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Scientific Method 


Call No.f.fl J. . . Accession No. 


Ti " e 


This Book should be returned on or before the date last 
marked belov)/ 

PriiM and lound in Great Britain 








This book is chiefly intended for those who feel interested in 
the methodical procedure of scientific investigation, and although 
some partte of it may appeal most strongly to science teachers, yet 
the fact that scientific method is now destined to play so great a 
part not only in the whole of the educational field but also in every 
other field of thought and activity, may suffice to make the book 
welcome to a much wider circle than those whose interests are con- 
fined to the laboratory and the lecture table. 

The method adopted by men of science in their work is far 
different now from what it was in the time of Aristotle or even 
in the time of Bacon. Fundamentally, the main processes of the 
method of science are, in character, not direct but inverse, and 
inverse processes almost always present great difficulties. The 
method of science has thus been a thing of exceedingly slow 
growth, and even now is by no means fully developed. We smile 
at v\e methods of Descartes, who himself found serious fault with 
the \ 'ethods of the ancients, and there is no doubt at all that our 
desce dants will greatly improve on the methods of the present 

Tl are are, however, a few original thinkers in the world's history 
who have wrought strongly upon opinion an<* practice in scientific 
method, and who, in their day, effected enormous improvements 
upon the methods of their predecessors. Among these, Aristotle 
and Bacon stand supreme. But Aristotle was a pupil of Plato, and 
Plato of Socrates; Bacon's method was in strong contrast to that of 
his contemporary, Descartes; and Locke and Hume also played im- 
portant parts in placing the method of science on firm foundations 
Locke, in tracing to its origin the knowledge we believe we possess, 
and Hume in developing correct notions of causation. Without some 
brief account of the parts all th 3 fattious men played in developing 

I 1 vil 


the subject now before us, it seemed hardly possible to give any 
adequate idea of the extraordinary difficulties that have faced one 
generation after another of men of science in their endeavour to 
formulate a method that might be of general application. 

All the writers just mentioned wrote on other subjects besides 
method. They were philosophers. And although the other sides 
of their work concern us here only indirectly, when they concern 
us at all, it is not possible, even were it desirable, to avoid touching 
upon certain differenc / philosophic faith, for these lie at the root 
of difference of method; and thus a preliminary chapter dealing 
with elementary philosophic notions and terminology seemed to be 

After all, philosophy in some of its aspects is pre-eminently 
a subject for teachers who would acquire a real mastery of the 
principles underlying their work. Teachers have too often been 
content to dip into introspective psychology and deductive logic, 
but both subjects are now largely discredited, and the teacher 
would do well to make an attempt to survey a somewhat wider 
field. (Unless at least science teachers give some attention to 
philosophy they are hardly likely ever to become conscious of the 
weaknesses of many of the foundations of their own subjects, weak- 
nesses which the metaphysician is only too quick to discover) No 
doubt the metaphysician occasionally leaves open to attack weak 
points in his own defence, but, on the other hand, we cannot deny 
that he sometimes deals a heavy blow at principles which men of 
science have regarded as altogether beyond challenge. 

Philosophy is an exacting taskmaster, but if the teacher would 
only take up the work of some one philosopher and really master it, 
he would probably be astonished at the amount of new light that 
would be thrown on his professional work. Philosophy is that sub- 
ject which, above all others, compels us to get down to the very 
bedrock on which rest the principles we profess to hold. Philo- 
sophy compels us to produce the authority for all our knowledge. 
Bacon, or Hume, or Mill, or perhaps Dugald Stewart, will probably 
appeal most to the science teacher. Plato will probably be found 
too visionary, and the German philosophers too obscure. William 
James will attract all practical men. And signs are not wanting 
that practical men will soon be able to derive a good deal of help 
also from the newer school of linglish philosophers, but most of the 



English philosophy of the latter half of the nineteenth century will 
be found a rather unprofitable study; for, in the first place, it is 
too esoteric and technical in character, and appeals to few except 
to its own small circle of votaries; in the second place, it is not 
sufficiently independent, and has compromised too much with 
German idealism; in the third, it contrives to conceal its funda- 
mental difficulties in an impenetrable obscurity of language; and, 
lastly, it seems to show an excessive dread of any kind of scientific 
law. ^ K 

The aim throughout the book has bee^., cts far as possible, to let 
authorities speak for themselves; and although, in quoting from 
many writers, the actual wording has often been modified for the 
sake of simplicity, clearness, and continuity, it is hoped that the 
spirit of the originals has always been preserved. In any case, the 
references have always been given, so that the reader can easily 
refer to the originals. 

The writer has no wish to impose his own views upon the reader. 
He rather desires to interest the reader in the works of the various 
authorities cited, and to induce him to look upon this work as of 
a purely introductory and preliminary nature. No doubt the 
writer has allowed his own views to escape him to some extent: 
this is almost unavoidable when praising or criticizing the work of 
others. He has not, however, made any attempt to conceal one 
very strong desire, and that is to convince the reader of the para- 
mount necessity nowadays of being perpetually on the alert to 
discard superseded methods, and to recognize the inner significance 
of all that is good in new methods and new ways of approach. 

The majority of the illustrations of the principles laid down have 
necessarily been drawn from science. As, however, during the last 
ten or fifteen years, the great majority of boys and girls have, before 
proceeding to the university, been through a fairly substantial course 
of elementary science, the matter of most of the illustrations will 
probably be quite familiar to the non-scientific reader. 

The chapters on the philosophy and on the logic of scientific 
method have been followed by examples of actual investigation by 
eminent men of science. 

The section on " Scientific Method in the Classroom " includes 
a few instances of attempts at investigation by intelligent young 
pupils. These, it is believed, indicate jvith some degree of accuracy 

(0415) 2 


the kind of success which may reasonably be expected from good 
average pupils who are well taught. 

The author desires to express the hope that nothing he has said 
in the course of the book will in any way wound humanistic sus- 
ceptibilities. He is strongly of opinion that there is probably no 
greater educational need at the present time than a reconciliation 
of humanist and realist ideals, If the Humanist and the Realist will 
but close their ranks, and cease their mutual recriminations, they 
may even yet succeed in checking the present general drift in the 
direction of an intense selfishness a selfishness which, clamouring 
for its rights while refusing more and more to recognize its duties, 
seems to be gradually eating its way into every department of the/ 
national life. 

The writer's thanks are due to Messrs. Macmillan for their kind- 
ness in allowing him to make use of (i) Jevons's Principles of Science, 
more especially for the purpose of chapters xxiii, xxiv, and xxv; 
and (ii) the figure on page 92 of C. L. Dodgson's Pillow Problems; 
also to Messrs A. & C. Black for their permission to make use 
of Mr. A. Sidgwick's books, The Process of Argument, and The Use 
of Words in Reasoning, more especially for chapters ii and xiii; and 
lastly to Mr. W. W. Rouse Ball for the figure taken from page 32 
of his very interesting book, Mathematical Recreations. 


Since the issue of the first edition, I have been asked from time 
to time not only to enlarge the scope of the first two sections but 
also to show how the principles of scientific method may be applied 
to the working out of human problems. To comply with the first 
request would mean an expansion of the volume to an unwieldy 
size, and it is in any case hardly necessary, for the reader can readily 
take up the references to the original sources. The second request 
seems to involve a task of peculiar difficulty. 

The difficulty arises from the fact that, in attempting to find 
a solution of any human problem, values have to be considered 
that cannot be brought under physical law and therefore fall out- 
side the scope of science. When we try to interpret such values 
in terms of objective fact, we seem to be up against a granite wall. 
The most abstruse problems of science seem to be simplicity itself 
compared with problems involving human interests. The human 
element is incalculable. 

It is an impressive fact that the deepest thought, the most 
brilliant talents, the shrewdest sagacity, the most earnest and 
scrupulous conscientiousness, have contributed to the problems of 
philosophy and history, and yet have come to no common agree- 
ment. Eternal enigmas are always reproducing themselves in such 
a form as to defy the logician's challenge. 

And yet, just as there are pre-eminently successful investigators 
in the world of science, so there are authorities equally well recog- 
nized for their impartial and searching investigations into problems 
involving the consideration of human values. Amongst these, Lord 
Balfour seems to hold a first place. His searching criticisms are 
always followed by fruitful and acceptable hypotheses. The late 
Lord Bryce and the late Lord Morley were also in the front rank 
of such men. It is a valuable exercise to take up some thesis 



expounded by one of these writers and to reduce it to a chain of 
syllogisms. Possibly we may not agree with the ultimate premisses , 
but with the rigorously logical reasoning, and with the final, scru- 
pulously impartial judgment based on those premisses, we are com- 
pelled to agree, even against all our preconceptions. To perform a 
similar exercise, daily for three months, with the first leading article 
of The Times, would probably conduce towards a better training in 
rigorous reasoning than would the reading of many books on formal 
logic. Speeches do not usually lend themselves so readily to the 
treatment. Mr. Asquith's speeches are, however, clear-cut, and 
models of logical reasoning. So were those of the late Mr. Chamber- 
lain. But oratory and sound reasoning seem seldom to be good 
friends. If, for instance, we strip a speech of the late Mr. Gladstone 
of all its wealth of rhetorical ornament (as of course we must, for 
the purpose mentioned), the residue is a little disappointing. 

I have ventured on the formal examination of three questions, 
two in history and one in philosophy. The known facts have been 
set forth, and explanatory hypotheses which seemed to be unsatis- 
factory have been examined and rejected. Even the hypotheses 
eventually accepted must be regarded as only provisional, for they 
are bound to involve some degree of non-calculable probability, and 
differences of opinion are therefore inevitable. 

Finally, a short section on Relativity has been included. With 
the appearance of Professor Nunn's book, most of the mathematical 
difficulties in anything like an elementary treatment of the subject 
have been cleared away, but Einstein's criterion of simultaneity 
still seems to give trouble, and an attempt has therefore been made 
to work put that criterion in some detail, according to the 
principles of logical method. The experience of the last three or 
four years has shown that much of the prevailing puzzlement 
concerning Relativity arises from a failure to grasp the logical and 
historical sequence of the various topics usually included in the 
ordinary textbooks. In a final chapter these topics have therefore 
been set out in the order which seems to lend itself best to a 
rational development of the subject. 

The reader's attention may be called again to Sir Richard 
Gregory's Discovery, a companion volume of rare interest. 

F. W. W. 

1st Jan., 1924- 




CHAP. Page 



1. Uncertainty in the Meaning of Words .... 7 

2. Indefiniteness and Ambiguity - - " / " " " ^ 

3. Translating from one Language to Another - - 10 

4. Classes and General Terms - - / - - - 18 

5. Connotation, Generalization, and Specialization - - 16 

6. Definition - ' 19 


1. Philosophy and its Sub-divisions 24 

2. The Borderland between Philosophy and Science - - 25 

3. Psychology, Metaphysics, and Logic 27 

4. The Contrast*F Subject and ObjecU " - 29 

6. The Different Schools of Philosophy 30 

6. Hypothetical and Natural Dualism ----- 33 

(a) Substance 34 

(6) Primary and Secondary Qualities ... - 35 

7. Monism : its Logical Consequences ----- 37 

(a) Idealism ---------37 

(b) Materialism 39 

Conclusion - - .?...- 40 



CHAP. Page 


1. Belief and Testimony 42 

2. Authority and Reason .......45 

3. The Nature of Truth 49 


1. First Attempts at Investigation - - - 61 

2. The Sophists 62 

3. Socrates and his Method 63 


1. Investigator or Dogmatist ? 69 

2. Plato's Doctrine of Ideas : Elementary Notions 61 

3. Elusive and Unacceptable Aspects of the Doctrine - - 63 

4. Plato's Method not really Scientific 64 

5. Plato's Works- 
fa) The Republic 66 

(6) The Timseus 66 

(c) The Thesetetus 67 

(d) The Parmenidas 68 

6. How far can we follow Plato's Method? .... 69 


1. Aristotle's Wide Knowledge 71 

2. His Rhetoric 72 

3. His Logical Treatises 73 

4. " Fact " and " Theory " : Aristotle's Notion of Induction - 14 
6. Aristotle's Science 

(a) His Works 78 

(6) Some General Notions ...... 79 

(c) His Theory of Projectiles 79 

(d) His Account of the Rainbow 80 

(e) An Example of Aristotle's Method of Reasoning - 81 

6. Aristotle's Blunders and Mistaken Notions - - - 82 

7. Aristotle's Method : Summary 83 

8. Plato and Aristotle : their Methods compared 84 


1. The Period of Scholasticism 87 

2. Some Characteristics of Scholasticism - - - - -87 

3. Aristotle followed, not Plato 88 

4. The Last Phase of Scholasticism 90 


CHAP. Page 

1. Bacon's Independence of Mind 92 

2. Bacon's Method : General Notions ..... 94 

3. His Philosophical Works 95 

4. The Four Classes of "Idols" 95 

5. Bacon's Method 

(a) Collection of Facts 98 

(b) Discovery of " Forms " 99 

(c) The " True Difference " 100 

(d) The Tables of Investigation 101 

(e) The Process of Exclusion 102 

(/) Other " Helps ". The " First Vintage " - - - 102 

6. Bacon's Investigation into Heat 103 

7. The Method a Failure in Practice 104 

8. Bacon's Errors and Oversights in Science .... 107 

9. His Rejection of the Copernican Theory - - - - 108 

10. Bacon's Critics 110 

11. Bacon and Aristotle 112 


1. Descartes dissatisfied with Existing Philosophic Systems - 114 
2. He considers a New Method of Procedure Necessary - -115 

3. His Organon is " Doubt " 117 

4. Cogito ergo sum --------- 117 

5. Clear and Distinct Ideas 119 

6. Descartes' Four Rules - - - - - - -119 

7. His Opinion of Logic 121 

8. His Mathematics and Physics 122 

9. His Theory of Vortices 123 

10. Why the Method fails 124 

11. The Cartesian Method and the Baconian Method - - 126 


1. Characteristics of Locke ....... 127 

2. His Toleration 129 

3. His Views on Education 130 

4. The Conduct of the Understanding 130 

5. Locke's " Essay " 131 

6. The Ambiguities of Language 132 

7. The Association of Ideas 132 

8. Locke the Founder of Modern Psychology - - - 133 

9. The Origin of our Ideas 134 

10. Simple and Complex Ideas 185 

11. Innate Ideas 137 

12. Locke's Critics 139 


CHAP. Page 


1. Hume's Philosophical Writings 141 

2. Hume's Scepticism 142 

3. His Method 143 

4. His Views of the Nature of Mind 143 

5. His General Theory of the Origin of Knowledge - - - 144 

6. His Theory of Causation 146 

7. Other Views of Causation 

(1) Reid 151 

(2) Hamilton 151 

(3) Brown 152 

(4) Mack 152 

(6) Clifford 153 

(6) Herbert Spencer 153 

(7) Professor Carveth Read 154 

(8) Professor Karl Pearson ...... 155 

(9) Bain 156 

(10) Mill 156 

8. Is " Time-sequence " an Element of Causation? - - - 159 




1. Deductive Reasoning : General Notions - - - 165 

2. Syllogistic Reasoning - - - - - - 166 

3. The Limited Value of Formal Logic - - - - 167 

4. " Forward " and <k Reflective " Reasoning - - - 169 

5. Deduction and Induction 171 

6. Some Common Logical Terms 172 

7. Conclusions as to the Value of Logic - - - - 174 


1. Whewell 175 

2. Mill 176 

3. Herschel 176 

4. Bain 177 

5. Jevons 177 

6. Professor Welton 177 

7. Mr. Alfred Sidgwick - - - - . - - 177 


CHAP. Page 

1. General Notions of Induction 178 

2. The Guiding Principles of Bacon, Newton, and 

Herschel 180 

3. Whewell's " Colligation of Facts " and " Explication of 

Conceptions" ....... 181 

4. Mill's Views of Induction 183 

5. How Mill Differs from Whewell - - . - 184 

6. Jevons's Views -----... 187 

7. Professor Welton's Views 188 

8. No Hard-and-fast Rules universally applicable - - 189 

9. The Ground of Induction 190 


1. Preliminary Notions 191 

2. " Varying the Circumstances " 193 

3. Observation 194 

4. Experiment 196 

5. Experiment not always Possible 198 

6. Experimental Researches 

(1) By Newton 199 

(2) By Faraday 200 

(3) By Brewster *200 

(4) By Franklin 201 

(5) By Davy 202 


1. The Basis of the Canons 203 

2. The Method of Agreement 203 

3. The Method of Difference 205 

4. The " Joint " Method 207 

5. The Method of Residues 208 

6. The Method of Concomitant Variations - - - 209 

7. Plurality of Causes 211 

8. Intermixture of Effects 212 

9. Criticism of Mill's Methods 212 


1. General Notions 215 

2. What Constitutes a Good Classification - - - 216 

3. "Kinds "and "Types" 217 

4. Principles of Logical Division - - - 219 

5. Definition 222 


CHAP. Pag* 


1. Unsuspected Associations of Phenomena - 224 

2. Herschel on the Analysis of Phenomena - - 226 

3. His Remarks on our Notions of Force - - - 227 

4. His Analysis of the Phenomenon of Sound - - 228 

5. The Limits of such an Analysis 230 


1. The Meaning of Generalization - - - - - 232 

2. Generalizations Vary in Degree .... 233 

3. Empirical Laws 234 

4. The " Joint Action " of Causes 235 

5. The Detection of Derivative Laws - - - - 237 

6. The Meaning of "Law" 239 


1. What an Hypothesis is 240 

2. The Varying Functions of Hypotheses - - - 242 

3. Verce Causce 243 

4. Conditions of a Good Hypothesis - - - -244 

6. Rival Hypotheses. Experimentum Crucis - - 246 

6. Emission versus Undulatory Theory of Light - 246 

7. The Deciding Crucial Experiment - 249 

8. The Use and the Misuse of Hypotheses - - - 249 


1. General Notions 250 

2. Points of Resemblance must be Weighed, not Counted 252 

3. " Essential " Resemblance 252 

4. Instances of Analogical Inference .... 254 

5. Illegitimate Analogy ---...- 256 

6. Hypotheses suggested by Analogy .... 257 


1. General Notions 258 

2. The Theory of Probability deals with Quantity of 

Knowledge 259 

3. Quantitative Aspects of the Theory .... 260 

4. Simple Mathematical Considerations - ... 262 

5. Experience and Theory Compared .... 264 

6. Inverse Probability 265 

7. Simple Rules of the Inverse Method - - - 267 

8. The Transmission of Historical Evidence - - - 268 

9. Coincidences which are Casual ----- 269 

10. Uncertainty almobt Inevitable 270 


CHAP. Page 


1. Precise Measurement Fundamental in Science - - 271 

2. Standards and Units 272 

3. Empirical Formulae 275 

4. Rational Formulae 279 

5. Variation in Simple Proportion 282 

6. Theory and Experimental Results .... 283 

7. Discordance between Theory and Direct Measurement 284 


1. Exact Measurement is virtually Impossible - - 285 

2. The Assumptions made by Science .... 286 

3. Interfering Causes 286 

4. Elimination of Error 287 

5. The Method of Means 289 

6. The Law of Error 292 

7. How the Law has been Arrived at - 293 

8, The Probable Error of Results 295 

9. The Method of Least Squares 297 

10. The Method of Curves 298 



Some of his Observations ------- 303 


The Migration of Birds - 305 


The Sensitiveness of Worms to Light .... 308 


The Power of Communication amongst Ants - - -311 


The Circulation of the Blood - -314 


The Production of Dew 316 


CHAP. Page 

Fixed Air in Lime and in Alkalis 321 


Fixed Air 326 


The Combination of Gaseous Substances ... - 329 

IS there Oxygen in Oxy muriatic Acid ? -334 


The Ascent of Water in Siphons .... - 337 


The Refrangibility of Light - - - % - - - 342 


Electricity by Friction of Water and Steam against other 

Bodies 350 


(1) Franklin 360 

(2) Cavendish , - 360 

(3) Davy 360 

(4) Brewster 360 

(5) Lord Kelvin 361 

(6) Lord Lister 361 

(7) Mendelteff 361 

(8) Lord Rayleigh 362 

(9) Clerk Maxwell 363 

(10) Tyndall 363 

(11) Huxley 364 

(12) Thomas Preston 364 

(13) Sir Oliver Lodge 364 

(14) Sir Joseph Larmor ------- 364 

(15) Sir J, J. Thomson 364 

(16) Professor Poynting and Sir J. J. Thomson- - - 364 

(17) Sir William Croo/ces 364 

(18) Lothar Meyer 364 

(19) Wilhelm Ostwald 365 

(20) Sir Archibald Geikie 365 

(21) Professor S. H. Vines 365 

(22) Rev. A. H. Cooke 365 

(23) Professor W. Ferrel 365 





1. The Heuristic Method 369 

2. Laboratory " Instructions " 373 

(1) By Professor Ganong 373 

(2) By Professor Hall 374 

(3) By Professor Alexander Smith . . . 375 

(4) By Professor Armstrong 377 

(5) By Mr. J. B. Russell 378 

(6) An Example of Instructions to be avoided - 379 

3. The Pupil's Notebook 380 

4. Manipulation 381 


1. An Instance from English Grammar - ... 383 

2. An Instance from the Art Room .... 387 

3. An Instance from Botany 389 

4. An Instance from Chemistry ..... 391 

5. An Instance from Physics ------ 396 


Examples 402 










Me vero primum dulces ante omnia Musae 
Accipiant : caelique vias et sidera monstrent, 
Defectus Soils varies, Lunaeque labores : 
Unde tremor terris : qua vi rnaria alta tumescant 
Objicibus ruptis, rursusque in se ipsa residant ; 
Quid tantum Oceano properent se tingere Soles 
Hiberni : vel quae tardis niora noctibua obstet. 
Felix qin potuu rerum cognoscere causas. 

Virg., Georg., ii. 475 ff. 

Qui tractaverunt scientias aut empirici aut dogmatici fuerunt. 
Empirici, formicae more, congerunt tantum, et utuntur: rationales, 
aranearum more, telas ex se conficiunt: apis vero ratio media est, 
quae materiam ex floribus horti et agri elicit ; sed tamen earn propria 
facultate vertit et digerit. Neque absimile philosophiae verum opi- 
ficium est; quod nee mentis viribus tantum aut praecipue nititur, 
neque ex historia naturali et mechanicis experiments praebitam 
materiam, in memoria integram, sed in intellectu mutatam et sub- 
actam, reponit. Itaque ex harum facultatum (experimentalis 
scilicet et rationalis) arctiore et sanctiore foedere (quod ad hue 
factum non est) bene sperandum est. 

Bacon, Nov. Organ., lib. i, Aph. xcv. 




ipulated statement of supposed facts, aided by a skilful use 01 iH 
guage, to give a plausible explanation by means of it. Yet this W 
exactly the kind of thing in which the shallower type of Humanist 
takes the keenest possible delight. 1 

'? } It is curious, too, how often the Humanist seems to attach jn*cateV 
^importance to the results than to the methods employed by the Greeks 
and Romans. 2 He treats a description of nature as literature; the 
words appeal to him far more than the things the words represent. 
"He never judges a new play by the Greek standard; he never 
brings his Aristotle to bear upon the politics of the day." And if, 
by chance, he finds under his microscope a little inexactitude in the 
phraseology of the Realist, he quite overlooks the deceptive nature 
of the magnified image, and the story of his great find he tells to 
all his friends for a week afterwards. 

"^ But the average Realist is just as unfair in estimating the 
worth of his rival's work, and always has available a plentiful supply 
of recent instances of the ''shocking ignorance" of the Humanist 
over the most commonplace of natural phenomena. Yet it has 
to be remembered that it is the Realist who is usually on the 
defensive. The patronizing attitude of the Humanist is sometimes 
a little provocative, and his wealthier vocabulary gives him an 
advantage; and of course the Humanist was first in possession, and 
naturally has a very strong interest in the preservation of the 
institutions ho represents. 

',, It is remarkable how Science is sometimes misconceived, and its 
functions entirely misunderstood, even by those whose sympathies 
are known to be on its side. Here are the views of Bain, a great 
personal friend of John Stuart Mill: "By Science, I understand 
the artificial symbolism and machinery requisite for expressing the 
'aws and properties of the world, as distinguished from the actual 
ppearance of things to the common eye". "The symbols of Arith- 
etic and Mathematics generally, the symbols of nomenclature of 
\emistry, &c., require a peculiar cast of intellect for their acqui- 
ion. They are a class of bare forms, not remarkably numerous, 
ich are to bo held in the mind with great ^enacity, and to be 
m as the sole representatives of all that is interesting in the 
1" Bain refers to two classes of "scientific minds", represented 
He "extreme terms Mathematics and Natural History, the 
artificial, and the concrete or real"; and he admits that, 

wart, Phil of the Human Mind, pj 1-33. 
, Essays, vol. i, p. 39, and Huxley, Science and Education, pp. 143, 152. 


in the latter, some part of the acquisition really consists in storing 
up the common appearances of animals, plants, and minerals. But* 
he is of opinion that the Chemist and the Physicist, no less than 
the Mathematician, "concentrate the whole of their brains upon 
algebraic symbols", and " immerse their minds in cheerless laby- 
rinths of uncouth characters", to the exclusion of "all those things 
that gratify the various senses and emotions". 1 If a friend of 
Science can thus hold such extraordinarily incorrect notions, the 
common enemy's notions are likely to be incorrect to the point of 

Yet Bain's words should be taken to heart by every young 
science teacher, who would do well to remember that, once a 
science lesson arrives at the stage of symbols, it may cease to be 
Science altogether; once a "law" is established, the subsequent 
work is likely to take the form of mere Algebra. It is astonishing 
how few, even of the older pupils of a school, are able to give an 
intelligent physical interpretation of a formula they have estab- 

It is a great misfortune that "most of the present science teach- 
ing in English universities seems to be directed to cultivating the 
deductive faculty". In essence, the training is mathematical. The 
man who is working for a science degree usually takes on trust 
nearly all he is told in the lecture theatre. He is not put in the 
position of an investigator at all. He receives his information on 
authority; his practical work is mainly intended to verify principles 
he has already accepted; and his whole training is thus very little 
calculated to imbue him with the scientific spirit. One university 
is notorious for the high standard it exacts in its paper examinations 
for a science degree, yet the practical examinations are of so trivial 
a character that candidates can prepare for them by spending les> 
than six months in a laboratory. The consequence is that man; 
young science teachers form, at the very outset, an entirely wroi 
conception of what scientific method really is. How can such 
teacher be expected to engage in successful heuristic, teaching wt 
he himself has never in his life undertaken the simplest piece 
research work 1 His outlook is altogether wrong. He sets to w 
in school exactly as he was taught to set to work at college. F 
indeed, can he be expected to do otherwise? He is entirely 
aware of the specific functions that science teaching is inte* 

i See Bain, The Senses and the Intellect, p. 444. 


perform. He teaches Science just as he would teach History. He 
considers it his sole duty merely to pass on information. The spirit 
of his work is, "Believe, and ask no questions". 

Such teaching is worth little. A boy is doing far more good 
in working his way, unaided, through a Latin author. His grammar 
and dictionary supply him with the "facts" he requires, and he 
learns from experience to suspend his judgment in regard to the 
author's meaning until he is in possession of these facts. He learns 
to reason correctly. He learns to test his conclusions. He is really 
solving problems by scientific method. Such work is of far greater 
value than the pseudo-science which finds expression in mere 
"lectures". 1 

It is sometimes urged that research is undesirable in the under- 
graduate stage, but there can be no doubt that some measure of 
research ought to enter into the training of every man who intends 
to take up science teaching. There is ample evidence to show that 
excellent work in this direction may be done by quite young men. 
One well-known Professor says, U I have always been struck by 
the quite remarkable improvement in judgment, independence of 
thought, and maturity, produced by a year's research. Research 
develops qualities which are apt to atrophy when the student pre- 
pares for examination, and, quite apart from the addition of new 
knowledge to our store, is of the greatest importance as a means 
of education." And successful research usually implies a complete 
mastery of all that is meant by scientific method. 

If the young teacher desires to master scientific method, he 
must follow the history of Science, and see how one faulty method 
has been superseded by another, which, in its turn, has itself been 
superseded, so difficult has it been to discover the principles of the 
true method; he must learn to get at the exact meaning of all his 
terms; he must learn to eliminate all personal bias from his facts; 
he must ever be on his guard against hasty generalizations; he must 
ever be ready to give up a pet hypothesis, once the facts are against 
him, and he must never, on any account, allow his hypotheses to 
masquerade as facts, "hypotheses are cradle-songs which lull the 
unwary to sleep"; he must acquire a knowledge of the laws of 
inductive reasoning; he must learn to balance probabilities; he 
must remember that even the best conclusions of Science are never 
more than in a high degree probable; and he must study the 

1 That is, continuous dogmatic assertion. A leather (as distinguished from a lecturer) at 
the demonstration table may, of course, do work of the very highest value. 


original records of successful investigators. And in all these things 
the following chapters are intended to help. 

Let the young science teacher never scoff at workers in other 
fields. It is not the method of Science to come to conclusions 
unwarranted by facts, and investigators in the field of psychology 
have many a weary year of work in front of them before their 
accumulated facts will enable us to decide the precise value of the 
different subjects of the school curriculum. It is all a question of 
opinion now, and those who dogmatize on the matter are putting 
themselves quite outside the pale of scientific method. 

A classical training is admittedly productive of one great ad- 
vantage over a training in Science, and that is in the power it 
confers in the balancing of probabilities in which the human element is 
dominant. Science can make no provision for this, though of course 
both History and modern Literature can. 

Science has, however, one enormous advantage over all other 
subjects. All facts can be obtained at first hand, and without 
resort to authority. The learner is thus put in the position of 
being able to reason with an entirely unprejudiced mind. It is 
;this possibility of self-elimination in for in ing a judgment that must 
Ibe regarded as the greatest possible speciiic result of science teach- 

The stray Humanist who still claims that a classical education 
is the only liberal education, we cnn afford to ignore. Centuries 
ago the claim must have been admitted, for then a classical edu- 
cation was the only education. But modern civilization has now 
lifted itself far above the ancient civilization, and its most charac- 
teristic feature is the enlightenment that has come from the great 
mathematical and physical researches of the last two or three 
centuries, an enlightenment which has permeated not only the 
practical arts and industries, but is also gradually finding its way 
into all fields of thought, Philosophy and History, Sociology and 
Literature. 1 A Humanist has few claims to culture nowadays, if 
he confines his tillage to the ancient fields. 

Probably the most successful teachers, in any subject, are those 
who have by research reached the inner life of something, great 
or small. The golden key of the investigator is mastery. But 
mastery does not come by listening, while somebody explains; it 
is the reward of strenuous effort. Mastery comes by attending 

i Cf. Mach, On the Classics and the Sciences, pp. 338-74 


long to a particular thing, by enquiring, by handling and doing, 
f by contriving and trying, by ordered system and good method, 
and especially by cultivating the habit of distinguishing between 
the things that signify and those that do not. 1 

Words and their Elusiveness 

i. Uncertainty in the Meaning of Words 

The late Professor William James 7 squirrel problem 2 appears to 
be the lineal descendant of one propounded many years ago by a 
well-known Scottish metaphysician : 

" A cart-wheel is placed horizontally upon a vertical axle. Seated 
on the wheel and facing each other are a cat and a dog, the 
former at the centre and the latter on the circumference. The 
wheel is made to rotate. Does the dog go round the cat?" 

For a moment the problem seems puzzling, but, as its conditions 
are quite simple, we are driven to suspect an ambiguity in the 
terms used, and at last the question arises: What are we to under- 
stand by going round 1 

If we mean passing from the north of the cat to (say) the east, 
then to the south, then to the west, and then to the north of the 
cat again, obviously the dog does go round the cat, for he occupies 
these successive and all intermediate positions. But if, on the con- 
trary, we mean being first in front of the cat, then on his right, 
then behind, then on his left, and fimlly in front again, it is quite 
as obvious that the dog does not go round the cat, for the cat's face 
is turned towards him all the time. Once this distinction is drawn, 
the difficulty disappears. The verbal phrase "to go round" is 

Cf Miall, n A. Report, Section L, 1908, p. 927. The reader may with advantage read 
through Strong, Lectures on the Methods of Science; Hand, Science in Public Affair*\ Karl 
Pearson, National Life; Carpenter, D. A. Presidential Address, 1872; Carpenter, Nature and 
Jfan, pp. 195, 217. etc'.; "Point'iire", Science and Hypotheses, Introduction; Huxley, Science and 
Education, p. 12V), &<;.; Whetham, Recent Advances in Physical Science, pp. 3U-6; Duke of 
Argyll, Reign of Law, p 89. Ac. 

2 Pragmatism, ch. ii. Similar problems, in different dress, are to be found in many old 


lacking in definiteness, and therefore introduces ambiguity into any 
statement containing it. 

Again: how can we "show whether the top part of the wheel 
of a carriage moves faster than the bottom part"? We first require 
to know the exact meaning of moves faster than. Is the motion 
to be taken as relative to the axle of the wheel, or relative to the 
general forward movement of the carnage? 

In such cases it is quite easy to see how necessary it is to know 
the precise meaning of the terms employed, but we are perhaps 
hardly conscious of the necessity for such precision in the discourse 
and converse of everyday life. The quarrels of the philosophers and 
the politicians are largely due to the element of doubt involved 
in the meaning of the terms peculiar to their respective creeds. 
So impregnated with indefiniteness, in fact, are most of such terms 
that their precise definition seems to be impossible. 

Who would venture to define, for instance, the term "socialist"? 
A score of different people might give a score of different answers. 
Are we supposed to think of the religious, the philosophical, the 
political, the juridical, the economic, or the sociological side of the 
term, which, to some people, seems to mean an aspiration, to others 
a speculation, to others a policy, to others a theory of rights, to 
others an economic doctrine, and to others a philanthropic move- 
ment? or are we to include all these things? or are we to eliminate 
the differences and base the definition on the collected residue 'I 
The term almost defies definition, yet it presents much less dilli 
culty than such words as, say, civilization, wealth, government, agnosti- 
cism, truth, cause, and many a hundred more. The rough, working 
definitions of the dictionary serve to throw some light on the 
meaning of isolated words, but it is when the words are actually 
used in assertions that their inherent indefiniteness leads to doubt, 
and to this is due nine-tenths of the wrangling that goes on in all 
the Council chambers of the country. 

" We cannot ", says Sigwart, 1 " have certain and firm possession 
of an idea, or use it in thought, unless we have a word by which 
to denote it. When the word is wanting to an idea, we always 
feel it as a want, and have a difficulty in grasping the idea in 
its individuality, and in reproducing it." Yet we can easily lend 
ourselves to the delusion of thinking that the learning of names 
adds to our knowledge of things, though we really gain very little 
from being told, for instance, that this plant is called fuchsia and 

i Logic, vol. i, p 41. 


that clematis. To a child there is a danger that a new name may 
be a mere empty sound. A child is little practised in apprehension 
and has but a scanty store of knowledge; hence, an image which 
enters into memory and is afterwards reproduced with the word, 
falls short of being a faithful and exhaustive copy of the thing 
presented to the senses. 1 Unless the child is trained to observe, 
he may grow. up and pass through life without ever seeing in a 
presented object more than a small fraction of what he ought to 
see. The traces which remain in his mind are no more than a 
rough and faded copy of the thing " in which, as in a hasty sketch, 
only the more prominent features appear". 2 A teacher can hardly 
expect to succeed if he fails to realize the importance of finding 
out, as far as it is possible to do so, what image the spoken word 
imprints on the child's mind. A child's progress consists, in no 
small measure, in his learning to apprehend more completely, in 
distinguishing differences more exactly, and in sorting out essentials 
more readily. 

2. Indefiniteness and Ambiguity 

"We do not, as a rule, notice the indefiniteness of a word 
until it has caused an ambiguity. Wherever a quality is on some 
occasions difficult to detect, there will be a tendency on the part 
of the many to identify that quality with its more obvious mani- 
festations only. To a hasty or careless or ignorant view, the good 
and the bad are the obviously good and the obviously bad, and, 
to the same sort of view, indefiniteness exists only when it has 
actually caused trouble. The most widely received opinion appears 
to be something of this kind: that indefiniteness (or ambiguity) 
which inheres in a word is either so slight as to be of no account, 
or else so great as to deserve the attention of sensible men; that 
theoretical Logic may, if it likes, amuse itself with the search for an 
accurate definition in either case, but that only where the indefinite- 
ness is great can there be any practical value in the search." 3 

These remarks apply with much force to the Englishman who 
boasts that he is " practical ", and is given to scoffing at what he 
calls "pedantry". But pedantry signifies a defective sense of 
relative values, a very different thing from precision and nicety. 4 

i Sigwart, Logic, vol. i, p. 43. 2 ib. 

Sidgwick, Use of Words in Reasoning, 40. 

< Clifford Allbutt, Notes on Scientific Papers, p. 32. 


The " practical" Englishman has been defined as one who keeps 
on the surface of things and never gets inside them. In his car& 
less use of words, he does much to impoverish his mother tongue. 
He regards synonyms as "different words for what is ' practically ' 
the same idea." He uses indifferently any one of such a group of 
words as entreat, implore, beseech', or excursion, trip, tour' or jeer, gibe, 
sco/) or attempt, endeavour, try; he says mistake when he means fault, 
intention when he means purpose, result when he means consequence, 
principle when he means rule, liberty when he means license, nation 
when he means race. Such instances might be multiplied to an 
almost unlimited extent. Even recognized masters of style are not 
guiltless of such offences. One such master, for instance, says, 1 
"But then the disciple must be also a critic, not some relation or 
friend ". Obviously, he meant relative. In this way is our vocabu- 
lary reduced from wealth to poverty. 

The distinction between indefiniteness and ambiguity is not 
always so carefully observed as it should be. The distinction is 
important. All words are alike indefinite but are not alike am- 
biguous, the latter defect being clue not to the words in themselves 
but to the occasion of their use. Indefiniteness is not itself am- 
biguity but is only a predisposing condition of it; and ambiguity 
arises only when indefiniteness is detected in a context. 2 Words 
with a descriptive meaning, when taken apart from the assertions 
in which they occur, are always indefinite, or capable of creating 
an ambiguity, but it is only when they have actually done so, and 
therefore when they are considered in reference to their context, 
that their indefiniteness has any effect on the meaning. And the 
effect it then has is absolutely destructive until the ambiguity is 
removed. 3 

J5 3. Translating from one Language 

to another 


The elusive character of words is always fell when an attempt is 
made to translate from one language to another. Referring to the 
difficulty of translating Shakespeare into French, Maeterlinck says: 
" Translators face to face with Shakespeare are like painters seated 
in front of the same landscape. Each will paint a different picture ; 

i Essays in Criticism, vol. i, p. 2. 2 Sidgwick, Use of Words, p. 186. 

#>., p. 203. The reader will flnd t nmch to interest him in Max MUller's Lectures on tht 
Science of Language. See e.g. vol. ii, pp. 247-61. 



and for this reason, that around the literal sense of the words there 
floats a secret life which is all but impossible to catch, and which is, 
nevertheless, more important than the external life of the words 
and of the images." The difficulty of translating poetry is ad- 
mittedly much greater than that of translating prose, for the literal 
sense of the words is but a small part of what they signify. Just 
us the strains of a cathedral chant, or the words of a great orator, 
produce in the mind an emotion which cannot be analysed, so it is 
with a poem; and the emotional power of the words produces 
different effects on different minds. Though the logical effect of 
the words of a poem translated into another language may be pre- 
served, their emotional power may be lost altogether, and will 
almost certainly lose in force and delicacy. 

In theory we may claim that intellectual sense and emotional 
sense are only different parts of the same thing; but, in practice, 
when they come to be expressed through the imperfect instrument 
of language they are often in conflict; and the poet has to decide 
whether he will sacrifice music to precision or precision to music. 
Like the artist the poet is incessantly struggling with his material. 
His finished poem is a mosaic^ put together after an infinite number 
of experiments and rejections. 

The translation of N prose is, of course, a different matter, but, 
here again, to catch ami reproduce exactly the intended meaning 
of the author is often sufficient to tax the resources of the ripest 
scholars. Consider, for instance, the following passages, chosen at 
random, from Aristotle's Rhetoric. The first is a translation by the 
late Sir R. Jebb, and the second by Bishop Welldon, both classical 
scholars of distinction. 


Let happiness, then, be prosperity 
combined with virtue or independence 
of life ; or that existence which, being 
safe, is pleasantest ; or a flourishing 
state of property and of body, with the 
faculty of guarding and rc/-rvducing 
this; for it may be said that all men 
allow Happiness to be one or more of 
these things. 1 


Happiness, then, may be defined as 
prosperity conjoined with virtue, or as 
an independent state of existence, or as 
the pleasantest life conjoined with 
safety, or as an abundance q" Jftbds and 
shires with the ability to pr \,crve them 
and make a practical use of theni; for 
it would be pretty generally admitted 
that happiness is one or more of these 

Rhetoric, Book I, ch. v. 



Or, again : 

The apparent character of the speaker 
tells more in debate, the mood of the 
hearer in law-suits. Men have not the 
same views when they are friendly and 
when they hate, when they are angry or 
placid, but views either wholly different; 
or different in a large measure. The 
friendly man regards the object of his 
judgment as either no wrongdoer, or a 
doer of small wrong; the hater takes 
the opposite view. The man who desirte 
and is hopeful (supposing the thing in 
prospect to be pleasant) thinks that it 
will be, and that it will be good: the 
man who is indifferent, or who feels a 
difficulty, thinks the opposite. 1 

The impression of the speaker's char- 
acter is especially serviceable in de- 
liberation, and the disposition of the 
audience in forensic matters; for our 
estimate of a speech is not the same, 
but either wholly different or different 
in degree, according as we regard a 
person with feelings of affection or dis- 
like, and are angrily or charitably dis- 
posed towards him. If we are friendly 
to the person upon whom we have to 
form a judgment, we regard him as 
either innocent or guilty of a very slight 
offence ; if we are inimical to him, the 
contrary is the case. Similarly when 
we are in an eager and sanguine mood, 
the result which is promised us is prob- 
able and advantageous in our eyes; 
when we are dispirited and out of 
humour, it is the reverse. 

Note in particular the striking differences of meaning in the 
parallel sentences in italics. 2 It matters not that the general tenor 
of the two renderings is roughly the same. Careful comparison 
shows marked differences, and different impressions must be left 
upon a reader's mind. 

It may be urged that part of the translator's difficulty in dealing 
with passages like the above is that the language translated is a 
dead language; that the evidence as to the meaning of any par- 
ticular word is therefore largely inferential and does not admit of 
the same kind of verification as in the case of a living language like 
French or German. This no doubt is true, and it is interesting to 
touch upon the kind of evidence actually available. Let us take, 
for example, any one of the thirty Characters of Theophrastw, say the 
thirteenth. Here is depicted that type of man "who will rise and 
promise things beyond his power, and who when an arrangement 
is adnfiT-ted to be just will oppose it and be refuted. He will insist, 
too, on the slave mixing more wine than the company can finish; 
he will separate combatants, even those whom he does not know; 
he will undertake to show the path, and after will be unable to find 
his way. Also he will go up to his commanding officer and ask 
when he means to give battle. When the doctor forbids him to 

Rhetoric, Book II, ch. i. 

2 The italics do not, of course, appear in the originals. 


give wine to the invalid, he will say that he wishes to try an experi- 
ment, and will drench the sick man. Also he will inscribe upon a 
deceased woman's tombstone the name of her husband, of her father, 
and of her mother, as well as her own, with the place of her birth; 
recording further that, 'All these were Estimable Persons'. And 
when he is about to take an oath, he will say to the bystanders, 
'This is by no means the first I have taken'/' 1 The desire to 
please, either by rendering an extraordinary service, or by perform- 
ing an ordinary one unusually well, is, as Jebb says, present in 
every act described. The problem is, then, to find an English 
equivalent for the Greek term (Tre/ncpyia) used to describe such a 
man. The nearest equivalent seems to be " officious", the term 
generally adopted. But, obviously, it is not quite the word we 
want, and we have to be satisfied with an approximation. 2 But if 
this be so in the case of a word the exact meaning of which, in the 
original, is known, how much more difficult it must be to find the 
precise English equivalent in a case where the evidence of the mean- 
ing is mainly analogical, and probably scanty at that. 

4. Classes and General Terms 

If we ask the pupils of an ordinary Third or Fourth Form, to 
define the name of some common object, say a box or a ball, we 
shall probably feel little surprise at many of the wild answers given. 
Unless a child has been taught how to define, it is absurd to expect 
a definition with any approach to accuracy. Let us consider for a 
moment what may at least appear to be a much easier term. What 
is an animal] 

If I think of a particular animal, say my fox-terrier Pompey, I 
have little difficulty in giving an exact description of him; but if I 
think of a fox-terrier generally, and not of a particular fox-terrier, 
I have a greater difficulty in finding a description at once clear and 
distinct. Do I, in these circumstances, describe, consciously or un- 
consciously, a particular fox-terrier, or do I attempt to give a general 
description of the many fox-terriers I have seen? Does an ordi- 
nary book -illustration of a fox-terrier represent some particular 
animal, or is it a sort of composite photograph of many f ox-terriers 1 
In the latter case, can it be said really to represent a fox-terrier 
at all? 

1 Jebb's translation. 

a Healey (1616) translates by "impertinent diligence"; La Bruyere (1687) by "1'air 
emprease*"; Howell (1824) by "Buaybody". 


Let us now advance a step further, and consider the more genera] 
term dog. We may be able to describe a dog in tolerably accu- 
rate language, but do the words we use convey an accurate repre- 
sentation of the image we are supposed to have formed in our 
minds? Is our description anything more than mere words, for 
can we conceive a kind of composite photograph of a "dog"? A 
book-illustration of a "dog" would certainly be that of a parti- 
cular breed, for no painter would attempt to produce anything of 
the nature of a "generalized" picture. A composite picture of a 
pomeranian, a poodle, a dachshund, and a deerhound would be an 
absurdity. L : , then, it is impossible to obtain a picture of a " dog" 
on canvas, is a mind-picture of a "dog" possible? 

We may regard the fox-terrier as a "variety" of the "species" 
common dog (canis familiaris), this species forming one member of 
the "genus" canis which includes other related species; for instance, 
the wolves and the jackals. Obviously a mental picture of a canis 
a composite photograph of, for instance, some common dog, a 
wolf, and a jackal is much more difficult to form than one of a 
"dog" alone. And as we work our way upwards through the 
"order" carnivora, the "class" mammalia, the "sub-kingdom" verte- 
brata, to the "kingdom" animal, the difficulty becomes greater and 
greater. When, then, we think of an "animal", we seem to think 
of a particular animal, or perhaps a succession of particular animals. 
We may think of a camel, a canary, a turtle, and a grasshopper, 
but we certainly do not form a composite mental picture of all four. 

It would thus seem that if we define an animal in the usual way, 
namely, "a living being possessing (1) locomotive power, which 
can be voluntarily exercised, (2) an internal cavity for the reception 
and digestion of solid food, and (3) a distinct nervous system", 1 
we are using a form of words which, though approximately accurate 
as a description, corresponds to no distinct mind-picture. Ap- 
parently, then, a "general term" is little more than a convenient 
label for tying on to a group of similar things. Now, in a group 
of things which, because they are "similar", are brought together 
into a class, there will almost inevitably be "differences" of some 
kind; and these differences, whether undiscovered, overlooked, or 
ignored, are nearly certain to lead to ambiguity in a greater or less 

Sidgwick defines a class-name as any imagined group of indivi- 
dual cases, whether material things or immaterial, whether real or 

i This is a sufficiently accurate definition at this stage. 


unreal, a group in which every individual is supposed to resemble 
all the others in some respects though differing in other respects; 
in fact any name which is used so as to admit of a plural. 1 And 
he points out that the defect of the popular view about classes is 
that it conceives them too rigidly, recognizes too little that the 
grouping is imaginary, changing with the changing purposes for 
which it is wanted. "There is a disinclination either to recognize 
any artificial element in 'natural' classes, or to admit the con- 
tinuity of nature, or to admit that all classes are indefinite." 2 

The Scholastic logicians knew so little of the laws of nature that 
they were unconscious of the real difficulties underlying definition. 
They professed to be able to distinguish between those qualities 
which belonged to the " essence" of a class, and those which were 
only "properties" or "accidents". "Natural classes, it was then 
habitually supposed, had no dependence upon man's way of regard- 
ing facts. The received idea was that natural classes were simply 
made for man, and made with clear-cut edges; and that man had 
nothing to do but to accept them and learn their names and their 
definitions. Doubts as to the application of a class-name were sup- 
posed to be the fault or misfortune of the doubter, not of the 
name." 3 It was forgotten that the invention of names was of 
human origin. 

Some classes, of course, are artificial, for instance, telescopes, 
teaspoons, and Territorials ; for we know all about the process 
involved in their production. But many people are still unwilling 
to admit that there is anything artificial about the so-called natural 
classes. Now natural classes as opposed to artificial ones can only 
mean those the precise limits of which are so clearly marked out 
that it is not optional but imperative to recognize them, 4 but when 
we ask what these classes are, our answer must largely depend on 
our adopted standard of clearness of division. Very few names 
are really safe against future changes of definition, for such 
changes almost always become necessary with increased knowledge. 
Usually, our knowledge is so imperfect that it is folly to attempt 
to draw between classes anything like a rigid line of demarcation. 

Since, as Sidgwick says, the world is, on the whole, wiser than 
the individual, the accepted sense of a word carries a presumption 
in its favour. There is thus something in the contention that class- 
names have a " correct" meaning. Yet, however 'widely the mean- 

i See Uie <nf Words, pp. 149-51. 2 t'6., pp. 161-3, i&. 

* #., pp. 16S-9. * 


ing of a name may be accepted by the best authorities, it by no 
means follows that this accepted meaning is so far satisfactory that 
we can with certainty learn the facts about any particular case 
where the name is applied. It may be a help in cases where pre- 
cision is not of much consequence, but it is certainly likely to be 
often a hindrance to the progress of real knowledge. 1 

5. Connotation, Generalization, and Specialization 

Some further light may perhaps be thrown on the inner signifi- 
cance of general names by considering the old logical term " con- 
notation ". 

"A connotative term is one which denotes a subject and implies 
an attribute. A non-connotative term is one which signifies a subject 
only, or an attribute only." ' London ', or ' England ', or * John \ 
are names which signify a subject only. * Whiteness', * length', 
'virtue', signify an attribute only. None of these names are 
therefore connotative. But the word 'man ' denotes Smith, Brown, 
Jones, and an indefinite number of other individuals, of whom, taken 
as a class, it is the name. But it is applied to them because they 
possess, or to signify that they possess, certain attributes; for 
instance, corporeity, animal life, rationality, and a certain external 
form. The word 'man' is therefore connotative; it signifies the 
subject directly, the attributes indirectly; it denotes the subject, and 
implies or connotes the attributes. 2 

Obviously, all concrete general names are connotative. But 
proper names are not c.onnotative ; they merely denote the indi- 
viduals that are called by them. Professor Welton makes this point 
clear: "When any general name is restricted in its application by 
some limiting word or phrase, of course its implication is not lost. 
Indeed, that implication is increased, and thus we have the class of 
significant individual names, which, though they denote only one 
object, yet imply the possession of many attributes by that one 
object. Thus, if we speak of a mountain, we imply the attributes 
'height', and 'composition of rock'; if we add 'in Asia', we 
increase the number of characteristics, though we limit the number 
of things to which the name applies; by adding 'high', we carry 
both theo' processes a stage further; and if, finally, we make the 

1 Use of Moid*, p. lf9. The reader may usefully compare the views of Mill, Lotze, Carveth 
Read, and Bain, on general and abstract terms. See the respective treatises on Logic. Of. 
also Locke, vol. i, p. 275, Ac. ' * Mill, Logic, Book I, ch. ii, 6. 


term singular and speak of ' the highest mountain in Asia ', we 
manifestly retain all the attributes previously implied, and add to 
them uniqueness. All tbese attributes are implied by the name, and 
anybody using the name must be supposed to intend to convey 
them to his hearers. But were we to use, instead of the significant 
name, the proper name * Everest', which we believe to be the 
name of the same object, no such information would be given. To 
anybody who knew the geographical fact that Everest is the highest 
mountain in Asia, the name * Everest' would doubtless suggest all 
that the words ' the highest mountain in Asia ' imply. But a word 
is not connotative because it may suggest facts or attributes other- 
wise known, but because it implies them." 1 

One of the chief sources of lax habits of thought is the custom 
of using connotative terms without a distinctly ascertained con- 
notation, and with no more precise notion of their meaning than 
can be loosely collected from observing what objects they are used 
to denote. It constantly happens that some general resemblance 
which a number of objects bear to one another leads to their being 
familiarly classed under a common name, although it is by no means 
immediately apparent what are the particular attributes upon the 
common possession of which their general resemblance depends. 
When this is the case, people use the name without any recognized 
connotation, i.e. without any precise meaning; they talk, and conse- 
quently think, vaguely. New objects are continually presenting 
themselves to people who class them on no other principle than that 
of superficial similarity. 2 

Most writers on Logic emphasize the fact that all cases of 
ambiguity of language are really instances of indeterminate con- 
notation. "If", says Lotzo, " wo pass our mental world in review, 
we shall be surprised to find that words of great significance betray 
an imperfect apprehension of their objects; for the more complex 
and important any matter is, the more easily will persuasive im- 
pressions derived from repeated observations awaken tfee feeling 
of its individuality, completeness, and self-inclusiveness, without 

1 Logic, vol. i, p. 63. 

2 Mill, Logic, Book I, en. ii, 5. Bain mentions many interesting examples, amongst 
Others the word stone. " It is applied to mineral and rocky materials, to the kernels of fruit, 
/to the accumulations in the gall-bladder and in the kidneys; while it is refused to rocks that 

nave the cleavage suitable for roofing (slates), and to baked clay (bricks). It ot *# in the 
designation of the magnetic oxide of iron (lodestone), and not in speaking of otrK metallic 
pres. Such a term is wholly unfit for accurate reasoning, unless hedged rounvou every 
occasion by other phrases, as building-stone, fruit-stone, gall-stone, <fec." (Logic, Induction, 
t- 72.) 

(C415) 4 


necessarily giving any real insight into its structure." 1 It is the 
unconsciousness of our ignorance of the terms in most frequent use 
that is the danger. 

Two counter movements are always taking place in language; 
one of generalization, by which words are perpetually losing portions 
of their connotation and becoming of less meaning and more general 
acceptation; the other of specialization, by which other, or even these 
same, words are continually taking on new connotation, acquiring 
additional meaning by being restricted to a part only of the occa- 
sions on which they might properly be used before. 2 If, then, we 
define " Denotation " as " the number of individual things to which 
the term is applicable in the same sense ", it will be clear that the 
denotation of a term is logically fixed by the connotation. Practi- 
cally, connotation and denotation help to determine each other, 
and a modification of the one usually leads to a modification of the 
other. As we augment the number of attributes implied by a name 
we diminish the number of things to which that name is appli- 
cable; there are, for instance, fewer trained teachers than teachers. 
Conversely, if we wish to include under a name a group of things 
not before included under it, and so to enlarge the borders of 
the class which the term denotes, we can, usually, only do so, by 
removing from the connotation of the name those attributes which 
before marked the difference between the two classes; for instance, 
if we wish to include both Elementary School teachers and Secondary 
School teachers under one common name, we must omit the points 
of difference, "Elementary School" and "Secondary School", and 
retain only the term "teacher", which will be applicable to all 
members of both classes, but which implies or connotes less than 
the separate name of either. In short, generally speaking, the 
less a name connotes the more groups of things it is applicable 
to; and the more it connotes, the narrower is its range of appli- 
cation. 3 

It will be seen, then, (1) that when we add an attribute not 
common to the whole class, we exclude some members of the class 
from participation in the class-name, and so decrease its denotation ; 
and (2) that when we introduce into a class some things not possess- 
ing all the attributes connoted by the class-name, we have to omit 

i Lotze, Logic, p. 29. 2 Mill, Logic, Book IV, ch. v, 2. 

* Cf. Welton, p. 64. The demand for a formal rule of interdependence between connota- 
tion and denotation was satisfied in traditional logic by the doctrine that one vanes as the 
other. But the term " varies as " suggests a mathematical relation, and such a relation is, of 
course, impossible. See Bosanquet, Logic, vol. i, pp. 68, 60, 67. 


part of its meaning, that it may cover the whole of the more ex- 
tended class; and thus we decrease the connotation. 1 

Thus specialization is increasing the connotation of a term and 
thereby limiting its application; while generalization is the opposite 
process of decreasing the connotation so as to embrace a larger 
number of objects. 

Enough has been said to show how variable is the precise con- 
notation of even the most ordinary terms. It remains to consider 
briefly Definition and its functions, 

6. Definition 

Although the whole object of any class - name is to group 
together similar individuals, yet a class may always be regarded 
as a sect, a portion cut out of a larger whole and placed in 
imaginary isolation. 2 In order to describe or to define a thing, we 
must first recognize clearly the class to which it belongs. As a rule, 
however, complete description or perfect definition is impossible. 
There conies a point at which even the most inquiring mind is 
willing to cease, for the time, from collecting further detail. 3 

Sidgwick draws a happy distinction between what he calls a 
"translation" and a definition proper. By a translation he means 
the general account of the meaning of a word, such as we find in a 
dictionary. Such translations are usually vague, as, naturally, no 
account of the meaning of thj term can be given with any reference 
to the particular statement in which the term occurs. A general 
description or definition of this kind must inevitably leave some 
particular difficulties untouched; like all other general statements 
it suffers from the defect of generality or "abstractness". 4 

If wo consider the various ways in which the meaning of any 
word can be verbally explained, the " translation" takes its p~ace at 
the lower end of the scale. At the other end of the scale, where 
explanation is most precise and definite, there is the process of dis- 
cussion by which a special difficulty of application (an "ambiguity") 
is dealt with after it has arisen. Between these two extreme types 
come the better kind of generally-useful definitions, which have 
evidently something in common with both ends of the scale. In 
face of a particular ambiguity which they foresee and remoy 
make good their claim to be called definitions; in fay 

i Sidgwick, Use of Words, p. 166. 2 &., pp. 162-7. 

i&., p. 176. * ti>., p. 148. 


particular ambiguity which they do not foresee and remove, they 
become, for the time, analogous to "translations". If we want the 
word " luxury " defined in order to apply in some doubtful case 
the rule that luxury is to be avoided, it is no use to be told 
that luxuries are the opposite of necessaries. That answer leaves 
our difficulty exactly where it was. It gives us merely a verbal 
expression for an equivalent to "luxury"; and perhaps we knew 
this before. 1 

The point of the distinction intended is that " a translation is not 
wanted except when a word to be translated is unfamiliar, while a 
definition is not wanted except when the rough meaning of a word 
is already known, and only then if an actual difficulty is felt in 
applying a word correctly in a given case or cases". 2 

It follows, therefore, that if words are taken out of their context, 
the "definitions" of such words can, as a rule, only be of a rough- 
and-ready character. 

To define a name, then, is, manifestly, to fix its connotation. 
This, of course, supposes a comparison of things, feature by feature, 
and property by property, in order to ascertain in what attributes 
they agree. Having discovered in what they agree, we have to 
determine which of these common attributes shall be selected to be 
associated with the name. The framing of a good definition is thus 
a matter of discussion, and the definition is always liable to improve- 
ment as our knowledge increases. 3 

Perhaps the best means of obtaining reasonably good definitions 
in the classroom is to fall back upon the method of Formal Logic, 
per genus et differ entiam.* 

In Logic, any class of things may be called a genus if it be 
regarded as made up of two or more species. " Line", for instance, 
is a genus as regards the species "straight" and "curved". On the 
other hand, species is any class which is regarded as forming part 
of the next larger class. Thus the terms genus and species are cor- 
relative, the genus being the larger class which is divided, and the 
species the two or more smaller classes comprising the divisions of 
the genus. It is evident that the connotation of the species contains 
more qualities than that of the genus, for the species must contain 
all the qualities of the genus, as well as a certain additional quality 
or qualities by which the several species are distinguished from each 

i Use of Words, pp 48-9. 2 #,., p . 49. a Mill, Logic, Book IV, eh. iv, g 3. 

* From what has been said, the somewhat artificial nature of this method will be readily 


other. These additional qualities form the difference, which may be 
defined as the quality or sum of qualities which mark out one part 
of the genus from the other part or parts. 1 Consider, for instance, 
the genus rectilineal figure: 

Rectilineal Figures. 

Three-sided Four-aided With more than four sides 

(Triangle). (Quadrilateral). (Polygon). 

Obviously, triangles have all the properties of rectilineal figures, 
and "three-sided" as well. Quadrilaterals have all the properties 
of rectilineal figures, and /w-sided as well. 2 Thus triangles and 
quadrilaterals are alike in being rectilineal figures, but they differ in 
the fact that the former are three-sided and the latter /owr-sided. 
We are thus able to define the " species" triangle by "adding" the 
"difference" three-sided to the "genus" rectilineal figure, "a triangle 
is a rectilineal figure with three sides". We now see the meaning 
of the old rule for framing a definition: Consider the thing the 
name of which is to be defined as a species; place this species under 
its genus and determine the difference-, the genus added to the differ- 
ence will give the definition. 3 

Children soon learn to use this rule with reasonably good results. 
Here are one or two actual examples given by girls in a Form II 
(average age, eleven years). They were asked to define the name 
"hat"; a few questions from the teacher elicited the genus "articles 
of dress", and the difference "for wearing upon the head". Thus 
the definition given was, "a hat is an ''article of dress for wearing 
upon the head". A little girl of nine in the same class defined a 
"chair" as "an article of furniture used for sitting on". For such 
a young child the definition was good, but the difference "for 
sitting on" is obviously too vague, for the same definition would 
apply to other kinds of seats. The definition of "book" proved 
more difficult, and the teacher wus a considerable time before she 
could obtain a suitable genus. When at last the genus "a number 
of printed sheets of paper of the same size" was suggested, the 

1 See Jevons, Logic, pp. 98-100. 

2 Attributes of things are very often found in groups, so that where one is found, others 
are found too. Thus when a triangle is equilateral it is also equiangular, and to speak of an 
equiangular equilateral triangle does not therefore limit the denotation given by equilateral. 
(Welton, Logic, vol i, p. 63 ) 

* Imperfect and rather misleading as this statement is, it is in common use. A warning 
has already been given about the use of mathematical terms in connection with connotation. 
For Mill's definition of " Difference ", see Logic, Book I, ch. vii, 6. 


teacher wisely refrained from quibbling over the suitability of the 
term "sheet" or of the words "the same size", and accepted the 
suggestion except as regards the word "printed". The difference 
finally decided upon was "bound together", though one child 
objected to this on the ground that bound together might mean 
bound at all four edges and thus signify a "drawing-block". The 
whole discussion was interesting, and showed how keenly even 
young children can be induced to try to enter into the real signifi- 
cance of words. 

Of course the definitions of the names of common objects like 
chair and look present more difficulty than the definitions of such 
terms as triangle or electrophone. In the former the denotative 
element predominates, and we are in the habit of using the names 
without any distinct idea of their connotation; in the latter, the 
connotation is the more important element, for the sole value of 
technical terms lies in a knowledge of their exact meaning. 1 

It should not be forgotten that the same class of things may 
be both a genus and a species at the same time. If, for example, 
we had to define "isosceles triangle" we should regard it as a 
species of the genus "triangle"; but if we had to define "triangle" 
we should regard it as a species of the genus rectilineal figure. It 
must also be borne in mind that, in logical division, we must never 
proceed from a high or wide genus at once to a low or narrow 
species. 2 The species should always be those of the proximate or 
next higher genus. 3 A child might be tempted to define the species 
chair by falling back upon the genus wooden thing, or even thing, in 
which case the "difference" is bound to be imperfect since m/iny 
necessary attributes would be omitted. As Professor Welton puts 
it: "If we define a class-term whose connotation is ABCI) by refer- 
ring it to the genus A (instead of to the proximate genus ABC) and 
adding the difference D, we plainly omit the attributes EC from our 
definition". 4 A definition should always state the essential attri- 
butes of the species defined. 5 

We may regard the definition of a conriotative name as the 
proposition which declares its connotation, 6 and this is the real 
advantage of a definition. The framing of a definition compels 
us to examine the precise connotation of a word, to get inside it, 
so to speak, and know it thoroughly. 

Cf. Welton, Logic, vol. i, p. 111. 2 JHvisio nonfaciat saltutn." 

* Jevons, Logic, pp. 100-1. * Welton, Logic, vol. i, p. 109. 

For an account of the "Predicates", including "Property" and "Accident", see Mill, 
Logic, 1-vii, or any other standard work on Logic. 6 See Welton, Logic, vol. i, p. 109 et seq. 


The practical impossibility of obtaining perfect definitions is, 
ultimately, due to the necessary indefiniteness of all general names. 
" Since the definition of any name P is an attempt to describe the 
difference between those things which are P and those which are 
not P, and since that difference, like everything else, can only be 
described in general terms and therefore incompletely, no definition 
can perfectly define. To put it another way, definition is an attempt 
to decide what amount and kind of difference is allowable between 
members of the class P, or what departure from the normal type is 
required to destroy a doubtful member's right to the name. There 
is no end to the inquiry except where we choose to make one/' 1 

The definite connotation of most scientific terms gives a con- 
siderable advantage to men of science, whose statements, however 
much lacking in literary form, are at least clear-cut, precise, and 
definite. This is less frequently the case in other departments of 
knowledge. 2 The lesson for the teacher is that he should always 
use words the exact significance of which he is certain his pupils 
fully apprehend. 1 low often one hears in the classroom such terms 
as the "constitutions" of Clarendon, the "causes" of the Refor- 
mation, "gerundial" infinitive, "varies as" the pressure, chemical 
"affinity", arid scores of others, which have but the slightest signifi- 
cance to the children. 

Few people are the masters of the words they use; most people 
are their slaves. 3 

1 Sulgwick, U*e of Won/*, p 17S 

2 Hut men of science occasionally accept terms, the exact meaning of which is open to 
considerable doubt. The writer iccently abked half a do/en chemists to define the term 
"ioni/ntion "; all six definitions differed in a most remarkable \\ay. Then, again, the term 
"anticyclone" (invented by Sir Francis alt on in 18<>'2; see his Memories of my Life) 
suggests, to the popular mind, some sort of opposition, the prefix being considered to signify 
the same meaning us in "antipodes" or " anti-viviset tion ", whereas the actual phenomenon 
referred to is of the most benign character. The prefix imports, not opposition, but alterna- 
tion, as in " antiphon " and " antistrophe ' . 

3 The reader may spend a useful half-hour in referring to pp 821-35 of Tart II of Herbert 
Spencer's Principles of /Vi/c/io {</</ Spencer takes from Berkeley's Principles of Human 
Kiwwh'tlue the sentence "By sight I have the ideas of liy,ht and colours". The various 
words of this sentence are subjected to minute analysis, and the exact significance of the 
assertion is thus microscopically examined. 


Philosophers and some of their Problems 

i. Philosophy and its Sub-divisions 

What is a Philosopher? In the Republic, Plato defines him as 
one who gets inside things and discovers the nature of their reality, 
and contrasts him with those who are content with mere appear- 
ances and with ready-made opinion. The philosophers, he says, are 
those who are able to grasp the permanent and immutable. 

But Plato makes no clear differentiation of the subsidiary in- 
quiries by which the question of the ultimate constitution of things 
may be approached. He fuses together in a semi-religious, semi- 
ethical fashion, Logic, Physics, Psychology, Metaphysics, and the 
Theory of Knowledge; and it was left to Aristotle to draw the 
necessary lines of separation. Aristotle was by nature much more 
methodical than Plato, and he may be regarded as the founder of 
Logic, Psychology, Ethics, and ^Esthetics, as separate philosophic 
disciplines. Those first principles which are common to, and pre- 
supposed in, those narrower fields of knowledge, he usually called 
"fitet philosophy", but this term has since given way to the term 
Metaphysics. 1 

A\istotle does not restrict Philosophy as a term of general 
application to the subjects just mentioned; under the title he in- 
cludes Mathematics and Physics. But, as the mass of knowledge 
accumulated, it gradually came about that the name Philosophy 
ceased to be applied to inquiries concerned with the particulars 
as such. The details of Physics, for instance, were abandoned to 
the Science specialist. 

In its modern sense, Philosophy is a term with a very variable 
connotation, but Mr. Balfour's definition is perhaps as acceptable as 
any. " Multitudes of propositions, all professing to embody know- 
ledge belonging to Science, Metaphysics, and Ethics, are being con- 
tinually put forward for our acceptance. And as no one believes all 
of them, so those who profess to act rationally must hold that there 
are grounds for rejecting the propositions they disbelieve and for 

ITO, /uera ra v<mca. The term means, merely, "the writings that came after the 


accepting those they believe. The systematic account of these 
grounds of belief and disbelief makes up what is here called 
Philosophy." 1 Sidgwick points out that Philosophy thus under- 
stood considers the fundamental principles of all departments of 
systematic thought, but considers them with the special object ol 
examining their validity and evidence. He does not much care 
for Mr. Balfour's grouping, but admits how wide is the variation, 
how vague the connotation, of nearly all philosophic terminology. 
Philosophy, as defined by Mr. Balfour, would seem to correspond 
to what is called Epistemology, or Theory of Knowledge, and is 
perhaps a rough equivalent to the Logic of Mr. Bradley and Mr. 
Bosanquet. 2 

2. The Borderland between Philosophy and Science 

It is a natural thing for the instructed plain man to place im- 
plicit reliance on the evidence of his senses. He sees the sun in 
its daily journey from east to west across the sky, and, like the 
ancient astronomers, he makes the assumption that the sun goes 
round the earth. To him the assumption involves no element of 
doubt; to him it is not an hypothesis it is a fact. When it is 
pointed out to him that the heliocentric hypothesis provides a 
simpler explanation of the celestial motions and is more consistent 
with ascertained facts, he is puzzled, and his respect for authority 
may make him feel that his senses, at all events his sense of sight, 
may sometimes deceive him. If he becomes a student of Science he 
finds that many of his established notions are hopelessly wrong. In 
thinking about ordinary material things, for instance, he had always 
thought that they were coloured and resonant, quite independently 
of their relation to himself. The evidence of his senses he soon 
learns to accept with greater caution, and he comes to understand 
that, so far as Physics distinguishes reality and appearance, its 
criterion is not sense -perception alone, but consistency with an 
elaborate and complex system of more or less definitely established 
facts which embody the combined results of many perceptions and 
inferences. Science has continually to explain to uninstructed com- 
mon sense that what really happens is often something quite different 
from what appears to happen. 

The chemist performs a number of quantitative experiments, 

1 A. Balfour, Defence of Philosophic Doubt, pp. 1, 2. 

H. Sidgwick, Philosophy, its Scope and Relations, p. 112. 


examines his results, and detects amongst them certain common 
quantitative relations, sums up these constant relations as "general- 
izations", and so establishes the "laws" of constant, multiple, and 
reciprocal proportion, and the "law" of Gay Lussac. These laws 
constitute important principles of chemistry, and form the basis of 
the theory of the subject. Their justification is a great number of 
definitely established facts. They involve no assumption, no hypo- 
thesis, save that of the great induction of the uniformity of nature. 

jBut the chemist now seeks for an "explanation" of these four 
laws. The atomic hypothesis covers and explains all the facts of the 
first three, and Avogadro's hypothesis covers and explains all the 
facts of the law of Gay Lussac. But these hypotheses are assumptions; 
they are constructions of the chemist's mind; they may or may not 
correspond to objective fact. In making these assumptions, the 
chemist is trying to get behind his observed facts, behind his 
phenomena, in order to discover the hidden secrets there. In doing 
this he is passing over the border-line between the domain of Science 
and the domain of Philosophy. 

Such assumptions often prove to be wrong. Again and again in 
the history of Science, one hypothesis has been discarded in favour 
of another. But each hypothesis served at the time to cover all the 
facts then known and to link them up. Sometimes a new hypothesis 
has superseded an old one because the latter did not cover new facts, 
and was therefore obviously wrong; sometimes an old hypothesis 
has been discarded because seen to be held on insufficient grounds; 
sometimes an old hypothesis has been reduced to a simpler form: 
the mind always prefers a simple explanation to an elaborate one. 
Around and beneath the more settled portions of Physical Science, 
in the region where knowledge is growing in range and depth, there 
is constant conflict and controversy as to the truth of new con- 
clusions, for the controversy centres round assumptions which are 
unproved, and often seem unprovable. Natural Science, so recent 
a growth, is necessarily infected with error. 

It has been said that the truths of Philosophy bear the same 
relation to the highest truths of Natural Science as each of these 
bears to the lower truths of Natural Science. But the term truth is 
hard to define, and it would be safer to say that, as each widest 
generalization of Science embraces and consolidates the narrowei 
generalizations of its own division, so the generalizations of Philo- 
sophy embrace and consolidate the widest generalizations of Science 
It has, however, to be borne in mind that the main concern of Science 


is with phenomena, for the investigations of Science yield mainly 
phenomenal knowledge. Philosophy aims at a knowledge of the 
concealed realities behind phenomena. There is, however, a great 
deal of common ground between Science and Philosophy, and the 
purely speculative side of Science properly belongs to Philosophy. 
A philosopher unversed in Science is like a man of Science unversed 
in Philosophy: neither can claim to be an authority in his own 

3. Psychology, Metaphysics, and Logic 

Nominally, Psychology differs from Physical Science only in the 
nature of its subject-matter, and not in its method of investigation. 
Regarded as an empirical study of-tlie, mind, it proceeds by methods 
of observation, experiment, and induction analogous to those used 
in Natural Science.' But the phenomena of the mind thoughts, 
cognitions, judgments, beliefs, the facts with which Psychology 
deals are obtained by introspection, not, as in the case of the 
phenomena of Natural Science, through the senses. The difficulties 
of ascertaining the facts are therefore greater, and psychological 
interpretation is not always easily distinguished from metaphysical 

The psychologist cannot begin at birth to register the history of 
his mental operations; he has to begin when a grown man, and the 
more cultivated his mind the farther away he is likely to be from 
the primitive mental operations of his early infancy. The system 
of knowledge which he attempts to formulate is thus of a highly 
problematical character, for about the beginnings of knowledge there 
can be no certainty. 

Textbooks on Psychology usually encroach on Metaphysics. For 
instance, they sometimes attempt to investigate valid beliefs as con- 
ceived to exist for an ideal mind independent of the peculiarities of 
development of particular minds. There is, in fact, often such an 
admixture of metaphysical speculation with the empirical facts of 
Psychology, that the intelligent reader is apt to attach a very scepti- 
cal value to the whole subject. Many of the ultimate problems 
of Psychology are, however, necessarily metaphysical, and are never 
likely to be brought within the range of experimental investigation 
find solved by the methods of Science. The newer experimental 
Psychology is laboriously accumulating valuable facts, but many 
competent authorities are of opinion that it is attacking an insoluble 


problem. At bottom, it is based on the fundamental hypothesis that 
every phase of consciousness has its counterpart in nerve changes. 
That our conscious life is inseparably associated with the changes 
that go on in the grey matter of the brain there is now hardly any 
room for doubt, but how the two are connected is unknown, and all 
explanations are conjectural. That our thoughts, cognitions, judg- 
ments, and beliefs are nothing more than mere molecular changes in 
the grey matter of the brain is an hypothesis unsupported by any 
acceptable evidence. 

Unlike positive Philosophy, which contemplates the world as a 
whole from the point of view of Natural Science, and is satisfied 
with empirical evidence and with such inferences as can be drawn 
therefrom, Metaphysics aims at ascertaining facts concerning matter 
and mind, and their relations beyond such knowledge as is based upon 
or is verifiable by particular empirical cognitions. The method of 
Metaphysics is a distinctive dialectic^] nflefood . it begins by making 
a priori pronouncements, and, by applying to these the rules of 
formal Logic, arrives at final conclusions which do not admit of 
any form of methodical proof or any sort of appeal to experience. 
Such conclusions, based as they are ultimately upon hypothesis 
which cannot be verified, are necessarily always uncertain. 

In mediaeval times, the most implicit trust was placed in formal 
Logic, and a correct chain of deductive reasoning from some original 
hypothesis dogmatically asserted was quite sufficient to stifle any 
doubts about strange conclusions; and gradually the opinion became 
almost universal that the most important truths concerning reality 
could, by mere thinking, be established with a certainty that no 
subsequent observation and experiment could shake. And even 
at the present day there are philosophers who claim that a priori 
reasoning can reveal otherwise undiscoverable secrets about the 
universe, and that, therefore, reality can be proved to be quite 
different from what by direct observation it appears to be. 

In the light of modern science, great numbers of old a priori 
errors have been refuted, and it is now natural to expect a fallacy 
in any deduction of which the conclusion appears to contradict 
patent facts. The fallacy is not usually in the actual chain of 
reasoning: philosophers do not often make elementary blunders of 
that kind. It is traceable rather to an untenable major premiss, 
adopted, perhaps, because of the royal confidence felt in some un- 
examined intuition, or because of some unsuspected prejudice, politi- 
cal, social, or theological. This major premiss, the original hypo- 


thesis adopted, may look plausible enough, but if the consequences 
logically traceable from it violate the first principles of common 
sense, the hypothesis must, without hesitation, be rejected. A con- 
clusion is by no means necessarily correct because the rules of formal 
Logic have been exactly observed. The unacceptable conclusions 
of educated men are far more frequently traceable to false premisses 
than to false reasoning. 

The formal Logic of tradition is merely a logic of consistency. 
As a well-known writer 1 on modern Logic says: "The trivial non- 
sense embodied in this tradition is still set in examinations, and is 
defended as a propaedeutic, that is, a training in those habits of 
solemn humbug which are so great a help in later life". Modern 
Logic is something very different. Its chief business is to examine 
the validity of premisses, and it deserves the closest attention. 

In ancient Philosophy the fundamental contrast was between 
things as they appear and things as they are supposed to be in 
themselves; between appearance and reality. In modern Philosophy 
the fundamental contrast is between mind and matter, between man, 
who knows and the things known to him. 

4. The Contrast of Subject and Object 

All consciousness must, in the first instance, present itself as a 
relation between the distinguishable parts of a duality, the person 
who is conscious and the thing lie is conscious of. In order to be 
conscious at all, u person must be conscious of something. This 
contrast has been indicated, directly or indirectly, by various names: 
mind and matter; person and thing; subject and object; self and 
not-self; the ego and non-ego. Mind, the ego, as knowing subject, 
may therefore be at once connected and contrasted with its known 
objects. That an external material world exists independently of 
our knowing it, and that its existence is not affected by our know- 
ledge of it, is a belief that seems at once instinctive, inevitable, and 

Introspectively, at any moment I am aware that I exist and 
continue to exist through changing states of consciousness. I know 
that I exist, but what I am, how my ego is constituted apart from 
my material organism I do not know. I am not justified in assum- 
ing, from the evidence of introspection alone, that my ego is, for 

* Bertram! Russell. 


instance, a self -existent entity indestructible by the forces that 
ultimately destroy my material organism, or that my consciousness 
is to be attributed to anything of the nature of a phantom -like 
double of the body. All that I can with certainty say is that, 
when I concentrate my attention on the simplest act of perception, 
I have the irresistible conviction that I exist and that something 
else exists, and that I am .conscious of both existences at the same 

We may therefore lay it down as a necessary conviction that 
consciousness gives us as an ultimate fact, a knowledge of both the 
ego and the non-ego in relation to and in contrast with each other; 
and it gives these elements in equal independence. In other words, 
mind and matter present themselves in absolute co-equality. This 
fact, however, is by no means universally accepted, arid even when 
it is accepted it is accepted with such qualifications as it suits a 
particular philosopher to devise. In short, there are almost as many 
philosophic systems originating in this fact as it admits of various 
possible modifications. As might be expected, therefore, no con- 
sistently logical classification of the different schools of Philosophy 
is possible. We may, however, give some indication of the broad 
distinctions amongst them. 

5. The Different Schools of Philosophy 

The first distinction may be drawn between those who accept, 
wholly and without reserve, the fundamental fact that mind and 
matter are separately distinct to consciousness, and those who do 
not. Thus we have 

A. Natural Dualists, who regard mind and matter as real entities 
distinct and separate from each other. 

B. Those who do not so accept the fact. 

Now it is undoubtedly true that the only positive knowledge we 
have of mind and matter is a knowledge of ithenmriena^ and we m$y 
therefore suppose and consequently assert that all our knowledge of 
mind and matter is only a consciousness of various groups of mere 
appearances. On the other hand, we may assert that the known 
phenomena of mind and matter must necessarily be referred to 
underlying substances or substrata of some kind, though actually 
unknown. Thus our class B may be subdivided into 

I. Nihilists, who deny that the testimony of consciousness can 


guarantee a substratum or substance underlying the phenomena of 
either the ego or the non-ego, and who assert that perceptions and 
ideas are the only realities. 

II. Realists, who affirm that the testimony of consciousness can 
guarantee the existence of a reality, a substance or substratum, 
underlying the phenomena of the ego and also of the non-ego. 

Realists are of many kinds, but they may be grouped into two 
main classes: 

1. Hypothetical Dualists, who accept the testimony of conscious- 
ness as to the ultimate duality of the ego and non-ego, but main- 
tain that our consciousness gives us no direct knowledge of anything 
beyond phenomena; that we therefore have no immediate know- 
ledge of the existence of matter or of mind, though we are com- 
pelled to assume both the existence of a substance or substratum in 
which the qualities of matter inhere, and also of an entity mind, 
subject, or spirit which perceives the facts of consciousness, though 
the nature both of the substance and of the perceiving entity is 

2. Monists, who reject the testimony of consciousness as to the 
ultimate duality of the subject and object, the ego and the non-ego. 
Monists fall into two classes, according as they do or do not preserve 
the equilibrium of subject and object: 

(i) Objective Idealists, who hold the doctrine of Absolute Identity. 
They admit the testimony of consciousness as to the co-equality of 
mental and material phenomena, but not as to the antithesis of 
mind and matter as existent entities. They maintain that mind 
and matter are only phenomenal modifications of the same unknown 
absolute reality; for, since the impenetrability of matter is intelligible 
only as a mode of resistance, the essence of matter must be some 
kind of power which it possesses in common with spirit. Matter 
and mind, or body and spirit, are therefore different aspects of a 
common substratum. 

(ii) Those who deny the evidence of consciousness as to the 
co-equality of mental and material phenomena, and subordinate the 
one to the other entirely. Thus we have: 

a. Idealists, who maintain that the subject, the ego, was the 
original, and is the only fundamental; the object, the non-ego, being 
evolved from it as its product. The fundamental reality is psychical; 
all matter is, at bottom, of the nature of thought. ' 

/?. Materialists, who maintain that the object, the non-ego, was 
the original, and is tho only fundamental; the subject, the ego, 


being evolved from it as its product. There is nothing but matter. 
Mind, thought, consciousness, are all by-products, epiphenomena, 
mere debris resulting from material processes. Life and conscious- 
ness cease absolutely with the disintegration of the matter with 
which they are associated. 

Thus both Idealists and Materialists believe in a reality, but iq 
a single reality. They are, therefore, at the same time Monists and 

It will be observed that all the different schools mentioned, 
Nihilists excepted, are Kealists of some kind. The four main 
schools may be grouped in this way: 

1. Dualists. 

(a) Natural Dualists (sometimes called simply Realists). 

(b) Hypothetical Dualists (sometimes called Phenomenalists). 

2. Monists. 

(a) Idealists. 

(b) Materialists. 

But the dividing lines are by no means so clear cut as this 
simple classification would seem to indicate. One school tends to 
shade off into another, and sometimes they are scarcely distinguish- 
able. Indeed, the terminology is most confusing, and is of a very 
varying connotation. 

A few other terms require brief explanation. 

Sensationalism maintains that all our knowledge comes to us 
through the senses, and refuses to admit that the mind is a co- 
contributor. Empiricism is sometimes confused with Sensationalism, 
but Empiricism admits that the mind must be something endowed 
with power to form judgments by comparing and contrasting the 
data supplied by the senses. All evidence derived from the senses 
is of particular truths. In every general truth there is an element 
of knowledge independent of such evidence, that is, independent of 
the data of the senses. Contrasted with Sensationalism is nationalism, 
which asserts that the knowledge which comes to us through the 
senses is fallacious, for perception and experience can give us infor- 
mation concerning only particular instances, and can therefore never 
provide us with universal truths. The rationalist claims that reason 
is the sole source of real knowledge. Metaphysical Rationalism must 
not be confused with Theological Rationalism, which is the doctrine 
that denies the existence of any supernatural revelation. But in 


both cases Rationalism is an uncompromising assertion of the absolute 
rights of reason throughout the whole domain of thought. Both 
Sensationalism and Rationalism are dogmatic, as with both it is an 
article of faith that we have the power of acquiring complete know- 
ledge, in the one case exclusively by perception, in the other ex- 
clusively by reason. In contrast with this dogmatism is Scepticism, 
which always doubts, and sometimes denies, the possibility of our 
acquiring true knowledge at all. N 

Agnosticism asserts that our knowledge is limited to the pheno- 
mena of the external world and of the mind," and that we know 
nothing of the* reality which may lie behind phenomena. The 
agnostic disagrees both with the man who asserts and with the 
man who denies the existence of reality underlying phenomena, 
for neither can prove his case. The agnostic says he "does not 
know " whether it exists or not. He will not agree even wit^, the 
hypothetical dualist, who assumes an unknowable. Agnosticism is 
negative. It differs from Atheism, which positively denies the 
existence of a personal God. Agnosticism "does not know" whether 
there is a personal God or not. 

The less liberal type of theologian naturally dislikes not only 
Atheism but also Materialism, for a materialist is necessarily an 
atheist. And he has no great love for agnostics, or even for pheno- 
menalists, and he invariably speaks of them in disparaging terms 
and of their "materialistic tendencies". Towards Idealism he is 
much less hostile, though this attitude he finds it impossible to 
defend logically. 

6. Hypothetical and Natural Dualism 

We have referred to the unknown real thing, the substratum 
or substance, which the Hypothetical Dualist assumes to underlie 
phenomena, the substance in which phenomena are supposed to 
"inhere". The term "phenomenon" is equivocal. In Science it 
refers to the positive facts of perception, as distinguished from their 
causes. Scientific thought, in dealing with the concrete things of 
Physical Science, investigates their nature, their causes, and their 
effects, and so goes beyond mere sense-perception. It assumes, for 
instance, the existence of atoms and of the aether, neither of which 
can be directly perceived at all. The atoms and the aether are 
inferred from a combination of observations and hypotheses. This 

(0415) " 5 


inferential process is an imaginable one, for any conceptual region 
is necessarily conceived as though it might he perceived; and by its 
means the atoms and the aether may bo seen as if under an indefinitely 
powerful microscope. We can verify perceptually only up to a cer- 
tain point; the weakness of our senses leaves a great deal unper- 
ceived and imperceptible. This conceptual region would, if our 
inferences and hypotheses are correct, and if our senses were suffi- 
ciently keen, be perceptible. It has to be admitted, unfortunately, 
that, while the human understanding attempts to construct concep- 
tual systems because it is not satisfied with the contents of sense- 
perception alone, it sometimes uses these conceptual systems of its 
own construction for the purpose of disparaging sense-perception as 
an illusion, although aware, of course, that the suppositions of the 
conceptual system derive, from the data of perception, the whole of 
their vitality. Sometimes attempts are made to construct concep- 
tual systems which are not clearly imaginable: that way lies 
inevitable danger. 

(a) Substance 

The Hypothetical Dualist's "Substance" is not phenomenal, for 
it cannot be made to appear to the senses. But although it is 
claimed to be more real than phenomena, its existence is merely 
inferred. Since, however, the inference is not verifiable, we may 
deny its legitimacy, especially as the "substance" cannot be made 
part of any conceptual system, for it is wholly unimaginable; and 
this really means denying the existence of the substance, and there- 
fore the existence of matter. Such a denial admits of no answer, 
though it certainly carries no conviction. It carries no conviction 
because we cannot bring ourselves to believe that the extcinal world 
would cease to exist if our minds were annihilated. We feel bound 
to believe in the existence of an external world quite independent 
of any percipient. 

"Substance", then, is the term given by the Hypothetical 
Dualist to that elusive yet necessary something, that obscure sub- 
stratum, common to all material things without being discoverable 
in any one of them, something which is never actually seen or in 
any other way experienced, yet something which is thought into 
things; nevertheless, a real thing though a transcendant thing. 
It is some kind of undiscovered basic reality, and the aether of Space 
may perhaps be regarded as the first stage of its phenomenality. 


(b) Primary and Secondary Qualities 

All the "phenomena" of the external world known to us in 
sense experience are logically reducible to a comparatively small 
number of common "attributes" or " qualities" which are (so the 
Hypothetical Dualist claims) inherent in the assumed underlying 
"substance". These qualities are distinguished as primary and 
secondary. Primary qualities are those derived from our muscular 
sense of resistance, such as solidity, extension or size, and motion. 
They are those attributes of the external world that are regarded as 
independent of the observer. Secondary qualities are those derived 
from our other senses, such as colour, sound, taste, smell, tempera- 
ture. Science teaches us that the things of the external world have 
only the primary qualities, and that these arc among the causes of 
the secondary qualities, though the secondary also depend upon the 
existence of a sentient being. The primary world is the seat of 
energy; permanent in time; the same whether we are present or 
absent; objective, and that about which there is no difference of 
opinion; measurable in three dimensions of Space, in duration of 
existencer^UKtln energy. The secondary world is not permanent 
in time, does not exist in the absence of a sentient being, and is not 
satisfactorily measurable in any way except by referring its pheno- 
mena to primary standards. The secondary qualities have no inde- 
pendent existence in the external world: this is a scientifically j 
established fact. If we think of the world or any part of it in 
the absence of all sentient beings, we think of it as absolutely dark 
and absolutely silent. 

The secondary qualities are really subjective reactions excited 
by the primary qualities and objectified by association with them. 
The primary qualities are the most constant and unconditional in 
experience. Illusions are chiefly of seeing and hearing, whereas to 
touch or grasp a thing usually produces conviction. Since it is in 
their primary qualities that things are most exactly measurable in 
dimensions, weight, and movement, it is natural that Science should 
regard the primary qualities as pre-eminently real. But it must 
never be forgotten that the primary qualities are, as truly as the 
secondary, grounded in sensations, and therefore liable to misinter- 

The nature of the Hypothetical Dualist's "substance" is, ad- 
mittedly, extraordinarily elusive; an unperceivable support of per- 


ceivable qualities necessarily seems to be something without assign- 
able character, resembling nothing in experience, and therefore 
explaining nothing. But if it exists at all, there is one quality 
we are bound to ascribe to it, and that is permanence in time, for 
this corresponds to the continuity of the experienced external world 
in the past and in the present. But, even so, permanence in time 
does not seem to help us establish any connection between the other 
primary qualities and the assumed substance, and such terms as 
"underlies" and " inhere" are metaphors, having no significant 
meaning. Still, the notion, though necessarily vague, of permanent 
transcendent substance does give coherence and unity to the pheno- 
mena of the external world we are familiar with. 

If we accept Hypothetical Dualism, it is best to regard " sub- 
stance" as a category as one of those unverifiable, unanalysable, 
fundamental, ultimate, concepts which the mind is driven by neces- 
sity to try to form. If we reject the category as illusory, the 
argument as to the possible coherence of phenomena is reduced to 
nothing. If we accept it, that is, if we recognize substance as a 
category indicating the reality which is not immediately given to 
us in perception, yet felt to be necessary for the understanding of 
phenomena, and accept it either a priori or as the result of reflection 
upon experience, the term seems to suggest something which is not 
very far removed from the ordinary matter of Natural Dualism 
after all. Yet the distinction may be usefully preserved. The 
distinction is just what is required to make intelligible the doctrine 
of transubstantiation, for a change in the substance of the sacramental 
elements, though unimaginable, would then not be inconceivable, all 
the qualities of the elements, primary and secondary, remaining un- 
changed. Ultimately, perhaps, Physical Science will solve the pro- 
blem of matter and substance, and there can be little doubt that the 
primary qualities of matter resistance, extension, weight, motion 
will give the key to the solution. 

The position of the Hypothetical Dualist, as contrasted with that 
of the Natural Dualist, ought now to be clear. Both Dualists are 
Realists. But in the case of the Hypothetical Dualist, the real is 
only inferred, and perceptions are the perceptions of qualities only. 
In the case of the Natural Dualist, the real is apprehended imme- 
diately; he takes the common-sense view; he kicks against a stone 
and perceives it immediately and objectively it is something solid 
and extended before him, and it can be measured and weighed : that 
object he takes to be matter. Common sense revolts against regard- 


ing the object merely as an idea, or as nothing beyond an integrated 
heap of sensations; and this is the view of Science. But the view 
is difficult to maintain in its entirety, for it is certain that our 
positive knowledge, the knowledge that admits of no question, of 
external reality, is limited to our perception of qualities. Whatever 
we know beyond these qualities is known by inference only, and 
inferences of this kind seldom admit of complete verification. 

7. Monism: its Logical Consequences 

The greatest antithesis in present-day Philosophy is that between 
the two monistic systems, Idealism and Materialism. Between these 
there is an unbridgable chasm. A particular system is, however, 
sometimes prevented from falling into absolute Idealism or absolute 
Materialism, and is held in a kind of vacillating equilibrium, because 
in some of its opinions an idealistic tendency is counteracted by a 
materialistic tendency in others. 

It will be understood that the term Monism applies to any 
philosophic system which seeks to exhibit all the complexities of 
existence, both material and mental, as modes of manifestation of one 
fundamental reality. Idealism assumes that all fundamental reality 
is psychical is, in fact, consciousness or mind. Materialism assumes 
that consciousness or mind is a mere by-product of the one funda- 
mental reality matter. Idealism reduces matter to mental elements. 
Materialism identifies thought or feeling with the nerve process 
which accompanies it. 

(a) Idealism 

We may consider Idealism first. Idealism maintains that what- 
ever we know directly is reducible to ideas, and that ideas have an 
existence more real than the fleeting transient objects of sense: the 
existence of matter is nothing but an illusion. But there are so 
many forms of Idealism, and its terms are used in so many senses, 
that it is difficult to come to close quarters with its fundamental 

If "consciousness" be regarded as denoting the recognition 
by the mind of its own acts, and "mind" as that which thinks, 
wills, and feels, it may be said that consciousness is to the mind 
what extension is to the body, Though the analogj is imperfect, 
it is suggestive, for both consciousness and extensior are essential 
qualities; we can neither conceive mind without consciousness noi 


body without extension. But "mind" is sometimes spoken of as if 
it were precisely synonymous with " spirit ". Yet while mind, like 
spirit, is always regarded as an unknown conscious something, mind 
is never conceived as extended in Space; whereas spirit, though 
incorporeal, immaterial, and invisible, is usually conceived as so 
extended, to be invested in human form, and to be a personality 
somehow associated with the body; it is always thought of as a 
substantial though immaterial entity which thinks, wills, and feels ; 
it is regarded as invisible merely because our human sense of vision 
is limited to material things. But whereas a spirit is always con- 
ceived as an entity distinct from, though during life closely asso- 
ciated with, the body, the mind is seldom spoken of as if it were 
something that could exist independently of the body. The reader 
who takes up a book on Idealism must assure himself of the precise 
meaning attached to these terms by the writer. 

All Idealists deny the existence of matter, though some of them 
say that all they really deny is the unknown substratum, 4< sub- 
stance". Some Idealists recognize the existence of spirit as an 
entity which thinks, wills, and feels. Others limit their recognition 
to the much vaguer thing, mind, still conceived, however, as an 
entity of some sort. Still others assert that, since all we positively 
know of mind are the facts of consciousness, we are not justified in 
assuming the existence of mind as any sort of separate entity; and 
they maintain that the only real things in existence are mental 
facts, ideas. They make vague statements about a universal con- 
sciousness, all men's minds being alike, and each mind being a sort 
of temporarily separated portion of this universal consciousness. 

Now if we are sure of anything, it is that consciousness is 
personal and individual; men's minds may in many respects be 
alike, but their differences are great and fundamental. A common 
consciousness is not only unimaginable, it is inconceivable. But 
more than this: Idealism altogether fails to explain the primary 
qualities of matter extension, inertia, impenetrability. Despite his 
clever paradoxes, the Idealist cannot get rid of matter by dissolving 
it in mind. When material objects are in question, common sense 
refuses to admit that esse and percipi are identical. It is impossible 
to accept the ultimate logical conclusion of Idealism, that, with the 
expiring breath of the last sentient being, the whole universe dis- 
appears into nothingness. 


(6) Materialism 

To Materialism the only real world is the world of matter, the 
world of atoms with their primary qualities and motions. Life and 
consciousness are the products of matter, and manifest themselves in 
complexities of atoms. From such complexities life is, in favourable 
circumstances, spontaneously generated, and spontaneously gene- 
mted living matter has, by blind chance, passed through the various 
stages of evolution until the human being reached his present state 
of development. There is no God, no soul, no freedom, no im- 
mortality. All psychical activity, all consciousness, is ultimately 
nothing more than a motion in and amongst the cells of the grey 
substance of the brain, possibly some form of wave-motion or 
of radiation set up by the movement. All thoughts and feelings are 
not merely accompaniments, but are identical with these nervous 
processes. The mind is nothing more than a function of the brain. 
All psychical facts are merely effects, though unexplained effects, of 
cell-movements in the brain. Thought bears much the same relation 
to the brain as bile does to the liver. 

The weakness of Materialism lies in its vast assumptions. It 
gives no explanation of the ultimate origin of either matter or 
motion. It is impossible to believe that the thinking, feeling self 
of which each one of us is conscious, is only an automaton, and 
even the materialist is forced to admit that whether there is any 
causal connection between the psychical xcts and the physical 
changes which accompany them, is wholly unknown. Materialism 
fails to give any satisfactory explanation of the nature and origin 
of life and consciousness. Common sense refuses to admit that 
consciousness is nothing but a movement of matter. 

The claims of Materialism lead to far-reaching logical conse- 
quences. For the materialist asserts that all our volitions are mere 
links in mechanical chains of blind causes and effects. Now men 
act in consequence of motives, and their motives are thus the results 
of preceding facts, so that if we knew the antecedents of these facts 
and the laws that connect them, we could \vith infallible certainty 
predict the consequences, immediate and remote. If Adam had 
been a super-mathematician he might, automaton though he was 
assuming that he was acquainted with all molar and molecular 
masses, their initial positions, direction of motions, velocities, and 
accelerations have predicted the whole course of the world's history. 


He might have written out a complete account, complete to the last 
detail, of the great European War; he might have predicted the 
date, place, and manner of death of the world's last mosquito; nay, 
he might have foretold the very terms of the marriage contract 
between the Tellurian Kaiser and the Martian Queen to be sealed 
a couple of centuries hence. To the materialist, the human will 
counts for nothing, and can affect nothing; our every decision is the 
infallible consequence of particular cerebral changes. The individual 
who, while balancing two courses, is under the impression that he is 
at liberty to pursue either, is completely under a delusion. The 
most calculating selfishness, the most heroic self-sacrifice, equally 
have been determined by chance aggregations of molecules. Newton 
did not write the Principia, or Shakespeare Hamlet] they were not 
creative personalities; they merely looked on while blind causes 
were at work. They were merely chance aggregations of molecules, 
constituting automata with fortuitously specially active cerebrations. 
So with all things that ever have been or ever will be produced. It 
is mere fancy, says the materialist, that we ever act from rational 
motives. No criminal is morally reprehensible; he is simply morally 
irresponsible. How can a materialist give his support to any sort 
of penal code? But to this question he can only logically answer 
that he, too, is irresponsible for his actions. 


It cannot be said that either Idealism or Materialism is a funda- 
mentally illogical system. Each is logically worked out, but neither 
is accepted because of the ultimate consequences traceable from its 
hypotheses; in each case the consequences are such that common 
sense declines to accept them, and this really means a rejection of 
the hypotheses on which the systems are constructed. In fact, 
every system breaks down that refuses to accept the cardinal facts 
of the duality of consciousness. Mind and matter are two entirely 
distinct things present to our consciousness; they cannot be reduced 
the one to the other, in the first place because resistance is incom- 
patible with the attributes of mind or spirit, arid in the second 
because consciousness is inexplicable by the qualities of matter. 
We may, if we like, recognize Materialistic Monism of body and an 
Idealistic Monism of spirit, combined in a unified Dualism of sub- 
stance, namely, the unified substance of body and spirit, or matter 


and mind, in the single personality of man. But the refusal to 
accept the great undei lying fact of duality of consciousness is an 
act of philosophic suicide. 

There is not a philosophic system but is open to attack, for 
<*very system rests on hypotheses which, ultimately, are not veri- 
fiable. Dualism of both kinds are attacked: Natural Dualism 
because it takes too much for granted, Hypothetical Dualism be- 
cause of the assumption of unknown and apparently unknowable 
entities. Still, the ultimate consequences of Dualism are not so 
destructive as are the consequences of Monism. 

No philosophic system is closed and final. Philosophic finality 
is still a philosophic dream. 

There are some philosophers who are less anxious to understand 
the world of Science than to convict it of unreality. They shrink 
from the laborious study of the detailed knowledge derived from 
the senses, and prefer to pin their faith on the wisdom, sudden and 
penetrating, which they believe will reach them by reflection and 
reasoning. In their more emotional moods, a belief in the unreality 
of the world of Science arrives with irresistible force, and when this 
emotional intensity subsides they seek for logical reasons in support 
of that belief. 

The attitude is altogether wrong. Like the man of Science, 
the philosopher must lay aside his hopes and wishes when he 
studies his subject. There must be no shrinking from hard 
facts, no demand in advance that the world shall conform to 
preconceived desires. Knowledge of the universe is not hidden 
by a flimsy veil that can be easily torn aside; it is very hard to 
come by. 

Common opinion prevails that metaphysical disquisition is idle, 
because the problems discussed are really never solved. It is quite 
true that Philosophy has made greater claims and achieved fewer 
results than any other branch of learning. It has made many rash 
assertions and many rash denials. Yet some of the greatest thinkers 
since the age of ancient Greece have devoted their lives to philoso- 
phical problems, and no one would dream of calling them either 
shallow or insincere. That progress has been slight is inevitable, 
for the great mass of Philosophy is necessarily purely speculative. 
There is very little philosophical truth finally established, and addi- 
tions can be made only at the cost of much labour, very slowly, and 
only then if the method of Science is made the method of Philosophy. 
Existing systems are often ingenious, even sublime, but they nearly 


always lay claim to finality and completeness. And it is for this 
reason that many philosophers are still the playthings of the gods. 1 

Opinion and Truth 

1. Belief and Testimony 

All beliefs 2 are to some extent influenced by the wish to believe, 
and the wish to believe has the strongest influence in many matters 
which closely concern us. " It has always been open to remark," 
says Bain, " how completely human beings are the slaves of circum- 
stances in the opinion that they entertain upon all subjects that 
do not appeal directly to the senses and daily experience. We 
see in one country one set of beliefs handed down unchanged for 
generations, and in another country a totally different set equally 
persistent." 8 There is very little independent judgment among 
mankind, and evidently, therefore, it must be possible by some 
means to make one opinion prevail rather than another. The arts 
of swaying men's convictions are, of course, numerous and well- 
known. " Look at the whole army of weapons in the armoury of 
the rhetorician. Look at the powers of bribery and corruption in 
party warfare. Consider also the effect of constantly hearing one 
point of view to the exclusion of all others." 4 Then, again, any 
strong feeling possessing the mind gives such a determination to 

1 The reader may usefully consult the following volumes : A. J Balfour, Defence of Philo- 
sophic Doubt, and Foundations of Belief \ T. Brown, Lectures on the Philosophy of the Human 
Mind; Sir W. Hamilton, Lectures on Metaphyics and Logic', Q W. Leibnit/:, New Essays 
concerning Human Understanding] G. H. Lewes, The Physical Basis of Mind ; J. M'Cosh, 
Examination of Mills Philosophy; J. S. Mill, Logic, and Examination of Sit W Hamilton's 
Philosophy ; K. Pearson, Grammar of Science', H. Poincare", Science and Hypothesis, and 
Science and Method ; Carveth Read, The Metaphysics of Nature ; F C. S Schiller, Riddles of 
the Sphinx-, H. Sidgwick, Philosophy, Its Scope and Relations-, H. Spencer, First Principles*, 
Dugald Stewart, Philosophy of the Human Mind; J. Ward, Naturalism and Agnosticism. 

