Early Invention. A paddle-wheel
vessel. From a sixteenth-century edition
of Vitruvius (first century a.i*:).

w

o

a

Makers of
SCIENCE

•3Iathematics "Physics
(^Astronomy

IVOR B. HART

WITH AN INTRODUCTION

BY

DR. CHARLES SINGER

Second Impression

LONDON

OXFORD UNIVERSITY PRESS

HUMPHREY MILFORD

1924

Printed in England

9

H3x

An early use of steam power by Heron
of Alexandria
? First century a.d.

AUTHOR'S PREFACE

The motives underlying the writing of this book have
been fully set out by Dr. Charles Singer in the Introduc-
tion. It merely remains for the author to express his
acknowledgements and to explain the limitations of the
work. Apart from the mode of presentation and the choice
of material, the book makes no claim to originality, and
the author freely acknowledges his indebtedness to existing
works on the subjects dealt with. A hst of these is given
in the bibliography at the end of the book.

This work is not intended as a series of detached
biographies. It is hoped that the reader will find the
various chapters linked to each other to form a chrono-
logical sequence of some of the broader movements in
scientific history so far as the physical and the mathe-
matical sciences are concerned.

Space has demanded a rigid limitation in the matter
treated. No attempt has been made to include either the
biological or the chemical sciences. For the same reason
much of the history of physics and mathematics has
necessarily been omitted, and the characters chosen for
biographical treatment have been so chosen rather from
the point of view of their suitability as * pegs ' from
which to ' hang ' the scientific history of their times than
from any superiority over their contemporaries.

The author desires to express his sincere thanks to his
friends ]\Iiss D. Turner and Mr. D. E. Williams for con-
siderable assistance in the reading of the proofs and
manuscript. More especially he is under a deep debt of
gratitude to Dr. Charles Singer for continuous advice,
encouragement, and helpful criticism throughout the whole
period of the author's labours at the book.

IVOR B. HART.

February 1923.

INTRODUCTION

There was a time — not so very long ago — when the general
scheme of education seemed stable and almost complete. To the
discovery of the classics in the fourteenth and fifteenth centuries
had succeeded that process by which the literary treasure of
Greece and Rome became accessible. The change in man's
outlook quickly affected education and the classical system
established itself firmly in the schools and remained practically
unchanged for wellnigh four centuries.

What an iUuminating system it was and how much truth it
provided ! It was Rome, the legatee of Greece, that had tamed
the barbarian and created civilization. It was to the Roman
tongue that the languages of the peoples of Europe surrendered
themselves and are still surrendering It was Roman law that
displaced and still displaces tribal custom. It was the religion, the
sacred books of which were written in Greek and the organization
of which was fashioned m Rome, before which the tribal rites
had receded. It was the Art and thought of Greece which seemed
so clearly to be the ancestor of much of what was best and most
beautiful in life. The consciousness of such an inheritance,
even when corrupted by ages of barbarism, gave men a sense
of the fullness of their own past. Purified by scholarship and
philosophy it provided a complex and ennobling scheme of life.

The educational system that thus arose served as the funda-
mental training until almost our own time. Only with extreme
slowness did new elements enter into the situation and the advent
of science had for long surprisingly little effect upon education.
The science of the sixteenth, seventeenth, and eighteenth cen-
turies was mainly the affair of amateurs, of men trained in the
old system who happened to interest themselves in pheno-
mena. For them the classical education, the only complete and
thought-out system of the day, was still the best available. The
ideas of Copernicus and Vesalius and even those of Galileo,
Kepler, Boyle, and Newton, were no obstacle. The great physical
synthesis established by such workers, while it emphasized the

Introduction 7

separation from the Middle Ages — which seemed ever darker
and darker as knowledge advanced — brought antiquity nearer to
men of the early modern period. If the physics of Aristotle fell,
yet much of his philosophy remained. Plato w^as untouched and
Greek letters and art stood yet as the model of all that was the
most beautiful. Latin was still the lingua franca of the learned.
Greek was the language ' of that ancient wisdom which was so
evidently the ancestor of the science of the day. In the eighteenth
and even in the earlier nineteenth century, a classical education
was by no means a bad preparation for a scientific career.

Two factors disturbed the situation, one practical and one
spiritual — firstly, certain later developments of the Industrial
Revolution and, secondly, the realization of the vastness and
complexity of man's past.

I say later developments of the Industrial Revolution because
the earlier developments, like the earlier developments of modern
science, had comparatively little influence on the manner of
thinking. The earlier factors in the Industrial Revolution, such
as the introduction of stone-coal, the flying-shuttle, the spinning-
jenny, steam-power, and new means of the preparation of iron,
certainly greatly increased the amenities of life and had their
influence on the manner of living, but they had no great efi^ect on
the intellectual situation. These early advances were almost
all technical — inventions rather than discoveries — innovations
depending on the application of known principles and not involv-
ing the introduction of new principles. It was at a later stage,
when a high degree of technical training became a common
demand, that the effect on the educational situation began to
be felt.

The unsettling elements in science, as in industry, hardly
began until the nineteenth centur}^ The views of Dalton on
the atomic nature of matter were expressed in the first decade.
The idea of the infinite complexity of matter was furthered by
the chemical discoveries of Davy, by Frauenhofer following up
Wollaston's work on the spectrum, by Mitscherlich's disclosure
of the existence of isomorphism, by Pelletier's synthesis of organic
compounds, and by Faraday's researches in electricity — all

8 Introduction

appearing before the first half of the century was over. In
1850 came the work of Joule which laid the experimental basis
of the modern doctrine of energy.

In Biological science the movement was a little later. Until
the work of Ehrenberg in the thirties and forties the knowledge
of minute life had remained much where Leeuwenhoek had left it.
With new and improved instruments was revealed an unexpected
variety and complexity of living things. The cellular theories of
Schleiden and Schwann — developed by Henle, Kolliker, and later
by Virchow — at last introduced effective general ideas into the
conceptions of vital phenomena. It was, however, the evolution-
ary view of Darwin and his followers that finally destroyed, in the
decades after i860, the possibility of thinking of a world in which,
outside the Bible, the whole debt lay to Greece and Rome. With
the spread of evolutionary views in the second part of the nine-
teenth century, with the development of archaeology and
especially with that department of pre-historic archaeology that
had been founded by Boucher de Perthes, with the enormous
increase in the complexity of scientific knowledge, and with the
demand for specially trained scientific workers, entirely new
needs arose. It was no longer true that the old classical education
supplied a clue to man's history, nor did it aid for vocational
purposes.

Classical learning in the old sense as the staple of education was
thus perhaps inevitably doomed. But Science — I use the word
for the moment in its restricted meaning — though it may displace
the Humanities, could not and cannot replace them, for it cannot
provide us with any clear record of how we have developed
mentally. For this we must turn to History, but History not in
the sense in which that word is customarily employed as equiva-
lent merely to Political History, nor even in the wider sense of
Sociological History. It is the history of mankind as a whole
that we need, the history of civilization, the history of man's
thoughts, of man's knowledge, of man's self.

Such history, we may hope, will ultimately take its place as the
central item in the curriculum even of the elementary schools.
Into that history will be interwoven the stories of Greece and

Introduction 9

Rome, but these will be presented not for themselves but as part
of a greater whole. The task of preparmg such a work is a very
great one and it must be many years before it will be forthcoming.
There are large areas of knowledge which must be reduced to
compassable form before it can even be attempted. In the mean-
time and as a preliminary stage we must look to separate works
on different aspects of history. The history of the earlier stages
of man's development as well as an account of the technology of
a later stage have been admirably set forth in an elementary
fashion by ^Ir. and Mrs. Quennell. There are several elementary
text books of Economic History available. The history of
Religion finds, or should find, its interpretation in the Sunday
school. There is still, however, very great need for an elementary
account of the development of Art throughout the ages and
almost as great a need for a school history of Science.

For those whose education is mainly grounded in Science, and
especially for that large and growing class that is destined to
follow Science as a career, the History of Science — even apart
from the reasons that have been urged — is itself surely an appro-
priate study. But there is another and more immediately
practical ground on which we may plead for the introduction of
Histor}^ into the scientific curriculum. We are well accustomed
to recognize that the store of acquired scientific knowledge is
a general treasury from which all men draw, by which alone it has
been possible for our material state to rise above that of the
savage. Yet we seldom remind ourselves that the guardianship
of this treasury, the heritage of all men, has always been in the
hands of a very small band, and this has been so in all its wander-
ings. From the peoples of the ancient East it passed to the
Greeks, then having dwelt awhile in Moslem lands it came to
Italy, and during the last three hundred years it has at last
penetrated to the West of Europe. In all these countries and at
all these periods the organic apparatus by which new knowledge
has been created has been the work of a mere handful. Surely
the contemplation of the conditions under which these men
worked and lived, the examination of their training and mental
history, of their environment and manner of development, must

10 Introduction

be of value — even in the practical everyday sense — to those who
would follow in their footsteps.

And the other side of the picture is also not without its applica-
tion. The study of those social and economic and philosophical
conditions that fail to produce effective scientific fruit, or that
yield only bizarre and deformed products, has also its lesson.
Some idea of the Science of these retrograde periods must also be
included in any course on the History of Science, and should form
an integral part of any scientific education worthy of the name.
The scientific student would thus be grounded in the elements
of what we may call the Embryology, the Physiology, and the
Pathology of his special study.

But there is yet another aspect of the History of Science. Our
scientific system of its nature claims an independence of all race,
nationality, or creed. It is of all studies the most truly inter-
national. The scientific man may, better than most, claim that
he is the true citizen of the world. Nevertheless, in all countries
and at all periods there has been a certain local and temporal
stamp in the Science that has been produced. These differences,
however, concern the interests and processes of the scientist
himself rather than the methods and aims of his science. Now
among the methods of Modern Science there are certain new
factors of an order that the world has not before seen ; and
though he must be sanguine indeed who believes that the scientific
treasury will always remain with its present guardians, yet these
new factors give us good hope of a permanence in our scientific
results and of a uniformity of scientific advance of a character
the like of which history has not yet seen.

Those factors are bound up with the manner in which we record
and present our knowledge as soon as it is acquired ; our mode
of storing our treasures for ready accessibility. One great lesson
of the history of science is that the influence of newly acquired
knowledge varies greatly with its presentation. Much of the
work of Thomas Young, for instance, one of the greatest scientific
intellects that this country has produced, has needed to be redone,
and modern discoveries are frequently * re-discovered ' in his
writings. The neglect of his material by later generations is

Introduction 1 1

largely the result of his own very imperfect method of presenting
his work. With the mass of knowledge so vast and growing, with
the evil and increasing tendency of the departments of knowledge
to separate farther and farther from each other and to dwell each
in its own house, the necessity for careful presentation of the
material grows ever greater and greater. One practical advantage
of even an elementary study of the history of science is that it
may tempt the student to the perusal of the great classics
of scientific investigation, to learn at first hand both the best
methods of research and the most appropriate modes of present-
ment. A pressing need for such students is a work containing
a series of extracts from the writings of the greatest investigators,
which could be used as a sort of commentary on such a book as
that of Mr. Hart, a work corresponding to the Aus der Werkstatt
grosser Forscher of Dr. Friedrich Dannemann.

Under our present system there are two possible channels by
which the history of science may reach the class-room, one is
through science, the other through history. On the whole the men
of science have proved themselves rather more active, if perhaps
less effective, than the historians. We have several elementary
accounts of the different sciences historically treated. Among
the more recent is Dr. Lowry's excellent Historical Introduction
to Chemistry. The self-imposed Hmitation of such works, how-
ever valuable they may be, prevents them from providing the
philosophical insight and wide general interest of, for instance,
Mr. F. S. Marvin's Living Past, which approaches the problem
primarily from the historian's standpoint. For a school History
of Natural Science as a whole we have to turn to the remarkable
work of the venerable Mrs. Buckley Fisher (Arabella Buckley),
first published in 1875.

Such works as those of Dr. Lowry, of Mrs. Buckley Fisher, and
of Mr. Marvin naturally appeal to a more developed intelligence
and to those who have already considerable command of the
scientific material itself. For an earlier stage the biographical
method is probably the best and most attractive. It has the
advantage of fixing in the student's mind the work and names of
the greater investigators, so that at a later stage he may be

12 Introduction

tempted to examine the originals. It appeals too to the ' human '
side and does something to prevent the abstraction of the
scientific from other points of view. It literally brings science
into the home.

Works prepared on lines like these help to bring some sort of
continuity and unity into the educational scheme. They point
to a time when the central element in education will be a great
outhne of history from which political history, civics, literature,
language, rehgion, art, science and other departments of know-
ledge will branch naturally, so as to give the student once again
a coherent view, as of old, of the great world into which he has
been born and the great heritage into which he has entered.

CHARLES SINGER.

University College, London,
31 January 1923,

A water-clock described by Vitruvius and
worked by a water tank and float

CONTENTS

TAGE

I. ARISTOTLE ^ iQ

II. THE SCHOOL OF ALEXANDRIA ... 33

III. ROGER BACON . . . . ^ . . 52

IV. COPERNICUS 67

V. JOHANN KEPLER 79

VI. WILLIAM GILBERT, FATHER OF MAGNETIC

PHILOSOPHY 93

VII. GALILEO, FOUNDER OF EXPERIMENTAL

SCIENCE 103

VIII. DESCARTES AND CO-ORDINATE GEOMETRY . 125

IX. SIR ISAAC NEWTON 138

X. ROBERT BOYLE 173

XL A]\IPERE AND MAGNETIC ELECTRICITY . . 193

XII. SIR HUMPHRY DAVY 210

XIII. OHM AND HIS FAMOUS LAW .... 233

XIV. MICHAEL FARADAY 248

XV. LORD KELVIN AND APPLIED SCIENCE . . 274

XVI. SCIENCE TO-DAY AND TO-MORROW . . 305

BIBLIOGRAPHY . .315

INDEX 317

LIST OF ILLUSTRATIONS

PAGE

An early paddle-wheel vessel ....... i

Dr. William Gilbert demonstrating his experiments to Queen
Elizabeth. From the picture in the Town Hall, Colchester, by
the late A. Acland Hunt. Reproduced by permission of the Town
Clerk of Colchester from a photograph by Benham & Co., Ltd.,
Colchester .......... 2

An early use of steam power. From the Pneumatics of the

Alexandrian mathematician Heron (? ist cent, a.d.) . . 4

A water-clock described by Vitruvius . . . . . .12

1. Map of Ancient Greece ....... 20

2. The Theorem of Pythagoras 22

3. Plato. From Herculaneum. Museo Nationale, Naples.

Photograph by Anderson, Rome ..... 24

4. Aristotle. From Herculaneum ; probably work of the fourth

century b. c. . . . . • • • -5

5. Aristotle teaching. From MS. Roy. 12 G. v., British Museum 27

6. Aristotelian Elements. From Singer in Hearnshaw, Mediaeval

Contributions to Civilization ...... 30

7. Scheme of the Universe, as developed by the early mediaeval

followers of Aristotle. From Singer in Hearnshaw, op. cit. 31

8. Map of the Mediterranean Sea and the adjoining lands . . 33

9. Euclid's Proof by Exhaustion . . . . . -37

10. Application of Idea of Limits to Area of a Circle ... 38

11. Archimedes. From the bust in the Capitoline Museum, Rome.

Photograph by Anderson, Rome ..... 39

12. Archimedes' Evaluation of the Area of a Parabolic Surface by

Method of Limits ....... 40

13. The Spiral of Archimedes . . . . . . -41

14. The Screw of Archimedes ....... 42

15. Claudius Ptolemaus and Boethius. Portion of a fresco drawing

by Raphael in the Royal Academy, Venice. The fresco
includes impressions of several philosophers of different
periods (Ptolemy is of the first century a.d., Boethius of
the sixth) . Photograph by Anderson, Rome ... 46

16. Ptolemy's Theory of the Motion of Planets .... 48

17. Ptolemy, by Giotto. From the Campanile del Duomo,

Florence. Photograph by Alinari .... 49

18. 'A Fire Engine'. From the Pneumatics of the Alexandrian

mathematician Heron (? ist cent. A. D.) . . . -51

19. Map showing University Towns in twelfth and thirteenth

centuries ....••••• 53

List of Illustrations 15

PAGE

20. Byrhferth's Microcosm and Macrocosm. From Singer in

Hearnshaw, op. cit. . . . . . . -55

21. Leaf from a yth-cent. Greek MS. believed to have been used by

Grosseteste. From MS. Ff. 7. 24, Universit}^ Library,
Cambridge ......... 56

22. A Scribe at Work. From a fifteenth-century MS. at Paris,

written by Jean Mielot . . . . . -57

23. Roger Bacon with a pupil taking observations from a window.

From a fifteenth-century MS. of his De Retardatione
Senectutis, Bodleian Librarj^ ..... 59

24. An Alchemist at Work, by Pieter Breughel, 1558 ... 62

25. Diagrams of Roger Bacon to illustrate optics of lens. From

Singer in Studies II ....... 64

26. Diagram of Roger Bacon to illustrate optics of burning-

glass. From Singer in Studies II . . . . -65

27. Nicolas Copernicus. Photograph supplied by Emery Walker . 69

28. An astrolabe of 1574. British Museum .... 74

29. Tycho Brahe. By permission of Mr. Aage Marcus . . 76

30. Tycho Brahe in 1587, with his astronomical instruments. In the

foreground, assistants and horologes. BDEC, the Great
Quadrant. Behind the Quadrant : T, Tycho Brahe ;
V, Part of Brahe' s Library ; X, Celestial Globe ; Y-Z,
Portraits of Frederick II of Denmark and Queen Sophia ;
1-4, Various Astronomical Instruments ; 5 and 8,
Astronomers ; 6-7, Large Celestial Globe, 6 feet in
diameter ; 9-1 1, Chemical Laboratory ; 12, Brahe's Dog.
From Cosmographia Blaviana, Amsterdam, 1662 (from
the copy in the Library of Worcester College, Oxford) . 77

31. Johann Kepler. Photograph supphed by Cassell & Co., Ltd. 79

32. Showing Kepler's approximate Law of Refraction for Glass . 84

33. Illustrating the application of Kepler's Rule of Refraction to

the Telescope ........ 84

34. Kepler's Principle of Continuity. The circle as a special case

of the ellipse ........ 85

35. Showing application of Infinitesimals to the area of a Circle . 86

36. Kepler's test of a circular orbit with the sun not at the centre 90

37. Illustrating Kepler's First Two Laws of Planetary Motion . 90

38. William Gilbert. From the engraving in Sylvester Harding's

Biographical Mirror, ii. 33 . . . . . .93

39. Gilbert's figure of a smith at his anvil, used by him to illustrate

his discovery that a piece of red-hot iron placed in the
north-south (septentrio-auster) position and struck by a
hammer becomes magnetic ...... 94

40. Showing Non-magnetized Needle ... .100

41. Showing Magnetic Dip . . . , , . ,100

1 6 List of Illustrations

PAGE

42. One of Gilbert's Terrellae or Spherical Loadstones, showing the

orb of virtue, the equator, the axis connecting the two
poles, and the dip of the magnet in various latitudes.
From ' Dr. William Gilbert ', by Charles Singer, repro-
duced by permission from the Journal of the Royal Naval
Medical Service, October 1916 . . . . .101

43. Galileo. From a portrait in the Bodleian Library, brought

from Florence in 1661 ....... 103

44. Galileo's Pulsilogium . . . . . . , .104

45. The Leaning Tower of Pisa. Photograph supplied by Cassell

& Co., Ltd. io5

46. Illustrating Galileo's method of proving that the path of

a projectile in space is a parabola . . . . .108

47. Galileo's Thermometer ....... 109

48. Effect of a Lens on Rays of Light . . . . .113

49. The principle of Galileo's Telescope . . . . .114

50. The proportions of Galileo's First Telescopes . . .115

51. The Moon as seen by Galileo, 1609-10. From Sidereus Nttnciiis 116

52. Facsimile of a design for a pendulum clock. Drawn by

Vincenzio Galilei from his father's dictation . . .118

Tailpiece : ' Two witches discovered '. From Matthew

Hopkins, Discoverie of Witches, 1647 . . . .124

53. Rene Descartes. Photograph supplied by Emery Walker . 125

54. Cartesian Geometry : The co-ordinates of a point with respect

to two axes of reference . . . . . • i33

55. Cartesian Geometry : Application to a straight line . . 134

56. Cartesian Geometry : Application to a circle . . .134

57. Cartesian Geometry : Intersection of straight line and circle . 135

58. Sir Isaac Newton. From an engraving by S. Freeman after

the original painting by Sir Godfrey Kneller . . .138

59. The Manor-house, Woolsthorpe ; the birthplace of Sir Isaac

Newton, showing the solar dials he made when a boy.
From J. Timbs, School-days of Eminent Men, 1858 . , 141

60. Grantham Free Grammar-school, restored 1857 ; the school of

Sir Isaac Newton. From J. Timbs, op. cit. . . .142

61. Deviation of light by prism ...... 146

62. Newton's experiment on the dispersion of white light . .146

63. Recombination of light by double prism . . . .147

64. Chromatic aberration in lenses . . . . . .148

65. The principle of the Reflecting Telescope . . . .149

66. Principle of Newton's Reflecting Telescope .... 149

67. Christian Huyghens. From a photograph supplied by Emery

Walker . . . . . . . . .151

68. Production of a Circular Orbit by a force constantly directed

towards the centre . . . . . . • I55

List of Illustrations 17

PAGE

69. Medal commemorating Edmund Halley. A memorial by

Dassier, struck in 1744. Photograph supplied by Cassell

& Co., Ltd 161

70. Illustrating Newton's Theory of Fluxions . . . .164

71. Gottfried Wilhelm Leibnitz. From a photograph supplied by

Emery Walker . . . . . . . .166

72. The Hon. Robert Boyle. From the portrait by F. Kerseboom.

By permission of the Royal Society . . . • I75-

73. Boyle's Pneumatic Engine or Air-pump. From New Experi-

ments, by Robert Boyle, 1662 . . . . . i8r

74. Diagram illustrating the principle of Boyle's air-pump . .182?

75. Boyle's determination of the weight of the air . . .183

76. Barometer readings at reduced pressure . . . .184

77. Boyle's experiment on Suction ...... 185

78-9. Experiments on Boyle's Law . . . . . .187

80. A Chemical Laboratory in 1747. Universal Magazine, 1747 ;

reproduced from Traill's Social England, v. 329, by per-
mission of Cassell & Co., Ltd. ..... 192

81. Andre Marie Ampere. Photograph supplied by Emery Walker 193

82. Benjamin Franklin. From the painting by D. Martin, by

permission of Cassell & Co., Ltd. . . . . .196

83 . Hans Christian Oersted. Photograph supplied by Emery Walker 1 99

84. Ampere's experiments illustrating deflexion of magnetic

needle ......... 204

85. Magnetic effect at centre of coil ...... 206

86. Theory of Galvanometer ....... 206

87. Theory of the Solenoid ....... 206

88. Humphry Davy. From the painting in the National Portrait

Gallery. Photograph by Emery Walker . . .210

89. Thomas Young. From the painting by H. P. Briggs ; by

permission of the Royal Society . . . . .216

90. One of Accum's Chemical Lectures. From a drawing of about

1820 by T. Rowlandson . . . . , .218

91. The First Davy Safety Lamp ...... 227

92. Davy and Stephenson Safety Lamps. Photograph supplied

by Cassell & Co., Ltd 228

93. Georg Simon Ohm. From Millikan and Gale's First Course in

Physics, by permission of Messrs. Ginn & Co. . . 233

94. The Thermo-Electric Circuit ...... 238

95. Ohm's Apparatus ........ 239

96. The first Membership Ticket of the British Association. From

O. J. R. Howarth, The British Association for the Advance-
ment of Science : A Retrospect, by permission of the author 247

97. Michael Faraday. From the painting by T. Phillips in the

National Portrait Gallery. Photograph by Emery Walker 248

2613 B

r8 List of Illustrations

PAGE

98. Lines of Force round a wire carrying a Current . . . 258

99. Faraday's experiment on Mutual Rotations of Magnet and

Wire carrying Current ...... 258

100. Faraday's discovery of Electro-Magnetic Induction . . 260

loi. Faraday's experiments on Electro-Magnetic Induction . . 261

«o2. Unpolarized Light- waves, showing various inclinations of the

plane of vibration ....... 268

103. William Thomson, afterwards Lord Kelvin, 30 April 1856.

From a photograph by Professor Blackburn . . .274

104. The principle of the Quadrant Electrometer . . . 280

105. Hermann von Helmholtz, by von Lenbach, 1876 . . . 281

106. James Clerk Maxwell. From a photograph supphed by

Cassell & Co.. Ltd 283

107. James Prescott Joule, by Alfred Gilbert, R.A. From a photo-

graph supplied by Cassell & Co., Ltd. .... 285

108. Five-needled instrument patented by Messrs. Cooke & Wheat-

stone in 1837. From a photograph supplied by Cassell

& Co., Ltd. 289

109. Sections of the second and third Atlantic Cables. From

a photograph supplied by Cassell & Co., Ltd. . . . 290

1 10. The Great Eastern leaving Sheerness with the Atlantic Telegraph

Cable on board, July 1866. Illustrated London News . 292

111. Lord Kelvin's early Siphon Recorder. Reproduced by per-

mission from Encyclopaedia Britannica, nth ed., vol. 26,

p. 623 293

112. Thomson's (Lord Kelvin's) Compass. Reproduced by per-

mission from Encyclopaedia Britannica, nth ed., vol. 6,

p. 804 296

113. Standard Mariner's Compass. From a photograph supplied by

Kelvin, Bottomley & Baird, Ltd 297

114. Lord Kelvin on board the Lalla Rookh, 23 September 1885.

From a photograph by Lady Kelvin .... 298

115. Telegraph by Semaphore, 1842. Illustrated London News . 300

116. A Central Telephone Exchange To-day. By permission of

Cassell & Co., Ltd 301

117. Buoys and Grapnels used in recovering the Atlantic Telegraph

Cable of 1865. Illustrated London News . . . 303

118. The Growth of Aviation. An early French print (1798), con-

templating Napoleon's descent on England through the

air. From a print belonging to the author . . . 304

119. Illustrating heavier-than-air flight ..... 306

120. Albert Einstein. From an etching by Hermann Struck . 310

ARISTOTLE

I. The Beginning of Knowledge — The Ionian School

During hundreds of years preceding the birth of Christ, at
a time when the inhabitants of our own country were ignorant
and uncivilized, there flourished in Greece a wonderful civiliza-
tion, characterized by culture, scholarship, and skill in warfare.
It is to this people that we must look for the first glimmerings
of scientific knowledge. True, judging by present-day standards,
the Greeks were in many ways ignorant. To them the world was
a large flat surface surrounded by water ; and the sun was the
God Apollo driving his chariot across the skies daily from east
to west. But aU things have their beginnings and our debt of
gratitude to the ancient Greek philosophers for the wonderful
heritage of learning which they have left to us cannot be over-
estimated.

Confining ourselves, as we shall in this book, to the story of
the progress of the physical and mathematical sciences, it may
of course be argued that in fact the earliest knowledge of these
subjects comes not from Greece but from Egypt, and Chaldea,
and Phoenicia, and China, and even from India. While it is
true that the beginnings of arithmetic may be found in Chaldea,
and that an empirical and crude sort of geometry was in use in
Egypt, these subjects were not developed in the abstract as
sciences, but were purely a result of practical needs. Thus the
periodic floodings of the river Nile, resulting as they did in the
inundations of large tracts of land, created the necessity for
a crude form of surveying, so giving rise to an empirical scheme of
geometry. For example, observations on the rising and setting
of stars enabled a north and south line to be laid along a plane
midway between these points, and they could set out a right

B 2

20 Aristotle

angle by fastening ropes round three pegs to form a triangle
the ratio of whose sides were 3:4:5, and so on. Similarly the
trade relations between the Phoenicians and the Chaldaeans
made the use of some scheme of reckoning necessary in order to
facilitate barter, so giving rise to the beginnings of arithmetic ;
whilst a certain amount of observational astronomy was carried
on to assist navigation.

ANCIENT GREECE

Fig. I.

The written records of all this are, however, very few, and much
is conjecture. But of the Greek initiation of these studies as
sciences, developed not from utilitarian motives but purely for
the sake of knowledge per se, there is no doubt whatever.

The Greeks were temperamentally well fitted for this mission.
They were of a naturally high order of intellect ; they were keen
observers ; the power of speculation was instinctive to their
being ; and above all they produced from amongst their numbers
great leaders of thought in whose hands these qualities could
not fail to make for tremendous progress.

The Ionian School 21

Pre-eminent amongst these people were the lonians, who
added to the other qualities of the Greeks that of a love
of adventure which prompted them to leave their homes and
found colonies, with the result that they came into contact with
other peoples, and with such culture as they found among these
peoples. It was in this way that Thales of Miletus (640 ?-550 ?
B. c), rightly regarded as the founder of the Ionian school of
philosophy, first developed a love of mathematics and science.
We are told of him that business took him to Egypt, where he
spent many years, and that when he returned to Miletus it
was with an enthusiasm for the Egyptian sciences which caused
him to abandon trade and to devote the remainder of his life to
philosophy. As a result we may say of him that he introduced
to the Greeks the serious study of geometry and of astronomy
— a noteworthy achievement was his successful prediction of the
solar eclipse of the 28th of May 585 B.C. — and he laid the
foundations of the study of electricity by his observations on the
electrification of amber by friction.

Amongst those who followed him we may mention Anaxi-
mander and Anaximenes, and more especially, Pythagoras of
Samos (? 572-497 B.C.).

2. The Pythagorean School

The teachings of Pythagoras and of the brotherhood which
he founded mark relatively a tremendous advance in mathe-
matical and scientific knowledge. Arguing, for instance, that
the sphere is the most perfect of all solid figures, the Pytha-
goreans were the first thinkers to assert the sphericity of the
earth, the sun, and the moon. But perhaps to the average
school-boy Pythagoras is best known for his discovery of the
proposition with regard to the right-angled triangle (Euclid I, 47)
commonly referred to as the ' theorem of Pythagoras ' . The
proof given by Euclid, and usually taught in schools, was of
course original to Euclid himself, but perhaps it will not be out
of place briefly to outline the demonstration which Pythagoras
most probably employed.

But make

M

Fig. 2. The Theorem of
Pythagoras.

22 Aristotle

Starting with the square A BCD (Fig. 2) we may split it up
into two squares EH and GF, and two equal rectangles AK
and KC. Join GE. Hence we may say

AB^ = EK^ + GK^ + 4^AGE (i).

BL = CM == DG = AE.

Then it is easy to see that the figure
GELM is a square, and that the tri-
angles AGE, BEL, CLM and DMG are
all equal.

Hence we have

AB'^^GE^ + ^l^AGE (2).

Equating (i) and (2) above, we there-
fore have

GE^ + 4l\AGE = EK'^ + GK^ + ^l^AGE,
whence

GE^ = EK^ + GK\
which proves the proposition.

The great advance which Pythagoras made in the study of
number was also very stimulating. We see in his treatment
of the subject a distinct geometrical bias. All numbers were
regarded as either odd or even, and the odd numbers were called
' gnomonic '. A gnomon, of course, is a figure such as ABCFKG
in Fig. 2, derived from a square by removing from it a smaller
square such as GKFD. Let us now see how Pythagoras built
up his scheme of odd numbers.

Representing i by a dot thus ., suppose we add three to

form a square, . We now have 1 + 3 = 2^ (where before we

« •
had I = i'^). Now add T^z;^ more dots at equal intervals, * T~
It will be noticed we have added a gnomonic figure, • — •

giving us 1 + 3 + 5=3^. The next gnomonic figure is ; i_

got by adding seven dots at equal intervals, giving 1 + 3 + 5 + 7
and so on, the general formula being

1 + 3 + 5 + 7 + (2n-i) = «2.

Pythagoras spoke of the sum of the gnomons from i to (2n- 1)
as a square number, and he regarded an odd number as the

The Pythagorean School 23

difference between two square numbers. This is evident from the

following: 1 + 3 + 5 + 7 + (2«-i) = nK

Now add the next odd number, i.e. (2n + i).

1 + 3 + 5 + 7 + (2n + i) = (n + i)2.

That is to say, (w + i)^ = n^+{2n + i).

i.e. (« + i2)-«2 = (2n + i),
giving an odd number (2n + i) as the difference between two
square numbers.

