 
Coulomb,     measurements    of,    i.    343, 

362,  368,  369  ;  founded  exact  science 


INDEX. 


763 


of  electricity,  347  ;  torsion  balance, 
360  ;  attraction  and  repulsion  of 
electritied  bodies,  361  ;  370 ;  two- 
fluid  theory  of  electricity,  ib.; 
electro-static  formula  of,  371  ;  Young 
and,  ii.  30  ;  modern  view  of  electrical 
phenomena,  67  ;  7-  ;  referred  to,  78, 
92  ;  laws  of,  79 ;  practical  school  of, 
100 ;  electrical  theory  of,  153 ;  the 
atomic  view  of  nature,  188,  191, 
193;  698. 

Counting  and  measuring,  ii.  732. 

Couper,  chemical  researches  of,  i.  447. 

Courcier,  geometrical  work  of,  i.  114. 

(Journot,  testimony  to  work  of  German 
universities,  i.  225. 

Cousin  guillotined,  i.  147. 

Cousin,  Victor,  testimony  to  work  of 
German  universities,  i.  225. 

Couturat,  L.,  ii.  734. 

Cowley,  Ode  on  Bacon,  i.  96. 

Cowper,  'The  Task,'  i.  285;  Letters, 
2S6. 

Cramer,  'Analyse  des  lignes  courbes,' 
&c.,  ii.  682. 

Crawford,  Dr,  influenced  by  Black's 
lectures,  ii.  102. 

Crell's  'Chennsche  Annalen,'  i.  41. 

Crelle's  '  .Journal  liir  die  reine  und 
angewandte  Mathematik,'  i.  41,  186, 
ii.  58 ;  correspondence  with  Gauss, 
185. 

Cremona,  i.  188 ;  quoted,  ii.  665  ; 
proves  Steiner's  theorems,  681. 

Critical  methods,  ii.  626. 

Crofton,  M.  W.,  "Probabilities,"  ii. 
569. 

Crome,  Prof.,  statistics,  ii.  579. 

Cronsted,  inventor  of  blow-pipe,  i.  117. 

Crookes,  Sir  William,  quoted  on  Prout's 
hypothesis,  i.  403 ;  sodium  vapour 
in  the  sun's  atmosphere,  ii.  48 ;  ex- 
periments and  discoveries,  190  ;  "cor- 
puscular" theory  of  cathode  rays, 
192  :  (see  Sir  Norman  Lockyer),  361. 

Cruveilhier,  French  medical  science,  i. 
208. 

Crystallographic  and  atomic  laws,  anal- 
ogy between,  i.  444. 

Crystallography,  i.  116,  441. 

Crystals,  laws  of  formation  of,  Haliy's, 
i.  117  ;  ii.  222. 

Cullen,  metaphysical  leaning  in  medi- 
cine, i.  126 ;  272. 

Culverwell,  ii.  595. 

Curie,  geometrical  treatment  of  crystal- 
lography, i.  443. 

Currie,  first  use  of  thermometer  at 
bedside,  ii.  388. 


Curtius,  Ernst,  '  Alterthum  und  Gegen- 
wart,'  i.  215;  on  English  archae- 
ologists, 294  ;  quoted,  295  ;  on  M.  W. 
Leake,  296. 

Curves,  degree,  class,  genus  of,  ii.  641. 

Cuvier,  Georges,  scientific  report  of, 
i.  42,  152,  1.54  ;  '  Tableau  '  and 
'Le9ons,'  82;  112;  on  Priestley  as 
chemist,  115  ;  on  Haliy,  118 ;  ad- 
vance in  study  of  organic  life,  119  ; 
services  of,  to  practical  science,  125 ; 
126  ;  Eloge  of  Halle,  127  ;  '  Le  Regne 
animal,'  128  ;  quoted,  129,  132,  141, 
146,  147,  150,  ii.  249  ;  makes  nervous 
system  of  animals  the  basis  of  classi- 
fication, i.  130 ;  training  of,  133 ; 
description  of  the  "  Karlschule,"  134; 
the  greatest  representative  of  the  aca- 
demic system,  136 ;  first  great  his- 
torian of  science,  137  ;  quoted  on 
science  and  revolution  ,138  ;  palfeon- 
tological  work  of,  139  ;  Eloge  of  Four- 
croy,  140  ;  elementary  scientific  text- 
books, 143  ;  report  of  French  Insti- 
tute, 149  ;  educational  institutions, 
155 ;  163,  171  ;  mistrusted  specu- 
lative spirit  in  science,  178  ;  his 
ideas  triumph  over  those  of  Geoffroy 
St  Hilaire,  179  ;  200  ;  in  praise  of 
French  science,  231  ;  quoted  on 
science  in  England,  235 ;  264  ;  and 
Brougniart,  founders  of  palaiontology, 
291  ;  306 ;  depreciated  by  Comte, 
310 ;  zoological  labours,  ii.  222  ; 
study  of  fossil  remains,  225 ;  ana- 
tomical dissection,  232 ;  zoological 
work,  235  ;  morphological  and  ana- 
tomical study  of  animal  life,  237 ; 
classifications,  238,  239,  254;  fos- 
sils, 240;  rejects  idea  of  "Echelle 
des  etres,"  243 ;  controversy  with 
Geoft'roy,  246,  253 ;  palaeontology, 
247  ;  "catastrophism,"  250,  251 ;  and 
"  theory  of  analogies,"  254 ;  the 
question  of  the  fixity  of  species, 
256 ;  comljats  influence  of  Oken, 
259  ;  extension  of  morphological 
view,  260,  266 ;  influence  of,  276 ; 
'Ossemens  fossiles,' 277  ;  exploration 
of  Paris  basin,  294 ;  one-sided  in- 
fluence, of,  300,  301  ;  and  Buflbn, 
309  ;  Eloge  <le  Lamarck,  316;  views 
of  Lamarck  and  Geoffroy,  320  ;  and 
Newton,  contrasted  with  Darwin, 
341  ;  a  founder  of  comparative  an- 
atomy, 386,  406;  "vortex,"  422; 
751. 

"Cyclical"  view,  ii.  286. 

Cyclopaedia,  Nichol's,  i.  330,  ii.  133. 


764 


INDEX. 


Cyclopaedias,  i.  273. 

Cyriacus  of  Ancona,  archseological 
pioneer,  i.  295. 

Czapski,  '  Theorie  der  optischen  lustru- 
mente  nach  Abbe,'  ii.  14,  229. 

Czermak,  language,  ii.  538. 

Czuber,  Emmanuel,  theory  of  probabili- 
ties, ii.  568  ;  method  of  least  squares, 
576. 

Dacier,  Report  on  the  progress  of  His- 
tory and  Classical  Literature,  i.  149. 

Daguerre,  photography,  ii.  506. 

Dahlmann,  "  theoretical  politician,"  i. 
311. 

D'Alembert,  contributions  to  the  En- 
cyclopedic, i.  34,  144  ;  his  import- 
ance in  French  literature,  105 ; 
theory  of  probabilities,  120 ;  215,  234, 
237  ;  the  cure  of  smallpox,  284  ;  319  ; 
mathematical  study  of  vibrations,  ii. 
16  ;  "measure  of  force,"  'Traite  de 
Dynamique,'  100  ;  statistics,  571 ;  on 
functions,  694. 

Dallas,  ii.  349. 

Dalton,  John,  'New  System  of  Chem- 
ical Philosophy,'  i.  83  ;  atomic  theory, 
189,  266,  385,  394,  415-417,  419,  425, 
426,  428,  ii.  180  ;  scientific  discov- 
eries of,  i.  229  ;  not  member  of  any 
university,  238,  272 ;  neglect  of,  in 
England,  245  ;  arithmetical  mind  of, 
246 ;  furnished  texts  for  lectures 
in  German  universities,  251  ;  265 ; 
science  of  meteorology,  286 ;  298, 
311,  313 ;  heat  a  material  substance, 
433  ;  formula  of,  436  ;  analogy  be- 
tween crystallographic  and  atomic 
laws,  444 ;  his  atomic  theory  insuffi- 
cient, 451  ;  atomic  theory  referred  to, 
ii.  19,  20,  37,  95,  153,  154;  colour 
blindness,  505. 

Dannecker  educated  with  Cuvier,  i. 
133. 

Dante,  i.  261. 

Danton,  i.  107. 

Darwin,  Charles,  constructive  ideas  of, 
i.  81  ;  eminence  of  writings  of,  105  ; 
179  ;  letter  from  Sir  Charles  Lyell  on 
British  Association,  240;  theory  of 
descent,  201,  ii.  321,  406  ;  furnished 
texts  for  lectures  in  German  univer- 
sities, i.  251,  310  ;  '  Cirripedia' mon- 
ograph, 283;  'Autobiography,'  ih.; 
nature  -  lover,  287  ;  and  Gilbert 
White,  290 ;  297,  312 ;  referred  to, 
ii.  136;  value  of  his  visits  to  distant 
countries,  207 ;  studies  of  organic 
life,   209  ;   law  of  descent,  214  ;  con- 


ceptions of,  246  ;  and  Owen,  267 ; 
theory  of  pangenesis,  271,  454  ;  writ- 
ings of,  301,  306  ;  309  ;  on  Lamarck, 
318;  'Origin  of  Species,'  326,  329; 
'Life  and  Letters,'  328;  and  Mal- 
thus,  331 ;  '  Origin  of  Species '  quoted, 
336;  Bates's  "Mimetic  Butterflies," 
339  ;  and  Newton  compared,  341 
et  seq.  ;  "natural  selection,"  351, 
354  ;  434,  437  ;  hybridisation,  373  ; 
"  final  causes,"  403  ;  408  ;  struggle 
for  existence,  418 ;  421  ;  environ- 
ment, 430  ;  conflict  in  nature,  431 ; 
435,  436,  451  ;  quoted,  457 ;  and 
Weismann,  460;  467,  470;  'Ex- 
pression of  Emotions,'  477 ;  511, 
514  ;  evolution,  530  ;  and  Herder's 
evolutionism,  533  ;  language,  540 ; 
587,  607  ;  variation  in  nature,  608  ; 
on  mental  phenomena,  609  ;  on  "  pan- 
genesis," 610;  621  ;  two  novel  points 
of  view  of,  624. 

Darwin,  Erasmus,  anticipated  Lam- 
arck, i.  201  ;  285  ;  colour  sensations, 
ii.  482. 

Darwin,  Francis,  '  Life  and  Letters  of 
Charles  Darwin,'  ii.  329. 

Darwin,  G.  H.,  '  The  Tides,'  u.  282. 

Darwin,  Robert  W.,  colour  sensation, 
ii.  482. 

Darwinism,  i.  251,  ii.  386  ;  and  final 
causes,  411  ;   in  Germany,  436. 

Daubenton  at  the  College  de  France, 
i.  107  ;  natural  history  at  the  Ecoles 
normales,  112  ;  113  ;  collection  of 
fossil  remains,  ii.  248. 

Daunou,  Academic  des  Sciences  mor- 
ales et  politiques,  i.  145  ;  152. 

Davy,  Sir  Humphry,  electro-chemical 
discoveries  of,  i.  83,  189,  363  ;  scien- 
tific work  of,  229  ;  science  in  Eng- 
land, 234  ;  not  member  of  any  uni- 
versity, 238,  272  ;  opposed  Dalton's 
atomic  theory,  245,  246  ;  studied  in 
laboratory  of  Royal  Institution,  249, 
264  ;  educated  Faraday,  265  ;  un- 
connected with  Cambridge  mathe- 
matical school,  266 ;  electric  action 
in  chemical  processes,  366 ;  decom- 
position of  soda  and  potash,  391, 
404  ;  electro  -  chemical  theory,  405, 
452  ;  salts  and  acids,  410  ;  attitude 
to  Dalton's  theory,  417 ;  attitude 
towards  the  atomic  theory,  418  ; 
428 ;  chemical  application  of  elec- 
tricity, ii.  92  ;  electro-chemistry,  93  ; 
heat  and  chemical  change,  102  ;  atti- 
tude to  science  that  of  a  medical 
man,   103  ;   vibratory  view   of  heat, 


INDEX. 


765 


104  ;  indestructibility  of  force,  111  ; 
the  dynamical  theory  of  heat,  128  ; 
154  ;  agricultural  chemistry,  391, 

Dawson,  John,  i.  267. 

De  Bary,  embryological  studies  of 
plant  life,  ii.  228. 

De  Blaiuville,  indebtedness  of  Cuvier 
to,  i.  130  ;  organisation,  ii.  236;  239  ; 
'  Cuvier  et  Geoflroy  Saint  Hilaire,' 
247,  255;  'Osteographie,'  257;  266; 
unity  of  organisation,  267  ;  ' '  com- 
2:)Osition  et  decomposition,"  421  ; 
school  of,  431. 

Decade  philosophique  ridiculed  the 
fall  of  meteors,  i.  327. 

De  CandoUe,  A.  P.,  botanist,  ii.  222; 
theories  of  symmetry,  223  ;  '  Organo- 
graphie  vegetale '  quoted,  230,  236, 
261,  265,  266  ;  '  Theorie  elementaire 
de  la  Botanique '  quoted,  235  ;  mor- 
phological view,  239 ;  quoted,  240, 
242,  269  ;  regularity  and  symnietry 
in  organic  nature,  241  ;  symmetry  of 
form,  243  ;  appreciation  of  Goethe's 
work,  quoted,  244  ;  influence  of,  276. 

Decher  (see  Clausius),  ii.  135. 

Decimal  fractions,  ii.  645,  731. 

Dedekind,  R.,  biographical  notice  of 
Riemann,  i.  352  ;  and  Dirichlet,  ii. 
721  ;  726,  729  ;  on  irrational  num- 
bers, 733,  734,  737. 

De  Gerando,  i.  149. 

De  Haen,  i.  208. 

Delage,  Yves,  history  of  the  study  of 
organic  life,  ii.  232  ;  '  L'Heredite  et 
les  grands  problemes  de  la  Biologie,' 
265,  364,  371,  372,  444,  4.55,  458,  459  ; 
'L'Heredite'  quoted,  271,  298,  348, 
349,  406,  421,  427,  447,  461 ;  structure 
of  protoplasm,  370;  school  of  "  or- 
ganicism,"  436. 

De  la  Hire,  ii.  664,  667. 

Delambre,  i.  113 ;  report  of  French 
Institute,  149  ;  quoted  on  statistical 
methods  in  France,  153. 

Delambre  and  Cuvier,  scientific  reports 
of,  i.  42. 

Delaunay,  lunar  theory,  i.  329. 

De  Luc,  attacks  on  Hutton,  ii.  291, 

Democritus  of  Abdera,  founder  of 
atomistic  theory,  i.  385  ;  animation 
of  all  matter,  ii.  369. 

De  Moivre,  doctrine  of  chances,  ii.  678. 

Derand,  geometrical  work  of,  i.  114. 

Derham,'^Dr  Wm.,  'Physical  Theology,' 
ii.  565. 

Descartes,  constructive  system  of,  i. 
75  ;  and  Bacon,  84 ;  123,  137  ;  and 
the  philosophy  of  Kant,  222 ;  Order 


of  Jesus,  256 ;  Harvey's  discovery, 
282 ;  discovery  of  reflex  action, 
292;  'Les  Passions  de  I'Ame,'  293; 
311,  313  ;  his  philosophy  and  New- 
ton's contrasted,  338;  qimlitates  oc- 
cultce,  351 ;  Snell's  experiments  in 
deflection  of  light  rays,  356  ;  develop- 
ment of  kinetic  view,  ii.  6  ;  Euler's 
opposition  to,  8  ;  theoretical  hydro- 
dynamics, 58 ;  older  vortex  theory 
and,  62  ;  the  measure  of  force,  100  ; 
influence  on  German  philosophy,  205  ; 
theory  of  vortices,  360  ;  a  founder  of 
modern  physiology,  378';  study  of 
biology,  379,  380  ;  idea  of  life,  409, 
410;  school  of  '•  organicisme,"  436, 
455  ;  470,  519,  638,  641,  697. 

Descent,  theory  of,  i.  201. 

Descriptive  geometry,  ii.  658  et  seq. 

Deshayes,  history  of  invertebrates,  ii. 
239;  Lamarck,  310. 

Destructive  spirit  in  writings  of  eigh- 
teenth century,  i.  78. 

Destutt  de  Tracy,  '  Ideologic,'  i.  83  ; 
alliance  with  medicine,  126 ;  152 ; 
ideologist,  ii.  472. 

Determinants,  ii.  682  ;  history  of,  ib. 

Development,  study  of,  ii.  264. 

Deville,  Sainte  Claire,  ii.  162. 

De  Wette,  theologian,  influenced  by 
school  of  Fries,  i.  209,  273. 

Diamagnetism,  ii.  74. 

Dickson,  J.  D.  H.,  quoted  byGalton, 
ii.  619. 

Diderot  on  the  genesis  of  new  words,  i. 
21  ;  his  Encyclopedie,  34,  144,  215. 

"  Dielectric,"  ii.  68. 

Differential  equations,  general  theory 
of,  ii.  692  ;  Sophus  Lie  on,  ib. 

"Diffraction,"  Fresnel's  memoir  on,  ii. 
25,  27. 

Dilthey,  '  Sclileiermacher,'  i.  279. 

Dingeldey,  '  Topologische  Studien,'  ii. 
64. 

Dingler's  '  Polytechnic  Journal,'  ii. 
134. 

Dini,  Ulisse,  on  theory  of  functions,  ii, 
704. 

Dionis  du  Sejour,  death  of,  i.  147. 

Dirichlet,  Lejeune,  lectures  on  mathe- 
matical physics,  i.  44  ;  discourse  on 
Jacobi,  185 ;  quoted,  186,  188,  189  ; 
Fourier's  series,  241  ;  on  Steiner,  ii. 
670  ;  680  ;  and  Fourier,  694  ;  his  and 
Thomson's  principle,  700,  704,  708 ; 
721,  726,  728. 

Dissociation,  ii.  163. 

Distribution,  ii.  566. 

Dobereiner,  i.  190. 


766 


INDEX. 


Dohrn,  Anton,  seaside  laboratory 
fonnded  at  Naples,  ii.  232. 

Dulliuger,  Tgnaz,  evolutionist,  and  the 
Naturphiiosophie,  i.  207;  scientific 
researches,  ii.  299  ;  303. 

DoUond,  not  member  of  any  university, 
i.  238 ;  astronomical  instruments, 
322. 

Domesday-Book,  ii.  555. 

Bonders, 'on  language,  ii.  538. 

Donner's  rendering  of  the  Greek  dram- 
atists, i.  213. 

Dopider,  enunciated  the  principle  of 
iUimer's  discovery,  ii.  10  ;  his  prin- 
ciple of  wave-motion,  49. 

Dove,  meteorology,  i.  205. 

Downs,  0.  G.,  ii.  579. 

Dreyfus-Brisac,  testimony  to  work  of 
German  universities,  i.  225. 

Driesch,  Hans,  ii.  342;  "  organicisme," 
455  ;  works  of,  456  ;  463,  549. 

Drobisch,  psychologist,  ii.  494,  497 ; 
pretensions  of  statistics,  586. 

Drude,  P.,  ii.  38. 

Drummond  and  Edinburgh  University, 
i.  269. 

Drummond,  Henry,  ii.  326. 

Drummond,  Thomas,  spectrum  analysis, 
i.  278. 

Duality,  principle  of,  in  geometry,  ii. 
665. 

Dublin  school  of  mathematicians,  i. 
274,  ii.  673. 

Du  Bois-Reymond,  Emil,  on  the  intro- 
duction of  new  ideas  from  abroad, 
i.  16  ;  45  ;  limits  of  the  knowable, 
53  ;  106  ;  the  speculative  tendency  in 
science,  179;  'Reden,'  188,  215,  ii. 
149  et  seq. ;  '  Gediichtnissrede  auf 
Joh.  Miiller,'  i.  198,  293;  voltaic 
elettricity,  199 ;  quoted,  216,  ii. 
270,  381,  469,  478  ;  mechanical  view 
of  biology,  i.  219  ;  Bell's  doctrine, 
293 ;  '  Akademie  der  deutschen 
Sprache,'  298  ;  '  Ueber  die  Grenzen  des 
Natnrerkennens,'  348  ;  objections  to 
Kirchhoff's  definition  of  "mecl,ianics," 
383  ;  researches  of,  ii.  208 ;  Eloge  of 
Johannes  Miiller,  384,  419,  482  ;"'391, 
revolution  in  physiological  studies, 
396 ;  '  Researches  in  Animal  Elec- 
tricity,' 397  ;  401 ;  position  in  vitalistic 
controversy,  403 ;  essay  on  Vital 
Force,  405;  408,  409,  411;  on  the 
principle  of  natural  selection,  quoted, 
414;  vitalism,  434;  "Darwin  versus 
Galiani,"  quoted,  4-35;  "Exercise," 
436 ;  active  nervous  system,  438 ; 
animal    electricity,    475,    476 ;  481  ; 


principle  of  reflex  action,  519  ;  546, 
743. 

Du  Bois  -  Reymond,  Paul,  services  to 
scientific  reasoning,  i.  45  ;  103 ; 
'  Grundlagen  der  Erkenntniss  in  den 
exacten  Wissenschaften,'  341  ;  377  ; 
gravitation  "  unknowable,"  852  ; 
kinetic  theory  of  gases,  433  ;  works 
of,  ii.  631,  705 ;  theory  of  functions, 
704  ;  on  arithmetising,  739. 

Du  Chatelet,  Madame,  letter  from  Vol- 
taire to,  i.  105. 

Duchesne,  physiognomy,  ii.  477. 

Duclos,  on  education,  i.  259. 

Ducos  quoted,  i.  109. 

Dufay,  controversy  on  electric  fluid,  i. 
362. 

Duhamel,  mechanics,,  i.  44;  taught 
metallurgy  at  the  Ecole  des  Mines, 
107. 

Duhem  (see  Prof.  Ostwald),  ii.  159  ; 
labours  of,  Horstmann,  170 ;  thermo- 
dynamic potential,  173  ;  '  Mecanique 
chimique,' 173  ;  chemical  equilibrium, 
175. 

Diihring,  E.,  '  Kritische  Geschichte  der 
allgemeinen  Principiien  der  Mechauik,' 
ii.  97,  101 ;  historical  and  controversial 
writings,  107. 

Dujardin,  Felix,  sarcode,  ii.  264  ;  defini- 
tion of  a  cell,  265. 

Dulong  and  Petit,  specific  heat  of  bodies, 
i.  428,  429. 

Dumas,  '  Le9ous  sur  la  Philosophie 
chimique,'  i.  114 ;  revives  Front's 
hypothesis,  402,  403 ;  explanation  of 
"isomerism,"  406;  the  "radicle" 
theory,  409 ;  attack  on  electro- 
chemical theory,  ib.  ;  410;  "type" 
theory,  411;  413;  attitude  towards 
the  atomic  theory,  418  ;  quoted,  421, 
ii.  370,  441;  i.  402,  428;  spectro- 
scopic observations,  ii.  361  ;  '  Essai 
de  Statique  chimique  des  Etres 
organises,'  392  ;  substitution  in  chem- 
istry, 393  ;  406. 

Duncker,  G.,  statistics  of  variation,  ii. 
622. 

Dlintzer,  ii.  531. 

Dupin,  Charles,  ii.  579  ;  658. 

Dutens,  '  Leibnitii  Opera  Omnia,'  ii. 
280. 

Dutrochet,  Bell's  theorem,  i.  293 ;  ii. 
230,  261. 

Dynamics,  ii.  5  ;  and  statics,  144. 

Eckermann  quoted,  ii.  253. 
Ecole  centrale  des  Travaux  publics,  i. 
112. 


INDEX. 


767 


Ecole  des  Fonts  et  Chaussees,  i.  107. 

Ecole  normale  superieure,  i.  112,   113, 

,  237. 

Ecole  polytechnique  of  Paris,  i.  112  ; 
used  as  model  for  German  poly- 
technic schools,  166. 

Ecole  veterinaire  d'Alfort,  i.  107. 

Ecoles  de  Sante,  i.  113  ;  founded  at 
Paris,  Strasbourg,  and  Montpellier, 
142. 

Economics  and  biology,  ii.  415. 

Edgeworth,  Prof.,  "  The  Law  of  Error," 
ii.  576. 

'  Edinburgh  Magazine  and  Review  ' 
issued,  i.  273. 

'  Edinburgh  Pieview,'  literary  criticism 
of,  i.  84  ;  233  ;  quoted,  234,  235,  236; 
on  English  universities,  254  ;  270  ; 
first  issued,  273 ;  Brougham's  attack 
on  Young,  ii.  19. 

Edison,  phonograph,  ii.  490. 

Education,  aud  instruction,  i.  258  ; 
liberal,  ideal  of,  255. 

Educational  conflict  on  discipline,  i. 
133. 

Educational  efforts  in  different  countries, 
i.  252  et  seq. ;  in  Scotland,  253  ;  liter- 
ature of  Switzerland,  ih. 

Educational  institutions,  French,  i.  112. 

Educational  organisations  in  England, 
i.  262. 

Edward,  Thomas,  shoemaker  aud  zool- 
ogist, i.  287. 

Edwards,  George,  'History  of  Birds,'  i. 
287. 

Edwards,  Milne,  '  History  of  Inverte- 
brates,' ii.  239  ;  Lamarck,  310  ;  Hux- 
ley on,  322;  "physiological  division 
of  labour,"  396. 

Ehrenberg,  '  Ueber  Leibnitzens  Meth- 
ode,'  ii.''280. 

Eighteenth  century,  one  of  revolution, 
i.  77. 

Eisenstein,  and  theory  of  numbers,  ii. 
684. 

Elasticity,  theory  of,  ii.  30,  40  ;  31  ; 
foundation  of  theory  of,  41. 

Electrical  and  magnetic  action,  i.  344. 

Electricity,  aud  magnetism,  ii.  64  et  seq.; 
velocities  of  light  and,  compared,  84  ; 
modern  researches,  189  ;  electric  dis- 
charges, 195  ;  animal,  475. 

Electro-dynamics,  Wilhelm  Weber's  law 
of,  i.  196  ;  ii.  149. 

Electro-magnetic  theory,  ii.  64 ;  in- 
definiteness  of,  93  ;  153. 

Electro-magnetism,  discovery  of,  i.  92. 

Electrolysis,  ii.  154  et  seq. 

Electron,  the  term,  ii.  193. 


"Electrotonic  "  state  of  matter,  ii.  68, 
81. 

Elizabeth,  England  under,  i.  67. 

Elliptic  functions,  history  of,  ii.  648 
et  seq. 

Ellis,  Alex.  T.,  on  terminology  of  sound, 
ii.  489. 

Ellis,  Robert  Leslie,  on  Bacon,  i.  94, 
96  ;  his  report,  ii.  649. 

Elphinstone,  Bishop,  started  Aberdeen 
University,  i.  268. 

Elster  aud  Geitel,  vacuum  tube  ex- 
periments, ii.   190. 

Emanations,  law  of,  i.  344. 

Embryology,  ii.  296. 

Ernpedocles,  relation  to  Galileo  and 
Newton,  i.  313  ;  attraction  and  repul- 
sion, 385  ;  recurrent  cycles,  ii.  287. 

Encke,  "calculus  of  probabilities,"  i. 
325. 

'  Encyclopadie  der  Mathematischen 
Wissenschaften,'  ii.  73. 

Encyclopadie,  lectures  on,  i.  37. 

'Encyclopedia  Britannica,'  article  on 
Napier,  i.  269  ;  first  published,  273  ; 
article  on  "Agriculture"  quoted, 
284;  article  on  F.  Mohr,  ii.  106; 
article  on  Sainte  Claire  Deville,  163  ; 
232,  279,  569. 

'  Encyclopaedia  Metropolitana,'  i.  236. 

Eucyclop;edia  of  Ersch  and  Gruber,  i. 
35. 

Eucyclopjedias,  origin  of,  i.  40. 

Encyclopedic  treatment  of  learning, 
age  of,  i.  34,  215  ;  view  necessary  in 
philosophy  ami  history,  203  ;  treat- 
ment of  scientific  subjects,  214. 

Encyclopiedists  followed  Newton,  i.  96  ; 
constructive  work  of  school  of,  110  ; 
educational  influence  of,  112. 

Energetics,  science  of,  ii.  141  ;  166 ; 
kinetics  and,  1>^Q. 

Energy,  conservation  of,  i.  199,  201  ; 
theory  of,  ii.  87,  96 ;  works  deal- 
ing with,  97  ;  dissipation  of,  97,  364  ; 
the  term  first  used  by  Young,  98  ; 
notion  of,  contained  in  Newton's 
'Principia,' 99  ;  the  term  introduced 
by  Thomson,  115;  and  "Force," 
115  ;  availability  and  dissipation  of, 
119;  doctrine  of,  124;  revolutions 
brought  about  by  idea  of,  137 ; 
"  potential  "  and  "actual,"  139,  398  ; 
influeuce  of  doctrine  of,  399  ;  circu- 
lation of,  420  ;  465 ;  availability  of, 
594. 

Engel,  F.,  on  taste  in  mathematics,  ii. 
632  ;  on  genesis  of  Lie's  ideas,  692. 

England,    science    and  philosophy  in, 


768 


INDEX. 


during  the  early  part  of  the  century, 
i-  75.  ^   . 

English  character,  individualism  of,  i. 

279  ;  changes  during  last  fifty  years, 

280  ;  love  of  nature,  284,  286  ;  Hankel 
on,  ii.  704,  711. 

Enneper,  '  Elliptische  Functionen,'  i. 
18.^  187. 

Entropy,  ii.  169  et  seq.,  181,  594. 

Enumeration,  ii.  561. 

"Environment,"  ii.  314,  430. 

Epicurus,  "essential  and  inherent 
gravity,"  i.  340;  natural  philosophy 
of,  ii.  4. 

Epigenesis  and  evolution,  ii.  298. 

Equations,  theory  of,  Abel,  ii.  681 ; 
general  solution  of,  687  et  seq. 

Equivalents,  chemical,  i.  399, 

Erasmus,  i.  163. 

Erdmann,  misprint  in  his  '  Grundriss 
der  Geschichte  der  Philosophic,'  i. 
50  ;  ii.  495,  512. 

Erlsberg,  ii.  271. 

Ernest  Augustus,  Elector  of  Hanover, 
i.  158. 

Ernest  II.,  Duke  of  Gotha,  i.  54,  176; 
patron  of  the  astronomer  von  Zach, 
177  ;  system  of  education  of,  256. 

Error,  element  of,  i.  323  ;  theory  of,  ii. 
568,  574. 

Ersch  and  Gruber,  Encyclopasdia  of,  i. 
35. 

Eschenburg,  representative  of  encyclo- 
paedic teaching,  i.  38. 

Ether,  luminiferous,  theory  of,  ii.  18  ; 
properties  of,  31  ;  nature  of,  36  ;  hy- 
pothesis of,  37 ;  Sir  0.  Lodge  on 
nature  of  the,  38 ;  nature  of,  40 
et  seq. ;  mathematical  and  experi- 
mental investigation  of,  44  ;  an 
"elastic  solid,"  54;  luminiferous, 
69,  70. 

Etymology,  value  of,  for  history  of 
Thought,  1.  20. 

Eucken,  R.,  on  philosophical  termin- 
ology, i.  21, 

Euclid    preferred  in  ^England    to    Le- 
gendre,   i.  44  ;  his   works  models   of 
scientitic  thought,    95 ;    120,    ii.    4 ; 
Proclus  on,  634  ;  Klein  on,  635  ;  718, 
733. 
Eudenms  of  Rhodes,  ii.  633. 
Eudo.xus,  Proclus  on,  ii.  634. 
Euler,    Leonhard,   freed  analysis  from 
geometrical    fetters,    i.     103 ;     135 ; 
competed  with  T.  Mayer,  158  ;  163 ; 
connection  of,  with  modern  science, 
175  ;     181,     183,     234  ;     analytical 
methods  of,  271 ;  mathematics,  44 ; 


819  ;  lunar  theory,  329 ;  Newton's 
gravitation  formula,  334  ;  "  Ur- 
sache  der  Gravitation,"  341  ;  ether 
theory  of  gravitation,  343,  346,  351  ; 
unfavoiu'able  to  Boscovich's  theory, 
358  ;  ii.  7  ;  '  Anleitung  zur  Natur- 
lehre,'8;  the  successor  of  Huygens, 
16,  17  ;  studies  in  elasticity,  30 ; 
spectrum  analysis,  46  ;  psycho-phy- 
sics, 474  ;  510,  637  ;  introduces  con- 
ception of  "function,"  639  ;  643,  646, 
648  ;  on  different  mathematical  inter- 
ests, 657  ;  669,  680,  692,  694,  695, 
721. 

Evelyn,  John  (see  Arundel  collection), 
ii.  564. 

Everett,  "character"  in  music,  ii.  489. 

Evohition,  ii.  210,  278. 

Ewald,  on  Humboldt's  geological  work, 
ii.  226 ;  253. 

Ewing,  'The  Steam-Engine,'  ii.  136. 