Also W B Carpenter, Nature and Man; J. Grote, Kxploratio Philosophica ; I. Kant, 
Critique of Pure Reason and Kritic of Judgment ; H. L. Mansel, Metaphysics, and Philosophy 
of the Conditioned; J. M'Cabe, Evolution of the Mind; T. Reid, Active fowers of the Human 
Mind; A. Riehl, Science and Metaphysics; J. Veitch, Dualism and Monism. 

2 It should be noticed that the real opposite of belief, as a state of mind, is not disbelief, 
but doubt, uncertainty; and the close alliance between this and the emotion of fear is 
stamped on every language. Bain, Emotions and the Will, p. 635. 

Bain,t&. p. 622. *Bain, ib. 


the thoughts and the active impulses as to pervert the convictions, 
and to dispose us to trust or distrust at that moment things that 
we should not trust or distrust at another time. In the elation of 
successful enterprise just achieved, we are apt to have a degree of 
confidence in our own powers that we do not feel in ordinary times, 
and very much in contrast to what we feel at some miscarriage or 
failure, or at a time when we are affected by some bodily ailment. 1 

Belief in testimony contains all the elements of experience, 
intuition, and emotion, in varying degrees, but there is also a more 
subtle element of influence, arising from the peculiar power exerted 
by one man upon another. All those circumstances which lend 
impressiveness to a speaker, and render the orator an artist, dispose 
the hearers to accept his statements with more than the deference 
due to the testimony of a single person. Emotion, in such cases, 
exercises an interference of its own kind. 2 The preacher and the 
politician often take an unfair advantage of this, and purposely 
forget that it is their duty to lead their followers to the truth. As 
Guyau says, 8 charlatans and orators are generally familiar with 
the contagious power of affirmation. It is interesting to watch 
the gradual development of emotion, becoming more and more un- 
controlled, as a clever party politician addresses a meeting. The 
psychology of a multitude is always an instructive study. 4 

"Pew, indeed, are ihe beliefs", says Mr. Balfour, "which any 
individual thinks himself called upon seriously to consider with a 
view to their possible adoption. The residue he summarily dis- 
poses of, rejects without a hearing, or, rather, treats as if they had 
not even that prima fane claim to be adjudicated on which formal 
rejection seems to imply. 

"Now can this process be described as a rational one? That 
it is not the immediate result of reasoning is, I think, evident 
enough. All would admit, for example, that once the mind is 
closed against the reception of any truth by 'bigotry 1 , or 'in- 
veterate prejudice*, the effectual cause of the victory of error is 
not so much bad reasoning as sometfiing which, in its essential 
nature, is not reasoning at all. But there is really no ground for 
drawing a distinction as regards their mode of operation between 
the 'psychological climates' which we happen to like and those 
of which we happen to disapprove. Por good or for evil, in 
ancient times and in modern, it is ever by the identic process that 

1 it), p. 544. 2 t'6. p. 549. 3 Education and Heredity, p. 17. 

Cf. Matthew Arnold on "Tolstoi", Essays, Second Series, p. 291. 


they have sifted and selected the candidates for credence, on which 
reason has been afterwards called to pass judgment; and that pro- 
cess is one with which ratiocination has little or nothing directly 
to do." 1 

Professor Carveth Read points out how Philosophy, coming to 
us late in life, meets at the outset with a great difficulty, how to 
begin the discrimination of truth and error, what to accept, what 
to reject. The mass of beliefs, ingrained in childhood and youth, 
abides with us and is necessarily amongst the foundation of reason. 
"The influence of social life in the various forms of education, 
tradition, authority, common sense, confirm alike our sciences and 
our superstitions. Family, school, church, and state, instruct the 
boy and the man what to think and what to do. Inheriting a 
nature fit for such a life, his instincts of imitation, honour, sym- 
pathy, reverence, and the rest, co-operate in delivering him over 
to the great tutor or arch-sophist (however you regard it) Society. 
The habit of believing assertion becomes almost instinctive, gives 
opportunity to liars and other imaginative persons. Falsehood and 
romance, imperfectly differentiated, flourish amongst children and 
savages; and this is quite natural, for deceit is common in organic 
nature." 2 

Most of our prejudices have become so ingrained that we are 
hardly conscious of them. And almost every day we are adding 
to them, for we cannot completely rid ourselves of the old habit 
of hastily taking up opinions which we have not properly examined, 
opinions from the daily press, opinions derived from the assertion 
of others, and opinions due to superficial observation. Unreasoned 
opinions are curiously infectious, and the presumption that any 
current opinion is not wholly false gains in strength according to 
the number of its adherents. Herbert Spencer thinks we must 
admit that the convictions entertained by many minds in common 
are the most likely to have some foundation, 3 but this is a dangerous 
doctrine to apply to the unreasoned opinions of the mob. As 
Dttgald Stewart says, if no test or criterion of truth can be pointed 
out but universal consent, may not all those errors which Bacon 
has called idola tribus claim a right to admission among the incon- 
trovertible axioms of Science? 4 We cannot, however, always avoid 
following current opinion, even if we would, and sometimes we 
follow it from deliberate choice. In this respect, fear of possible 

i Pom lations of Belief, p. 205. 2 Metaphysics of Nature, pp. 12-3. 

First Principles, p. 4. * Works, p. 322. 


ridicule is often the determining factor. Mr. Balfour, speaking, for 
instance, of aesthetic, remarks that the inclination to admire what 
squares with some current theory of the beautiful rather than what 
appeals to any real feeling for beauty, is so common that it has 
ceased even to amuse. 1 Opinions are influenced by the prevailing 
fashion. Men fear singularity more than error; they accept numbers 
as the index of truth; and they follow the crowd. The dislike of 
labour, the fear of unpopularity, the danger even of setting up 
individual opinion against established convictions and the voice of 
the multitude, contribute to strengthen this inclination. 2 

2. Authority and Reason 

It seems clear that our opinions and beliefs are for the most 
part borrowed, and that the common tendency is to repose blindly 
.on authority. Now ought we to put our trust in authority, or 
ought we always to appeal to Reason? To what extent can we 
accept Huxley's dictum that the mental power which will be of 
most importance in our daily life is the power of seeing things as 
they are without regard to authority'? 3 

The argument of those who urge that we cannot trust our 
Reason, and that we must inevitably fall back upon authority, is 
something of this kind: since we cannot throw over the engineer, 
the lawyer, the doctor, and others with expert knowledge, are we 
not bound to resort to authority ? how can Reason possibly help us 
in cases where a lifetime must be spent in acquiring a knowledge 
of the technicalities in every one of a score of different profes- 
sions? But such an argument is beside the point; the illustration is 
misleading, as illustrations often are. Expert opinion is one thing; 
opinion on everyday affairs another. The man in the street will- 
ingly accepts on trust the work of the mathematician, the man of 
science, the historian, the engineer, the jurist, and the medical man; 
but as long as human nature remains what it is, the opinions of the 
social reformer, the politician, and the theologian, will never be 
accepted by a large number of people, who, rightly or wrongly, 
think they are entitled to their own "opinion" on all such subjects 
as social matters, politics, and religion, subjects which, as we all 
know, form topics of perennial discussion. 

Now the statement that the rival opponent of authority is 

i Foundations of Belief, p. 254. 

a Sir G. 0. Lewis, Influence of Authority in Matters of Opinion, p. 16. 

* Science and Education, p. 96. 


Reason seems to most persons, says Mr. Balfour, 1 equivalent to a 
declaration that the latter must be in the right and the former in 
the wrong; while popular discussion and speculation have driven 
deep the general opinion that authority serves no other purpose 
than to supply a refuge for all that is most bigoted and absurd. 

The current theory by which these views are supported may 
be summarized in this way. "Everyone has a 'right' to adopt 
any opinions he pleases. It is his 'duty' before exercising this 
right critically to sift the reasons by which such opinions may be 
supported, and to adjust the degree of his convictions in such a 
manner that they shall accurately correspond with the evidences 
adduced in their favour. Authority, therefore, has no place among 
the legitimate causes of belief. If it appears among them, it is as 
an intruder, to be jealously hunted down and mercilessly expelled. 
Reason and Reason only can be safely permitted to mould the con- 
victions of mankind." 

"Sentiments like these are among the commonplaces of political 
and social Philosophy. Yet, looked at scientifically, they seem to 
me," Mr. Balfour continues, "to be not merely erroneous but absurd. 
Suppose for a moment a community of which each member should 
deliberately set himself to the task of throwing off as far as possible 
all prejudices due to education, where each should consider it his 
duty critically to examine the grounds whereon rest every positive 
enactment and every moral precept which he has been accustomed 
to obey; to dissect all the great loyalties which make social life 
possible, and all the minor conventions which help to make it easy; 
and to weigh out with scrupulous precision the exact degree of 
assent which in each particular case the results of this process might 
seem to justify. To say that such a community, if it acted upon 
the opinions thus arrived at, would stand but a poor chance in the 
struggle for existence, is to say far too little. It could never even 
begin to be ". 2 

Thus does Mr. Balfour fill would-be consistent thinkers with 
feelings of discomfort. Must we, then, forbear to question our 
prejudices lest we should bring about a social cataclysm? But is 
Mr. Balfour's supposition, with all its dreaded consequences, so 
destructive of the main argument as at first it seems? Is he not 
himself an excellent example of such a community as he imagines ? 
Does he accept authority? Has he not spent his life in bidding 
people appeal to Reason? 

i Foundations of Belief, p. 195. a ft. p. 196. 


But let us hear him again: "The identification of Keason with 
all that is good among the causes of belief, and authority with all 
that is bad, is a delusion so prevalent that a moment's examination 
into the confusions which lie at the root of it may not be thrown 
away. The first of these confusions may bo dismissed almost in 
a sentence. It arises out of a tacit assumption that reason means 
right reason. Such an assumption, it need hardly be said, begs 
half the point at issue. Keason, for purposes of this discussion, 
can no more be made to mean right reason than authority can be 
made to mean legitimate authority". 1 

Here we are all bound to agree with Mr. Balfour. And, as he 
points out elsewhere, when we reason we are the authors of the 
effect produced; we have ourselves set the machine in motion, and, 
for its proper working, we alone are responsible. If, therefore, the 
machine is imperfect if our reasoning is faulty or our knowledge 
defective we should probably be wiser to put our trust in autho- 
rity. But the important thing is to choose safe and able guides in 
matters which we cannot or ought not to judge for ourselves. 2 It 
has, however, to be remembered that, in choosing our guides, we are 
choosing them by the light of our own reason, and, more probably 
than not, we shall allow our prejudices or our affections to operate 
even in making this choice. 

We are sometimes deceived when we think that certain beliefs 
we entertain are the rational product of strictly intellectual pro- 
cesses. We have, in all probability, only got to trace back the 
thread of our inferences to its beginnings in order to perceive that 
it finally loses itself in some general principle which, describe it as 
we may, is in fact due to no more defensible origin than the influ- 
ence of authority. For authority moulds our ways of thought in 
spite of ourselves and usually unknown to ourselves. " The power 
of authority is never more subtle and effective than when it pro- 
duces a psychological * atmosphere' or ' climate ' favourable to the 
life of certain modes of belief, unfavourable and even fatal to the 
life of others." 8 

To Spencer's mind, remarks Professor Sadler, scientific teaching 
seemed inseparably connected with discovery, with the overthrow 
of false authority, with liberation. But it is quite conceivable that, 
in future, when physical science sits on the throne of undisputed 
authority, she may impose on education as heavy a weight of pre- 

i Foundations of Belief, p. 202. 2 cf. Sir G. C. Lewis, Influence of Authority, dfcc., p. 65. 
Cf . Foundations of Belief, pp. 203, 206, 228. 


scribed belief as did any earlier regime. All true education strikes 
a balance between authority and independent research. It is there- 
fore expedient always to have a due place in education lor that 
subject or group of subjects in which the most strenuous movement 
of enquiry and investigation is going forward. The spirit of search 
is caught from teachers who are themselves researching, not simply 
by artificially reproducing the methods of search in provinces of 
knowledge already accepted. 1 

It is the claim of authority to unchallenged acceptance that we 
are all bound to dispute. In the Middle Ages the search after a 
causative explanation of phenomena was represented by its oppo- 
nents as hostile to the authority of the State and subversive to 
the Christian faith, and such views are not entirely unknown even 
at the present day. 2 It is perhaps natural that persons in autho- 
rity should dislike their authority questioned, and here perhaps 
lies the clue to the dislike, felt in some quarters, to any general 
adoption of scientific method, since such method cannot but result 
in independent judgment. Children who are taught to think for 
themselves, to sift evidence, to get at all essential facts, are likely, 
later on, to prove formidable opponents to illogical systems. But 
many a generation will pass away before Mr. Balfour's community 
of intellectual anarchists will be born. The mass of mankind will 
never have any ardent zeal for seeing things as they are; very 
inadequate ideas will always satisfy them. Whoever sets himself 
to see things as they are will find himself one of a very small 
circle, but it is only by this small circle resolutely doing its own 
work that adequate ideas will ever get current at all. 3 

Authority, then, we must treat with respect; yet we must 
always be on our guard against its too arrogant claims. Whilst 
we may credit it with being sincere, we must ask it to produce its 
credentials. We should beware of the limitations of Reason, but 
we should never hesitate to use Reason. We should always make 
an insistent demand for facts, and do our utmost to search amongst 
them for the Truth. As Schiller says, the real philosopher is one 
who always loves truth better than his system. We should, then, 
throw away our systems as soon as we have convicted them of 
error; we should never hesitate to revise our opinions in the light 
of fresh facts. Change of mind is not inconsistency. 4 

1 Science in Public A/airs, p. 58. 2 Cf. Lectures on the Method of Science (Strong), p. 86. 
* Cf. Matthew Arnold, Essays, vol. i, p. 26; and Locke, Conduct of the Understanding, g 12. 
*"Ncmo doctus unquam mutationem consilii inconatantiain dixit esse." (Cicero). Cf. 
Arnold, Essays, vol. i, p. 31. 


3. The Nature of Truth 

Perhaps a teacher's most imperative duty is to inculcate the 
desire of probing a thing to its depths. The desire for thorough 
work is one and the same thing with the desire of finding the truth, 
for a little experience forces us to recognize that the truth is never 
near the surface, and that we must always dig and labour before 
reaching it. 1 

To define Truth is difficult and is really unnecessary, for, in its 
more general sense, it is perfectly well understood. Professor 
Baldwin tells us that he once put to a sixteen-year-old girl the 
question, "What would you say it is that the true is true to?" 
After some thought she said, "It is true to itself." "Why?" 
"Because the truth is that which doesn't pretend to be anything 
else." 2 There it is, in a nutshell. 

The cultivation of such a cardinal virtue as truth must tell in 
every department of life, and its cultivation depends, in no small 
degree, upon the work of the Science teacher. The moral disposi- 
tion to veracity can avail little without the tests and methods of 
distinguishing true from false, while men well versed in these 
seldom quarrel about matters of fact. The disputes of the scientifi- 
cally educated are narrowed to some very special and difficult 
issues. 3 The Science teacher should tell his pupil that it is his 
duty to doubt until he is compelled, by the absolute authority 
of nature, to believe what other people tell him about Science. 
Pursue this discipline carefully and conscientiously, and we may 
make sure that, however scanty may be the measure of information 
which we have poured into the boy's mind, we have created an 
intellectual habit of priceless value in practical life. 4 

"The philosopher", says Faraday, "should be a man willing to 
listen to every suggestion, but determined to judge for himself. He 
should not be biased by appearances ; have no favourite hypotheses ; 
be of no school; and in doctrine have no master. He should not be 
a respecter of persons but of things. Truth should be his primary 
object. If to these qualities be added industry, he may, indeed, 
hope to walk within the veil of the temple of nature." The ideal 
intellect is a clear cold logic engine, as Huxley would say. 6 

Every teacher should realize that all Truth is relative and cannot 

1 Cf. Guyau, Education and Heredity, p. 175 

2 Thought and Things, vol. ii, p. 367. 3 Bain, Science of Education, p. 162. 
< Cf . Huxley, Science and Education, p. 123 5 Science and Education, p. 86. 

(0415) 6 


be absolute. As our knowledge grows we have to revise our ideas. 
The truth of yesterday may be falsehood to-day. Meanwhile we 
have to live to-day by what truth we can get to-day, and be ready 
to-morrow to call it falsehood. " Ptolemaic astronomy, Aristotelian 
logic, scholastic metaphysics, were expedient for centuries, but 
human experience has boiled over those limits, and we now call 
these things only relatively true, or true within those borders of 
experience. Absolutely', they are false, as everyone now knows." 1 
The history of thought consists of little more than an accumulation 
of abandoned explanations, yet these explanations passed as Truth 
within the limitations of the experience of their own day. 

"The truth of an idea is not a btagnant property inherent in it. 
Truth happens to an idea. It becomes true, it is made true by 
events. Its verity is, in fact, an event, a process, the process, 
namely, of its verifying itself. 

"The 'absolutely true', meaning what no further experience 
will ever alter, is that ideal vanishing point, towards which we 
imagine that all our temporary truths will some day converge. It 
runs on all-fours with the perfectly wise man, and with the abso- 
lutely complete experience; and if these ideals are ever realized, 
they will all be realized together." 2 But that goal is a long, long 
way off. 

The teacher should bear in mind that Science is the most perfect 
embodiment of the Truth, and of the means of getting at the Truth. 
More than anything else does it impress the mind with the nature 
of evidence, with the labour and precautions necessary to prove a 
thing. It is the best possible corrective of the laxness of the 
natural man in receiving unaccredited facts and conclusions. It 
exemplifies the devices for establishing a fact or a law in every 
variety of circumstances; it saps the credit of everything that is 
affirmed without being properly attested. 3 The method of Science 
is, in short, above all things the method of discovering the truth. 

Let the Science teacher, then, be on his guard against dogmatiz- 
ing. His chief business is to teach, not to lecture ; to guide, not to 
tell. Let him remember the maxim, " In primis, hominis est propria 
veri inquisitio atgue investigatio".* To lead his scholars to the pursuit 
and investigation of Truth should be his highest aim. 

i Pragmatism, p. 223. 

* ib. Cf. also William James, The Meaning of Truth, especially ch. il. 

Bain, Ed\ication as a Science, p. 147. * Cicero, De Offlciis, i, 13. 


The Sophists and Socrates 1 

i. First Attempts at Investigation 

It was with the most unbounded confidence that the early philos- 
ophers of Greece entered upon the work of physical speculation, and 
they quite expected to be able to divine, at a single glance, the 
whole import of Nature's book. The smaller problems of Science 
they usually scorned to try to solve; they aspired to a complete and 
immediate knowledge of the origin and the controlling principles of 
the universe itself. According to Thales, water was the origin of all 
things; according to Anaximines, air; arid Heraclitus considered jfir0 
as the essential principle of the universe. And about these con- 
clusions they had no doubt at all. 

There are, however, to be found more limited examples of in- 
quiry concerning the causes of natural phenomena, and in these we 
are able occasionally to discern some slight anticipation of the true 
spirit of the scientific investigator. One of the most striking 
instances of this kind is to be found in the speculations which 
Herodotus records relative to the cause of the floods of the 

Although Herodotus questioned the Egyptians closely about this 
matter, ho learned very little from them. They appear not only to 
have had no theory about the cause of the floods, but to have felt 
no want of a theory. The Greeks, on the other hand, had shown 
more curiosity, but their hypotheses were so far unacceptable to 
Herodotus that he substituted one of his own. Not only, however, 
did Herodotus' own hypothesis not cover all the facts, but it spoke 
of the sun drawing the water, and exactly what was meant by this 
ambiguous term, the historian neglected to say. It is, in fact, 
obvious that he had but the vaguest notions of evaporation, and 
we are forced to conclude that, despite his inquiry into the facts, 
his hypothesis was merely a loose conjecture. And this was typical 
of the Greek speculators. As soon as they had formed any general 
conceptions, they proceeded to scrutinize these by the internal light 
of the mind alone, without any longer looking abroad into the 
world of sense. They quite underestimated the value of observation, 

l Socrates, about 468-399 B.C. 


and quite neglected verification. They put their faith in a priori 
methods, and they failed utterly. 1 

2. The Sophists 

The Sophists were teachers of Rhetoric, and the litigious quib- 
bling nature of the Greeks was the soil on which an art like that of 
disputation was easily made to flourish. But the only testimony 
we have of the Sophists is that of the Philosophers, their opponents, 
and as a strong dislike is so often the inevitable consequence of any 
marked difference of creed, we feel bound to accept with consider- 
able hesitation the evidence by which alone we are able to judge of 

Certain passages from Plato suggest that the Sophists were held 
in profound contempt generally, but it is very doubtful if this was 
actually the case. They were certainly wealthy and powerful; they 
were men of quite exceptional ability; they were, in large measure, 
the intellectual leaders of their age; and they were often selected 
as ambassadors on very delicate missions. No doubt they were 
objects of aversion to some successful men always are; and no 
doubt they were more than a little unscrupulous. But the general 
feeling towards them was probably one of dislike, possibly also of 
fear, rather than of contempt, except, of course, on the part of the 
Philosophers, who despised them for their insincerity, superficiality, 
and shallowness, and hated them for the popularity which their 
specious and dazzling rhetoric easily secured and maintained. 

The great boast of the Sophists was that they taught the art of 
"making the worse appear the better reason", but in this it is 
doubtful if they can be said to have been guilty of anything specially 
reprehensible in a Greek, however much such serious thinkers as 
Socrates and Plato might despise the shallow philosophy from which 
it sprang. 

Lewes puts in a strong defence of the Sophists, and calls to his 
aid Macaulay's essay on Machiavelli, in order that we may see 
how their doctrines might have been held by very virtuous men. 
" Habits of dissimulation and falsehood, no doubt, mark a man of 
our age and country as utterly worthless and abandoned ; but it by 
no means follows that a similar judgment would be just in the case 
of an Italian in the Middle Ages." Lewes also bids us look at home, 
and asks, Does not every barrister exert his energy, eloquence, 

i Cf . Whewell, History of the Inductive Sciences^ i, pp. 10-28 ; and Herodotus, Book II. 


subtlety, and knowledge "to make the worse appear the better 
reason" 1 Indeed there seems to be little to choose between the 
Sophists and the present-day pleaders in our courts of justice. If 
a barrister has a bad case, does he not set himself deliberately to 
deceive the jury? does he not use every device known to Rhetoric 
to appeal to the emotions and to obscure the facts'! does he not try 
to injure the character of his opponent's witnesses? He is not paid 
to establish the truth but to win his case, and, if he does this, no 
matter how unscrupulous his methods, few will think any the worse 
of him. In private life he may be the most moral, perhaps the 
most religious of men. His professional work is supposed to meet 
a public want, and in any case it forms an admirable training for 
the political platform. Who, then, would deny him his reward? If 
the honours due to an honourable profession are thrust upon him, 
may we not assume that the Sophists were similarly esteemed? 

The Sophists appear to have given up Philosophy because they 
had come to the conclusion that there was no possibility of discover- 
ing Truth; any attempt to penetrate the mysteries of the universe 
they believed to be utterly vain. It was this that caused them to 
begin to consider their relations to other men, and so it came about 
that they devoted themselves to Politics and Rhetoric. If, they 
thought, there was no possibility of Truth, there only remained the 
possibility of Persuasion. They were convinced that there were no 
such things as Right and Wrong by nature, but only by convention. 
As orators they treated Truth with disdain, and devoted their 
talents to perfecting the mere outward form of expression. They 
were, it is true, a standing protest against the absurd metaphysical 
science of their day, but there can be no doubt even if Plato is 
guilty of great exaggeration that they were pretentious and in- 
sincere to the last degree. 1 

3. Socrates and his Method 

Whilst the Sophists were teaching the word-jugglery which they 
called Disputation, there suddenly appeared among them a strange 
antagonist. Outwardly the stranger's appearance was mean. Short 
of stature, thick-necked and somewhat corpulent, with prominent 
eyes, with nose upturned and nostrils outspread, with large mouth 

1 According to Plato the office of the Sophist was to teach immorality and openly to avow 
immorality. But this statement carries its own contradiction, since no set of men could 
preach doctrines acknowledged to be subversive of all morality, without incurring the 
heaviest penalties of the State. 


and coarse lips, he seemed the embodiment of stupidity. "But, 
inwardly, he was so just that he never did an injury to any man; 
so temperate that he never preferred pleasure to right; so wise, that 
in judging of good and evil he was never at fault." His self-control 
was absolute; his powers of endurance were unfailing; he had so 
schooled himself to moderation that his very scanty means easily 
satisfied all his wants. With a shrew for his wife, he submitted to 
her violent temper with an equanimity which is proverbial. Such 
was Socrates; and his intellectual gifts were hardly less remarkable 
than his moral virtues. Naturally observant, acute, and thoughtful, 
he developed these qualities by constant and systematic use. But 
though intellectually the acutcst man of his age, he liked to repre- 
sent himself in till companies as the dullest person present. 1 

Socrates soon became known to every citizen in the market- 
place, but he always declared that he knew nothing. " When you 
professed knowledge on any point, especially if admiring crowds 
gave testimony to that profession, Socrates was sure to step up to 
you and, professing ignorance, entreat to be taught. Charmed 
with so humble a listener, you began. Interrogated, you unsus- 
pectingly assented to some very evident proposition; a conclusion 
from that, almost as evident, received your assent. From that 
moment you were lost. With great power of logic, with great 
ingenious subtlety, and sometimes with daring sophistication, he 
weaved a web from which you could not extricate yourself. Your 
own admissions were proved to lead to monstrous conclusions, and 
you could not see where the gist of the sophism lay. The laughter 
of all bystanders bespoke your defeat. Before you was your adver- 
sary, imperturbably calm, apparently innocent of all attempt at 
making you ridiculous. Baflled and disgusted you left the spot in- 
dignant with yourself, and vowing vengeance upon your adversary." 2 

Socrates found men confidently making affirmations with words 
which they had never troubled themselves to define, and persuaded 
that they required no further teaching, yet at the same time unable 
to give clear or consistent answers to his questions, and so showing 
themselves to be destitute of real knowledge. 3 Socrates did not 
attempt to dogmatize; his system was simply that of question and 
answer. By a systematic cross-examination, his opponent was com- 
pelled to pass judgment upon himself, and perhaps induced to sub- 
stitute a better opinion for a worse. If, as often happened, the 

* Of. Lewes, Biog Hist, of Phil., pp. 130-9; and Adolph Harnack, "Socrates", Ency. Brit 

* Lewes, Biog. Hist, of Phil, pp. 139-40. Cf. Grote'a Plato, Preface, p. ix. 


respondent, defeated, withdrew from the inquiry, he had in Socrates* 
judgment gained something, for he had in some measure become 
conscious of his ignorance. If, however, he did not shrink from 
a new effort, Socrates was ready to help him with further ques- 
tions of a constructive sort. Such were the peculiar features of the 
Socratic method, and the method was adopted by Plato. Plato's 
writings are thus cast in Dialogue form, and the introduction of 
Socrates himself into the Dialogues seems to invest them with 
special interest and authority. 

The Dialogues are seldom easy to follow, and it will suffice 
here to give an imaginary one, expressed in terms as simple as 
possible. We will suppose Socrates engaged in discussion with 

Soc. I am afraid, Kuclides, I know nothing of Geometry, though 
the subject interests me greatly, for I believe you said that the 
whole science has for its basis a number of axioms. 

Euc. That is so. 

S. You said, did you not, that these axioms carry with them an 
inherent authority, that their truth is self-evident] 

E. Yes. 

S. So that if anyone ventured to deny the truth of an axiom, if, 
for instance, anyone said that the whole is not always greater than 
its part, you would say 

E. I should say he was a fool. 

S. Evidently your convictions are planted on a rock. Few 
branches of knowledge appear to have such firm foundations as 

E. That is generally admitted. 

S. I feel so much interested that I should like to refer to the 
problems you were working with your pupils this morning. You 
were making squares, bisecting lines, and so on, afterwards proving 
that your constructions were correct. The work was, I suppose, 
comparatively simple ? 

E. It was of the most elementary character. 

S. Let me then draw the square AI3CD. Does my figure satisfy 

E. You are a most promising pupil, Socrates. 

S. 1 may, perhaps, vary the problem you were working in your 
last lesson, and will therefore draw AE outside the square, equal to 
AB, and making an acute angle with AB. And I will join CE. 

* That is with Euclid the mathematician, not with Socrates' own pupil. 



E. Your construction is perfectly clear. 

S. Suppose, now, I bisect CB in H, and through H draw HO 
at right angles to CB. Suppose, too, that I bisect CE in K, and 
through K draw KO at right angles to CE. Since CB and CE are 
not parallel, the lines HO and KO must meet, must they not, in 
some point 0? 
E. Evidently. 

S. Let me give the figure a more finished appearance by joining 
OA, OE, OC, and OD. I will now try to examine this figure, as 

nearly as possible following your 
own method. Perhaps you will 
help me if I get into difficulties? 
E. Willingly. 

S. Since KO bisects CE and 
is perpendicular to it, OC is 
equal to OE? 

E. Excellent, so far. 
S. And since HO bisects CB 
and DA, and is perpendicular 
to them, OD is equal to OA? 
E. You are quite correct. 
S. And, by construction, DC 
is equal to AE? 
E. Certainly. 

S. Therefore the three sides 
of the triangle ODC are equal, 
respectively, to the three sides 
of the triangle OAE, so that, by 
the 8th proposition of your First 
Book, the angle ODC is equal to the angle OAE. 
E. I have never known a clearer demonstration. 
S. But since OD is equal to OA, therefore the angle ODA is 
equal to the angle OAD? 
E. Obviously. 

S. Hence the angle ADC (the difference of the angles ODC and 
ODA) is equal to the angle DAE (the difference of the angles OAE 
and OAD)? 

E. I suppose I must admit that. 

S. But is not the angle ADC equal to the angle DAB, both 
being right angles? 
E. I cannot deny it. 


S. Therefore the angle DAB is equal to the angle DAE, or the 
part is equal to the whole *? 

E. It certainly appears so. 

S. So that at least one of your axioms is not true? 

E. That, you have demonstrated. 

S. You will admit, then, Euclides, that some of the claims of 
mathematicians cannot be substantiated? 

E. You have clearly proved, Socrates, that mathematical truth 
is sometimes, if not always, a fiction. 1 

Socrates became the most formidable antagonist the Sophists 
ever encountered. While the Sophists denied the possibility of 
Truth, Socrates sought to make Truth evident, and he never 
neglected an opportunity of refuting them. In a manner at once 
playful, ironical, and often quibbling, he seemed to take a delight 
in covering them with ridicule. 2 

" Socrates, though esteemed and admired by a select band of 
adherents, incurred a large amount of general unpopularity. The 
public do not admit the claim of independent exercise for individual 
reason. In the natural process of growth in the human mind, belief 
does not follow proof, but springs up apart from and independent 
of it; an immature intelligence believes first and proves (if, indeed, 
it ever seeks proof) afterwards. The community, themselves deeply 
persuaded, will not hear with calmness the voice of a solitary 
reasoner, adverse to opinions established; nor do they like to be 
required to explain, analyse, and reconcile those opinions." 3 

Socrates was a reformer, and therefore had to combat with exist- 
ing prejudices. Pure as his intentions were, his actions and opinions 
were offensive. He incurred the hatred of party spirit, and by that 
hatred fell. At the age of seventy-two he had to appear before his 
judges to answer the charges of impiety and immorality. His con- 
demnation was a foregone conclusion. 4 

Socrates is usually credited with having produced a revolution 
in thought, in consequence of which he is regarded by some as the 
founder of Greek philosophy, properly so called. 

As Socrates reflected, he began more and more clearly to per- 
ceive that words, besides being the instruments by which we govern 
others, are means by which we may become acquainted with our- 

1 With apologies to Mr. Rouse Ball, and all other mathematicians. The fallacy ia, of 
course, obvious The interested reader may now turn to some of Plato's Dialogues, where ho 
will mid some much harder nuts to crack. See the next chapter. 

2 Biog. Hint, of Phil, pp. 138-140. * Grote, Plato, vol. i, p. 251. 
4 Of. Lewes and Uarnack. 


selves. In trying really to understand a word, to ascertain the 
precise meaning which he himself gave it, he found that he gained 
more insight into his own ignorance, and at the same time that he 
acquired more real knowledge, than by all other studies together. 
He therefore decided that he must lead his disciples to inquire what 
they actually meant by the words of the propositions they were 
using, and no time could possibly be wasted which was honestly 
spent in such labour. 

No doubt an opponent who had adopted a certain proposition 
and was provided with abundance of arguments in defence of it, 
would be irritated and vexed beyond measure by finding himself 
not fairly encountered upon those arguments, but led back into a 
question which he had assumed, forced to give account of a word 
which he fancied everyone was agreed upon, and not permitted 
after all to bring any of his own resources into play. It was most 
perplexing for a disciple who had come expecting that a certain 
doctrine would be either established or refuted, to find that he got 
no decision either way, and moreover that he had been talking all 
his life in a language which he did not understand, and using words 
as if they were algebraic characters. 1 

The aim and purpose of Socrates was confessedly to withdraw 
the mind from its contemplations of the phenomena of nature and 
to fix it on its own phenomena. He sought truth by looking in- 
wards, not outwards. His main instruments were Definitions. 2 By 
Definitions he separated the particular thought he wished to express 
from the myriad of other thoughts which clouded it. 

Socrates did not occupy himself with any particular branch of 
Science, but directed his attention to Science in general, to method. 
"Man is the measure of all things," said Protagoras; "and as men 
differ there can be no absolute Truth." "Man is the measure of all 
things," replied Socrates; "but descend deeper into his personality, 
and you will find that underneath all varieties, there is a ground 
of steady Truth. Men differ, but men also agree; they differ as to 
what is fleeting; they agree as to what is eternal. Difference is 
the region of opinion; agreement is the region of Truth: let us 
endeavour to penetrate that region." 

Socrates did not invent systems but only a method. He believed 
that in each man lay the germs of wisdom. He believed that " no 
science could be taught but only drawn out". "To borrow the ideas 

i Maurice, Moral and Metaphysical Philosophy, vol. i, pp. 126-7. 
Cf. Aristotle, Met. xiii, c. 4 ; and G. H. Lewes, op. cit. p. 162. 


of another was not to learn; to guide oneself by the judgment of 
another was blindness." Each man must conquer truth for himself, 
by rigid struggle with himself. And this is Socrates 1 great lesson 
for the teacher. It is not what the teacher does for the pupil, but 
what the pupil does for himself, that matters. 

Socrates 7 method, which constitutes his real philosophical impor- 
tance, has long since been discarded. Science was bound to discard 
it. Distinctions in words were mistaken by Socrates for distinctions 
in things. The nature of a thing can never be adequately exhibited 
in a Definition. We must go to the thing itself. This Socrates 
failed to do. And this the modern metaphysician also sometimes 
fails to do. 1 


(427-347 B.C.) 

i. Investigator or Dogmatist? 

From the age of twenty to the age of thirty, Plato was the 
devoted pupil and friend of Socrates. The discourses of such a 
master naturally gave the pupil's studies a definite direction, and 
determined the course of his after-life. From him Plato learned to 
understand himself, and thence to understand his predecessors and 
contemporaries. So completely, in fact, has Plato identified himsell 
with his master that it is difficult to discover with any certainty the 
events and circumstances of his own life. 2 

We sometimes hear Plato described as the great Idealist. He 
was, however, anything but an Idealist, as that phrase is usually 
understood. He was a great dialectician ; he was a severe and 
abstract thinker; his metaphysics were of the most subtle kind; 
and his morals and politics were hard and uncompromising to the 
last degree. Plato had learned to look upon human passion almost 
as a disease, and human pleasure as a frivolity: the only thing 
worth living for was the truth. His opposition to poets was deep 
and constant, for he saw in them an indifference to truth, and a 

i Cf. Lewes, Bwg. Hist, qf Phil., pp. 162-64. 

Cf. Maurice, Moral and Metavh. PhU. t vol. i, pp. 138-9; and Diog. Laer., lib. Ill, c. I, s. 7, 


preference for the arts of expression; poetry was therefore a dan- 
gerous rival to Philosophy. 1 

Plato is not to be measured, says Jowett, by the standard of 
any philosophical system. "He is the maker of ideas, satisfying 
the wants of his own age, providing the instruments of thought 
for future generations. He is no dreamer, but a great philosophical 
genius struggling with the unequal conditions of light and know- 
ledge under which he is living. His truth may not be our truth, 
and nevertheless may have an extraordinary value and interest for 
us." 2 

There is a common spirit in the writings of Plato, but not a 
unity of design. The hypothesis of a general plan worked out is 
an after-thought of the critics, who have attributed a system to 
writings belonging to an age when system had not as yet taken 
possession of Philosophy. 3 It is, indeed, questionable whether Plato 
ever attempted to elaborate a consistent doctrine, and thus to cull 
passages here and there from his writings with the object of making 
up a doctrine must inevitably lead to error. Like Socrates, Plato 
occupied himself with method, rather than with results. Like 
Socrates, he devoted his life to the search for Truth. 4 

We saw in the last chapter that, as a teacher, Plato adopted 
the method of his master, and that he not only cast his writings 
in dialogue form, the better to suit the method, but invested 
the Dialogues with a peculiar authority by introducing into them 
Socrates himself. It is characteristic of the Dialogues that the 
notion of authority, instead of being invoked and worked up, as is 
generally done in Philosophy, is formally disavowed, and practically 
set aside. "I have not made up my mind; I give you the reasons 
for and against; you must decide for yourself." And again: " Why 
are you so curious to know what / myself have determined on the 
point? Here are the reasons pro and con; weigh the one against 
the other, and then judge for yourself." 5 

Some critics of antiquity regard Plato as essentially a Sceptic, 6 
that is, a Searcher or Investigator, not reaching any assured or 
proved result. They deny to him the character of a dogmatist; 
they maintain that he neither established nor enforced any affirma- 
tive doctrine. This latter statement is, however, carried too far. 
Plato is sceptical in some Dialogues, dogmatic in others, though 

i Cf. Lewes, Bwg. Hist, of PhU. t pp 185-92. 2 Preface to Plato. 8 ft. 

* Cf. Lewes, op. dt. p. 201. Cf. Grote, Plato, i, p. 289; and Prolog., 314 B. 

6 Not to be confused with the sceptic in the sense of an unbeliever. 


the sceptical Dialogues (Dialogues of search or investigation) are 
more numerous than the dogmatic (Dialogues of exposition), as 
they are also, speaking generally, more animated and interesting. 1 

To teachers, the truths arrived at by Plato are of much less value 
than the mode in which the truth is sought. As Mill says, although 
Plato continually starts most original and valuable ideas, it is seldom 
that these, when they relate to results of inquiry, are stated with an 
air of conviction, as if they amounted to fixed opinions. But when 
the topic under consideration is the proper mode of philosophizing, 
then the views inculcated are definite and consistent and always the 
same. The inference seems to be that, in regard to the investigation 
of Truth, Plato had not only satisfied himself that his precedessors 
were in error, and how, but had also adopted definite views of his 
own; while on all or most other subjects he contented himself with 
confuting the absurdities of others, pointing out the proper course 
for inquiry and the spirit in which it should be conducted, and 
throwing out a variety of ideas of his own. 2 

2. Plato's Doctrine of Ideas: Elementary Notions 

Plato was convinced of the fundamental necessity for an un- 
tiring investigation into the nature of general terms. 3 

Long before Plato's time, meditative men had perceived that 
knowledge derived from the senses can only bo knowledge of 
appearances, of phenomena. Now phenomena, Plato said, are, 
by their very nature, fleeting and transitory; they are not true 
existences, they are only images of true existences. We must there- 
fore examine and classify them; discover what qualities they have 
in common; discover that which is invariable and necessary amidst 
all that is variable and contingent. Discover the One in the Many, 
and we have penetrated the secret of true existences. 4 

Everyone will admit that we can form some kind of conception 6 
of a genus, that we do think of and reason about " man " quite 
independently of Smith and Brown. If we have such a conception, 
whence did we derive it? Our experience has only been with the 
Smiths and Browns; we have known only men. Our senses tell us 
nothing of man. Individual objects give only individual knowledge. 
According to the Realists, our knowledge of man is derived from 

> Grote, Plato, i, p. 212. 

2 Cf. Lewes, op. cit. p. 215 8 Or, as the Schoolmen would say, abstract terms. 

* Cl. Lewes, p. 207 ; and Philebus, 233-6. Cf. ch. ii, 4. 


a different source altogether, namely, from the mind. Now man is 
a general term, and general terms, Plato said, stand for the only 
real existences. The separate existences denoted by general terms 
he called Ideas. 1 

The Realists found the One in the Many, in other words, found 
certain characteristics common to all men, and not only common 
to them but necessary in their being men; they abstracted these 
general characteristics from the particular accidents of the indivi- 
dual men, and out of these characteristics made what they called 
Universals. These Universals existed per se. They were more than 
conceptions of the mind; they were, so to speak, projected out of 
the mind and so became images or entities which could be looked 
upon; perceptions of them were formed in the same manner as 
perceptions of things. If, then, the conception of genera be thus 
rendered objective transformed into perceptions of real existing 
things we have, as before, Plato's Ideas. 2 

These Ideas Plato maintained to be the only things that had 
a real existence; they were the noumena* of which all individual 
things were the phenomena. The Platonic Idea is thus a kind of 
"Substantial Form". 4 

Practically, the whole doctrine is comprised in Plato's answer 
to Diogenes, who thought he demolished the theory of Ideas by 
exclaiming, " I see a table and a cup but I see no Idea of a table or 
a cup". Plato replied, "Because you see with your eyes and not 
with your Reason ". 6 

Thus, according to Plato, the phenomena which constitute what 
we perceive by means of our senses are but the participations of 
matter in "Ideas". In other words, Ideas are the "Forms" of 
which material things are the copies; they are the noumena, of which 
all that we perceive are the Appearances (phenomena). But we must 
not suppose these copies to be exact; they not only do not partici- 
pate in the nature of their models; they do not even represent them, 
otherwise than in a superficial manner. 6 

1 This term Idea must not be confused with the term in the modern popular sense, 
a Cf. Lewes, op. cit. pp. 209-11. Cf. chap iii, 2. < Cf. Lewes, p. 209. 

* Cf. Lewes, p. 211 ; and Bosauquet, Companion to Plato's Republic^ p. 16. 
Cf. Lewes, p. 211. 


3. Elusive and Unacceptable Aspects of the Doctrine 

Walter Pater reminds us that the expression " theory of ideas " 
is due to Plato's commentators rather than to himself, and he 
considers that Platonism (as he calls it) is not so much a formal 
theory or body of theories as a tendency or group of tendencies, 
a tendency to think or feel and to speak about certain things in a 
particular way. It is a fashion of regarding and speaking of all 
those terms or notions which represent under general forms the 
particular presentations of our individual experience ; or to use 
Plato's own frequent expression, which reduces "the Many to the 
One". 1 

The actual relationship of these general terms and abstract 
notions to the individual, the unit, the particulars they include, is 
the great problem. Realism supposes the general name animal, for 
instance, to be not a mere name, as with the nominalists, nor a 
mere subjective thought, as with the conceptualists, but to be res, 
a thing-in-itself, independent of the particular instances which come 
into and pass out of it, as also of the particular mind which enter- 
tains it. 2 

A modernized view of the doctrine might be obtained, perhaps, 
by imagining, with Pater, the existence of a kind of permanent 
common sense, independent, indeed, of each one of us, but with 
which we are, each one of us, in communication. It is in this that 
those general ideas really reside. Abstract or common notions 
come to the individual mind through language, through general 
names, into which one's individual experience, little by little, drop 
by drop, conveys their full meaning or content; and by the instru- 
mentality of such terms and notions, thus locating the particular in 
the general, and mediating between our individual experience and 
the common experience of our kind, we come to understand each 
other and assist each other's thoughts, as in a common mental 
atmosphere, an " intellectual world ", as Plato calls it. 3 

Plato's Realism, however, seems, at times, to pass into such an 
extreme form that it becomes absolutely unacceptable. "From the 
simple and easily intelligible sort of Realism, seeking in ideas only 
a serviceable instrument for the distinguishing of what is essential 
from what is unessential in the actual things about him, Plato 
passes by successive stages, which we should try to keep distinct as 
we read him, to what may be rightly called a 'transcendental', what 

i See Pater's Plato, p. 136. a 16. t'6. 


to many minds has seemed a fantastic and unintelligible habit of 
thought; those abstractions, indeed, seem to become for him not 
merely substantial things-in-themselves, but little short of living 
persons, to be known as persons are made known to each other 
by a system of affinities, these persons constituting together that 
common intellectual world, a sort of divine family or hierarchy, 
with which the mind of the individual, so far as it is reasonable 
or really knows, is in communion or correspondence. And here 
certainly is a theory about which the difficulties are many." 1 

Plato's Ideas as transcendental existences have been compared 
to objects of contemplation in painting, music, poetry, sculpture, 
where the representations of art, framed apart by themselves, induce 
in the spectator that dream-image of reverie, which was previously 
the ideal-pattern of the artist himself. Plato, with his extraordinary 
powers of visualization, seemed to individualize his abstract con- 
cepts and to give them a fantastical embodiment. 2 

In its essence, the doctrine of ideas may be regarded as an 
attempt to solve a problem which in all ages has forced itself upon 
the notice of thoughtful men, How can certain and permanent 
knowledge be possible for man, since all his knowledge must be 
derived from transient and fluctuating sensations? And the doc- 
trine answers the question thus, that certain and permanent 
knowledge is not derived from Sensations but from Ideas? To 
what extent the doctrine is acceptable by other Philosophers, we 
shall see later. 

4. Plato's Method not really Scientific 

The reader of Plato may at first fail to discover any evidence 
of a mastery of what we now call scientific method, but a careful 
search will reveal a very considerable insight into such method. 
Mill found the materials of his experimental methods in Herschel's 
Natural Philosophy, but at least the germs of these methods were 
created by Plato. For, sometimes, Plato's Idea is equivalent to 
what the man of science calls " Cause", " Explanation'', "Law", and 
the like. But in addition to such Ideas as these Causes, Explana- 
tions, or Laws, to be discovered by Science Plato deals with " Ideas 
which are not to be discovered but are in our possession to start 
with", the native "Categories of the Mind", which are employed 

i Cf. Pater, pp. 136-9. 2 Classical Keview, Aug. 1910. 

* Whewell's Philosophy of the Inductive Sciences, p. 12. 


in the process of discovering the Ideas before mentioned. These 
native Categories, supposed to be apprehended by the Mind itself, 
are given as " Unity, Plurality, Identity, Difference, Similarity, 
Dissimilarity, Rest, Motion". It is by scrutinizing these in the 
data supplied by our senses that we discover the particular cause, 
or explanation, or law, belonging to the data, it being always 
assumed that the data are manifestations of real existences. "It 
is in much the same way as that suggested by Plato here that 
modern science employs its methods of Agreement, Difference, and 
Concomitant Variations, to explain the data of sense, to discover 
the Laws of Nature governing them." 1 

In one sense, then, the doctrine of Ideas may be regarded as a 
method, the method of discovering special Ideas or Laws of Nature, 
discovered always by means of the application, to the phenomena 
presented, of certain general Ideas, Unity, Plurality, Identity, 
Difference, Similarity, &c. But the important point is that ex- 
perience is apprehended in a scientific way only when the Categories 
(Unity, Plurality, &c.) are made clearly explicit, as they are in 
what we now speak of as the method of Agreement, the method 
of Difference, &c. These formal realizations of his Categories Plato 
is evidently feeling his way to and Aristotle actually reached. 2 

But the statement that the Categories are " apprehended by the 
mind itself" opens up a very large question; the man of science is 
Always suspicious of intuitive methods. The Science teacher must 
certainly not assume that the Categories are clearly " apprehended" 
by the minds of his pupils. 8 

Though Plato saw that scientific truths of great generality 
might be obtained, he overlooked the necessity of a gradual and 
successive advance from the less general to the more general. Whew- 
ell at first ascribed this to Plato's " dimness of vision", but after- 
wards acknowledged that the phrase was not very appropriate, 
since no acuteness of vision could have enabled Plato to see that 
gradual generalization in Science of which, as yet, no example had 
appeared. 4 But Plato did certainly fail to see the extent to which 
experience and observation are the basis of all our knowledge of the 
universe. The ascent from the particular to the general must be 
gradual, and each step upwards requires time and labour, and a 
patient examination of actual facts. But Plato, by a pure effort of 

1 See J. A. Stewart's Plato's Doctrine of Ideas, pp. 119-23; and Mill's Logic. 

* Ct Stewart, %&.; and Aristotle, Topics, ii, 10 and 11. See the chapter on Locke. 

Cf. Whewell's Philosophy of Discovery, p. 13. 

(0*16) 7 


thought, always seized upon the highest generality at once, and 
afterwards filled in all the intermediate steps between that and 
the special instances. This was his cardinal error. 1 

5. Plato's Works (a) The Republic 

Brief reference may now be made to such of Plato's works 2 as 
most nearly concern those who are interested in scientific method. 

However great may have been Plato's speculative interest, it 
was his practical enthusiasm as a reformer that lay deepest within 
him. He imagined a form of society in which the ideal man might 
find himself at home, and so the Republic was constructed. 

Although the Republic is rather long, and sometimes a little 
tedious, it will repay careful reading. But no part of it is likely to 
be of greater interest to teachers than Book VII, wherein is con- 
tained the famous Allegory of the Cave. Here Plato brings out 
clearly the false sense of reality which uncritical associations acquire 
for a mind which has never been led to feel their inconsistency: 
and he shows how strong is the reciprocal repulsion between the 
man who himself gets to the heart of things and the mob who are 
contented with traditional opinion and conventional views. 3 

5. (V) The Timseus 

The Timwus has been described as "an outbuilding of the great 
fabric of original Platonism". Of all the writings of Plato, it is 
the most obscure, and the obscurity is due to Plato's scanty know- 
ledge of Physical Science. Physical Science at that time was in 
its infancy, yet Plato attempted to give a detailed account of the 
structure and nature of the universe. 

"The time had not yet arrived", says Jowett, "for the slower 
and surer path of the modern inductive philosophy. Although 
the ancient philosophers no doubt often fell into strange and fanci- 
ful errors, it remains to be shown that they could have done more 
in their age and country, or that the contributions which they 

i Whewell, Phil, of Disc , pp. 9-17. 

ajowett's translation is considered the best; and his introductions to the different 
Dialogues should be read again and again. 

* Cf. Lewis Campbell on "Plato" in Ency. Brit.\ Maurice, Moral and Metaph. Phil, vol. i, 
p. 166; Rejjublie by Davis and Vaughan, pp 235-8; Jowett's translation of and introduction 
to the Republic \ Nettleship's Lectures on Plato* * Republic, p. 261, <fcc.; Bosanquet's Com- 
panions to Plato's Republic, p. 263, <fec. ; also G rote's Plato. 


made to the sciences with which they were acquainted are not as 
great upon the whole as those made by their successors/ 1 

No doubt Plato intended to include in the Timceus such know- 
ledge as he had then acquired concerning the various parts of the 
universe, and he gives us an extensive scheme of mathematical and 
physical doctrines. The Dialogue treats, in fact, not only con- 
cerning the laws of " harmonical sounds", of " visual appearances", 
and of the motions of planets and stars, but also concerning heat 
and light; water and ice; iron, rust, gold, gems, and other natural 
objects; concerning odours, tastes, hearing, sight, and the powers 
of the senses generally; and concerning practically all the obvious 
points of Physiology. 2 Now while those of the doctrines which 
depend upon geometrical and arithmetical relations are either 
portions or preludes of those branches of knowledge which have 
since assumed a mathematical form for the expression of truth, the 
opinions on such subjects as Physics, Chemistry, and Physiology 
will bear hardly a moment's examination. Plato's notions of 
Physiology are of the most fantastic kind. It seems almost in- 
credible that such an explanation as that given, for example, of 
the causes of respiration could have emanated from such a mind 
as Plato's. 

Here and there may be found elements of truth in his hypo- 
theses, but these must be ascribed to his previous studies in other 
directions. His hypotheses as a whole involved such tremendous 
assumptions that the necessary conclusions which logically followed 
from them did not and could not possibly square with the facts. 
Instead of accumulating facts first and then framing hypotheses to 
cover the facts, the method of modern investigation Plato ignored 
the facts and started off with the hypotheses. Such a method could 
not but end in failure. 8 

5. (c) The Thesetetus 

The Thecftetus is an inquiry into the nature of knowledge, and 
the greater part of the Dialogue is devoted to setting up and throw- 
ing down definitions of Science and Knowledge. 4 It is remarkable, 
how, in this Dialogue, Plato holds the balance between experience, 

1 Jowctt's Introduction to the Tima>m. 

2 Cf. Whewell's History of the Inductive Sciences, vol. i, p. 849. 
8 Cf. Maurice, Moml and Mctaph. Phil , vol. i, p. 175. 

4 Cf. Jowett's Introduction to Thccetetus: and Whewell's Hist, of the Indue. Sci. t vol. i 
p. 349. 


imagination, and reflection. He seems almost to have made "a 
compact with himself to abstain rigidly from snatching at the 
golden fruit that had so often eluded his grasp, and to content 
himself with laboriously cutting steps towards the summit that was 
still unsealed ". 

The part played by the mind and the part played by the senses 
in the acquisition of knowledge are minutely examined, but the 
light which Plato throws on the subject is indirect, and we only 
catch occasional glimpses of the probable truth. The theory that 
" knowledge is sense-perception" seems to be regarded as the anti- 
thesis of that which derives knowledge from the mind, but Socrates 
is designedly held back from giving us any final positive solution of 
the problem. The saying of Theretetus that "knowledge is sense- 
perception " is probably responsible for much of the misunder- 
standing of the empiricist position. The modern term " experience" 
while implying a point of departure in sense, and a return to sense, 
also includes all the processes of reasoning and imagination whict 
have intervened. But the man of science is under no illusion that 
if he looks into the mind he will find there accurate records of 
perfect knowledge. We ought, in fact, to be on our guard against 
using the phrase " looking into the mind". It is a figure of speech, 
very misleading in character. It would be more correct to say 
looking "out of" the mind. Recognition of anything within us is 
of the most shadowy and fleeting character. We must not be 
misled by the terminology of a worn-out introspective Psychology. 1 

5. (d) The Parmenides 

In the Parmenides, Plato assails his own theory of Ideas, and 
does this so vigorously that many of his interpreters have con- 
sidered the Dialogue to have been written by another hand. 
Whewell is amongst the number. The arguments advanced in 
the Dialogue are nearly, if not quite, those of Aristotle; they are 
the objections which naturally occur to a modern student of Philos- 
ophy. But Jowett is undoubtedly right when he says that the 
objection to Plato as the writer is really fanciful and rests on the 

i See Thecetetus, especiaMy 184-6, and Jowett's Introduction (Jowett, vol. tv). There 
is, of course, no doubt whate^ er about Plato's general views. Throughout his works he draws 
a strong distinction between those aspects of things which are sensibly perceived, and that 
which is not seen and heard but thought and understood, and he regards the latter as more 
trustworthy than the former. His whole tendency is to exalt Ideas above Facts, to find a 
Reality which is more real than phenomena, to take hold of a permanent truth which is 
more true than the truth of observation. (Cf. Whewell's Phil, of Disc., p. 424.) 


assumption that the doctrine of ideas was held by Plato throughout 
his life in the same form. The truth is that the Platonic ideas were 
in constant growth and transmutation. 1 

Grote is of the same opinion. It is true, as Grote says, that 
in the case of most philosophers we expect to find a preconceived 
system and a scheme of conclusions to which everything is made 
subservient. But Plato's search or debate has a greater importance 
in his eyes than the conclusion. He never hesitates to set forth 
what can be said against a given conclusion, even though not pre- 
pared to establish anything in its place. 2 

The discussion of Socrates and Parmenides forms one of the 
most remarkable passages in Plato. Few writers have ever been 
able to anticipate "the criticism of the morrow" on their favourite 
notions. But Plato may here be said to anticipate the judgment, 
not only of the morrow but of all after-ages, on the Platonic ideas. 3 
Probably no one but Plato ever ventured on such an experiment 
the experiment of showing that his own fundamental principle 
was practically untenable. 4 He deliberately sets forth everything 
that could possibly be said against his own conclusions, fully recog- 
nizing that reasoned truth never rests upon any better title than the 
superiority of the case made out on its behalf over the case that 
may be made out against it. 

6. How far can we follow Plato's Method? 

Plato lived in an age when little was known of Science, and still 
less of the method of investigating it. He thus had to devise 
methods for himself, and so it came about that he underestimated 
the value of observation and experiment, though, temperamentally, 
perhaps, he was averse from the laborious work of accumulating 
details. When in the Timceus he constructed the Universe, he did 
not begin with facts and then construct a hypothesis; he began 
with a hypothesis; his Universe was the outcome of a pure effort 
of thought. Such a method could not be expected to produce 
anything but an absurd result. 

Socrates is represented in The Clouds 5 as hoisted up in a basket 
gazing at the sky, and, no doubt, Plato is thinking of this when he 
speaks of the absurdity of supposing that star-gazing will reveal the 

1 Jowett'a Introduction to Panne nides. * Qrote's Plato. ' Jowett, ib. 

* See Maurice, Moral and Metaph. Phil , vol. i, p. 155. 
6 Aristophanes, Clouds, 171 et seq. 


laws of the stars. Now suppose an untrained observer watches the 
course of the sun across the sky. What is the difference between the 
result of his observation and, for instance, that of Kepler? Assuredly 
the simple observation that the sun occupies different places in 
the sky at different times of the day is a true observation. But 
Kepler's interpretation of the observation is very different from 
that of the untrained observer, for he puts his observation with a 
large number of others previously made. The untrained observer 
sees the sun sweep daily across the sky from East to West, and 
constructs the hypothesis that the sun goes round the earth once 
in twenty-four hours. His hypothesis covers the facts, and is 
absolutely correct as the facts go. But Kepler's multitude of 
additional facts causes him to construct a totally different hypo- 
thesis, and the untrained observer's hypothesis is seen to be wrong. 
No one imagines that Socrates in his basket will ever get at the 
truths of astronomy by simple looking ; but a certain type of meta- 
physician l denies the necessity of looking at all. True, the mind 
interprets; but the facts must first be gathered to be interpreted. 
The interpretation is then checked by new facts, and so the simpler 
generalization is gradually included in a generalization of a higher 

But although Plato as a scientific investigator is not to be 
imitated, there are certain aspects of his method of investigation 
that no teacher who desires to work on scientific lines can afford 
to ignore. 

In the first place, he insists, as we have already seen, upon the 
fundamental importance of understanding the exact significance of 
all the general and abstract terms we use. Such terms as animal 
and plant, wisdom and justice, suggest different notions to different 
minds, and the notions are almost always vague and indefinite. 
The important thing is to examine such terms, and to get clear 
and definite notions concerning them. 

In the second place, Plato urges attention to the so-called 
"categories". How we all assume that a child knows exactly 
what we mean by such a term as " like ". But do we know pre- 
cisely what it signifies? One of the axioms of Formal Logic is, 
"whatever is true of a thing is true of its like"; but what does 

i We all know, for example, the young man who bubbles over with his first metaphysical 
enthusiasm, talking about analysis and synthesis to his father and mother and the neighbours, 
and hardly even sparing the dog. He despises facts and constructs his phantom systems out 
of nothing. Cf. Jowett's Introduction to Philebus; and Nettleship'a Lectures on the Republic, 
pp. 270-6. 


"like" mean? Are we supposed to refer to things which appear 
alike, or which really are alike? 

Thirdly, Plato constantly warns us against seeing things from 
only one point of view, to be on our guard against superficial im- 
pressions, and never to accept an opinion merely because it happens 
to be held by many people in common. The evidence on which 
such opinions are based must always be carefully scrutinized. 

Finally, Plato tells us never to fear being charged with incon- 
sistency. He was a searcher after truth. He knew that his work 
was imperfect, and he never feared to make corrections when correc- 
tions were required. Additional experience often rendered neces- 
sary some modification of ideas already formulated, and Plato never 
hesitated to make the change. We English people are much too 
prone to "stick to our opinions", and to ignore inconvenient facts. 
Let Plato teach us the necessary lesson. 1 


(About 384-322 B.C.) 

i. Aristotle's Wide Knowledge 

Aristotle's father was a physician, and claimed descent trom the 
gens of the Asclepiads or supposed descendants of ^Esculapius; and 
no doubt the scientific tendencies of Aristotle's mind are in some 
measure to be attributed to early environment and family tradition. 
Amongst the Asclepiads there seems to have been a certain amount 
of training in observation and in dissection, imparted traditionally 
from father to son, thus serving as preparation for medical practice. 
Probably in this way Aristotle acquired that liking for physiological 
study which so many of his works indicate, but it is doubtful if he 
ever dissected the human subject, as Greek prejudices would hardly 
have tolerated such a course. 

i Besides the Republic, Tiinatus, Thecetetns, and Parnienides, the reader will find much 
to interest him in Protagoras and Phcedrus. 

The teacher should beware of introducing the Socratlc method in the classroom. The 
great object of Socrates was to get his victims into a corner. The reasoning was always his; 
their business was merely to assent to the propositions which he formulated. His was the 
active mind ; theirs were passive. 


Aristotle was a pupil of Plato's, but probably owing to his 
marked opposition to many of Plato's views, he was not appointed 
head of the school when his master died. 1 

In the history of European thought, down to the period of the 
revival of letters, the name of Aristotle was supreme. Aristotle not 
only treated of almost every subject which came within the range 
of ancient knowledge, but also initiated many new branches of 
inquiry dependent on observation and induction. He not only 
represented in himself the culmination of Greek speculative philos- 
ophy, but was also, as far as possible, the forerunner of modern 
Science. 2 

It is characteristic of Aristotle that before laying down his own 
views on any subject, he examines with almost minute care the 
views of his predecessors, and it not infrequently happens that his 
own opinions seem rather brought out in his criticisms than dog- 
matically affirmed. 3 But the first thing that must strike anyone 
who examines his writings is the unparalleled extent of his know- 
ledge. In all branches of Science then cultivated he was proficient. 
He wrote on Politics, giving the outline of no less than two hundred 
and fifty Constitutions. His treatise on Metaphysics would alone 
have made him famous. His Ethics, Rhetoric, and Logic are still 
held by many to be authoritative and unsurpassed. 4 

2. His Rhetoric 

Perhaps no work of Aristotle's is better known than his Rhetoric- 
Plato had regarded Rhetoric as the mere embodiment of the tricks 
of procedure used by the Sophists, and he refused to countenance 
the study of it. But Aristotle, "who often exhibits less moral 
earnestness but greater intellectual breadth than Plato", considered 
it necessary to cultivate all intellectual fields, this included. He 
had abundance of materials available, illustrating in the greatest 
variety of forms how speakers had been able to move their audiences, 
and from this mass of materials he decided to generalize. " Let us 
deduce rules," he said, "by applying which a speaker shall always 

* See Galen, De Anatom. Admin., ii, 1; and for early life see G rote's Aristotle and 
Maurice's Moral and Metaph. Phil.; also article "Aristotle" In Eney. Brit. 

Cf. Ency. Brit, " Aristotle". 3 Cf. Lewes, Biog. Hist, qf Phil., p. 237. 

*Cf. Lewes, Aristotle, p. 20. The catalogue of Diog. Laer. contains a list of 148 works, 
hardly one of which seems to correspond with any of the 40 works which are now ascribed to 
Aristotle and with which we are acquainted. But only about one -half of the latter number 
appear to be genuine works of Aristotle. There is no doubt that a very large number of his 
works are loat. 


be able to persuade the reason or to move the feelings, and when 
we have got our rules we will construct a true art." There is no 
doubt that "Aristotle's principles of Rhetoric are the results of 
extensive original induction". 1 It was, clearly, Aristotle's intention 
to systematize the whole subject on a scientific plan. 

3. His Logical Treatises 

Aristotle's Logical treatises were placed by his earliest known 
editor 2 at the commencement of the collected works, it being thought 
that these treatises, taken collectively, were not so much a part of 
Philosophy as an Organon* or instrument, the use of which must 
be acquired by the reader before he became competent to grasp 
or comprehend Philosophy ; they formed an exposition of method 
rather than of doctrine. 

Aristotle tells us that the theory of the syllogism was his own 
work altogether and from the beginning; that no one had ever 
attempted it before, that he therefore found no basis to work upon ; 
and was thus obliged to elaborate, by long and laborious preparation, 
his own theory from the very rudiments. 4 

It was undoubtedly Aristotle who first told the world how, in 
deduction, the mind proceeds from some universal proposition. A 
process of deductive reasoning having been once thus recognized, 
it was obviously an advantage that the laws should be clearly 
ascertained, if only in order that any flaw in the process as prac- 

i Edward Coppleston, Reply (Oxford, 1810). Aristotle's Rhetoric is worth reading for its 
own sake. In it are catalogued all the ordinary tricks of the platform speaker, which pass 
under the name of "Rhetorical devices". Aristotle openly advocates dishonest methods. 
See, for example, Bishop Welldon's translation, pp. 65, 68, 286. See also Archbishop Whate- 
ley's Introduction to his own Rhetoric, and his excuse there given for writing such a volume. 

a Andronicm 

3 The Organvn includes six different treatises: (1) "The Categories"; (2) "On Interpreta- 
tion"; (S)" The Prior Analytics"; (4) "The Posterior Analytics"; (6) " The Topics "; <e) " On 
Sophistical Refutations ". The first two deal with Propositions ; the " Prior Analytics" and 
41 Posterior Analytics" with the Syllogism and with Demonstration; the "Topics" give rules 
of debate, it being supposed that the object of the debates is not to prove truth or disprove 
falsehood, but to secure victory. The sixth treatise deals with Fallacies. 

The second treatise (" On Interpretation ") is the source of much of the matter of the 
elementary Logic of modern times, and the substance of the "Prior Analytics" has become 
the common property of all modern books on deductive Logic. Hardly anything has ever 
been added to or detracted from what Aristotle wrote about the Syllogism. " Both Kant and 
Hegel acknowledge that from the time of Aristotle to their own age, Logic had made no 
progress. The fourth figure was added to the Syllogism, uselessly; and Sir William Hamilton 
introduced his quantification of the predicate: voild tout." See Grote's AristotU, iii, iv, 
pp. 87, 141, <fec.; Hamilton's Logic, vol. iii, pp. 87-91; also Ency. Brit. ("Aristotle"), and Stahr. 

* Of. with the Rhetoric. See Sophis. Xefut. % pp. 183-4. Sir W. Hamilton points out that 
the Principles of Contradiction and Excluded Middle can be traced back to Plato (Logic, Hi, 
pp. 87-91). 


tised might be instantly detected. But no one would have repudi- 
ated more strongly than Aristotle himself that the formula of the 
syllogism can be used to test or explain anything beyond the process 
of reasoning from certain premisses possessed or assumed, and he is 
never tired of telling us that the only means of obtaining premisses 
is by experience and observation of facts. " When the facts of each 
branch of science or art are brought together, it will be the province 
of the logician to set out the demonstration in a manner clear and 
fit for use". 1 

Now those who attempt to keep Logic purely formal explain 
that when they speak of a piece of reasoning as being " formally 
valid", they mean that its validity is determined solely by its form, 
and is in no way dependent upon the particular subject-matter to 
which it relates. They regard the process of reasoning as something 
distinct from the subject-matter about which it is employed, and the 
errors of reasoning which they contemplate are those only which 
occur in the process so conceived. 2 But the mere process is a com- 
paratively simple thing; it is the determination of the precise signifi- 
cance of the subject-matter, the exact meaning of all our terms and 
of the statements containing them, the precise correspondence of 
what we say with what we mean, and the unquestioned truth of 
the assertions contained in our propositions: these are the real diffi- 
culties. These difficulties once overcome, Aristotle's rules for the 
subsequent process of reasoning are almost as perfect as they can 
be made. But these rules form little more than an elaborate piece 
of mechanism, so much so in fact that a modern logician 3 has actually 
constructed a logical machine by means of which it may be shown 
conclusively how entirely mechanical the process of deductive reason- 
ing really is. But the value of formal logic is a subject which must 
be left for consideration in a future chapter. 4 

1 Analy. Prior., i, 30-3; and cf. Maurice, Mor. and Met. Phil, vol. 1, p. 189 

2 Sidgwick, Use of Words in Reasoning, p. 9. 
8 Jevons. See his Principles of Science. 

4 Aristotle regarded the Sophists as mere charlatans, and he collected, classified, and 
exposed their fallacies. So exhaustive is he that the human mind has hardly invented any 
fallacious argument since, which may not be brought under some head of the Sophistical 
Refutations. The reader should go through this treatise (which is not a large one) and then 
through the corresponding section in some modern textbook on Logic. Here is a sample 
from Aristotle's collection of fallacies, taken at random: "If the knowledge of a thing is 
good, it is a good thing to learn ; the knowledge of evil is good, therefore evil is a good thing 
to learn ; but evil is evil and a thing to learn ; therefore it is an evil thing to learn ". 


4. "Fact" and "Theory". Aristotle's Notion of 


The part of Logic which most closely concerns scientific investi- 
gation is Induction, and we must now consider Aristotle's views on 
Induction and on Scientific Method generally. 

Aristotle taught that the very first essential of Science is to 
collect "facts": we must "first classify them, bring particular facts 
under general heads, and co-ordinate them into theories". 

But what are "Facts"? And are we justified in drawing a 
sharp distinction between a Fact and an Idea, or between Fact 
and Theory? The distinction seems to fade away on examination. 
Facts are commonly understood to relate exclusively to the objective 
world, to phenomena existing externally; Ideas, on the contrary, 
to consciousness, to conceptions we form of external things. But 
we cannot consistently maintain such distinctions. So far from any 
fact being the unadulterated image of its object, the conditions of 
our consciousness are necessarily mingled with it. An analysis 
shows in the simplest fact an inextricable blending of inference with 
sensation. A fact has been defined as a bundle of inferences tied 
together by one or more sensations. Take a case so simple as that 
of an apple on the table. 1 All that is here directly certified by 
consciousness is the sensation of a coloured surface; with this are 
linked certain ideas of roundness, sweetness, and fragrance, which 
were once sensations and are now. recalled by this of colour; and 
the whole group of actual and inferred sensations clusters into the 
fact which is expressed in "there is an apple' 1 . Yet any one of 
these inferences may be erroneous. The coloured object may be an 
imitation apple in wood or stone; the inference of roundness and 
solidity would then be correct, those of sweetness and fragrance 
erroneous: the statement of fact would be false. 2 

Clearly, then, the common distinction between Fact and Theory 3 
is misleading. For some purposes, perhaps, it would suffice to say 
that Fact is the equivalent of Description of the order of phenomena, 
and Theory the explanation of that order. But on examination we 
see that a correct explanation is only a fuller description. As I sit 
in my chair I hear a noise; this is a "fact". But I proceed at once 
to draw a number of inferences, to form a "theory": (1) that the 

1 Cf. ch. iii, 2. 2 Of. Lewes, Aristotle, p. 72. 

8 In this chapter the term "theory" is used in its looser and more popular sense. See 
ch. xjti, on Hypotheses. 


noise came from the next room; (2) that a picture has fallen down; 
(3) that a servant has dropped the picture. On proceeding to the 
next room I find that my inferences my "theory" are correct. 
But had I been in the room and seen the picture fall, the careless 
action of the servant would have become part of the "fact", part 
of the description; the completed fact contains the former theory. 
Of course my suggested theory or explanation might have proved 
incorrect; the falling of the picture might have been due, for 
instance, to the snapping of the supporting wire. Some day, Sir 
J. J. Thomson's interesting theory of the constitution of the atom 
may, conceivably, become a matter of actual observation, in which 
case what is now "theory" would become "fact". 

We seem, then, to have a succession of links in the chain. With 
some of these we are acquainted by the operation of our "senses", 
with others only by the reason; and the boundary line between 
Theory and Fact is sometimes hardly distinguishable. 1 

Science having collected and classified its facts, has to find a 
hypothesis to bind the facts together. But until the hypothesis is 
verified it is only a guess, and may turn out to be an absurd error 
instead of a great truth. Deductions drawn from unverified hypo- 
theses are necessarily always open to doubt. The great danger of 
accepting such deductions was entirely overlooked by Aristotle, 
whose blunders, in consequence, are often grotesque. 2 

Aristotle was intent on seeking scientific explanations of phe- 
nomena, though he lived at a time when such explanations were 
novelties; and to achieve this object he decided that the indispens- 
able thing to do first was to collect facts, and to arrange them and 
classify them. From classification he proceeded, by induction, tc 
generalizations, these being indispensable for furnishing the pre- 
misses necessary for deduction. In theory, then, he was wholly 

But in practice he was wrong. He was wrong because he quite 
misunderstood the nature of the process of Induction. In the first 
place, he neglected to suspect phenomena, or to suppose that they 
need sifting and probing if the facts they really denote are to be 
known; 8 and in the next place he always assumed as given,* the 
ideas which entered into his propositions, whereas the most im- 
portant feature in induction is the introduction of a new idea. That 

i Cf. Lewes, Aristotle, pp. 72-6. * ib. pp. 114-5. 

Cf. Maurice, Moral and Metaph. Phil, vol. i, p. 191. 

* Aristotle's Induction is that of "Simple Enumeration ". See ch. xv. 


peculiar sagacity in some men which seizes upon the conceptions 
by which the facts may be bound together seems to be hardly 
recognized by Aristotle. 1 In short, Aristotle did little towards 
elucidating the actual methods by which the mind legitimately 
arrives at general facts or laws of nature. 2 

It may seem somewhat remarkable that, while he so frequently 
proclaims the necessity of careful induction, he did not acquire a 
completer mastery of the principles underlying the actual process, 
especially as he bestowed such elaborate care upon the analysis of 
the process of deduction and upon the rules for its use. It is true 
that he attempted to resolve induction into a peculiar variety of the 
syllogism, but the scheme is hopelessly unpractical. He really 
made one half of Logic to look like the whole, and this dispropor- 
tionate treatment of the subject has been adopted and perpetuated 
by writers on formal logic almost to the present day. Many of our 
most important works on the subject treat Induction as if it were of 
no real consequence whatever. 

We must, however, remember that, in Aristotle's day, little was 
known of Science, and far too little experience had then been 
accumulated from which effective generalizations could be made. 
For, after all, when a new hypothesis is conceived, the conception 
depends very largely upon the stores of previous experience already 
in the mind. Further, Aristotle was of a naturally impatient 
nature; no doubt, too, he was often unable to garner all the facts 
he felt to be necessary. At all events he jumped to conclusions. 
Eager, as most men are, to solve the problems which present them- 
selves, he solved them a priori, he applied his syllogism before he 
had ascertained the certainty of his premisses. Instead of fusing 
together accumulated facts by means of verifiable hypotheses 
patiently thought out, he satisfied himself with vague and hastily- 
formed generalizations; and ho constantly allowed himself to be 
drawn away from considerations of objective fact to foolish specu- 
lations of a metaphysical character. 3 But at that time the verbal 
disputations of the Sophists had infected all learning, and it is pro- 
bably due to this rather than to any inherent intellectual short- 
comings in himself, that Aristotle was led too readily to accept 
vague and loose notions drawn from general and superficial obser- 
vation, instead of seeking carefully, in well-arranged and thoroughly 
considered instances, for the true laws of nature. 4 

1 Cf. Whewell, Phil, of Disc., p. 20. * cf. Sney. Brit., " Aristotle ". 

1 Cf. Lewes, Biog. Hist, qf Phi*., p. 240. * Cf. Herschel, Philosophy, p. 109. 


Yet Aristotle was so far consistent with his own doctrine of the 
derivation of knowledge from experience, that he made in almost 
every province of human thought a vast collection of special facts, 
and these collections are almost unrivalled oven to the present day. 
In Political Economy, for instance, where almost everything depends 
upon observation and extended experience, it would be difficult to 
find in later times any writer by whom Aristotle has been surpassed 
or equalled. 1 And in his Natural History we have not only an 
immense and varied collection of facts and observations, but a 
sagacity and acuteness in classification which it is impossible not to 
admire. On the other hand, in those departments of knowledge 
when to the facts we must, in order to obtain truth, add the right 
inductive Idea, we find little of value in Aristotle's works. 2 The 
superlative excellence of the one side of his work forms an extra- 
ordinary contrast to the practical worthlessncss of the other. 

5. Aristotle's Science. (a) His Works 

Aristotle's treatises on Science were numerous, arid included a 
large number of researches into Physics and Biology. But it may 
be said at once that, from a modern point of view, most of the actual 
results are so meagre as to be almost unworthy of notice. Yet it 
seems a little unjust to treat him with such disparagement as Lewes 
did, to go so far as to say that he was utterly false in method 
and puerile in his views of nature. Comparatively little could, 
of course, be expected from an investigator of 2000 years ago, in 
respect of experimental science, for, no matter how excellent his 
method, advance could be made but gradually and from one 
vantage-point to another. Aristotle's results would probably have 
been very different, could he have had at his disposal any modern 
scientific instrument. But Physical Science was then in its infancy, 
and he could start only where his predecessors left off. 3 

The principal Physical treatises of Aristotle are the eight books 
of Physical Lectures, the four books of the Heavens, the two books 
of Production and Destruction, the Meteorologies, and the Mechanical 
Problems. There are also numerous treatises on different branches 
of Natural History. 4 

i Of. Posted Introduction to Post. Analy. 2 cf. Whewell, Phil, of Disc., pp. 21-2. 

* Cf. Envy. Brit., "Aristotle ". * Cf. Whewell, Hist, of Indue. Sci., vol. i, p. 82. 


5. (b) Some General Notions 

Aristotle shows a marked tendency to take his facts and general- 
izations as they are implied in the structure of language. He 
decides, for instance, that motion is impossible in vacua by such 
arguments as this: "In a voiJ there could be no difference of up 
and down; for, as in nothing there are no differences, so there are 
none in a privation or negation; but a void is merely a privation or 
negation of matter; therefore in a void bodies could not move up 
and down, which it is in their nature to do". 1 Clearly, facts are here 
entirely subordinated to mere words, and the reasoning is absurd. 2 

The widely accepted ancient doctrine of the Four Elements 
appears to have been founded on the opposition of the adjectives 
hot and cold y wet and dry. Aristotle puts the matter in a more 
systematic form than his predecessors: u We seek", he says, "the 
principles of sensible things, that is, of tangible bodies. We must 
take, therefore, not all the contrarieties of quality, but those only 
which have reference to the touch. Thus black and white, sweet 
and bitter, do not differ as tangible qualities, and therefore must 
be rejected from our consideration. The contrarieties of quality 
which refer to the touch are these: hot, cold; dry, wet. 8 

"Now in four things there are six combinations of two; but the 
combinations of two opposites, as hot and cold, must be rejected. 
We have, therefore, four elementary combinations, which agree 
with the four apparently elementary bodies. Fire is hot and dry; 
air is hot and wet (for steam is air); water is cold and wet; earth is 
cold and dry." 4 This disposition to assume that some common 
elementary quality must exist in the cases in which we habitually 
apply a common adjective, survived the Aristotelian philosophy for 
many centuries. As Whewell points out, even Bacon fell into the 
error. 5 Thus were great minds misled by mere words. 

5. (c) His Theory of Projectiles 

Having argued that motion in vacuo is impossible, Aristotle 
proceeded to maintain that projectiles continue moving after the 

i Aristotle, Physic. Ausc., lv, 7, 215. 2 cf. Whewell, ib. p. 34. 

8 Aristotle also includes heavy, light; hard, soft; unctuous, meagre; rough, smooth; 
dense, rare. But he rejects these : heavy and light because they are not active and passive 
qualities; the others because they are combinations of the four qualities accepted, which 
therefore he infers to be the four elementary qualities. 

< Aristotle, DC Oen. et Corrup., ii, 2; cf. Whewell, i, p. 86. Whewell, ib. p. 37 


original motor ceases to be in contact with them, " either, as some 
say, by reaction, or by the motion of the moved air, which fe more 
rapid than that of the natural tendency of the body to its proper 
place ". 

" In vacua, on the contrary, there will be nothing of the kind ; no 
body can have motion there unless it be carried and supported as in 
a chariot." How the chariot is to be moved in vacua, Aristotle does 
not explain. Moreover, he adds, " no one can say why in vacua a 
body once set in motion should ever stop; since why rather here than 
there? Consequently it must either remain in necessary rest, or, 
if in motion, in endless motion, unless some stronger interferes," 

Aristotle had by no means overlooked the fact of the resistance 
of the air, since he compares it with the resistance of water. Yet 
the air is made to keep up rather than destroy the motion of a pro- 
jectile. He had also, as wo see, got a glimpse of inertia, at least as 
regards bodies in vacua. But it never occurred to him to connect 
the two ideas and make inertia keep up the continuity of motion, 
and resistance of the air destroy the motion. He was forced to 
seek for some continuous external motor for continuous motion; "the 
pulses of the moved air " was the first cause which presented itself, 
and was immediately accepted. That such a hypothesis could have 
been seriously put forward seems almost incredible nowadays. 1 

5. (d) His Account of the Rainbow 

In Aristotle's account of the Rainbow, not only is his explana- 
tion valueless, but even his observation of facts, so common and so 
palpable, is inexact. He says: "The Rainbow is never more than a 
semicircle. And at sunset and sunrise, the circle is least, but the 
arch is greatest; when the sun is high, the circle is larger, but 
the arch is less." This as regards the circle is, of course, wrong, 
and it seems almost amazing that Aristotle should have failed to 
observe the constancy of the angular diameter 2 of the circle of 
which the arch of the Rainbow forms a part. " After the autumnal 
equinox," he adds, "it appears at every hour of the day; but in 
the summer season, it does not appear about noon." Whewell 
thinks it is curious Aristotle did not see the reason for this, but 
the fact that Aristotle failed to observe the constancy of the angular 
diameter of the Rainbow sufficiently explains why the reason, now 

t See Aristotle, Phys. Awe., iv, 7, and viii, 10; and cf. Lewes, Aristotle, p. 138. 
* Approximately 82*. 


so familiar to us, did not occur to him. Aristotle's further remarks 
concerning the colours show a certain amount of careful observa- 
tion: "Two rainbows at most appear, and, of these, each has three 
colours; but those in the outer bow are duller, aud their order 
opposite to those in the inner. For in the inner bow the first and 
largest arch is red; but, in the outer bow, the smallest arch is red, 
the nearest to the inner, and the others in order. The colours are 
red, green, and purple, such as painters cannot imitate." 

In Aristotle's attempt to " explain " these phenomena, there is 
much loose speculation. "It is produced", he says, "by Reflection, 
from a cloud opposite to the sun, when the cloud forms into 
drops." And as a reason for the red colour he says that "a bright 
object seen through darkness appears red, as the flame through the 
smoke of a fire of green wood ". This notion hardly deserves notice, 
though it was taken up again in our own times by the famous 
German poet, Goethe. 1 But absurd as the "explanation" now 
seems, we must remember that even if Aristotle's observations had 
been more complete, his facts would still have been too few to 
suggest a hypothesis very closely in accordance with the actual 
explanation as we now know it. But Aristotle hastily jumped to 
conclusions; his hypothesis was totally unwarranted from the facts 
at his disposal; and the result shows that the methods he practised 
were entirely at variance with the methods he advocated. 2 

5. (e) An Example of Aristotle's Method of Reasoning 

Aristotle's style of reasoning is unsparingly exposed by Galileo. 
We append a typical example. Aristotle's object is to prove "the 
immutability and incorruptibility of the heavens": 

1. Mutation is either generation or corruption. 

2. Generation and corruption only happen between contraries. 

3. The motions of contraries are contrary, 

4. The celestial motions are circular. 

5. Circular motions have no contraries. 

a. Because there can be but three simple motions. 

1. To a centre. 2. Round. a centre. 3. From a centre. 
/?. Of three things, one only cau be contrary to one. 

1 Whose rather astonishing claims to be an authority on Optics, readers of his life by 
Lewes will remember. 

act. Aristotle, Meteorolog., Ill, ii-iv; and Whewell, vol. i, pp. 346-7. 

(0415) 8 


y. But a motion to a centre is manifestly the contrary to 

a motion from a centre. 
8. Therefore a motion round a centre (i.e. a circular motion) 

remains without a contrary. 

6. Therefore celestial motions have no contraries ; 

7. Therefore among celestial things there are no contraries; 

8. Therefore the heavehs are eternal, immutable, and incor- 


it is evident that this string of nonsense is the result partly 
of absurd hypotheses and partly of the use of the vague and 
ambiguous terms, generation, corruption, contrariety, &c., on which 
the changes are rung. 1 

6. Aristotle's Blunders and Mistaken Notions 

Aristotle made many blunders, some of them quite inexcusable. 
He describes, for instance, the human kidney as lobed like that of 
an ox; he speaks of the heart as having only three chambers; he 
says that the brain is bloodless, and that it does not extend to the 
back part of the skull. Such mistakes as these are almost innumer- 

His method of diagnosing scarlet fever is both curious and 
interesting: "If a woman suffering from scarlet fever looks at 
herself in a mirror, the surface of the mirror will become suffused 
with a blood-red mist, and this mist, if the mirror be quite new, 
cannot be rubbed off without difficulty". This was doubtless one 
of the old women's tales current in his day. It is almost incon- 
ceivable that he did not think of testing the truth of the statement. 
Instead of this he proceeded to " explain " it, and did so in various 
ways. 2 

We may quote one or two of his remarkable "problems": 

"What is the reason that lime is set on fire, and on a greater 
heat, by casting water on it?" "Lime is hot of nature, and there- 
fore when water is cast on it, it flies from the cold, and, by uniting 
of its force, gathers a greater heat and strength, and so is set on 
fire. And that is also the reason that a candle burns faster in 
the winter than in the summer; for then by reason of the encom- 

i See Galileo, Sy 'sterna Cosmicum, Dial. I, p. 30. (flerschel, Phil., p. 110.) 
* Aristotle, De Intomniis, ii, 450; cf. Lewes, Arittotle, p. 172. 


passing cold, the heat unites itself and gathers the closer to the 
tallow or wax, and so consumes it the faster." 

" What is the reason that, if you cover an egg over with salt, 
and let it lie in it for a few days, all the meat within it is con- 
sumed?' 7 "The great dryness of the salt consumes the substance 
of the egg; but in sand, some say, they may be kept long, as the 
mariners practise." 

And here are two specimens of the hundreds that might be 
mentioned of his quaint ideas:- 

1. "The earth is composed of the noblest matter, which has 
three dimensions, for three is the most perfect number: Of it we 
say first, beginning, middle, end." 

2. " A man bonds when he rises, because a right angle is con- 
nected with equality and rest." 1 

7. Aristotle's Method: Summary 

The reader ought now to be able to form a fair conclusion as to 
the value of Aristotle's method. Bacon sums up the method thus: 
" He had made up his mind beforehand. He did not consult 
experience in order to make right propositions and axioms, but 
when he had settled his system to his will, he twisted experience 
round, and made her bend to his system." 2 

We must, however, give Aristotle full credit for the method he 
taught. Over and over again he urges us to accumulate facts first; 
over and over again he insists upon the necessity for careful observa- 
tion and generalization as alone capable of furnishing correct ideas. 
Speaking, for example, of the parthenogenesis of bees, he says, 
"There are riot facts enough to warrant a conclusion, and more 
dependence must be placed on facts than on reasonings, which must 
agree with fact." 3 Again, "Let us first understand the facts, and 
then we may speak for their causes ". 4 Almost any number of 
such warnings might be quoted from his writings. No one was 
ever more keen to make " facts " the basis of his theories. But the 
art of experimenting, and the exact quantitative record of observa- 
tions, had not been developed, and Aristotle was often quite desti 
tute of the appropriate facts for a particular enquiry, and was 
sometimes even deceived in the " facts " on which he relied. His 

1 See Nichol's Bacon, p. 28. 2 Nov. Organ., Aphor. 63; cf. Whewoll, vol. i, p. 345. 

Aristotle, De G<*n. Aniin., iii, 700; cf. Lowes, Aristotle, p. 111. 

* Aristotle, De Part., i, 103ci; and cf. Lewes, ib. 


training as a dialectician was a disadvantage to him as an investi- 
gator, for he was thus led to depend too much on the evidence of 
language, in forming his theories of nature. 

As Lewes says, Aristotle was, in spite of himself, practically a 
metaphysician, assuming without misgiving the validity of all prin- 
ciples that were clear and logically consistent, no matter if they 
were merely verbal propositions, wholly without correspondence 
in fact. He argued from these principles, and only scrutinized 
the logical dependence of his deductions, instead of scrutinizing the 
principles themselves, and verifying his conclusions. Thus, from 
the assumption that the circle is the most perfect form, he deduced 
the conclusion that the motions of the planets must be circular. 
From the assumption that the centre is the "noblest place", he 
deduced the conclusion that the heart, being central, must be the 
seat of the noblest faculty, the soul. 1 

Lewes thus sums up Aristotle: "It is difficult to speak of 
Aristotle without exaggeration; he is felt to be so mighty and is 
known to be so wrong. History, surveying the whole scope ol 
his pretensions, gazes on him with wonder. Science, challenging 
these separate pretensions, and testing their results, regards them 
with indifference. His intellect was piercing and comprehensive; 
his attainments surpassed those of every known philosopher; his 
influence has been exceeded only by the great founders of Religions. 
Nevertheless, if we now estimate the product of his labours in the 
discovery of positive truths, it appears insignificant, when not 
erroneous. None of the great germinal discoveries in Science are 
due to him." 2 

8. Plato and Aristotle. Their Methods Compared 

It has often been stated that Aristotle was not only ungrateful 
but actually antagonistic to Plato. But this is going too far. 
That in many things Aristotle differed fundamentally from Plato, 
there is, of course, no doubt; that his opposition to Plato was often 
resolute, there is equally no doubt. But, as Lewes remarks, it is 
not necessary to construe opposition as an offence. While it is true 
that Aristotle's criticisms and allusions to Plato are not always 
remarkable for judicial calmness, they never show any approach to 
irreverence, and certainly not contempt. Aristotle undoubtedly 
looked upon Plato as the very greatest of thinkers. 3 

i Lewes, Aristotle, p. 120. 2 cf. Lewes, ib. p. 1. ib. p. 11. 


Plato's rich and varied contributions to Logic, Psychology, Meta- 
physics, Ethics, and Politics were so much scattered up and down 
in his works, and often so subtly and slightly indicated, that they 
required a process of codification. Aristotle, with the greatest gifts 
for the analysis and systematization of Philosophy that have ever 
been known, applied himself to the required task. He treated the 
Platonic dialogues as quarries out of which he got the materials 
wherewith to build up in consolidated form all the departments of 
thought and science, so far as they could at that time be conceived. 
It is true that he did the work rather ungraciously, seeming to 
dwell by preference on the difference of view between himself and 
Plato, but he probably did this unconsciously, apparently hardly 
perceiving how much the substance of his own thought, in all his 
non-physical researches, was derived from Plato. The attitude and 
aims of the two writers were, of course, different. Plato was a 
Dialectician; Aristotle was a man of Science. 1 Plato stood apart 
from induction and systematization; Aristotle's aim, almost from 
first to last, was to be scientific. Plato's dialogues are masterpieces 
of literary art; mere form, Aristotle entirely disregarded. 2 Plato 
held that the deceptions of sense justified scepticism of all sense 
knowledge; Aristotle, more correctly, taught that error did not 
arise from the senses being false media, but from the wrong inter- 
pretations we put on their testimony. Both agreed that Science is 
mainly concerned with " universals ", but it was Aristotle alone who 
insisted that these could only be reached through experience. 8 

Until the time of Hegel, the general explanation of the funda- 
mental difference between Plato and Aristotle was that Plato was 
an Idealist, Aristotle a Materialist; the one a Rationalist, the other 
an Empiricist; one trusting solely to Reason, the other solely to 
Experience. This explanation Hegel crushed by showing that 
although Aristotle laid much more stress upon Experience than 
did Plato, yet he also expressly taught that Reason was absolutely 
indispensable to form Science. It was Plato's Ideal theory to which 
Aristotle was so strongly opposed. Aristotle did not deny to Ideas 
a subjective existence; on the contrary, he made them the materials 
of Science; but he was completely opposed to their objective exis- 
tence, and called them empty and poetical metaphors. He said that 
on the supposition of Ideas being Existences and models, there 
would be several models for the same thing, since the same thing 

1 Cf Sir Alex. Grant's Ethics of Aristotle, vol. i, p. 182. * Cf. Ency. Brit. 

Cf. Davidson's Aristotle, p. 162; and Ency. Brit. 


may be classed under several heads. 1 He saw clearly that Ideas 
are nothing but the productions of the Reason. 

Mr. J. A. Stewart's sympathies are, as we should expect, wholly 
with Plato; but when he speaks of Plato as a " great man of science 
and a connoisseur of scientific method ", 2 it seems impossible to agree 
with him. Lewes calls Plato's conception of method " disastrous ", 
and regards him as one of the worst of investigators among men 
of great eminence. 3 Aristotle's method, though imperfect, was not 
utterly wrong, but wrong only in certain important particulars ; in 
general direction it was right, for he did insist upon the pre- 
liminary accumulation of necessary facts. But his royal confidence 
in formal reasoning prevented due circumspection. He relied far 
too much on logical deduction, and accepted evidence without cross- 
examination. Aristotle's maxim, that "to know truly is to know 
the causes of things", is a doubtful guide in scientific research. We 
may aspire to know at last why things are, but we must be content 
for a long time with knowing hoiv they are. 

On the whole we must admit that while Aristotle had the 
truer notions of scientific method, Plato had the truer views of the -. 
nature of Science. Although Plato's notion of a real intelligible 
world, of which the visible world was a fleeting and changeable 
shadow, was absurdly extravagant, yet it led him to seek to de- 
termine the "forms of Intelligible Things", which are really the 
laws of visible phenomena. On the other hand, Aristotle was led 
to pass lightly over such laws, because they did not at once reveal 
the causes which produced the phenomena. 4 

To some extent we may regard the methods of Plato and 
Aristotle as mutually complementary. Plato disregards facts, but 
he does try to get to the heart of things. Aristotle insists on the 
facts, but then he constantly makes guesses which he does not 
trouble to verify and which are never substantiated. We can learn 
much from both philosophers, but we have still far to travel before 
we get any real insight into true scientific method. 5 

i Lewes, Bioy. Hist. Phil., p 238. 2 Stewart, Plato's Doctrine of Ideas. Lewes, ib. 

* Cf. Wbewell's Phil, of Disc., p. 29. 

6 For Aristotle's views on Education, the reader may consult Wilkins's Nat Educ. in 
Greece, Davidson's Aristotle, and Burnet's Aristotle on Education It will be seen that the 
problem as to whether the end of education is culture or whether it is to fit us for the 
business of life, is a problem over which the ancients were divided just as much as are the 



i. The Period of Scholasticism 

The Athenian Schools were closed by order of the Emperor 
Justinian in the year 529 A.D., a date which may be regarded as 
marking the termination of the period of Ancient Philosophy. 
After centuries of intellectual darkness, during which the settlement 
of the new races and their conversion to Christianity proceeded, 
and the foundations of the modern European order were being 
laid, the first symptoms of renewed intellectual activity appeared 
jit about the same time as the consolidation of the Empire of the 
West in the hands of Charlemagne. That great monarch opened 
schools for the prosecution of philosophical studies, and from these 
Schools (scholce) Scholasticism derives its name. For the most part 
the schools appear to have been established in connection with the 
abbeys and the monasteries; and as in those days the clergy were 
almost the only persons who had leisure or inclination for the 
studies provided, the schools were really ecclesiastical institutions 
from the beginning. 1 

Scholasticism, in the widest sense, extended from the eighth to 
the fifteenth centuries, but its fortunes during that period were 
various. It became really active in the eleventh and twelfth cen- 
turies, and reached its zenith in the thirteenth. As an active force 
it began to decay rapidly after about 1350. 2 

2. Some Characteristics of Scholasticism 

The characteristic of early Scholascicism was the absolute sub- 
ordination of Philosophy to Theology. To quote Erigena: "There 


1 Cf Lewes, Biog. Uixt. Phil, p. 345; and Ency. Brit., vol. xxi, p. 417. 

2 Cousin divides Scholasticism into three epochs. The first of these extends over the 
ninth and tenth centuries and includes the one great name of Erigena, who lived in the 
earlier half of the ninth century. The tenth century was a kind of intellectual interregnum. 
The second period covers the eleventh and twelfth centuries and includes the names of 
Roscellinus, Anselm, William of Champeaux, and Abclard. The third period extends over 
the thirteenth and fourteenth centuries; in the thirteenth century the names of Albertus 
Magnus, Thomas Aquinas, and Duns Scotus represent the culmination of scholastic thought; 
while William of Occam (died 1347) may be regarded as the representative of the last 
stage of Scholasticism. (Cf. Ency. Brit., p. 417, <fce.; and Lewes, p. 346. For Cousiii'i 
general views, see Victor Cousin's Philosophy, by Jules Simon.) 


are not two studies, one of philosophy and the other of religion; 
true philosophy is true religion, and true religion is true philosophy". 

It has been said 1 that there was no such thing as Philosophy in 
the Middle Ages; there were only Logic and Theology. But, after 
all, logical discussion commonly leads up to metaphysical problems, 
and this was pre-eminently the case with the Logic of the schoolmen. 
Yet the saying draws attention in a forcible way to the two great 
influences which shaped mediaeval thought, on the one side the 
traditions of Ancient Logic, on the other side the system of Christian 
Theology; and it is the attitude of the schoolmen towards these two 
influences that yields the general characteristics of the period. Their 
attitude throughout is that of interpreters rather than of those con- 
ducting an independent investigation. And though they are at the 
same time the acutest of critics, and offer the most ingenious develop- 
ments of the original thesis, they never step outside the circle of the 
system they have inherited. They contemplate nature not at first 
hand but through the medium of Aristotelian logical formulae. 
Their problems and solutions alike spring from Aristotle's dicta, 
for they felt the need of reconciling these with one another and 
with the conclusions of Theology. 2 

In the Middle Ages, Reason had not the free play which char- 
acterized its activity in Greece, and in the Philosophy of modern 
times: it was subject to authority. Its conclusions were predeter- 
mined, and the initiative of the individual thinker was therefore 
confined, in the treatment of his thesis, to the consideration of little 
more than mere formal details. From the side of the Church this 
characteristic of the period is expressed in the saying that " Reason 
has its proper station as the handmaid of Faith" (ancilla fidei). In- 
tellectual activity was confined to methodizing and demonstrating 
the truths of dogmas founded by the Church. No mediaeval philos- 
opher thought of questioning the truth of a religious dogma, even 
when he found it philosophically false and indemonstrable. 3 

3. Aristotle Followed, not Plato. 

Surprise has sometimes been felt that Aristotle rather than Plato 
should have swayed the minds of the Middle Ages. But it has to be 
borne in mind that Plato was then almost unknown, 4 and even had 

i By Prantl. (See Ency. Brit.) Cf. Ency. Brit., vol. xxi. 

Cf. Veitch, Descartes, p. xvi. 

* It was not until about the end of the twelfth century that even the whole of the 
Organon of Aristotle was available. The introduction of Aristotle's works at this time wai 
due to the Arabians. 


he been known he would almost inevitably have been rejected. No 
doubt, the Philosophy of Plato was, at bottom, more in accordance 
with the doctrine of the Church, but the form was so original, so 
independent, and so provocative of liberty of thought, that it would 
have been adjudged inadmissible. On the other hand, the Philos- 
ophy of Aristotle had perfected the only thing about which men 
then dared to occupy themselves, namely, form. Scholastic Philos- 
ophy, such as it was, was a form of Theology ; and that which tended 
to perfect the form perfected Theology. 1 

Aristotle was the great authority on all matters of reasoning, 
as the Bible was the great authority on all matters of Faith. For 
along time Reason and Faith marched side by side, and "the con- 
stant effort of Scholasticism to be at once philosophy and theology" 
seemed at last satisfactorily realized. 2 But as time went on, doctrine 
after doctrine was withdrawn from the possibility of rational proof, 
and relegated to the sphere of faith; and so at last it came about that 
Scholasticism failed in its great task of rationalizing the doctrines 
of the Church. Logic and Theology refused to be reconciled. "The 
Aristotelian form refused to fit a matter for which it was never 
intended; the matter of Christian theology refused to be forced 
into an alien form." The ultimate result was that, although at 
the outset of Scholasticism Philosophy was absolutely subordinated 
to Theology, and although later on the two agreed to walk hand in 
hand, Philosophy began to feel an imperative need for independence. 
Complete and final separation was then only a question of time. 3 

It must always be borne in mind that Scholasticism had formed 
a body of thought remarkable for its order and symmetry, well-knit 
and squared, solid and massive, and capable for centuries of defend- 
ing itself from all attacks. But it was formed for conservation and 
defence, not for progress, and the day was therefore bound to come 
when new forces, making for progress, would inevitably prevail 
against it. 4 Yet it would be unjust to look upon Scholasticism as 
philosophically barren, and to speak as if Reason, 6 after hibernating 
for a thousand years, woke up again at the Renaissance. In spite 
of their initial acceptance of authority the scholastics cannot be 
regarded as the antagonists of Reason ; on the contrary, they fought 
many battles on its behalf. It has often been well pointed out that 

i Cf. Lewes, Biog. Hist. Phil., p. 347 Cf. Milman, Latin Christianity, Ix, 101. 

:{ Cf. Lewes, i&. pp. 346-8; and Ency. Brit., p. 418. 
* Cf Veitch, Descartes, p. xviii. 