To Pythagoras we also owe the beginnings of the study of
sound. The story goes that while passing a blacksmith's shop
he was attracted by the musical notes emitted by the anvil on
being struck with the hammer, and subsequent experiments
on the stretching force applied to strings of the same materials,
length, and thickness, to produce notes whose intervals are
fourths, fifths, and octaves were as i : | : f : J. He also experi-
mented on stretched strings of varied lengths, and found that the
necessary length-ratio to produce an octave was 2:1; to produce
a fifth, 3:2; and to produce a fourth, 4 : 3.

3. Plato and his Academy

In due course the centre of Greek learning shifted from Ionia
and southern Italy to Athens. Here the immortal Socrates
thought and taught, and among his pupils was Plato, destined,
like his master, to be recognized as one of the greatest of Greece's
noble sons. Plato founded a school at Athens in a pleasant grove
with shady walks and seats, and here he discoursed daily to his
disciples and wrote those many dialogues for which he is justly
famous. It was called 'Academy ' after some almost forgotten
hero Academus who is said to have once dwelt there.

It is not our purpose to give here a detailed account of the
life of Plato. Great as a philosopher, he was not in the strict
sense of the term a * maker of scientific history ' . Plato was,
however, both a lover and a student of the science of geometry.
Indeed he had caused to be written over the door of his
Academy, in large capitals, the following inscription :

LET NO ONE PRESUME TO ENTER HERE UNLESS HE
HAS A TASTE FOR GEOMETRY AND THE MATHEMATICS.

24 Aristotle

Plato's claim to mention in this book lies in the fact that
one of his disciples was a youth named Aristotle, whose later
teachings were destined to exert a dominating influence over
the * western * world for nearly two thousand years.

Before, however, we pass on to a detailed consideration of
the life and teachings of Aristotle, it is as well to note that it is
to Plato that we probably owe some of the earliest additions to
geometrical knowledge. He shares with ^lenaechmus the credit
for creating the study of conic sections. Hitherto the circle had
been the only curve which had been studied. But Plato per-
ceived that if a cone be cut by a plane
under certain conditions, the section
obtained took the form of certain
peculiar curves, and a little further
I St^^S^^^F study assured him that there were

only three types of these, which he
named the parabola, the ellipse, and
the hyperbola.

A much later Greek follower of Plato

(Proclus, A. D. 410-485) tells us that

to Plato also belongs the credit for in-

v^^^^^~^-~ .-.■*-..*^^ venting that method of mathematical

Fig. 3. PLATO investigation known as 'geometrical

analysis' — a process familiar to every

school-boy. Given a certain problem or theorem, assume it to

be true ; on this assumption deduce step by step a series of

logical consequences, until a statement is reached which is

definitely known to be true. Now retrace the steps one by one,

and the required proof is obtained.

]\Iost great men have their detractors and Plato was no excep-
tion to the rule. Thus an unjust charge was that he stole his
knowledge from the valuable writings of Philolaus, a Pytha-
gorean, which he had purchased in Sicily. The taunt was made
by Timon in the following terms :

You, Plato, with the same affections caught.

With a large sum a little treatise bought.

Where all the knowledge that you own was taught.

Plato and his Academy 25

There is little doubt, however, that such charges were unjust
and without foundation. At all events, whilst his detractors are
comparatively unknown, Plato's fame will live for ever.

4. Aristotle's Early Life

Aristotle was bom in the year 385 b. c. in the city of Stagira,
in Macedonia. He was the son of Nicomachus, a celebrated
physician of his day, and a favourite at the court of King
Amyntas III. His parents died
when he was but a youth, and
he was left under the careful
guardianship of Proxenus of
Atarneus, who, recognizing in the
lad an inherited taste for philo-
sophy, sent him at the age of
seventeen to Athens, knowing
that with the ample fortune his
father had left him he would be
able to pursue his studies without
financial embarrassments of any
kind.

Accordingly we find Aristotle
entered as a student in Plato's
Academy, and here for twenty
years he studied diligently, lay-
ing for himself the solid foundation for a great career which
was to make scientific history. There is a story that his thirst
for knowledge was so great that he even denied himself sleep in
order to study. Diogenes Laertius tells us that to help him to
reduce the amount of his sleep to a minimum, he always placed
beside his bed a brass basin, and when he lay down to read and
rest, he would hold in his hand extended over the basin a leaden
weight. When he was overcome by sleep, the weight would fall
from his inert hand, and the sound of its dropping into the basin
would immediately awaken him.

Aristotle, so we are told by the same writer, was a young man

Fig. 4. ARISTOTLE

26 Aristotle

who, in spite of such disadvantages as an effeminate lisping
voice, small eyes, and ' spindle shanks ' , took considerable pains
over his dress and his appearance. He very soon established
himself at the Academy as the most brilliant of a band of young
students, all of whom looked up to him, and, it is said, frequently
preferred his private opinion in debate to that of Plato himself.

On the death of Plato, in 347 B. c, the leadership of the
Academy fell to his nephew, Speusippus, and possibly in con-
sequence of this Aristotle left Athens, accompanied by Xeno-
crates, a fellow student. They went to Atarneus in Asia Minor,
the home of Aristotle's guardian, and there formed a friendship
with Hermeias, the remarkable prince ruler of that area, whose
niece Pythias Aristotle afterwards married. Hermeias was
shortly afterwards killed, and Xenocrates returned to Athens,
whilst Aristotle and his wife went to Mitylene. Here they
obtained the favour of King Philip of Macedon, at whose invita-
tion our philosopher became tutor to the young prince Alexander,
known to history as Alexander the Great.

It is not evident to what extent the Crown Prince was influ-
enced by his tutor, but there can be no doubt about the satis-
faction which this intercourse must have given to King Philip,
for we read that, out of gratitude and affection for Aristotle, he
ordered the latter' s birthplace, Stagira, which had been laid in
ruins in recent wars, to be rebuilt.

5. The Peripatetic School

In the year 336 B. c. King Philip was murdered, and Alexander
was called to the throne of Macedonia. Aristotle's duties as
tutor accordingly ended abruptly, and after an affectionate
leavetaking he returned to Athens. Just at this time the leader-
ship of the Academy had again faUen vacant owing to the death
of Speusippus, and Aristotle, who considered his claims to be such
as fully to entitle him to the position, found himself passed over
in favour ol Xenocrates. He therefore started an independent
institution. He chose a spot known as the Lj^ceum, which
was attached to the Temple of Apollo Lycaeus, and here he

The Peripatetic School 27

founded his new school. Its success was immediate. He was
soon joined by some of the most distinguished members of the
Academy, and for the next twelve years he gave himself up to
speculations and researches in almost every branch of inquir}^ —
researches the results of which completely dominated the world
for the next eighteen hundred years.

At the entrance to the Lyceum there was a covered portico,
or ' peripatos ' , leading from which was a gravel walk with an
avenue of trees, and it was Aristotle's custom to walk up and
down this avenue with his pupils, and discuss with them the
various problems which pre-
sented themselves for study.
On this account his school
was called the Peripatetic
School, and his followers
were spoken of as the Peri-
patetic Philosophers.

In later years Aristotle
seems to have fallen foul
of King Alexander, the
difference arising out of his
support of and interest in
a distant relative named
Callisthenes, who, it seems,
had been brought up and
educated by Aristotle. As a
result of his guardian's recommendation, Callisthenes had been
accepted as historiographer to Alexander, but instead of playing
the part of the polite courtier, he had expressed his real opinions
somewhat too freely, and had openly condemned Alexander's
attempts to impose upon his Macedonian subjects the worship of
himself which he had been able to exact from the conquered
Persians.

Alexander resolved to get rid of Callisthenes. He was suspected
of being involved in an imaginary plot against the king's life, and
was executed. This began, it is said, a period of active enmity
between Aristotle and Alexander which only ended with the
latter's death in 323 B. c.

"'li^

SB^fe^l

1

^m

|V

3K^^

L^

WI^KSB/^K^^K^^'^*^^

Fig. 5. ARISTOTLE TEACHING
as conceived by a late i3th-cent.
illuminator.

28 Aristotle

Alexander's death was followed by an Athenian rising against
the ]\Iacedonians, and this brought with it the final downfall of
Aristotle. For despite his estrangement from Alexander, the
people only remembered his friendly connexions with both the
late king and Philip his father, and on a trumped-up charge of
impiety against the gods, he was threatened with immediate
prosecution. He accordingly withdrew with his disciples to
Chalcis, where he remained until his death at the age of sixty-
two, in the following year.

Aristotle was twice married, to Pythias, and after her death
to Herpyllis, who survived him, and by whom he had a son,
Nicomachus, and a daughter. Both marriages were happy, and
his last will, still extant, testifies to the goodness of Herpyllis,
and to the success of his first marriage by the request that his
remains and those of Pythias should be placed in the same tomb.
That he died in reasonably wealthy circumstances is also shown
by the numerous bequests to his many servants and friends.

After his death it is said that the natives of Stagira, the city of
his birth, erected altars to his memory, and paid him the tribute
of divine adoration.

6. Aristotle's Scientific Work and Teachings

Let us now consider some of the teachings of this great
philosopher. Much of his work deals with subjects which lie
beyond the scope of this book — politics, ethics, and metaphysics.
In all these subjects Aristotle's influence was great. However,
we are concerned mainly with his influence in the mathematical
and mechanical sciences, although, as a matter of fact, his main
contributions were to the biological sciences. Here, indeed,
Aristotle excelled, and the care he bestowed upon the tedious
task of collection of specimens, and their classification into
suitable groups, and the scientific efficiency of his descriptions,
are such as to excite our admiration and respect.

What, then, were his teachings ? As a preliminary to clear
and ordered thinking, Aristotle realized that some scheme of
classification of the sciences was necessary, and accordingly

Scientific Work and Teachings 29

began by adopting two broad divisions — Speculative or Theo-
retical Science, and Practical Science. In the first division the
object is to ' know ', in the second the object is to ' do ', or to
know for the purpose of doing.

Aristotle now proceeded to subdivide his first group, Theo-
retical Science, into three main sub-groups. The first of these he
called First Philosophy, corresponding to what we now speak of as
Theology, his second group was Mathematics, and his third Physics.
Aristotle's classification of the sciences is given diagrammatically
as follows :

Science

I

Theoretical Practical
I

First Philosophy Mathematics Physics

or Theology *"

Turning then to his treatment of physics, and using the term
in its broadest sense, we find that Aristotle's pronouncements
contain a remarkable admixture of sense and what must now
appear as non-sense.

He taught that all terrestrial bodies are composed of four
elements — earth, water, air, and fire, although for celestial
bodies he introduced the idea of a fifth element. That is to say,
he made an absolute distinction between ' celestial matter '
and 'terrestrial matter', and he claimed as a fundamental
distinction between them that the natural motion of celestial
bodies was always circular, whilst for terrestrial bodies it tended
to be rectilinear. Again, to talk of terrestrial matter as being com-
posed of four elements implies a variety of possible combinations
and disintegrations within the limits of those four elements.
But not so with celestial matter, for which there was only
a single fifth element. There could be, therefore, no such thing
as change of any kind in the sun or planets, and no break in
their uniformity. No wonder, therefore, that it was a rude
shock for the Aristotelians when Galileo's telescope showed
irregularities on the moon, spots on the sun, and variability in
some of the stars.

30 Aristotle

Aristotle also developed a theory of gravity of a kind. Plato
had already attempted such a theory, his idea being that a down-
ward motion was really a motion towards the centre of the earth,
and that there existed a tendency for all bodies to be attracted
to larger masses of the same material. Hence, for example,
a stone ' falls ' to the earth, but a ' vapour * rises to the larger
masses of vapour above. Aristotle, however, departed from this
explanation by insisting on the distinctions between two classes
Qi^^^ of bodies — heavy bodies,

which have a natural ten-
dency to move ' down *
towards the centre of the
earth, and light bodies,
whose natural tendency
is to move ' up ' , and
away ffom the centre of
the earth. Further, the
heaviest bodies tend to
move nearer to the centre
of the earth than the less
heavy bodies. So, for
example, earth being
heavier than water, we
expect to find the water
over the earth, as indeed
it is. Both, however, belong to the ' heavy ' group of bodies.
On the other hand, whilst fire and air both belong to the ' lighter '
group, so that their natural tendency is '-up-', yet; since fire is
lighter than air, we get the air above the water, and the fire
above the air and nearest to the celestial regions. This theory
had at least the advantage of appealing to the imagination, and
it went unchallenged.

Aristotle's treatment of the study of motion was very inter-
esting. We have already seen that he speaks of two kinds of
* natural ' motion — circular for celestial bodies, and rectilinear
for terrestrial bodies. But confining ourselves to his treatment
of terrestrial bodies alone, he classifies motions as ' natural '
and ' unnatural ' . There was no need for such a classification

Fig. 6. Aristotelian elements
It should be noted that the addition of the
four humours of blood, black bile, red bile,
and phlegm was not due to Aristotle, but
to the early mediaeval followers of the peri-
patician.

Scientific Work and Teachings 3 1

in the case of celestial bodies, whose motions could, according
to Aristotle, be nothing but perfect and natural, so that they
persisted in their uniform circular paths for ever. ' Falling *
was a natural motion — so much so indeed, that ' falling * bodies
were even accelerated, so very natural was this type of motion.
* Unnatural ' motions, however, were those that were imposed
upon a body by some external agency, and as a consequence,
could not persist. Thus if a stone be thrown an unnatural motion
is imposed upon it, and
this being contrary to
nature, the motion
speedily diminishes,
and the stone again
comes to rest. We see
here something in the
nature of a principle of
inertia.

Aristotle's explana-
tion of why falling
bodies are accelerated
is also extremely inter-
esting. Motion, he says,
is caused by something
in contact with the
body moved. The more
persistent the contact
the more natural the motion, and the body will even get speeded
up. Now, in the case of falling bodies, there is continual contact
with the air, which therefore not only causes the motion, but
produces an acceleration. From this followed, too, his famous
doctrine that the acceleration depends upon the mass of the
faUing body — the greater the mass, the greater its acceleration,
and it is amazing to think that a doctrine so fallacious as to be
refutable by the simplest of experiments, held complete sway
for centuries. It is a striking testimony to the thoroughness
with which his doctrines ruled the civilized world.

To Aristotle is also due the famous statement ' that nature
abhors a vacuum ' .

Fig. 7. Scheme of the Universe, as developed
by the early mediaeval followers of Aristotle.

32 Aristotle

Another point worthy of mention with regard to Aristotle's
work in mechanics concerns his notions of the ' doctrine of
force ' . He definitely records, for the particular case when two
forces are at right angles, the principle of the parallelogram of
' motions ' — regarding the ' motions ' as being caused by forces,
somewhat as follows : Supposing two forces, in a given finite
ratio to each other, to act upon a body in directions at right
angles, then assuming straight lines in those directions to be
drawn to represent by their length the intensities of the two
acting forces, then if the rectangle be completed, the diagonal
will express in direction and quantity the resulting motion.

The value of this lies not so much in the arguments he employs,
which are, in fact, of doubtful value, as in the statement itself.
Enough has been given of Aristotle's teachings in physics and
mechanics to indicate the general nature of his work, and the
general trend of his scientific thought. But the reader must
again be reminded that only a very small fraction of his teachings,
even in the subjects dealt with, has been here included. Of his
wonderful work on the study of animals, of his thoughtful dis-
cussion on the subject of geological change, and of his researches
in embryology, no mention has been made, because space does
not permit. Aristotle is, of course, known mainly for his teachings
in social ethics and in moral philosophy. These are aspects of his
activities with which we are not concerned in this book.

Aristotle lived over two thousand years ago. The history of
science in the interval between then and now is studded with
the brilliant work of many lives. It would not be untrue to say
that the work of many of the pioneers of science has been far
superior to the scientific work of Aristotle. Indeed it would
even be true to say that in many respects Aristotle's influence
was (partly perhaps owing to his ' mis- ' translators) retrogade.
But where, throughout the whole of the period between then
and now, can we find another case of a single scientist whose
influence and whose teachings received such a blind and unanimous
acceptance throughout the whole civilized world for so long a time
after his death ? The record is truly an astonishing one, and fully
entitles our philosopher to a prominent place as a pioneer of science.

II

THE SCHOOL OF ALEXANDRIA

I. The SchooVs Inception

Among the many military achievements for which Alexander
the Great became famous was the conquest of Egypt. This took
place while Aristotle was teaching at Athens. Alexander, to
commemorate his victories, founded a city on the southern
shores of the Mediterranean Sea, and caused it to be named

THE MEDITERRANEAN SEA

English Miles

100 200 300 too

Fig. 8.

Alexandria. Its success was almost immediate, and in a very
short time Alexandria became a populous city and a flourishing
port.

Now the death of Alexander was followed by the division of
his empire among his more powerful officers, and fortunately for
the world's subsequent scientific history, Egypt fell to the lot
of one Ptolemy Lagus, who, powerful general though he had been,

2613 C

34 The School of Alexandria

was also a lover of learning. As a consequence he soon gathered
around him a line band of philosophers and students.

On his death he was succeeded by his son, Ptolemy Phila-
delphus, who luckily inherited his father's wisdom and taste for
learning — so much so, indeed, that he caused to be erected a
magnificent block of buildings comprising a library, an observa-
tory, and a school of science, and here philosopher after philoso-
pher received his training. A solid foundation was laid to the
study of mathematics and mechanical science, and a spirit of
inquiry was fostered such as was unequalled in enthusiasm and
achievement until the seventeenth century.

It is not our purpose here to give a connected history of the
scientific achievements of those times. It is proposed, therefore,
to make a selection of a few of the more remarkable from this
Alexandrian School of philosophers, and to offer, as far as is
possible in a brief space, a few biographical details in the hope
that the reader may be stimulated to further study.

2. Euclid

Euclid was one of the great teachers of Mathematics in the
Alexandrian School. Unfortunately, history records very little
indeed of his life, such details as are available being derived
from the writings of the later authors Pappus and Proclus.
According to these, Euclid was bom in Alexandria somewhere
about the year 300 b. c. and he lived in the reign of King Ptolemy
Lagus of Egypt. He was the first of a long line of eminent
mathematicians, and was the source of inspiration, through the
medium of his writings, for such later men as Eratosthenes,
Archimedes, Apollonius, Ptolemy, and a host of others. Proclus
tells us that Euclid was a man of courteous bearing and agreeable
behaviour, and was much liked by King Ptolemy. The king once
asked him if there was a shorter way of studying Geometry than
by his Elements, and he received the answer ' There is no royal
way to Geometry ' .

His best-known work is the Elements, in which he presents
a complete system of elementary geometry. But it must not
be supposed that he was the creator o'f a system of elementary

Euclid 35

geometry. Indeed, from the point of view of the mathematical
and physical sciences, the development of the study of geometry
by a long succession of illustrious philosophers constitutes one
of the chief features of the Greek age in scientific history. ^ We
have already referred to Thales and the Pythagoreans, and
mention should also be made of Hippocrates of Chios (470-400
B. c, not to be confused with Hippocrates of Cos, the father of
Medicine), the first-known compiler of a book of 'Elements',
and the discoverer of the theorem that the areas of circles are
to one another as the squares of their diameters, through
which he introduced to the Greeks the fascinating and insoluble
problem of 'squaring the circle' ; of Eudoxus (408-355 B.C.),
who discovered the great theory of proportion which forms the
basis of Euclid's Book V, and who was the originator of the
well-known ' proof by exhaustion ' ; ^ of Archytas of Tarentum
(430-360 B. c), who addressed himself to the study of the problem
of ' doubling the cube ' , as a consequence of the finding of two mean
proportionals between two given lines, and who greatly advanced
the study of the geometry of three dimensions ; of Menaechmus
(c. 350 B.C.), who shares with Plato the credit for the discovery
of the three conic sections ; and of Theatetus and others.

Euclid's ' Elements ' were therefore, with the exception possibly
of Book X, rather in the nature of a ' review of the position ' —
a linking together of the works of his predecessors into a united
whole. His task was splendidly accomplished and, quite apart
from the question of the suitability of the presentation of his
scheme of geometry to boys and girls for instruction, the wonderful
sequence of ordered demonstrations, deductions, and truths, the
thoroughness and the clarity which permeate, with one or two

I exceptions only, the whole of his work, have excited the wonder

i and the admiration of the whole of the civilized world from his

\day to ours.

I The ' Elements ' consist of fifteen books, but it is now generally
irecognized that the last two are not Euclid's own, but have been

\ * In this connexion the reader is recommended to read Allman's Greek
Gteometry from Thales to Euclid, DubUn, 1889 ; and the recently published
Hijjtory of Greek Mathematics by Sir T. L. Heath (Oxford, Clarendon
Press, 1922). « See p. 37.

C 2

36 The School of Alexandria

added to the other books, probably by Hypsicles (about A. D. 150);
for they are certainly not up to the same standard as the first
thirteen. It is probable that the ' Elements ' are a combination
of at least two distinct works, for they deal not only with geo-
metry, but also with the theory of arithmetic and its applications
to geometry. As is well known, the first four books treat of plane
figures, the fifth of magnitudes in general, the sixth of the
proportion of plane figures, the seventh, eighth, and ninth of the
fundamental properties of numbers, the tenth of the theory
of commensurable and incommensurable lines and spaces, and
the remainder of the theory of solids.

There are weaknesses here and there, and of course in schools
there are now taught systems of geometry more suited to the
needs of boys and girls. Nevertheless as a philosophical scheme of
geometry, Euclid still remains unchallenged.

Euclid gave great prominence to the problem of ' squaring
the circle'. That is to say, to draw by geometrical methods
a square equal in area to a given circle. The problem arose from
the famous demonstrations of the proportionalitj/ of the areas
of circles to the squares of their diameters, and of the volumes
of spheres to the cubes of their diameters. The point is of interest
from the fact that this problem so attracted the attention of
the mathematically inclined of those days as to give a refreshing
and in many respects fruitful stimulus to the study of mathe-
matics in general and geometry in particular.

Euclid clearly saw the relationship between geometry and
arithmetic — that is to say, between the properties of plane
figures, lines, &c., and the numerical figures representing their
dimensions. Thus, for example, it is well known that a right-
angled triangle may be drawn whose sides are 3'', 4'', and 5''.
It is proved geometrically that the square (i. e. the actual
rectilineal figure known as a square) on the hypotenuse is equal
in area to the sum of the squares on the remaining two sides
But it is also obvious that the corresponding relationship is true;
with regard to the numerical figures representing these length.',
namely, in the example chosen above,

52=42 + 32.

Euclid 37

It is much to Euclid's credit that he fully grasped the significance
of this, that he generalized the problem, and that he realized to
what important developments he could extend this idea.

Plato, it is interesting to note, is credited with having found
the general rule by which such a relationship could be found
between whole numbers. Let n be any number, then we always
have the three whole numbers. 2n, n^ — i, and n^ + i such that

so that any triangle whose sides are drawn proportioned to these
numbers must be right-angled.

Euclid's thorough treatment of the comparison of areas,
based on his famous Proposition 47 of the First Book (originally
the invention of Pythagoras) led
naturally to an attempt to express
the areas of curvilinear figures in
terms of rectilinear figures, and a
proper appreciation of this is neces-
sary if the true significance of Euclid's
work is to be realized. For we find
here the first applications of the idea ^^^- 9' ^^^^^^^Xif '''''^ ^^
of 'limits' — and of course the study

of ' limits ' may fairly be regarded as the starting-point of
what we vaguely speak of to-day as ' higher mathematics ' .

The simplest case of limits is seen in the well-known method of
proof by ' exhaustion ' discovered by Eudoxus ^ (fourth century
B. c). As an example take the proof of the proposition that ' the
angle opposite the greater side is greater than the angle opposite
the lesser ' . Omitting all preliminaries, and referring to the figure,
in which AB is given greater than AC, Euclid says ' The angle B
must be either greater than, equal to, or less than the angle C ' . He
states every possibility, and then proceeds to consider each in turn.

Using, for the sake of brevity, the usual mathematical symbols,
he says : — First suppose ^B > ^C.

. *. By the previous proposition, side AC > side AB,

But this is impossible, by hypothesis.

The choice is accordingly narrowed down.
» Seep. 35.

38 The School of Alexandria

Secondly, suppose ^C = IB.

. '. the triangle is isosceles, and AC = AB.

This again is impossible.

He has exhausted all the possibilities except one.

In other words, he has approached the limiting case, and the
only remaining possibility must be true.

The principle of superposition, so beautifully developed by
Euclid, is bound up with his treatment of the comparison of
areas, and we will give just one further example of Euclid's
use of the idea of limits — the case of the circle — before we pass
to another of the great Alexandrian School of philosophers.

If a regular polygon — say a pentagon — be inscribed in a circle.

Fig. 10. Application of Idea of Limits to Area
of a Circle.

it is obvious (a) that the perimeter of the pentagon is less than
the circumference of the circle, and (b) that the area of the
pentagon is less than the area of the circle. Further, the differ-
ences are relatively considerable in each case.

But suppose we inscribe instead a regular polygon of many
more sides — say twelve. Statements (a) and (b) above remain
true, but the differences are now much smaller than before.

It is seen that the more we increase the number of sides of the
inscribed polygon, the more nearly does the figure coincide with
the circle, so that the polygon will in the limit become the circle.
Euclid clearly realized, however, that the limit can never actually
be reached (a very important point) but can only be approached
more and more closely by continually increasing the number of
sides in the inscribed polygon.

39

3- Archimedes

The name of Archimedes stands out as one of the most illus-
trious of the philosophers of the Alexandrian epoch. From the
point of view of the mathematical and physical sciences, he ranks
superior to Aristotle, for while the latter propounded doctrines
and theories which, long dominant as they were, have now
been more or less completely
abandoned, the discoveries and
doctrines with which the name
of Archimedes is associated are
being taught in schools to this
day. His record is a standing
example of the true greatness
which may be achieved by a
life devoted to one particular
branch of scientific stud}^ In
the history of Mathematics and
Mechanics, Archimedes de-
serves a very high place indeed.

We know very little of his life.
He was possibly a contemporary
of Euclid, and was bom in the
city of Syracuse, in Sicily, about
the year 287 b. c, at a time
when Hiero was its king. He
received his education at Alex-
andria, probably under Euclid himself, and this is an interesting
testimony to the fame which the School of Alexandria had
achieved. For a journey from Sicily to Alexandria, particularly
for a youth such as Archimedes must have been at that time,
was no light undertaking. It was a very different thing from
travelling as we know it to-day, having regard to the size and
type of the ships of those days.

Archimedes very quickly established a reputation, and his
future career became clearly marked out for him. He returned
to his native city, and here he stayed for the remainder of his

Fig. II. ARCHIMEDES

40 The School of Alexandria

life, devoting himself whole-heartedly to study, experiment, and
research.

Archimedes is best known for his work in hydrostatics and
mechanics, but his work in the field of pure mathematics is equally
important and praiseworthy. Working from the consideration
of the subject of limits so ably begun by Euclid, he found a
means of obtaining the areas of figures bounded by some of the
conic sections. As an example let us consider his treatment of
the parabolic surface ABC. If we inscribe in it the triangle

^ ACB, and if in the segments
which it leaves we inscribe
triangles CBD and ACD^,
then it is known that the
combined area of CBD and
ACD^ is equal to one-quarter
of the triangle ABC.

Again, if in each of the four
smaller segments now left,
triangles CDE, DBE^, &c., be
inscribed, the sum of the areas
of these four triangles is one-
quarter of the sum of the
former two triangles. Suppose
we continue this process. The
next set of eight triangles have
a united area one-quarter of the previous four, and so on.
Obviously, in the limit, we shall have completely covered the
area of the original figure with sets of triangles such that if we
represent by i the area of the triangle ABC, then the area of
the whole figure will be represented by the sum of the series

taking in an infinite number of terms.

Now Archimedes knew that the sum of this series * to infinity *
works out to exactly f , and so he deduced that the area of the
parabolic curve in question must be four-thirds of the area of
the triangle ABC, or what is the same thing, two- thirds of the
area of the circumscribing rectangle.

Fig. 12. Archimedes' Evaluation
of the Area of a ParaboHc Surface
bv Method of Limits.

Archimedes 41

This is only one, of course, of many similar investigations for
which we are indebted to Archimedes. One of his most celebrated
demonstrations was as to the famous relationship between the
surface areas and volumes of a sphere inscribed in an equilateral
cone, and a cylinder circumscribing a sphere. To Archimedes,
too, is due the well-known evaluation of ir, the ratio of the
circumference of a circle to its diameter. Actually, his investiga-
tion proved that this ratio was less than 37^ and greater than

37TtOI.

The curve known universally as Archimedes' Spiral was
undoubtedly developed by him, but the original idea appears
to have been suggested to him by his
friend Conon. This curve may be
defined as the locus of a point which
moves uniformly towards or from the
centre of a circle along its radius, at
the same time as the radius revolves
uniform^. Thus in the figure, let OA
be the rotating radius. Consider suc-
cessive eighths of its length. As the
moving point in succession reaches ^^^ ^^ j\^^ gp-^^^ ^^
these positions, marked i, 2, 3, 4, &c. Archimedes.

along the radius, the line OA is itself

revolving, and taking up the positions i, 2, 3, 4, &c., round 0.
The construction for drawing the curve is therefore obvious, and
may possibly afford the reader some amusement.

4. Archimedes' Teachings in Mechanics

Turning from the activities of Archimedes in pure mathematics
to those in mechanics, we come upon another rich field of investi-
gation. This is particularly the case in that branch that we speak
of as statics, or the study of forces in equilibrium. His outstand-
ing discovery is the principle of the lever. ' Give me ' , said he,
' where to stand, and I will move the earth.' His line of reasoning,
beginning with the truth that two equal masses suspended at
the ends of a uniform rod suspended at its centre will balance

42 The School of Alexandria

each other, is flawless in its logic and accuracy ; and from this
he proceeds to a careful study of centres of gravity, and works
out a number of standard cases.

But perhaps the most famous of Archimedes' discoveries are
those which deal with hydrostatics, a subject which had been
somewhat neglected by his predecessors. The story of the dis-
covery of what is now generally called the Principle of Archimedes,
namely, that a solid body when immersed in a liquid ' loses '
a portion of its weight equal to the weight of the liquid it displaces,
has many different versions, of which the following is one.

Fig. 14. The Screw of Archimedes.

It seems that Hiero, the King of Syracuse, intended to make
an offering to the gods of a golden crown, and he accordingly
engaged an artificer skilled in such matters to fashion one, the
king supplying the gold for the purpose. In due course the crown
was finished and delivered. The weight was found to be correct,
but for some reason, the artificer came under suspicion of having
appropriated some of the gold for himself, substituting for it
an equal weight of silver. To Archimedes, therefore, was
entrusted the task of discovering whether this suspicion was
justified.

Archimedes w^as a very absent-minded man. So absorbed was
he at times in the problems which interested him that he would

Archimedes' Teachings in Mechanics 43

frequently lose all sense of his immediate surroundings. He was
in such a fit of abstraction one day over the problem the king had
set him when he went to his bath, and he did not notice at first
that the bath was full to the brim with water. He went in, and
the first inkling of the fullness of the bath came when the water
overflowed ; like a flash the full significance of its meaning came
to him. He could not contain himself for excitement, and for-
getting in the absorption of his enthusiasm that he was both
wet and naked, he jumped out of the bath, and ran through the
streets shouting ' Eureka ! Eureka ! ' (I have found it ! I have
found it !)

As a matter of fact, his discovery was twofold and led later to
his very able work on floating bodies. He saw first that when
a body was immersed in a vessel of liquid, it displaced its own
bulk of liquid, and secondly, that its ' loss ' in weight was equal
to that of this displaced ' bulk ' of liquid.

He now saw how to tackle the problem he had been set. He
obtained two balls, one of gold and one of silver, each weighing
the same as the crown. He noticed that the two balls were of
different sizes, because gold is heavier than silver, so that less
of it would be required to make up the same weight as the silver.
But he could tell this exactly by taking a basin of water, and
noting the height of the water in it, and then immersing say the
gold ball. The water rose by displacement, and he marked the new
level. He now took out the gold ball and placed in the basin the
silver ball. The water now rose higher than before owing to the
silver being lighter, and occupying more room, and he noted
the new level. Finally, he took out the silver ball and inserted
the crown. The level of the water was now higher than for the
gold, but lower than for the silver, thus proving that the crown
was made of material lighter than gold and heavier than silver.
Clearly, it contained both gold and silver, and the artificer stood
condemned. Further, by making a series of balls of gold and
silver mixed, all of the same weight as the crown, but each
containing different proportions of gold to silver, and immersing
each in turn, Archimedes was able to find one which would cause
the water to rise to the same height as obtained in the case of

44 The School of Alexandria

the crown, and so he was able to say exactly how much gold had
been stolen.