Exner,    'Repertorium    der   Physik,'   i. 
323. 

Exploration,  the  spirit  of,  ii.  206  et  seq. 

Externalisation,  ii.  525. 

Fabricius  of  Acquapendente,  teacher  of 
Harvey,  i.  282. 

Fagnano,  Count,  Euler  on,  ii.  657. 

Falk,  Johannes,  follower  of  Pestalozzi, 
i.  258. 

Faraday,  electrical  theories  of,  i.  199  ; 
electrical  researches,  201,  ii.  86 ; 
electrical  and  other  discoveries  of,  i. 
230 ;  science  in  England,  236 ;  not 
member  of  any  university,  239,  272  ; 
and  Pllicker,  242  ;  neglected  in  Eng- 
land, 246  ;  studied  in  laboratory  of 
Royal  Institution,  249 ;  furnished 
texts  for  lectures  in  German  univer- 
sities, 251 ;  at  Royal  Institution, 
264,  ii.  80 ;  educated  by  Davy,  i. 
265;  "lines  of  force,"  266,  ii.  68, 
182  ;  not  connected  with  Cambridge 
mathematical  school,  i.  266 ;  neglect 
of  his  writings,  277  ;  279,  297  ;  gravi- 
tation, 344  ;  electricity,  345  ;  sym- 
bolism, 347  ;  nature  of  matter,  358  ; 
discovery  of  electrical  induction,  363 ; 
method  of  measuring  the  electric 
current,  365 ;  electrical  action  in 
chemical  processes,  366 ;  discovery 
of  magnetic  induction,  368,  371  ;  his 
influence,  380;  discovery  of  "iso- 
merism," 406;  his  attitude  towards 
the  atomic  theory,  418  ;  431  ;  theory 
of  chemical  affinity,  452  ;  researches 
of,  ii.  35  ;  modern  view  of  electrical 
phenomena,    66;    "magnetisation   of 


INDEX. 


769 


light,"  74  ;  electro-magnetic  radiation, 
77  ;  and  Thomson,  78  ;  galvanic  cur- 
rents, 79  ;  and  Clerk  -  Maxwell,  80  ; 
" electrotonic  state"  of  matter,  81  ; 
tubes  of  force,  83  ;  electricity  in 
motion,  93  ;  and  Poggendorf,  107  ; 
referred  to,  111 ;  indestructibility  of 
force,  lb. ;  correlation  and  inter- 
cbangeability  of  natural  forces,  119  ; 
"force,"  125;  "  regelation  of  ice," 
127  ;  indestructibility  of  force,  130  ; 
electricity  in  space,  145  ;  electro- 
magnetic field,  146  ;  electrolytic  law, 
154,  157 ;  results  of  experimental 
work  of,  161  ;  law  of,  165 ;  atomic 
view,  189 ;  observations  of  vacuum 
tube  phenomena,  190  ;  191,  193. 

Faudel  and  Schwoerer,  '  Life  of  Him,' 
ii.  134. 

Fay,  Du,  referred  to  by  Voltaire,  i. 
106. 

Faye,  '  Sur  I'Origiue  du  Monde,'  ii.  282, 
357,  360. 

Fechner,  Gnstav  Theodor,  '  Elements 
of  Psycho-physics,'  i.  200  ;  andBosco- 
vich's  theory,  359  ;  Ohm's  law,  365  ; 
electrical  theory  of,  371;  'Atomen- 
lehre,'  433  ;  ii.  369  ;  psycho-physics, 
469,  493 ;  psychical  research,  508 ; 
'  Psychophysik,'  511  ;  514,  546,  743. 

Felbiger,  Von,  educational  work  of, 
i.  256, 

Fellenberg,  Von,  follower  of  Pestalozzi, 
i.  258. 

Fenelon,  i.  253. 

Fermat,  Pierre,  the  theory  of  probabil- 
ities, i.  120  ;  arithmetical  discoveries, 
181  ;  187 ;  his  theorems,  ii.  680, 
721. 

Ferrier,  functions  of  the  brain,  ii.  479. 

Fertilisation  of  plants,  ii.  338. 

Fertilisers,  invention  of  artificial,  i.  92. 

Fessel,  fellow-worker  with  Pllicker,  ii. 
76. 

Fichte,  I.  H.,  and  Lotze,  i.  49. 

Fichte,  J.  G.,  the  province  of  j^hil- 
osophy,  i.  36  ;  influence  on  academic 
teaching,  37,  38 ;  idealism  of,  60 ; 
'  Wissenschaftslehre,'  83  ;  doctrine  of, 
170;  'Nature  of  the  Scholar,'  171; 
172  ;  influenced  liy  Spinoza,  212  ;  edu- 
cational significance  of  his  writings, 
258  ;  263,  264  ;  system  of,  ii.  500 ;  and 
Herder,  532. 

Fiedler,  German  translations  of  Sal- 
mon's works,  i.  275,  ii.  669 ;  685 ; 
expounds  von  Staudt's  method,  669. 

Fiedler  and  Salmon,  i.  44. 
"Field,"  magnetic,  ii.  68. 

VOL.  II. 


Finnie,  John,  agricultural  chemistry,  i. 

Fischer,  Emil,  ii.  437. 

Fischer,  E.  G.,  first  table  of  standard 
equivalents,  i.  393  ;  398. 

Fischer,  Kuno,  'Geschichte  der  neueren 
Philosophic,'  i.  67. 

Fitton,  ii.  294. 

Fitzgerald,  G.  F.,  ii.  193. 

Fizeau,  velocity  of  light,  ii.  45,  85. 

Flamsteed,  Newton's  correspondence 
with,  i.  98. 

Flemming,  ii.  444. 

Fletcher,  L.,  'The  Optical  Indicatrix,' 
ii.  14,  42,  55. 

Flourens,  '  Histoire  des  Travaux  de 
Georges  Cuvier,' i.  130,  139;  'Eloges 
Historiques,',  1.35  ;  and  de  Blainville, 
ii.  247  ;  "  Eloge  "  of  Geoftroy,  255  ; 
doctrine  of  descent,  322  ;  quoted  on 
Gall,  477  ;  phrenology,  478. 

Fluorescence,  ii.  52. 

Fluxions,  invention  of  method  of,  i. 
101;  method  of,  ii.   706. 

Pol,  on  fertilisation,  ii.  228. 

Fontanes,  conversation  of  Napoleon 
with,  i.  153. 

Fontenelle  popularised  science,  i.  106 ; 
literary  influence  of.  111  ;  123,  134, 
135,  142,  144,  279  ;  '  Eloge  de  Leib- 
niz '  quoted,  ii.  280. 

Forlies,  Edward,  naturalist,  i.  283,  288. 

Forbes,  J.  D.,  i.  272  ;  on  radiant  heat, 
ii.  105. 

"Force,  lines  of,"  ii.  68;  Lord  Kelvin 
on,  71  ;  and  "energy,"  115. 

Force,  matter  and,  mathematically  de- 
fined, i.  334. 

Forces,  correlation  of,  ii.  105. 

Forms,  theory  of,  ii.  678,  684. 

Forster,  Georg,  Humlroldt's  view  of 
nature,  i.  52  ;  naturalist,  services  of, 
179  ;  the  term  "  phrenology,"  ii.  477  ; 
influences  Herder,  532. 

Forster,  Johann  Reinhold,  i.  179. 

Forsyth,  A.   R.,  theory  of  functions,  ii. 

704. 
'Fortnightly  Review,'  ii.  558. 
'  Fortschritte  der  Physik '  started,  ii, 
58. 

Foster,  Sir  Michael,  'Text -Book  of 
Physiology '  quoted,  ii.  289,  446 ; 
physiology,  3^6;  'Text-Book,'  417; 
"Metabolism,"  421,  442;  "General 
Physiology,"  423,  430  ;  quoted,  428, 
Foucault,  spectrum  analysis,  i.  278; 
speed  of  light,  ii.  36,  45 ;  prismatic 
analysis  of  the  voltaic  arc,  50 ; 
"gyroscope"  and  "gyrostat,"  61. 

3  c 


770 


INDEX. 


Foucher,  '  Hypothesis  Physica,'  ii.  5. 

Fouiuiatious  of  science,  historical  and 
logical,  ii.  671  ;  of  mathematics  re- 
vised by  Weierstrass,  703  ;  examina- 
tion of,  709. 

Fourcroy,  '  Annales  de  Chinjie,'  i.,  41  ; 
at  the  Jardin  des  Plantes,  107  ;  Ecole 
des  Travaux  pnbliques,  112;  113; 
services  of,  to  the  Republic,  148 ; 
criticisms  of  Baumes's  essay,  ii.  390. 

Fourier,  Fr.  M.  C,  and  co-operation, 
ii.  566. 

Fourier,  J.  B.  Jos.,  i.  187  ;  neglected 
by  Paris  Institute,  241  ;  '  Tlieorie  de 
la  Chaleur,'  322,  ii.  175;  theory  of 
dimensions,  i.  323  ;  his  mathematics 
employed  by  Lord  Kelvin,  330 ; 
"dynamic  equilibrium,"  ii.  79; 
quoted,  120;  dedication  of  'Phil- 
osophic Positive,'  239 ;  heat,  487  ; 
analysis  of  periodic  phenomena,  6"23  ; 
on  Jacobi  and  Abel,  657  ;  definition 
of  function,  693  ;  697,  699. 

Fox-Talbot,  light,  ii.  11. 

France,  home  of  scientific  thought  in 
the  early  part  of  the  century,  i.  75. 

Francis  I.'  founded  College  de  France, 
i.  107. 

Francke,  A.  H.,  influence  of,  at  Halle 
University,  i.  160  ;  educational  work 
of,  256  ;  257. 

Francceur's  mathematics  introduced 
into  England  and  Germany,  i.  44  ; 
influenced  German  thought,  ii.  101. 

Frank,  i.  208. 

Frankland,  Sir  Edw.,  chemical  re- 
searches of,  i.  413,  447  ;  atomicity  of 
chemical  compounds  discovered  by, 
414. 

Franklin,  controversy  on  electric  fluid, 
i.  362  ;  Davy's  speculations  on  heat 
and  light,  ii.  104. 

Fraunhofer  lines,  i.  278  ;  theory  and 
practice  of  measuring,  322  ;  spectro- 
scopic observations,  ii.  47. 

Frederick,  Elector,  reconstitutes  Uni- 
versity of  Heidelberg,  i.  159. 

Frederick  the  Great,  popular  education, 
i.  256  ;  population  statistics,  ii.  563. 

Frederick  II.  of  Denmark  and  Tycho, 
i.  157. 

Freewill,  ii.  583. 

Frege,  G.,  ii.  737. 

Freind,  John,  molecular  attraction,  i. 
355. 

French,  the,  masters  in  science  at  the 
beginning  of  the  century,  i.  41. 

Fresenius,  text-books  of,  i.  188. 

Fresnel,  Augustin,  neglected  by  Paris 


Institute,  i.  241 ;  and  Young,  theories 
of,  244  ;  dynamical  view  of  light,  370 
revival  of  kinetic  view  of  nature,  ii.  8  ; 
optical  phenomena,  13,  14  ;  undula- 
tory  theory  of  light,  21,  36  ;  views  on 
"sidedness"  of  rays  of  light,  24; 
Memoir  on  Diffraction,  25,  26  ;  trans- 
verse vibrations,  28  ;  elastic  theory 
of  light,  31  ;  nature  of  the  ether,  40 ; 
theory  of  elasticity,  41  ;  definition  of 
motion  of  light,  42  ;  theory  of  light, 
43  ;  vibrations  of  the  ether,  56  ;  the 
dielectric  and  luminiferous  ether,  69, 
70,  89  ;  "  elastic  medium  "  in  space, 
84  ;  reference  to,  86,  91  ;  344,  467. 

Freytag,  '  Bilder  aus  der  deutschen 
Vergangenheit,' i.  256. 

Frezier,  geometrical  work  of,  i.  114. 

Fries,  Jacob,  i.  195  ;  school  of,  208  ; 
psychology,  ii.  495. 

Fritsch,  'Theorie  der  Newtou'schen 
Gravitation,'  i.  343. 

Frobel,  founder  of  the  Kindergarten,  i. 
258. 

Frost,  Scheiner's  'Astronomical  Spec- 
troscopy,' ii.  46  ;  362. 

Function,  mathematical,  introduced  by 
Euler,  ii.  639. 

Functions  of  living  substance,  ii.  429. 

Functions,  theory  of,  ii.  693  et  seq.; 
two  schools,  693  ;  non-difterentiable, 
Hankel  and  Weierstrass  on,  705 ; 
oscillating,  706  ;  analytic,  712. 

Fundamentals  in  mathematics,  ii.  649 
et  seq.;  geometrical  and  logical,  651 
et  seq.;  Gauss  on,  652. 

Galen,  i.  293  ;  ii.  207. 

Galileo,  Bacou's  indebtedness  to,  i.  94  ; 
mechanical  laws  of,  317  ;  318  ;  stimu- 
lated star-gazing,  327  ;  formula3  of, 
335  ;  described  phenomena  of  falling 
bodies,  353;  389,  424;  'Sidereus 
Nuncius,'  discovered  the  moons  of 
Jupiter,  ii.  10 ;  12 ;  inertia,  124 ; 
astronomical  work  of,  227. 

Gall,  J.  F.,  i.  136  ;  extolled  by  Comte, 
310 ;  phrenology,  ii.  477,  479. 

Galle  and  the  discovery  of  Neptune,  i. 
277.     . 

Galois,  Evariste,  Theory  of  Equations, 
ii.  686  ;  his  life  and  works,  ib. ;  his 
letter  to  Chevalier,  ib.  ;  and  theory 
of  groups,  687  ;  692. 

Galton,  Francis,  on  heredity,  ii.  574, 
612 ;  on  variation,  609  ;  his  works, 
ib.  ;  combines  Quetelet  and  Darwin, 
ih. ;  on  statistical  treatment,  612 ; 
on  pangenesis,  614 ;   forestalls  Weis- 


INDEX. 


71 


mann,  ib.  ;  on  "particulate"  inheri- 
tance, 615  ;  on  law  of  distribution, 
617  ;  on  law  of  regression,  618. 

Galvani,  discoveries  of,  i.  363,  ii.  150  ; 
galvanic  current,  233 ;  animal  elec- 
tricity, 474. 

"Gamma"  function,  ii.  696. 

Garnett,  R.,  on  Georg  Forster,  1.  52  : 
179. 

Garnett,  W.,  and  Campbell,  'Life  of 
Clerk-Maxwell,'  ii.  599. 

Gartner,  investigations  of,  ii.  415. 

Gases,  liquefaction  of,  i.  316 ;  the 
kinetic  theory  of,  425,  ii.  34 ;  i. 
433. 

Gaskell,  Dr,  cerebro-spinal  nerves,  ii. 
429;  analysis  of  process  of  "meta- 
bolism," 44"2. 

Gassendi  taught  at  the  College  de 
France,  i.  107  ;  385. 

Gassiot,  experiments  with  vacuum 
tubes,  ii.  190. 

Gatterer  of  Gottingen  University,  i. 
165. 

Gauss,  Carl  Fr. ,  i.  44,  45 ;  orbit  of 
Ceres,  54  ;  works  of,  82  ;  and  Weber, 
the  telegraph,  92,  367  ;  "  Disquisi- 
tiones  Arithnieticte,'  105,  120,  ii.  682; 
Lobatchevski  and  Bolyai,  i.  161 ;  and 
Humboldt,  167 ;  and  Zach,  177  ; 
178  ;  mathematical  researches,  181 ; 
182 ;  least  squares,  183  ;  184,  185, 
188,  189,  191,  2U0,  207,  211  ;  "exact 
habit  of  thought,"  222  ;  231,  238,  247  ; 
measurement  of  magnetic  action,  265  ; 
303 ;  absolute  measurements,  309, 
369  ;  astronomical  work  of,  314,  331  ; 
measurements  of,  322 ;  '  Theoria 
motus  corporum  ccelestium,'  324; 
calculus  of  probabilities,  325  ;  352  ; 
Coulomb's  methods,  36(»,  362  ;  365 ; 
importance  of  his  work,  384  ;  "Top- 
ologie,"  ii.  63  ;  researches  into  elec- 
trical phenomena,  67  ;  76  ;  electro- 
magnetic measurements,  78  ;  system 
of  absolute  measurements,  117  ;  arith- 
metical discoveries  of,  124  ;  influences 
Helmholtz,  150  ;  197,  254  ;  science 
of  chances,  568  ;  theory  of  error,  574  ; 
575  ;  method  of  least  squares,  576  ; 
doctrine  of  probabilities,  577  ;  law 
of  error,  616  ;  and  Newton  compared, 
630 ;  rediscovery  of  Ceres,  ib.  ; 
pioneer  of  modern  mathematics,  636  ; 
Bessel  on,  ib.  ;  his  style  criticised  by 
Abel,  637  ;  640 ;  his  fundamental 
theorem,  644,  688  ;  on  convergency, 
646  ;  his  work  on  higher  functions, 
648  ct  seq.  ;   on  fundamentals,   652  ; 


his  influence  on  Bolyai,  Lobatchevski, 
and  others,  652  ;  anticipates  the  work 
of  others,  ib.  ;  compared  to  Goethe, 

653  ;  on  extended  system  of  numbers, 

654  ;  reforms  theory  of  numbers,  680 
et  seq.,  720;  on  determinants,  682; 
686,  688,  693,  695,  697,  698  ;  on  con- 
formal  images,  701  ;  on  non-Euclidean 
geometry,  710,  713  ;  measure  of 
curvature,  714 ;  theory  of  congru- 
ences, 723  ;  on  mathematical  calculi, 
724;  on  bi-quadratic  residues,  725; 
732  ;  not  a  great  teacher,  646,  743. 

Gauss  and  Gerling,  ii.  713. 

Gauss  and  Schumacher,  correspondence, 
ii.  710. 

Gauss  and  Weber,  telegraph,  i,  92, 
367 ;  school  of,  ii.  702. 

Gay-Lussac,  Memoirs  of,  1.  83  ;  '  An- 
nales  de  Chymie  et  de  Physique,' 
189 ;  190 ;  organic  analysis,  ib.  ; 
chemical  discoveries,  398,  407 ;  ex- 
periments, 425  ;  426  -  429  ;  Fresnel's 
'  Memoire  sur  la  Ditt'raction,'  ii.  25  ; 
visit  to  England,  27  ;  experiment  in 
heat  measurement,  109  ;  155,  592. 

Geddes  and  Thomson,  'The  Evolu- 
tion of  Sex,'  ii.  227,  454,  458,  459; 
sexual  selection,  344  ;  "  Reproduc- 
tion," 348. 

Gegenbaur,  school  of  Darwinism  in 
Germany,  ii.  436. 

Gehlen,  '  Allgemeines  Journal  flir 
Chemie,'  i.  41. 

Geikie,  Sir  Archd.,  quoted  on  Playfair's 
'  Huttonian  Theory  of  the  Earth,'  i. 
283 ;  G.  Wilson  and,  '  Memoir  of 
E.  Forbes,'  288. 

Geissler,  fellow  -  worker  with  Plucker, 
ii.  76 ;  electrical  researches,  189 ; 
vacuum  tubes,  190. 

Geitel  (see  Elster),  ii.  190. 

Generalisation,  process  of,  in  mathe- 
matics, ii.  638  ;  650. 

Generalised  co-ordinates,  Pliicker,  ii. 
673. 

"  Genesis,"  ii.  279. 

Genetic  view  of  nature,  ii.  276,  290  ; 
in  Germany  and  France,  321 ;  triumph 
of,  328  ;  on  a  large  scale,  S45 ; 
strengthened  by  physics  and  chem- 
istry, 355. 

Genetics,  ii.  213. 

Genius,  latent  thought  the  material  of, 
i.  8. 

'  Gentleman's  Magazine,'  ii.  679. 

Geography,  historical,  i.  294. 

Geological  Society,  i.  290. 

Geology,  ii.  290. 


772 


INDEX. 


Geometrical  axioms,  i.  199,  352  ;  ii.  649, 

et  seq. 
Geometry,    deficiency   of    organisation 
of  research  in  England,  i.  243  ;  two 
schools  of,  ii.  668. 
Geophysics,  ii.  363. 
George,  Duke  of  Saxony,  reconstituted 

University  of  Leipzig,  i.  159. 
Gergonne,   ii.    660  ;    Hankel   on,    666  ; 

673. 
Gerhardt,  C.  F.,  revives  Front's  hypoth- 
esis, i.  402  :  attack  on  electro-chemical 
theory,   409;    "type"  theory,    411; 
413;  on  the  constitution  of  substances, 
419  ;  "types,"  423  ;  Gmelin's  system 
of  equivalents,  426  ;  characteristic  of 
hydrogen  atoms,  430. 
Gerhardt,  C.  J.,  on  the  invention  of  the 
calculus,  i.  101  ;  edited  Leibniz,  'Phil- 
o.sophische  Schriften,'  ii.  5. 
Germ  plasma  and  body  plasma,  ii.  457, 

458  ;  plasma,  ditt'erentiation  of,  459. 
German  Association,  character  and  de- 
cline of,  i.  238. 
German  language,  peculiarity  of,  i.  22. 
German  universities,  i.  226. 
Germany  leads  in  the  history  of  thought, 

i.  46. 
Gervinus  on  Herder,  i.  51  ;  connection 
of  political  and  literary  history,  59  ; 
'  Georg  Forster's   Werke,'  179;  rela- 
tions of  philosophy  and  history,  206  ; 
"theoretical  politician,"  311. 
Gesner  of  Gottingen  University,  i.  165. 
"Gewerbeschulen,"  i.  166. 
Gibbon,  i.  47;  'Roman  Empire,'  169; 
influence  of,  on  German  thought  and 
literature,    212 ;    in   German  univer- 
sities, 251. 
Gibbs,  J.  Willard,  energetics,  ii.   166, 
171;    "free  energy,"  173;   chemical 
equilibrium,   175,  177 ;    formulae   of, 
185 ;    on    directional    calculus,    655 ; 
656. 
Gibson,  George  A.,  "Fourier's  series," 

i.  241. 
Giese,    vacuum-tube   experiments,    ii. 

190. 
Gilbert,  Sir  J.  H.,  agricultural  experi- 
ments and  publications  of,  i.  284. 
Gilbert,  Wm.,  Bacon's  indebtedness  to, 

i.  94. 

Glaciers,  Helmholtz's  theory  of,  ii.  127. 

Glaisher,  Prof.,  quoted  on  invention  of 

logarithms,  i.  269  ;  321  ;  law  of  error, 

ii.  576. 

Glazebrook,  Prof.,  'Report  on  Optical 

Theories,'     ii.     54 ;     Lord     Kelvin's 

theory  of  ether,  55  ;    '  James  Clerk- 


Maxwell   and   Modern  Physics,'  77  ; 
indefiniteness   of  Maxwell's   electro- 
magnetic theory,  94. 
Gmelin,  Chr.,  chemist,  i.    188  ;  hand- 
book of  chemistry,  208. 
Gmelin,     Leopold,     '  Handbuch      der 
Chemie,'  i.    43,    ii.    158  ;    system   of 
equivalents  of,  i.  426,  430. 
Goebel,  Prof.,  on  biology,  ii.  313. 
Goethe  quoted  on  history,  i.  7  ;  quoted 
on  the  success  of  the  few,  9 ;  made 
modern  German   language,  22  ;  atti- 
tude of,  to  national  idealism  of  Ger- 
many, 39  ;  style   of,    51  ;    his  work, 
61 ;    influence    of,     on    taste,     67 ; 
'Faust,'  76  ;  school  of,  84  ;    Lewes's 
Life  of,  166  ;  179  ;  as  a  scientist,  180  ; 
influenced  by  the  Naturphilosophie, 
207  ;  212  ;  introduced  hexameter  into 
German  poetry,  213;  quoted  251,  286, 
ii.   3,  254,  258  ;    educational   signifi- 
cance of  his  writings,    i.    258  ;  261  ; 
corresjjondence    of,    279  ;    on    Luke 
Howard,    286 ;    introduction    of    the 
term     morphology,     ii.    210  ;    213  ; 
theory  of   metamorphosis,  223,   243, 
267  ;  influence  of,  225  ;   theories  of, 
246  ;  influence  of  Linnajus,  252  ;  253  ; 
the  genetic  view,  317,  321  ;  subjective 
colour  sensations,  482  ;    foundations 
of  the  study  of  language,  538. 
Goldstein,    vacuum-tube    experiments, 
ii.  190;  "ether"   theory  of  cathode 
rays,  192. 
Goltz,    experiments   on   the   brain,    ii. 

478  ;  479. 
Goodsir,  cell  theory,  ii.  265. 
Gordon,    Lewis,     Carnot's    'Puissance 

motrice,'  ii.  118. 
Gottingen,  prize  essays  on  principles  of 

dynamics,  ii.  97. 
'Gottinger     Gelehrte      Anzeigen'     of 

Haller,  i.  176. 
Gough,  John,   the  blind  naturalist,  i. 

287. 
Gourand  quoted,  ii.  571. 
Grrevius,  recognition  of  Bentley,  i.  169. 
Graff,     Prof.     L.    von,     on     Haeckel's 

'Stammbaume,'  ii.  337. 
Graham,    Thomas,    chemistry,    i.    44 ; 
salts   and  acids,    410  ;    experimental 
work  of,  ii.  161  :  164  ;  discoveries  of, 
224. 
Grandi,  series  of,  ii.  646. 
Grant,  Sir  A.,  '  Story  of  the  University 
of  Edinburgh,'  i.   160,  232,  267,  269, 
283 ;    on    David    Gregory,    270 ;    on 
Bell,  '293. 
Grant,  Prof.,  natural  selection,  ii.  330. 


INDEX. 


773 


Grassraann,  Hermann,  geometry,  i.  44  ; 
geometrical  labours  of,  neglected  in 
Germany,  243,  247  ;  '  Ausdelinungs- 
lehre,'  275  ;  mathematical  labours 
of,  ii.  73  ;  630  ;  Hankel  on  his  science 
of  forms,  640  et  seq.;  his  comprehen- 
sive calculus,  655  ;  gradual  apprecia- 
tion of  his  work,  656  ;  710. 

Graunt,  John,  statistics,  i.  122 ;  "Tables 
of  Mortality,  "ii.  564. 

Graves,  R.  P.,  'Life  of  Sir  W.  R. 
Hamilton '  quoted,  i.  106,  289 ;  ii. 
722. 

Gravitation,  formula  of,  i.  319  ;  lines  of 
thouc;ht  emanating  from  it,  321  ;  not 
an  ultimate  property  of  matter,  338  ; 
difBculty  of  measuring  directly,  353. 

Gray  (the  poet),  i.  285. 

Gray  quoted  on  David  Robertson,  i. 
289. 

Gray,  Asa,  criticism  of  '  Vestiges, '  ii. 
3i9  ;  332. 

Greard,  educationalist,  i.  260. 

Green,  George,  important  generalisation 
in  statics  and  dynamics,  i.  230 ;  his 
"potential  function,"  231  ;  246,  272, 
331  ;  important  papers  lost,  277 ; 
properties  of  ether,  ii.  31,  33 ;  in- 
spired by  Cauchy,  43 ;  analytical 
method  of,  45  ;  referred  to,  54 ;  theory 
of  electric  and  magnetic  phenomena, 
74  ;  698. 

Gregoire  proposed  Bureau  des  Longi- 
tudes, i.  113. 

Gregory,  David,  introduced  Newtonian 
philosophy  into  the  University  of 
Edinburgh,  i.  232  ;  Professor  of  Astro- 
nomy, Oxford,  270,  272  ;  astronomical 
instruments,  322. 

Gregory,  F.,  Hankel  on,  ii.  712. 

Gren's  'Journal  der  Physik,'  i.  41. 

Grew,  Nehemiah,  used  the  term  "  cell," 
i.  195  ;  microscopic  investigations  in 
biology,  283  ;  embryological  re- 
searches, ii.  227  ;  microscopical 
studies,  260  ;  observations  of,  261. 

Griesbach,  "Animal  and  Plant  Geo- 
graphy," ii.  226. 

Griesinger,  Mayer's  "right  of  priority," 
ii.  115. 

Grimaldi,  polarisation  of  light,  ii.  18. 

Grimm,  Jacob,  'Ueber  Schule,  Univer- 
sitat,  Akademie,'  i.  100  ;  language,  ii. 
540,  542. 

Groth,  'Pliysikalische  Krystallographie, ' 
i.  443. 

Groups,  theory  of,  ii.  632,  686,  687 ; 
Burkhardt  on,  688 ;  689  et  seq,  ; 
continuous  and  discontinuous,  691. 


Grove,  "  Correlation  of  Physical  Forces," 

ii.  Ill;  "force,"  125,  130. 
Gruber,    Ersch   and,    Encycloijredia  of, 

i.  35  ;  representative  of  encyclopaedic 

teaching,  38. 
Guardia  quoted,  i.  106;    'Histoire   de 

la  Medicine,'  126. 
Guerry,  A.  M.,  statistics,  ii.  579. 
Guhrauer,    'Leibniz,    eine   Biographic," 

i.  158,  ii.  280. 
Guizot,  education,  law  of,  i.  183,  257. 
Guldberg,  law  of  mass-action,  i".  157  ; 

ideas  of  Berthollet,  177. 
Guyton  de  Morveau,  i.  116,  131  ;  gun- 
powder, iron,  steel,  148. 
Gyroscope  and  gyrostat  invented,  ii.  61. 

Haacke,  ii.  271. 

Hacker,  DrVal.,  'Praxis  und  Theorie 
der  Zellen-  und  Befruchtungslehre,'  ii. 
265,370;  371,447. 

Haeckel,  Ernst,  i.  179;  'Generelle 
Morphologic  der  Organischen  Wesen,' 
ii.  213,  214,  270,  271,  349  ;  Goethe's 
ideas,  244,  246;  "Ontogenesis"  and 
"Phylogenesis,"  307;  'Natiirliche 
Schopfungs  -  Geschichte,'  313,  323; 
'History  of  Creation,'  332;  genea- 
logical trees,  337  ;  sexual  selection, 
343  ;  347  ;  evolution,  348,  455  ;  Dar- 
win and  Lamarck,  350 ;  351,  361  ; 
conception  of  universal  animation, 
369  ;  biological  theories  of,  371  ;  414  ; 
school  of  Darwinism  in  Germany, 
436;  "germinal"  element,  457  ;  and 
Weismann,  460  ;  and  Herder's  evolu- 
tionism, 533  ;  man  and  brute,  541  ; 
546,  608  ;  kinetic  hypothesis,  611. 

Haeser,  'Geschichte  der  Mediciu,'  i. 
126,  308,  ii.  388,  390,  401;  on 
homceopathy,  i.  210  ;   on  Kant,  219. 

Hahn,  "Cuvier"  in  'Grande  Encyclo- 
pedic,' i.   130. 

Hahnemann's  homceopathy  .i.  210. 

Hales,  improvements  in  microscopy,  ii, 
230. 

Hall,  Marshall,  ii.  519. 

Halle,  University  of,  i.  165. 

Haller,  Albrecht  von,  i.  163  ;  of  Gottin- 
geu  University,  165;  connection  of, 
with  modern  science,  175  ;  '  Gottinger 
Gelehrte  Anzeigen,'  176;  '  Ele- 
menta,'  193  ;  194  ;  zoological  labours 
of,  ii.  220,  230 ;  study  of  separate 
organs,  233;  "evolutionist,"  278; 
279  ;  epigenesis,  298  ;  299,  308  ;  vital - 
istic  conceptions,  384  ;  discovery  of  ir- 
ritability, 429 ;  psycho-physical  view, 
471  ;  influences  Herder,  532  ;  533. 


774 


INDEX. 


Hallej-,  Edmund,  "reciprocal  dupli- 
cate "  ratio,  i.  98 ;  270 ;  Newton's 
'Principia,'  283;  orbits  of  comets, 
324  ;  calculates  return  of  comet,  327  ; 
Newton  to,  342  ;  pendulum  experi- 
ments of,  354 ;  statistician,  ii.  565. 
Halsted,    6.    B. ,    on    non  -  Euclidean 

geometry,  ii.  652  ;  714. 
Hamanu,  Johann  Georg,  ii.  535,  536. 
Hamilton,  Sir  W.,  '  Discussions,'  i.  203  ; 
'Dugald     Stewart's     Works,'     359; 
"  Philosojjhy  of  the  Unconditioned," 
ii.  326. 
Hamilton,  Sir  W,  R.,  used  the  notation 
of  Newton,  i.   101 ;   Life  of,  quoted 
from,   106 ;   paper  on  caustics,   230  ; 
important    generalisation    in    statics 
and  dynamics,  231  ;    Dublin  Mathe- 
matical  School,   274 ;   originality  of, 
ib. ;  "characteristic  function,"  316; 
theory  of  optical  phenomena,  ii.  13, 
42 ;   mathematical    labours    of,    73 ; 
dynamics,  139;  195;  his  quaternions, 
654 ;     656,     709 ;     introduces    term 
"associative,"  711;  722. 
Hank,  Theodore,  suggested  idea  of  the 

Royal  Society,  i.  227. 
Hankel,  Hermann,  generalising  aspects 
of  the  sciences,  i.  46  ;  quoted  on 
the  establishment  of  analysis  as  a 
science,  103  ;  '  Die  Entwickelung  der 
Mathematik,'  175  ;  '  Theorie  der  com- 
plexen  Zahlensysteme,'  185  ;  ii.  710  ; 
'  Die  Elemente  der  Projectivischen 
Geometric, '  i.  188  ;  ii.  632  ;  on  the 
two  processes  of  algebra,  640 ;  on 
Grassmann,  ih.,  656;  on  Peacock 
and  de  Morgan,  641  ;  on  Gauss's 
theorem,  645 ;  on  imaginaries,  653, 
664  ;  Poncelet's  principle,  661  ;  on 
Gergonne's  principle  of  duality,  666  ; 
on  Steiner,  668 ;  compares  von 
Staudt  with  Chasles,  669  ;  on  Mobius, 
682  ;  on  fundamentals,  703  et  seq.  ; 
on  English  mathematics,  704,  711  ; 
on  oscillating  functions,  706 ;  on 
Bolzano  and  Cauchy,  709  ;  principles 
of  arithmetic,  711 ;  on  principle  of 
permanence,  712 ;  on  quaternions, 
ib.,  717;  726. 