6 The exercise of "reason " must of course be distinguished from the reasoning of formal 


.the attempt to establish by argument the authority of Faith is, in 
reality, the unconscious establishment of the authority of Reason; 
and Reason, if admitted at all, must ultimately be admitted al- 
together. On the other hand, the successive results of Scholasticism 
are not the free products of speculation; they are modified versions 
of Aristotle. Each new result is, however, a fresh recognition of the 
rights of Reason, and Scholasticism as a whole may be justly regarded 
as the history of the growth and gradual emancipation of Reason, 
an emancipation which was completed in the movements of the 
Renaissance and the Reformation. 1 

4. The Last Phase of Scholasticism 

With the fifteenth century an epoch commences which may be 
regarded as one of transition from Scholasticism to Modern Phi- 
losophy. Scholasticism was now beginning to be identified with 
obscurantism. The taking of Constantinople and the revival of 
ancient letters hastened materially the development of the human 
mind ; the works of Plato became known and were enthusiastically 
studied. The different nations and languages of modern Europe 
began to assert their individuality; the sudden contact with new 
men, new lands, and new faiths, awakened the slumbering intelli- 
gence of Europeans and roused their curiosity; and men's interests 
ceased to be predominantly ecclesiastical. Scholasticism, therefore, 
which was in its essence ecclesiastical, began to die of inanition. 
The sixteenth century brought Luther and the Reformation, the 
result of which was to place the Bible in the hands of the people, 
just as the revival of letters had placed the writings of the Greek 
philosophers in the hands of the students. Authority, already 
feeble, was quickly thrown to the ground, and Philosophy trans- 
ferred its allegiance from the Church to antiquity. 2 Erasmus, in 
his Praise of Folly f , pours out his exultation over the old world of 
ignorance and bigotry, now beginning to vanish away before light 
and knowledge. Folly in cap and bells mounts a pulpit and pelts 
with her satire the absurdities of the world around her, the super- 
stition of the monk, the pedantry of the grammarians, and the 
dogmatism of the doctors of the schools. 3 

Science also began to make advances. Galileo in 1609 invented 

1 Cf. Ency. Brit., "Scholasticism". 

2 Cf. Lewes, op. cit.; and Ency. Brit., ib. p. 430. 

Cf. Green's History, "The New Learning"; and Erasmus, Praise of Folly (the Interest 
ing edition with Holbein's drawings can sometimes be obtained for a few shillings). 


the telescope, which enabled him to discover the satellites of Jupiter. 
Kepler was engaged in those discoveries which have immortalized 
him. Gilbert published his speculations on the magnet. Algebra 
was developed, in fact, Mathematics generally was sedulously 
cultivated, and had already been applied to Astronomy, Mechanics, 
and Physics, thus effectually ruining the authority of both Aristotle 
and the Schoolmen. Elements were at work which made the age 
ripe for the appearance of Bacon and Descartes. Had Bacon or 
Descartes appeared earlier, " their influence would have been com- 
paratively trifling; but the age was ready for them, the age wanted 
them, and the age adopted them. The special want of the age was 
a method, and these men furnished it." 1 

Bacon and Descartes threw off the trammels of their time and 
opened a new era. Both are often called philosophers, but it seems 
preferable to regard Bacon primarily as a man of science and Des- 
cartes as a metaphysician. Bacon is sometimes called the Father of 
Experimental Philosophy, just as Descartes is called the Father 
of Metaphysical Philosophy. The titles are apt, for Bacon's philo- 
sophical instrument is Induction; that of Descartes, Deduction. 

But although these two famous men did separate themselves 
from the reigning dogmas of the day and did open new paths of 
inquiry, in which they travelled far beyond their contemporaries, 
we must not suppose them unindebted to their contemporaries. 
They were the creatures no less than the creators of their epoch. 
They founded new schools, but they founded them on the ruins and 
out of the materials around them. 2 

1 Cf. Lewes, op. cit p. $49. 

2 Cf. Lewes, p S4o it ^as at this period that Physics and Metaphysics first stood up 
openly against each oiner: consequently it is now that the ambiguous nature of the term 
Philosophy becomes im8t npparent. When Physics was jumbled with Metaphysics there 
was no impropriety m designating all men's speculations by the name of Philosophy. But 
when the separation tooK place, men were anxious to indicate that separation even in their 
language. And so it is that whenever a History of Philosophy is spoken of, a History of 
Metaphysics is almost invariably meant. (Lewes, Bitty. Hist. Phil , p. 344.) 

Perhaps the most intelligible and satisfactory idea of the method, objects, and results of 
Scholasticism is to be gained from the analysis of Ahc~luid's works, which fills a volume and 
a quarter of Remusafs Abttard, Paris, 1845. See also Victor Cousin, flfet. ile la Phil., ii. 




i. Bacon's Independence of Mind 

We have seen that one of the distinguishing characteristics 
of Scholasticism had been the attempt to acquire a knowledge of 
Natural Philosophy by mere thinking and arguing, without coming 
into contact with the contradictions, or corrections, or verifications 
of experience; but men were now beginning to see the necessity 
for pursuing their inquiries into nature by careful observation, and 
there were already successful workers in Italy, in Germany, and 
in England. It was, however, Bacon who first systematized the 
new method, and proclaimed it from the housetops as the key to 
the secret of interpreting nature. 1 

It is scarcely likely that anyone will, nowadays, accept 
Macaulay's estimate of Bacon as a man; but should there still be 
any lurking suspicion that there is some discordance between the 
character and the intellect of Bacon, it would be well to bear in 
mind, not only that character arid intellect are never necessarily 
related, but also that there is a complete explanation of Bacon's 
general acceptance of conventional standards. This explanation 
is to be found in Bacon's absolute interest in knowledge and his 
want of interest in man. In this respect Bacon and Shakespeare 
are as the poles asunder. To Bacon, nature was the supremely 
absorbing fact, just as man was to Shakespeare. And it is this 
that gives us the key to Bacons life. 

Of Bacon's independence as a thinker we have evidence as far 
back as his undergraduate days, when he spoke of the "unfruitful- 
ness" of Aristotle. And in his paper "On Controversies of the 
Church", which he wrote at the age of twenty-eight, his attitude 
is entirely that of a disinterested observer. He had been brought 
up in a Puritan household of the straitest sect, and he got to see 
the inside of Puritanism, its best as well as its worst side; he saw 
its learning, its labour, and its hatred of wrong, and he saw its 
aggressiveness, its intolerance, and the personal ambition of its 
leaders. But in the paper just mentioned, it is easily seen that 

i Cf. Nichol's Bacon, vol. ii, pp. 10-11. 


Bacon had ceased to feel as a Puritan, he was too tolerant and 
too neutral. 1 His attitude was that of an impartial judge. He 
had already become imbued with the true scientific spirit. 

Bacon not only refused to accept the authority of ecclesiasticism, 
but he also treated with disdain the results of the labours of the 
Greek philosophers. He was quite ready to admit that "things 
are not what they seem"; but, apart from the inscrutable truths 
of religion, he had no faith in anything that was not physical. 
With metaphysical modes of thought he had no sympathy at all. 2 
" When it comes to the questions which have attracted the keenest 
thinkers," says Dean Church, " the question, what it is that thinks 
and wills, what is the origin and guarantee of the faculties by which 
men know anything at all and form rational and true conceptions 
about nature and themselves, whence it is that reason draws its 
powers and materials and rules, what is the meaning of words 
which all use but few can explain Time and Space and Being and 
Cause Bacon is content with a loose and superficial treatment of 
them. Bacon was certainly not a metaphysician, nor an exact and 
lucid reasoner. The subtlety, the intuition, the penetration, the 
severe precision, and even the force of imagination which make a 
man a great thinker on any abstract subject were not his." 8 But 
this criticism is unreasonable and unjust, though it is part of the 
price Bacon has still to pay because his attitude towards Meta- 
physics was that of a disinterested scepticism. Bacon knew full 
well that the acutest intellects of 2000 years had tried to solve 
the problems of Metaphysics, and had tried in vain. Why, then, 
should he waste time in trying to solve the insolvable? As Fowler 
says, a deep sense of the unprofitable character of metaphysical 
speculations has been a characteristic not only of the Baconian 
Philosophy in particular but of British Philosophy in general, which, 
with a healthy instinct, has usually either avoided them altogether, 
or discussed them solely with the view of showing that they lie 
outside the limits of human knowledge. 4 Bacon assumed the ordi- 
nary distinction of mind and matter, a universe of objects to be 
known, and a thinking subject capable of attaining to a knowledge 
of them; and he set himself the task of solving those problems 
which he felt really were within the range of human powers. 

i Cf. Church's Bacon, pp. 1-14. * of. Nichol, vol. ii, pp. 98-101. 

8 Church, pp. 204-5. 4 Fowler, Nov. Org. t p. 15. 


2. Bacon's Method: General Notions 

Hitherto, the mode of demonstration had been by the syllogism, 
but "the syllogism is, in many respects, an incompetent weapon, 
since it is compelled to accept its first principles on trust". Bacon 
was convinced that a radical change of method by which Science 
was pursued was indispensable, arid the boldness and definiteness of 
his views of the change that was requisite are truly remarkable. 1 
A cardinal principle of Bacon's method was the necessity not only 
of proceeding from experience but of proceeding cautiously and 
gradually, and this is the essential difference from the mediaeval 
and ancient methods. The ancient method certainly did begin with 
facts of observation, but rushed at once, with no gradations, to the 
most general principles; and the same course had been followed 
by all those speculative reformers who had talked so loudly of the 
necessity of beginning Philosophy from experience. Whenever any 
of these men had attempted to frame a physical doctrine, they had 
caught up a few facts of observation and had erected a universal 
theory upon the suggestions which these offered. They anticipated 
instead of interpreting nature. 2 

Bacon called men, as with the voice of a herald, 8 to lay them- 
selves alongside of Nature, to study her ways, and imitate her pro- 
cesses. To use his homely simile, he rang the bell which called 
the other wits together. He insisted on the importance of experi- 
ment, as well as on observation. He insisted on the necessity of 
collecting facts. He urged that authority must be disregarded. 
The office of Keason, he said, ought riot to be limited to an exami- 
nation of the conclusions and their dependence on the premisses; 
we must insist on examining the premisses themselves. And ho 
insisted on the importance of a gradual ascent from propositions 
of a lower to those of a higher degree of generality. 4 

Bacon also urged the subordination of scientific enquiries to 
practical aims, to the increase of man's comforts, and to the general 
convenience of life. This attitude has been severely criticized; but 
when we recollect the frivolous character of many of the questions 
which men of the most brilliant abilities were then in the habit 
of disputing, and the profound misery in which the mass of man- 

1 Cf. Whewell, Phil, of Disc., p. 370. 

2 Cf. Nov. Org., Aph. 20, 22; and Whewell, Phil, of Disc., p. 133. 

8 Cf. De Aug., iv, 2. * Cf. Fowler, Nov. Org., pp. 86, 126. 


kind, then even more than now, were sunk, we can hardly feel 
surprise or regret that a great statesman and great philosopher 
should have suggested the application of man's intellectual gifts 
to the improvement of his material condition. 1 

3. His Philosophical Works 

It is very difficult to give an account of Bacon's philosophical 
writings at once clear and sufficient. This arises, first, from the 
fact that his work is very incomplete. Of the three main contri- 
butions to his scheme, the De Auymentis (practically an expansion 
of the Advancement of Learning) alone is finished. The Novum 
Organum is only a fragment; and the Si/fat Sylvarum is a mass of 
disjointed though interesting observations. 2 The second obstacle 
to a satisfactory analysis is Bacon's habit of repeating himself. 
It seems preferable, therefore, instead of considering the separate 
works, to consider Bacon's method as developed in the works as a 

4. The Four Classes of " Idols" 

Preliminary to the method itself are the discussions of the First 
Book of the Novum Organum, and the most important of these 
concern our common intellectual vices and tricks of self-deception, 
the Idols, as Bacon, in his figurative language, calls them. The 
word Idolon or Idolum is manifestly borrowed from Plato. It is 
used twice by Bacon in connection with the Platonic Ideas. The 
$>a>A,oi> of Plato is the fleeting transient image of the real thing. 3 
"Idola" is usually translated Idols, but it would be more correct 
to speak of "phantoms of the mind", " false notions", or "false 
appearances". Bacon never refers to the common meaning of the 
word, namely, the image of a false god. Idols are with him pladta 
quaedam inania. The doctrine of Idols stands, he says, in the 
same relation to the interpretation of Nature as the doctrine of 
fallacies to ordinary Logic. 4 

Fowler, Nov. Org , p. 127. Sec also Whewell, Phil , pp. 142-3. 

2 There is also a volume of posthumously published discourses and discussions, for the 
most part forecasts of the Orgamtm. Its precise place in the author's scheme is often hard 
to determine. 

8 Bacon evidently refers to the passage in the Itepublic, vii, 616 A. Cf. ch. vi, 5. See 
also Nov On/., 23, 124; and Kncy. Brit , "Bacon". 

Cf. Ellis, Pref. to Nov. Org., p. 223; Hallam, Hist, of Europe, Hi, 194-6; Lewes, Biog. 
Hitt. Phil, p. 864; Nichol, Bacon, ii, p. 163. 


Bacon divides the Idols into four classes: 

1. Idola Tribus, i.e. Idols of the Tribe, 

2. Idola Specus, i.e. Idols of the Den. 

3. Idola Fori, i.e. Idols of the Market Place. 

4. Idola Theatri^ i.e. Idols of the Theatre. 

"The Idola Tribus are inherent in human nature and the very 
tribe or race of man." " The mind is not like a plane mirror, which 
reflects the images of things exactly as they are; it is like the 
mirror of an uneven surface, which combines its own figure with the 
figures of the objects it represents." 1 

Among the Idols of this class is the propensity which there is in 
all men to find a greater degree of order, simplicity, and regularity 
than is actually indicated by observation, and to be diverted from 
the truth by an unconscious love of uniformity. Thus, as soon as 
men perceived the orbits of the planets to return into themselves, 
they immediately supposed them to be perfect circles, and the 
motion in those circles to be uniform; and to these hypotheses the 
astronomers and mathematicians of antiquity laboured to reconcile 
their observations. Then, again, most men are warped by the 
strength of first impressions, and, having adopted opinions, hold 
them tenaciously; or they look only to affirmatives and not to nega- 
tives. " It was a good answer made by one who, on being shown 
in a temple the votive tablets suspended by such as had escaped 
from shipwreck, and being pressed as to whether he would now 
recognize the powers of the gods, asked, *But where are the 
portraits of those who have perished in spite of their vows?'" 2 

The IdoJa Specus are those which spring from the peculiar char- 
acter of the individual. Besides the causes of error common to all 
mankind, each individual has his own dark cavern or den, into 
which the light is imperfectly admitted, and in the obscurity of which 
a tutelary idol lurks, at whose shrine the truth is often sacrificed. 

These Idols of the Den take their rise in peculiarities of mental 
or bodily structure, in education, habit, or accident. Among them 
are professional zeal, the narrow devotion of men to certain studies, 
either because they have bestowed much thought on them, or, as 
it were, have lived all their lives in the midst of them. Some 
love the old, others the new. " Profound understandings are dis- 

Nov. Org., t, 41. 

*Ct Nw. Org. t i, Aph. 46-62; Nichol, Bacon, ii, p, 164; Lewes, op, cit. p. 366; and Kney. 


posed to attend carefully, to proceed slowly, and to examine the 
most minute differences ; while those that are abnormally active are 
ready to lay hold of the slightest resemblances." Each of these 
easily runs into excess, the one by catching continually at distinc- 
tions, the other at resemblances. " Let every student of nature take 
this as a rule, that whatever the mind seizes and dwells upon with 
particular satisfaction is to be held in suspicion." 1 

The Idola Fori are those which arise out of intercourse with 
society, and those also which arise from language. Bacon calls these 
delusions of the "Market Place" on account of the consort of men 
there. Men believe that their thoughts govern their words, but it 
often happens that " words, like the arrows from a Tartar bow, are 
shot back and react upon the mind". "Words being commonly 
framed and applied according to the capacity of the vulgar, follow 
those lines of division which are most obvious to the vulgar under- 
standing." 2 

The Idola Theatri are the false notions which have arisen from 
the dogmas of different philosophers. They are called Idols of the 
" Theatre" because all the received systems are " but so many stage- 
plays representing worlds of their own creation after an unreal and 
scenic fashion". They do not enter the mind imperceptibly like 
the other three; a man must labour to acquire them. Examples 
of false systems are "those which, from a few and random experi- 
ments, leap at once to general conclusions"; or "those which corrupt 
philosophy by poetical and theological notions"; or those like Aris- 
totle's, "which substitute formulae for the investigation of nature". 8 

It is evident that the Idols "the spectres of the mind" may 
either act together or separately in the same person and in refer- 
ence to the same thing. If I say, " the sun moves round the earth", 
because my eyes tell me so, it is an Idol of the Tribe; if because 
common language says so, it is an Idol of the Market Place; if be- 
cause Ptolemy says so, it is an Idol of the Theatre; if because that 
view agrees with other theories of my own, as was the case with 
Bacon himself, it is an Idol of the Den. 4 

i Nov. Org., Aph. 42, 54-8; Lewes, p. 366; Nichol, ii, p. 165; Ency. Brit., p. 212. 

a Nov. Org., Aph. 43, 64, 80; Lewes, p. 366; Nichol, ii, p. 166; Spedding, p. 224; Fowler, 

* Nov. Org., Aph. 44, 61, <fec.; Lewes, pp. 366-6; Nichol, ii, p. 157. Cf. also Bacon, 
"Redargutio" and "Cogitata et Vita". * Cf. Nichol, ii, pp. 167-8. 



5. Bacon's Method. (a) Collection of Facts 

These preliminary discussions completed, Bacon proceeds in the 
second book of the Organum to describe and exemplify the nature 
of Induction. 

The indispensable preliminary to Induction is the observation 
and collection of facts. " Man the servant and interpreter of Nature, 
can do and understand so much, and only so much, as he has ob- 
served in fact or in thought of the course of nature; beyond this he 
neither knows anything nor can do anything." 1 "Our first object 
must therefore be to prepare a 4 history' of all the phenomena to be 
explained." The history is to include both observations and experi- 
ments; "it ought to be composed with great care; the facts accu- 
rately related and distinctly arranged; their authenticity diligently 
examined; those that rest on doubtful evidence, though not rejected, 
yet noted as uncertain, with the grounds of the judgment so formed. 
The last is very necessary, for facts often appear incredible only 
because we are ill-informed, and cease to appear marvellous when 
our knowledge is further extended." 2 

Bacon dwells upon the importance of this part of his scheme, 3 
declaring that, without such a register or "history" of the facts of 
nature, nothing can be done, even "if all the wits of all the ages 
shall meet in a world university". "Let such a history be once 
provided, and the investigation of nature and of all sciences will be 
the work of a few years." But Bacon completely underestimated 
the magnitude of such a task. No one acquainted with the history 
of Natural Philosophy would now think it possible to form a collec- 
tion of all the "facts" which are to be the materials of any " science", 
antecedently to the formation of the "science" itself. "Fact" and 
"theory" cannot be separated in this way. 4 Yet Bacon thought it 
possible so to sever observation from theory that the process of col- 
lecting facts, and that of deriving consequences from them, might 
be carried on independently and by different persons. His opinion 
seemed to be that the connection between fact and theory was merely 
an external one; and that the facts, being comparatively few, might 
be observed and recorded within a moderate length of time by persons 
of ordinary intelligence. Now it is true that when the laws of nature 
have been caught sight of, much may be done by ordinary observers 

1 Nov. Org. t Aph. 1. 

2 Cf. Lewes, op. cit p. 366. * See his Essay, the Parasceve. 
* Cf . Nlchol, ii, p. 163 ; and Kuno Fischer Bacon, pp. 96-7. 


in verifying and exactly determining them; but, as Whewell points 
out, when a real discovery is to be made, this separation of the 
observer and the theorist is not possible, the questioning temper 
and the busy suggestive mind being needed at every step to direct 
the operating hand or the observing eye. 1 Mere observers cannot 
supersede the discoverer who is to introduce into the facts a new 
principle of order, though it is of course true that persons of moderate 
powers may, when properly trained, make observations which may 
be used by greater discoverers than themselves. 

5. (b) Discovery of " Forms" 

Bacon's next step is to discover, by a comparison of the different 
facts, the "Form" of the phenomena under investigation. But he 
seems to find great difficulty in giving an adequate and exact defini- 
tion of what he means by a Form, though, as a general description, 
the following passage is pretty clear. " The Form of any nature is 
such that, given the Form, the nature infallibly follows. Again, the 
Form is such that, if it be taken away, the nature infallibly vanishes. 
Lastly, the true Form is such that it deduces the given nature from 
some essence inherent in many natures." 2 From this it would 
appear that since by a nature is meant some sensible quality, super- 
induced upon, or possessed by, a body, so by a Form we are to 
understand the cause of that nature, which cause is itself a manifesta- 
tion of some quality inherent in a greater number of objects. 

Lewes explains the Forms thus: "The Form of any quality in a 
body is something convertible with that quality; that is, where it 
exists, the quality exists. Thus, if transparency in bodies be the 
thing inquired after, the Form of it is something found wherever 
there is transparency. Thus Form differs from Cause in this only: 
we call it Form or Essence when the effect is a permanent quality; 
we call it Cause when the effect is a change or event." 3 

This is not very illuminating, and it is really difficult to under- 
stand precisely wliat Bacon intended his Forms to signify. It cer- 
tainly does not mean the outward shape, which is a mere matter of 
sight and touch. Nor can it be the Platonic Idea, or any abstraction 
separable from concrete realities. Nor is it a Law of nature, as now 

1 See Bacon, Phenomena Universi ; and cf. Ellis, p. 35. See also Whewell's criticism of 
Bpedding's views in Phil, of Disc., pp. 154-6. 

2 Nov. Org., ii, 4. Cf. JBncy. Brit., p. 213. 

8 Lewes, op. cit. p. 866. Cf. Bacon, Valerius Terminus, ch. xi. 


understood. 1 Fowler says that at one time he thought Bacon 
attached to the term two entirely distinct meanings, which may 
be represented roughly by cause and essence, but later he concluded 
that it had various shades of meaning in different places, all of these 
admitting of derivation from a single conception. 2 Ellis was dis- 
posed to believe that the doctrine of Forms is in some sort an 
extraneous part of Bacon's system. Certainly the second part of 
the Novum Oryanum is rendered more or less vague and obscure by 
the employment of the term, instead of the more precise expressions, 
such as Law, Cause, Conditions, &c., by which it is now replaced. 3 

One thing is certain, and that is that Bacon not only had a firm 
grasp of particular physical properties, but was able to form a clear 
conception of generalized physical properties; and we may perhaps 
look upon his Forms as physical properties of a highly generalized 
character. "Though Bacon uses the word cause,, and even identifies 
Form with cause, it is evident that, to him, effects were manifesta- 
tions and not consequents. Notions of cause as dynamical were 
foreign to him; in his view, nature had a ourely statical aspect." 4 

5. (c) The "True Difference" 

The next point to be considered is the particular method, 
employed by Bacon, of comparing the collected facts of any given 
phenomena and of discovering the Form or Cause concealed among 
them. We are told to ascend from the experience of facts to the 
experience of causes: 5 and so we come to Bacon's theory of 

In our examination of the collected data, we must, by some 
means or other, discover and set aside whatever is non-essential 
and contingent. Clearly, if this be done, the residue will consist of 
what is really essential to the phenomena under investigation. To 
this residue of data thus left over and constituting the essential 
conditions of the phenomena, Bacon applies the term " true differ- 
ence", 6 which he further designates as "the fountain of things", 
the Form of the phenomena. If, then, we are to arrive at the 

i Cf. Nlchol, ii, p. 184; and Maurice, Moral and Metaph. Phil, ii, p. 223. 
a Fowler, p. 63. ib. p. 131. 

* Cf. JBncy. Brit., p. 213. For some account of Bacon's "simple natures", cf. Nov. Org. t 
ii, 5; Ellis, p. 16, and the illustration concerning the natures of gold in the Sylva Sylvarum; 
also De Aug., iii. 

* 01, for instance, " Recte ponitur: vere scire ease per causas scire ", <fcc. 

* ' Differentia, vera" 

BACON 101 

Natural Law underlying the phenomena to discover the Form of 
the phenomena the problem to be solved is the discovery and elimi- 
nation of the non-essential. 

Bacon was of opinion that the discovery of the Form or Cause 
thus concealed among the facts presented to sense, could be made 
with absolute certainty and with mechanical ease. The form of 
induction hitherto used by logicians he regarded as useless, since 
it was a mere catalogue of a few known facts, made no use of 
exclusions or rejections, and so was always liable to be overthrown 
by a negative instance. Now this last point Bacon looked upon as 
of fundamental importance, and therefore directed special attentior 
to it in his own Method. 1 

5. (d) The Tables of Investigation 

In order that the necessary preliminary classification of facts 
might be systematic and complete, Bacon suggested three "Tables 
of Investigation ''. 

1. The Table, of Affirmatives. This is to contain a collection ot 
all the known instances that agree in having the same quality. If, 
for example, the subject to be enquired into is heat, we should 
include in our Table the sun, lightning, flame, burning-glasses, the 
blood of mammals, hot-iron, &c. 2 We are advised, in forming the 
Table, to collect instances from all quarters, and from varied and 
dissimilar objects. 8 But any conclusion arrived at from an inspec- 
tion of this Table will be a guess; for Bacon curiously remarks, only 
God and the angels can tell the cause from the contemplation of the 
affirmatives. 4 We are bound to make use of 

2. The Table of Negatives, "a collection of examples of bodies 
otherwise similar (else the list would be endless), which do not 
agree in the same nature". Thus, the negative Table of Heat 
would contain such instances as the moon's rays, blood of fish, dead 
animals, &c. 

The stress Bacon lays on negative instances is one of the earliest 
applications to Philosophy of the principle "Audiatur et altera pars". 
He constantly urges that the cardinal defect of the old induction 
was the neglect of this; that "our conclusions can never be legiti- 
mate or secure till they have passed through the sieve of this table 
and have no more to apprehend from an unforeseen exception". 6 

i Cf. Nov. Org., I, 60. 2 s c c Bacon's investigation into "Heat", Nov. Org. t ii. 

Cf. Mill's "First Canon of Induction " (see ch. xvli). * Nichol, vol. ii, p. 166. 

Cf. Nichol, ii, p. 166; and Mill's "Joint Method " (see ch. xvii). 


3. The Table of Comparison, i.e. "a collection of instances 
where the phenomenon sought to be explained is present in various 
degrees ". Thus " heat is unequal in various kinds of flame, rising 
in degree from that of burning spirits of wine to that of a blast- 
furnace ; it varies in the same animals under different circum- 
stances "; and so on. 1 

This form of Table often throws suggestive light on the relation 
of antecedents and consequents, but its efficacy largely depends on 
the skilful use of experiment, in which Bacon, while recognizing its 
importance, was in practice unskilled. 

5. (e) The Process of Exclusion 

After the formation of these Tables we are to apply what is 
perhaps the most valuable part of Bacon's method, and that which 
the author regarded as the corner-stone of his system, the process of 
exclusion or rejection. 2 Suppose, for instance, we check the first Table 
by means of the second, we may be able to correct, and perhaps 
have to reject, a generalization already provisionally made from the 
first Table alone. Thus when it appears that the blood of terrestrial 
animals is hot and that of fish cold, the hasty conclusion that the 
blood of all animals is hot is rejected. Then, again, if we are trying 
to discover the cause of transparency in bodies, we should, from the 
fact that the diamond is transparent, immediately exclude rarity 
and fluidity from possible causes, the diamond being a very solid 
and dense body. 

This elimination of the non-essential is the special feature wherein 
Bacon's method differs from that of previous philosophers. It is 
evident that if the Tables were complete, and our notions of the 
respective phenomena clear, the process of exclusion would be a 
mere mechanical counting out, and would infallibly lead to the detec- 
tion of the Cause or Form. But it is evident that these conditions 
can never be adequately fulfilled. Bacon saw this, and therefore 
set to work to devise new " helps ". 8 

5* (/) Other "Helps". The "First Vintage" 

There is, naturally, great difference in the value of facts. Some 
of them show the thing sought for in the highest degree, some in 

i Cf. Mill's "Method of Concomitant Variations" (see ch. xvii); and see Nichol, II, p. 166. 
See Nov. Org. t I, 69, 106; ii, 15, 16, 19 Cf. Kmy. Brit., " Bacon ", p. 210. 

BACON 103 

the lowest; some exhibit it "simple and uncombined", in others 
"it happens confused in a variety of circumstances". Bacon's 
scheme of "Prerogative Instances" 1 was the outcome of his considera- 
tion of this comparative value of facts. He enumerates twenty- 
seven different species, but few of these add much to our know- 
ledge of his Method, though one is well worth mentioning, viz. the 
Imtantia Crucis. 

When, in any investigation, the understanding is placed in 
eyuilibrio, as it were, between two or more possible causes, each of 
which seems to account equally well for the phenomena, nothing 
remains to be done but to look out for a fact which can be explained 
by one of these causes and not by the other. Such facts perform 
the office of a rms'x, erected at the junction of two or more roads, to 
direct the traveller which road to take. They are therefore called 
crucial instances. 

The Experimsntum Crucis is of such importance in inductive 
investigation that, in all those branches of Science where it cannot 
be resorted to, there is often great want of conclusive evidence. 2 

Of the other " helps " enumerated by Bacon we have but 
scattered hints. And although the rigorous requirements of Science 
could only be fulfilled by the employment of all these means, yet, 
in their absence, it was permissible to draw from the various Tables 
a hypothetical conclusion, the truth of \\hich might be verified by 
the use of the other processes. Such a hypothesis Bacon quaintly 
'called the "First Vintage". 8 

$ 6. Bacon's Investigation into Heat 

Bacon's inductive method, so far as exhibited in the Organum^ 
is exemplified by an investigation into the nature of Heat. 4 He 
throws into a Table of Exclusions everything about Heat which is 
not present in the Table of Affirmative Instances, or which is 
present in the Table of Negative Instances, everything which in- 
creases when the phenomenon decreases, and vice versa. From the 
possible causes of Heat he is now able to throw aside Light, Fluidity, 
and Quiescence, and at last arrives at the hypothetical conclusion 
that the essential nature of Heal is imtwn. Flame is perpetually 
in motion; so are hot or boiling fluids. Heat is increased by 
motion, as in bellows or blasts; all bodies are destroyed or have the 

i Cf. A'ow. Org , II, 21. * PUyfalr. See Lewes, pp. 

" Kwulrmiatto". See Xncy. Brit., p. 216. JVov. Org , ii. 


position of their parts altered by Heat; when it escapes, as in death, 
the body rests. Motion is therefore clearly the genus of heat. 
This conclusion is not, of course, very far wrong, though it is 
defective in detail and obtained by a very imperfect process. 1 But 
the conclusion is only the " first vintage ", beyond which, as a 
matter of fact, Bacon was never able, in any of his investigations, 
to advance. He had worked up to Mill's Canon of the Method of 
Residues, but he failed properly to apply it. Instead of proceeding 
with further testing experiments, he was hurried on by the very 
impatience, misled by the same love of uniformity, which in his 
predecessors he denounced. 2 

7. The Method a Failure in Practice 

It is not correct to say that Bacon ignored the deductive side of 
reasoning altogether, for whenever he saw its value for the purpose 
of applying the truths already arrived at by induction, he seems to 
have assigned it an almost co-ordinate iank. 3 Hut he did reject 
deductive reasoning in his process for establishing general principles. 
He scoffed at the old scholastic notion that it was possible to estab- 
lish by a priori methods the first principles of any ' science ", 4 and 
then to deduce by syllogism all the propositions which that science 
could contain. 6 In this he was, of course, abundantly justified, 
though sometimes he went rather too far in assigning to deductive 
reasoning such a strictly subordinate function. " We reject the 
syllogistic method", he says, "as being too confused and allowing 
nature to escape out of our hands. In everything relating to the 
nature of things we make use of induction for both our major 
and minor propositions." 6 Bacon felt, as we now all feel, that in 
the Middle Ages an absurd importance had been attached to the 

i A careful examination of this investigation will show, an Ellis points out, that Bacon's 
provisional conclusion is not really the result of the method of Exclusion, but rent* itnint* 
diately on the three Tables of Investigation Hence it does not pretend to be the rt'hult of 
formal proof, but only a sort of probable hypothesis, based upon the consideration and com- 
parison of a large number of instances. Whewell's opinion of the investigation is that it is a 
complete failure. Yet the essential part of the conclusion is that Heat is an expansive motion 
amongst the minute particles of bodies, so that, in any case, Bacon did divine the true nature 
of Heat. But, after all, the conclusion was more the result of a lucky guess than of good 
method, and the investigation which occupies so much of the second book of the N&vum 
Organum does not afford us much insight into a method that is really practicable. Cf. 
Appendix to Tyndall's Heat, and Aph 20 of the Nov. Org.\ also Whewell's Phil, of Ditc., 
pp. 136-8; Ellis, vol. i, pp. 36-7; Fowler, pp. 36-43. 

* Cf. Nichol, vol. ii, pp. 168-9. 

* Cf. Fowler, p. 130; Nov. Org. t i, 93, 106, ii, 21 ; and K^musat, p. 224 

* The objection to the term " sciences " has already been mentioned. 

* Cf. Ellis, p. 3a Cf. Bacon's Prtjace\ Devey, p. 12. 

BACON 105 

syllogism, but apparently he did not quite realize the important 
part that deductive reasoning still had to play in scientific investi- 

Bacon was not the first to tell men that they must collect know- 
ledge from observation, from experience, but he had no rival in 
his peculiar office of teaching them how knowledge must thus be 
gathered. With great clearness, he insists on " a graduated and suc- 
cessive induction ", as opposed to a hasty transit from particular facts 
to the highest generalizations. 1 As Whewell points out, it is a truly 
remarkable circumstance to find this recommendation of a continuous 
advance from observation, by limited steps, through successive gra- 
dations of generality, given at a time when speculative men in 
general had only just begun to perceive that they must begin from 
experience in some way or other. There is no vagueness in Bacon's 
assertion of this important truth. He repeats it over and over again, 
and illustrates it by a great number of emphatic expressions. Thus 
he speaks of the successive "floors" (tahulata) of induction; and he 
makes use of a further happy simile when he speaks of each "science" 
as a pyramid 2 which has observation and experience for its base, 
with the lower generalizations gradually converging to the highest 
generalization at the apex. 8 

Bacon made a great advance on Aristotle, in that, instead of 
being satisfied with a "simple enumeration" of facts, he insisted on 
an assemblage and codification of sifted and tested facts; but his 
method of induction is a long way behind that of Mill, Whewell, 
Herschel, Faraday, and Darwin, and does not form a suitable instru- 
ment for the successful investigation of the laws of nature. Bacon 
thought his method as certain in its results as a demonstration in 
Euclid; and so mechanical that, when once understood, all men 
might employ it. 4 But in practice it is entirely unworkable. 

Bacon underestimated the part played by mind in the con- 
stitution of knowledge. "Our method of discovering the sciences 
is one which leaves not much to acumen and strength of wit, but 
nearly levels all wits and intellects." 5 While it is true that Bacon 
does not entirely neglect to consider the formation of scientific con- 
ceptions, yet he gives us no single hint as to the manner in which 
induction is to bo employed for this particular purpose, and by this 
circumstance alone our knowledge of his method is rendered im- 

i Xov Org., I, 19. * A\tg. Sci , ill, 4, U>4 ; and Nov. Org. t I, 104. 

See Whewell'i Phil, of Dwc., pp. 132, 144 

* iVop. Org., ii, 1, 5; NIchol, II, pp. 181, 231, * Nov. Org., I, 01. 

Of. Nov. Org. t 1, 16; 11,19. 


perfect and unsatisfactory. And perhaps Bacon never, even in idea, 
completed his method thus far. 

Now, although in the process of scientific discovery the forma- 
tion of conceptions is the part with respect to which it is practically 
impossible to lay down general rules, yet its importance in practice 
is so great, that Bacon's avoidance of the difficulty has reduced the 
value of his method almost to vanishing point. In fact, not only 
has the method never produced any appreciable result, but the pro- 
cess by which many scientific truths have been established cannot, 
as a rule, be so presented as even to appear to be in accordance with 
it. The process always involves an element to which nothing corre- 
sponds in Bacon's Tables of Comparison and Exclusion, namely, the 
application to the facts of observation of an idea, call it a scientific 
conception, a hypothesis, a general principle, or what we will, from 
the mind of the discoverer. The finding of an appropriate idea the 
formation of a hypothesis explanatory of the collected facts is the 
very essence of the inductive act. If, for instance, we consider 
Kepler's discovery that Mars moves in an ellipse, we see that the 
core of the difficulty lay in bringing into connection with the facts 
of observation the idea of motion in an ellipse. The hypothesis once 
found, it is verified by a further appeal to facts, a point we shall 
have to consider in detail in a future chapter. 

Bacon failed because he thought it possible to make the process 
of induction mechanical; because he did not recognize that Science 
must progress by the application of ideas to facts; and because 
nature is practically infinite and not reducible to a mere "alphabet". 1 
"Bacon inherited the mental diseases of those he imagined himself 
to have slain." " In the act of arraigning Aristotle, he is nowhere 
more Aristotelian than when he speaks of dense and rare, light and 
heavy, as if they were absolute qualities, instead of terms as relative 
as up and down, broad and narrow." 2 Bacon had little experimental 
skill, and his facts were drawn more from hooks than from nature, 
and he was therefore able only to suggest, not to realize. Then 
he set before himself an unattainable goal. He set out to become 
master of all nature. His audacity in this respect contrasts with 
the 'modest aims of more practically successful men of science, such 
as Leonardo da Vinci, Copernicus, Galileo, and Newton, who owed 
their triumphs in large measure to self-restraint. 8 As Bacon under- 
rated the vastness and subtlety of nature, so he overrated his own 
appliances to bring it under his command. Cowley compared him 

i Of. Nichol, ii, p. 171. * ib. p. 195. 0>. pp. 171, 196, 196, 227. 

BACON 107 

to Moses on Pisgah surveying the promised land; it was but a dis- 
tant survey, and Newton was the Joshua who began to take posses- 
sion of it. 1 

Although Bacon's method excites our admiration historically, 
it excites no admiration for its present intrinsic value. We have 
a much more perfect method now, the processes of scientific in- 
vestigation being far better understood. But we are never in com- 
munion with his vast and penetrating intellect without acknowledg- 
ing his greatness, for much of his teaching is as applicable now as 
when first written. 2 

As De Morgan says, Bacon was eminently the philosopher of 
error prevented, rather than of progress facilitated? 

8. Bacon's Errors and Oversights in Science 

It is often said that Bacon was very imperfectly acquainted 
with the Science of his own day. Spedding gives numerous de- 
tails of his errors and oversights, and some of these are worthy of 

Bacon paid great attention to Astronomy, but he appears to 
have been quite ignorant of the discoveries that had just been made 
by Kepler's calculations. Though he complained in 1623 of the 
want of compendious methods for facilitating arithmetical computa- 
tions, he does not say a word about Napier's logarithms, which had 
been published only nine years before. He complained that hardly 
any advance had been made in Geometry beyond Euclid, without 
taking any notice of what had been done by Archimedes and Apol- 
lonius. He saw the importance of determining accurately the specific 
gravities of different substances, and attempted to form a table of 
them by a rude process of his own, without knowing of the more 
scientific though still imperfect methods previously employed by 
Archimedes and others. He speaks of the "principle" of Archi- 
medes in a manner which implies that he did not understand the 
nature of the problem to be solved. In reviewing the progress 
of Mechanics, he makes no mention either of Archimedes, or of 
Stevinus, or of Galileo. He observes that a ball of one pound weight 
will fall nearly as fast through the air as a ball of two, without 
alluding to the theory of the acceleration of falling bodies, which 
had been made known by Galileo more than thirty years before. 

i Church, p. 179. 2 cf. Whewell, Phil., p. 151 ; and Lewes, p. 877. 

Budget cf Paradoxes, p. 60. 


He makes no allusion to the theory of equilibrium. He proposes 
an inquiry with regard to the lever, though the theory of the 
lever was as well understood in his own time as it is now. He 
speaks of the poles of the earth as fixed, in a manner which seems 
to imply that he was not acquainted with the precession of the 
equinoxes; and, in another place, of the North pole being above, arid 
the South pole below, as a reason why, in our hemisphere, the north 
winds predominate over the south. 1 

Then Bacon believed, with qualifications, not only in Natural, 
but in Judicial, Astrology. He believed that air and water, under 
certain conditions, were mutually convertible. He makes no men- 
tion of the circulation of the blood, which Harvey began to teach 
in 1616. He believed in the existence of bodies of positive levity, 
and held that air has no weight. He gave his countenance to , 
many of the most absurd fancies of the time, as that an ape's 
heart, "applied to the neck or head, helpeth the wit". 2 He speaks 
of Astronomy as being degraded by Alathematics. He says that 
"wood and metal are not equally cold". 3 He lays it down that 
the phosphorescence sometimes seen in the sea is due to its being 
struck violently by the oar, or agitated by storms. 4 

We thus see how over-confident was Bacon's temper, and how 
little he did in his own practice to rectify the fallacious methods 
of which he so eloquently complained. 5 The fact is, he never 
divested himself of a prejudice in favour of the simplicity of nature, 
and this disposed him to exaggerate the facility of its analysis.* 5 

9. His Rejection of the Copernican Theory 

Perhaps the most important and at first sight least excusable of 
Bacon's scientific errors was his persistent rejection of the Copernican 
theory. 7 It seems strange that such a great reformer of Science 
should have steadily refused to admit the greatest reform in scien- 
tific conceptions which had been proposed for many generations, and 
which had already been before the world for eighty years. But it 
cannot be said that, till the laws of formal astronomy were connected 
by Newton with the physical laws of matter and motion, the motions 
of the earth or its relations to the rest of the solar system could in 

i See Ellis, vol. i, pp. 672, 578, 625, 631, notes, Ac.; also Fowler, pp 23-5. 

a See Nov. Org. t II, 40, 48, 111, Ac. See De Aug., ill, 4; and Nov. Org , H, ia 

* De Aug., iv, 3; and Nov. Org., II, 12 * Robertson, pp. 80-2. 

Cf. Abbott, p. 408. 7 i.e. the heliocentric theory. 

BACON 109 

any way be regarded as placed beyond the range of dispute. The 
following sentences from De Morgan read us a useful lesson in esti- 
mating the scientific judgments of men of past ages. "By invest- 
ing Copernicus with a system which requires Galileo, Kepler, and 
Newton to explain it, and their pupils to understand it, the modern 
astronomer refers the want of immediate acceptance of that system 
to ignorance, prejudice, and over-adherence to antiquity. No doubt 
all these things can be traced; but the ignorance was of a kind 
which belonged equally to the partisans and to the opponents, and 
which fairly imposed on the propounder of the system the onus of 
meeting arguments which, in the period we speak of, he did not and 
could not meet. It must bo remembered that, in the sixteenth cen- 
tury, the wit of man could not imagine how, if the earth moved, a 
stone thrown directly upwards would fall down upon the spot it was 
thrown from. Easy experiments verify the law of motion which 
now explains this; but, to be proved by experiment, a law must be 
conceived and imagined. To be put under discussion it must be 
proposed. Now the advocates of the earth's motion never, before 
the time of Galileo, even conceived this law, never proposed it, and 
of course never proved it." l 

It is true that Bacon once spoke of " these carmen who drive the 
earth about",* but he was then a young man, and Hume goes too 
far in saying that Bacon rejected the Copernican system "with 
positive disdain ". No doubt in early life Bacon conceived, like the 
majority of his scientific contemporaries, a strong prejudice against 
the theory, and equally no doubt, as he ^ot older, the reasons 
against the theory appeared to him more and more decisive. But 
it would be unreasonable to think that Bacon did not weigh the 
evidence, for and against the theory. To parallel cases of the rejec- 
tion 3 of a proposed theory there is scarcely any limit. The Cam- 
bridge mathematicians, for instance, adhered to the Cartesian system 
long after the publication of Newton's discoveries; and Leibnitz 
obstinately declined to accept the Newtonian doctrine of gravita- 
tion. Many theories now universally accepted were at first sup- 
ported only by the slenderest evidence, and assuredly cautious men 
showed their wisdom by suspending judgment. Consider the many 
scientific theories floating in the air at the present time. Assuredly 
some, perhaps most, will have to bo rejected, while evidence will 

1 Companion to Rntittk Almanac for 1S65. pp. 21-2. 

9 Of. Praise o/ Knwltdtje and TVmpori* /'artiu Matculu*. (See Ellii and Speddlng. L 
p. 124, and lit, 636; Fowler, p. 84.) 

* It would perhaps be fairer to say " luapenaion of judgment". 


gradually accumulate to lead to the general adoption and final ac- 
ceptance of others. 1 

Bacon is sometimes regarded as a dilettante in Science, but he 
never pretended to have any claims to the distinction of being a 
great discoverer. His main business was with the logic, of Science. 
Yet the wealth of illustration exhibited in the Novum Organum and 
the vast number of subjects reviewed in the De Angmcntis show a 
range of knowledge probably quite unequalled by any other man 
then living. He was not a Specialist, but he throw out many 
suggestions of rare sagacity. He suggested the necessity of a closer 
union between formal and physical astronomy. 2 He recognized 
the possible influence of the moon on spring and neap tides. 3 He 
conjectured that light requires time for its transmission. 4 Ho 
anticipated some of the optical investigations of Newton. 5 His 
experiment with the hollow globe of lead to determine the ques- 
tion of the compressibility or incompressibility of water, preceded 
by nearly fifty years the celebrated Florentine experiment of a 
similar nature. Humboldt complimented Bacon on having con- 
sidered the direction of the winds in connection with temperature 
and aqueous phenomena. 6 And he seems even to have had a 
glimpse of the fallacy of the doctrine of the fixity of species. 7 

It is of course an error to think that Bacon took no interest 
at all in experimental work. In fact, as Macaulay points out, he 
was destined to be the martyr of experimental Science. It had 
occurred to him that snow might be used with advantage for the 
purpose of preventing animal substances from putrefying; and on 
a very cold day early in 1626 he alighted from his coach near 
Highgate to try the experiment. He went into a cottage, bought 
a fowl, and with his own hands stuffed it with snow. While thus 
engaged he caught a chill and, after a week's illness, died. 8 

10. Bacon's Critics 

Like all great men, Bacon has been subjected to much criticism, 
and, of his frankly hostile critics, Macaulay is perhaps the most 

* Cf. Fowler, p. 36. 

a See Deter. Glob. Intell., v. (Ellis and Spedding, vol iii, 734 ; Fowler, p. 37.) 

Nov. Org. t ii, 45-8. * ib. 46. * ib 22. 

*ib. 45, 50; and Hist. Dens. Rar. (Ellis and Spedding, ii, 299, 300; Fowler, p. 46); Hum- 
boldt, Kosmoa, Ii, 322, 379. 1 Nov. Org., i, 66. 

8 Macaulay, Essay on Bacon. For an excellent example of Bacon's experimental work, ie 
Nov. Or?., ii, 40. 

BACON 111 

unfair. Macaulay almost leads us away by his ingenuity and 
plausibility. But his puerile arguments about mince-pies and about 
Jacobinism, as illustrations of the futility of induction, u the in- 
ductive method has been practised ever since the beginning of the 
world by every human being", reveal his total incompetence to 
examine Bacon's method. That all men in all ages have practised 
"induction" is true; but Macaulay confounds induction as an "art 
of life", with the inductive method as a scientific process. The 
induction as practised by ordinary people is that of simple enumera- 
tion, and is fundamentally different from that of the scientific 
investigator. Impartial readers of Macaulay \s Ebsay will be forced 
to the conclusion that the author's "monstrous absurdity" is to be 
found in his own argument rather than in the inductive process 
which ho tries to ridicule. 1 

Mill's criticism is searching, but fair. "Some have preferred to 
assert that all rules of induction are useless, rather than suppose 
that Bacon's rules are grounded upon an insufficient analysis of the 
inductive process. Such, however, will be seen to be the fact as 
soon as it is ascertained that Bacon entirely overlooked plurality 
of causes. All his rules tacitly imply the assumption, so contrary 
to all we know of nature, that a phenomenon cannot have more than 
one cause." 2 

The Novum Oryanum appears to have received, at first, a wider 
recognition on the Continent than in England. Descartes, writing 
to Mersenne, said, <4 You desire to know how best to make ex- 
perience useful; on this point 1 have nothing to add to Verulam". 
The opponent of Descartes, (iasscndi, yet praises him for his points 
of resemblance to Bacon. Puffendorf, the Jurist, declared that it 
was Bacon " who raised the standard and urged on the march of 
discovery ". As time went on Bacon's work began to receive due 
recognition in England. Boyle, Hooke, and others admitted Bacon's 
greatness, but if Newton owed anything to Bacon he does not 
acknowledge it. Yet Walpole is probably fully justified in saying, 
"Bacon was the prophet of things that Mew ton revealed". 

The majority of German metaphysicians, repelled by Bacon's 
scoffing protests against a priori views, have criticized him harshly. 
Spinoza regards his school as that of superficial industrialism; Hegel 
is equally uncomplimentary; but Leibnitz shows a marked apprecia- 

i Of. the K*say on /taioti, with Nirhol, pp. 2, 3, 24, 25 ; Lewes, Riog., p. 380. On Mfccaulajr't 
reference to Bacon's " utility ", see J. Grote, Explor. PhU., vol. i, p. IS. 
* Mill, Logic, ii, pp. 127, 878, Ac.; Lewes, op. cit. p. 388, 


tion of Baconian philosophy. Of more recent German thinkers 
Schopenhauer is one of the most sympathetic. 1 

A few other critics may receive passing mention. Condillac 
is quite complimentary, and D'Alembert extremely so. Cowley 
describes how Bacon chased away authority 

" Nor suffered living men to be misled 
By the vain shadows of the dead." 3 

Hume's praise was of a modified character. 8 Voltaire's was ex- 
cessive. De Maistre was frankly hostile, and so were Krewster 4 
and Liebig. 6 

Concerning Bacon as a man it would be easy to quote from a 
large number of writers. Spedding is Bacon's greatest defender; 
Sortain is "piously hostile"; Hepworth Dixon is an admirer and 
a friend, but too partisan; Dr. Abbott is both ungenerous and' 
unfair. Sir Sidney Lee pronounces Abbott's book as u the best 
summary of Bacon's life and work", without even making a refer- 
ence to Spedding's far greater performance. Dean Church comes 
to the conclusion, though apparently with regret, that "it is vain 
to fight against the facts of Bacon's life". Mr. S. II. Reynolds 
says, "For accuracy of detail Bacon had no care whatever, and 
this may be set down as probably part of his craft ". Such a 
reckless assertion carries its own condemnation. Mr. J. M. 
Robertson's attitude towards Bacon is that of an impartial judge. 7 

The hostility of some of Bacon's critics is due to their un- 
favourable opinion of his personal character; of others, because 
they were under the impression that he was a Materialist; and of 
still others, because of his " utilitarian " philosophy. But his im- 
partial critics brush aside all such issues, as not being germane 
to the case before them. In the main their reasoned opinions of 
Bacon as a man are entirely favourable, arid they have the deepest 
respect for him as a philosopher. 

11. Bacon and Aristotle 

Two men stand out, says Church, "the masters of those who 
know", without equals up to their time the Greek Aristotle and 
the Englishman Bacon. They agree in the universality and com- 

i Cf. Nichol, ii, pp. 232-43. a Ode to the Royal SocUty, 

8 Hist, of Eng. , Appendix to Reign of James I. * Life of Newton, 

* Ueber Francis Bacon. Essays, t'lar. Press Edition, Introduction, p. xxxiv. 

1 Ct. Robertson, Bacon, pp. 45, 47, 51, djc. 

BACON 113 

prehensiveness of their conception of human knowledge; and they 
were absolutely alone in their serious practical ambition to work 
out this conception. In the separate departments of thought, of 
investigation, of art, each is left far behind by numbers of men, 
who in these separate departments have gone far deeper than 
they, have soared higher, have been more successful in what they 
attempted. But Aristotle first, and Bacon after him, ventured on 
the daring enterprise of " taking all knowledge for their province"; 
and in this way they stood alone. The new world of knowledge 
has, however, turned out in many ways very different from what 
Aristotle or Bacon supposed; but their industry, their courage, 
their genius, in doing what none had done before, makes it equally 
stupid and idle to impeach their greatness. 1 

Aristotle condemned the methods of his predecessors; Bacon 
condemned Aristotle's; we condemn Bacon's; and no doubt ours 
will in time also be condemned. The perfection of method comes 
with the completion of experience. 

" What Bacon says of Plato is pre-eminently true of himself. 
* He was a man of sublime genius, who took a view of everything 
as from a high rock.' 2 Now to the young student I know nothing 
of so much impottunce as to be brought into contact with works of 
real genius, arid there must be many men who recollect the transi- 
tion from dry manuals of Logic to the brilliant pages of Bacon as 
forming one of the eras in their lives." 3 

Finally, what are the lessons which Bacon communicates 1 
"The duty of taking nothing upon tiust which we can verify for 
ourselves; of rigidly examining our first principles; of being care- 
fully on our guard against the various delusions arising from the 
peculiarities of human nature, from our various interests and pur- 
suits, from the force of words, and from the disputes and traditions 
of the different schools of thought; the duty of forming our conclu- 
sions slowly and of constantly checking them by comparison with 
facts; of avoiding merely subtle and frivolous disputations; of 
confining our inquiries to questions of which the solution is within 
our power; and of subordinating all our investigations to the wel- 
fare of man and society." 4 And what greater lessons have been 
taught by any philosopher of any age? 

Church, pp. 201-4. De A \tg. , ill, 4. 3 Fowler, p. 129. 

4 Fowler, p. 120. It ! a remarkable thing how one reviewer after another will accept 

Macaulay's estimate of Bacon's personal character. Two main charjres are commonly brought 

against Bacon, viz , treachery to Essex, and bribery. As regards the first, Bacon's duty an 

head of the State was far greater than his very limited obligations to Esacx. As regards the 

(0415) 10 




x. Descartes Dissatisfied with Existing Philosophic 


KemS Descartes Duperron was born in Touraine in 1596. Bacon 
had then reached his thirty-sixth year. 

The remark sometimes made that, for the man of genius, there 
is no education but what he gives himself, seems to apply with 
peculiar force to Descartes, who, on leaving the Jesuit College' of 
La F16che, declared that he had derived no other benefit from his 
studies 1 than that of a conviction of his utter ignorance, and a pro- 
found contempt for the systems of Philosophy then in vogue. The 
incompetence of philosophers to solve the problems with which they 
occupied themselves, the fact that no two thinkers could agree upon 
fundamental points, the extravagance of the conclusions to which 
some accepted premisses led, " determined him to seek no more to 
slake his thirst at their fountains". 2 

"As soon as my age permitted mo to pass from under the 
control of my instructors, I entirely abandoned the study of letters 
and resolved no longer to seek any other science than the knowledge 
of myself, or of the great book of the world. I spent the remainder 
of my youth in travelling, in visiting courts and armies, in holding 
intercourse with men of different dispositions and ranks, in collect- 
ing varied experience, and, above all, in making such reflection on 
the matter of my experience as to secure my improvement. For it 

second, there is no doubt that Bacon did accept gifts from suitors, but in riot a single CMC 
is there any reason to believe that he was corruptly swayed by the gifts, ami in taking 
these he was simply following the judicial practice of his day Pope's gibe that Bacon 
was "the meanest of mankind" probably explains, in some measure, Al.-iiaulay's prejudice 
The dislike shown to Bacon by Sortain and Dr. Abbott probably arose from tbe fact that 
Bacon did not champion any particular creed, but there is absolutely no doubt about the 
sincerity of his religious convictions. Roscoe's opinion that Bacon was "a crafty man " may 
be measured by his fulsome flattery of Coke, who was one of "the most truculent and un- 
scrupulous of English lawyers". No doubt Bacon was ambitious, and no doubt lie wan, as 
Dean Church says, " a pleaser of men ". These are admitted faults. But most of the charges 
usually levelled against Bacon have no foundation in fact, and Spedding has no difficulty at 
all in tearing Macaulay's case to pieces. The reader should refer to the works of Mr. Sped 
ding and to those of Mr. J. M. Robertson. 

* In " Mathematics, Physics, Logic, Rhetoric, and the ancient languages". 

* Ct Lewes, Biog. Hist. Phil., pp. 891-2. 


occurred to me that I should find much more truth in the reasonings 
of each individual with reference to the affairs in which he is per- 
sonally interested, and the issue of which must presently punish him 
if he has judged amiss, than in those conducted by a man of letters 
in his study, regarding speculative matters that are of no practical 
moment, and followed by no consequences to himself, further, per- 
haps, than that they foster his vanity the better the more remote 
they are from common sense; requiring, as they must in this case, 
the exercise of greater ingenuity and subtlety to render them 
plausible." 1 

For many years Descartes thus led a roving unsettled life, now 
serving in the army, now making a tour; now studying Mathematics 
in solitude, now conversing with scientific men. At the age of thirty- 
three he retired into Holland, there in silence and solitude to arrange 
his thoughts into a consistent whole. When, several years later, the 
results of his meditations were given to the world, in the shape 
of his celebrated Discourse on Method, the sensation produced was 
immense. It was evident to all men that ?in original and powerful 
thinker had arisen, and although, as might be expected, this origi- 
nality could not but rouse much opposition, just as originality almost 
always does, yet Descartes soon gained the day, and his fame 
became European.' 2 

2. He Considers a New Method of Procedure 

We have already seen that Scholasticism had, before this time, 
quite worked itself out. Even in Italy itself many men 3 were 
deeply inspired by the spirit of revolt against authority, and were 
asserting the freedom, individuality, and supremacy of thought. 
And the far-reaching speculative tendencies of the time were re- 
inforced by the new spirit of inquiry applied to nature by Coper- 
nicus, Kepler, Galileo, and Huron. Bacon's Xorum Organum appeared 
in 1620; Descartes' Mdhod seventeen years later. 4 

Descartes had none of the outspoken boldness which we are 
accustomed to associate with great reformers, and one of his 
biographers goes so far as to say that he was "timid to servility". 5 

i Ducourte on JfrfAod, Part I Cf Veitoh, Descartes, p. 10; and Lewes, op. cif. p. 892. 

* C!f. Lewea, op cit. pp. 302-3. 

* For Instance, Kruno, Vanini, and Campanula, whose ll\es will interest the reader. The 
attack on Aristotle by Karnus is also interesting. 

* Cf. Veitch, Descartes, xvi-xxi. Descartes had not seen the Organum before thinking out 
his Method. * Cf . Lewes, p. 393. 


He certainly did not care perhaps he did not dare to encounter 
the powerful opposition of the Church. As far as possible he 
avoided the appearance of an innovator, although this is exactly 
what he was in the truest sense of the word. When he attacked 
an old dogma, it was not by a daring march up to the face of 
it, but rather by a quiet process of sapping the foundations. He 
got rid also of traditional principles not so much by direct attack 
as by substituting for them new proofs and more acceptable 
grounds of reasoning. 

Though Descartes probably read more than some of his admirers 
supposed, he was not in any strict sense a reader. His wisdom grew 
mainly out of his own reflections, calmly yet ceaselessly pursued. 
Of mere learning and scholarship he had no esteem. He was in 
many ways typical of the self-reliant, somewhat harsh and in- 
tolerant, man of science, to whom erudition and all the heritage 
of the past seem to be mere trifling. 1 The very first sentence 
of his philosophy contains this celebrated declaration: " Since we 
begin life as infants, and have contracted various judgments con- 
cerning sensible things before we possess the entire use of our 
reason, we are turned aside from the knowledge of truth by many 
prejudices; from which it does not appear that we can be any 
otherwise delivered, than if once in our life we make it our 
business to doubt of everything in which wo discern the smallest 
suspicion of uncertainty". 2 All authority he threw aside, and 
boldly attempted to solve by reason alone the problems which 
hitherto had been solved by faith. 3 

" I had become aware/' he said, " even so early as during my 
college life, that no opinion, however absurd and incredible, can 
be imagined, which has not been maintained by some one of the 
philosophers; and afterwards I was led to infer that the ground 
of our opinions is far more custom and example than any certain 
knowledge. And I remarked that a plurality of suffrages is no 
guarantee of truth where it is at all difficult of discovery, as in 
such cases it is much more likely that it will be found by one 
than by many. I could, however, select from the crowd no one 
whose opinions seemed worthy of preference, and thus I found 
myself constrained, as it were, to use my own Keason in the 
conduct of my life." 4 

i Of. Ency. Brit, "Descartes", p. 118. 

a Prin of Phil , I (i). Cf. Veitch, p. 193 ; and Whewell, Phil, of Disc., p. 163. 

Cf. Morel, Phil vol. i, p. 152; and Lewes, p. 394. 

* Discourse on Method, Part II. Cf. Veitch, pp. 16, 17. 


3. His "Organon" is "Doubt" 

Descartes considered it necessary to examine the premisses of 
every conclusion, arid to believe nothing but upon the clearest 
evidence of reason, evidence so convincing that he could not by 
any effort refuse to assent to it. 1 Yet he could find no criterion 
of positive certainty in any existing philosophic system. The great 
question to him, therefore, was, "Is there in knowledge an ultimate 
basis which I can regard as absolutely true and certain]" "And, 
supposing this found, can I obtain from it a criterion of truth and 
certainty ? " 

In the settlement of these questions, doubt was the great instru- 
ment which Descartes pressed into his service. He began with an 
examination, by reflection, of the facts of consciousness. Of what, 
and how far, can we doubt? We can doubt, Descartes would say, 
whether it be true, as our senses testify, or seem to testify, that 
a material world really exists; we can doubt even of mathematical 
truths, at all events when the evidence is not directly present to our 
minds. But in the pursuit of a reflective doubt, we are bound at 
last to reach the boundary line which divides doubt from certainty. 
This dividing line Descartes found in self -consciousness; for self- 
consciousness implies self-existence, and about this there can be no 
doubt at all. We thus have a method which seems to make the 
least possible assumption. It starts simply from the fact of a 
conscious questioning; it proceeds to exhaust the sphere of the 
doubtable ; and at last it reaches that truth or principle which is 
its own guarantee. 2 

Descartes has told us how he found that he could plausibly 
enough doubt of everything, except of his own existence. He 
pushed his scepticism to the verge of self-annihilation. There he 
stopped: there in Self, there in consciousness, he found at last 
irresistible Certainty. 3 "The reality of the 'Ego' of Descartes 
is inseparably bound up with the fact of the definite act of con- 
sciousness." "The act and the Ego are the two inseparable factors 
of the "same fact or experience." 4 

4. "Cogito ergo sum" 

Descartes felt that he might doubt the existence of the external 
world and treat it as a phantom. But of the existence of his 

i Cf. Lewes, op. cit. p. 305. * Cf. Veitch, pp. xxii, xxiii. 

Cf. Lewes, p. 395. * Veitch, p. xxiL 


thinking, doubting mind, no sort of doul>t was possible. He, the 
doubter, existed, if nothing else existed. The existence that was 
revealed to him in his own consciousness was the first absolute 
certainty. Hence his famous cogito ergo sum: I think, therefore 
I am. 1 

The object of Descartes was to find a starting-point from which 
to reason, to find an irreversible certainty; and he found this in 
his own consciousness : " Doubt as I may, I cannot doubt of my 
own existence, because my very doubt reveals to me something 
which doubts. You may call this an assumption if you will; I 
point out the fact to you as a fact above and beyond all logic, 
a fact which logic can neither prove nor disprove, a fact which 
must always remain an absolute certainty, and as such a fitting 
basis for philosophy. Je pense, done je suis. I exist. This is 
a certainty if there be none other. It is in vain to ask a proof 
of that which is so irresistibly self-evident." 2 

We are assured of our own existence because the conception 
of existence is at once involved in the consciousness of self. We 
can distinguish the two elements but we cannot separate them; 
whenever we clearly and distinctly conceive the one, we are forced 
to think of the other along with it. But this gives us a rule for 
all judgments whatever. Whatever we cannot separate from the 
clear and distinct conception of anything, necessarily belongs to 
it in reality; and, on the other hand, whatever we can separate 
from the clear and distinct conception of anything, does not neces- 
sarily belong to it in reality. If, then, we set an object clearly 
before us, and separate it in thought as far as is possible from 
all other objects, we shall at once be able to determine what pro- 
perties and relations are essential, and what are not essential to 
it. And if we find empirically that any object manifests a pro- 
perty or relation not involved in the clear and distinct conception 
of it, we can say with certainty that such property or relation 
does not belong to it except by arbitrary arrangement of things 
which have no natural affinity or connection. 3 This is Cartesianism 
in a nutshell. 

1 Lewes, p. 395. Cf. Discourse on Method, Part IV; and Veitch, p. 33; also Maurice, Jfor. 
and Metaph. Phil., vol. ii, p. 299; and Grote, Expl. Phil., ii, pp. 35, 41, 79, 178-9. 

2 Lewes, p. 396; and cf. Eticy. Brit., "Descartes", p. 122. In regard to Oaasendi's 
objection, see Lewes, p. 395, and Veitch, p. xxiv. As to Huxley's criticism, see Veitch, 
pp. xrvi-xxvii. s Cf. Caird, Cartesianism, p. 143. 


5. Clear and Distinct Ideas 

Descartes, then, introduced a new method. It was indeed but 
another shape of the old formula "Know thyself", but it gave that 
formula a precise significance. It is of little use to tell a man to 
know himself by examining the nature of his thoughts: that had 
been done without success. Or by examining the process of his 
thoughts; that, too, had been accomplished, and the logic of Aris- 
totle was the result. The formula needed a precise interpretation, 
and that Descartes supplied. Thus, the vital portion of his system 
lies in this axiom: ivhatewr is clearly and distinctly conceived is true. 
This axiom he regarded as the foundation of all Science. 1 

Knowledge, then, must be "clear and distinct". Descartes has 
defined this test in the following words: "I call that clear which is 
present and manifest to the mind giving attention to it, just as we 
are said clearly to see objects, when, being present to the eye look- 
ing on, they stimulate it with sufficient force, and it is disposed to 
regard them ; but the distinct is that which is so precise and different 
from all other objects as to comprehend in itself only what is clear". 2 
By clear Descartes moans with plenty of light upon the idea, so that 
it is riot dim or obscure; by distinct he means standing out in bold 
relief, so that there is no difficulty in distinguishing one idea from 
other ideas, and no confusing it with them. But we must not, of 
course, think that the clearness of its perception in any way con- 
stitute s the truth of the idea. Against the possibility of this error, 
Locke's view as to the aggregation of our knowledge, which sets 
plainly before us the dependence of truencss on fact, should always 
be kept in mind. 3 

6. Descartes' Four Rules 

Descartes having laid down his fundamental axiom, his next step 
was to determine the rules for the proper detection of the ideas. 
" As a multitude of laws often only hampers justice, so that a state 
is best governed when, with few laws, these are rigidly administered; 
in like manner, instead of the great number of precepts of which 
Logic is composed, I believed that the four following would prove 

i Descartes, Prin. Phil, Part IV; and Cf. Lowes, p. 397. 

a Prin. Phil., Part I; cf. Vettch, Iv. Cf. also Leibnitz on Knowledge in Meditations d* 
Cognitione, Veritatc et ldei\ and Veitch, p. Ivi. Grote prefers the axiom, "False ideas can- 
not present themselves clearly and distinctly ". See Explor. Phil., ii, p. 206. 

Cf. Grote, Kxplor. Phil., ii, pp. 41, '200-7. 


perfectly sufficient for me, provided I took the firm and unwavering 
resolution never in a single instance to fail in observing them. 

" ' 1. Never to accept anything as true but what is evidently so; 
to avoid precipitancy and prejudice; and to admit nothing but what 
so clearly and distinctly presents itself as true that there can be no 
reason to doubt it/ 

" ' 2. To divide each of the difficulties under examination into as 
many parts as possible; that each part being more easily conceived, 
the whole may be more intelligible/ (Analysis.) 

" ' 3. To conduct the examination with order, beginning by that 
of objects the most simple and therefore the easiest to be known, 
and ascending little by little to knowledge of the more complex.' 

" ' 4. To make enumerations so complete and reviews do general, 
as to be confident that nothing essential has been omitted/" 1 

It is true, say the Port Royalists, 2 that there is much difficulty 
in observing these rules, but it is always advantageous to have them 
in the mind, and to observe them as much as possible when we try 
to discover the truth by means of reason, and as far as our mind is 
capable of knowing it. 

The four rules were Descartes' substitute for Logic. He had 
learned from Geometry to believe that all the subjects of human 
knowledge stood in a certain sequence, which may be detected if 
we are watchful never to assume as true what we have not ascer- 
tained to be true, and if we are on our guard against all " hasty 
jumps". 3 Descartes' mathematical studies profoundly influenced his 

"There is no question more important to solve", says Descartes, 
"than that of knowing what human knowledge is and how far it 
extends." "This is a question which ought to be asked at least 
once in their lives by all who seriously wish to gain wisdom." And 
he points out " wherein consists all the knowledge we now possess, 
and what are the degrees of wisdom at which we have arrived. 
The first degree contains only notions so clear of themselves that 
they can be acquired without meditation; the second comprehends 
all that the experience of the senses dictates; the third that which 
the conversation of other men teaches us; to which may be added 
as the fourth, the reading, not of all books, but especially of such 

i Discourse on Method, Part II. Cf. Veitch, p. 19; Lewes, p. 397; and Welton, Logic, ii, 
p. 216. 

Port Royal Logic, pp. 316-6. Cf . Maurice, U or. and Metaph. Phil., 11, p. 297. 


as have been written by persons capable of conveying proper in- 
struction. And it seems to me that all the wisdom we in ordinary 
possess is acquired only in these four ways. " Descartes then pro- 
ceeds to castigate the philosophers, men who in all ages have 
vainly endeavoured to find a fifth road to wisdom, by their search 
for " first causes and true principles from which might be deduced 
the reasons of all that can be known by man". 1 And a little further 
on, he says, "they who have learned the least of all that has been 
hitherto distinguished by the name of philosophy are the most fitted 
for the apprehension of truth". 2 

Professor Veitch thinks that the most liberal and probably the 
fairest interpretation of the criterion of Descartes is, that it is the 
assertion of the need of eridmw, whatever be its kind, as the ground 
of the acceptance of a statement or proposition. As such, it is the 
expression of the spirit not only of the philosophy of Descartes but 
also of modern research. 3 

Descartes was fully aware of the general destructive tendency 
of his method, and he felt that there was a necessity, while he 
was seeking for new foundations, for the adoption of a provisional 
morality, that he might not remain irresolute in his actions whilst 
he was occupied in this search for principles. This provisional 
morality consisted of a few simple maxims; for instance, obedience 
to his country's laws, adherence to the faith of his childhood, and so 
on. And having thus secured himself, as he conceived, against the 
perils of scepticism, he had less dilliculty in waiting for the assurance 
that he was always looking for. For nothing, he says, was less his 
desire than to doubt for doubting's sake. Instead of loving that 
shifting sand, he was impatient of it. lie always believed there was 
a rock and that it could be found. 4 

7. His Opinion of Logic 

Descartes set great value upon the proper development of the 
reasoning powers. "Those to whom the faculty of Reason is pre- 
dominant," he said, " and who most skilfully dispose their thoughts 
with a view to render them clear and intelligible, are always the 
best able to persuade others of the truth of what they lay down." 5 
But he had a very poor opinion of Logic. " I found that its syllo- 

l Cf. Kncy. Brit., "Descartes", pp. 122-3. 

2 Of. Veitch, Preface to Principles, pp. 170, 179. Veitch, p. 69. 

* Cf. Maurice, Mor. and Metaph. Phil., vol. ii, p. 298. 

* Discourse, i. Cf. Veitch, p. 8. 


gisrns and the majority of its other precepts are of avail rather 
in the communication of what we already know, or in speaking 
without judgment of things of which we are ignorant, than in the 
investigation of the unknown; arid although the science contains 
indeed a number of correct and very excellent precepts, there are, 
nevertheless, so many others, and these either injurious or super- 
fluous, mingled with the former, that it is almost quite as difficult to 
effect a severance of the true from the false as it is to extract a 
Diana or a Minerva from a rough block of marble." 1 In another 
place, 2 he says, " The logic of the schools is only a dialectic which 
teaches the mode of expounding to others what we already know, 
or even of speaking much, without judgment, of what we do not 
know ". 

8. His Mathematics and Physics 

Although, in later life, Descartes gave up the study of Mathe- 
matics, and was " anxious not to lose any more time in the barren 
operations of Geometry and Arithmetic", 3 yet he was one of the 
most eminent mathematicians of his age, and his mathematical 
training influenced to an enormous extent his views on things 
generally. His fame as a mathematician rests mainly on the appli- 
cation of Algebra to Geometry. Descartes must be considered not 
only as the founder of analytic Geometry, but also as the pioneei 
in the path which led up to the discovery of the Differential Cal- 
culus by Newton and Leibnitz. 4 It was Descartes who showed, in 
the most general manner, that every equation may be represented 
by a curve or figure in space, and that every bend, point, cusp, 
or other peculiarity in the curve, indicates some peculiarity in the 
equation. 6 

Descartes being convinced of the certitude of mathematical 
reasoning, gradually came to the conclusion that the method of 
Mathematics was capable of a much more extended application. 
As consciousness was his basis of certitude, so mathematical reason- 
ing should be his method of certitude. His demonstrations were 
thus made to take the form of gradual and successive deductions 
from "clear and distinct ideas" which served as starting-points. The 
whole system was rigorously deductive and, as might be expected 
from a mathematician, was based on the smallest possible number 

1 ib. ii, p. 18. 2 Preface to Principia. Cf. Veitch, p. 183. 

* Hamilton, Discussions, pp. 277-8. 

Cf. Mahaffy, Descartes, pp. 208-9; and Ency. Brit., "Descartes", p. 121. 

* Jevons, Prin. of Science, p. 632. 


of assumptions. He applied this method oven to Physics. When, 
for instance, in his Principia he announces his intention of giving 
a short account of the principal phenomena of the world, he says, 
"we desire to deduce effects from causes, not causes from effects". 1 
Thus, he arrives at his results by pure a priori reasoning, in direct 
opposition to the method of observation and experiment. Descartes 
was convinced that Geometry furnished the one model of proof. 

Descartes proceeds to apply his method to particular cases. In 
his Dioptrics he professes to deduce the laws of reflection and refrac- 
tion of light from certain arbitrary comparisons, in which the radia- 
tion of light is represented by the motion of a ball impinging upon 
the reflecting or refracting body. It is a curious instance of the 
caprice of fortune that Kepler, one of the greatest men of science 
of his day, failed to detect the law of refraction; while Descartes, 
who professed to be able to despise experiment, actually claimed 
to have discovered it. There is, however, good reason to believe 
that Descartes really learned the law of sines from Snell's papers. 2 
But whether this be so or not, it is certain that, notwithstanding 
the profession of independence of experience which his philosophy 
made, in reality experience constantly guided and instructed him. 
Descartes' reasonings and explanations were, consciously or uncon- 
sciously, often directed by the known facts, which he had observed 
for himself or learnt from others. 3 He certainly often did seek in 
facts for the law that lies at the foundation of them. And to this 
extent, of course, he departed from the method he had been so 
careful to lay down. 

9. His Theory of Vortices 

Descartes' famous theory of vortices is perhaps the best-known 
example of his method. 

He begins by banishing the notion of a vacuum, not, as his con- 
temporaries said, because Nature has a horror of a vacuum, but 
because the essence of substance being extension, wherever there 
is extension there must be substance. The infinite universe must 
therefore be infinitely full of matter; it is an absolute plenum. Con- 
sequently, empty space must be a chimera. The substance which 
thus fills all space must be assumed to be set in motion; 4 the parts 

i Cf. Mahaffy, Descartes, pp. 146, lf>0; Lewes, pp. 328-9; Whewell, Phil , p. 161. 
a But cf. Mahaffy, p. 200. a Cf. Whewoll, Mil., p. 162. 

4 I.e. by the Deity. The reader will be interested in Descartes' own exposition in hia 
Principia Philvsophice, where it is illustrated by diagrams. 


will then necessarily be ground into a spherical form, and the 
corners thus rubbed off, like filings or sawdust, form a second and 
more subtle kind of substance. There is, besides, a third kind of 
substance, coarser and less fitted for motion. Now we seem to 
have no alternative but to assume that the motions thus set up are, 
in form, like whirlpools, or vortices. Such circular motion will cause 
the " first matter " to collect at the centre of each vortex and make 
luminous bodies, such as the sun and fixed stars; the "second 
matter" will surround it, and by its centrifugal force constitute 
light and form the transparent substance of the skies. The third 
kind of substance is the material of opaque bodies, such as the earth 
and the planets. An innumerable series of vortices of matter will 
thus be produced, in which are carried along the grosser bodies 
situated in them. Our solar system is such a vortex, and the 
planets are carried round the sun by the motion of this vortex, each 
planet being at such a distance from the sun as to be in a part of 
the vortex suitable to its solidity and mobility. The motions arc 
prevented from being exactly circular and regular by various causes. 
For instance, a vortex may be pressed into an elliptical shape by 
contiguous vortices. 1 

Now vortices are on the whole plausible suppositions; for planets 
and satellites bear at first sight much resemblance to objects carried 
round in whirlpools, an analogy which doubtless suggested the theory. 
The system is not, then, intrinsically absurd and inconceivable, but it 
breaks down because it does not give results in accordance with the 
actual motions of the heavenly bodies. And the very first requisite 
of a hypothesis is its agreement with observed facts.' 2 Thus Descartes' 
method fails, as indeed it fails in practicallv all his investigations 
into Science. 

10. Why the Method Fails 

Although all knowledge of the external world is in reality only 
to be obtained by observation and induction, the mind conforms to 
these conditions reluctantly, and is ever ready to rush to general 
principles and then to employ itself in drawing conclusions from 
these by deductive reasoning. Men therefore readily overlooked 
the precarious character of Descartes 7 fundamental assumptions, in 
their admiration of the skill with which a varied and complex uni- 

1 See Lewes, pp. 402-8; Ency. Brit., "Descartes", p. 124; Mahaffy, pp. 15S-9; and Prin 
cipia, ill, 47. a See Jevons, Prin. of Sci., pp. 611, 617. 


verse was evolved out of them. As Mackintosh says, 1 " A system 
which attempts a task so hard as that of subjecting vast provinces 
of human knowledge to one or two principles, if it presents some 
striking instances of conformity to superficial appearances, is sure 
to delight the framer, and for a time to subdue and captivate the 
student too entirely for sober reflection and rigorous examination. 
Consistency passes for truth. When principles in some instances 
have proved sufficient to give an unexpected explanation of facts, 
the delighted reader is content to accept as true all other deductions 
from the principles. Specious premisses being assumed to be true, 
nothing more can be required than logical inference." 

Descartes' system was, at bottom, a glaring example of that 
error which Bacon had called Anticipation, that illicit generalization 
which leaps at once from special facts to principles of the widest 
and remotest kind. Yet Descartes believed that his demonstrations 
equalled, and even surpassed, the demonstrations of Geometry, such 
belief being founded on the very nature of certitude as conceived by 

Now, is Descartes right or wrong in his assumption that con- 
sciousness is the ultimate ground of certitude? Can ideas be re- 
garded as the internal copies of external things'? 

Lewes, in no uncertain terms, declares that Descartes is wrong. 
"Consciousness is the ultimate ground of certitude for me; if I am 
conscious that I exist I cannot doubt that I exist; if I am conscious 
of pain, I must be in pain. This is self-evident But what ground 
of certitude can consciousness be respecting things which are 'twt- 
me'1 The principle can only extend to things which relate to me. 
I am conscious of all that passes within myself] but I am not con- 
scious of what passes in not-self: all that I can possibly know of 
the not-self is its effects on me. Consciousness is therefore 'cabin'd, 
cribb'd, confin'd ; to me, and to what passes within me. So far does 
the principle of certitude extend, and no farther. Any other idea's 
we may have, any knowledge we may have respecting not-self, can 
only be founded on inferences, and directly we leave the ground of 
consciousness for that of inference, our knowledge becomes question- 
able. Thus the mathematical certainty which Descartes attributes 
to these inferences becomes a great uncertainty." 2 

Descartes says that not only do we know things exclusively 
through the medium of ideas, but also that, in consequence of this, 

i Dissertation on Ethical Sciences. Cf. Whewell, Phil., p. 164. 
* Lewes, p. 405. 


whatever we find in the ideas must necessarily be true of the things. His 
reason is that, as ideas are caused in us by objects, and as every 
effect must have as much reality as the cause, so must ideas 
have the same reality as things. But this is a fallacy. Descartes 
assumes that the mind is a passive recipient, a mirror in which 
things reflect themselves. In truth, however, we are utterly unable 
to apprehend the real nature of things external to us. " When we 
are placed in contact with external objects, they operate upon us; 
their operations we know, themselves we cannot know." Wo have no 
right to infer that the ideas excited are exact copies of the exciting 
causes, or that they apprehend the whole nature of the causes. 1 

ii. The Cartesian Method and the Baconian Method 

Metaphysicians join hands with Descartes and turn their backs 
on Bacon because Descartes held the doctrine of the existence of 
Innate Ideas. 2 But the assumption that we have ideas absolutely 
independent of all experience is one of the fundamental errors of 
metaphysical speculations. That we have no such ideas seems now 
to be clearly established. 3 It may be urged that Descartes hardly 
seemed to realize the importance of Innate Ideas to his system, but 
the fact remains that such Ideas form the very basis of the Cartesian 
doctrine. And Cartesianism would be unacceptable to Science from 
this fact alone. 

Bacon and Descartes lived at a time when reforms were urgently 
wanted. When Bacon urged attention, and ever-repeated attention, 
to nature, to fact, to observation, to experiment, he was performing 
a most useful and greatly needed task; but when he advised less 
attention to books, and to reflection or self -concentrated thought 
("idle cobwebs of the brain"), it is less safe to follow him. For, 
after all, what was wanted in regard to books and thought was 
exactly the same as was wanted in regard to observation, not at all 
less attention, but a wiser, better applied, more real attention, which 
would really help, instead of hindering, observation of nature and 
fact. Of this wiser and better reflection or thought, Descartes was 
the apostle, as Bacon was of better and more abundant observation. 4 

Science must employ deduction as well as induction, and Bacon's 
greatest error was in not sufficiently acknowledging it. Hence, we 

1 Cf . Lewes, p. 406. 

2 Dugald Stewart denies that Descartes held the doctrine, but see Lewes, p. 407. 

3 Cf. Lewes, pp. 407-8, and see the next chapter. 
* Ot Grote, Explor. Phil., voL i, p. 224. 

LOCKE 127 

may partly account for the curious fact that Bacon, with his cautious 
method, made no discoveries, while Descartes, with his rash method, 
made important discoveries. But of course Descartes' knowledge 
of Mathematics had much to do with this, for the discoveries were 
of a kind to which the mathematical method was strictly applicable. 

In Bacon's view, the important thing about truth was its closeness 
to fact; in Descartes' view, clearness and distinctness of thought. 1 
Bacon teaches us one great lesson, Descartes another. The lessons 
are complementary and we need them both. 

As we have seen, Bacon's method is of little value because it is 
impracticable. But Descartes' method is not only impracticable but 
also dangerous, for it teaches us to deduce conclusions from general 
principles assumed independently of all experience?, to deduce effects 
from imagined causes rather than causes from known effects. The 
special danger of the Cartesian method is its attractiveness and its 

Cartesianism took but slight hold in England. Towards the 
close of the seventeenth century, its only remnants were "an over- 
grown theory of vortices, which received its deathblow from Newton; 
and a dubious phraseology about Innate Ideas, which found a witty 
executioner in Locke ". 2 



i. Characteristics of Locke 

From Westminster School, which he entered at fourteen, Locke 
passed on to Christ Church, but the strong attachment of the Uni- 
versity to all that was old, and its hardly disguised contempt for 
anything new, seem to have irritated him. Though now utterly 
routed elsewhere, Scholasticism was still strongly entrenched at 
Oxford, and scholastic studies and disputations were maintained 
with an ostentatious formality entirely unsuited to Locke's inquisi- 

1 Of. Orotc, Explor. Phil., vol. i, pp !5-rt. 

2 Ency. Brit., " Descartes", p. 128. The method of Descartes was pushed to its ultimate 
concluiion by Spinoza, whoso works the reader should consult. 


tive temper. Like his great predecessor Bacon, he soon imbibed a 
profound contempt for university studies, and in after-life regretted 
that so much of his time should have been wasted on such profit- 
less pursuits. So deeply convinced was he of the vicious method of 
college education that he ran into the other extreme and thought 
self-education the best. 1 

When considering Locke as a philosopher, it is important to 
realize that he was no mediaeval monk but an English gentleman 
and a man of the world. He represented all that was best and 
most accomplished in the English lay mind, and he was exactly the 
man then wanted to resist the clerical or university mind. But 
tenacious and effective as this resistance was, it was absolutely 
untinged with any form of fanaticism. 2 

As a writer, Locke is clear, truthful, direct. " He indulges in 
no vague formulas, no rhetorical flights, no flattery of prejudices, 
arid no word jugglery." 3 Yet his language is sometimes ambiguous 
and sometimes even contradictory, 4 and no attempt should therefore 
be made to gather his opinions from isolated and casual expressions, 
since these often require to be interpreted on the general analogy of 
his system. Locke was anxious to make himself intelligible, and to 
this end he varied his expressions and stated his meaning in a 
variety of forms. He must be read more than once, or he will 
almost inevitably be misinterpreted. 

The essence of Locke's philosophy is the reasonableness of taking 
probability as the ultimate guide in all the really important concerns 
of life. A repugnance to believe blindly what rested on authority, 
as distinguished from what was seen to be sustained by self-evident 
reason, or by demonstration, or by good probable evidence, runs 
through his life. He is a typical man of science in his reverence 
for facts, in his tendency to turn away from merely verbal reason- 
ings, and in his ready submission to truth. 5 Locke sought anew for 
himself a solid foundation for human knowledge. Like Bacon, he 
turned away with aversion from Scholasticism, which seemed to him 
to encourage the two chief hindrances to the intellectual liberty of 
the individual, empty verbalism, and unverified assumption. 7 

i Of. Lewes, Biog. Hist. Phil., pp. 448-9; Ency. Brit., "Locke", p. 752; Alexander, Locke t 
p. 4. 

a Cf. St. John, Locke, vol. i, p. 17; Maurice, Mor. and Met. Phil., vol. ii, p. 440. 

Of. Lewea, p. 464. * Cf. Hamilton, Discussions, p. 78. * Cf. Ency. Brit., p. 765. 

*Cf. Morel, Phil., vol. i, p. 91. * Cf. Frazei; Locke, pp. 40-41, 105-6. 

LOCKE 129 

2. His Toleration 

Locke had found all parties and sects disposed towards persecu- 
tion. Brought up, like Bacon, in a Puritan household, his first 
sympathy was, very naturally, with the Puritans, but this was 
gradually lessened by what he saw of the intolerance of the Presby- 
terians and the fanaticism of the Independents. He found, he says 
characteristically, that " what was called general freedom was really 
general bondage". 1 And in his books he directly encouraged resis- 
tance to " masters or teachers who t&ke men off the use of their own 
judgment, and put them upon believing and taking upon trust with- 
out further examination". That every man should be able to see 
things as things are, and not merely through the eyes of others, 
was his greatest wish. He pleaded strenuously for toleration; and 
his Epistola de Tolerantia has been called the most original of all his 

The toleration for which Locke argued then implied a complete 
revolution in the previously received view of human knowledge and 
belief. It implied a protest against those who demand absolute 
certainty in questions where balanced probability alone is within the 
reach of human intelligence. Locke argued that the foremost duty 
of the Church was to promote goodness and to give no counten- 
ance to theological wranglings. "No man", he maintains, "is hurt 
because his neighbour is of a different religion from his own, and 
no civil society is hurt because its members are of different religions 
from one another." An encouragement of variety in individual 
opinion may be advantageous to society because it tends to develop 
the intellectual resources of mankind and thus adds to the security 
for the discovery of truth. 

But even Locke did not teach the duty of an unlimited tolera- 
tion by the State. He argues for the forcible suppression of 
opinions that operate to the dissolution of society, or which subvert 
those moral rules which are necessary to the preservation of order. 
He even applies this principle so as to exclude from toleration all 
who are themselves Intolerant. 2 

i Cf. Eticy. Brit , " Locke", p. 752. 

a See Fraser, Locke, pp. 88-94; and Ency. Brit., xiv, 752-0. 

(0415) 11 


3. His Views on Education 

Locke's philosophical works are: Some Thoughts on Education; 
The Conduct of the Understanding; and An Essay Concerning Human 

In Thoughts on Education, information and mere learning are 
subordinated to the formation of character and practical wisdom. 
Accumulating facts in the memory without using the power to 
think, and without accustoming the youthful mind to apply reason 
to the evidence by which individual thoughts mast be tested, is 
always referred to as the cardinal vice in teaching. "Truth needs 
no recommendation/' says Locke, "and error is not mended by it; 
in our inquiry after knowledge, it little concerns us what other men 
have thought." 1 

4. "The Conduct of the Understanding " 

The Conduct of the Understanding was designed as an additional 
chapter to the Essay, but the main theme on which it treats is con- 
nected rather with the work of self-education than with the analysis 
of knowledge. The suggestive nature of this little volume will be 
seen from the following passages, culled almost at random: 

" Let not men think there is no truth but in the sciences that 
they study, or the books that they read. To prejudge other men's 
notions before we have looked into them is not to show their 
darkness but to put out our own eyes." 2 

"To those who would shake oft* the great and dangerous 
monster, prejudice, who dresses up falsehood in the likeness of 
truth, I shall offer this one mark whereby prejudice may be known. 
He that is strongly of any opinion must suppose that his persuasion 
is built upon good grounds, and that his assent is no greater than 
what the evidence of the truth he holds forces him to, and that they 
are arguments and not inclination or fancy that make him so confi- 
dent and positive in his tenets. Now if, after all his profession, he 
cannot bear any opposition to his opinion, if he cannot so much as 
give a patient hearing, much less examine and weigh the arguments 
on the other side, does he not plainly confess it is prejudice governs 
him?" 8 

1 Cf. Ency. Brit., xiv, p. 75C. The whole of Thoughts on Education is well worth reading. 
The teacher will pick up many valuable hints, though, of course, much of the advice Locke 
gives is now only of historical interest. Locke's views should he compared with those of 
Comenius, then with those of Rousseau. (See Fowler, pp. 173-6.) 

a Section iii, " Reasoning ". * Section x, " Prejudice ". 

LOCKE 131 

" Reading furnishes the mind only with materials of knowledge; 
it is thinking makes what we read ours. The memory may be 
stored, but the judgment is little better, and the stock of knowledge 
not increased, by being able to repeat what others have said." 1 

" I do not say but a man should embrace some opinion when he 
has examined, else he examines to no purpose; but the surest and 
safest way is to have no opinion at all till he has examined, and that 
without any the least regard to the opinions or systems of other men 
about it." 2 

5. Locke's "Essay" 

The object of Locke's great philosophical work, Essay Concerning 
Human Understanding, was " to inquire into the original, certainty, 
and extent of human knowledge". Locke desired to make a faithful 
report, based on what he actually found, as to the extent to which 
we can share in certain knowledge, and in what cases we can " only 
judge and guess" on grounds of probability. The Essay was in- 
tended to be a defence of intellectual freedom. Locke waged war 
against dogmas which refuse to be verified by facts; and against 
words and phrases for which there are no corresponding ideas or 
meanings. He believed that by insisting upon a recognition of 
"experienced" ideas, he was helping to put demonstration and 
well - calculated probabilities in the room of blind repose upon 
authority. 8 

Although discovery of the nature and extent of the few cer- 
tainties that are within the scope of human understanding and of 
the ground and office of probability, is announced as the aim of the 
Essay, it is curious that only the last of the four books into which 
the Essay is divided is directly concerned with this subject. But 
before reference is made to the main theme of the Essay, there are 
two subsidiary topics which deserve passing mention: (1) the im- 
perfections of language, which Locke deals with in his third book; 
and (2) the association of ideas, which forms the subject of the last 
chapter of the second book. 

i Section xx, " Reading ". a Section xxxv, " Ignorance with Indifferencj ". 

Of. Kncy. Brit., p. 767; and Frazer, op. cit. p. 107. 


6. The Ambiguities of Language 

To the ambiguities of language Locke gave special attention. 
We make two or three typical extracts from the Essay. 

"To make words serviceable to the end of communication, it 
is necessary that they excite in the hearer exactly the same idea 
they stand for in the mind of the speaker. Without this, men fill 
one another's heads with noise and sounds, but convey not thereby 
their thoughts, and lay not before one another their ideas. Names 
of very compound ideas, such as for the most part are moral words, 
have seldom in two different men the same precise signification." 1 

" Men take the words they find in use amongst their neighbours; 
and that they may not seem ignorant what they stand for, use them 
confidently, without much troubling their heads about a certain fixed 
meaning; whereby, besides the ease of it, they obtain this advan- 
tage, that, as in such discourses they seldom are in the right, so 
they are as seldom to be convinced that they are in the wrong." 2 

"All the art of Khetoric, besides order and clearness, all the 
artificial and figurative applications of words eloquence hath in- 
vented, are for nothing else but to insinuate wrong ideas, move 
the passions, and thereby mislead the judgment, and so indeed are 
perfect cheats ; and therefore however laudable or allowable oratory 
may render them in harangues and popular addresses, they are 
certainly in all discourses that pretend to inform or instruct, wholly 
to be avoided; and where truth arid knowledge are concerned, 
cannot but be thought a great fault either of the language or 
person that makes use of them. It is evident how much men love 
to deceive and be deceived, since rhetoric, that powerful instrument 
of error and deceit, has its established professors and is publicly 
taught." 3 

"Toga, tunica, pallium, are words easily translated by gown, 
coat, and cloak; but we have thereby no more true ideas of the 
fashion of those habits amongst the Romans than we have of the 
faces of the tailors who made them." 4 

7. The Association of Ideas 

The chapter on the Association of Ideas at the end of the second 
book of the Essay, was introduced in the second edition, "not in 
any way philosophically explanatory either of the thoughts or of 

* Ch. ix, | 6. 2 ch. x, 4. Ch. x, 34. * Ch. xi, 26. 

LOCKE 133 

the knowledge and probable beliefs of men, but as the chief source 
of human prejudices, as a cause of human errors against which men 
need, in an especial manner, to be warned". This useful chapter 
was a kind of afterthought. 1 

The term Association of Ideas is used to denote the tendency 
which one thought in our minds has to introduce another thought. 
Such an association is apt, as Dugald Stewart points out, 2 to warp 
our opinions both by blending together in our apprehensions things 
which are really distinct in their nature, and by connecting in the 
mind erroneous opinions with truths which command our assent. 

"Some of our ideas have a natural correspondence and con- 
nexion one with another; it is the office and excellency of our 
reason to trace these and hold them together in that union and 
correspondence which is founded in their peculiar beings. Besides 
this there is another connexion of ideas wholly owing to chance 
or custom; ideas that, in themselves, are not all of kin, come to be 
so united in some men's minds that it is very hard to separate 
them; they always keep in company, and the one no sooner at any 
time comes into the understanding, but its associate appears with 
it; and if they are more than two which are thus united, the whole 
gang, always inseparable, show themselves together." 3 

The chapter abounds in interesting illustrative examples. For 
instance: children are often taught to associate figure and shape 
with the idea of the Deity, and in later life have the greatest 
difficulty in severing the two notions. Again : although goblins 
and sprites have no more to do with darkness than with light, yet 
children are often afraid of the dark because a foolish maidservant 
has perhaps associated the dark with the existence of goblins and 
sprites. 4 

Further reference to the Association of Ideas will be made in 
the next chapter. Meanwhile we must touch upon the main feature 
of Locke's philosophy. 

8. Locke the Founder of Modern Psychology 

Locke was the founder of modern introspective Psychology. 
He was the first " to watch patiently the operations of the mind 

1 This chapter should be compared with ITobbes, Human Nature, ch. iv, and Leviathan, 
I, iii; Hume, Human Nature, i, 4, and Essays on Hum. Und., 3; Condillac, Essai sur 
Vorigine de* Connaitxance Humaines, I, iii. See Fowler, Locke, p. 141. Locke appears to 
have been the first to use the exact expression " Association of Ideas ". The reader will find 
some beautiful lines on this subject in Byron, Childe Harold, iv, 23-4. 

Dugald Stewart, Works, Part I, ch. v, ii, (1), p. 184. 6. * | 10, 17. 


in order that he might, if possible, surprise the evanescent thoughts 
and steal from them the secret of their combinations". Others 
before him had cast a hasty glance inwards, but they dogmatized 
on what they saw; they contented themselves with the thoughts 
as they found them. Locke's object, however, was to discover 
the origin of the thoughts, 1 to find the origin of " ideas " in the 
individual man and their connection in constituting knowledge. 

There are two propositions on which Locke is constantly insist- 
ing: one, that the object of his investigation is his own mind; the 
other, that his attitude towards this object is that of mere observa- 
tion. He speaks of his own mind just as he might of his own body. 
He regards the "minds" of different men as so" many different 
things " thinking things". This " thinking thing", as he finds it 
in himself, the philosopher has merely and passively to observe, in 
order to understand the nature of knowledge. 2 We thus see that 
Locke had imbibed the spirit of the Baconian method: just as with 
the study of matter, so with the study of mind; observation of 
facts must come first, then classification, then reasoning. 

Locke's philosophy is pre-eminently a philosophy of "experi- 
ence". It accepts nothing on authority, and no foregone conclu- 
sions. "It digs, as it were, into the mind, detaches the ore, 
analyses it, and asks how the various constituents come there." 3 

9. The Origin of our Ideas 

Hobbes and Gassendi believed that all our ideas are derived 
from sensations; nihil est in intelledu quod non prms fuerit in sensu. 
But Locke's fundamental proposition was that there are two sources, 
not one source, and that these were Sensation and Reflection. He 
separated himself decisively from the upholders of the doctrine of 
innate ideas of truths independent of experience and declared 
that all our knowledge is founded on experience. And he separated 
himself equally decisively from those who saw no source of ideas 
but Sensation, declaring that although Sensation was the great 
source of most of our ideas, yet there was "another fountain from 
which experience furnisheth the understanding with ideas"; and 
this source, " though it bo not sense, as having nothing to do with 
external objects, yet it is very like it, and might properly enough 
be called internal sense"; this he calls Reflection* 

i Cf. Lewes, 455, 466, 459. a cf. Green and Grose, Hume, pp. 6-7. 

Fowler, Locke, p. 160. Cf . Lewes, p. 403. 

LOCKE 135 

" Since there appear ", says Locke, 1 " not to be any ideas in the 
mind before the senses have conveyed any in, I conceive that ideas 
in the understanding are coeval with Sensation-* which is such an 
impression, made in some part of the body as produces some per- 
ception in the understanding. It is about these impressions made 
on our senses by outward objects that the mind seems first to 
employ itself in such operations as we call remembering, considera- 
tion, reasoning, &c. In time the mind comes to reflect on its own 
operations about the ideas got by Sensation, 3 and thereby stores 
itself with a new set of ideas which I call ideas of Reflection. These 
impressions which are made on our senses by outward objects ; and 
the mind's own operations, proceeding from powers proper to itself, 
are the original of all knowledge." 

By Sensation Locke understands "the simple operation of ex- 
ternal objects through the senses". The mind is herein wholly 
passive. The senses, therefore, may be said to furnish the mind 
with one portion of its materials. 

By Reflection he understands that internal sense by means of 
which the mind observes its own operations. This furnishes the 
second and last portion of the materials out of which the mind 
frames knowledge. 4 

10. Simple and Complex Ideas 

"When the understanding is once stored with simple ideas, it 
has the power to repeat, compare, and unite them, even to an 
almost infinite variety, and so can make at pleasure new complex 
ideas. But it is not in the power of the most exalted wit, or 
enlarged understanding, by any quickness or variety of thought, 
to invent or frame one new simple idea in the mind not taken in 
by the ways aforementioned." 5 

Of " simple ideas of sensation ", some come into our minds by 
one sense only. Such are the various colours, sounds, tastes, and 
smells. The ideas we get by more than one sense are those of size, 
shape, 6 number, rest, motion. 

* Essay, II, 1, 23-24. 

2 For a carefully reasoned criticism of this assertion, see Lewes, p. 466. Reference should 
then be made to the chapters on Sensation and Perception in Herbert Spencer's Psychology, 
followed by the corresponding chapters in Prof. W. James's Psychology 

The words " operations about the ideas " are a little obscure, but the general drift of the 
whole sentence is pretty obvious. 

* Of. Lewes, hiotj. Hint. Phil., p. 466; Whewell, Phil, of Disc., p. 202; Green and Grose, 
Hume, pp. 8, 9. Cf. Essay, Book II, ch. i. Orig., exUiwwn, figure. 


The " simple ideas of reflection" which the mind acquires when 
"it turns its view inward upon itself, and observes its own actions 
about those ideas it has received from without", are mainly two, 
namely, Thinking and Willing. 

"There be other simple ideas which convey themselves into the 
mind by all the ways of Sensation and Reflection, namely, Pleasure 
or Delight, Pain or Uneasiness, and so forth." 1 

In the reception of these simple ideas, the mind is regarded by 
Locke as merely passive. It can no more refuse to have them, 
alter or blot them out, than a mirror can refuse to receive, alter, 
or obliterate the images reflected on it. But having once received 
its simple ideas, the mind is able to create out of them complex 
ideas, and that in an infinite variety; this it does chiefly by com- 
bining, comparing, and separating them. 2 In other words, while 
the mind is passive in respect of its two sources of experience, 
sensation and reflection, it is also active, in that it can compare, 
distinguish, and abstract. Thus simple ideas are the ultimate con- 
stituents of experience, the uncompounded appearances of things; 
complex ideas are the workmanship of the mind. 3 The mind mani- 
pulates the materials derived from sensation and reflection, and so 
manufactures the complex ideas. Or the complex ideas may be 
regarded as resolvable into these elements of sensation and reflec- 
tion, together with an active element of construction referable to 
the mind itself. 

As an instance of the manner in which Locke attempts to 
resolve a complex idea into simple ones, we may take the idea of 
"substance". 4 

If we examine our idea of, say, a horse, a man, or a piece of 
gold, we are able to resolve it into a number of simple ideas, 
such as size, shape, solidity, weight, colour, &c., coexisting together. 
But we feel that there must be, in addition to all these qualities, 
a substratum, 5 as Locke says, "wherein they do subsist, and from 
which they do result". Now of the various qualities, we can 
form a clear idea and give a more or less intelligible account. 

i Essay, Book II, ch. vii, 1. 2 Fowler, Locke, p. 136 ; and Essay, II, xii, 1. 

* Alexander, Locke, p. 33. In regard to simple ideas of sensation, Locke distinguishes 
between the ideas of the primary qualities (size, shape, number, rest, and motion) and ideas 
of secondary qualities of bodies (colour, taste, smell, <fec.) Bodies possess primary qualities, 
no matter what change they undergo ; but secondary qualities change with varying circum- 
stances. Lewes thinks the real distinction should be that the former are invariable conditions 
of a sensation, and the latter variable. Cf. Lewes, pp. 468-9; and Alexander, pp. 34-6. 

4 For Locke's division of Complex Ideas (modes, substances, relations), see Essay, II, xii, 
8, Ac. Cf. also Green and Grose, Hume, p. 82, <fec. 

Cf. ch. iii, 2, and ch. vii, 4. 

LOCKE 137 

But can we form a clear idea or give an intelligible account of 
the substratum? A complex idea of an unsubstantial aggregate of 
sensible qualities, without a centre of unity to which they may 
be " attributed", Locke finds unthinkable. An adjective without 
a substantive is meaningless; and when we say that all adjectives 
necessarily presuppose substantives, we express in another way this 
obligation to substantiate our simple ideas. But Locke confesses 
candidly that we cannot form an idea-image of the substratum. 
If we ask what the " substance" is to which this colour or that 
odour belongs, and are told that it is the solid and extended par- 
ticles of which the coloured and odorous mass consists, this indeed 
gives a substance that is picturable, as such particles are; but then 
it is inadequate to the genuine idea of substance, for we find that 
we are mentally obliged to ask in turn what their substance is, and 
having got in reply only something else that is picturable, we have 
to repeat the question for ever, as long as we get nothing which 
transcends the imagination. We are, says Locke, " in a difficulty 
like that of the Indian who, after explaining that the world rested 
on an elephant, which in its turn was supported by a broad-backed 
tortoise, could at last only suppose the tortoise to rest on 'some 
thing' / know not wJiat". Locke was baffled, as we are all baffled, 
by this endless incomprehensible regress. Curiously enough, Locke 
does not seem to have asked himself the question why we are 
mentally unable to refrain from thinking more than we can 
mentally picture. 1 

ii. Innate Ideas 

We have already noticed that Locke waged war against "innate" 
ideas. Locke believed that by insisting upon a recognition of 
"experienced" ideas only, he was helping to put demonstration and 
well-calculated probabilities in the room of blind repose on authority. 
That a part of human knowledge, and this the most important part, 
exists from the first, ready made consciously in our minds, inde- 
pendently of experience and prior to experience, might be an 
opinion eminently calculated to "ease the lazy from the pains of 
search", but would not bear examination at all. A blind prejudice 
that their assumptions were "innate" was enough "to take men 
off their own reason and judgment and to put them upon believing 
and taking upon trust without further examination". 

i See Fraser, Locke, pp. 147-50; Fowler, Locke, pp. 187-8; Essay, II, xxiii, $ 2, and I, Iv, 
18; Ency. Brit., " Locke ", vol. xiv, p. 700. Cf. ch. iii, 2. 