Archimedes was gifted with much mechanical skill, and this
taken in conjunction with his theoretical knowledge, enabled
him to devise many ingenious contrivances, one of the most
famous of which was a form of pump known as the Cochlea or
' Screw of Archimedes ' . This simple device was in effect a pipe
twisted in the form of a corkscrew. It was held inclined with one
end dipping below the water to be pumped up. It was then
made to revolve about its axis, thus drawing the water up
at each successive winding of the ' screw ' until it came out at
the top.

He is also reputed to have made a sort of glass model of the
universe — a sphere of glass through which the heavenly bodies
could be seen in motion — presumably by revolving the sphere
on its axis. The truth of this is doubtful, though it is asserted
that he ordered a record of it to be engraved on his tomb, together
with his discoveries concerning the geometrical properties of the
sphere and cylinder.

The poet Claudian wrote an epigram on this reputed invention,
of w^hich the following is a translation :

When in a glass's narrow space confin'd,

Jove saw the fabric of th' almighty mind,

He smil'd and said : Can mortal art alone

Our heavenly labours mimic with their own ?

The Syracusan's brittle world contains

Th' eternal law, which through all Nature reigns,

Fram'd by his art see stars unnumber'd burn,

And in their courses rolling orbs return.

His suns through various signs describe the year,

And every month his mimic moons appear.

Our rival's laws his little planets bind.

And rule their motions with a human mind.

Salmoneus could our thunder imitate,

But Archimedes can a World create.

Another contrivance with which Archimedes has been credited
was an arrangement of ' burning-glasses ' , or mirrors, which he
caused to be trained on to the hostile Roman Fleet then lying

Archimedes' Teachings in Mechanics 45

outside the harbour, but there is considerable doubt as to the
truth of this.

These were troublous times for Sicily. The Roman power was
then in the early days of its expansion, and ]\Iarcellus was Consul
at Rome. The siege of Syracuse with which is associated the
latter days of our philosopher occurred during the second Punic
war. Reference has alreadj/ been made to the absent-minded
reveries into which Archimedes permitted himself to sink, and
it was this which, unfortunately, cost him his life. The story is
well knowTi.

In spite of all the heroism of the besieged people, and of all
the mechanical skill and ingenuity of their great philosopher,
Syracuse at last fell, taken by storm in the year 212 b. c. Mar-
ceilus, in recognition of the respect due to the fame of Archimedes,
had given strict orders that his life was to be spared, and that he
was to be accorded due honour. But alas, the attack took place
at a moment when Archimedes was engrossed on a geometrical
problem for which he had traced a figure on the sand. A common
soldier rushed up, and demanded his name. He was told to
be gone and not to spoil his circle, whereat the soldier slew him.

If this story can be trusted, it is literally true, therefore, that
Archimedes died ' in harness ' — he was the scientist to his last
moment.

Many of his works are lost, but the following list of those of
which we know speaks for itself : Two books of the Sphere
and Cj^linder — The Dimensions of a Circle — Of Equiponderants,
or Centres of Gravity — Of Spheroids and Conoids — Of Spiral
lines — The Quadrature of a Parabola — Of the Number of the
Sand — Of Bodies that Float on Fluids.

It is difficult to give adequate praise to the brilliant qualities
of this great man, and we will conclude merely with the opinion
that his work and record amongst the ancients may justly be
likened to the achievements of Newton in later times.

46

The School of Alexandria

5. Ptolemy

As a final example of the great philosophers of the Alexandrian
period, we now proceed to an account of the life and works
of Claudius Ptolemaus, or Ptolemy, as he was more commonly
called. He was no relation to the line of kings who founded
the famous school, Ptolemy being in fact quite a common name
of the period. He was born about a hundred years after Christ

1

1 iG. 15. CLAUDIUS PTOLEMAUS and BOETHIUS

Imaginative portraits by Raphael

See note on p. 14

at Pelusium, in Egypt. The Alexandrian school had by that
time passed through many vicissitudes. Egypt had become
a province of the Roman Empire, and for a long time the study
of science had received a serious set-back. The Roman taste lay
more in the direction of poetry and moral philosophy and the
study of law. But a revival came later with the advent of the
Emperor Marcus Aurelius Antoninus, who, luckily, was of a philo-
sophical turn of mind. A fresh impetus was now given to scientific

Ptolemy 47

study and research, and anew band of thinkers picked up the loose
threads in the web of knowledge and began to weave them anew.
Ptolemy, Diophantus, Pappus, and Proclus all belonged to this
period, and each in his own way added renewed lustre to the
glory of Alexandria.

Ptolemy is known to fame chiefly as an astronomer. Astro-
nomy had been sadly neglected for the previous three hundred
years, the last work of any importance having been done by
Hipparchus, who in particular had compiled a valuable star
catalogue. Ptolemy revived the study. He collected the works
of Hipparchus and his predecessors, and built out of them a
complete celestial system which, based as it was on Aristotelian
doctrines, received blind and undisputed acceptance for cen-
turies. We speak of it to-day as the Ptolemaic System, and it
was set forth in detail in a great work called the ' Great System ' ,
originally written in Greek. It was translated by Arabian astro-
nomers under the title 'Almagest' (al = Arabic for the, magest =
Greek megiste, greatest), and it is by this name that it is usually
knowTi nowadays. (The Latin translation was many centuries
later than the Arabic, and was first made from the Arabic.)

At the root of his theory are the teachings of Aristotle, to
which we have already referred, that the motions of the celestial
bodies are ' perfect ' , and that the most perfect type of motion
is circular. It is almost tragic to think that Ptolemy made his
teaching to fit this theory, for there is no doubt that with all
the ability and originality displayed by him in his writings, the
history of astronomy would have made very different reading
but for the influence of Aristotle on his premises.

The earth, said Ptolemy, was a sphere, and was at the centre
of the universe, and was immovable. His arguments as to why
the earth is spherical were perfect, and are much the same as
are taught in schools to-day ; there was nothing in the teachings
of the peripatetic philosophers to prevent this. But for the rest,
he was indeed blinded by their teachings, which included the
doctrine that lighter bodies move more slowly than heavier ones.
This being so (notice he did not say, ' If this were so '), he argues
that if the earth were to move, the loose bodies upon it, including

48 The School of Alexandria

of course the air, being lighter than the earth would be left
behind, which obviously was not in fact happening. Hence he
satisfied himself that the earth was immovable. But if the
earth is immovable, and is spherical in shape, then indeed it
must be poised in space. We can imagine with what wonder
and delight Ptolemy reached this striking conclusion. But the
remainder of his theory followed almost automatically from the
Aristotelian doctrines of motion in a circle.

As a matter of simple observation, the sun and moon and stars
were seen to rise in the east and set in the west daily. The
explanation by relative motion due to the earth's rotation could

not even enter into the argument,
since it had been showai that the
earth was immovable. Therefore
the celestial bodies were in motion,
and their motion being ' perfect '
they must be moving in circles round
the earth, for the absolute uniformity
with which the stars were seen to

^"■'^^ ^^^ move could only be possible if the

Fig. 16. Ptolemy's Theory of earth were the centre of their rotation,
the Motion of Planets. Ptolemy was a careful observer of

the heavens. His observations did indeed appear to bear out his
theory. But the movements of those stars which had long been
known as the planets, or wanderers, could not be so easily
explained. Ptolemy, with that blind faith in the fundamental
assumptions in his theory, therefore sought out some other scheme
of circles which would answer the purpose of explaining these more
complicated motions. He hit upon the idea of the planets revolving
in a circle round a moving c^xiXx^ C (Fig. 16), this centre having, in
fact, a circular orbit about the earth. This circular orbit he called
the deferent, and by a careful choice of dimensions, this did in fact
explain sufficiently approximately the variable motions (in some
cases, as is well known, retrograde in the skies, instead of
' forward ' ) of the planets, of which five only were known in those
days. It is not necessary for us here to go further into the details
of this theory. Readers who are sufficiently interested will have

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1
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1

\ V ^/

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\»

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Ptolemy

49

no difficulty in obtaining all the information they desire from
astronomical text-books. Sufficient has been said to enable the
reader to appreciate the fertile genius of Ptolemy in presenting
to the world a complete and self-contained theory as to the
structure of the universe.

There is, however, one point of interest which we must here
interpose. Some four hundred years before Ptolemy's days
there had flourished a Greek philosopher named Aristarchus of
Samos, whose great achievement was the putting forward of
a theory that the sun, and
not the earth, was the centre
of the universe, and that the
earth revolved round the
sun in a circular orbit. Here
was something almost ap-
proaching the truth, ' in a
nutshell ' , yet unfortunately
it met with no favour. The
voice of the Aristotelian
school was too strong, and
so the views of Aristarchus
were lost. Many centuries
were to pass before they
were destined to be revived
by Copernicus.

Ptolemy's activities were
not confined to astronomy,
and he greatly distinguished himself as a geographer. The book
he wrote on this subject was indeed, for centuries afterwards, the
standard work on the subject. It contained maps of all the known
parts of the world, and described countries as far apart as India,
China, and Norway. Our own country was described under the
name of Albion. Lines of latitude and longitude were marked on
his maps, calculated on the basis of rules devised by an earlier geo-
grapher of great fame, named Eratosthenes, and the whole book
indicates clearly the patient student and the diligent scientist.

To Ptolemy is also ascribed — perhaps wrongly — a work on

2613 D

Fig. 17.

PTOLEMY as conceived
by Giotto.

50 The School of Alexandria

Optics. The chief feature of this book is a valuable inquiry into
the subject of refraction. There is no doubt that in this pursuit
he was actuated by a desire to understand and allow for the
influence of this phenomenon in the displacement of the heavenly
bodies from their real positions, but whatever his motive, the
results were invaluable. Actually, Euclid was the real pioneer
of the study of light, and was responsible for the statement that
light travels in straight lines. Ptolemy went much farther. He
carefully worked out the angles of refraction corresponding to
all angles of incidence from o° to 80° for rays from air to water,
and from air to glass, and from these results he built up a theory
of astronomical refractions which worked out very well indeed
in practice. He did not, however, deduce a generalized law of
sines such as we all use to-day.

According to Gauricus, one of the commentators on his hfe,
Ptolemy died in the seventy-eighth year of his age.

6. Last Days of Greek Science

We have so far confined ourselves to special examples of the
great thinkers of the Alexandrian School, but before leaving this
subject we must draw attention to a few other names of those
who contributed to the greatness of this later phase of Greek
scientific history. Thus we have the celebrated Apollonius of
Perga (265-190 B. c. ?), probably contemporary with Archimedes,
whose researches on conic sections carried the subject far beyond
the point at which it had been left by Plato and Menaechmus ;
Ctesibus and his contemporary Hero of Alexandria, who were
both successors of Archimedes in their study of such various
mechanical appliances as the forcing pump, the air-gun, the
water clock or clepsydra, the siphon-fountain, &c., and the
theodolite ; and Posidonius, who wrote on the tides and interested
himself in the subject of atmospheric refractions.

But with the Roman ascendancy the period of intellectual
decline was now definitely in evidence. Great as were the Romans
in war, social ethics, literature, and above all perhaps in law, they
were emphatically not scientists. The scientific activity which

Last Days of Greek Science 51

recommenced with the advent of the Emperor Marcus AureUus
Antoninus did not persist, and beyond such isolated exceptions
as the astronomer Gallus, the historian Pliny, the geographer
Strabo, and the physicist Seneca (whose Naturalmm quaestio-
num lihri VII was used as a text-book throughout the Middle
Ages), we come upon a rather barren era.

In the study of mathematics the record is a little brighter,
for with this era is associated the famous name of Diophantus,
often referred to as the founder of the study of Algebra. He
lived probably early in the fourth century a. D. and he greatly
enriched the world by his refreshing methods of analysis. He
was preceded by Pappus, a geometrician of great power, whose
misfortune it was to be surrounded by a people in whom the
taste for geometry was seriously on the decline, and was followed
by Theon (c. a. d. 370) and his daughter Hypatia, both able
commentators of the fifth century.

Finally we must mention Boethius, the great Roman writer
of the sixth century, who formed the main link in the slender
chain which connected up mediaeval science with the Greek
ages. He was essentially a commentator, contributing nothing
original (except perhaps in music), but writing on the mathe-
matical sciences as he knew them from his studies of the original
Greek sources.

Fig. 18. 'A Fire Engine.'

D 2

Magic and the —

Black A rts

III

ROGER BACON

I. Science in the Middle Ages

The history of science in the Middle Ages makes but sorry
reading. It was, so far as science is concerned, a period of
ignorance, misunderstanding, and neglect. The decline of the
Roman Empire brought with it an inevitable decay in the Alex-
andrian School. The influence of Greek learning gradually faded.
Then came the final fall of the Roman Empire, and with it the
last fiickerings of philosophical inquiry in Europe came to an end.

But although the light of learning had left Europe, it had not
left the world altogether. For it now began to burn brightly
in the East. The Nestorians, ]\Ioors, Jews, SjTians, and other
Arabic-speaking peoples ^ had always exhibited a leaning
towards scientific inquiry, and when later the military hordes of
the ]\Iohammedan rulers pushed their conquering way into
Spain and northern Africa, these peoples knew better than to
destroy the valuable records which they found. Instead they
translated many of these works into their own language, and
derived therefrom an encouragement to further inquiry which
brought many fruitful results. Foremost among the Arab leaders
responsible for this enlightened policy we may mention the Caliphs
El-Mansour, Haroun El-Raschid, and El-Mamoun in the eighth
and ninth centuries A. D. It was the last of these, in fact, who
ordered in a. d. 827 the translation to be made of Ptolemy's great
work into Arabic which passed under the title of the ' Almagest '.

^ The Arabs themselves were not philosophers, as is popularly supposed,
and what is spoken of as Arabian learning is attributable almost entirely
to subject peoples under the Arabs who wrote in the Arabian language,
and it is through this fact that the misconception has grown up.

Science in the Middle Ages 53

Accordingly, during this period, we read of a number of Arabian
philosophers pursuing their researches diligently in Astronomy,
Mathematics, Physics, and Alchemy (that ' mystic ' forerunner
of chemistry), and making valuable contributions to the world's
knowledge in these subjects. In particular mention should be
made of the great Moorish philosopher Alhazen, who flourished
in Spain in the eleventh century, and who produced well-known

UNIVERSITY TOWNS

in 12 ^& 13"^ Centuries

English Miles

Univs. founded in 12^ Cent.

Fig. 19.

works on Optics (he tells us of lenses, or rather segments of glass
spheres, and their magnifying powers) and Geometry.

Meanwhile, as we have already pointed out, Europe had sunk
to its lowest depths of intellectual ignorance and inertia. There
were no original writers, and very few readers. Such very little
learning as existed was confined to the clerics. At most it com-
prised a few bad Latin translations of the writings of Aristotle,
together with the works of Pliny, and the teachings in these books
were accepted without question. Such records of other ancient
teachings as survived were relegated to the unused shelves of

54 Roger Bacon

the monastic libraries. From one point of view this was fortunate,
for, in an era of tumult and disorder, the monasteries were at
least regarded as sacred ground by all parties, and so the records
were saved from an otherwise inevitable destruction.

The effect, however, of this scientific activity of the Arabic-
speaking peoples was to stimulate a few of the more enlightened
men of the West to curiosity. As a consequence, the books of
the ancients were taken down from the shelves of the monastic
libraries, and they were studied anew, and the men who shared in
this now became the pioneers of a new movement of restoration.
Amongst these should be mentioned Gerbert, a monk from the
Netherlands, who in the tenth century journeyed to Spain, to
acquire at first hand the wisdom of the Moors. Under the title
of Silvester II he afterwards became pope, and the story of his
life appears as a ray of light in a world of darkness.

The first real signs of a return to intellectual activity in Europe
was the establishment in various centres of the institutions known
as universities. This began in the twelfth and was at its height
in the thirteenth century. To these universities students and
teachers began to gravitate in increasing numbers. All the
European nations were represented, and Latin was the universal
language employed. One of the most famous of these universities,
particularly from the point of view of science, was at Paris,
where, although it had long before been the seat of some con-
siderable learning, a university was constituted in the year
A. D. iioi. The favourite studies pursued at these universities-
were almost entirely theology and metaphysics, and the prevailing
influence was of course Aristotelian. There was no attempt
made to seek out new truths, or to question old dogmas, and the
blind worship of the Peripatetics was general throughout Europe.

It was in such a world, and in such an atmosphere, that there
was born, to the glory of England and of science, a man destined
to rise superior to his times. As herald of a new era of inquiry
and activity the memory of Roger Bacon, visionary and scientist,
will live for ever.

55

2. The State of Philosophy in the Dark Ages

It will help us to appreciate the value of Roger Bacon's
scientific record if we review the general position in which
philosophy found itself in the eleventh and twelfth centuries.
So far as the problem of the nature of the universe, and of man's
place within it, is con-
cerned, the governing
views were those laid
down by Plato in his
Timaeiis, as translated
by Apuleius and com-
mented upon by Chal-
cidius, and included that
central doctrine around
which practically the
whole of mediaeval
science was built — that
of the ' macrocosm and
microcosm ' . This doc-
trine taught that man's
fate was governed by a
completely knowable in-
terplay of the forces of
nature and character.
The microcosm, man,
reflected the macrocosm,
the world around him, and the problem which presented itself to
the ' dark age' and ' mediaeval ' philosophers was the manner and
the extent of this reflection, and the study of this subject was known
by the name of ' astrology ' . Having derived the problem from
Plato, the development of it was largely governed by Aristotle's
views as to the structure of the universe. The later Greek philo-
sophers taught that for the cause of changes in bodies on the earth
below, one had to look for parallel changes in the heavens above.
They held that such regular alternations as that of night and day,

Fig. 20.

Byrhtferth's Microcosm
Macrocosm.

and

56 Roger Bacon

winter and summer, growth and decay, were governed by the
regular movements of the stars in circles ; whilst on the other
hand the many variable and less predictable elements of daily
life and experience were governed by the irregular planetary
movements. Writer after writer elaborated on all this, until
the position by the end of the tenth century Vv^as very much as

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y^f^-^v''

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KAj Yioi r^.'jLtjp

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-lOJCUf'^iTti^ <<•- K'l.

Fig. 21. Leaf from a yth-cent. Greek MS. believed
to have been used by Grosseteste.

is shown in the figure on p. 55, after Byrhtferth (c. 1000).
The reader will notice from this figure how the Aristotelian
doctrine of the four elements had become incorporated in this
scheme.

This, then, was the position and the standpoint of the world
of philosophy in those days, and it will be noticed that the
astrology which grew up from it, and at which we are nowadays

State of Philosophy in the Dark Ages 57

somewhat hastily wont to scoff, was a perfectly natural and
inevitable outcome of the times. It was destined later to
degenerate into a charlatanism which was to bring it into deserved
disrepute, but in the early Middle Ages it was a pure philosophy,
and as such must command our respectful attention.

We have mentioned how the spirit of learning, slowly and
haltingly, began to revive when Graeco-Arabic culture began to
percolate through into Europe ; and by the thirteenth century.

Fig. 22. A Scribe at work.

during what is known as the ' scholastic period ', a new spirit was
beginning to assert itself, fostered by such people as Alexander
of Hales {d. 1245), Robert Grosseteste {d. 1253), Albertus Magnus
(i 193-1280), and St. Thomas Aquinas (1225-74). The univer-
sities had by now been firmly established, the Greek language
was beginning to be studied, and the scientific works of Aristotle
were becoming more accessible.

For the development of this new spirit much credit is due to
a group of Franciscan Friars who, headed by the great Robert
Grosseteste, afterwards Bishop of Lincoln, studied and wrote upon

58 Roger Bacon

mathematics, optics, natural philosophy, literature, and the
foreign and ancient languages. It was as a member of this band
that Roger Bacon did much of his work, and so to him and his
labours we now turn.

3. Roger Bacon

Roger Bacon was born near Ilchester, in Somersetshire,
probably in the year 12 14, and appears to have belonged to
a wealthy family of ancient and honourable descent, whose
members later sacrificed their fortunes in the cause of King
Henry III in his struggle with the Barons from 1258 to 1265.
He began his studies at home at the early age of thirteen years,
and then proceeded to the University at Oxford. Here he
attended the lectures of Edmund Rich (subsequently Archbishop
of Canterbury), on Aristotle, and he quickly asserted himself as
a young student of unusually brilliant qualities. Whilst at
Oxford he came under the influence of another of Rich's pupils,
Robert Grosseteste. Grosseteste had made a careful study of
the Greek language, having had the advantage of intercourse
with a Greek monk, and at his promptings Roger Bacon also
sought to learn this language, and so to gain access to a wealth
of scientific literature which must have stood him in excellent
stead in his later career. One of the great claims of Roger on
our memory is the attention that he drew to the importance of
getting good texts of the existing scientific works translated
direct from the Greek.

Following the fashion of the times. Bacon passed on from
Oxford to Paris, then the premier university of Europe and the
centre of attraction for the intellectual world, and he had here
a most distinguished career.

He returned to Oxford in 1250, and embarked upon an ex-
tended course of study and research over a very wide field. He
pursued his investigations far beyond the stage in which he found
his subjects, which were accordingly greatly enriched by his
labours. He spent, he tells us, no less a sum than two thousand
pounds in the course of twenty years on books, instruments, and
apparatus — a prodigious sum, having regard to the value of

Roger Bacon 59

money in those days, although as a matter of fact much of this
sum was contributed by his friends and admirers.

During this period he was undoubtedly at the height of his
fame. But fame brings with it its penalties. There were those
who envied Bacon, and there were others who were even ready
to do him injury, particularly after the death in 1253 of his most
influential patron, Bishop Grosseteste. It must be remembered

Fig. 23. ROGER BACON with a pupil taking observations from
a window.

that Bacon lived in a very ignorant age. The real students were
few indeed — the quacks and pretenders many. The Church was
the dominating influence of the time, and looked askance at
the practice of what were vaguely termed the ' magical arts ' .
It was this fact which was seized upon by Bacon's traducers as
their opportunity to encompass his downfall.

One can well understand that it was easy for these people to
persuade the men who ruled in the Church of that day how
closely allied to the practice of magic was the use of retort stand
and crucible. Unfortunately, too, Friar Bacon had written of
the clergy with more candour than tact. He had spoken freely

6o Roger Bacon I

of their ignorance and their want of character, and had even
gone so far as to write to Pope Innocent IV on the subject of
the necessity for a reformation. These were hardly the writings
which his enemies would peacefully receive, but Friar Bacon,
like so many other pioneers of science, was a conscientious
thinker, and he had the courage of his convictions. Indeed, it is
contended that his motive in embracing a monastic life was to
obtain such increased leisure for research as to enable him to
achieve discoveries that would be ' of the highest consequence
to the honour and peace of the Church ' . For, he continued,
' the surest method of extirpating all heresies, and of destroying
the Kingdom of Antichrist, and of establishing true religion in
the hearts of men, is by perfecting a true system of natural
philosophy ' .

As a reward for his pains. Bacon found himself inhibited from
lecturing to the students of the University by command of the
General of the Franciscan Order, Bonaventura the ' seraphic*,
as he was afterwards called. Later, in 1257, he was sent to Paris
and was kept in close confinement at the Franciscan house near
the Porte Saint-Michel. Here he stayed, under strict surveillance,
for ten long years.

There seemed at first but little possibility of his release, but,
after a few years, Bacon heard that there had been sent to
England a papal legate, one Guy de Foulques, a man who for
his time was singularly broadminded. Guy had heard of the
great philosopher, and this, added to the fact that his political
tendencies in England were on the side of King Henry III and
against the Barons, brought him into sympathetic contact with
Bacon's family.

In 1265 Guy de Foulques was elected Pope under the title of
Clement IV, and Roger, when he heard this news, saw at last
opportunity of release. Knowing the new Pope's philosophical
tendencies, he sent him a petition in the course of which he pro-
posed ' out of a reverence due to his high dignity, which ought
to engage him in seeking to procure the benefit of the whole world,
he was willing, as far as the impediments he laboured under
would permit, and his memory would allow, to deduce a regular
system of true philosophy to the utmost of his power ' . His offer

Roger Bacon 6i

fell on willing ears, and in the year 1266 the Pope wrote to his
' beloved son, Friar Roger named Bacon, of the Order of the Friars
Minor ' , inviting him to send, with all speed, a copy of his works.

Roger Bacon set to work on his self-imposed task. To appre-
ciate its magnitude, we must remember that he was a prisoner,
and that for years he had been without instruments, with prob-
ably very few books, and without the assistance of expert copyists.
His only materials were his excellent memory and his indomitable
courage. In the space of eighteen months he produced the three
large treatises on which the main part of his reputation is based.
They were called the Opus Mains, the Opus Minus, and the
Opus Tertium, respectively. They gained him his long-sought
release. In the year 1268, after an absence of over ten years,
Bacon was at last permitted to return to Oxford.

A fresh period of fruitful intellectual activity now set in for
our philosopher, and in 1271 he produced the first part of an
encyclopaedic work called Compendium Studii Philosophiae.
His freedom was, however, doomed to be once more limited.
Bacon always had his enemies, and the well-known friendliness
of the Pope to him was his only safeguard against attack. But
unfortunately. Pope Clement IV died very soon after, and the
storm clouds of biased and jealous ignorance once more gathered.
Once again Roger was arraigned on the charges of meddling
with the magical arts. He was tried by the new General of the
Franciscans, Jerome de Esculo. His writings were again con-
demned, and he was once more imprisoned in the Franciscan
house in Paris. This was in the year 1278.

Bacon was now sixty- four and obviously less able than before
to endure the rigours of confinement. He was again cut off from
the opportunity of experiment and research, though possibly he
was permitted access to books. It speaks much, therefore, for
his courage and perseverance that during the fourteen years of
this second confinement he continued to write books on a wide
range of philosophical subjects.

Bacon was released in 1292. He was now an old man, but he
was by no means broken. He returned to Oxford, to the college
of his Order, and wrote his last great work, a Compendium of
Theology. He spent his last days in peace and died in the

Roger Bacon 63

eightieth year of his age, on the nth of June 1294. He was
interred in the Church of the Franciscans, all trace of which has
since vanished.

' Of this son of Oxford, who with his " almost prophetic gleams
of the future course of science " had only a Pisgah sight of the
promised land of long deferred discovery, we may say that " no
man knoweth of his sepulchre unto this day".' ^

4. Bacon's Scientific Writings

Bacon's writings have come to light but slowly. With his
death his books appear to have been suppressed, though luckily
not destroyed. One of the earliest to be printed (at Paris in
1542) was a treatise On the marvellous power of art and nature,
a book that was perhaps responsible for the accusations of
' magic ' which were hurled at him during his life. One can
imagine the effect on his contemporaries of the following striking
passages which we reproduce from an old translation.

' First, by the figurations of art, there may be made instruments
of navigation without men to rowe them, as great ships to brooke
the sea, only with one man to steere them, and they shall sayle
far more swiftly than if they were full of men ; also chariots that
shall move with unspeakable force, without any living creature
to stirre them. Likewise, an instrument may be made to fly
withall if one sit in the midst of the instrument, and doe turne
an engine, by which the wings, being artificially composed, may
beat the ayre after the manner of a flying bird. . . .

* But physicall figurations are farre more strange : for by that
may be framed perspects and looking-glasses, that one thing
shall appeare to be many, as one man shall appeare to be a whole
army, and one sunne or moone shall seem divers. Also perspects
may be so framed, that things farre off shall seem most nigh
unto us.'

When it is remembered that this was written in the thirteenth
centur}^ and that some of those ' visions ' Bacon saw then have
only achieved reality in the twentieth century, one may realize
how far ahead of his times he must have been.

By many educated people Bacon is best remembered for his
supposed connexion with the invention of gunpowder. There

^ John Sandys, Roger Bacon, British Academy, vol. vi, 1914.

64 Roger Bacon

is no doubt that he was a close student of the subject of alchemy,
the forerunner of chemistry. Alchemy was a serious business in
his days. It was a study largely developed by the Arabians, and
may be said to have had a twofold object— the transmutation of
all metals into gold, and the search for the elixir of life. John
Freind, a seventeenth-century scientist and student of Bacon,
claims that the Friar succeeded in discovering a tincture of gold
for the prolongation of life.

With regard to gunpowder, we find the following passage in
his Secrets of Nature and Art : ' From Salt Petre, and other

Eve.nR.

Centre FSTiii"

Fig. 25. Diagrams of Roger Bacon to illustrate optics of lens.

ingredients, we are able to make a fire, that shall bum at what
distance we please.' Then again later :

* That sounds like thunder, and corruscations, may be formed
in the air, and even with greater horror, than those which happen
naturally ; for a little matter, properly dispersed, about the
bigness of a man's thumb, makes a dreadful noise, and occasions
a prodigious corruscation, and this is done in several ways ; by
which a city, or an army, may be destroyed after the manner of
Gideon's Stratagem, who having broke the pitchers and lamps,
and the fire issueing out with an inexpressible noise, killed an
infinite number of the Midianites.'

There is no doubt whatever, in view of these passages, that
Bacon must have been fully aware of the formula for the compo-
sition of gunpowder, and such a formula has been found in
a cryptogram in his work.^

* See A. G. Little, English Franciscan Studies.

Scientific Writings

65

Bacon was not a mathematician in the highest sense of the
term, that is to say, although he made himself familiar with the
subject in so far as it had then been developed, he made no
original contributions to it, his interests being rather in the direc-
tion of its applications. Nevertheless, he had a true perspective
of its value, on which he never ceased to write, and he referred
to it as ' the gate and the key ' of all the other sciences.

Bacon, too, was skilled in astronomy, though he followed the
universal rule of his day which regarded the movements of the
stars as affecting the lives of men. He was, in fact, a believer in
astrology, and he even held that the origin of religions depended

Fig. 26. Diagram of Roger Bacon to illustrate optics of burning-glass.

upon the conjunction of the planets. Yet in spite of the fact
that we now know astrology to be nonsense, the superiority
of Bacon as an astronomer over his contemporaries is
indisputable.

Finally we come to Bacon's work in ' Opticks'. Here again
there is no doubt of his brilliance. There is ample evidence that
he was acquainted with the properties of lenses and spherical
mirrors. The extract given below speaks for itself. It comes in
a part of his Opus Maius, where he is discussing the angle sub-
tended to the eye by the image of an object as viewed through
a refracting plane or spherical medium. He applies to this
discussion such cases as the crooked appearance of an oar in
water, and again he describes how a piece of money in the bottom
of a basin which is concealed by the rim may be made visible by
pouring in water, and he discusses why the sun and the moon

2613 E

1

66 Roger Bacon

appear larger when near the horizon. He then proceeds as
follows :

' If the letters of a book, or any minute objects be viewed through
a lesser segment of a sphere of glass, or crystal, whose plane
base is lade upon them, they will appear far better and larger.
Because by the fifth canon about a spherical medium, its con-
vexity is towards the eye, and the object is placed below it, and
between the convexity and its centre, all things concur to magnify
it. For the angle under which it is seen is greater and its image
is also greater, and nearer the eye than the object itself ; because
the object is between the centre and the eye ; and therefore this
instrument is useful to old men, and to those that have weak
eyes ; for they may see the smallest letters sufficiently magnified.'

Here clearly we have an attempt at the theory of spectacles,
and we find in fact that the adaptation of lenses for use as spec-
tacles was certainly an invention of his time.

Great controversy has raged around the question of whether or
no Bacon knew of the telescope. The consensus of opinion is on
the whole against the view that Bacon actually made or invented
such an instrument. Nevertheless, his writings show that he was
at least aware of the possibilities of lens combinations, such as
have produced in later times both microscope and telescope. It
shows how very far ahead of his times this great man lived and
thought, for remember that it was actually not until the seven-
teenth century that the telescope was effectively constructed, and
first turned to the skies by Galileo.

We have tried to impress upon the reader some real idea of the
state of ignorance with which Baconwas surrounded, and without
this it is impossible to do adequate justice to his memory. Bacon
stands out as a bold champion of inquiry, experiment, and observa-
tion, and his life was a lasting protest against the ' trammels of pre-
judiced authority ' which hindered progress in science and learning.

There is a general idea prevalent, and it finds encouragement
in most commentaries on Bacon's life and work, that his efforts
were wasted owing to the intellectual inertia of those around
him. This view is, however, unfair and incorrect. ' Bacon was
not an isolated phenomenon, but an important link in the chain
of scientific development.' ^ For example, his pupil, John Pecham,

^ See Little's Studies in English Franciscan History, Manchester, 191 7,
pp. 220-1.

Scientific Writings 67

lectured to the Franciscans at Oxford ; Herber, also a lecturer
there, carefully collected all Bacon's manuscripts; we find evi-
dences, in the shape of ' school ' copies of the Perspecliva, that this
work was authoritative in the fourteenth and fifteenth centuries,
and looking still farther ahead, both Columbus and Copernicus^
through intermediary writings, were influenced by Bacon.