Hanle's  '  Magazin,'  i.  43. 

Hanselmaun,  '  K.  F.  Gauss,'  i.  181. 

Hansen,  lunar  theory,  i.  329. 

Harcourt,  Vernon,  i.  236. 

Harding,  discovery  of  planets,  i.  182. 

Harkness     and     Morley,     theory     of 
functions,  ii.  704. 

Harmonic  functions,  ii.  696. 

Harriot,  a  forerunner  of  Bacon,  i.  94. 


Harris,  James,  language,  ii.  536. 

Harris,  Snow,  referred  to  by  Faraday, 
ii.  69. 

Harrison,  received  prize  of  Board  of 
Longitude  for  his  chronometers,  i. 
158  ;  astronomical  instruments,  322. 

Hart,  J.  M.,  testimony  to  work  of 
German  universities,  i.  225. 

Hartmanu,  ii.  470,  60S. 

Hartnack  and  Nachet,  improvement  in 
immersion  system,  ii.  228. 

Harvey,  contemporary  with  Bacon,  i. 
94  ;  discovery  of  the  circulation  of 
the  blood,  193  ;  272  ;  contributions 
to  biology,  282  ;  292 ;  study  of  sep- 
arate organs,  ii.  233;  "metamor- 
phosis," 278  ;  embryology,  297  ;  349, 
444. 

Hatchett,  not  member  of  any  univer- 
sity, i.  238. 

Haukesbee,  Francis,  capillary  phenom- 
ena, i.  346  ;  experiments  of,  355,  356. 

Hauptmann,  C,  'Die  Metaphysik  in  der 
modernen  Physiologic,'  ii.  401,  438  ; 
quoted,  407,  444. 

Hausser,  L.,  i.  59. 

Haiiy,  Abbe,  physics  at  the  Ecole  nor- 
male,  i.  112 ;  crystallography  of, 
116,  117  ;  services  of,  to  mineralogy, 
118 ;  136  ;  created  the  science  of 
crystallography,  441  ;  labours  of,  ii. 
222 ;  founder  of  crystallography, 
240 ;  241  ;  crystallography,  264 ; 
building  up  of  crystals,  270. 

Haym,  Rudolf,  'Leben  W.  v.  Hum- 
boldts,'  i.  38;  chief  authority  on 
Herder,  51 ;  biographies  of  Hegel 
and  others,  ■  279 ;  '  Herder  nach 
seinem  Leben  und  seinen  Werken,' 
ii.  531,  533,  537. 

Hayward,  algebra  of  'Coplanar  Vec- 
tors,' ii.  656. 

Heat,  Tyndall's  dynamical  theory  of, 
ii.  57 ;  dynamical  theory  of,  73 ; 
Black,  Rumford,  and  Davy,  102  ;  the 
non-mechanical  nature  of  heat-phen- 
omena, 120  et  seq. ;  and  perpetual 
motion,  126  et  seq.  ;  of  the  sun,  357. 

Heaviside,  Oliver,  popularisation  of 
Maxwell's  electro  -  magnetic  theory, 
ii.  72  ;  193  ;  his  directional  calculus, 
655,  656. 

Hecker,  .J.  J.,  established  "  Realschule" 
at  Berlin,  i.  166. 

Heeren  of  Gcittingen  University,  i.  165  ; 
and  Ukert,  collections  of  Histories  of 
all  countries,  167. 

Hegel,  G.  W.  F.,  on  the  province  of 
philosophy,    i.    36 ;    treated    science 


INDEX. 


775 


from  a  metaphysical  standpoint,  43 ; 
philosophy  of,  intiuenced  by  Herdei-, 
51  ;  ridiculed  search  for  new  planets, 
54 ;  on  status  of  philosophy,  60 ; 
his  definition  of  philosophy,  61 ;  re- 
lation of  philosopliy  to  religion,  73  ; 
'  PhJinomenologie  des  Geistes,'  83; 
spontaneous  development  of  thought, 
85;  'Geschichte  der  Philosophie,' 
145 ;  162 ;  speculative  tendency  of, 
178  ;  philosophy  of,  204,  ii.  279,  346, 
500  ;  i.  207,  208  ;  encyclopajdic  lec- 
tures on  philosophy,  214  ;  benefac- 
tions to  historical  sciences,  215 ; 
Schelling's  scheme  of  evolution,  ii. 
354  ;  495  ;  dialectics,  530  ;  60S,  751. 

Hegelianism,  failure  of,  i.  72. 

Heidenhain,  Prof.,  function  of  gland- 
cells,  ii.  429. 

Heine,  E.,  ii.  704,  733. 

Helm,  Dr  Georg,  'Die  Lehre  von  der 
Energie,' ii.  97,  142,  185,  186;  'Die 
Energetik  nach  ihrer  gescliichtlichen 
Entwickelung,'  97,  106,  108-111,  125, 
127,  133,  138 ;  controversies  as  to 
priority  of  discovery  in  theory  of 
energy,  97,  98  ;  influence  of  Poucelet 
on  practical  mechanics,  101  ;  heat 
nnit,  109 ;  labours  of  Horstmann, 
170;  methods  of  W.  Gibbs,  171; 
criticism  of  mechanical  view,  183 ; 
188. 

Helmholtz,  metaphysical  foundations 
of  geometry  and  dynamics,  i.  45 ; 
'Eeden'  quoted,  175;  on  speculative 
tendency  in  science,  179  ;  on  Goethe 
as  a  naturalist,  180  ;  '  Vortrage,'  193  ; 
198,  199  ;  doctrine  of  the  conserva- 
tion of  energy,  2')1  ;  on  the  relations 
of  mathematical  and  experimental 
science,  205 ;  '  Wisseuschaftliche 
Alihandlungen,'  ib.  ;  'Vortrage  und 
Reden '  quoted,  209  ;  '  Ueber  das 
Deiiken  in  der  Medicin,'  210  ;  revival 
of  doctrine  of  conservation  of  force, 
218  ;  on  Kant,  219  ;  220  ;  '  Journal 
fur  Mathematik,'  231  ;  Fourier's 
series,  241 ;  "sense  perceptions,"  243 ; 
on  Young,  244  ;  '  Ueber  die  Erhaltung 
der  Kraft,'  265,  309  ;  on  Faraday's 
ideas,  266 ;  vortex  motion,  313,  ii. 
35,  60  ;  on  the  gravitation  theory,  i. 
352  ;  375  ;  objection  against  Weber's 
law,  376,  377  ;  "action  at  a  distance," 
380  ;  on  the  electro-chemical  theory, 
405  ;  investigations  of  fluid  motion,  ii. 
58;  articles  on  acoustics,  ib. ;  "vor- 
tex filaments,"  61  ;  influence  of  his 
speculations  in  England,    62  ;    illus- 


trations of  his  theories,  63;  suggested 
vortex-atom  theory,  66 ;  '  Faraday 
Lecture  '  quoted,  ib.  ;  adopted  views 
of  English  scientists,  93  ;  independ- 
ence of  Mayer's  writings,  97 ;  his 
work  theoretical,  99  ;  "  physical  me- 
chanics," 101  ;  scientific  services  of, 
106  ;  memoirs  refused  by  Poggendorf, 
107 ;  classical  character  of  his  in- 
vestigations into  the  nature  of  heat, 
112;  'Gesammelte  Abhandlungen,' 
113  ;  his  recognition  of  the  claims  of 
Mayer,  114;  117;  and  Sadi  Carnot, 
123  ;  perpetual  motion,  124  ;  conser- 
vation of  energy,  125,  127,  130,  142, 
438;  "death"  of  the  universe,  131; 
mathematical  treatment  of  power  and 
work,  137  ;  on  tension,  138 ;  141 ; 
energetics,  148  ;  electro  -  dynamics, 
149  ;  theories  of  electro-dynamic  phen- 
omena, 152  ;  Faraday  Lecture,  154  ; 
dissociation,  163  ;  thermal  measure- 
ments, 172;  "free  energy,"  173; 
chemical  equilibrium,  175  ;  quoted, 
182  ;  atomic  view,  189  ;  atom  of  elec- 
tricity, 193  ;  memoir  of,  195  ;  ether 
theory,  196  ;  imperfections  of  tlie  eye 
as  an  optical  instrument,  215  ;  micro- 
scopic work,  229  ;  Goethe's  theory  of 
colours,  245 ;  Kant's  theory,  282 ; 
appreciation  of  Kant,  284  ;  "energy," 
355 ;  physical  laws,  356 ;  cosmical 
origin  of  life,  369 ;  on  vitalism, 
388  ;  391  ;  'Physiological  Optics,' 397, 
480,  508;  'Physiological  Acoustics,' 
397  ;  nature  of  living  forces,  398  ; 
403,  421,  467 ;  animal  magnetism, 
476;  quoted  on  "specific  energies," 
482  ;  optics,  483,  506  ;  psycho-physi- 
cal science,  485;  "Timbre,"  488; 
aiTangement  of  tones,  490  ;  and  Kant, 
491  ;  psycho  -  jihysical  phenomena, 
496  ;  space  perception,  504  ;  "  Ueber 
das  Sehen  des  Jlenschen,"  506  ;  hear- 
ing and  seeing,  512  ;  language,  538  ; 
on  liarmonics,  623 ;  on  foundations 
of  geometry,  710  ;  letter  to  Schering, 
ih.  ;  on  axioms  of  geometry,  711  ; 
and  Riemann  on  geometry,  713. 

Helvetius,  ignorance  of  physiology,  ii. 
471. 

Henle,  Jacob,  reconstruction  of  "gen- 
eral anatomy,"  i.  195  ;  198  ;  anthro- 
pological lectures  of,  215;  mechanical 
views  in  biology  of,  219  ;  on  demon- 
stration of  Bell's  doctrine,  293 ; 
'  AUgemeine  Auatomie,'  ii.  401. 

Henrici,  ii.  656. 

Henry,  Dr,  not  member  of  any  univer- 


776 


INDEX. 


sity,  i.  239;  'Life  of  Daltou,'  246; 
on  Charles  Bell,  292. 
Heraclitus  of  Ephesns,  i.  314 ;  the 
"kinetic  theory,"  385  ;  conception  of 
eternal  motion,  ii.  3 ;  conception  of 
changing  world-periods,  286. 
Herapath,      "mechanical      theory     of 

gases,"  i.  310;  434. 
Herbart  repudiated  by  Lotze,  i.  49 ; 
208 ;  educational  influence  of,  in 
Germany,  257  ;  phrenology,  ii.  478  ; 
anticipated  Helmholtz,  491  ;  influ- 
ence of  his  philosophy,  494 ;  on 
"faculty -psychology,"  495;  psycho- 
logical research,  496  ;  mathematical 
psychology,  498  ;  500 ;  psychical 
mechanism  of,  504 ;  space  percep- 
tion, 506  ;  507,  512,  515  ;  introspec- 
tive method,  527;  "  Volkerpsych- 
ologie"  and  "  Sprachwissenschaft," 
530. 
Herbert,   Dean,    natural   selection,    ii. 

330. 
Herder,    i.  50  ;   History  of  Humanity, 
51;    'Ideen,'53;    '  Metakritik,'  83  ; 
indebtedness  to   Gibbon,    169 ;   171  ; 
cited  on   Georg  Forster,  179  ;   scien- 
tific ideal  of,  211 ;   212  ;  Alcaic  and 
Sapphic    metres,     213  ;    educational 
influence  of,  in  Germany,  257  ;  258  ; 
scientific  work  of,   ii.  210 ;  influence 
of,   225 ;    280 ;    philosophy  of,    346  ; 
psycho-physical  view  of  nature,  531  ; 
quoted,  533  ;  'History  of  Mankind,' 
534 ;  538,  563. 
Heredity,  problem  of,  ii.  343,  613. 
Hering,  ii.  442  ;   '  Ueber  das  Gedacht- 
niss  als  eine  allgemeine  Funktion  der 
organischen  Materie,'  544. 
Hermann,   Gottfried,    indebtedness   to 
Bentley,   i.  169;    162,   172;    science 
for    its   own    sake,   211  ;    212,   214  ; 
classical  learning  of,  222. 
Hermann,    Jac,    Leibniz's    letter    to, 

quoted,  ii.  646. 
Hermite,   researches   of,   ii.  124  ;   649  ; 
on  determinants,  683  ;  on  transcend- 
ent numbers,  731. 
Herodotus   referred    to  on  division   of 

History  into  centuries,  i.  13  ;  296. 
Herrmann,  Cr.,  quoted,  ii.  266. 
Herschel,  Caroline,  discovers  her  eight 

comets,  i.  229  ;  285. 
Herschel,  Sir  John,  i.  177  ;  quoted  on 
Laplace,  123;  astronomical  work  of, 
230 ;  introduction  of  knowledge  of 
Continental  mathematics  to  Cam- 
bridge by,  233  ;  science  in  England, 
234  ;  236  ;  and  Airy,  article  in  '  En- 


cyclopedia      Metropolitana,'      236 ; 
quoted  on  Fresnel,  241  ;  educational 
movement    jjromoted    by,    261  ;    '  A 
Preliminary  Discourse  on  the  Study 
of    Natural    Philosophy,'   263,    306  ; 
founded    Anal}i;ical    Society,     271  ; 
spectrum   analysis,    278 ;    stands    on 
Bacon's  philosophy,  307  ;   376  ;  phe- 
nomenon   of    fluorescence    observed 
by,    ii.    52 ;    criticism    of    the    term 
"potential  energy,"  140;   295;    'In- 
troduction to  the  Study  of  Natural 
Philosophy,'  328  ;  experiments  at  the 
Cape,  357  ;  "sound,"  488;  theory  of 
probabilities,  569  ;  606. 
Herschel,  Sir  William,  '  On  the  Proper 
Motion  of  the  Sun  and  Solar  System,' 
i.   176  ;    astronomical   discoveries   of, 
229  ;  238,  285  ;  discovery  of  Uranus, 
324;    'Observations  of    Nebulaj,'   ii. 
283  ;  nebular  theorv,  295. 
Hertwig,  0.,   'The  Cell,'  ii.  224,  265, 
297,  370,  371,  373,  420,  427,  444,  461  ; 
embryological  researches,  228  ;  '  The 
Biological  Problem  of  To-day,'  298, 
459  ;  '  Zeit  und  Streitfragen  zur  Bi- 
ologic,' 401  ;  quoted,  409  ;  '  The  Cell,' 
quoted,  425,  446,  448  ;  "  idioplasma, " 
448  ;  ' '  organicisme, "  455. 
Hertz,  H.,  electric  theory,  i.  344 ;  elec- 
trical wave-motion,  ii.  77  ;  electrical 
view    of   light,    88,    92;    "physical 
mechanics,"    101;    electro  -  magnetic 
wave-motion,  148  ;  193. 
Hess,  a  founder  of  physical  chemistry. 

ii.  152;  157. 
Hesse,  Otto,  his  elegant  work,  ii.  677  ; 
introduces  determinants,  682  et  seq.; 
and  invariants,  684. 
Hessel,  '  Krystallometrie,'  i.  443. 
Hettner,  history  of  the  idea  of  humanity, 
i.    50  ;   literary  history  of  the  eigh- 
teenth century,  59  ;  cited  on   Georg 
Forster,  179. 
Heun,    '  Jahresbericht    der    deutschen 

Mathematiker-Vereinigung,'  ii.  101. 
Heussler,  Hans,  on  Bacon,  i.  94. 
Heyne  of  Gottingen  University,  i.  165  ; 

indebtedness  to  Bentley,  169. 
Hicks,  'Report  on  Hydrodynamics,' ii. 
58 ;    contribution  to  vortex  theorv. 
63.  ■" 

Higgins,  theory  of,  i.  398. 
Hilbert  on  algebraic  numbers,  ii.  729. 
Hildebrand,  Bruno,  statistics,  ii.  561. 
Hillebrand,  Karl,   '  Zeiten,  Volker,  und 

Menschen,'  quoted,  i.  311. 
Hippeau,  C,  '  Public  Education  during 
the  Revolution  in  France,'  quoted,  i. 


INDEX. 


777 


108  ;  109  ;  quotes  Condorcet,  111  ; 
'  L'Instruction  publique  en  France 
pendant  la  Revolution,'  259. 

Hippocrates,  ii.  470. 

Hirn,  the  steam-engine,  i.  331,  ii.  133  ; 
indestructibility  of  force,  111  ;  con- 
troversy with  Zeuner,  135  ;  179. 

Hirsch,  DrA.,  'Gesch.  d.  medicinischen 
Wissenschaften  in  Deutschland,'  i. 
210,  ii.  390,  401. 

Hirzel,  Sal.,  i.  167. 

His,  VV.,  ii.  271. 

Histology,  Huxley  on,  i.  196. 

Historians,  supposed  objectivity  of,  1. 
7. 

Historical  geography,  i.  294. 

History,  contemporary,  to  what  extent 
possible  and  valuable,  i.  6  ;  Goethe 
quoted  on  re-writing  of,  7  ;  periods 
of,  13  ;  philosophy  of,  due  to  Con- 
tinental thinkers,  25 ;  periods  of, 
take  their  name  from  some  gi-eat 
event  or  movement,  58  ;  and  science, 
relations  of,  206. 

Hittorf,  W.,  on  attraction  in  chemical 
phenomena,  i.  380  ;  fellow  -  worker 
with  Pllicker,  ii.  76  ;  electrolysis, 
164  ;  vacuum-tube  experiments,  190. 

Hobbes,  philosophy  of,  i.  48  ;  '  De  Cor- 
pore  '  quoted  on  Harvey,  282  ;  385,  ii. 
473. 

Hobsou,  on  the  infinite,  ii.  736. 

Hoff,  Prof,  van't,  i.  431,  450  ;  '  Journal 
ftir  physicalische  C'hemie,'  ii.  158 ; 
(see  Ostwald),  159 ;  researches  of, 
164  ;  discovery  of,  165  ;  carbon  tetra- 
hedron of,  424. 

Hoffmann,  F.,  animist,  1.  126. 

Hofmaun,  A.  W.  von,  on  Liebig,  i.  18, 
188  ;  scientific  experiments  under,  92  ; 
chemical  researches  of,  412;  "Fara- 
day "  lecture,  ii.  391  ;  393. 

Hofmeister,  Wilhelm,  the  genetic  con- 
ception of  plant  life,  ii.  224  ;  induc- 
tive school  of,  321. 

Hogg,  'The  Microscope,'  ii.  228. 

Holbach,  'Systeme  de  la  Nature,'  i. 
144. 

Holger,  von  (see  Baumgartner),  ii.  107. 

Holman,  Prof.  S.  W.,  '  Matter,  Energy, 
Force,  and  Work,'  ii.  182. 

Holtzmann,  investigations  into  nature 
of  heat,  ii.  112;  and  Clausius,  135. 

Holtzmiiller  on  isogonal  relations,  ii. 
701. 

Homer,  i.  261,  296. 

Homoeopathy,  i.  210. 

Homogeneous  formulae,  ii.  681  ;  co- 
ordinates, Mobius,  681, 


Homologj',  study  of,  ii.  258;  in  geo- 
metry, 663. 

Hooke,  Dr  Robert,  "reciprocal  dupli- 
cate "  ratio,  i.  98  ;  used  the  term 
"  cell,"  195  ;  283,  434  ;  referred  to  by 
Young,  ii.  18  ;  theory  of  elasticity, 
30  ;  compound  microscope,  228. 

Hooker,  Sir  J.  D.  (see  Darwin),  ii.  329  ; 
Darwin  to,  406. 

Hopital,  Marquis  de  1',  adopted  the 
calculus,  i.  101. 

'  Horen '  of  Schiller,  i.  84. 

Horner,  'Edinburgh  Review,'  i.  273, 

Horsley,  edition  of  "  Newton's  Works," 
i.  355. 

Horstmann,  labours  of,  ii.  170;  free 
energy,  173. 

Houil  referred  to,  ii.  653  ;  on  non- 
Euclidean  geometry,  714. 

Hovelacque,  Abel,  '  La  Linguistique,' 
ii.  540. 

Howard,  Luke,  classification  of  clouds, 
i.  286. 

Huber,  investigations  of,  ii.  415. 

Huggins,  Sir  William,  light,  ii.  11. 

Hugo,  Prof.,  of  Gottingen,  translated 
44th  chapter  of  Gibbon's  '  Roman 
Empire,'  i.  169. 

Humboldt,  A.  von,  on  scientific  state 
of  Paris  at  the  close  of  the  eighteenth 
century,  i.  17;  '  Kosmos,'  51,  53,  ii. 
277,  284,  328,  329,  532  ;  '  Life '  by 
Bruhns,  i.  207,  253,  263  ;  travels  in 
America,  i.  83  ;  eminence  in  scien- 
tific literatiire  of,  105  ;  his  influence 
as  pojiulariser  of  the  study  of  natural 
history,  106  ;  133,  155  ;  and  Gauss's 
scheme  for  a  network  of  magnetic 
observations,  167 ;  171,  175,  176 ; 
uninfluenced  by  speculative  spirit  in 
German  science,  178  ;  cited  on  Georg 
Forster,  179 ;  183,  190 ;  supported 
scientific  institutions  at  Berlin,  238  ; 
Bell's  theorem,  293  ;  founded,  with 
Oken,  "  Naturforscher  -  Versamm  - 
lung,"  298;  and  Gay-Lussac,  425; 
popular  work  of,  ii.  149 ;  explorations, 
206 ;  travels,  222,  247  ;  morphology, 
225,  226  ;  252 ;  extension  of  mor- 
phological view,  260 ;  and  Robert 
Brown,  265  ;  266  ;  influence  of,  276  ; 
293,  .300;  341,  390,  467;  animal 
electricity,  475,  476  ;  514,  607. 

Humboldt,  W.  von,  creator  of  Berlin 
University,  i.  38  ;  203,  206,  212,  253, 
263 ;  comparative  jjhilologv,  ii.  538  ; 
542. 

Hume,  David,  transition  from  the  logi- 
cal   to    the    historical    view,   i.   46 ; 


778 


INDEX. 


opposed  metaphysics,  75 ;  influence 
of,  on  German  thought  and  literature, 
212 ;  sceptical  philosophy  of,  replied 
to  by  Kant,  ib.  ;  and  Kant,  219  ;  in- 
tercourse with  French  thought,  268  ; 
influence  of, '273;  ii.  279  ;  and  German 
criticism,  323  ;  326  ;  psychology,  497  ; 
genetic  view,  506 ;  the  study  of 
mankind,  529  ;  quoted,  555. 

Hunter,  John,  English  medical  science, 
i.  208  ;  anatomist,  283  ;  ii.  247. 

Hunter,  John  and  William,  no  connec- 
tion with  the  English  universities,  i. 
272. 

Hutton,  James,  a  follower  of  Boscovich, 
i.  359 ;  study  of  fossil  remains,  ii. 
225  ;  Cuvier's  "catastrophism,"  250  ; 
school  of  geology,  291  ;  genetic  view 
in  geology,  330 ;  364  ;  and  Jameson, 
services  to  the  study  of  natural  his- 
tory, i.  283  ;  290. 

Huxley,  T.  H.,  'Lay  Sermons'  and 
other  writings,  i.   193,  201 ;   quoted, 

193,  292,  ii.'^252,  256,  257,  348,  376, 
405,   448;    'American  Addresses,'  i. 

194,  ii.    364 ;    on    individuality    of 
English  scientists,    i.  250 ;    '  Science 
and   Culture,'  282;    'Essay  on  Geo- 
logical    Reform,'    283;     'Geological 
Reform  '  quoted,  291 ;  '  Critiques  and 
Addresses,'    298;    'Life    of    Charles 
Darwin,'  310  ;   on  Whewell  and  the 
mechanical  equivalent  of  heat,  ih.  ; 
'Scientific    Aspects    of    Positivism,' 
310;  onComte,  'Lay  Sermons' quoted, 
ii.  37  ;  extract  from  "  Lecture  on  the 
Study  of  Biology,"   217  ;    quotation 
from   'Life  of  Richard  Owen,'  222; 
Goethe's    ideas,    244,    246 ;    Cuvier's 
work,     248 ;     quoted    on     vertebral 
theory  of  the  skull,  251  ;   on  Hum- 
boldt,  253;    the  term   "homology," 
259 ;    on    Cuvier    and    Oken,    260 ; 
268;    "Evolution   in   Biology,"  278, 
297,  347  ;  controversy  with   Kelvin, 
284;    on    Hutton,     291,     292;    and 
Von  Baer,  299,  302;  305;  historical 
connection  of  Lamarck's  ideas,  309  ; 
"Biology,"  313;  321  ;  theory  of  de- 
scent in  France  and  Germany,  322 ; 
"Agnosticism,"  326  ;  "Reception   of 
the    'Origin  of  Species,'"   327  ;  329  ; 
address  to  the    Geological    Society, 
363;    'On  Descartes,'    378;    "vital- 
ism," 406;  411  ;  "On  the  Cell  Theory," 
423  ;  history  of  Biogenesis,  451  ;  the 
ubiquity  of  life,  452  ;  psycho-physi- 
cal parallelism,  519  ;  theory  of  reflex 
action,  520. 


Huygens,  Chr.,  variation  of  gravity  in 
different  latitudes,  i.  99 ;  103 ;  the 
theory  of  probabilities,  120  ;  mechan- 
ical laws  established  by,  317  ;  New- 
ton and,  ib. ;  formulte  of,  335 ; 
mechanical  explanation  of  gravita- 
tion ;  342,  351  ;  phenomena  of  gravi- 
tation, 353 ;  389 ;  kinetic  view  of 
nature,  ii.  6  ;  8  ;  followed  by  Young, 
9  ;  the  theory  of  light,  13,  14,  17  ; 
periodic  wave-motion,  21 ;  'Traite  de 
la  Lumiere,'  22  ;  motion  of  light,  42  ; 
conservation  of  energy,  99,  100  ;  on 
probability,  565,  568. 

Hyatt,  A.,  neo-Lamarckian,  ii.  351. 

Ideal  elements,  ii.  664  ;  Poncelet  on, 
674  ;  numbers,  727  ;  Kummer's,  728. 

Ideals  of  life  during  nineteenth  cen- 
tury, i.  32. 

Ideas,  migration  of,  i.  29. 

Ideologues,  Napoleon  and  the,  i.  152 ; 
ii.  3'23. 

Imaginary,  the,  Cayley  on,  ii.  716. 

'  Index  Lectionum '  of  Gottingen  Uni- 
versity, i.  165. 

Individualism  of  English  character,  i. 
279. 

Individuality  the  centre  of  interest  of 
the  sciences,  i.    125  ;  ii.  746. 

Individuation,  ii.  415. 

Inductive  reasoning  in  England,  i.  103. 

Infinite,  the,  ii.  643,  735  ;  Hobson  on, 
736. 

Infinitesimal  methods,  necessity  of  de- 
veloping, i.  373. 

Infinitesimals,  method  of,  ii.  706. 

Inheritance,  inarticulate,  ii.  615. 

Inquiry,  scientific  method  of,  i.  30. 

Institute,  French,  reports  of,  i.  149. 

Institution,  Royal,  i.  264. 

Interests,  human,  unity  of,  i.  33. 

Introspective  method,  ii.  527. 

"Invariants,"  doctrine  of,  ii.  140,  676  ; 
MacMahon  on,  676  ;  history  of,  677  ; 
unknown  to  Pliicker,  677  ;  Sylvester 
on,  684 ;  diflerent  methods  in,  ib. 

Inventions,  accidental,  in  sixteenth, 
seventeenth,  and  eighteenth  centuries, 
i.  91. 

Inverse  operations,  ii.  639,  727. 

"Ions,  migration  of,"  ii.  164;  198. 

Ireland,  Alexander,  on  authorship  of 
the  'Vestiges,' ii.  318. 

Irvine,  Dr,  the  term  "capacity"  first 
used  by,  ii.  102. 

Isenkrahe,  C,  'Das  Rathsel  von  der 
Schwerkraft,'  i.  341,  342,  343,  377  ; 
refers  to  Euler's  ether  theory,  ii.  8. 


INDEX. 


779 


Isherwood,  researches  of,  ii.  135. 

Isonierisni,  discovery  of,  ii.  405. 

Isomorphism,  ii.  444. 

Ivory,  scientific  work  of,  i.  229  ;  well 
known  among  Continental  mathema- 
ticians, 232 ;  not  member  of  any 
university,  238 ;  maintaiue'i  reputa- 
tion of  British  mathematicians,  270. 

Jacobi,  C.  G.  I.,  i.  44  ;  '  Werke,'  185  ; 
187,  189 ;  inJiuence  on  Helmholtz, 
199  ;  200,  205,  ii.  637  ;  his  relation  to 
Legendre  and  Abel,  648  ;  on  deter- 
minants, 683,  686 ;  Theta  function, 
696,  728. 

Jacobi,  F.  H.,  'Offener  Brief  an  Fichte,' 
i.  83  ;  162  ;  influenced  by  Spinoza, 
212  ;  psychology,  ii.  495. 

Jaeger,  Dr,  "gerunnal"  element,  ii. 
457. 

'  Jahresberichte '  of  Berzelius,  i.  167. 

James,  Alex.,  process  of  cellular 
division,  ii.  445. 

James,  King,  charter  to  Edinburgh 
University,  i.  268. 

James,  Prof.  W.,  '  Principles  of  Psy- 
chology,' ii.  479,  513,  519  ;  quoted, 
522,  539. 

Jameson  founded  Wernerian  Society, 
i.  118  ;  288. 

Janiin,  speed  of  light,  ii.  45. 

Januschke,  Hans,  '  Das  Princip  der 
Erhaltung  der  Energie,'  ii.  152. 

Japp,  Prof.,  "Stereo -chemistry  and 
Vitalism,"  ii.  437;  selective  action 
of  certain  organisms,  598. 

Jardin  des  Plantes,  i.  107. 

Jeffrey,  '  Edinburgh  Review,'  i.  273. 

Jenner,  Edward,  no  connection  with 
the  English  universities,  i.  272 ;  284. 

Jevons,  Stanley,  '  Principles  of  Science,' 
i.  37,  308  ;  on  theory  of  probabilities, 
120  ;  325  ;  Bacon's  "  method  of  in- 
stances," ii.  558,  559  ;  '  Principles  of 
Science '  quoted,  560,  569  ;  737. 

Joachim  of  Brandenburg,  founds  Uni- 
versity of  Kouigsberg,  i.  159. 

John  Frederick,  Duke  of  Hanover,  i. 
158  ;  founds  University  of  Jena,  159. 

John,  v.,  'Gesch.  d.  Statistik,'  ii.  555, 
587 ;  statistics,  563  ;  564 ;  quoted,  579. 

Jones,  Bence,  'The  Royal  Institution,' 
i.  90. 

Jordan,  Camille,  his  'Theorie  des 
Substitutions,'  ii.  686,  692. 

Joseph  II.,  i.  256. 

Joule,  James  Prescott,  the  mechanical 
equivalent  of  heat,  i.  93  ;  doctrine  of 
the    conservation    of    energy,    201  ; 


"J"  or  Joule's  equivalent  of  heat, 

265  ;  and  Dalton,  ib.  ;  not  connected 
with  Cambridge  Mathematical  School, 

266  ;  not  member  of  any  uiuversity, 
272  ;  determination  of  the  equival- 
ent of  heat,  309  ;  "mechanical  theory 
of  gases,"  310;  313;  paper  on  mol- 
ecular action,  433 ;  calculations  of, 
434  ;  435,  437  ;  ii.  Ill  ;  kinetic 
theory  of  gases,  34,  162  ;  dyn- 
amical theory  of  heat,  73 ;  inde- 
pendence of  Mayer's  writings,  97  ; 
and  Tyudall,  107 ;  heat  unit,  109  ; 
scientific  work  of,  110  et  seq.  ;  a  pupil 
of  Dalton,  111  ;  indestructibility  of 
force,  ib.  ;  revival  of  interest  in  the 
ideas  of  "Energy,"  ll4  ;  his  measure- 
ments utilised  by  Clausius  and  Thom- 
son, 116  ;  practical  foundation  of  his 
researches,  117 ;  perpetual  motion, 
124  ;  two  laws  of  thermo-dynamics, 
128  ;  force,  130  ;  subjection  of  physi- 
cal phenomena  to  dynamical  laws, 
132 ;  measurements  of,  133  ;  and 
experiments,  137;  "Thermal  Unit," 
139 ;  conservation  of  energy,  142 ; 
electrical  phenomena,  146 ;  law  of, 
147  ;  electrical  measurements,  156  ; 
heat,  178;  "energy,"  355;  statistics 
in  physics,  590,  592. 