Locke challenged the defenders of innate ideas to produce them 
and show what and how many there are. Did men find such innate 
ideas "stamped on their minds" when they came into the world, 
nothing could be more easy than this. Those who attempt such 
an enumeration differ in the lists which they draw up, and give no 
sufficient reason why many other propositions which they regard 
as secondary and derived should not be admitted to the same rank 
with the so-called innate principles, which they assume to be 
primary and independent. It is, of course, impossible clearly to 
discriminate between those propositions which appear to be axio- 
matic and those which are derived. Race, temperament, capacity, 
habit, education, produce such differences between man and man, 
that a proposition which to one man appears self-evident arid un- 
questionable will by another be admitted only after much hesita- 
tion, while a third will regard it as false. Especially is this the 
case with many of the principles of religion and morals, which have 
now been received by so constant a tradition in most civilized 
nations, that they have, for the most part, come to be regarded 
as independent of reason, and if not " engraven on the mind" from 
its birth, are at least exempt from discussion and criticism. But 
the fact that they are not universally acknowledged shows that 
to mankind, in general, at any rate, they are not axiomatic, and 
that, however clear and convincing the reasons for them may be, 
at all events those reasons require to be stated. 1 

Although the Essay attacks imiateness in human knowledge, 
yet the "self-evidence" which comes to us gradually, "in the slowly 
growing light of educated reason", of much that we know is 
vigorously asserted. Locke says that in some cases the intellect 
becomes able to perceive a truth, as the eye does light, by being 
directed to it by intuition alone. The innate principles which he 
so persistently attacks are entirely different from those intuitive 
elements of knowledge, which are, by degrees, seen by growing 
reason to be either self-evident or demonstrable. 2 

Locke left much unexplained, and, in spite of all the ingenuity 
of subsequent thinkers, 8 we are still profoundly ignorant of tho 
precise nature of the so-called a priori element of our knowledge. 
But modern investigation seems to suggest that considerable light 

i See Fowler, Locke, pp. 129-32. 

a Iraser, Locke, pp. 115-6. Cf. Morel, Phil., pp. 101-4 ; Fowler, Locke, pp. 129-31 ; Maurice, 
Mor. and Metaph. Phil., p. 441. 

* Kant, for instance, tried to prove that it was only through certain a priori elements in 
the mind that our a posteriori experiences were intelligible. 

LOCKE 139 

may be thrown on the subject by the principle of Heredity. It is 
possible that what are called innate ideas are certain tendencies of 
the mind "to group phenomena under certain relations and to 
regard them under certain aspects; and the existence of such ten- 
dencies, so far as the individual is concerned, seems to be explained 
by the principle of hereditary transmission. And it seems probable 
that we must assign the formation of these tendencies to the con- 
tinuous operation, through a long scries of ages, of causes acting 
uniformly, or almost uniformly, in the same direction, in a word, 
of Evolution." 1 A more positive answer cannot at present be given; 
for we are forced to admit that the beginnings of our intellectual 
life are still enshrouded in mystery. 

12. Locke's Critics 

The majority of Locke's numerous critics have woefully misre- 
presented him. Their attitude has usually been quite unreasonable, 
for he spoke plainly and sought the truth, and never attempted to 
mystify anyone. " All those men who still seek to penetrate im- 
penetrable mysteries, and who refuse to acknowledge the limits 
of man's intelligence, treat Locke with the same superb disdain as 
the ambitious alchemists treated the early chemists. The tone in 
which modern Frenchmen and Germans speak of Locke is painful; 
the tone in which many Englishmen speak of him is disgraceful. 
To point out any error is honourable, but to accuse him of errors 
which are not to be found in his work, and to misinterpret his 
language and then accuse him of inconsistency and superficiality, 
deserve the severest reprobation." 2 

Victor Cousin's criticisms were, as Lewes conclusively shows, 
shallow and unfair, but Cousin did at all events take the trouble 
to read the Essay with some care; whereas another critic, Dr. 
Whewell, impatiently remarked, "We need not spend much time 
in pointing out the inconsistencies into which Locke fell, as all 
must fall, who recognize no source of knowledge except the senses". 
But this is, of course, a misrepresentation. Whewell must have 
known that Locke did recognize another source, namely, in Reflec- 
tion, and his criticism is therefore quite beside the mark. 3 

Locke's greatest critic was Leibnitz, who was a great mathe- 

i Fowler, Locke, pp. 145-6 See also M'Cabe, Evolution of Mind ; M action aid, The Child't 
Inheritance ; and the works of Gallon and Weismann. 

a Lewes, pp. 478-4. Cf. Lewes, pp. 474-9. 


matician and a Cartesian. Leibnitz was a follower of Plato, and 
was therefore naturally repelled by Locke's doctrines. Schlegel 1 
has well observed that every man is born either a Platonist or 
an Aristotelian, and Leibnitz and Locke were examples of this an- 
tagonism. "Our differences", says Leibnitz, "are important. The 
question between us is whether the mind in itself is entirely empty, 
like a tablet upon which nothing has been written (tabula rasa) 
according to Aristotle and the author of the Essay, and whether 
all that is there traced comes wholly from the senses and experi- 
ence; or whether the mind (soul) originally contains the principles 
of several notions and doctrines, which the external objects only 
awaken on occasions, as I believe with Plato." 

Perhaps we must admit that there is some little justification 
for the attitude taken up by Locke's critics, despite the prejudice 
exhibited by most of them. For there undoubtedly is in the Essay 
a tendency to bring into prominence the passive receptivities of the 
mind, and to ignore, to some extent, its activity. The metaphor of 
the tabula rasa, the "sheet of white paper", exercises an influence 
over the whole work. The author is so busied with the variety of 
impressions from without, that he seems sometimes almost to forget 
the reaction of the mind from within. 2 But Locke was fighting for 
a reform of method, and he felt the necessity of laying stress on the 
hitherto neglected and despised factor in our means of obtaining 
knowledge. Perhaps, too, he did rather underrate the importance 
of the mental reaction which is essential to the formation of even 
the simple ideas of sensation. But, at that time, Physiology was in 
far too backward a state to throw much light upon Psychology, and 
Locke probably knew little or nothing of nerve-action or nerve- 
energy. 3 

"Few books", says Mackintosh, 4 "have contributed more than 
Locke's Essay to rectify prejudice, to undermine established errors, 
to diffuse a just mode of thinking, to excite a fearless spirit of 
inquiry. In the mental and moral world, which scarcely admits 
of anything that can be called discovery, the correction of the 
intellectual habits is probably the greatest service which can be 
rendered to science. In this respect, Locke is unrivalled: his writ- 
ings have diffused throughout the civilized world the spirit of tole- 

* Qeschichte der Literatur. Coleridge used to pass off this aphorism as his own. See 
Lewes, p. 481. 

a Cf. Fowler, Locke, p. 147. Cf. Fowler, pp. 147-8. 

* Ed. Rev., Oct. 1821, p. 243. See also Lewes, pp. 467-8 ; and cf. Fox Bourne's Life of 
Locke, vol. ii, p. 136. 

HUME 141 

ration and charity in religious differences; the disposition to reject 
whatever is obscure or fantastic in speculation; to reduce verbal 
disputes to their proper value; to abandon problems which admit of 
no solution; to distrust whatever cannot be clearly expressed; to 
render theory the simple expression of facts; and to prefer those 
studies which most directly contribute to human happiness. If 
Bacon first discovered the rules by which knowledge is improved, 
Locke has most contributed to make us observe them. If Locke 
made few discoveries, Socrates made none. Yet both did more for 
the improvement of the understanding, and not less for the progress 
of knowledge, than the authors of the most brilliant discoveries." 

It has been well said that nothing but good can result from com- 
munion with such a mind as Locke's. If the teacher desires to 
obtain "clear and distinct ideas" of the inner nature of his work, 
let him read Locke again and again. 1 


i. Hume's Philosophical Writings 

When, at the age of fifteen, David Hume left the University ol 
Edinburgh, he had become keenly interested in " books of reasoning 
and philosophy", and, in his early speculations on the nature and 
certainty of knowledge, he was probably directed largely by the 
writings of Cicero, Seneca, and Bacon. 2 At the age of twenty-three 

* But not witli the idea of acquiring a knowledge of Psychology. Locke's method is all 
right, but he had no knowledge of practical Physiology, and, as in hib time scarcely anything 
was known ahout physiological function, he could hardly have hccn conscious of the necessity 
of making Physiology the basis of his Psychology. Introspective Psychology has now, for the 
most part, been thrown overboard, and the newer experimental Psychology is still only in its 
infancy. It would be absurd now to attempt a study of Psychology unless it were preceded by 
and based upon a practical knowledge of Physiology. But if we consider the fundamental 
unit of living matter the cell -we have to admit that our knowledge of its physiological 
function is of the slightest, and derived for the most part from mere morphological research. 
Living matter has no analogue in the inorganic world, and the secrets involved in its actions 
and activities seem to be insoluble enigmas. To talk of " vital force " existing in protoplasm 
is a scientific periphrasis whereby we affect to conceal our iirnorance It seems, however, to 
be possible that a further study of the surface tension in cells will throw a good deal of light 
upon the origin of energy in the human machine. See any recent standard work on Phy- 
siology, and cf. Prof. Macallum's Brit. Assocn. Address, 1910. 

a Cf. Huxley, Hume-, Hill Burton, Life of Hume ; Knight, Hume\ Ency. Brit., "Hume". 


he went to France and settled at La Fl&che, where he worked up 
his speculations into systematic form in the Treatise of Human 
Nature, which he published in 1739, a year or two after he had re- 
turned to England. In telling the tale of this first venture, Hume 
said, "never literary attempt was more unfortunate; it fell dead- 
born from the press". The work undoubtedly failed to do what 
the author expected from it. His expectations had been great, and 
his disappointment was therefore keen. In later years he was 
accustomed to explain his want of success as due to the immature 
style of his early thoughts and exposition, to the rashness of a young 
innovator in an old and well-established province of literature. 
Hume's reference to the Treatise, in his preface to the Inquiry Con- 
cerning Human Understanding, 1 is well known; but none of the prin- 
ciples of the Treatise are given up in the later writings, and no 
addition was made to them. Nor can the superior polish of the 
more mature productions overbalance the freshness and vigour of 
the earlier work. Hume is at his best in the Treatise. 12 

2. Hume's Scepticism 

There are those who maintain that Hume was a sceptic, since he 
regarded all definite opinion as to "first principles" to be a trans- 
gression of the limits of the knowable. "Nothing", he said, "can 
be more unphilosophical than to be positive or dogmatical on any 
subject. Where men are most sure and arrogant, they are commonly 
the most mistaken." 3 But his scepticism was really of the kind 
which stands apart, and declines to speculate on ultimate problems 
because of the apparent impossibility of penetrating the haze in 
which the whole region is enshrouded. Hume did not say that 
we should never make any definite assertions concerning the truth 
of things, nor did he make the positive affirmation that we can 
possess no knowledge of the sphere of reality. 

It is the general misconception of the real nature of Hume's 
scepticism that is the cause of the antipathy felt by many people 
towards his teaching. His arguments are, however, directed, not 
against the truths of religion, but against metaphysical speculations. 
He desires to " confound those dangerous friends or disguised enemies 
to the Christian religion who have undertaken to defend it by the 

i Published as Essays in 1749. 2 cf. Ency. Brit., " Hume ", p. 348. 

Inquiry Concerning the Principles of Morals, Section IX (this was published in 1761) ; 
and cf. Treatise, Part IV, L 

HUME 143 

principles of human reason. Our most holy religion is founded on 
faith, not on reason." Both Locke and Hume have told us on what 
questions we must be content to remain in darkness, all which 
relate to Metaphysics, all which involve the inner nature of essences 
and causes; and this metaphysical scepticism is maintained by the 
great majority of thinking men, some from conviction, others from 
a vague sense of the futility of ontological speculation. To say that 
Hume was wanting in religious conviction is not only unjust, it 
is untrue. 1 

3. His Method 

"To me", says Hume, "it seems evident that the essence of 
mind being equally unknown to us with that of external bodies, it 
must be equally impossible to form any notions of its powers and 
qualities otherwise than from careful and exact experiments, and the 
observation of those particular effects which result from its differ- 
ent circumstances and situations. And though we must endeavour 
to render all our principles as universal as possible by explaining 
all effects from the simplest and fewest causes, 'tis still certain we 
cannot go beyond experience ; and any hypothesis that pretends to 
discover the ultimate original qualities of human nature, ought at 
first to be rejected as presumptuous and chimerical." 2 This is the 
spirit that prevails throughout Hume's writings. Hume had a true 
insight into scientific method. lie saw clearly that Philosophy 
ought, in great measure, to be the exponent of the logical conse- 
quences of data established on the basis of experience. 

4. His Views of the Nature of Mind 

Hume was keenly interested in Berkeley's 3 attack on the received 
notion of " substance ". Philosophers had assumed the existence 
of a noumenon 4 underlying all phenomena, a substratum support- 
ing all qualities. Locke had declared such a substratum to be a 
necessary inference from our knowledge of qualities, but that we 
must always remain ignorant of its actual nature. Berkeley, how- 
ever, denied the existence of the substratum entirely, declaring it 

i Of course Hume was anything but orthodox, though he was most certainly not irreli- 
gious. The reader should refer to his Dialogues on Natural Religion, bearing in mind that 
Cleanthes is Hume's mouthpiece. Cf. Lewes, pp. 511-2; Maurice, 3/or. and Met. PhU. t vol. ii, 
p. 676; Ueberweg, PML, vol. ii, pp. 378-9; Ency. Bnt., "Hume", p. 355; Knight, pp. 231-2. 

* Cf. Huxley, Hume, p. 56. 

Berkeley (1684-1763), Bishop of Cloyne. * Cf. ch. lii, ft 2. 


to be a mere abstraction. "If", he says, "by matter you under- 
stand that which is seen, felt, tasted, and touched, then I say matter 
exists; if, on the contrary, you understand by matter that occult 
substratum which is not seen, not felt, not tasted, and not touched, 
then I say I believe not in the existence of matter." Berkeley did 
not contradict the evidence of the senses; on the contrary he confined 
himself exclusively to the evidence of the senses. 1 He could see no 
necessity for Locke's inference, and got rid of substance ("matter") 
altogether by identifying " objects " with " ideas ". 

Locke had shown that all our knowledge was dependent upon 
experience. Berkeley had pronounced matter to be a mere abstrac- 
tion. Hume, probing more deeply than Berkeley, decided that not 
only was matter an abstraction, but mind was no less so. If the 
occult substratum which men had inferred to explain material 
phenomena could be denied, because not founded on experience, so 
also, said Hume, must we deny the occult substratum (mind) which 
men have inferred to explain mental phenomena. All that we have 
any experience of are " impressions and ideas ". The substance of 
which these are supposed to be impressions, is occult, is a mere 
inference; the substance in which these impressions are supposed to 
be, is equally occult, is a mere inference. In short, *mind is but 
a succession of impressions and ideas? 

5. His General Theory of the Origin of Knowledge 

Hume's general theory of the origin of knowledge it will be 
best to give in his own words. 

" All the perceptions of the human mind resolve themselves into 
two distinct kinds which I shall call Impressions and Ideas. The 
difference betwixt these consists in the degree of force or liveliness 
with which they strike upon the mind, and make their way into our 
thought or consciousness. Those perceptions which enter with most 
force and violence we may name impressions] and under this name 
I comprehend all our sensations, passions and emotions, as they 
make their first appearance in the mind. 3 By ideas I mean the faint 
images of these in thinking and reasoning. 

* Cf. Berkeley, Principles of Human Knowledge, Sections 35-37, 40. See also "Berkeley 
and Idealism", Blackwood's Magazine, June, 1842; also Reid, Enquiry, ch. vl, p. 20; Knight, 
Hume, p. 122; Lewes, pp 490-1 Berkeley used the term matter ambiguously, but his 
intended meaning will have been gathered from what has been said above. He is often 
ridiculed by those who do not understand him: "And coxcombs vanquish Berkeley with a 

a 01 Lewes, Biog. Hist. Phil, p. 507. Orig., "soul". 

HUME 145 

" The circumstance that strikes the eye is the great resemblance 
betwixt our impressions and ideas in every other particular except 
their degree of force and vivacity. The one seems to be in a 
manner a reflection of the other. 

" Every simple idea has a simple impression which resembles it, 
and every simple impression a correspondent idea. * 

"All our simple ideas in their first appearance are derived 
from simple impressions, which are correspondent ^o them, and 
which they exactly represent. The simple impressions always take 
precedence of their correspondent ideas, but never appear in the 
contrary order. The constant conjunction of our resembling per- 
ceptions is a convincing proof that the one are the causes of the 
other; 1 and this priority of the impressions is an equal proof that 
our impressions are the cause of our ideas, not our ideas of "our 

" Impressions may be divided into two kinds those of Sensation 
and those of Reflection. An impression first strikes upon the senses. 
Of this impression there is a copy taken by the mind, which remains 
after the impression ceases; and this we call an idea. This idea, 
when it returns, produces new impressions of reflection, because 
derived from it. These, again, are copied by the memory and 
imagination and become ideas, which, perhaps, in their turn, give 
rise to other impressions and ideas. So that the impressions of 
reflection are posterior to those of sensation, and derived from 
them." 2 

When complex impressions or complex ideas are reproduced t is 
memories, it is probable that the copies never give all the details of 
the originals with perfect accuracy, and it is certain that they rarely 
do so. No one possesses a memory so good, that if he has only 
once observed a natural object, a second impression does not show 
him something that he has forgotten. Almost all, if not all, our 
memories are therefore sketches, rather than portraits, of the 
originals, the salient features arc obvious, while the subordinate 
characters are obscure or unrepresented. 8 

i Cf , Mill's definition of cause. 

* Treatise, Part I, i-iii Cf. Ueberweg, PJiil., vol ii, pp. 132-3; and Knight, Hume, 
pp. 136-6. For some very acute, though unconvincing, criticism of Hume's theory, see 
Green and Grose, Introduction to fiume, especially pp. 161-6. 

8 Cf. Huxley, Hume, p. 94 Huxley gives in his own words the " broad outlines " of Hume's 
philosophy. Hiwtample of the " flashing red light " leads on to a very lucid explanation of 
Hume's general position See in particular pp. 68-73. The reader should compare the very 
divergent views of Huxley and Knight. Huxley is perhaps a little too dogmatic, but Knight's 
position is frankly that of tho " pure metaphysician " with his back to the wall. He says, for 
instance, " No physiological explanation of mental states a*d processes is worthy of serious 
(0415) 12 


Hume continues: "Were ideas entirely loose and unconnected, 
chance alone would join them; and 'tis impossible the same simple 
ideas should fall regularly into complex ones (as they commonly do) 
without some bond of union among them, some associating quality by 
which one idea naturally introduces another. The qualities from 
which this association arises, and by which the mind is after this 
manner conveyed from one idea to another, are three, namely, 
Resemblance, Contiguity in Time or Place, and Cause and Effect. Of 
the three relations, that of Causation is the most extensive." 1 

The general drift of Hume's meaning is perfectly clear, but his 
loose phraseology his varying meaning of such terms as " quality ;; 
and "relations" often obscures his arguments and gives many 
verbal victories to his critics. 

6. His Theory of Causation 

It is Hume's great effort to prove that the relation of cause 
and effect is a particular case of the process of association; and no 
part of Hume's philosophy is more important to the teacher than his 
theory of causation. 

We hear a particular sound succeed the discharge of a gun; and, 
when we have done so repeatedly, we come to associate the two 
together; but we are not thus warranted in setting down the firing 
of the gun as the cause of the sound we hoar. Again, we take a 
flower and smell it; the sweet odour we experience we attribute to 
the flower, but this also is merely due to habit, and the sequence of 
the pleasant sensation from the proximity of the flower is all that we 
are warranted in affirming. In these two instances, the senses 
of sound and of smell take note only of antecedence and sequence. 
Any link of causality or causal connection between the phenomena 
is not in the objects but in ourselves who subsequently, by dint of 
habit and association, read into the objects what is not really there. 
My belief that the sound comes from the gun and the scent from 
the flower is due merely to the fact that I have had a reiterated and 
vivid "impression" of the conjunction of the two things. It is the 

regard in the domain of philosophy"; and again: "To tell us, as the physiologists do, that 
the brain is the organ of mind, and that molecular changes of the brain always accompany 
mental acts, is to explain nothing ". Let us grant that the case of the physiologist has not 
been absolutely proved. But what about that of the metaphysician? Whilst there is any 
amount of available evidence tending to confirm the hypothesis of the physiologists, there is 
nothing but introspective Psychology to support the metaphysician. It is merely a question. 
therefore, of balancing probabilities, and which side has the stronger case is fairly obvious, 
i Treatite, Book I, 4. Cf . Huxley, p. 72, Ac. 

HUME 147 

vivacity of the impression, its force and liveliness, that is the sole 
warrant (according to Hume) for my calling the antecedent which 
I have been in the habit of associating with the consequent a cause, 
and for naming that consequent its effect. 

Hume did not deny that we are in the habit of attributing some 
kind of causality to the antecedent which produces the consequent. 
What he denied was that we have any philosophical justification for 
doing so. Of the supposed "necessary connection" he wished for 
an explanation. The problem lay in finding a reason for the fact 
that, given any particular phenomenon, another phenomenon must 
of necessity follow from it. Hume could discover no reason for the 
existing sequence of events except custom, and therefore no reason 
except the accident of habit for attributing efficiency to any single 
phenomenon. For the proposition that "every effect must have 
some cause", and that there is therefore a tie of necessity between 
the sequences of nature, altogether independent of the result that 
happens to emerge, Hume could see no speculative warrant what- 
soever. 1 

"We can never by our utmost scrutiny", says Hume, 2 "discover 
anything but one object following another, without being able to 
comprehend any force or power by which the cause operates, or any 
connection between it and the supposed effect. All events seem 
entirely loose and separate. One event follows another, but we 
never can observe any tie between them. They seem conjoined but 
never connected. But as we can have no idea of anything which 
never appeared to our outward sense or inward sentiment, the 
necessary conclusion seems to be that we have no idea of connec- 
tion or power at all, and that those words are absolutely without 
any meaning when employed either in philosophical reasonings or 
common life. 

"The first time a man saw the communication of motion by 
impulse, as by the shock of two billiard balls, he could not pro- 
nounce^ that the one event was connected, but only that it was 
conjoined with the other. After he has observed several instances 
of this nature he then pronounces them to be connected. What 
alteration has happened to give rise to this new idea of connection^ 
Nothing but that he now feeh these events to be connected in his 
imagination, and can readily foretell the existence of one from the 
appearance of the other." 

It is, however, very difficult to get rid of the idea from our 

i Cf. Knight, pp. 150-3. 2 Inquiry, 7. 


minds that there is something of the nature of Force or Power or 
Energy resident in the cause which produces the effect. Hume 
explains Force and Power as the results of the association, with 
inanimate causes, of the feelings of endeavour or resistance which 
we experience when our bodies give rise to or resist motion. 

" If I throw a ball, I have a sense of effort which ends when the 
ball leaves my hand; and if I catch a ball, I have a sense of resis- 
tance which comes to an end with the quiescence of the ball. In 
the former case there is a strong suggestion of something having 
gone from myself into the ball; in the latter, of something having 
been received from the ball. Let anyone hold a piece of iron near 
a strong magnet, and the feeling that the magnet endeavours to 
pull the iron one way in the same manner as he endeavours to pull 
it in an opposite direction, is very strong." 1 As Hume says, "No 
animal can put external bodies in motion without the sentiment of 
a nisus, or endeavour; and every animal has a sentiment or feeling 
from the stroke or blow of an external object that is in motion. 
These sensations, which are merely animal, and from which we 
can, a priori, draw no inference, we are apt to transfer to inanimate 
objects, and to suppose that they have some such feelings whenever 
they transfer or receive motion." 2 It is obviously as absurd to 
suppose the sensation of warmth to exist in a fire as it is to imagine 
that the subjective sensation of effort or resistance in ourselves can 
be present in external objects, when they stand in the relation of 
causes to other objects. 

To the argument that we have a right to suppose the relation 
of cause and effect to contain something more than invariable 
succession, because, when we ourselves act as causes, we are con- 
scious of exerting power, Hume replies that wo know nothing of 
the feeling we call power except as effort or resistance; and that 
we have not the slightest means of knowing whether it has any- 
thing to do with the production of bodily motion or mental changes. 
And he points out that when voluntary motion takes place, that 
which we will is not the immediate consequence of the act of 
volition, but is something which is separated from it by a long 
chain of causes and effects. If the will is the cause of the move- 
ment of a limb, it can be so only in the sense that the guard who 
gives the order to go on is the cause of the transport of a train 

1 Cf. Huxley, pp. 116-7. 

2 Inquiry, Section VII, Part ii, 60, note (Selby-Bigge's edition, p. 77). Cf. also Ueberweg, 
Phil., vol. ii, pp. 133-4; and article on "Axiom ", Ency. Brit., vol iii, p. 161. 

HUME 149 

from one station to another. 1 "We learn from anatomy that the 
immediate object of power in voluntary motion is not the member 
itself which is moved, but certain muscles and nerves and animal 
spirits, and perhaps something still more minute and unknown, 
through which the motion is successively propagated, ere it reach 
the member itself, whose motion is the immediate object of volition. 
Can there be a more certain proof that the power by which the 
whole operation is performed, so far from being directly and fully 
known by an inward sentiment or consciousness, is to the last 
degree mysterious and unintelligible'?" 2 

Needless to say, Hume meets with a good deal of criticism from 
the opposite school of thought. Even Lewes expresses disagree- 

Hume's theory, says Lewes, is neither a complete expression of 
the facts nor a correct analysis of the origin of our belief. When 
he says that invariable succession of antecedent arid consequent is 
all that is given us in our experience of causation, he asserts that 
which every man who examines the matter attentively may con- 
tradict. " Ask yourself whether you have not a sense of power 
also given in the experience of causation. You cannot hesitate. 
You believe that fire has the power to burn your finger, that one 
billiard ball has the power of moving another when impinging on 
it." "The idea of power may be vague if by idea we understand 
anything like an image, but it is precise enough if we understand 
by it merely a conception formed by the mind. We cannot, indeed, 
frame an image of power any more than we can frame an image of 
mind or of substance; but we have a strong conviction of the exis- 
tence of them all." 3 Possibly: but proof requires something more 
than personal conviction. 

Professor Knight's criticism is, as might be expected, based upon 
the supposition that Hume attaches undue importance to knowledge 
derived from sense experience. "We are told that, in imagining 
efficiency, or causality, or productiveness (name it as you will) to be 
lodged within an antecedent, or even within a group of antecedents, 
as co-operative con-causes, we arc the dupes of custom. But we 
know the cause as productive of the effect, or we do not know it at 
all; and we know the effect as produced by the cause, or we do not 
know it at all; and since all phenomena are, alternatively, both 

i Huxley, p. 127. 

a Inquiry, Selby-Bigge's edition, p. 66. Cf. also Selby-Bigge's Treatise, p. 632. See also 
Maurice, Mor. and Met. Phil., ii, p. 670; Green and Grose, Treatise, i, p. 248, <fcc. 
* See Lewes, Biog. Hist. Phil., pp. 618-20. 


causes and effects, according as we regard them the cause being 
just the effect concealed and the effect being merely the cause re- 
vealed we find an interior power or causality within every link of the 
chain. Take any small section of the continuous area of pheno- 
menal succession (for we must remember that the chain is never 
broken), select two or three links. You apply a match to gun- 
powder, and you see the flame and smoke and hear the sound of an 
explosion. You perceive a violent change in the position of and 
the relations of certain particles of matter. The application of the 
spark to the powder you call the cause; the explosion you name the 
effect; but there were many things besides the application of the 
spark that were equally influential in determining the result, arid 
without which the result could not have taken place, elements, 
states and conditions, indefinitely necessary, but all concurring and 
co-operating. And all the result lay potentially within the cause, 
or the sum of the con-causes : the explosion merely made it visible. 
It displayed the working of the cause or causes in a certain manner. 
In other words, the force which separated the atoms formerly 
slumbered within them. It was latent and it became active. Of 
course we are not to suppose that there is a non-material entity 
lying in some sort of crypt amongst the material atoms, alternately 
caught and released, now passive and again active in its wanderings 
to and fro; but within every atom, as its interior essence, and there- 
fore throughout the whole area of nature, this force or causal power 
resides. The special point to be noted is that while the senses take 
note of phenomenal succession only, the intellect strikes through 
the phenomenal chain, and it discerns the inner vinculum, the tie of 
causality binding antecedent to sequent in the grip of an a priori 
necessity." x This is dogmatism with a vengeance ! 

Professor James Ward considers that Hume has settled once for 
all one point in the analysis of the causal relation,- that it does not 
rest upon or contain any immediate intuition of a causal nexus? 
But the whole subject of causation is so difficult that it is advisable 
to quote the opinions of several recognized authorities. 

i Knight, pp. 158-66. Cf Morel, Phil, vol. i, pp. 274-84. On ulterior causes and the 
Supreme Cause, see Whe well's Nov. Org. lien., pp 250-6. Cf. also Huxley, pp. 182-96, 120-3 
a See Ency. Brit, vol. xx, p. 82. 

HUME 151 

7. Other Views of Causation 

1. Reid. We can derive little light from the events which we 
observe in the course of nature. We perceive changes innumerable 
in things without us. We know that these changes must be pro 
duced by the active power of some agent, but we neither perceive 
the agent nor the power, but the change only. Whether the things 
be active or merely passive is not easily discovered. 

We see an established order in the succession of events, but we 
see not the bond that connects them together. 

Those very philosophers who attribute to matter the power of 
gravitation, and other active powers, teach us, at the same time, 
that matter is a substance altogether inert, and merely passive; 
that gravitation and the other attractive or repulsive powers which 
they ascribe to it, are not inherent in its nature, but impressed 
upon it by some external cause, which they do not pretend to know 
or explain. Now when we find wise men ascribing action and active 
power to a substance which they expressly teach us to consider as 
merely passive, and acted upon by some unknown cause, we must 
conclude that the action or active power ascribed to it are not to be 
understood strictly, but in some popular sense. 

In all languages, action is attributed to many things which all 
men of common understanding believe to be merely passive. Thus 
we say the wind blows, the rivers flow, the sea rages, the fire burns, 
bodies move and impel other bodies. 1 

2. Hamilton. When we are aware of something which begins 
to be, we are, by the necessity of our intelligence, constrained to 
believe that it has a cause. But what does the expression, that it 
has a cause, signify? If we analyse our thought we shall find that 
it simply means, that as we cannot conceive any new existence to 
commence, therefore, all that now is seen to arise under a new 
appearance, had previously an existence under a prior form. We 
are utterly unable to realize in thought the possibility of the com- 
plement of existence being either increased or diminished. We are 
unable, on the one hand to conceive nothing becoming something, 
or, on the other, something becoming nothing. "Ex nihilo nihU, 
in nihilum nil posse reverti", 2 expresses in its purest form the whole 
intellectual phenomenon of causality. The mind is compelled to 
recognize an absolute identity of existence in the effect and in the 

i Reid, Active Powers, Essay I, ch. v, vi, vii (Wright's edition, pp. 98, 103-7). 
&t ill, 84. 


complement of its causes, between the causatum and the causce. 
We think the causes to contain all that is contained in the effect; 
the effect to contain nothing but what is contained in the causes. 1 

3. Brown. We see in nature one event followed by another. 
The fall of a spark on gunpowder, for example, followed by the 
deflagration of the gunpowder; and, by a peculiar tendency of our 
constitution, we believe that, as long as all the circumstances con- 
tinue the same, the sequence of events will continue the same; that 
the deflagration of gunpowder, for example, will be the invariable 
consequence of the fall of a spark upon it. 

There is nothing more, then, understood in the train of events, 
however regular, than the regular order of antecedents and conse- 
quents which compose the train; and between which, if anything 
else existed, it would itself be a part of the train. All that we 
mean when we ascribe to one substance a susceptibility of being 
affected by another substance, is that a certain change will uni- 
formly take place in it when that other is present. All that we 
mean when we ascribe to one substance a power of affecting another 
substance, is that, where it is present, a certain change will uni- 
formly take place in that other substance. Power, in short, is 
significant not of anything different from the invariable antecedent 
itself, but of the mere invariableness of the order of its appearance 
in reference to some invariable consequent, the invariable ante- 
cedent being denominated a came, the invariable consequent an 
effect. A cause is, perhaps, not that which has merely once pre- 
ceded an event; but we give the name to that which has always 
been followed by a certain event, is followed by a certain event, 
and according to our belief will continue to be in future followed 
by that event, as its immediate consequent; and causation, power, 
or any other synonymous words which we may use, express nothing 
more than this permanent relation of that which has preceded to 
that which has followed. 2 

4. Much. In speaking of cause and effect, we arbitrarily give 
relief to those elements to whose connection we have to attend in 
the reproduction of a fact in the respect in which it is important to 
us. There is no cause or effect in nature; nature simply 'is. Recur- 

1 Lectures on Metaphysics, vol. ii, p. 377; Discussions on Philosophy, pp. 610, 621, 622. See 
also pp. 378-413 of former, and pp. 611-633 of latter. For Mill's criticisms of Hamilton's views, 
see Mill's Examination of Hamilton, pp. 844-363. 

2 Physical Enquiry (Phil, of Human Mind), p. 36. For a criticism of Brown's views, see 
Professor Wilson in Black wood' 8 Magazine, vol. xl, p. 122, <fec.; or Hamilton's Metaphysics, 
vol. ii, pp. 379-94. 

HUME 153 

rences of like cases in which A is always connected with B, that is, 
Kke results under like circumstances, that is again, the essence of 
the connexion between cause and effect, exist but in the abstraction 
which we perform for the purpose of mentally reproducing the facts. 
Let a fact become familiar, and we no longer require this putting 
into relief of its connecting marks, our attention is no longer at- 
tracted to the new and surprising, and we cease to speak of cause 
and effect. A person of experience regards an event with different 
eyes from a novice. The new experience is illuminated by a mass 
of old experience. The notion of the necessity of a causal connection 
is probably created by our voluntary movements in the world, and 
by the changes which these indirectly produce, as Hume supposed. 
Cause and effect are things of thought, having an economical office. 
It cannot be said why they arise. 1 

5. Clifford. The word represented by "cause" has sixty-four 
meanings in Plato and forty-eight in Aristotle. These were men 
who liked to know as near as might be what they meant, and it 
would only be the height of presumption in me to attempt to fix the 
meaning of a word which has been used by so grave authority in so 
many and various senses; and I shall evade the difficulty by telling 
you Mr. Grote's opinion. You come to a scarecrow and ask, what 
is the cause of this? You find that a man made it to frighten the 
birds. You go away and say to yourself, " Everything resembles 
this scarecrow; everything has a purpose". And from that day the 
word " cause" means for you what Aristotle meant by "final cause". 
Or you go into a hairdresser's shop, and wonder what turns the 
wheel to which the rotatory brush is attached. On investigating 
other parts of the premises, you find a man working away at a 
handle. Then you go away and say, "Everything is like that 
wheel. If I investigated enough, I should always find a man at a 
handle." And the man at the handle, or whatever corresponds to 
him, is from henceforth known to you as "cause". 2 

When we say that every effect has a cause, we mean that every 
event is connected with something in a way that might make some- 
body call that the cause of it. But I, at least, have never yet seen 
any single meaning of the word that could be fairly applied to the 
wfwle order of nature. 3 

6. Herbert Spencer. When we inquire what is the meaning of 
the various effects produced upon the senses, we are compelled to 

i Science of Mechanics, pp. 483-5, 679. 2 Cf . Grote's Plato, vol. ii (Phcedo). 

Clifford, Lectures and Essays, vol. i, pp. 149-51. 


regard them as the effects of some cause. Be the cause we assign 
what it may, we are obliged to suppose some cause. And we are 
not only obliged to suppose some cause but also a First Cause. 
Whatever we assume to be the agent producing on us these various 
impressions must either be the First Cause of them or not. If it 
is the First Cause the conclusion is reached. If it is not the First 
Cause, then by implication there must be a cause behind it; which 
thus becomes the real cause of the effect. We cannot think at all 
about the impressions which the external world produces on us 
without thinking of them as caused; and we cannot carry out an 
inquiry concerning their causation, without inevitably committing 
ourselves to the hypothesis of a First Cause. 

But now if we go a step further, and ask what is the nature 
of this First Cause, we are driven by an inexorable Logic to 
certain further conclusions. Is the First Cause finite or infinite? 
If we say finite, we involve ourselves in a dilemma. To think of 
the First Cause as finite is to think of it as limited. To think of 
it as limited necessarily implies a conception of something beyond 
its limits; it is absolutely impossible to conceive a thing as bounded 
without conceiving a region surrounding its boundaries. What now 
must we say of this region? If the First Cause is limited, and 
there consequently lies something outside of it, this something must 
have no First Cause must be uncaused. But if we admit that 
there can be something uncaused, there is no reason to assume a 
cause for anything. If beyond that finite region over which the 
First Cause extends there lies a region which we are compelled to 
regard as infinite, over which it docs not extend if we admit that 
there is an infinite uncaused surrounding the finite caused; we 
tacitly abandon the hypothesis of causation altogether. Thus it is 
impossible to consider the First Cause as finite. And if it cannot 
be finite it must be infinite. Another inference concerning the 
First Cause is equally unavoidable. It must be independent. If 
it is dependent it cannot be the First Cause; for that must be the 
First Cause on which it depends. 

These are inferences forced upon us by arguments from which 
there appears no escape. But it might easily be proved that the 
materials of which the argument is built, equally with the con- 
clusions based on them, are merely symbolic conceptions of the 
illegitimate order. 1 

7. Professor Carveth Read. Occult causes were regarded as enter- 

i Firtt Principles, pp. 8d-46. 

HUME 155 

ing into the tissue of natural processes, but as essentially unsearch- 
able; and under the name of powers or virtues were the discourage- 
ment of induction, the refuge of ignorance, and a fastness of 
scepticism. Hume's great service was to supersede occult causes by 
the notion of a sequence of phenomena. His definition of Cause 
amounts to this, that the cause of a phenomenon is its constant 
antecedent. 1 

There is not in nature one ^et of things called causes and another 
called effects, but everything is both cause of the future and effect 
of the past; and whether we consider an event as the one or the 
other, depends upon the direction of our curiosity or interest. Still, 
taking the event as effect, its cause is the antecedent process; or, 
taking it as a cause, its effect is the consequent process. This 
follows from the conception of causation as essentially motion; for 
that motion takes time is an ultimate intuition. But, for the same 
reason, there is no interval of time between cause and effect, since 
all the time is filled up with motion. 2 

8. Professor Karl Pearson. That a certain sequence has occurred 
and recurred in the past is a matter of experience to which we give 
expression in the concept causation; that it will continue to recur in 
the future is a matter of belief to which we give expression in the 
concept probability. Science in no case can demonstrate any inherent 
necessity in a sequence nor prove with absolute certainty that it must 
be repeated. Science for the past is a description; for the future 
a belief. 

Some more or less superficial works on natural science give 
currency to the notion that mechanics supply a code of rules which 
nature of inherent necessity obeys. We are told that mechanics is 
the science of force, that force is the cause that produces or tends 
to produce change of motion, and that force is inherent in matter. 
Force thus appears to the popular mind as an agent inherent in 
unconscious matter producing change. Mechanics is the science of 

The whole tendency of modern Physics has been to describe 
natural phenomena by reducing them to conceptual motions. From 
these motions we construct the more complex motions by aid of 
which we describe actual sequences of sense-impressions. But in 
no single case have we discovered why it is that these motions are 
taking place. Science describes how they take place, but the why 
remains a mystery. Science knows nothing of first causes. Causa- 

i Metaphysics of Nature, p. 329. 2 Logic, p. 170. 


tion, says Mill, is uniform antecedence, and this definition is per- 
fectly in accord with the scientific concept. 1 

9. Bain. The Law of Causation may be expressed thus: In 
every change there is a uniformity of connection between the 
antecedents and the consequents. 

In Causation, the same cause always produces the same effect; 
but the converse does not hold; the same effect is not always pro- 
duced by the same cause. There may be a plurality of causes. 
A sufficiently severe blow on a man's head will always cause death; 
but death is not always caused by a blow on the head. The fact 
of plurality renders the causation of an event ambiguous; there 
may be several alternative antecedents. But plurality of causes 
is more an incident of our imperfect knowledge than a fact in the 
nature of things. As knowledge extends we find less of plurality. 

In common language, the cause of an event is some one circum 
stance selected from the assemblage of conditions, as being practi- 
cally the turning-point at the moment. A man slips on a ladder, 
falls, and is killed. The cause of the fatality is said to be the 
slipping; for, if this one circumstance had been prevented, the 
effect would not have happened. Yet, in order to the result, many 
other conditions were necessary: the weight of the body (gravity), 
the height of the position, the fragility of the human frame. Yet, 
for practical purposes, we leave out of sight at the moment all the 
elements that are independent of us and secure. By a common 
ellipsis, all arrangements that are fixed and settled are passed over 
in silence. 

But when in the statement of a cause there is not merely the 
ellipsis of understood circumstances, but an omission of some essen- 
tial fact, the consequence is positive error. When, for example, the 
healthy effects of residence at a medicinal Spa are attributed exclu- 
sively to the operation of the waters, there is a fallacy of causation; 
the whole circumstances and situation being the cause. 2 

10. Mill. When I speak of the cause of any phenomenon, I do 
not mean a cause which is not itself a phenomenon. I make no re- 
search into the ultimate cause of anything. The causes with which 
I concern myself are not efficient but physical causes. They are causes 
in that sense alone in which one physical fact is said to be the cause 
of another. Of the efficient causes of phenomena, or whether such 
causes exist at all, I am not called upon to give an opinion. 

i Grammar of Science, pp. 113, 114, 120, 128, 131. 

* Inductive Logic, pp. 15-20; Senses and the Intellect, pp. 428-434. 

HUME 167 

The Law of Causation, the recognition of which is the main 
pillar of inductive science, is but the familiar truth that invariability 
of succession is found by observation to obtain between every fact 
in nature and some other fact, which has preceded it, independently 
of all considerations respecting the nature of "things in themselves". 

To certain facts, certain facts always do, and, as we believe, will 
continue to succeed. The invariable antecedent is termed the cause; 
the invariable consequent the effect. 

It is seldom between a consequent and a single antecedent that 
this invariable sequence subsists. It is usually between a consequent 
and the sum of several antecedents, the concurrence of all of them 
being requisite to produce, that is to be certain of being followed 
by, the consequent. In such cases it is very common to single out 
one only of the antecedents under the denomination of cause, calling 
the others merely conditions. Thus, if a person eats of a particular 
dish, and dies in consequence, people would be apt to say that eating 
of that dish was the cause of death. There needs not, however, be 
any invariable connection between eating of the dish and death; but 
there certainly is, among the circumstances which took place, some 
combination or other, in which death is invariably consequent; as, 
for instance, the act of eating of the dish, combined with a particular 
bodily constitution, a particular state of present health, and perhaps 
even a certain state of the atmosphere; the whole of which circum- 
stances perhaps constituted in this particular case the conditions of 
the phenomenon, or, in other words, the set of antecedents which 
determined it, and but for which it would not have happened. The 
real cause is the whole of these antecedents; and we have, philo- 
sophically speaking, no right to give the name of cause to one of 
them exclusively of the others. Nothing can better show the absence 
of any scientific ground for the distinction between the cause of a 
phenomenon and its conditions than the capricious manner in which 
we select from among the conditions that which we choose to deno- 
minate the cause. 

For example, a stone thrown into the water falls to the bottom. 
What are the conditions of the event? In the first place, there 
must be a stone and water, and the stone must be thrown into 
the water. The next condition is, there must bo an earth, and 
accordingly it is often said that the fall of a stone is caused by 
a force exerted by the earth. It is not, however, enough that 
the earth should exist, and we have another condition in the fact 
that the body must be within that distance from the earth, in which 


the latter's attraction preponderates over that of any other body. 
A further condition is that, if the stone is to reach the bottom, its 
specific gravity must exceed that of the surrounding fluid. Each 
and every condition of the phenomenon may be taken in its turn, 
and, with equal propriety in common parlance, though not in scien- 
tific discourse, as if it were the entire cause. And, in practice, 
that particular condition is usually styled the cause, whose share in 
the matter is superficially the most conspicuous, or whose requisite- 
ness to the production of the effect wo happen to be insisting on 
at the moment. So great is the force of this last consideration, 
that it sometimes induces us to give the name of cause even to 
one of the negative conditions. We say, for example, that the army 
was surrounded because the sentinel was absent from his post. 

It is necessary in our using the word cause that we should be- 
lieve not only that the antecedent always has been followed by the 
consequent, but that as long as the present constitution of things 
endures, it always mil be so. We do not believe, for instance, that 
night is the cause of day and day the cause of night; for we do 
not believe that night will be followed by day under all ima^irnible 
circumstances, but only that it will be so provided the sun rises above 
the horizon. Therefore, we do not call night the cause or even 
a condition of day; for day does not follow night independently of 
the rising of the sun. The succession of day and night is conditional 
on the occurrence of other antecedents. That which will bo followed 
by a given consequent when and only when some third circumstance 
also exists, is not the cause. Invariable sequence, therefore, is not 
synonymous with causation, unless the sequence, besides being in- 
variable, is unconditional. 

Philosophically speaking, the cause is the sum total of the con- 
ditions, positive and negative, taken together; the whole of the 
contingencies of every description, which being realized, the con- 
sequent invariably follows. 1 It is the antecedent, or the concurrence 
of antecedents, on which the phenomenon is (1) invariably, and (2) 
unconditionally, consequent. 2 

If we accept Professor Bosanquet's amendment of Mill's defini- 
tion and say that, cause is the "totality of the conditions", instead 
of "sum of the conditions", we have a definition generally acceptable 
to, and accepted by, men of science. As Professor Bosanquet says, 

i "The negative conditions, however, of any phenomenon, a special enumeration of which 
would generally be very prolix, may be all summed up tinder one head, viz., the absence of 
preventing or counteracting causes." 2 Mill, Logic, Book III, ch. v, 3-6. 

HUME 159 

the word "sum" is unfortunate because it indicates a special way, 
which may be inappropriate, of combining the factors. 1 

8. Is "Time- sequence " an Element of Causation? 

It will be observed that the weight of opinion is all on the side 
of Mill's conception of the nature of causation. Mill has, it is true, 
been repeatedly attacked by the rationalist school, but he has, in the 
long run, invariably proved the victor. 2 It will be sufficient here to 
touch upon the strictures of Professor Welton. 

"It is", says Professor Welton, "the continual endeavour to re- 
tain time-sequence at any cost, which vitiates Mill's discussion, an 
endeavour due to his fundamental position that reality is nothing 
but phenomena in the sense of mere transitory sensuous impres- 
sions which are in their nature distinct and separate and only 
conjoined for consciousness by the operation of psychological asso- 
ciation." 3 

Professor Welton himself defines cause as " a totality of condi- 
tions whose existence secures the effect". It is not "a phenomenal 
event in time". "Whenever the cause is present, the effect is pre- 
sent". " Cause and effect are not two but one. In content they are 
absolutely identical." Now let us briefly examine one or two of 
the illustrations he uses to support his views that time -sequence 
is not an element of causation. 

1. "The weight of the atmosphere", Professor Welton says, "is 
the cause of the height of the mercury in the barometer, but the 
two are coexistent." Let us then suppose that the barometer has 
been standing steadily for a considerable period at 30 inches. At a 
given instant, additional pressure makes itself felt. Is the increase 
in the height of the mercury absolutely simultaneous with the in- 
crease of pressure 1 ? Is it not rather that the mercury instantly 
responds to the increased pressure? 

2. "The cause of the formation of water is the combination in 
definite proportions of hydrogen and oxygen, but this combina- 
tion does not precede the formation of water, it is that formation." 
"The combination of hydrogen and oxygen . . . determines that 
the effect shall be water, but the combined elements and the water 

i Boaanquet, Logic, vol. i, pp 264-5, &c.; vol. ii, pp. '212, 221-5. Of course the term 
11 factors " is used here in a very loose sense. It is interesting to compare Sigwart's opinions 
with those of Bosanquet. See Sigwart's Logic, vol. i, pp. 71, 371 ; vol. ii, pp. 10, 96-121, 384-61. 

i See, for example, Mill's Examination of Hamilton's Philosophy. 

Logic, vol. ii, p. 19. 


are one and the same identical substance, and this substance is the 
content both of the cause and of the effect." Now let us suppose 1 
that the molecules of oxygen and hydrogen have been brought into 
contact under such conditions that they are just about to exchange 
atoms, to " combine". Can we conceive the contact and the ex- 
change to take place simultaneously? Is it not rather a question of 
successive instants of time? Does not the act of combination involve 
a processl If so, can a process be absolutely time-lessl 

3. Professor Wei ton thinks that the plain man would admit 
that in certain cases (for instance, the barometer) cause and effect 
are synchronous and not successive, but would point to other cases 
"in which what he calls the effect is subsequent to that which he 
calls the cause. Thus, for example, he will say that a man takes 
poison first, and that death follows at a longer or shorter interval. 
But here the words ' cause' and 'effect' are used very arbitrarily. 
By cause is meant the beginning of a chain of subsequent events, 
and by effect one of those events selected because of its interesting 
character. But an infinite number of intermediate links can be in- 
serted in the chain, each of which may be equally well regarded as 
the effect of that which precedes and the cause of that which follows, 
and thus the * cause ' is, at best, only the remote cause and is sepa- 
rated from its ' effect* by many intermediate proximate causes." 
That such a chain must be conceived is obvious. If our knowledge 
of Physiology was perfect, arid we could watch the succession of 
physiological changes between the time the poison was taken and 
the time when death took place, we should see that the conception 
of such a chain was justified. But let us suppose that the poison 
was taken at 9.0 and that death resulted at 9.30. Granting the 
chain, how can we totally eliminate time from its successive con- 
stituent elements? 

It would, of course, be entirely inadmissible to interpose an 
interval of time, however small, between the action of the cause 
and the production of the immediate effect. As Sir John Herschel 
says, "In the production of motion by force, though the effect be 
cumulative, with continued exertion of the cause, yet each elemen- 
tary or individual action of the force is, to our apprehension, instanter 
accompanied with its corresponding increment of momentum in the 
body moved". 2 

We may conclude this chapter with some remarks by Mr. F. H. 

i Accepting the atomic theory, as Professor Welton does. Cf . p. 890. 
* Herschel, Estays, pp. 200-7. 

HUME 161 

Bradley: "To apprehend causation we must first distinguish the 
elements before they have come together. And thus we get to 
perceive what may be called the conditions. But these conditions, 
when asunder, are not yet the cause. To make the cause they must 
come together, and their union must set up that process of change 
which, when fixed artificially, we call the effects.'' 

" Though the effect succeeds, it succeeds immediately. Causation 
is really the ideal reconstruction of a continuous 1 process of change 
in time. Between the coming together of the separate conditions 
and the beginning of the process, is no halt or interval. Cause and 
effect are not divided by time in the sense of duration, or lapse, or 
interspace. They are separated in time by an ideal line which we 
draw across the indivisible process/' 2 They are thus immediately 
successive in time, rather than identical, as Professor Welton seems 
to say. 

All the ingenuity of all the metaphysicians has failed to throw 
any real light on the inner nature of cause. We must, at all events 
for the present, be content to know how things happen; for we can- 
not find out why they happen. Beyond Mill's definition we cannot 
go. Students of Science, when dealing with causes and effects, must 
be particularly careful to rid their minds of any lurking notions 
of concealed "agents" or "powers". Matter contains no hidden 

i If it were not continuous, we could then take a solid section from the flow of events, 
solid in the sense of containing no change. But any such section, being divisible, must have 
duration. But, if so, we should have our cause enduring ^urn-hanged through a certain 
number of moments and then suddenly changing But this is clearly impossible, for what 
could have altered it? If the cause can endure unchanged, even for ever so short a time, it 
must endure for ever; it cannot pass into the effect, and therefore is not cause at all. See 
Prof. Bradley's " Dilemma", Appearance and Reality t pp. 60-61. 

* Bradley, Principles of Logic, pp. 485-8. 

(0415) 13 




The Function of Logic in Scientific 


i. Deductive Reasoning: General Notions 

The Geometry of Euclid is often referred to as one of the most 
perfect examples of continued logical development, and if we 
examine any particular proposition, say the thirty-second of the 




3 4 

I I 






10 | 













first book, it is easy to follow back the chain of reasoning 1 which 
leads to the conclusion, until we come to the first and fourth pro- 
positions, and so at last to the first and tenth axioms on which 
these propositions respectively depend. 2 If we accept these axioms, 8 
we feel bound to accept the whole of the subsequent reasoning, 
for at each step we are merely bringing a particular case under a 
generalization, the truth of which we consider to have been estab- 
lished at the previous step. There seems to be no danger, and no 
difficulty, until we get back to our first assumptions, the axioms; 
and the truth of these it is our general practice to accept unques- 
tioned. Whether this is legitimate or not, we shall see presently. 

2. Syllogistic Reasoning 
Let us- examine a simple argument of a rather different kind: 

- All schoolmasters are scholars; 
*" Smith is a schoolmaster, 

' Therefore Smith is a scholar. , 

^A (*^*( t ***- 

The first proposition tells us that schoolmasters form a part, but not 
the whole, of the class scholars. The fact may be represented by 
one of Euler's diagrams : 

Fig. 2 

The small circle is supposed to contain the schoolmasters and no- 
thing else. The large circle is supposed to contain the scholars and 
nothing else. But as the small circle is wholly within the larger one, 
it follows that all the schoolmasters must be counted as scholars. 

i Cf. Euclid and his Modern Rivals, by C. L Dodgson (Lewis Carroll). 

* Unfortunately Euclid sacrificed his Geometry to his Logic. 

* The definitions, as distinguished from the axioms, are purposely ignored here ; so are 
the so-called postulates. 


It should, however, be noticed that we know nothing at all about 
that part of the circle of scholars outside the circle of schoolmasters. 
Bishops, statesmen, and others may be there, but of this possible 
fact we have no knowledge. 

Now if Smith is contained amongst the schoolmasters, he must 
obviously be contained amongst the scholars, so that the essence of 
our argument consists in showing that a given particular case falls 
under a general rule. This is Formal Logic in a nutshell. The 
leading idea of the syllogism is the recognition that when any fact 
is produced as sufficient to prove a conclusion, the sufficiency of such 
fact for such purpose depends on the acceptance of a generaliza- 
tion which covers it and connects it with the conclusion. We seem 
almost instinctively to feel that every particular case has a general 
rule behind it, and therefore that proof consists in finding a general 
rule to cover the particular case. 1 

The supposition underlying the syllogism of Formal Logic is, 
then, that every assertion, regarded as disputable, requires for its 
proof two others related to it in a particular manner and accepted 
as true; these are known as the major and minor premisses. The 
assertion supposed to be proved by them is called the conclusion, and 
the three assertions together form a syllogism. 

- Smith is a scholar (conclusion); 
< "~ For Smith is a schoolmaster (minor premiss), 
/ -~ And all schoolmasters are scholars (major premiss). 

It will be clear that this process of syllogizing consists in showing 
the conclusion to be a particular case coining under a general rule. 

In the typical syllogism, the statement of the general rule is the 
major premiss, and the function of the minor premiss is to connect 
the conclusion with it. 2 

3. The Limited Value of Formal Logic 

Nowadays Formal Logic is greatly discredited, and many of our 
acutest thinkers and ablest reasoners openly scoff at it. Why is 

1 Sidgwick, Use of Words in Jteasoning, pp. 71-4. 

2 Formal Logic admits that the value of the syllogistic process stands or falls by that of Us 
typical form, which therefore need alone concern us here 

Logicians have a convenient custom of typifying arguments by using letters instead of 
words ; for instance. SMP. Thus, the typical syllogism is often written : All M are P; 8 is M, 
therefore S is P. (S - subject of conclusion ; P = predicate of conclusion ; M = middle term, 
i.e. the common term of the two premisses, connecting them with each other; it does not 
appear la the conclusion.) 


this, seeing that it has been in almost constant use, with very few 
modifications or additions, ever since the time of Aristotle? 

When the logicians of the older school speak of a piece of reason- 
ing as being formally valid, they mean that its validity is determined 
solely by its form, and is in no way dependent upon the particular! 
subject-matter to which it relates. They try to regard the process 
of reasoning as something distinct from the subject-matter about which 
it is employed, and the errors of reasoning which they contemplate 
are those only which occur in the process so conceived. 1 Archbishop 
Whately, for instance, would readily admit the conclusion of the 
following syllogism, simply because the syllogism is formally valid: 

All good men are wise; 
Smith is a good man, 
Therefore Smith is wise. 

He would maintain that it is no part of the business of Logic to 
consider the truth of the premisses. He restricts the process of 
reasoning to syllogizing, or concluding from generals to particulars; 
and he regards errors in reasoning as simple failures in verbal 
consistency. 2 It is a remarkable thing that such logicians should 
overlook the fact that, in order to get an assertion expressed in 
" logical form", they are usually bound to consider its meaning, and 
therefore cannot, to this extent at least, escape the necessity of 
" material " 3 considerations. 4 

Formal Logic commits itself to the assumption that the mere 
form of a sentence is sufficient to bind asserter and defender to a 
single indisputable meaning. It cannot therefore hope to be of any 
great practical service in dealing with the chief differences of opinion 
about matters of fact. For in the vast majority of cases, fallacies 
and disputes are due to the difficulty of making our meanings clear. 5 

Formal Logic is, in short, merely a Logic of consistency. When 
we apply Logic to the investigation of objective reality, we are in the 
domain of Material Logic. 

Let us consider the syllogism 

All disciplinarians are martinets; 
Smith is a disciplinarian, 
Therefore Smith is a martinet. 

i Cf. Sidgwiok, Fallacies, pp. 18-19. 2 cf. Sidgwick, Use of Words, pp. 9, 10. 

s " Material " is opposed to " Formal ". * Cf. Use of Words, pp. 10, 11. 

6 ib. p. 19. 


If the truth of the premisses be granted, and if the " middle term" 
disciplinarian has precisely the same meaning in the two premisses, 
any schoolboy will draw the correct conclusion, for he has merely 
to engage in the mechanical operation 1 of fitting a particular case 
under a general rule. But are we sure of the truth of the state- 
ment ("the theory") contained in the major premiss? How do 
we know that "all disciplinarians are martinets"? Is this a mere 
assumption, or a carefully established induction? Are we sure of 
the truth of the "fact" contained in the minor premiss? Have we 
verified the supposed fact that Smith is a disciplinarian? Do we use 
the term "disciplinarian" in exactly the same sense in each of our 
assertions? Do we agree as to the exact significance of the term 
"martinet"? These are the points about which we are likely to 
differ in opinion, these the points likely to render our reasoning 

In Formal Logic, the conclusion is always implicitly contained 
in the premisses, and mere consistency compels assent to the con- 
clusion if the premisses are once admitted. As Dr. Keynes says, 2 
"Of context and subject-matter, Formal Logic has no cognizance". 
And for this very reason, Formal Logic has no appreciable practical 
value. Its reasoning operations are restricted to the manipulation 
of ready-prepared material, sentences in "logical form", pairs of 
sentences with a common term (M) which we drop out of account 
in the "conclusion". It is quite true that syllogizing may prove 
a very interesting pastime, but we delude ourselves if we think it is 
likely to be of any real service in the serious business of reasoning. 

4. "Forward" and " Reflective " Reasoning 

It is necessary to draw a distinction between "Forward" and < 
"Reflective" reasoning, and Mr. Sidgwick makes the distinction 
clear. " ' Forward* reasoning starts from facts accepted as true and 
asks what unseen conclusion they point to. 'Reflective' reasoning 
starts from a questioned conclusion, and examines its truth by 
exploring its grounds." 8 

" Forward" reasoning is the only kind of reasoning which Formal 
Logic cares about. "Reasoning is thus regarded as a process of 
building a structure by putting together isolated bricks of thought" 

1 Reference has already been made to Jevons'a Logical Machine. Cf. also the "Dictum de 
omni et nullo " of Aristotle. See, for instance, Whately, Logic, p. 23. 

2 Logic, pp. 1-3. s Use of Words, p. 59. 


Chief among these are mathematical reasonings or rather mathe- 
matical demonstrations 1 but these form virtually a class by them- 
selves. There are, it is true, occasionally " other cases where we 
get a piece of knowledge and then another piece of knowledge, and 
then suddenly see that these are premisses and yield a logical con- 
clusion"; 2 and in Science we often require the forward use of the 
syllogism for the purpose of deducing conclusions from a hypothesis 
in order to compare them with facts. But whenever doubt arises as 
to whether a given conclusion is justified by its premisses, the use of 
the syllogism has already ceased to be forward deductive reasoning, 
and become "reflective". Hence syllogistic reasoning as a move- 
ment of thought from seen truth to truth not yet seen, applies only 
to cases which are comparatively free from doubt and difficulty. 8 

In ordinary cases we suspect a truth before we prove it; "our 
reasonings lag behind our guesses, and are an attempt to review the 
grounds of belief which has already begun to take shape". 4 The 
occasions on which we get premisses before we have an inkling of 
the conclusion are by no means so frequent as Formal Logic com- 
monly supposes. 

In reflective reasoning we call for the production of facts suffi- 
cient to support the conclusion, the sufficiency being made up partly 
of the truth of the facts produced and partly of their relevance. Thus 
a syllogism used for proof is a conclusion expanded so that the two 
disputable elements of it shall be open to inspection. In a reflective 
syllogism, the premisses come out of the conclusion rather than 
precede it. Of course this view materially alters the notion of 
proof as popularly conceived, for the superstition still prevails that 
" proof" is bound to take the form of " mathematical demonstration ". 

The most that any proof can do, in the case of disputed conclu- 
sions, is to challenge the objector to find definite fault with the 
reasons given for belief. If our assertion that "Smith is a scholar" 
is disputed, we bring forward our reasons: "Smith is a schoolmaster, 
and all schoolmasters are scholars"; and we challenge a denial of 
these reasons. Thus the truth of the premisses now becomes the 
basis of the argument. When, then, we question the truth of a 
conclusion, we call for facts on which it may rest. After the facts 
are produced, they may still be open to objection on one of two 
grounds; we may dispute their truth, or we may dispute their 

i We shall see later on that analysis plays a far larger share than synthesis in the work of 
the mathematician. 

a Use of Words, p. 128. Use of Words, pp. 280-9, Ac. * ib. 


relevance (even if true), to prove the conclusion. And whichever 
line of objection is adopted, a new question is thereby raised, which 
takes precedence of the question originally in dispute. Till this 
new question is answered, the argument is at a standstill. 1 

If we leave the simplest cases of argument out of account, it is 
easy to see that the whole process, as between two persons arguing, 
is the search on the part of each for false views held by the other as 
to the way in which certain things are connected in the ordinary 
course of nature. The personal aim in every, disputed question is 
to show not only that your opponent's general knowledge is somehow 
defective, but also that in consequence of his ignorance he has 
reached a false conclusion in this particular case. 

A accuses B, in effect, of being misled by appearances, or by 
words. B accuses A of making too much of some small differences. 
How is Logic, with its merely mechanical rules, to decide between 
them? The argument turns upon the real meaning of the subject- 
matter, and until agreement on this point is reached, Logic can 
nly stand still and look on. Whenever matters of real doubt and 
dispute arise, it is one of the hardest things in the world to provide 
a perfectly unambiguous syllogism that will support either side. So 
uncertain and treacherous are the words we use. 2 

5. Deduction and Induction 

Many logicians separate their books into two portions, called, 
respectively, deductive and inductive logic, but there is some danger 
in drawing too sharp a line of distinction between deduction and 
induction: the two processes are so closely Intel-related. Broadly 
speaking, we may distinguish between them by saying that deduc- 
tion includes all reasoning in which, from given particulars, we draw 
a conclusion supposed to be contained in their meaning, while induc- 
tion includes all reasoning in which we reach a conclusion from 
observation of facts. Induction is therefore the interpretation of 
facts, while deduction is the interpretation of sentences assumed 
to be true. 3 

We shall see later that the great weapon of induction, and there- 
fore of scientific method, is the so-called "method of difference"; 
but just as the "formal logician" 4 pays almost exclusive attention to 

the mere machinery of the syllogism, so he seems to think that tb * 


i Cf. Use of Words, pp. 59-61. 2 Of. Use of Words, pp. 79-80. ib. p 

4 This unfortunate term is now in rather common use. 


virtue of the "method of difference" lies in the method itself, in- 
stead of in the care and knowledge with which the material for the 
application of the method has been previously prepared. The very 
best rules of inductive logic may lead us astray. Men of science 
of one generation have often been at the utmost pains to establish 
an important induction by a rigorous application of accepted 
methods to such facts as were known, but the next generation has 
discovered the complexity of some circumstance which was supposed 
formerly to be simple, and the old induction has in consequence 
broken down. The important thing is to recognize that Science 
rests on a limited but constantly increasing knowledge of facts. 
Inquiry is never finished. Science is ever reviewing its facts and 
theories in the constant effort to make them harmonize, for there 
is always the possibility of error being concealed in accepted truths; 
imperfections are therefore constantly sought, and, when discovered, 
are removed. While, therefore, induction is the great instrument 
of scientific research, we must concentrate our attention upon the 
preparation of the materials rather than upon the inductive process 
itself, and we must always be ready to revise an induction in the 
light of new facts. It must always be remembered that inductive 
methods are of use rather in a Logic of Proof than in a Logic of 
Discovery. 1 

6. Some Common Logical Terms 

There are in common use certain logical terms which sometimes 
appear to be wanting in definite connotation. To these we must 
briefly refer. 

"Inference" is a very ambiguous word. "When we infer one 

fact from another or others, we believe that fact * by reason of ' our 

belief in those others; and when we prove one fact by means of 

another, exactly the same expression is commonly used. In both 

cases there is * reasoning ', and, accordingly, both that from which 

the inference is drawn and that on which the proof is based, are 

indiscriminately called, in popular language, the reason. We reason 

when we proceed from premisses to conclusion, arriving at new 

truths by means of old ones; and we reason when, having already 

n assertion before us, we produce arguments to support it, even if 

ich arguments be then for the first time thought of. Again, the 


the mat. Use of Words, pp. 27-30, 321-30; and W. L. Courtney, Life of John Stuart Mill, 


term * premisses' is sometimes used for the grounds of proof , and 
sometimes for the data of inference; * conclusion' sometimes means 
that which is discovered arid sometimes that which is proved." 

Inferences are of very varying degree. They may be merely 
our first vague guesses; they may be the final and certain results of 
the most careful enquiry. 

It would bo convenient to restrict the term Inference to the 
process of reaching a belief, and to speak of a Conclusion following 
from its "premisses" or "data"; and to regard Proof as the process 
of establishing a belief on a firm foundation after it is already some- 
how reached. Thus, in the case of Proof we should speak of an 
assertion "guaranteed by" its "reasons", or "resting upon" its 
"grounds". The problem of Proof is thus narrower and more 
definite than that of Inference. Instead of asking at large, "what 
conclusion may be drawn?" Proof asks, "Is such and such a reason 
warranted*!" 1 

It is evidently immaterial to an argument whether the conclu- 
sion is placed first or last. But a premiss placed after its conclusion 
is usually called the reason of it, and is introduced by a causal con- 
junction (since, because, &c.). The illative adverbs (therefore, &c.) 
designate the conclusion. 

Perplexity often arises from the fact that these conjunctions and 
adverbs have also another signification, being employed to denote, 
respectively, cause and effect, as well as premisses and conclusion. For 
example : 

(1) The soil is rich because the trees on it are flourishing; 
or (2) The trees are flourishing and therefore the soil must be rich. 

In both examples the italicized words denote the connection between 
premisses and conclusion-, for clearly the luxuriance of the trees is not 
the cause of the soil's fertility but only the cause of my knowing it. 
But if I say : 

(1) The trees flourish because the soil is rich; 
or (2) The soil is rich and therefore the trees flourish; 

I use the same words 2 to denote the connection of cause arid effect, for 

in this case the luxuriance of the trees, being evident to the eye, 

would hardly need to be proved, but might need to be accounted for. 

In some cases the cause is employed to prove the existence of the 

i Sidgwick, Fallacies, pp. 32-5. 2 i.e. because and therefore. 


effect. For instance, when from favourable weather anyone argues 
that the crops are likely to be abundant, the cause and the reason 
coincide. And this contributes to their often being confounded 
together in other cases. 1 

The reader should spare no pains in acquiring an accurate know- 
ledge of common terms used in the process of argument. The word 
why, for instance, as an interrogative, is employed in three senses, 
viz., "By what proof?" (or reason); "From what cause f; "For 
what purpose?" "Why is the triangle ABC equal to the triangle 
DBF ?" " Why does a stone fall to the earth?" " Why did you go 
to London?" 2 

7. Conclusions as to the Value of Logic 

Logic is of little use for the purpose of enabling us to reason; 
it rather enables us to know whether in a given case we have 
reasoned correctly, or at least to discover where the weak point in 
our reasoning must lie. Logic does not discover, but it tests dis- 
coveries which claim to be already made. 3 It is also a useful 
instrument for combating fallacy and sophism. 4 

Whether students of Science can profitably spend much time in 
the study of deductive logic is open to serious doubt. Obviously 
the mathematician will feel no such need, although it certainly 
has to be remembered that Mathematics is an extremely abstract 
branch of reasoning. The "pure" mathematician may possibly be 
less apt in detecting fallacy than the trained logician, for the latter is 
the more accustomed to deal with " facts " that are not certainties. 
But the study of induction is quite another matter. No student of 
Science can afford to ignore it, or even to be content with a super- 
ficial knowledge of it; and his wisest course, perhaps, is to begin 
with some elementary treatise on deduction, and follow that up by 
wide reading of inductive logic, and perhaps by some standard work 
on the theory of knowledge. The essentials of induction are, how- 
ever, dealt with in the next few chapters. 

As Herbert Spencer and others remind us, the very first condi- 
tion for avoiding fallacy is a calmness which is ready to recognize 

1 Whately, Logic, p. 18, and compare his Rhetoric, pp. 53-7. 

ib. p. 230. The whole chapter on ambiguous terms is well worth reading. 
Fallacies, pp 18-20. 

* " Fallacy is honest error ; sophism is intentional deception." Syllogisms involving 
"fallacies" have been manufactured by all logicians from Aristotle downwards, and are 
the examiners' stock-in-trade. A few instances are given at the end of the chapter. 


or to infer one truth as readily as another. If we make sure of our 
facts, if we can agree upon the precise significance of the general 
and abstract terms we use, if we can conduct our arguments frankly 
and dispassionately, we need have little fear of the reasoning pro- 
cess, and can well afford to give Formal Logic a long holiday. 1 

The Methodologists * 

We shall frequently have occasion to refer, in the next few 
chapters, to various authorities on the logic and the method of 
Science. Brief personal reference may here be made to the follow- 
ing writers who hold first place amongst such authorities. 

i. Whewell 

William Whewell (1794-1866) was the son of a Lancaster 
carpenter. He obtained a local Exhibition which enabled him to 
proceed to Trinity College, Cambridge, in 1812. He graduated as 
second Wrangler in 1816, was elected Fellow in 1817, and in 1841 
was appointed Master of the College. Of his numerous works, the 
chief are the Philosophy, and the History of the Inductive Sciences, and 
the Novum Organoti Renovatum* Whewell's wide acquaintance with 
the different branches of Science enabled him to write a compre- 
hensive account of their development, an account which, in fact, has 
never been superseded. 

i The reader will find examples of syllogisms involving " fallacies " in almost any textbook 
on Formal Logic. Here are ji few, chosen at random: 

1. All fixed stars twinkle ; yonder star twinkles; therefore it is fixed. (Bain.) 

2. You are not what I am ; I am a man ; therefore you are not a man. (Port Royal Logic.) 

3. All birds are animals with feathers ; but all birds are animals with a heart ; therefore 

all animals with a heart are animals with feathers. (Hamilton.) 

4. He who says that you are an animal speaks truly ; he who says that you are a goose says 

that you are an animal ; therefore he who says that you are a goose speaks truly. 
(Port Koyal.) 

The detection of the fallacies is left as an exercise for the reader. (It may be mentioned 
that ambiguity of the Middle Term is recognized generally as the most fruitful source of 

* Aristotle wrote the Organon, Bacon the Novum Or g anon, and Whewell the Novum 
Or g anon Renovatum. 


WhewelFs philosophy of Science was opposed to the so-called 
"empiricist tendency" prevalent among many English thinkers. 
He maintained the distinction between necessary and contingent 
truths, the former involved in the innate constitution of the mind, 
the latter coming from experience. On this and other points he had 
a sharp controversy with Mill. He defended the a priori necessity 
of axioms attacked by the latter, and in his inductive theory attri- 
buted more importance to the function of the mental idea in the 
colligation of facts than Mill did. 

2. Mill 

John Stuart Mill (1806-1873) was the son of James Mill the his- 
torian and political philosopher. The son's education was from first 
to last undertaken by the father, and is likely long to remain a 
standing subject for wonder and discussion. 1 From very early 
childhood his greatest pleasure seemed to consist in overcoming 
intellectual difficulties, and the wonderful mastery which, as a boy, 
he acquired in getting at the exact meaning of general terms, seems 
to account for the singular and quite unparalleled ease with which 
he treated of politics and sociology, always in close relation with 
facts. Mill's knowledge seems to have been encyclopaedic. 

l was in 1837, on reading WhewelFs Inductive Sciences, and re- 
reading Herschel, that Mill at last saw his way clear to formulating 
the methods of scientific investigation. His great work, Logic, was 
regarded as epoch-making, from the multitude of new views opened 
up. Mill has been described as the father of Induction, just as 
Aristotle is sometimes called the father of Deduction. He has been 
assailed by many critics, but although a few unimportant outworks 
have been taken, his main position is as secure as ever. 

3. Herschel 

Sir John Herschel (1792-1871) was the son of Sir William 
Herschel. Both father and son were famous astronomers. The 
son graduated as Senior Wrangler in 1813. His book, Discourse on 
Natural Philosophy, though of very modest proportions, is one of the 
best treatises on scientific method ever written. 

i The reader should turn to Mill's Autobiography, a delightfully interesting book. 


4. Bain 

Alexander Bain (1818-1003) was* for many years Professor of 
Logic at the University of Aberdeen, and was famous as a Logician 
and as a Psychologist. Bain and Mill were lifelong friends, and the 
two had much in common. Bain's Inductive Logic is a well-known 
standard work. 

5- Jevons 

William Stanley Jevons (1835-1882) graduated at the University 
of London, and in 1866 was elected " Professor of Logic and Mental 
and Moral Philosophy and Cobden Professor of Political Economy" 
at Owens College. He felt the absurdity at having to deal with 
so many branches of knowledge, and was glad to exchange in 1876 
for the professorship of Political Economy at University College, 
London. Although Political Economy appears to have been his 
principal subject, he had in his early days been greatly interested 
in Science, and he gave special consideration to the logic of induc- 
tive science. His Principles of Science is his important work, and 
we shall have to refer to it frequently. Jevons's views of induc- 
tion were very similar to those of Whewell, and, like Whewell, he 
attacked Mill. His life was prematurely cut short by drowning at 

6. Professor Welton 

Professor Welton occupies the Chair of Education at the Univer- 
sity of Leeds. The second volume of his Manual of Logic deals at 
length with the various logical aspects of the method of Science. 

Although Professor Welton's dearest wish seems to be to con- 
sign, with bell, book, and candle, the "mere" empiricist to utter 
darkness, the mere empiricist will gain much by reading the second 
volume of the Logic, which is a mine of useful hints^to those who 
wish to master scientific method. 

7. Mr Alfred Sidgwick 

The present writer owes a great deal to the various works of 
Mr. Alfred Sidgwick, perhaps the best known among modern logi- 
cians to show conclusively how extremely limited is the value of 
Formal Logic. His works include Fallacies, The Process of Argur 
went, The Use of Words in Reasoning, and The Application of Logic. 

(0415) 14 




i. General Notions of Induction 

Induction has been defined as the legitimate inference of pro- 
positions applicable to cases hitherto unobserved and unexamined, 
from propositions which are known to be true of the cases observed 
and examined. In every argument it is implied that, wherever and 
whenever the same circumstances are repeated, the same effects will 
follow. Induction, therefore, may also be defined as the legitimate 
inference of the general from the particular ', or of the more general from 
the less general. 1 

To illustrate this definition, Fowler makes use of the well- 
known "guinea and feather" experiment. 2 A guinea and a feather 
are placed at the same height under the exhausted receiver of an 
air-pump. When released they are observed to reach the bottom 
of the vessel at the same instant of time, or, in other words, to fall 
in equal times. 

From this fact, we infer that a repetition of the experiment, 
either with the same two bodies or with any other bodies, would 
be attended with the same result, and that, if it were not for the 
resistance of the atmosphere and other impeding circumstances, all 
bodies, whatever their weight, would fall through equal vertical 
spaces in equal times. 

Now here we have performed an experiment, we have arranged 
that, for purposes of observation, a certain thing shall happen under 
certain conditions; and we have drawn an inference. What assump 
tions underlie this inference, and on what grounds does it rest? 

Clearly there was some definite object in working the experi- 
ments. The question had previously been asked whether bodies, 
if subject to the action of gravity alone, would fall in equal or 
unequal times. By exhausting the air in the receiver, it wag 
possible to isolate the phenomenon, all circumstances affecting the 
bodies, except the action of gravity, being thus removed; the effect 
of this cause acting alone could then be watched. 

We are, however, assuming that the ^effect, whatever it may be, 
will be entirely due to the cause (or causes) then and there in action, 

i Fowler, Inductive Logi$, pp. 9-10. a ib. 


In other words, we are assuming that nothing can happen without 
a cause. 1 

But why do we infer that if the experiment be repeated, the 
same two bodies, or any other bodies, will behave in the same way ? 
Because we feel assured that the same cause will invariably be 
followed by the same effect, or, to speak more accurately, that the 
same cause or combination of causes will, if unimpeded by the 
action of any other cause or combination of causes, be invariably 
followed by the same effect or combination of effects. We assume 
the "uniformity of nature". 2 

Our argument, then, turns upon the truth of two important 
assumptions, viz. the Law of Universal Causation and the Law of the\ 
Uniformity of Nature. 

The general argument may be summarized as follows: 

1. We observe that the two bodies, though of unequal weight, 
reach the bottom of the receiver at the same moment. 

2. The fact must be due to some cause, or combination of causes. 3 

3. The only cause operating in this instance is the action of 
gravity. 4 

4. Therefore the fact that these two bodies reach the bottom of 
the receiver at the same moment is due to the action of gravity 
operating alone. 

5. But whenever the same cause, or combination of causes, is in 
operation, and that only, the same effect will invariably follow. 5 

6. Therefore when these two bodies, or any other two or more 
bodies, even though of unequal weight, are subject to the action of 
gravity only, they will reach the bottom of the receiver at the same 
moment, or, in other words, will fall in equal times. 6 

It is exceedingly important to notice exactly how in this way 
we are able, if we assume the truth of the Laws of Universal Causa- 
tion and the Uniformity of Nature, to make a great generalization 
from a single experiment. Unfortunately, however, it is very 
seldom that we can eliminate all operating causes save one, and 
induction is generally far more subtle and difficult than this easy 
example seems to suggest. 

There are other so-called inductions which are not really induc- 

1 2 These two assumptions will be considered presently. 
8 Law of Universal Causation. 

* Of course we have no knowledge of the nature of gravity, which may be a complex, and 
not a simple, phenomenon. It is possible, therefore, that if and when we discover the nature 
of gravity, we shall have to revise many of our scientific conceptions. 

* Law of Uniformity of Nature. Fowler, Inductive Logic t pp. 1-7. 


tions at all, though the opinion commonly prevails that induction 
is in some way connected with the collection or counting of a large 
number of instances. Suppose, for example, we wish to establish 
the fact that every month contains more than twenty-seven days. 
We simply examine an almanac, get at the actual fact for every 
month, and make a complete record. In such a case there is no 
inference of any sort or kind, and no induction. 

But suppose we make the statement that "all swans are white". 
We may have examined ten, perhaps a hundred, perhaps a thou- 
sand, instances, but, even so, we are not justified in making any such 
generalization. It would at the best be only a probability, for we 
are not acquainted with any causal connection between a swan and a 
particular colour of plumage. And the first black swan we saw or 
knew to exist would, of course, show the generalization to be false. 

Take another instance. Gold is known to have a definite specific 
gravity and to melt at a certain temperature, but these are merely 
coexisting facts, which may possibly be due to some causal connec- 
tion; but, if so, such connection is at present entirely unknown to 
us. Such facts of coexistence are arrived at by "simple enumera- 
tion". There is no inference, no real induction at all. 

Yet inductions of this class inductions of simple enumeration 
really include the Laws of the Uniformity of Nature and Causa- 
tion, as well as the axioms of Mathematics and such facts of co- 
existence as that already referred to. We shall have to refer to 
this point again. 

So much for induction in its broader and simpler aspects. 

2. The Guiding Principles of Bacon, Newton, 
and Herschel 

It will be remembered that Bacon's great merit was his insistence 
on the necessity of basing all generalizations on a patient collection, 
classification, and comparison of facts. He did not, however, pro- 
vide us with inductive machinery of any appreciable value. 

Newton, like Bacon, made little by way of direct contribution to 
the methods either of Discovery or Proof, but he set an example 
of scrupulously careful and cautious inquiry, and raised the standard 
of proof enormously. His "Kules of Philosophising" were long 
quoted as authoritative. 1 

i For instance : (1) " Only real causes (verce causes, actually existing causes) are to he 
admitted n explanation of phenomena"; (2) "No more causes are to be admitted than 


Herschel insists that experience is our sole source of knowledge. 
He urges the importance of recording observations with numerical 
precision, dwells upon the value of classification, and gives several 
rules which are useful aids to Discovery. 1 

3. Whewell's "Colligation of Facts " and 
"Explication of Conceptions " 

But it is not until we come to Whewell that we find a method 
worked out in detail. His Novum Organon' 2 lienovatum claims to be 
"a revision and improvement of the methods by which Science 
must rise and grow ". 

Whewell considered that the great problem of Science is to 
"superinduce" Ideas or Conceptions 8 upon Facts. The business 
of the discoverer is, first, to familiarize himself with facts, then to 
compare them with conception after conception, in order to find out 
after a longer or shorter process of trial and rejection, what con- 
ception is (1) clear and distinct, and (2) exactly "appropriate" to 
the facts under consideration. When the investigator has at length, 
by a happy guess, hit upon the appropriate conception, he is said 
to "colligate" the facts, to "bind them into a unity". 

Throughout Whewell's scheme there is a sharp antithesis be- 
tween Ideas or Conceptions, and Facts. With him generalization 
consists not in evolving notions from a comparison of facts, but 
in "superinducing" upon facts conceptions supplied by the mind. 
The particular facts are not merely brought together, but there is 
a new element added to the combination by the very act of thought 
by which they are combined. There is a conception of the mind 
introduced, which did not exist in any of the observed facts. 4 

Let us take one of Whewell's examples with which he illustrates 
his arguments. Why do we infer that the earth is of globular form? 

Our chief fads are these: (1) As we travel to the north, we find 
that the apparent pole of the heavenly motions, and the constella- 

such as suffice to explain the phenomena". In other words, when one cause is proved to be 
present in sufficient amount for the effect, we are not at liberty to suppose the presence of 
other causes. (Cf. the maxim known as Occam's razor: " Entia non *unt multiplicanda 
praeter necessitate".) (3) " In as far as possible, the same causes are to be assigned for the 
ame kind of natural effects "for instance, the respiration in man and beasts; the fall of 
stones in Europe and in America. 

i One such rule recommends the tabulation of facts "in the order of intensity in which 
some peculiar quality subsists M . See Phil, of Disc., Part II, ch vi ; and cf. Bain, pp. 40&-11. 

a Whewell used the Greek word, Bacon the Latin (Organum). 

* Ideas " the higher generalities " ; Conceptions" the lower ge eralitlea". 

* Nov. Org. Ren., pp. 72-4, 106-7. Cf. Bain, pp. 411-2. 


tions which are near it, seem to mount higher; and as we proceed 
southwards, they descend. (2) If we proceed from two different 
points, considerably to the east and west of each other, and travel 
directly northwards from each, as from the south of Spain to the 
north of Scotland, and from Greece to Scandinavia, these two north- 
and-south lines will be much nearer to each other in their northern 
than in their southern parts. 

These facts, namely, the visible descent of the North pole of the 
heavens as we travel south, and the convergence of the meridians 
to the north, are seen to be consistent with the supposition that the 
surface of the earth is convex, and with no other supposition. If 
the earth be supposed globular, the facts at first brought forward 
are at once seen to be mere consequences. And the supposition 
is further confirmed by observing that the boundary of the earth's 
shadow upon the moon is always circular. 1 

Upon the actual facts, then, we superinduce the conception that 
the earth is globular in form. Or we may say that we have con- 
ceived a new and general proposition which includes the more 
particular ones. But these particulars constitute ^he general truth, 
not by being merely enumerated and added together, but by being 
seen in a new light. The inductive truth is made into something 
more than the sum of the facts by the introduction of a new 
mental element; and the mind, in order to be able to supply this 
element, must already be stored with appropriate knowledge. In 
order, for instance, that an investigator may see that a convex sur- 
face of the earth necessarily follows from the facts above brought- 
forward, he must have a sound knowledge of Geometry, especially 
the geometry of the sphere. The conception that the earth is 
globular would never occur to an investigator ignorant of Mathe- 
matics. 2 

We see, then, that Whewell considered the inductive step to 
consist in the suggestion of a new conception for binding the facts 
together. But precisely how such conceptions really originate, he 
does not clearly say. He speaks of them as being gradually worked 
out by the discussions and reflections of successive speakers, a view 

* It being supposed to be already established that the moon receives her light from the 
sun, and that lunar eclipses are caused by the interposition of the earth. 

The further illustration of the fact that the earth in globular, often given, viz. that the 
horizon is always circular, is a little dangerous. The eye may be misled by mere perspective 

a To "explain" to children, who are entirely ignorant of the geometry of the sphere, that 
the earth is globular in fojm is a mere waste of words. 


not inconsistent with their gradual development from the comparison 
of particulars. But he says also that they are supplied by the mind, 
while facts are supplied by sense; and he seems tacitly to assume that 
the mind is a sort of storehouse of conceptions accumulated there 
independently of the experience of particulars. 1 

4. Mill's Views of Induction 

Mill defines indifctioi>as that operation of the mind by which 
we infer that what we know to be true in a particular case or cases 
will be true in all cases which resemble the former in certain assign- 
able respects. In other words, induction is the process by which 
we conclude that what is true of certain individuals of a class is 
true of the whole class, or that which is true at certain times will 
be true in similar circumstances at* all times. 

Induction is thus a process of inference; it proceeds from the 
known to the unknown; and any operation involving no inference, 
any process in which what seems the conclusion is no wider than the 
premisses from which it is drawn, does not fall within the meaning 
of the term. 

Such a definition therefore excludes the so-called " perfect" induc- 
tions, or inductions of "simple enumeration". If, for instance, we 
were to say, All the planets shine by the sun's light, from observa- 
tion of each separate planet; or, all the Apostles were Jews, because 
this is true of Peter and Paul and every other Apostle; these, and 
such as these, would, in mediaeval phraseology, be called "perfect", 
and the only perfect, inductions. But such an induction is not an 
inference from facts known to facts unknown, but a mere shorthand 
registration of facts known. The two simulated arguments quoted 
are not generalizations; the propositions purporting to be conclu- 
sions from them are not really general propositions. "A general 
proposition is one in which the predicate is affirmed or denied of 
an unlimited number of individuals, viz. all, whether few or many, 
existing or capable of existing, which possess the properties con- 
nected by the subject of the proposition." "All men are mortal" 
does not mean merely all now living, but all men past, present, and 
to come. 

In short, Mill regards induction as " the operation of discovering 
and proving general propositions". 2 

i Cf. liaiu, p. 41'2. 

a Mill, Logic, Book III, ch. ii. Cf. Aristotle's views (see ch. vii, 4). 


5. How Mill Differs from Whewell 

Mill's view of induction differs materially from Whewell's. The 
difference will be best understood by referring to Kepler's "First 

The ancients noticed, just as untrained observers now notice, 
that the stars maintained an apparently constant position on the 
uniformly rotating star-sphere, but amongst them was to be seen a 
number of other bodies (which they called planets) moving in paths 
made up of a series of successive loops. They, very naturally 
perhaps, regarded the earth as the common centre of both solar 
and planetary orbits, the looped paths of the planets being explained 
by supposing each planet to travel, in a circle, round a centre which 
itself travelled, in a circle, round the earth. In other words the 
path of each planet was an epicycle 1 . Copernicus 2 was not satisfied 
with this old geocentric theory, and he conceived the sun, instead 
of the earth, to occupy the centre of the solar system, a conception 
which much simplified the real planetary movements. But the old 
axiom that the celestial motions must be circular and uniform ap- 
peared to Copernicus to have strong claims to acceptance, and he 
therefore felt bound still to regard the planetary paths as epicyclic. 
But Kepler 3 , the disciple of Tycho Brahe, 4 was convinced that the 
theory of epicycles was wrong, and, making use of his master's great 
mass of accurate observations of the orbit of Mars, set to work to 
discover the truth. On a firm basis of actual facts of observation, 
he constructed hypothesis after hypothesis, all modifications of the 
old theory of epicycles, till he was finally led to change the epi- 
cyclical into an elliptical theory. 5 The failure of many of his earlier 
hypotheses was due to his acceptance of the old notion that the path 
of a planet was a perfect circle. Altogether he made no less than 
nineteen hypotheses with regard to the motion of Mars, and with 
enormous labour calculated the results of each, before he finally estab- 
lished the fact that the planet's path is an ellipse. It must not, 
however, be thought that Kepler made any serious alterations of 
relations which occurred in the first hypothesis. His elliptical theory 
of Mars' motion involved relations of lines and angles much of the 
same nature as all his previous false hypotheses. 6 

1 The reader should construct an epicycle for himself. The epicycle describes, with ap- 
proximate correctness, the apparent motion of a planet when the earth is assumed as /teed, 
a 1478-1643. 8 1571-1630. * 1646-1601. 

5 Cf. Whewell, Hist. Ind. Sci , vol. i, pp. 316-26. 

Nov. Org. Hen., pp. 65-6. Cf. the section on the " Method of Curves ", ch. xxv, 10. 
The non-mathematical reader may hardly appreciate the difficulties encountered when 


Before examining this example as a possible instance of induc- 
tion, Mill gives what he considers to be an analogous case: 

A navigator sailing in the midst of the ocean discovers land; ho 
cannot, at first, or by any one observation, determine whether it is 
a continent or an island; but he coasts along it, and, after a few 
days, finds that he has sailed completely round it. He then pro- 
nounces it an island. Now there was no particular time or place of 
observation at which he could perceive that this land was entirely 
surrounded by water; he ascertained the fact by a succession of 
partial observations, and then selected a general expression which 
summed up in two or three words the whole of what he so observed. 
But there is nothing of the nature of an induction in this process. 
He inferred nothing that had not been observed, from something 
else which had. He had observed the whole of what the proposition 
asserts. That the land in question is an island is not an inference 
from the partial facts which the navigator saw in the course of his 
circumnavigation; it is the facts themselves; it is a summary of 
those facts; the description of a complex fact, to which those simpler 
ones are the parts of a whole. 

Now Whewell maintained that Kepler had established by induc- 
tion the fact that Mars' orbit is an ellipse. But Mill urged that 
there was no difference in kind between the navigator's simple 
operation and that by which Kepler ascertained the nature of the 
planetary orbit; that Kepler's operation, or at least the character- 
istic part of it, was not more an inductive act than that of our sup- 
posed navigator. 

Kepler's object was to determine the real path described by the 
planet Mars. To do this there was no other mode than that of 
direct observation; and all that observation could do was to ascertain 
a great number of successive places of the planet, or rather of its 
apparent places. That the planet occupied successively all these 
positions., and that it passed from one of them to another without 
any apparent breach of continuity, thus much the senses could 
ascertain. What Kepler did more than this was to find what sort 
of a curve would result, supposing a line drawn through all these 

the heliocentric theory was first suggested. If we could watch the motions of the planets, 
from some point right outside the solar system, we might determine their orbits as easily as 
we do those of Jupiter's satellites. Even if we could observe them from the sun, our task 
would be comparatively easy. But our observations have to be made from one of the moving 
planets themselves; and the consequent apparent motions of the other planets are so compli- 
cated that the real motions are exceedingly difficult to determine exactly. The apparent 
motion of, for instance, Mars amongst the stars is far more suggestive of an epioycle than an 


points. He unified the whole series of observed positions of Mars 
by what Whewell calls the "general conception" of an ellipse. 1 
This operation, though much more difficult than our supposed navi- 
gator's, is, Mill says, the very same sort of operation ; and if the one 
is not an induction but a description, this must also be true of the 
other. Kepler merely found an expression for a set of facts; he 
made no inference. Nor did he (which is the true test of a general 
truth) add anything to the power of prediction already possessed. 
Astronomers had long known that the planets periodically returned 
to the same places. Thus Mill argues. 

Mill agrees that Whewell's expression "colligation of facts" is 
aptly chosen for the descriptive operation which enables a number 
of details to be summed up in a single proposition. But he denies 
that such colligation is induction at all. He also agrees that, for 
such descriptive operations, a conception of the mind is required; 
the conception of an ellipse must have presented itself to Kepler's 
mind before he could identify with it the orbit of Mars. According 
to Whewell, the conception was something added to the facts. But 
Kepler did not, says Mill, put something into the facts by his mode 
of conceiving them. The ellipse was in the facts before Kepler 
recognized it, just as the island was an island before it had been 
sailed round. Kepler did not put what he had conceived into the 
facts, but saw it in them. If the elliptic path were visible, no one, 
Mill thinks, would dispute that to identify it with an ellipse is to 
describe it; and Mill cannot see why any difference should be made 
by its not being directly an object of sense, when every point in it 
is as exactly ascertained as if it were so. 

Mill admits that Whewell's account of the manner in which a 
conception is selected to express the facts is probably just; and 
believes that the experience of all thinkers will testify that the 
process is tentative; that it consists of a succession of guesses, many 
being rejected, until at last one occurs fit to be chosen. Successive 
expressions for the colligations of observed facts, or, in other words, 
successive descriptions of a phenomenon as a whole, which has been 
observed only in parts, may, though conflicting, be all correct as 
far as they go. "But it would surely be absurd to assert this of 
conflicting inductions." "Different descriptions may be all true, 

i The reader should bear in mind that, in textbooks on Astronomy, the illustrations of the 
planetary orbits are, as regards eccentricity, grossly exaggerated. If, for instance, the orbit 
of the earth be accurately drawn, it IB quite impossible for the untrained eye to see that it if 
not a perfect circle. 


but not, surely, different explanations." " Colligation is not always 
induction, but induction is always colligation." 

Whewell, in reply, denied that there was any validity discover- 
able in the distinction which Mill attempts to draw between descrip- 
tions like Kepler's Law of Elliptical Orbits, and other examples of 

But Mill again insisted that such distinction is necessary. Dr. 
Whewell " allows of no logical process in any case of induction other 
than what there was in Kepler's case, namely, guessing until a guess 
is found which tallies with the facts; he considers the process of 
invention, which consists in framing a new conception consistent 
with the facts, to be not merely a necessary part of all induction, 
but the whole of it". But, says Mill, "induction is generalization 
from experience. It consists in inferring from some individual in- 
stances in which a phenomenon is observed to occur, that it occurs 
in all instances of a certain class, namely, in all which resemble the 
former, in what are regarded as the material circumstances." 1 

The real difference between Mill and Whewell is mainly one of 
definition, though of course there is the further fundamental differ- 
ence of philosophic faith. To the practical man the difference is 
of no particular consequence. 2 

6. Jevons's Views 

Jevons defines induction as the inference of general from par- 
ticular truths, and regards the process as the inverse operation of 
deduction. He admits, however, that the inverse operation is incom- 
parably more difficult than the direct, just as integration is more 
difficult than differentiation, or just as finding the factors of a given 
large number is more difficult than finding the product of such 
factors. Exactly the same difficulty exists in determining the law 
which certain things "obey". Given a general mathematical ex- 
pression, we can easily ascertain its value for any required value 
of the variable, but given a series of numbers like the following, 

I 1 1 1 5 691 7 3617 43867 JP 7r , 

~ ~~ 

i See Mill, Logic, Book III, ch. i, ii. 

Mill has often been attacked because of his "empiricist" attitude. Professor Welton, 
for instance, says that Mill has two incompatible theories of inference : (1) Inference is based 
on resemblance between phenomena; (2) inference is grounded in the essential conditions of 
phenomena " In the former view Mill keeps fairly close to the empiricist position. But the 
latter position is quite inconsistent with empiricism ; for analysis of conditions necessarily 
involves the synthetic activity of thought." But such an argument suggests considerable 
misapprehension of the reU empiricist position. Of. ch. xi. 


a series which seems to set all regularity and method at defiance, 
and it would puzzle anyone not a mathematician to detect any form 
of symmetry in the relations amongst them. 1 "Induction is the 
deciphering of the hidden meaning of natural phenomena." 

Jevons calls an induction perfect " when all the objects or events 
which can possibly come under the class treated have been examined". 
In all other cases, " induction is imperfect and is affected by more or 
less uncertainty ". Thus, Jevons's views of what constitutes induc- 
tion are almost diametrically opposite to those of Mill. In answer 
to the objection that the process of " perfect induction " can give us 
no information, and is merely a summing up, in a brief form, of a 
multitude of particulars, Jevons says, " but mere abbreviation of 
mental labour is one of the most important aids we can enjoy in the 
acquisition of knowledge". No doubt; but a mere shorthand regis 
tration of facts is a very different thing from inference. 

Jevons considers that we pass from perfect to imperfect induc- 
tion "when once we allow our conclusions to apply, at all events 
apparently, beyond the data on which it was founded ". But " imper- 
fect induction never makes any real addition to our knowledge, in 
the meaning of the expression sometimes accepted. The results of 
imperfect induction, however well authenticated and verified, are 
never more than probable." " The theory of probability shows how 
far we go beyond our data in assuming that new specimens will re- 
semble the old ones." 2 

In Jevons's opinion, " there are but three steps in the inductive 
process: (1) Framing some hypothesis as to the character of the 
general law; (2) Deducing consequences from that law; (3) Observ- 
ing whether the consequences agree with the particular facts under 
consideration ". 8 But our final conclusion, he thinks, never passes 
from the realm of probability to that of absolute certainty. 

7. Professor Welton's Views 

Professor Welton's views are clearly expressed and very sug- 
gestive, though he constantly shows impatience with the empiricist 

He considers there is general agreement that " induction Is 
essentially an analysis of the process by which a universal judg- 

1 The numbers are known as those of Bernouilli. The first thirty-one of these numbers 
were published by Ohm in vol. xx of Crelle's Journal. Prof. J. C. Adams has calculated the 
next thirty-one. See the Bnt. Assoc. Rpt. for 1877. 

a See Principle* of Science, pp. 146-61, 218-19. ib. pp. 265-S. 


merit about reality can bo established, and that this process starts 
with the particular ". Owing, however, to the complexity of the 
data of experience, the process of analysis is very liable to error. 
There is thus an advantage of plurality of instances, for the observer 
is then more likely to detect unessential elements. If, however, the 
conditions can be exactly ascertained in a single instance, plurality 
of instances is unnecessary. This is often the case in chemical 
experiments. "The only cases in which an inference is made from 
number of instances as such is when it is impossible at any rate 
for the time to ascertain the conditions of the phenomenon in 
question; and then the inference is not inductive, but belongs to 
the domain of mathematical probability." This view should be 
compared with Jevons's. 

Professor Welton gives the following as the essential steps in 
the inductive process: 

1. The formation of a hypothesis suggested by a first observation 
of facts. 

2. The deduction of the consequences of this hypothesis. 

3. The testing of these consequences by a careful analysis of 

4. The consequent exact definition of the hypothesis, which 
then, as expressing the true universal nature of reality, is verified 
and received as an established theory or law. 1 

8. No Hard-and-fast Rules Universally Applicable 

It is clear that there is considerable divergence of views as to 
the nature and method of induction. Since, however, induction 
is an inverse process, it is practically impossible to reduce the pro- 
cess to any stereotyped method. Every case presents its own 
difficulties, and sometimes these are so great as apparently to defy 
solution. For instance, despite the ingenuity of some of the most 
brilliant men of science, we are still absolutely ignorant of the real 
nature of gravitation. Although, therefore, Professor Welton has 
given us a set of admirable rules for the general solution of the 
inductive problem, we shall find that men of science by no means 
always work exactly on these lines, and that Mill's Canons of in- 
duction are certainly not to be tossed away as useless lumber, as 
logicians of a certain school of thought demand. Nature presents 
her problems to us in an almost infinite variety of ways, and it 

i See Welton, Manual of Logic, vol. ii, pp. 65-60. 


is a great mistake to think that those problems can all be solved 
by any single set of simple rules. It is amazing to find what a 
number of expedients are adopted by men of science for pursuing 
their work. Research is not such a simple tusk as many theorists 
regard it. 

g. The Ground of Induction 

It remains to consider the ground of induction. 

The induction of the ancients, like the induction of unlettered 
moderns, consisted in ascribing the character of general truths to 
all propositions which are true in every instance that happens to 
be known. It is the "perfect" induction of "simple enumeration"", 
and is the kind of induction natural to the mind when unaccustomed 
to scientific methods. The unprompted tendency of the mind is to 
generalize its experience, provided this points all in one direction, 
and provided no other experience of a conflicting character happens 
to present itself. The notion of interrogating nature is of much. 
later growth. "The observation of nature by uncultivated intel- 
lects is purely passive; they take the facts which present themsdves 
without taking any trouble of searching for more. It is only a 
superior mind which asks itself what facts are needed to enable 
it to come to a safe conclusion, and then looks out for these." l 

Yet, even in the most scientific induction, we are making a 
tremendous assumption, an assumption with regard to the course 
of nature and the order of the universe, that what happens once 
will, under a sufficient degree of similarity of circumstances, happen 
again, and not only again, but as often as the same circumstances 

This universal assumption which is our warrant for all inferences 
from experience, is often referred to as the uniformity of nature-, and 
it must be regarded as the fundamental principle, or general axiom, 
of induction. 2 

It is exceedingly difficult to justify such an assumption. Can 
we regard such a vast generalization as itself an instance of induc- 
tion ? Mill thinks we can. But Professor Welton and his school will 
not admit this at all. 