All honour, therefore, is due in these days to the man who, in
the words of a great Oxonian, ' was perhaps the first of the long
list of the victims of ecclesiastical persecution, and is associated
with that illustrious band of patriots in the republic of letters and
science who maintained the cause of intellectual and moral liberty
against the odious encroachment of spiritual despotism.' ^

IV

COPERNICUS

I. The Revival of Scientific Inquiry

We have seen how the thirteenth century brought the first
faint signs of the return of a spirit of inquiry. Slowly but surely
this spirit developed, halting no doubt when it came into antago-
nistic contact with the accepted theological views of the time,
but nevertheless gaining in impetus, until it attained a culminating
pitch of brilliance in the seventeenth and eighteenth centuries.

One science there was which, even in the darkest days of
ignorance and neglect, was never completely abandoned — the
science of astronomy. And we need not go far to seek the reason
for this. Astronomy was essential for the determination of the

1 Baden Powell, in his Historical View of the Physical and Mathematical
Sciences. See also articles by R. R. Steele and by C. Singer in Studies in
the History and Method of Science, vol. ii, ed. C. Singer, Oxford, 1921.

E 2

68 Copernicus

dates of the Church festivals, the accurate celebration of which
was a matter of great importance in mediaeval days. Moreover,
bound up with the ignorant superstitions of the Middle Ages was
a profound belief in the art of astrology. This art, sister to the
science of astronomy, was regarded as being the more important
of the two. Indeed, the value of astronomy was often measured
solely by the assistance which astronomical observation could
render to the astrological art. Later, when the claims and
pretensions of astrologers had been exploded and their exponents
held up to ridicule, this untenable system brought a measure of
discredit upon the more legitimate science, but in the earlier
days there is no doubt that much of the stimulus to astronomical
inquiry was due directly to the superstitious interest in astrology.

Throughout the whole of this period the influence of Ptolemy
in astronomy and of Aristotle in other departments of science
was always paramount. Their teachings were brought into
further prominence with the invention of the art of printing about
the middle of the fifteenth century. Two names in particular are
associated with these Ptolemaic teachings — they are George
Purbach and his famous pupil, John Miiller, of Konigsberg
( = King's hill), better known by his Latin pseudonym of Regio-
montanus^ ( = King's mountain). Purbach was professor of
astronomy at the University of Vienna about 1450, and he
realized the necessity for an accurate translation of Ptolemy into
Latin. He died before this project was very far advanced, but
his pupil and admirer, Regiomontanus, carried on and completed
the work. There is no doubt that this philosopher had serious
doubts as to the truth of Ptolemy's fundamental statement that
the earth was fixed, immovable, and the centre of the universe,
but, in refraining from openly challenging it and working from
it to its logical conclusion, he lost a great opportunity.

It was left for a quiet but thoughtful cleric to do this, and to
begin for the world a new era of philosophical belief. As a conse-
quence Nicolas Copernicus will go down in scientific history as
the man who accomplished a revolution in astronomy by the
final and complete overthrow of the Ptolemaic doctrine.

^ The practice of the learned in latinizing their names was natural in
view of the fact that they wrote in Latin.

69

2. Nicolas Copernicus

Nicolas Copernicus was born in the town of Thorn on the
Vistula at the Prussian frontier, on the 19th of February 1473.
His father, also named Nicolas, was a successful tradesman, and
his mother was a sister of Lucas Watzelrode, afterwards Bishop
of Ermeland, a relationship which turned out later to be a very
useful one for the subject of our study.

Little is known of the childhood and early youth of Copernicus.
It appears that his early education, chiefly in the Latin and Greek
languages, was undertaken at
home, but as soon as he was
sufficiently proficient to profit
thereby, he proceeded to the
University of Cracow with the
object of training for the
medical profession. He soon
discovered in himself a natural
liking for mathematics and
natural philosophy, and it was
not long before he-was working
just as hard at these subjects
as at medicine. His mathe-
matical studies carried him
into a discussion on the theory
of perspective, and as a con-
sequence he also became an
able draughtsman.

Having graduated at Cracow as doctor in both arts and
medicine, Copernicus, after a short stay at his home in Thorn,
proceeded first to Bologna, where he came under the influence
of the astronomer Domenico Maria Novara, and then, at the
age of twenty-three, to Rome, which was ringing with the name
of Regiomontanus. Here Copernicus rapidly established himself
as an earnest mathematician and astronomer, and it was not long
before he experienced the signal honour of being instituted, before
a full assembly of doctors and great men, professor of mathe-
matics in the University of Rome.

Fig. 27. NICOLAS COPERNICUS

70 Copernicus

Rome did not keep hrm at her University for very long, for his
uncle, Lucas Watzelrode, Bishop of Ermeland, gratified at the
position achieved by his nephew, invited Copernicus to return
to his own country, and take up a canonry at the cathedral of
Frauenberg. Before doing this, however, Copernicus went to
the University of Padua, at whose medical school he studied
till 1505.

He did not proceed immediately to Frauenberg, but resided
first at the episcopal palace of Heilsberg as his uncle's physician.
His early days here were none too comfortable. As so often
happens when a man obtains a position by influence his presence
was resented by some. But his natural gentleness, his love of
peace and quiet, and his obvious scholarship soon had their
effect, and on his appointment after his uncle's death to the
canonry of the cathedral of Frauenberg he found himself in
peaceful possession, honoured and respected. His daily routine
was characteristic of the man. It was made up of three ' activi-
ties ' — devotional exercises and the diligent performance of his
divine offices, the tending of the sick poor who required his
medical assistance, and the employment of all his spare time in
philosophical study and meditation.

There were occasions when the peace and solitude of his daily
routine were not permitted to Copernicus. He was occasionally
called into consultation by those in charge of the affairs of the
State. He had been chosen by the College of Canons as their
representative in the State Assembly at Grodno, and although
he never went out of his way to disturb the ordered scheme of his
daily life, he never attempted to deny the State the benefit of
his wisdom and learning when called upon to offer them. The
following example is of peculiar interest in connexion with
certain post-war problems. The many wars in which the country
had become involved had considerably diminished the value of
money, and had in consequence created much financial and
economic distress among the people. The Diet was greatly con-
cerned about this, and a committee of Senators were appointed
to investigate the matter, but they had to confess themselves
beaten. They appealed, however, to Copernicus for his advice

Nicolas Copernicus 71

and opinion. He accordingly drew up a rule for reducing to
a definite standard all the various kinds of money then in circula-
tion throughout the provinces of the kingdom, and this was
immediately adopted by the Senate and inserted in its public Acts.

3. Copernicus as an Astronomer
Nicolas Copernicus is known primarily as an astronomer. He
gave to the study of the heavens all the time he could spare
from his normal duties. His instruments were few and poor, but
this did not dishearten him. He proved himself a most patient
and painstaking observer, utilizing his slender resources to the
best of his ability. The modem observatory is equipped with
a telescope known as a transit instrument. This is mounted on
two massive pillars and can only swing in one vertical plane — the
plane of the meridian, which is defined by a great circle passing
through the north and south points and the point overhead
(' zenith '). This is the plane which the sun crosses approximately
at twelve noon. Sooner or later, in the course of every twenty-
four hours, all stars cross this meridian, and the exact time at
which this happens for any particular star is an important
determination in astronomy. Copernicus had no transit instru-
ment— telescopes were not yet invented — and so he arranged
slits in the walls of his home through which, by suitably placing
himself for observation, he could note the ' transit ' of the stars
across the meridian. Further, he measured the altitude of these
stars above the horizon, at the moment of ' transit ', by means
of a quadrant which he devised, and which he set up in front of
the slits or apertures mentioned.

Copernicus was soon attracted to a careful study of the motions
of the planets. He recorded all his observations, and the tables
of planetary motions which he compiled therefrom were easily
the best of his times, and remained in general use for long after-
wards. Of more importance than these tables was the train of
thought to which his observations of the planets led him, for
from it was gradually evolved that theory of the solar system
universally referred to to-day as the Copernican System.

It is a matter of some interest to all students of science and of

72 Copernicus

human nature to ask themselves the question, with regard to any
important discovery, invention, or theory, ' What started the train
of thought which led to the final achievement ? ' The answer is
usually interesting, and frequently surprising. An accident,
a dream, an apparent speck of dust in an instrument, the falling
of an apple from its tree — how remarkable may be the results
when these small things and simple occurrences are experienced
by genius !

Rheticus, friend, pupil, admirer and commentator of Coper-
nicus, tells us that the whole of his master's speculations arose
from his observation of the planet Mars. He was profoundly
impressed by the fact that its brightness and its magnitude
varied so very considerably at different times. Now, according
to the Ptolemaic System, unquestionably accepted, the earth,
iixed and immovable, is the centre of the universe, and the sun
and the planets revolve round the earth. If the reader refers back
to Fig. 1 6 he will recall that according to Ptolemy the planets
move round the earth in epicyclic orbits — that is to say, the
planets move in circular orbits round a point C, which itself
moves round the earth in a circular path known as the ' deferent '
circle. A planet, therefore, is not at a constant distance from
the earth, but the variation is not very great. Copernicus felt
very definitely that the marked variations in brightness and
magnitude which he observed in Mars and in the other planets
were out of all proportion to what might be expected from the
Ptolemaic doctrine of the universe. Now Copernicus knew from
the literature of the ancients of a theory of the solar system put
forw^ard by the distinguished Greek philosophers, Pythagoras
(572-497 B.C.) and Aristarchus (310-230 B. c), according to which
the sun, and not the earth, is the centre of the universe, the
planets, including the earth, revolving round the sun annually,
and rotating about their axes diurnally. The teachings of
Pythagoras and Aristarchus became completely submerged under
the flood of the Aristotelian and Ptolemaic doctrines which
formed the staple scientific material of succeeding ages. So the
truth had laid hidden in obscurity for about two thousand years,
till Copernicus again brought it to light. Let there be no mis-

as an Astronomer 73

understanding about this all-important fact. Copernicus did
not create the system which bears his name. He knew that its
fundamentals had been given out to the world by Pythagoras,
but the world had not listened.

Copernicus revived this theory, and so supported it with
argument and exposition as to force its acceptance. Thus began
a new era in scientific thought.

How did Copernicus work out his theory ? Pondering over
Ptolemy's writings, he was first struck by the somewhat laboured
claim that with the earth immovable and fixed, the whole of the
vast expanse of the heavens, with all the stars, sun, and planets,
are carried completely round the earth every twenty-four hours.
If there were no alternative explanation, Copernicus, too, would
perforce have accepted it as true, but he realized clearly the
elementary facts of relative motion. Thus, he instanced, when
a ship is moving parallel to the shore in smooth water, to a person
on board, the ship appears to be at rest whilst the objects on the
shore move past the ship in the opposite direction from that of
the ship's real motion. Scores of similar examples will readily
occur to the reader.

Similarly, therefore, the daily movements of the heavenly
bodies could be explained by supposing that it is not the celestial
sphere which is rotating, but the earth which is rotating once in
twenty-four hours in the opposite direction. Here were two
alternatives. Which was the more plausible ? Surely the
simpler of the two, and so Copernicus definitely rejected the
clumsy idea of a gigantic universe revolving round the earth.
It remained for him to consider what logical consequences must
follow from his acceptance of the other alternative.

To appreciate properly the frame of mind into which Coper-
nicus had been drawn, the reader must again be reminded that
the doctrines of Aristotle and Ptolemy were still paramount
everywhere, and that it was tantamount to heresy to question even
a single utterance of the great Greek philosopher. If Copernicus
had not, so to speak, ' caught them out ' on one point, he probably
would not have attempted to question any other point. Now
Aristotle had taught that the earth was ' fixed, immovable, and

74 Copernicus

the centre of the universe '. Copernicus had satisfied himself
that, on the contrar}^ the earth was neither fixed nor immovable,
but that it was rotating in space on its own axis. He, therefore,
would be naturally led to ask himself, ' If Aristotle was wrong in
stating that the earth is fixed and immovable, perhaps, too, he
was wrong in declaring it to be the centre of the universe.' His
observations on the varying brightness of the planet Mars

Fig. 28. AN ASTROLABE of 1574.

strengthened his doubts, and his reading of the Pythagorean view
evidently settled them once and for all.

We find, then, after eighteen hundred years of unbroken rule,
the first great departure from the teachings of Aristotle. The
sun, declared Copernicus, is the centre of the solar system.
Round it at varying distances revolved the planets, and these
also rotated about their axes. Yet even with Copernicus the
Aristotelian influence was strong. He made no attempt to break
away from the ' circle-worship ' of the Greek philosopher, and said
that the planets moved in circular orbits round the sun. Where
observation showed a planet's motion to, be inconsistent with
this Jn its irregularity, he freely introduced Ptolemy's device of

as an Astronomer 75

a ' deferent ' circle, and, indeed, before very long a complicated
scheme of epicycles grew up, keeping pace in its increase of
complexity with every improvement in observation, and it
remained for Kepler in the next century to sweep all this away
and substitute for it the simple ellipse.

The great achievement of Copernicus was, therefore, that he
* put the earth in its proper place ' in the cosmical scheme of
things, and that although, as we shall see later, his suggestions
were made with much timidity, he was the first to break away
from the ' Aristotle-worship ' which had impeded scientific
progress for so many centuries.

4. De Revolutionibus Orbium Caelestium, 1543

The book in which Copernicus stated and proved his theorj^
that the sun is the centre of the solar system was published in the
year of his death, 1543. It was called The Revohttions of the
Celestial Orbs, and its publication was undoubtedly a landmark
in scientific history. Yet we know that Copernicus began his
speculations on the subject thirty years before this, and that the
book had been practically completed by about 1530. Why, then,
was there a delay of thirteen years in the publication of the
book ? The story is very interesting and characteristic of the
times in which Copernicus lived.

We have already referred to the strong hold of the Church upon
the people of those days. Nothing could exceed the rigidity
of its outlook or the iron of its discipline in those days, and its
notion of the exalted place and functions of mankind in the
universe demanded unquestioned recognition that the home of
man, the earth, was fixed, immovable, and the centre of the
universe. There is little doubt that if Copernicus had been
anything but the retired, unobtrusive student and churchman,
that if he had shouted his views from the house-tops, and had,
as we sometimes put it nowadays, ' rushed into print,' his book
would have been seized and destroyed, his views condemned, his
teachings suppressed, and he himself punished. But Copernicus
did not seek fame, and only those with whom he came into

76 Copernicus

contact could gather, from direct conversation and discussion,
the trend of his thoughts and his views.

There was, however, another factor of importance which made
for delay in publication. Copernicus w^as himself a canon of the
Church, and he was, moreover, deeply religious. As a true man
of science he was above the narrow prejudices of his colleagues,
but nevertheless he was strongly influenced against publication
by his knowledge of the great offence it would give. His w^as too

modest and gentle a nature
easily to override such a
consideration, and it accord-
ing 1}^ took many years of
earnest persuasion on the
part of his friends and ad-
mirers before a reluctant
permission to publish was
drawn from him.

Justice to Copernicus de-
mands that we should point
out that there was in him
no element of fear in the
statement of his views. He
dedicated his work to the
ro])e, Paul III, in a preface
which concludes in the fol-
lowing terms :

' If there be some w^ho, tho'
ignorant of aU mathematics,
take upon them to judge of these, and dare to reprove this work,
because of some passage of Scripture, w^hich they have miserably
warped to their purpose, I regard them not, and even despise
their rash judgement. . . . What I have done in this matter,
I submit principally to your Holiness, and then to the judgement
of all learned mathematicians. And that I may not seem to
promise your Holiness more concerning the utility of this work
than I am able to perform, I pass now to the work itself.'

There is some irony, let us note in passing, in the fact that
this eulogy, which greatly pleased Pope Paul III, was succeeded

IiG. 29. TYCHO BRAHE

Fig. 30. TYCHO BRAKE, in 1587, with his astronomical instruments
See note on p. 15

78 Copernicus

eight years later by a similar eulogy to his successor, Pope Sextus,
in a preface to a Latin edition of Ptolemy's Almagest, and was
received by the latter with equal pleasure.

The manuscript was entrusted by Copernicus to his friend and
pupil, Rheticus, who took it to Nuremberg, where some years
before he had printed a treatise by Copernicus, Concerning the
Sides, and Angles of Triangles, Planes, and Spheres. Here the
book was printed, and a copy was sent to the illustrious author.
But while it was yet on its way, Copernicus, at the age of seventy
years, was smitten by a paralytic stroke which rapidly weakened
him. The book, the fruits of his life, arrived but a few hours
before his death, on the 23rd of May 1543.

We may fittingly conclude this brief note on his life and work
by a mention of the fact that in his early days Copernicus painted
his own picture — a half-length portrait. This picture was given
later to the famous astronomer and poet, Tycho Brahe, who
placed it in his museum at Uraniborg over an inscription of
which the following is a translation :

Phoebus no more his bounding Coursers drives
Sublime in Air ; the task to Earth he gives.
Amidst the world enthron'd he sits in State,
And bids the Heav'ns obey the Laws of Fate ;
Yet thro' all Nature is his Aid the same.
And changing Seasons still his Guidance claim.
Erratic Stars have now their Courses known.
By this rare System of the station'd Sun ;
They stand, go retrograde, are swift, or slow.
Just as the Earth directs them what to do.
The great Copernicus (the Man behold).
This heavy Orb in rapid Motion roll'd.
But why, you'll say, was not his Wit portray'd ?
But that is partly in the Heav'n display'd.
Partly in Earth ; for neither can confine
The boundless Searches of his daring Mind.
Again you'll say — But half his Figure 's shown,^
A Man so worthy to be wholly known.
True ; yet 'tis he who bore the earth entire
Thro' Space immense around the Solar Fire ;
The spacious Earth in vain would hold the Man
Who measures Heaven with his ample Span.

' Referring to the fact that the portrait was only half-length.

JOHANN KEPLER

I. Early Life

Kepler's chief claim to memory lies in his enunciation of the
laws of planetary motion. The record of this faithf al follower of
science is remarkable. The whole of his life is one long story
of domestic trouble, ill-health, and financial worry. Yet through
all he displayed a genius and an enthu-
siasm for mathematics and astronomy
which led him to the highest pinnacles
of scientific achievement. Kepler was
denied the joy of astronomical observa-
tion. In his youth a serious illness
had permanently injured his eyesight.
Telescopes and other instruments of
observation were for him ' forbidden
fruit ' . He conquered, but his victory
was won in the battlefield of geometry
and statistics with the aid of his cal-
culations, his drawing instruments, and
above all his wonderful perseverance in
the face of repeated failure.

Johann Kepler was born at Weil in
the Duchy of Wiirtemberg on the 21st of December 1571. His
father, though probably of good family, was idle and unreliable ;
his mother ignorant and of violent temper. Moreover, Johann
was a sickly child ; and an attack of small-pox, which nearly
killed him at the age of four, left him with an enfeebled con-
stitution.

He went to a local school at a very early age, but it was not
long before the first check to his studies appeared. It seems
that his father had become surety for a friend who proved to be
a defaulter. As a consequence he lost what little money he had
and was obliged to keep a tavern. So we see the sorry spectacle

Fig. 31.
JOHANN KEPLER

1

8o Johann Kepler

of a future professor of astronomy withdrawn from school
at the age of nine and employed as a pot-boy in his father's
inn. For three years this state of affairs continued, but
eventually, owing to the kindly intervention of friends, young
Johann Kepler was enabled to attend a monastic school at
Maulbronn. The ability which he displayed enabled him to be
passed on, at the age of seventeen, to the University of Tubingen,
where it was intended that he should prepare himself for the
Church. Fortunately for the world, he here came under the
influence of Michael Maestlin, then professor of mathematics at
the university, who soon detected Kepler's genius.

Maestlin was an outspoken convert to the Copemican doctrine
of the solar system, and in this doctrine Kepler may therefore be
said to have been brought up. Its simplicity made a powerful
appeal to his imagination, and he was its vigorous defender in
lecture and debate. All this helped to build up for him a con-
siderable reputation, so that when, in 1594, a professorship of
mathematics fell vacant at the University of Graz, in Styria,
it was immediately offered to Kepler, who accepted it with some
hesitation. From the point of view of pay and prestige,
astronomy was none too highly rated in the universities of those
days, and the professors were expected to devote more time to
the revelations of astrology than to . anything else. It was
because of this fact, and because of his bitter recollections of the
acute poverty of his childhood that Kepler was so diffident in
accepting the professorship, and he fully made up his mind that
when anything better offered itself he would accept it.

2. Kepler's Early Theories

In 1597, at the age of twenty-six, John Kepler wooed and
married a lady from Styria. It is not known whether he thought
that, with her ' dowry ' she might have eased his financial
position, for she had been twice married before. Be that as it
may, it proved none too happy a union. There were three
children of the marriage, and Kepler's financial cares were on
the whole considerably increased in consequence.

Early Theories 8i

At Graz, he busied himself with speculations as to the general
scheme of the solar system. There were at the time six known
planets — Mercury, Venus, Earth, Mars, Jupiter, and Saturn,
and Kepler knew that these were at successively greater distances
from the sun. Moreover he knew that the farther a planet was
from the sun, the slower seemed its motion. It was Kepler's
strong feeling that there was in all this some governing scheme.
The unravelling of this problem he made his life work. His-
final efforts were indeed crowned with brilliant success, but his
first theory, developed at Graz, was fantastic. He was a keen
student of geometry, but his mathematics, in those days of
astrology, were not unnaturally tinged with mysticism. Between
six planets there are five spaces, and for some reason or other
Kepler felt that this held the clue which he sought. The five
spaces led him to think of the five symmetrical solid figures —
the tetrahedron, the cube, the octahedron, the dodecahedron,
and the icosahedron, with four, six, eight, twelve, and twenty
faces respectively. Accordingly his scheme took the following
form. Beginning with a sphere to represent the earth's orbit,
he drew round it a dodecahedron, and round this another sphere
to represent the orbit of Mars ; about that a tetrahedron, and
around that a larger sphere for Jupiter ; about that a cube, and
round that a final sphere for the orbit of Saturn. Again, returning
to the sphere representing the earth's orbit, he drew within that
an icosahedron, and inside that another sphere for Venus ;
inside that an octahedron, and finally inside that a sphere for
the orbit of Mercury.

Kepler's delight is well worth recording. ' The intense pleasure
I have received from this discovery can never be told in words.
I regretted no more the time wasted ; I tired of no labour ; I
shunned no toil of reckoning, days and nights spent in calcula-
tion, until I could see whether my hypothesis would agree
with the orbits of Copernicus or whether my joy was to vanish
into air.'

Kepler published his theory (as to the absurdity of which it
will suffice for us to point out that we now know of eight large
planets and a host of planetoids) in 1596 in a book called

2613 F

§2 Johann Kepler

Mysterium Cosmographicum, and it brought him the enthusiastic
applause of a wondering world. Of more immediate importance
to Kepler, however, was a cordial invitation which he now
received from a man at Prague who was destined to affect his
whole future career. This man was the famous Tycho Brahe.

Tycho Brahe may justly be termed the pioneer of accurate
astronomical observation. He was a Dane of noble family,
and had created in 1576 with the co-operation of his King,
Frederick II, a wonderfully equipped observatory at Uraniborg
Castle, in the Island of Hven, near Elsinore. Here he laboured
for twenty years, accumulating the most complete records of
planetary observations thus far existing. Naturally his success
brought him enemies, and when Frederick died in 1596, his
successor was induced to withdraw his patronage from Tycho,
who accordingly retired to Prague, in Bohemia. Here, under
the patronage of Rudolph II (who, as befitting the times, valued
his services as an astrologer rather than an astronomer) he
continued his wonderful record of observations.

To Kepler, then, Tycho extended a cordial invitation to come
to Prague and test his fantastic theory with the observations in
Tycho's possession. Tycho was not a follower of Copernicus
but he nevertheless had sound advice to offer Kepler. ' Do not
build up abstract speculations concerning the system of the
world,' he advised, ' but rather first lay a solid foundation in
observations, and then by ascending from them, strive to come
at the causes of things.'

Kepler paid his visit, studied the records, and did not hesitate
to abandon his theory when he realized it was not consistent
with the accurate observations he knew himself to be handling.
But he had earned the respect of his host, and when his professor-
ship at Graz was rendered exceedingly uncomfortable owing
to a religious change in the regime of the University, Kepler
(who was a Protestant) gladly accepted in 1601 the offer of
a post as imperial mathematician to King Rudolph II, his duty
being to assist Tycho Brahe. This was a wonderful combination
of talents. Tycho was a splendid observer, but a poor mathe-
matician, Kepler was a splendid mathematician but a poor

Early Theories 83

observer ; both had unbounded enthusiasm for their work and
admiration for each other. What might they not have achieved
together had the alHance continued! But it was not to be.
Tycho had never recovered from the disappointment of his
dismissal from Uraniborg, and he died soon after Kepler joined
him.

3. Kepler as Physicist and Geometer

All this time, Kepler was in continuous financial straits, and
periodically he was seized with illness. Tycho's generosity had
tided him over his troubles, but at his colleague's death they
broke out afresh. Bohemia was in a sorry state at that time ;
misgovernment and wars had brought the national exchequer
to a low state and Kepler's salary was more often promised than
paid. Yet he stuck to his post. A solemn duty had been
entrusted to him by Tycho on his deathbed. Tycho, engrossed
in the preparation of an elaborate set of planetary tables, had
charged Kepler to complete them, and they were to be known
as the Rudolphine Tables, in honour of his patron. They
entailed enormous work and considerable expense. The latter
consideration involved such delay that Kepler perforce had time
to devote to other matters.

In 1604, he published a work called Paralipomena in Vitel-
lionem} in which the question of refraction came up in connexion
with the theory of lenses. The telescope had but recently been
invented, and Kepler clearly saw the necessity for such investiga-
tions. He tried to work out a relation between the angle of
incidence and the angle of refraction. All schoolboys know of
Snell's Law, which says that the ratio of the sine of the angle
of incidence to the sine of the angle of refraction is a constant
for any given pair of media. For glass, for example, this ratio,
known as the refraction index, comes out somewhere about 1-5.
Kepler did not discover this law, though there is no doubt but
that his work inspired Snell to take up the subject so successfully.
He did, however, discover a useful approximation to it. In the

^ Vitello was a thirteenth-century Polish philosopher who commented
on Alhazen and studied the subject of refraction.

F 2

84 Johann Kepler

case of glass, when the angle of incidence is small, he found the
ratio of the angle of incidence to the angle of refraction is almost
always about 1-5. Thus in the figure (Fig. 32) the
angle of incidence, measured in radians, is the ratio
arc Ip

10
perpendicular

Fig. 32. Show-
ing Kepler's
approximate
Law of Refrac-
tion for Glass.

by Ptolemy.

whereas the sine of this angle is the ratio
IP

j^ , and it is at once evident that

provided the angle i is small, there will be little
difference between the arc Ip and the perpendicular
IP. Similarly, of course, for the angle of refrac-
tion r. The approximate truth of Kepler's rule is
therefore established. For the purpose which Kepler
had in view, namely the application of the subject
to the case of the telescope, the rule as he stated
it sufficed, for (as shown in Fig. 33) an object P
viewed through such an instrument will necessarily
involve only a small angle of incidence.

Kepler also studied atmospheric refraction, and

greatly improved on the treatment of this subject

He worked out an approximate formula to allow

for this error for all angles from 0° to 90^

4^P^

Fig. 33.

Illustrating the application of Kepler's Rule of
Refraction to the Telescope.

It is convenient at this stage to do homage to Kepler's great
influence on his contemporaries in the realms of mathematics,
and particularly in geometry. This branch of mathematics had
suffered some neglect at the expense of a great advance in
algebra, the theory of equations, and trigonometry. The seven-
teenth-century revival in geometry was largely due to the influence
of Kepler. In chapter 4 of his Paralipomena, for example, he
introduced to the world of mathematics for the first time what
has been called the principle of continuity.

Physicist and Geometer 85

As an instance of this, he regarded the circle as a special case
of the ellipse. For, keeping the major axis AA' (Fig. 34 (a)) of
constant length, suppose we construct a series of ellipses with
the two foci SS' (Kepler was the originator of the term ' focus ')
successively closer together, we find that the minor axis becomes
longer and longer, making the ellipse resemble the circle more
and more closely, until we reach the limiting case in which the
foci coincide with the centre, when the curve becomes a circle.

We have another example when we regard the parabola as
continuous with the ellipse. This is seen by keeping A and S
(Fig. 34 («)) fixed, and gradually moving the other focus S'
and the extremity A' farther and farther to the right. In the
limit, when S' is at an infinite distance to the right, the curve
becomes a parabola.

■^^'

Fig. 34. Kepler's Principle of Continuity,
case of the ellipse.

The circle as a special

In 1615 Kepler published a book called Stereometria. He
was led to some investigations on the volumes and areas of
certain solid forms through noticing by accident the blunders
made by an ignorant ganger in measuring his wine casks. Kepler
submitted a large number of solids for the solution of geome-
tricians, only solving a few himself. It speaks much for his
influence, however, that these suggestions were at once taken
up by others. Kepler, in his own solutions, introduced the idea
of infinitesimals as an application of the law of continuity.
This was reaUy a simple extension of the method of limits in
vogue as far back as the days of Euclid and Archimedes, but
it had far-reaching consequences later, for it paved the way to
the invention of the calculus by Newton and Leibnitz. By way
of illustration of Kepler's introduction of the term ' infinitely
small quantity ', a single case will suffice. He regarded a circle

86 Johann Kepler

as being made up of an infinite number of triangles all with
vertices at the centre 0 (Fig. 35) and with infinitely small bases
on the circumference. The sum of the areas of the infinitely
small triangles gives the total area of the circle, whilst the sum
of the lengths of the infinitely small bases gives the length of
the circumference.

4. Kepler's Later Life

Meanwhile Kepler's financial worries and domestic miseries
were continual. His salary was always in arrears, and it was
with difficulty that he could make both ends meet. His wife

was suffering from long fits of
despondency, and finally, in 1612,
a series of misfortunes produced a
crisis in his affairs. His patron.
King Rudolph, died, and his salary
now ceased. But worse was to come.
Within a very short time, all his
children fell ill, and small-pox
carried off one of them. A few days
later his wife also died. Yet when
his fortune seemed at its lowest
ebb, he was offered a professor-
ship at the University of Linz, and
without hesitation he accepted it,
and off to Linz he went with his two remaining children, leaving
due to him a sum of 8,000 crowns in respect of arrears of
salar^^

There was little money in a professorship, and at Linz he had
to supplement his income somehow. So he published a sort of
Old Moore's Almanac, and told people's fortunes, and generally
practised the arts of the astrologer in a way which in these
days would have earned for him a prosecution, at any rate in
England.

Having settled in Linz, Kepler did a somewhat bold thing in
view of his unhappy experience of married life. He deliberately

Fig. 35. Showing application
of Infinitesimals to the area of
a Circle.

Later Life 87

looked round him for a second wife, and he set about it very
thoroughly and scientifically. There were, it seems, no less than
eleven candidates for the privilege, and Kepler, statistician to
his finger-tips, carefully set forth his estimate of the merits and
demerits of each ! That he was honest in all this, and free from
any mercenary motives, is evidenced by the fact that he chose
the poorest of them all — an orphan girl without dowry. Appar-
ently it turned out a much more satisfactory marriage than his
first one, though judging from the fact that his wife bore him
seven children, his continuously scanty resources must have been
taxed to the uttermost in his efforts to pay his way. Always
something seemed to turn up to increase his difficulties. Thus,
about this time, news reached him that his bad-tempered old
mother had managed to get herself accused of sorcery at her
home in Wiirtemberg. She was found guilty and was con-
demned to imprisonment and torture. Kepler hurried off to
Wiirtemberg to intercede on her behalf, and although he failed
to obtain her release, he at least saved her from torture. It
took him another twelve months, however, before he could get
her released from prison. She died shortly after, bellicose to
the last.

At the same time Kepler was applying his mind to the pro-
blems of the solar system, and one by one, at long intervals,
he gave to the world his three wonderful laws of planetary
motion (see p. 89).

Nor did Kepler forget his promise to Tycho Brahe to complete
the Rudolphine Tables of planetary motions. Year after year
he worked at these, all the time puzzling as to how to raise the
necessary funds for their publication. Time and again he
applied to the court for assistance, but always without result.
Yet strange to say, with all his poverty, with all his yearnings
for the wherewithal to discharge his debt of gratitude to his
dead friend and benefactor, when an opportunity did arise for
him to take up a lucrative and honourable position, he refused
because it entailed his leaving his own country to go to England.
In 1620 Sir Henry Wotton, English Ambassador to Venice,
a man of very wide culture and interests and a poet of no mean

88 Johann Kepler

merit, invited Kepler to come to England, guaranteeing him
a good post and an enthusiastic reception. But the prospect
of life in a foreign country among a strange people appears tc
have been too much for him ; and this refusal came in spite of
the fact that he had but recently incurred the violent dis-
pleasure of the Church for publishing a work on the Coper-
nican System — a book which having been promptly banned, did
not even yield him the sorely needed financial benefits from
its sales.