Jousse,  geometrical  work  of,  i.  114. 
Julius  of  Brunswick  founds  University 

of  Helmstadt,  i.  160. 
Juugfleisch,  ii.  437. 
Jurin,    Dr,    experiments    in    capillary 

attraction,  i.  356. 
Jussieu,    Ant.    Laurent  de,    author  of 

'  Genera    Plantarum,'    ii.    222,    235, 

265. 
Jussieu,   Bernard  de,  contributions  to 

the  study  of  natural  history,  i.  116  ; 

119  ;  botanical  work  of,  126  ;  referred 

to,  265. 
Justi,  'Winckelmann,' i.  279, 

Kane,  his  work  overlooked,  i.  414. 

Kant,  scientific  methods  insulBcient  by 
themselves,  i.  36  ;  influenced  popu- 
larity of  lectures  on  "Encyclopiidie," 
37  ;  a  century  before  his  time,  45  ; 
style  of,  51  ;  decadence  of  philosophi- 
cal thought  after,  78  ;  radicalism  of 
thought  of,  81  ;  ideas  of,  developed 
by  Schiller  and  others,  83 ;  Helm- 
holtz and  the  philosophy  of,  199 ; 
influenced  by  political  movements  in 
France  and  America,  203  ;  influence 
on  development  of  German  schools  of 
medicine,  208  ;  211,  212  ;  mathemati- 


780 


INDEX. 


cal  and  physical  sciences  affected  by, 
216  ;  infiuence  of,  on  the  development 
of  modern  German  science,  219  ;  and 
Hume  and  Descartes,  222 ;  influence 
of,  on  education  in  Germany,  257  ; 
was  inspired  by  Rousseau,  259 ;  in- 
fluenced by  Hume,  273 ;  philosophy 
of,  dispelled  Cartesian  philosophy  in 
Germany,  433  ;  cosmological  genesis 
of  planetary  system,  ii.  209  ;  nebular 
theory,  277,  282 ;  late  development 
of,  309  ;  '  Critique  of  Pure  Eeason,' 
326 ;  philosophical  theories,  346 ; 
metaphysics,  354;  "si^ecific  ener- 
gies." 482  ;  science  of  sensation,  484  ; 
time  and  space,  491,  492  ;  the  mind, 
497 ;  space  perception,  506 ;  and 
Herder,  532,  535;  freewill,  584; 
634  ;  751. 

Kastner  of  Gottingen  University,  i. 
165. 

Kater,  scientific  work  of,  i.  230. 

Kaufmann,  W.,  Hamburg  Address,  ii. 
190,  197. 

Kaup,  Jacob,  'Skizzirte  Entwickelungs- 
geschichte  und  natiirliches  System  der 
Europaischen  Thierwelt,'  ii.  317. 

Kayser,  spectroscopic  observations,  ii. 
361,  362. 

Keill,  John,  molecular  attraction,  i. 
355. 

Kekule,  chemical  researches  of,  i.  412  ; 
'  Lehrbuch  der  organischen  Chemie ' 
quoted,  421,  448 ;  explains  pheno- 
menon of  multiple  proportions,  447  ; 
theory  of  aromatic  compounds,  449 ; 
benzine  ring,  ii.  424. 

Kellaud's  edition  of  Young's  writings 
quoted,  ii.  98,  104. 

Kelvin,  Lord.  See  Sir  William  Thom- 
son. 

Kepler,  Bacon's  indebtedness  to,  i.  94  ; 
118  ;  three  laws,  157,  318  ;  received 
logarithms  with  enthusiasm,  269 ; 
Newton  and,  317 ;  374 ;  father  of 
modern  astronomy,  386  ;  astron- 
omical work  of,  ii.  227 ;  634. 

Kerner  von  Marilaun,  '  The  Natural 
History  of  Plants '  quoted,  ii.  376. 

Kerry,  B.,  on  G.  Cantor  and  mathe- 
matics, ii.  634 ;  734. 

Ketteler,  '  Theoretische  Optik,'  ii.  54. 

Kielmeyer  and  the  Naturphilosophie, 
i.  207  ;  ii.  349. 

Kieser,  D.  G.,  and  the  Naturphilosophie, 
1.  207  ;  ii.  230  ;  phytotomic  researches 
in  Germany,  261. 

ELinetic,  view  of  nature,  ii.  3  ;  the  word 
introduced  by  Ampere,  5  ;  revival  of 


kinetic  view  in  nineteenth  century, 
7  ;  theories,  34  ;  theory  of  gases,  ib.  ; 
view  of  nature,  insufficiency  of,  96  ; 
the  term  substituted  for  "actual," 
139;  "kinetics"  and  "energetics," 
180 ;  465,  574. 

Kirchhoff,  Gustav,  'Mechanik,'  i.  45; 
'  Vorlesungen  iiber  Mathematische 
Physik,'  231  ;  discovery  of  spectrum 
analysis,  277  ;  coincidence  between 
electrical  wave  -  motion  and  light, 
372;  Weber's  law,  380;  definition 
of  "mechanics,"  382;  Frauuhofer's 
lines,  ii.  48  ;  '  Gesammelte  Abhand- 
lungen,'  ib. ;  caesium  and  rubidium, 
49  ;  emission  and  absorption  of  light 
rays,  50  ;  51  ;  spectrum  analysis,  56  ; 
"physical  mechanics,"  101. 

Kirwan,  i.  117,  ii.  291. 

Klaproth,  i.  117 ;  forerunner  of  Berze- 
lius,  391  ;  393. 

Klein,  'G.  Forster  in  .Mainz,'  i.  179. 

Klein,  Felix,  pupil  of  Pliicker,  ii.  76  ; 
his  geometrical  tract,  632  ;  on  the 
period  of  Euclid,  635;  'Evanston 
Colloquium'  quoted,  ib. ;  on  abridged 
mathematics,  636  ;  686  ;  his  '  Erlangen 
Programme,'  690;  and  Lie,  691,  692, 
718,  720 ;  his  tract  on  Riemann's 
theory,  698,  699  ;  on  Riemann's  in- 
fluence, 700  et  seq. ;  on  Riemann 
and  Weierstrass,  707  ;  on  Dirichlet's 
principle,  708  ;  on  non-metrical  rela- 
tions, 713 ;  on  non-Euclidean  geom- 
etry, 715  ;  on  Cayley  and  von  Staudt, 
718 ;  on  generalised  notion  of  dis- 
tance, ib.  ;  on  famous  problems,  721, 
731  ;  on  arithmetising  tendency,  738,  1 

740.  I 

Klopstock,  Alcaic  and  Sapphic  metres 
of,  i.  213.  a 

Knapp,  statistics,  ii.  563,  566.  ■ 

Knott  on  directional  calculus,  ii.  656.  ■ 

Knowledge,  accumulation  of,  in  nine- 
teenth century,  i.  28 ;  method  and 
unity  of,  29. 

Knox,  John,  creator  of  Scotch  educa- 
tional system,  i.  253  ;  '  First  Book  of 
Discipline,'  255. 

Kobell,  'Geschichte  der  Mineralogie,'  i. 
117. 

Kochly,  i.  162;  'Gottfried  Hermann,' 
169. 

Kohlrausch,  F.,  electrolysis,  ii.  164. 

Kohlrausch,  R.,  electrical  measure- 
ments, i.  369;  ii.  84. 

Kolbe,  chemical  researches  of,  i.  412 ; 
attacks  of,  on  'Modern  Chemistry,' 
455. 


INDEX. 


781 


Kolliker,  von,  quoted,  ii.  401;  "idio- 

plasma,"  448. 
Konig,  Ed.,  on  Wundt,  ii.  513. 
Kcinig,   H.,    '  G.   Forster  in   Hans  und 

Welt,'  i.   179. 
Konigsberger,  L.,   'Zur  Geschichte  der 

Theorie    der    elliptischen    Transceu- 

denten,'  i.  185,  ii.  648. 
Kopke,    Rudolf,     '  Die    Griindung   der 

Koniglichen-Wilhelms-Universitat  zu 

Berlin,'  i.  263. 
Kopp,    Hermann,    on    the    reports    of 

Berzelius,  i.  42  ;    '  Die  Entwiclceluug 

der  Chemie,'  115,  246,  418,  419,  ii.  154 ; 

'Geschichte  der  Chemie,'  i.  175,  188, 

191,  308  ;   quoted  on  Lavoisier,  386, 

387;    quoted,    391,    393,    398,   407, 

421,   422;    electro  -  chemical   theory, 

405 ;    408   et  seq.,    413  ;    Avogadro's 

hypothesis,  428  ;  on  J.  Black,  ii.  102  ; 

founded  physical  chemistry,  153 ;  157. 
Kossak,  E.,  on  Weierstrass,  ii.  712  ;  734. 
Kotter,  E.,  on   Poncelet's   principle   of 

continuity,   ii.   660 ;  on   von   Staudt, 

661. 
"  Kreislauf  des  Lebens,"  ii.  395. 
Kronecker,  ii.  727,  729  ;   on  arithmetis- 

ing,  738. 
Kronig,  A.,  '  GrundzUge  einer  Theorie 

der  Gase,'  i.  433  ;   ii.  162  ;  179. 
Krug,    representative    of    encyclopaedic 

teaching,  i.  38. 
Kunimer,  ii.  680,  726 ;   ideal  numbers, 

728. 
Kundt  (see  Christiansen),   '  Die  neuere 

Entwicklung    der   Electricitatslehre,' 

i.  380. 
Kuntze,    quoted    in    reference    to    the 

brothers  Weber,  i.  197  ;  biography  of 

G.  T.  Fechner,  200 ;  ii.  608. 

La  Beche,  de,  palaeontological  work  of, 
i.  139. 

Lacepede,  i.  119. 

Lacroix,  geometry,  i.  44  ;  '  Differential 
and, Integral  Calculus,'  233;  student 
at  Ecole  normale,  237  ;  ii.  643,  686. 

Ladeuburg,  '  Vortriige  iiber  die  Ent- 
wicklungsgeschichte  der  Chemie,'  ii. 
158. 

'  Ladies'  Diary,'  i.  236,  238,  ii.  679. 

Laennec,  French  medical  science,  i.  208. 

Lagrange,  mechanics,  i.  44 ;  general 
methods  of,  45  ;  adapts  the  calculus 
to  the  problems  of  the  'Principia, ' 
102;  '  Mecanique  analytique,'  ,105, 
ii.  100;  mathematics  at  the  "Ecole 
normale,"  i.  112;  113,  148,  181,  200, 
233 ;    237 ;    analytical    methods    of, 


271;  "  potential  function,"  316 ;  319 
theories  elaborated    by  Gauss,    331 
ii.  5  ;  mathematical  study  of  vibra 
tions,  16  ;  analytical  school  of,  100 
dynamics,    138 ;    his    system   mathe 
matical,  144;   467,  510,  572;  theory 
of  error,  575  ;  637  ;  on  fundamental 
questions,   656;    669,  680,  690;   and 
Weierstrass,  693-695,  706. 

Laguerre,  ii.  715.  , 

Lakanal  on  the  Ecole  normale,  i.  109, 
112;  quoted.  111;  113;  obtained  a 
decree  from  Convention  to  continue 
sittings  of  the  Academy  during  sus- 
pension, 148;  "  Museum,"  ii.  311. 

Lalande  at  the  College  de  France,  i. 
107;  113,  167,  177;  Clairault's  at- 
tempt to  alter  gravitation  formula, 
334. 

Lamarck,  '  Philosophie  Zoologique,'  i. 
S3,  ii.  309  et  seq.;  beginnings  of  Dar- 
winian theory,  i.  137 ;  temporary 
neglect  of  suggestions  of,  179 ; 
'  Hydrogeologie,'  194;  and  the 
'Origin  of  Species,'  201;  '  Hydro- 
geologie  '  quoted,  ii.  217 ;  natural 
history  of  vertebrates,  239  ;  247  ;  and 
Geoffroy  Saint-Hilaire,  255  ;  and  Von 
Baer,  316  et  seq.;  321,  322,  327; 
natural  selection,  330,  351  ;  adapta- 
tion, 353;  "environment,"  394;  his 
.school,  431  ;  460,  470,  607,  621. 

Lambert,  J.  H.,  i.  175  ;  'Photometry,' 
'Pyrometry,' 176  ;  319;  cosmological 
letters,  ii.  282. 

Lame,  treatises  on  mathematics  and 
physics,  i.  45  ;  theories  of,  360  ;  379  ; 
synthetic  method,  ii.  100 ;  influenced 
German  thought,  101. 

La  Mettrie,  '  L'Homme  Machine,'  i. 
144;  '  Histoire  naturelle  de  I'Ame,' 
lb.;  ii.  699. 

Landen,  scientific  services  of,  i.  229  ; 
well  known  among  Continental  mathe- 
maticians, 232 ;  maintained  reputa- 
tion of  British  mathematicians,  270. 

Lange,  F.  A.,  '  History  of  Materialism,' 
i.  145,  385,  ii.  323,  513,  584  ;  "psy- 
chology without  a  soul,"  523. 

Langley,  function  of  gland  cells,  ii. 
429. 

Language  portrays  changes  of  thought, 
i.  11  ;  conventional,  inadequate  for 
original  thought,  12  ;  the  problem  of, 
ii.  536. 

Lankester,  Ray,  "Zoology,"  ii.  232; 
the  term  "  homology,"  259. 


Lapeyronie 
Chirurgie, 


founded 
107. 


Academic     de 


782 


INDEX. 


Laplace,  works  of,  i.  82,  97  ;  Newton's 
ideas  elaborated  by,  96  ;  mathematics 
at  the  Ecole  normale,  112,  237;  113, 
115;  crystallography,  116  ;  'Systeme 
du  Monde,'  119,  319;  'Tbeorie  analy- 
tiqiie  des  Probabilite-s,'  120,  325  ;  his 
own  iiopulariser,  122  ;  statistics,  124  ; 
126;  and  Cuvier  contrasted,  132;  148, 
154,  177,  181,  187,  200  ;  "exact  habit 
of    thought,"    222;    potential    func- 
tion, 231,  316  ;  241 ;  Ualton's  atomic 
theory,    246  ;    264  ;    researches    of, 
281 ;  306,  311 ;   '  Mecanique  celeste,' 
319 ;    358 ;    gravitation,    321  ;    least 
squares,  324;  326;    the  Tides,  330; 
Gauss,    331  ;    mathematical    expres- 
sion of  astronomy,   333  ;    emanation 
theory   of    light,    344  ;    346  ;    mole- 
cules, 347  ;  gravitation  theory,  349  ; 
molecular  attraction,  354;    'Theorie 
de  I'Action  capillaire,'  355  ;  quoted, 
356  ;  St  Veuaut    quoted,   359  ;    362  ; 
corpuscular    theory    of    light,    370 ; 
measurement    of     electrical     action, 
371  ;  value  of  Newton's  formula,  373  ; 
Newton's    law,     378 ;    astronomical 
view    of   nature,    380 ;    opposed    to 
undulatory  theory,   ii.   16  ;  on  New- 
ton's emission  theory,  17  ;  theory  of 
light,  20  ;  opposed  undulatory  theory 
of  light,  24  ;  on  the  commission  which 
crowned   Fresnel's    'Memoire  sur  la 
Diflraction,'  25  ;  extension  of  gravita- 
tion   into     molecular    physics,    29 ; 
theory  of  capillarity,  33  ;  'researches 
into      electrical      phenomena,      67 ; 
methods  of,  70  ;   school  of,  referred 
to,   93,    100,    101  ;   the  material  and 
dynamical  conceptions  of  heat,  118  ; 
cosmological    genesis    of    planetary 
system,  209;  215;  astronomical  work 
of,      227;     228;     nebular     theory, 
277,  284  ;  quoted,  285  ;  290  ;  genesis 
of   the    cosmos,    320 ;    genetic    view 
anticipated  by,  330  ;  theory  of,  357  ; 
hypothesis  of,  360  ;  stability  of  solar 
system,  386  ;  animal  heat,  390,  433  ; 
analysis   of    phenomena    of    nature, 
399 ;    474,    487  ;    science  of  chances, 
568  ;  569,  571,  572,  575  ;  method  of 
least  square,  576  ;   doctrine  of  prob- 
abilities,    578 ;    influence     of,    581  ; 
statistical  method  in  social  questions, 
599 ;  curve  of  error,  616  ;  634,  637  ; 
his  '  Mecanique  celeste '  and  '  Theorie 
des   Probabilites,'  642;  functions  of, 
696  ;  751. 
Larmor,  Jos.,  vortex  theory,  ii.  63,  64  • 
'  ^ther  and  Matter,'  89,  195  ;  mathe- 


matical theory  of   electricity,    193 ; 
his  position,  195  ;    197  ;    atomic  and 
energetic  views,  198  ;  595  ;  on  vectors, 
656. 
Lasswitz,    'Geschichte  der  Atomistik,' 
i.  433,  ii.  5;    'G.  T.  Fechner,'  369, 
508;  Fechner's  philosophy,  513. 
Laurent,  revives  Front's  hypothesis,  i. 
402 ;    attack    on     electro  -  chemical 
theory,    409;    "type    theory,"  411; 
413;    quoted,    419;    "substitution" 
in  chemical  combination,  429. 
Laurillart,  Bell's  theorem,  i.  293, 
Lavater,      Caspar,      '  Physiognomische 

Fragmente,'  ii.  477. 
Lavoisier,    i.    114,    147 ;    services    to 
France,  148  ;  170,  188,  200  ;  scientific 
method  of,  306,  365  ;    influenced  by 
Laplace,  380  ;  theory  of  combustion, 
386,  393  ;   chemical  researches,  391  ; 
392,  399,  400  ;  organic  analysis,  407  ; 
chemical    balance,    ii.    152";    atomic 
view,  153  ;  379  ;  and  his  school,  382  ; 
animal  heat,  390,  433 ;  chemical  ele- 
ments, 398. 
Lawes,  Sir  J.  B.,  experiments  and  pub- 
lications in  agriculture,  i.  284. 
Layard,  i.  294. 
Lazarus,    psychologist,    ii.    497 ;     the 

objective  mind  in  history,  530. 
Leake,  M.  W.,  explorations  of,  i.  296. 
Learning,  apparent  disintegration  of,  i. 

30. 
Least  squares,  method  of,  i.  120 ;  183 ; 

ii.  576. 
Le  Bel,  the  carbon  tetrahedron,  i.  450. 
Leblanc  invents  soda  process,  i.  92. 
Le  Breton,  report  on  Fine  Arts,  i.  149. 
Le  Chatelier,  '  Journal  de  Physique,'  ii. 

169,  173. 
Lecoq    de    Boisbaudran,    discovery    of 

gallium,  i.  315,  423. 
Legallois,  ii.  519. 

Legendre  reforms  geometry,  i.  44 ; 
'  Theorie  des  Nombres,'  82  ;  method 
of  least  squares,  120,  183,  ii.  576  ;  i. 
181  ;  '  Traite  des  Nombres,"  182  ; 
'Nouvelles  methodes  pour  la  deter- 
mination des  orbites  des  cometes,'  183  ; 
'Traite  des  fonctions  elliptiques,' 
185  ;  187  ;  potential  function,  231 ; 
on  elliptic  integrals,  ii.  648  ;  his  rela- 
tion to  Abel  and  Jacobi,  ib.  ;  Konigs- 
berger  on,  ih. ;  on  foundations  of 
geometry,  656  ;  on  svnthetic  method, 
670;  functions  of,  696;  721. 
Lehmann,  '  Molecularphysik '  quoted,  1. 

Leibniz,    i.    49 ;    essay    on,     by    the 


INDEX. 


783 


author,  50 ;  on  thought,  66 ;  or- 
gauises  scientific  eft'ort,  100;  "cal- 
culus," 101 ;  modern  analytical  spirit 
of,  102  ;  letter  to  Huygens  on  cal- 
culus, 103  ;  letter  to  Bodenhausen, 
104;  105;  'Schriften,'  122;  137;  at 
the  court  of  Brunswick,  158 ;  the 
Uuiversity  of  Halle,  160 ;  encyclo- 
paedic view  of  '  Wissenschaft,'  171; 
modern  science,  175  ;  reaction  against 
his  philosophy,  212 ;  notation  of, 
233  ;  247,  283,  311  ;  "energy,"  312  ; 
337  ;  gravitation,  340  ;  358  ;  letter  to 
Foucher,  ii.  5  ;  Euler's  opposition  to, 
8  ;  "vis  viva,"  100  ;  indestructibility 
of  force,  111  ;  inHuences  German 
philosophy,  205  ;  scientific  work  of, 
210;  'Protogfea,'  277,  280,  293; 
' '  evolutionist, "  278  ;  '  Protogcea ' 
quoted,  281  ;  288  ;  epigenesis,  298  ; 
genetic  view  anticipated  by,  330 ; 
364,  365  ;  animation  of  all  nature, 
369  ;  403  ;  idea  of  life,  409  ;  monad- 
ology,  500 ;  507  ;  doctrine  of  pre- 
established  harmony,  519 ;  (see 
Herder),  535  ;  the  theory  of  language, 
537 ;  statistical  information,  546 ; 
555 ;  Neumann's  statistical  tables, 
565  ;  science  of  chances,  568  ;  theory 
of  probabilities,  573  ;  638,  643  ;  his 
dyadic  system,  645  ;  on  convergency, 
646 ;  letter  to  Huygens,  659 ;  on 
determinants,  682 ;  706  ;  science  and 
religion,  742. 

Leitch,  '  Miscellaneous  Works '  of  Dr 
Young  cited,  i.  244. 

Lelievre,  i.  136. 

Lemonnier  at  the  .Jardin  des  Plantes,  i. 
107. 

Lenard,  discoveries  of  light  rays,  ii. 
92 ;  observation  of  cathode  rays, 
192. 

Lenz,  electrical  phenomena,  ii.  146. 

Le  Sage,  "ultramundane  corpuscles," 
i.  342 ;  344 ;  quoted  on  Epicurus, 
ii.  4. 

Leslie,  scientific  work  of,  i.  229,  230  ; 
Scotch  university  professor,  272. 

Lessing,  moralising  style  of,  i.  51  ;  and 
Gibbon,  169  ;  171  ;  the  scientific  ideal 
of,  211  ;  212. 

Leuckart,  Rudolf,  ii.  322  ;  law  of  limit 
of  growth,  445. 

Leuweuhoek,  perfection  of  simple  micro- 
scope, ii.  228  ;  reference  to,  281. 

Leverrier  and  the  discovery  of  Neptune, 
i.  277;  "Association  scientifique," 
298  ;  astronomical  achievements  of, 
314  ;  meteoric  hypothesis,  ii.  357. 


Lewes,  G.  H.,  on  Herbert  Spencer,  i. 
48;  'Life  of  Goethe,'  166;  ii.  470; 
phrenology,  478  ;  "specific  energies," 
483  ;  512  ;  spinal  chord,  519  ;  608. 

Lexis,  Prof. ,  '  Die  deutsclieu  Universi- 
tateu,'  i.  226  ;  statistics,  ii.  566. 

Lhuilier  referred  to  by  Steiner,  ii. 
669. 

Lichtenberg  of  Gottingen  University,  1. 
165 ;  electricity  and  the  Geissler 
tubes,  ii.  191  ;  physiognomy,  477. 

Lichton,  John,  Louvain  University,  i. 
268. 

Lie,  Sophus,  ii.  686 ;  and  theory  of 
groups,  690;  and  Klein,  691,  692, 
718  ;  on  differential  equations,  696  ; 
on  fundamental  problem  of  geometry, 
718 ;  720. 

Liebig,  J.  von,  laboratory  at  Giessen,  i. 
18;  '  Jahresbericht  der  Chemie,'  42; 
works  on  chemistry,  43 ;  chemical 
predictions  of,  92 ;  on  Bacon,  93 ; 
115 ;  162,  174 ;  temporarily  in- 
fluenced by  speculative  spirit  in 
German  science,  178  ;  establishment 
of  chemical  laboratories,  188  ;  quoted, 
190  ;  his  organic  analysis,  191  ;  and 
Wcihler,  192 ;  194 ;  metaphysical 
leanings  of,  196  ;  200  ;  influenced  by 
the  JWUurphilosophie,  207  ;  freed 
under  the  influence  of  French  science, 
208 ;  underlying  idea  in  foimding 
chemical  laboratory,  214;  "vital 
force,"  218  ;  Dalton's  atomic  theory, 
246  ;  agricultural  exi:ieriments,  285  ; 
'Familiar  Letters  on  Chemistry' 
quoted,  389;  discovery  of  "isomer- 
ism," 406;  the  "radicle"  theory, 
409 ;  the  hydrogen  and  the  oxygen 
theory  of  acids,  410  ;  412  ;  quoted  on 
chemical  research  in  England,  414 ; 
his  attitude  towards  the  atomic 
theory,  418  ;  .scientific  work  of,  ii. 
105;  '  Annalen  der  Pharmacie,'  107, 
163,  170 ;  Mohr's  and  Helm's  first 
papers  published,  lo9  ;  appreciation 
of  Mohr  and  Mayer,  114;  'Die 
Organische  Chemie,'  115 ;  organic 
chemistry,  117,  391  ;  dynamical 
theory  of  he.at,  128  ;  popular  work  of, 
149;  152;  (see  Thos.  Graham),  161; 
biological  studies,  208  ;  physiological 
processes,  390 ;  393  ;  his  influence, 
394 ;  396 ;  attempt  to  extend  the 
idea  of  "  Stoffwechsel,"  397  ;  '  Chemi- 
cal Letters,'  398  ;  practical  study  of 
nature,  404;  "vitalism,"  405;  406, 
411,  420;  Bacon's  "method  of 
instances,"  558. 


784 


INDEX. 


Leibisch,  '  Physikalische  Krystallogra- 
phie,'  i.  443. 

Liebreich,  Oscar,  discovered  action  of 
chloral,  i.  93. 

Life  and  mind,  ii.  216  ;  what  are  they  ? 
462  ;  mental,  496. 

Life,  problem  of,  ii.  352 ;  what  is  it  ? 
381  ;  Bichat's  definition  of,  383  ;  394  ; 
and  mind,  .548. 

Light,  the  undulatory  theory  of,  i.  241, 
ii.  153  ;  i.  229,  236  ;  theories  of,  ii.  8  ; 
undulatory  and  emission  theories, 
11  ;  undulatory  theory  prepared  by 
acoustics,  12  ;  and  sound,  mechanical 
difl'erence  between,  30;  speed  of,  36  ; 
corpuscular  theory  of,  ib.  ;  speed,  45  ; 
magnetisation  of  (Faraday),  74. 

Limits,  method  of,  ii.  706  ;  Hankel  on, 
ih. 

Lindemann,  researches  of,  ii.  124 ;  on 
transcendency  of  number  tt,  731. 

Link,  ii.  230  ;  observations  of,  261. 

'Linnajan  Society,  Transactions  of,'  i. 
41. 

Linnseus,  contributions  to  study  of 
natural  history,  i.  116;  beginning  of 
geometrical  crystallography,  117 ;  119 ; 
system  and  nomenclature  of,  126;  145; 
classification  of  living  beings,  288  ; 
system  of  classification,  ii.  220,  221, 
232 ;  basis  of  classification  of  veget- 
able and  animal  kinfjdom,  234  ;  first 
four  classes  of,  238  ;  243,  251 ;  classifi- 
cations, 254,  336 ;  311. 

Lionardo  da  Vinci,  rules  of  perspective, 
ii.  663. 

Liouville  recognised  merits  of  Green's 
work,  i.  247 ;  publishes  Galois' 
works,  ii.  686  ;  726,  727. 

Lister,  improvements  in  microscope,  ii. 
228. 

Listing,  J.  B.,  'Vorstudien  zur  Topo- 
logie,'  ii.  63. 

Literature,  French,  influence  of  science 
on,  i.  104. 

Lloyd,  Humphrey,  experiments  in  re- 
fraction, ii.  43. 

Lobatchevsky,  Vasiliev  on,  i.  161  ;  ii 
635  ;  and  Gauss,  652 ;  pupil  of  Bar 
tels,  653  ;  710,  713,  718. 

Locke,  David  Hume  and,  i.  47  ;  144  , 
influence  of,  on  German  thought  and 
literature,  212 ;  and  Kant,  219 
school  of,  250  ;  influence  on  educa 
tional  views  in  England,  253  ;  influ- 
ence on  French  philosophy,  273  ;  new 
line  of  thought  adopted  by,  311  ; 
sensualistic  philosophy,  ii.  323  ; 
psycho-physical  view,  471 ;  genesis  of 


space  perception,  473  ;  497  ;  genetic 
view,  506  ;  516  ;  language,  536  ;  751. 

Lockyer,  Sir  Norman,  nature  of  ele- 
ments, ii.  192  ;  282  ;  genesis  of  the 
cosmos,  360;  'Inorganic  Evolution,' 
369. 

Lodge,  Sir  01.,  "The  Second  Law  of 
Thermodynamics,"  i.  331;  370;  on 
"action  at  a  distance,"  380;  on  the 
ether,  '  Modern  Views  of  Electricity,' 
ii.  38,  90,  163 ;  popularisation  of 
Maxwell's  electro  -  magnetic  theorj^, 
73  ;  illustrations  of  Maxwell's  theory, 
90,  94. 

Lommel,  Ohm's  'Gesammelte  Abhand- 
lungen,'  i.  365. 

Longet,  Bell's  theorem,  i.  293. 

Longitude,  Board  of,  i.  113 ;  prize 
offered  by,  158. 

Longitudes,  Bureau  des,  i.  113. 

Lorentz,  H.  A.,  mathematical  theories 
of  electricity,  ii.  193  ;  195 ;  quoted, 
195,  197. 

Lorenz,  0.,  quoted  on  division  of  history 
into  centuries,  i.  13  ;  '  Die  Geschichts- 
wissenschaft,'  206. 

Loria,  Gino,  i.  275. 

Lotze,  Hermann,  definition  of  "reality," 
i.  32  ;  contrasted  with  Herbert  Spen- 
cer, 48  ;  quotation  from  '  Microcos- 
mus,'  52  ;  definition  of  philosophy, 
65  ;  constructive  ideas  of,  81  ;  and 
Fechner,  200;  lectures  on  "encyclo- 
pedia" of  philosophy,  215 ;  mechanical 
view  in  biology  of,  219 ;  220  ;  phil- 
osophy of,  ii.  288  ;  401 ;  "Leben  und 
Lebenskraft, "  401  ;  405  ;  vitalism  and 
animism,  407  ;  purpose  and  will,  408, 
409  ;  vitalism,  434  ;  anticipated  Helm- 
holtz,  491  ;  492  ;  influence  of  Herbart 
on,  494  ;  physiology  of  the  soul,  500  ; 
psycho-physics  of  vision,  504  ;  theory 
of  "local  signs,"  508;  medical  psy- 
chology, 512  ;  psycho-physics,  517  ; 
'  Microcosmus,'  532;  549;  quoted, 
585  ;  on  non-Euclidean  geometry,  716. 

Louis  XV.,  i.  107  ;  and  botany,  ii.  235. 

Love,  A.  E.  H.,  'Dynamics,'  ii.  183. 

Lowth,  'Lectures  on  Hebrew  Poetry,' 
ii.  537. 

Lubbock,  Sir  John,  ii.  415  ;  anthropol- 
ogist, 497. 

Lucretius,  scientific  speculations  of,  i. 
313;  the  "atomic  theory,"  385; 
quoted,  ii.  4. 

Ludwig,   F.,   mathematical   botany,  ii 
622. 

Ludwig,  K.  F.  W.,  Eloge  of  Weber,  ii. 
396 ;  ' '  automatic  curve-plotting, "  403. 


INDEX. 


785 


Luminiferous  ether,  theory  of,  ii.  18  ; 
69,  70. 

Lunar  theory,  i.  329. 

Liiroth,  on  von  Staudt,  ii.  669 ;  and 
Shepp,  translation  of  Dini's  work, 
704. 

Luther,  educational  work  of,  1.  255. 

Lyell,  Sir  Chas.,  i.  229 ;  quoted  on 
British  Association,  240  ;  '  Travels  in 
North  America,'  263  ;  '  Principles  of 
Geology,'  291,  ii.  277,  317;  on  Cuvier 
and  the  fixity  of  species,  256  ;  291  ; 
"  uniformitarian  "  school  of  geology, 

292  ;  beginnings  of  the  genetic  view, 

293  ;  quoted,  296,  559  ;  genesis  of  the 
cosmos,  320 ;  327  ;  genetic  view  in 
geology,  330  ;  335,  608. 