Yet our sole guarantee for inductive inference is the uniformity 
of nature, or indeed for inference of any kind. If we put a piece of 
wood into the fire and see it burned, we infer that another piece will 

i Mill, Logic, Book III, ch. iii, 2. a tf>. m, m, i. 


be consumed in like manner. This is to take for granted that what 
has happened will, in the same circumstances, happen again; in other 
words, that nature is uniform. 1 We are bound to pass across the 
gulf, from the experienced known, either present or remembered, to 
the unexperienced and unknown; we must perform the leap of real 
inference. We are doiug the same kind of thing, and making just 
the same kind of fundamental assumption, every day of our lives. 

We can give no final logical reason for our assumption that 
nature is uniform. But we make the assumption, and feel bound 
to make it, though at the same time we are forced to admit that 
by so doing we are begging the whole question. Theoretical proof 
seems to be absolutely impossible, but the probability of the truth 
is so enormous that the practical man does not hesitate to accept 
it. For though it be admitted that the assumption is the outcome 
of an induction of mere simple enumeration, the facts enumerated 
are coextensive with all human experience. 2 


Some General Principles of Investigation 
Observation and Experiment 

i. Preliminary Notions 

When a railway accident takes place, an enquiry is held as to 
its cause. This may prove no easy matter, may in fact be so difficult 
that the cause never is absolutely determined. The accident may 
have been due to an error of a signalman, to an oversight of the 
engine-driver, to a defect in the permanent way, to an obstruction, 
to the collapse of a wheel, or to any one or more of a large number 
of possible other causes. A witness may suggest what he considers 
to have been the cause; the suggestion is made a working hypo- 
thesis, the consequences of which are traced out, and a comparison 
made with known facts; the hypothesis is thus verified or shown to 
be wrong: and so on. The important point to notice is that the 

i See Bain, vol. i, p. 19. 

a ib. pp. 273-4. The reader may usefully consult Dugald Stewart, Phil, of Human Mind t 
pp. 469-92; Reid, Active Powers, p. 22, Ac.; Hamilton, Metaph., vol. i, pp. 96-109; Sigwart, 
Logic, pp. 334 et seq.\ Clifford, Essays, vol. i, pp 131, 155; Karl Pearson, Gram, qf Sci. 
pp. 63-9; De Morgan, Logic, pp. 211-26; MacColl, Symbolic Logic, pp. 100-10L 


procedure is often exceedingly difficult when we are given an effect 
and have to discover the cause. On the other hand, if we are given 
a cause, it is usually a comparatively simple matter to produce an 
effect. We see a dead bird lying on the roadside; to discover the 
cause of its death might be impossible; but if we knew the cause, if, 
for instance, we knew that death resulted from the shot of a sports- 
man's gun, we could quite easily bring about a similar effect by 
bringing the known cause into action. Or, we might decide to use 
heat as a cause, in which case we could devise experiments to show 
its various effects; but if we discover heat as an effect, say, in a fer- 
menting mass, we cannot, by any simple and certain means, deter- 
mine the cause. We have, first, to conjecture a cause; we then devise 
experiments to find out the effect of that conjectured cause; then, if 
these tally with the effect in question, we have probably determined 
its cause. 1 So generally: given an antecedent, the consequent is 
easily determined; but, given the consequent, the antecedent is usu- 
ally determined only with difficulty. It is this latter operation which 
is perhaps the greatest problem of induction. 

The problem is rendered more difficult by the fact that, in prac- 
tice, circumstances are nearly always of a complex character, and 
it is more than probable that the apparent simplicity of even a 
very easy experiment may be quite deceptive. Let us, for instance, 
consider Jevons's experiment of rubbing two sticks together, and 
make an exhaustive statement of the conditions. There are the 
form, hardness, organic structure, and the numerous chemical 
qualities of the wood; the pressure and velocity of the rubbing; 
the temperature, pressure, and chemical qualities of the surround- 
ing air; the proximity of the earth with its attractive and electric 
powers; the temperature and other properties of the persons pro- 
ducing the motion; the radiation from the sun; and so forth. 
On a priori grounds, it is unsafe to assume that any one of these 
circumstances is without effect, and it is only by experience that we 
can single out those precise conditions from which the observed heat 
of friction proceeds. 

Obviously we must, if we can, remove one at a time those 
conditions which may be suspected of having an influence on the 
result. To decide, for instance, in the above experiment, whether 
the presence of air is a contributory factor to the result, we repeat 
the experiment exactly as before except that it is done in vacuo. 
If heat still appears, we infer that air is not, in the presence of the 

i Cf. Bain, Inductive Logic, p. 44. 


other circumstances, a requisite condition. The conduction of heat 
from neighbouring bodies may be a condition ; to determine this we 
make all the surrounding bodies ice-cold, which is what Davy aimed 
at in rubbing two pieces of ice together. And so on. 1 

Again, suppose we wish to determine why meat putrefies when 
exposed to the air. We know that the atmosphere contains oxygen, 
nitrogen, carbon dioxide, water vapour, ammonia, numerous other 
gases, and solid particles, partly dust and partly living germs; and 
we know that it possesses at any given moment a certain tem- 
perature, a certain pressure, a certain electrical condition, and no 
doubt other peculiarities. Evidently the possible variety of ante- 
cedents is very great, and this must always be the case when the 
air is presented to us as a cause or agency. As before, we try to 
adopt the method of elimination, though the disentangling process 
may prove to be both tedious and difficult. And the same thing 
is true generally.' 2 

2. " Varying the Circumstances" 

In order to discriminate the necessary from the unnecessary 
elements of cause and effect, our only course is to vary the circum- 
stances. We suspect a plurality of antecedents, arid a plurality of 
consequents, or both, and the problem is to single out the connected 
couples of antecedent and consequent. This requires us to look for 
other instances where the groupings are different, and to note what 
happens when particular antecedents and consequents are wanting. 3 
It will be readily seen that _^ 

(1) Whatever antecedent can be left out without prejudice to the 
effect, can be no part of the cause; and \ 

(2) When an antecedent cannot be left out without the consequent 
disappearing, such antecedent must be the cause or part of the 
cause. 4 

Let A represent a cause, and a an effect. In nature we seldom 
have A followed by a alone. What we find is A in combination 
with other things, as ABL\ and a also in combination, as abc. But 
these conjunctions are not rigid and invariable, or our task would 
be easy, the fact being that, though a cause may always be in com- 
bination with other agents, it is not always in the same combination. 
At one time the union is ABC, at another time ABD, and again 

* Cf. Jevons, Principles of Science, pp. 416-7. * Cf. Bain, pp. 42-5. 

Cf. Bain, p. 43. ib. pp, 47-8. 
(C415) 15 


ACEy there being corresponding conjunctions in the effects aJc, 
abd, ace. 

If we suppose, then, the instances ABC giving ale, ABD giving 
abdy ACE giving ace, we reason thus: so far as the first instance is 
concerned, ABC giving abc, the effect a may be produced by A or 
by B or by C. In the second instance, ABD giving abd, the cause 
C is absent, the effect a still remaining; hence C is not the cause 
of a. In the third instance, ACE giving aw, B is absent, a remain- 
ing; hence B is not the cause of a. The only antecedent persisting 
through all the instances is A\ when a is present as a consequent, 
A is always present as an antecedent. If, then, we are sure that 
every other antecedent circumstance has been removed in turn, the 
consequent a still surviving, we have conclusive evidence that A is 
a cause, condition, or invariable accompaniment of a. 1 

It is scarcely possible to pay too much attention to this line of 
argument, as it is the kind of reasoning that occurs in all scientific 
investigations. We shall have to consider it further in connection 
with Mill's Canons. 2 

Of course we must not assume the conditions to be indepen- 
dent: 8 they seldom are. And this is one of the investigator's 
greatest difficulties. It is often impossible, too, to alter one con- 
dition without altering others at the same time, and thus we may 
not get the pure effect of the condition in question. Perhaps, 
however, the most treacherous source of error is the existence of 
unknown conditions which, of course, we cannot remove except 
by accident. Even the greatest investigators have failed because 
of the existence of unsuspected conditions. 4 

3. Observation 

The first work of the investigator is, however, the recording of 
all necessary facts, and it will be convenient at this stage to consider 
a little more clearly the nature of observation and experiment. 

i Cf. Bain, p. 60. 2 See the next chapter. 

8 Suppose we have five or six or more antecedents. We ought to try the effect of the 
absence of each condition, both in the presence and absence of every other condition, and 
every selection of those conditions (excluding, of course, the case where the whole of the con- 
ditions might be imagined to be absent together). Perfect and exhausti>e experimentation 
would, in short, consist in examining natural phenomena in all their possible combinations. 
But Buch exhaustive investigation is practically impossible because the number of experi- 
ments would be so great. Six antecedents would require 2*-l or 63 experiments. The 
experimenter therefore has to fall back upon his own insight and experience in selecting 
those experiments which are most likely to yield him significant facts. (See Jevons, pp. 417-8.) 


Let us suppose we are early arrivals at a theatre. Our attention 
at first is of a general character; our eyes wander round the audi- 
torium, and we feel no special interest either in the building or in 
the people present. The curtain rises: our attention is at once 
confined to the stage. An actor enters: our attention is withdrawn 
from the stage itself and concentrated upon him, his dress, and his 
bearing. He takes a letter from his pocket, and our attention is 
still further narrowed down to that particular act. From first to 
last there has been observation, but the observation has gradually 
become more intensive; the act upon which the attention is last 
concentrated has become isolated. For close observation, we select 
and isolate. If anything distracts the attention and renders the 
isolation less complete, the observation is rendered imperfect. 

But with even the closest attention, our observations may be 
entirely incorrect. Any one of our organs of sense is easily de- 
ceived, a fact which enables the magician to make his living. Then 
it is seldom that we see the whole of any event that occurs: a cab 
and a bicycle collide, and half a dozen " witnesses 5 ', all perfectly 
honest, may probably will give accounts which differ materially 
and may be mutually destructive. It is always difficult to keep 
fact and inference distinctly apart. In the middle of the night we 
"hear a dog bark in the street". But really all that we hear is a 
noise; that the noise comes from a dog, and that the dog is in the 
street, are inferences, and the inferences may be wrong. For in- 
stance, a boy may be imitating a dog; and everybody knows how 
easily the ear is deceived in regard to the direction of sound. It is 
almost impossible to separate what we perceive from what we infer; 
and we certainly cannot obtain a sure basis of facts by rejecting all 
inferences and judgments of our own, for in all facts such inferences 
and judgments form an unavoidable element. Even when we seem 
to see a solid body occupying, as it does, space in all dimensions, 
we really see only a perspective representation of it, as it appears 
depicted on a surface. Our knowledge of its solid form is obtained 
by inference. A clever painter may deceive us even here. 

But wo can do one thing at least, and that is to make all facts 
depend upon the intellect alone, and not to allow ourselves to be 
in the least swayed by any feelings of admiration, fear, and the 
like. 1 A scientific observer always records all evidence against as 
well as for, and he immediately abandons a hypothesis or view as 
soon as any new facts demand it. 

i Cf. Whewell, Nov. Org. Ren., pp. 50-6. 


It is the essence of good observation that the eye shall not only 
see a thing itself, but of what parts that thing is composed. And 
if an observer is to become a successful investigator in any depart- 
ment of Science, he must have an extensive acquaintance with what 
has already been done in that particular department. Only then 
will he be prepared to seize on any one of those minute indications 
which often connect phenomena apparently quite remote from each 
other. His eyes will thus be struck with any occurrence which, 
according to received theories, ought not to happen; for these are 
the facts which serve as dues to new discoveries. The deviation of the 
magnetic needle, by the influence of an electric current traversing 
a wire, must have happened hundreds of times to a perceptible 
amount, under the eyes of persons engaged in electric experiments, 
with apparatus of all kinds standing around them, but it required 
the eye of Oersted to seize the indication, refei it to its origin, and 
thereby connect two great branches of Science. 1 

4. Experiment 

By observation alone it is often impossible to find out precisely 
what conditions are operative, and thus, when possible, we call in 
the aid of experiment. The object of an experiment is to get one 
or more of the conditions under our control, to set them in action 
or stop them, to raise or to lower their intensity, and to eliminate, 
if and when possible, the unessential conditions of the phenomenon 
under investigation. 

The great rule in experiment is to vary only erne circumstance at 
a time^^nd to maintain all other circumstances rigidly unchanged. 
Evidently there are two reasons for this rule: in the first place, if 
we vary two conditions at a time, and find some effect, we cannot 
tell whether the effect is due to one or the other condition, or to 
both jointly; in the second place, if no effect ensues, we cannot 
safely conclude that either of them is indifferent; for the one ma} 
have neutralized the effect of the other. 2 If we want to prove that 
oxygen is necessary to life, it is useless to put a mouse into a vessel 
from which the oxygen has been removed by a burning candle. 
We should then have not only an absence of oxygen, but the pre- 
sence of carbon dioxide, and the carbon dioxide itself might cause 
the animal's death. For a similar reason, Lavoisier avoided the use 

1 Cf Mill, Logic, Book III, ch. vii, 2; and Herschel, Phil, p. 132. 

2 Cf . Jevons, Principles of Science, p. 423. 


of atmospheric air in experiments on combustion, because air was 
not a simple substance, and the presence of nitrogen might impede 
or even alter the effect of oxygen. 1 

An observation does not necessarily become an experiment when 
we call in the aid of an instrument. When, for instance, we use a 
telescope for viewing a distant object, or a microscope for observing 
a small object, we are clearly not performing an experiment, for we 
have no sort of control o\er any of the conditions which determine 
the phenomenon under observation. As Bosanquet says, 2 experi- 
ment is observation under artificial conditions, that is, conditions 
produced or arranged by human action. But observation with the 
telescope or microscope is observation under natural and not arti- 
ficial conditions. Yet observation tends gradually to take on the 
character of experiment, and the transition between the two is 
quite gradual. We may consider experiment to begin when we 
pass on to actual interference with the conditions that determine 
the phenomenon under observation, though even before this line 
is reached observation passes into something which may properly 
be called "natural experiment". "When the earliest astronomers 
simply noticed the ordinary motions of the sun, moon, and planets, 
they were pure observers. But astronomers now select precise times 
and places for important observations. They make the earth's orbit 
the basis of a well-arranged natural experiment, as it were, and take 
well-considered advantage of motions which they cannot control. 
Meteorology might seem to be a science of pure observation, because 
we cannot possibly govern the changes of weather which we record. 
Nevertheless we may ascend mountains, or rise in balloons or aero- 
planes, and may thus so vary the points of observation as to render 
our procedure experimental." 3 

Again, a microscope is, par excellence, an observing instrument, 
but the moment we modify the object under observation (for in- 
stance, by applying chemical reagents on the stage of the micro- 
scope), we are experimenting. 4 If a student is told to dissect a 
rabbit, expose the recurrent laryngeal nerve, and show that it 
loops round the subclavian artery, he does not perform an experi- 
ment; he is merely clearing away obstructions for the purpose of 
adequate observation. But if he is told to cut the sympathetic 
nerve in order that the muscles of the bloodvessels of the ear may 
become relaxed, and the vessels themselves dilated and filled with 

i Jevons, Prin. of Sci., p. 423. 2 Logic, vol. ii, p. 143. 

Jevons, Prin. of Sci., pp. 400-1 4 Cf. Bosanquet, Logic, vol. ii, pp. 144-5. 


blood (for the purpose of producing artificial "blushing"), he is 
performing an experiment, for the act of cutting the nerve has 
brought under his control certain conditions determining the phe- 
nomenon under investigation. And if, further, he irritates the cut 
end of the sympathetic trhich remains connected with the vessels, 
in order to cause contraction of the latter, he is again performing 
an experiment, for again he is controlling some of the determining 

5. Experiment not always Possible 

It need hardly be pointed out that there are many operations in 
nature which we cannot imitate by experiment. Our object is to 
study the conditions under which a certain eflect i produced, but 
one of these conditions may involve a great length of time. All 
metamorphic rocks, for example, have doubtless endured high tem- 
peratures and enormous pressure for inconceivable periods of time, 
so that at least one part of Geology is quite outside the scope of 
experiment. A similar remark applies to Darwin's theory of the 
origin of species, 1 and in fact to hundreds of other questions in the 
domain of Geology, Botany, arid Natural History generally. Why, 
for instance, is the average height of a horse greater than that of a 
dog? How can we answer such a question? We may put forward 
a conjecture, but we have no possible means of proving its truth. 
These branches of knowledge, in contrast to such branches as 
Chemistry and Physics, are essentially observational ; experiment 
can play only a minor part. Hence their state of relative uncer- 
tainty and undevelopment. 

Observers should be on their guard against coming to the con- 
clusion that non-observation of a phenomenon necessarily implies 
its non-occurrence. There are sounds which we cannot hear, rays 
of heat we cannot feel, multitudes of worlds we cannot see, and 
myriads of minute organisms of which not even the most powerful 
microscopes can give us a view. Inferences have often been drawn 
from the non-occurrence of particular facts or objects, but a more 
extended and careful examination has often proved their falsity. 
It must not, however, be supposed that negative arguments are 
of no force or value, though negative conclusions are by their very 
nature treacherous. In Natural History, for instance, the utmost 
patience will not enable an observer to watch the behaviour of a 
particular living thing in all circumstances continuously for a great 

i See Jevons, pp. 437-8. 


length of time. There is always a chance that the initial act or 
change may take place when the observing eyes are withdrawn. 
Darwin himself adopted one conclusion on negative evidence, 
namely, that certain orchids secrete no nectar, .But his caution 
and unwearying patience in verifying the conclusion give an im- 
pressive lesson to the observer. For twenty-three consecutive days 
he examined flowers in all states of the weather, at all hours, in 
various localities. Flowers of different ages were subjected to 
irritating vapours, to moisture, and to every condition likely to 
bring on the secretion, and only after invariable failure of this 
exhaustive enquiry was the barrenness of the nectaries assumed 
to be proved. 1 

We may conclude this chapter by reference to a few well-known 
experimental researches, from which we may learn useful lessons. 

6. Experimental Researches. (i) By Newton 

(i) Newton's work in connection with the spectrum teaches us 
a particularly valuable lesson, the fundamental necessity, in ex- 
perimenting, of varying the circumstances. Newton says, 2 "The 
different magnitude of the hole in the window shut, and different 
thickness of the prism where the rays passed through it, and 
different inclinations of the prism to the horizon, made no sensible 
changes in the length of the image. Neither did the different 
matter of the prisms make any; for in a vessel made of polished 
plates of glass cemented together in the shape of a prism, and filled 
with water, there is the like success of the experiment according 
to the quantity of the refraction." Yet even Newton overlooked 
one important point. Throughout his researches on the spectrum, 
he was quite unsuspicious of the fact that if he reduced the hole 
in the shutter to a narrow slit, all the mysteries of the bright and 
dark lines were within his grasp, provided, of course, that his prisms 
were sufficiently good to define the rays. He forgot to vary the cir- 
cumstances of one condition, though he took the greatest pains to vary 
them in the case of all the other conditions. 3 

(ii) In many experiments we wish to study only one condition, 
the other conditions being interfering forces which we avoid if 
possible. One of the determining conditions of the motion of a 

1 Darwin, Fertilization of Orchids, p. 48. Cf. Jevons, Prin. of Sci. t p. 413. 

2 Opticks, p. '25. 

Cf. Jevons, Prin. of Sci., pp. 418, 420, 424 ; Newton, Opticks, p. 26. See also eh. xxxvll 


pendulum is the resistance of the air or other medium in which it 
swings. But when Newton desired to prove the "equal gravitation 
of all substances", he had to avoid this interfering resistance, foi 
his object was to observe the result of the action of the one force 
due to gravitation only. He therefore made his pendulums, of 
which the oscillations were to be compared, of equal boxes of wood, 
hanging by equal threads, and filled with different substances, so 
that the total weights should be equal, and the centres of oscillation 
at the same distance from the points of suspension. Hence the 
resistance of the air became approximately a matter of indifference; 
for the outward size and shape of the pendulums being the same, 
the absolute force of resistance would be the same, so long as the 
pendulums vibrated with equal velocity ; and the weights being 
equal, the resistances would diminish the velocity equally. Hence 
if any inequality were observed in the vibrations of the two pen- 
dulums, it must arise from the only circMmstance which was different, 
namely, the chemical composition of the matter within the boxes. 
But no inequality was observed, and the conclusion therefore was 
that the chemical composition of substances could have no appreci- 
able influence upon the force of gravitation. 1 

6. (2) By Faraday 

An experiment of Faraday's shows how the alteration of a single 
circumstance sometimes conclusively explains a phenomenon. It 
was known that lycopodium powder scattered on a vibrating plate 
collected together at the points of greatest motion, whereas sand 
and all heavy particles collected at the nodes where the motion was 
least. It occurred to Faraday to try the experiment under the 
exhausted receiver of an air-pump, and it was then found that the 
light powder behaved exactly like the heavy powder. The obvious 
conclusion was that the presence of air was the differentiating and 
determining factor, doubtless because it was thrown into eddies by 
the motion of the plate, and carried the lycopodium to the points 
of greatest agitation. Sand was too heavy to be carried by the air.- 

6. (3) By Brewster 

One of Brewster's experiments may be quoted as an example of 
the possibility of none of the most obvious of the antecedents taking any 

1 Priticipia, III, vi ; and cf. Jevons, pp. 443-4. 

2 See Jevons, Prin. of Sci. , p. 419. (See also ch. xxxviii.) 


part in the production of a phenomenon. If we were asked to account 
for the peculiar colours of mother-of-pearl, we should most probably 
suggest that they must be due to some peculiarity in the chemical 
composition of the substance. Brewster himself was ignorant of 
the real explanation, but he had occasion to fix a piece of mother- 
of-pearl to a goniometer with a cement of resin and beeswax, and 
upon removing it was surprised to see the whole surface of the wax 
shining with the prismatic colours of the mother-of-pearl. He first 
thought that a film of the substance had been left on the wax; but 
this was soon found to be a mistake, and it became manifest that 
the mother-of-pearl really impressed upon the cement its own power 
of producing coloured spectra. Further investigation showed that 
the colours were produced by a particular configuration of the 
surface. The surface, examined with a microscope, presented a 
grooved structure, like a section of the annual growths of wood, 
the grooves being obviously the sections of all the concentric strata 
of the shell. If we examine the actual surface of any one stratum 
(and the ordinary surface of the pearl itself is such a stratum) none 
of the colours are seen. 1 Of course, the grooves having been de- 
tected, the proper explanation of the colours was obvious. 2 The 
point to notice is that the easily observed antecedents were all mis- 
leading; the real antecedent might, but for accident, have remained 
concealed until this day. 3 

6. (4) By Franklin 

Experiments sometimes lead to wrong conclusions because of the 
impossibility of carrying out the rule of varying one circumstance at a time. 
Franklin's experiment concerning the comparative absorbing powers 
of different colours is well known. He took a number of little 
square pieces of broadcloth from a tailor's pattern-card, of various 
colours. He laid them all out upon the snow on a bright sunny 
morning. " In a few hours, the black being the most warmed by 
the sun, was sunk so low as to be below the stroke of the sun's 
rays; the dark blue was almost as low; the lighter blue not quite 
so much as the dark; the other colours less as they were lighter. 
The white remained on the surface of the snow, not having entered 
it ut all." To the uninitiated, the inferences to be drawn seem to 

Brewster, Optics, pp. 118-20 Cf. Jevons, p. 419. 

* See any standard textbook on Light. 

Cf. Camb. Nat. History, "Mollusea", pp. 253-4; Carpenter, B. A.. Address, p. xiii, ff. 


admit of little doubt, but Leslie, in his researches upon the nature 
of heat, was forced to the conclusion that the colour of a surface 
has very little effect upon the radiating power, the mechanical 
nature of the surface appearing to exert a greater influence. He 
considered the question incapable of solution, since no substance 
can be made to assume different colours without at the same time 
changing its internal structure, that therefore it was impossible 
to vary one circumstance at a time. The whole subject is, of 
course, complicated and difficult. 1 

6. (5) By Davy 

Sometimes, unsuspected conditions may lead to erroneous results. 
The early alchemists were misled by the unsuspected presence of 
traces of gold and silver in the substances they proposed to trans- 
mute. The unsuspected presence of common salt in the air at one 
time gave great trouble, and, in the earlier work on electrolysis, 
led to the erroneous conclusion that electricity had the power of 
generating acids and alkalis. Davy undertook a systematic investi- 
gation of the circumstances, by varying the conditions. For his 
glass vessel he substituted one of agate or gold, and then found that 
far less alkali was produced; excluding impurities by the use of 
distilled water, he found that the quantities of acid and alkali were 
still further diminished \ and having thus obtained a clue to the 
cause, he completed the exclusion of impurities by avoiding contact 
with his fingers, and by placing the apparatus under an exhausted 
receiver, no acid or alkali being then formed. He thus detected 
a previously unsuspected antecedent? 

i Jevons, pp. 424-5 ; Leslie, Enquiry into the Nature of lleat, p. 95, Of also any standard 
work on Heat. 

* Works of Sir Humphry Davy, vol. v, pp 1-12. Cf. Jevons, p. 429. The reader may 
usefully compare these dillerent investigations with modern views of the phenomena men- 
tioned, and see if any additional facts have KUDU to light rendering new explanations 


Mill's "Canons" 

i. The Basis of the Canons 

Let us suppose that, by observation and comparison of a number 
of cases of an effect, we have found an antecedent which appears to 
be, and perhaps is, invariably connected with it. Whether this 
antecedent is the cause we do riot yet know, and cannot know until 
we have reversed the process and by experiment produced the effect 
by tneans of the antecedent. Observation without experiment is 
very unlikely to prove causation. In the case of most of the 
phenomena which we find conjoined, we cannot know with certainty 
which is cause and which effect, or whether either of them is so, 
or whether they are not both effects of causes yet to be discovered. 
Ye thus resort to experiment, in the hope of being able to isolate 
,nd examine separately the different conditions. 1 

But, as we have seen, isolation is often impossible, and experi- 
(lental enquiry cannot therefore be reduced to any form of mechani- 
al routine. Although Mill was well aware of the difficulties of such 
inquiry, he thought rules of general procedure ought to be possible, 
,nd set himself the task of formulating them. 

As he says, the simplest and most obvious modes of singling out, 
from among the circumstances which precede or follow a phenome- 
non, those with which it is really connected by an invariable law, 
are two in number: (1) by comparing together different instances in 
which the phenomenon occurs ; (2) by comparing instances in which 
the phenomenon does occur with instances in other respects similar 
in which it does not. Thus we have a Method of Agreement, and 
a Method of Difference; and these form the basis of all Mill's rules. 

2. The Method of Agreement 

If two or more instances of the phenomenon under investigation have 
only one circumstance in common, ttiat circumstance may be regarded as 
the probable cause (or effect) of the phenomenon.- (Mill's first Canon.) 

The following are illustrations: 

1. After taking a particular kind of food, whatever else I may 

1 Cf. Mill, Book III, ch. vii, g 4. 

2 The wording of the various Canons 1ms been slightly simplified. Fowler's modified forma 
will serve for purposes of comparison 


eat or drink, and however various my general state of health, the 
climate in which I am living, and my other surroundings, I am 
invariably ill. I am therefore justified in regarding the food as the 
probable cause of my illness, and avoid it accordingly. 

2. I find that a certain plant always grows luxuriantly on a 
certain kind of soil; if my experience of the other conditions be 
sufficiently various, I am justified in concluding that the soil probably 
possesses certain constituents which are peculiarly -favourable to the 
production of the plant. 1 

3. We compare instances in which bodies are known to assume 
a crystalline structure, but which have no other point of agreement. 
In the great majority of instances, though not in all, we find that 
these bodies have assumed their crystalline structure during the 
process of solidification from a fluid state, and, so far as can be 
observed, these cases have no other circumstance in common. We 
may therefore reasonably infer that the passage from a fluid to a 
solid state is a probable cause, though not the only cause, of 
crystallization. 2 

In all such cases, we have only probability, not certainty. All 
our inferences may turn out to be wrong, for we can never be sure, 
by the Method of Agreement alone, that we have eliminated all the 
casual circumstances. The difficulty is especially felt when we are 
attempting to find the cause of a given effect. The same event may 
be due to a great number of distinct causes (as is exemplified in the 
familiar cases of motion, disease, death, &c.). We are not justified, 
therefore, in neglecting to take account of what is sometimes called 
Plurality of Causes, though by the multiplication and variation of 
instances, the possible error due to the Plurality of Causes may be 
rendered less and less probable. In practice, of course, we generally 
have a great number of antecedents and a great number of conse- 
quents (or rather a great number of antecedents contributing to 
a complex effect), and it often becomes virtually impossible to find 
in a collection of instances of a phenomenon one circumstance 8 in 
which alone they all agree. The Method of Agreement, then, has 
a "characteristic imperfection". 4 

It should be noticed that the Method of Agreement is mainly, 
though not exclusively, a method of Observation rather than of 

i Cf. Fowler, Indue. Log., pp. 138-9. a ib. p. 146. 

* Really one other circumstance, not the circumstance that brought the instances together 
for comparison. 

4 It will be understood that when we say " one circumstance in common ", we ordinarilj 
exclude such common circumstances as gravity, exposure to the atmosphere, Ac. 


Experiment, and is usually applied for the purpose of inquiring 
into the causes of given effects, rather than into the effects of given 
causes. 1 But it is essentially a method for suggesting a due] it is 
rarely final. 

3. The Method of Difference 

If an instance in which the phenomenon under investigation occurs, 
and an instance in which it does not occur, have every circumstance in 
common save one, that one occurring only in tlie former ; the circumstance 
in which alone the two instances differ is the effect, or the cause, or an 
indispensable part of the cause, of the phenomenon. (Mill's second 

Both the Method of Agreement and the Method of Difference 
are methods of elimination. This term, borrowed from the theory 
of equations, is employed to denote the process of excluding, one 
after the other, the various circumstances which are found tc 
accompany a phenomenon in a given instance. 

The Method of Agreement stands on the ground that whatever 
can be eliminated is not connected with the phenomenon by any 
law; the Method of Difference, that whatever caniwt be eliminated 
is connected with the phenomenon by a law. 

Difference plays a great part in our everyday inferences. The 
usual form is the sudden introduction of some limited and definite 
agency or change, followed by an equally definite consequence. 

(1) We drink some water, and there is a cessation of thirst; we do 
not hesitate to pronounce the former fact the cause of the latter; 

(2) we make a noise, and a sleeping child awakes; (3) we rub a 
match, and it bursts into flame. In every case the new agency is 
followed by the new effect. 

A large part of our knowledge of nature is gained by making 
experimental changes and watching the consequences. An immediate 
response is usually satisfactory evidence. In fact, wherever Differ- 
ence can be resorted to, a knowledge of causes is gained at once. 
We introduce a new antecedent x, to which the new consequent y 
must be due. But if the omission of one circumstance be attended 
by the omission of another, we may argue with equal confidence. 
A man is deprived of food and ho dies, and we do not hesitate to 
ascribe the disappearance of what we call life to the withdrawal of 
the means by which it is maintained. 2 

i Cf. Fowler, Indue. Log., pp. 180-48; Bain, pp. 49-67; Mill, Book III, Till, 1, . 
Cf. Bain, pp. 68-0. 


The Method of Agreement is often of great use for suggesting 
applications of the Method of Difference. If the former, for instance, 
suggests that A is an invariable antecedent, we try to produce a by 
experiment, and so find out whether A is an unconditional invariable 
antecedent, i.e. the cause, of a. For example, on the first use of 
some new coal, we notice in the case of the five or six fires in the 
house, rather frequent slight "explosions", fragments of burning 
material being projected into the room. An examination shows 
that in each fire there are one or more stones. This one common 
circumstance suggests, by the Method of Agreement, the probable 
cause of the " explosions ". We now try the experiment of actually 
putting a stone in the fire. An " explosion " follows; and so we get 
a decisive test by the application of the Method of Difference; for 
A is now seen to be the real cause of a. 

The Method of Difference is very extensively used in experi- 
mental Science, especially Chemistry. We mix, for instance, a solu- 
tion of chloride of mercury with a solution of potassium iodide; 
the result is a red precipitate in a colourless liquid. We at once 
infer that the change produced (the effect, the consequent) is due to 
the mixing (the cause, the antecedent). Of the truth of this infer- 
ence we are absolutely certain from the experiment alone. But any 
further inference (for example, as to the composition of the red pre- 
cipitate) is not legitimate from the experiment, though it may be from 
our stock of previous knowledge. 

Any textbook of Science will afford an abundance of further 
examples. We may mention one other. --Arago, having suspended 
a magnetic needle by a silk thread and set it in vibration, observed 
that it came much sooner to a state of rest when suspended over 
a plate of copper than when no such plate was beneath it. In 
the two experiments there was but one Difference, the presence or 
absence of the plate of copper. Clearly, therefore, the retarding 
influence was exerted by the copper itself. 

In the employment of the Method of Difference, the greatest 
care should be taken to introduce only one new antecedent, or at 
least only one new antecedent which can influence the result. As 
the whole force of the argument based on this method depends on 
the assumption that any change that takes place in the phenomenon 
is due to the antecedent then and there introduced, clearly we can 
place no reliance on our conclusion unless we feel perfectly assured 
that no other antecedent has intervened. Had the ancients recog- 
nized that instead of one cause acting on falling bodies, as appeared 


to them to be the case, there were really two, the action of gravity 
tending downwards and the resistance of the atmosphere pressing 
upwards, they would probably never have fallen into the gross error 
of supposing that bodies fall in times inversely proportional to their 
weights. 1 

4. The " Joint " Method 2 

If two or more instances in which tlw phenomenon occurs have only one 
circumstance in common, while two or more instances (in the same depart- 
ment of investigation), in which it does not occur, have nothing in common 
save the absence of that circumstance, the circumstance in which alone the 
two sets of instances differ is the effect, or the cause, or an indispensable 
part of the cause, of the phenomenon. (Mill's third Canon.) 

This method is simply an extension of the Method of Agreement, 
by extending it to agreement in absence. When such cases are con- 
joined with those where the agreement is in presence, there is an 
approach to the conclusiveness of the Method of Difference. We 
first of all compare cases in which the phenomenon occurs, and, so 
far as we can ascertain, find them to agree in the possession of only 
a single circumstance. 3 But though we may not be justified in 
regarding this inference as certain, we may increase our assurance 
by proceeding to compare cases in which the phenomenon does not 
occur. By our positive instances we are, as it were, put on the 
track of the one circumstance in which the instances agree, and by 
our negative instances we strengthen the probability of the accuracy 
of our conclusion. 

1. When I take a particular kind of food, I suffer from a par- 
ticular form of illness; when I leave it off I cease to suffer, and my 
suspicion that the food is the cause of my illness is confirmed. 

2. I notice that a particular plant is invariably plentiful on a 
particular soil; 1 fail to find it growing on any other soil; my belief 
that there is in this particular soil one or more chemical constituents 
favourable to the growth of the plant is thus strengthened. 

3. Suppose I am asked why it is that a north-east wind is 
specially injurious to many persons. T already know that winds 
are characterized by various qualities, such as velocity, temperature, 
humidity, electricity, ozone, itc., but on investigation I find that no 
one mode of any one of these qualities uniformly accompanies the 

i Cf. Fowler, pp 148-69; Rain, pp. 67-61; Mill, Rook III, eh. viii, 3. 

* Sometimes called "Joint Method of Agreement and Difference", or "Method of Double 
Agreement ". 

* Rather, a single other circumstance. Cf. 2, ante. 


north-east wind. But further examination shows that the wind, 
which blows from the Pole towards the Equator, travels for several 
thousand miles close upon the surface of the ground. This single cir- 
cumstance is common to all north-east winds, and, on this point 
alone, the agreement seems to be constant. I now apply the second 
part of the Joint Method. I examine other winds, for instance the 
south-west wind, and find it does not blow for a long distance close 
to the surface of the ground, and that it is not noxious. My first 
tentative inference, that the north-east wind, during its contact with 
the ground, picks up dust, germs, &c., and so becomes noxious, is 
thus confirmed by negative instances. 

Of course the evidence necessary to give absolute proof is not 
yet complete, but the Joint Method has taken us a long way on the 
road towards absolute proof. 1 

5. The Method of Residues 

Subtract from any phenomenon such part as is known to be the effect of 
certain antecedents, and the residue of the phenomenon is the effect of the 
remaining antecedents. (Mill's fourth Canon.) 

If we know that a total result is due to a certain number of 
antecedents, and that part of the result is due to a portion of those 
antecedents, the residue of the result must necessarily be due to 
the remaining antecedents. This method is extensively used in the 
present advanced state of Science. 

Herschel makes a suggestive remark when he says, " It was a 
happy thought of Glauber to examine what everybody else threw 
away ". 2 

1. The discovery of the precession of the equinoxes resulted, as 
a residual phenomenon, from the imperfect explanation of the return 
of the seasons by the return of the sun to the same apparent place 
amongst the fixed stars. 3 

2. The Method of Residues was employed in the discovery of 
the planet Neptune. From the year 1804 it had been noticed that 
the orbit of the planet Uranus was subject to an amount of per- 
turbation which could not be accounted for from the influence of the 
known planets. There was an unknown residual disturbance, beyond 
the disturbances produced by Jupiter and Saturn. 4 Astronomers 

i Ct Bain, pp. 61-2; Mill, III, viii, 4; Fowler, pp. 160-73. 

' Herachel, A' at. Phil., p. 158. * Herschel, Outlines of Attronomy, | 866. 

* The only two of the old planets exercising any sensible action on Uranui. 


therefore suspected tiie existence of an unknown planet, and they 
were faced with the difficult inverse problem, u given the disturbances, 
to find the orbit and the place in that wbit of the disturbing planet ". The 
problem was successfully solved by two different astronomers, 1 
working quite independently, and Neptune was located on Sep- 
tember 23, 1846. 2 

3. The inquiry into the cause of sound had led to conclusions 
respecting its mode of propagation, and from these its velocity in the 
air could be precisely calculated from purely theoretical considera- 
tions. The calculations were performed, but when compared with 
known experimental fact, though the agreement was quite sufficient 
to show the general correctness of the assigned cause and mode of 
propagation, yet the whole velocity could not be shown to arise from 
this theory. There was still a ic^idual velocity to be accounted for. 
At length Laplace struck on the happy idea that this might arise 
from the heat developed in the act of that condensation which 
necessarily takes place at every vibration by which sound is con- 
veyed. The matter was subjected to exact calculation, with the 
result that the residual phenomenon was completely explained. 3 

S 6. The Method of Concomitant Variations 

ffhatever phenomenon varies in any manner whenever another 
phenomenon varies hi some particular manner, is cither a cause or an 
effect of that phenomenon, or is connected with it through some fact of 
causation. (Mill's fifth Canon.) 

This method is really a peculiar application or series of applica- 
tions of the Method of Difference. It is employed in those cases 
where a phenomenon cannot be made to disappear altogether, but 
where we have the power of augmenting or diminishing its quan- 
tity, or at least where Nature presents it in greater or smaller 

1. We know that, if we confine some mercury in a suitable 
tube, every sensible increase of the temperature of the surrounding 
atmosphere is accompanied by a sensible increase of the volume of 
mercury in the tube, and vice versa. Now each successive experi- 
ment is an application of the Method of Difference, and we arrive at 
last at the conclusion that the volume of the mercury is invariably 
dependent on the temperature of the surrounding medium ; in other 

i Mr. Adams and M. Lc Vervier. - Hcrschcl, op. cit., 707-8. 

CL Mill, III, ix, 6; Tymlall, Sound, ch. i; Fowler, Indue. Logic, p. 181. 

(0415) 16 


words, that augmentation of temperature is the cause of expansion 
It should be noticed that we cannot in such a case employ the 
Method of Difference, because the phenomenon is one which is 
only capable of augmentation or diminution, and cannot bo made 
to vanish. We may more and more diminish the heat of a body, 
but we cannot wholly deprive the body of its heat. 

The Method of Concomitant Variations may be used for two 
purposes, either to establish a causal connection, or to determine 
the law according to which the phenomena vary. Thus, it may 
either establish the fact that any increase of temperature causes 
mercury to expand, or it may determine the exact rate according 
to which this expansion takes place, a determination which is, in 
fact, effected by the ordinary thermometer. But when attempt- 
ing to determine the numerical relations according to which two 
phenomena vary, the utmost caution is required as soon as our 
inference outsteps the limits of our observations. There is always 
the possibility of the intervention of some counteracting cause. For 
instance, water at 39, instead of continuing to contract as it 
becomes colder, ceases at that point to do so, and thenceforward 
begins to expand. Then, again, whenever the range of our obser- 
vations is confined within comparatively narrow limits, there must 
be an element of uncertainty. Different laws of variation may pro- 
duce numerical results which differ but slightly from one another 
within narrow limits; and when, therefore, such variations in the 
quantity of the antecedents as we have the means of observing are 
small in comparison with the total quantities, there is much danger 
lest we should mistake the numerical law, and be led to miscalculate 
the variations which would take place beyond the limits. 

2. The experimental proof of the First Law of Motion affords 
an interesting case of the method. Obviously we cannot entirely 
remove the various obstacles (friction, resistance of the atmosphere, 
&c.) which retard motion; we can only diminish them. For 
instance, we may cause a pendulum to oscillate for a considerable 
period by reducing the friction at the point of suspension. Borda 
contrived to reduce this friction to such an extent in the case of 
a pendulum arranged to oscillate in vacuo, that the oscillation con- 
tinued for more than thirty hours. From such an experiment we 
do not hesitate to draw the inference that the whole of the retarda- 
tion to continued motion is due to the obstacles. 1 

i Cf . Aot>. Ory. lien , III, viii, 2, 9 ; and Fowler, p. 195. Sec also Fowler, pp. 183-200 : 
and Mill, Book HI, ch. viii 7 


7. Plurality of Causes 

It will be seen that, for all practical purposes, Mill's five Rules 
reduce to two, Agreement and Difference, the last three being 
really modifications or variants of the others. 

The Rules take two conditions for granted: first, that an effect 
has only one cause, or set of antecedents; secondly, that different 
effects are kept apart and are distinguishable. But both these 
conditions may be wanting and the methods therefore frustrated. 
We have then to consider what is sometimes called " Plurality of 
Causes" and "Intermixture of Effects". 

In many cases the same effect may be produced by a Plurality 
of Causes; as motion, or heat. We see a body in motion, but it 
may be quite impossible to say which one of many possible agents 
may have set it in motion. We discover a hot body, and it may 
be equally impossible to say how it became heated. 1 

The operation of Plurality is to give uncertainty to the Method 
of Agreement. For example, we observe numerous cases of un- 
healthy human beings whose parents were unhealthy; this fact 
suggests a possible inference from Agreement. But many un- 
healthy persons are the children of perfectly healthy parents. We 
cannot, therefore, draw any safe inference. Ill-health may be due 
to one or more of many causes. 

One remedy for this failure of the Method of Agreement is 
multiplication of instances. This will tend to bring out all the causes, 
and inquiry is narrowed down to determining, in a given case, 
which of the causes are present and whether these are free to 
operate. If, for instance, we are aware of the various antecedents 
of dyspepsia, bad food, too much food, too little food, hard labour, 
want of exercise, intemperance, mental wear and tear, bad air, hot 
climate, &e., we can infer with considerable certainty what brought 
on the disease in a given instance. 

The second remedy is the use of the " Joint Method ". We 
should seek out cases of Agreement in absence, which are of a very 
decisive nature. If, in all cases where a particular effect fails, one 
particular cause is absent, there is, in spite of possible plurality, 
a strong presumption that these two circumstances are cause and 
effect in those instances. 

1 In a great number of inferences in over) day affairs, politics for instance, elimination 
is vitiated by plurality, and we have the fallacy pott hoc ergo proptcr hoc. 


8. Intermixture of Effects 

Mill's methods suppose different effects to remain separate and 
distinguishable, whereas cases frequently arise when the effects of 
different causes unite in a homogeneous total. 

An invalid goes to some health resort and adopts every possible 
means of restoration to health. Many influences combine to the 
result, but the effect is one and indivisible. A good crop of wheat, 
the general prosperity of a country, or the demand for some new 
legislative enactment, is seldom the effect of any one cause exclu- 
sively, yet we commonly regard such effects as homogeneous. 

The intermixture of effects is a serious obstacle to the successful 
use of the experimental methods. ABC acting together yield not 
abc but a; and if AtiD yield still a, nothii g is eliminated, and there 
is no progress. We have zinc, sulphuric acid, and water in a flask; 
hydrogen is generated, and we wish to discover the source of the 
hydrogen. We replace the zinc by magnesium; the result is the 
same as before, and no inference is therefore possible. We replace 
the sulphuric acid by hydrochloric acid; again the result is the same, 
and again we can draw no inference. 1 

In many cases of this kind we have no alternative but to devise 
some other form of experiment and set to work in an entirely 
different way. But use may often be made of the Method of Con- 
comitant Variations. For instance, the assigning of the respective 
parts of the sun and moon, in the action of Tides, may be effected, 
to a certain degree of exactness, by the variation of the amount 
according to the positions of the two attracting bodies. 2 

9. Criticism of Mill's Methods 

Whewell's opinion of Mill's Methods of Inquiry was unfavour- 
able, mainly because "they take for granted the very thing which 
is most difficult to discover, the reduction of the phenomena to 
formulae. When we have any set of complex facts offered to us, 
and when we would discover the law of nature which governs them, 
where are we to look for our ABC arid abc ( \ Nature does not 
present to us the cases in this form, and how are we to reduce them 
to this form? You say when we find the combination ABC with 

1 Of course in practice we should not stop at this point in such a case. Continued sub- 
stitution would soon furnish us with suggestive data, although the final solution of the 
problem would be effected another way. 

a Cf. Bain, pp. 76-84 ; Mill, Book III, ch. x. 


abc 9 and ABD with abd, then we may draw our inference. Granted, 
but when and where are we to find such combinations?" 1 

But Mill himself points out that his Methods are, primarily, 
rules and models to which, if inductive arguments conform, those 
arguments are conclusive, and not otherwise. He not only makes 
no claim that the Methods are infallible; he admits their many 
imperfections. He particularly points out how the plurality of 
causes and intermixture of effects may frustrate the Methods. He 
freely admits the difficulty and the frequent impossibility of dis- 
entangling Nature and reducing it to the form of ABC, abc. 
Whewell's criticisms are based on the assumption that Mill in- 
tended his methods to be the very last word in induction, to be 
final and absolute. Mill plainly shows that he had no such 
intention. 2 

Professor Wei ton is also somewhat unduly critical of the 
Methods. He enumerates the various claims that Mill makes on 
behalf of the Methods, and then states that these claims are by 
no means granted by logicians. But he immediately admits 8 that 
Mill himself clearly pointed out the strictly limited possibilities 
of the Methods. Further, he says, " Mill himself supplies us with 
abundant evidence that the Methods can never prove any general 
law " ; " he also undermines the authority of his Canons and 
practically destroys it." But it seems beside the mark to criticize 
Mill for pointing out what his Canons were never intended to do. 
No one ever saw more clearly than Mill the limitations of the 
Methods he had taken so much trouble to formulate. 

Professor Welton admits, though a little grudgingly, that " the 
Methods are not worthless. It is true they are not inductive in 
the empiricist sense, but they are inductive in the sense that they 
are based upon principles which are operative in inductive inquiry, 
though in every case they need more exact formulation. The 
Methods suggest hypotheses." 4 

There is, in actual practice, little to choose between the two 
schools of logical thought as represented by Mill and Professor 
Welton. Both admit that the inductive method must begin with 
an examination of facts. The latter tells us we are now to form 
a hypothesis, as suggested by such examination. The former tells 
us how to examine our facts, to discover points of agreement and 

l Phil, of Disc., p. 262. 

a The reader should refer to the controversy in Mill's Logic and Whewell's Philosophy of 
Discovery. * Logic, vol. ii, pp. 140-7. 4 ib. pp. 166-7. 


points of difference, and gives us "methods" for discovering clues 
for framing tentative hypotheses. Both now tell us to deduce the 
consequences of our hypotheses. And both point out the impor- 
tance of final comparison with fact, of verification. 

The fact is, the Methods have two entirely different functions 
to perform. In the first place, they afford us a general line of inquiry 
in scientific investigation. In using them for this purpose, we have 
to be particularly on our guard against their imperfections and their 
inherent dangers; and many of these, though pointed out by Mill 
himself, are wisely emphasized by Professor Welton, as well as by 
such well-known logicians as Bradley 1 and Sigwart 2 . In the second 
place, they form admirable tests of logical proof in scientific investiga- 
tion, just as the syllogism is a useful testing instrument when doubt 
has arisen over a particular deductive inference. The Methods " set 
us on the road " to discovery, though they uo not take us quite to 
the goal. 

Professor Welton will not for a moment accept "time sequence" 
in the causal relation : such acceptance would carry him straightway 
into the enemy's camp. But if we will consent to regard ante- 
cedent and consequent not as implying time sequence but simply 
as the respective equivalents of "determining" and "determined", 
he will meet us willingly. Assuredly we can meet him thus far. 3 

But let the philosophers quarrel. For the practical man it will be 
sufficient to bear in mind that all scientific investigation is, at bottom, 
the seeking of points of agreement and points of difference. 

i Bradley, Logic, p. 331. 2 Sigwart, Logic, vol ii, p 341 

* Cf. Welton, Logic, ii, pp 158-9. The reader should, if possible, read the chapter in Mill, 
and then Prof. Welton's criticism in Logic, vol. ii. The criticisms involve objections which 
are largely of a theoretical character, but they are m-vertheless suggestive in many ways. 

Mr. A. Sidgwick makes some useful ciiticnl it-marks on Mill's im'thods In the Method of 
Difference we should he careful to distinguish " between any attempt to apply the Method in 
the concrete, and the Method itself as an abstract ideal. In the abstract, no fault can be 
found with the rule, but it is always in concrete cases that any rule must be applied, and 
nothing is easier than to apply it wrongly What is insufficiently dwelt on in the formal 
account of the method is that the guarantee of correctness is not to be found in the Method 
of Difference itself, but in the wisdom and care with which we apply it." (Use oj Wordy in 
Reasoning, pp 88-95.) 



i. General Notions 

Let us imagine a not over-intelligent young servant sent to a 
room containing a miscellaneous collection of books, and told to 
arrange them on some available shelves. There is little doubt that 
she would arrange them according to their size or to the colour of 
their binding. Her principle of classification would be determined 
by the immediately obvious points of resemblance, and would not 
in any way be the result of that kind of careful examination we 
should expect from a trained librarian. Mere words, "large", 
"small ", " red ", " green ", and the like, would, in the main, control 
her labours. Her groups would be a mere incidental effect conse- 
quent on the use of names intended for a totally different purpose. 
In a word, her classification would not be scientific. 

In scientific classification we endeavour to avoid being led away 
by the fact that general names imply the recognition of classes of 
things corresponding to them. AYc begin by a careful examination 
of the properties of the objects to be classified, in order to find some 
natural connecting link amongst them. We try to detect some 
form of identity, and then bring together those objects amongst 
which the identity has been detected. The naming of the groups 
avowedly conforms itself to the actual distribution into the groups; 
it does riot govern the distribution. 1 

There is no property of objects which may not be taken, if 
desired, as the foundation of a classification. We might, for in- 
stance, classify animals according to the colour of their eyes, or 
houses according to the number of windows they contain. But, 
clearly, such classifications would have no practical value. Our 
aim should be to form objects into groups respecting which the 
most important and the greatest number of general propositions can 
be made. The properties, therefore, according to which objects are 
classified should as far as possible be those which are sure marks of 
them. The test of the scientific character of a classification is the 
number and importance of the properties which can be regarded 
as common to all the objects included in a group. Properties on 
which the general aspect of things depends, are sometimes of com- 

1 See Jevons, Prin. of Sci., pp. 673-4, 


paratively trifling importance and are likely to lead us astray. 
The old division, for instance, into trees, shrubs, and herbs, answers 
to so few differences in the other properties of plants, that a classi- 
fication founded on it would be both artificial and useless. 1 It 
often happens that natural groups must be founded not on the 
more obvious but on the less obvious properties of things, when 
these are of greater importance; and this suggests, what is certainly 
the fact, that an extensive knowledge of the properties of objects is 
almost always necessary for making a good classification of them. 

2. What Constitutes a Good Classification 

Bain gives us the following rule of classification: Place together in 
classes the things that possess in common the greatest number of attributes. 2 
Thus the vertebrate animals have been classed according to the 
leading points of their anatomy and physiology, rather than accord- 
ing to the " element" they live in (earth, water, and air). The bat 
flies in the air but has more real affinities with quadrupeds than 
birds; the whale, seal, and porpoise have warm blood and suckle their 
young like land quadrupeds, although living in the sea as fishes. 

But importance of attributes is to a certain extent governed by 
purpose in view. For practical purposes, whales are classed as fishes 
(we speak of the whale fishery), because their living in the sea 
determines the manner of their being caught. So trees, shrubs, 
flowers, grasses, and weeds form groups of practical importance to 
the gardener, but do not coincide with the classifications of botany. 3 

There is evidently an almost unlimited number of modes of 
classifying a group of objects. From time to time different ways 
have been adopted of classifying plants, none completely satisfactory. 
Some authorities have made the form of the fruit the basis of classi- 
fication; others, the number and arrangement of the parts of the 
corolla; others, the calyx; others, the leaves; and so forth. 4 Again, 
the elements may be classified according to their atomicity; accord- 
ing as they are metallic or non-metallic; useful or useless; abundant 
or scarce; solid, liquid, or g&seous. Obviously, however, elements 
cannot be defined as solid, liquid, or gaseous absolutely, but only 
within certain degrees of temperature. 5 

How much is implied in a good classification maybe seen by con- 
sidering the grouping of the metals that has been made by chemists. 

i Cf Mill, Logic, IV, vii, g 1, 2. 2 Inductive Logic, p. 186. ib. p. 18C 

* Cf. Jevons, Prin. of Set , pp. 677-8. 8 Cf. Carveth Bead, Logic, p, 310. 


Take, for example, the alkaline metals, potassium, sodium, rubidium, 
caesium, and lithium. On comparing the qualities of these metals, 
they are all found to combine very energetically with oxygen, to 
decompose water at all temperatures, and to form strongly basic 
oxides which are highly soluble in water, yielding powerfully caustic 
and alkaline hydrates from which water cannot be expelled by heat; 
their carbonates are also soluble in water, and each metal forms only 
one chloride. Such a class provides us with a powerful instrument 
for possible future inference. If, for example, we discovered a new 
metal possessing one or two of the above properties in a marked 
degree, we should infer that it possessed the other properties; we 
should, however, at once proceed to verify such inference practically. 

3. " Kinds" and "Types" 

We often find that, after "natural" groups have been deter- 
mined, especially in Botany and Zoology, one group seems gradu- 
ally to shade off into the other, and that many members are on the 
border line of both groups. According to Dr. Whevvell, natural 
groups cannot be circumscribed within a Definition, for they are 
determined by characters which do not admit of being precisely 
expressed in words; they are determined rather by Type. Propo- 
sitions concerning them state not what happens in all cases, but 
only usually. The classes are not left quite loose; they are steadily 
fixed though not precisely limited; each is determined not by a 
boundary line without but by a central point within. 1 In Natural 
History we often find anomalous members of groups, which neither 
conform to the verbal definition nor yet differ sufficiently from the 
other members to be excluded from the group. We may imagine 
a group formed upon the basis, say, of ten qualities, but consisting 
of individuals that vacillate, some differing in one quality and some 
in another, while yet agreeing in by far the greater number. We 
may even make the extreme supposition that the vacillation is such 
that no single quality of the ten persists in every individual; hence, 
in strictness, there would bo no common feature, and yet there 
would be a very large amount of resemblance. 2 

The difficulty is constantly felt by all students of Botany and 
Zoology. Mill himself felt it but disliked Whewell's method of 
overcoming it. Mill discussed at some length the possibility of dis 

* Cf. Mill, Logic, Book IV, ch. vii f 3; and Whewell, Hist /nd. Set., vol. 11, pp, 120-2. 
a Cf. Bain, pp. 191-2. 


tinctions of "kinds", that is, classes between which there is an 
impassable barrier; and was of opinion that the element of uncer- 
tainty could sometimes be eliminated. 1 But if we admit continuity 
in Nature, there must always be a doubtful margin between our 
groups, 2 and the notion of absolutely separate and distinct kinds 
must be accepted with great limitations. 

Of course the recognition of a "type" is bound to involve 
illogical consequences. The type itself is an individual, not a class, 
and no other object can be exactly like the type. If some objects 
resemble the type in some points, and others in other points, then 
each definite collection of points of resemblance virtually constitute 
a separate class. The naturalist in his endeavour to mark out living 
forms in definite groups is constantly perplexed by the discovery of 
forms of an intermediate character. The only remedy is the frank 
recognition of the fact that, according to the theory of hereditary 
descent, gradation of characters is probably almost always the rule, 
and precise demarcation between groups the rare exception. 8 

The general recognition of the theory of evolution has exploded 
all notions about natural groups resulting from specific creations. 
Naturalists long held that every plant belonged to some species, 
marked out by invariable, never-changing characters. They acknow- 
ledged variable differences as well, and so explained sub-species and 
varieties. Similarly, a natural genus was a group of species, and was 
marked out from other genera by eternal differences of still greater 
importance. We now perceive, however, that the existence of any 
such groups as genera and species is an arbitrary creation of the 
naturalist's mind. All resemblances of plants are natural so far as 
they express hereditary affinities; but this applies as well to the 
variation within the species as to the species itself or to the larger 
groups. All is a matter of degree. The deeper differences between 
plants have been produced by differentiating action extending over 
probably millions of years; sub-species may sometimes have arisen 
within historical times, and varieties approaching to sub-species 
may often be produced by the horticulturist in a few years. 4 It is 
thus easy to see how specific differences may arise among the descen- 
dants of a common stock. 6 

The fixity of species in the organic world is, in fact, now entirely 
discredited. During a given period of a few thousand years, 
" kinds " may be recognized, because, under such conditions as now 

i Of. Mill, IV, vli, 4, 6. * Cf. Bain, p. 192. Cf. Jevons, Prin. of Sci , pp. 122-4. 
* Cf. Jevons, Prin. of Sci. t pp. 724-8. * Cf. Bain, p. 190. 


prevail in the world, that period of time is insufficient to bring 
about great changes. The horse, the dog, and the cat 1 have had 
a common ancestor from whose type they have gradually diverged, 
and their present distinctness results only from the destruction of 
intermediate types. Could we restore all the descendants of the 
common ancestor, we should find nowhere a greater difference than 
between offspring and parents. Of "kinds" there would be none. 2 

In practice, then, natural groups must be determined by con- 
sidering not only those qualities which are strictly common to all 
the objects included in the group, but the entire body of qualities, 
all of which are found in most of those objects, and most of them in 
all. And hence the image which we conceive in our minds to repre- 
sent the class is that of a specimen possessing the whole of the 
qualities in a high degree, for such a specimen is alone really fitted 
to show clearly what those qualities are. It is by a mental reference 
to this standard that we usually and advantageously determine 
whether any individual or species belongs to the class or not. 3 

4. Principles of Logical Division 

In order that a classification may facilitate the study of a par- 
ticular phenomenon, we must first bring into one class all kinds of 
things which exhibit that phenomenon, in whatever variety of forms 
or degrees; and secondly we must nrrange these kinds in a series 
according to the degree in which they exhibit it. \Ve must there- 
fore be able to recognize the essential similarity of a phenomenon, 
in its minuter degrees and obscurer forms, with what is called the 
same phenomenon in its most complete development. 

The main principle of division must of course be natural ailinity; 
the classes formed must, as far as possible, be natural groups, but 
the principles of natural grouping must be applied in subordination 
to the principles of a natural series. The groups must not be so con- 
stituted as to place in the same group things which ought to occupy 
different points of the general scale. The precaution necessary to 
be observed for this purpose is that the primary divisions must 
be grounded not on all distinctions indiscriminately, but on those 
which correspond to well-marked variations in the degree of the 

1 This is, of course, quite a haphazard choice ; any or all animals might be mentioned 

2 Of. Carveth Bead, Logic, p. 314. But there are many perplexing difficulties and many 
unsolved problems in connection with the accepted doctrine of evolution through the medium 
of natural selection. For some of these, the reader may refer to Professor Bateson's six 
lectures on Genetics, given at the Royal Institution in Jan. and Feb., 1912. 

Ct Mill, IV, vli, 5. 


main phenomenon. In classifying animals, for example, the series 
as a whole should be broken into parts at the points when the varia- 
tion in degree begins to be attended by conspicuous changes in the 
various animal properties. 1 Such well-marked changes take place, 
for instance, where the class mammalia ends; at the point where the 
fishes are separated from insects; insects from mollusca; and so on. 2 

Apart, however, from the strictly logical difficulties already men- 
tioned, no classification of animals can ever be perfect until the pre- 
sent great gaps in our knowledge of animal life are filled up. For 
a perfect classification of animals, two conditions are necessary: 
(1) a full knowledge of the adult structures of every animal, recent 
and extinct; (2) the mode of development of every animal. For, as 
Huxley says, it is the sum of all the structural conditions of an 
animal which constitutes the totality of its structure; and if two 
animals, similar in their adult state, were unlike in their development, 
it is clear that the latter circumstance would have to be taken into 
account in determining their position in a classification. 3 Now these 
conditions are impossible to meet, for our knowledge is still Very 
incomplete. Thus it comes about that whatever classification of the 
animal kingdom is adopted, it is open to logical criticism. The very 
best grouping is necessarily subordinate to our present state of 

To obtain a strictly logical division, every superior class should 
be divided into two inferior classes, distinguished by the possession 
or non-possession of a single specified difference. Each of these 
minor classes is again divisible by any other quality whatever which 
can be suggested. Every such classification may be called bifurcate. 
Theoretically, such a method is alone productive of a system logically 
perfect. For example - 

Parts of Speech 

Nouns Not Nouns 

Pronouns Not Pronouns 

Verbs Not Verbs; &c. 

* Applied to animals, the logical term "properties" seems awkward, hut the meaning is 

a Cf. Mill, Book IV, ch. viii, g 4, 6. 

* Ct Mill, IV, viii, | 6; and Huxley, "Animal Kingdom", Ency. Brit. 


But such a plan is usually cumbrous, and at each step the negative 
term is entirely undefined in its extent. 1 In practice, therefore, it 
is seldom used, though its logical necessity was insisted on by Ben- 
tham, who took, for an example, the vertebrate animals and divided 
them into four classes as follows : 

Mammals : having mammae and lungs. 

Birds : having lungs and wings but not mammae. 

Fish: not having lungs. 

Reptiles : having lungs but not mammae or wings. 

We have then, according to Bentham, this bifurcate division: 



With lungs Without lungs 

With mammae Without mammae 

' mammals) \ 

With wings Without wings 

( = birds ) ( = rept ties) 

But, as Jevons points out, even this scheme is theoretically im- 
perfect. The sub-class mammals must either have wings or not; 
we must either subdivide this class, or assume that none of the 
mammals have wings, which is, as a matter of fact, the case (the 
wings of bats riot being true w r ings in the sense of wings applied to 
birds). Fish, again, ought to be considered with regard to the pos- 
session of mammae and wings; and in leaving them undivided we 
really imply that they never have mamma} or wings (the wings of 
flying-fish being again no exception). Although the example affords 
an illustration of logical division which, for practical purposes, is 
perfect, it shows the extreme difficulty of conforming to the rigorous 
demands of theory. 2 

The strictly bifurcate form of division may often be dispensed 
with, and yet the logical aspects be strictly maintained; for 

example : 


I I t 

Commissioned Officers Non-commissioned Officers Rank and File 

See Welton, Logic, vol. ii, p. 130. 

2 Cf. Jevons, /Yin. o/Sci., pp. 694-8; Bentham, New System of Logic, p. 115. 


And it is quite unnecessary to adopt the bifurcate plan to classify 
things admitting of numerical discrimination; for example: 

Plane Rectilineal Figures 1 

1 i i i ; i 

Triangles Quadrilaterals Pentagons Hexagons Figures of more than 6 sides 

And perhaps the same remark applies in the case of a classification 
of, for instance, the different countries of Europe. On the other 
hand, we might make our first step consist of France and not- 
France; then not-France might be divided into Germany and not- 
Germany; and so on. Absurd as this seems, logicians are by no 
means unanimously of opinion that we could, with strict logical 
consistency, adopt any other basis of division. 2 

The ordinary rules of logical division should always be borne in 
mind: (1) there must be only one basis of division (and the sub- 
classes will therefore be mutually exclusive; (2) the division must 
be exhaustive; (3) in continued division, each step must be a proxi- 
mate one; and (4) the division must be appropriate. 3 The necessity 
for the last rule will be seen if a proposal be made to classify, for 
instance, the boys in a school according to whether their names con- 
sisted of one or more syllables. 

Difficult and practically impossible as strictly logical classification 
is in Botany and Zoology, it is comparatively simple in Chemistry. 
Taking nature generally, however, rigorously logical grouping is 
more often impossible than not. There are, for instance, substances 
varying by insensible degrees; the granites are a case in point. 
Similar difficulties confront us in any attempt to classify odours, 
the emotions, human faces, personal characters, and so forth. In 
such cases, diversity is far too great for logical classification to be 

5. Definition 

Closely associated with Classification is the question of Defini- 
tion. We have already referred to the Scholastic mode of defining, 
and it will suffice here to add, by way of further suggestion, an 
instructive instance of Bain's method of working out the definition 
of a common term. We will take the term Food. 

We begin by assembling representative examples of all the sub- 
stances ever recognized under this name. We have before us the 
flesh of animals, the esculent roots, fruits, leaves, &c. We have also 
a number of substances of purely mineral origin, as water and com- 

* Cf. p. 21. 2 ib * See Bain, p. 10G, or any standard work on Logic. 


mon salt. Our work lies "in generalizing these, in detecting com- 
munity in the midst of much difference". 

Were man a purely carnivorous feeder, his food might he general- 
ized as " the flesh of animals taken into the mouth and passed into 
the stomach, to be there digested and thence to be applied to the 
nourishment and support of the system". But when we include 
vegetable and mineral bodies, we must leave out " flesh", and substi- 
tute "animal, vegetable, and mineral substances"; the other part of 
the statement being applicable. Even as amended, however, the 
definition is still tentative, and needs to be verified by comparison 
in detail with everything that is ever put forward as food. We 
must challenge all informed critics to say where the definition fails. 
Thus, nourishment is afforded by substances absorbed through the 
skin, a fact which would invalidate the exclusive mention of the 
medium of the mouth and stomach, and narrow the definition to 
nourishing and supporting the system. Again, it is doubtful 
whether alcohol and tea nourish the system. This is a far more 
serious objection; and the manner of dealing with it will illustrate 
the principles of defining. 

In the first place, there may be a contest as to the matter of fact. 
Could it be shown that these substances do give nourishment and 
support to the system, the difficulty is at once overcome; in that case 
they fall at once under the definition. On the contrary supposition 
that they do not nourish and support the system, two courses are 
open. First, we may exclude them from the class "food", and retain 
the definition. Or, secondly, we may include them, and alter the 
definition. As modified to suit the extension, the definition would 
bo, " substances that either nourish and support or stimulate the 
system". To decide between those two courses, we must refer to 
the golden rule of classification, which recommends the adherence to 
a smaller class based on the greatest number of important qualities, 
rather than to a larger where the properties in common are reduced 
to comparative insignificance. It is better, therefore, to retain two 
groups Foods and Stimulants each with its own Definition. In 
that way we should derive much more information respecting any 
individual thing designated either "Food" or "Stimulant", than if 
the word "Food" covered both. It may be that some substances, 
beef tea, for instance, combines both functions, which would entitle 
them to be named in both classes. 1 

1 See ttain, Indue. Logic, pp. 158-9. Of course much more is now known about Foods and 
Stimulants than when Bain wrote this, but the principle underlying the general argument id 


It has already been pointed out that the need for exact definitions 
of terms very seldom arises, until the terms are actually used in 
assertions. 1 

The Analysis of Phenomena 

i. Unsuspected Associations of Phenomena 

In a former chapter 2 it was stated that the association of ideas, 
by blending together things that are really distinct in their nature, 
tends to introduce perplexity and error into every process of reason- 
ing in which we may be engaged. 

One intimate association between two ideas which have no 
necessary connection is that which exists in every person's mind 
between colour and extension. The word "colour" expresses a sensa- 
tion in the mind; " extension" denotes a quality of an external 
object. There is no more real connection between two such notions 
than between pain and solidity. And yet, in consequence of our 
always perceiving extension at the same time as the sensation of 
colour is excited in the mind, we find it impossible to think of that 
sensation without conceiving extension along with it. 3 

Again, most people are under the impression that the relation 
which the different notes of the musical scale bear to one another, 
and the relation of high and low position among material objects, 
are analogous. They seem to think that the notes to the right of 
the piano are " higher " than those to the left, that an acute sound 
is higher than a grave sound. But the association is entirely mis- 
leading, and is, in fact, the very reverse of an association once 
equally prevalent. The more ancient of the Greek writers looked 
upon grave sounds as high, and acute ones as low; the present mode 
of expression is a later innovation. 4 There is, of course, no scientific 
reason for calling acute or grave sounds high or low, though the 
practice perhaps arose from the relative positions of the strings in 
ancient instruments. 6 

i See ch. ii. a On Locke. 

* Cf. Dugald Stewart, Phil, of Human Mind, p. 184. 

* Cf. Dugald Stewart, op. cit. p. 185, and Gregory's Euclid, preface. 

* Cf. Dr. Beattie's Essay on Poetry and Music \ and Dugald Stewart, p 560. 


If, then, such erroneous associations remain unsuspected, and we 
proceed to reason from the underlying " facts", our reasoning will 
probably be fallacious. The necessity for disentangling our facts 
thus becomes evident. It has been well said that progress in scien- 
tific investigation depends much more on that severe and discrimi- 
nating judgment which enables us to separate ideas that nature or 
habit has closely combined, than on acuteness of reasoning or fer- 
tility of invention. Whenever two subjects of thought are intim- 
ately connected in the mind, it requires the most determined effort 
of attention to conduct any process of reasoning which relates to 
only one. 

Since one of the main objects of Science is to ascertain the laws 
which regulate the succession of events in nature, the investigator 
has constantly to deal with different events presented to him nearly 
at the same time, and he has the: ef ore to be particularly careful 
that phenomena closely connected in time do not mislead him into 
thinking that they are necessarily invariably conjoined. The dis- 
position to confound together accidental and permanent connections 
is one great source of popular superstitions, palmistry, phrenology, 
planetary influence, haunted houses, miraculous wells, unlucky days, 
and so on. Such combinations are confined, in great measure, to 
uncultivated and unenlightened minds, but there are other acci- 
dental combinations which are apt to lay hold of the minds of 
even the very ablest of investigators. 1 

We have already seen that when a phenomenon is preceded by 
a number of different circumstances, we cannot determine, by any 
a priori reasoning, which of these circumstances are to be regarded 
as the constant, and which the accidental, antecedents of the effect. 
If, in the course of our experience, the same combination of circum- 
stances is always exhibited to us without any alteration, and is 
invariably followed by the same result, we must necessarily remain 
ignorant whether the result be connected with the whole combina- 
tion, or with only one or a few of the circumstances combined; and 
therefore if at any time we wish to produce a similar effect, there 
is no alternative but to imitate in every particular circumstance the 
combination which we have seen. 

Let us suppose, for instance, that a savage who, on some occa- 
sion, had found himself relieved of some bodily ailment by a draught 
of cold water, is a second time afflicted with a similar disorder and 
is desirous of repeating the same remedy. With the limited degree 

i Cf. Dugald Stewart, op. cit. pp. 186-7. 
(0415) 17 


of knowledge and experience which we have here supposed him to 
possess, it would be impossible for the greatest of modern investi- 
gators, in his situation, to determine, whether the cure was due to 
the water which was drunk, to the cup in which it was contained, to 
the fountain from which it was taken, to the particular day of the 
month, or to the particular age of the moon. In order, therefore, 
to ensure the success of the remedy, the savage will, very naturally 
and very wisely, copy, as far as he can recollect, every circumstance 
which accompanied the first application of it. He will make use of 
the same cup, draw the water from the same fountain, hold his body 
in the same position, and turn his face in the same direction; and 
thus all the accidental circumstances in which the first experiment 
was made, will come to be associated equally in his mind with the 
effect produced. The fountain from which the water was drawn 
will be considered as possessed of Darticular virtues; and the cup 
from which it was drunk will be set apart for exclusive use on 
all future similar occasions. 

Now the mind cannot be cured of these associations by any 
progress in the art of reasoning; the cure can be effected only by 
an enlargement of experience. It is experience alone which will 
teach us to break up, and how to break up, complex phenomena 
into its parts, to combine them together again in various ways, 
and to observe the effects which result from these different experi- 
ments. It is only after we have eliminated from physical causes 
their accidental and unessential concomitants that we can ascertain 
with precision the general laws of nature. 1 

But in spite of every care we may take in analysing the pheno- 
menon under investigation, we may quite probably find it impos- 
sible to effect the pure connection between the conditions and their 
consequences, unimpeded by any irrelevant details. Much of the 
"residue" in the phenomenon, which we are presuming to be in- 
different and leaving out of account, is incapable of actual removal. 
The exclusion from consideration of this residue is, therefore, only 
justified as far as the residue has been analysed. 2 

2. Herschel on the Analysis of Phenomena 

Herschel's remarks 3 on the analysis of phenomena are so valu 
able and instructive that we cannot do better than summarize them 

i Cf. Dugald Stewart, op. cit. pp. 188-9. 

Cf. Welton, Logic, vol. ii, pp. 121-41. flat. Phil, Part II, ch. ill. 


Phenomena, or appearances, as the word is literally rendered, 
are, says Herschel, the sensible results of processes carried on among 
external objects, of which they are, so to speak, signals, conveyed by 
the wonderful mechanism of our sense organs to our minds, which 
receive and review them, and by habit and association connect them 
with corresponding qualities in the objects; just as a person writing 
down and comparing the signals of a telegraph might interpret their 

Now these processes themselves may be in many instances 
analysed and shown to consist in the motions or other affections 1 
of the external objects. For instance, the phenomenon of the 
sound produced by a musical string, or a bell, when struck, may 
be shown to be the result of a process consisting in the rapid 
vibratory motion of its parts communicated to the air, and thence 
to our ears; though the intermediate effect on our organs of hearing 
does not seem to suggest the slightest idea of such a motion. 

On the other hand, there are innumerable instances of sensible 
impressions which we seem to be incapable of tracing beyond the 
mere sensation; for example, the sensations of bitterness and sweet- 
ness. These, therefore, if we were inclined to form hasty decisions, 
might be regarded as ultimate qualities; but the instance of sounds, 
just mentioned, alone would teach us caution in such decisions, and 
incline us to believe them to be mere results of some secret process 
going on in our organs of taste, too subtle for us to trace. 

3. His Remarks on our Notions of Force 

There seems to be little hope of attaining a knowledge of the 
ultimate and inward processes of Nature. Let us, for instance, 
consider the production of motion by the exertion of force. We 
are conscious of a power to move our limbs, and, by their inter- 
vention, other bodies. We are also conscious that this effect is the 
result of a certain inexplicable process by which we exert force. 
And even when such exertion produces no visible effect, as when 
we press our two hands violently together in such a way as just 
to oppose each other's effect, we still perceive, by the fatigue and 
exhaustion, that something is going on within us, of which the 
will is the determining cause. The impression which we receive 
of the nature of force from our own effort and the sense of fatigue 
is quite different from that which we obtain of it from seeing the 

* i.e. those qualities of bodies by which they directly affect the senses. 


effect of force exerted by others in producing motion. Were there 
no such thing as motion, had we, for instance, been from infancy 
shut up in a dark dungeon and every limb encrusted with plaster, 
the internal consciousness would give us a complete idea of force; 
but when set at liberty, habit alone would enable us to recognize its 
exertion by its signal, motion, and tlwt only by finding that the same 
action of the mind which in our confined state enables us to fatigue 
and exhaust ourselves by the tension of our muscles, puts it in our 
power, when at liberty, to move ourselves and other bodies. But 
how obscure is our knowledge of the process going on within us 
in the exercise of this movement (by virtue of which alone we act 
as direct causes), we may judge from the fact that when we put any 
limb in motion, the seat of the exertion seems to us to be in the 
limb, a conclusion which is demonstrably wrong. 

This one instance of the obscurity which hangs about the only 
act of direct causation of which we have an immediate consciousness, 
will suffice to show how little prospect there is that, in the investi- 
gation of nature, we can ever arrive at a knowledge of ultimate 
causes. We must be satisfied with a knowledge of laws, and to 
obtain these we begin by analysing every particular complex pheno- 
menon presented to us, and continuing the process until the resolved 
constituents are the most simple and elementary obtainable. 

4. His Analysis of the Phenomenon of Sound 

Herschel now proceeds to give an instance of the analysis of a 
complex phenomenon. Let us, he says, take the phenomenon of 
sound, and, by considering the various cases in which sounds of 
all kinds are produced, we shall find that they all agree in these 
points : 

1. The excitement of a motion in the sounding body. 

2. The communication of this motion to the air or other 

medium which is interposed between the sounding body 
and our ears. 

3. The propagation of such motion from particle to particle of 

such medium in due succession. 

4. Its communication, from the particles of the medium adja- 

cent to the ear, to the ear itself. 

5. Its conveyance in the ear, by a certain mechanism to the 

auditory nerve. 

6. The excitement of sensation. 


Now in this analysis we notice that two principal matters must be 
understood before we can have a true and complete knowledge of 
sound : 

1. The excitement and propagation of motion. 

2. The production of sensation. 

These, therefore, appear to be the elementary phenomena into which 
the complex phenomenon of sound resolves itself. 

But, again, if we consider the communication of motion from body 
to body, or from one part to another of the same body, we shall 
perceive that it is again resolvable into several other phenomena: 

1. The original setting in motion of a material body, or any 

part of one. 

2. The behaviour of a particle set in motion, when it meets 

another lying in its way, or is otherwise impeded or influ- 
enced by its connection with surrounding particles. 

3. The behaviour of the particles so impeding or influencing it 

in such circumstances. 

The last two suggest another phenomenon which it is 
necessary also to consider, viz. : 

4. The phenomenon of the connection of the parts of material 

bodies in masses, by which they form aggregates, and are 
enabled to influence each other's motions. 

Thus we see that an analysis of the phenomenon of sound leads to 
the enquiry 

1. Into two causes, viz., 

(a) The cause of motion, 

(b) The cause of sensation, 

these being phenomena which we seem to be unable to 
analyse further, and we therefore set them down as simple, 
elementary, and referable, for anything we can see to the 
contrary, to the immediate action of their causes. 

2. Into several questions relating to the connection between the 

motion of material bodies and its cause; for example, 

(a) What will happen when a moving body is surrounded 
on all sides by others not in motion? 

(6) What will happen when a body not in motion is ad- 
vanced upon by a moving one? 

It is evident that the answers to such questions as these 
can be no others than laws of motion. 


Lastly, we are led, by pursuing the analysis and considering the 
phenomenon of the aggregation of the parts of material bodies, and 
the way in which they influence each other, to two other general 
phenomena, namely, the cohesion and elasticity of matter; and these 
we have no means of analysing further, and must therefore regard 
them (until we see reasons to the contrary) as ultimate phenomena, 
and referable to the direct action of causes, namely, an attractive 
and a repulsive force. 1 

5. The Limits of such an Analysis 

Of force, as counterbalanced by opposing force, we have, as 
already said, an internal consciousness; and though it may seem 
surprising that matter should appear capable of exerting on matter 
the same kind of effort, yet we feel bound to accept the direct 
evidence of our senses; and this seems to show us that when we 
keep a spring stretched with one hand, we feel our effort opposed 
exactly in the same way as if we had ourselves opposed it with 
the other hand, or as it would be by that of another person. The 
inquiry, therefore, into the aggregation of matter resolves itself 
into the general question, What will be the behaviour of material 
particles under the mutual action of opposing forces capable of 
counterbalancing each other? and the answer to this question can 
be no other than the announcement of the law of equilibrium, what- 
ever law that may be. 

With respect to the cause of sensation, it must be regarded as 
much more obscure even than that of motion, inasmuch as we have 
no conscious knowledge of it. 2 

Dismissing, then, as beyond our reach, the inquiry into causes, 
we must be content, at present, to concentrate our attention on the 
laws which prevail among phenomena, and which seem to be their 
immediate results. From the instance just given, it is evident that 
every inquiry into the intimate nature of a complex phenomenon, 
branches out into as many different and distinct inquiries as there 
are elementary phenomena into which it may be analysed; and 
that, therefore, it would greatly assist us in our study of nature, 
if we could, by any means, ascertain what are the ultimate pheno- 
mena into which all the composite ones presented by it may be 

1 id. pp. 88-90 

2 The chasm between the physical and the psychical is still unbridged. Subjective Psy- 
chology can throw no light whatever on the cause of sensation, and Physiology so far very 


resolved. Clearly this can be ascertained if at all only by going 
to Nature itself; and just as the analytical chemist accounts every 
ingredient an element until it can be resolved into others, so, in 
investigation generally, we must account every phenomenon as an 
elementary or simple one till we can analyse it and show that it is 
the result of others, which in their turn become elementary. Thus, 
in a modified and relative sense, we may still continue to speak of 
causes, not intending thereby ultimate causes, but those proximate 
causes which connect phenomena with others of a simpler, higher, 
more general, or elementary kind. For example, we may regard the 
vibration of a musical string as the proximate cause of the sound 
it yields, receiving it so far as an ultimate fact, and deferring 
the inquiry into the cause of vibrations, which is of a higher and 
more general nature. It may, however, often happen that although 
we become fully aware of the complexity of a phenomenon, we are 
entirely unable to analyse it. 1 

In pursuing the analysis of any phenomenon, the moment we 
find ourselves stopped at a point beyond which further analysis 
seems impossible, we are forced to refer, at least provisionally, the 
constituent element we have now reached to the class of ultimate 
facts; and the study of this elementary constituent and of its laws 
becomes a separate branch of Science. On those phenomena which 
are most frequently encountered in an analysis of nature, and which 
most decidedly resist further decomposition, it is evident that the 
greatest pains and attention ought to be bestowed. They furnish 
the key to the greatest number of inquiries, and in them we must 
look for the direct action of causes. Now by far the most general 
phenomenon with which we are acquainted, and that which occurs 
most constantly, in every inquiry upon which we enter, is motion. 
Dynamics, then, is a branch of knowledge, a thorough study of which 
is imperative. Happily, it is one in which a very high degree of 
certainty is attainable, a certainty in no way inferior to mathematical 

Unfortunately, no general rules of procedure can be laid down 
for the analysis of a complex phenomenon into simpler ones. 2 
Success comes from experience, patience, insight, and a careful 
study of the work of successful investigators. 

i op. cit. pp. 90-3. 2 ib. pp. 93-6. 


Generalization and Empirical Laws 

9 i. The Meaning of Generalization 

The Scholastic Logicians " generalized " by merely omitting all 
those qualities which distinguished the observed particulars from 
one another. But the term generalization as now commonly used, 
seems to include two distinct processes, though these are often 
closely associated together. 

In the first place, the term is used when, even in two objects, 
there is a recognition of something in common. The slightest simi- 
larity seems almost of necessity to lead to an inference of some kind 
from one case to another. 1 

In the second place the term generalization is often used to 
denote the process of passing from a limited number of facts, or 
from a partial law, to a multitude of unexamined cases, which we 
believe to be subject to the same conditions. In the cases actually 
examined, we have done more than merely recognize similarity; we 
feel that we have been able to detect the conditions which invari- 
ably accompany and determine those cases. Hence, in generaliza- 
tions of this kind, we may be said to endow ourselves with a power 
of prediction of more or less probability. Having observed, for 
example, that many substances assume, like water and mercury, 
the three states of solid, liquid, and gas, and having assured our- 
selves by frequent trial that the greater the means we possess of 
heating and cooling, the more substances we can vaporize and 
freeze, we pass confidently in advance of fact, and assume that all 
substances are capable of these three forms. 2 

It is generalization in this second sense that enters so largely 
into the work of Science. The essence of the process consists in the 
discovery, in a group of observed phenomena, of those invariable 
conditions which determine the common nature of the phenomena. 
We do not generalize from number of instances as such ; validity in 
no way depends on the mere number of instances examined. Com- 
plete knowledge may, in favourable cases, be attained by the careful 
analysis of a single instance. The validity of the generalization 
rests upon the fundamental assumption that every elementary fact 

i Cf. Welton, Logic, vol. ii, pp. 191-2. * Cf. Jevons, Prin. of Sci., pp. 697-8. 


of Nature is always definitely determined in precisely the same way, 
so that the relation between a phenomenon and its conditions cannot 
vary. 1 

2. Generalizations Vary in Degree 

In the earlier stages of scientific inquiry, generalizations are 
necessarily more or less empirical. We have first to be satisfied 
with " facts ", which we check and correct, label and classify, and 
thus do our best to ensure accuracy and orderliness. All this must 
necessarily precede any discovery of determinate conditions. That 
which has to be " explained " must be clearly and distinctly set out 
before we can attempt to explain it. In other words, empirical 
generalizations must precede generalizations of strict determination; 
we must first ascertain the Laws of phenomena; the consideration 
of Causes must come later. 2 Obviously, then, our generalizations vary 
greatly in finality; but as our knowledge grows, so they increase in 
comprehensiveness and certainty. 8 

Certain established natural laws are held to be true of all matter 
in the universe absolutely, without exception, no instance to the 
contrary ever having been noticed. This is conspicuously true of 
the law of universal gravitation, and of Newton's laws of motion. 
These, therefore, we may regard as ultimate laws, at all events for 
the present. But by far the greater number of properties of matter 
vary in degree; substances are more or less dense, more or less 
transparent, more or less magnetic; and so on. One common result 
of the progress of Science is to show that qualities once supposed to 
be entirely absent from many substances are really present, though 
in so low a degree of intensity that the means of detection were 
insufficient. Newton, for instance, believed that most bodies were 
quite unaffected by the magnet. Faraday and Tyndall have rendered 
it very doubtful whether any substance whatever is wholly devoid 
of magnetism. 4 Thus <are generalizations, once commonly accepted, 
shown to be incorrect. 

Then phenomena which are in reality of a closely similar or even 
identical nature may present to the senses very different appear- 
ances, and so, again, we may be led to make false generalizations. 
Without a careful analysis of the changes which take place, we may 

i Cf. Welton, Logic, ii, p. 194; also ch. xv, 1 and 9. 

See Welton, ii, p. 196; and Whewell, Nov. Org. /ten., p. 118. 

Cf. Jevons, Prin. of Sci., p. 600. 

* id. pp. 603-7. Magnetism here includes "diamagnetUm 


often be in danger of widely separating facts and processes, which 
are actually instances of the same law. Extreme difference of degree 
or magnitude is a frequent cause of error. It is, for instance, diffi- 
cult, for the moment, to recognize any similarity between the gradual 
rusting of a piece of iron and the rapid combustion of a heap of 
straw. Yet Lavoisier's chemical theory was founded upon the 
similarity of the oxidizing process in the two cases. We have only 
to take iron in a finely divided state to show that it is the more 
combustible of the two. 1 

3. Empirical Laws 

Scientific investigators give the name of Empirical Laws to those 
uniformities which observation or experiment has shown to exist, 
but on which they hesitate to rely in cases varying much from those 
which have been actually observed, because they have not yet been 
able to see any reason why such a law should exist. It will be seen, 
therefore, that the very notion of an empirical law implies that it is 
not an ultimate law; that, if true at all, there must be an explanation, 
which should be sought and found. It is a derivative law, the deriva- 
tion of which is not yet known. To state the explanation, the ivhy, 
of the empirical law, would be to state the laws from which it is derived. 
And if we know these, we should also know under what conditions 
it would cease to be fulfilled. But these higher laws may not yet 
be identical with the ultimate laws of causation; they may be of an 
intermediate class, requiring still further derivation. 

1. That snow is always to be found on high mountains was at 
one time an empirical law. The law was* based on observation, but 
was not susceptible of being explained or referred to any higher gene- 
ralizations. We can now resolve it into the laws connected with 
radiant heat passing through the atmosphere, and we may therefore 
regard it as being derived from such laws. These may not them- 
selves be the highest attainable generalities; still they are much 
more general than the stated uniformity connecting snow and height. 

2. The fact that water always rises in pumps was an empirical 
law previous to the discovery of the pressure of the atmosphere. 
The application of the Method of Agreement, in different coun- 
tries, and with pumps of different bores, proved that no pump could 
draw water beyond about 33 ft. The law could be relied on within 
the wide limits of place and circumstances where it had been tried. 

i Cf. Jevons, op. cit. p. 611. 


It could not have been extended to other planets, but it might be 
extended with apparent safety to any part of the earth. But on the 
discovery of the pressure of the atmosphere, the empirical law passed 
into a law of higher generalization; its limits of operation were pre- 
cisely defined. The new discovery explained why the water could 
not rise much beyond 33 ft.; why the height varied at different 
times; why, on a high mountain, the rise was considerably less than 
at the sea level; and so on. It is conceivable that, some time or 
other, these explanations might have been empirically discovered by 
sufficiently wide and careful experiments, but it is very unlikely. In 
any case the derivation superseded such a laborious task. 

3. That our breathing animals are hot-blooded is a law formerly 
empirical, but now derived from the general law of the dependence 
of temperature on the oxygenation of the blood. 

4. The periodical return of eclipses, as originally ascertained by 
the observation of the early astronomers, was an empirical law until 
the general laws of the celestial motions had explained it. 

The following are empirical laws still waiting to be resolved into 
the simpler laws from which they are derived. The local laws of 
the flow and ebb of the tides in different places; the succession 
of certain kinds of weather to certain appearances of the sky; the 
apparent exceptions to the almost universal truth that bodies ex- 
pand by increase of temperature; the law that gases have a strong 
tendency to permeate animal membranes; the law that when dif- 
ferent metals are fused together the alloy is harder than the various 
elements; the law that substances containing a very high proportion 
of nitrogen (such as morphia and hydrocyanic acid) are powerful 

An empirical law, then, is an observed uniformity, presumed to 
be resolvable into simpler laws, but not yet resolved into them. It 
is a law which awaits explanation. 1 

4. The " Joint Action 1 ' of Causes 

All possible empirical laws, and all possible uniformities of less 
generality, seem to be resolvable into a very limited total number of 
ultimate laws of causation. Conversely, from this limited number 
of ultimate laws of causation, a vast number of uniformities, both of 
succession and coexistence, must necessarily be derived. Now the 
order of succession or coexistence which obtains among effects neces- 

i Cf. Mill, Logic, Book III. ch. xvi, 1,2; Bain, Inductive Logic, pp. 104-8. 


sarily depends on their causes. "If they are effects of the same 
cause, it depends on the laws of that cause; if on different causes, it 
depends on the laws of those causes severally, and on the circumstances 
which determine their coexistence" If we trace the coexistence of these 
causes back, the different effects may meet at a point, and the whole 
is thus shown to depend ultimately on some common cause; or they 
may terminate in different points, and the order of succession and 
coexistence of the effects is thus proved to have arisen from the 
" collocation " l or joint action of some of the primeval causes or 
natural agents. 

Derivative laws, therefore, do not depend solely on the ultimate 
laws into which they are resolvable; they mostly depend on those 
ultimate laws and an ultimate fact, namely, the mode of coexistence 
or joint action of some of the component elements of the universe. 
For example, the order of succession and coexistence among the 
heavenly motions, which is expressed by Kepler's Laws, is derived 
from the coexistence or joint action of two primeval causes, the 
sun's attractive force, and the original projectile force belonging to 
each planet. But the sun's attraction and the original projectile 
force coexist and act together in a certain ratio, a ratio which is 
productive of regular elliptical motions. But this ratio might have 
been entirely different, in which case the motions would have been 
different, though still regular. 

Now why the sun's attraction and the force in the direction of the 
tangent coexist and act together in the exact proportion they do, 
we do not know, and we cannot trace any coincidence between it 
and the proportions in which any other elementary powers in the 
universe thus coexist or act together. The utmost disorder is, in fact, 
apparent in the combination of causes generally. In the resolution 
of derivative laws, then, we have to consider not only the ultimate 
laws from which they are derived, but also an element which is not 
a law of causation, an element in which there is no uniformity, no 
principle, no rule. It is an elusive element of joint action, and it 
defies explanation. 

We now see why investigators place only a limited degree of 
reliance upon derivative laws. A derivative law which results 
wholly from the operation of some one cause will be as universally 
true as the laws of the cause itself, but where the law results from 

i This term of Mill's is not a very happy one ; " co-action " would be better, except that 
as commonly used it implies a certain amount of compulsion ; " joint action " seems most 
nearly to suggest the correct idea. 


effects of several causes, there may be a variation in the mode of 
coexistence or joint action of these causes; and as we are necessarily 
ignorant of the nature of this coexistence or joint action, we are not 
safe in extending the law beyond the limits of time, place, and cir- 
cumstances, in which we have actual experience of its truth. 1 The 
elliptic motion of the planets, for example, would be fundamentally 
modified if some great disturbing body were sufficiently near to 
counteract solar attraction, or if the tangential force were made 
different from what it is. Hence we cannot extend the law of the 
ellipse to every body that may now or at any future time revolve 
about the sun. 2 

We have seen that, by the Method of Agreement alone, we can 
never arrive at causes. Hence, no generalization can be more than 
an empirical law when the only proof rests on that method. It 
therefore follows that almost all results obtained by simple observa- 
tion without experiment must be considered empirical only, deri- 
vative laws, the derivation of which has not been traced. 3 

5. The Detection of Derivative Laws 

Suppose we have determined, in an observed uniformity, some 
law of causation. By what signs arc we to judge that it is not an 
ultimate law but an unresolved derivative law 1 

One sign would be any evidence, between the antecedent a, and 
the consequent b, of some intermediate link, some phenomenon of 
which we can surmise the existence, though from the imperfection 
of our senses or of our instruments, we are unable to ascertain its 
precise nature and laws. If we denote the link by x, it follows 
that, even if a be the cause of A, it is but the remote cause, and that 
the law a causes b is resolvable into at least two laws, a causes x, 
and x causes b. This is frequently the case, since the operations of 
nature mostly take place on so minute a scale that many of the suc- 
cessive steps are either imperceptible or very indistinctly perceived. 

Take the case, for instance, of the " explosion " of a mixture 
of oxygen and hydrogen to form water. 4 All that we see of the 
process is, that the two gases are mixed in certain proportions, that 
an electric spark is passed, an explosion takes place, the gases dis- 
appear, and water vapour comes into being, and that there is diminu- 
tion of volume. There is no doubt about the law, no doubt about 

i Cf. Mill, Logic, Book ill, ch. xvi, 2, 3, 4. * Cf. Bain, p. 107. 

Mill, ft. * 01 ch. xii, a 


the causation. But between the antecedent (the mechanical mixture 
of gases to which the electric spark is applied) and the consequent 
(the production of water), there must be an intermediate process 
which we do not see. We find that every portion of the water 
vapour, even the smallest portion our instruments are capable of 
appreciating, contains oxygen and hydrogen in the ratio of 1:2, and 
we feel no doubt that the minutest perceptible portion contains the 
same elements in the same ratio. Hence, we are driven to the con- 
clusion that still more minute portions of oxygen and hydrogen 
must have come together in every such minute portion of space; 
and, since the volume of water vapour is less than the original mix- 
ture, they must have come closer together. If we grant the truth 
of the atomic theory, there must have been a breaking asunder of 
the combined atoms in each oxygen and hydrogen molecule, a re- 
arrangement of all these atoms, and a recombination into water 
molecules. ' If the whole process could be slowed down from the 
fraction of a second to, say, an hour, and rendered visible, can we 
doubt that a succession of wonderfully interesting phenomena would 
be presented to us? There is probably a chain of innumerable in- 
tervening links between a and J, the antecedent and consequent 
with which alone we are familiar. And so it must be generally, in 
all chemical processes both in the inorganic and organic worlds. 

A second sign from which a law of causation, though hitherto 
unresolved, may be inferred to be a derivative law, is when the 
antecedent is a complex phenomenon. Take the case of a diminu- 
tion of the pressure of the atmosphere (indicated by the fall of the 
barometer) followed by rain. The antecedent is a complex pheno- 
menon: the column of atmosphere consists of a column of air and 
a column of aqueous vapour mixed with it; and the change in the 
two together, shown by a fall in the barometer and followed by 
rain, must be either a change in one of these, or in the other, or in 
both, We might, then, even in the absence of any other evidence, 
form a reasonable presumption, from the invariable presence of both 
these elements in the antecedent, that the sequence is probably not 
an ultimate law but a result of the laws of the two different agents, 
a presumption only to be destroyed when we had made ourselves so 
well acquainted with the laws of both as to be able to affirm that 
those laws could not by themselves produce the observed result. 1 

1 Ct Mill, Logic, III, xvi, ft 6. 


6. The Meaning of " Law ". 

A great deal has been written about the precise significance of 
the term "Law", and as objection is often raised to its use in 
scientific investigation, a few remarks on the subject will not be 
out of place. 

According to Sidgwick, "Laws'" may be defined as Rules of 
Conduct which we are morally bound to obey; or, more briefly, 
commands imposed by Rightful Authority. 1 

"It is essential to the idea of law that it be attended with a 
sanction; or, in other words, a penalty or punishment for dis- 
obedience." 2 

Our human laws, says Froude, are but the copies, more or less 
imperfect, of the eternal laws, so far as we can read them, and 
either succeed and promote our welfare, or fail and bring confusion 
and disaster, according as the legislator's insight has detected the 
true principle, or has been distorted by ignorance or selfishness. 

The eminent jurist, Blackstone, regarded "the law of gravita- 
tion, the law of nature, and the law of England", as different 
examples of the same principle, as rules of action or conduct im- 
posed by a superior power on its subjects. The Creator " endued 
matter with a principle of mobility, and established certain rules 
for the perpetual direction of that motion; so, when he created 
man, he laid down certain immutable laws of human nature". 3 

But Austin, the great writer on jurisprudence, insisted, with 
much energy, on the necessity for a distinction; he pointed out 
that some of these laws are commands, while others are not com- 
mands. The so-called laws of nature are not commands; they are 
uniformities which resemble commands only in so far as they may 
be supposed to have been ordered by some intelligent being. But 
they are not commands in the only proper sense of the word, they 
are not addressed to reasonable beings who may or may not will 
obedience to them. Laws of nature are not addressed to anybody, 
and there is no possible question of obedience or disobedience to 
them. Austin pronounces these as laws improperly so called. 

But law in the scientific sense has acquired a position of its own 
from which it is impossible to dislodge it; and it involves none 
of the ambiguities and confusions against which Austin protested. 
The conceptions of law by the jurist and by the man of science are 

i Method of Ethics, p. 269. a A. Hamilton, Federalist, pp. 210-5. 

* Blackstone, Extracts, p. 10. 


now entirely distinct. 1 We may regard the word law in its scientific 
sense to be a borrowed metaphor; a law in the judicial sense has the 
characteristic of uniformity, and it is from this characteristic alone 
that " law " can be employed to signify order in nature. 2 


i. What an Hypothesis is 

In the earlier years of the last century, a Manchester school- 
master named John Dalton, who had undertaken an investigation 
into the chemical composition of various substances, analysed two 
gases, olefiant gas and marsh gas, both of which consist of carbon 
and hydrogen, and obtained the following results: 

Olefiant gas, 85*7 % of carbon and 14*3 % of hydrogen. 
Marsh gas, 75 % of carbon and 25 % of hydrogen. 

On comparing these numbers, he found that the ratio of carbon to 
hydrogen in olefiant gas is 6:1, whereas in marsh gas it is 3:1 or 
6:2. The mass of hydrogen, combined with a given mass of carbon, 
is therefore exactly twice as great in the one case as in the other. 
This research was followed by those on the composition of the 
oxides of carbon and nitrogen. In all these compounds a regularity 
of composition was found, and the uniformity led Dalton to formu- 
late the empirical law of " Multiple Proportions ". 

Dalton now cast about for an explanation of the composition of 
matter, an explanation which would entail this formulated law as 
a mere consequence. He therefore made the assumption that all 
elements consist of very minute indivisible particles, termed atoms, 
having a definite weight; that the atoms of each elementary 
substance are alike among themselves and are different from the 
atoms of every other element; that the atoms of a chemical com- 

i Ed. Robertson, Ency. Brit , xiv, p 335. As Dr. Robertson points out, the opposed con- 
ceptions are still entangled in the field of political economy. Some people speak of certain 
economical principles as if they were laws of nature, and any measures that would violate 
these principles are regarded as particularly heinous. 

Cf. Bain, Logic, vol. ii, p. 9. See also Welton, Logic, vol. ii, p. 200. Professor Wei ton 
objects to the term "empirical laws" altogether; he thinks that the generalizations are too 
loose, and express no necessity, and that therefore the term " law" ia out of place. 


nothing, or it may be a perfect and conclusive induction. In the 
example given, the essence of the supposed relation is the manage- 
ment of a b asiness by a few persons specially chosen from amongst 
the much larger number actually interested. Now some may con- 
tend that this circumstance, with its various consequences, is the 
chief factor in determining all the effects which make up what we 
call good or bad administration. If they can establish this, their 
argument has the force of a rigorous induction; if they cannot, they 
have failed in proving' the analogy between the two cases! 

$But it is more usual to extend the name of analogical evidence 
to arguments from any sort of resemblance, provided they do not 
amount to a complete induction. "Two things resemble each other 
in one or more respects; a certain proposition is true of the one; 
therefore it is probably true of the other." The distinction between 
analogy^ and induction is, then, that in the case of a complete in- 
duction, by due comparison of instances it is established that there 
is an invariable conjunction between the former points of resemblance 
and the latter; but in what is called analogical reasoning, no such 
conjunction has been made outj An argument from analogy really 
amounts to this: a fact m, known to be true of A y is more likely 
to be true of B if B agrees with A in some of its properties (even 
though no connection is known to exist between m and those pro- 
perti^s), than if no resemblance at all could be traced between B and 
any other thing known to possess the attribute m. 1 

Suppose, for instance, we infer that there are probably inhabi- 
tants (m) in the moon (B) because there are inhabitants on the 
earth (A). Now the moon resembles the earth in being a solid, 
opaque, nearly spherical body; appearing to contain, or to have 
contained, active volcanoes; receiving heat and light from the sun 
relatively in about the same quantity as our earth; revolving on its 
axis; and obeying the laws of gravitation. If this were all that was 
known of the moon, the existence of inhabitants in that luminary 
would derive from these various resemblances to the earth a fairly 
high degree of probability. 