Yet Kepler never abandoned his determination to publish his
Rudolphine Tables, and at last, tired of further waiting, he
determined to find the money himself. How he succeeded
remains a mystery. It has been asserted that he had accumu-
lated a secret hoard of money, the fruits of years of fortune-
telling as an astrologer ; but it is difficult to believe that he
deliberately and unnecessarily subjected his wife and children
to years of miserable poverty in the accumulation of such
a hoard. Be that as it may, however, the Rudolphine Tables
were published, and published handsomely too, in 1627. They
were of the utmost importance. Their accuracy rendered them
indispensable to the navigators of the seventeenth century, by
whom they were used for practically the same purpose as is
served to-day by the Nautical Almanac. Even had he produced
nothing beyond this Kepler would deserve our lasting remem-
brance.

But the publication of the Tables left Kepler a broken man. The
long strain of ill-health, poverty, worry, and constant study began
to have its effect, and at last, in November 1630, in his sixtieth
year, whilst on his return from a fruitless mission to Prague for
the purpose of recovering the money so long due to him, he
caught a chill and died. He was buried in St. Peter's Church at
Ratisbon, and it is no credit to the country of his birth that so
little was done to perpetuate his memory. ' A century ago
a proposal was made to erect a marble monument to his memory,
but nothing was done. It matters little one way or the other
whether Germany, having almost refused him bread during his
life, should, a century and a half after his death, offer him

Later Life 89

a stone.* ^ It matters little indeed. Kepler's true monument
is not of stone. It stands in those brilliant laws of planetary
motion which gave to the world for the first time a complete
view of the cosmic scheme as far as it concerns the solar system
of which our earthly home forms so integral a part.

5. Keple/s Laws of Planetary Motions

We will conclude our study of Johann Kepler by a consideration
of his three laws of planetary motions. He had always felt
that there was some profound law which controlled the motions
of the planets round the sun. * There were three things ', he
wrote, while still at Linz, * of which I pertinaciously sought the
causes why they are not other than they are : the number, the
size, and the motion of the orbits.' He fully realized the funda-
mental importance of his self-imposed task, and in his book.
Treatise on the Motions of the Planet Mars, he took care to
' wan. off ' the anti-Copernicans : ' If any one be too dull to
comprehend the science of astronomy, or too foolish to believe
in Copernicus without prejudice to his piety, my advice to him
is, that he should quit the astronomical school, and condemning,
if he will, any or all the theories of philosophers, look to his own
affairs, and leaving this worldly travail, go home and plough
his fields.'

Kepler's materials were the invaluable records of Tycho
Brahe's observations, and his own knowledge of geometry.
His was essentially the method of trial and error. Every con-
ceivable relationship between distance, the rate of motion, and
the path of the planets he tested in the light of Brahe's results,
only to reject them one after the other. Through all he saw one
ray of hope. ' I was comforted,' writes he, ' and my hopes of
success were supported, as well by other reasons which will
presently follow, as by observing that the motions in every case
seemed to be connected with the distances, and that when there

^ Sir O. Lodge, Pioneers of Science, London, 1893. It is fair to note
that the Germans have since made partial amends in the issue of a complete
edition of Kepler's works, Joannis Kepleri Astronomi Opera Omnia,
Dr. Ch. Frisch, Frankfurt, 1883, 9 vols.

Fig. 36. Kepler's test of a cir-

dth the sun not at

90 Johann Kepler

was a great gap between the orbits, there was the same between
the motions.' Like Copernicus, Kepler followed in particular the
movements of the planet Mars, these being sufficiently rapid to
provide adequate data for testing purposes. What was the
correct orbit of Mars ? He soon convinced himself that if it

were a circle, then at any rate
the sun could not be at its centre.
After much labour he got a step
farther. He noticed that when
the planet's distance from the
sun diminished, the planet went
faster, and w^hen the distance
increased, it went slower, and
this brought him to the idea that
the planet must sweep out equal
areas in equal intervals of time.
Suppose, therefore, that he were
to represent the orbit by a circle,
with the sun not at the centre
(Fig. 36), would the planet under
such conditions sweep out equal
areas in equal times ? He tested
it for innumerable positions of
the sun, but it never quite fitted.
He next tried an oval orbit, but
this, too, never quite fitted the
facts. At last, however, he hit
upon the right solution. Why not
try an ellipse ? He tested it with Brahe's observations, and it
fitted beautifully. At last the long-sought secret was his. The
path of the planet is that of an ellipse with the sun at one focus, and
the variations in speed are such that in equal times the planet sweeps
out equal areas. A reference to Fig. 37 will at once show the
idea. 5, representing the sun, is at the focus of an ellipse
ABCD &c. This ellipse represents the orbit of any planet.
Then obviously the distance of the planet will be a minimum
at A and a maximum at F, and observation shows that the

cular orbit
the centre

Fig. 37. Illustrating Kepler's
First Two Laws of Planetary
Motion.

Laws of Planetary Motions 91

speed of motion is, on the contrary, a maximum at A and
a minimum at F, so that, ii A, B, C, D, E, &c., be the positions
of the planet at equal intervals of time, and we join these points
to S, then the areas swept through by the planet will be respec-
tively ABS, BCS, CDS, DES, and EFS, and these areas are found
to be exactly equal.

Kepler was fully entitled to his triumph, but his work was
not yet complete. He had yet to unravel the relationship which
he felt existed between the distances of the different planets
and their average speeds round the sun. Why he felt such
a relationship to exist we can hardly say, but he had a feeling
that simple mathematical laws were traceable in all natural
phenomena. He had little to go upon. It was part of his genius
that he felt intuitively that not only was there such a relation-
ship, but also that he would find it out sooner or later. And
find it out he did, though later rather than sooner. Let him
speak for himself :

' WHiat I prophesied two-and-twenty years ago, when I dis-
covered the five solids among the heavenly orbits (see p. 8i) — •
what I firmly believed long before I had seen Ptolemy's " Har-
monies " — what I had promised my friends in the title of this
book, which I named before I was sure of my discovery— what
sixteen years ago, I urged as a thing to be sought — that for which
I joined with Tycho Brahe, for which I settled in Prague, and
for which I have devoted the best part of my life to astronomical
contemplations, this at length I have brought to light. It is not
eighteen months since the first glimpse of light reached me,
three months since the dawn, very few days since the unveiled
sun, most admirable to gaze upon, burst out upon me. Nothing
holds me ; I wiU indulge in my sacred fury ; I will triumph over
mankind by the honest confession that I have stolen the golden
vases of the Egyptians to build up a tabernacle for my God, far
away from the confines of Egypt. If you forgive me, I rejoice ;
if you are angry, I can bear it ; the die is cast ; the book is
written ; to be read either now or by posterity, I care not which ;
it may well wait a century for a reader, as God has waited 6,000
years for an observer. . . .

' If you would know the precise moment, the idea first came
across me on the 8th of March of this year, 1618 ; but, chancing
to make a mistake in the calculation, I then rejected it as false.
I returned to it again with new force on the 15th of May ; and

92 Johann Kepler

it has dissipated the darkness of my mind, by such an agreement
between this idea and my seventeen years' Labour on Brake s
Observations, that at first I thought I must be dreaming, and had
taken my result for granted in my first assumptions. But the
fact is certain, that the proportion existing between the periodic
times of any two planets is exactly the sesquiplicate proportion of the
mean distances of the orbits.'

And now let us put this into simple language. Kepler's
discovery was this : that for all planets, the squares of the times
of revolution round the sun are as the cubes of the mean distances.
Let us try it, for example, in the case of Mars.

The data are as follows, taking the Earth's distance as one
unit, and the Earth's year (i. e. time of one comiplete revolution)
also as unity :

Earth's Distance from Sun . . i-ooo units

Mars' „ „ „ . . 1-5237 >>

Earth's Period of Revolution . . i-ooo years

Required, the period of revolution for Mars. We have by
Kepler's Third Law

(Mars' Period)2 (Earth's Period)2

Hence

(Mars' Distance)^ (Earth's Distance)*
(Mars' Period )2 12

(1-5237)3 i3

Mars' Period of Revolution = ^1-5237*

= I -8808 years,
which is true.

And so with all planets.

This then was Kepler's life work, and no more fitting tribute
to his memory could be given than to conclude this chapter with
a restatement of his laws :

Law I. All the planets move round the sun with elliptic orbits

with the sun at one focus.
Law 2. The radius vector, or line joining the planet to the

sun, sweeps out equal areas in equal intervals of time.
Law 3. For all planets, the square of the time of one complete
revolution (or year) is proportional to the cube of the
mean distance from the sun.

VI

WILLIAM GILBERT, FATHER OF
MAGNETIC PHILOSOPHY

I. The Founding of Experimental Science

In the sixteenth century two names stand out clearlj^ in the
initiation of a revolution in scientific method. They are Wilham
Gilbert of Colchester, the father
of the magnetic philosophy,
and Galileo Galilei of Pisa, the
founder of modern physics.
With these two we must now
concern ourselves.

To the average schoolboy of
to-day, with his organized
scheme of studies, an integral
part of which is concerned with
experimental work in properly
equipped laboratories, the con-
ditions under which the six-
teenth - century student of
natural philosophy studied his
subject must indeed seem
strange. The text-books were
almost entirely inferior translations of Aristotle ; the lectures
were frankly Aristotelian ; the experiments performed were nil.
Such a thing as a laboratory was unheard of. When a problem
came up for solution, the treatment was simple. What did
Aristotle say about it ? The point was looked up in the text-
book, and whatever the Greek Philosopher said was accepted
with absolute finality. Against the centuries-old judgement
of Aristotle, not only was there no appeal, but there was
no thought of appeal. If, for example, the question is asked,
' Which falls to the ground the quicker from the same height,
a heavier body, or a lighter one ? ' the natural answer to-day

Fig. 38. WILLIAM GILBERT

94

William Gilbert

is, ' Let us drop them and see '. In those days such an answer
was unthinkable. Instead they would say, ' Let us see what
the ancient philosophers said'. The position was even worse
than this, as we shall see in the next chapter, when we deal
with Galileo. For if such a scientific revolutionary were to
suggest, ' Well, let us drop them, if only to verify what these

Fig. 39. Gilbert's figure of a smith at his anvil
See note on p. 15

men said ', he was branded as a heretic. The very suggestion
implied a wicked doubt as to the wisdom of the ancients.
Obviously, only by rude shocks could such a stumbling-block to
scientific progress be swept away.

The name of William Gilbert, the first eminent man of science
in England since Roger Bacon, must fittingly go down in scientific
history on account of his brave stand for verification by experi-
ment. He did not hesitate to trounce his opponents in outspoken
terms. Referring to his reasons for delay in the publication of his
results, he writes in the preface to his De Magnete :

The Founding of Experimental Science 95

' Why should I submit this noble science and this new philoso-
phy to the judgement of men who have taken oath to follow the
opinions of others, to the most senseless corrupters of the arts,
to lettered clowns, grammatists, sophists, spouters, and the
wrong headed rabble, to be denounced, torn to tatters, and heaped
with contumely ! To you alone, true philosophers, ingenuous
minds, who not only in books but in things themselves look for
knowledge, have I dedicated these foundations of magnetic
science — a new style of philosophizing.'

And again later :

' To the early fathers of philosophy let due honour be paid,
for by them wisdom has been handed down to posterity. But
our age has detected and brought to light many facts which they,
were they alive, would gladly have accepted. Therefore have
I not hesitated to expound by demonstration and theory those
things which I have discovered by long experience.'

2. Biographical Details

William Gilbert (he himself wrote it Gilberd) was born at
Colchester in 1544. He was the son of Jerome Gilberd, a man
whose family had resided for centuries in Suffolk, but who had
migrated to Colchester. Jerome was greatly respected by his
fellow townsfolk, and in 1553 he became a free burgess of the
town. Later he rose to be the Recorder of Colchester. He had
four or five sons, of whom, curiously enough, two were called
William. The one with whom we are here concerned was, how-
ever, the elder of these. Gilbert became a student at St. John's
College, Cambridge, at the age of eighteen years, and probably
began his academic career by studying mathematics. He took
his degree of B.A. in 1560, became a fellow of his college in
1561, and proceeded to his M.A. in 1564, afterwards becoming
a mathematical examiner. But evidently he had now seriously
turned his attention to medical science, for in 1569 he graduated
as M.D. and on the 21st of December of the same year he was
made a senior fellow.

Gilbert now left Cambridge, and as was the custom of educated
men of his day he travelled on the Continent, especially with
a view of visiting Italy, the intellectual centre of the world in

96 William Gilbert

the sixteenth century. He returned to England in 1573, and
settled down to the practice of medicine in London. In this he
was very successful, quickly establishing himself as a prac-
titioner of repute. He was elected a Fellow of the Royal College
of Physicians in 1573, and later to the position of Treasurer to the
College. He had for some time held the appointment of physician-
in-ordinary to Queen Elizabeth, and in order the better to
combine his duties in this office with those of his private practice,
he took a house on St. Peter's Hill, near St. Paul's Cathedral.
This house became the rendezvous of a Society or College of
philosophers, probably the first of its kind in Europe, and
certainly the first in this country. There is no doubt, too, that
here was the scene of most of his famous experiments and
researches, at first in chemistry, but later in electrical and
magnetic phenomena. His reputation grew prodigiously, both
as a physician and as an experimentalist, and may be said to
have reached its highest point in 1600. This year saw him
elected President of the Royal College of Physicians, it saw the
publication of his epoch-making book, and finally, it was in the
same year that he received the appointment of Chief Physician
to the Court of Queen Elizabeth.

As a consequence Dr. Gilbert gave up his house on St. Peter's
Hill, and joined the Court about February 1600. The publication
of De Magnate had a mixed reception. Offending, as the preface
naturally did, very many of his scientific contemporaries, there
were nevertheless those who were greatly impressed by its
contents. In his Magneticall Advertisements, 1616, William
Barlowe speaks of a letter he received from Gilbert which
reads,

* There is heere a wise learned man, a secretary of Venice, he
came sent by the State, and was honourably received by Her
Majesty. He brought me a Lattin letter from a gentleman of
Venice that is very well learned, whose name is Johnnes Franciscus
Sagredus ; he is a great magneticall man, and writeth that hee
hath conferred with divers learned men of Venice, and with
the readers of Padua, and reporteth wonderful liking of my
booke/

Biographical Details 97

The great Galileo was certainly emphatic in his praise, ' I ex-
tremely admire and envy the author of De Magnete,' wrote he,
' I think him worthy of the greatest praise for the many new
and true observations which he has made, to the disgrace of so
many vain and fabling authors, who wrote not from their own
knowledge only, but repeat everything they hear from the
foolish and vulgar, without attempting to satisfy themselves
of the same by experience.'

Queen Elizabeth died in ]\Iarch 1603, but her successor,
James I, retained William Gilbert in his office of Chief Physician
to the Royal Court. But his service under his royal master
was of very short duration, for Dr. Gilbert died on the 30th of
November, of the same year. His death probably occurred in
the town of his birth, Colchester. He bequeathed his books,
instruments, loadstones and other minerals to the College of
Physicians, which was then housed at Amen Corner. Unfor-
tunately all were destroyed in the Great Fire of 1666.

In his Worthies of England, 1662, that delightfully semi-
conscious humorist Thomas Fuller writes thus of Gilbert:

He had the clearness of Venice glass without the hrittleness
thereof ; soon ripe and long lasting in his perfections. He com-
menced doctor in physick, and was physician to Queen Elizabeth,
who stamped on him many marks of her favour, besides an
annual pension to encourage his studies. He addicted himself
to chemistry, attaining great exactness therein. One saith of
him that he was stoicall, but not cynicall, which I understand
reserv'd but not morose ; never married, purposely to be more
beneficial to his brethren, such his loyalty to the queen, that,
as if unwilling to survive, he dyed in the same year with her 1603.
His stature was tall, complexion cheerful, an happiness not
ordinary in so hard a student and retired person. He lyeth
buried in Trinity Church, in Colchester, under a plain monument.
Mahomet's tomb at Mecha is said strangely to hang up, attracted
by some invisible loadestone ; but the memory of this doctor
will never fall to the ground, which his incomparable book, De
Magnete, will support to eternity.'

2613

98

3- De Magnate

The complete title of Gilbert's treatise, published in London in
1600, was ' De magnete magneticisque corporibus, et de magno
magnete tellure ; Physiologia nova '. ('Of the magnet and mag-
netic bodies, and of that great magnet the earth ; a new physio-
logy.') Quite apart from the fact that this book threw a flood
of light upon a hitherto little-known subject, it insisted with
much-needed emphasis on the urgent necessity for an experi-
mental basis to scientific inquiry. If for no other reason, this
plea, backed by the example of his own experiments, entitles
Gilbert to a permanent place in the history of science. When
an argument or a statement is verifiable by experiment, then,
Gilbert holds, its truth must stand or fall by the result of the
experiment, performed not once alone, but many times over, to
eliminate chance errors, and to be the more convincing.

For example, Giovanni Battista Porta, an Italian philosopher,
had taught that iron rubbed with diamond behaves in exactly the
same way as if it had been rubbed with loadstone. That is to
say, it would be endowed temporarily with the property we
speak of to day as ' polarity ', so that when suspended freely it
would come to rest pointing to ' magnetic ' north and south.
Gilbert administers his chastisement to Porta in the following
terms :

' We made the experiment ourselves with seventy- five diamonds
in presence of many witnesses, employing a number of iron bars
and pieces of wire, manipulating them with the greatest care
while they floated in water, supported by corks ; but never was
it granted me to see the effect mentioned by Porta.'

Gilbert's doctrine of the experimental method of investigation
may weU be expressed in his own words :

' In the discovery of secrets and in the investigation of the
hidden causes of things, clear proofs are afforded by trustworthy
experiments rather than by probable guesses and opinions of
ordinary professors and philosophers. In order, therefore, that
the noble substance of that great magnet, the earth, hitherto
quite unknown, and the exalted powers of this globe of ours may

De Magnete 99

be better understood I shall first of all deal with common magnets,
stones, and iron materials, and with magnetic bodies, and with
the near parts of the earth, which we can reach with our hands
and perceive with our senses. After that I shall proceed to show
my new magnetic experiments, and so I shall penetrate for the
first time into the innermost parts of the earth. . . .

' Whoever wishes to try the same experiments, let him handle
the substance, not carelessly, but prudently and deftly, and in
the proper way, and when the thing does not succeed let him
not in ignorance denounce my discoveries, for nothing has been
set down in these books which has not been many times performed
and repeated.'

Some slight knowledge of magnetism and frictional electricity
certainly dates back to the time of Thales of Miletus.^ Thales
probably knew something of it from the fact that amber (the
Greek word for which, elektron, has given us our word ' electricity ' ),
when rubbed, attracts such things as small pieces of paper. He
also knew of the magnetic properties of ' lodestone ' . But he
considered that both were possessed of ' soul ' . This was typical
of the ideas held by many of his successors all through the
Middle Ages. The phenomena of magnetism were mingled
in men's minds with the fancies of magic to an almost hopeless
degree.

' The lodestone was accused of producing melancholy, of
making love philtres, of losing its power when rubbed with garlic,
and regaining it when smeared with goat's blood, of declining to
attract iron in presence of diamond.'

One by one Gilbert took all such statements and by the rigid
test of experiment he proved each to be so much nonsense. But
his work was by no means confined to the mere refutation of
other people's statements. Take the case of frictional electricity
as an example. His extensive tests showed that amber was not
the only substance which when rubbed would attract ver^^ light
objects. Using a carefully pivoted light needle as his attracted
object, he held up in succession various substances which had
been rubbed. Some immediately attracted the needle, such as
glass, jet, sulphur, sealing-wax, resin, diamond, sapphire, opal,

* See p. 21, ch. i.
G 2

100 William Gilbert

and amethyst. To these he gave the name of 'Electrics'.
Others, such as marble, ebony, ivory, flint, pearl, coral, and the
metals, he termed ' non-electrics ' . This classification was, as
we now know, incorrect ; but Gilbert did not know of the
properties of electrical conductivity and insulation, or he
would have realized that what he termed a non-electric could
in fact be electrified by rubbing, provided it were properly
insulated.

In the realms of magnetism Gilbert's achievements were of the
highest importance. Indeed, apart from his pioneer work as an
exponent of experimental methods, he will always be remembered
as the first to realize that the earth is itself a magnet. We know

^ZZZZZZZZ2

Fig. 40. Showing Non-mag- Fig. 41. Showing

netized Needle. Magnetic Dip.

that in Europe the mariner's compass, originally a piece of load-
stone floated by means of corks in a vessel of water so as always
to point nearly north and south, was used by Peter Peregrinus
as early as 1269. But no one knew why a compass always pointed
in one direction. Again, the phenomenon known as ' dip ' had
been recently discovered by George Hartmann of Nuremberg
(1489-1564) . If a needle be suspended about its centre of gravity,
so as to be able to rotate freely about a horizontal axis, then it
should be able to come to rest in a horizontal position (Fig. 40).
But if the needle is magnetized, we find that, when made to
rotate in the plane of the magnetic meridian (that is to say, in
the plane which includes the ' magnetic ' north and south poles),
it never comes to rest in a horizontal position, but instead the
north pole of the magnet ' dips ' downwards, the angle its axis
makes with the horizontal being called the ' angle of dip ' (Fig. 41).
An instrument for detecting and measuring this is known as

De Magnete loi

a ' dip-circle ' , and the first account of such an instrument was
given by Robert Norman, a compass-maker, in his book, the
Newe Attractive, printed in London in 1581. It was known,
moreover, that the angle of dip differed from place to place, and
in the region of the equator it was zero.

The explanation of these phenomena was given by Gilbert,
who said that the earth is itself a big magnet. He had asked
himself whether it were possible for a magnet to be of spherical
shape, and he fashioned one of iron and magnetized it by rubbing
it with loadstone. Not only did he find that it behaved like
a magnet, possessing its magnetic poles, but also that, on bringing
up to it a carefully-suspended small mag-
netic needle : (i) the needle always came to
rest with one of its poles pointing directly
to the opposite pole of his * terrella ' (as he
called his spherical magnet), and (2) the
suspended magnet came to rest at various
angles of ' dip ' with respect to the terrella,
varying from ninety degrees at the poles
to zero dip at points midway between the
poles (Fig. 42). Gradually the full signi-
ficance of this came to Gilbert's mind.
The earth itself is a giant magnet, with magnetic poles in
the region of the geographical north and south poles, and
from this fact all the commonly observed phenomena of com-
pass-property and dip were at once explicable. Since like
poles repel each other, and unlike poles attract, a suspended
magnet will obviously come to rest with its north-seeking pole
pointing to the earth's magnetic north pole. Gilbert insisted on
the proper use of the terms ' north-seeking ' and ' south-seeking '
poles, rather than ' north ' and ' south ' poles, rightly realizing
that since unlike poles attract, then if we speak of the earth's
' north ' magnetic pole, the end of a magnet facing it must
necessarily be the opposite ' south ' pole, unless the term ' north-
seeking ' be introduced.

So, by the logic of experiment, all the myth and magic which
the mystery-loving philosophers had called in to explain why the

Fig. 42. One of Gil-
bert's Terrellae.
See note on p. 16.

102 William Gilbert

needle points north were swept away. Speaking of this, Gilbert
remarks in his book :

' The common herd of philosophers, in search of the causes of
magnetic movements, called in causes remote and far away.
Martinus Cortesius . . .dreamt of an attractive magnetic point
beyond the heavens, acting on iron. Petrus Peregrinus holds
that direction has its rise at the celestial poles. Cardan was of
the opinion that the rotation of iron is caused by the star in the
tail of the Ursa Major. The Frenchman Bossard thinks that
the magnetic needle turns to the pole of the zodiac. ... So has
ever been the wont of mankind : homely things are vile ; things
from abroad and things afar are dear to them and the object of
longing.'

In spite of its value, Gilbert's De Magnete suffered neglect
after his death. The reason is perhaps that with all the care and
accuracy of his experiments, he strained the applications of his
theory of terrestrial magnetism. He was a strong supporter of
the Copernican system, and in his anxiety to assist this with his
own arguments, he ' overdid ' it. Thus, for example, he tried to
prove that magnetism was the actual cause of the earth's rotation
on its axis. Such assertions as these considerably damaged his
reputation after his death, so that there was no reprint of De
Magnete, after that of 1638, for more than two hundred and fifty
years ; and for all this time the memory of this true pioneer of
science lay neglected.^ In 1889 a ' Gilbert Club ' was formed in
London for the purpose of celebrating the tercentenary publica-
tion of De Magnete, and the work was retranslated and pub-
lished, whilst in recent years the late Sylvanus P. Thompson has
made an exhaustive study of his writings.

^ It is interesting to note that Descartes in his Regulae (probably written
in the winter of 1628-9) refers two or three times with obvious admiration
to Gilbert's work on the magnet. The Regulae was unfinished, and was
first published in a Flemish translation in 16S4, and in Latin in 1701 in
Opusciila Posthuma.

VII

GALILEO GALILEI, FOUNDER OF
EXPERIMENTAL SCIENCE

I. Early Life

Galileo Galilei was born at Pisa, in the province of Tuscany
in Italy, on the i8th of February 1564. His father, Mncenzo
Galilei, was an impoverished
Florentine nobleman of much
culture, high ideals, and breadth
of mind. He was a poor man,
and he was naturally anxious
that his son should adopt some
definitely lucrative career. He
saw his little Galileo exhibiting
marvellous ingenuity in making
toy contrivances, and he was
much troubled by the thought
that his son might wish to
take up a scientific career.
Vincenzo knew how hard it
was to make a living in such
a career, and he determined ' ^

that if he could divert Galileo's mind from any such tendencies
he would do so. Accordingly he decided to make of his son a cloth-
dealer. Luckily fate was against him. Galileo went to a convent
school, and whatever he did, he did well. His father gave up the
unequal struggle. The idea of making a merchant of such a boy
was preposterous. A university career was inevitable ; but at least,
if he must take up a profession, then it should be as lucrative as
possible. All this pointed to the medical profession, so to the
University of Pisa went Galileo, at the age of seventeen years,
to study for his medical degree.

However, fate would not be denied. Mechanical skill was there,
and mathematical genius was there. Galileo knew no mathe-

GALILEO

I04 Galileo Galilei

matics, but his genius could not be suppressed. Thus during
a service in the Cathedral at Pisa, his attention was diverted from
his devotions by the swinging of a chandelier above him. Its
regularity of movement set him thinking. Galileo timed its
swings. He had no watch — such things had not yet been in-
vented— so he felt his own pulse and used that as his time-
index. What particularly interested him was the fact that,
although the oscillations were dying down,

\^ the time of swing yet remained unchanged.
^^ This fact is now universally recognized as
'^ what is known as the principle of isochron-
■H\ ism in pendulums, and is applied in the
working of the modem clock. But Gali-
leo's interest in it at the time was purely
medical. He experimented at home with
a metal ball suspended by a string of vary-
ing length, and found that the time of
swing changed with the length — it was
faster for shorter lengths and slower for
longer. The outcome was his invention
of the ' pulsilogium ' — an instrument for
recording the pulse-rate of a patient
(Fig. 44). It was a simple enough con-
trivance. By rotating an index or pointer,
a simple pendulum was wound up or un-
wound until its time of swing] ust coincided
with the pulse-rate of the patient. The
scale over which the pointer moved was graduated to give a direct
reading of the number of beats per minute. One day Galileo, while
calling on a friend of the family, one Ottilio Ricci, a mathematical
tutor to the Court of Tuscany, accidentally heard through an open
door a lesson in Euclid being given to some pages. That chance
lesson decided Galileo's fate. He begged his friend to give him
some lessons, and soon he was deeply engrossed in his new-
found joy ; for joy it was to him. It was not long before he had
mastered Euclid's first six books. Nor was it long before the
elder Galileo saw how things were going, and the career of
medicine was finally abandoned.

Fig. 44. Galileo's
Pulsilogium.

Early Life 105

Galileo now gave himself up whole heartedly to a study of
mathematics and physics. Among other things, he became a
close student of Archimedes, and he wrote a thesis on the * hydro-
static balance ' , suggesting improvements on the Syracusan
philosopher's original design. This brought Galileo to the notice
of Guido Ubaldi, at that time the premier mathematician of
Italy, and through him to Ferdinand dei Medici, grand duke of
Tuscany. It was the patronage of this latter gentleman which
secured for him, at the age of twenty-six years, his first pro-
fessional appointment — that of professor of mathematics in his
own university of Pisa.

2. Galileo at Pisa

Galileo was not long in asserting for himself that independence
of mind which we have seen to be so rare in those days. He was
not indeed alone in his indictment of Aristotelian physics. For
example, the writings of Copernicus were making silent headway
amongst somewhat timorous adherents, who seldom spoke out,
so many were there to offend. Galileo, however, did not hesitate.
With a born genius for experiment, a trenchant pen for the
recording of facts, and an honesty which refused "to permit his
conscience to saxiction as fact that which his laboratory proved
to be fiction, there could be only one result.

Galileo's older colleagues knew nothing of experiments. The
very idea implied to them a sort of hideous witchcraft — a pro-
fanation of the sanctity of the Aristotelian doctrine. One part
of the doctrine, it will be remembered, stated that a heavy body
will fall to the earth more rapidly than a lighter one. Thus
a 100 lb, weight will fall in one-hundredth the time it will take
a I lb. weight to fall through a given distance. One would
scarcely dare claim much pluck or originality for the idea of
dropping two such weights simultaneously from a given height
in order to put the great Aristotle to the test ; yet this simple
experiment was in fact one of the outstanding achievements of
scientific history. It is astonishing to think that such an experi-
ment had not been deliberately performed for at least two
thousand years. Thinkers had come and gone, yet this absurd

io6 Galileo Galilei

fiction of the great Greek philosopher had persisted through the
ages. And the men who were considered par excellence the great
minds of the sixteenth century refused the evidence of their own
senses ! It is a problem for the psychologist.

The story of the experiment at the leaning tower of Pisa is
well known. It speaks volumes for the vigorous personality
of young Galileo that he got his audience together at all. There
is real humour in the thought. What an unwilling audience they
must have made ! What angry mutterings must have accom-
panied the preliminaries as this young up-
start slowly mounted the tower. And then,
no doubt, a hush of unwilling expectancy
as the signal was given for the simultaneous
release of heavy and light weights. Surely
it is difficult to believe that these aged
philosophers had not, at some time or
other in their lives, seen two such weights
drop in more or less the same time. They
must surely have felt, in their heart of
hearts, that they were fighting a losing fight,
and that this young firebrand of a Galileo
was a true herald of a new era.

Crash ! With simultaneous thud those
two weights did indeed reach the ground
at the same time. It was truly a great
moment in the history of the world. Yet
the blind prejudice of an unreasoning
hero-worship was too strong even for the evidence of the senses
of sight and sound. ' Let us go home again', said they, ' and
look it up.' So back they went to their old books, and there
sure enough it was — a heavy body faUs faster than a lighter body.
Besides, and the thought was like balm to their wounded sensi-
bilities, does not the Church sanction the views of the great
Aristotle ? So the net result of it all was that whilst they secretly
feared Galileo, they openly disliked him. It was but the beginning
of his career, yet his enemies multiplied rapidly.

Galileo persevered in his study of motion — particularly the

^\\ W 1 1 li

-mm

Fig . 45 . Leaning Tower
of Pisa

Galileo at Pisa 107

motion of falling bodies. He saw clearly that falling bodies have
accelerated motion — that is to say, the velocity is increasing.
He sought out what was the law of this increase in velocity. He
soon satisfied himself that the velocity is proportional to the time
of falling ; that is to say, that a falling body received equal
increments of velocity in equal increments of time. He tested
this experimentally by means of an inclined plane — a board
twelve yards long, down the centre of which was cut a trough one
inch wide. This trough was lined with smooth parchment so as
to minimize frictional errors. A highly polished and well-rounded
brass ball was allowed to run down this plane, and the time was
carefully noted for a wide range of varying inclinations. Galileo
had no clock with which to measure time, but he was too gifted
an experimentalist to be beaten by that fact. He arranged a water
pail with a small outlet at the bottom. The escaping water was
caught in a cup, the period of flow being timed to begin and end
for the exact duration of his experiment — namely, the period of
roll of his brass ball down the inclined plane. He then carefully
weighed the water, and of course this weight was a measure of
the time of descent of the ball down the inclined plane.