M'Aulay,  A.,  on  directional  calculus,  ii. 
656. 

Macaulay  eulogises  Bacon,  i.  93. 

M'Cormack,  Thomas,  translation  of 
Prof.  E.  Mach's  Works,  i.  318;  ii. 
183. 

M'Cosh,  James,  ii.  513. 

M'Cullagh,  James,  i.  274  ;  properties  of 
ether,  ii.  31 ;  analytical  method  of,  45  ; 
referred  to,  54  ;  contribution  to  vortex 
theory,  63  ;  195. 

MacCulloch,  J.  R.,  '  Statistical  Account 
of  the  British  Empire,'  ii.  563. 

Macfarlane  on  directional  calculus,  ii. 
656. 

Mach,  Prof.  Ernst,  '  Mechanik  in 
ihrer  Entwickehmg '  quoted,  i.  318, 
383,  ii.  97,  100  ;  '  Die  Geschichte  und 
die  Wurzel  des  Satzes  von  der 
Erhaltung  der  Arbeit,'  97;  'Prin- 
cipien  der  Warmelehre,'  102,  106, 
109,  111,  175  ;  popularisation  of 
Fourier's  heat  theory,  121  ;  criticism 
of  mechanical  view,  183  ;  185,  737. 

Machiavelli,  a  model  historian,  i.  7. 

M'Kendrick  on  Helmholtz,  ii.  396,  485; 
quoted,  490. 

Maclaurin,  Colin,  tribute  by  Playfair 
to,  i.  232 ;  '  Treatise  on  Fluxions,' 
&c.,  270  ;  272  ;  series  of,  ii.  646  ; 
theorem  of,  670. 

MacMahon,  Major,  Address  to  Mathe- 
matical Section  of  British  Association, 
Glasgow,  ii.  140  ;  on  combinational 
analysis,  643  ;  679. 

Madrin  despaired  of  Newton's  theory  of 
gravitation,  i.  334. 

Mageudie,  Bell's  theorem,  i.  293 ;  ex- 
perimental school  of,  ii.  384  ;  385  ; 
experimental  or  vivisectional  school, 
406 ;  experiments,  481. 

VOL.  n. 


Magnus,  Gustav,  chemist,  i.  188  ;  205  ; 
chemical  researches  of,  208. 

Mairan,  referred  to  by  Voltaire,  i.  106. 

Malpighi  used  the  term  "cell,"  i.  195  ; 
embryological  work  of,  ii.  227,  260  ; 
(s^ee  De  Candolle),  261 ;  "  epigenesis," 
278. 

Malthns,  'Principles  of  Population,'  i. 
84,  ii.  331  et  sea.;  conflict  in  nature, 
431. 

Mains,  polarisation  of  light  discovered, 
i.  S3;  introduced  the  word  "polar- 
ity," ii.  22;  "polarity"  acquired  by 
light  by  reflexion,  23  ;  on  polarisa- 
tion, ih. ;  referred  to  by  Young,  27. 

Man,  and  brute,  the  dividing  line,  ii. 
541  ;  the  "mean,"  580. 

Manchester  Literary  and  Philosophical 
Society,  i.  265. 

Manifold,  ii.  713. 

Mansel,  Dean,  'On  the  Limits  of  Re- 
ligious Thought,'  ii.  326. 

Mantegazza,  physiognomy,  ii.  477. 

Mantell,  G.,  ii.  318. 

Marat,  i.  107. 

Maria  Theresa,  i.  256. 

Marine  laboratories,  ii.  232. 

Mariniui,  animal  electricity,  ii.  475. 

Marion,  '  Grande  Encyclopedie '  quoted, 
ii.  495. 

Mariotte,  Boyle's  law  of  pressures,  i. 
425  ;  427  ;  experimental  formulae  of, 
436. 

Markgraf,  Andreas  Sigismund,  i.  175. 

Martin,  Charles,  Lamarck's  views,  ii. 
310  ;  "  Introduction  Biographique  "  of 
Lamarck,  311. 

Maser,  H.,  edition  of  Abel  and  Galois, 
ii.  686. 

Maskelyne,  N.,  i.  177 ;  scientific  work 
of,  229 ;  not  member  of  any  uni- 
versity, 238  ;  measurement  of  force 
of  gravitation,  320  ;  personal  equation 
unknown  to,  .325  ;  discoveries  of,  354. 

Maskelyne,  Story,  '  The  Morphology 
of  Crystals,'  ii.  222. 

Mass,  weight  and,  i.  336. 

Massieu,  mathematical  formulae  of  "  free 
energy,"  ii.  173. 

Mathematical  methods.  Continental,  in- 
troduced into  England  by  Babbage 
and  others,  i.  18. 

Mathematical,  spirit,  i.  314  ;  first  intro- 
duced into  science,  317 ;  formulae, 
focalising  effect  of,  332  ;  definition  of 
matter  and  force,  334. 

Mathematicians,  Kiinigsberg  school  of, 
i.  186  ;  ancient,  catalogue  of,  ii.  633. 

Mathematics,  Continental,  methods  in, 

3  D 


786 


INDEX. 


i.  100;  modern  changes  in  conception 
of,  221  ;  impetus  to  study  of,  given 
by  French  Revolution,  237  ;  pre- 
judices against,  ii.  628 ;  Sylvester 
on,  629,  631  ;  use  of,  630 ;  Huxley 
on,  ib. ;  Lord  Kelvin  on,  ih.  ;  Gauss 
on,  631  ;  Cay  ley  on,  ih. ;  twofold 
interest  in,  632 ;  origin  of,  634 ; 
Euler  on,  657 ;  Abel  and  Jacobi's 
school  of,  ih. 

Mathurin,  geometrical  work  of,  i.  114. 

Matter  and  force  mathematically  de- 
fined, i.  334. 

Matter,  circulation  of,  ii.  420  ;  living, 
mobility  of,  438. 

Matteucci,  animal  magnetism,  ii.  475. 

Matthew,  Patrick,  'Naval  Timber  and 
Arboriculture,'  ii.  334  ;  347. 

Maudsley,  Dr  H.,  'Physiology  and 
Pathology  of  Mind,'  ii.  512. 

Maupertuis  followed  Newton,  i.  96 ; 
referred  to  by  Voltaire,  105  ;  prin- 
ciple of  least  (or  stationary)  action, 
231 ;  astronomical  constants,  322. 

Maury,  Alfred,  '  Les  Academies  d'autre- 
fois,'  i.  90,  99,  105  ;  quoted  on  Vol 
taire    and    scientific  progress,    106 ; 
quoted,    127,    135,    147,    148;    143; 
226. 

Mauvein,  i.  92, 

Maxwell,  Transactions  of  Society  of 
Agriculture,  i.  284. 

Maxwell,  James  Clerk-,  on  probabilities, 
i.  120;  'Science  and  Freewill,'  124; 
his  theories  followed  up  in  Germany 
and    France,     251 ;    and    Faraday's 
"lines  of  force,"  266;  contributions 
to  study  of  natural  philosophy,  274  ; 
'Heat,'   315,    ii.     173;    'Electricity 
and    Magnetism,'    i.    323 ;    electric 
theory,     344  ;     "  the     astronomical 
method,"    347 ;     '  Action   at  a   Dis- 
tance,'  348  ;    '  Electrical   Researches 
of  Cavendish,'  363  ;   '  Physical  Lines 
of  Force,'  372  ;  'Equilibrium  of  Elas 
tic  Solids,'  379  ;  Weber's  theory,  380 
"  energy  "  a  substance,  388  ;  '  Dynam 
ical  Evidence  of  the  Molecular  Con 
stitution    of   Bodies '    quoted,    424 
kinetic  theory  of  gases,  433,  ii.   34 
the  statistical  view  of  nature,  i.  438 
'Kinetics,'  ii.  5;   'Scientific  Papers 
quoted,   33,    175 ;    treatise    on   elec- 
tricity and  magnetism,  35  ;  followed 
on  the  lines  of  Stokes,  55  ;  quoted  on 
Rankine's  theory   of  molecular  vor- 
tice.s,   62;   "Atom,"    'Encyclopedia 
Britannica,'    66  ;     electro  -  magnetic 
theory,    73,    153 ;    labours    of,    76 ; 


theory  of  electricity,  78  ;  "  tubes  of 
force,"  80  ;  electrotonic  state  of  mat- 
ter, 81 ;  "On  Physical  Lines  of  Force," 
82,  83;  "elastic  medium"  in  space, 
84;  "elastic  disturbances"  of  that 
medium,  85,  86  ;  theory  of  energy, 
87,  88,  89  ;  indefiniteness  of  electro- 
magnetic theory,  93  ;  physical  view 
of  nature,  141,  144  ;  and  Faraday's 
views,  145 ;  electro-magnetic  field, 
147  ;  148  ;  theory  of  electro-dynam- 
ical phenomena,  151  ;  '  Theory  of 
Heat,'  167;  Willard  Gibbs,  172; 
"available  energy,"  174;  179,  182; 
triumphs  of  atomic  view,  188  ;  191, 
193  ;  difiiculties  of  his  theories,  194  ; 
Ampere,  341  ;  statistical  view,  574, 
603  ;  theory  of  probabilities,  590  ; 
statistical  methods,  592,  593 ; 
"  Sorting  Demon,"  594  ;  quoted,  605, 
606 ;  on  historical  and  statistical 
methods,  613  ;  624  et  seq.,  630 ;  on 
vector  analysis,  655. 

Mayer,  A.  M.,  Young's  colour  theory, 
ii.  480. 

Mayer,  Julius  Robert,  i.  218,  265,  309 ; 
theory  of  energy,  ii.  97  ;  his  work 
theoretical,  99  ;  scientific  services  of, 
106  ;  memoirs  refused  by  Poggendorf, 
107;  measurement  of  "energy," 
108  ;  indestructibility  of  force.  111  ; 
neglect  of  earlier  writings  of,  113, 
114  ;  his  views  extended  and  elabor- 
ated by  Thomson  and  Clausius,  116  ; 
117 ;  correlation  and  interchange- 
ability  of  natural  force,  119 ;  per- 
petual motion,  124  ;  the  dynamical 
theory  of  heat,  128,  130 ;  first  phil- 
osophical generalisations  on  power 
and  work,  137  ;  "  Kraft,"  169  ;  207  ; 
"energy,"  355;  meteoric  theory  of 
the  sun's  heat,  357,  358 ;  conserva- 
tion of  energy,  397  ;  398. 

Mayer,  Tobias,  Professor  of  Mathe- 
matics and  Economics  at  Gottingen, 
i.  158  ;  connection  of,  with  modern 
science,  175  ;  176 ;  method  of  least 
squares,  183 ;  astronomical  calcula- 
tions of,  324 ;  lunar  theory,  329  ; 
368. 

Measurements,  Weber's  fundamental, 
i.  368. 

Mechain,  i.  113. 

Mechanical  view  of  nature,  ii.  183. 

Mechanism,  ii.  399. 

Meckel,  anatomist,  ii.  248  ;  morphologi- 
cal analogies,  250 ;  308  ;  quoted  by 
Huxley,  348:  law  of  "biogenesis," 
349. 


INDEX. 


787 


Medical  faculty,  &c.,  in  German  uni- 
versities, i.  197 ;  science  and  phil- 
osophy of  nature,  209 ;  medical 
interest,  the,  ii.  207  ;  thermometry, 
389. 

Medicine,  i.  126  ;  Austrian  school  of, 
198  ;  German  schools  of,  208  ;  influ- 
ence of,  ii.  379. 

Medium,  internal,  ii.  432. 

Melanchthon,  and  the  first  Protestant 
universities,  i.  159  ;  educational  work 
of,  255. 

Meldola,  R.,  analytical  and  synthetical 
methods  in  chemical  research,  i.  457. 

Melloni,  radiant  heat,  ii.  105. 

Mendeleeff,  D.,  classification  of  the 
elements,  i.  315 ;  j^eriodic  laws  of, 
403,  422,  423,  448;  ii.  362. 

Mental  life  of  mankind,  i.  55. 

Mentelle,  geography  at  the  Ecole 
normaie,  i.  112. 

Mercator,  i.  157  ;  his  projection,  ii. 
701. 

Merck,  '  Annalen  der  Pharmacie,'  ii. 
107. 

Mere,  Chevalier  de,  i.  120. 

Merey,  C.  H.,  on  foundation  of  anal- 
ysis, ii.  704,  734. 

Meridian,  measurements  of  arcs  of,  i. 
99. 

Merkel,  'Jacob  Henle,'  i.  215,  293. 

Mersenne,  original  member  of  Paris 
"Academic  des  Sciences,"  i.  228. 

Mesmer,  animal  magnetism,  ii.  476. 

Metabolism,  ii.  421,  422,  442. 

Metajihysical  treatment  of  science  in 
Germany,  i.  43. 

Methods  have  their  day  and  are  dis- 
carded, i.  56. 

Metrical  and  projective  geometry,  ii. 
668. 

Meusnier,  i.  115. 

Meyer,  E.  von,  'History  of  Chemistry,' 
i.  405,  406,  413  ;  quoted,  411;  memoirs 
of,  ii.  257. 

Meyer,  Franz,  his  history  of  Invariants, 
i.  247,  308  ;  ii.  677 ;  684  ;  on  Lie  and 
'Tlieory  of  Groups,'  691 ;  on  poten- 
tial theory,  698. 

Meyer,  Lothar,  classification  of  chemical 
elements,  i.  315  ;  '  Modern  Theories 
of  Chemistry,'  393  ;  periodic  laws  of, 
403,  422,  423  ;  427  ;  '  Die  Atome  und 
ihre  Eigenschaften,'  429,  445  ;  456  ; 
'  Moderne  Theorien  der  Chemie,'  ii. 
65. 

Meyer,  0.  E.,  'Die  Kinetische  Theorie 
der  Gase,'  i.  434,  435,  437  ;  quoted 
on  Maxwell,  438  ;  ii.  593. 


Meyer,  Victor,  on  change  of  chemical 
views,  ii.  165. 

Michaelis  of  Gottingen  University,  i. 
165. 

Michell,  apparatus  to  measure  force  of 
gravitation,  i.  320. 

'  Microcosmus '  of  Lotze,  i.  52. 

Microscope,  ii.  228. 

Miething,  E.,  '  L.  Euler's  Lehre  vom 
Aether,'  i.  343,  352,  ii.  8. 

Mill,  John  Stuart,  leintroduces  phil- 
osophy of  Comte  to  France,  i.  18  ; 
'  Logic,'  37,  ii.  307,  308  ;  on  theory  of 
probabilities,  i.  120,  ii.  569  ;  i.  306  ; 
'  Autoliiography,'  307;  opposed  to 
undulatory  theory  of  light,  ii.  37  ;  on 
A.  Bain,  511  ;  513,  571,  608. 

Millar,  W.  J.,  Rankine's  '  Miscellaneous 
Scientific  Papers,'  ii.  133,  139. 

Miller,  Hugh,  stonemason  and  geologist, 
i.  288. 

Miller,  W.  A.,  spectrum  analysis,  i. 
278  ;  ii.  47,  48  ;  '  Chemical  Physics,' 
i.  316. 

Milnes-Marshall,  ii.  349. 

Milton,  influence  on  German  thought 
and  literature,  i.  212  ;  influence  of,  on 
educational  views  in  Ens^land,  253. 

"Mimicry,"  ii.  338. 

Mind,  ii.  216,  455  el  seq.;  the  objective, 
529 ;  5,48. 

Mines,  Ecole  des,  i.  107. 

Minnigerode,  geometrical  treatment  of 
crystallography,  i.  443. 

Mirabeau,  higher  aims  of,  not  realised,  i. 
112. 

Mii-bel,  ii.  230 ;  observations  of,  261 ; 
cellular  theory,  262. 

INIitchell,  P.  C'ii.  459. 

Mitchelson,  speed  of  light,  ii.  36. 

Mitscherlich,  E.,  i.  174  ;  chemist,  188  ; 
190  ;  discovery  of  isomorphism,  191, 
444  ;  services  of,  to  chemistry,  208  ; 
Dalton's  atomic  theory,  246 ;  discovers 
polymorphism,  446. 

Mivart,  St  George,  ii.  546. 

Mobility  of  living  matter,  ii.  438. 

Mcibius,  A.  F.,  his  geometry,  i.  44  ;  a 
pupil  of  Gauss,  181,  187;  his  writings 
unknown  to  Pliicker,  ii.  76 ;  and 
Gauss,  652  ;  his  barycentric  calculus, 
655,  724 ;  introduces  homogeneous 
co-ordinates,  681. 

Mohl,  Hugo  von,  "protoplasm,"  i.  309  ; 
improvements  in  micrometric  pro- 
cesses, ii.  229  ;  cellular  theorv,  '262, 
299  ;  protoplasm,  264,  265,  422,  443  ; 
inductive  school  of,  321. 

Mohr,  Karl  Friedrich,  i.  413  ;  scientific 


788 


INDEX. 


work  of,  ii.  106;  "On  the  Nature 
of  Heat,"  107  ;  indestructibility  of 
force,  111  ;  neglect  of  early  writings 
of,  113,  114  ;  referred  to,  117  ;  corre- 
lation and  interchangeability  of  nat- 
ural forces,  119,  124;  "force,"  125, 
130 ;  tirst  philosophical  generalisa- 
tions on  power  and  work,  137 ; 
'Gesch.  der  Erde,'  289;  heat  and 
animal  energy,  398. 

Moivre,  De,  the  theory  of  probabilities, 
i.  120 ;  ii.  568  ;  572. 

Molar  dimensions,  special  interest  at- 
tached to,  i.  350. 

Molecular  action,  i.  346  ;  phenomena, 
astronomical  view  of,  354. 

Molecules,  internal  energy  of,  i.  436. 

Moleschott,  materialistic  works  of,  i. 
60;  LifeofGeorgForster,  179;  'Kreis- 
lauf  des  Lebens,'  ii.  289,  323. 

Moll,  Prof.,  of  Utrecht,  favourable 
criticism  of  science  in  England,  i. 
236  ;  ignorance  of  foreign  languages 
in  England  and  France,  237. 

Molyneux,  space  perception,  ii.  473. 

Monadology,  ii.  500. 

Monboddo,  Lord  (James  Burnett),  ii. 
531  ;  '  On  the  Origin  and  Progress  of 
Language, '  536,  537. 

Monge,  Gaspard,  descriptive  geometry, 
i.  44,  ii.,658,  664,  675,  685  ;  geometry 
at  the  Ecole  normale,  i.  112,  237  ; 
'Descriptive  Geometry,'  114;  115, 
147  ;  brass  and  iron  cannons,  148  ; 
152,  187  ;  306  ;  practical  school  of,  ii. 
100. 

Monro.  Alexander,  Edinburgh  Univer- 
sity,' i.  268  ;  ii.  247. 

Monro,  John,  at  Edinburgh  University, 
i.  268. 

Montagu,  Lady  Mary  W.,  inoculation, 
i.  284. 

Montesquieu  reflects  the  thought  of  the 
eighteenth  century,  i.  61  ;  107  ;  study 
of  human  culture,  ii.  529. 

Montgolfier,  indestructibility  of  force, 
ii.  111. 

Montgomery,  Edmund,  '  Space  and 
Touch,'  ii.  472;  article  in  'Mind' 
quoted,  484. 

Montmort,  Remont  de,  letter  to  Brook 
Taylor,  i.  101  ;  original  member  of 
Paris  "Academie  des  Sciences,"  228. 

Montucla,  '  Histoire  des  Mathema- 
tiques '  quoted,  i.  114,  307,  334,  358. 

'  Monumenta  Germanise,'  i.  167. 

Moore,  Thomas,  on  an  English  charac- 
teristic, i.  240. 

Morgan,  A.  de,  theory  of  probabilities, 


i.  120  ;  calculus  of  probabilities,  325  ; 
essay  on  probabilities,  ii.  569  ;  641, 
650,  709,  711. 

Morley,  John,  '  Diderot,'  i.  34. 

Morphogenesis,  ii.  549. 

Morphological  view  of  nature,  ii.  200 ; 
insufficiency  of,  270 ;  period,  274 ; 
structural  analysis  of  elements,  423. 

Morphology,  ii.  212  ;  defined,  219  ;  of 
crystals,  223  ;  on  a  large  scale,  224  ; 
on  a  minute  scale,  227  ;  and  classifi- 
cation, 231  ;  549. 

Morveau,  Guyton  de,  '  Annales  de 
Chimie,'  i.  41. 

Mosander,  pupil  of  Berzelius,  i.  188. 

Moser,  perfection  of  stereoscope,  ii. 
506. 

Mosheim,  "  libertas  docendi,"  i.  164. 

Motion,  atomic  and  molecular,  i.  437  ; 
in  ancient  jihilosophy,  ii.  3 ;  per- 
petual, impossible,  124. 

Motivity,  thermodynamic,  ii,  168,  594. 

Muir,  Thomas,  ii.  643. 

Miiller,  Fritz,  'Facts  and  Arguments 
for  Darwin,'  ii.  349. 

Miiller,  Johannes,  physiology  at  Berlin, 
i.  174  ;  temporarily  influenced  by 
speculative  spirit  in  German  science, 
178;  'Handbuch,'  193;  195;  meta- 
physical leanings  of,  196  ;  school  of, 
197,  ii.  397,  403 ;  i.  198,  200,  201 ; 
influenced  by  the  Naturphilosophie, 
207  ;  freed  under  influence  of  French 
science,  208  ;  211 ;  upheld  the  method 
of  historical  survey  in  science,  215 ; 
his  achievements  in  physiology,  217  ; 
"reflex  action,"  263;  292;  Bell's 
theorem,  293,  294 ;  scientific  re- 
searches of,  ii.  106  ;  117  ;  influences 
Du  Bois  -  Reymond  and  Helmholtz, 
150  ;  physiological  studies,  208  ;  the 
cellular  theory,  263;  "vital  force," 
269;  301;  'Physiology,'  308,  417, 
420,  443,  491;  381,  384;  chemical 
processes  in  the  living  body,  391  ; 
396;  cellular  theory,  &c.,  418; 
animal  magnetism,  475,  476 ;  481 ; 
"specific  energies,"  482,  483;  519; 
Herder's  'Werke,'  537;  study  of 
language,  538  ;  on  Steiner,  670. 

Miiller,  K.  0.,  i.  215. 

Miiller,  Max,  quoted  on  definition  of 
thought,  i.  4  ;  'Science  of  Language,' 
23,  ii.  540  ;  608. 

Miiuchausen,  von,  founded  University 
of  Gottingen,  with  "libertas  docendi," 
i.  164. 

Munk,  experiments  on  the  brain,  ii, 
478  ;  479. 


INDEX. 


789 


Munro,  '  Lucretius,'  ii.  4. 

Mliusterberg,  Dr  Hugo,  psycho-physics, 
ii.  518  ;  experiments,  521. 

Murdoch,  W.,  not  member  of  auy  uni- 
versity, i.  239. 

'  Musenalmanaoh '  of  Schiller  and 
Goethe,  i.  84. 

Museum  d'Histoire  naturelle,  i.  112. 

Nageli,  C.  von,  co-editor  with  Schleiden 
of  'Zeitschrift   i'iir  wissenschaftliche 
Botanik,'  i.   195  ;  mechanical  theory 
of  organic   structures,   ii.    224 ;    per- 
fection of  micrometric  processes,  229 
271  ;  inductive  school  of,   321  ;  351 
'Micellar    Theory,'    425,    427,    611 
Weismaun  on,  435  ;  process  of  intus 
susception,  443;  "  idioplasma,"  448 
613. 

Nansen,  Fridjof,  arctic  exploration,  ii. 
207 ;  quoted  on  the  ubiquity  of 
organic  germs,  453. 

Napier,  John,  logarithms,  i.  94,  269 ; 
272,  282. 

Napoleon  I.,  relation  to  science,  i.  42; 
offered  prize  for  discovery  of  a  process 
of  manufacturing  carbonate  of  soda, 
92 ;  107  ;  his  influence  on  science, 
149  ;  quoted  from  Thibaudeau,  150  ; 
founded  Universite  Imperiale,  151  ; 
favoured  mathematical  sciences,  ih.  ; 
152 ;  his  scientific  glory  derivative, 
154  ;  statistical  methods  employed  by, 
153  ;  206  ;  animal  magnetism,  ii.  476. 

Napoleon  III.,  scientific  reports,  i.  42. 

Narboune,  i.  151. 

Nasse,  Chr.  Fried.,  physiological 
method  in  medicine,  ii.  388. 

Nations,  work  of  the  three,  compared,  i. 
298  ;  disappearance  of  national  differ- 
ences, 305. 

Natural  history,  first  public  course  in 
Paris,  i.  143. 

Naturalistic  school  in  France,  i.  75. 

Nature,  history  of,  how  to  be  under- 
stood, i.  2 ;  philosophy  of,  204 ; 
philosophy  of,  and  medical  science, 
209  ;  English  love  of,  284  ;  statistical 
view  of,  438  ;  kinetic  view  of,  ii.  1  et 
seq.  ;  physical  view  of,  95  et  seq. ;  mys- 
tery of  the  actual  processes  of,  366. 

Naturphilosophie  of  Schellingand  Hegel, 
i.  178,  207;  ii.  315. 

Naumann,  C.  F. ,  "  morphology  of  the 
surface  of  the  earth,"  ii.  212. 

Navier,  mecanique  moleculaire,  i.  359  ; 
360,  379  ;  theory  of  elasticity,  ii.  31, 
41 ;  properties  of  the  ether,  33  ;  syn- 
thetic method,  100. 


Nees  von  Esenbeck,  ii.  265. 

Neptune,  discovery  of,  i.  277. 

Neptunists  and  Plutonists,  i.  283,  290. 

Nernst,  'Theoretical  Chemistry,'  i.  448, 
ii.  186. 

Neumann,  Carl,  development  of  astron- 
omical view  of  nature,  i.  366  ;  quoted 
on  provisional  character  of  electrical 
formulre,  375  ;  '  Die  Principien  der 
Electrodynaniik,'  376  ;  ii.  186  ;  on 
potential,  698  ;  and  Dirichlct's  prin- 
ciple, 708. 

Neumann,  Franz,  the  elder,  mathe- 
matical physics,  i.  44  ;  199  ;  experi- 
ments in  chemistry  of,  429  ;  proper- 
ties of  ether,  ii.  31  ;  analytical  method 
of,  45;  "elastic"  theory  of  ether, 
54  ;  influences  Helmholtz,  150 ; 
theory  of  electro-dynamic  phenom- 
ena, 151 ;  193. 

Neumann,  Kaspar,  statistical  tables  of, 
ii.  565. 

Newlands,  periodic  law  of,  i.  422,  423. 

Newport,  his  discovery,  ii.  227. 

Newton,  value  of  work  of,  i.  93  ;  cor- 
rected the  thought  of  Bacon,  95  ;  his 
work  completed  and  amplified  by 
Laplace,  97  ;  mathematical  reason- 
ings of,  substantiated,  99  ;  invention 
of  "fluxions,"  100;  influence  on  the 
popular  miud  inappreciable,  105;  118, 
119,  123 ;  contrasted  with  Cuvier,  132 ; 
137  ;  Cuvier  on  the  gravitation  theory 
of,  146  ;  Gauss's  appreciation  of,  181  ; 
discoveries  of,  frequently  forestalled 
by  others,  184  ;  '  Principia,'  188,  189, 
227,  ii.  6  ;  pre-eminent  as  an  exact 
thinker,  i.  222 ;  indebtedness  of 
French  science  to,  226  ;  notation  of, 
233  ;  and  Young,  244,  ii.  9  ;  Flam- 
steed's  observations,  i.  250  ;  267,  279, 
282,  311;  "energy,"  312;  317; 
astronomical  instruments,  322  ;  323, 
325  ;  lunar  theory,  329  ;  332  ;  mathe- 
matical expression  of  astronomy, 
333;  matter  and  force,  334;  "de- 
scription and  explanation  "  of  phen- 
omena, 337;  gravity  not  "essential 
and  inherent,"  340  ;  mechanical 
explanation  of  gravitation,  342  ; 
emanation  hypothesis  of  light, 
344  ;  actio  in  distans,  345  ;  gravita- 
tion, 351,  353  ;  molecular  attrac- 
tion, 354  ;  Horsley's  edition  of 
his  works.  355  ;  correspondence 
with  Cotes  on  molecular  attraction, 
lb. ;  Hauksbee's  experiments,  356  ; 
358  ;  St  Venant  on,  and  Boscovich, 
359 ;   idea  of  mass,   362 ;   370,  372, 


790 


INDEX. 


374 ;  universality  and  accuracy  of 
his  law,  377,  380,  382,  384;  385, 
389,  394,  424  ;  calculation  of  molar 
and  cosmical  phenomena,  439  ;  "  me- 
chanical cause "  of  gravitation,  ii. 
4  ;  5  ;  and  Huygens,  6  ;  method  of, 
8  ;  Euler's  opposition  to,  ih.;  insuffi- 
ciency of  emission  theory,  14,  15  ; 
suggested  both  theories  of  light,  17 ; 
recognised  ' '  polarity  "  of  light  rays, 
22  ;  general  laws  of  motion,  28  ;  for- 
mula of  attraction,  44  ;  referred  to, 
62  ;  and  the  French  school  of  physi- 
cal astronomy,  79  ;  scientific  terms, 
95  ;  '  Principia '  and  the  modem  no- 
tion of  energ}^  99,  100,  140  ;  vibra- 
tory view  of  heat,  104  ;  laws  of  mo- 
tion, 143  ;  astronomical  researches, 
227 ;  Darwin  and,  compared,  341 
et  seq. ;  344  ;  universal  gravitation, 
351 ;  364,  467  ;  optics,  480  ;  and 
Gauss  compared,  630  ;  634,  638,  643  ; 
his  theorem  on  equations  proved  by 
Sylvester,  681 ;  706,  733  ;  science  and 
religion,  742 ;  751. 

Newtonian  formula  the  basis  of  physi- 
cal astronomy,  i.  375  ;  unique  as  to 
universality  and  correctness,  377  ;  is 
it  a  universal  law  ?  378. 

Newtonianism  created  by  Voltaire,  i. 
250,  251  ;  dispelled  Cartesian  physi- 
cal philosophy  in  France,  433. 

Nichol,  John,  on  Francis  Bacon  and 
his  forerunners,  i.  94. 

Nichol's  'Cyclopsedia,'  ii.  133. 

Nicholas  V.,  Pope,  and  the  University 
of  Glasgow,  i.  268. 

Nicholson  and  Carlisle,  scientific  dis- 
covery of,  i.  229. 

'  Nicholson's  Journal,'  i.  41,  ii.  104. 

Nicol,  'Crystallography,'!.  117. 

Nicomachus,  ii.  207. 

Niebuhr,  B.  G.,  his  indebtedness  to 
Gibbon,  i.  169  ;  212. 

Niebuhr,  Karsten,  on  Tobias  Mayer,  i. 
158. 

Niepce,  photography,  ii.  506. 

Nietzsche,  idea  of  recurrent  cj'cles,  ii. 
287. 

Nilson,  discovery  of  scandium,  i.  423. 

Nineteenth  century  not  one  of  revolu- 
tion, i.  77. 

Nobili,  animal  electricity,  ii.  475. 

Nomenclature,  importance  of,  in 
science,  i.  131. 

Non-Euclidean  geometry,  ii.  652  et  seq.; 
Klein  on,  653  ;  712,  715 ;  Halsted 
and  Schlegel  on,  714 ;  criticised  by 
Lotze,  716. 


Nordenskiold,  pupil  of  Berzelius,  i. 
188. 

'  North  British  Review '  quoted  on 
Scotch  educational  movement,  i.  254. 

Norwood,  determined  length  of  a  de- 
gree, i.  97. 

Nbther,  M.,  onSophus  Lie,  ii.  690,  691  ; 
and  Klein,  720.     See  Brill. 

Number  tt,  ii,  721  ;  and  e,  transcendent 
nature  of,  731. 

Numbers,  theory  of,  ii.  680 ;  revived 
by  Legendre;  and  Gauss,  ib.  ;  general- 
ised, 726  ;  transcendental,  727,  730  ; 
corpus  of,  728  ;  algebraic,  729. 

Objective  mind,  ii.  529. 

Observation,  insiifficiency  of  mere,  i. 
328. 

Observatory,  Greenwich,  built,  i.  98i; 
Pulkowa,  i.  99. 

Odling,  chemical  researches  of,  i.  414. 

Oersted  referred  to,  i.  238  ;  discovery 
of  electro-magnetism,  92,  207,  370, 
371  ;  discoveries  of,  366  ;  electric  cur- 
rents, 367  ;  importance  of  his  dis- 
coveries, 372 ;  indestructibility  of 
force,  ii.  Ill,  125  ;  electrical  phenom- 
ena, 146. 