But any dissimilarity between A and B furnishes a counter- 
probability. ' There will b$ a competition between the known point* 
of agreement and the known points of difference. The moon, for 
instance, differs from the earth in being smaller, in having its sur- 
face more unequal and apparently volcanic throughout, in having 
(at least on that side next the earth) no atmosphere sufficient to 

* See Mill, Book III, ch. xx, 1, 2. 


refract light, no clouds, and presumably no water. These differ- 
ences might perhaps balance the resemblances, so that the analogy 
would afford no presumption either way. But considering that 
some of the circumstances which are wanting on the moon are 
among those which, on the earth, are indispensable to animal life, 
we are forced to conclude that if there is animal life in the moon, it 
must be an effect of causes totally different from those on which it 
depends here. But the important point to notice is the competition 
between analogy and diversity. A probability arising out of points 
of agreement may be cancelled, or at all events greatly affected, by 
known differences; and it is often enormously reduced by the large 
element of the unknownjJ 

2. Points of Resemblance must be Weighed, not 


It is, however, necessary to bear in mind that, in analogy, as 
indeed in inference generally, the mere number of points of resem- 
blance may be of little importance; such points ought to be weighed 
not counted* The pbints of resemblance contain no common factor 
which admits of any form of mathematical treatment. As 'Pro- 
fessor Weltoh says, properties are not isolated or separate indi- 
vidualities which we can count and enumerate as we can balls and 
books. 3 - There is, in fact, no pbpular error frcto which the student of 
Science must more resohitely shake himself free than the notion that 
resemblance and differencd can be estimated as un "amount". A 
resemblance or difference is great or small not according either to its 
power of striking the observer's notice, or to the number of "points" 
(or details) into which it may be analysed, but according to the 
importance of its details in regard to the matter in hand. 4 

3. "Essential" Resemblance 

There is a danger in all analogical argument that the resem- 
blance between the cases supposed to be analogous is only a super- 
ficial one; or even perhaps that the resemblance, though on the 
whole real and deep, is not essential for the purpose intended. So 
far as an "argument professes to rest on analogy, we must first ascer- 
tain, if possible, the exact points of resemblance and difference, and in- 
quire whether the resemblance hafs>any right to be considered essential.? 

i Cf. Mill, to. 2, 3; Bain, Logic, vol. ii, p. 147. 

Cf. Bosanquet, Logic, vol. ii, p. 90. Cf. Welton, Logic, vol. ii, pp. 76-80 

See Sidgwick, Process of Argument, p. 194. Cf. Sidgwick, Fallacies, p. 263. 


To illustrate this point, Mr. Sidgwick makes use of the argument 
sometimes employed against Sunday closing, that, since the upper 
classes have their clubs open on that day, it would be unfair to 
deprive the poor of their only places of resort and refreshment. 
It is clear at once that we have here a case of double analogy, 
"essential resemblance" being considered to exist (1) between clubs 
and public-houses, and (2) between the upper classe ( s and the lower. 
Now "essential resemblance" means that, for the purposes imme- 
diately in view, we may neglect points of difference; but if we do 
this we begin to generalize. If we neglect points of difference 
between clubs and public-houses, or between one class of men and 
another, we speak of them as members of some wider class. In the 
case of clubs and public-houses, it is the fact of their being places of 
" resort and refreshment " that is considered essential. And although 
the key to the analogy between the upper and lower classes is not 
expressly given, no doubt some such maxim as that " the law is no 
respecter of persons" is implied. If, then, this account of the 
analogy is a correct one, if it is only as being places of resort and 
refreshment that public-houses arc to be kept open for the benefit of 
the poor in their sole capacity of citizens of the State, we imply the 
generalization, "all citizens of the State are equally entitled to their 
places of resort and refreshment". By means of this, if true, the 
original proposition may now\bc deductively proved. 1 

Although analogy rarely ^ives more than a slight presumption of 
Proof, it is more widely used in common discourse than any other 
form of argument; and even for purposes of Proof as well as for 
purposes of Inference. This seems to be due to the slackness with 
which our examination of evidence is commonly carried on. It 
is so much less trouble to see that two things bear a " striking 
resemblance" than to discriminate accurately how far the resem- 
blance really goes, and the points wherein they differ. There is 
probably nothing that is more characteristic of the higher intellect, 
as contrasted with the lower, than its greater power of discrimi- 
nating, that is, of seeking points of difference. Knowledge begins 
with a vague blur, which gradually becomes distinct. The trained 
eye, the analytic mind, is always able to detect finer shades of 
difference than are visible to the multitude; it is, in fact, neglect of 
differences that marks the ruder nature. 2 Of course, any neglect of 

i See Sidgwick, Fallacies, pp. 254-6. 

3 This, perhaps, requires some qualification. For instance, the remarkable forest-lore ol 
the Red Indian, or the equally remarkable knowledge of animal spoors shown by the 7.nlu, 
be attributed to an intelligent observation and an appreciation of minute differenced 


real resemblance would result in serious error, but the inducements 
to over-generalize are usually much stronger than those to indulge 
in excessive hair-splitting. And it is always less trouble to avoid 
distinguishing, even when we have attained the power. Anything 
that appeals to our idleness, anything that flatters our sense of 
"breadth of view", will invariably meet with a friendly reception. 1 

We see, then, that, in strength, an analogical argument may 
approach, but not reach, a valid induction. The value of such an 
argument increases with the extent of ascertained essential resem- 
blance, and this is determined by a careful comparison of points 
of resemblance and points of difference. We cannot "neglect" 
points of difference until they have been carefully scrutinized; 
should there be essential difference, no analogical inference is likely 
to be acceptable. And if there is a large "unexplored region of 
unascertained properties", in other words, if our knowledge of the 
subject-matter is only slight, the extent of our ascertained essential 
resemblance is, in any case, likely to be so small as to lead to an 
inference of doubtful or no value. 2 

4. Instances of Analogical Inference 

Analogy naturally plays a great part in discovery, often giving 
hints that are followed up in a most fruitful way. There are 
analogies which connect whole branches of Science in a parallel 
manner, and enable us to infer of one class of phenomena what 
we know of another. It has thus happened on several occasions 
that the discovery of an unsuspected analogy between two branches 
of knowledge has been the starting-point for a rapid course of dis- 

No two branches of Science might seem at first sight more 
different in their subject-matter than Geometry and Algebra, and, 
prior to the time of Descartes, they were developed slowly and 
painfully in almost entire independence of each other. But that 
great philosopher showed that every algebraic equation may be 
represented by a geometric curve; and this discovered analogy be- 
that would put an ordinary civilized white man to shame. We are apt to gauge the intelli- 
gence of primitive races by their conception of abstract ideas, coupled with their adaptability 
when confronted with civilizing influences. No doubt, the nobler conceptions of human life 
are totally incomprehensible to the average aboriginal, who, however, is a much more intelli- 
gent person, and possesses far more ral knowledge, than some of those who affect to despise 

* See Sidgwick, Fallacies, pp. 256-8. 

a Cf . Mill, Book III, ch. xx, 2, 3 ; and Bosanquet, Logic, vol. ii, pp. 98-9. 


tween Geometry and Algebra soon led to many new developments 
in mathematical methods. 

Then, again, the different forms of wave-motion provide us with 
striking instances of analogy. All waves, whatsoever be the matter 
through which they pass, obey the principles of rhythmical or 
harmonic motion, and the subject presents a fine field for mathe- 
matical generalization. Each kind of medium will, however, prob- 
ably allow of waves with specific characteristics, so that it is a good 
exercise in analogical reasoning to decide how, in making inferences 
from one kind of medium to another, we must make allowance for 
difference of circumstances. The waves of the ocean are large and 
visible, and there are the yet greater tidal waves which extend 
round the globe. From these we pass to waves of sound, varying 
in length from about 32 ft. to a small fraction of an inch. If, now, 
we can imagine the fortieth octave of the middle C of a piano, 
we reach the undulations of yellow light, the ultra-violet being 
about the forty-first octave. Thus we pass from the obvious to the 
obscure. Yet the same phenomena of reflection, interference, and 
refraction, which we find in some kinds of waves, may be expected 
to occur, mutatis mutandis, in other kinds. But while light travels 
186,000 miles a second, sound in air travels only 1100 ft. in the 
same time, that is, nearly a million times as slowly. We are, there- 
fore, prepared to find great differences of some kind, both in the 
form and in the character of the vibrations. 

In Astronomy, too, analogy has played an important part. 
When the scientific world was divided in opinion between the 
Copernican and Ptolemaic systems, Galileo discovered, by the use 
of the telescope, four small satellites revolving round Jupiter. The 
analogy from this miniature planetary world was irresistible. Then 
our speculations concerning the physical conditions of the planets 
and their satellites depend largely upon analogies. We do not hesi- 
tate to infer that the moon has mountains and valleys, and we infer 
with considerable probability that Mars has Polar seas. These are 
comparatively safe inferences, but speculations have also been made 
on the existence of life in other planets. Huyghens even went so 
far as to enter into an inquiry whether the inhabitants of other 
planets would possess reason and knowledge of the same sort as 
ours; and he concluded that, although their intellectual power 
might be different, they would at least have the same Geometry if 
they had any at all. Laplace entertained a strong belief in the 
existence of inhabitants in other planets, considering that the benign 


influence of the sun would tend to be the same in the case of other 
planets as in the case of the earth. Even if it be objected that, in 
certain planets, the extreme heat or the extreme cold would render 
life, as we know it, impossible, it has to be remembered that many 
metals and other elements never found in organic structures are 
yet capable of forming compounds with substances of vegetable or 
animal origin; and it is therefore quite within the bounds of possi- 
bility that creatures formed of different yet analogous compounds 
(compared with those of earth creatures) might exist in tempera- 
tures vastly different from ours. Still, we must admit that all such 
speculations rest on weak analogies, and are hardly admissible 
within the portals of true Science. Nevertheless, as Jevons points 
out, such speculations are far more reasonable and acceptable than 
dogmas which assert that the thousand million of persons upon the 
earth, or rather a small fraction of them, are the sole object of care 
of the Power which designed this limitless Universe. 1 

5. Illegitimate Analogy 

In public speaking, analogy is often put forward to raise a vague 
presumption; arid it may be done in such a manner that, if objec- 
tions should be raised, it remains easy to claim that only an illustra- 
tion was intended, and to grant with much candour that possibly as 
an illustration it fails to fit the case exactly; a process which closely 
resembles the parliamentary practice of first using and then with- 
drawing an offensive expression. The words " because ", or " for ", 
or "since" are, as a rule, omitted by the speaker; the connection 
will be readily supplied, as every experienced rhetorician knows, 
by any average audience, and being thus voluntarily supplied, 
will probably be less exposed to immediate criticism. Whately, for 
example, did not write "Inductive Logic can never be a rival to the 
Aristotelian Logic, since a plough can never be substituted for a 
flail"; but he wrote that Inductive Logic "would not have the same 
object proposed with the Aristotelian Logic; nor be in any respect 
a rival to that system. A plough may be a much more ingenious 
and valuable instrument than a flail, but it can never be substituted 
for it." 2 Such a rhetorical device often comes perilously near the 
border-line of intentional deception. 

* See Jevons, Prin. of Set., pp. 627-41. 

a It should be noticed that this is not given as an instance of necessarily faLe analogy. It 
is given as an instance of the usual method of getting an analogy (true or false) accepted 
by an audience. It it usually difficult to decide whether the analogy is really relied on as 


Proverbs, again, are frequently employed in arguing from a 
shadowy resemblance. Any "striking" analogy will so easily pass 
muster that proverbs can always be freely and safely used. To 
assume that some case comes under some well-known proverb, with- 
out a shadow of evidence to show that it does so beyond what may 
be gathered from the crudest superficial inspection, is, with some 
people, quite a favourite practice. 1 

6. Hypotheses Suggested by Analogy 

Hypotheses are very frequently suggested by analogy. Even 
the simplest phenomenon may present so many points that suggest 
comparison, that we often have a choice from among many hypo- 
theses. Analogy has been aptly compared to a guide-post. 2 

Although the cases in which analogical evidence affords in itself 
any very high degree of probability are only those in which the 
resemblance is essential and extensive, yet there is no analogy, how- 
ever faint, which may not be of the utmost value in suggesting 
experiments or observations that may lead to more positive conclu- 
sions. We may feel that it is impossible to accept as positive truths 
any hypotheses which are unsusceptible of being ultimately brought 
to the test of actual induction. Yet " any hypothesis which has so 
much plausibility as to explain a considerable number of facts, helps 
us to digest these facts in proper order, to bring new ones to light, 
and make experimenta cruets for the sake of future inquiries". If an 
hypothesis both explains known facts and has led to the prediction 
of others previously unknown, and since verified by experience, the 
analogy which extends so far may probably extend further, and 
nothing is more likely to suggest experiments tending to throw 
light upon the real properties of the phenomenon than the follow- 
ing out of such a hypothesis. But to this end it is by no means 
necessary that the hypothesis be mistaken for a scientific truth. 
That illusion would be an impediment to the progress of real know- 
ledge. Yet analogy should readily bo allowed to play its part in 
bringing up new phenomena for comparison with the old; an hypo- 
thesis may thus receive additional strength, and be one step nearer 

eyidence, or genuinely and legitimately put forward as an illustration merely, or to point a 
quaint and semi-serious fallacy. A still more difficult question arises when we attempt to 
fix the line between the metaphorical and the direct use of words. See Hidgwick, Fallacies, 
pp. 263-4. The worthy Archbishop was rather unfortunate in his choice of a figure, and 
could hardly have foreseen how soon tho flail was to be relegated, with Aristotelian Logic, to 
a museum 

i Cf. Sidgwick, Fallacies, p. 266. Cf. Jevons, p. 630; and Mill, III, xx, 3. 

(C415) 19 


scientific truth. On the other hand, it may be weakened, and perhaps 
even destroyed. 1 " 


i. General Notions 

Let us suppose- that there are three perfectly sincere persons, 
A, B, and C, and that, on some particular subject, A holds one 
opinion, B another, and C has no opinion at all. One of them, say 
A, proceeds to burn B arid C, or to hang them, or imprison them, 
or, at the least, to libel them in the newspapers, according to what 
the feelings of the age will allow; the pretext being that A, B, and 
C are morally inexcusable for not believing what is true. If A is 
shown the absurdity of his own arguments, he promptly contends 
for a sort of absolute truth external to himself, which B or C, he 
declares, might attain if they pleased. Now let it be granted for a 
moment that the intellectual constitution of A, B, and C is precisely 
the same, and that there is ground for declaring that any difference 
of opinion resulting from the same arguments must be one of moral 
character. If, then, it were quite certain A is right, and if it be 
granted that State punishments are reformative of immoral habits 
as well as repressive of immoral acts, A might be justified in using, 
with B and C, methods which are reformative of moral character, 
even if these methods amounted to direct persecution. But, as De 
Morgan says, anyone who is able to sec with the eyes of his body 
that the same weight will stretch different strings differently, and 
with the eyes of his mind that the same arguments will affect 
different minds differently by difference not of moral but of in- 
tellectual construction will also see that the only legitimate process 
of effecting a change of conviction must be that of argument and 
discussion. 3 

Intolerance arises, as a rule, from inability to see how differently 
different persons are affected by real probabilities. It therefore be- 
comes interesting to ask what it is that mathematicians, in their 

i Cf. Mill, to. 2 See De Morgan, Essay on Probabilities, pp. 7, 8. 

8 The common assertion that opinions dangeious to the existence of public order must not 
be promulgated, is hardly germane to our subject. 


theory of Probabilities, actually number, measure, and calculate. Is 
it belief, or opinion, or doubt, or knowledge, or chance, or necessity, 
or what? Does probability exist in the things which are probable, 
or in the mind which regards them as such? 

Now it must be clear, at the outset, that the subject of the theory 
cannot be "chance". Chance does not exist in Nature. The exact 
form of every pebble on the seashore is the resultant effect of a 
succession of definitely acting antecedents. Chance is merely an 
expression, as Laplace remarked, for our ignorance of the causes in 
action, and our consequent inability to predict the result or to bring 
it about infallibly. In Nature, "all is causal, nothing is casual"; 1 
in her laws there can never be any uncertainty. Such deficiency as 
there may be must lie wholly in our knowledge. 

Clearly, then, probability is no inherent property of any set of 
circumstances, it is a feeling of the mind. 2 This may be seen from 
the fact that different minds may regard the very same event at the 
same time, with widely different degrees of probability. A steam 
vessel, for instance, is missing, and some persons believe that she 
has sunk in mid-ocean; others think differently, though all have 
the same scanty information concerning her last-known movements 
But in the event itself there can be no uncertainty; the vessel has 
sither sunk or not sunk, and no amount of subsequent discussion of 
the probable nature of the event can alter the fact. Yet the prob- 
ability of the event will really vary from day to day and from mind 
to mind, according as the slightest information is gained regarding 
the vessels met at sea, the weather prevailing there, wreckage found, 
and so on. Probability, then, belongs wholly to our minds, to the 
light in which we regard events, the occurrence or non-occurrence 
of which is, in themselves, absolutely certain. 3 

2. The Theory of Probability deals with Quantity of 


Jevons disagrees with De Morgan, who says that " by degree of 
probability we really mean or ought to mean degree of belief"; and 
with Donkin's opinion that probability is "quantity of belief"; for, 
says Jevons, " the nature of belief is not more clear to my mind than 
the notion which it is used to define. The theory of probability 

i See Welton, Logic, vol. ii, p. 165. 2 De Morgan, op. cit. p. 7. 

Ct Jevons, Prin. of Set., pp. 197-8; Lotze, Logic, p. 367; and Welton, Logic, vol. ii, 
t>p. 166-70. 


does not measure what the belief is but what it ought to be." 1 Venn also 
refers to the difficulty of obtaining any measure of the amount of 
our belief. In the first place, there is the disturbing influence pro- 
duced on the quantity of belief by any strong emotion or passion; 
and in the second place, there is the extreme complexity and variety 
of the evidence on which our belief of any proposition depends. 
It follows, therefore, that our actual belief at any given moment is 
one of the most fugitive and variable things possible, so that we can 
scarcely ever get sufficiently clear hold of it to measure it. Directly 
we begin to think of the amount of our belief, we have to think of 
the arguments by which it is produced, in fact, these arguments 
will intrude themselves without our choice. As each in turn flashes 
through the mind, it modifies the strength of our conviction. 2 

Jevons prefers to avoid the term "belief" as being obscure, and 
he regards the theory of probability as dealing with quantity of 
knowledge. An event is only probable, he says, when our knowledge 
of it is diluted with ignorance, and exact calculation is needed to 
discriminate how much we do and do not know. The theory of 
probability measures the comparative amounts of our knowledge 
and ignorance. 3 

3. Quantitative Aspects of the Theory 

" When we say that the probability that an event will happen 
in a certain way is 1/n, what we mean is that the relative amounts 
of knowledge and ignorance we possess as to the conditions of 
the event justify the amount of expectation. The event itself will 
happen in some one definite way, exactly determined by causation; 
the probability does not determine that, but only our subjective 
expectation of it." "It is from this combination of knowledge and 
ignorance that the calculation of probability starts." 4 

Fundamentally, the theory of probability consists in putting 
similar cases on an equality, and distributing equally among them 
whatever knowledge we possess. Throw a penny into the air, and 
consider what we know in regard to its way of falling. We know 
that it will certainly fall upon a side, so that either head or tail will 
be uppermost; but as to whether it will be head or tail, our know- 
ledge is equally divided. Whatever we know concerning head, we 
know also concerning tail, so that we have no reason for expecting 

i Jevons, Prin. of Sci. , p. 199. 2 Cf . Venn, Logic of Chance, pp. 126-7. 

Jevons, t&. pp. 199-200. * Cf. Welton, Logic, vol. ii, pp. 166-70. 


one more than the other. The least predominance of belief to 
either side would be irrational; it would consist in treating un- 
equally things of which our knowledge is equal. We must treat 
equals equally. 1 

The theory does not require that we should first ascertain by 
experiment the equal facility of the events we are considering. 
The more completely we could ascertain and measure the causes 
in operation, the more would the events be removed from the 
sphere of probability. The theory comes into play where ignorance 
begins, and the knowledge we possess requires to be distributed 
over many cases. Nor does the theory show that the coin will fall 
as often on the one side as the other. It is almost impossible that 
this should happen, because some inequality in the form of the 
coin, or some uniform manner in throwing it up, is almost sure 
to occasion a slight preponderance in one direction. But as we do 
not previously know in which way a preponderance will exist, we 
have no reason for expecting head more than tail. 2 

Suppose that, of certain events, we know that some one will 
certainly happen, and that nothing in the constitution of things 
determines one rather than another; in that case, each will recur, 
in the long run, with a frequency in the proportion of one to the 
whole. Every second throw of a coin, for example, will, in the 
long run, give heads. Every sixth throw of a die will, in the long 
run, give ace. 8 

The method which we employ in the theory consists in calculat- 
ing the number of all the cases or events concerning which our 
knowledge is equal. 4 

Let us suppose % that an event may happen in three ways and 
fail in two ways, and that all these ways are equally likely to occur. 
Clearly, in the long run, the event must happen three times and fail 
two times out of every five cases. The probability of its happening 
is therefore f , and of its failing, f . Thus the probability of an event 
is the ratio of the number of times in which the event occurs, in the 
long run, to the sum of the number of times in which the events of 
that description occur and in which they fail to occur. 

An event must either happen or fail. Hence the sum of the 
probabilities of its happening or failing is certainty. We therefore 
represent certainty by unity. 

i Cf. Jevons, Prin. cf Sci. t p. 200. 2 cf. Jevons, op. cit. p. 201. 

* Cf. Bain, Inductive Logic, p. 91. 4 Jevons, op. cit p. 201. 


4- Simple Mathematical Considerations 

The usual algebraic definition of probability is as follows. If an 
event may happen in a ways and fail in b ways, and all these ways 

are equally likely to occur, the probability of its happening is ., 

d + u 

and the probability of its failing is ,.. (In mathematical works, 

the word "chance" is often used as synonymous with probability.) 

It should be noticed that H - = 1 : also that 1 - 

a + b a + b 


*L-~ = Thus, if p be the probability of the happening of 

a + b a -f b 

an event, the probability of its not happening is 1 -p. 

When the probability of the happening of an event is to the 
probability of its failure as a is to b, the odds are said to be a to b 
for the event, or b to a against it, according as a is greater or less 
than b. 

Suppose that 2 white, 3 black, and 4 red balls are thrown pro- 
miscuously into a bag, and a person draws out one of them, the 
probability that this will be a white ball is |, a black ball,, f , and a 
red ball, *. 

A few simple problems will help to illustrate the principles in- 

1. What is the probability of throwing 2 with an ordinary die? 
Any one face is as likely to be exposed as any other face; there 
are therefore one favourable and five unfavourable cases, all equally 
likely. The required probability is therefore . 

2. What is the probability of throwing a number greater than 
two with an ordinary die ? Obviously there are 4 possible favourable 
cases out of a total of 6. The probability is therefore or f . 

3. A bag contains 5 white, 7 black, and 4 red balls. What is 
the probability that 3 balls drawn at random are all white? We 
have 16 balls altogether. The total number of ways 1 in which 3 balls 
can be drawn is therefore 16 C 3 , and the total number of ways in 
which 3 white balls can be drawn is 5 C 8 . -Therefore, by definition, 
the probability is 5 C 3 / 16 C 3 , that is -g^- 

By a compound event, we mean an event which may be decomposed 
into two or more simpler events. Thus, the firing of a gun may be 

* It is assumed that the reader is acquainted with the elementary theory of Combination! 
and Permutations. 


decomposed into pulling the trigger, the fall of the hammer, the 
explosion of the cartridge, &c. In this example, the simple events 
are not independent, because, if the trigger is pulled, the other events 
will, under proper conditions, necessarily follow, and their proba- 
bilities are therefore the same as that of the first event. Events 
are independent when the happening of the one does not render the 
other either more or less probable than before. Thus the death of 
a person is neither more nor less probable because the planet Mars 
happens to be visible. When the component events are independent, 
a simple rule can be given for calculating the probability of the 
compound event, thus : Multiply together the fractions expressing the 
probabilities of the independent component events. 1 

If, for instance, A occur once in 6 times, its probability is , or 
1 for and 5 against; if B occur once in 10 times, its probability is 
T ^, or 1 for and 9 against. The probability, or relative frequency 
in the long run, of the concurrence of the two is ^, that is, 1 for 
and 59 against. 2 

The justification of the rule may be shown thus. 8 If two dice 
are thrown, the side which the one shows uppermost has nothing to 
do with the side which the other shows uppermost; but each die 
has 6 sides, each of which may fall uppermost, and each of these 
may with equal possibility coincide with any one of the 6 sides of 
the other; there are thus 36 possible cases, and the probability of 
each single one of them is ^ ( = J x ^). 

We may add one or two more problems. 

1. What is the probability of throwing an ace in the first only 
of two successive throws of a single die? Here we require a com- 
pound event to happen, namely, at the first throw the ace is to 
appear, at the second throw the ace is not to appear. The proba- 
bility of the first simple event is -J-, and of the second . Hence 
the required probability is $ ( = ^ x ). 

2. A party of 23 persons take their seats at a round table. 
Show that it is 10 to 1 against two specified individuals sitting next 
to each other. The probability that a given person A is on one side 
of a given person B is -J$; the probability that A is on the other 
side of B is also ^ ; hence, the probability of A being next to B 
is /2 = yY. Thus the odds are 10 to 1 against A and B sitting 

3. Find the probability of throwing 8 with two dice. With 
two dice, 8 can be made up of 2 and 6, 3 and 5, 4 and 4, 5 and 3, 

i Of Jevons, op. cit. p. 204. CI. Bain, Logic, vol. ii, p. 92. Cf. Lotze, Logic, p. 368. 



and 6 and 2, that is 5 ways. The total number of ways is 36. The 
probability is therefore ^\, and the odds 31 to 5 against. 

5. Experience and Theory Compared 

" The Laws of Probability rest upon the fundamental principles 
of reasoning, and cannot be really negatived by any possible experi- 
ence. It might happen that a person should always throw a coin 
head uppermost, and appear incapable of getting tail by chance. 
The theory would not be falsified because it contemplates the possi- 
bility of the most extreme runs of luck." 1 But the probability of 
the occurrence of extreme runs of luck is excessively slight. When- 
ever we make any extensive series of trials, as in throwing a die or 
coin, the probability is great that the results will agree pretty nearly 
with the predictions yielded by theory. Precise agreement must 
not, of course, be expected, for that, as the theory shows, is highly 
improbable. Buffon caused a child to throw a coin many times in 
succession, and he obtained 1992 tails and 2048 heads. The same 
experiment performed by a pupil of De Morgan's resulted in 2044 
tails to 2048 heads. In both cases the coincidence with theory is as 
close as could be expected. Jevons himself made an extensive series 
of experiments. He took 10 coins, and made 2048 throws in two 
sets of 1024 throws each. Obviously, the probability of obtaining 
10, 9, 8, 7, &c., heads is proportional to the number of combinations 
of 10, 9, 8, 7, &c., things chosen from 10 things. The results may 
therefore be thus conveniently tabulated : 

Character of Throw. 



JSei oinl 



10 Heads, Tails 

10 C = 1 




+ 1 

9 1 , 

10 d = 10 




+ 74 

8 2 , 

10 C. 2 = 45 




+ 20 

7 3 

10 C 8 = 120 




+ 6 

6 4 

10 C 4 = 210 





5 5 

10 O 6 = 252 




- 74 

4 6 

10 C 6 =210 





3 7 

10 C 7 = 120 




- 5 

2 8 

W 0g = 45 




+ 6 

1 9 

10 C y = 10 




+ 8 


10 Cio = 1 



- * 






i Jevons, Prin. of Sri., p. 206. 



The present writer repeated the same series of experiments, with 
the following results : 

Character of Throw. 






10 Heads, Tails 

10 C = 1 



+ 1 


10 d = 10 




+ 3 


10 C, = 45 




- 5 

7 3 

10 C 8 = 120 




- 3J 

6 4 

10 C 4 = 210 




+ 13 

6 5 

10 C 6 = 252 





4 6 

10 C 6 - 210 




+ 22 

3 7 

10 C 7 = 120 




- 9 

2 8 

10 C 8 = 45 




- 1 

1 9 

10 C 9 = 10 





lo c lo - i 




+ 2 





The whole number of single throws of coins amounted to 2048 x 10, 
or 20,480 in all, one half of which, or 10,240, should theoretically 
give heads. The total number of heads obtained by Jevons was 
10,352 (5130 in the first series, and 5222 in the second). The 
number obtained by the present writer was 10,234 (5098 in the 
first series, and 5136 in the second). The coincidence with theory 
is in each case fairly close. 1 

6. Inverse Probability 

From the known character of certain events, we may argue back- 
wards to the probability of a certain law or condition governing 
those events. When it is known that an event has happened, and 
that it must have followed from one of a certain number of causes, 
the determination of the probabilities of the different possible causes 
is said to be a problem of inverse probability. 

If, for instance, it was known that a black ball was drawn from 
one or other of two bags, one of which was known to contain 
2 black and 7 white balls, and the other 5 black and 4 white balls, 
what was the probability that the ball was drawn from the first 

Let us suppose a great number, 2N, of drawings to be made; 
there will in the long run be N from each bag. But in N draw- 

i See Jevons, Prin. of Sci., pp. 206-9. It was the writer's intention to perform several 
experiments of this kind ; but if the reader will undertake one such experiment for himself, 
he will probably conclude that one is sufficient to satisfy one person. 


ings from the first bag there are, on the average, f-N which give 
a black ball; and in N drawings from the second bag there are f N 
which give a black ball. Hence, in the long run, f N out of a 
total of f N -f |N black balls are due to drawings from the first 
bag. Thus, the probability that the ball was drawn from the first 
bagis|N/(|N-f |N) = f 1 

The general problem may be thus stated : If it is certain that one 
07' other of the supposed causes exists, the probability that any one does exist 
is the probability that if it exists the event happens, divided by the sum of 
all the similar probabilities. 

If, for instance, there be three boxes, each containing 10 balls in 
all, and respectively containing 7, 4, and 3 white balls, then on mix- 
ing all the balls together we have 14 white ones; and if we draw 
a white ball, that is, if the event happens, the probability that it 
came out of the first box is T 7 T ; which is exactly equal to jVCrV + 
/P -f T \), the fraction given by the rule. 2 

The inverse problem is complex and difficult, but the principle of 
the method is frequently used in cases of scientific investigation. If 
only two, or at the most a few, hypotheses may be made as to the 
origin of certain phenomena, we may sometimes easily calculate the 
respective probabilities. It was thus, as Jevoris points out, that 
Bunsen and Kirchhoff established with a probability almost equal to 
certainty that iron exists in the sun. 3 Then, again, the probability 
has been calculated as to whether the six brightest stars of the 
Pleiades came by accident into such close proximity, Michell's esti- 
mate is that the odds are nearly 500,000 to 1 against casual conjunc- 
tion. 4 Then extremely interesting cases have been worked out in 
regard to the similarity of direction of the orbital motions and axial 
rotations of the planets, and in regard to the near approximation of 
the orbits of the planets to a common plane. The numbers in these 
cases representing the odds are so great as to be altogether beyond 
the comprehension of the non-mathematical mind. Suflice it to say 
that the enormous probability that the constitution of the planetary 
system arose from some common cause, amounts to practical cer 
tainty. 6 

i See C. Smith's Algebra, p. 521. Cf. Chrystal's Algebra, vol. il, ch. xxxvi. 

* See Jevons, Prin. of Sci., pp. 243-4. 

* See Kirchhotf, Researches on the Solar System, i, pp. 18, 19. 
Phil Tram , vol. Ivii, p. 431. 

* Cf Laplace, E>ii>ai Philosophique, p. 65; and Todhunter, History of Theory of Probability \ 
p 543. For details of these and other interesting cases, see Jevons. pp. 244-50. 


7. Simple Rules of the Inverse Method 

Although the general solution of the inverse problem is outside 
tue scope of this work, two useful rules may be mentioned. 

1. To find the probability that an event which has not hitherto been 
observed to fail will Juippen onct more, divide the number of times the 
event has been observed increased ly one, by the same number increased by 

Continued recurrence of an event testifies to the persistence of 
the conditions which produce the event; and even though we do not 
know what these conditions are, yet, as evidence of their existence 
increases, we are justified in expecting more and more strongly 
their continued existence. If, for example, an event has happened 
once, that is one reason for expecting its recurrence. But let us 
put that on one side for a moment. We may now argue that the 
chance of the event riot occurring is in itself just as likely as that 
it will. There are therefore two reasons for expecting the event 
to recur, and only one for expecting it not to recur. The odds for 
its recurrence are consequently '2 to 1, and the probability of the 
event happening again is, by definition, f . So generally, if an event 
has happened m times, and we consider the possibility that it may 
occur again, we have a total number of alternatives of m 4- 2, of 
which m -f 1 are favourable. The probability that the event will 
occur once more is therefore (m H- 1 )/(m + 2). If, for instance, we 
suppose the sun to have risen one thousand million times, the prob- 
ability that it will rise again, on the ground of this knowledge 
merely, is 1, 000,000,001/1, 000,000,002 a probability extremely 
close to certainty. 1 

2. To find the probability that an event which his not hitherto failed 
will not fail for a certain number of new occasions, divide the number 
of times the event has happened increased by one, by the same number 
increased by one and the number of times it is to happen.* 

If, for instance, we suppose the sun to have risen one thousand 
million times, the probability that it will continue to rise for another 
thousand million times is only 1,000,000,001/2,000,000,001, or almost 
exactly |. The probability that it will continue so rising a thousand 
times as long is only about 1/1001 a very low degree of probability. 

We thus see that with wide and uncontradicted experience, the 
probability that an empirical law which summarizes that experience 

t Cf. Lotze, Logic, $ 282 (5); Welton, Logic, vol. ii, pp. 180-1 ; and .Tevons, pp. 257-9 
a Cf. Jevons, Prin. of Sci. t p. 257. 


will hold good in one more case is very high. But we also see that 
extension of the law beyond the realm of actual experience becomes 
increasingly uncertain with increase in the width of that extension. 1 
Of course, without demonstration or decisive experiment, proba- 
bility can never reach absolute certainty. Fermat, for example, 
sought a formula in connection with prime numbers. An examina- 
tion of several instances led him to think that 2 raised to a power 
which was itself a power of 2 would, if increased by unity, result in 
a prime number. Thus, 2 2 + I = 5; 2 4 + 1 = 17; 2 8 + 1 = 57; 
2 16 -h 1 = 65537; all prime numbers. Fermat thereupon concluded 
that there was a great probability of the result being general. Abso- 
lute certainty, however, could only come with demonstration. In 
point of fact, there is a breakdown at the very next step, as Ealer 
showed; 2 82 + 1 = 4,294,967,297, which is the product of 6,700,417 
and 641, and is therefore not prime. 2 

8. The Transmission of Historical Evidence 

Laplace points out that, since the successive powers of a fraction 
less than unity continue to diminish, an event which depends upon 
a series of very great probabilities may at last become extremely 
improbable. " Suppose", he says, 3 "an incident to be transmitted 
to us by twenty witnesses in such manner that the first has trans- 
mitted it to the second, the second to the third, and so on. Sup- 
pose, again, the probability of each testimony to be equal to the 
fraction T 9 ^. The probability of the incident resulting from all the 
testimonies will be (yV) 20 , or less than |", an enormous diminution 
in the probability. Now we all know that the farther news travels 
the more distorted it becomes, but it is extremely doubtful if calcu- 
lation will really help us to decide the degree of trust we may repose 
in a transmitted statement. In the first place we make the large 
assumption that the probability of each testimony is (to take the 
above case) equal to T 9 ^, that is, that a particular person speaks the 
truth 9 times out of 10. Then, again, any given statement is either 
right, or it deviates more or less from the truth; and we might 
assign to it a greater or less degree of credibility according as it 
deviates more or less, supposing it to be possible to measure against 
one another the different amounts of those deviations. But this we 
can seldom do. As Lotze points out, 4 the falsification of a state- 

i Ct Welton, Logic, ii, pp. 180-2. Ct Laplace, Theory of Probabilities, p. 177. 

> Laplace, op. cit. p. 13. * See Lotze, Logic, pp. 370-1. 


meat depends not on the number of times it has been passed on, 
but on the size and sort of errors made in it each time it has been 
passed on. The eyewitness A may or may not have wished to com- 
municate aright what he has rightly observed ; his hearer B has or 
has not understood him aright, or he may have understood him and 
yet desire to hand it on himself in a distorted form; a third person 
C, who intended to distort afresh what he already misunderstood, 
may chance to hit upon the actual truth in what he communicates. 
It is hardly conceivable that the trustworthiness of a communication 
depends, in any regular manner, merely on the number of times it 
has passed from mouth to mouth. 

g. Coincidences which are Casual 

It will not, of course, be thought that the theory of probability 
is ever likely to furnish us with an infallible guide. All that it can 
give is the result in the long run, as it is called, and this virtually 
means an infinity of cases. During any finite experience, however 
long, chances may be against us. Yet the theory is the best guide 
we can have, and, if we follow it, we shall have the best chance of 
escaping error. 

But no rule can be given for discriminating between coincidences 
which are casual and those which are the effects of law. Facts casu- 
ally conjoined are separately the effects of causes, but of different 
causes, and causes not connected by any law. While, therefore, it 
is incorrect to say that any phenomenon is produced by chance, we 
may add that two or more phenomena are conjoined by chance, that 
they coexist, or that the one succeeds the other only by chance. 1 

It is, for example, only by chance that the ratio of the sun's 
diameter to the earth's diameter, the ratio of the mean distance of 
the earth from the sun to the sun's diameter, and the ratio of the 
mean distance of the moon from the earth to the moon's diameter, are 
all very approximately 110 to 1. Curious coincidences often occur 
in historical matters. If, for example, to 1794, the number of the 
year in which Robespierre fell, we add the sum of its digits, the 
result is 1815, the year in which Napoleon fell; the repetition of 
the process gives 1830, the year in which Charles X abdicated. 
Then the Bacon-Shakespeare controversy arose from a number of 
curious coincidences; the Baconian advocates, lacking insight into 

i Cf. Jevons, Prin. ofSci., pp. 261-2; and Mill, Logic, Book III, ch. xvii. (Cf. also ch. xx, 
4, on Joint Action of Causes.) 


scientific method, mistook the casual for the causal. 1 The subject 
of Phrenology affords another instance of the manner in which 
numerous coincidences may mislead the unscientific mind. The 
assumption is made that the outside of the skull is so finely and accu- 
rately modelled to the surface of the brain that it is an exact copy 
of that surface, an assumption which has been absolutely disproved. 
The great majority of phrenologists have had no serious scientific 
training at all; they are mere collectors of casual facts. Many of 
these facts when tabulated suggest, it is true, a rather high degree 
of probability, but this is the only solid claim that can be put 
forward. The work of the phrenologists is of the nature of a series 
of guesses, followed by deduction; it has no scientific basis what- 
ever. Another assumption they make is that the grey matter of 
the brain is divided into a number of regions corresponding to 
certain universal habits, propensities, passions, and so on. This is 
a pure guess on their part; it is not based on scientific know- 
ledge. The greatest living physiologists are at the present time 
laboriously accumulating facts in regard to cerebral localization, 
but an enormous amount of work yet remains to be done before 
we have anything like complete knowledge. Well may the physi- 
ologist regard with amused contempt the phrenologists and their 
absurd pretensions. 

10. Uncertainty almost Inevitable 

If, in estimating the probability of events, the only data we have 
are the mere frequency of events in the past, our inferences are 
necessarily much more precarious than they would be if they could 
be deduced from an accurate knowledge of the frequency of the oc- 
currence of the causes of the events. But it is a fact that, in almost 
all cases in which chances admit of estimation sufficiently precise 
to render their numerical appreciation of any practical value, the 
numerical data are not drawn from knowledge of the causes, but 
from experience of the events themselves. The probabilities of life 
at different ages; the probabilities of recovery from a particular 
disease; the chances of the destruction of property by fire; the 
chances of the loss of a ship on a particular voyage; are derived 
from statistics on mortality, returns from hospitals, registers of fires, 

* For instance, the word honor ificabilitudinitatibus (Love's Labour 's Lost, V, i), which 
yields the anagram, "Hi ludi orbi tuiti F. Baconis nati", has given rise to much misplaced 
ingenuity of computation. (See The Associated Accountants' Journal.) 


of shipwrecks, &c. ; that is, from the observed frequency not of the 
causes but of the effects. In all these classes of facts, the causes 
are not amenable to precise observation, and whatever inferences we 
draw are necessarily drawn from frequency of effects. 1 

The element of uncertainty should always be borne in mind. 
If, for example, we are considering the prospect of a given particular 
man living another year, and we know from statistics that 9 out 
of 10 of his age do survive, it does not necessarily follow that he 
will; we say that our belief in his surviving is diminished from 
certainty to -j^. Not only is there an element of uncertainty in the 
empirical law that has resulted from generalization, but there is the 
further element of uncertainty in the inference we draw from such 
a law. 2 

A curious prejudice exists in some quarters against the study of 
the theory of probability, it being considered that such study is 
likely to foster a love of gaming and gambling. There may or may 
not be some truth in this, but the very great practical value of the 
theory must not be lost sight of. The whole business of insurance 
of all kinds is based upon it. And as regards Science, not only is 
the exactness of our present knowledge of Astronomy largely owing 
to the applications of the theory, but the theory acts as a fine correc- 
tive to false impressions and doubtful hypotheses in all branches of 
Science. Although its direct results may not be very obvious, its 
final importance cannot be denied. 3 


i. Precise Measurement fundamental in Science 

The ultimate aim of Science is to reduce the complexities of 
nature to their fundamental elements, and to express in an exact 
and quantitative form the relations amongst those elements. The 
more that exact measurement enters into any branch of Science, the 

1 Cf. Mill, Logic, Book IIT, ch. \viii, 3. 

2 Cf. Venn, The Logic of Chance, pp. 192-3 

* See De Morgan, op. cit. pp. 18-19. The reader who feela interested in the subject should 
turn to the works of De Morgan, Venn, Laplace, and Quetelet. See also Sir J. Herschel'i 
paper on "Estimation of Skill in Target-shooting". 


more highly is that branch developed. It is for this reason that 
Chemistry and Physics are so far in advance of Botany and Geology. 
And the reason why we can obtain so much clearer notions of, for 
instance, an area or a weight, than of, say, wisdom or chivalry, is 
because the former are measurable, the latter not. It is of the first 
importance in Science that we should, whenever possible, obtain 
precise quantitative statements of phenomena, 1 and thus we see 
why it is that the introduction of a new scientific instrument so 
often leads to a marked advance in our knowledge. 2 There is no 
doubt that with the instruments now available we are able to take 
note of quantities at least a million times as small as in the time of 
the Chaldeans. 3 

The great majority of questions in physical Science are complex, 
and an investigation often includes a number of steps, any one of 
which may suddenly lead to one or more subsidiary investigations. 
The kinds of questions likely to arise are so varied that no general 
rules of guidance can be laid down, though occasionally the sequence 
best followed will be fairly obvious. Suppose, for instance, we 
have to make an investigation into the question of the solution of 
common salt in water. The first point that would, perhaps, suggest 
itself would be, Does the solubility vary with the temperature? 
Then we should probably go on : Does the quantity of salt dissolved 
increase or diminish with the temperature? What is the amount of 
variation? Is there a law of variation, and, if so, what is it? Do 
different salts show different results? Does solubility vary with the 
pressure? Does the presence of other salts affect the result? Will 
different solvents lead to the same or to different results? And so 
one question leads to another, exact measurement being necessary 
at nearly every stage. 4 

2. Standards and Units 

The immediate result of every actual measurement is to give us 
a purely numerical ratio, namely, that between the magnitude to be 
measured, and a certain other magnitude, which should, when pos- 
sible, be a fixed standard unit or magnitude. 

When the standard unit is greater than the magnitude to be 
measured, we often divide the unit, until we get a magnitude equal 
to that measured. To measure minute objects, for instance, we use 

i Cf. Henchel, Phil., pp. 122-3; De Morgan, Logic, p. 176 ff.; Welton, Logic, If, pp. 160-3. 
a Cf. Jevons, Prin. of Set'., p. 270. ib. p. 271. ib. pp. 278-282. 


the micrometer screw, and so divide the inch or centimetre. But 
frequently we have to multiply the unit until we get a magnitude 
equal to that to be measured; for instance, in ordinary measurements 
with the footrule or chain. 

In other cases we multiply or divide a magnitude until we get 
what is equal to the unit or easily comparable with it. To measure 
the velocity of a falling body, for example, we diminish the velocity 
by letting the body roll down an inclined plane. 

A third method consists in multiplying both magnitudes to be 
compared until some multiple of the first is found to coincide very 
nearly with some multiple of the second. This method of repeti- 
tion is naturally employed whenever quantities can be repeated or 
correctly repeat themselves. The oscillation of the pendulum, for 
example, admits of almost endless repetition, and since the force of 
gravity never ceases, there is no interval between the oscillations. 
It is thus possible, by comparing the oscillations of two exactly 
similar pendulums, to compare the force of gravity at the top and 
at the bottom of a mine; and by the aid of electric- clock signals 
this can be done with remarkable precision. In an experiment at 
Harton Colliery, Airy was able to measure a total difference in th 
vibrations at the top and bottom of the shaft of only 2*24 seconds 
in 24 hours, with an error of less than one-hundredth of a second, 
or one part in 8,640,000 of the whole day. 1 

Exact quantitative laws can occasionally be obtained without in- 
strumental measurements. For instance, we learn that sounds of 
different pitch have exactly equal velocities, by observing that a 
peal of bells is heard harmoniously at any distance to which the 
sound penetrates. This could not be the case if one sound overtook 
the other. 

Experiments are sometimes devised for the purpose of indirectly 
measuring quantities, which, in their extreme greatness or smallness, 
are beyond the powers of our senses. Thus Faraday measured the 
thickness of gold-leaf by weighing 2000 leaves 3f inches square; 
the weight was 384 grammes. From the known specific gravity of 
gold, it was easy to calculate that the average thickness of the leaves 
was less than a quarter of a millionth of an inch. 2 

Systematic measuring on an extensive scale often involves a 
large number of separate determinations, and care therefore has to 

1 Jevons, Prin. of Sci., p. 291; and cf. Phil. Trans. , vol. cxlvi. 

2 Faraday, Chem. Res., p. 293. Gold leaf may be beaten out so fine that the thickness of 
a single sheet is only aorfooo P&rt of an inch, or about one-sixth part of the length of a wave 
length of green light 

(0415) 20 


be taken to adopt a system whereby any initial error is not only 
not increased in subsequent measurements, but actually detected, if 
possible. For instance, in the trigonometrical survey of a country, 
the most scrupulous care is taken to ensure the accuracy of the base- 
line; few laymen can appreciate the enormous trouble taken over 
chis particular measurement. A principal triangulation now fixes, 
with the utmost possible accuracy, the relative positions and dis- 
tances of a few points. A minor triangulation refers every promi- 
nent hill or village to one of the principal points, and thus the 
details are filled in by reference to the secondary points. Again, in 
ascertaining the specific gravities of substances, all gases are referred 
to atmospheric air at a given temperature and pressure; all liquids 
and solids are referred to water. We therefore require to compare, 
with the greatest accuracy, the densities of water and air, and the 
comparative densities of any two substances whatever can then be 

Few measurements of any kind are exact to more than six 
significant figures, and it is very seldom that even this degree of 
accuracy can be hoped for. Time is the magnitude which until 
recent years seemed capable of the most exact estimation. Astro- 
nomers have been able to ascertain the ratio of the mean solar to 
the sidereal day to the 8th place of decimals, or to one part in 
100,000,000. Thirty years ago, this was probably the most accu- 
rate result of measurement in the whole range of Science. But 
determinations of weight seem now to come first in exactness, and 
balances have been constructed to detect one part in at least 
250,000,000.! Determinations of length are open to much error in 
the junction of the measuring bars. Even in measuring the base- 
line of a trigonometrical survey, where extraordinary care is taken, 
the accuracy generally attained is only that of about one part in 
60,000, or one inch in the mile. But Sir J. Whitworth was able to 
detect (by the use of a remarkably well turned screw) a change of 
dimension in a bar, amounting to no more than one-millionth of an 
inch. 2 Electrical measurements, too, are now carried out with an 
extraordinary degree of exactness 

1 For instance, the balance constructed by Rueprecht for the International Bureau of 
Weights and Measures. 

2 See Jevons, Prin. of Sci. t pp. 270-30-1. Cf. also rhil. Tram., vol oxlvi, pp 330-1 ; First 
Annual Report of the Mint, p. 106; Watts, Dictionary of Chentiittr!/, vol. i, p. 483; Brit. 
Assocn. Report, 1856, Address of President of Mech. Section ; Pro. l\oy Soc , vol. Ixxxiii, 
p. 81, on JDr Tutton's reference to Mr. Grayson's line rulings of 40,000 to the inch. 


3. Empirical Formulae 

In quantitative experiments we endeavour to obtain the relation 
between the different values of one quantity which is varied at will, 
and another quantity which is caused thereby to vary. The former 
may be called the variable, and the latter the variant. The variable 
is that one of the two measured quantities which is an antecedent 
condition of the other. When we are examining the effect of heat 
in expanding bodies, heat 1 is the variable, length the variant. If 
we compress a body to observe how much it is thereby heated, 
pressure, or it may be the dimensions of the body, is the variable, 
heat the variant. 2 Having once obtained, from a series of experi- 
ments, a number of values of a variable, and a corresponding 
number of values of the variant, we endeavour to determine what 
mathematical function the variant is as regards the variable. It is 
usual, therefore, first to discover whether there is any constant 
relation between the variable and the variant, and then to determine 
the empirical formula which expresses the relation between them. 
This empirical formula may or may not lead to the discovery of the 
rational formula expressing the law of nature involved. 3 

It is, of course, characteristic of quantitative investigations in 
physical Science that they are approximate only. As a general 
rule, a function can be developed or expressed as the sum of quan- 
tities, the values of which depend upon the successive powers of the 
variable quantity. If y be a function of x, then we may say that 

y - A + Bx + Gc 2 -f Dtf + #z 4 + . . . 

In this equation, the terms may be infinite in number, or, after 
a time, may cease to have any value. The coeflicients A, B, C, D, 
&c., are fixed quantities, of different values in different cases, and 
may happen to be zero or negative. The quantity #, on the other 
hand, is, of course, variable. Let us suppose a particular instance in 
which x and y are both lengths; and let us assume that y^^ P ar ^ 
of an inch is the least that we can take note of. Thus, when x is 
T ^ of an inch, x 2 = TTOtftf ^ an lnc ' 1 > anc * ^ G is less than unity, 
the term Cx 2 is inappreciable, being less than we can measure. 
Unless any of the quantities D, E, &e., should happen to be very 
great, it is evident that all the succeeding terms will also be in- 
appreciable, because the powers of x become rapidly smaller in geo- 

1 Or, one of its dimeiihiuus, temperature. 

a Jevons, op. cit. p. 440. 8 ib. pp. 483-7. 


metrical ratio. Thus when x is made small enough, the quantity y 
seems to obey the equation y A + Bx. If x should be still less, 
if, for example, it should become as small as Y^^^TTT ^ an " lc h> 
and B should not be very great, then y would appear to be the 
fixed quantity A> and would not seem to vary with x at all. On 
the other hand, were x to grow greater, say equal to y 1 ^ of an inch, 
and C not be very small, the term Cx* would become appreciable, 
and the law would be more complicated. 1 

Or, if we take any curve and consider a portion of it to be free 
from any kind of discontinuity, we may represent the character of 
such portion by an equation of the form 

y - A + Bx + Cx* + Dx* + ... 

If, now, we restrict our attention to a very small portion of the 
curve, the eye will be unable to distinguish its difference from a 
straight line; in other words, the term Cx 2 in the portion examined 
has no value appreciable to the eye. In this case y = A + JT. 

If we take a larger portion of the curve, curvature will become 
obvious, but it may be possible to draw a parabola or ellipse so that 
the curve shall apparently coincide with a portion of that parabola 
or ellipse. Similarly, if we take larger and larger arcs of the curve, 
it may assume the character successively of a curve of the third, 
fourth, or perhaps higher degrees; that is, it corresponds to equa- 
tions involving the third, fourth, and higher powers of the variable 
quantity. 2 

In abstract mathematical theorems, the approximation to absolute 
truth is perfect, because we can treat of infinitesimals. In physical 
Science, on the contrary, the least quantities we can treat of are 
those which are perceptible to the senses; but if the measured 
effects are really small, any joint effect is likely to be altogether 
imperceptible. For instance, in the expansion of a solid body, we 
regard the cubic expansion as three times as great as the linear 
expansion. The coefficients of expansion are so small, and so 
imperfectly determined, that when we expand (1 -f a) 8 , we neglect 
the minute quantities specified by the second and third powers of a. 
For a being a very small fraction, its square becomes an entirely 
negligible quantity, and still more so its higher powers. 3 

In order to establish an empirical formula, we may generally 

1 Jevous, op. cit. pp. 471-2. 

a Cf. Jevons, ib. p. 473. * ib. p. 47& 



assume, in actual practice, that the quantities involved will approxi- 
mately conform to a law of the form 

y = A + Bx + Cx\ 

in which x is the variable and y the variant. From the experi- 
mentally determined series of corresponding values, which should be 
arranged in a table, of the variable x and the variant y, we select 
three pairs, and, substituting them in the general equation, we solve 
the three resulting equations, and so obtain the values of the 
constants A, JJ, and C. We can now write down the empirical 
formula. It will usually be found that the formula thus obtained 
will yield the other numbers of the table to a considerable degree of 

As an example, we may take one of Perot's determinations of 
the densities of saturated vapours. 1 Perot's method depended, in 
principle, on the isolation and weighing of a certain volume of 
the particular saturated vapour. The results for ether are given 
in the following table: 










Temperature ... 








Specific Volume 








We now select any three of these results, say, (ft), (d\ and (0), 2 
and, substituting their respective values in the general equation 
A + Bx + Cx 2 = y, we have 

A + 307? + 900(7 = 400) 
A 4- 31-9J3 + 1017-61(7 - 373V 
A + 57-9# + 3352-41(7 - 168J 

Solving in the usual way, we find that A - 1043-27, B = - 28'24, 
and C = *227. Hence our empirical formula is 

v = 1043-27 - 28-24* + '227* 2 . 

The next step is to see if the empirical formula thus found agrees 
with the remaining experimental results. We find that it does 

* See Perot, Journal de Physique, torn, vii, p. 129. Cf. Preston, Heat, pp. 344-5. 
a Such a selection is not very likely to produce an acceptable formula. The results 
delected should always be far apart, and as far as possible equidistant. 


agree with (a) and (c). It therefore covers the first five cases, (a), 
(6), (c), (d), and (e). But it fails in the case of both (/) and (g), 
and in these instances the approximation is so slight that we are 
driven to the conclusion either that the experimental results are 
wrong, or that the underlying law is more complex than would 
appear from the formula established/ The best plan now is to take 
a new group of three cases, say (a), (e), and (g), 1 and see how nearly 
the formula derived therefrom, viz., 

v = 802-62 - 15'47< + -079* 2 , 

covers the remaining cases. This new formula will be found hardly 
more satisfactory than the other. It thus becomes necessary to 
formulate an equation involving higher powers of the variable, 
though, of course, to solve an equation with as many as six or seven 
unknowns, especially with such numbers as those given*, is a some- 
what formidable task. 2 It is always possible that some of the 
experimental results may be wrong, owing to experimental errors 
which are either beyond control or perhaps unsuspected. For in- 
stance, if in the series of experiments just mentioned, water vapour 
had been under examination, temperatures much above 100 could 
not be employed, on account of the solvent action of water vapour on 
glass, at high temperatures. 

It will often happen that even the second power of the variable 
will be unnecessary. Regnault found that the results of his inquiry 
into the latent heat of steam at different pressures were represented 
with sufficient accuracy by the formula 

Q - 606-5 + 0-305*, - *'* 

*# , 
where Q is the total heat of the steam and t the temperatur^J * 

On the other hand, it is sometimes necessary to include the 
third power of the variable. In the expansion of liquids, for in- 
stance, physicists assume the law to be of the form 

8 = at + bP + cP, 
and they calculate from the results of observation the value of the 

* These are the best three. See the last footnote. 

2 The reader would do well to face this task. To work out a series of results, to compare 
them, and to discover exactly why they differ, will throw much light upon the principles 
underlying empirical formulae. 

* See Preston, Heat, p. 313. The pressures varied from *22 to 13*625 atmospheres. In 
thirty-eight experiments made under the ordinary atmospheric pressure, the mean value of 
the total heat was found to be 637*67, the extreme values in the series being 635*6 and 638*4. 



three constants fl, 6, and c, which are usually very small quantities. 
In the case of water, Kopp used the formula 

V = 1 - at + W - ct* 

for the volume at any temperature t of a mass occupying unit 
volume at zero. For liquids at temperatures above the normal 
boiling-point, Him expressed the dilatation A by means of formulae 
of the type 1 

A - at + bfl + cP + dl*. 

Thus, in the case of water, the volume being taken equal to unity at 
zero, the volume at any temperature between 100 U (J, and 200C, 
was given by the formula 

v = 1 + 0-000108678750 + 0-0000030073653 2 

+ 0-0000000028730422 3 - 0-0000000000066457031 4 . 

Theoretically speaking, the process of empirical representation might 
be applied with any degree of accuracy; we might include still 
higher powers in the formula. In a similar manner, periodic varia- 
tions may be represented, to any required degree of accuracy, 
by formulae involving the sines and cosines of angles and their 

4. Rational Formulae 

It must be clearly understood that all these empirical formulae 
do not coincide with natural laws. They are only approximations 
to the results of natural laws, and it is upon the general principles 
of approximation that they are founded. We do not learn what 
function the variant is of the variable^ but we obtain another function, 
which, within the bounds of observation, gives nearly the same 

Let us consider the case of a stone which is projected vertically 
downwards. Five observations are made, and the results are as 
follows : 

Number of seconds after the start ... 






Number of feet covered after the start 






Taking the general formula s = a + U + cP, and substituting the 

1 For details, see Preston, Heat, p. 186. 

2 See, for example, On Tides and Waves, by Sir G. B. Airy. 


first, third, and fifth of the pairs of results (the best selection 
possible), we have 

a 4- 2i + 4c = 88] 

16a + 606 + 225c - 4320 \ 

a + 66 + 36c = 648J 

which gives a ~ 0, b = 12, c = 16. The formula therefore is 

5 = 12* -h 16/ 2 . 

This will be recognized at once as the ordinary formula connecting 
space and time in the case of falling bodies. (The value of g in 
this case is 32; and 12 represents, of course, the initial velocity of 

But it need hardly be said that the above numbers were not 
obtained from actual experiments. They were made up from pre- 
vious knowledge, and specially for purposes of illustration. Actual 
experiments, no matter how carefully performed, would have 
yielded results only approximately accurate, and the consequent 
complex empirical formula might or might not have given a clue 
to the rational formula s - j^tf 2 . But this particular relation has 
long passed the empirical stage, and our knowledge of the action of 
gravity not only enables us to establish the relation in a different 
way, but clearly to see the reason underlying the relation. 

The graph of an empirical formula will be a curve approximating 
the true curve, but will give us no information concerning the pre- 
cise nature of the true curve. Indeed, the curve obtained may be 
such a fragment, so to speak, of the whole curve, that it gives us 
scarcely the slightest clue to the relation between the quantity of 
the cause and the quantity of the effect. 

What we are seeking is the rational formula or function, 1 which 
will exhibit the exact nature and origin of the law connecting the 
phenomena. Given the quantities, we want the function of which 
they are the values. The discovery of this function is often ex- 
tremely difficult, and not infrequently it seems absolutely impossible 
to make any headway whatever beyond the empirical law. 

We may, it is true, discover the rational function by purely 
haphazard trial, for we are always at liberty to invent any mathe- 
matical formula we like, and then try whether, by the suitable 

i Any quantity which depends upon and varies with another may be called a function of 
it, and either may be considered a function of the other Literally, a rational formula show* 
the " reason " of the law connecting the phenomena. 


selection of values for the unknown constant quantities, we can 
make it give the required results. But the chance of succeeding in 
this manner is very small, for the number of possible functions is 
practically without limit, and even the number of comparatively 
simple functions is so large that the possibility of falling on the 
correct one by mere chance is only slight. We do, however, 
usually obtain the law by a deductive process of some kind, not by 
showing that the numbers give the law, but that the law gives the 
numbers. 1 

The better plan is to note the general character of the variation 
of the quantities, trying, by preference, functions which give a 
similar form of variation. A survey of the numbers will often give 
us a general notion of the kind of law they are likely to obey, and 
we may gain much assistance by drawing their graph. We can 
in this way ascertain with some probability whether the curve is 
likely to return into itself, or whether it has infinite branches; 
whether such branches are asymptotic; whether it is logarithmic 
in character, or trigonometric. This indeed we can only do if we 
remember the results of previous investigations, and a complete 
familiarity with different classes of curves is indispensable. Once 
we can discover the class of functions to which the required law 
belongs, our chances of success are much increased because our work, 
whether by haphazard trial or otherwise, is then brought within 
much narrower limits. But unless we have the greater part of the 
curve before us, the identification of its character must be a matter 
of great uncertainty ; for limited portions of curves of almost any 
character can be made to approximate to one another. Clearly, 
then, both insight and mathematical knowledge are needed to obtain 
the correct form of the function; but its form once obtained, the 
remaining work is mere computation, the unknown constants being 
determined, in the mariner already explained, by making selections 
from our experimental results. We thus get the function itself, 
and now try, as before, whether it gives with sufficient accuracy the 
remainder of our experimental results. 

It is obvious, then, that to discover the form of function most 
Jikely to suit, we shall almost always have to draw freely upon our 
previous knowledge and to depend upon analogical reasoning. The 
general nature of the phenomenon will often show at once whether 
the law is one of direct simple proportion, or of an exponential form; 
and so on. Any influence which spreads freely through tridimen- 

i Cf. Jevons, pp. 489-90. 


sional space will, of course, be subject to the law of the inverse 
square of the distance. But no general rules can be given. Know- 
ledge and insight are alone likely to ensure success. 

Success, however, is by no means always certain. In many 
important branches of Science it seems almost impossible to detect 
the precise laws, and the rational formulae are, therefore, necessarily 
unknown. The pressure of saturated vapours at different tempera- 
tures, for instance, has been determined by experiments conducted 
with extraordinary care, but no incontestable general law has been 
established. All sorts of formula) have been suggested, 1 but none 
can be said to correspond very closely with the actual experimental 
results. Then, again, some of the greatest men of Science 2 have 
spent much labour in trying to discover some general law of atmo- 
spheric refraction, but all to no purpose. 

5. Variation in Simple Proportion 

In quantitative investigations our first impression is often likely 
to be that one quantity varies directly as another, thus obeying the 
law y = mx -f n, and this is often actually the case. For instance, the 
heat produced by friction is exactly proportional to the mechanical 
energy absorbed; and if electricity is converted into heat we have 
again simple proportion. Wherever, in fact, one thing is but 
another thing with a new aspect, we may expect to find this law. 
But it is necessary to distinguish between the cases where this pro- 
portionality is really true and where it is only apparently true. A 
small portion of any curve, for instance, will appear to be a straight 
line, and when our modes of measurement are comparatively rude, 
we must expect to be unable to detect the curvature. Kepler made 
many attempts to discover the law of refraction of light, and he 
approximated to it when he observed that the angles of incidence 
and refraction, if small, bear a constant ratio to each other; for 
angles, when small, do, of course, vary nearly as their sines. It 
would be well to look upon every law of simple proportion as only 
provisionally true until reason to the contrary is shown. 8 

i For instance, Young suggested p = (a+bO) m , in which a, b, and m are constants to be 
determined by experiments. Biot suggested log. p = a + 6a*.+ cpO. Roche used a formula 

of the type p = aa m + n O. (See Jamin, Cours de Physique, vol. ii., p. 138 ; Young, A'af. 
Phil., vol. ii , p. 440; Biot, Connaiwance des Temps, 1844; Dulong and Arago's Memoir, JfliJi. 
de Vlnttttut, torn x , p. 227; Preston, Heat, pp. 330-1; Jevons, Prin. ofSci., pp. 499-501.) 

2 For instance, Kepler, Newton, and Laplace. 

Cf. Jevons, Prin. of Sci., pp. 483-603. 


6. Theory and Experimental Results 

It should be noticed that the great bulk of quantitative facts 
recorded by scientific investigators, have not been brought under 
any theoretical system. The results are empirical only. A phe- 
nomenon may be measured, but no explanation may be forthcoming as 
to why it should possess any particular quantity, or to connect it by 
theory with other quantities. The tables of numerical results which 
abound in books on Chemistry and Physics, the records of observa- 
tions of public Observatories, the numerous tables of meteorological 
observations, are, for the most part, results of a merely empirical 
character; either theory is defective, or the labour of calculation and 
comparison is too formidable. Of course, purely empirical measure- 
ments may have a direct practical value, as when tables of specific 
gravities, or strengths of materials, assist the engineer; or when a 
knowledge of the refractive index of various kinds of glass enables 
the optician to make achromatic lenses; but, in such cases, the use 
made of the measurements is not scientific but practical. 1 

If, by means of a theory, we can not only predict the nature of 
a phenomenon, but also assign the precise quantity of a phenomenon, 
we have an excellent test of the probable truth of the theory. It 
was in this manner that Newton first attempted to verify his theory 
of gravitation. He knew approximately the velocity produced in 
falling bodies at the earth's surface; and if the law of the inverse 
square of the distance held true, and the reputed distance of the 
moon was correct, he could infer that the moon would fall towards 
the earth at the rate of 15 ft. in one minute. Now the actual 
divergence of the moon from the tangent of its orbit appeared to 
amount only to 13 ft. in one minute. This discrepancy of 2 ft. 
caused Newton to " lay aside at that time any further thoughts on 
this matter". Many years afterwards, he obtained more precise 
data from which he could calculate the size of the moon's orbit, and 
he then found the discrepancy to be inappreciable. His theory of 
gravitation was thus verified as far as the moon was concerned. 
This was to him only the beginning of a long course of deductive 
calculations, each ending in a verification. 2 

It may happen that we are able from certain quantitative ex- 
periments and a correct theory, to determine the amount of a 
phenomenon which we either cannot measure at all, or cannot 
measure with sufficient accuracy to verify the prediction which the 

* Jevons, op. cit. pp. 651-3. 2 ib. pp. 656-6. 


theory enables us to make. For instance, the specific heat of air 1 
was believed, on the grounds of direct experiment, to amount to 
0*2669, but the methods of experiment were open to sources of 
error. Rankine calculated in 1 850, from the mechanical equivalent 
of heat and other thermodynamic data, that the number ought to be 
0*2378. This determination was then accepted, though not verified. 
Subsequently Regnault obtained by direct experiment the number 
0*2377, proving that Rankine's estimate was well grounded. 

It is evident that, in quantitative questions, verification is a 
matter of degree and probability. Many quantities are assigned 
on theoretical grounds which we are quite unable to verify with 
corresponding accuracy. The thickness of gold leaf, the average 
depths of the oceans, the velocity of a star's approach to the earth, 
are cases in point. Physicists have measured light-undulations, and 
we also know the velocity with which light travels ; from these data 
we can estimate that about 600,000,000,000 undulations must strike 
the retina of the eye in one second. But how by direct counting 
could we verify such a number? 

7. Discordance between Theory and Direct 

It frequently happens that there is a serious want of accordance 
between the theory adopted and the results of direct measurement. 
There are several possible causes of this : the direct measurements 
may be erroneous; theory may be correct as far as regards the 
general form of the supposed laws, but some of the constant numbers 
or other quantitative data employed in the theoretical calculations 
may be inaccurate; the theory may be false, in the sense that the 
forms of the equations assumed to express the laws of nature are 
incorrect; the theory and the quantities concerned may be approxi- 
mately correct, but some regular unknown cause may have interfered 
so that the divergence may be regarded as a residual effect representing 
possibly a new phenomenon. 

No precise rules can be laid down whereby the investigator can 
overcome such difficulties. He must depend on his own insight and 
knowledge, though certain points will always suggest themselves to 
him. He will, for instance, increase the number of his experiments; 
he may find it necessary to devise other apparatus or to modify his 
materials; or he may approach the subject in an entirely new way. 

1 That of water being taken as unity. 


He must continue to vary the circumstances, in the hope that the 
source of the inconsistency will at last reveal itself. Of course he 
may, finally, have to abandon his original hypothesis, but not until 
he can form another which yields a more accurate accordance, in 
which case the new one will have first claim upon his attention. 1 

Error and its Correction 

i. Exact Measurement is virtually Impossible 

It will have become evident that the knowledge we acquire in 
experimental investigation is only of an approximate character; it 
is, in fact, a rare thing to reach laws which are absolutely true, and 
exact to the last degree. Some people, for example, consider it 
proved that planets move in ellipses; but to "prove", that is to 
demonstrate with certainty, that the orbits are elliptical, is beyond 
our resources; all that we can do is to show that the orbit of an un- 
perturbed planet approaches very nearly to the form of an ellipse, 
and more nearly the more accurately our observations are made. 
But to assert that the orbit is an ellipse is to pass beyond our data 
and to make an assumption which cannot be verified by observation. 
And, as a matter of fact, no planet docs move in a perfect ellipse; 
the mutual perturbations of the planets distort the elliptical paths. 

We could never prove the existence of perfectly circular or para- 
bolic movement, even if it existed. The circle is a particular case 
of the ellipse, for which the eccentricity is zero; but if the orbit of 
a planet were a circle we could never prove the entire absence of 
eccentricity; we could not do more than declare that the divergence 
from the circular form was inappreciable. Again, we can conceive 
the existence of a comet moving in a parabolic orbit; but owing to 
the particular limit which the parabola occupies between the ellipse 
and hyperbola, 2 we could never prove that the comet so moved. 8 

i Cf. Jevons, op. cit. pp. 558-60. The whole of ch. xiii, xiv, xxii, and xxv of Jevons will 
repay careful reading. 

* The hyperbola should be considered in its most general sense, the curve formed by the 
intersection of a plane and a double cone, and not confined to the case where the plane cuts 
the cone parallel to its axis The plane must make a greater angle with the base of the cone 
than the Bide of the cone makes. (With an equal angle we have a parabola, with a smaller 
angle an ellipse.) * See Jevons, Prin. of Sci. t pp. 450-8. 


2. The Assumptions made by Science 

We seldom realize, perhaps, what great assumptions we make in 
scientific investigation, and how our knowledge must therefore be 
largely of a hypothetical and merely approximate character. We 
base calculations upon the assumed existence of inflexible bars, in- 
extensible lines, heavy points, homogeneous substances, perfect fluids 
and gases; but as probably none of these things have any real exis- 
tence, we cannot say that our problems are ever finally solved. And 
even the very best of the instruments with which we perform our 
measurements are imperfect. We assume a plumb line gives a 
vertical line, but this can never be true in the absolute sense, owing 
to the attraction of mountains and other inequalities in the surface 
of the earth. We assume the surface of mercury to be a perfect 
plane, but even in a breadth of five inches there is a divergence from 
a true plane of about one ten-millionth part of an inch; we assume 
that in the torsion balance the force of torsion of a wire is propor- 
tional to the angle of torsion, but this is true only for infinitely 
small angles. Even the pendulum our most perfect instrument 
is not theoretically perfect, except for infinitely small vibrations. 1 

There is not, of course, any inexactness in the laws of nature; 
the inexactness is in our data. And so far as assumption enters in, 
so far want of certainty will attach to our conclusions. Yet there 
are occasions when we seem warranted by our data in assuming the 
existence of an exact law, and using it in preference to the numerical 
results which are at best only approximate. Dalton's laws of definite 
combining proportions never have been exactly proved; but chemists 
having shown, to a considerable degree of approximation, that the 
elements combine together as if each element had atoms of an in- 
variable mass, assume that this is exactly true. Chemists thus 
step beyond their data; they throw aside their actual experimental 
numbers and boldly assume that the discrepancies are due to ex- 
perimental errors. 2 

3. Interfering Causes 

When we wish to attain rigid accuracy, it is surprising how many 
possible causes of error may enter into even the simplest experi- 
ments. We cannot, for instance, perform the common experiment 
of testing the truth of Boyle's Law, without paying regard to (1) 

i Jevons, op. cit. pp. 466-61. 2 Cf. Jevons, ib. pp. 462-5. 


the variations of atmospheric pressure which are communicated to 
the gas through the mercury; (2) the compressibility of mercury, 
which causes the column of mercury to vary in density; (3) the 
temperature of the mercury throughout the column; (4) the tem- 
perature of the gas, which is with difficulty maintained invariable; 
(5) the expansion of the glass tube containing the gas. Although 
Regnault took all these circumstances into account in his examina- 
tion of the law, there is no reason to suppose that he exhausted the 
sources of inaccuracy. 1 

A measurement which aims at any considerable degree of exact- 
ness is a very delicate and usually complex operation, and much of 
the difficulty arises from the fact that it is scarcely ever possible to 
measure a single effect at a time. Thus, if we wish to measure the 
expansion of a liquid by heat, we observe the rise of a column of 
liquid in a narrow glass tube. But we cannot heat the liquid with- 
out heating the glass, so that the change observed is really the differ- 
ence between two expansions. Careful investigation will show the 
necessity of allowing for further effects, for example, the compression 
of the liquid, and the expansion of the bulb due to the increased 
pressure of the column as it becomes lengthened. The variation in 
the height of the barometer is another complex effect, being partly 
due to the real variation of the atmospheric pressure and partly to 
the expansion of the mercurial column by heat. 2 

As, however, our object in an experiment is to measure a single 
effect only, we always endeavour to obtain that effect free from 
interfering effects; and if we cannot get rid of the interfering effects 
altogether, we reduce them to a minimum. We try, then, to adopt 
some means of counteracting interfering causes. It should, however, 
be noted that those quantities which are called errors in one case 
may become important phenomena in another investigation. When 
we speak of "eliminating error", we really mean isolating a par- 
ticular phenomenon and freeing it, as far as possible, from interfering 
causes. Several methods of eliminating error are recognized. 

4. Elimination of Error 

In the first place we may devise an experiment, or opportunity 
of observation, in which error is avoided, or at all events rendered 

i See Jevons, op. cit. p. 468; and Jamin, Cours de Physique, 1, pp. 282-3. 
a Cf. Jevons, ib. pp. 336-8. The term "expansion" is here used in its general sense, con- 
traction being regarded as negative expansion. 


inappreciable. An astronomer, for example, is unable to assign any 
satisfactory law to atmospheric refraction; he therefore avoids, as 
far as possible, making observations of an object when near the 
horizon, and waits till it reaches the highest point of its daily course. 
An astronomer also places his principal controlling clock in a cellar 
or other place where the changes of temperature, being very slight, 
will not affect the length of the pendulum. 1 Dulong and Petit's 
method of measuring the expansion of mercury enabled them to 
avoid the difficulty arising from change of dimension in the contain 
ing tubes. 

Sometimes an experiment may be rendered valueless owing bo 
the existence of error which cannot be avoided. Foucault's experi- 
ment for demonstrating the rotation of the earth, for instance, is 
of no use for purposes of exact measurement; it is practically im- 
possible to avoid giving the pendulum a slight lateral motion; the 
consequence is an elliptic path with a progressive motion of the axis 
of the ellipse, a motion which disguises that due to the rotation of 
the earth. 2 

In the second place, we may sometimes measure phenomena in 
such circumstances that the error remains very nearly the same in 
all the observations. This method is available when we want a 
difference between quantities, and not the absolute quantity of either. 
In Leslie's Differential Thermometer, for instance, any alterations 
of the temperature of the air will affect the equal bulbs equally, arid 
produce no change in the indications of the instrument. Only that 
radiant heat which is purposely thrown upon one of the bulbs will 
produce any eifect. 3 

A third method is known as the method of corrections. Whenever 
the result of an experiment is affected by an interfering cause to 
a calculable amount, it is sufficient to add or subtract this amount. 
We are said to "correct observations" when we thus eliminate what 
is due to extraneous causes. The variation in the height of the 
barometer, for instance, is partly due to the change of temperature, 
but since the coefficient of absolute expansion of mercury is known, 
the necessary correction for temperature is a simple matter. 

When we come to use instruments of great accuracy, there are 
many minute sources of error which must be guarded against. If a 
thermometer, for example, has been graduated when vertical, it will 

1 This is an additional check to the compensatory arrangement for the change of tempera- 

2 Cf. Jevons, op. cit. pp. 340-4. See also Phil. Mag., 1851, fourth series, vol. ii. 
8 Cf. Jevons, ib. p. 345, and Leslie, Inquiry into the nature of Heat, p. 10. 


read somewnat differently when laid flat, since the pressure of a 
column of mercury is removed from the bulb. The reading may also 
be somewhat altered if it has recently been raised to a higher tempera- 
ture than usual, if it be placed under an exhausted receiver, or if 
the tube be unequally heated as compared with the bulb. For these 
minute causes of error we may have to introduce troublesome correc- 
tions. Again, the measurement of quantities of heat is a matter of 
great difficulty because there is no known substance impervious to 
heat, and the correction of the consequent experimental errors often 
taxes the resources of our ablest physicists; it is very much like 
trying to measure liquids in porous vessels. 1 

A fourth method is that of compensation. Here we adopt some 
means of neutralizing the interfering cause by balancing against 
it an exactly equal and opposite cause of unknown amount. We 
cannot, for instance, weigh an object with great accuracy unless we 
make a correction for the weight of the air displaced by the object. 
When a chemist wishes to weigh gas in a large glass globe, he 
avoids the error and the labour of correcting it by attaching to the 
opposite scale of the balance a dummy sealed glass globe of equal 
capacity to that containing the gas to be weighed. In the astatic 
galvanometer, we have another illustration of the principle of the 

A fifth method of eliminating error may be adopted when we 
can so reverse our mode of procedure as to make the interfering 
cause act alternately in opposite directions. If we can get two ex- 
perimental results, one of which is as much too great as the other 
is too small, the error is equal to half the difference, and the true 
result is the mean of the two apparent results. It is by this method 
that we are able to ensure accuracy in, for example, the use of the 
dip-needle. 2 This leads us to the consideration of the "Method of 

5. The Method of Means 

Any person who uses a scientific instrument of great precision 
and registers successive observations in an unbiased manner, will 
invariably find that the results differ. Only the careless investi- 
gator will think that his observations agree. The more accurate 
our modes of observation are rendered, the more numerous are the 
sources of minute error which become apparent. We may, in fact, 
look upon the existence of error in all measurements as the normal 

i Cf. Jevons, op. cit. pp. 346-50. 2 See Jevons, ib. pp. 354-6. 

(C415) 21 


state of things. Experimental results which agree too closely 
should raise our suspicions. If, then, we cannot get exactly the 
same result twice over, the question arises, how can we ever attain 
the truth, or select the result which may be supposed to approach 
most nearly to it? It is clear that if the quantity of a certain 
phenomenon is expressed in several differing numbers, only one 
at most can be true, and very likely all are false. Common sense 
suggests that we must take the mean, and mathematical reasoning 
shows that the mean is very likely to bring us near the truth. 

There are several kinds of means, 1 the commonest of which is 
the arithmetic mean. This is often referred to as "the mean". The 
arithmetic mean of a series of quantities is, of course, the sum of 
the series divided by their number. If a and b be two numbers, 
their arithmetic mean is ^(a + b). The geometric mean is \/ab. 

The geometric mean is necessarily adopted in certain cases. 
When we estimate the work done against a force which varies 
inversely as the square of the distance from a fixed point, the mean 
force is the geometric mean between the forces at the beginning and 
end of the path. When in an unperfect balance we eliminate error 
by adopting the method of Gauss, weighing first in one pan and 
then in the other, the true weight is the geometrical mean of the 
two apparent weights. 2 

A mean result sometimes signifies a merely representative number, 
expressing the general magnitude of a series of quantities. Such a 
number is sometimes called the fictitious mean or the average result. 
In popular usage, however, the terms mean and average are synony- 
mous; and even in Science they are sometimes indifferently used. 
But although the term average, when employed in the sense of a 
fictitious mean, represents no really existing quantity, it is yet of 
great scientific importance, as enabling us to imagine a number of 
particular details generalized in a single result. The weight of a 
body, for example, is the sum of the weights of a number of in- 
finitely small particles, each acting at a different place, but we may 
regard the weight of all the particles as concentrated in a particular 
point, the Centre of Gravity, and the behaviour of the whole 

1 The old mathematicians recognized ten. 

2 Thus, if a body of true weight W weighs A when placed in the right-hand pan, and B 
when place,d in the left-hand pan, then calling R and L the lengths of the respective arms, 
we have WR = AL; WL = BR; .-. \V2 = AB; .-. W = v'AB. Since A and B are as a rule 
very nearly equal, we may in moat cases use the arithmetic mean instead. Thus the arith- 
metic mean of I'OOO and I'OOl is 1*0005, whilst the geometrical mean is 1-0004908. It would be 
impossible to detect the difference between the two by the balance. See Stewart and Gee, 
Practical Physics, vol. i, p. 89, or Qlazebrook and Shaw, Practical Physics, pp. 99-118. 


body will be exactly represented by the behaviour of this imaginary 
heavy point. Terrestrial gravity is a case of approximately parallel 
forces, and the centre of gravity is but a special case of the more 
general Centre of Parallel Forces. Wherever a number of forces 
of whatever amount act in parallel lines, it is possible to discover 
a point at which the algebraic sum of the forces may be imagined 
to act with exactly the same effect. Thus we have the Centre of 
Pressure, the Centre of Percussion, and so on. 

But we ought to distinguish between those cases in which an 
invariable centre can be assigned, and those in which it cannot. 
Strictly speaking, there is no such thing even as an invariable 
centre of gravity. As a general rule, a body is capable of possess- 
ing an invariable centre only for perfectly parallel forces, and 
gravity never does act in absolutely parallel lines. Again, we 
familiarly speak of the poles of a magnet. But, strictly, the poles 
are not the ends of the magnet, nor any fixed points within, but the 
variable points from which the resultants of all the forces exerted 
by the particles in the bar upon exterior magnetic particles may 
be considered as acting. The poles are, in short, Centres of Mag- 
netic Forces; but as these forces are never really parallel, the 
centres will vary in position according to the relative position of 
the object attracted. 1 

One mode of employing the mean result is analogous to the 
method of reversal, a method which is extensively practised in some 
branches of physical Science. We have a simple instance in the 
determination of the latitude of a place by observation of the Pole 
Star. If the elevation of any circumpolar star be observed at its 
higher and lower passages across the meridian, half the sum of the 
elevations gives the height of the pole, which, of course, is equal 
to the latitude of the place. Such a star is as much above the pole 
at its highest passage as it is below at its lowest, so that the mean 
must give the height of the pole free from doubt, except as regards 
incidental errors. 2 

Sometimes we are able to eliminate fluctuations and take a mean 
result by purely mechanical arrangements. The daily variations of 
temperature, for instance, become imperceptible one or two feet below 
the surface of the earth, so that a thermometer placed with its bulb 
at that depth gives very nearly the true daily mean temperature. 8 

i Cf. Jevons, op. cit. pp. 363-5. Cf. also Venn, Logic of Chance, ch. xviii (on averages). 
The distinction between "average" and "mean" is perhaps a little artificial, 
a Cf . Jevons, #. p. 866. * <&. p. 368. 


It is frequently very difficult to determine exactly the zero 
point from which we desire to measure, and in some cases it is 
actually better to determine it by the average of equally diverging 
quantities, than by direct observation. In delicate weighings with 
a chemical balance, for instance, it is requisite to ascertain exactly 
the point at which the beam comes to rest, but it is often better 
to let the beam vibrate and observe the terminal points of the 
vibrations. The mean between two successive extreme positions 
will nearly, but not quite, indicate the position of rest; for the 
swings gradually decrease, owing to friction and to resistance of 
the air. We therefore observe a third terminal point, on the same 
side as the first, and then reason thus: the single swing to the 
right is, say, 125; the two swings to the left, 63 and 69; we may 
therefore assume that the mean of 63 and 69, that is 66, would 
have been the left-hand turning-point at the moment at which it 
was 125 on the other, had the pointer been swinging in the opposite 
direction. The mean of 125 and 66 is 95*5, which may therefore 
be regarded as the res ting -point. AVe may, if we wish, observe 
another turning-point to the right, say, 120; then we have another 
such series. Proceeding thus, we get a set of determinations of 
the resting-point, the mean of which will give us the true position 
with great accuracy. 1 

6. The Law of Error 

It will have been understood that the term error, as here used, 
merely means discordance, of which the cause is unknown. The 
error may arise from some law of nature not known to the observer; 
it may arise from the imperfection of the observer's senses; it may 
arise from the personal constitution of the observer, that is, his 
particular habit or temperament which causes him to differ from 
other persons in his method of observing; it may arise from some 
imperfection peculiar to the apparatus employed, a graduated 
metal scale, for instance, undergoes daily expansion and contraction 
by variations of temperature. Now before any trials are made, 
that is, before anything is known of the character of the observer 
or of the apparatus he uses, we can have no reason to suppose that 
any one observation is more likely to exceed the truth than to fall 
short of it. When any observation is greater than reality, the error 

i That is, the resting-point when the pans are empty. See Glazebrook and Shaw, Practical 
Physics, pp. 110, 111. 


is called positive; when less, negative. The hypothesis, therefore, 
of an equal presumption for positive and negative errors, is one 
with which we must commence; and it follows from the suppo- 
sition that the mean is the most probable result of a number of 
discordant observations. The sum of all the observations will be 
without error itself if the amount of the positive errors be equal 
to that of the negative ones. This last supposition, though not 
probable in itself, is nevertheless more probable than any other, 
and the odds are very much in favour of its being very nearly true. 
Now whatever may be the error of the sum of observations, say 
100 in number, the average, or the hundredth part of the sum, con- 
tains only the hundredth part of that error; and the presumption 
that such an average is very close indeed to the truth greatly ex- 
ceeds the probability in favour of any one of the observations. 1 
All this seems to suggest the possibility of reducing error to Law. 

In point of fact, mathematicians have established a "Law of 
Error", a law which not only enables us, among discordant results, 
to approximate to the truth, but to assign the degree of probability 
which fairly attaches to this conclusion. Mathematicians agree, 
however, far better as to the form of the Law than they do as to 
the manner in which it can be deduced and proved. They agree 
that, among a number of discordant results of observation, that 
mean quantity is probably the best approximation to the truth, which 
makes the sum of the squares of the errors as small as possible. But the 
whole subject is much too difficult for general treatment here, and 
can be touched upon only in some of its more elementary aspects. 2 

7. How the Law has been Arrived at 

Mathematicians have arrived at the Law in different ways. 
Gauss proceeds much upon assumption; Herschel depends upon 
geometrical considerations; Laplace and Quetelet regard the Law 
as a development of the doctrine of combinations. The last- 
mentioned method is happily illustrated by Jevons. The illustra- 
tion, simplified and shortened, is as follows. 

Let us assume that a particular observation is subject to six 

1 Cf. De Morgan, Probability, pp. 128-34. 

2 The standard Law of Error, commonly called the Exponential Law, la expressed In the 
formula y - Yc~ cac2 , in which x is the amount of the error, Y the maximum ordinate of the 
curve of error, and c a number constant for each series of observations and expressing the 
amount of the tendency to error, varying between one series of observations and another; 
e is the mathematical constant. See Jevons, pp. 374-82. 



chances of error, each of which will increase the result 1 inch if 
it happens. Each of these errors is to be regarded as an event 
independent of the rest, and we can therefore assign, by the theory 
of probability, the comparative probability and frequency of each 
conjunction of errors. By giving x in 6 C X all values from to 6, 
we see that no error at all can happen in only 1 way; an error of 
1 inch can happen in 6 ways; and the ways of happening of errors 
of 2, 3, 4, 5, and 6 inches will be 15, 20, 15, 6, and 1 in number, as 
in the following table : 

Amount of Error, in inches 







Number of Errors ... 








Obviously the error most likely to occur is that of 3 inches, and will 
occur in the long run in 20 cases out of 64. Errors of 2 and 4 inches 
will be equally likely, but will occur less frequently ; errors of 1 and 
5 inches still less frequently; while no error at all and one of 6 inches 
will be a comparatively rare occurrence. 

Let us now suppose the errors to act as often in one direction 
as in the other. There will thus be three positive causes of error and 
three negative causes, and we may tabulate the numbers of errors of 
various amounts thus: 

Positive Error. 

Negative Error. 

Amount of Error, in inches 

3 2 1 

1 2 3 

Number of Errors ... 

1 6 15 


15 6 1 

From this table we easily ascertain the probability of any particular 
amount of error under the conditions supposed. The probability of 
a positive error of exactly 1 inch is , in which fraction the nume- 
rator is the number of combinations giving 1 inch positive error, 
and the denominator the whole number of possible errors of all 
magnitudes. By adding together the appropriate numbers we can 
get the probability of an error not exceeding a certain amount. 
Thus the probability of an error of 2 inches or less is (6 + 15 + 20 
f 15 -f 6)/64 or 62/64. Evidently, the probability of small errors 
is far greater than of large ones; for example, the odds are 62 to 2 
or 31 to 1 that the error will not exceed 2 inches. 

But to assume any special number of causes of error is an arbi- 


trary proceeding, and mathematicians have chosen the least arbitrary 
course by imagining the existence of an infinite number of infinitely 
small errors. 1 Upon this basis they have proceeded to establish the 
Law of Error already mentioned. It should be noticed that the 
Law allows of the possible existence of errors of every assignable 
amount, a fact in itself sufficient to show that it is only approxi- 
mately true. Although we may fairly say that in measuring a mile 
it would be impossible to commit an error of a thousand miles, yet 
the general Law of Error would assign a probability for an error of 
even that amount, and more, but such a probability would be almost 
inconceivably small. All that the Law claims to do is to represent 
the errors in any special case to a very close approximation. 2 

One important fact following immediately from the Law of Error 
is that the mean result is the most probable one] and when there is only 
a single variable, this mean is found by the familiar arithmetic 
process. The "Method of Means" may be regarded merely as a 
special application of the general case, that is, of the " Method of 
Least Squares ". 3 

8. The Probable Error of Results 

When, however, we are dealing with cases of importance, we 
must not be content with finding the simple mean and treating it as 
true. We must also ascertain the degree of confidence we may place in 
this mean. In some cases the mean may be approximately certain 
and accurate; in other cases it may be worth little or nothing. The 
Law of Error enables us to ascertain the degree of confidence proper 
in any instance, for it shows how to calculate the probability in the 
case of a divergence of any amount from the mean, and we can thence 
ascertain the probability that the mean in question is within a certain 
distance of the true number. By probable error mathematicians mean 
the limits within which it is as likely as not that the truth will fall. 
Thus, if 5*45 be the mean of all the determinations of the density of 
the earth, and '20 be approximately the probable error, the meaning 
is that the probability of the real density of the earth falling between 
5*25 and 5*65 is |. Any other limits might, of course, have been 

i This course is quite justifiable, considering that "there may exist infinitely numerous 
causes of error in any act of observation ". 

* Cf Jevons, pp. 374-85. 

3 Whewell stated that the Method of Least Squares is a Method of Means, but, as Jevons 
pointed out, this is incorrect. Cf. Whewell, Phil, of 2nd. Sci., ii, pp. 408-9; and Jevons, 
Prin. of Sci. , p. 386. 


selected; for instance, we might calculate the limits within which 
it was 10 to 1 or 100 to 1 that the truth would fall; but there is 
a convention to take the even odds of 1 to 1, as the quantity of 
probability of which the limits are to be estimated. 1 

For making the necessary calculations, works on probability give 
the following rules : 

1. Find the mean of the observed results. 

2. Find the difference, that is the error, between the mean and 
each observed result. 

3. Find the sum of the squares of these errors. 

4. Divide by one less than the number of observations. This 
gives the square of the mean error. 

5. Take the square root of this last result; this is the mean error 
of a single observation. 

6. Divide by the square root of the number of observations; this 
gives the mean error of the mean result. 

7. Multiply by the natural constant 0*6745; this gives the prob- 
able error of tJie mean result. 

For purposes of illustration Jevons gives the following example : 
Suppose the five measured heights of a hill to be 293, 301, 306, 307, 
and 313 ft. We require to know the probable error of the mean. 

1. The mean is 304. 

2. The differences ("errors") between this mean and the mea- 
sured heights are 11, 3, 2, 3, and 9. 

3. The squares of these errors are 121, 9, 4, 9, and 81, the sum 
of which is 224. 

4. Divide by 1 less than 5, that is 4, and we get 56, the square 
of the mean error. 

5. The mean error of a single observation is thus ^/56 = 7 '48. 

6. Divide by /^/5, that is by 2*236, and we have 3*35, the mean 
error of the mean result. 

7. Multiply by 0*6745, and we get 2-259, the probable error of 
the mean result. (Approximately 2.) 

The meaning of this is that the probability is , or the odds are 
even, that the true height of the hill lies between 301 f and 306^ ft. 
We thus have an exact measure of the degree of credibility of our 
mean result. 2 

In these calculations, the object is only to give a notion of the 
degree of confidence with which we view the mean; it is therefore of 
little use to carry them to any great degree of precision. And it 

i Cf. Jevons, op. cit. p. 387. 2 Cf. Jevons, ib. p. 388. 


should be remembered that the probable error has regard only to 
those causes of errors which, in the long run, act as much in one 
direction as another; it takes no account of constant errors. The 
true result accordingly may often fall far beyond the limits of 
probable error, owing to some unknown constant error or errors. 
It is always necessary to bear in mind that the mean of any series 
of observations is the best, that is, the most probable approximation 
co the truth, only in the absence of knowledge to the contrary. The 
selection of the mean rests entirely on the probability that unknown 
causes of error will, in the long run, act as often in one direction as 
the opposite, and will therefore balance one another. 1 

9. The Method of Least Squares 

When two or more unknown quantities are so involved that they 
cannot be separately determined by the simple Method of Means, we 
can yet obtain their most probable values by the Method of Least 
Squares. A simple example of Herschel's 2 illustrates the principle 
admirably, and the same example is mentioned by Venn. 

Suppose that a man had been firing for some time with a pistol 
at a small mark, say a wafer on a wall. We may take it for 
granted that the shot-marks would tend to group themselves about 
the wafer as a centre, with a density varying in some way inversely 
with the distance from the centre. But now suppose that the wafer 
which marked the centre was removed, so that we could see nothing 
but the surface of the wall spotted with the shot-marks; and that we 
were asked to guess the position of the wafer. Had there been only 
one shot, common sense would suggest our assuming (of course very 
precariously) that this marked the real centre. Had there been two, 
common sense would suggest our taking the mid-point between 
them. But if three or more were involved, common sense would be 
at a loss. It would feel that some intermediate point ought to be 
selected, but would not see its way to a more precise determination, 
because that on which it is accustomed to rely, the arithmetical 
average, does not seem at hand here. The rule of Least Squares 
tells us how to proceed. It directs us to select that point which 
will render the sum of the squares of all the distances of the shot- 
marks from it the least possible. 

In practice such a problem would reduce itself to taking what 
may be conveniently called the "centre of gravity" of the shot- 

i Jevons, op. cit. pp. 388-9. * Nat. Phil, pp. 217-8. 


marks, all being regarded as of equal weight. Such a centre is, in 
reality, the "average" of all the marks, as the elementary geometri- 
cal construction for obtaining the centre of gravity of a system of 
points will show. 1 

The Method of Least Squares is the most general mode of find- 
ing the true magnitude from a number of divergent measurements, 
but when these measurements involve one magnitude only, the 
simplest mode of applying the method is to take the arithmetical 
mean. 2 

The Law of Error and the Method of Least Squares are things 
of an entirely distinct kind and must not be confused. The Law 
of Error is the formulated statement of a precisely ascertained fact ; 
it assigns, with more or less of accuracy, the relative frequency with 
which errors or deviations of any kind are found in practice to 
present themselves. It belongs therefore to what may be termed 
the physical foundations of the science of Probability. The Method 
of Least Squares, or its simplified application, the arithmetical 
average, is no law whatever in the scientific sense. It is rather a 
precept or rule for our guidance. It directs us how to treat the 
errors which tend to occur, when any number of them are presented 
to us. There is, of course, a relation between the Law and the 
Method; nevertheless, they are absolutely distinct. 8 

10. The Method of Curves 

A further brief reference may be made to the Method of Curves. 
Every equation involving two variable quantities corresponds to 
some kind of plane curve, and every plane curve may be repre- 
sented symbolically in an equation. In an experimental research, as 
we saw in the last chapter, we obtain a number of values of the 
variant corresponding to an equal number of values of the variable. 
The variant, or quantity whose change we would consider, is made 
the ordinate of the curve; and the variable, or the quantity which we 
vary at will and on which the changes depend, we make the abscissa. 
If a curved line be drawn through all the points, or ends of the 
ordinates, it will probably exhibit irregular inflections, owing to the 

i The reader should take such a series of marks, draw convenient axes, and find, by the 
usual methods, what for convenience 1 sake is here called the Centre of Gravity. He should 
then join each of the marks to this centre, and prove that the sum of the squares of these 
distances is the least possible. The geometrical construction and algebraic solution are 
exceedingly simple. See Venn, Logic of Chance, pp. 466-8; Welton, pp. 185-7; Whewell, 
Nov. Org. Ren. t pp. 216-6 Cf, Welton, p. 187. Cf. Venn, p. 41. 


errors which affect the numbers. But when the results are numerous, 
it becomes apparent which results are more divergent than others; 
and, guided by a so-called " sense of continuity ", it is possible to 
trace a line among the points-which will approximate to the true law 
more than the points themselves. We draw the curve " not through 
the points given by observation, but among them ". l 

The value of the Method of Curves depends upon the fact that 
order and regularity are more readily and clearly recognized when 
pictorially exhibited to the eye than they are when presented to 
the mind in any other manner. And the curve often enables us to 
infer numerical results more free from accidental errors than any of 
the numbers obtained directly from experiment. Further, the form 
of the curve sometimes indicates the class of function to which our 
results belong. 2 

* See Jevons, op. cit. pp. 492-4; Whewell, Nov. Org. Ren., pp. 204-10 Most readers will 
probably be quite familiar with ordinary graphic algebra. Those who are not should read 
through Professor Gibson's Treatise on Graphs, which not only deals with the subject in a 
very lucid manner, but provides a large variety of examples of physical applications. Ch. xi 
of Earl'a Physical Measurements will prove helpful to the beginner 

s Jevons, op. cit. p. 494. On the danger of interpolation, see Jevons, pp. 495-9. 

The subject-matter of this chapter is difficult, and the reader who desires to follow it up 
must be prepared for a serious task. The nature and theory of average is well dealt with by 
Venn (Logic of Chance, ch. xviii and xix), and several chapters in Jevons's Principles of 
Science are suggestive. Compare also Whewell, Novum Organum Renovatum, ch. vii. The 
Law of Krror is admirably dealt with in Ency. Brit., vol. xxviii, pp. 280-91, and the same 
work has an exhaustive article on " Probability " (vol. xix, pp. 708-88). For some instructive 
elementary remarks on the Exponential Curve, see Venn, Logic of Chance, pp. 29 seq.\ 
Jevons, Principles of Science, ch xvii; and De Morgan, Probability, ch. vii Reference may 
also be made to Quetelet, Letters on the Theory of I'lububilities (translation by Downes). On 
the Method of Least Squares, the works of Gauss and Encke are amongst the best known, but 
Todhunter's contribution to this subject is considered by mathematicians to rank high ; it 
will be found in the Transactions of the fJamb. Phil Soc , vol. xi, Part II; a reprint in 
pamphlet form can sometimes be purchased for four or five shillings. Comstock's Method of 
Leant Squares is more recent; some typical Error Curves are shown in the frontispiece, and 
the book contains numerous typical examples. There is a very readable translation of 
Laplace's Essay on Probabilities by Truscott and Emory. Todhunter's Uistory of Probability 
is, of course, a standard work. 




If the reader desires to become acquainted with the practice of scientific 
discovery, he must do more than make himself familiar with the principles 
of method. He must acquire a first-hand knowledge of the work of men 
who have been famous for success in the field of research. From the 
records of the researches of not a few of these men, it is easily possible 
to gather clear notions of the methods they adopted. But however 
careful be his study of the work and methods of a great master, the 
ordinary man is never likely to rival him. In the first place, there are, 
of course, enormous differences in degree, between one man and another, 
of intellectual endowment. In the second place, the successful discoverer 
always seems able to detect a difference where the ordinary man sees 
none, and to detect a resemblance where the ordinary man sees only a 
difference. But let the reader judge for himself. We have room for 
only a few extracts, but all the works from which the extracts are taken 
should be read right through. Newton, Faraday, and Darwin should be 
read again and again. 

White of Selborne 


[Gilbert White was a Hampshire curate who wrote a Natural History of his 
own parish of Selborne. The History consists of miscellaneous jottings of all 
kinds, written in letter form to brother naturalists. White possessed remarkably 
keen powers of observation, as the following passages, selected at random, will 

From Letter XXVII. 1 Hedgehogs abound in my gardens and 
fields. The manner in which they eat their roots of the plaintain in 
my grass-walks is very curious: with their upper mandible, which 
is much longer than their lower, they bore under the plant, and so 
eat the roots off upwards, leaving the tuft of leaves untouched. In 
this respect they are serviceable, as they destroy a very troublesome 
weed; but they deface the walks in some measure by digging little 
round holes. It appears that beetles are no inconsiderable part of 
their food. In June last I procured a litter of four or five young 
hedgehogs, which appeared to be about five or six days old; they, 
I find, like puppies, are born blind, and could not see when they 
came to my hand. No doubt their spines are soft and flexible at 
the time of their birth, but it is plain they soon harden; for these 
little pigs had such stiff prickles on their backs and sides as would 
easily have fetched blood, had they not been handled with caution. 
Their spines are quite white at this age; and they have little hang- 
ing ears, which I do not remember to be discernible in the old ones. 
They can, in part, at this age, draw their skin down over their faces; 
but are not able to contract themselves into a ball as they do, for 
the sake of defence, when full grown. The reason, I suppose, is 
because the curious muscle that enables the creature to roll itself up 
into a ball was not then arrived at its full tone and firmness. Hedge- 
hogs make a deep arid warm hybernaculum with leaves and moss, in 

1 To Thomas Pennant. 


which they conceal themselves for the winter: but I never could find 
that they stored in any winter provision, as some quadrupeds cer- 
tainly do. 

From Letter XXXV. 1 Happening to make a visit to my neigh- 
bour's peacocks, I could not help observing that the trains of those 
magnificent birds appear by no means to bo their tails; those long 
feathers growing not from their uropygium, but all up their backs. 
A range of short brown stiff feathers, about six inches long, fixed in 
the uropygium, is the real tail, and serves as the fulcrum to prop 
the train, which is long and top-heavy, when set on end. When the 
train is up, nothing appears of the bird before but its head and neck, 
but this would not be the case were those long feathers fixed only 
in the uropygium, as may be seen by the turkey-cock when in a 
strutting attitude. By a strong muscular vibration these birds can 
make the shafts of their long feathers clatter like the swords of a 

From Letter XVI. 2 About the middle of May, if the weather 
be fine, the house-martin begins to think in earnest of providing 
a mansion for its family. The crust or shell of this nest seems to 
be formed of such dirt or loam as comes most readily to hand, and 
is tempered and wrought together with little bits of broken straws 
to render it tough and tenacious. As this bird often builds against 
a perpendicular wall without any projecting ledge under, it requires 
its utmost efforts to get the first foundation firmly fixed, so that 
it may safely carry the superstructure. On this occasion the bird 
not only clings with its claws, but partly supports itself by strongly 
inclining its tail against the wall, making that a fulcrum; and thus 
steadied, it works and plasters the materials into the face of the 
brick or stone. But then, that this work may not, while it is soft 
and green, pull itself down by its own weight, the provident architect 
has prudence and forbearance enough not to advance her work too 
fast; but by building only in the morning, and by dedicating the 
rest of the day to food and amusement, gives it sufficient time to 
dry and harden. About half an inch seems to be a sufficient layer for 
a day. Thus careful workmen when they build mud walls (informed 
at first perhaps by this little bird) raise but a moderate layer at 
a time, and then desist; lest the work should become top-heavy, 
and so be ruined by its own weight. By this method in about ten 
or twelve days is formed an hemispheric nest with a small aperture 
towards the top, strong, compact, and warm; and perfectly fitted 

To Thomas Pennant. a To the Hon. Daines Harrington. 


for all the purposes for which it was intended. But then nothing 
is more common than for the house sparrow, as soon as the shell 
is finished, to seize on it as its own, and to line it after its own 
manner. The shell or crust of the nest is a sort of rustic work full 
of knobs or protuberances on the outside : nor is the inside of those 
that I have examined smoothed with any exactness at all; but is 
rendered soft arid warm, and fit for incubation, by a lining of small 
straws, grasses, and feathers, and sometimes by a bed of moss inter- 
woven with wool. 