Galileo found that, within the limits of experimental error, the
distance of descent was proportional to the square of the time. This
is in accordance with the well-known formula for falling bodies

Galileo had no difficulty in realizing that the results for the
inclined plane would apply equally to falling bodies, since by
gradually increasing the steepness of slope to ninety degrees, the
latter case emerges as a special limit of the general problem.

Galileo, too, was the first to realize that the path of a projectile
in space is a parabola. This was not a new problem. Early
writers on gunnery had remarked that for certain distances of
the objective, the gun must be pointed upwards ; whilst Thomas
Digges, in his New Artillerie, published in 1591, had pointed out
that the ball had a downward tendency right from the beginning
of its course, and that it was the persistence of this tendency
which ultimately produced a deflexion from the original direction.
Galileo's contribution to the problem was of a much more positive

io8 Galileo Galilei

character. He had shown that for a falling body the fall was
proportional to the square of the time. Representing then equal
increments of time by AB, BC, CD, DE, &c. (Fig. 46), if BF be
the fall in the first interval, the fall in twice the time would be
four times BF, namely CG, and in three times this interval the
fall would be DH, equal to nine times the fall BF, and so on.
So that if AB, BC, CD, &c. represent also the equal forward
displacements of the projectile ejected initially in a horizontal
direction, then in fact the successive actual positions in space
occupied by the projectile at these equal intervals of time would
he A, F, G, H, K, &c., and this path
Galileo had no difficulty in showing to
be a parabola. It will be noticed that
actually Galileo was making use here of
the principle of the composition of forces,
but he did not definitely enunciate this,
evidently not fully recognizing its scope.
One other important principle in
mechanics was brought out by Galileo at
this period, in his Delia Scienza Meccanica,
published in 1592. It is concerned with
the theory of mechanical powers, and
his statement in effect was this : that
a force which can move a weight of two
pounds through one foot will also move a weight of one pound
through two feet. That is to say, the lighter the weight to be
overcome, the greater is the distance in the corresponding ratio
through which the force will move it, but under no circumstances
can this advantage be exceeded.

This is a most important proposition in Statics, and was one
which, much about this time, was also being investigated by the
famous Stevinus, of Bruges, from a somewhat more practical
standpoint.

The days of Galileo at Pisa were numbered, as things were
fast reaching a climax. He had, by his outspoken criticisms,
multiplied his enemies rapidly. The end came as a result of
a difference he had with one Giovanni dei Medici, an influential

Fig. 46. Illustrating
Galileo's method of prov-
ing that the path of a
projectile in space is a
parabola.

Galileo at Pisa 109

personage who had invented a scheme for cleansing the port
of Leghorn. Galileo's opinion was sought, and honest man that
he was, he condemned it outright. Later experience of the
scheme fully justified Galileo's condemnation, but the mischief
was done. The inventor was mortally offended, and his hostile
influence proved too strong for Galileo, who was compelled to
resign his chair at Pisa. The death of his
father at this period left him with some
responsibility in the matter of assisting to
provide for his sisters, so that when in 1592
the Senate of Venice offered him the professor-
ship of mathematics at the University of Padua,
Galileo eagerly accepted, and so began for
himself a new era of brilliance and fame.

3. Padua

Galileo went to Padua in 1592 in no chastened
spirit. Pisa was his native city, and the call
of home was strong in him. There is no doubt
that he keenly felt his exile, for such it really
was. Yet he threw himself whole-heartedly
into his professional duties. His inaugural
lecture was a triumph of eloquence, and his
fame rapidly increased. People of the highest
rank flocked to hear him, and his school of
natural philosophy was filled to overflowing,
so that frequently he had to abandon his class
room and lecture in the open air.

One of the first-fruits of his labours at Padua was the inventian
of what was perhaps the first thermometer. This consisted of
a flask A with a long narrow neck (Fig. 47), inverted, with its end
B dipping into a small reservoir of coloured water. Some of the
air within the flask having been withdrawn, the decreased pressure
of the air so produced causes the water to rise in the neck. The
position of the head of the column was indicated by a scale SS at
the side. The effect of heat is much greater upon air than upon

Fig. 47. Galileo's
Thermometer.

no Galileo Galilei

water, and hence, when the temperature rose, the liquid fell in the
stem, and vice versa. The chief error in this instrument arises
from the fact that not only does the position of the liquid in
the stem depend upon the temperature, but also upon the baro-
metric pressure. Galileo, however, was probably unaware of this,
as the barometer was not invented till about 1642.

It was whilst Galileo was at Padua that he began to come into
world-wide prominence as a disciple of Copernicus. It is evident
that, so far as his public lectures were concerned, he made no
attempt in the first years of his professorship to depart from the
current Ptolemaic hypothesis as usually taught. He first testified
to his belief in the Copemican system in 1597, when he wrote to
Kepler to thank him for a copy of the latter's Mysterium Cosmo-
graphicum. ' I have been for many years ', wrote he, ' an adherent
of the Copernican system, and it explains to me the causes of
many of the appearances of nature which are quite unintelligible
on the commonly accepted hypothesis.' He then goes on to
explain why, in spite of this belief, he has remained silent.
' I have collected many arguments for refuting the latter ; but
I do not venture to bring them to the light of publicity, for fear
of sharing the fate of our master, Copernicus, who, although he
has earned immortal fame with some, yet with very many (so
great is the number of fools) has he become an object of ridicule
and scorn.'

Galileo was not wanting in courage, but his appointment at
Padua was for a term of six j^ears only, and he evidently had no
intention of jeopardizing his prospects of re-election. Presumably
he was justified, for in 1598 he was not only re-elected, but his
salary was considerably increased, and he felt more secure in
consequence.

There was, however, another fact — a black incident in the
history of the Church of those days — which must have pro-
foundly influenced Galileo against too free a pronouncement of
his Copernican views. Giordano Bruno, an eminent philosopher,
had boldly pronounced for Copernicus. This, as we all know,
was regarded as heresy b}^ the Church, and Bruno took refuge
from anger by residing for a time in the republic of Venice.

Padua III

Nevertheless, in 1594 Bruno was tried and convicted and cast
into prison. He refused to recant. At last, after six years, it
became evident to the ecclesiastical authorities that imprisonment
would not suffice, and so this martyr of science was passed on to
'have his soul cleansed '. He was condemned to death at the
stake, but he remained true to his convictions to the last. ' You
who sentence me ', said he, ' are in greater fear than I who am
condemned.' There is something really fine about Bruno's dying
words. ' I have fought, that is much — victory is in the hands of
fate. Be that as it may, this at least future ages will not deny me,
be the victor who he may — that I did not fear to die. I yielded
to none of my fellows in constancy and preferred a spirited death
to a cowardly life.'

His death was a shock to all high-minded people who dared to
think about it at all. Padua, now a tram-ride from Venice, was
near enough then for Galileo to have been profoundly affected by
the whole affair. We know he was a Copernican, but it was some
years after the death of Bruno before he ventured to be really
outspoken on the subject.

At first he confined his denunciations to the general Aristotelian
philosophy of the immutability of the heavens. An almost ideal
opportunity offered itself in 1604, when a brilliant new star
literally blazed into view. Such stars appear at varying intervals
in the skies, and astronomers speak of them as novae, or temporary
stars. They are obvious evidences of great cosmic upheaval of
some kind or other, and they are the subject of considerable
speculation and scientific interest whenever they appear.

So far as Galileo was concerned, here was a splendid object-
lesson for his obstinate pro-Aristotelian contemporaries. Here in
the ' unchanging ' heavens (for the heavens in the old view were
the seat of all that is changeless) was shining with a brilliance far
exceeding that of Jupiter at his brightest, a something where
there had been nothing ! A star where there had been no
star ! What was Aristotle's immutable sky worth in the face
of this ?

Before enraptured audiences of greater numbers than ever
before, Galileo discussed this phenomenon and pointed the

112 Galileo Galilei

moral. His opponents took up the challenge, and Padua
became the storm-centre of a controversy which could only carry
Galileo one way ; and so we find him boldly proclaiming for
Copernicus and his system, and definitely committing himself
to a campaign in which, as we shall see later, the whole of the
forces of the Church were arrayed against him, and which brought
tragedy to his later life.

4. The Telescope

It was a trick of fate which placed at this period a most power-
ful weapon in Galileo's hands, and enabled him to adduce
illustration after illustration in support of his pro-Copernican
campaign. In 1609 he heard interesting rumours of a remark-
able contrivance which had been devised in Holland, whereby
objects, viewed through the instrument, appeared to be enlarged
and brought considerably nearer than they actually were when
seen by the naked eye.

There has been much controversy as to the origin of the
telescope. We know that lenses had been used as long ago as
Roger Bacon's time as an aid to vision, but the actual combination
of lenses to produce a telescope was an invention of the beginning
of the seventeenth century. There have been many claims for
the honour of the invention. On the whole, evidence appears to
favour the claims of Hans Lippershey, a manufacturer of spec-
tacles in Middelburg, as having been at least the first to produce
such an instrument. Details are regrettably vague. It is said
that the necessary combination of lenses was accidentally arranged
by one of Lippershey's apprentices, and was regarded by the
spectacle-maker rather as a toy than anything else. In some
vague way, the novelty began to be talked about, and in due
course rumours of it reached Galileo. The significance of such an
instrument as a weapon of science was fully evident to him. The
problem of its design haunted him, and he could not rest until
he had solved it. His only data for a solution were the existing
treatises on the structure of the eye, and his own vague knowledge
of the theory of lenses. But these with his genius for mechanical

The Telescope 113

contrivance sufficed. He sat up for a whole night, and before the
morning he had solved the problem. His own words are definite
enough. Writing to a relative, he said :

*' I have a piece of news for you, though whether you will be
glad or sorry to hear it I cannot say. . . . You must know then,
that two months ago there was spread a report here that in
Flanders some one had presented to Count ]\laurice of Nassau
a glass manufactured in such a way as to make distant objects
appear very near, so that a man at the distance of two miles
could be clearly seen. This seemed to me so marvellous that
I began to think about it. As it appeared to me to have a
foundation in the Theory of Perspective I set about contriving
how to make it, and at length I found out, and have succeeded
so well that the one I have made is far superior to the Dutch
telescope. It was reported in Venice that I had made one, and

t c

Fig. 48. Effect of a Lens on Rays of Light.

a week since I was commanded to show it to his Serenity and
to all the members of the senate, to their infinite amazement.
Many gentlemen and senators, even the oldest, have ascended at
various times the highest bell-towers in Venice to spy out ships
at sea making sail for the mouth of the harbour, and have seen
them clearly, though without my telescope they would have been
invisible for more than two hours. The effect of this instrument
is to show an object at a distance of say fifty miles, as if it were
but five miles.'

It is worth noting that the Dutch instrument was of a totally
different type from that which Galileo designed. The former
gave an inverted image ; the latter an erect image. Galileo's
type of instrument is still in use in the opera-glass. The principle
of Galileo's telescope is shown in Figs. 48 and 49. To avoid
confusion it will suffice to remember that the effect of interposing
a lens in the path of a ray of light is to produce a bending or
refraction towards the thicker part of the lens. Thus in the
Fig. 48, if a, b, and c are rays from a distant object, the lens L^,

2613 H

114 Galileo Galilei

will bend the bounding rays a and c inward (because the lens is
thickest in the middle) and will give an image I^. Such a lens
is spoken of as a convex or converging lens.

Suppose now we prevent the formation of this image by inter-
posing a concave or diverging lens L.^ (as shown dotted in Fig. 48).
The effect of this interposition is shown in the next figure. The
rays are not permitted to come to focus at I^, but are each bent
outward towards the thicker portion of the lens L^, the divergence
being the greater as we get farther from the middle of the lens.
That is to say, ray h is bent farther down than a, and c farther
down than h. Consequently the rays emerge diverging, as in
a, b\ and c', in Fig. 49. The eye looking along these ^ays sees

Fig. 49. The principle of Galileo's Telescope.

the image where the rays, produced backward (as shown by
dotted lines in the figure), come to focus, and it will be seen that
the result is a much more magnified image 1 2 than was produced
by the first lens L^ alone. Such an image is known as a virtual
image, and it is erect or upright instead of inverted as was /j.
Galileo's original instrument gave a magnification of three and
his second of eight. It was not long before he had considerably
extended these magnifications, and with his assistants he became
very expert in telescope manufacture. He presented some to
various noblemen, and some he sold, and with such unbounded
delight and wonder was this novelty received that an admiring
senate promptly increased his salary to one thousand florins and
granted it for the duration of his life.

It should not be difficult to realize how astonishingly impressive
the invention of this instrument must have been to those privi-
leged to gaze through it for the first time. To see a ship where
the naked eye sees nothing, to see a man a mile away smiling or
making some slight movement ordinarily invisible at a distance ;

The Telescope 115

such experiences must of course have appeared wonderful to all
concerned. Of far more importance is it that when Galileo turned
his instrument to the heavens at night, he discovered new wonder
after new wonder, and each new fact helped to controvert the
Aristotelian philosophy, and afforded added proofs of the truth
of the Copernican doctrine of the solar system as modified by
Kepler.

A few examples of these discoveries — there are too many to
deal with within the compass of this book — will suffice. Thus
Aristotelians had regarded the face of the moon as being steadily
even and uniformly bright. Galileo found instead the irregularity,
both in surface and in brilliance, of mountain and crater and

< "m

Fig. 50. Diagram to illustrate the proportions of Galileo's First
Telescopes.

valley and sea. The reference to Galileo's observations is clearly
indicated in Milton's Paradise Lost :

. . . the moon, whose orb
Through optic glass the Tuscan artist views
At evening from the top of Fesole,
Or in Valdarno, to descry new lands.
Rivers or mountains in her spotty globe.

Again, the Aristotelians said that all heavenly bodies revolved
round the earth. Yet Galileo turned his telescope to Jupiter and
to his amazement and delight discovered four moons revolving
round it. The extravagances of opposition which these observa-
tions elicited read to-day like a childish novel. Thus Sizzi argued
that since these moons were invisible to the naked eye, therefore
they can exercise no influence on the earth, and therefore they
are useless, and, therefore, they do not exist. Another opponent
went farther. He absolutely declined to look through the
telescope at all.

' Oh, my dear Kepler,' writes Galileo, ' how I wish that we
could have one hearty laugh together. Here at Padua, is the

H 2

ii6

Galileo Galilei

principal professor of philosophy whom I have repeatedly and
urgently requested to look at the moon and planets through my
glass, which he pertinaciously refuses to do. Why are you not
here ? What shouts of laughter we should have at this glorious
folly. And to hear the professor of philosophy at Pisa labouring

before the grand duke with
logical arguments, as if with
magical incantations, to
charm the new planets out
of the sky.'

One further instance may
be quoted. Galileo examined
the surface of the sun, and
saw spots. Heinous offence !
He examined them and saw
them moving, and so proved
the rotation of the sun on
its own axis. A thoughtful
monk named Scheiner veri-
fied these observations, and
communicated an account
of the spots to the superior
of his order. And what was he told for his pains ? ' I have
searched through Aristotle ', wrote the superior, * and can find
nothing of the kind mentioned. Be assured, therefore, that it
is a deception of your senses, or of your glasses.'

Fig. 51,

The Moon as seen by Galileo,
1609-10.

5. Florence

Meanwhile Galileo's fame grew. He was the idol of the Venetian
Republic. We have seen that in 1609 he had his salary doubled
and confirmed for life. In Padua, too, children had been bom
to him — one son, Vincenzo, and two daughters, one of whom,
Polissena, was afterwards to become the comfort of his old age.
Yet he was never quite happy in Venetia. Galileo was a Tuscan,
and for him Tuscany spelt home and Venetia exile. The people
of Tuscany, too, had long since regretted that they had driven
this great man from them. Galileo had never quite lost touch

Florence 117

with Pisa, and when his position at Padua had become reasonably
secure, he began paying hoHday visits to his native home, and
thus came into friendly contact with the Grand Duke of Tuscany,
Cosimo 11. Cosimo expressed the popular desire in his efforts
to induce Galileo to return to Tuscany, and in 1610, after the
famous discovery of Jupiter's satellites, he offered our philosopher
the appointment of Mathematician and Philosopher to the
Grand Duke, and Galileo accepted.

It was a fateful decision. The joy of freedom from the daily
routine of lectures and the remembrance of long years of yearning
for a return to his native country overrode all other considerations,
and so we find him in 16 10 installed in the city of Florence, there
to continue his career of successful research in astronomy and
mechanics.

Why was it such a fateful decision ? Galileo was a Copemican
in a land which was officially anti-Copernican ; and where the
Church ruled, to dabble with doctrines which it regarded as
heresies was to play with fire. It was not so very many years
since Bruno was burnt at the stake for such an offence. In
Venice Galileo had been reasonably safe. It was a land of relative
tolerance in religious matters. But Tuscany was different. It
came more under the influence of Rome. And so behind Galileo's
return from a land of freedom to a land of religious tyranny there
lurked tragedy.

Of course the Venetians were much offended at his departure
from them, and rightly so. It was scarcely a year since they had
voted Galileo an annuity for life. They had always treated him
well, and his departure hurt them. So Galileo left behind him
many enemies amongst those who had been his friends.

In 161 1 he paid a brief visit to Rome, and was enthusiastically
received. On his return to Florence, he turned his attention to
the subject of hydrostatics, and published an excellent treatise
on floating bodies. This was followed by more astronomical
activity. He discovered and commented on Saturn's remarkable
' appendages ', later known as Saturn's rings ; he wrote upon the
problem of the determination of longitude ; he discovered the

ii8 Galileo Galilei

phenomenon known as the ' libration of the moon'. And all
the time he attacked the Aristotelian philosophers with unceasing
vigour ; and meanwhile his clerical enemies were at work, trying
to stir up Rome against him.

They were so far successful that Galileo was in 1615 sum-
moned to Rome to explain
his views. He went. It was
a delicate situation, fraught
with possibilities. He found
himself arrayed against the
cream of the Aristotelian talent
of the day. But he excelled
in argument and carried his
points. If only he could have
remained in the presence of
his opponents no doubt all
would have been well, for Pope
Paul V was well-disposed to-
wards him. When, however,
he withdrew from the de-
bating chamber the magic of
his arguments went with him,
and the College of Cardinals
decided definitely to ban the
writings of Copernicus and
Kepler, and to instruct Car-
dinal Bellarmine to repri-
mand Galileo for his support
of their doctrines. This was

Fig. 52. Facsimile of design for a
pendulum clock.

done, and on the 26th of February 1616 Galileo found himself
enjoined, under the threat of imprisonment and torture, ' to
abandon and cease to teach his false, impious, and heretical
opinions ' . Galileo bowed to the inevitable ; he gave his promise
and was permitted to return to Florence.

119

6. The Inquisition

The years which followed Galileo's return to Florence were
peaceful enough in their way. He vigorously continued his
researches but carefully avoided anything which would give
offence to his watchful enemies. He was getting on in years, and
at this period of his life found much comfort in the proximity of
one of his daughters, who had become a nun in the Convent
of St. Matthew at Arcetri, just outside the town of Florence. So
Galileo took a small villa in Arcetri, and here he passed much
of his time, frequently visiting the Convent and when unable to
do so maintaining a steady correspondence with his daughter.
Her letters to her father, many of them still extant, constitute
a most touching record of this period of the philosopher's life.

So we come to the year 1623, to the death of the Pope Paul V.
He was succeeded by Urban VHI, who, as Cardinal ]\Iaffeo
Barberini, had been one of Galileo's cordial friends and well
wishers. His elevation to the Papacy was a source of much
gratification to Galileo, who hoped that the new regime would
spell for him an era of tolerance. One of his friends tactfully
sounded the Pope on his behalf, and as a result advised Galileo
to come to Rome to offer to the Pope his personal congratulations.
Galileo came, and the visit was a success. So much so, that on
his return to Florence, he found that Urban VIII had dispatched
a letter of commendation to Ferdinand, Co^imo's young successor
to the ducal throne of Tuscany.

' We find in Galileo ', wrote he, ' not only literary distinction,
but also the love of piety, and he is also strong in those qualities
by which the pontifical good- will is easily obtained. And now,
when he has been brought to this city to congratulate us on our
elevation, we have very lovingly embraced him ; nor can we
suffer him to return to the country whither your liberality calls
him, without an ample provision of pontifical love. And that
you may know how dear he is to us, we have willed to give him
this honourable testimonial of virtue and piety. And we further
signify that every benefit which you shall confer upon him,
imitating or even surpassing your father's liberality, will conduce
to our gratification.'

120 Galileo Galilei

This was surely a splendid testimonial, and it was only natural
for Galileo to hope that the tide had turned, and that he might at
last venture a little more outspokenly to record his real thoughts
and opinions. However, Galileo made the fatal mistake of
forgetting to differentiate between the Pope himself and the
powerful ecclesiastical authorities who surrounded him. It was
a mistake for which he was to pay heavily.

He now set to work and prepared the great book of his life.
It was called Dialogues on the Ptolemaic and Copernican Systems,
and he completed it by the year 1630. The form which this work
took was determined by the fact that in 1616 he had been made
to promise, under threat of imprisonment, never to teach the
Copernican doctrine. He wrote what purported to be an impartial
discussion in dialogue form, between Salviati, a Copernican,
Simplicio, an Aristotelian, and Sagredo, a sort of good-natured
chairman. It is claimed by some writers that this work was in
no way antagonistic to the promise which had been extorted
from him, but it is difficult to believe this. At best one can only
say that if it did not conform to the spirit of the promise, it did
to the letter. The fact remains that as a pretence to a detached
impartiality it was little more than a pretext, for throughout
the work Salviati has much the better of the argument. It was
a brilliantly written work, and was undoubtedly a masterpiece of
common sense and a fine literary effort, but it did not deceive
Galileo's enemies. Indeed it is remarkable that he ever got so
far as to obtain preliminary permission to publish the book.
Looking at it from their very narrow and prejudiced point of
view, the permission to publish could only have been due to
some very careless bungling on the part of the Master of the
Sacred Palace, the man who acted as censor in these matters.
The book appeared in 1632, and was dedicated to the Grand Duke
of Tuscany. It was received by an eager public and read with
avidity. It was then realized by the Master of the Sacred Palace
that he had blundered, and he at once ordered the sequestration of
the book. Too late Galileo saw how strong were the forces against
him, and in spite of such friendly assistance as the Grand Duke
Ferdinand cind others tried to offer, the tide of fury was irresistible.

The Inquisition 121

Even Pope Urban, former friend and well-wisher of Galileo,
turned against him. His Holiness was persuaded that the
character of Simplicio was intended as a deliberate caricature
of himself. Galileo was peremptorily summoned to Rome on
a charge of heresy. He was now an old man, his health was
failing, the plague was abroad and it was winter. In those days
the journey from Florence to Rome was no light undertaking,
and Galileo pleaded for delay. His plea was refused and he arrived
in Rome in February 1633. He was permitted to be received as
the guest of his old friend Niccolini, the Tuscan ambassador, but
he was recommended to keep indoors. The proceedings of the
Inquisition were protracted till June. They were of course
conducted in secret. Throughout this time Galileo's friends
urged upon him the advisability of submission. It must have
been a time of mental torture for the aged philosopher. What
was he to do ? How could he, in the circumstances in which
he was placed, do other than remember the fate of such men
as Bruno ? The old man, broken in spirit, gave in, and declared
his ' free and unbiassed ' willingness to recant. Clothed in
the regulation garb of the penitent, he was brought before the
assembly of cardinals to receive the judgement of the Inquisition.
They condemned his works, but out of their mercy and in con-
sideration of his voluntary recantation, they extended to him
their gracious pardon, and merely imposed the sentence of
imprisonment at the Papal discretion.

Then followed the famous recantation :

' . . . But because I have been enjoined by this Holy Office
altogether to abandon the false opinion which maintains that the
sun is the centre and immovable, and forbidden to hold, defend,
or teach the said false doctrine in any manner, and after it hath
been signified to me that the said doctrine is repugnant with the
Holy Scripture, I have written and printed a book, in which
I treat of the same doctrine now condemned, . . . that is to say,
that I held and believed that the sun is the centre of the universe
and is immovable, and that the earth is not the centre and is
movable ; willing, therefore, to remove from the minds of your
Eminencies, and of every Catholic Christian, this vehement
suspicion rightfully entertained towards me, with a sincere heart

122 Galileo Galilei

and unfeigned faith, I abjure, curse, and detest the said heresies
and errors, and generally every other error and sect contrary
to the Hoty Church, and I swear that I will never more in future
say or assert anything verbally, or in writing, which may give
rise to a similar suspicion of me. . . .'

What are we to say of this disgraceful scene ? Who, dis-
passionately reading the facts, can do aught but feel deeply for
the pathetic victim ? Who can but feel profound indignation
against an organization which could act thus in the name of God ?
Yet in common fairness the reader should be reminded that, so
far as the Church was concerned, there was in reality no motive
of either punishment or persecution behind what might be called
the ' theory ' of the Holy Inquisition.

' The Inquisition was not a court of justice to try heresy as
a crime ; but rather a sort of spiritual board of health, whose
ofhce was to apply a salutary remedy, possibly a painful one, to
stop the contagion of error, and if possible, to restore the heretic
to the pale of salvation. The object was not conviction, but
submission : not truth, but profession : this being once obtained,
by whatever means, the sole end was accomplished.' ^

Knowledge of Galileo's almost world-wide influence as a scholar
and a philosopher prompted the most elaborate methods of
bringing to the notice of Europe the fuU text of the recantation.
It w^as read to all congregants from every pulpit ; it was read
to all students by the professors at universities ; it was read
publicly to all Galileo' s friends and sympathizers in his own town
of Florence.

7. Galileo's Last Years

The Pope interpreted the sentence of imprisonment mercifully.
So far as close confinement was concerned, it lasted but four days,
after which he was permitted a modified exile in the palace of
the Archbishop Piccolomini at Siena.

Meanwhile the anxieties of the trial had broken the health of
Galileo' s daughter. As she lay dying, her last wish was naturally
to see her father, so Galileo asked for permission to return to

^ Powell's Historical View of the Mathematical and Physical Sciences,
1834. P- 177.

Galileo's Last Years 123

Arcetri. The wish was mercifully granted, and for the last time
the two were permitted to see each other. A few days later she
died. The grief- stricken old man now asked to be permitted to
return to Florence, but fear of his possible influence at the scene
of his former triumphs brought a stem refusal and a warning
that he must content himself with confinement in the Villa
Arcetri. So here he stayed on, broken by grief and by the
infirmities of old age. Nevertheless, his intellect was as brilliantly
active as ever, and he returned to his work. He devoted the next
few years to the study of dynamics, and in his famous Dialogues
on Motion, published under great difficulties (owing to the
ecclesiastical ban on his works) in Amsterdam in 1636, he con-
solidated his earlier work on the subject at Pisa, and did all the
spade work which later resulted in the enunciation of Newton's
Laws of Motion, justly considered to be the foundation of the
study of mechanics.

Virtually a prisoner — his own son was appointed to act as his
warder — and with rapidly failing health, Galileo was at last
seized with blindness. He accepted this misfortune, as he had
done so many others before, with philosophic resignation.

' Your dear friend and servant, Galileo,' he wrote to Diodati
in 1638, ' has been for the last month perfectly blind, so that this
heaven, this earth, this universe, which I by my marvellous
discoveries and clear demonstrations have enlarged a hundred
thousand times beyond the belief of the wise men of bygone
years, henceforward is for me shrunk into such a small space as
is iiQed by my own bodily sensations. So it pleases God ; so
also shall it therefore please me.'

Apparently he was now considered to be somewhat less dan-
gerous to civilization, as we now find him permitted to receive
friends. The highest in his own country vied with the eminent
men of all other parts of Europe to do him homage and to express
sympathy and admiration for him. Among others, by a strange
irony of fate, Milton, doomed to blindness himself, visited
Galileo. All who came were delighted to find his gift of conversa-
tion and old charm of manner unimpaired by his bodily infirmities.
But the end was approaching. To his blindness there was added

124 Galileo Galilei

deafness, and at last he was seized with a low fever. He died
on the 8th of January 1642, aged seventy-eight years.

Even in death his persecution was continued. At first the
authorities refused him burial. Later they sanctioned an obscure
burial, but permitted no monument over his grave. They then
disputed his will, and even this did not suffice. They seized all
the unpublished manuscript in the possession of his family, and
what little they actually returned was ' offered up ' as a ' burnt
offering' by Galileo's grandson, Cosimo, as a preliminary act
of devotion at the beginning of his career as a missionary.

Nowadays there exists a monument to his memory in the church
of Santa Croce at Florence. Yet what finer monument to
Galileo's memory can there be than the old leaning tower at
Pisa — that silent witness of a great experiment by the man of
whom it may truly be said ' he was the founder of experimental
science'.

M;jttliewHopkin5 WikJi VmAcr Gencmll

An age which still believed in witch-
craft. Two Witches discovered.

^VIII

REN£ DESCARTES AND
CO-ORDINATE GEOIMETRY

I. Early Life

Contemporary with the latter half of Galileo's career there
lived a man who, without rising to the brilliance in experiment
and invention of the great _
Italian philosopher, neverthe-
less played a very significant
part in the scientific history of
the seventeenth century. Rene
Descartes was a Frenchman of
wide attainments, who greatly
enriched the world by his
writings in many branches of
knowledge. He was a great
metaphysician and he had also
an important influence on bio-
logy. He wrote the first text-
book of physiology. To him
we are indebted for the origin
of that branch of mathematical
inquiry known as co-ordinate
or analytical geometry.

Rene Descartes was born at
La Haye, near Tours, on the 31st of March 1596. He was the
younger son of Joachim Descartes, a wealthy man of widej^ilture
andjioblehneage, who was accustomed to spend six months of
the year at i^eimes, in the local ' parliament ' in which he was
a councillor, and the remaining half on his family estate of Les
Cartes, at La Haye.

There were two misfortunes attendant on the upbringing of
young Rene. One was the death of his mother soon after he was
born. The other was the fact that he was a delicate child.
Bereft of her gentle guidance, and granted every wish by an over-

FiG. 53. RENE DESCARTES

Rene Descartes

afetious father, he developed a mild selfishness which displayed
itself throughout his later life. Joachim Descartes was sufficiently
wealthy to deny his children nothing ; they were brought up
in the lap of luxury. He was, however, an observant man, and
it was not long before he detected in Rene signs of unusual
ability. Most healthy children continually ask questions. But
the everlasting stream of questions which this child asked — there
were no encyclopaedias for parents in those days — were almost
too much for the harassed father. The type of question showed
a high order of mentality in the child, and the elder Descartes
jokingly called him ' the philosopher'.

At the age of eight Rene was sent to the Jesuit school at La
Fleche, and was placed under the tuition of Father Charlet. The
discipline and the education in this school were both excellent,
and Descartes had little difficulty in mastering the ' learned
languages and polite literature ' which formed the backbone of
the course of studies there. He was allowed much licence on
account of his delicate health. Thus he was permitted to remain
in bed late in the mornings. This was a habit which persisted
with him throughout his life, and he tells us that the best of his
thinking was always done there ! Yet in spite of all the advantage
offered by his school, and of the ease with which he mastered any
work which was put before him, Rene Descartes seemed to derive
no personal satisfaction from his studies. He developed neither
enthusiasm nor hobbies, and if one can use the expression with
regard to a youth of fifteen or sixteen, he seemed very much
bored with life. His was evidently a very difficult personality,
and with all its excellences, the Jesuit school at La Fleche failed
to discover his S5mipathies.

When Rene left school in August 1612, it was without the
slightest inclination on his part to pursue his studies any farther.
For a short time he devoted himself to outdoor exercises, ' in
learning to ride the great horse and to fence, and other such like
actions suitable to his quality'. His health, however, did not
permit him to continue this for very long, and so he was sent
under the care of a kind of companion-tutor to Paris, there to
play the gentleman in ajmanner befitting his station. The tutor-

Early Life 127

companion seemed to have had very little to do other than to
ensure by a sort of judicious chaperonage, that the generous
formula as to behaviour which Joachim Descartes had laid down
for his son — namely, absolute freedom from all restrictions
consistent with virtue and quality — was properly carried out.

2. The Call to Science

Descartes' whole upbringing had been that of an idle gentleman
of wealth and station, and he had never taken life very seriously.
Denied nothing, and thrown when still but a youth into the
gaieties of Parisian life, and into the companionship of pleasure-
loving people of his own age, it is probable that but for that
abnormality of personality which had proved a puzzle to his
tutors at school he might have sunk to a low level of profligacy.
Evidently that same something in his character which bored
him at work equally bored him at idle pleasure.