Oettingen,  von,  ii.  185 ;  statistician, 
557,  562,  585. 

O'Connell,  Daniel,  i.  240. 

Ohm,  G.  S.,  Fourier's  series,  i.  241  ; 
anticipated  by  Cavendish,  363  ;  ac- 
curacy of  his  law,  365 ;  electro-mag- 
netic measurements,  ii.  78  ;  galvanic 
currents,  79  ;  electrical  phenomena, 
146 ;  law  of,  147 ;  resonance,  487  ; 
508  ;  on  harmonics,  623. 

Oken,  originated  scientific  associations 
in  Germany,  i.  42  ;  exponent  of  the 
Naturphiloso2}hie,  207  ;  238  ;  '  Ele- 
ments of  Physio -philosophy,'  283; 
founded  "  Naturforscher  -  Versamm- 
lung,"  298  ;  anatomical  analogies,  ii. 
251  ;  development  of  Goethe's  views, 
255  ;  influences  Owen,  308  ;  natural 
philosophv,  315 ;  the  genetic  view, 
317,  321  ;  'evolution,  354  ;  508. 

Olbers,  Heinr.  Wilh.  Mat.,  rediscovers 
Ceres,  i.  54,  82  ;  astronomical  work 
of,  176  ;  biographical,  177  ;  calculates 
orbit  of  Ceres,  182  ;  correspondence 
with  Gauss,  185,  304. 

Oldenburg,  i.  283. 

Oltramare  on  Abel,  i.  187. 

Operations,  inverse,  ii.  639 ;  different 
kinds  of  mathematical,  640  ;  calculus 
of,  ib.,  655,  684;  Hankel  on,  640; 
Peacock  on,  ii. 


INDEX. 


791 


Operator,  ii.  655. 

Oppolzer,  Vienna  school  of  medicine,  i. 
198  ;  208. 

Opthalmoscope,  Helmholtz's  invention 
of,  i.  200. 

Optics,  ii.  484. 

Order,  ii.  556 ;  theory  of,  678 ;  and 
unity,  742  et  seq.;  745. 

Organic  substance,  first,  produced  arti- 
ficially, i.  92 ;  compound,  preparation 
of,  by  Wcihler,  191  ;  substances,  syn- 
thesis of,  ii.  425. 

Organisation,  problem  of,  ii.  236  ;  415. 

Organs,  study  of  separate,  ii.  233. 

Ossian,  i.  212. 

Ostwald,  '  Die  Energie  und  ihre  Wand- 
lungen,'  i.  380;  "energy"  a  sub- 
stance, 388 ;  on  Berthollet's  views, 
393  ;  '  Classiker  der  exacten  Wissen- 
schaften,'  427  ;  'Allgemeine  Chemie,' 
443,  ii.  176;  'Allgemeine  Chemie' 
quoted,  i.  444,  445;  "  Physikalische 
Chemie,"  457,  ii.  158,  160;  principle 
of  energetics,  125,  142  ;  physical 
chemistry,  153 ;  chemical  affinity, 
157, 159  ;  165  ;  memoirs  of  W.  Gibbs, 
171  ;  second  law^  of  thermo-dynamics, 
175  ;  criticism  of  mechanical  view, 
183  ;  quoted,  187. 

Otto,  translation  into  German  of  Thos. 
Graham's  '  Elements  of  Chemistry, 
ii.  161. 

Owen,  Robert,  co-operation,  ii.  566. 

Owen,  Sir  Richard,  i.  42 ;  palseontol- 
ogical  work,  ii.  257  ;  the  term  "  hom- 
ology," 258 ;  influenced  by  Oken, 
259  ;  extension  of  morphological 
view,  260 ;  Cuvier's  position  unten- 
able, 266  ;  quoted,  268  ;  morphol- 
ogical view  of  nature,  276  ;  parthen- 
ogenesis, 456. 

Packard,  A.  S.,  'Lamarck,  his  Life  and 
Work,'  ii.  312,  351. 

Page,  '  Text-Book,' ii.  363. 

Paine,  Thomas,  'Age  of  Reason,'  i. 
84. 

Paleontology,  science  of,  created  by 
Cuvier,  i.  131  ;  Cuvier's  work  in,  ii. 
247  ;  363. 

Paley,  philosophy  in  English  universi- 
ties represented  by,  i.  254. 

Pallas,  travels  of,  ii.  247,  337. 

Pambour,  de  (see  Zeuner),  ii.  133. 

Pander,  ii.  299,  303. 

Pangenesis,  ii.  271,  454,  610  et  seq. 

Paper  duties,  i.  237. 

Paradoxes  in  mathematics,  ii.  732. 

Parallel  lines,  axiom  of,  ii.  518,  717. 


Paris,  the  focus  of  scientific  thought,  i. 
17. 

Paris  Academy  ridiculed  the  fall  of 
meteors,  i.  327 ;  competition  on 
"  Difl'raction,"  ii.  25. 

Paris  Institute,  i.  226. 

Parker,  Prof.,  quoted,  ii.  345. 

Parmenides,  unity  of  all  existence,  ii.  3. 

Parthenogenesis,  ii.  456. 

Pascal,  Blaise,  his  contributions  to 
science  beyond  those  of  Bacon,  i.  94  ; 
the  theory  of  probabilities,  120,  ii. 
668 ;  667. 

Pasteur,  discoveries  of,  i.  431 ;  the  car- 
bon tetrahedron,  451;  "redintegra- 
tion," ii.  387  ;  414  ;  bacteriological 
investigations,  415  ;  discovery  of 
"  chirality,"  437. 

Pathology  pre  -  eminently  a  German 
science,  i.  216. 

Pattison,  Mark,  meaning  of  "thought," 
i.  25  ;  on  Bentley,  quoted,  169. 

Paulmier,  first  maps  of  Greece,  i.  '295. 

Paulsen,  F.,  '  Geschichte  des  gelehrten 
Unterrichts  auf  den  deutschen  Schu- 
len  und  Universitiiten,'  i.  159,  160, 
163,  164,  166  ;  on  Lotze  and  Fechner, 
200;  'Die  deutschen  Universitaten,' 
214. 

Peabody,  C.  H.,  'Thermodynamics  of 
the  Steam -Engine,'  ii.   136. 

Peacock,  G. ,  i.  18;  introduction  of 
Continental  mathematics  to  Cam- 
bridge by,  233  ;  '  Life  of  Dr  Young ' 
quoted,  245,  417,  ii.  20,  21,  23,26; 
educational  movement  promoted  by, 
i.  261  ;  and  the  Analytical  Society, 
271;  Young's  'Miscellaneous  Works,' 
ii.  9;  his  "report"  quoted,  640, 
645  ;  referred  to  by  Hankel,  641  ; 
his  history  of  arithmetic  referred  to, 
645;  654;  709,  711. 

Peano,  G.,  ii.  656,  734,  737. 

Pearson,  Prof.  Karl,  i.  398,  ii.  30; 
Todhunter's  'History  of  Elasticity,' 
33  ;  '  History  of  Elasticity  '  quoted, 
43  ;  quoted  on  labours  of  Neumann, 
54  ;  modern  theory  of  elasticity,  56  ; 
'  Grammar  of  Science,'  183  ;  phenom- 
ena of  heredity,  574  ;  mathematical 
theory  of  evolution,  621  et  seq. ;  and 
Bateson,  623 ;  737. 

Pearson,  William,  i.  289. 

Peel,  Sir  Robert,  ii.  265. 

Pelletan,  a  founder  of  comparative 
anatomy,  ii.  386. 

Peltier,  phenomenon,  ii.  143. 

Percival,  A.  S.,  'Optics'  quoted,  ii.  53. 

Percy,  Ballads,  i.  212  ;  ii.  537. 


792 


INDEX. 


Purier,  Edmond,  '  La  Philosopliie  Zool- 

o^que  avant  Darwin'  quoted,  ii.  309, 

322. 
Periodic  law  of  Mendeleeff,  i.  315,  422. 
Periodicals,  scientific,  the  oldest,  i.  41. 
Permanence  of  formal  rules,  principle 

of,  Hankel's,  ii.  712. 
Perrault,  i^lan  of  co-operation  proposed 

by,  i.  99. 
Perry,  calculus  for  engineers,  ii.  636. 
Perthes,    C.   T.,    'Politische    Zustande 

und  Personen  in  Deutschland  zur  Zeit 

der  franzbsischen  Herrschaft,'  i.  133, 

256. 
Perthes,  Frederick,  Memoirs  of,  i.  39, 

279. 

Pertz,  first  editor  of  '  Monumenta  Ger- 
manise,' i.  158. 

Peschel,  0.  F.,  'Geschichte  der  Erd- 
kunde,'  i.  291. 

Pestalozzi,  i.  163,  253  ;  his  educational 
influence  in  Germany,  257  ;  began  the 
purely  educational  movement,  258  ; 
inspired  by  Rousseau,  259. 

Peter  the  Great,  i.  153. 

Petermann,  geographical  establishment 
at  Gotha,  i.  167. 

Petit,  i.  107. 

Petty,  Sir  William,  statistics,  i.  122  ; 
(see  Arundel)  collection  of  relics,  295  ; 
'  Political  Arithmetic,'  ii.  562  ;  564. 

PfefiFer,  W.,  labours  of,  ii.  165 ;  cellular 
substances,  373. 

Pfleiderer,  E.,  '  Philosophie  des  Heraklit 
von  Ephesus,'  ii.  3. 

Pflliger,  E.,  "proteid"  theory,  ii.  426; 
"  laws  of  reflex  action,"  519  ;  on  com- 
pound organic  molecule,  611. 

Phalaris,  Epistles  of,  Bentley's  con- 
troversy about  the,  i.  169. 

"  Philanthropinism  "  of  Basedow,  i.  166. 

Philip  of  Hesse,  first  Protestant  uni- 
versity founded  by,  i.  159. 

Phillips.     See  Combes. 

Philosophical  faculty,  development  of, 
in  German  universities,  i.  164,  197. 

'  Philosophical  Magazine  and  Journal  of 
Sciences,'  i.  41,  ii.  48,  50,  55,  58,  69, 
75,  85,  97,  109 ;  on  Carnot  the  elder, 
139  ;  480. 

Philosophical  theories,  ii.  346 ;  prob- 
lems, 352,  743  ;  thought,  geographical 
centre  of,  750. 

Philosophy,   definition    of,    i.    62,    65  ; 
intermediate    between    science    and 
religion,  71,  73  ;  and  science,  conflict 
between,  205  ;  and  science,  311. 
Phlogiston,  i.  388,  ii.  153. 
Phonetics,  ii.  539. 


"Phoronomie,"  ii.  5. 

Phrenology,  ii.  476. 

Phylota.xy  and  phylogenesis,  ii.  308. 

Physical   and  chemical  reasoning  con- 
trasted, i.  424. 

Physical  view  of  nature,  ii.  95. 

"Physical"  method,  ii.  428. 

Physics  and  statistics,  ii.  589. 

'Physik,  Annalen  der,'  Gilbert's,  i.  41. 

'Physik,  Journal  der,'  Gren's,  i.  41. 

'  Physikalische  Gesellschaft '  of  Berlin, 
i.  42. 

Physiocrats,  so-called,  referred  to,  i. 
16  ;  ii.  529. 

Physiological,  units,  ii.  272  ;  division  of 
labour,  396  ;  psychology,  512. 

Physiology  pre  -  eminently  a  German 
science,  i.  216. 

'  Physique,  Journal  de,'  i.  41. 

'  Physique,  Observations  sur  la,'  i.  41. 

Phjrtotomy,  ii.  260. 

Piazzi  discovers  Ceres,  i.  54,  82,  177, 
182,  423. 

Picard,  Ch.  E.,  'Traite  d' Analyse,'  ii. 
690. 

Picard,  Jean,  calculations  of,  i.  97  ;  as- 
tronomical constants,  322  ;  "  methods 
of  dealing  with  astronomical  errors  of 
observation,"  324. 

Picavet,  F.,  '  Les  Ideologues,'  i.  149, 
152,  ii.  470 ;  quoted,  472. 

Pictet,  condensation  of  permanent  gases, 
i.  316. 

Piderit,  Ph. ,  mimicry  and  physiognomy, 
ii.  477. 

Pinel,  medical  nomenclature  of,  i.  131. 

Pitcairn,  medicine  in  alliance  with 
mechanics,  i.  126. 

Plana,  lunar  theory,  i.  329. 

Planck,  Max,  'Das  Princip  der  Erhal- 
tung  der  Energie,'  ii.  97,  99,  106, 
197;  'Thermodynamik,'  142,  186; 
159  ;  labours  of,  165  ;  works  of,  184. 

Planta,  Martin,  the  forerunner  of 
Pestalozzi,  i.  258. 

Platen,  i.  213. 

Plato,  constructive  system  of,  i.  75 ; 
views  of  Heraclitus,  ii.  3  ;  4,  246 ; 
archetypes,  259  ;  his  mathematics, 
633. 

Playfair,  John,  scientific  work  of,  i. 
229 ;  criticisms  of,  on  science  in 
England,  231 ;  review  of  Laplace's 
'  Mecanique  celeste '  quoted,  232  ; 
biographical,  ib. ;  tribute  to  Colin 
Maclaurin,  ib.  ;  234  ;  quoted,  236  ; 
270,  272  ;  '  Huttonian  Theory  of  the 
Earth,'  283,  ii.  292,  356  ;  579. 

PlUcker,  Julius,  geometry,  i.  44  ;  187  ; 


INDEX. 


793 


geometrical  labours  of,  neglected  in 
Germany,  242 ;  spectrum  analysis, 
278  ;  researches  of,  ii.  75  ;  electrical 
researches,  189;  on  "singularities  of 
curves,"  641  ;  670 ;  new  geometry, 
671  ;  672  ;  deficient  in  elegance,  677, 
682  ;  and  Sophus  Lie,  692  ;  on  higher 
curves,  700. 

Plutonists.     See  Neptunists. 

Poggendorf,  'Annalen,'  i.  43,  ii.  128, 
133,  169,  487  ;  refused  Helmholtz's 
'Ueber  die  Erhaltung  der  Kraft,'  i. 
205  ;  Dictionary  of,  silent  about  Avo- 
gadro,  428  ;  refused  Mohr's  '  Ueber 
die  Natur  der  Warme,'  ii.  107. 

Poincare,  H.,  lectures  on  Maxwell's 
theories,  i.  251  ;  on  indefiuiteuess  of 
electro-magnetic  theory,  ii.  93 ;  as- 
tronomical mechanics,  101  ;  Paris 
Address,  1900,  188 ;  discourse  of, 
199  ;  quoted,  635  ;  quoted  on  Weier- 
strass,  638  et  seq.;  703,  705;  on 
"function,"  639;  686,  690;  on  Rie- 
mann  and  Weierstrass,  707,  708  ; 
737. 

Poinsot,  ii.  5  ;  "geometrical mechanics," 
101  ;  on  synthetic  method,  670. 

Poisson,  mechanics,  i.  44 ;  188,  345 ; 
electricity,  347;  "mecanique  mole- 
culaire,"  359  ;  360  ;  analysis  of,  362  ; 
370 ;  Newton's  law,  379 ;  Fresnel's 
calculations,  ii.  25 ;  retired  from 
commission  on  Fresnel's  theory  of 
transverse  vibrations,  26  ;  theory  of 
elasticity,  31,  41  ;  32  ;  properties  of 
ether,  33  ;  referred  to  by  Faraday,  69  ; 
formula  of,  72  ;  theory  of  electric  and 
magnetic  phenomena,  74  ;  '  Memoire 
sur  la  Theorie  du  Magnetisme' 
quoted,  75 ;  referred  to,  76 ;  474 ; 
science  of  chances,  568 ;  on  conver- 
gency,  646 ;  on  Jacobi,  657 ;  on 
synthetic  method,  670  ;  686. 

Polarisation  of  light,  ii.  22. 

"  Polarity,"  origin  of  the  word,  ii.  22. 

Polymorphism,  i.  446. 

'  Polytechnic  Journal,'  Dingler's,  ii. 
134. 

'  Polytechnique,  I'Ecole,  Journal  de,'  i. 
41. 

Poncelet,  J.  V.,  mathematics,  i.  45 ; 
new  science  of  geometry,  114  ;  187  ; 
definitions  of  horse-power  and  work, 
310;  360,  ii.  5;  'Traite,'  76,  660; 
'  Mecanique  industrielle,'  100  ;  practi- 
cal school  of,  ib.;  his  influence  on 
practical  mechanics,  101  ;  thermotics, 
118  ;  first  definite  use  of  new  con- 
ceptions   of   power  and  work,   137 ; 


658  et  seq.;  his  principle  of  continuity 
criticised,  660 ;  quoted,  662 ;  on 
"homology"  and  "reciprocity," 
663  ;  673  ;  on  ideal  elements,  674  ; 
684,  685,  692. 
Pond,  not  member  of  any  university,  i. 

2iOO. 

Poole,  '  Index  to  Periodical  Literature,' 
i.  40. 

Pope,  influence  of,  on  German  thought 
and  literature,  i.  212. 

Popper,  Jos.,  ii.  185. 

Positivism,  i.  307. 

Potential,  ii.  698. 

Pouillet,  Ohm's  law,  i.  365 ;  influenced 
German  thought,  ii.  101  ;  heat  experi- 
ments, 357. 

Poulton,  Weismaun's  Essays,  ii.  372. 

Power  Series,  Infinite,  ii.  707. 

"Power,"  the  term,  .introduced  by 
Watt,  ii.  99. 

Poynting,  Prof.,  contributions  to 
Maxwell's  electro-magnetic  theory,  ii. 
72;  193;  and  Thomson's  'Text-book 
of  Physics,'  Sound,  489. 

Practical  problems,  solidarity  of,  i. 
32. 

Preston,  T.,  ii.  361. 

Prevost,  theory  of  exchanges,  ii.  46. 

Preyer,  Prof.  W.,  theory  of  "Pans- 
permia," ii.  369  ;  school  of  Darwinism 
in  Germany,  436  ;  470. 

Priestley,  chemical  discoveries  of,  i.  115 ; 
155 ;  scientific  discoveries  of,  229 ; 
not  member  of  any  university,  238, 
272  ;  '  History  of  Optics,'  358,  ii.  9  ; 
follower  of  Boscovich,  i.  359 ;  and 
Lavoisier,  386,  387  ;  effect  of  plants 
on  air,  ii.  391. 

Prime  numbers,  ii.  722  et  seq. 

Pringle-Pattison.     See  Seth. 

Pringsheim,  A.,  on  theory  of  functions, 
ii.  693  ;  734,  739. 

Pringsheim,  N.,  observations,  ii.  447. 

Pritchard,  "immersion"  system  in 
microscope,  ii.  228. 

Probability,  theory  of,  i.  118,  ii.  566. 

Prochaska,  "reflex  action,"  i.  292;  ii. 
519. 

Proclus  on  Greek  mathematicians,  ii. 
634. 

Progress,  intellectual,  two  factors  of,  i. 
27. 

Projection,  method  of,  ii.  663. 

Projective   and   metrical  geometry,   ii. 

668  ;  properties,  717. 
Proportions,  fixed,  rule  of,  i.  392 ;  mul- 
tiple, rule  of,  398. 
'  Protogsea '  of  Leibniz,  ii.  277,  280. 


794 


INDEX. 


Protoplasm,  i.  309,  ii.  264 ;  theory  of, 

444. 
Proust,  theory  of  fixed  proportions,  i. 

393  ;  defeated  Berthollet's  doctrine  of 

chemical  affinity,  394  ;  398,  416. 
Prout,    organic    analysis,    i.    190 ;    on 

hydrogen,   230 ;   hypothesis  of,   402 ; 

theory  of  nature  of  elements,  ii.  192  ; 

Bridgewater  Treatise,  325. 
Psychology,  ii.  465  el  seq.;  mathemati- 
cal, 49S. 
Psycho-physical  aspect   of   nature,    ii. 

218,  465. 
Psycho-physics,  E.  H.  Weber's  law  of, 

i.  196  ;   198,  ii.   465  et  seq.,  469;  of 

vision,    504 ;    three    facts    imi^ressed 

by,  545. 
Purkinje,    founded    first    physiological 

laboratory,  i.  18S  ;  198,  208  ;  follower 

of  Baer,  ii.  300. 
Pusey,  E.  B. ,  quoted  on  English  and 

German  writers,  i.  261. 
Putter  of  Gotting-en  University,  i.  165. 
Pythagoras,  unity  of  all  existence,   ii. 

3  ;  school  of,   286  ;  the  octave,  490  ; 

his  mathematical  ideas,  633. 

Quantics  and  "  tactics  "  in  mathematics, 
ii.  683. 

'Quarterly  Review,'  literary  criticism 
of,  i.  84  ;  236,  239  ;  quoted  on  educa- 
tional matters  in  England,  255 ;  Young 
quoted,  ii.  20. 

Quaternions,  ii.  654 ;  introduced  into 
Germany  by  Hankel,  712  ;  717. 

Quatrefages,  de,  of  the  "Association 
Frangaise,"  quoted,  i.  298. 

Quesnay,  economic  system  of,  i.  16, 
107. 

Quet,  experiments  with  vacuum  tubes, 
ii.  190. 

Quetelet,  statistics,  i.  122,  ii.  563,  588  ; 
555,  556,  557  :  theory  of  error,  574  ; 
theory  of  probabilities,  579  ;  quoted, 
580,  581,  587,  607,  609;  the  "mean 
man,"  617. 

Quincke,  foam  theory  of,  ii.  427. 

Rademacher,  his  empiricism  in  medical 
science,  i.  210. 

Rammelsberg,  i.  174. 

Ramsay,  Prof.,  discovery  of  argon,  i. 
423. 

Ramsden,  i.  177 ;  astronomical  instru- 
ments, 322. 

Rankine,  Macquorn,  improvement  in 
steam-engines,  i.  93;  "thermo- 
dynamic function,"  316,  ii.  169  ;  the 
steam-engine,  i,  331,  ii.  133 ;   theor- 


etical thermo-dynamics,  62 ;  mole- 
cular vortices,  63,  82 ;  technical 
mechanics,  101  ;  revival  of  interest  in 
the  ideas  of  "energy,"  114;  on  the 
mechanical  equivalent  of  heat,  128  ; 
Prof.  Unwin's  account  of  theories  of, 
135 ;  elaboration  of  Joule's  and  Reg- 
nault's  experiments,  137 ;  energy, 
"potential"  and  "actual,"  139,  140, 
174 ;  reply  to  Sir  J.  Herschel,  139 ; 
physical  view  of  nature,  141  ;  theory 
of  energy,  166;  168, 173  ;  heat  engines, 
175 ;  mechanical  analogies  of  heat, 
178 ;  entropy,  169,  180 ;  thermo- 
dynamics, 603. 

Raoult,  researches  of,  ii.  164,  165. 

Rathtke,  ii.  300. 

Ran,  A.,  'Theorien  der  modernen 
Chemie,'  i.  406,  414,  430,  455. 

Rauber,  '  Formbildung  und  Form- 
storung  in  der  Entwickelung  von 
Wirbelthieren,'  ii.  401. 

Ray,  John,  botanist,  i.  282 ;  classifica- 
tion of  living  beings,  288. 

Rayleigh,  Lord,  discovery  of  argon,  i, 
423  ;  quoted,  ii.  170  ;  "  free  energy," 
173  ;  optical  researches,  229  ;  'Sound,' 
488,  490. 

"Realschule,"i.  166. 

Reaumur,  referred  to  by  Voltaire,  i. 
105. 

Reciprocity  of  figures,  ii.  663 ;  Ger- 
gonne  on,  666. 

Records,  contemporary,  value  of,  i.  8. 

Redtenbacher,  '  Dynamiden  System,'  i. 
433  ;  influenced  by  Poncelet,  ii.  101 ; 
heat,  178. 

Registration,  ii.  561. 

Regnaud,  i.  150. 

Regnault,  chemistry,  i.  44 ;  245 ;  in- 
vestigated specific  heat  of  chemical 
compounds,  429  ;  influenced  German 
thought,  ii.  101 ;  experimental  work 
of,  137;  "Observations  on  Steam," 
139  ;  a  founder  of  physical  chemistry, 

Rehnisch,  statistics,  ii.  587. 

'Reid,  Thomas,  Life  and  Writings  of,' 

by  Dugald  Stewart,  i.  84. 
Reifi",  R.,  his  history  of  series,  ii.  646. 
Reiz,  indebtedness  to  Bentley,  i.  169. 
Renaissance,  period  of  the,  i.  67. 
Renan,  testimony  to  work  of  German 

universities,  i.  225. 
Rendu,  Ambroise,  '  Code  Universitairej' 

quoted,  i.  150.  w,n  = 

Reports,  annual,  on  scientific  progress, 

i.  42. 
Reproduction,  ii.  443. 


i 


INDEX. 


795 


Repsold,  measurements  of,  i.  322. 

Retrospect  and  prospect,  ii.  741  et  seq. 

Reuchlin,  i.  163. 

Revett.     See  Stuart. 

Revolution,  French,  added  the  modern 

practical  popularisation  of  science,  i. 

145. 
Revolutionary  theories  not  practical,  i. 

79. 
Reye,  'Geometric  der  Lage,'  ii.  669. 
Ribbeck,    'Friedr.    Wilh.    Ritschl.,'  i. 

169,  172. 
Ribot,   'Modern  German  Psychology,' 

ii.     495 ;     '  Psychologic     Allemande 

Contemporaine,'  511  ;  513. 
Richelieu,    his    "metallic"   interest   in 

science,     i.      105 ;      first     statistical 

bureau,  ii.  561. 
Richelot  at  Konigsberg  with  Neumann 

and  Bessel,  ii.  54. 
Richer,  astronomical  constants,  i.  322  ; 

pendulum  experiments  of,  354. 
Richet,   Ch. ,  '  Physiologic  des  Muscles 

et  des  Nerfs,'  i.  293,  ii.  519. 
Richter,  J.  B.,  chemical  equivalents,  i. 

189  ;  313  ;  theory  of  fixed  proportions, 

393  ;   398  ;  atomic   theory,   416  ;   the 

"equivalent"  of  an  element,  419. 
Richter,  W.,  theory  of  "Panspermia," 

ii.  369. 
Rie,cke,    memoir    of    Pllicker,    ii.    75 ; 

Eloge  of  Weber,  197. 
Riemann,  B.,  i.  45;    '  Hypothesen  der 

Geometric,'    200  ;     Fourier's     series, 

241  ;  celebrated  dissertation  of,  243  ; 

views     on     ideas     of     space,     352  ; 

'  Werke,'    ii.    63  ;     researches     into 

electrical  phenomena,  67 ;  254,  635  ; 

and   Cauchy,   693,   699;    on   Abelian 

functions,    699 ;   his   work,   700 ;   his 

surface,   701 ;  704,   706  ;   and  Weier- 

strass  compared,  707  ;  on  hypotheses 

of  geometry,  710;  717,  718. 
Riess,    frictional     electricity,    i.    205  ; 

statical  electricity  and  the  Geissler 

tubes,  ii.  191. 
Rindfleisch,   Ed.   von,    'Arztliche  Phil- 

osophie,'  ii.  379,  437. 
Ritschl,  Friedr.  Wilh.,  indebtedness  of, 

to  Bentley,  i.  169  ;  quoted,  172  ;  con- 
ducted philological  seminaries,  214  ; 

language,  ii.  540. 
Ritter,  Karl,  comparative  geography,  ii. 

226  ;  extension  of  morphological  view, 

260  ;  300. 
Rober,  construction  of  the  heptagon,  ii. 

722. 
Robertson,   Groom,   calls  Hobbes's   the 

first  English  system  of  philosophy,  i. 


48  ;  282  ;    '  Mind,'  ii.  512  ;  on  Mlin- 
sterberg's  work,  522. 

Robertson,  David,  naturalist,  i.  288. 

Roberval,    referred   to  by   Voltaire, 
105  ;  taught  at  the  College  de  France, 
107. 

Robespierre,  i.  107. 

Robin,  'Traite  d' Anatomic  generale,'  ii. 
266. 

Robison,  John,  on  Boscovich's  theory, 
i.  358,  359  ;  publisher  of  Black's 
lectures,  ii.  102. 

"  Rochdale  Pioneers,"  ii.  566. 

Rochow,  von,  educational  work  of,  i. 
256. 

Rogers,  W.  G.,  illustrations  of  Helm- 
holtz's  theories,  ii.  63. 

Rokitansky,  Vienna  school  of  medicine, 
i.  198,  208. 

Roman  system  of  registration,  ii.  561. 

Romanes,  'Darwin  and  after  Darwin,' 
ii.  346 ;  436. 

Romanticism,  reactionary  movement  of, 
i.  82. 

Romberg,  medical  school  of,  i.  208. 

Rome  de  I'lsle,  contributions  to  crystal 
lography,  i.  117,  118,  ii.  241. 

Romer,  Glaus,  motion  of  light,  ii.  10. 

Romme,  Gilbert,  quoted,  i.  110. 

Rontgen,  discovery  of  X  rays,  ii.  92. 

Roscher,  '  Gesch.  d.  National-Oekono- 
mik,'  ii.  555  ;  statistics,  563. 

Ruschlaub  influenced  by  the  JVatur- 
2)hilosophie,  i.  207. 

Roscoe,  Sir  H.,  '.John  Dalton,'  i.  417. 

Rose,  H.,  i.  174  ;  the  greatest  analyt- 
ical chemist  of  the  century,  399. 

Rose,  H.  and  G.,  chemists,  i.  188. 

Rosenberger,  'Geschichte  der  Physik,'i. 
308,  359,  433,  ii.  8,  11,  178,  506; 
'  Die  moderne  Entwickelung  der 
elektrischen  Principien,'  90  ;  physical 
nature  and  "perpetual  motion,"  124. 

Rosenkranz  on  the  encyclopedists,  i.  34. 

Ross,  Sir  James,  confirms  calculations 
of  Gauss  as  to  south  magnetic  pole,  i. 
331. 

Rothmann,  i.  157. 

Rousseau,  influence  on  Herder,  i.  50  ; 
gospel  of  Nature,  51  ;  and  the  "  Auf- 
kliirung  "  period,  60  ;  107  ;  destruc- 
tive revolutionary  work  of,  110  ; 
popularised  botanising,  127 ;  centre 
of  reaction  against  school  of  Voltaire, 
Buftbn,  &c.,  145  ;  163  ;  influence  of, 
on  German  thought  and  literature, 
212  ;  253,  257  ;  valuable  side  of  his 
ideas  developed  outside  of  France, 
259  ;  285,  ii.  415  ;  language,  536. 


1 


796 


INDEX. 


Roux,  Wilhelm,  '  Entwickelungsmech- 
anik  des  Embryo,'  ii.  401 ;  '  Struggle 
of  the  Parts  in  the  Organism,'  436  ; 
quoted,  444  ;  "organicisme,"  455. 

Rowland,  spectroscopic  observations, 
ii.  361. 

Royal  Institution  founded,  i.  89,  264, 
ii.  139. 

Royal  Society  of  Edinburgh,  i.  269. 

Royal  Society  Catalogue  of  Scientific 
Papers,  i.  40  ;  '  Transactions '  of,  41  ; 
founded,  89  ;  227,  228  ;  unfavourably 
criticised  by  Babbage,  233  ;  favour- 
ably criticised  by  Cuvier,  235 ;  by 
Prof.  Moll  of  Utrecht,  236  ;  ii.  69  ; 
Kaspar  Neumann's  statistical  tables, 
565. 

Rubidium  found  by  Kirchhoff  and  Bun- 
sen,  ii.  49. 

Riickert,  imitation  of  oriental  poetry, 
i.  213  ;  "Chidher"  quoted,  ii.  289. 

Rudolf  II.,  Emperor,  and  Tycho,  i. 
157. 

Rudolph,  '  Grundriss  der  Physiologic,' 
ii.  499. 

Rudolphi,  ii.  230,  261. 

Ruffini,  Paolo,  and  theory  of  groups,  ii. 
688. 

Riihlmann  influenced  by  Poncelet,  ii. 
101. 

Rumford,  Count  (Benjamin  Thompson), 
mechanical  theory  of  heat,  i.  83 ; 
155  ;  experiments  of,  229  ;  not  mem- 
ber of  any  university,  238 ;  246 ; 
founded  Royal  Institution,  248,  264  ; 
the  steam-engine,  331  ;  the  kinetic 
view  of  nature,  ii.  7  ;  investigations 
of  the  nature  of  heat,  102  ;  "  Inquiry 
concerning  the  Source  of  the  Heat 
which  is  excited  by  Friction,"  103; 
Davy's  speculations  on  light  and 
heat,  104  ;  experiments  utilised  by 
Helm  in  his  '  Energetik,'  109. 

Runge,  C,  spectroscopic  observations, 
ii.  361,  362. 

Russell,  Hon.  Bertrand,  his  writings,  ii. 
653  ;  718,  720,  734,  737. 

Russell,  Lord  John,  Royal  Commission 
of  Inquiry  into  University  Reform,  i. 
254. 
Rutherford,  spectroscopic  observations, 
ii.  361. 