Alfred Russel Wallace, O.M., F.R.S. 

(Born 1823) 

[Dr. Wallace, who enjoyed the friendship of Darwin for twenty-five years, is 
our greatest living naturalist. He is the author of Man's Place in the Universe^ 
Dariuinism, and several other standard works. A good many people dislike his 
views on Vaccination and on " Spiritualism", but they readily admit the soundness 
of his reasoning from the facts adduced in support of these views. The following 
extract is from his latest work, The World of Life, written at the age of eighty- 
seven. Note how he insists upon the distinction of fact and inference.] 

Pp. 148-162. Before quitting the subject of migration, on 
which Mr. Seebohm's observations throw so much light, I will 
shortly describe the most wonderful exhibition of migration pheno- 
mena in the world that of the small island of Heligoland, 40 miles 
off the mouth of the Elbe in about the same latitude as Scarborough. 
Most of the migratory birds from Scandinavia and Arctic Europe 
pass along the coasts of the German Ocean, and the lighthouse on 
Heligoland serves as a guide, and the island itself as a resting-place, 
during bad weather. Mr. Seebohm's account of what he witnessed 
in the island, during nearly a month spent there in September to 
October, 1875, is most interesting; and I refer to it here chiefly for 
the sake of pointing out a very important error as to the cause of a 
very singular fact recorded there by Herr Gatke, who for fifty years 
observed and registered the migrations both in spring and autumn 
with great accuracy, and formed a collection of birds there, perhaps 
more extensive than could be made at any other station in Europe. 

(0415) 22 


The fact observed was, that, during the autumn migration, as 
regards many of the most abundant species, the young birds of the 
year, that is, those that had been hatched in the far north in the 
preceding June or July, and who were, therefore, only about three 
or four months old, arrived in Heligoland earliest and alone, the 
parent birds appearing a week or two later. This is the fact. It 
has been observed on Heligoland for half a century; every resident 
on the island knows it, and Mr. Seebohm declares that there can be 
no doubt whatever about it. The inference from this fact (drawn 
by Herr Gatke and all the lleligolanders, and apparently accepted 
by almost all European ornithologists) is, that these young birds 
start on their migration alone, and before their parents, and this 
not rarely or accidentally, but every year and they believe also 
that this is a fact, one of the most mysterious of the facts of migra- 
tion. Neither Mr. Seebohm nor Professor Lloyd Morgan (in his 
Habit and Instinct) expresses any doubts about the inference any 
more than about the fact. Yet the two things are totally distinct; 
and while I also admit the fact observed, I totally reject the infer- 
ence (assumed to be also a fact) as being absolutely without any 
direct evidence supporting it. I do not think any English observer 
has stated that the young of our summer migrants all gather to- 
gether in autumn and leave the country before the old birds; the 
American observers state that their migrating birds do not do so; 
while many facts observed at Heligoland show that no such infer- 
once is required to explain the admitted fact. Let us see what these 
additional facts are. 

The enormous rushes of migratory birds which rest at Heligoland 
always occur at night and are very intermittent. They usually take 
place on dark nights, sometimes in millions; at other times a week 
will sometimes pass with only a few stragglers. Of one such pitch- 
dark night, Mr. Seebohm writes: 

"Arrived at the lighthouse, an intensely interesting scene pre- 
sented itself. The whole of the zone of light within range of the 
mirrors was alive with birds coming and going. Nothing else was 
visible in the darkness of the night, but the lanthorn of the light- 
house vignetted in a drifting sea of birds. From the darkness in 
the east, clouds of birds were continually emerging in an uninter- 
rupted stream; a few swerved from their course, fluttered for a 
moment as if dazzled by the light, and then gradually vanished with 
the rest in the western gloom. ... I should be afraid to hazard 
a guess as to the hundreds of thousands that must have passed in 


a couple of hours; but the stray birds that the lighthouse man 
succeeded in capturing amounted to nearly 300." 

He also tells its that 15,000 skylarks have been caught on 
Heligoland in one night; and all agree that the countless myriads 
that are seen passing over Heligoland are but a minute fraction 
of those that really pass, high up and quite out of sight. This is 
shown by the fact, that if, on a dark night, it suddenly clears 
and the moon comes out, the swarms of birds immediately cease. 
Another fact is, that, on what the islanders call "good nights", the 
birds that come to rest seem to drop down suddenly out of the sky. 
One other fact is mentioned by Mr. Seebohm. It is that every year 
the regular migration season is preceded by a week or two during 
which a few stragglers appear; and these are all old birds and many 
of them slightly crippled, or partially moulted, or without some 
of their toes, or only half a tail, or some other defect. These are 
supposed to be mostly unmated birds, or those whose young have 
been destroyed. It is also supposed that, during favourable weather 
(for the birds), migration goes on continuously during the season of 
about six weeks, though for the most part invisible at Heligoland, 
but often audible when quite invisible. 

Now, the fact of the young birds only appearing on Heligoland 
for the first week or so of the season of each species is easily expli- 
cable. Remembering that the autumnal migration includes most 
of the parent birds and such of their broods as have survived, it is 
probable that the latter will form at least half or, more often, two- 
thirds of each migrating flock. But the young birds, not having 
yet acquired the full strength of the adults, and having had little, 
if any, experience in long and continuous flights, a considerable 
proportion of them on the occasion of their first long flight over the 
sea, on seeing the lighthouse and knowing already that lights imply 
land and food-crops below them, and being also much fatigued, will 
simply drop down to rest just as they are described as doing. The 
old birds and the stronger young ones, however, pass high overhead, 
till they reach the north coast of Holland, or, in some cases, pass 
over to our eastern coasts. We must also remember that the longer 
the birds are in making the journey overland, the more young birds 
are lost by the attacks of birds of prey and other enemies. Hence 
the earliest flocks will have a larger proportion of young birds than 
the later ones. The earlier flocks also, being less pressed for time, 
will be able to choose fine weather for the crossing, and thus it will 
be only the young and quickly fatigued birds that will probably 


fly low and come down to rest. Later on, every recurrence of bad 
weather will drive down old and young alike for temporary shelter 
and rest. Thus, all the facts are explained without having recourse 
to the wildly improbable hypothesis of flocks of immature birds 
migrating over land and sea quite alone, and a week in advance of 
their parents or guides. 



[Charles Robert Darwin, the famous English naturalist, and in some ways the 
greatest Englishman of the nineteenth century, did much to mould the form of 
modern thought. Of his many works, the Origin of Species is the best known. 
"He had a marvellous faculty of observation, and collected masses of facts to an 
extent that is almost incredible." " His calm unbiased mind and his love of 
truth enabled him immediately to abandon his own hypotheses when they ceased 
to be supported by observation." The following extract is taken from his book 
on Vegetable Mould and Earthworms (pp. 19-26). It will be noticed that, in this 
case, observation is aided by simple experiment.] 

The Sensitiveness of Worms to Light 

Worms are destitute of eyes, and at first I thought that they 
were quite insensible to light; for those kept in confinement were 
repeatedly observed by the aid of a candle, and others out of doors 
by the aid of a lantern, yet they were rarely alarmed, although 
extremely timid animals. Other persons have found no difficulty 
in observing worms at night by the same means. 

Hoffmeister, however, states that worms, with the exception of 
a few individuals, are extremely sensitive to light; but he admits 
that in most cases a certain time is requisite for its action. These 
statements led me to watch on many successive nights worms kept 
in pots, which were protected from currents of air by means of glass 
plates. The pots were approached very gently, in order that no 
vibration of the floor should be caused. When, in these circum- 
stances, worms were illuminated by a bull's-eye lantern having slides 
of dark red and blue glass, which intercepted so much light that 
they could be seen only with some difficulty, they were not at all 
affected by this amount of light, however long they were exposed 


to it. The light, as far as I could judge, was brighter than that 
from the full moon. Its colour apparently made no difference in 
the result. When they were illuminated by a candle, or even by a 
bright paraffin lamp, they were not usually affected at first. Nor 
were they when the light was alternately admitted and shut off. 
Sometimes, however, they behaved very differently, for as soon as 
the light fell on them, they withdrew into their burrows with almost 
instantaneous rapidity. This occurred perhaps once out of a dozen 
times. When they did not withdraw instantly, they often raised 
the anterior tapering ends of their bodies from the ground, as if 
their attention was aroused or as if surprise was felt; or they moved 
their bodies from side to side as if feeling for some object. They 
appeared distressed by the light; but I doubt whether this was 
really the case, for on two occasions after withdrawing slowly, they 
remained for a long time with their anterior extremities protruding 
a little from the mouths of their burrows, in which position they 
were ready for instant and complete withdrawal. 

When the light from a candle was concentrated by means of a 
large lens on the anterior extremity, they generally withdrew in- 
stantly; but this concentrated light failed to act perhaps once out of 
half a dozen trials. The light was on one occasion concentrated on 
a worm lying beneath water in a saucer, and it instantly withdrew 
into its burrow. In all cases the duration of the light, unless 
extremely feeble, made a great difference in the result; for worms 
left exposed before a paraffin lamp or candle, invariably retreated 
into their burrows within from five to fifteen minutes; and if in the 
evening the pots were illuminated before the worms had come out 
of their burrows, they failed to appear. 

From the foregoing facts it is evident that light affects worms 
by its intensity and by its duration. It is only the anterior ex- 
tremity of the body, where the cerebral ganglia lie, which is affected 
by light, as Hoftmcister asserts, and as I observed on many occasions. 
If this part is shaded, other parts of the body may be fully illumi- 
nated, and no effect will be produced. As these animals have no 
eyes, we must suppose that the light passes through their skins, and 
in some manner excites their cerebral ganglia. It appeared at first 
probable that the different manner in which they were affected on 
different occasions might be explained, either by the degree of ex- 
tension of their skin and its consequent transparency, or by some 
particular incidence of the light; but I could discover no such rela- 
tion. One thing was manifest, namely, that when worms were em- 


ployed in dragging leaves into their burrows or in eating them, and 
even during the short intervals whilst they rested from their work, 
they either did not perceive the light or were regardless of it; and 
this occurred even when the light was concentrated on them through 
a large lens. 

When a worm is suddenly illuminated and dashes like a rabbit 
into its burrow to use the expression employed by a friend we 
are at first led to look at the action as a reflex one. The irritation 
of the cerebral ganglia appears to cause certain muscles to contract 
in an inevitable manner, independently of the will or consciousness 
of the animal, as if it were an automaton. But the different effect 
which a light produced on different occasions, and especially the 
tact that a worm when in any way employed and in the intervals 
of such employment, whatever set of muscles and ganglia may then 
have been brought into play, is often regardless of light, are opposed 
to the view of the sudden withdrawal being a simple reflex action. 
With the higher animals, when close attention to some object leads 
to the disregard of the impressions which other objects must be pro- 
ducing on them, we attribute this to their attention being then 
absorbed; and attention implies the presence of a mind. Every 
sportsman knows that he can approach animals whilst they are 
grazing, fighting, or courting, much more easily than at other times. 
The state, also, of the nervous system of the higher animals differs 
much at different times ; for instance, a horse is much more readily 
startled at one time than another. The comparison here implied 
between the actions of one of the higher animals and of one so low 
in the scale as an earthworm, may appear far-fetched; for we thus 
attribute to the worm attention and some mental power, neverthe- 
less I can see no reason to doubt the justice of the comparison. 

Although worms cannot be said to possess the power of vision, 
their sensitiveness to light enables them to distinguish between day 
and night; and they thus escape extreme danger from the many 
diurnal animals which prey on them. Their withdrawal into their 
burrows during the day appears, however, to have become an habitual 
action; for worms kept in pots covered by glass plates, over which 
sheets of black paper were spread, arid placed before a north-east 
window, remained during the daytime in their burrows and came 
out every night; and they continued thus to act for a week. No 
doubt a little light may have entered between the sheets of glass 
and the blackened paper; but we know from the trials with coloured 
glass, that worms are indifferent to a small amount of light. 


Worms appear to be less sensitive to moderate radiant heat than 
to a bright light. I judge of this from having held at different 
times a poker heated to dull redness near some worms, at a distance 
which caused a very sensible degree of warmth in my hand. One 
of them took no notice; a second withdrew into its burrow, but not 
quickly; the third and fourth much more quickly, and the fifth as 
quickly as possible. The light from a candle, concentrated by a 
lens, and passing through a sheet of glass which would intercept 
most of the heat-rays, generally caused a much more rapid retreat 
than did the heated poker. Worms are sensitive to a low tempera- 
ture, as may be inferred from their not coining out of their burrows 
during a frost. 1 

Lord Avebury, F.R.S. 


[Lord Avelflivy-- the Sir John Lubbock of former years was a well-known 
naturalist, banker, politician, and man of affairs. His nuinerou^ works include 
British Wild Flowers ; Ants, JJees, and Wasps', and The Senses, Instincts, and In- 
telligence of Animals ; all of which abound with suggestions for teachers of Nature 
Study. The following extract (Ants, Bees, and Wasps, pp. 176-81) is a good illus- 
tration of the method of the naturalist who calls in the aid of simple experiments. 
This chapter should be compared with the last.] 

The Power of Communication amongst Ants 

One rather cold day, when but few ants were out, I selected a 
specimen of Atta testaceopilosa, belonging to a nest which I had 
brought back with mo from Algeria. She was out hunting about 
six feet from home, and I placed before her a large dead bluebottle 
fly, which she at once began to drag to the nest. I then pinned the 
fly to a piece of cork, in a small box, so that no ant could see the 
fly until she had climbed up the side of the box. The ant struggled, 
of course in vain, to move the fly. She pulled, first in one direction, 

1 Other interesting examples of Darwin's methods may be found on almost any page of 
any of his hooks. One or two may be mentioned : (1) Intelligence shown by worms in their 
manner of plugging their burrows (Earthworm, pp. 64-98); (2) The struggle of animals and 
plants for existence (Origin of Species, pp. 48-61); (3) Special expressions of animals (Expres- 
sion of the Emotions, pp. 116-46); (4) Comparison of mental powers of man and the lower 
animals (Descent of Man. pp. 98-147). 


and then in another, but, finding her efforts fruitless, she at length 
started off back to the nest empty-handed. At this time there were 
no ants coming out of the nest. Probably there were some few 
others out hunting, but for at lenst a quarter of an hour no ant 
had left the nest. My ant enteied the nest, but did not remain 
there; in less than a minute she emerged 1 accompanied by seven 
friends. I never saw so many come out, of that nest together before. 
In her excitement the first ant soon distanced her companions, who 
took the matter with much more sang-froid^ and had all the appear- 
ance of having come out reluctantly, or as if they had been asleep 
and were only half awake. The first ant ran on ahead, going 
straight to the fly. The others followed slowly and with many 
meanderings ; so slowly, indeed, that for twenty minutes the first 
ant was alone at the fly, trying in every way to move it. Finding 
this still impossible, she again returned to the nest, not chancing 
to meet any of her friends by the way. Again she emerged in less 
than a minute with eight friends, and hurried on to the fly. They 
were even less energetic than the first party ; and when they found 
they had lost sight of their guide, they one and all returned to the 
nest. In the meantime several of the first detachment had found the 
fly, and one of them succeeded in detaching a leg, with which she 
returned in triumph to the nest, coming out again directly with four 
or five companions. These latter, with one exception, soon gave up 
the chase and returned to the nest. I do not think so much of this 
last case, because as the ant carried in a substantial piece of booty in 
the shape of the fly's leg, it is not surprising that her friends should 
some of them accompany her on her return; but surely the other 
two cases indicate a distinct power of communication. 

Lest, however, it should be supposed that the result was acci- 
dental, I determined to try it again. Accordingly, on the following 
day I put another large dead fly before an ant belonging to the 
same nest, pinning it to a piece of cork as before. After trying in 
vain for ten minutes to move the fly, my ant started off home. At 
that time I could only see two other ants of that species outside 
the nest. Yet in a few seconds she emerged with no less than 
twelve friends. As in the previous case, she ran on ahead, and 
they followed very slowly and by no means directly, taking, in fact, 
nearly half an hour to reach the fly. The first ant, after vainly 
labouring for about a quarter of an hour to move the fly, started off 

i Lord Avebury marked his ants, for purposes of identification, by means of a small dab of 
paint on the back (op. cit. p. 6). 


again to the nest. Meeting one of her friends on the way, she con- 
versed with her a little, then continued towards the nest, but, after 
going about a foot, changed her mind, and returned with her friend 
to the fly. After some minutes, during which two or three other 
ants came up, one of them detached a leg, which she carried off to 
the nest, coming out again almost immediately with six friends, 
one of whom, curiously enough, seemed to lead the way, tracing it, 
I presume, by scent. I then removed the pin, and they carried oft 
the fly in triumph. 

Again, on June 15, 1878, another ant belonging to the same nest 
had found a dead spider, about the same distance from the nest. I 
pinned down the spider as before. The ant did all in her power to 
move it; but after trying for twelve minutes, she went off to the 
nest. Although for a quarter of an hour no other ant had left the 
nest, yet in a few seconds she came out again with ten companions. 
As in the preceding case, they followed very leisurely. She ran on 
ahead and worked at the spider for ten minutes; when, as none of 
her friends had arrived to her assistance, though they were wander- 
ing about, evidently in search of something, she started back home 
again. In three-quarters of an hour after entering the nest she 
reappeared, this time with fifteen friends, who came on somewhat 
more rapidly than the preceding batch, though still but slowly. By 
degrees, however, they all came up, and after most persevering 
efforts carried off the spider piecemeal. On July 7, I tried the same 
experiment with a soldier of Pheidole megacej'/iaht. She pulled at 
the fly for no less than fifty minutes, after which she went to the 
nest and brought five friends exactly as the Alia had done. 

On a subsequent day at three o'clock I again put a dead fly 
pinned on a bit of cork before a Formica fusca, who was out hunting. 
She tried in vain to carry it off, ran round and round, tugged in 
every direction, and at length at ten minutes to four she returned 
to the nest. Very soon after she reappeared, preceded by one and 
followed by two friends; these, however, failed to discover the fly, 
and, after wandering about a little, returned to the nest. She then 
set again to work alone, and in about forty minutes succeeded in 
cutting off the head of the fly, which she at once carried into the 
nest. In a little while she came out again, this time accompanied by 
five friends, all of whom found their way to the fly; one of these, 
having cut off the abdomen of the fly, took it into the nest, leaving 
three of her companions to bring in the remainder of their prey. 

These exDeriments certainly seem to indicate the possession by 


ants of something approaching to language. It is impossible to 
doubt that the friends were brought out by the first ant; and as she 
returned empty-handed to the nest, the others cannot have been 
induced to follow her merely by observing her proceedings. In face 
of such facts as these, it is impossible not to ask ourselves how far 
are ants mere exquisite automatons; how far are they conscious 
beings? When we see an ant-hill, tenanted by thousands of indus- 
trious inhabitants, excavating chambers, forming tunnels, making 
roads, guarding their home, gathering food, feeding the young, 
tending their domestic animals, each one fulfilling its duties indus- 
triously, and without confusion, it is difficult altogether to deny to 
them the gift of reason; and the preceding observations tend to con- 
firm the opinion that their mental powers differ from those of men, 
not so much in kind as in degree. 1 

William Harvey 


[We now pass to a subject where experiment plays a more important part. 
William Harvey, after graduating at Cambridge, studied medicine at Padua. He 
took his M.D at the age of twenty -four, and soon afterwards obtained the post 
of physician to St. Bartholomew's Hospital. Later on, he became physician to 
both James I and Charles I. In 1628 he published his famous treatise on the 
circulation of the blood, Excrcitatio de motu Oordis et Sanguinis. The method 
by which Harvey arrived at his complete and almost faultless solution of what is 
perhaps the most fundamental and difficult problem in Physiology, is deserving of 
the closest examination. We append two short extracts, but the whole volume, 
a cheap reprint of which can now be obtained, should be read.] 

The Circulation of the Blood 

From Chapter IX. Let us assume either arbitrarily or from 
experiment, the quantity of blood which the left ventricle of the 
heart will contain when distended, to be, say two ounces, three 
ounces, one ounce and a half, in the dead body I have found it to 
hold upwards of two ounces. Let us assume further, how much less 

* The whole of the volume forms most Instructive reading to the student of scientific 
method. The same remark applies to the other volumes mentioned at the head of the 


the heart will hold in the contracted than in the dilated state; and 
how much blood it will project into the aorta upon each contrac- 
tion; and all the world allows that with the systole something is 
always projected, a necessary consequence obvious from the struc- 
ture of the valves; and let us suppose as approaching the truth that 
the fourth, or fifth, or sixth, or even but the eighth part of its 
charge is thrown into the artery at each contraction; this would 
give either half an ounce, or three drachms, or one drachm of blood 
as propelled by the heart at each pulse into the aorta; which quan- 
tity, by reason of the valves at the root of the vessel, can by no 
means return into the ventricle. Now, in the course of half an 
hour, the heart will have made more than one thousand beats, in 
some as many as two, three, or even four thousand. Multiplying 
the number of drachms propelled by the number of pulses, we shall 
have either one thousand half-ounces, or one thousand times three 
drachms, or a like proportional quantity of blood, according to the 
amount which we assume as propelled with each stroke of the heart, 
sent from this organ into the artery; a larger quantity in every case 
than is contained in the whole body! In the same way, in the 
sheep or dog, say that but a single scruple of blood passes with each 
stroke of the heart, in one half-hour we should have one thousand 
scruples, or about three pounds and a half of blood injected into the 
aorta; but the body of neither animal contains above four pounds 
of blood, a fact which I have myself ascertained in the case of the 

Upon this supposition, therefore, assumed merely as a ground 
for reasoning, we see the whole mass of blood passing through the 

From Chapter X. If a live snake be laid open, the heart will be 
seen pulsating quietly, distinctly, for more than an hour, moving 
like a worm, contracting in its longitudinal dimensions, (for it is of 
an oblong shape,) and propelling its contents; becoming of a paler 
colour in the systole, of a deeper tint in the diastole; and almost all 
things else by which I have already said that the truth I contend 
for is established, only that here everything takes place more slowly, 
and is more distinct. This point in particular may be observed 
more clearly than the noon-day sun : the vena cava enters the heart 
at its lower part, the artery quits it at the superior part; the vein 
being now seized either with forceps or between the finger and 
thumb, and the course of the blood for some space below the heart 
interrupted, you will perceive the part that intervenes between the 


fingers and the heart almost immediately to become empty, the 
blood being exhausted by the action of the heart; at the same time 
the heart will become of a much paler colour, even in its state of 
dilatation, than it was before; it is also smaller than at first, from 
wanting blood; and then it begins to beat more slowly, so that it 
seems at length as if it were about to die. But the impediment to 
the flow of blood being removed, instantly the colour and the size 
of the heart are restored. 

If, on the contrary, the artery instead of the vein be compressed 
or tied, you will observe the part between the obstacle and the 
heart, and the heart itself, to become inordinately distended, to 
assume a deep purple or even livid colour, and at length to be so 
much oppressed with blood, that you will believe it about to be 
choked; but the obstacle removed, all things immediately return 
to their pristine state the heart to its colour, size, stroke, &c. 

Here then we have evidence of two kinds of death: extinction 
from deficiency, and suffocation from excess. Examples of both 
have now been set before you, and you have had opportunity of 
viewing the truth contended for with your own eyes in the heart. 

[The experiments with ligatures in ch. xi, and the demonstration 
of the function of the valves in the veins in ch. xiii, are excellent 
examples of methodical investigation.] 

William Charles Wells 


[Dr. Wells was a London physician to whom we are indebted for the true 
theory of Dew. In 1814 he published his admirable Essay on this subject. A 
long series of experiments, happily conceived and skilfully executed, enabled him 
to propound his theory, which has stood the test of all subsequent criticism. The 
Essay is a model of wise enquiry, lucid exposition, and scientific method. The 
success of the investigation was largely due to the very careful use of the Method 
of Agreement and the Method of Ditterence, combined with a well-thought-out 
logical plan of continually varying the circumstances. The Essay extends over 
160 pp. A copy can occasionally be bought for three or four shillings.] 

Wells* observations and experiments were made in a Surrey 
garden "not more than 1J miles from a densely built part of the 


suburbs" of South London. The garden was level and half an acre 
in extent. "At one end was a dwelling house of moderate size, at 
the other a range of low buildings; on one side a row of high trees, 
on the other a low fence, dividing it from another garden." Within 
it were some small fruit trees. Towards one end there was a grass- 
plat, 62 feet by 16 feet, the herbage of which was kept short. The 
rest of the garden was given up to the growing of vegetables. " All 
these circumstances, however trifling they may appear, had influence 
on my experiments." 

In one part of his investigation Wells used, for collecting the dew, 
little bundles of wool, which, when dry, weighed 10 grains each. 

Influence of Situation on the Production of Dew 

I now proceed to relate the influence which several differences in 
the situation have upon the production of dew. 

One general fact relative to situation is, that whatever diminishes 
the view of the sky, as seen from the exposed body, occasions the 
quantity of dew, which is formed upon it, to be less than would 
have occurred if the exposure to the sky had been complete. 

Experiment with elevated board. I placed, on several clear and 
still nights, 10 grains of wool upon the middle of a painted board, 
4i feet long, 2 feet wide, and 1 inch thick, elevated 4 feet above 
the grass -plat, by means of four slender wooden props of equal 
height; and, at the same time I attached, loosely, 10 grains of 
wool to the middle of its under side. The two parcels were, conse- 
quently, only an inch asunder, and were equally exposed to the 
action of the air. Upon one night, however, I found, that the 
upper parcel had gained 14 grains in weight, but the lower only 4. 
On a second night the quantities of moisture, acquired by like 
parcels of wool, in the same situations as in the first experiment, 
were 19 and 6 grains; on a third, 11 and 2; on a fourth, 20 and 4; 
the smaller quantity being always that which was gained by the 
wool attached to the lower side of the board. 

Experiment with bent pasteboard. I bent a sheet of pasteboard into 
the shape of a house roof, making the angle of flexure 90 degrees, 
and leaving both ends open. This was placed one evening, with its 
ridge uppermost, upon the same grass plat, in the direction of the 
wind, as well as this could be ascertained. I then laid 10 grains 
of wool on the middle of that part of the grass, which was sheltered 
by the roof, and the same quantity on another part of the grass- 


plat fully exposed to the sky. In the morning the sheltered wool 
was found to have increased in weight only 2 grains, but that 
which had been exposed to the sky, 16 grains. 

In these experiments, the view of the sky was almost entirely 
cut off from the situations in which little dew was formed. In 
others, where it was less so, the quantity gained was greater. Thus, 
10 grains of wool, placed upon the spot of the grass-plat which was 
directly under the middle of the raised board, and which enjoyed, 
therefore, a considerable oblique view of the sky, acquired during 
one night 7, during a second 9, and during a third 12 grains of 
moisture, while the quantities gained, during the same times, by 
equal parcels of wool, laid upon another part of the grass-plat, which 
was entirely exposed to the heavens, were 10, 16, and 20 grains. 

As no moisture, falling like rain from the atmosphere, could, on 
a calm night, have reached the wool in any of the situations, where 
little dew was formed, it may be thought that the board and the 
pasteboard under which the wool was placed, prevented, mechani- 
cally, the access of that fluid. But on this supposition it cannot be 
explained why some dew was always found in the most sheltered 
places, and why a considerable quantity occurred upon the grass 
under the middle of the raised board. A still stronger proof of 
the want of justness in this supposition is afforded by the following 

Experiment with hollow cylinder. I placed, upright, on the grass- 
plat, a hollow cylinder of baked clay, the height of which was 
2 feet, and diameter 1 foot. On the grass, surrounded by the 
cylinder, were laid 10 grains of wool, which, in this situation, as 
there was not the least wind, would have received as much rain 
as a like quantity of wool fully exposed to the sky. But the 
quantity of moisture obtained by the wool surrounded by the 
cylinder, was only a little more than 2 grains, while that acquired 
by 10 grains of fully exposed wool was 16. This occurred on the 
night, during which the wool under the bent pasteboard gained 
only 2 grains of moisture. 

Other varieties of situation. Dew, however, will, in consequence 
of other varieties of situation, form in very different quantities, upon 
substances of the same kind, although these should be similarly 
exposed to the sky. 

(1) In the first place; it is requisite, for the most abundant 
formation of dew, that the substance attracting it should rest on a 
stable horizontal body of some extent. Thus, upon one night, while 


10 grains of wool, laid upon the raised board, increased 20 grains 
in weight, an equal quantity, suspended in the open air, 5| feet 
above the ground, increased only 11 grains, notwithstanding that 
it presented a greater surface to the air than the other parcel. On 
another night, 10 grains of wool gained on the raised board 19 grains, 
but the same quantity suspended in the air, on a level with the 
board, only 13; and on a third, 10 grains of wool acquired, on the 
same board, 2 grains of weight, during the time in which other 
10 grains, hung in the air, at the same height, acquired only half 
a grain. 

(2) In the second place; the quantities of dew attracted by equal 
masses of wool, similarly exposed to the sky, and resting on equally 
stable and extended bodies, oftentimes vary considerably, in conse- 
quence of some difference in the other circumstances of these bodies. Ten 
grains of wool, for instance, having been placed (a) on the grass-plat, 
on a dewy evening; 10 grains upon (b) the gravel walk which bounded 
the grass-plat; and 10 grains upon (c) a bed of bare garden mould, 
immediately adjoining the gravel walk; in the morning the wool 
on the grass was found to have increased 16 grains in weight, but 
that on the gravel walk only 9, and that on the garden mould 
only 8. On another night, during the time that 10 grains of wool 
laid upon grass, acquired 2 grains of moisture, the same quantity 
gained only half a grain upon the bed of garden mould, and a like 
quantity, placed upon the gravel walk, received no accession of 
weight whatever. 

Two objections will probably be made against the accuracy of 
these, as well as my other experiments with wool, (a) One is that 
wool placed on grass may, by a kind of capillary attraction, receive 
dew previously formed on the grass, in addition to its own. To 
this I answer, that wool in a china saucer, placed on the grass, 
acquired very nearly as much weight, as an equal parcel imme- 
diately touching the grass, (b) The second objection is, that a part 
of the increased weight in the wool might arise from its imbibing 
moisture, as a hygroscopic substance. I do riot deny that some 
weight was given to the wool in this way; but it may be safely 
affirmed that this quantity must have been very small. For, on 
very cloudy nights, apparently best fitted to increase the weight 
of hygroscopic substances, wool upon the raised board would, in 
the course of many hours, acquire little or no weight; and in 
London I have never found 10 grains of wool, exposed to the air 
on the outside of one of my chamber windows, to increase, during 


a whole night, more than half a grain in weight. When this weight 
was gained, the weather was clear and still; if the weather was 
cloudy and windy, the wool received either less or no weight. This 
window is so situated as to be, in great measure, deprived of the 
aspect of the sky. 

It being shown that wool, though highly attractive of dew, was 
prevented, by the mere vicinity of a gravel walk, or a bed of garden 
mould, for only a small part of it actually touched those bodies, 
from acquiring nearly as much dew, as an equal parcel laid upon 
grass, it may be readily inferred, that little was formed upon them- 
selves. In confirmation of this conclusion, I shall mention, that 
I never saw dew on either of them. Another fact of the same 
kind is that, while returning to London from the scene of my 
experiments about sunrise, I never observed, if the atmosphere 
was clear, the public road, or any stone pavement on the side of it, 
to be moistened with dew, though grass within a few feet of it, and 
painted doors and windows of houses not far from it, were fre- 
quently very wet. If, indeed, there was a foggy morning, after a 
clear and calm night, even the streets of London would sometimes 
be moist, though they had been dry the day before, and no rain 
had in the meanwhile fallen. This entire, or almost entire, freedom 
of certain situations from dew depends, however, much more upon 
extraneous circumstances, than upon the nature of the substances 
found there; for river-sand, though of the same nature as gravel, 
when placed upon the raised board, or upon grass, attracted dew 

(3) A third difference, from situation, in the quantity of dew 
collected by similar bodies, similarly exposed to the sky, depends 
upon their position with respect to the ground. Thus, a substance 
placed several feet above the ground, though in this situation later' 
dewed, than if it touched the earth, would, notwithstanding, if it 
lay upon a stable body of some extent, such as the raised boanl 
lately mentioned, acquire more dew during a very still night, than 
a similar substance lying on grass. 

(4) A fourth difference of this kind occurred among bodies placed 
on different parts of the same board. For one, that was placed nt the 
leeward end of it, generally acquired more dew than a similar body 
at the windward extremity. 1 

Space cannot be spared for further extracts, but the rccider is 

i Edition of 1818; pp. 135-44. 


strongly urged to go through the whole Essay. Wells was never 
tired of varying the circumstances in every possible way. Consider, 
for instance, his experiments with metals, in connection with the for- 
mation of dew. He varied the kind of metal, the size of the metal, 
the thickness of the metal, and the position of the metal with respect 
to the ground; he exposed the metal alone, and the metal closely 
attached to some other substance; he exposed the metal dry, and 
the metal purposely first moistened; he removed the metal from 
place to place during the night; and so on, seemingly almost inde- 
finitely. He varied one circumstance at a time-, the detection of a 
difference enabled him to form a hypothesis, which he then promptly 
checked by means of further experiment. 

Joseph Black 


[We now give a few instances of experimental investigations by famous 
chemists. It is a little difficult to make a choice from the large number of 
eminent men whose names appear in every textbook dealing with the history 
of Chemistry ; but Black, Priestley, Gay - Lussac, and Davy may certainly be 
regarded as worthy representatives of the others. 

Black was Professor of Chemistry in the University of Edinburgh from 1766 
to 1797. He graduated at that University in 1754, and immediately afterwards 
revealed himself as a great scientific discoverer. At that time the causticity of 
the alkalis was attributed to their absorbing an imaginary fire-essence known as 
ptdoyiston, an hypothesis which Black overthrew. Black showed, for example, 
that the causticity acquired by " crude lime" on ignition is due to the expulsion 
of a ponderable gas, carbonic acid, which he named " fixed air ", meaning that 
it was found not only as a separate fluid, but as fixed in solid bodies. The dis- 
covery was embodied in a Paper, which Black read in 1755, "Experiments upon 
Magnesia Alba, Quicklime, and other Alkaline Substances ". There are very few 
finer examples of inductive investigation iiv the whole range of Science. The 
following extract is taken, with slight omissions and modifications, from Part II 
of the Paper.] 1 

Fixed Air in Lime and in Alkalis 

It is sufficiently clear [from previous experiments] that the cal- 
careous earths in their native state, and that the alkalis and mag- 

1 The whole paper is reproduced in the Alembic Club Reprints, which the reader should 

(0415) 23 


nesia 1 in their ordinary condition, contain a large quantity of fixed 
air, 2 and this air certainly adheres to them with considerable force, 
since a strong fire is necessary to separate it from magnesia, and the 
strongest is not sufficient to expel it entirely from fixed alkalis, 3 or 
take away their power of effervescing with acid salts. 

Hypothesis. These considerations led me to conclude that the 
relations between fixed air and alkaline substances, were somewhat 
similar to the relation between these and acids; that as the calca- 
reous earths and alkalis attract acids strongly and can be saturated 
with them, so they also attract fixed air, and are in their ordinary 
state saturated with it: and when we mix an acid with an alkali or 
with an absorbent earth, that the air is then set at liberty, and 
breaks out with violence ; because the alkaline body attracts it more 
weakly than it does the acid, and because the acid and air cannot 
both be joined to the same body at the same time. 

Further Hypothesis. I also imagined that, when the calcareous 
earths are exposed to the action of a violent fire, and are thereby 
converted into quicklime, they suffer no other change in their com- 
position than the loss of a small quantity of water and of their fixed 
air. The remarkable acrimony which we perceive in them after this 
process, was not supposed to proceed from any additional matter re- 
ceived from the fire, but seemed to be an essential property of the 
pure earth, depending on an attraction for those several substances 
which it then became capable of corroding or dissolving, which 
attraction had been insensible as long as the air adhered to the 
eaith, but discovered itself upon the separation. 

This supposition was founded upon an observation of the most 
frequent consequences of combining bodies in chemistry. Commonly, 
when we join two bodies together, their acrimony or attraction for 
other substances becomes immediately either less perceivable or 
entirely insensible; although it was sufficiently strong and remark- 
able before their union, and may be rendered evident again by dis- 
joining them. A neutral salt, which is composed of an acid and 
alkali, does not possess the acrimony of either of its constituent 
parts. It can easily be separated from water, has little or no effect 
upon metals, is incapable of being joined to inflammable bodies, and 
of corroding or dissolving animals and vegetables; so that the attrac- 
tion both of the acid and alkali for these several substances seems to 
be suspended till they are again separated from one another. 

Crude lime was therefore considered as a peculiar acrid earth 

* That is, magnesia alba. 2 That is, carbon dioxide. * That is, potash and soda. 


rendered mild by its union with fixed air; and quicklime as the 
same earth, in which, by having separated the air, we discover that 
acrimony or attraction for water, for animal, vegetable, and for in- 
flammable substances. 

The General Theory Considered. According to our theory, the 
relation of the calcareous earth to air and water appeared to agree 
with the relation of the same earth to vitriolic and vegetable acids. 
As chalk, for instance, has a stronger attraction for the vitriolic than 
for the vegetable acid, and is dissolved with more difficulty when 
combined with the first than when joined to the second: so it also 
attracts air more strongly than water, and is dissolved with more 
difficulty when saturated with air than when compounded with 
water only. 

A calcareous earth deprived of its air, or in the state of quick- 
lime, greedily absorbs a considerable quantity of water, becomes 
soluble in that fluid, and is then said to be slaked; but as soon as 
it meets with fixed air, it is supposed to quit the water and join 
itself to the air, for which it has a superior attraction, and is there- 
fore restored to its first state of mildness and insolubility in water. 

When slaked lime is mixed with water, the fixed air in the water 
is attracted by the lime, and saturates a small portion of it, which 
then becomes again incapable of dissolution, but part of the remain- 
ing slaked lime is dissolved and composes lime water. 

If this fluid be exposed to the open air, the particles of quick- 
lime which are nearest the surface gradually attract the particles of 
fixed air which float in the atmosphere. But at the same time that 
a particle of lime is thus saturated with air, it is also restored to its 
native state of mildness and insolubility; and as the whole of this 
change must happen at the surface, the whole of the lime is suc- 
cessively collected there under its original form of an insipid calca- 
reous earth, called the cream or crusts of lime water. 

When quicklime itself is exposed to the open air, it absorbs the par- 
ticles of water and of fixed air which come within its sphere of attrac- 
tion, as it meets with the first of these in greatest plenty, the greatest 
part of it assumes the form of slaked lime; the rest is restored to its 
original state; and if it be exposed for a sufficient length of time, 
the whole of it is gradually saturated with air, to which the water 
as gradually yields its place. 

If quicklime be mixed with a dissolved alkali, it shows an attrac- 
tion for fixed air superior to that of the alkali. It robs the salt of 
its air, and thereby becomes mild itself, while the alkali is conse- 


quently rendered more corrosive, or discovers its natural degree of 
acrimony or strong attraction for water, and for bodies of the inflam- 
mable, and of the animal and vegetable kind; which attraction was 
less perceivable as long as it was saturated with air. And the vola- 
tile alkali when deprived of its air, besides this attraction for various 
bodies, discovers likewise its natural degree of volatility, which was 
formerly somewhat repressed by the air adhering to it, in the same 
manner as it is repressed by the addition of an acid. 

Consequences of the Theory. This account of lime and alkalis re- 
commended itself by its simplicity, and by affording an easy solution 
of many phenomena, but appeared upon a nearer view to be attended 
with consequences that were so very new and extraordinary, as to 
render suspicious the principles from which they were drawn. 

I resolved, however, to examine, in a particular manner, such 
of these consequences as were the most unavoidable, and found 
the greatest number of them might be reduced to the following 
propositions : 

Proposition I. If we only separate a quantity of air from lime 
and alkalis, when we render them caustic they will be found to lose 
part of their weight in the operation, but will saturate the same 
quantity of acid as before, arid the saturation will be performed 
without effervescence. 

Proposition II. If quicklime be no other than a calcareous earth 
deprived of its air, and whose attraction for fixed air is stronger 
than that of alkalis, it follows that, by adding to it a sufficient quan- 
tity of alkali saturated with air, the lime will recover the whole of 
its air, and be entirely restored to its original weight and condition; 
and it also follows, that the earth separated from lime water by an 
alkali, is the lime whick was dissolved in the water now restored to 
its original mild and insoluble state. 1 

These are necessary conclusions from the above suppositions. 
1 determined to inquire into the truth of them by way of experi- 
ment. I therefore engaged myself in a set of trials; the history of 
which is here subjoined. 

The Consequences Proved to be Consonant with the Theory. Desiring 
to know how much of an acid a calcareous earth will absorb, and 
what quantity of air is expelled during the dissolution, I saturated 
120 grains of chalk with diluted spirit of salt; 421 grains of the acid 
finished the dissolution, and the chalk lost 48 grains of air. 

This experiment was necessary before the following, by which 
i Three other Propositions are also stated, making five in all. 


I proposed to inquire into the truth of the first proposition, so far 
as it relates to quicklime. 

120 grains of chalk were converted into a perfect quicklime, and 
lost 52 grains in the fire. This quicklime was slaked, or reduced to 
a perfect liquor with an ounce of water, and then dissolved in the 
same manner and with the same acid as the 120 grains of chalk in 
the preceding experiment; 414 grains of the acid finished the 
saturation without any sensible effervescence or loss of weight. 

It therefore appears from these experiments that no air is 
separated from quicklime by an acid, and that chalk saturates 
nearly the same quantity of acid after it is converted into quick- 
lime as before. 

With respect to the second proposition, I tried the following 
experiments : 

A piece of perfect quicklime made from 120 grains of chalk, and 
which weighed 68 grains, was reduced to a very fine powder, and 
thrown into a filtrated mixture of an ounce of a fixed alkaline 
salt and two ounces of water. After a slight digestion, the powder 
being well washed and dried, weighed 118 grains. It was similar 
in every trial to a fine powder of ordinary chalk, and was there- 
fore saturated with -air which must have been furnished by the 

60 grains of pure salt of tartar 1 was dissolved in 14 pounds of 
lime water, and the powder thereby precipitated, being carefully 
collected and dried, weighed 150 grains. When exposed to a violent 
fire, it was converted into a true quicklime, and had every other 
quality of a calcareous earth. 

This experiment was repeated with the volatile alkali, and also 
with the fossil or alkali of sea-salt, and exactly with the same 
event. 2 

* That is, potassium carbonate. 

a The remaining three Propositions are similarly dealt with, and the investigation con- 
tinues. Hut the logical finality of Black's conclusions can hardly be realized unlesa the 
whole paper is read. 


Joseph Priestley 


[Joseph Priestley, though not a professional man of science, devoted a good 
deal of attention to Chemistry, and contributed greatly to our knowledge of gases. 
In 1774 he discovered oxygen. But his researches on Different Kinds of Air are 
usually considered to be more remarkable for the impulse they gave to contro- 
versy and experiment than for their concrete results. Whatever success he gained 
was probably due almost as much to good luck as to good method, for he held 
that all discoveries are made by chance. He possessed great insight, but ap- 
parently he failed to see the need of constant and rigorous verification. Yet 
his exceedingly important results went far to build up Chemistry into a Science. 
At Leeds he lived next door to a brewery, and amused himself with experiments 
on the "fixed air" (CO 2 ) produced there. Thus his researches began. His works 
are well worth reading if only because of the naivete" with which he tells the whole 
story of his experiments. The following extract gives a good general idea of hia 

Fixed Air 

It was in consequence of living for some time in the neighbour- 
hood of a brewery, that I was induced to make experiments on 
fixed air, of which there is always a large body, ready formed, upon 
the surface of the fermenting liquor, generally about 9 inches or 
a foot in depth, within which any kind of substance may be very 
conveniently placed; and though, in these circumstances, the fixed 
air must be continually mixing with the common air, and is there- 
fore far from being perfectly pure, yet there is a constant fresh 
supply from the fermenting liquor, and it is pure enough for many 

A person, who is quite a stranger to the properties of this 
kind of air, would be agreeably amused with extinguishing lighted 
candles, or chips of wood in it, as it lies upon the surface of the 
fermenting liquor; for the smoke readily unites with this kind of 
air, probably by means of the water which it contains; so that very 
little or none of the smoke will escape in the open air, which is 
incumbent upon it. It is remarkable that the upper surface of this 
smoke, floating in the fixed air, is smooth and well defined; whereas 
the lower surface is exceedingly ragged, several parts hanging down 
to a considerable distance within the body of the fixed air, and 


sometimes in the form of balls, connected to the upper stratum by 
slender threads, as if they were suspended. 

Making an agitation in this air, the surface of it is thrown into 
the form of waves; and if by this agitation any of the fixed air be 
thrown over the side of the vessel, the smoke which is mixed with 
it will fall to the ground, as if it were so much water, the fixed air 
being heavier than common air. 

The red part of burning wood was extinguished in this air, but 
I could not perceive that a red-hot poker was sooner cooled in it. 

Fixed air does not instantly mix with common air. Indeed, if it 
did, it could not be caught upon the surface of the fermenting liquor. 
A candle put under a large receiver, and immediately plunged very 
deep below the surface of the fixed air, will burn some time. But 
vessels with the smallest orifices, hanging with their mouths down- 
wards in the fixed air, will, in tirnv, have the common air, which 
they contain, perfectly mixed with it. 

Considering the near aflinity between water and fixed air, I con- 
cluded that if a quantity of water was placed near the yeast of the 
fermenting liquor, it could not fail to imbibe that air, and thereby 
acquire the principal properties of Pyrmont, and some other medi- 
cinal mineral waters. Accordingly I found that when the surface 
of the water was considerable, it always acquired the pleasant 
acidulous taste that Pyrmont water has. The readiest way of 
impregnating water with this viitue, in these circumstances, is to 
take two vessels, and to keep pouring the water from one into the 
other when they are both of them held as near the yeast as possible. 
In this manner I have sometimes, in the space of two or three 
minutes, made a glass of exceedingly pleasant sparkling water, 
which could hardly be distinguished from very good Pyrmont, or 
rather Seltzer water. 

But the 'rnoxt effectual way of impregnating water with fixed air 
is to put the vessels which contain the water into glass jars, filled 
with the purest fixed air, made by the solution of chalk in diluted 
oil of vitriol, standing in quicksilver. In this manner, I have in 
about two days made a quantity of water to imbibe more than an 
equal bulk of fixed air, so that it must have been stronger than 
the best imported Pyrmont. If a sullicient quantity of quicksilver 
cannot be procured, oil may be used with sufficient advantage, for 
this purpose, as it imbibes the fixed air very slowly. 

The readiest method of preparing this water for use is to agitate 
it strongly with a large surface exposed to the fixed air. By this 


means, more than an equal bulk of air may be communicated to a 
large quantity of water in the space of a few minutes. 

Water thus impregnated with fixed air readily dissolves iron; 
so that if a quantity of iron filings be put in it, it presently becomes 
a strong chalybeate, and of the mildest and most agreeable kind. 

I have recommended the use of chalk and oil of vitriol as the 
cheapest, and, upon the whole, the best materials for the purpose. 

Whereas some persons had suspected that a quantity of the oil 
of vitriol was rendered volatile by this process, I examined it, by all 
the chemical methods that are in use; but could not find that water 
thus impregnated contained the least perceivable quantity of that 

The heat of boiling water will expel all the fixed air, if a phial 
containing the impregnated water be held in it; but it will often 
require above half an hour to do it completely. 

Having succeeded so well with artificial Pyrmont water, I 
imagined that it might be possible to give ice the same virtue, 
especially as cold is known to promote the absorption of fixed air 
by water; but in this I found myself quite mistaken. I put several 
pieces of ice into a quantity of fixed air, confined by quicksilver, 
but no part of it was absorbed in two days and two nights. 

I then took a quantity of strong artificial Pyrmont water, and 
putting it into a thin glass phial, I set it in a pot that was filled 
with snow and salt. This mixture instantly freezing the water that 
was contiguous to the sides of the glass, the air was discharged 
plentifully, so that I caught a considerable quantity in a bladder 
tied to the mouth of the phial. 

The pressure of the atmosphere assists very considerably in 
keeping fixed air confined in water; for in an exhausted receiver, 
Pyrmont water will absolutely boil, by the copious discharge of its 
air. This is also the reason why beer and ale froth so much in vacuo. 
I do not doubt, therefore, that by the help of a condensing engine, 
water might be much more highly impregnated with the virtues of 
the Pyrmont spring. 

Insects and animals which breathe very little are stifled in fixed 
air, but are not soon quite killed in it. Flies and butterflies will 
generally become torpid, and seemingly dead, after being held a few 
minutes over the fermenting liquor; but they revive again after 
being brought into the fresh air. But there are very great varieties 
with respect to the time in which different kinds of flies will either 
become torpid in the fixed air, or die in it. A large, strong frog 


was much swollen, and seemed to be nearly dead, after being held 
about six minutes over the fermenting liquor; but it recovered upon 
being brought into the common air. A snail treated in the same 
manner died presently. 

Fixed air is presently fatal to vegetable life. At least sprigs of 
mint growing in water, and placed over the fermenting liquor, will 
often become quite dead in one day, or even in a less space of time; 
nor do they recover when they are afterwards brought into the 
common air. I am told, however, that some other plants are much 
more hardy in this respect. 1 

Joseph Louis Gay-Lussac 


[Gay-Lussac was one of the most distinguished of French physicists and 
chemists. From 1808 to 1832 he was Professor of Physics at the Sorbonne, 
and afterwards Professor 6f Chemistry at the Jardin des Plantes. His work was 
remarkable not only for its range, but for its intrinsic worth, its accuracy of detail, 
its experimental ingenuity, its descriptive clearness, and the soundness of its infer- 
ences. His name is closely associated with the law of gaseous volumes, with the 
law of variation of gaseous volume with temperature, with researches on iodine 
and cyanogen, and with many analytical methods (for instance, the method of 
titration). The following extract 2 is from a Paper he read before the Philomathic 
Society in 1808.] 

On the Combination of Gaseous Substances with each 


Substances, whether in the solid, liquid, or gaseous state, possess 
properties which are independent of the force of cohesion; but they 
also possess others which appear to be modified by this force, and 
which no longer follow any regular law. The same pressure applied 
to all solid or liquid substances would produce a diminution of 

i From Experiments and Observations on Different Kinds of Air (1774), pp 26-43. Priest- 
ley's paper on the discovery of Oxygen is included in the Alembic Club Reprints (No. 7); it 
should be read in conjunction with Scheele's paper on the same subject (Reprint No. 8). 

Priestley's account of the apparatus he devised and used will be found in the volume 
above mentioned (pp. 6-22). A copy of this volume may sometimes be discovered in a second- 
hand book-shop. The old plates are interesting. 

See Alembic Club Reprint No, 4, and Memoires de la SocUte d'Arcueil, ii (1809), pp. 207-34. 


volume differing in each case, while it would be equal for all elastic 
fluids. Similarly, heat expands all substances; but the dilatations 
of liquids and solids have hitherto presented no regularity, and it is 
only those of elastic fluids which are equal and independent of the 
nature of each gas. The attraction of the molecules in solids and 
liquids is, therefore, the cause which modifies their special properties; 
and it appears that it is only when the attraction is entirely de- 
stroyed, as in gases, that bodies under similar conditions obey simple 
and regular laws. At least it is my intention to make known some 
new properties in gases, the effects of which are regular, by showing 
that these substances combine amongst themselves in very simple 

It is a very important question in itself, and one much discussed 
amongst chemists, to ascertain if compounds are formed in all sorts 
of proportions. M. Proust, who appears first to have fixed his 
attention on this subject, is of opinion that the metals are suscep- 
tible of only two degrees of oxidation, a minimum and a maximum \ 
but led away by this seductive theory, he has seen himself forced 
to entertain principles contrary to physics in order to reduce to 
two oxides all those which the same metal sometimes presents. 
M. Berthollet thinks, on the other hand, that compounds are always 
formed in very variable proportions, unless they are determined by 
special causes, such as crystalli/ation, insolubility, or elasticity. 
Lastly, Dalton has advanced the idea that compounds of two bodies 
are formed in such, a way that one atom of the one unites with one, 
two, three, or more atoms of the other. It would follow from this 
mode of looking at compounds that they are formed in constant pro- 
portions, the existence of intermediate bodies being excluded, and 
in this respect Dal ton's theory would resemble that of M. lYoust; 
but M. Berthollet has already strongly opposed it, and we shall see 
that in reality it is not entirely exact. Such is the .state of the 
question now under discussion; it is still very far from receiving Its 
solution, but I hope that the facts which I now proceed to set forth, 
facts which had entirely escaped the notice of chemists, will contri 
bute to its elucidation. 

Suspecting from the exact ratio of 100 of oxygen to 200 of 
hydrogen, which M. Humboldt and I had determined for the pro- 
portions of water, that other gases might also combine in simple 
ratios, I have made the following experiments. I prepared fluoboiic 1 ^ 
muriatic, and carbonic gases, and made them combine successively 

* "Obtained by distilling pure fluoride of lime with vitreous horaeic acid." 


with ammonia gas. (1) 100 parts of muriatic gas saturate precisely 
100 parts of ammonia gas, and the salt which is formed from 
them is perfectly neutral, whether one or other gases is in excess. 
(2) Fluoboric gas, on the contrary, unites in two proportions with am- 
monia gas. When the acid 1 gas is put first into the graduated tube, 
and the other gas is then passed in, it is found that equal volumes 
of the two condense, and that the salt formed is neutral. But if 
we begin by first putting the ammonia gas into the tube, and then 
admitting the fluoboric gas in single bubbles, the first gas will then 
be in excess with regard to the second, and there will result a salt 
with excess of base, composed of 100 of fluoboric gas and 200 of 
ammonia gas. (3) If carbonic gas is brought into contact with 
ammonia gas, by passing it sometimes first, sometimes second into 
the tube, there is always formed a sub-carbonate composed of 100 
parts of carbonic gas and 200 of ammonia gas. It may, however, 
be proved that neutral carbonate of ammonia would be composed 
of equal volumes of each of these components. M. Berthollet, who 
has analysed this salt, obtained by passing carbonic gas into the sub- 
carbonate, found that it was composed of 73*34 parts by weight of 
carbonic gas and 26*66 of ammonia gas. Now if we suppose it to 
be composed of equal volumes of its components, we find from their 
known specific gravity, that it contains by weight 71*81 per cent of 
carbonic acid and 28*19 per cent of ammonia, a proportion differing 
only slightly from the preceding. 

If the neutral carbonate of ammonia could be formed by the 
mixture of carbonic gas and ammonia i^.is, as much of one gas as 
of the other would be absorbed; and since we ran only obtain it 
through the intervention of water, wo must conclude that it is the 
affinity of this liquid which competes with that of the ammonia to 
overcome the elasticity of the carbonic acid, and that the neutral 
carbonate of ammonia can only exist through the medium of water. 

Thus we may conclude that muriatic, fluoboric, and carbonic 
acids take exactly their own volumes of ammonia gas to form neutral 
salts, and that the last two take twice as much to form sub-salts. It 
is very remarkable to see acids so different from one another neu- 
tralize a volume of ammonia gas equal to their own; and from this 
we may suspect that if all acids and all alkalis could be obtained in 
the gaseous state, neutrality would result from the combination of 
equal volumes of acid and alkali. 

It is not less remarkable that whether we obtain a neutral salt 
i "Alkaline" in the original 


or a sub-salt, their elements combine in simple ratios which may be 
considered as limits to their proportions. Accordingly, if we accept 
the specific gravity of muriatic acid determined by M. Biot 1 and 
myself, and those of carbonic gas and ammonia given by MM. Biot 
and Arago, we find that dry muriate of ammonia is composed of 
100 parts of ammonia to 1607 parts of muriatic acid (i.e. 38*35 per 
cent to 61*65 per cent), a proportion very far from that of M. Ber- 
thollet, viz., 100 of ammonia to 213 of acid. 

In the same way, we find that sub-carbonate of ammonia con 
tains 100 parts of ammonia to 127*3 of carbonic acid (i.e. 43*98 per 
cent to 56*02 per cent); and the neutral carbonate 100 parts of am- 
monia to 254*6 of carbonic acid (i.e. 28*19 per cent to 71*81 per cent). 

It is easy from the preceding results to ascertain the ratios of 
the capacity of fluoboric, muriatic, and carbonic acids; for since 
these three gases saturate the same volume of ammonia gas, their 
relative capacities will be inversely as their densities, allowance 
having been made for the water contained in muriatic acid. 

We might even now conclude that gases combine with each other 
in very simple ratios; but I shall still give some fresh proofs. 

According to the experiments of Berthollet, ammonia is com- 
posed of 100 parts of nitrogen to 300 of hydrogen (by volume). 

I have found that sulphuric acid is composed of 100 parts of sul- 
phurous gas to 50 of oxygen gas. 

When a mixture of 50 parts of oxygen and 100 of carbonic 
oxide is inflamed, these two gases are destroyed and their place 
taken by 100 parts of carbonic acid gas. Consequently, carbonic, 
acid may be considered as being composed of 100 of carbonic oxide 
gas to 50 of oxygen gas. 

Davy, from the analysis of various compounds of nitrogen with 
oxygen, has found the following proportions by weight: 

Nitrous oxide 63'30 of nitrogen to 3670 of oxygen 

Nitrous gas 44'05 55'95 

Nitric acid ... . 29*50 70'50 

Reducing these proportions to volumes we find, respectively, 100 to 
49'5, 100 to 108*9, and 100 to 204*7. The first and last of these 
proportions differ only slightly from 100 to 50 and 100 to 200; it is 
only the second which diverges somewhat from 100 to 100. The 
difference, however, is not very great, and is such as we might 

i " As muriatic acid contains | Ita weight of water, we must only take *J of the density foi 
that of real muriatic acid." 


expect in experiments of this sort; and I have assured myself that 
it is actually nil. On burning the new combustible substance from 
potash in 100 parts by volume of nitrous gas, there remained over 
exactly 50 parts of nitrogen, the weight of which, deducted from 
that of nitrous gas, yields as result that this gas is composed of 
equal parts by volume of nitrogen and oxygen. 

We may then admit the following numbers for the proportions 
by volume of the compounds of nitrogen and oxygen : nitrous oxide, 
100 of nitrogen to 50 of oxygen; nitrous gas, 100 to 100; and nitric 
acid, 100 to 200. 

From my experiments, osygenated muriatic acid 1 is composed of 
22'92 parts of oxygen to 77 'OS of muriatic acid (by weight). Con- 
verting these quantities into volumes, we find that oxygenated muri- 
atic acid is formed of ,'500 of muriatic acid to 103 '2 of oxygen, a 
proportion very nearly 300 to 100. 2 

Thus it appears evident to me that gases always combine in the 
simplest proportions when they act on one another; and we have 
seen in reality in all the preceding examples that the ratio of com- 
bination is 1 to 1, 1 to 2, or 1 to 3. It is very important to observe 
that in considering weights there is no simple and finite relation 
between the elements of any one compound; it is only when there 
is a second compound between the same elements that the new pro- 
portion of the element that has been added is a multiple of the first 
quantity. Oases, on the contrary, in whatever proportions they 
may combine, always give rise to compounds whose elements by 
volume are multiples of each other. 8 

i Chlorine. 

* " In the proportion by weight of oxygenated muriatic acid, the muriatic arid is supposed 
to b.> free from water, whilht in the piopoition by volume, it is supposed to be combined with 
Jt of its weight of water, which I have proved to be absolutely necessaTy for its existence in 
the Ktiseoug state " With this statement of (Say Lusnac's, compare the next chapter. 

* Uay-Lussac now proceeds to deal with " the apparent contraction of >olume which pases 
experience on combination ". ami to show that tins follows a general law. 'I he render should 
refer to the paper. Alembic Oftift Reprint No 4 contains, in addition to this paper, extracts 
from papers by Dalton and Avogadro, also dealing with the molecular theory 


Sir Humphry Davy 


[The name of Davy is popularly associated with the safety-lamp, but his fame 
is mainly due to his discoveries in electro-chemistry. He was appointed Profess* r 
of Chemistry at the Royal Institution in 1802, and the liberality of the Committee 
of that Institution supplied Davy with two enormously powerful batteries, with 
the help of which he conducted the brilliant investigations which resulted in 
the discovery of potassium and sodium. In a lecture given in 1809, he brought 
forward proofs that oxymuriatic acid is a simple body, termed by him chlorine, 
and that muriatic acid is a compound of that element with hydrogen. The famous 
chlorine controversy raged during the early years of last century, and the extracts 
below are from some of Davy's papers bearing on the subject. 

As an experimenter, Da\y was renwikably qui^k and resourceful. lie was a 
Complete master of scientific method. IVfore he was twenty-one he wrote, "It 
is only by forming theories, and then comparing them with facts, that we car 
hope to discover the true system of nature ".] 

Is there Oxygen in Oxymuriatic Acid? 

I have made many new experiments with the hope of decom- 
posing chlorine, but they have been all unavailing; nor have I been 
able to gain the slightest evidence of the existence of that oxygen 
which many persons still assert to be one of its elements. 

I kept sulphuret of lead for some time in fusion in chlorine, the 
results were sulphurane (Dr. Thomson's liquor) and plumbane (mu- 
riate of lead); not an atom of sulphate of lead was formed in the 
experiment, though if any oxygen had been present, this substance 
might have been expected to have been produced. 

I heated plumbane (muriate of lead) in sulphurous acid gas, and 
likewise in carbonic acid gas, but no change was produced; now, if 
oxygen had existed either in chlorine, or in its combination with 
lead, there is every reason to believe that the attractions of the 
substances concerned in these experiments would have been such as 
to have produced the insoluble and fixed salts of lead, the sulphate 
in the first case, and the carbonate in the second. 

I shall not enter into any discussion upon the experiments in 
which water is said to be produced by the action of muriatic gas on 
ammonia: there is, I believe, no enlightened and candid person who 
has witnessed the results of processes in which large quantities of 


muriate of ammonia, made by the combination of the gases in close 
vessels, have been distilled, without being satisfied that there is no 
more moisture present than the minute quantity which is known 
to exist in the compound vapours diffused through ammoniacal and 
muriatic acid gases, which cannot be considered either as essential to 
the existence of the gases, or as chemically combined with them. 

One of the first experiments that I made, with the hope of 
detecting oxygen in chlorine, was by acting upon it by ammonia, 
when I found that no water was formed, and that the results were 
merely muriate of ammonia and azote; and the driest muriate erf 
ammonia, I find, when heated with potassium, converts it into 
muriate of potassa, which result would be impossible on the hypo- 
thesis of oxymuriatic gas being a compound of oxygen, for, if there 
w;ts a separation of water during the formation of the muriate, the 
same oxygen could not be supposed to be detached in water, and yet 
likewise to remain so as to form part of a neutral salt. 

If water had been really formed during the action of chlorine on 
ammonia, the result would have been a most important one ; it would 
have proved either that chlorine or azote was a compound, and con- 
tained oxygen, or that both contained this substance; but it would 
not have proved the existence of oxygen in chlorine till it had been 
shown that the azote of the ammonia was unchanged in the opera- 

Some authors continue to write and speak with scepticism on the 
subject, and demand stronger evidence of chlorine being undecom- 
pounded. These evidences it is impossible to give. It has resisted 
all attempts at decomposition. In this respect it agrees with gold, 
silver, hydrogen, and oxygen. 

By the same mode of reasoning as that in which oxygen is con- 
ceived to exist in chlorine, any other species of matter might be sup- 
posed to form one of its constituent parts ; and by multiplying words 
all the phenomena might bo satisfactorily explained. Thus in the 
simple view of the formation of muriatic acid, it is said one volume 
of chlorine combines with one of hydrogen, and they form two 
volumes of muriatic acid gas. In the hypothesis of chlorine contain- 
ing oxygen, it is said, the oxygen of the chlorine combines with the 
hydrogen to form water, and this water unites to an unknown some- 
thing, or dry muriatic acid, to produce a gaseous body. If it were 
asserted that chlorine contained azote, oxygen, and this unknown 
body, then it might be said that in the action of hydrogen on 
chlorine, the azote, the oxygen, and the chlorine, having all attrac- 


tions for hydrogen, enter into union with it, and form a quadruple 

Berzelius has lately adduced some arguments, which he conceives 
ctre in favour of chlorine being a compound of oxygen from the laws 
of definite proportions; but I cannot regard these arguments of my 
learned and ingenious friend as possessing any weight. By trans- 
ferring the definite proportions of oxygen to the metals, which he 
has given to chlorine, the explanation becomes a simple expression 
of facts; and there is no genera! canon with respect to the multiples 
of the proportions in which different bodies combine. Thus, azote 
follows peculiar laws in combining with every different body; it 
combines with three volumes of hydrogen, with half a volume of 
oxygen, with one, two, arid one and a half of the same body, and 
with four volumes of chlorine. 

The chemists in the middle of the last century had an idea that 
all inflammable bodies contained phlogiston or hydrogen. It was 
the glory of Lavoisier to lay the foundations for a sound logic in 
chemistry, by showing that the existence of this principle, or of other 
principles, should not be assumed where they could not be detected. 

In all cases, in which bodies support combustion or form acids, 
oxygen has been supposed by the greater number of modern chemists 
to be present; but as there are many distinct species of inflammable 
bodies, so there may be many distinct species of matter which com- 
bine with them with so much energy as to produce heat and light; 
and various bodies appear capable of forming acids; thus hydrogen 
enters into the composition of nearly as many acids as oxygen, and 
three bodies, namely, sulphuretted hydrogen, muriatic acid, and 
fluoric acid, which contain hydrogen, are not known to contain 
oxygen. The existence of oxygen in the atmosphere, and its action 
in the economy of nature, and in the processes of the arts, have 
necessarily caused it to occupy a great portion of the attention of 
chemists, and, being of such importance, and in constant operation, 
it is not extraordinary that a greater number of phenomena should 
be attributed to it than it really produces. 

In the views that I have ventured to develop, neither oxygen, 
chlorine, or fluorine, are asserted to be elements; it is only asserted 
that, as yet, they have not been decomposed. 1 

i From the Phil. Trans, for 1814, vol. civ, pp. 02-73. Nee pp. 71-5 of Alembic Club Reprint 
No. 9. In the same reprint will be found a particularly interesting extract from another 
paper of Davy's: "On the Fallacy of the Experiments in which Water is said to have been 
formed by the Decomposition of Chlorine" (Phil. Tranx. for 1818, vol. cvilt). Atembic Club 



Robert Boyle 


[Robert Boyle was one of the founders of the Royal Society. He was the first 
great investigator who carried out in his lalxiura the principles of the Novum 
Organum. His strength lay in his patient research and observation of facts. 
Boyle's name is perhaps lK\st known in connection with the Law concerning the 
relation of the volume and the pressure of a gas. His numerous works (of which 
Dr. Peter Shaw's classified abridgment is the most useful edition) include New 
Experiments touching the Spring of the A ir, and Ifydrostatical Paradoxes. One of 
;hese paradoxes, so called, has been selected for inclusion here. 

The pressure of the air was quite unknown to the ancients, and was only first 
perceived by Galileo on the occasion of an ordinary pump refusing to draw water 
alx)ve a certain height. Before that time it had always been supposed that water 
rose by suction in a pipe because nature abhorred a vacuum, and so obliged the 
water to enter in order to supply the plave of the air sucked out. Although the 
crue cause of the phenomenon eventually occurred to Galileo, it was not satis- 
factorily demonstrated until his pupil Torricelli, in Iti42, thought of using mercury 
.\s a substitute for water. But Torricelli's discovery was much disputed, and at 
last Pascal proposed a crucial experiment. Pascal could see that if the column of 
mercury varied with the pressure of the air, the height of the column would be 
diminished if the experiment were made at a higher elevation, say on a mountain. 
In 1647 Pascal caused the experiment to be performed on the Puy de Dome, and 
the point at issue was settled once for all. 

Boyle "presented" his Paradoxes to the Royal Society in 1664. It would 
appear from the following that t\i?n at that date the old notion that ** nature 
abhors a vacuum" had not entirely disappeared.] 

Paradox X. The cause of the accent of water in syphons, and of its 
flowing through M/'w, way be explicated without having recourse to nature s 
abhorrency of a. racninn. 

Both philosophers and mathematicians having too generally con- 
fessed themselves reduced to fly to aftiya vacui, for an account of the 
cause of the running of water and other liquids through syphons; 
and even those moderns that admit a vacuum, having either left 
the phenomenon unexplained, or endeavoured to explain it by dis- 
putable notions; I think the curious will be much obliged to Mon- 

Reprint No. gives extracts from Davy's papers on " The Decomposition of the Alkalis and 
Alkaline Earths". 

The reader is strongly advised, especially if he is interested in Chemistry, to refer to the 
other reprints of tho Alembic Club. Researches by Cavendish, Wollaston, Dalton, Hooke, 
Priestley, Scheele, Orahnm, Jean Hey, Faraday, IttTthollct, Paateur, and others, are reprinted 
in convenient form ; and the labour of hunting out original records in the great national 
libraries or libraries of the learned societies may thus be avoided. 

(0415) 34- 



sieur Pascal for Having ingeniously endeavoured to show, that this 
difficult problem need not reduce us to have recoiusc to a fuya 
vacui. And indeed his explanation of the motion of water in 
syphons seems to me so consonant to hydrostatical principles that I 
think it not necessary to alter anything in it. But as for the ex- 
periment he proposes to justify his reasoning, I 
fear his readers will scarce be much invited to 
attempt it. For besides that it requires a great 
quantity of quicksilver, and a new kind of 
syphon 15 or 20 feet long, the vessels of quick- 
silver must be placed 6 or 7 yards under water, 
that is, at so great a depth, that I doubt whether 
men who are not divers will bo able conveniently 
to observe the progress of the trial. 

Wherefore we will substitute a way. Provide 
a glass jar A BCD, of a good wideness, and half a 
yard or more in depth; provide also a syphon of 
two legs F K and K (;, to which is joined at the 
upper part of the syphon a pipe E K, in such 
manner that the cavity of the pipe communi- 
cates with the cavities of the sypbon. To each 
of the two legs of this new syphon must be tied 
with a string a glass tube, J and H, sealed at one 
end; the open end of each tube admits a good 
part of the leg of the syphon to which it is 
fastened, which leg must reach a pretty good 
way beneath the surface of the water, with 
which the said tube is to be almost filled. But 
as one of these legs is longer than the other, so 
the surface of the water iu the .suspended tube i 
which is fastened to the shorter leg K F, must bo 
,, higher (that is, nearer to K or' A u) than the sur- 
face of the water in the tube H suspended from 
Fig. s the longer leg KG; that (as usual in syphons) the 

water may run from a higher vessel to a lower. 

All things being thus provided, and the pipe K K being made 

fast that it may not be moved, pour oil of turpentine into the jar 

A BCD, 1 till it reach higher than the top of the syphon FKG (whose 

orifice E you may, if you please, in the meantime close with your 

* If you have not much oil, pour in water beforehand till it reaches near the bottom of the 
suspended tubes, aa to the level XY. 


finger, or otherwise, and afterwards unstop), and then the oil press- 
ing upon the water will make it ascend into the legs of the syphon, 
and pass through it, out of the uppermost vessel J into the lower- 
most H; and if the vessel J were supplied with water, the course of 
the water through the syphon would continue longer than here (by 
reason of the paucity of water) it can do. 

Now in this experiment we manifestly see the water made to 
take its course through the legs of a syphon from a higher vessel 
into a lower, and yet the top of the syphon being perforated at K, 
the air has free access to each of the legs of it, through the hollow 
pipe EK which communicates with them both. So that, in our case, 
where there is no fear of a vacuum, the fear of a vacuum cannot 
with any show of reason be pretended to be the cause of the water 
running. Wherefore, we must seek out some other. 

And it will not be very difficult to find, that it is partly the 
pressure of the oil, and partly the contrivance and situation of the 
vessels, if we will but consider the matter attentively. For the oil 
that reaches much higher than K presses upon the surface of the 
external water in each of the suspended tubes J and H. I say the 
external wafer, because the oil floating upon the water has no access 
to the cavity of either of the legs F and <;. Wherefore, since the oil 
gravitates upon the water outside the legs, and not upon that inside 
them, and since its height above the water is great enough to press 
up the water into the cavity of the legs of the syphon and impel it 
as high as K, the water must by that pressure be made to ascend. 

And this raising of the water happening at first in both legs, 
there will bo a kind of conflict about K betwixt the two ascending 
portions of water, and therefore we will now examine which must 

And if we consider that the pressure sustained by the two 
parcels of water in the suspended tubes J and H depends upon the 
height of the oil that presses upon them respectively, it may seem 
at the first view that the water should be driven out of the lower 
vessel into the higher. For if we suppose that part of the shorter 
leg that is un-immersed under water to be 6 inches long, and the 
un-immersed part of the longer leg to be 7 inches, then, because the 
surface of the water in the vessel ,1 is an inch higher than that of the 
water in the vessel 11, it will follow that there is a greater pressure 
upon the water in which the longer leg is dipped by the weight of 
an inch of oil; so that that liquid being an inch highor upon the 
surface of the water in the tube H than upon that in the tube J it 


seems that the water ought rather to be driven from H towards K 
than from J towards K. 

But then we must consider that though the descent of the water 
in the leg G be more resisted than that in the other leg by as much 
pressure as the weight of an inch of oil can amount to, yet being 
longer by an inch than the water in the leg F, it tends downwards 
more strongly by the weight of an inch of water, by which length it 
exceeds the water in the opposite leg. So that an inch of water 
being (ceteris paribns) heavier than an inch of oil, the water in the 
longer leg, notwithstanding the greater resistance of the external 
oil, has a stronger endeavour downwards than has the water in the 
shorter leg, though the descent of this be resisted but by a depth of 
oil less by an inch. So that all things computed, the motion must 
be made towards that way where the endeavour is most forcible, 
and consequently the course of the water must be from the upper 
vessel and the shorter leg, into the longer leg and so into the lower 

The application of this to what happens in syphons is obvious enough. 
For, when once the water is brought to run through a syphon, the 
air (which is a fluid and has some gravity, and has no access into 
the cavity of the syphon) must necessarily gravitate upon the water 
in which the legs of the syphon are dipped, and not upon that which 
is within the syphon; and consequently, though the incumbent air 
has a somewhat greater height upon the water in the lower vessel 
than upon that in the upper, yet the gravitation it thereby exercises 
upon the former more than upon the latter, being very inconsider- 
able, the water in the longer leg much preponderating (by reason of 
its length) over the water in the shorter leg, the efilux must be out 
of that leg, and not out of the other. And the pressure of the ex- 
ternal air being able to raise water (as we find by suction pumps) to 
a far greater height than that of the shorter leg of the syphon, the 
efflux will continue, for the same reason, until the exhaustion of the 
water or some other circumstance alters the case. But if the legs of 
the syphon should exceed 34 or 35 feet of perpendicular altitude, the 
water would not flow through it, the pressure of the external air 
being unable to raise water to such a height. And if a hole being 
made at the top of a syphon, that hole should be unstopped while 
the water is running, the course of it would presently cease. For in 
that case the air would gravitate upon the water, inside as well as 
outside the cavity of the syphon; and so the water in each leg 
would, by its own weight, fall back into the vessel belonging to it. 


But because this last circumstance, though clearly deducible from 
hydrostatical principles and experiments, has not, that I know of, 
been verified by particular trials, I caused two syphons to be made, 
the one of tin, the other of glass, each of which had, at the upper 
part of the bend, a small round hole or socket, which I could stop 
and unstop, at pleasure, with my finger. So that when the water 
was running through the syphon, if I removed my finger, the water 
would presently fall, partly into one and partly into the other of 
the vessels underneath. And if the legs of the syphon were so 
unequal in length, that the water in the one had a far greater height 
than in the other, there seemed to be, when the liquid began to take 
its course through the syphon, some light pressure from the external 
air upon the finger with which I stopped the orifice of the socket 
made at the bend. 

And on this occasion I will add what I more than once tried, 
to show at how very minute a passage the pressure of the external 
air may be communicated to bodies fitted to receive it. For, having 
for this purpose stopped the orifice of one of the above-mentioned 
syphons (instead of doing it with my finger), with a piece of oiled 
paper, carefully fastened with cement to the sides of the socket, I 
found as I expected that though by this means the syphon was so 
well closed that the water ran freely through, yet, if I made a hole 
with the point of a needle, the air would, at so very little an orifice, 
insinuate itself into the cavity of the syphon, and thereby gravitat- 
ing inside as well as outside, make the water in the legs to fall 
down into the vessels. And though, if 1 held the point of the 
needle in the hole 1 made, and then caused someone to suck at the 
longer leg, this small stopper sufficed to make the syphon fit for use; 
yet, if I removed the needle, the air would get in at the hole and 
put a final stop to the course of the water. Nor was I able to take 
out the needle and put it in again so nimbly, but that the air found 
time to get in at the syphon; and, till the hole were again stopped, 
render it useless, notwithstanding that the water was by suction 
endeavoured to be set a running. 


Sir Isaac Newton 


[Sir Isaac Newton, one of the greatest mathematicians and physicists the world 
has ever known, was elected a Fellow of Trinity College, Cambridge, in 1667, and 
a Fellow of the Royal Society in 1672. Of his numerous works, the famous Prin- 
cipia is the best known. Despite his remarkable powers and his penetrating 
intellect, he was a singularly modest and unassuming man. A short time before 
his death he uttered this memorable sentiment: "I seem to have been only like 
a boy playing on the seashore and diverting myself in now and then finding a 
smoother pebble or a prettier shell than ordinary, whilst a great ocean of truth 
lay all undiscovered before me ", 1 His character as a man was almost beyond 
reproach, though his behaviour towards Leibnitz relative to the discovery of the 
calculus shows that he was quite capable of asserting and defending his rights. 
The following investigation is from the First Book of the Opticks^ in which branch 
of Science Newton made many important discoveries.! 

The Light of the Sun consists of Rays differently 
Refrangible. 2 The Proof by Experiments 

Experiment 1. In a very dark chamber, at a round hole about one- 
third part of an inch broad made in the shutter of a window, I placed 
a glass prism, whereby the beam of the sun's light which came in at 
thd hole might be refracted upwards toward the opposite wall of the 
chamber, and there form a coloured image of the sun. The axis of 
the prism was in this and the following experiment perpendicular to 
the incident rays. About this axis 1 turned the prism slowly, and 
saw the refracted light on the wall, or coloured image of the sun, 
first to descend and then to ascend. Between the descent and 
ascent, when the image seemed stationary, I stopped the prism and 
fixed it in that position. For in that position, the refractions of the 
light at the two sides of the refracting angle, that is at the entrance 
of the rays into the prism, and at their going out of it, were equal 
to one another. So also in other experiments, as often as I would 
have the refractions on both sides the prism to be equal to one 
another, I noted the place where the image of the sun formed by 
the refracted light stood still between its two contrary motions; and 
when the image fell upon that place, I made fast the prism. And in 
this position it is to be understood that all the prisms are placed in 

* firewater's Life qf Newton, vol. ii. a " Prop. II, Theor. II " (considerably abridged). 


the following experiments, unless some other position is described. 
The prism, therefore, being placed in this position, I let the refracted 
light fall perpendicularly upon a sheet of white paper at the oppo- 
site wall of the chamber, and observed the figure and dimensions 
of the solar image formed on the paper by that light. This image 
was oblong and not oval, but terminated with two rectilinear and 
parallel sides, and two semicircular ends. On its sides it was 
bounded pretty distinctly, but on its ends very indistinctly, the 
light there decaying and vanishing by degrees. The breadth of this 
image answered to the sun's diameter, and was about 2 inches, 
including the penumbra. For the imago was 18 feet distant from 
the prism, and at this distance that breadth if diminished by the 
diameter of the hole in the window shutter, that is by ^ inch, sub- 
tended an angle at the prism of about half a degree, which is the 
sun's apparent diameter. But the length of the image was about 
10 J inches, and the length of the rectilinear sides about 8 inches; 
and the refracting angle of the prism whereby so great a length was 
made, was 64 degrees. With a less angle, the length of the image 
was less, the breadth remaining the same. If the prism was turned 
about its axis that way which made the rays emerge more obliquely 
out of the second refracting surface of the prism, the image soon 
became an inch or two longer, or more; and if the prism was turned 
about the contrary way, so as to make the rays fall more obliquely 
on the first refracting surface, the image soon became an inch or two 
shorter. And therefore in trying this experiment I was as curious 
as I could be in placing the prism by the above-mentioned rule 
exactly in such a position that the refractions of the rays at their 
emergence out of the prism might be equal to that at their incidence 
on it. This prism had some veins running along within the glass 
from one end to the other, which scattered some of the sun's light 
irregularly, but had no sensible effect in increasing the length of the 
coloured spectrum. For I tried the same experiment with other 
prisms with the same success. 

Now the different magnitude of the hole in the window shutter, 
and different thickness of the prism where the rays passed through 
it, and different inclinations of the prism to the horizon, made no 
sensible changes in the length of the image. Neither did the dif- 
ferent matter of the prisms make any: for in a vessel made of 
polished plates of glass cemented together in the shape of a prism 
and filled with water, there is the like success of the experiment 
according to the quantity of the refraction. It is farther to be 



observed that the rays went on in right lines from the prism to the 
image, and therefore at their going out of the prism had all that 
inclination to one another from which the length of the image pro- 
ceeded, that is the inclination of more than 2 degrees. And yet 
according to the laws of Optics commonly received, they could not 
possibly be so much inclined to one another. 

Let EG represent the window shutter, F the hole therein through 
which a beam of the sun's light was transmitted into the darkened 
chamber, and ABC a triangular plane whereby the prism is sup- 
posed to be cut transversely through the middle of the light. And 
let XY be the sun, MN the paper on which the solar image or spec 

Fig. 4 

trum is cast, and PT the image itself whose sides towards v and w 
are rectilinear and parallel, and ends towards P and T semicircular. 
YKHP and XL IT are two rays, the first of which comes from 
the lower part of the sun to the higher part of the image, and is 
refracted in the prism at K and H, arid the latter comes from the 
higher part of the sun to the lower part of the image, and is 
refracted at L and I. Since the refractions on both sides of the 
prism are equal to one another, that is, the refraction at K equal to 
that at I, and the refraction at L equal to that at H, so that the 
refractions of the incident rays at K and L taken together are equal 
to the refractions of the emergent rays at H and I taken together: it 
follows, by adding equal things to equal things, that the refractions 
at K and H taken together are equal to the refractions at I and L, 
taken together, and therefore the two rays being equally refracted 
have the same inclination to one another after refraction which they 
had before, that is an inclination of half a degree answering to the 
sun's diameter. So then, the length of the image PT would by the 
rules of common optics subtend an angle of half a degree at the 
prism, and consequently be equal to the breadth vw, and therefore 
the image would be round. Thus it would be, were the two rays 


XLIT and YKHP, and all the rest which form the image 
alike refrangible. And therefore seeing by experience it is found 
that the image is riot round, but about five times longer than broad, 
the rays which, going to the upper end P of the image, suffer the 
greatest refraction, must be more refrangible than those which go to 
the lower end T, unless the inequality of refraction be casual. 

This image or spectrum PT was coloured, being red at its least 
refracted end T, and violet at its most refracted end P, and yellow, 
green, and blue in the intermediate spaces. Which agrees with the 
proposition that lights which differ in colour do also differ in re- 

It appears, then, that in equal incidences there is a considerable 
inequality of refractions. But whence this inequality arises, whether 
it be that some of the incident rays are refracted more and others 
less, constantly, or by chance, or that one and the same ray is by 
refraction disturbed, shattered, dilated, and, as it were, split and 
spread into many diverging rays, as Grimaldo supposes, will appear 
by the experiments that follow. 

Experiment 2. Considering that, if in the last experiment, the 
image of the sun should be drawn out into an oblong form, either by 
a dilatation of every ray, or by any other casual inequality of the 
refractions, the same oblong image would, by a second refraction 
made sideways, be drawn out as much in breadth by the like dilata- 
tion of the rays, or other casual inequality of the refractions side- 
ways, I tried what would be the effects of such a second refraction. 
For this end I ordered all things as in the last experiment, arid then 
placed a second prism immediately after the first in a cross position 
to it, that it might again refract the beam of the sun's light which 
came to it through the first prism. In the first prism this beam was 
refracted upwards, and in the second sideways. And I found that 
by the refraction of the second prism, the breadth of the image was 
not increased, but its superior part which in the first prism suffered 
the greater refraction, and appeared violet and blue, did again in 
the second prism suffer a greater refraction than its inferior part, 
which appeared red and yellow, and this without any dilatation of 
the image in breadth. 

Let s represent the sun, F the hole in the window, ABC the first 
prism, D H the second prism, Y the round image of the sun made by 
a direct beam of light when the prisms are taken away, PT the 
oblong image of the sun made by that beam passing through the 
first prism alone when the second prism is taken away, and p t the 



image made by the cross refractions of both prisms together. Now 
if the rays which tend towards the several points of the round image 
Y were dilated and spread by the refraction of the first prism, so 
that they should not any longer go in single lines to single points, 
but that every ray being split, shattered, and changed from a linear 
ray to a superficies of rays diverging from the point of refraction, 
and lying in the plane of the angles of incidence and refraction, they 
should go in those planes to so many lines reaching almost from one 
end of the image PT to the other; and if that image should thence 
become oblong, those rays and their several parts tending towards 
the several points of the image PT ought to be again dilated and 
spread sideways by the transverse refraction of the second prism, so 
as to compose a four-square image, such as is represented at TT T. 

For the better understanding of which let the image PT be dis- 
tinguished into five equal parts p Q K, K Q R L, L R s M, M s v N, N v T. 
And by the same irregularity that the orbicular light Y is by the 
refraction of the first prism dilated and drawn out into a long image 
PT, the light PQK, which takes up a space of the same length and 
breadth with the light Y, ought to be, by the refraction of the second 
prism, dilated and drawn out into the long image irqkp; and the 
light KQRL into the long image kqrl] and so with the rest; and 
all these long images would compose the four-square image TTT. 
Thus it ought to be, were every ray dilated by refraction, and 
spread into a triangular superficies of rays diverging from the point 
of refraction. For the second refraction would spread the rays one 
way as v much as the first does another, and so dilate the image in 
breadth as much as the first does in length. And the same thing 
ought to happen, were some rays casually refracted more than 
others. But the event is otherwise. The image P T was not made 




broader by the refraction of the second prism, but only became 
oblique, as it is represented by p t, its upper end p being by the 
refraction translated to a greater distance than its lower end T. So 
then the light which went towards the upper end p of the image was 
(at equal incidences) more refracted in the second prism than the 
light which tended towards the lower end T, that is the blue and 
violet, than the red and yellow ; and therefore was more refrangible. 
The same light wab by the refraction of the first prism translated 
farther from the place Y to which it tended before refraction; and 
therefore suffered as well in the first prism as in the second a 
greater refraction than the rest of the light, and consequently was 
more refrangible than the rest 
even before its incidence on the 
first prism. 

Sometimes I placed a third 
prism after the second, and 
sometimes also a fourth after 
the third; but the rays which 
were more refracted than the 
rest in the first prism were also 
more refracted in all the others, 
and that without any dilatatkn 
of the image sideways. 

But that the meaning of the 
experiment may more clearly 
appear, it is to be considered that the rays which are equally re- 
frangible do fall upon a circle answering to the sun's disc. For 
this was proved in the first experiment. Let therefore A G re- 
present the circle which all the most refrangible rays, propagated 
from the whole disc of the sun, would illuminate and paint upon 
the opposite wall if they were alone; EL the circle which all the 
least refrangible rays would in like manner illuminate and paint 
if they were alone; BH, ci, DK, the circles which so many inter- 
mediate sorts of rays would successively paint upon the wall if they 
were singly propagated from the sun in successive order, the rest 
being always intercepted; and conceive that there are other inter- 
mediate circles without number, which innumerable other inter- 
mediate sorts of rays would successively paint upon the wall if the 
sun should successively emit every sort apart. And seeing the sun 
emits all these sorts at once, they must all together illuminate and 
paint innumerable equal circles, of all which, being according to 


i \ 


Fig 6 


their degrees of refrangibility placed in order in a continual series, 
that oblong spectrum P T is composed which I described in the first 
experiment. Now if the sun's circular image Y which is made by 
an unrefracted beam of light was by any dilatation of the single 
rays, or by any other irregularity in the refraction of the first 
prism, converted into the oblong spectrum FT, then ought every 
circle A G, B H, &c., in that spectrum, by the cross refraction of the 
second prism again dilating or otherwise scattering the rays as 
before, to be in like manner drawn out and transformed into an 
oblong figure, and thereby the breadth of the image P T would now 
be as much augmented as the length of the image Y was before by 
the refraction of the first prism; and thus by the refractions of both 
prisms together would be formed a four-square figure pirtr, as I 
described above. Wherefore, since the breadth of the spectrum Pi 
is not increased by the refraction sideways, it is certain that the rays 
are not split or dilated or otherwise irregularly scattered by that 
refraction, but that every circle is by a regular and uniform re- 
fraction translated entire into another place, as the circle AG by 
the greatest refraction into the place ag\ the circle BH by a less 
refraction into the place b h-, and so of the rest; by which means a 
new spectrum pt inclined to the former PT is in like manner com- 
posed of circles lying in a right line; and these circles must be of 
the same size as the former*, because the breadths of all the spec- 
trums Y, P T, and p t at equal distances from the prisms are equal. 

Experiment 3. In the middle of two thin boards I made round 
holes one-third part of an inch in diameter, and in the window 
shutter a much broader hole to let into my darkened chamber a 
large beam of the sun's light. I placed a prism behind the shutter 
in that beam to refract it towards the opposite wall, and close behind 
the prism I fixed one of the boards, in such manner that the middle 
of the refracted light might pass through the hole made in it, and 
the rest be intercepted by the board. Then at the distance of about 
12 feet from the first board I fixed the other board in such manner 
that the middle of the refracted light which came through the hole 
in the first board and fell upon the opposite wall might pass through 
the hole in this other board, and the rest being intercepted by the 
board might paint upon it the coloured spectrum of the sun. And 
close behind the board I fixed another prism to refract the light 
which came through the hole. Then 1 returned speedily to the first 
prism, and by turning it slowly to and fro about its axis, I caused 
the image which fell upon the second board to move up and down 



upon that board, that all its parts might successively pass through 
the hole in that board and fall upon the prism behind it. And in 
the meantime I noted the places on the opposite wall to which that 
light after its refraction in the second prism did pass; and by the 
difference of the places I found that the light which being most 
refracted in the first prism did go to the blue end of the image, was 
again more refracted in the second prism than the light which went 
to the red end of that image. And this happened whether the axes 
of the two prisms were parallel or inclined to one another and to the 
horizon in any given angles. 

Let F be the wide hole in the window shutter, through which 
the sun shines on the first prism ABC, and let the refracted light 

Fig. 7 

fall upon the middle of the board D K, and the middle part of that 
light upon the hole Q made in the middle of that board. Let this 
trajected part of the light fall again on the middle of the second 
board dc, and there paint such an oblong coloured image of the sun 
as was described in the first experiment. By turning the prism 
ABC slowly to and fro about its axis, this image will be made to 
move up and down the board de, and by this means all its parts 
from one end to the other may be made to pass successively through 
the hole g which is made in the middle of the board. In the mean- 
while another prism abcis to be fixed next after that hole g to re- 
fract the trajected light a second time. And these things being thus 
ordered, I marked the places M and N of the opposite wall upon 
which the refracted light fell, and found that whilst the two boards 
and second prism remained unmoved, those places by turning the 
first prism about its axis were changed perpetually. For when the 
lower part of the light which fell upon the second board d e was cast 
through the hole <?, it went to a lower place M on the wall; and 
when the higher part of that light was cast through the same hole 


g, it went to a higher place N on the wall; and when any inter- 
mediate part of the light was cast through that hole, it went to 
some place on the wall between M and N. The unchanged position 
of the holes in the boards, made the incidence of the rays upon the 
second prism to be the same in all cases. And yet in that common 
incidence, some of the rays were more refracted and others less. 
And those were more refracted in this prism which by a greater 
refraction in the first prism were more turned out of the way, and 
therefore for their constancy of being more refracted are deservedly 
called more refrangible. 1 

In this way Newton at last arrives at his great generalization 
that the light of the sun is not homogeneous but consists of rays 
of different refrangibility. 

Michael Faraday 


[Faraday was appointed assistant to Sir Humphry Davy at the Royal Institu- 
tion in 1813, and became Director of the laboratory at the same Institution in 
1825, and Fullerian Professor of Chemistry in 1833. With no Mathematics be- 
yond simple Arithmetic, Faraday displayed powers of experiment and generaliza- 
tion so extraordinary that in these respects he stands on the same level as Newton 
himself. "The rare ingenuity of his mind was ably seconded by his manipulative 
skill, while the quickness of his perceptions was equalled by the calm rapidity of 

1 For the completion of this investigation, the reader must turn to the original 
There are few facts in the history of optics more singular than that Newton should have 
believed that different bodies when shaped into prisms all produced prismatic spectra of 
equal length, or dispersed the red and violet rays to equal distances, when the mean refrac- 
tion, or the refraction of the middle ray of the spectrum, was the same. This opinion, which 
he deduced from no direct experiments, and into which no theoretical views could have led 
him, seems to have been impressed on his mind with all the force of an axiom. In one of 
his experiments he had occasion to counteract the refi action of a prism of glass by a prism 
of water. Had he completed the experiment and studied the result of it when the mean 
refraction of the two prisms was the same, he could hardly have failed to observe that the 
prism of water did not correct the colour of the prism of the glass, and would thus have been 
led to the great truth that different bodies have dilferent dispersive powers It is curious to 
observe, as happened in this experiment, what trifling circumstances often arrest an investi- 
gator when on the very verge of a discovery. Newton had mixed with the water which he 
used in his prism a little sugar of lead, in order to increase the refractive power of the water ; 
but the sugar of lead having a higher dispersive power than water, made the dispersive 
power of the water prism equal to that of the prism of glass , so that if Newton had com- 
pleted the experiment, the use of the sugar of lead would have prevented him from making 
the important discovery which was almost within his possession. (See Brewster's L\fe oj 
Newton, vol. i, ch. v.) 



his movements." Dr. Bonce Jones, 1 Professor Tyndall, 2 and Dr. J. H. Gladstone, 8 
all speak of his sweetness of disposition and nobility of character, and refer time 
after time to hia amazing fertility of resource as an investigator. His Experi- 
mental Researches in Electricity have been well described as imperishable. The 
following investigation forms the eighteenth series of the second volume.] 

On the Electricity Evolved by the Friction of Water 
and Steam against other Bodies 

2075. Two years ago an experiment was described by Mr. 
Armstrong and others, in which the issue of a stream of high- 
pressure steam into the air produced abundance of electricity. The 
source of the electricity was not ascertained, but was supposed to 
be the evaporation or change of state of the water, and to have a 
direct relation to atmospheric electricity. I have at various times 
since May of last year been working upon the subject, and the 
Royal Society may perhaps think a compressed account of my 
results and conclusions worthy its attention. 

2076. The apparatus I have used was not competent to furnish 
me with much steam or a high pressure, but I found it sufficient 

Fig. 8 

for my purpose, which was the investigation of the effect and its 
cause, and not necessarily an increase of the electric development. 
The boiler I used would hold about ten gallons of water. A pipe 
4 feet long was attached to it, at the end of which was a large 
stop-cock (A) and a metal globe (B), of the capacity of 32 cubic 
inches, which I will call the steam-globe, and to this globe by its 
mouthpiece (c), could be attached various forms of apparatus, serv 

1 Life of Faradai/, by Dr Benco Jones. 

2 Fa radii n </.s a Discoverer, by Professor Tyndall. 
s Michael Faraday, by Dr. J. fl. Gladstone. 



ing as vents for the issuing steam. 1 Thus, (a) a cock could be con- 
nected with the steam-globe at c, and this cock bo used as the 
experimental steam-passage; or (b) a wooden tube could be screwed 
in; or (c) a small metal or glass tube put through a good cork and 
the cork screwed in ; and in these cases the steam way of the globe 
arid tube (D) leading to the boiler was so large that they might be 
considered as part of the boiler, and these terminal passages (from c) 
as the obstacles which, restraining the issue of steam, produced 
any important degree of friction. 

2077. Another issue piece (for 
screwing in at c) consisted of a metal 

K |-fiR^ %%^.-f-** tube (G) terminated by a metal funnel 

(H), and of a cone (j) advancing by a 
screw (K) more or less into the funnel, 
so that the steam as it rushed forth 
beat against the cone; and this cone 
could either be electrically connected with the funnel and boiler, 
or be insulated. 

2078. Another terminal piece consisted of a tube (L) with a 
stop-cock (M) &i\d feeder (N) attached to the top part of it, by which 
any fluid could be admitted into the passage, 
and carried on with the steam. (The feeder 
was a glass-tube or retort-neck, fitted by a cork 
into the cap of the stop-cock.) 

2079. In another terminal piece, a small 
cylindrical chamber (p) was constructed, into 
which different fluids could be introduced, so 
that, when the cocks were opened, the steam 
M ^^ S passing on from the steam-globe should then 

Fig. 9 

Fig. 11 

enter this chamber and take up anything that was there, and so 
proceed with it into the final passage (Q), or out against the cone (,T), 
according as the apparatus had been combined together. 

2080. The pressure at which I worked with the steam was from 

i In the diagram, D represents the 4^-ft. pipe coming from the boiler; E is a drainage tube 
and P its cock, for removing the water condensed in the pipe D. 


8 to 13 inches of mercury, never higher than 13 inches, or about two- 
fifths of an atmosphere. 

2081. The boiler was insulated on three small blocks of lac. 
The insulation was so good that when the boiler was attached to a 
gold-leaf electrometer and charged purposely, the divergence of the 
leaves did not alter either by the presence of a largo fire, or the 
abundant escape of the results of combustion. 

2082. When the issuing steam produces electricity, there are 
two ways of examining the effect; either the insulated boiler may 
be observed, or the steam may be examined, but these states are 
always contrary one to the other. I attached to the boiler both 
a gold-leaf and a discharging electrometer; the first showed any 
charge short of a spark, arid the second, by the number of sparks in 
a given time, carried on the measurement of the electricity evolved. 
The state of the steam may be observed either by sending it through 
an insulated wide tube in which are some diaphragms of wire gauze, 
which serves as a discharger to the steam, or by sending a puff of it 
near an electrometer when it acts by induction; or by putting wires 
and plates of conducting matter in its course, and so discharging it. 
To examine the state of the boiler or substance against which the 
steam is excited, is far more convenient than to go for the electricity 
to the steam itself; and in this paper I shall give the state of the 
former, unless it be otherwise expressed. 

2083. Proceeding to the cause of the excitation, I may state first 
that I have satisfied myself it is not due to evaporation or conden- 
sation, nor is it affected by either the one or the other. When the 
steam was at its full pressure, if the valve were suddenly raised and 
taken out, no electricity was produced in the boiler, though the 
evaporation was for the time very great. Again, if the boiler were 
charged by excited resin before the valve was opened, the opening 
of the valve and consequent evaporation did not affect this charge. 
Again, having obtained the power of constructing steam passages 
which should give either the positive, or the negative, or the neutral 
state (2102, 2110, 2117), I could attach these to the steam way, 
so as to make the boiler either positive, or negative, or neutral at 
pleasure with the same steam, and whilst the evaporation for the 
whole time continued the same. So that the excitation of electricity 
is clearly independent of the evaporation or of the change of state. 

2084. The issue of steam alone is not sufficient to evolve elec- 
tricity. To illustrate this point I may say that the cone apparatus 
(2077) is an excellent exciter; so also is a boxwood tube, soaked in 

(0415) 25 


water, and screwed into the steam-globe. If with either of these 
arrangements the steam-globe be empty of water, so as to catch and 
retain that which is condensed from the steam, then after the first 
moment (2089), and when the apparatus is hot, the issuing steam 
excites no electricity; but when the steam-globe is filled up so far 
that the rest of the condensed water is swept forward with the 
steam, abundance of electricity appears. If then the globe be 
emptied of its water, the electricity ceases; but upon filling it up to 
the proper height, it immediately reappears in full force. So when 
the feeder apparatus (2078) was used, whilst there was no water in 
the passage tube, there was no electricity; but on letting in water 
from the feeder, electricity was immediately evolved. 

2085. The electricity is due entirely to the friction of the particles 
of water which the steam carries forward against the surrounding 
solid matter of the passage, or that which, as with the cone, is pur- 
posely opposed to it, and is in its nature like any other ordinary 
case of excitement by friction. As will be shown hereafter, a very 
small quantity of water properly rubbed against the obstructing or 
interposed body, will produce a very sensible proportion of electricity. 

2086. Of the many circumstances affecting this evolution of elec- 
tricity, there are one or two which I ought to refer to here. Increase 
of pressure greatly increases the effect, simply by rubbing the two 
exciting substances more powerfully together. Increase of pressure 
will sometimes change the positive power of a passage to negative ; 
not that it has power of itself to change the quality of the passage, 
but as will be seen presently (2108), by carrying off that which gave 
the positive power; no increase of pressure, as far as I can find, can 
change the negative power of a given passage to positive. 

2087. The shape and form of the exciting passage has great influ- 
ence, by favouring more or less the contact and subsequent separa- 
tion of the particles of water and the solid substance against which 
they rub. 

2088. When the mixed steam and water pass through a tube or 
stop-cock (2076), they may issue, producing either a hissing smooth 
sound, or a rattling rough sound; and with the cone apparatus these 
conditions alternate suddenly. With the smooth sound, little or no 
electricity is produced; with the rattling sound, plenty. The rattling 
sound accompanies that irregular rough vibration, which casts the 
water more violently and effectually against the substance of the 
passage, and which again causes the better excitation. I converted 
the end of the passage into a steam-whistle, but this did no good. 


2089. If there be no water in the steam-globe, upon opening 
the steam-cock tt\Q first e/ect is very striking; a good excitement of 
electricity takes place, but it very soon ceases. This is due to water 
condensed in the cold passages, producing excitement by rubbing 
against them. Thus, if the passage be a stop-cock, whilst cold it 
excites electricity with what is supposed to be steam only ; but as 
soon as it is hot, the electricity ceases to be evolved. If, then, 
whilst the steam is issuing, the cock be cooled by an insulated jet of 
water, it resumes its power. If, on the other hand, it be made hot by 
a spirit-lamp before the steam be let on, then there is no first effect. 

2090. We find, then, that particles of water rubbed against other 
bodies by a current of steam evolve electricity. For this purpose, how- 
ever, it is not merely water but pure water which must be used. On 
employing the feeding apparatus (2078), which supplied the rubbing 
water to the interior of the steam passage, I found, as before said, 
that with steam only I obtained no electricity (2084). On letting in 
distilled water, abundance of electricity was evolved; on putting a 
small crystal of sulphate of soda, or of common salt into the water, 
the evolution ceased entirely. Re-employing distilled water, the 
electricity appeared again; on using the common water supplied to 
London, it was unable to produce it. 