Conflicting forces, indeed, appear to have been at work during
his stay in Paris. In 1615 he met with two men who influenced
him strongly. One was Claude Mydorge, and the other an old
friend of his schoolboy days. Father Marin Mersenne. Both were
mathematicians of some note, and both saw the genius latent in
the idler. They succeeded in rousing him to a liking for mathe-
matics and philosophy sufficient to persuade him to devote
himself to a detailed course of study. The effect was no doubt
lasting, but at the time it seemed little more than a spurt, for
in 1616 we again find him in the hands of his former friends,
who appeared to have lured him back to the world of fashion.
But this lapse did not last very long, and soon Descartes looked
around him for a career of some kind. For men of his social
standing, however, there was very little choice. The Army and
the Church were practically the only alternatives. There was
nothing of the churchman about Rene Descartes, and so the
problem solved itself. Accordingly in 1617 he joined the army of
Prince Maurice of Orange as a volunteer, and he became involved
in the campaign then in progress between the Spanish and the
Dutch.

128 Rene Descartes

It was whilst he was stationed in the garrison town of Breda,
during a period of truce between the two armies, that a very
significant incident occurred in his hfe. It seems that an anony-
mous person had mounted a placard in one of the main streets of
the town, challenging the world to find a solution to a problem
in geometry. Such challenges were to become very frequent
later on in the same century, and indeed were destined to be the
medium for considerable research in mathematics ; but in
Descartes' early days a challenge of this kind was a distinct
novelty.

Chance prompted him to stop and look at the placard. It was
written in Dutch, and he was unfamiliar with the language,
so he stopped the first passer-by with a request to translate the
notice to him into French or Latin. As luck would have it,
this passer-by was Isaac Beeckman, Principal of the Dutch College
at Dort, and he offered to supply the translation on condition
that Descartes would attempt a reply. Descartes took the problem
home to his quarters and worked at it for a few hours, and to his
delight succeeded in obtaining a correct solution. It was a revela-
tion to him. He had enjoyed the tussle, and had discovered in
himself a mathematical ability which he had not suspected,
despite his previous work with Mersenne. He took the solution
to Beeckman, who, too, was delighted with it, and a warm
friendship sprang up between these two.

The remainder of Descartes' stay in Breda was very fruitful.
He had little to do in the way of military duties, and he devoted
himself to mathematical study and discussion in an ever-growing
circle of friends of a philosophic turn of mind. Among other
things he wrote a treatise on music. He would definitely have
abandoned his military career, but family tradition impelled him
to stay on. However, he tired of Breda, and took advantage of
the beginning of the Thirty Years' War to leave Holland and
volunteer early in 1619 in the army of the Duke of Bavaria.

So we find him at Neuberg after a season of campaigning on
the Danube, and here, on the night of the loth of November 1619,
there occurred that emotional experience which determined his
future career as a philosopher and mathematician. Something

The Call to Science

turned his thoughts in the direction of mathematics, and presii!
ably he was thinking of a possible relationship between the
hitherto separate subjects of algebra and geometry. The idea
suddenly flashed through his mind of the fixing of a point in.
a plane by referring it to two lines at right angles to each other.
His powerful mental vision fastened on this, and upon all the
possible developments to which it could give rise, and soon the
idea became an obsession. That night, so he tells us, he dreamt
three separate dreams which he regarded as a clear call to him
to abandon his former mode of life, and to take up the mission
of developing his new line of mathematical reasoning, and from
that to explain the mystery of the universe.

3. Holland — The Vortex Theory

Descartes did not immediately abandon his military career,
but he never lost sight of his great idea and his new purpose.
The campaign of 1620 was a busy one for him. He was present at
the sieges of Prague, Pressburg, Tirnaw, &c., but he was rapidly
tiring of this kind of life, and in 162 1, after the raising of the siege
of Neuhausel, he resigned his commission and definitely aban-
doned the profession of arms. He was twenty-six years of age,
and even now he did not settle down. For five years he travelled,
dividing his time between sight-seeing and the study of mathe-
matics.

/ In 1626 he returned to Paris, a very different Descartes from the
/one who had lived an aimless life of gaiety there ten years before.
1 He shunned his old haunts, and devoted himself to the theory
and construction of optical instruments, which, it will be remem-
bered, were attaining general prominence about this time. Soon
his presence began to be known, and men of science and learning
sought him out. Cardinal de BeruUe, the Pope's Nuncio, in
particular was much impressed by the general trend of Descartes' s
views, and successfully urged upon him the task of devoting his
life seriously to their development and presentation to the world.
Descartes acquiesced, and decided to take up his residence in
Holland for that purpose, and thither he went in 1628, the year

2613 I

130 Rene Descartes

which may be regarded as the real beginning of his active career
as a scientific publicist in mathematics and philosophy.

What were his methods ? He was not a member of the
experimental school of Galileo and Gilbert. He had very little
to do with the laboratory, except perhaps in his work on anatomy.
His methods were essentially those of the mathematician. He
would start with a statement of fact — an enunciation of a definite
principle, and working from it, he would develop, step by step,
a logical sequence of deductions until he had built up a complete
scheme. He was in a sense a pioneer of the mathematical study
of nature. ' Comparing the mysteries of nature with the laws
of mathematics, he dared to hope that the secrets of both could
be unlocked with the same key.' To guide himself in developing
his scheme of work, he compared the problems of nature to a tree
of which metaphysics was the root and physics the trunk. The
three chief branches dealt with the external world (mechanics),
the human body (medicine), and human conduct (morals), and
to these subjects he rigidly confined himself.

As a result of his first four years of labour in Holland, Descartes
had practically completed a work which he called the System of
the World. It contained his theory of ' vortices ' which was later
to bring him the widest possible notice. Yet he never published it.
The reason is interesting. The book neared its completion in 1633,
just at the time of Galileo's famous trial before the Holy Inquisi-
tion at Rome, followed by the recantation. The news took
Descartes by surprise. He was not of the stuff of which heroes
are made. He had no ambitions for any conflict with the Church,
for he had no illusions as to its power. He liked his theories, and
he liked publicity, but he had no desire for martyrdom. So
he decided at once against publication. He wrote to Father
Mersenne : ' I confess that if the opinion of the earth's movement
be false, all the foundations of my philosophy are so also, because
it is demonstrated clearly by them. It is so bound up with every
part of my treatise that I could not sever it without making the
remainder faulty ; and although I consider all my conclusions
based on very certain and clear demonstrations, I would not for
all the world sustain them against the authority of the Church.'

Holland— The Vortex Theory 131

He did not burn his manuscript, as he at first threatened to
do, but extended it, for eleven years later, in 1644, he did in fact
publish the book under the title of Principia Philosophiae,
having found some ' formula ' which he thought might reconcile
the Church to its acceptance. As a matter of fact it did not do
so, and the work was placed on the ' Index ' of prohibited
books. In spite of this, however, it obtained a wide publicity.

Descartes's theory of vortices caused a great stir in the world
of philosophy. According to this theory, matter was endowed
with the properties of extension, impenetrability, and inertia.
Such matter, said Descartes, fills all space. This is the first point
he makes. His second point is this, that every portion of this
matter is endowed with motion, or the possibility of motion, in
every conceivable direction. Arguing from this, he held that such
a combination of motions made rectilinear or straight line motion
absolutely impossible. On the other hand, there was a continual
tendency to deflexion from such motion ; a continual tendency,
in other words, to circular motion, and hence to the phenomenon
we speak of as centrifugal force.

From this to the formation of multitudes of whirlpools or
vortices was but one step, the lighter portions of matter forming
the real vortex, and the heavier portions ' floating ' within ;
and each vortex, in addition to its own rotary motion, is carried
round bodily with its heavy nucleus. The universe, therefore,
consisted of vast numbers of these vortices, all limiting and
circumscribing each other.

Applying this to the Solar System, Descartes held that the
planets (including the earth) are carried round in the great vortex
of which the sun is the main nucleus. The normal pressure
exerted on the planets by the ' light ' matter composing the solar
vortex (the modem substitute for which is the ether) would tend
to draw the planets (i. e. make them fall) into the sun, but this
is counterbalanced by the equal and opposite and centrifugal
force normally outwards. In the same way, each planet is itself
the nucleus of a lesser vortex, and so on.

There is something very remarkable in the eager and almost
universal acceptance which this theory received, particularly in

I 2

132 Rene Descartes

England. It will be noticed that the theory leads to circular orbits
only, and yet Kepler had definitely established his laws of plane-
tary motion beyond all doubt. There was evidently something
in it which satisfied the philosophic hunger of those times, and
it probably lies in the fact that the theory of vortices was a com-
plete theory with explanations, as compared with Kepler's bald
facts without explanations. It made a powerful and an effective
appeal to the imagination.

In these days, Descartes's theory is a relic in the museum of
scientific literature, but, abandoned as it is to-day, it served
an important purpose then. From the time of Copernicus
there had been attempts to break away from the Aristotelian
tradition, yet no such attempt had received universal acceptance.
In spite of all, Aristotle still held the field. But Descartes's theory
of vortices brought about a remarkable change. Everybody
accepted it, and almost in the space of a generation it began to
be taught in the universities.

4. Cartesian Mathematics

In 1637 Descartes published at Leyden the book which contains
his invention of co-ordinate geometry. Its full title was Discours
de la methode pour bien conduire sa raison et chercher la verite dans
les sciences, but it is more commonly referred to as the Discours.

The first portion of the book is not devoted to mathematics,
however, but to optics, and it is right that we should note the
more important contributions he made in this subject. He took
up the subject of refraction, and enunciated the law now spoken
of as Snell's Law. It has been suggested that he derived this law
from Snell.

Descartes next investigated the problem of the focus of a
spherical lens. The usual formula given is

using the customary notation.

If the reader is sufficiently interested to follow up the proof
of this simple formula, he will find that it is only an approxima-
tion, and that it is based on the assumption that all rays are taken

Cartesian Mathematics 133

very near to the axis. In fact there is no real point-focus to a
spherical lens. There is instead a focal region, and Descartes
tackled the problem of finding out what must be the shape of
a lens to give a real point-focus. He proved the answer to be
a curve of the fourth degree, and in certain cases a curve of the
second degree, i. e. a conic. However, owing to the practical
difficulties of workmanship in fashioning such a lens, Descartes's
work was of little practical value in his own time.

Descartes also tackled the problem of the rainbow. This, so
far as the primary bow was concerned, had already been explained
by Antonio de Dominis, Archbishop of Spalatro, in 1611, in a
work, De Radiis Visits et Liicis. y
Now all careful observers of the
phenomenon of the rainbow
know that above the usual
bright bow there is another,
sometimes very faint, at other
times much more distinct,
spoken of as the ' secondary
bow '. Descartes succeeded in

y

L_

explaining this bow, and he Fig. 54. Cartesian Geometry,

prrnratplv trnrpH nut thp nath^ ^^^ co-ordinates of a point with

accurately traced out tne patns j-ggpe^t to two axes of reference.
of the rays which produce it.

We now turn to the mathematical portion of the Discours ;
that which deals with Descartes's discovery of the principle of
co-ordinate geometry. The basic feature is that a point in a plane
can be completely fixed if we know its perpendicular distances
from two arbitrarily chosen lines of reference OX and OY
(Fig. 54). These distances, usually designated by x and y, are
termed the co-ordinates of the point, and given such co-ordinates,
the point is as surely fixed in the plane as is a place on the
earth's surface when its latitude and longitude are given.

Again, suppose we are told nothing more definite about a point
than that one co-ordinate is always twice as much as the other ;
that is to say, that x is always equal to 2y. As a statement in
algebra we may put it thus :

X = 2y.

134 Rene Descartes

We may now try to represent such a point with regard to
Descartes's two axes of reference, OX and OY. We have only
the one fact to go upon, that x = 2y, and we find that there
are any number of points, Pi, P2, P3, &c. (Fig. 55), for which
this is true, and we quickly see that all these points lie upon
a straight line passing through the origin 0 (the point of inter-
section of OX and OY), and
having its inclination to OX such
that tan 0 = 1

This straight line is in fact the
geometrical representation of the
algebraical statement that x = 2y;
and conversely, the equation
x = 2y is the algebraical represen-
tation of the geometrical fact that
a line is such that every point on
it has its x co-ordinate twice the
length of its y co-ordinate. So
we see how Descartes succeeded
in welding together the hitherto
separate subjects of algebra and
geometry.

Let us take another example.
Suppose we are again not defi-
nitely told what are the co-ordi-
nates of the point, but that the
point is to be such that the sum
of the squares of the two co-
ordinates gives a constant answer.

Fig. 55. Cartesian Geometry.
Application to a straight line.

Fig. 56. Cartesian Geometry.
Application to a circle.

For example, suppose we are told that x^ +y^ = 2S. Clearly any
point on a circle of centre 0 (the origin) and radius 5 units will
satisfy the required condition, since if we consider any right-
angled triangle such as POM (Fig. 56), where PM is the y of
the point and OM is its x co-ordinate, we must always have

OP^ = OAl^ + PM^

= x^ +y^

Cartesian Mathematics 135

and if OP = 5, OP'^ will be 25, giving the required condition.
Here again we may say that the equation x^+y'^ = 2S is the
algebraical representation of a geometrical fact, namely, a circle
of radius 5 units, with centre at the origin ; or we may put it
that drawing such a circle is a geometrical representation of the
algebraical fact that x^ +3/^ = 25.

But it would be a mistake to say that analytical geometry is
the mere application of algebra to geometry, or of geometry to
algebra. It is the linking up of the two subjects into what becomes
a completely new branch of mathematical inquiry. So we may
speak of a;^ +jy^ = 25 as a circle,
and we should by so doing be
speaking just as correctly as we
should if we were to call x^ +3/^ = 25
an equation. It is a circle, and it
conveys indirectly all the informa-
tion which the word ' circle ' con
veys to the mathematical student.
Any particular property of the
circle which can be brought out by
a careful geometrical construction
can be just as surely brought out
by direct algebraical processes with-
out even so much as drawing a figure.

As an example, for the benefit of those readers who care to
have one, suppose we consider the problem of the intersection of
a circle and a straight line. We know that x^ +3;- = 16 is a circle ;
and that :v + 23/ = 4 is a straight line. To see where they intersect,
we could draw them, as in Fig. 57, and see from the figure where
they cut. But we can dispense with a drawing. For the points
A and B lie on both the circle and the straight line simultaneously,
so that the two statements x~ +y'^ = 16
and x + 2y = 4

are simultaneously true. Hence we can treat the problem as the
solution of two simultaneous equations in algebra.

From the second equation, a; =4 — 2jy.

Fig. 57. Cartesian Geometry.
Intersection of straight line and
circle.

136 Rene Descartes

Substituting this value for x in the first equation, we get :

(4-2>')'+J^^ = 16
i. e. i6-i6j^ + 43'2+3'^ = 16

i. e. sy^—'^^y = o

i. e. jy(5v-i6) = o

whence 3/ = o or .

. . 12

giving .1; = 4 or — ^

So that the two points of intersection of the Hne and the circle

are those whose co-ordinates are

/ \ A I 12 16

(x = 4,3/ = o) and (;v = - — , y = — ).

There is no need for us to discuss Descartes's development of this
line of thought, or his application of it to tangents. The main
thing is to appreciate the enormous value of the fundamental idea
as a contribution to mathematical inquiry. It is for this that he
is included in these pages.

5. Descartes's Later Life

After the publication of the Discours in 1637, Descartes
worked steadily on, publishing his Meditations in 1641 and the
Principia Philosophiae in 1644. This latter, it will be remem-
bered, contained his famous theory of vortices, and so enthusiastic
was its reception in his own native France that in 1647 the French
Court granted him a pension as a reward for his labours.

Descartes was taking his life seriously. It will be remembered
that as a child of very delicate health he had contracted the
habit of early thinking and late rising. The habit stuck to him.
He thought out all his problems in bed, rose late, and devoted
his afternoons to social functions and exercise. He was always
scrupulously careful about his health, and it was his definitely
expressed ambition to die of a ripe old age.

It was an ambition which did not materialize, for in 1649 tie
was invited by Queen Christina of Sweden to join her Court in
the role of philosophic tutor. Christina was a somewhat shallow-
minded lady who liked to be surrounded by great minds.

Later Life 137

Descartes hesitated. He was fifty-three years of age, and he
dreaded the cold cUmate of a Swedish winter. Moreover, Queen
Christina was a very early riser, and he was faced with the
prospect of giving lessons in philosophy at five in the morning !
To break the lifelong habit of late rising was naturally a most
serious matter, and there is no wonder that he hesitated. How-
ever, Descartes loved adulation, and the idea of intimate
proximity with royalty proved too tempting. So he went to Stock-
holm. It was a fatal decision. The strain proved too great for
so delicate a man, and he broke down under it. He developed
inflammation of the lungs, and the Court physician could do
nothing for him. He died on the nth February 1650. He was
at first buried in Stockholm, but seventeen years later his body
was removed to Paris, where a magnificent monument was
erected to his memory in the Church of Ste. Genevieve.

Descartes was a very great man. We have said nothing here of
his eminent contributions to anatomy, biology, and moral philo-
sophy. In these, as in mathematics and physics, he left his mark.

In appearance he ' was a small man with large head, projecting
brow, prominent nose, and black hair coming down to his eye-
brows. His voice was feeble. Considering the range of his
studies he was by no means widely read, and he despised both
learning and art unless something tangible could be extracted
therefrom '.^

There was much that was selfish in his character, and he was
very jealous of his rivals. He was so far influenced by this as
purposely to obscure his meanings and his language. In his
Discours he freely confesses ' Je n'ai rien omis qu'a dessein . . .
j'avois prevu que certaines gens qui se vantent de sgavoir tout
n'auroient pas manque de dire que je n'avois rien ecrit qu'ils
n'eussent sgu auparavant, si je me fusse rendu assez intelligible
pour eux '. On the other hand, he does not always give credit to
his contemporaries when credit is fairly due to them. Thus,
when he wrote on the rainbow, he made no mention of Father
Dominis and his work, although he must have been considerably
indebted to him on the subject.

* Rouse Ball, History of Mathematics.

IX

SIR ISAAC NEWTON

I. Science in the Seventeenth Century

We may now pause to take stock of the scientific position in
the middle of the seventeenth century. That position, fortunately,
was a very different one from that of a hundred years before. It
was much more favourable to further progress. The outstanding

fact was the overthrow of the
Aristotelian tradition. The
first warning blast of the
attacking forces was sounded
by the publication of Coper-
nicus'sD^ revolutionihus orbium
caelestiwn in the year of his
death 1543, and for one hundred
years the fight had been carried
on, at first by Kepler and his
followers, and later by the ex-
perimental school of philoso-
phy headed by Galileo on the
Continent and Gilbert in
England. It was an uphill
fight of reason against prejudice, and although the forces of
prejudice were strong, the logic of reason was stronger. The result
was never more than a question of time. The world was ready for
a new doctrine, and we have seen what a powerful effect was
produced by Descartes' s Theory of Vortices. It is curious that
after the spade-work of investigation, experiment, and observation
had been done by Kepler, Galileo, and Gilbert, the final overthrow
of the Aristotelians should have been produced by what has since
proved to be a futile speculation, having foundation in neither
fact nor experiment.

There is no question of the reality of the deep interest which
was developing in the realms of scientific inquir}^ at this time.
Much of this development was undoubtedly due in particular

Fig. 58. SIR ISAAC NEWTON

Science in the Seventeenth Century 139

to the writings of two men — Francis Bacon (1561-1626) in
England, and Rene Descartes in France and Holland. Much
controversy has raged round the question of Francis Bacon's
merits as a leader of scientific thought. He was not a scientist,
but he wrote on scientific method in his Novum Organum, and laid
down a comprehensive scheme of principles which he considered
should guide procedure in scientific inquiry. Apart from their
intrinsic value (probably in these days very little), his writings
achieved a wide publicity and commanded an attention, the
effect of which must not be underestimated. There is no doubt
that Francis Bacon gained for science the receptive ear of the
public at large, and contributed to an interest in research which
made smoother the thorny path of the student of nature.

Descartes, too, in his Discourse on Method gave an equally
great impetus to scientific inquiry on the Continent. He taught
clearly and successfully that no statement was necessarily true
because some one of authority in the past had made it.

A sign of the times was the appearance during this period, for
the first time in history, of various learned societies in different
European centres, whose object it was to bring together men of
a philosophic turn of mind for friendly discussion and argument.
Thus in 1603 there was founded in Italy the Lincean Society,
under the patronage of the Marchese Federigo Cesi. Galileo was
himself an active member of it, and after a period of decline it
was succeeded by the famous Florentine School of physicists
who in 1657 banded together to form the Accademia del Cimento,
with which were associated such illustrious names as Viviani and
Torricelli and their disciples. In France the Royal Academy of
Sciences was founded in 1666, during the reign of Louis XIV, and
much about the same time the Institute of Bologna was also formed.

The formation of such institutions was first advocated by
Francis Bacon in his writings, so it is not a matter for surprise
that England, too, early developed its learned society. In 1645
there began to gather together a body of men in Oxford, who
afterwards united again in London under a royal charter of
incorporation by Charles II in 1662, to form the Royal Society
for the Advancement of Learning.

140 Sir Isaac Newton

Finally, mention should be made of the fact that during this
period observational astronomy received its first recognition in
the establishment of the great national observatories — that of
Paris in 1667 and of Greenwich in 1675.

Such, then, were the conditions under which the pursuit of
knowledge was fostered in the middle of the seventeenth century.
It is not surprising, therefore, that the latter half of the century
and the beginning of the eighteenth century proved to be an era
of remarkable scientific activity, characterized by tremendous
strides in mathematics and physics. This period, too, produced
a galaxy of brilliant philosophers and mathematicians of the first
magnitude. Boyle, Hooke, and Halley in England ; Leibnitz,
Huyghens, Torricelli, Pascal, Cassini, and Guericke on the Conti-
nent, were but a few of them. Towering head and shoulders
above all his contemporaries, a veritable giant among the giants,
a man whose intellect and whose contributions to knowledge are
incomparably greater than those of any other scientist of the
past, was that prince of philosophers, Sir Isaac Newton.

2. Newton's Early Life

The Newtons were yeomen of Lincolnshire, with a local
tradition dating back to the fifteenth century. Theirs was not
a very 'arge estate, but such as it was it had always been
zealously husbanded and passed on from generation to generation.
It was situated in the manor of Woolsthorpe, near Grantham,
and it was here that Isaac Newton was born on Christmas Day
1642, the year of Galileo's death. His father, unfortunately, had
died just before this at the very early age of thirty-six, and the
responsibility for Isaac's upbringing devolved upon his mother.

He was by no means a healthy baby. His life was despaired
of on more than one occasion. However, with the watchful care of
his mother, he must have soon thrown off these ' symptoms of
an early death ', since he lived to be eighty-five years old.

Isaac's mother did not long remain a widow. She married
again, and went to live with her new husband, the Rev. Barnabas
Smith, at North Witham. Isaac did not accompany her, but was

Early Life 141

looked after by his grandmother, Mrs. Ayscough, who came to
Woolsthorpe.

At the age of twelve, Isaac was sent to the King's School at
Grantham, staying meantime at the home of the local apothecary.
At first he did not shine at school, nor had he any inclination to
do so. Indeed he tells us that he was for some time the lowest
boy in the lowest class but one. He was just a healthy, normal,
mischief-loving boy, without a care. Like his Continental

Fig. 59. The Manor-house, Woolsthorpe ; the birthplace of Sir
Isaac Newton, showing the solar dials he made when a boy.

predecessor, Galileo, however, he very soon manifested a strong
inclination for the making of mechanical models — kites, wind-
mills, and the like. There is a story that he once tied paper
lanterns to the tail of a kite he had made, and sent it up at night
with the object of deluding the people into believing that they
were watching a comet ; and another, that after days of watching
some workmen construct a windmill in the neighbourhood he
made an excellent working model of one for himself.

An important little event in school life now happened which
was something of a revelation to both Newton himself and those
around him. He fought a fight against odds and won. It seems

142 Sir Isaac Newton

that a bigger boy kicked him. No one worth an ounce of salt
takes a kicking lying down. So Newton fought the boy and
thrashed him. The affair set young Newton thinking. The boy
was higher up in the class than he, and he argued to himself
that if he could thrash the fellow at fists he could thrash him at

Fig. 60. Grantham Free Grammar-school, restored 1857
The school of Sir Isaac Newton.

work. He set to work to do it, and did more. He rose to the top
of his class !

At the age of fifteen he was withdrawn from school by his
mother owing to the death of her second husband. She had now
returned to Woolsthorpe, and was anxious to maintain the
yeoman traditions of the Newtons. As Isaac Newton was to own
his property in the near future, it was just as well, she thought.

Early Life 143

that he should start early at farming and husbandry. But there
was nothing of the farmer in Isaac. He had developed the study
of mechanical contrivances and all that pertained thereto into
an absorbing interest. However, he kept the fact to himself.
He evidently felt that if his mother were to know of it he would
have to do a little more farming and far less studying. So he
said nothing, but every week, when he was sent in to Grantham
with an old servant on market days to do the necessary buying
and selling for the farm, he managed to steal a few hours for his
books and models. He had evidently got on the right side of the
old servant, who was prevailed upon to go alone to Grantham,
leaving young Newton to his books at some convenient point on
the way.

If his mother saw nothing of his student proclivities, she at
least saw he was making a poor farmer, and being puzzled as to
what to do about it she turned to a brother for advice and help.
This gentleman, a parson, sought out Isaac to have a chat with
him. He expected to find him farming. Instead, he found him
reading a book on mathematics. He was sensible enough to
realize the impossibility of the position, and as a result of his
subsequent talks with his sister, back went Isaac Newton to the
Grantham Grammar-school, this time with the definite object
of preparing himself for a university career at Cambridge, and
here he pursued the usual course of classics common to the
schools of those times. At the age of eighteen, in the year 1660,
he left Grantham with the blessings of his head master and the
good wishes of his fellow pupils, and entered Trinity College,
Cambridge.

3. At Cambridge

Hitherto young Newton had had no opportunity of displaying
his great intellect. It is very probable that he was unconscious
of his own mental powers. Nevertheless his chance had now
come. I^ectures were of little use to him. His mind worked far
more rapidly than the prescribed pace laid down by a scheme
of lectures. He worked through a series of books, starting with
Euclid's Elements, which he found very easy. Kepler's Optics,

144 Sir Isaac Newton

too, gave him no difficulties. He next tackled Descartes's
Geometry, and this, though he confesses that he did so with
difficulty, he mastered too.

From this he passed on to other books, and now he was
sufficiently sure of himself to become somewhat critical in his
reading, and his criticisms and comments (and frequently
improvements) were to be seen in the form of marginal notes
completely filling all the available blank spaces of the books
he read.

The Lucasian Professor of Mathematics under whom Newton
worked was Dr. Isaac Barrow. He was an eminent mathe-
matician and a discerning man of science, and it was not long
before he noticed Newton's remarkable abilities. He encouraged
Newton to see him frequently and to discuss his work with him.
The warm friendship that sprang up between them had far-
reaching results later in the invention of the calculus — that
branch of higher mathematics which has so completely revolu-
tionized practically every branch of science.

For the first few years he devoted himself mainly to mathe-
matics. They were fruitful years, but we will defer our record
of his mathematical discoveries for the moment. At the age of 22
he took his B.A. degree, and a year later, in 1665, an outbreak of
plague caused the university to be temporarily closed. So
Newton retired to the quiet of his own home in Woolsthorpe,
Lincolnshire, staying there till 1667.

It was during this period that he turned his thoughts to those
speculations on the subject of gravity which resulted in his
famous enunciation of the inverse square law of universal gravita-
tion, and enabled him later to give a definite proof of the three
laws of planetary motion discovered, but left unexplained, by
Kepler.

In 1667 Isaac Newton, now a Fellow of his college, returned
to Trinity and went ahead at his researches in mathematics,
optics, and dynamics. There was little that his fertile brain did
not tackle, and when he was still in his twenties he had achieved
more than would have been considered a brilliant lifework in
many another man of fame. The differential calculus, the

At Cambridge 145

perfection of the reflecting telescope, the beginning of spectrum
analysis, the law of universal gravitation, were but a few of a host
of different original investigations for which he was responsible.
And he did it all quietly. His notes were voluminous, but he
published little, and for a time only those with whom he came
into intimate contact knew of his researches. Much of the work
had only reached its early stages, and a portion of Newton's later
life was to be spent in n^aturing and perfecting his earlier
investigations.

Nevertheless his genius was fully apparent to his professor,
Dr. Isaac Barrow. Barrow was a churchman as well as a mathe-
matician. There were many problems in theology of interest to
him, for which he desired more time. He fully recognized in
Newton a man superior to him in mathematical and scientific
ability. So in 1669 he resigned his professorship in Newton's
favour. Newton was twenty-six years of age on the date of his
appointment, and he held the professorship for the next twenty-
five years.

Let us consider briefly a few of the more important of his
contributions to knowledge, taking in turn his work in optics, in
dynamics, and in mathematics.

4. Newton's Work in Optics

Newton's work in optics may be said to have dated from 1664,
in which year he is known to have purchased a prism, ' to try the
celebrated phenomenon of colours '. His work, however, could
not have been of great value until 1669, for in the year previous
to this his friend Dr. Barrow had published a very faulty Theory
of Colours in the preparation of which we know him to have
freely consulted Newton.

It will be remembered that Descartes had investigated the
problem of determining the correct surface of a lens which would
possess a proper point-focus, i. e. which would be free from the
error known in optics as spherical aberration ; and he found
that under certain conditions a paraboloidal surface would do.
Newton attempted to foUow this up practically by trying to grind

146 Sir Isaac Newton

lenses in the laboratory to the required shape. It was difficult, but
it soon led Newton to a discovery of importance, for he saw that,
however accurately the grinding was performed, he kept getting
what we may vaguely term ' colour troubles ', and what students
of optics will recognize by the name of ' chromatic aberration '.

Newton thought this over and began
to suspect a relationship of some
kind which could produce different
refrangibilities for different colours.
This led to his famous experiments
with the prism which were the his-
torical beginnings of the vast modern
subject of spectrum analysis. It is,
of course, well known that when a ray of light AB (Fig. 61) passes
through a triangular prism of glass it undergoes two successive
bendings, or refractions BC and CD, each being a deflection
towards the thicker portion of the prism.

Newton's experiment was as follows. He arranged a smaU
round hole H (Fig. 62) in the window shutter AB of a darkened
room. A narrow beam of sunlight was admitted through the

Fig. 61. Deviation of light
by prism.

Fig. 62. Newton's experiment on the dispersion of white hght.

shutter at H, and gave a spot of white light on a screen S opposite
the shutter.

Newton now interposed a prism CDE as in the figure. The
effect was twofold. The light was, of course, refracted or bent
as in Fig. 61. But, further, the circular spot became elongated
into a band of coloured light nearly five times its breadth, the
succession of tints passing insensibly from one to another, and

Work in Optics 147

showing different degrees of refrangibility for different colours.
Newton detected seven main colour t^^pes — red, orange, yellow,
green, blue, indigo, and violet, the red being bent least and the
violet most.

Mark how carefully Newton tackled the problem of inter-
preting this experiment. Why were the rays spread out ?
Perhaps, thought he, because the rays nearer the vertex E have
less glass to pass through and so suffer less bending. He tried
sending one ray through a thin portion of the prism, and another
through the thicker portion. From each he got a spectrum, and
both were of the same length. That settled that question. Then,
perhaps, the elongated band is produced by a flaw in the glass.
So he tried other prisms, but always he obtained the spectrum
band. Further, he argued that if it
were due to a flaw, then the trouble
would be doubled by doubling the
prism, i. e. having two of the same
vertical angle. He arranged these
with one reversed, as in Fig. 63, and fig. 63. Recombination of
found that so far from doubling the light by double prism.
effect of colour, they appeared to

nullify each other. He got neither band nor colour effect, but
a normal undistorted image. So this explanation, too, had to be
rejected.

He next thought that possibly it may be due to the fact that
the rays entering the hole H in Fig. 62, from different portions
of the sun's disk, would be slightly inclined to each other. But
calculation showed even this to be a negligible consideration.
However, he had still not exhausted the possibilities. Perhaps
the effect of the prism was to bend the rays into curves which
would strike the screen at different degrees of obliquity, pro-
ducing the effect of elongation. So he tested the length of the
spectrum at different distances from the prisms. It was always
in direct proportion to the distance, however, proving the rays
to be rectilinear.