Rydberg,  ii.  362. 

Sabine,  magnetic  experiments,  i.  230. 

Sachs,  Julius,  the  effect  on  biological 
science  of  the  discovery  of  the  cell,  i. 
195;  'Geschichte  der  Botanik,'  209 
ii.  212,  223,  227,  230,  231,  246,  260, 


265,  269 ;  importance  of  the  spiral 
theory,  224 ;  cellular  theory,  262 ; 
of  Hofmeister,  321  ;  quoted,  338 ; 
'Lectures  on  Plant  Physiology,' 408. 
Sacro  Bosco,  Joannes,  ii.  287. 
Saint-Hilaire,  Auguste  de, ' '  Morphologic 

vegetale,"  ii.  ,224. 
Saint-Hilaire,  Etienne  Geoffroy,  germ 
of  Darwinian  theory,  i.  137  ;  200 ; 
and  the  "Origin  of  Species,"  201; 
and  Cuvier,  ii.  239  ;  appreciation  of 
Goethe's  work,  244  ;  controversy  with 
Cuvier,  246  ;  morphological  analogies, 
251  ;  labours  of,  253  ;  quoted,  258  ; 
unity  of  organisation,  267  ;  301  ;  and 
Buffon,  309  ;  321,  322  ;  natural  selec- 
tion, 330  ;  364. 

Saint-Hilaire,  Isidore  Geoffroy,  ii.  322. 

Saint  Pierre,  ,Bernardin  de,  taught 
morals  at  the  Ecole  normale,  i.  112. 

Saint  Simon,  co-operation,  ii.  566. 

Saint  -  Venant,  Barre  de,  quoted  on 
Boscovich's  theory,  i.  359  ;  properties 
of  ether,  ii.  33;  "elastic  solid" 
theory  of  ether,  54  ;  synthetic  method, 
100. 

Salisbury,  Lord,  Oxford  Address,  ii. 
347. 

Salmon,  George,  text-books  on  geometry 
translated  by  Fiedler,  i.  44  ;  scientific 
work  of,  and  PlUcker,  242  ;  Dublin 
mathematical  school,  275 ;  German 
edition  of  his  works,  ii.  669,  685 ; 
introduces  Chasles's  work,  673  ;  great 
merit  of  his  text-books,  685 ;  Meyer 
on,  ih. ;  Italian  edition  of  his  works 
by  Brioschi,  ib. 

Sameness  and  variation,  ii.  607. 

Sampson,  R.  A.,  'Proceedings  of  the 
Society  of  Antiquaries,'  ii.  282. 

Sanderson,  Sir  J.  Burdon,  quoted,  ii. 
428,  429,  439  ;  "Elementary  Problems 
of  Physiology  "  quoted,  442  ;  565. 

Sanskrit,  discovery  of,  ii.  538. 

Santi-Linari,  animal  magnetism,  ii.  475, 

Sarcode,  ii.  264. 

Sartorius  von  Waltershausen  on  Gauss, 
i.  181,  183,  ii.  631. 

Saussure,  de,  ii.  247  ;  experiments,  391. 

Sauveur,  referred  to  by  Voltaire,  i,  105. 

Savage  tribes,  history  of,  i.  3. 

'Savants,  Journal  des,'  i.  41. 

Savart,  theory  of  elasticity,  ii.  31  ;  193. 

Savigny,  i.  162;  indebtedness  of,  to 
Gibbon,  169. 

Sayce,  '  Introduction  to  the  Science  of 
Language '  quoted,  ii.  539,  540. 

Scaliger,  Joseph  J.,  influence  of,  on 
German   thought    and    literature,  i. 


INDEX. 


797 


212,  226 ;  services  to  classical  learning 
and  criticism,  222  ;  295. 

Scheele,  forerunner  of  Berzelius,  i.  391. 

Scheidt,  edition  of  '  Protogfea,'  ii.  280. 

Scheiner,  J.,  'Astronomical  Spectro- 
scojiy,'  ii.  46,  362  ;  quoted,  49  ;  '  Der 
Ban  des\Veltalls,'282. 

Schelling,  F.  W.  J.  von,  on  the  province 
of  philosophy,  i.  36 ;  on  position  of 
philosophy,  38  ;  treated  science  from 
a  metaphysical  standpoint,  43  ;  phil- 
osophy of,  influenced  by  Herder,  51 ; 
philosophical  writings  of,  83 ;  162 ; 
speculative  tendency  of,  178  ;  '  Ideen 
zu  einer  Philosophie  der  Natur,'  179  ; 
philosophy  of,  204  ;  207  ;  influenced 
by  Spinoza,  212 ;  benefactions  to 
historical  sciences,  215  ;  influence  of, 
ii.  225,  494,  500  ;  and  Goethe's  views, 
245,  255;  '  Natur-philosophie,'  304, 
315  ;  evolution,  354  ;  508. 

Schenstone,  W.  A.,  'Justus  von 
Liebig,  his  Life  and  Work,'  ii.  391, 
393. 

Schering,  E.,  '  C.  F,  Gauss  und  die 
Erforschung  des  Erdmagnetisnuis,'  i. 
181,  331  ;  address  on  Gauss's  cen- 
tenary, 304 ;  corresi^ondeuce  with 
Helmholtz,  ii.  710  et  seq. 

Scheuchzer,  correspondence  with  Leibniz 
quoted,  ii.  281. 

Schiller,  style  of,  i.  51  ;  writings  of, 
83,  84  ;  educated  with  Cuvier,  133  ; 
"The  German  Muse"  quoted,  157; 
Kant's  sesthetical  philosophy,  ii.  535  ; 
'  Wallenstein's  Tod  '  quoted,  586. 

Schimper,  K.  F.,  "spiral  theory,"  ii. 
223. 

Schlegel,  A.  W.  von,  Berlin  lectures,  i. 
84  ;  on  Georg  Forster,  1 79  ;  263  ; 
researches  of,  ii.  542. 

Schlegel,  Fr.,  on  Goethe's  school,  i.  84  ; 
made  Shakespeare  familiar  to  German 
readers,  212. 

Schlegel,  Victor,  '  Hermann  Grass- 
mann,'  i.  243 ;  on  Grassmann,  ii. 
656  ;  on  non-Euclidean  geometry,  714. 

Schleicher,  August,  '  Morphology  of 
Language,'  ii.  540,  541. 

Schleiden,  Mathias,  cellular  theory  of, 
i.  194,  309,  ii.  262,  263,  299  ;  i.  200  ; 
'  Botany  as  an  Inductive  Science,' 
209;  biological  discoveries  of,  217; 
mechanical  view  in  biology,  218  ;  220  ; 
refers  to  Brown'.s  discovery,  ii.  264  ; 
theory  of  cell  formation,  265  ;  ulti- 
mate identity  of  structure  of  animals 
and  plants,  267  ;  definition  of  a  cell, 
370  ;  402,  403,  408. 


Schleiermacher,  F.,  new  era  of  education 
in  Germany,  i.  38 ;  philosophical  writ- 
ings of,  83  ;  religious  revival  preached 
by,  203;  scientihc  ideal  of,  211; 
educational  significance  of  his  writ- 
ings, 258  ;  263  ;  psychology,  ii.  495. 

SchlOmilch,  0.,  i.  209. 

Schlosser,  F.  Chr.,  'History  of  the 
Eighteenth  Century,'  i.  59. 

Schltizer,  Ludwig  August,  of  Guttingen 
University,  i.  165  ;  statistics,  ii.  555. 

Schmidt,  F.,  and  P.  Stackel  publish 
Bolyai's  correspondence,  ii.  652. 

Schmidt,  Johannes,  on  August  Schlei- 
cher, ii.  540. 

Schmidt,  Karl,  '  Geschichte  der  Pada- 
gogik,'  i.  166,  256. 

Schonflies,  A.,  ii.  734;  on  G.  Cantor's 
work,  736. 

Schonlein,  Lucas,  metaphysical  lean- 
ings of,  i.  196  ;  198  ;  influenced  by 
the  NaturphUosophie,  207  ;  freed 
under  the  influence  of  French  science, 
208. 

School  literature,  reform  in,  i.  44. 

School  of  Oriental  Languages  in  France, 
i.  113. 

School  of  philology,  modern  German,  i. 
172. 

School,  polytechnic,  German,  first  es- 
tablished at  Vienna,  i.  166. 

Schools,  German,  i.  166. 

Schools  of  thought  in  Germany,  i.  167. 

Schopenhauer,  A. ,  animation  of  all 
nature,  ii.  369  ;  470. 

Schriider,  E.,  ii.  737. 

Schubert,  H.,  ii.  734. 

Schultze,  Ma.x,  protoplasmic  theory,  ii. 
371,  443. 

Schumacher,  H.  C,  i.  45;  '  Astronom- 
ische  Nachrichten,'  167  ;  correspond- 
ence with  Gauss,  185,  ii.  652  ;  letter 
from  Gauss  on  telegraph,  i.  304. 

Schiitte,  German  translation  of  Gino 
Loria's  work  on  geometry,  i.  275. 

Schwann,  Theodor,  extended  cell  theory 
to  animals,  i.  195  ;  198,  200  ;  the  head 
of  the  modern  physiological  school, 
217 ;  mechanical  view  in  biology, 
320;  cellular  theory,  309,  ii.  263; 
identity  of  all  living  structure,  209  ; 
discovery  of  the  nucleus  referred  to, 
264  ;  theory  of  cell  formation,  265 ; 
ultimate  identity  of  structure  of  ani- 
mals and  plants,  267  ;  definition  of 
a  cell,  371  ;  402,  403  ;  microscopical 
researches,  418  ;  '  Microscopical  Re- 
searches,' 419,  420,  423  ;  conception 
of  the  cell,  422  ;  "Metabolism,"  44'2. 


798 


INDEX. 


Schwarz,  H.  A.,  on  Dirichlet's  prin- 
ciple, ii.  703  ;  Weierstrass's  letter  to, 
ib.;  on  Bolzano,  709. 

Schweikart,  ii.  713. 

Schwerd,  'Die  Beugungserscheinuugen 
aus  den  Fundamentalgesetzen  der 
Undulationstheorie  analytisch  ent- 
wickelt'  (luoted,  ii.  26. 

Schwoerer  (see  Faudel),  ii.  134. 

Science  now  international,  i.  19,  303  ; 
and  life,  31  ;  and  poetry,  ib.;  as 
opposed  to  other  thought,  69  ;  the 
meaning  and  use  of  the  word,  89,  90  ; 
English  and  Continental  notions  of, 
91 ;  schools  of,  in  France,  106 ;  schools 
of,  promoted  by  Governments  of 
Revolution,  108  ;  during  the  Revolu- 
tion and  under  the  First  Empire, 
138 ;  popularised  by  France,  142 ; 
German,  not  patronised  by  royalty, 
157  ;  and  "Wissenschaft,"  168  ;  and 
exact  science,  171  ;  German,  cosmo- 
politan, 189  ;  in  Germany,  202  ;  and 
philosojihy,  conflict  between,  205  ;  and 
history,  relations  of,  2o6  ;  for  its  own 
sake,  211 ;  thoroughness  of  German 
men  of,  213  ;  and  teaching,  214  ;  and 
philosophy,  215,  311  ;  organisation 
of,  abroad,  226  ;  English,  in  the  early 
part  of  nineteenth  century,  229 ; 
alleged  decline  of,  in  England,  230  ; 
French,  praised  by  Cuvier,  231  ; 
English,  criticisms  of  Playfair,  ib.; 
criticisms  of  Babbage,  233 ;  decline 
of,  in  England,  '  Edinburgh  Review ' 
quoted  on,  234 ;  in  England  favour- 
ably criticised  by  Cuvier,  ib.;  by 
Prof.  Moll  of  Utrecht,  235;  Prof. 
Moll  on  difference  between  culture  of, 
in  France  and  England,  237;  English, 
individual  character  and  practical 
tendency  of,  251 ;  English,  peculiar- 
ities more  marked  in  early  part  of 
century,  252  ;  importance  of  British 
contributions  to,  276 ;  diffusion  of 
scientific  knowledge  on  the  Continent, 
276 ;  isolation  of  English  men  of 
science,  277 ;  philosophy  of,  306 ; 
interests  which  promote,  326  ;  prac- 
tical interest  in,  328  ;  physical,  ap- 
plied to  medicine,  ii.  208  ;  abstract, 
550  ;  of  large  numbers,  555. 

Science,  exact,  reception  of,  in  Ger- 
many, i.  175  ;  absent  from  German 
universities  in  the  eighteenth  cen- 
tury, 178. 

Sciences,  the  descriptive,  ii.  203  ;  na- 
tural and  mental,  separation  of  the, 
534. 


Scientific,  reasoning,  1.  45 ;  periodicals, 
180 ;  associations,  dates  of,  227 ;  spirit 
in  the  first  and  second  half  of  the 
century,  302 ;  ideas,  special,  306 ; 
antiquity  of  leading  ideas,  312 ; 
spirit  in  business,  ii.  553. 

Scotch  school  of  natural  philosophy, 
ii.  141  ;  activity  of,  148. 

Scott,  Sir  Walter,  i.  82  ;  romantic  school 
of,  84  ;  '  Edinburgh  Review,'  273. 

Secchi,  spectroscopic  observations,  ii. 
361. 

Sedgwick,  A.,  'A  Discourse  on  the 
Studies  of  the  University  of  Cam- 
bridge,' i.  263 ;  267 ;  worked  in 
harmony  with  Analytical  Society, 
271  ;  criticism  of  '  Vestiges,'  ii.  319. 

Seebeck,  electricity  and  heat,  i.  363  ; 
thermo-electricity,  ii.  143  ;  the  siren, 
487. 

Seeley,  J.,  '  Life  of  Stein,'  i.  38. 

Seguin,  heat  units,  ii.  109 ;  indestruc- 
tibility of  force.  111  ;  physiological 
processes,  390. 

Selborne,  White's  '  Natural  History  of,' 
i.  2S7. 

Selection,  "natural"  and  "sexual,"  ii. 
336 ;  natural,  within  the  organism, 
435 ;  Maxwell's  j^rocess  of,  598. 

Sellmeier,  W.,  anomalous  dispersion  of 
wave-motion,  ii.  53 ;  researches  of, 
54. 

Seminaries  in  Germany,  i.  214. 

Semler,  Archdeacon,  established  the 
first  "  Realschule  "  at  Halle,  i.  166. 

Sensation,  Johannes  MUller's  law  of 
specific  energies,  i.  198 ;  Weber's  law 
of,  200  ;  localisation  of,  ii.  507. 

Sense-perception,  i.  199. 

"Sensualistes,"ii.  323. 

Serres,  'Anatomic  Comparee  du  Cer- 
veau,'  ii.  317;  "law  of  biogenesis," 
349. 

Serret,  his  'Algebre  Superieure,'  ii. 
686. 

Servois,  ii.  660,  711. 

Seth,  A.,  on  Fr.  Nietzsche,  ii.  287. 

Shaftesbury,  i.  145. 

Shakespeare,  infiuence  of,  in  German 
thought  and  literature,  i.  212 ;  261, 
ii.  251  ;  the  word  "statist,"  555. 

Shelburne,  Lord,  quoted,  ii.  562. 

Shelley,  P.  B.,  freshness  of  individual 
thought  of,  i.  76. 

Siemens,  Werner,  submerged  cables,  i. 
329. 

Siemens,  William,  ii.  179. 

Silvius,  chemistry  in  alliance  with 
medicine,  i.  126. 


1 
I 


f 


INDEX. 


799 


"Simplex  sigillum  veri,"  i.  401. 

Simpson,  Sir  J.  Y.,  introduced  clilor- 
otorm,  i.  93. 

Simson,  Robert,  Scotch  university  pro- 
fessor, i.  272 ;  and  Stewart,  ii.  658. 

Skoda,  i.  198,  208. 

Sloman  on  tlie  invention  of  the  calculus, 
i.  101. 

Sniellie,  William,  'Edinburgh  Magazine 
and  Review,'  i.  273. 

Smiles,  'Life  of  Thomas  Edwards,'  i. 
287. 

Smith,  Adam,  imported  ideas  from 
France,  i.  16  ;  intercourse  with  French 
thought,  268  ;  272  ;  influence  of,  273  ; 
ii.  415  ;  human  culture,  529. 

Smith,  H.,  translation  of  Schwann's 
principal  work,  ii.  263 ;  on  con- 
gruence, 723  ;  his  report,  ib. 

Smith,  Sydney,  lectured  at  Royal  In- 
stitution, i.  249,  264 ;  '  Edinburgh 
Review,'  273. 

Smith,  William,  on  'Strata,'  i.  230; 
father  of  English  geology,  291  ;  study 
of  fossil  remains,  ii.  225 ;  tabular 
view  of  the  British  strata,  293. 

Snell,  deflection  of  rays  of  light,  i. 
356. 

Societe  Philomatique,  bulletin  of,  i. 
41. 

Society,  Royal,  i.  227. 

Socrates,  ethical  philosophy  of,  ii.  4. 

Soemmering,  ii.  247  ;  influences  Herder, 
532. 

Sohnke,  L.,  '  Entwickelung  der  Theorie 
der  Krystallstructur,'  i.  443. 

Sommer,  edition  of  Herschel  '  On  the 
Construction  of  the  Heavens,'  ii. 
283. 

Sophocles,  i.  261. 

Sound  and  colour,  analogy  between,  ii. 
489. 

Sound  and  light,  mechanical  difference 
between,  ii.  30. 

South,  not  member  of  any  university,  i. 
239. 

Southey,  'Thalaba,'i.  84. 

Spanheim,  recognition  of  Bentley,  i. 
169. 

Species,  changes  of,  services  of  Lamarck 
and  Saint  Hilaire  to  the  study  of, 
debatable,  i.  201. 

Spectrum  analysis,  i.  277,  ii.  45  et  seq.; 
clue  to,  47  ;  359. 

Speculation,  meaning  and  scope  of  the 
term,  i.  64. 

Spedding,  James,  i.  282. 

Spencer,  Herbert,  first  English  system 
of  philosophy,   i.   48  ;   on  the   "  Un- 


knowable," 53,  ii.  326  ;  constructive 
ideas  of,  i.  81  ;  system  of,  ii.  205 ; 
works  of,  210  ;  vocabulary  and  ideas 
of  evolution,  214 ;  conceptions  of, 
246;  'Principles  of  Biology  '  quoted, 
270  ;  "physiological  units,"  '272,  424, 
610  ;  philosophy  of,  279,  346  ;  ([uoted, 
288;  'Biology,'  322,  323,  406,  438; 
351;  "survival  of  the  fittest,"  ib.; 
"Factors  of  Organic  Evolution,"  353  ; 
dynamical  aspect  of  science,  355 ; 
"On  the  Nebular  Hypothesis,"  358; 
"direct  equilibration,"  436;  law  of 
limit  of  growth,  445  ;  theory  of  evolu- 
tion, 455 ;  and  Weismann,  460 ; 
anthropological  work,  497  ;  511  ; 
study  of  sociology,  530 ;  607,  608, 
749. 

Si^iuoza,  influence  of,  on  German 
thought  and  literature,  i.  212 ;  on 
German  philosophy,  ii.  205  ;  251  ; 
animation  of  all  matter,  369  ;  psycho- 
physical parallelism,  519  ;  5-35. 

Spix,  morphological  analogies,  ii.  251. 

Spon,  Jacob,  archajologist,  i.  295. 

Sprengel,  Chr.  C,  ii.  230,  261  ;  fer- 
tilisation of  plants,  338  ;  investiga- 
tions of,  415. 

Spurzheim,  Joh.  Chr.,  i.  136  ;  phren- 
ology, ii.  477,  479. 

Squares,  metliod  of  least,  ii.  576. 

Staid,  Mme.  de,  and  German  literature, 
i.  17  ;  225 ;  writings  of  Herder,  ii. 
531. 

Stiigemann,  i.  45. 

Stahl,  animist  (medicine),  i.  126 ; 
elaborated  the  phloi^istic  theory,  387  ; 
"Anima,"ii.  388,  503. 

Stair,  Earl  of,  first  agricultural  or- 
ganisation in  Scotland,  i.  284. 

Stas,  J.  S.,  measurements  of,  i.  403. 

Statics,  ii.  5  ;  and  dynamics,  144. 

Statistical,  methods,  used  largely  by 
Napoleon,  i.  153  ;  view  of  nature, 
i.  438,  ii.  546,  548  ;  application  in 
physics,  589  ;  knowledge  of  nature, 
600. 

Statistics,  beginning  of  science  of,  i. 
121  ;  ii.  548  et  seq.  ;  in  France, 
Germany,  and  England,  562  ;  social, 
583  ;  pretensions  of,  586. 

Staudt,  0.  G.  C.  von,  his  geometry,  i. 
44,  181,  275 ;  and  Gauss,  ii.  652 ;  on 
imaginary  elements,  661  ;  669  ;  his 
work  expounded  by  Reye,  Luroth, 
and  Fiedler,  ib.;  and  Cayley,  718  ; 
Klein  on,  ib. 

Stebbing,  Thomas  R.  R.,  '  Naturalist 
of  Cumbrae,'  i.  289. 


800 


INDEX. 


StefFens,  H.,  on  Paris  at  the  close  of  the 
eighteenth  century,  i.  17  ;  '  Autobio- 
graphy,' 39  ;  development  of  Goethe's 
views,  ii.  256 ;  natural  philosophy, 
315;  evolution,  354;  508. 

Stein,  H.  Fr.  K.  von,  attitude  of,  to 
national  idealism  in  Germany,  i.  39  ; 
quoted  on  Humboldt,  263. 

Steiner,  Jacob,  geometry,  i.  44  ;  new 
science  of  geometry,  114  ;  163  ;  and 
Crelle,  186,  187 ;  neglect  of,  in  Ger- 
many, 243  ;  against  analysis,  ii.  632  ; 
his  method,  662  ;  Geyser  on,  ib.;  his 
great  work,  667  ;  on  isoperimetrical 
problems,  669  ;  672 ;  his  theorems 
proved  by  Cremona,  681. 

Steinheil,  measurements  of,  i.  322. 

Steinthal,  psychologist,  ii.  497 ;  the 
objective  mind  in  history,  530. 

Stephen,  Leslie,  i.  25  ;  on  liume,  47. 

Stephenson,  George,  the  "Racket,"  i. 
303. 

Stereo-chemistry,  i.  447. 

Stevin,  Simon,  'La  Disme,'  ii.  645; 
recommends  decimal  system,  ib. 

Stewart,  Balfour,  spectrum  analysis,  i. 
278;  "radiant  heat,"  ii.  46;  physical 
view  of  nature,  141,  601. 

Stewart,  Dugald,  works  of,  i.  83  ; 
quoted,  359;  ii.  287,  601. 

Stewart,  Matthew,  forerunner  of  Car- 
not,  ii.  658. 

Stieda,  L.,  'Life'  of  von  Baer,  ii. 
300. 

Stirling,  James,  ii.  572. 

Stirp,  theory  of  the,  ii.  614. 

"Stoflfwechsel,"  ii,  395;  older  ideas 
corrected,  397. 

Stoics,  "cyclical"  view  of  the,  ii.  286. 

Stokes,  Sir  G.  G.,  i.  274 ;  spectrum  analy- 
sis, 277,  ii.  49  ;  properties  of  ether, 
31 ;  quoted,  32,  592  ;  33 ;  '  Burnett 
Lectures  on  Light '  quoted,  37 ; 
"double  refraction,"  43;  lines  of 
sodium,  47,  48  ;  translation  of  Fou- 
cault's  and  Kirchholf's  memoirs,  48  ; 
on  emission  and  absorption  of  light 
rays,  50,  51  ;  invented  the  term 
fluorescence,  52  ;  referred  to,  54,  55  ; 
on  whirling  motion,  58  ;  on  iin- 
dulatory  theory,  195;  optical  re- 
searches, 229;  630. 

Stoll,  Max.,  i.  '208. 

Stolz,  0.,  '  Grossen  und  Zahlen,'  i.  275  ; 
and  Weierstrass,  ii.  703  ;  on  Bolzano, 
709  ;  726. 

Stiilzle,  'K.  E.  von  Baer  und  seine 
Weltanschauung,'  ii.  300. 

Stoney,  Dr  Johnstone,  introduces  the 


term    "electron,"    ii.    193;    use    of 
recent  microscopic  appliances,  229. 

Stout,  G.  F.,  "Herbart  compared  with 
English  Psychologists  and  with 
Beneke,"  ii,  495,  497;  'Analytic 
Psychology, '  528. 

Stow,  Normal  School  at  Glasgow,  i. 
257. 

Strasburger,  E.,  embryological  studies 
of,  ii.  227  ;  "idioplasma,"  448  ;  459. 

"Struggle  for  Existence,"  ii.  332,  333. 

Struve  on  methods  of  the  astronomers 
of  Greenwich  Observatory,  i.  99. 

Stuart,  Gilbert,  'Edinburgh  Magazine 
and  Review,' i.  273. 

Stuart  and  Revett,  archaeological  ex- 
plorations of,  i.  295. 

Study,  E.,  referred  to,  ii.  654. 

Sturm,  J.  C.  Fr,,  recognised  merits  of 
Green's  work,  i.  247  ;  appreciated 
educational  work  of  the  "Order  of 
Jesus,"  256. 

Substitution,  chemical,  i.  409. 

Substitution,  principle  of,  in  mathe- 
matics, ii.  686. 

Substitutions,  Jordan's  treatise  on,  ii, 
686,  689,  692. 

Sully,  Due  de,  doctrine  of  averages, 
ii.  561  ;  political  statistics,  563. 

Sully,  James,  article  "Evolution"  in 
'Encyclopedia  Britannica,'  ii.  279; 
"Herder,"  533. 

Sun,  heat  of,  ii.  357. 

Siissmilch,  Pastor,  the  divine  origin  of 
language,  ii.  536 ;  '  On  the  Divine 
Order,'  557,  563;  political  arith- 
metic, 585. 

Svieten,  G,  v.,  i.  208. 

Swan,  spectrum  analysis,  i.  278. 

Sybel,  H.  von,  'historische  Zeitschrift,' 
i.  159. 

Sydenham,  i.  272. 

Sylovv,  L.,  on  Abel,  ii.  649;  on  Abel 
and  Galois,  686. 

Sylvester,  J.  J.,  developed  theories  of 
Boole,  i.  247 ;  on  mathematics,  ii, 
629  ;  631  ;  on  invariants,  676 ;  the 
proper  business  of  mathematics,  679  ; 
proves  Newton's  theorem,  681  ;  on 
determinants  and  Hesse,  683  ;  691, 

Symbolism,  chemical,  i.  417. 

Syme  of  Edinburgh  [Jniversity,  i.  272. 
Symington    built  the  tug   "Charlotte 

Dun  das,"  i.  303. 
Symmetrical  formulge,  ii.  681. 

Tacitus,  a  model  historian,  i.  7. 
Tait,   P.   G.,   'Sketch  of  Thermodyn- 
amics,' i.  376,  ii.  167,  173,  175 ;  on 


I 


INDEX. 


801 


"  action  at  a  distance,"  i.  380  ;  '  Pro- 
perties of  Matter,' 388, 425  ;  "Kinetic 
Theory  of  Gases,"  438  ;  "kinetics," 
ii.  5;  'Light,'  11,  592;  'Light' 
quoted,  13,  36  ;  criticism  of  Tyndall's 
theory  of  heat,  57 ;  translation  of 
Helmholtz's  memoir  on  vortex  motion, 
58  ;  memoir  of  Rankine,  62  ;  '  Recent 
Advances  of  Physical  Science,'  63, 
106,  108  ;  '  On  Knots,'  64  ;  '  Recent 
Advances  of  Physical  Science'  quoted, 
66;  'Sketch  of  Thermodynamics,' 
controversy  regarding,  97  ;  '  Dyna- 
mics,' 99  ;  and  Tyndall  and  others, 
107  ;  computations  of  Seguin,  109  ; 
quoted  on  the  relative  values  of  the 
terms  "force"  and  "energy,"  116; 
perpetual  motion  defined,  124  ;  pre- 
face to  Rankine's  papers,  133 ;  (see 
Clausius),  135  ;  physical  view  of 
nature,  141  ;  '  Heat '  quoted,  591. 

Tait  and  Crum  Brown,  Memoir  of 
Thomas  Andrews,  ii.  162. 

Tait  and  Steele,  '  Dynamics  of  a  Par- 
ticle,' i.  101,  ii.  144. 

Tait  and  Thomson.  See  Thomson  and 
Tait. 

Tait's  '  Edinburgh  Magazine '  published, 
i.  273. 

Talbot,  solar  spectrum,  i.  278. 

Talleyrand,  public  instruction,  i.  109  ; 
higher  aims  of,  not  realised,  112. 

Tannery,  Jules,  his  lectures  on  theory 
of  functions,  ii.  704  ;  737. 

Tauchuitz,  edition  of  ancient  classics,  i. 
167. 

Taylor,  Bayard,  '  Faust '  quoted,  i.  52. 

Taylor,  Brook,  i.  101. 

Taylor,  Charles,  on  continuity,  ii. 
660. 

Taylor,  'Scientific  Memoirs,' i.  325,  ii. 
263  ;  series  of,  646. 

Telegraph,  first,  i.  92. 

Tennyson,  mature  thought  of,  i.  76. 

Tenon,  i.  107. 

"  Tension,"  ii.  138. 

Terquem,  ii.  660. 

Terrestrial  view,  ii.  369. 

Teubner,  editions  of  the  ancient  classics, 
i.  167. 

Tliewtetus,  Proclus  on,  ii.  634. 

Thenard,  practical  discoveries  of,  i. 
147  ;  organic  analysis,  190  ;  '  Chem- 
istry,' 200  ;  ii.  508. 

Theological  faculty  in  German  univer- 
sities, ii.  197. 

Thermodynamics,  ii.  62 ;  two  laws  of, 
128. 

Thermo-elastic  phenomena,  ii.  142. 

VOL.  II. 


Thermo-electric  phenomena,  ii.  142. 

Theta  function,  Jacobi's,  ii.  649  ;  696. 

Thevenot,  original  member  of  Paris 
"  Academic  des  Sciences,"  i.  228. 

Thibaud,  i.  162. 

Thibaudeau  quoted,  i.  113  ;  '  Le  Con- 
sulat  et  I'Empire,'  149,  152. 

Thiersch,  Fr.,  i.  162  ;  conducted  philo- 
logical seminaries,  214. 

Tholuck,  '  Das  akademische  Leben  des 
n^™  Jahrhunderts,'  i.  163. 

Thomasius  represents  spirit  of  Bacon 
and  Leibniz  at  Halle,  i.  160. 

Thompson,  Benjamin.  See  Count  Rum- 
ford. 

Thomsen,  V.  L.  P.,  a  founder  of  phys- 
ical chemistry,  ii.  152  ;  chemical 
affinity,  171. 

Thomson  and  Tait,  '  Natural  Phil- 
osophy,' i.  45,  101,  274.  316,  318, 
376,  ii.  61,  99,  144,  1.52,  1.53,  184, 
358  ;  the  term  "kinetics,"  5  ;  referrecl 
to,  62,  148  ;  influence  of,  145. 

Thomson,  J.  A.,  'Science  of  Life,'  ii. 
228,  271,  337,  338,  348,  349,  370,  436, 
447;  the  term  "homology,"  259; 
"  Cell  and  Protoplasm,"  266  ;  298  ; 
"embryology,"  299;  quoted  on  von 
Baer,  303  ;  ''Evolution  of  Sex,'  344  ; 
'Science  of  Life'  qiioted,  448,  455, 
458;  459;  on  ".stirps,"  614. 

Thomson,  James,  harmonic  aualysis,  i. 
330;  heat  and  "perpetual  motion," 
ii.  126  ;  prediction,  126,  170;  physical 
view  of  nature,  141  ;  "Crystallization 
and  Liquefaction,"  142;  theory  of 
energy,  166. 

Thomson,  J.  J.,  on  vortex  motion,  ii. 
63,  65,  183 ;  Princeto\vn  lectures, 
190;  'Researches,'  191;  'Discharge 
of  Electricity  through  Gases,'  192; 
electrical  researches,  362. 

Thomson  (the  poet),  i.  285. 

Thomson,  Prof.  Thos.,  i.  188  ;  and  Dal- 
ton,  245  ;  the  atomic  theory,  425. 