2091. Again, using the steam-globe and a boxwood tube (2076), 
which excites well if the water distilling over from the boiler be 
allowed to pass with the steam, when I put a small crystal of sul- 
phate of soda, of common salt, or of nitre, or the smallest drop of 
sulphuric acid, into the steam-globe with the water, the apparatus 
was utterly ineffective, and no electricity could be produced. On 
withdrawing such water, and replacing it by distilled water, the 
excitement was again excellent; on adding a very small portion of 
any of these substances, it ceased; but upon again introducing pure 
water it was renewed. 

2092. Common water in the steam-globe was powerless to excite. 
A little potash added to distilled water took away all its power; so 
also did the addition of any of those saline or other substances which 
give conducting power to water. 

2093. The effect is evidently due to the water becoming so good 
a conductor, that upon its friction against the metal or other body, 
the electricity evolved can be immediately discharged again, just as 
if we tried to excite lac or sulphur by flannel which was damp instead 
of dry. It shows very clearly that the exciting effect, when it occurs, 
is due to water and not to the passing steam. 


2094. As ammonia increases the conducting power of water only 
in a small degree, I concluded that it would not take away the 
power of excitement in the present case. Accordingly, on intro- 
ducing some to the pure water in the globe, electricity was still 
evolved though the steam of vapour and water was able to redden 
moist turmeric paper. But the addition of a very snKill portion of 
dilute sulphuric acid, by forming sulphate of ammonia, took away 
all power. 

2095. When in any of these cases, the steam-globe contained 
water which could not excite electricity, it was beautiful to observe 
how, on opening the drainage cock which was inserted into the 
steam-pipe before the steam-globe (the use of which was to draw off 
the water condensed in the pipe before it entered the steam-globe), 
electricity was instantly evolved; yet a few inches further on the 
steam was quite powerless, because of the small change in the 
quality of the water over which it passed and which it took with it. 

2096. When a wooden or metallic tube (2076) was used as the 
exciting passage, the application of solution of salts to the outside 
end of the tube in no way affected the evolution. But when a 
wooden cone (2077) was used, and that cone moistened with the 
solutions, there was no excitement on first letting out the steam, 
and it was only as the solution was washed away that the power 
appeared; soon rising, however, to its full degree. 

2097. Having ascertained these points respecting the necessity 
of water and its purity, the next for examination was the influence of 
the substance against which the stream of steam and water rubbed. For 
this purpose I first used cones (2077) of various substances, either 
insulated or not; and the following, namely, brass, boxwood, ivory, 
linen, kerseymere *, white silk, sulphur, caoutchouc, oiled silk, melted 
caoutchouc and resin, all became negative, causing the stream of 
steam and water to become positive. The fabrics were applied 
stretched over wooden cones. The melted caoutchouc was spread 
over the surface of a boxwood or a linen cone, and the resin cone 
was a linen cone dipped in a strong solution of resin in alcohol and 
then dried. A cone of wood dipped in oil of turpentine, another 
cone soaked in olive oil, were at first inactive, and then gradually 
became negative, at which time the oil of turpentine and olive oil 
were found cleared off from the parts struck by the stream of steam 
and water. A cone of kerseymere, which had been dipped in alco- 
holic solution of resin and dried two or three times in succession, 

i A woollen fabric. 


was very irregular, becoming positive and negative by turns, in a 
manner difficult to comprehend at first, but easy to be understood 
hereafter (2113). 

2098. The end of a rod of shell-lac was held a moment in the 
stream of steam, and then brought near a gold-leaf electrometer; it 
was found excited negatively. The corner of a plate of sulphur 
showed the same effect. 

2099. Another mode of examining the substances rubbed was 
to use it in the shape of wires, threads, or fragments, holding them 
by an insulated handle in the jet whilst they were connected with 
a gold-leaf electrometer. AH the substances thus examined 1 were 
rendered negative, though not in the same degree. This apparent 
difference in degree did not depend only upon the specific tendency 
to become negative, but also upon the conducting power of the 
body itself whereby it gave its charge to the electrometer; upon 
its tendency to become wet, by which its conducting quality was 
affected; and upon its size or shape. 

2100. For the purpose of preventing condensation on the sub- 
stance, I made a platinum wire white-hot by an insulated voltaic 
battery, and introduced it into the jet: it was quickly lowered in 
temperature by the stream of steam and water to 212, but of course 
could never be below the boiling-point. No difference was visible 
between the effect at the first instant of introduction or any other 
time. It was always instantly electrified and negative. 

2101. The threads I used were stretched across a fork of stiff 
wire, and the middle part of the thread was held in the jet of 
vapour. In this case the thread, if held exactly in the middle of 
the jet, and looked at endways to the thread, was seen to be still, 
but if removed the least degree to the right or left of the axis of the 
stream, it (very naturally) vibrated, or rather rotated, describing a 
beautiful circle, of which the axis of the stream was the tangent. 
The interesting point was to observe that when the thread rotated, 
travelling as it were with the current, there was little or no electri- 
city evolved, but that when it was nearly or quite stationary, there 
was abundance of electricity, thus illusti Ating the effect of friction. 

2102. The difference in the quality of the substances (2099) 
gives a valuable power of arrangement at the jet. Thus if a metal, 
glass, or wood tube 2 (2076) be used for the steam issue, the boiler is 

i Faraday gives a Hst of thirty different substances he actually tried, e.g. various metals, 
fabrics, hair, glass, ivory, sulphur, charcoal, asbestos, fluor-spar, &c. 

A boxwood tube 3 in. long, and one-fifth of an inch inner diameter, well soaked in dfc. 
tilled water and screwed into the steam-globe, is an admirable exciter. 


rendered well negative and the steam highly positive; but if a quill 
tube, or better still, an ivory tube be used, the boiler receives 
scarcely any charge, and the stream of steam is also in a neutral 
state. This result not only assists in proving that the electricity 
is not due to evaporation, but is also very valuable in the experi- 
mental enquiry. It was in such a neutral jet of steam and water 
that the excitation of the bodies already described (2099) was 

2103. Substances, therefore, may be held either in the neutral 
jet from an ivory tube, or in the positive jet from a wooden or 
metal tube; and in the latter case effects occurred which if not 
understood, would lead to great confusion. Thus an insulated wire 
was held in the stream issuing from a glass or metal tube, about 
half an inch from the mouth of the tube, and was found to be un- 
excited; on moving it in one direction a little further off, it was 
rendered positive; on moving it in the other direction nearer to the 
tube, it was negative. This was simply because, when near the 
tube in the forcible part of the current, it was excited and rendered 
negative, rendering the steam and water more positive than before, 
but that when further off, in a quieter part of the current, it served 
merely as a discharger to the electricity previously excited in the 
exit tube and so showed the same state with it. Platinum, copper, 
string, silk, wood, plumbago, but not quill, ivory, and bear's hair, 
could, in this way, be made to assume either one state or the other, 
according as they were used as exciters or dischargers, the difference 
being determined by their place in the stream. A piece of fine wire 
gauze held across the issuing jet shows the above effect very beauti- 
fully; the difference of one-eighth of an inch either way from the 
neutral place will change the state of the wire gauze. 

2104. If instead of an excited jet of steam and water (2103), 
one issuing from an ivory tube (2102), and in the neutral state, be 
used, then the wires, &c., can no longer be made to assume both 
states. They may be excited and rendered negative (2099), but at 
no distance can they become dischargers ; or show the positive state. 

2105. We have already seen that the presence of a very minute 
quantity of matter able to give conducting power to the water took 
away all power of excitation (2090, &c.) up to the highest degree 
of pressure, i.e. of mechanical friction that I used (2086); and the 
next point was to ascertain whether it would be so for all the bodies 
rubbed by the stream, or whether differences in degree would begin 
to manifest themselves. I therefore tried all these bodies again, at 


one time adding about 2 grains of sulphate of soda to the 4 ounces 
of water which the steam-globe retained as a constant quantity 
when in regular action, and at another time adding not a fourth of 
this quantity of sulphuric acid (2091). In both cases all the sub- 
stances (2099) remained entirely unexcited and neutral. Very prob- 
ably great increase of pressure might have developed some effect 

2106. With dilute sulphuric acid in the steam-globe, varying 
from extreme weakness to considerable sourness, I used tubes and 
cones of zinc, but could obtain 710 trace of electricity. Chemical 
action, therefore, appears to have nothing to do with the excitement 
of electricity by a current of steam. 

2107. Having thus given the result of the friction of the steam 
and water against so many bodies, I may here point out the re- 
markable circumstance of water being positive to them all. It very 
probably will find its place above all other substances, even cat's 
hair and oxalate of lime. We shall find hereafter that we have 
power not merely to prevent the jet of steam and water from be- 
coming positive, as by using an ivory tube (2102), but also of 
reducing its own power when passing through or against such sub- 
stances as wood, metal, glass, &c. Whether with a jet so reduced 
we shall still find amongst the bodies above mentioned (2099) some 
that can render the stream positive and others that can make it 
negative, is a question yet to be answered. 

For the remainder of the investigation, the reader must refer to 
the original. Briefly, Faraday proceeds as follows: 

2108-2122. Various substances (e.g. turpentine, olive oil) are 
introduced into the Feeding Apparatus (2078), or Cylindrical 
Chamber (2079), in order to see what other bodies, than water, 
would do if their particles were carried forward by the current of 

2123-2128. Theoretical considerations. 

2129-2137. Compressed air used instead of steam. 

2138-2140. Experiments with the air current and dry powders. 

2141-2143. Remarks concerning electrification by friction. 

Faraday thus concludes his investigation : Finally, I may say 
that the cause of the evolution of electricity by the liberation of confined 
steam is not evaporation; and further, being, I believe, friction, it has no 
effect in producing, and is not connected with, the general electricity of the 
atmosphere : also, that as far as I have been able to proceed, pure gases, 


that is, gases not mingled with solid or liquid particles, do not excite elec- 
tricity by friction against solid or liquid substances. 

Almost any of Faraday's researches will be found to be of 
absorbing interest. One that used to appeal strongly to the writer 
was Faraday's attempt to discover a possible relation between 
Gravity and Electricity. See Researches, vol. iii, 2702-2717. 

Other Investigators and Writers 

Limits of space do not permit of extracts from the works of 
other investigators, but the reader himself may, with profit, refer 
to all or any of the following: 

1. Benjamin Franldin (1706-1790) was perhaps the most eminent 
American statesman and philosopher of his time. He was the first 
to demonstrate the identity of lightning with electricity. His work 
Observations and New Experiments on Electricity, made at Philadelphia 
in America, includes investigations full of suggestive matter and 
method, all very interesting and quaintly expressed. 

2. Henry Cavendish (1731-1810) was a chemist and physicist 
whose researches went far to place chemical investigation upon a 
thoroughly sound basis. The Alembic Club reprints include two of 
Cavendish's papers, Experiments on Air, read in 1784 and 1785. 
His Electrical Researches, in 696 articles, have been edited by Clerk 
Maxwell. In this volume reference may specially be made to the 
famous experiment now commonly known as the "Cavendish" ex- 
periment but sometimes associated with the name of Biot, 218- 
231; and to the investigation of the Electrical effects in the torpedo 
fish, 395-437. 

3. Sir Humphry Davy (1778-1829). See Ch. XXXV. A little 
book of 148 pages, The Safety Lam,p, with some Researches an Flame, 
published by Davy in 1818, forms an excellent model of investiga- 

4. Sir David Brewster (1781-1868) was an accurate observer 
whose general method was empirical rather than mathematical. His 
Treatise on Optics is a general work on the subject, but much of it is 


the result of Brewster's own investigation. See, in particular, the 
chapters on "Polarisation", pp. 157-243. 

5. Lord Kelvin (William Thomson) (1824-1907) held the Chair 
of Natural Philosophy in the University of Glasgow for fifty-three 
years, and was universally recognized as one of the greatest 
physicists of his time. He published hundreds of original papers 
bearing on almost every branch of physical science. Many of these 
papers are difficult to read, but the following, amongst others, will 
be found to be fine examples of investigation: (1) "Atmospheric 
Electricity", in Papers on Electrostatics and Magnetism, Art. xvi, pp. 
192-236; (2) "Elasticity", in vol. iii. of Mathematical and Physical 
Papers, pp. 3-84. (Pp. 84-112 of the latter deal with the mathe- 
matical theory of Elasticity, and is beyond the ordinary reader.) 

6. Lord Lister (1827-1912), the famous surgeon, became a Fellow 
of the Royal College of Surgeons at the age of twenty-five, and was 
elected a Fellow of the Royal Society at the age of thirty-three. He 
was created a baronet in 1883, was raised to the peerage in 1897, 
and was one of the original members of the Order of Merit (created 
1902). From 1860 to 1877 he held appointments in the Universities 
of Glasgow and Edinburgh, and then came to London. From an 
early period of his professional career he had been deeply impressed 
by the great mortality which was then commonly attendant upon 
surgical operations, and, having decided that the cause must be 
discoverable, he set about making the search. Deriving hints from 
Pasteur's work, his profound acumen and untiring patience soon 
narrowed down the investigation to the best methods of protecting 
wounds from injurious organisms. How brilliant was his ultimate 
success, all the world knows. The main results of his life's great 
work are embodied in The Collected Papers of Joseph, Baron Lister. 
The following papers, amongst others, may be recommended for 
careful study. Vol. i, "An Inquiry regarding the parts of the 
Nervous System which regulate the Contractions of the Arteries" 
(pp. 27-47); "On the Appreciation of a Knowledge of Hydrostatics 
and Hydraulics to Practical Medicine" (pp. 186-188); vol. ii, 
" Observations on Ligature of Arteries on the Antiseptic System " 
(pp. 86-101); "On the Principles of Antiseptic Surgery" (pp. 

7. D. I. MendeUeff (born 1834) was appointed Professor of Chem- 
istry in the University of St. Petersburg in 1864. His original 
work covers a wide range, from questions in applied chemistry to 
the most general problems in Chemical and Physical Theory. The 


reader may be referred to his Faraday lecture, delivered at the 
Royal Institution, 1889, on "The Periodic Law of the Chemical Ele- 
ments" (see pp. 489-508 of vol. ii of his Principles of Chemistry}] 
and to a paper he wrote in 1902, "An Attempt towards a Chemical 
Conception of the Ether" (ib. pp. 509-529). 

8. Lord Eayleigh, O.M., F.B.S. (born 1842), was Senior Wrangler 
in 1865, succeeded Clerk Maxwell as Cavendish Professor of Physics 
in 1879, and was appointed Professor of Natural Philosophy at the 
Royal Institution in 1887. His work has ever been remarkably 
noteworthy for its extreme accuracy and precision. He " combines 
the highest mathematical acumen with refinement of experimental 
skill". "His textbook on Sound is one of the finest examples of 
a scientific treatise extant." In conjunction with Sir W. Ramsay 
he discovered argon. This discovery was the outcome of a long 
series of delicate weighings and of minute experimental care in the 
determination of the relative density of nitrogen, undertaken in 
order to determine the atomic weight of that gas. Lord Rayleigh's 
Scientific Papers are published in four volumes. Some of the papers 
are of a very specialized character, but amongst those of more general 
interest may be mentioned those on (a) " Harmonic Echoes ", vol. i, 
pp. 188-9; (b) "On the Dark Plane which is formed over a Heated 
Wire in Dusty Air", vol. ii, pp. 151-4; and (c) "Foam", vol. iii, 
pp. 351-62; and there are numerous other papers which will strongly 
appeal to many readers. The papers on the density of nitrogen and 
on argon are in vol. iv, Nos. 197, 201, 210, 214, 215, 218, and 219. 
No serious student of physical science can afford not to read, with 
the utmost care, the four volumes mentioned. 

There have been and still are many eminent men of science 
whose work is better known by its results than by the methods 
actually used. It is possible to turn over the pages of volume after 
volume of the Proceedings of the Royal Society, without getting 
any real insight into the methods of the various contributors. 
There is almost an entire absence of that self-revelation which 
appears on every page of Newton or Faraday. Exigencies of space 
no doubt partly account for this, but there is the further reason 
that the contributions are intended for specialists who are content 
to know the general lines of procedure adopted and the conclusions 
arrived at. 

It is, however, very necessary for young teachers to distinguish 
between textbooks which are mere compilations and those which 


are written by men acknowledged to be leading authorities in their 
own departments. The fullness of knowledge and the mastery of 
the subject in the latter case, lead to an entirely different type of 
presentation a presentation illuminated by a thousand side-lights 
the existence of which will probably not even be suspected by the 

It may be useful to refer the reader to a few instances of the 
work of eminent men of science, selected specially because worthy 
of very careful study. In these instances the actual method adopted 
by the different writers will, as far as the reader is concerned, be 
largely inferential. Most of the instances are, primarily, examples 
of the elucidation or demonstration of principles, and should be read 
not so much for the sake of the actual facts recorded as for the 
general lines of procedure, the illustrations, the logical development 
and arrangement, the logical argument, the logical conclusions, and 
so forth. Many other excellent examples from the works of the 
same writers could, of course, easily be selected. 

9, /. Clerk Maxwell, F.R.S. (1831-79), was the first holder of the 
Professorship of Experimental Physics at Cambridge, and it was 
under his direction that the plans of the Cavendish laboratory were 
prepared. His treatise on Electricity and Magnetism was pronounced 
by the late Professor Tait to be "one of the most splendid monu- 
ments ever raised by the genius of a single individual ". The reader 
may refer to this treatise, Part I, ch. i, "Description of Phenomena" 
(pp. 31-67); ch. ii, "Elementary Mathematical Theory of Statical 
Electricity" (pp. 68-95); Part II, ch. iv, " Electrolysis " (pp. 345-55); 
and " Electrolytical Polarisation " (pp. 356-66). 

10. John Tyndall, F.E.S. (1820-93), was a colleague of Faraday 
at the Royal Institution, having been appointed Professor of Natural 
Philosophy there in 1854. He succeeded Faraday as superintendent 
on the latter's death in 1867. Tyndall was noted for his remarkable 
power of exposition to the unlearned, and in this respect far excelled 
all his contemporaries. But he lacked the cultivated caution of a 
Faraday, or the depth of a Clerk Maxwell. Any of the following 
will be found full of interest : Heat a Mode of Motion, chapters 
on "Radiant Heat" (pp. 269-423); "The Azure of the Sky" 
(pp. 468-95) *; the same subjects in Contributions to Molecular Physics 

* Beat a Mode of Motion is written in a popular form. Tyndall's original papers may, 
however, be obtained in a convenient volume, Contributions to Molecular J'hyxics in tht 
Domain of Radiant Heat. 


in the Domain of Radiant Heat] Sound, "Acoustic Transparency of 
the Atmosphere in Relation to the Question of Fog-signalling " 
(pp. 284-358); Fragments of Science, vol. i, "Dust and Disease" 
(pp. 131-93); vol. ii, "Spontaneous Generation" (pp. 292-336). 

11. T. H. Huxley, F.K.S. (1825-95), like his friend Tyndall, 
possessed very exceptional powers of lucid exposition. His mind 
was a " clear, cold, logic-engine ". Dr. A. R. Wallace, speaking from 
intimate personal knowledge, recently said that, in sheer intellectual 
power, Huxley was superior to Darwin. Reference may be made 
to Danviniana, "Causes of the Phenomena of Organic Nature" 
(pp. 303-475); Physiography, "Geology of the Thames Basin" 
(pp. 272-98). 

12. Thomas Preston, F.R.S., for some time an esteemed colleague 
of the present writer's, was cut off, a few years ago, in the very 
prime of life. His Theory of Heat and Theory of Light are standard 
works. In the former, the "Preliminary Sketch" (pp. 1-100), 
and in the latter, "Diffraction, Graphic Methods" (pp. 243-74), 
are well worth reading, 

Selections from the works of living writers are made with some 
diffidence, lest the authors should feel that the selections are not 
sufficiently representative. But most, if not all, of the following 
will appeal to those who delight in close reasoning and clear ex- 
position : 

13. Sir Oliver Lodge, F.R.S.: Modern Views of Electricity (1889 
edition), "The Dielectric" (pp. 18-29); Electrons, "Electric View of 
Matter "(pp. 146-62). 

14. Sir Joseph Larmor, F.R.S.: Aether and Matter, "The Scope 
of Mechanical Explanation; The idea of Force" (pp. 268-88). 

15. SirJ. J. Thomson, O.M., F.R.S.: British Association Presidential 
Address, 1909; and Elements of Electricity and Magnetism, "Electrical 
Images and Inversion" (pp. 138-83). 

16. Professor J. H. Poynting, F.R.S., and Sir J. J. Thomson, 
O.M., F.R.S.: Properties of Matter, "Capillarity" (pp. 135-72). 

17. Sir William Crookes, O.M., F.R.S. : Select Methods in Chemical 
Analysis, "Electrolytic Analysis; and Gas Analysis " (pp. 616-47). 
These are admirable models of lucid instructions. 

18. Lothar Meyer: Outlines of Theoretical Chemistry (translated by 
Bedson and Williams), "Valency", "Atomic Linking", " Isom- 
erism" (pp. 65-111). 


19. Wilhelm Osticald: The Principles of Inorganic Chemistry 
(translated by Findlay); the chapters on "Water" (pp. 106-52); 
"Sulphur" (pp. 253-305); and one of the metals, for instance, 
"Mercury" (pp. 656-72). 

20. Dr. Harold Wager, F.R.S. : Vegetable Cytology. (Ency. Brit.) 

21. Professor S. H. Vines, F.R.S. : Text Book of Botany, "Physi- 
ology of Plant Movement" (pp. 735-66). 

22. Rev. A. II. Cooke: Cambridge Natural History, vol. on Mol- 
lusca, "Enemies of the Mollusca, Means of Defence, Mimicry, and 
Protective Coloration" (ch. iii); "Form, Composition, and Growth 
of the Shell of Mollusca " (ch. ix). 

It is rather an invidious thing to make selections of this kind, 
and there are numerous other workers in the world of Science whose 
names are well worthy of inclusion in such a list as the above. But 
those given are sufficiently representative. 




Some Elementary Principles of Science 


i. The Heuristic Method 

"No heuristic method here, if I can help it 7 ', said an angry 
Science master. "What does Professor Armstrong know about 
teaching? He says to a boy who cannot yet distinguish a test-tube 
from a totem, 'Here is a laboratory and here is a piece of rusty 
iron. I am going to lock you up in the laboratory and keep you 
there until you have discovered the cause 1 of the rusting of iron 1 !" 

Like most reformers, Professor Armstrong has often been mis- 
represented and maligned, but as he is quite capable of taking care 
of himself, there is no need to put in any kind of defence on his 
behalf here. Brief reference to the heuristic method is, however, 

As Professor Armstrong himself puts it, " Heuristic methods of 
teaching are methods which involve our placing students as far as 
possible in the attitude of discoverers, methods which involve their 
finding out instead of being merely told about things ". 2 The main 
question is not " the teaching of this or that science, but of giving 
training in the A B C of scientific method, of making all education 
scientific; with the object of putting thinking heads on the shoulders 
of the rising generation". 3 ^ 

Thirty or forty years ago, such practical Science as was attempted 
in the few school laboratories then existing was of no appreciable 
value; the teaching was confined mainly to the lecture-room. This 

i It Is singular how the notion still prevails that the problem in connection with the 
rusting of iron is to discover the cause of the rusting. So far as I know, Professor Armstrong 
has never set such an impossible problem to elementary pupils. His suggested problem 
is to find the general conditions under which iron rusts. (Those interested in this particular 
matter, apart from the teaching question, may refer to a recent investigation by Dr Newton 
Friend, published in the Journal of the Iron and Steel Institute ) 

a Th* Teaching of Scientific Method, p. 23(5. 3 ib. p. 33. 

(0415) 369 26 


"teaching" had certain well-marked characteristics: all facts were 
told; principles were stated, and then occasionally verified; and 
the reasoning, so far as reasoning was employed at all, was entirely 
deductive. The lessons took the form of lectures ; the teacher 
talked, and the boys sometimes listened. 1 Of scientific method 
there was none whatever. 

Professor Armstrong was one of the first to point out the 
necessity for a radical alteration of method. From the very outset 
his plea was for a method that would involve sustained intellectual 
effort on the part of the pupils; he urged that passive observation 
and didactic statement should be replaced by active observation 
and original investigation. And thus the old order of things began 
gradually to give place to the new. 

"Young scholars cannot be expected", says Professor Armstrong, 
"to find out everything for themselves, but the facts must always 
be so presented to them that the process by which results are 
obtained is made sufficiently clear as well as the methods by which 
any conclusions based on the facts are deduced^ 

The first essential step in an experiment is " to have a clear con- 
ception of the nature of the quest in which it is proposed to engage. 
When the motive is clear, some clue must be sought for and fol- 
lowed up." 2 

The rusting of iron investigation is not, of course, the first task 
which the teacher of Chemistry will set to the beginner, as is so 
often stated to be the case. In point of fact, the sequence actually 
suggested is as follows: (1) Lessons on common objects and common 
substances; (2) lessons on measurement; (3) studies of the effect of 
heat on substances; (4) the problem stage, the rusting of iron, the 
burning of chalk, the action of acids on oxides, &c. Quantitative 
work, almost from the first, enters largely into the teaching, and 
data are gradually accumulated which lead, gradually, to the enun- 
ciation of theoretical principles. 

"The essential feature in the Chemistry scheme is that students 

i The writer received his first Science lesson, at the age of ten, from the local County 
Analyst, who was engaged by the School Authorities as a visiting master to teach Chemistry. 
There was no laboratory available, but there was a well-fitted lecture-room, and in later 
lessons a few gases were prepared. But the first lesson, which extended over an hour, wns 
frankly a lecture on the atomic theory. No experiments whatever were performed, but tho 
formula) and equations which covered the blackboard greatly impressed at least one small 

3 Professor Armstrong suggcbts that teachers should master Baden-Powell's Aids to 
Scouting, and read detective stories. Of the latter it is preferable to read Poe's stories (for 
example, The murders in the Rue Morgue and The mystery of Marie Roget), than to read 
those of Poe's English imitators. 


are to be set to work to solve problems experimentally." " Quanti- 
tative experiments are introduced at the outset and are insisted on 
as all-important." "Each student receives a paper of instructions, 
which are advisedly made as bare as possible, so as to lead him to 
find out for himself how to set to work." But "in teaching chil- 
dren to experiment, a teacher must exercise extraordinary self- 
restraint in withholding information; however slowly the subject 
may develop, it must be allowed to develop solely on the basis of the 
facts established in the course of the inquiry taken in conjunction 
with common knowledge". 1 It is the function of the teacher to 
guide, not to tell; he should never help a boy over a stile until the 
boy has had at least one good try to get over himself. 

Dr. Alexander Smith, Professor of Chemistry in the University 
of Chicago, is one of the recognized authorities on scientific method 
in America. His sympathies are wholly on the side of the heuristic 
method, though, as might be expected in any man with an original 
and independent mind, he has his own opinion over many details. 
His general views are fairly represented by the following extracts : 

There are "parts of the subject to which the heuristic method 
is not applicable. If, for instance, we suggest that a pupil should 
discover the fundamental laws of the subject for himself, we are 
putting upon him an impossible task. Verification is the term more 
applicable to work in this direction." 

In Professor Armstrong's first problem, "pupils must not only 
find out for themselves, but as far as possible be led to imitate the 
detective's method and find out how to find out for themselves". 
" It is evident that the nature of the directions will have much to 
do with the attitude of the pupil towards his work. In the ideal 
application of this method, however, no book and no directions are 

"While work exclusively on heuristic lines does not furnish the 
knowledge of Chemistry which is expected in Secondary Schools, it 
is evident that the attitude is one to be cultivated. Practically, 
the effort will be to include as much heuristic work as possible in 
the school course." 2 

Another well-known American writer on Scientific Method is 

i The Teaching of Scientific Method, pp. 206, 241; see also pp. 300-66 ("The British 
Association Course"). 

a Alexander Smith, The Teaching of Chemistry, p 100, Ac. See the same writer's Labora- 
tory Outline of General Chemistry, a book which is full of suggestive hints for dealing with 
laboratory problems. The first three chapters of his Introduction to Inorganic Chemistry 
should also be read. 


Dr. E. H. Hall, Professor of Physics in Harvard University. His 
views of the heuristic method will be gathered from the following : 

" What are the conditions of success ? A very competent teacher 
who knows the ground thoroughly, and will not delude himself or 
his pupils with exaggerated notions of their independence and origi- 
nality in Science; and a very small class. The method sometimes 
advocated of teaching children to swim by throwing them into deep 
water, will surely be fatal to a very large proportion of the unhappy 
youngsters unless there is some experienced person with every group 
of three or four. Usually I am sure that the teacher who thinks to 
iet his pupils 'find out everything for themselves' will find out for 
himself that he has somehow got the hardest part of the under- 
taking. For visible progress must be made, tangible results must 
be reached." 

"I would keep the pupils just enough in the dark as to the 
possible outcome of his experiment, just enough in the attitude of 
discovery, to leave him unprejudiced in his observations; and then 
I would insist that his inferences, so far as they profess to be derived 
from his own seeing, must agree with the record, previously made, 
of these observations." 1 

When due allowance is made for the essential difference of 
treatment that must necessarily be made in the teaching of many 
sections of Physics, as compared with Chemistry, it is ^uite obvious, 
from Professor Hall's own work as practised at Harvard, that the 
difference between himself and Professor Armstrong is mainly one 
of words. (A specimen of his laboratory instructions is given on 
p. 374.) 

Professor Hall is unquestionably right when he says that the 
heuristic method presupposes a very competent teacher. In the 
hands of an unskilled teacher the method is almost certain to result 
in disaster. 

It is now generally conceded that the introduction of the heuristic 
method has led to an enormous improvement in the teaching of the 
elementary stages of Science. But in the more advanced stages it 
would seem that the method has still to be worked out. In those 
schools where the standard of attainments in Science is fairly high, 
dogmatic teaching is, not infrequently, allowed gradually to super- 
sede the heuristic teaching of the Lower and Middle Forms. 

There is no cast-iron about the method. It is not hemmed in by 
a body of inelastic rules. In essence it implies simply an orienta 

1 The Teaching of Physics, p. 278, Ac. 


tion of mind towards the subject in hand. That orientation secured, 
the details are of relatively little importance. But some teachers 
misconceive the real intention of the method, arid seem to think 
that Professor Armstrong would regard them as guilty of a particu- 
larly heinous crime if, for example, they ever took their pupils into 
the lecture-room. It is true that many successful teachers now dis- 
pense almost entirely with formal lecture-table work, and instead 
make use of the first and last quarter hours of each laboratory 
period. This answers very well with elementary pupils, but, as the 
work progresses, occasional hours at the demonstration-table become 
almost indispensable; for the teacher must find time for generaliza- 
tion, for formally establishing laws, for performing such experiments 
as are beyond the pupils' skill, for going over difficulties, for driving 
home fundamental principles; and so forth. All this is, however, 
merely supplementary to the laboratory work. The term " lecture- 
room " is responsible for much misconception of the proper function 
of Science teaching. 

2. Laboratory "Instructions" 

The Laboratory " instructions" or " directions" provided by a 
Science teacher for his pupils always afford a clue to the worth of 
his work. If the instructions contain too little information, the 
pupils' investigation necessarily comes to a stop or proceeds on a 
wrong track; if too much, the work tends to degenerate into me- 
chanical routine. The form of the instructions must always depend 
upon the exact stage of the pupils 7 previous knowledge, though the 
particular form in which a series of problems are cast will depend 
much upon the pupils' general intelligence and their previous and 
collateral training. The following sets of instructions should be 
carefully compared. 

1. Dr. W. F. Ganong, Professor of Botany in Smith College 
(Mass.), says that his first object in teaching is to form the scientific 
instinct, the habit of observation, comparison, and experiment. 
He presents to his class every new topic in the form of "a problem 
so arranged as to be solved through proper inductive processes by 
the pupils' own efforts". These problems, which form a series of 
original investigations, are introduced by questions asked in a form 
to direct attention to the leading facts and phases of the subject. 
Here is his first paper 1 of instructions: 

i Ganong, The Teaching Botanist, pp. 161-2. 


1. a. Study the outside of the dry Lima Beans; compare several 

specimens, and observe what features are common to 
all and what are individual; minutely observe: 

(1) What is the typical shape? 

(2) What is the colour? 

(3) What markings have they? 

Answer, as far as possible, by drawings made twice the 
natural size; add notes to describe features which draw- 
ing cannot express. 

b. Remove the coatings from soaked seeds. 

(1) What effect has the soaking had upon the mark- 

ings, size, and shape ? 

(2) How many coats are there? 

(3) Do the external markings bear any relation to the 

structures inside ? 

(4) What shapes have the structures inside, and how 

are they connected with one another ? 

Answer, as before, by drawings and notes. 

II. Study fully in the same way the Horse Bean. 

III. Describe the resemblances and the differences of the Lima arid 
the Horse Beans. 

Two two-hour periods are required for this investigation ; three, 
if possible. 

2. The Allowing is taken from the List of Exercises in Physics, 
by Professor Hall, required of Candidates for admission to Harvard. 


Apparatus-, a spring balance of about 250 gm. capacity; a rec- 
tangular wood-block about 8 cm. x 8 cm. x 4 cm.; a smooth sheet 
of paper about 18" x 12". 

(1) First consider the velocity of the motion; that is, ask whether Hie 
force required to keep up a slow steady motion is greater or less than that 
required to keep up a more rapid steady motion. 

Lay the block upon one of its broad sides, and attach it to the 
spring balance by a thread passing around but not under the block. 
Load the block with weights until the force required to maintain a 
slow steady motion is about 3 oz. Draw the block parallel to its 


grain along the sheet of paper several times with a very slow steady 
motion, and then several times with an equally steady motion two 
or three times as fast. (As the paper is likely to grow somewhat 
smoother under the repeated rubbing, do not make all the slow 
trials first, but change from slow to fast and fast to slow a number 
of times.) 

Record your conclusion as to whether the slow or the more rapid 
motion requires the greater force. 

(2) Next try to find out whether, the total weight being the same as 
before, it is easier or harder to draw the block on a narrower side than on 
a broad side. 

Use the same block and the same load of weights, pulling it now, 
as before, parallel to its grain. (The sides of the block must always 
be clean, and the broad and narrow sides as equally smooth as 

Record your conclusion as to whether the broad side or the 
narrow side offers the greater resistance to the motion. 

(3) Finally, ask what connection there is between the total mass drawn 
and the force required to draw it. 

For this purpose, vary the weights placed upon the block, using 
not less than 6 oz. for the least, and as much as 16 oz. for the 
greatest load. 

Add to the load in each case the weight of the block itself, and 
make the record in the following form, W being the load, and b the 
weight of the block : 

W + b. F (Force required). 

Look for any simple relation between (W + b) and F. 

(In the next part of the investigation, the block was made to 
slide down a sloping board covered with a sheet of paper, arrange- 
ments being made for varying the steepness of the board.) 

3. Professor Alexander Smith quotes the following instructions 
from "a well-known laboratory outline": "Treat a few small 
crystals of potassium iodide with concentrated sulphuric acid. What 
do you notice ? Compare with the results obtained when potassium 
bromide and sodium chloride are treated in a similar way." This 


brief statement constitutes the whole of the directions foi the in- 
vestigation, and Professor Smith has found by experience that it is 
hopelessly inadequate. Without further instructions in regard to the 
materials used and the general method of setting to work, anything 
like uniformity of results cannot possibly be expected; and no 
elementary student is ever likely to realize without a good deal of 
guidance that there are several distinct products concerned, though 
much will depend, of course, upon what he already knows about 
HC1, H 2 S, and S0 2 . 

Professor Smith's own directions for the investigation are as 
follows : 

Place about a gram of potassium iodide in a test-tube, and 
moisten it with concentrated sulphuric acid. Warm, if necessary. 
Investigate the result as follows: 

(1) Breathe across the mouth of the test-tube to ascertain the 
effect of the gas on moist air. What gas previously made showed 
the same behaviour? Remembering the similarity between the 
halogens and between their corresponding compounds, what do you 
infer in this case? To confirm this conclusion, lower a glass rod 
dipped in ammonia hydrate into the test-tube ; also a strip of filter 
paper dipped in lead nitrate solution [It]. 1 

(2) What is the colour of the gas, or any part of it? What is 
the coloured body? 2 Was there any corresponding product when 
sulphuric acid acted on a chloride? By what kind of chemical 
action could this coloured substance be formed from the one iden- 
tified in (1)? 

(3) Study the odour of the gas and describe it. Was there any 
effect on the lead nitrate which remained unexplained in (1)? Can 
you now explain it [R]? 3 

The work in (1) and (2) leads to the recognition of two distinct 
gaseous products. That in (3) will yield one, and perhaps two 
others. Still another distinct solid product may be observed on the 
walls of the tube. Construct separate equations representing the 
formation of the first product from the original materials, and of 
each of the others from this product and sulphuric acid. What two 
properties of sulphuric acid and what property of hydrogen iodide 
are illustrated by this set of experiments? 4 

1 [R] indicates that the pupil needs information he cannot have gained in previous work, 
and must therefore refer to some book or to his teacher. Here he is ignorant of the action 
of iodides on lead salts. 

2 This assumes that Iodine has been handled before. 

8 This assumes that hydrogen sulphide has not yet been studied. 
* The Teaching of Chemistry and Physics, pp. 102-4. 


4. We next give a paper of directions, for the comparative study 
of lead arid silver, by Professor Armstrong. " The experiments are 
chosen so as to afford an insight into the principles of the methods 
ordinarily employed in qualitative and quantitative analyses." 1 


SILVER. Symbol, Ag (Argentum). Atomic weight, 107*67. Specific 
heat, -05701. 

LEAD. Symbol, Pb (Plumbum). Atomic weight, 206-47. Specific 
heat, -03140. 

(1) Determine the relative density of lead and silver at a known 
temperature by weighing in air and in water. 

(2) Separately heat known weights of lead and silver for some 
time in the air, allow to cool, then weigh. 

(3) Separately convert known weights of lead and silver into 
nitrates; weigh the latter. From the data thus obtained, calculate 
the equivalents of lead and silver. 

(4) Convert the known weights of nitrates thus obtained into 
chlorides; weigh the latter. 

(5) Compare the action on lead and silver of chlorhydric acid; of 
dilute and concentrated sulphuric acid, using the acid both cold and 
hot; and of cold and hot nitric acid. 

(6) Using solutions of the nitrates, compare their behaviour with 
chlorhydric and sulphuric acids, hydrogen sulphide, potassium iodide, 
and potassium chromate. Ascertain the behaviour of the precipitate 
formed by chlorhydric acid when boiled with water and when treated 
with ammonia solution. 

(7) Compare the behaviour of lead and silver compounds on 
charcoal before the blowpipe. 

(8) Tabulate the results of your experiments with lead and silver 
in parallel columns. 

(9) Ascertain whether the substances given you contain lead or 

(10) Determine silver in an alloy of lead and silver by cupel- 

(11) Study the method of determining silver volumetrically by 
means of a standard solution of ammonium thiocyanate. Determine 
the percentage of silver in English silver coinage. 

(12) Determine silver as chloride by precipitation. 

i The Teaching of Scientific Method, p. 230. * <&. pp. 233-4. 


(13) Dissolve a known weight of lead in nitric acid, precipitate 
it as sulphate, collect and weigh the latter. 

(14) What are the chief ores of lead and silver? How are lead 
and silver extracted from their ores ? How is silver separated from 
lead ? How is it separated from burnt Spanish pyrites ? What are 
the chief properties and uses of lead and of silver ? State the com- 
position of the chief alloys of lead and silver. 1 

The stage in the students* course of work when this investigation 
would be given is pretty obvious, It is quite clear that during such 
an investigation the average student would constantly experience 
doubt and difficulty. The skilled teacher would, in such circum- 
stances, always give him a bare minimum of information, would 
indeed give him a mere hint, or perhaps ask a leading question, 
rather than give him information of a direct kind. 

5. Mr. J. B. Russell, in his book Notes on the Teaching of Elemen- 
tary Chemistry, provides us with numerous examples of admirably 
worked out laboratory instructions. The one reproduced here is, 
as will be seen, intended for young beginners: 


Heat, one at a time, each of the substances named in the list 
as directed, and try to see all that happens. 

Mercury. Soda. Lead nitrate. 

Nitre. Borax Sal-ammoniac. 

Iodine. Red lead. Blue Vitriol. 

(1) Describe the substance in such a way that a person after 
reading your description might readily pick out the right substance 
from among the others. 

(2) Place on a strip of paper, bent in the form of a shoot, about 
sufficient of the substance to cover a shilling, and introduce it into 
a clean dry test-tube without soiling the sides. 

(3) Heat the tube at first gently and then more strongly. 
Watch all that happens. Allow to cool and examine the residue. 

* Ot course an investigation of this kind requires a considerable amount of time. But it 
not infrequently happens that time is badly economized in a chemical laboratory, pupils 
standing idle during such processes as filtering:, drying, Ac. A well-taught pupil can often 
keep two or three different operations going at the same time. 


(4) Immediately after each experiment, write down an account 
of all that you have observed, and in addition answer the following 
questions : 

(i) Does the substance left in the tube appear to you to be 
the same as, or different from, the original substance? 
(ii) Does any substance appear to leave the tube? if so, de- 
scribe it. 

(iii) From which of these substances are two, or more, distinct 
substances obtainable ? 

6. Finally, we give an example of laboratory directions of a 
totally different kind. It is taken from a textbook in common 


(1) Notice the offensive odour of bromine, taking care not to 
expose the eyes to the vapour, and only to smell it when freely 
diluted with air. 

(2) Place a cork in a bottle containing bromine, and observe that 
the cork is rapidly destroyed. 

(3) Put a drop of bromine in some water. Notice that it sinks, 
partly dissolving and giving a yellow solution. 

(4) Cool some bromine water to 4 U . Crystals having the com- 
position Br 2 ,10H 2 0?, will form. 

(5) Add a drop of bromine water to solution of iodide of potas- 
sium containing starch. Iodine will be liberated and form blue 
iodide of starch: 2KI + Br 2 = 2KBr + I 2 . 

(6) Pass hydrogen through a U-tube containing fragments of 
pumice-stone soaked with bromine, and provided with a jet; ignite 
the mixture which escapes. Clouds of dense colourless acid fumes, 
resembling those of damp hydrogen chloride, will testify to the for- 
mation of an acid fuming gas. This is hydrogen bromide (HBr). 

(7) Place some Dutch gold in bromine. The metal will combine 
with the bromine, but much less readily than with chlorine. 

(8) Place a strip of Turkey-red twill in some bromine water. 
It will be bleached much less rapidly than when chlorine is 

With such instructions as these, pupils would engage in mere 
mechanical routine; for the instructions give away the whole case 


and the pupils know exactly what is going to happen, or at any rate 
what is supposed to happen, before they perform an experiment. 
Work of this kind is of no appreciable value whatever, and is admir- 
ably designed to make the hostile humanist scoff at the "intellectual 
claims of science ". 

However good the instructions may be, the work will never pro- 
ceed successfully unless the teacher is constantly in touch with every 
pupil. Unexpected difficulties are bound to arise, and different 
difficulties with different pupils. It must be borne in mind that, 
without frequent suggestions and warnings from the teacher, the 
average pupil is seldom capable of giving, with any degree of pre- 
cision and accuracy, concrete interpretation to laboratory instruc- 
tions, however carefully these may be drawn up. 

3. The Pupil's Notebook 

An essential part of the training in the laboratory is the syste- 
matic writing up of notes. These notes should be a faithful record, 
in the pupils' own words, of all that is done, and should be written 
out in ink as th6 work proceeds. 

Except when really difficult points of theory are being dealt 
with points requiring great precision of expression notes should 
never be dictated. A Science teacher who dictates notes advertises 
his own incompetence. In Professor Armstrong's words, the dicta- 
tion of notes by a teacher should be regarded as a criminal offence. 1 

" As an incident to the writing, the pupil usually finds that his 
thoughts on the subject were not so perfectly organized as he had 
supposed. In framing written answers to the questions in the labo- 
ratory instructions, he is stimulated to group the facts in new ways, 
and is assisted in studying the subject by the discovery of gaps in 
his thoughts and in his observations." 2 

The exact recording of laboratory notes affords " training in pre- 
ciseness and proportion in exposition of original data ", and " imposes 
direction, definiteness, and completeness in observation". "It enables 
the teacher to make sure that the student has actually and fully 
worked out his topics." 

"It is only when the motive is clearly written out that it is 
clearly understood, that the meaning or intention of the experi- 

1 The Teaching of Scientific Method, p. 265 ; see also p. 266. 
* Alex. Smith, The Teaching of Chemistry , p. 125. 


ment is fully grasped, and this is equally true of the result." "The 
thing to be impressed on the pupils is that a record should tell a 
plain tale to people who are not present when the record is made." 1 
The correction of the notes is a very important part of the 
teacher's duties, but such correction sometimes becomes a most 
grievous burden. The burden is often much heavier than it need 
be. If the notes are written out, as they certainly should be, 
during the actual progress of the work, all mistakes can be pointed 
out at the bench; for the teacher can quite easily arrange to glance 
through the notes last made, never more than a few lines, every 
time he goes to the pupil to see what progress he is making. But 
the teacher himself ought not, as a rule, to make the correction. 
He should have a code of symbols for indicating different types of 
mistakes, and all corrections should be made by the pupil himself. 
The pupil's own act of correction necessarily calls forth his sustained 
attention, much more forcibly than any correction by the teacher. 
But of course the notebooks require a thorough examination periodi- 
cally, say two or three times a Term. 

4. Manipulation 

Manipulative skill comes only with much practice, and those 
Science teachers whose laboratory training has been slight, should 
spare no efforts to acquire a sound knowledge of laboratory practice 
and of laboratory arts. Want of acquired manipulative skill too often 
leads to an evasion of the most telling form of laboratory instruction, 
and to courses of work which are entirely unworthy of Upper Form 
boys. If a Science teacher is to do justice to his professional work, 
anything less than two or three years of constant laboratory prac- 
tice, under the direction of a professor of recognized eminence, is of 
little use. 

Those teachers who have not had this good fortune, and who 
cannot even now find an opportunity of undergoing the necessary 
training in Institutions of University rank, should, by dint of much 
practice and by means of all the help they can obtain from text 
books written by men who are recognized authorities in their own 
departments, add to their practical knowledge and skill. There are 
several excellent modern books now obtainable, written specially for 
the solitary worker, who, however, should obtain, if possible, Fara- 
day's Chemical Manipulation. This book, although written as far 

i Hall, The Teaching of Physics, p. 216, <fec. 


back as 1828, is still a veritable gold-mine for all students of practical 
science, for in its 650 pages are to be found minute practical instruc- 
tions for all sorts of experiments, instructions which in many cases 
have never been improved upon. 

The simplicity of the means by which Faraday made his experi- 
ments is often astonishing, and he took a keen delight in showing 
how easily apparatus might be extemporized. He once exhibited to 
a large audience all the rudimentary experiments in statical elec- 
tricity by using an electrical machine which he thus improvised at 
a few minutes' notice. He inverted a four-legged stool to serve for 
a stand, and took a white glass-bottle for the cylinder. A cork was 
fastened into the mouth of this bottle, and a bung was fastened with 
sealing-wax to the other end. Into the cork was inserted a handle 
for rotating this bottle, and in the centre of the bung was a wooden 
pivot on which it turned; while with some stout wire he made 
crutches on two of the legs of the stool, for the axles of this glass 
cylinder to work upon. The silk rubber he held in his hand. A 
japanned tea canister resting on a glass tumbler formed the con- 
ductor, and the collector was the head of a toasting-fork. 1 

To the uninitiated all this may seem very simple, but such in- 
genuity comes only of prolonged practical experience; it is not 
innate in the novice. 


Instances of Investigation Attempted 
by Pupils 

The circumstances in which the following problems were set are 
stated in each case. Strictly speaking, perhaps, neither the term 
"investigation" nor the term "research" is applicable to the in- 
stances given, as in no case was the pupil wholly ignorant of the 
particular matter he had to take in hand. But then this is usually 
the case in school work.' 2 

i See J. H. Gladstone's Life of Faraday, and G. lies' Inventors at Work. 

* In order to facilitate the following of the arguments in these examples, some slight 
alterations have been made in the English and in the numbering of the sections. But the 
actual matter and the reasoning are entirely unchanged, and are the pupils' own. Most of 
the problems were given by the author, a good many years ago, to his own pupils He is 
naturally debarred from making use of examples drawn from schools with which he is now 
officially associated. 


i. An Instance from English Grammar 

The following was given to an Upper Form during the slack 
week between the annual examination and the holidays. Books of 
reference were allowed. 

"Distinguish between the different kinds of ' connective' words 
in English grammar, and show clearly the difference between adverbs 
and conjunctions. Use the following words for purposes of illus- 
tration, making up sentences showing their ordinary, and not any 
exceptional, usage: accordingly, because, before, consequently, lest, since, 
then, there, therefore, until, when, where, which, while, who, why. Frame 
definitions of an adverb and a conjunction, in accordance with the 
functions you consider the words actually discharge." 

Here is one of the more successful results : 

The following sentences show the different possible uses of the 
given words: 

1. I received a pressing invitation to go; accordingly I went. 

2. He will succeed because ho is trusted. 
3a. He is standing before the fire. 

36. I have heard that report before. 
3c. Do not go before I come. 

4. My pocket has been picked ; consequently I have no money. 

5. I will not make a noise lest I disturb you. 
6a. I have not seen him since. 

66. He has been here twice since Tuesday. 
6c. He has not smiled since his son died. 
6d. I must believe it since you say so. 

7. Then the clock struck. 

8. He was standing there for an hour. 

9. He has been idle; therefore he must be punished. 
10. He did not speak until the people became silent, 
lift. When will you start? 

116. You were out when I called. 

12a. Where shall we go ? 

126. Show me the shop where you bought the book. 

1 3a. Which do you prefer ? 

136. I received the book which you sent me. 

14. Hold the horse while I put on my gloves. 

15a. Who called this morning? 


156. I asked him who called this morning. 
16a. Why did you strike the dog? 
166. He asked me why I struck the dog. 

These sentences may be grouped, according to tho grammatical 
meaning of the words, as folLws: 

3a. He is standing before the fire. 

66. He has been here twice since Tuesday. 

In these sentences, before and since are prepositions. 

36. I have heard that report before. 
6a. I have not seen him since. 

In these sentences, before and sinte Are simple adverbs, 
modifying the verbs heard and seen, respectively. 

1. I received a pressing invitation to go; accordingly I went. 
4. My pocket has been picked; consequently I have no money. 
9. He has been idle; therefore he must be punished. 

In these sentences, accordingly, consequently, and there- 
fore, are simple adverbs. Therefore, for example, is the 
exact grammatical equivalent of for that reason, and evi- 
dently modifies the verb punished. "He has been idle" 
and "he must be punished" are, grammatically, two 
complete and independent sentences. There is a con- 
tinuity in thought, but no grammatical connection. Hence 
the grammatical function of therefore is in no sense con- 
junctive but only adverbial. It is wrong to class it 
either amongst the conjunctions or amongst the con- 
junctive adverbs. 

13a. Which do you prefer? 
15a. Who called this morning? 

Which and who are here interrogative pronouns. 

136. I received the book which you sent me. 
156. I asked him who called this morning. 

Here, which and who perform two functions: (1) the 
function of a pronoun, as in 13a and 15a; (2) the func- 
tion of a connective between two sentences. As, how- 
ever, their primary function is that of a pronoun, we 
call them connective pronouns, instead of pronominal con- 
nectives. They are also called relative pronouns. " Which 


you sent me" is the equivalent of a descriptive adjective 
attached to book] "who called this morning" is the equi- 
valent of a noun, the object of asked (cf. the sentence 
"I asked him a question"). 

7. Then the clock struck. 

8. He was standing t/iwe for an hour. 
110. When will you start? 

l'2a. Where shall we go? 

16a. Why did you strike the dog? 

Then> there, when, where, and why are simple adverbs, 
limiting the action of the verbs in the respective sen- 
tences; then and when are adverbs of time; there and 
where, of place; why, of reason. 

116. You were out when I called. 

126. Show me the shop where you bought the book. 

166. He asked me ivhy I struck the dog. 

In these cases, when, where, and why perform the func- 
tion of an adverb exactly as in Ha, 12a, and 16a; they 
modify the verbs in the subordinate sentences they intro- 
duce. But they perform a second function; they join a 
subordinate to a principal sentence, i.e. they are connec- 
tives. But their primary function is that of an adverb, 
and we therefore call them connective adverbs or conjunc- 
tive adverbs, not adverbial conjunctions. They might be 
called relative adverbs, just as connective pronouns are 
called relative pronouns, for they have an antecedent, 
expressed or implied. (You were out then [ at the 
time] when 1 called.) 

In 116 the adverb when modifies the verb called in 
the subordinate clause it introduces, and the subordinate 
clause itself (when I called) has the force of an adverb 
with respect to the principal sentence. In 126, where 
you bought the book is the equivalent of an adjective 
qualifying the noun shop. In 166, why I struck the dog 
is the equivalent of a noun, the object of the verb asked. 

2. He will succeed because he is trusted. 

5. I will not make a noise lest I disturb you. 

6c. He has not smiled since his son died. 

6rf. I must believe it since you say so. 

(0416) 27 


10. He did not speak until the people became silent. 
14. Hold the horse while I put on my gloves. 
3c. Do not go before I come. 

In these sentences, because, lest, since, until, while, and 
before are conjunctions (of cause, purpose, and time). 
They are not adverbs; they^do not modify the meaning 
of any word in the sentences containing them; their 
function is to connect dependent sentences to principal 
sentences; and these dependent sentences have the force of 
adverbs limiting the action of the verbs in the respective 
principal sentences. In 2, for instance, because does not 
by itself modify the verb is trusted; but the clause be- 
cause he is trusted is an adverbial clause modifying the 
verb will succeed. 

There are thus three sorts of words connecting sentences to- 
gether : 

1. Connective or relative pronouns. 

2. Conjunctive adverbs. 

3. Conjunctions. 

We must therefore define conjunctions as connective words which Jiave 
neither a pronominal nor an adverbial signification. They usually join 
sentences together, but the conjunction and sometimes joins words 
only, as in the sentence, " The school is between the house and the 

Adverbs (1) add to the meaning, and (2) limit the application of, 
the word to which they are attached. Rains heavily means all that 
rains means, and heavily as well; the adverb thus adds to the mean- 
ing of the verb. Heavily also limits the application of the verb 
rains ; for rains applies to all occasions, rains heavily to fewer 

An adverb may in this way be attached to 

(1) A verb: she walks slowly. 

(2) An adjective : her pace is too slow. 

(3) An adverb : she walks very slowly. 

(4) A preposition: she found her purse just outside the door. 

(Here, just is attached to the preposition outside, rather 
than to the whole phrase outside the door.) 



(5) A conjunction : she has done her best ever since she went 

(Here, the adverb is attached more closely to the con- 
junction since than to the whole sentence since she went 

(6) A complete sentence: Evidently, she knew her way about. 

Thus an adverb may be defined as a word which adds to the meaning 
and limits the application of verbs, adjectives, adverbs, prepositions, con- 
junctions, and complete sentences. Adverbs may be (1) simple, (2) con- 
junctive. Both kinds may be classified according to their meaning, 
time, place, manner, degree, &c. 

For good or for ill, English grammar occupies a much less pro- 
minent place in the curriculum than when this exercise was attempted, 
and the exercise would no doubt now be regarded as a waste of 
time. Nevertheless the result certainly does show a nice apprecia- 
tion of the function of words. There may be differences of opinion 
about the boy's conclusions, but that does not matter. 

2. An Instance from the Art Room 

The following was given to a Sixth Form boy who, a year or 
two later, won an open mathematical scholarship: 

"The accompanying figure (fig. 12) represents the usual per- 
spective drawing of a cylinder standing on its base 
on the ground, a few feet from the observer. It is 
sometimes said that the original of the major axis 
x Y of the ellipse is a diameter of the circle forming 
the top of the cylinder. Is this right? Investigate 
the mathematical relations generally." 

Let AEBF (fig. 13) be the plan of the cylinder, Fig 12 

D the position of 
the observer, DE and DF the 
plans of two tangent planes 
drawn from the observer to 
touch the cylindrical surface, 
and R J L s the picture plane. 
13 It is evident that the line EF is 



s 1 

the original of the major axis J L of the ellipse. (Any other line in 
the circle, parallel to EF, even a diameter through P, would when 
projected on the picture plane, be represented by a line shorter 
than JL. This is evident from the figure.) 

Now E F is the polar of the point D with respect to the circle, or 
C and D are inverse points with respect to the circle. 

.', P C. P D - r B 2 , or A, c, B and D form a harmonic range. Take 
a vertical plane through A D, i.e. through the diameter of the cylin- 
der and the observer (fig. 14). Let Y represent the observer's eye, 
K'GHS' the picture plane, YA, YC, YB rays from the observer's eye 

to A, c, and B, and Y D a vertical 
through the observer. A M N B is 
a medial section of the cylinder. 

Now Y . A c B D is a harmonic 
pencil. And since G H is a trans- 
versal parallel to the ray YD of the 
pencil, G H must be bisected by 
YC, the conjugate of YD, i.e. G K 
K H. Thus the minor axis G H is bisected at K, 
and the original of G K is A C, and of K H is c B. 
Thus the unequal sections AC and CB of the 
diameter AB of the circle become the equal 
semi-minor axes of the ellip&e. 

Hence the major axis of the ellipse is the 
projected polar E F, and the semi-minor axes 
are the projected unequal sections of the diameter AB. In other 
words, the lines AB and EF in the plan are the originals of the 
minor and major axes respectively, and their point of intersection c 
is the original of the intersection of the elliptic axes. Also the lines 
XV and Y w in the perspective sketch are the lines of contact of the 
tangent planes (from the eye) and the cylinder. It is evident that 
the portion of the cylindrical surface seen by the observer is less 
than that portion unseen, i.e. the portion beyond the lines of con- 
tact of the tangent planes from the eye. 

This was the result of twenty-five minutes' work. The boy had 
been working problems in harmonic division, and the solution gave 
him little trouble. But he had, at the outset, entirely wrong notions 
of the perspective projection of a circle. This appeared to be due to 
the fact that when he had been taught to draw the cylinder, he had 
been told that the original of the point of intersection of the elliptic 

Fig. 14 


axes was the centre of the circle. The same boy afterwards investi- 
gated the more difficult case of the cylinder lying on the ground, 
oblique to the picture plane. He did not at first see that precisely 
the same principle applies as in the former case. His solution, 
though correct, was rather clumsy, and is not worth reproducing. 

3. An Instance from Botany 

The pupil, a girl of sixteen, knew .already that warmth and 
moisture are necessary for the germination of seeds. She knew 
how to prepare oxygen and carbon dioxide, and had some knowledge 
of the properties of these gases; she knew that alkaline pyrogallol 1 
absorbed oxygen, that caustic potash absorbed carbon dioxide, and 
knew the lime-water test for carbon dioxide. She was told that a 
living plant sometimes takes in and sometimes gives out oxygen, 
and sometimes takes in and sometimes gives out carbon dioxide. 
She was also told that when one was given out the other was usually 
taken in. The problem set was to discover the process that went 
on in germinating seeds. 

The laboratory instructions were based upon Professor Ganong's 
experimental course on Respiration, and his U-tube form of respiro- 
scope was used. This consists of a common U-tube, inverted; one 
end is closed with a cork on which is placed some wet sphagnum to 
support the germinating seeds. The open end dips into a tall bottle, 
the tube fitting into the neck suiliciently closely to prevent any 
appreciable chemical action on the part of the atmosphere on the 
reagent in the bottle, but not so close as to interfere with the atmo- 
spheric pressure on the surface of the reagent. The seeds used were 
oats which had already been allowed to begin to germinate, the 
radicles being from J to $ in. long. 

The girl had been previously shown how to use the respiroscope. 

1. I removed the cork from the mouth of a bottle in which some 
oat seeds had been germinating, and plunged a lighted taper into 
the bottle. The taper was immediately extinguished. This may 
have been due to CO 2 given off from the seeds; or, if the had 
been absorbed by the seeds, to the N of the air; or to both these 
things; or to the presence of some other gas that does not support 

i She was provided with a concentrated mixture of pyrogallic acid and caustic potaab. 



combustion. The conclusion from the experiment is therefore un- 

2. I put some oat seeds in the respiroscope, the open end of 
which I placed in a tall bottle of KHO solution; and I put the 
apparatus on one side for examination two or three days later. On 
examination, I found that ihe seeds had grown considerably, and 
that the KHO solution had risen in the respiroscope about J- of its 
length. On a further examination, two days still later, the KHO 
had risen in the respiroscope about \ of its length, and the seeds had 
grown still more. 

The conclusion is that the KHO rose to take the place of a por- 
tion of the air that had been used up by the seeds, though whether 
any C0 2 had been given out and absorbed by the 
KHO, it is not possible to say. 

If the KHO had risen i the length of the re- 
spiroscope, I should have felt pretty certain that 
had been used up. And it does seem certain that 
more of the air was used up than }, seeing that 
the rise of the KHO cannot correctly represent 
the total amount of what seems to have disap- 
peared. For the pressure at the level A (fig. 15) 
within the bottle is the pressure of the atmos- 
phere, and therefore the pressure at the same level 
A within the arm of the respiroscope is also equal to that of the 
atmosphere; but within the respiroscope this pressure is represented 
by a column of KHO (between the levels A and u), in addition to a 
certain pressure due to the enclosed gas. The density of this gas 
must therefore be less than that of the atmosphere; and the higher 
the KHO rises in the respiroscope, the less dense must the enclosed 
gas become. This makes me think that although only about } 
appears to be absorbed, perhaps as much as \ has really been ab- 
sorbed. If this is so, there can be hardly any doubt that the 
oxygen has been used up. 

3. I had arranged a similar respiroscope with germinating seeds, 
but with its open arm placed in water instead of in KHO. The 
seeds germinated almost as well as they did before, but the water 
within the tube remained at just about the same level as at the 
start, all the time. As in this case the liquid does not rise, some 
gas must be given out as well as some gas taken in by the seeds. 
From the last experiment we are now bound to conclude that the 
gas given out was C0 2 , and that it must have been absorbed by the 

Fig. 15 


KHO, for it is the only gas absorbed by KHO; and the amount oi 
gas used up by the seeds seems to be just about equal to the gas 
given out by them. 

4. In a bottle holding some clear lime-water, I suspended a piece 
of wire netting supporting some wet blotting paper on which were 
placed a few germinating seeds. I fixed the stopper of the bottle 
tightly in, and placed the apparatus in the conservatory. The lime- 
water became milky after a day or two. This conclusively proved 
that C0 2 was given out. 

But we do not yet know that it was really that was taken in 
by the seeds. 

5. So I tested the gas remaining in the respiroscope after Experi- 
ment 2. No oxygen seemed to be present. 

6. I tried to make seeds grow in jars of N, H, and C0 2 . There 
was no growth in either case. 

7. 1 took another respiroscope and placed the open arm in alka- 
line pyrogallol. In a short time the solution rose up the tube about 
I the length of the tube. This showed that the O had been ab- 
sorbed. The germinating seeds did not appear now to grow at all. 
So there seems to be no doubt that is necessary and is taken in 
by the germinating seeds. 

The general conclusion is that in the germinating of oat seeds, 
is used up, and CO. 2 is given out; and that the two gases thus taking 
part in the exchange are about equal in quantity. The action seems 
to be a good deal like the action of breathing in animals. 

4. An Instance from Chemistry 

The work previously done and the stage reached by the pupil 
responsible for the following, as well as the form given to the labora- 
tory directions provided, may be inferred with sufficient accuracy 
from the general result. The problem set was to discover the nature 
of bleaching by 1>1 caching powder. As will be seen, the experi- 
mental investigation was followed by a search for additional evidence 
from the books of the school library. 

Jars of H, 0, 01, 1IC1 gas, and Chlorine water provided. 

1. The Cl gas easily distinguished by its colour and smell. 

2. Breathed across the mouths of the jars of H, 0, and CL No 
noticeable result. 


3. Lowered a jet of burning H into a jar of Cl. The H burnt 
with a pale yellow flame. Fumes escaped from the mouth of the jar. 
These were recognized as HC1. 

4. Took two jars, one of H and one of Cl, each covered with a 
glass plate, and placed them mouth to mouth, plates being then with- 
drawn. Jars shaken to ensure mixture of gases. Lighted taper ap- 
plied to one. A sharp explosion occurred. Whitish fumes appeared ; 
recognized as HC1. 

5. Covered the mouth of the second jar and exposed to diffused 
daylight. After a few hours, the greenish colour of the gas had dis- 
appeared. Removed plate. Breathed across the mouth of the jar; 
dense fumes appeared; recognized as HC1. 

These three experiments show that Cl has a powerful affinity 
fr H. 

6. Placed some dry coloured calico in jars of dried H and O, by 
fastening it to a cork cemented to the under side of the covering 
glass plate. Colour in each case unchanged. 

7. Repeated the last experiment, the jars containing a little 
water as well as the respective gases. Colour of calico still un- 
changed, whether calico itself was kept dry or made wet. 

8. Exposed coloured calico to I1C1 gas, also to HC1 solution. 
Colour unchanged. 

9. Placed some dry coloured calico in a jar of Cl. Some lumps 
of CaCl 2 had been placed in the jar, to dry the Cl. Colour of calico 
very slightly changed. 

10. Repeated the last experiment, substituting concentrated 
H 2 S0 4 for CaClg, and first allowing the jar of gas to stand for some 
hours, to ensure complete drying before inserting the calico. Colour 
entirely unchanged. 

11. Moistened the coloured calico and inserted it in a jar of un- 
dried Cl. Calico bleached almost immediately. 

These experiments seem to show that neither II, 0, HC1, nor Cl 
alone, has any more power than water to bleach coloured calico; 
and a similar remark applies to II, 0, and HC1 acting with water. 
But bleaching is immediately effected by the combined action of Cl <wd 

12. With common writing ink, wrote on a piece of printed paper 


and inserted paper into a jar of moist Cl. Writing bleached; print- 
ing unchanged. As the blackness of the writing ink is said to be 
due to organic colouring matter, and that of printers' ink to carbon, 
it seems that Cl and OH 2 acting together can attack organic colour- 
ing matter, but not carbon. 

13. Filled a long glass tube, sealed at one end, with a solution of 
Cl and OH 2 ; inverted it over a shallow vessel of the same solution, 
and exposed it to sunlight. Bubbles of gas were evolved, and col- 
lected at the top of the tube. Liquid gradually lost its colour. The 
disappearance of the colour suggests the disappearance of the Cl, 
and as there is nothing present but Cl and OH 2 , the gas at the top 
of the tube must be cither H or O; but Cl is known to have a strong 
affinity for II ; the gas is therefore probably 0. Tested this gas and 
proved it to be 0. Tested the liquid and found it acid. Acid 
proved to be HC1, as expected. 

This experiment seems to show that in the action of bleaching by 
Cl and OH 2 , the colour is destroyed either by the newly formed 0, 
or by the newly formed IIC1. From what I have already learnt of 
chemistry, I do not see how the latter is possible; and Experiment G 
has shown that ordinary free O can have no effect. But I know 
that " nascent " gases are said sometimes to be very powerful, and 
it seems likely, therefore, that the newly formed atoms of 0, before 
they have recombined into molecules, are the active agent here. 
Perhaps, then, the bleaching takes place by the Cl withdrawing the 
II from the OH 2 and leaving the "atomic" free to oxidize the 
coloured compound and so render it colourless. 

14. Made some bleaching powder by passing Cl into slaked lime. 
The following is said to be the reaction: 

2Ca(011) 2 + 2C1 2 - CaCL, + Ca(OCl), + 2H 2 0, 
or Ca(OH), + CL, = Ca(OCl)Cl " + H 2 0. 

15. If bleaching powder is a mi. f litre of calcium chloride (CaCl 2 ) 
and calcium hypochlorite (Ca(OCl).,), the CaCl 2 ought to be dis- 
solved out by alcohol, in which it is easily soluble. Tried this ex- 
periment; shook up some bleaching powder in alcohol, filtered, and 
evaporated. Scarcely any residue. Therefore the CaCl 2 is not 
soluble, and therefore bleaching powder is not a mixture. This is 
confirmed by bleaching powder showing little sign of being deliques- 
cent, whereas CaCl 2 is strongly deliquescent. 

The relation in which bleaching powder stands to CaCl 2 on the 



one hand, and to Ca(OCl) 2 on the other, seems to be indicated by 
the thick lines in the following diagrams: 

Fig. 16 

16. Made a mixture of bleaching powder in water. Added 
dilute H 2 S0 4 . Cl evolved. Therefore acid seems to be capable of 
turning Cl out of bleaching powder. 

17. Shook up some bleaching powder in water, and decanted the 
clear solution. Dipped some coloured calico in the solution, then in 
dilute acid. The calico was bleached. 

The bleaching is apparently due to the combined action of Cl 
and OH 2 . Since Cl is evolved, and since, with HJS0 4 , CaS0 4 is 
certainly precipitated, perhaps the following equation represents the 
reaction : 

Ca(OCl)Cl + H, 2 S0 4 - CaS0 4 + H 2 + C1 2 . 

Reference to Books in Library: 

18. The great majority of organic compounds are said to be 
colourless, and the molecules of such compounds are usually very 
complex. Hence even a slight chemical change in the molecules of 
a coloured compound, affecting only one or two of the atoms of the 
molecule, is almost sure to result in a colourless material. Thus, 
if Cl unites with the H of water und sets free O, this O will, in 
" oxidizing" the coloured compound, not "destroy" it, but will very 
probably be productive of a colourless compound. 

19. One book says that dry Cl may sometimes bleach, that then 
the Cl unites with the H of the dye, and so converts the dye into 
a non-coloured compound. But I have tried a good many coloured 
fabrics in dry Cl and could get no result worth mentioning. 

20. Another book says that the so-called bleaching action of Cl 
io almost always due to oxidation by hypochlorous acid (HC10). 
When Cl is dissolved in water, a small part of the Cl interacts with 
a little of the water : 


H 2 

C1 2 - HC10 


But only traces of HC1 and HCIO are produced, the change coining 
quickly to a standstill, the interaction being reversible. The pro- 
ducts IIC1 and HCIO interact more vigorously to produce, reversely, 
Cl arid OH 2 again. But when the solution is exposed to sunlight, the 
HCIO decomposes, and is produced. The removal of the HCIO 
prevents the reverse action proceeding, so that the direct action con- 
tinues, under continued exposure to sunlight, to completion. 

21. I took some Cl water that had been standing for a little 
while in diffused daylight and tested for HCIO, by shaking up well 
with Hg. A precipitate slightly brownish but nearly white was 
formed. Warmed this precipitate with dilute HC1. The brownish 
portion seemed to dissolve; the white insoluble precipitate that re- 
mained was mercurous chloride. The brownish precipitate that dis- 
solved indicated the presence of HCIO, but there was not much of 
it, and I did. not feel very certain. I did not know of any confirma- 
tory test. 

22. It seems probable that although is proved to be the direct 
agent in the action of bleaching, this is not released directly by 
the action of Cl upon the H of 1I 2 0, but is released from HCIO, 
which itself is formed, with HC1, by the action of Cl upon OH 2 . 

(1) C1 2 + U 2 HCIO + I1C1. 

(2) HCIO HC1 + 0. 

If this is so, it is not necessary to consider the meaning of "nascent" 
oxygen, which nobody seems to understand really. It is better to 
consider the HCIO as a powerful oxidizing agent, than to consider 
that the required energy comes from " atomic " oxygen just released 
by the action of Cl upon the water molecules. 

23. It was shown (in 17) that the action of acid on bleaching 
powder was to liberate Cl, and an equation was constructed showing 
that the complete action might be as follows: 

Ca(OCl)Cl + H 2 S0 4 - CaS0 4 + H 2 + C1 2 . 

One book states that the bleaching is then brought about by the Cl 
generated within the fibres of the wet cloth, and there setting free 
the from the water. But, from what we have just learned, the 
real action seems to consist in the acid liberating HCIO: - 

Ca(OCl)Cl + H^O, - CaS0 4 + HCIO + IIC1. 
Most of the HCIO now temporarily interacts with the HC1: 
HCIO + HC1 - H.O + 01* 


but as a certain portion of the HC10 gives up its 0, the reverse 
action is able to begin : 

C1 2 + H 2 = HC10 + HC1, 

and so the process continues until the Cl is all used up, the HC1O 
meanwhile giving up its and oxidizing the coloured fabric. 

It therefore seems wrong to say that bleaching is directly effected 
by Cl ; it is more correct to say by HC10. 

The investigation does not quite end at this point. Experiments 
involving crystallization and dialysis were performed with the object 
of proving whether bleaching powder is a " mixture " or a " com- 
pound ". But either the experiments were beyond the pupil's skill, 
or the directions given in the books consulted were inadequate. At 
all events the conclusions were negative, save that it was suggested 
that dry bleaching powder is a compound, but that in aqueous solu- 
tion it becomes dissociated into chloride and hypochlorite. 

5. An Instance from Physics 

The boy who did the following illustrated his notes with a large 
number of diagrams, but it is not necessary to reproduce many of 
these. The boy had done some good, fairly advanced work in Elec- 
tricity and Magnetism, Heat, and Inorganic Chemistry, but all he 
knew of Hydrostatics was the usual small amount done in connection 
with densities, &c., three years before. 

" Determine in the case of the syphon barometer, (1) whether 
the tube must be of uniform bore; (2) whether it must be placed in 
a vertical position; (3) whether the tube may be irregular in shape; 

(4) whether the height of the mercury column will be affected if 
a piece of iron be allowed to float upon the mercury in the cistern ; 

(5) whether the barometer will give correct readings (a) if in a 
sealed room, (b) if the cistern is closed except by a pinhole ; and (6) 
show how to correct a scale to give direct readings of the barometric 
height. As far as possible you are to prove everything experi- 
mentally from first principles. You may consult what books you 
like, but you may not accept any assumptions made by the writers 
of the books; nor may you make any assumptions from your own 
previous knowledge." 


1. Liquids take up the shape of their containing vessels, and 
if poured out on a level surface, spread themselves out on that sur- 
face; and the more perfect the liquid the more quickly do its parts 
act. Water, for instance, acts more quickly than glycerine. All 
this is a matter of common observation. In a perfect liquid, if there 
was one, we may assume there would be no resistance to change of 
shape, i.e. one part could slide over another without any friction 
whatever. Since, then, a liquid yields immediately to the slightest 
force, a fluid at rest cannot exert any frictional or tangential force 
against the surface in contact with it. Therefore the pressure of a 
fluid at rest is always perpendicular to the surface with which it is in 
contact. (Principle I.) 

2. Experimented with a glass globe containing (a) a neck fitted 
with a piston, and (b) a series of small holes above, below, and at 
the sides. Fjlled the globe with water and applied pressure to the 
piston. The issuing jets showed that the pressure was transmitted 
about equally in all directions. 

3. Experimented with a larger glass globe containing four necks, 
each neck fitted with a cork containing half-inch glass tubes so 
arranged as to test the pressure at the top, bottom, side, and centre 
of the globe, by means of water columns. Filled the globe with 
water, and applied additional pressure by pouring more water into 
one of the necks. The result showed that the pressure was trans- 
mitted through the liquid equally in all directions. 

4. The conclusion is that when. ]n ensure is communicated to any 
part of a liquid, it is transmitted without change of intensity e(fually in 
all directions through the liquid. (Principle II.) 

5. It follows that a pressure applied to any unit area, will be felt 
ivilhout change of intensity on every other unit area. (Principle III.) 
Hence, in a closed vessel filled with water and containing two 
pistons, A and B, B having x times the area of A, if unit force be 
applied to A, x units must be applied to B to keep it from being 
forced out. 

6. If one brick rests on a second, the second is subjected to the 
pressure of the first. If a third brick is added, the bottom brick is 
subjected to the pressure of the other two, the middle brick to the 
pressure of one. If a fourth be added, the bottom one is now sub- 
jected to a pressure of three; and so on. From this we may infer 
that we should probably experience an increase of pressure with an 
increase of depth in a liquid. 

7. Experimented with a glass tube, 12" x 2", open at both 


ends. A movable base consisting of a metal disk was pressed 
against one end of the tube and the whole was lowered vertically 
into a jar of water. The disk was maintained in position. In- 
ference: water exerts an upward pressure. 

8. By means of a string attached to the disk and passing through 
the tube, the disk was connected to the scale-pan of a balance, and 
counterpoised by shot placed in the second pan. Different weights 
were now placed in the second pan, and just sufficient water poured 
into the tube each time to make the disk fall off. Each time this 
happened the weight added always showed the same ratio to the 
height of the water poured in. 

9. Counterpoised the movable disk as in the last experiment, 
but, instead of adding weights, plunged the tube and disk into the 
jar of water (as in Experiment 7). The disk always fell off when 
the levels of the water in the tube and the jar were the^ same. Thus 
the water in the jar exerts an upward pressure on the disk, and the 
greater the depth of the disk the greater the pressure. 

10. With Professor Hall's pressure gauge (thistle funnel covered 
with membrane and connected by rubber tubing with horizontal 
glass tube containing a liquid index), tested the pressure in various 
parts and in various directions of a large vessel of water. 

Inferences from these experiments: 

11. The pressure in a liquid varies directly as the depth. (Prin- 
ciple IV.) 

12. The pressure at a given point is equally great in all directions. 
(Principle V.) 

13. The pressure is equally great at all points in tJie same horizontal 
plane. (Principle VI.) 

14. Experimented with Pascal's vases, the bases being of the 
same area, but the shapes of the vases differing greatly, In all 
cases, for the same weight in the scale-pan, the disk fell off when 
the water rose to a particular level. The experiment proved 

15. That the pressure mi the base of the vessel depends solely upon the 
height of the liquid above the base. (Principle VII.) The pressure is 
independent of the shape of the vessel and of the quantity of liquid 
in the vessel. 

16. That whatever be the shape of the vessel^ the pressure on the base 
is equal to the weight of a cylindrical column of water with a base equal to 
the base of the vessel and a height equal to the height of tlie contained water. 
(Principle VIII.) 

17. The truth of Principle VIII is obvious when the vessel is 



cylindrical, as at A. When the vessel is shaped like B the result 
may be explained thus: the pressure at any point x is perpendicular 
to the side (Principle I), and produces a reaction equal in magnitude 
and opposite in direction. Resolving this force into horizontal and 
vertical components m and n, we are able to see how all such hori- 
zontal components may be neglected, and how all the vertical corn- 

Fig. 17 

Fig 18 

Fig. 19 

ponents act upwards to support the water over the slant side. Thus 
the pressure on the base is less than the weight of the whole of the 
liquid in the vessel, the difference being .supported by the slant sides. 

18. When the vessel is shaped like C, the component n' acts 
downwards, and so increases the pressure on the base; the base is 
thus subjected to a pressure greater than the weight of the liquid. 

(The pressure thus exerted must not be confused with the pres- 
sure which the vessel and its contents exert on 
the table or other supporting body.) 

19. In 17 and 18 it will be seen that if the 
area of the base is increased the pressure on it 
will increase. 

20. Observation shows that a liquid always falls 
from a higlwr level to a lower level. (Principle IX.) 

21. Experiments with variously shaped vessels 
showed that the surface of a liquid in equilibrium is 
always horizontal (Principle X); and that 

22. All liquids seek their level (Principle XL) 

23. Thus in a U-tube, whether the arms are of equal or unequal 
cross section, the contained liquid will maintain a level. 

24. The sectional area of the right arm DB of the U-tube CABD 
(fig. 20) was four times that of the left arm CA. Mercury was 
poured into the tube until it reached the level AB. If water is 
poured into the arm CA, the pressure on the surface A is trans- 
mitted equally to B, and in order that the mercury may retain its 
original level in the arm DB, we must pour into DB an amount of 
water four times as great as was poured into CA. (Principles II 

Fig. 20 


and III.) Experiment showed this to be the case; also that the 
water in the two arms now reached the same level CD. 

25. If, then, we poured two different kinds of liquids in the 
respective arms, say one twice as dense as the other, the less dense 
liquid column ought to be twice as high as the more dense, if the 
mercury retained its original level AB. 

26. Found, by using the specific-gravity bottle, that the relative 
density of alcohol was % 8. Poured water into the arm a A of the 
U-tube, and then alcohol into the right arm DB until the mercury 
was restored to its original level. The height of the water column 
to the height of the alcohol column was, as expected, 4 : 5. There- 
fore the U-tube may be used for finding the relative densities of 
two liquids by measuring only the heights of the respective columns 
above the mercury level. 

27. If the liquids do not mix, we might dispense with the mer- 
cury and measure the heights of the columns from the horizontal 
plane passing through the surface of separation of the liquids. 

28. Experimented with inverted U-tubes (Hare's apparatus), 
using water and alcohol. Varied the experiments as follows: (a) 
Upright tubes of the same bore; (b) upright tubes of different bores; 
(c) sloping tubes of different bores; (<l) irregular tubes of different 
bores; (e) levels of liquids in beakers the same; (/) levels of liquids 
different; (g) beakers at different levels. The results were always 
the same; the heights of the columns of alcohol and water, measured 
vertically from the surfaces of the liquids in the beakers, were always 
in the ratio of 5 to 4. The size, shape, and position of the tubes, 
the position of the beakers, the levels of the liquids in the beakers, 
made no difference at all to the result. This was expected, consider- 
ing the various Principles already established experimentally. The 
apparatus can therefore be used for finding the relative densities of 

29. The pressure of the atmosphere may bo ignored, since it 
affects both columns in exactly the same way. Inside the tube the 
reduced pressure is exactly the same on each column; on the surface 
of the liquids in the beakers, the outer atmospheric pressure is also 
just about the same in the two cases; one beaker would have to be 
very much higher than the other for the difference in the atmospheric 
pressure to be at all measurable. 

30. So in the case of each liquid, we have the outer atmospheric 
pressure balanced by a pressure due to a liquid column increased by 
the pressure due to the rarefied air. Thus one liquid column balances 


another, or the pressure due to the one on unit area is equal to the 
pressure due to the other on unit area. 

31. The questions about the barometer can now be answered. 
The barometer is an instrument for transmitting the pressure of 

the atmosphere, and this pressure is transmitted to, and the amount 
indicated by, a column of mercury. It is practically a long U-tube, 
one arm containing a column of air extending from the earth to the 
upper surface of the atmosphere, and the other containing mercury. 
Therefore, what applies to the ordinary U-tube containing balancing 
columns also applies to the barometer. 

32. The tube need not be of uniform bore. The pressure will 
depend merely upon the vertical Iieighl of the mercury column. From 
the previous experiments it is clear that the shape of the tube, the 
position of the tube, and the regularity of the tube will not in any 
way aflect tj^e vertical height of the column of mercury. (See 
Principles II, IV, VII, and VIII.) 

33. Floated a piece of iron in the cistern of mercury of a baro- 
meter. The mercury rose in the tube. This was to be expected, 
as the column of mercury now bus to support the pressure of the 
atmosphere and a piece of iron. 

From this it follows that, in the wheel barometer, since the iron 
float is necessarily rather heavier than the counterpoise, any diminu- 
tion of atmospheric pressure which is less than the difference be- 
tween these weights would not be sufficient to raise the iron float, 
with the consequence that the diminished pressure would not be 
indicated on the dial. If r>nly for this reason, the wheel barometer 
is not to be relied upon. 

34. The barometer will not give correct readings of the outer 
atmosphere if placed in a sealed room, i.e. a room which has abso- 
lutely no communication with the outer air. But usually, however 
carefully doors, windows, and chinks may be fastened and stopped 
up, air will force its way through the porous walls, ceiling, and 
floor, and the barometer will register the pressure of the outside 
atmosphere correctly. 

35. A pin-hole is quite sufficient for the atmosphere to exert its 
full force. The size of the aperture is quite immaterial. This is 
an application of an extreme case of one of Pascal's vases (fig. 19). 

36. The height of the barometer is best taken by means of two 
readings, viz. the readings of the heights of the mercury in the two 
limbs of the U-tube; and taking their difference. But a direct 
scale may be constructed as follows. Suppose the cross section of 

(0415) 28 


the open limb (supposed uniform) be ten times the area of the cross 
section of the closed limb. Then when the mercury in the tube 
(the closed limb) rises one inch, the level in the cistern (the open 
limb) will sink one-tenth of an inch. Thus there is now an increased 
difference between the mercury levels of l T \y in. It follows, there- 
fore, that a length which is actually one real inch on the scale must 
be marked 1^ in. And so on in proportion. 

If there is no simple relation between the cross sections of the 
cistern and tube, the scale must be made by trial. 

It is a very easy matter to criticize the result of this investi- 
gation. For instance, "principles" have been established that are 
not afterwards used, and assumptions have been made that what 
applies to the pressure of a liquid applies also to the pressure of a 
gas; there is no differentiation of "fluid" pressures. ,And so on. 
Yet, for a boy, the result cannot but be regarded as very satis- 
factory. The subject is difficult, and very few textbooks deal with 
it adequately. The phrase "pressure at a point" is responsible for 
much vague thinking on the part of those beginning hydrostatics 


Solving Mathematical Problems in the 


"The profound study of Mathematics seems to injure the more 
general and useful mode of reasoning, that by induction. Mathe- 
matical truths being, so to speak, palpable, the moral feelings become 
less sensible to impalpable truths." 1 

"Nothing is less applicable to life than a mathematical argument. 
A proposition couched in ciphers, is decidedly either true or false. 
In all other relations the true and the false are so intermingled that 
frequently instinct alone can decide us in the strife of motives, some- 
times as powerful on the one side as on the other." 2 

"He who is styled a mathematician very frequently succeeds in 
passing for a deep thinker, although under that name are included 
the veriest dunderheads in existence, incapable of any business what- 

i Walpole, in Walpoliana, vol. i, p. 113. * De Stael, De I'Allcmagne, vol. I, p. 163. 


soever which requires reflection, since this cannot be immediately 
performed by the easy process of connecting symbols, which is more 
the product of routine than of thought." l 

Thus spoke three of Sir William Hamilton's " cloud of witnesses" 
who were brought forward to prove to the world that Mathematics 
was a wholly unprofitable study. Sir W. Hamilton himself looked 
upon Mathematics as altogether beneath the attention of intellectual 
men, the subject being "so easy that it affords no real discipline". 
His temerity in discussing a subject about which he knew practically 
nothing at all is little short of amazing, and Mill had a very easy 
task in demolishing the whole of the arguments of the famous Scot- 
tish metaphysician. 2 

Yet the fact remains that, oven to this day, a considerable 
number of people are inclined to speak slightingly of the study of 
Mathematiqp and of the usefulness of mathematical knowledge. 
This is perhaps due not so much to the survival of the old opinion 
that the subject affords no practice in the estimation of conflicting 
probabilities, and therefore does nothing towards developing the 
kind of sagacity most required in the conduct of practical affairs; it 
is rather that, when the ordinary synthetical demonstration of a 
mathematical problem is, step by step, followed out, the whole thing 
seems so simple, every step following directly arid logically from 
the previous step, that the process seems to demand no real intel- 
lectual effort at all. 

Now this synthetic or deductive method is the method by which 
the mathematician exhibits the, result of his work. Such a demonstra- 
tion rarely or never reveals the secret whereby he discovers the 
method by which he attains the result. Actually, the problem is 
always solved by tumli/sis, not by synthesis; the reasoning is, in the 
main, inductive, not deductive. Although it is true that deductive 
reasoning appears to form the very essence of all mathematical ex- 
position, it is a mistake to think that the actual work of the mathe- 
matician is entirely, or even primarily, of a deductive character. 
His work is largely inductive, and is therefore in important respects 
akin to that of the man of science. 3 

* LIchtenberg, Vermuchte SchrifUn, II., p. 187. 

*See Hamilton's DMCIIMIOIM on Philosophy, pp. 263-340; ami Mill'* Examination of 
Hamilton's Philosophy \ pp 591-616 

It la not intended to suggest here that Mathematics 1ms now become a " practical" sub- 
ject. With the arguments of the extreme advocates of the two mathematical schools of 
thought- the advocates of the ultra-academic school on the one side, and those who, on the 
other side, would reduce Mathematics to a number of "tips" and "formulae" for engineering 
practice-thls chapter has nothing to do The extent to uhich Mathematics should, for 
teaching purposes, be made a " concrete " subject is still a matter of dispute. 


Let us suppose that a teacher, finding his class unable to solve a 
particular mathematical problem he has set them, " works out" the 
problem himself. No doubt the pupils will, as a rule, be able to 
follow without difficulty the different steps of the solution and be 
convinced of its accuracy. But what have they gained? They have 
had no real share in the work. They are still ignorant as to the 
way in which the teacher discovered how to solve the problem. To 
work through, in this way, a whole problem for a class is not only 
unnecessary; it is a teaching blunder of a serious kind. All that the 
pupils really require, or, at all events, ought to be given, is a clue 
by which they may set to work themselves. The art of teaching 
Mathematics consists, at bottom, in telling the children just enough, 
but no more, to enable them to initiate a plan for successfully 
assailing the central difficulty of a problem. To tell them more 
than this is, psychologically, altogether wrong, , 

Although, when a problem has to be solved, the procedure to be 
followed is that of analysis, it is a fallacy to think that, for effecting 
such an analysis, explicit and final directions can be given which 
would enable a pupil to proceed, with certainty of success, to the 
solution of any proposed problem or to the demonstration of any 
proposed theorem. No such instructions are possible, though, 
according to the ordinary textbooks, all we have to do is to assume 
the truth of the theorem or the solution of a problem, deduce con- 
sequences from this assumption, and combine them with results 
which have been already established. If a consequence can be 
deduced which coincides with some result already established, it 
may happen that by starting from the consequences which we 
deduced and retracing our steps, we can succeed in giving a 
synthetical demonstration of the theorem or solution of the prob- 
lem. But such a rule is altogether too vague for general applica- 
tion, because no exact instructions can be formulated by which 
we are to combine our assumptions with results already estab- 
lished. 1 

1. Suppose the following well-known exercise in Geometry be 
given to a class of young pupils: 

The opposite sides AD, BC of the parallelogram A BCD are bisected 

* For further remarks on Geometrical Analysis, see almost any textbook on Geometry. 

For some admirably-worked-ont examples of geometrical analysis, see Euclid, Book XIII, 
Heath's edition, vol. iii, "Propositions on the Kegular .Solids", especially the alternative 
solutions of Pappus. (The term Geometrical Analysis must not, of course, be confused with 
Analytical Geometry.) 


in E and F; AF and EC are joined, cutting BD in G and H. Show 
that BO, GH, and HD are equal 

We begin in the usual way by assuming that BG, GH, and HD 
are equal. The first question that would probably occur to us to 
ask, is, How have we sometimes been able, in previous exercises, to 
prove two or more lines equal? and the answer almost certain to be 
forthcoming is, By means of congruent triangles. The symmetry 
of the figure will now suggest how BG and HD may probably be 
proved equal, since the triangles BGF and EHD appear to be con- 
gruent. The quicker boys will soon observe that GH may be 
similarly dealt with by drawing a parallel through G or through H. 
The slower boys may require the help of a few suggestive questions 
on this point, which is the only possible real difficulty likely to be 
experienced by them in the whole exercise. The apparent congru- 
ence of th^ three triangles being now seen, the teacher will leave the 
remainder of the work entirely to 
the class. Any further help in com- 
pleting the analysis ought to be quite 
unnecessary; and to give any help in 
setting out the subsequent deductive 
demonstration would be unwise. 
The whole of the teacher's work 
ought, in fact, to be confined to 
two or three questions; and the form he makes these questions 
take, and the way in which he deals with the answers, will be a 
searching test of his skill. He should tell the boys nothing that 
they can, reasonably, discover for themselves. 

2. Or, suppose the given problem to be, Divide a given line into 
extreme and mean ratio. Without some kind of a hint, the ordinary 
boy will probably be unable to make a start; and if he is merely 
shown the construction given in many textbooks on modern Geo- 
metry, he is as much mystified as to how such a method could have 
oeen devised, as he is if he is referred to Euclid ii, 11, or vi, 30. 
But if he is told to solve the problem algebraically, and so, if 
possible, obtain a hint for the geometrical solution, he sees at once 
that the whole thing really depends upon discovering a method of 
drawing a line ^/5 units in length. And if he has previously been 
taught how to find the square roots of numbers graphically, he 
can now solve the given problem without any further aid whatever. 
Further, he will obtain the clue to the origin of the textbook con- 



structions, Euclid's included. To explain these constructions to him, 
therefore, would be a confession of a lack of teaching skill. 

3. We may take as a third example, To inscribe a square within 
a given triangle. 

In working through an examination paper in geometry, a boy 
naturally prefers a rider which is appended to a proposition, for 
he knows that he probably has to deal with an application of the 
general principle underlying that proposition, and he is therefore 
supplied with the key. 

This particular problem would, in such a case, probably be 
appended to a proposition concerning similar polygons, more par- 
ticularly the inscribing of one polygon within another; a quicker 

boy would sec that the application was straightforward, and he 
would proceed with his synthesis at once. He would gather from 
the proposition that he might draw any square whatsoever with its 
base in the base of the triangle and a corner on one of the other 
sides of the triangle, say the square PQRS or ALNM (when the 
side AL conveniently coincides with the altitude of the triangle). 
By joining BS and producing towards /, or by joining BM; and 
either allowing the square PQRS to expand, the point s running 
along BZ; or allowing the square ALNM to contract, the point M 
running along ZB; the point G in AC is determined, and the rest 
follows at once. (Fig. 22.) 

But suppose the boy did not know the general principle of 
which the rider is an application. An analysis would be essential, 
involving perhaps a number of trials. Unless the boy had pre- 
viously done something to similar triangles and to proportional 
division, he would fail to obtain the solution. But in any case he 
would probably first ask himself, how is the point o to be deter- 
mined in A o (or D in A B) in the completed figure? (Fig. 23.) Once 


he had decided that similar triangles might give him the clue, 
he would not improbably follow up the fairly obviously direct 
course : 

AG AK _ AK _ AL 

GO G"F "~ DG ~ EC' 

that is, the line AC is divided at o (or AB at D) in the ratio 
altitude/base. He can now set out his work synthetically, in its 
usual deductive dress. 

4. Although the analytical method of approaching a problem 
applies to other branches of Mathematics generally, the method 
will vaiy materially, according to the particular circumstances. In 
teaching how to solve, for instance, problems producing algebraic 
equations, a great deal depends upon the plan adopted for making 
a pupil see* how to apply certain general principles to all particular 
cases. The pupil must be taught not only how to set down his data 
systematically, but how to search for the given alternative condi- 
tions whereby the equation can be formulated. Take, for instance, 
the following well-worn problem producing a quadratic: Whai is the 
juice of eggs per dozen when tir<) lets in the shilling 1 s worth raises the price 
one penny a dozen? Pupils who have been well taught and have had 
a fair amount of practice with easy examples, solve this problem 
offhand; pupils who have been taught without insistent reference to 
general principles find it a little ditlicult. 

The well taught pupil will see at once that he has 

(1) To consider (a) the price per dozen eggs, and (b) a shilling's 

worth of eggs. 

(2) To discover a relation between these two things. (An in- 

telligent pupil may see the relation at once; a slower pupil 
will have to take the intermediate step of finding the cost 
of a single egg.) 

(3) To formulate an equation either between 

(i) Numbers of eggs for a shilling; or, 
(ii) Prices of eggs per dozen; or, 
(iii) Prices of one egg. 

He therefore tabulates his data and the consequent derivative 
relations, and then equates, as follows: 



First method: 



Price of eggs per dozen 
/. Price of one egg 

/. No. of eggs for Is. 

x pence 

x -h 1 pence. 

12 " 

x + l 

Hence the equation : -f- 2. 
x x -f 1 

/. * - 8. 

or, Second method: 



No. of eggs for Is. 
.*. Price of one egg 



x - 2 

a: - 2 f 

.*. Price of a dozen eggs. . . 



* -2 " 

TT 4i * 144 144 n 
Hence the equation: -- 1. 
x x - 2 

w, 27tM'd method: 

= 18. 



Price of one egg ... 
.*. Price of a dozen eggs. . . 

/. No. of eggs for Is. ... 

cc pence 

y pence. 
12y ,, 


Hence the equations: 12* = 12y - 1; and 1? = 1? + 2. 
* 3/ 

and so with other possible methods, all based on the same general 
principles. The whole procedure of tabulation is virtually mechani- 
cal, and the only point that ought, ordinarily, to require elucidation 
on the part of the teacher is the derivation of the step (a) number of 


eggs for a shilling from the step (I) the price of a dozen eggs; or 
vice versa. A few preliminary "mental" exercises would probably 
suffice to make this point clear. 

5. Of course, the successful solving of problems will depend, to a 
considerable extent, upon the amount of previous practice in problems 
of a similar, if simpler, kind. We could not, for instance, expect a 
boy to attack the following problem, until he had learned, by work- 
ing easier examples, to formulate an equation involving angular 
measurements as determined by the usual initial and final positions 
of the hands of a watch. Suppose it is now between ten and eleven 
o'clock, ami that minutes hence the minute hand of a watch will be 
exactly opposite to the place where the hour hand was 3 minutes ago. 
Find the time. The real difficulty here would probably consist in the 
drawing of a satisfactory figure, considering the number of angles 
that are involved and the close proximity of the positions of the 
hour hand now, three minutes ago, and at ten o'clock; and a 
hint would probably be necessary as to the means of discovering 
the approximate present position of the minute hand. Clearly from 
the question this position must be somewhere in the neighbour- 
hood of a quarter past the hour. Hence a figure may now be drawn 
upon the blackboard, and the angular measurements briefly discussed. 
Any further help ought to be unnecessary, except perhaps a reminder 
that in this type of problem the equation is usually formulated by 
breaking up the composite angle in two different ways. 1 The boys 
must not lose sight of the general principle in the particular problem, 
and must be made to apply that principle themselves. 

6. Or another problem : From the top of a mast of a ship, which is 
88 ft. above the sea, the light of a lighthouse which is known to be 132 ft. 
high can just be seen. How far is it aim//?- -As this is a simple and 
direct application of Euc. iii, 36, the teacher's work ought to be con- 
fined to the elucidation of the fact that the mast and the lighthouse 
are virtually prolongations of two radii of a great circle. If the 
class wanted more help than this, they would probably not have 
realized the full purport of Euc. iii, 36. ? 

1 If the teacher found it absolutely necessary to formulate the equation himself, for 
instance, g ~ 8 + 50 = * + + 30, he would afterwards insist on the boys giving one or two 

alternative forms of equation, using the same figure 

2 The ordinary approximation method of the textbooks (on problems involving the Dip 
of the Horizon) would, of course, be de^lt with after the general principle had been fully 
grasped. The simplification of the usual formula might then well be given to the class as a 
separate and distinctive problem. 


7. Or a harder problem 1 : A cylindrical vessel is filled with water. 
With what velocity must it be whirled round its axis that half the water 
may be thrown out? Obviously this problem requires the solver to 
be familiar with the following principles: 

(1) If a cylindrical vessel of water revolve about its axis, the 

cavity formed in the fluid will be a paraboloid. 

(2) In order that any particle of water on the surface of the 

paraboloid may remain at rest relatively to the ground, the 
particle must revolve, in a horizontal plane, with a velocity 
which would be acquired by a body falling through a space 
equal to the abscissa of the point. 

(3) The content of a paraboloid " inscribed " within (and there- 

fore touching the base of) a cylinder is equal to half the 
content of the cylinder. 

He ought then to be able to see that 

(1) The quantity of water thrown out will always be equal to 

the paraboloid thus formed ; 

(2) The greater the velocity of the cylinder, the greater will be 

the quantity of water thrown out, i.e. the lower will the 
vertex descend; 

(3) The cylinder must be whirled with such a velocity that the 

vertex of the paraboloid may descend till it just touches 
the bottom of the cylinder. 

The solution at once follows, viz., that the velocity must be equal to 
that acquired by a body falling freely through a space equal to the 
height of the vessel. 

The problem was given as a rider to a class of students who 
were already familiar with Principles 1 and 3, and to whom Prin- 
ciple 2 had just been demonstrated in connection with problems on 
centrifugal force. Only one student was successful ; the others had 
not quite grasped Principle 2, which was then demonstrated again, 
and several other students got out the solution successfully. The 
real point of interest was the teacher's attitude towards his students; 
he took care to see that they were thoroughly familiar with the 
necessary general principles, but he positively refused to help them 
in applying these principles. 

8. The writer was once much struck by the mathematical work 

* See Carr's edition of Newton's Principia, Sections I-III, p. 161. 


of a class of boys in a French school. It was remarkable how little 
help the teacher responsible seemed to give, yet the boys showed 
an unusual facility in attacking problems. They were at that time 
doing solid geometry and were not only quite familiar with the 
content of Euclid, Book XI, but had done some fairly advanced 
work in orthographic projection, including exercises in interpene- 
tration. The Headmaster asked the writer to give them some kind 
of problem, and accordingly Lewis Carroll's 63rd "pillow problem" 
was proposed: 

Given two equal squares in different horizontal planes, having their 
centres in the same vertical line y and so placed that the sides of each are 
parallel to the diagonals of the oilier and at 
such a distance apart tfiat, by joining neigh- 
bouring vertices^ eight equilateral triangles 
are formed. 9 Find the volume of the solid 
thus enclosed. 

Only one boy was able to draw a man- 
ageable figure, and he was then made to 
draw it on the blackboard. During the 
next three minutes no boy made any 
progress; then the master went to the 
board and put in J K, and by a question 
or two got some of the boys to point out 

that the solid was built symmetrically about JK as an axis. They 
were, however, still battled, and eventually they were given a further 
hint, the master indicating that the midpoint o of JK might be made 
a possible starting-point for the dissection of the solid. Almost im- 
mediately three boys saw there were eight similar pyramids having the 
equilateral triangles for their bases, and their vertices at 0; and it now 
soon came out that the solid contained still two other pyramids, the 
bases consisting of the two original squares, and the vertices being at o. 

The whole class now saw that the problem resolved itself into find- 
ing the volume of one of the former and one of the latter pyramids. 

They decided first to find the volume of ABCD.O, and were 
told to let each side of each square be 2 units in length. Almost 
without exception they quickly found the length of JK by finding 
LM from the triangle LMG (LG = ^/3 and MG = ^/2 1; there- 
fore LM = 2*). Thus JK = 2* and therefore JO = -j. Hence 


the volume of ABCD. o = . . 



They now took in hand the pyramid CDG. O. The area of the 
base CDG was obvious, but the perpendicular distance OR from the 
vertex to the base puzzled them for a time. Eventually two boys 
suggested the same expedient, viz., the drawing of OS parallel to 
KG. Thus the triangles ORS and LMG are similar, and as OS is known 

/2 -I- 1 

(being half the sum of JL and KG), OR can be found and = v , , 
V 8 ' 2 i . v /3. 

/2 -4- 1 

Therefore the volume of the pyramid CDG.O = V^^T . The 

* y 2*. 3 

volume of the whole solid is now easily estimated, and is equal to 
8.2*^/2 + 1) 


In a class of twenty-three boys there were fifteen correct solu- 
tions. The times varied from fourteen to twenty-one minutes. No 
other help was given than that indicated. It will be 4 noticed that 
the boys' solution is really neater than Lewis Carroll's own, though 
of course the actual key to the boys' solution was provided by the 
teacher. And the large-scale figure on the board was made very 
clear by a few suggestive shading lines. 1 

Briefly, then, scientific method applied to the teaching of solving 
mathematical problems means the method of discovery, the method 
of induction, the method of analysis. The pupil is taught to realize 
at the outset what the problem gives him by way of working ma- 
terials, and what the problem requires him to do. The method does 
not mean placing the pupil in the attitude of a passive listener, of 
one who merely follows out the working of the teacher's mind. The 
teacher's work is limited to giving the pupils hints and clues, and 
these by means