Thomson,  Wm.  (Lord  Kelvin),  on 
chemical  laboratories,  i.  188  ;  and 
Helmholtz,  199,  ii.  149  ;  the  conserva- 
tion of  energy,  i.  201,  ii.  128,  142; 
Fourier's  series,  i.  241  ;  Green's  treat- 
ise, 246  ;  and  Joule,  265,  434,  ii.  110  ; 
Faraday's  "lines  of  force,"  i.  266,  ii. 
71  ;  referred  to,  i.  272 ;  his  work, 
274,  ii.  133  ;  on  discovery  of  spectrum 
analysis,  i.  277  ;  telegraphic  connec- 
tion with  America,  i.  303 ;  absol- 
ute .scale  of  temperature,  309,  315  ; 
"vortices,"  312,  313  ;  absolute  meas- 
urements,     323 ;     submarine     tele- 

3  E 


802 


INDEX. 


graphy,  329 ;  '  Popular  Lectures  and 
Addresses,'  330,  ii.  61 ;  improve- 
ments in  mariner's  compass,  i.  331 ; 
mechanical  theory  of  gravitation, 
344  ;  Boscovich's  theory,  358  ;  elec- 
trical measurements,  366 ;  cohesion 
aud  capillary  attraction,  376 ;  on 
"capillary  attraction"  quoted,  425; 
"chirality,"  432,  ii.  22;  "On  the 
Size  of  Atoms,"  i.  437;  "Steps  to- 
wards a  Kinetic  Theory  of  Matter," 
456;  quoted,  ii.  39,  182,  184,  190; 
sodium,  48  ;  wave-motion,  53  ;  optics, 
55  ;  vortex  theory,  57,  58,  63  ;  on  gyro- 
stat, fil  ;  thermodynamics,  62,  603  ; 
diamagnetism,  74 ;  on  "permeability," 
75  ;  electro-magnetics,  77  ;  Faraday 
and  Clerk-Maxwell,  78,  79  ;  reprints 
of  papers  quoted,  803 ;  physical 
lines  of  force,  81  ;  electrical  re- 
searches, 86;  "vortex  filaments," 
89 ;  vibrations  of  the  ether,  91  ;  in- 
dependence of  Mayer's  writings,  97  ; 
and  Mayer's  hypothesis,  109;  "en- 
ergy," 114;  "work  "and  "energy," 
115 ;  Mayer,  and  Joule,  116 ;  ab- 
solute measurements  in  thermotics, 
117;  Carnot's  'Puissance  motrice,' 
118;  dissipation  of  energy,  119,  131, 
132,  364,  598 ;  Sadi  Carnot's  heat 
theory,  123 ;  perpetual  motion,  124- 
126 ;  experiment,  127 ;  Sadi  Carnot, 
130 ;  experiments  of  Joule  and  Eeg- 
nault,137 ;  " potential "  and  "actual " 
energy,  139  ;  physical  view  of  nature, 
141 ;  Kegnault's  measurements,  152  ; 
167;  thermodynamic  "motivity," 
168,  169,  594;  "free  energy,"  173; 
"available  energy,"  and  "entropy," 
174,  594;  175,  179,  184  ;  ether  theory, 
196  ;  recognition  of  Kant,  284  ;  296  ; 
"On  Geological  Time,"  356;  "Me- 
chanical Energies  of  the  Solar  Sys- 
tem," 358  ;  on  the  spectroscope,  362  ; 
Glasgow  Address  quoted,  363 ;  cos- 
mical  origin  of  life,  369 ;  on  the 
dissipation  of  energy,  i.  309 ;  ii.  52, 
404 ;  irreversibility  of  natural  pro- 
cesses, 593 ;  699 ;  his  theorem  and 
Dirichlet,  700  ;  704,  708. 

Thomson,  William,  aud  Sir  G,  G. 
Stokes,  contributions  to  mathematical 
physics,  i.  274  ;  and  Tait :  '  Natural 
Philosophy,'  ib. 

Thorpe,  'Essays  in  Historical  Chem- 
istry,' ii.  158. 

Thought,  the  hidden  world,  i.  1  ;  the 
only  moving  principle,  2 ;  Max 
Miiller   on  definition    of,    4 ;    many 


meanings  of,  5 ;  forgotten  and  unex- 
pressed, 8 ;  value  of  contemporary 
records  of,  10 ;  unity  of,  a  product  of 
the  nineteenth  century,  16 ;  equi- 
valents in  German  and  French,  24  ; 
conception  of,  not  specifically  Eng- 
lish, 26 ;  definition  of,  33 ;  not  ex- 
hausted by  science  or  philosophy, 
66 ;  unmethodical,  68  ;  religious,  69  ; 
personal  or  subjective,  70  ;  scientific, 
philosophical,  and  individual,  72  ;  of 
nineteenth  century  characterised,  77  ; 
constructive,  not  destructive,  80 ; 
exact,  historical,  and  critical  habits 
of,  222 ;  characteristics  of  higher 
mental  work  in  England,  239 ;  char- 
acteristics of  English,  249  ;  scientific, 
absence  of  schools  of,  in  England, 
250  ;  history  of,  ii.  627  ;  not  history 
of  knowledge,  628. 

Thouin,  agriculture  at  the  Ecole  nor- 
male,  i.  112. 

Thucydides,  a  model  historian,  i.  7. 

Tiedemann,  Fr.,  chemistry  of  the  living 
body,  ii.  391 ;  317. 

Tilloch,  'Philosophical  Magazine,' i.  41. 

"  Timbre,"  ii.  488. 

Tisserand,  'Comptes  Rendus,'  i.  377; 
quoted  on  Newton's  law,  378. 

Titchener,  E.  B.,  criticism  of  Miinster- 
berg's  work,  ii.  522. 

Titius,  Daniel,  astronomical  formula  of, 
i.  422. 

Tocqueville,  A.  de,  quoted  on  contem- 
porary records,  i.  10. 

Todhunter,  Isaac,  his  '  Histories,'  i. 
91 ;  '  History  of  the  Theories  of 
Attraction,'  98,  99,  308,  ii.  698  ; 
theory  of  probabilities,  i.  120,  ii. 
568  ;  '  History  of  the  Theory  of  Prob- 
ability,' i.  234;  'Life  of  Whewell,' 
236,  262,  306  ;  theory  of  elasticity,  ii. 
30 ;  on  Young's  style,  ib. ;  on  Eng- 
lish science,  ib.  ;  '  History  of  Elas- 
ticity,' 33 ;  quoted,  43. 

Todhunter  and  Pearson,  '  History  of 
the  Theory  of  Elasticity,'  i.  376,  ii.  43, 
56. 

Tooke,  Home,  on  words,  i.  21 ;  the 
'  Diversions  of  Purley,'  ii.  537. 

Tour,  Cagniard  de  la,  the  siren,  ii.  487. 

Traube,  medical  thermometry,  ii.  389. 

Treitschke,  '  Deutsche  Geschichte,'  i. 
312 

Trembly,  ii.  418. 

Trench,  Archbishop,  on  words,  i.  21. 

Treviranus,  G.  R.,  'Biologie,'  i.  194; 
identity  of  all  sciences  of  organic 
life,    ii.    217 ;    230,    261  ;    biological 


♦ 


INDEX. 


808 


researches  of,  313 ;  genetic  view,  321  ; 
evolution,  327. 

Treviranus,  L.  C,  botanical  laboiirs  of, 
ii.  218. 

Truth,  the  search  after,  not  the  end  of 
knowledge,  i.  29. 

Tschirnhausen,  refeiTed  to,  i.  101. 

Tubingen  school  of  theological  criti- 
cism, i.  162. 

Turgot,  founded  the  Ecole  des  Fonts  et 
Chaussees,  i.  107 ;  neglect  of,  by- 
Napoleon,  149  ;  statistics,  ii.  571 ; 
573. 

Turner  disproves  Prout's  hypothesis,  i. 
402. 

Tycho,  a  forerunner  of  Bacon,  i.  94  ; 
of  Kepler,  157 ;  317 ;  discovered 
variable  stars,  327. 

Tylor,  E.  B.,  anthropologist,  ii.  497. 

Tyndall,  John,  'Heat,'  ii.  57;  and 
Faraday,  77  ;  on  Mohr's  and  Mayer's, 
&c.,  scientific  work,  107 ;  computa- 
tions of  Seguiu,  109  ;  his  works  trans- 
lated into  German,  148  ;  405  ; 
ubiquity  of  life,  452;  "tone,"  488. 

Type  theory  in  chemistry,  i.  411. 

Ueberweg  and  Beneke,  ii.  495  ;  512. 

Ukert  (see  Heeren),  i.  167. 

Ulrich,  Duke,  reconstituted  University 

of  Tubingen,  i.  159. 
Units,  living  and  lifeless,  ii.  620. 
Unity  of  human  interests,  terms  for,  i. 

33. 
Universities  and  high  schools,  relations 

of,  i.  166. 
Universities,  Belgian,  i.  161. 
Universities,  British,  and  others,  dates 

of,  i.  228. 
Universities,  Danish,  i.  161. 
Universities,  Dutch,  their  influence  on 

German  culture,  i.  160  ;  161. 
Universities,  English,  unique  character 

of,  i.  254. 
Universities,  German,  foundation  of,  i. 

158 ;   162,   197  ;   testimonies   to   the 

gi-eat  work  of,  225. 
Universities,  Norwegian,  i.  161. 
Universities,  Russian,  i.  161. 
Universities,  Scotch,  i.  160,  267,  271. 
Universities,  Swedish,  i.  161. 
Universities,  Swiss,  retarded   develop- 
ment of,  i.  163. 
University,      Johns     Hopkins,     Lord 

Kelvin's  lectures,  ii.  55. 
University  of  Athens,  i.  161. 
University  of  Geneva,  i.  160. 
University  of  Giittingen,  i.    164,   165, 

175  ;  prize  essays  on  dynamics,  ii.  97. 


University  of  Halle,  i.  165. 
University  of  Kasan,  i.  161. 
University  of  Maros  Vasarhely,  i.  161. 
"  Unknowable,"  ii.  326 ;  or  unknown 

factor,  375. 
Unwin,  W.  C.,  "The  Development  of 

the    Experimental    Study    of    Heat- 

Engines,"  i.  331  ;  theories  of  Rankine 

and  Clausius,  ii.  135. 

Valenciennes,  Bell's  theorem,  i.  293. 

Valency,  i.  447. 

Valmont  de  Bomare,  i.  143. 

Valson,  his  Life  of  Cauchy  quoted,  ii. 

637. 
Van't  Hoff,  '  La  Chimie  dans  I'Espace,' 

i.  397  ;  '  Die  Lageruug  der  Atome  im 

Raume,' 431  ;  the  carbon  tetrahedron, 

450,  451. 
Variation,  ii.  331,  343 ;  discontinuous, 

623. 
Variations,  calculus  of,  ii.  670. 
Varnhagen   von   Ense   quotes  Kant,  i. 

45  ;  memoirs  of,  279. 
Vasiliev,  A.,  Address  on  Lobatchevsky, 

i.  161. 
Vauquelin,  practical  discoveries  of,  i. 

147. 
Vector,  ii.  655  ;  analysis,  73,  655. 
Venn,  John,  'The  Logic  of  Chance,"  ii. 

569. 
Verdet,  M.,  'CEuvresdeFresnel,' quoted 

on    Euler,    ii.    9  ;    referred    to,    14 ; 

quoted,   25 ;    history   of    undulatory 

theory,  26  ;  '  ffiuvres  de  Fresnel,'  26  ; 

quoted,  27,  41,  42. 
Veronese,  G.,  ii.  737. 
Versification,  German,  catholicity  of,  i. 

213. 
Verworn,  Max,  quoted,  ii.  423  ;  quoted 

on  foam  theory,  427  ;  '  General  Physi- 
ology '  quoted,  445. 
'  Vestiges   of    Creation,'  published,   ii. 

318  ;  323,  327  ;  and  natural  selection, 

330. 
Vicq    d'Azyr,    i.    107 ;    forerunner   of 

Cuvier,    147 ;    200 ;    pioneer  of   the 

mechanical    view    in    biology,    219 ; 

anatomist,  ii.  248  ;  quoted,  255. 
Vieweg,  publishers,  ii.  300. 
Villemain,   review   of    eighteenth -cen- 
tury   literature,    i.    59 ;    quoted    on 

Napoleon's  educational  projects,  151. 
Villers,  '  Coup-d'a?il  sur  les  Universites 

d'Allemagne,'  i.  225. 
Vinci,  Lionardo  da,  mathematics  and 

science,  ii.  5  ;  vision,  506. 
Vines,  S.  H.,  ii.  459. 
Virchow,  Rudolf,  "cellular  pathology," 


804 


INDEX. 


i.  195,    ii.  265,  376;   i.   198,    208 
"Autonomy  of  the  Cell,"    ii.   395 
'  Cellular    Pathology '    quoted,    402 
444  ;  progress  of  biology,  463  ;  quoted 
by  Darwin,  610. 

Virey,  indebtedness  of  Cuvier  to,  i. 
130  ;  importance  of  nervous  system, 
ii.  237. 

Virgil  quoted,  ii.  287. 

Vischer,  Fr.  T.,  i.  162. 

Vital  force,  i.  218. 

Vitalism,  extreme,  ii.  388. 

Vitalistic,  aspect  of  nature,  ii.  217 ; 
353 ;  view  of  nature,  368 ;  idea  of 
Bichat,  383 ;  386. 

Vogel,  A.,  address  on  Liebig,  ii.  391. 

Vogel,  H.  C,  spectrum  analysis  of  the 
stars,  ii.  362. 

Vogt,  Karl,  materialistic  works  of, 
i.  60 ;  vertebral  theory  of  the  skull, 
ii.  251  ;  '  Bilder  aus  deni  Thierlebeu,' 
323;  407;  '  Physiologische  Briefe,' 
469;  503. 

Volkmann,  W.,  psychologist,  ii.  494, 
497. 

Volney,  history  at  the  Ecole  normale, 
i.  112. 

Volta,  electric  pile,  i.  83,  ij.  104  ;  dis- 
coveries of,  i.  363,  ii.  150  ;  animal 
electricity,  475. 

Voltaire  imported  new  ideas  into  France 
from  England,  i.  16  ;  century  of,  59  ; 
reflects  the  thought  of  the  eighteenth 
century,  61 ;  an  essayist  and  man  of 
the  world,  93 ;  popularised  the  ideas 
of  Newton,  96  ;  importance  in  French 
literature  of,  105  ;  on  the  progress  of 
the  philosophical  spirit  in  France, 
ih.;  influenced  by  Newton  and 
Descartes,  106 ;  constructive  work 
influenced  by,  110  ;  philosophical  and 
philanthropic  influence  of.  111 ;  123  ; 
'Siecle  de  Louis  XIV.,'  135;  142; 
'  Elemens  de  la  Philosophic  de  New- 
ton,'144  ;  'Lettres  sur  les  Anglais,' 
ib.;  created  Newtonianism,  250 ;  cor- 
respondence of,  279 ;  the  cure  of 
smallpo.x,  284  ;  quoted  on  the  Car- 
tesian and  Newtonian  philosophies, 
340,  ii.  324. 

Vortex,  motion,  i.  199,  ii.  35  ;  earlier 
researches,  61  ;  filaments,  ib.;  theory 
developed  in  England,  62 ;  ring 
theory,  difficulties  of,  64 ;  atom 
theorv',  Helmholtz  and  Thomson,  57, 
66.  ■ 
Voss,  A.,    on   principles   of  calculus, 

quoted,  ii.  706. 
Voss,  J.  H.,  hexameters,  i.  213. 


Vries,  de,  labours  of,  ii.  165;  "muta- 
tion," 364. 

Waage,  Guldberg  and  law  of  mass- 
action,  ii.  157 ;  ideas  of  Berthollet, 
177. 

Waals,  von  der,  researches  of,  ii.  164. 

Wagner,  A.,  on  freewill,  ii.  584. 

Wagner,  Pvudolf,  '  Physiological  Let- 
ters,' iL  323;  '  Handworterbuch  der 
Phvsiologie,'  401,  501  ;  controversy 
with  Karl  Vogt,  469. 

Waitz,  psychology,  ii.  497,  530. 

Wald,  F.,  'Die  Energie  und  ihre  Ent- 
werthuiig,'  ii.  169. 

Wallace,  Alfred  Russel,  i.  179  ;  '  Intro- 
duction of  New  Species,'  310 ;  ii. 
327,  329;  'Darwinism,'  330,  339; 
"Struggle  for  Existence,"  332,  333; 
Darwin,  341  ;  sexual  selection,  343 ; 
351  ;  quoted,  365 ;  546  ;  variation  in 
nature,  608 ;  621. 

Wallis,  Dr,  quoted  in  'History  of  the 
Royal  Society,'  i.  227. 

Walther,  Ph.  von,  physiological  method 
in  medicine,  ii.  388. 

Walton,  Izaak,  i.  285. 

Wand  (see  Clausius),  ii.  135. 

Wappaus,  statistics,  ii.  563. 

Ward,  James,  '  Naturalism  and  Agnos- 
ticism,' ii.  188,  519  ;  modem  psychol- 
ogy', 522,  523  ;  quoted,  606. 

Ward,  T.  H.,  '  Reign  of  Queen  Victoria,' 
i.  310. 

Wardlaw,  Bishop,  founded  University 
of  St  Andrews,  i.  268. 

Wardrop,  ii.  505. 

Waring,  Ed.,  of  Cambridge,  quoted,  i, 
234  ;  ii.  688. 

Wamkonig,  Prof.,  of  Liege,  translation 
of  Gibbon's  'Romau  Empire,'  i. 
169. 

Waterston,  J.  J.,  meteoric  theory  of 
the  sun's  heat,  ii.  358. 

Watson,  Hewett  Cottrell,  '  Cybele 
Britannica,'  ii.  3-35  ;  595. 

Watt,  James,  an  inventor  with  scien- 
titic  training,  i.  91  ;  not  member  of 
any  university,  238 ;  definitions  of 
horse-power  and  work,  310 ;  use  of 
term  "horse -power,"  ii.  99,  156; 
technical  mechanics,  101 ;  (see 
Zeuner),  134  ;  heat  measurement,  156. 

Wattenbach,  W.,  'Zum  Andenken 
Lessings,'  i.  169. 

Weber  Brothers,  theory  of  elasticity,  ii. 
31 ;  biological  studies,  208 ;  experi- 
mental research,  396  ;  psycho-physi- 
cal investigations,  492. 


INDEX. 


805 


Weber,  Eduard,  i.  196,  519. 

Weber,  Ernst  Heinrich,  i.  196  ;  school 
of,  200  ;  law  of  sensation,  ib. ; 
"science  of  life,"  ii.  396;  402; 
psycho  -  physical  phenomena,  496  ; 
60*0 ;  psycho-physics  of  vision,  504  ; 
508;  "touch  and  bodily  feeling," 
509 ;  psycho-physics,  517,  519. 

Weber,  H.,  biographical  notice  of 
Wilhelm  Weber,  i.  304. 

Weber,  Heinrich,  his  treatise  on  algebra, 
ii.  729,  730. 

Weber,  Wilhelm,  of  Gottingen  and 
Gauss,  telegraph,  i.  92 ;  quoted, 
171,  172,  196,  199,  211;  'Electro- 
dynamische  Maasbestimnmngen,'  265, 
303  :  365  ;  absolute  measurements, 
309,  323,  ii.  117  ;  perfected  Coulomb's 
methods,  i.  360  ;  astronomical  view 
of  nature,  366  ;  electrical  researches 
of,  367,  368,  369  ;  quoted,  370,  373 ; 
measurements  of,  371,  ii.  149 ;  im- 
portance of  his  labours,  i.  384  ;  law 
of,  ii,  67 ;  76  ;  electro  -  magnetic 
measurements,  73  ;  79  ;  statical  and 
current  electricity,  84  ;  theory  of,  87  ; 
researches,  92  ;  97  ;  electric  measure- 
ments, 143 ;  electrical  phenomena, 
146 ;  influences  Helmholtz,  150 ; 
theory  of  electro-dynamic  phenomena, 
151 ;  electrical  theory  of,  153  ;  atomic 
view  of  nature,  188 ;  Helmholtz 
quoted,  189;  191,  192;  electric 
particles,  197. 

Webster,  Daniel,  the  term  "  statist,"  ii. 
555. 

Webster,  Thos.,  palaiontological  work 
of,  i.  139. 

Wegele,  'Gesch.  d.  deutschen  Historio- 

graphie,'  i.  206,  ii.  555. 
Weidmann,    editions    of    the    ancient 

classics,  i.  167. 
Weierstrass,  ii.  630  ;  Poincare  on,  638, 
703  ;  and  Lagrange,  693  ;  his  theory 
of  functions,  694 ;  his  pure  analysis, 
702 ;    genesis    of    his    ideas,     703  ; 
Lampe  on,  ih.  ;  on  non-differentiable 
functions,    705  ;   706  ;   aud   Riemann 
compared,    707  ;   on   Riemann,    708  ; 
his    letter   to   Schwarz,    ih. ;    proves 
Gauss's  statements,  726  ;  733. 
Weight  and  mass,  i.  336. 
Weis,  Samuel  Christian,  mentioned  by 

Verdet,  ii.  41. 
Weismann,  A.,  '  Essays  upon  Heredity,' 
ii.  372  ;  idio plasma  theory,  448,  611  ; 
on  heredity,  450  ;  on  pangenesis,  455  ; 
theory  of  evolution,  ih.  ;  "On  the 
Duration  of  life,"  457;  'Essays  on 


Descent  and  Heredity,'  459  ;  versus 
Lamarck,  460. 
Weissbach,  influenced  by  Poncelet,  ii. 
101.  ' 

Weisse,  Chr.  H.,  influence  on  Lotze,  ii. 
500  ;  508. 

Weld,  '  History  of  the  Royal  Society,'  i. 
90,  127,  227,  228,  2.S3  ;  quoted  on  the 
publication  of  the  'Principia,'  98. 

Weldon,  W.  F.  R.,  on  crabs,  ii.  621  ; 
on  Pearson's  methods,  623. 

Wells,  'Essay  on  Dew,'  i.  230  ;  'Two 
Essays  upon  Dew  and  Single  Vision,' 
ii.  334 ;  347. 

Werner,  A.  G.,  Freiberg  Mining  Aca- 
demy, i.  17  ;  school  of  geology  of, 
116  ;  Cuvier  on,  118  ;  155  ;  connection 
of,  with  modern  science,  175  ;  scien- 
tific strife  with  Hutton,  283j  290; 
study  of  fossil  remains,  ii.  225  ;  266  ; 
and  Hutton,  291  ;  describes  mineral 
character  of  rocks,  294. 

Wernicke,  language,  ii.  539. 

Wessel,  Caspar,  on  imagiuaries,  ii. 
653. 

Weyrauch,  Jacob  J.,  'KleinereSchriften 
und  Briefe  von  Robert  Mayer,'  ii,  97, 
108. 

Wheatstone  and  Cooke,  first  telegraph 
lines,  i.  303. 

Wheatstone,  Ohm's  law,  i.  365 ; 
quoted.  366 ;  stereoscope,  ii.  4S6, 
505;  506. 

Whewell,  Wm.,  on  relations  of  the 
sciences,  i.  37 ;  identification  of 
thought  with  philosophy,  62  ;  '  Writ- 
ings and  Correspondence,'  91;  crys- 
tallography, 117;  236  ;  quoted,  ib.;  his 
influence,  "261 ;  '  History  of  the  In- 
ductive Sciences,'  262,  277,  306,  365  ; 
270  ;  Analytical  Society,  271 ;  '  His- 
tory of  the  Inductive  Sciences ' 
quoted,  291,  292,  ii.  12;  influenced 
by  Kant,  i.  307  ;  origin  and  variation 
of  species,  310 ;  Avogadro's  hypo- 
thesis not  mentioned  by  him,  428  ; 
the  final  establishment  ot  the  undula- 
tory  theory,  ii.  26  ;  '  Philosophy  of  the 
Inductive  Sciences,'  205 ;  his  divisions 
abandoned,  210  ;  quotation  from  Lin- 
njeiis,  220;  account  of  vertebral  theory, 
251  ;  268 :  the  study  of  functions, 
269  ;  318  ;  Bridgewater  Treatise,  325, 
327  ;  Bacon's  "method  of  instances," 
558. 

Whiston,  on  reluctance  of  Cambridge 
to  accept  theories  of  Newton,  i.  270. 

White,  Gilbert,  of  Selborne,  i.  179; 
'Natural  History  of  Selborne,'  286; 


806 


INDEX. 


nature  lover,  287  ;  288  ;  biographical, 

289  ;  quoted,  290. 
Whitehead,     A.    N.,     his     'Universal 

Algebra,'  ii.  641 ;  656,  737. 
Whittaker,  Thos.,  on  "cyclical"  view, 

i.  286. 
Wichern,  .J.  H.,  follower  of  Pestalozzi, 

ii.  258. 
Wiechert.  E.,  'Grundlagen  derElektro- 

dynamik,'  ii.  193,  197. 
Wiedemann,   Georg,  'Die  Electricitat,' 

i.  370 ;    '  Annalen,'  ii.  186  ;  on  Helm- 

holtz,  410. 
W'ien,    W.,   electro  -  dynamic    view    of 

ether,  ii.  195. 
Wigand,    A.,    Darwin,     Newton,    and 

Cuvier  compared,  ii.  341. 
Wilberforce,  William,   associated  with 

Rumford's  philanthropic  schemes,  i. 

249. 
Will,  H.,  text-books  of,  i.  188. 
William  IV.  of  Hesse,  astronomer,  i. 

1.57. 
William  the  Conqueror,  ii.  555. 
Williamson,  chemical  researches  of,  i. 

414 ;  quoted,  ii.  163. 
Willis,  "reliex  action,"  i.  292. 
Willoughby  and  Ray,  botanical  travels 

of,  i.  283  ;  '  Historia  Piscium,'  283. 
WUson,  E.  B.,  'The  Cell  in  Develop- 
ment and  Inheritance,'  ii.  370,  456, 

458. 
Wilson,  G.  (see  A.  Geikie),  i.  288. 
Winckelmann,  classic   style  of,    i.  51  ; 

171  ;  founder  of  archaeology  in  Ger- 
many, 295. 
Winkler,   discovery  of   germanium,   i. 

315,  423. 
Winter,    W.,     "astronomical    magni- 
tudes," i.  323. 
"  Wissenschaft,"  meaning  and  scope  of 

the  word,  i.  90,  168  ;  evolution  of  the 

idea  in  German  literature,  170  ;  202  ; 

combines  the   exact,   historical,    and 

critical    methods    of   thought,    222 ; 

moral  value  of,  223. 
"  Wissenschaftslehre  "  of  Fichte,  i.  170. 
Witt,  John  de,  tables  of  mortality,  ii. 

665. 
Wohler,  his  works  on  chemistry,  i.  43  ; 

prepares  organic  substances,  92,  191  ; 

ii.    440 ;   i.   188  ;   194,   200  ;  ^services 

to    chemistry,    208;     "vital    force," 

218  ;  discovery  of  "  isomerism,"  406  ; 

412,  414  ;  uric  acid  and  its  derivatives, 

ii.  393  ;  vitalist,  405. 
Wolf,   C,    'Les    Hypotheses    Cosmog- 

oniques,'  ii.  282. 
Wolf,  F.  A.,  indebtedness  to  Bentley, 


i.  169 ;  171  ;  philology,  203 ;  212, 
214  ;  evolved  the  science  of  antiquity 
from  vaguer  beginnings,  220  ;  classical 
learning  of,  222 ;  educational  ideal 
differs  from  that  of  Pestalozzi,  258 ; 
263,  264;  ii.  538. 

Wolf,  R.,  'Geschichte  der  Astronomie,' 
i.  54,  157,  167,  171,  177,  277,  328; 
'Handbuch  der  Astronomie,'  319, 
324,  ii.  282,  358,  362. 

Wolff,  Caspar  Friedrich,  used  the  term 
"cell,"  i.  195;  anticipated  Goethe, 
ii.  212;  metamorphosis,  267;  "epi- 
genesis,"  278,  299;  'Theoria  genera- 
tionis,'298;  494. 

Wolff,  Christian,  philosophy  of,  i.  212  ; 
astronomical  formula  of,  422  ;  ii.  563. 

Wollaston,  scientific  discoveries  of,  i. 
229,  230 ;  not  member  of  any  uni- 
versity, 238 ;  contributions  to  the 
atomic  theory,  245  ;  272 ;  prophecy 
of,  397,  450 ;  his  attitude  towards 
Dalton's  views,  417 ;  experiments 
supporting  undulatory  theory  of 
light,  ii.  19,  45 ;  Fraunhofer's  lines, 
47. 

Words,  new,  and  new  thoughts,  i.  23. 

Wordsworth,  his  visit  to  Germany,  i. 
17 ;  influence  of,  on  taste,  67 ;  fresh- 
ness of  individual  thought  of,  76 ; 
healthy  spirit  of,  78;  179,  285; 
a  friend  of  Wm.  Pearson,  289. 

Work,  the  term  introduced  by  Clausius, 
ii.  115. 

World,  outer  and  inner,  how  related,  i. 
5. 

Wright,  Ed.,  length  of  a  degree,  i.  97. 

Wright,  Thos.,  of  Durham,  cosmical 
theories,  ii.  282. 

Wunderlich,  medical  thermometry,  ii. 
389. 

Wundt,  Wilh.,  Fechner'swork  continued 
by,  i.  200  ;  220  ;  animal  electricity, 
ii.  475  ;  physiognomy,  477  ;  '  Physio 
logische  Psychologic,'  479,  490,  519 
520,  521;  '"'specitic  energies,"  483 
influence  of  Herbart,  494  ;  497,  508 
510,  512  ;  '  System  der  Philosophie, 
513  ;  514,  515  ;  consciousness,  516 
517  ;  psychology,  525  ;  526. 

Wurtz,  A.,  quoted,  i.  114  ;  '  La  Theorie 
atomique'  quoted,  394,  421,  427, 
429  ;  on  Dalton,  398 ;  413. 

'  Xenien  '  of  Schiller  and  Goethe,  i.  84. 

Young,  Dr  Thos.,  the  undulatory 
theory  of  light,  i.  83,  229,  ii.  16, 
36 ;  light  and  hieroglyphics,  i.  236  ; 


i 


INDEX. 


807 


not  a  member  of  a  university,  238, 
272;  and  Fresnel,  241  ;  inadequate 
appreciation  of,  243,  244,  277 ;  246  ; 
lecturer  at  the  Royal  Institution, 
249,  264  ;  recognition  of,  by  Frencli 
scientists,  251  ;  quoted  on  universi- 
ties, 261  ;  not  connected  with  the 
Mathematical  School  of  Cambridge, 
266  ;  294  ;  dynamical  view  of  light, 
370  ;  revival  of  kinetic  view  of  nature, 
ii.  8  ;  Euler's  ether  theory,  9  ;  '  Out- 
lines of  Experiments  and  Inquiries 
respecting  Sound  and  Light,'  17 ; 
quoted,  lb.,  20  ;  interference  of  light, 
18 ;  accuracy  of  Newton's  experi- 
ments, 19  ;  methods  of  Laplace,  20  ; 
"interference,"  21;  polarisation  of 
light,  22;  rejects  projectile  theory  of 
light,  ib.;  quoted  on  Malus's  discovery 
of  polarisation  of  light  by  reflection, 
23  ;  24  ;  memoir  of,  26  ;  '  Works ' 
quoted,  27 ;  transverse  vibrations  of 
light,  28 ;  futility  of  astronomical 
view  of  nature,  28  ;  theory  of  elas- 
ticity, 30  ;  theory  of  capillarity,  33  ; 
nature  of  the  ether,  40,  43 ;  analogy 
of  optical  and  acoustical  phenomena, 
50;  "  luminiferous  ether,"  69,  70, 
89  ;  "elastic  medium"  in  space,  84; 
referred  to,  86,  91,  95  ;  hrst  used 
the  term  "  energy,"  98, 115  ;  his  work 
theoretical,  99  ;  value  of  one  horse- 
power,  99;    'Lectures,'  102;  theory 


of  heat,  103  et  seq.;  heat  a  form  of 
motion,  104  ;  undulatory  theory, 
180;  341,  344;  (see  Sir  Norman 
Lockyer),  361  ;  colour  theory,  480  ; 
'Essay  on  Music,'  489. 

Zach,  von,  '  Monatliche  Correspondenz,' 
i.  41  ;  54  ;  first  international  organ 
for  astronomical  observations,  167  ; 
astronomical  achievements,  176;  bio- 
graphical, 177;  182;  422. 

Zeemann,  magnetism  and  light,  ii.  197. 

Zeiss,  Carl,  improvements  in  the  micro- 
scope, ii.  229. 

Zeller,  E.,  i.  162;  'Philosophie  der 
Griechen,'  ii.  3,  207  ;  quoted,  286. 

Zeno,  unity  of  all  existence,  ii.  3 ; 
286. 

Zeuner,  the  steam-engine,  ii.  133  ;  con- 
troversy with  Hirn,  135  ;  (see  Claus- 
ius),  ib. ;  heat  engines,  175 ;  185  ; 
statistics,  566. 

Ziegler,  'Doctrine  of  Descent,'  ii.  349. 

Zittel,  A.  von,  '  Gesch.  der  Geologic,'  ii. 
212. 

Zcillner,  F.,  historical  and  controversial 
writings,  ii.  107 ;  Poggendorf  and 
Mayer's  MS.,  114 ;  speculations  of, 
192 ;  '  Wissenschaftliche  Abhand- 
lungen,'  716. 

Zschokke,  H.,  educational  influence  of, 
in  Germany,  i.  257. 

Zwingli,  educational  work  of,  i.  255. 


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