Note how carefully the problems were being reduced to
narrower limits. Newton was forced to conclude that the

K2

148 Sir Isaac Newton

question of colour must vitally affect the explanation of the
whole phenomenon, and he determined to isolate the rays of one
colour only, and experiment upon each in turn. How was he to
do this ? Refer back to Fig. 62. Suppose we have a hole pricked
in the screen 5 at the place where one of the rays, say the green,
falls on it. Then, whilst all other colours are stopped by the
screen, the green ray passes on and can be experimented upon.
Newton did this. He isolated each colour in turn, and made it
pass through a second prism, and in each case carefully measured
the refraction produced. He was careful to arrange for each
colour to enter the same point of the prism at the same angle,
in order to make the comparisons scrupulously fair. He was
delighted to find that, proceeding along the spectrum colours from
red to violet, the refrangihility steadily increased.

The conclusion was, therefore, that sunlight, or white light, is
not homogeneous, but is ' made up ' of many differently coloured
rays of differing refrangibilities (or refractive indices), these being
least for red rays and most for violet rays, and that as a conse-
quence the effect of a prism will be to separate out these primary
rays or colours by their different degrees of refraction. This
spreading out of the rays is spoken of as the phenomenon of
dispersion of light.

It will not be difficult for the reader to see now that an arrange-
ment of two prisms such as is shown in Fig. 63 will cause a
reuniting of the rays separated out by the first prism, and giving
as a result no colours or dispersion of any kind whatever.

Nor was it difficult for Newton to perceive why lenses produce
* colour trouble' (chromatic aberration), no matter how perfect

the shape might be from the
point of view of ' spherical
aberration '. For to each
different colour there would
correspond a different point-
FiG. 64. Chromatic aberration in focus, the nearest being, say,
^^"^^^- V (Fig. 64) for the most re-

frangible violet rays, and the farthest R for the least refrangible
red rays. So that, instead of a sharp point-focus, there could
only be a coloured patch VR.

Work in Optics 149

Newton came to the conclusion that the use of the principle
of refraction in optical instruments was undesirable, and he
turned his attention accordingly to the construction of reflecting
telescopes. Now this question had also been attempted by James
Gregorj^ The whole matter was a question of design. For,
given a good speculum or spherical mirror M (Fig. 65), the rays

From distant
object.

Fig. 65. The principle of the Reflecting Telescope.

falling on it from a distant object would produce an image / near
the focus F, and this could be suitably magnified by a small lens
of some kind. Nothing could be simpler. But there is a real
difficulty nevertheless. Where can the head of the observer be
placed so as to view the image without interfering with the
incident rays ?

Gregory's suggestion was one which involved cutting a small
circular hole in the middle of the mirror, and telescopes of this

Fig. 66. Pnnciple of Newton's Reflecting Telescope.

kind are occasionally seen. But Newton's suggestion was
somewhat simpler. The image /, having been formed, a small
mirror M, supported at an angle of 45° to the axis, produced
a further horizontal image I^, and this could be viewed directly
through a small lens L in the side of the case of the instrument,
giving both increased magnification and comfort of observation.
Newton's first telescope was small — one inch in diameter and
six inches long — yet it gave a magnification of forty. The

150 Sir Isaac Newton

concave mirror was prepared from a mixture of copper and tin,
and gave a very clear image. His second instrument was better,
and was presented by him to the Royal Society in 1671. They
were delighted with it, and expressed their thanks by electing
Newton a Fellow. As to the actual importance of Newton's work
on reflecting telescopes it will suffice to point out that all the
giant telescopes of the world's best observatories are made on
the reflecting principle.

Yet how was Newton's work on optics received by his contem-
poraries ? Newton communicated an account of his experiment
on colour to the Royal Society in 1671, and in a letter to Olden-
burgh, the secretary to the Royal Society, he described his work
as ' an account of a philosophical discovery which induced me
to the making of the telescope : and I doubt not but will prove
much more grateful than the communication of that instrument ;
being, in my judgement, the oddest, if not the most considerable
detection which hath hitherto been made in the operations of
nature ' .

In England these communications were at first well received,
but on the Continent there developed an extraordinary outburst
of petty antagonism to Newton, the arguments advanced by
way of criticism being frequently as ignorant as they were
persistent. Newton was exceedingly sensitive to these criticisms.
He never courted publicity in any shape or form, and he preferred
to leave these criticisms unanswered. But Oldenburgh prevailed
upon him to reply, and having vanquished his Continental
'critics*, he prepared to withdraw himself from publicity once
more. But a formidable critic now appeared at home in the
person of Dr. Hooke, an able Fellow of the Royal Society.
Looking back on the records of those times it must be confessed
that Hooke was prompted by motives of jealousy at Newton's
success in problems which had balfled him. It is immaterial
what exactly were Hooke' s arguments and contentions. Newton
answered them both with di jnity and force, but it left his sensitive
nature somewhat outraged. ' I find it yet against the grain to
put pen to paper any more on that subject', wrote he to Olden-
burgh, whilst to the illustrious Leibnitz he expressed himself

Work in Optics 151

thus : * I was so persecuted with discussions arising from the
pubHcation of my theory of light, that I blamed my own impru-
dence for parting with so substantial a blessing as my quiet, to
run after a shadow.'

Newton' s activities on the subject of optics continued unabated.
He took up the subject of colours as seen on viewing a soap film,
and he developed the subject
of ' Newton's Rings', as they
are now called.

5. Rival Theories of
Light

Mention must, however, be
made of Newton's views as to
the nature of light. It is, of
course, obvious that the ques-
tion, ' What is light ? ' must
have presented itself to New-
ton as it did to many others,
and he tried to supply an
answer. His answer, as it
turns out, was wrong. The
matter is historically inter-
esting, since round it there
centred a scientific controversy whose solution depended upon
a test which was in fact only supplied after the death of both
Newton and his illustrious opponent in the controversy, Huy-
ghens.

Christian Huyghens was a Dutch scientist of this period. He
was bom at the Hague in 1629 and excelled both as a physicist
and a mathematician. One of his best-known pieces of work was
his continuation of Galileo's researches on the pendulum. The
original form of the pendulum was such that to obtain isochronism
— that is to say, continuously equally-timed beats — it was
necessar}'' to have small swings in a circular arc. But as a result
of Huyghen's investigations into the mathematical properties

Fig. 67. CHRISTIAN HUYGHENS

152 Sir Isaac Newton

of the curve known as the cycloid he was able in 1658 to invent
the cycloidal pendulum, and this was able to keep accurate time
swinging over wide distances or amplitudes. Huyghens had also
done valuable work in astronomy with a ten-feet-long telescope
he had made in 1659, accurately describing the rings round
Saturn for the first time. He came to England in 1660 at the
invitation of the Royal Society, and his friendship with Newton
began some years later. He afterwards settled in France, and
it was in the year 1678 that he presented to the ' Academic des
Sciences ' his famous ' undulatory theory ' of light which repre-
sented his attempt to answer the question ' WTiat is light ? '
and which became the opposition side to Newton' s in the historic
controversy of their rival theories.

What was Huyghen's undulatory theory ? Curiously enough,
it was based on one of Newton's discoveries. Newton had shown
that the phenomenon of sound is caused by the vibration of air
particles being transmitted from the object producing the sound
to the ear receiving it, the vibrations being propagated in ' waves '
very much in the same way as * waves ' are transmitted outward
in a pond from some point of disturbance. If the sound is
' excited ' by striking a harp string, for example, then the shorter
and tighter the string, the more rapid will be the vibrations, and
as a consequence the more shrill the note.

' Light ' , said Huyghens, ' is a phenomenon of vibrations like
sound, but simply on a different scale of size, the vibrations
being ever so much smaller and more rapid.' ' Yes,' was the
answer of his critics, ' but if that is so, then what is the vibrating
medium corresponding to the air in sound, since, for example,
there is no air between the sun and the earth in the millions of
miles of space, and therefore there is no medium to pass on the
vibrations of the sun's light to the earth ? ' Huyghen's answer
was of profound importance. ' There is a medium,' said he, ' and
it pervades all space. It is highly elastic and extremely attenu-
ated, passing between the particles of solid objects just as freely
as it occupies outer space.' This universal medium Huyghens
called the etJier, and any source of light, e. g. the sun, sets up the
vibrations in the ether, and these vibrations are passed on with

Rival Theories of Light 153

tremendous rapidity (186,000 miles per second, as we now know).
When these undulations or waves strike the eye they affect us
physiologically with the sensations of vision. ' But', asked his
critics, ' if the light waves are travelling in the sky, why do we
have darkness ? ' The answer again was simple and decisive.
' You cannot hear soimd unless your ear drum stops a sound-
wave. The wave may pass you without touching your ear, and
you hear nothing. A stick may move rapidly, and if you stop it
with your head it will affect you physiologically with the sensation
of pam ; yet if it passes you by you feel nothing. Similarly with
light. The wave may be there, but unless it impinges on your
eye it will not affect you physiologically with the sensation of
light.' The waves, in fact, produce an effect as though light
travels in straight lines.

And what, on the other hand, was Newton's rival theory ?
He called it the ' Emission ' or ' Corpuscular Theory ' . According
to this light is composed of streams of minute invisible particles
of matter emitted from the luminous source in straight lines at
very high velocity. It is the impinging of these streams of
particles upon the retina of the eye which produces the sensation
of light.

Round these two theories, then, there developed a storm of
controversy. Both without doubt were ingenious. Both were
able to account for all the ordinarily observed phenomena of
reflection and refraction known at that time. Nowadays we
know of other phenomena which Newton's theory could not
explain, but which the undulatory theory can. But how were
the rival claims of the two theories to be tested ?

Now it was known that as a logical consequence of Newton's
theory light must travel faster in a medium such as glass or water
than it will in air. On the other hand, it follows from Huyghens's
theory that the speed of light in these media must be less than
for air. Here, then, was the test — definitely to measure these
velocities in the different media. But how ? Alas, the experi-
ment was beyond the scientists of Newton's day. Both Newton
and Huyghens died without the application of this crucial test,
and the weight of Newton's superior reputation alone served to

154 Sir Isaac Newton

produce a balance of opinion in favour of the corpuscular theory
and against the wave theory. Such phenomena as the inter-
ference of light were unknown then, or more justice might have
been done to Huyghens, and it was not till 1850 that Jean Leon
Foucault, of France, finally settled the whole controversy by his
experiment which showed that light travels at a rate of 186,000
miles per second in air, and only about three-quarters of this
speed in water.

6. Newton's Researches on Gravitation

We turn now to another branch of Newton's activities — that
of dynamics. It will be remembered that in 1665, owing to
an outbreak of plague, the University was closed, and Newton
returned to his home at Woolsthorpe, near Grantham. Here he
spent a quiet eighteen months of meditation on various problems,
and it was here that he thought out that great law of universal
gravitation which so profoundly changed the whole character of
the science of d3mamics.

The problem of gravity was not a new one. Speculations on
the subject had interested almost every philosopher of note from
the time of Plato. What had been called the power of gravity
was familiar to all. It remained to discover the law which
presumably this ' power ' obeyed. Newton, like his predecessors,
found the problem of fascinating interest. ^

It will be remembered that Kepler, after a lifework of patient
analysis of Tycho Brahe's famous record of observations, had
enunciated his three famous laws of planetary motion. The
third of these laws, it will be recalled, was that for every planet,
the cube of the distance is proportional to the square of the periodic
time ; or, expressing this mathematically,

Y2 is constant for all planets.

Why should this be so ? This was what Newton asked himself.
To understand this further, let us vary Kepler's statements

^ The familiar story of the faUing apple, originating from Voltaire, is
of such doubtful authenticity that it is purposely omitted from the text.

Researches on Gravitation 155

a little. He told us that the orbits of the planets are elliptical.
It will simplify the problem, without upsetting the argument in
any way, if we adhere to circles. Suppose the orbits are circular.
What ' binding ' force is there in a body like the sun which will
keep a planet constantly moving round it in circular orbit ? One
finds a similar problem in the twirling of a mass in a circular
path by means of a string. Referring to Fig. 68, suppose the
string is held at C, then initially, taking the point A as the mass
in question, its direction of motion is along the tangent AB.
That is to say, unless otherwise restrained, it will ' fly off at
a tangent * , as the popular phrase goes. But it is so restrained —
by the string AC, which, by tending
to pull the mass into itself, brings it
in a given time to E on the circle
instead of to D on the straight line.
In effect, in the given time in ques-
tion, it has pulled the mass inward
towards the centre through a dis-
tance DE. The new direction of
motion is now EF, the tangent at
E, and the whole argument con-
tinually repeats itself, and the force
along the string directed towards
the centre C constantly pulls the body out of its ' straight line '
tendency, and keeps it moving in a circular path or orbit.

Let us now apply a little mathematics and elementary
mechanics to the problem, and it will then be seen why Newton
was seeking for the existence of a constant force directed towards
a centre.

In his famous book, the Principia, Newton enunciated the
three laws of motion which, as we have before pointed out,^ were
primarily due to the spade-work of Galileo's researches at Arcetri,
and which constitute the basis of modem mechanics. The first
of these tells us that in a world of no forces, if such a thing could
be imagined, a body would do only one of two things ; it would
either be at rest, or, if moving at all, it would move continually

1 Ch. vii.

Fig. 68. Production of a
Circular Orbit by a force con-
stantly directed towards the
centre.

156 Sir Isaac Newton

in a straight line with uniform speed ; and this simply because
there are no forces to make it do otherwise. A force continuously
applied to a body at rest will start it moving with continually
increasing speed, and a force applied to a moving body will change
its motion ; that is to say, it will speed it up, or slow it down, or
swerve it from its original direction. The force will in fact
produce in the body an acceleration (or, of course, a retardation,
which mathematically is merely a negative acceleration).

This was Newton's first law of motion. His second was in part
nothing but a common-sense law, and said in effect that the amount
of acceleration produced in a body depends upon the magnitude
of the force ; a big force must have a big effect — a small force
a small effect. The acceleration (or rate of change of motion)
produced, then, is proportional to the impressed force. This is
algebraically the F = ma formula well known to all students
of elementary mechanics.

His third law, that ' to every action there is an equal and
opposite reaction ' , does not concern us at the moment, and we
therefore do no more than make bare mention of it here.

Returning to the problem of a body being whirled round

a circular orbit (Fig. 68) about a given centre C, we have seen

that the circular orbit is produced through the exertion of

a constant force along the string directed towards the centre. As

a matter of common sense, it must be obvious that the swifter

the speed (let us call it v) with which the body tends to ' fly off

along the tangent*, the greater must be the controlling force

to give it the necessary change of speed of motion (or acceleration)

inward to keep it in its circular path. Both Huyghens and

Newton showed in fact that the acceleration required must

V-
be — where r is the radius of the circle, and v velocity of the mass.
r

The investigation of this problem would be out of place here.

Students of elementary mechanics will be quite familiar with it,

and others will, it is hoped, be content to accept the result as

here stated.

Now since the force F = ma, we have obviously

F= —
r

Researches on Gravitation 157

giving us the measure of the centripetal force, as it is called,
necessary to hold any given mass m moving with a speed v in
a circular orbit of radius r, and this force is always directed towards
the centre of the orbit.

We are now in a position to see a little light with regard to
Kepler's third law of planetary motion. He talks of the periodic
time ; he means, of course, the time for one complete revolution.
If the speed is v, and the circumference 27rr, then obviously we
must have

. ,. ^. „ 27rr ^ . distance gone X

periodic time T = — (since time taken = :f )

V ^ speed -^

whence

27rr
v= ^,

and hence, since

r

we can substitute

2-r .
^ for?;,

and we get

as an expression for the constant force required to hold a body
in its circular orbit.

Now compare this with the constant expression required by

r^

Kepler's third law — namely, —^.

To get a correspondence between these two expressions, we want
an r^ term to come into the numerator of the former one. The

reader must be reminded that the expression F = Z,'^ - is con-
cerned with the problem of a body whirled round a circular
path at the end of a string, the force F being the inward force
exerted along the string. Kepler's expression, on the other hand,
is for the actual planets, where there are no strings connecting
the body to the central sun. We want, in this latter case, a substi-
tute for the force along the string. Let us assume, therefore,
that in the case of the planet moving round the sun in a circular
orbit (we are still regarding the orbits as circular instead of

158 Sir Isaac Newton

elliptical) there is a constant force directed towards the sun,
exerted, so to speak, along an imaginary string. If we can take
this force as being inversely proportional to the square of the
radius, we shall have achieved our object of a proper correspon-
dence between these two expressions. Let us see how it works out.
Let us suppose that, in fact, there is a law according to which
a body is naturally attracted to a ' central ' mass with a force
which is inversely proportional to the square of the distance
between them, and is directly proportional to the masses of the
two bodies, M being the mass of the central or attracting body.
If we express this algebraically, we have

F = K -^^, where K is constant.
But we have seen that
Hence we may say that
which gives us _„ _ „ .

If we examine the right-hand side of this equation it will be seen

that it is a constant quantity, sinCe K is the constant factor of

proportionality already mentioned, and M is the mass of the

central attracting body.

We therefore have

r^ (Distance)^ „

^0 = jYy — ^^r — ^- r? = Constant

T^ (Periodic Time)^

and this is nothing more nor less than Kepler's Third Law.

To sum up, what we have so far said reduces to this : that it
follows from a consideration of the elementary mechanics of
central orbits ' that it would he quite easy to explain Kepler's
third law of planetary motion if there could he found to exist a force
of attraction towards the central hody whose magnitude is inversely
proportional to the square of the distance ' .

For the sake of simplicity we have confined ourselves to the
case of circular orbits only. But although the mathematics is
more complicated for elliptical orbits, the result is the same, so

F =

mj^ir'^r

J2 '

m^ir'^r

KMm

J2

- y2

^3

MK

Researches on Gravitation 159

the problem is perfectly general. Whatever truth there may have
been in the well-known story of the falling apple, it is extremely
probable that Newton must at least have considered as significant
the every-day experience of the behaviour of an object such as
a freely-falling stone. Why was such an experience so fraught
with significance ? It was because it enabled Newton to link up
•certain facts. Here was an example of a force exerted by the
earth on the stone. So far as the planets are concerned, the force
he sought was to be exerted by the sun. Yet in the case of
Jupiter, say, an exactly similar problem presented itself in the
seeking of such a force towards that planet to account for the
orbits of her then-known four moons.

Was it possible, thought Newton, that in every case the force
of attraction was inversely proportional to the square of the
distance ? In that case would it account too for the motion of
our own moon round the earth ? For surely if the earth attracts
the stone it must also attract the moon ?

Here was a splendid chance of applying a test. The earth's
pull or attraction falls off as the square of the distance. The moon
was known to be distant sixty times the earth's radius from the
earth's centre. Hence the attraction exerted by the earth on

the moon must be (^ ^1 of the attraction it will exert on a body

v6ox6o^ -^

at its own surface (since a body on the earth's surface is -p- of

the distance of the moon from the earth's centre).

Now a body on the earth's surface is pulled to it (i. e. ' drops ')
a distance of i6 feet (or more exactly 193 inches) in one second.

Therefore the moon should ' drop ' a distance of (r f- ^ feet

^ ^00x60

in one second. But this can be tested. We know by observa-
tions exactly how long the moon takes to go once round, and
we know the distance between the earth and moon. There-
fore we could draw a diagram like Fig. 68, to scale to repre-
sent the moon's motion round the earth C, and we could
calculate how much arc AE (still referring to Fig. 68) could
be traversed by the moon in one second. All we have to do

t6o Sir Isaac Newton

is to calculate the ' drop ' DE, and assure ourselves that it

works out to (p ^) feet.

^60 x6o^

By a tragedy of misfortune for which Newton was not to blame,
his test was doomed at first to disappointment. The accuracy of
the result depended upon the accuracy of the value taken as the
radius of the earth. Newton could only take the accepted value
of the times, and it was, alas, wrong. It was assumed to be
3,436 miles, whereas the correct value is 3,963 miles. Conse-
quently, instead of getting the required drop for the moon of

(7 T") feet in one second, he only got (^ — -^-\ feet in one

^60 x6o^ -^ ^ ^60 x6o^

second.

Newton's disappointment was keen. He had no reason to
suspect his data, and so he found himself obliged to abandon the
basic assumption of an inverse square law. This was in 1666.

For the next step in the story we are carried to the year 1682,
when Picard, at a meeting of the Royal Society, communicated
the results of his more accurate determinations of the value of
the earth's radius. Newton was present, and he made a careful
note of Picard's results. Immediately he began to recall his work
and hopes of sixteen years ago. He hurried home and routed
out his old papers and calculations on the subj ect. His excitement
at the anticipation of complete success to his theory was too
much for him. He was too agitated to finish his calculations,
and he got a friend to do them for him. The result was a complete
triumph. The value for the moon's ' fall ' per second was exactly

( r ^ ) feet. At last he had discovered both the true law of

\6o x6o^

universal gravitation and the true explanations of Kepler's laws

of planetary motion. And all this would have been definitely

achieved sixteen years before but for an inaccurate determination

for which he was not responsible.

Yet despite the magnificence of this achievement, Newton said

nothing about his discovery. He was now, as always, chary of

publicity. He hated alike both adulation and attack. How then

did his discovery ultimately receive the wide publicity which its

Researches on Gravitation i6i

importance demanded ? The story is an interesting one. The
problems which Newton had solved so successfully were also
being attempted by his contemporaries. All the chief members
of the Royal Society were intensely interested. Three men in
particular who were giving much time and trouble to the problems
of gravitation and the solar system were Hooke, Sir Christopher
Wren, and Edmund Halley, a distinguished astronomer and
mathematician.

In January 1684 Wren made an offer of a present of a book
to the cost of forty shillings if
either of the others would bring
him within two months a proof
of the statement that if a planet
be attracted to the sun with a
force obeying the inverse square
law, its path would be an ellipse.
They both failed to supply the
proof. But in August of the same
year Halley had decided to con-
sult Newton about it, not knowing
that Newton had even thought of
the problem before, but convinced
nevertheless that his genius would
help to find a solution.

There were few preliminaries to the conversation,
came straight to business. ' What will be the curve described
by the planets on the supposition that gravity diminishes as the
square of the distance ? ' he asked. Newton's immediate repty
was ' An ellipse '. ' But how do you know ? ' retorted the amazed
Halley. ' W^hy,' said Newton, ' I have calculated it.' He began
searching for the papers containing the calculations. He could
not iind them immediately, but promised to send them as soon
as possible. Halley hurried back to London, and in the following
November received the calculations. They were communicated
to the Royal Society early in 1685, and it was therefore to Edmund
Halley that the world was indebted for bringing to light what must
always remain one of the most important documents 'in the world's

2613 L

Fig. 69.

Medal commemorating
Edmund Halley.

Halley

1 62 Sir Isaac Newton

scientific history. As Halley proudly put it, he was ' the Ulysses
who produced this Achilles '.

The importance of Newton's work was by no means lost on the
Roj^al Society. They wrote to Newton and asked for permission
to publish his researches. Newton consented, and as a conse-
quence the world has his epoch-making Principia, or Mathematical
Principles of Natural Philosophy. It is without exception the
most important work in natural philosophy extant.

Halley spared neither trouble nor expense in seeing the work
through the press, and he was justified. The work on the whole
was well received by those in a position to judge it. Yet
there were some detractors who did not hesitate to attack Newton.
Hooke in particular was especially virulent in his attack, as he
had been on a former occasion in connexion with Newton's
work in optics. Here, as before, Hooke claimed priority, declaring
that Newton had derived his solution from his (Hooke's) work.
This was an unjust claim, as all are now agreed. In a second
edition, however, Newton acknowledged the part Wren, Hooke,
and Halley had each played in the researches on gravitation and
the solar system generally. We can well imagine, from what
has previously been said, how painful the whole controversy was
to Newton. He was near suppressing the whole of the third
book entirely. ' Philosophy ', wrote he to Halley, ' is such an
impertinently litigious lady that a man had as good be engaged
in lawsuits as have to do with her. I found it so formerly, and
now I can no sooner come near her again, but she gives me
warning.' Halley, fortunately, succeeded in dissuading him from
this step, and so the world has the whole work complete and
unabridged.

And what was the result ? Here was an entirely new philosophy
presented to a world which had been slowly weaned from the
Aristotelian School, and which had by now been taught to accept
the Cartesian view. Even Newton himself had been taught
Descartes 's Vortex Theory as a ' real live ' thing. We have seen
that the world does not abandon a theory in a hurry. So we
cannot be surprised that on the Continent Newtonian physics made
but slow progress, until Voltaire stirred up his contemporaries

Researches on Gravitation 163

and aroused them to face facts. In England, however, the
abandonment of Descartes in favour of the Newtonian philosophy
was much more rapid, as one may w^ell suppose, and by the time
Newton had died the scientific opinion of the country was solid
for his teachings.

7. Newton's Mathematical Researches

We have, so far, considered in turn New^ton's researches in
optics and in mechanics. We have now to consider his contribu-
tions to pure mathematics. He began as early as the year 1665,
at the age of twenty-three, with the discovery of the binomial
theorem. The actual nature of it is hardly a matter for this work.
We will merely remark that it was but a stepping-stone in the
progress of Newton's mind : that it was merely a weapon —
a mathematical weapon, which he required to help him to solve
the age-old problem of finding the area of a figure bounded by
a curve ; and of finding the length of a curved line.

The binomial theorem was, in fact, but a step towards the
creation of that wonderfully fertile scheme of investigation
which Newton called his theory of fluxions, and which to-day we
speak of as the differential and integral calculus.

It is difficult to speak of this branch of Newton's work in terms
intelligible to the non-mathematical reader, and perhaps the
wisest course for such a reader would be to take it all ' as read ',
and pass straight on to the next section. The word ' fluxion '
indicates a flow. According to Newton, all types of geometrical
quantities could be regarded as being generated by a continuous
flow or motion. Thus a line is generated by the motion or a
point, a surface by the motion of a line, a solid by the motion of
a surface, and so on. That being so, Newton next went on to
speak of the speed or velocity of any of these moving magnitudes
as i]\Q fluxion of the magnitude generated, e. g. the speed of a moving
line is the fluxion of the surface created, the speed of the moving
surface is the fluxion of the solid so produced, and so on.

As a matter of convenience, Newton employed Cartesian
co-ordinates to help him in this conception. So if we take the

L 2

164 Sir Isaac Newton

case of a moving point P whose co-ordinates are x and y respec-
tivel}^ referred to two axes at right angles, and whose velocity is
the fluxion of the arc so created, then since the velocity can be
resolved into two velocities parallel to each axis respectively,
each of these resolved velocities will give the fluxion of % and y
respectively.

The converse conception is also possible, and we speak of the
arc as the fluent of the velocity of the moving point with which
it is described ; and the surface is the fluent of the velocity of
the moving arc with which it is described, and so on.

Now suppose that the fluxion of a curve is constant, that is to
say, suppose the curve is described by the point moving along it
with uniform velocity. Then the ratio
of the fluxion of the x co-ordinate (or
abscissa, as this co-ordinate is called) to
the fluxion of the y co-ordinate (or or-
dinate as this co-ordinate is called) will
be determined solely by the nature of
^ ^ the curve. The ratio will be small if the

Fig. 70. Illustrating New- ^^^^^ -^ ^^^^^^ ^^^ ^^le ratio will be big
ton's Theory of Fluxions. -r , , • i n 2. > /t-- \

•^ if the curve IS Hat (l^ig. 70).

Conversely, still considering the case of a curve of constant
fluxion, if we know the ratio of the fluxions of the co-ordinates
at any given instant, the nature of the curve can be built up,
or in other words the equation to the curve can be found. The
former operation Newton called the ' Method of Fluxions '. It
corresponds to the differential calculus of to-day. The latter
operation was the ' inverse method of fluxions ', and forms th^
starting-point of the modern integral calculus.

Now a word as to Newton's notation. Suppose :v is a given
fluent. Then he denoted its fluxion by i". Further, if x is in its
turn a variable or fluent quantity, then its fluxion was denoted
by i' ; so that x was a fluxion of a fluxion, or, as Newton expressed
it, a fluxion of the second order, or more shortly, a second fluxion.
Obviously, if x is such that it varies directly with the time, then
.r is a constant, and therefore x = 0.

Conversely, since x can itself be considered a fluxion of another

Mathematical Researches 165

quantity which would be its fluent, Newton denoted this fluent
by %' in some books and by \_%\ in others ; and from these in
their turn he got the second fluents %" or [[;t]], and so on.

Finally, Newton spoke of the infinitely small increases in the
magnitude of the variable in indefinitely small intervals of time
as the ' moments ' of the fluent. Newton denoted the small
interval of time by o. Hence if x be the fluent, since x is
the fluxion, the increase in the value of the fluent in time o must
be the product io, and this quantity is the ' moment ' of x. That
is to say, after an indefinitely small interval of time x has assumed
the value x +.fo.

This, in brief, and, it is feared, in somewhat vague terms, is
the outline of the fundamental ideas underlying Newton's theory
of fluxions. It was not entirely a result of Newton's unaided
genius. Mention has already been made of his tutor and professor
at Cambridge, Dr. Isaac Barrow. To him history must apportion
some of the credit for Newton's theory, for he had himself been
interested in this question and there is no doubt but that Newton
derived many of his notions from conversations and discussions
with Barrow.

Students of the differential calculus wfll have noticed that the
notation Newton used in his fluxional calculus is not that which
is used to-day. The notation of the calculus of to-day is the
invention of Gottfried Wilhelm Leibnitz, and indeed the mathe-
matical history of this period is almost entirely a history of a long
and painful controversy between these two great men on the
subject of their rival claims to the invention of the calculus.

8. The Battle of the Calculus

As usual, the trouble was probably largely due to Newton's
reticence and hesitation to publish his papers. We know that he
used his theory of fluxions in 1666. We also know that a manu-
script circulation of the theory existed amongst friends and
pupils in 1669. Yet no full publication of the theory occurred
till 1693. Compare these facts with those of Leibnitz's version
of the calculus. He used it in his note books in 1675, nine years

1 66 Sir Isaac Newton

after Newton first used his theory of fluxions. He wrote to Newton
about it in 1677, and he first pubHshed it in 1684, nine years before
Newton's theory was published.

Who then really invented the calculus ? There appears to
be no doubt but that Newton was the first with his theory of
fluxions. The question then becomes, did Leibnitz invent it
independently of Newton, or did he in fact get the idea from
Newton ? The answer is largely a question of Leibnitz's good

faith. Was this open to doubt ?
Let us try to examine the facts.

In 1673 Leibnitz visited England
and met Oldenburgh, the secre-
tary to the Royal Society. At
this time he knew little of mathe-
matics, but when, shortly after,
he became interested in the sub-
ject, his remarkable mental talents
soon enabled him to grasp all that
was then known on the subject.
On leaving England he main-
tained a friendly correspondence
with Oldenburgh, and in 1676
the latter forwarded to Leibnitz
an account of Newton's theory
of fluxions, concealed under an
anagram. A year later, in 1677,
Leibnitz replied to Oldenburgh with ' a short account of an equally
general method which he had invented, which he called the differ-
ential calculus '. This Leibnitz definitely published in 1684 in his
journal, the Acta Eruditoriim.

The position was now that whilst Leibnitz's calculus was
published and was spreading rapidly on the Continent, Newton's
* fluxions ' was unpublished and unknown except to a few friends.
Indeed, it is somewhat ironical that the first book to appear in
England connected with the subject was a treatise by Craig,
who definitely acknowledged Leibnitz as his source.

At first there was little dispute between the two rivals. Each

Fig. 71. GOTTFRIED \\ I LllJ^LM
LEIBNITZ

The Battle of the Calculus 167

appeared to agree that the two systems were honestly invented
independently of each other. But external circumstances
gradually drove them into controversy. The beginning of this
was seen in the growing rivalry in this period between the English
and the Continental mathematicians. For this there was no
definite foundation ; yet it was there. Leibnitz's differential
calculus had spread so rapidly abroad that mathematicians here
who knew Newton felt that a great injustice was being done to
their premier philosopher.

Of the later developments in this unfortunate controversy we
will say very little. Before the matter was finally dropped,
there were even open accusations against Newton on the part
of Continental mathematicians to the effect that he had derived
his own ideas from Leibnitz. The Royal Society, at the request
of Leibnitz, held an inquiry into the whole question. From
this Newton's reputation emerged unblemished.

One further remark we will make. The world can never
know the real facts, for the vital witnesses, the only two who
really knew the whole truth, the two men who in 1676 had
passed on Newton's papers to Leibnitz, were John Collins and
Oldenburgh ; the former died in 1683, the latter in 16S4, whilst
Leibnitz's theory of the differential calculus was published
immediately after.

And what was the result after all ? The personal feeling which
had been aroused by these serious events was so strong that in
England only the theory of fluxions was taught, whilst on the
Continent the differential calculus made rapid progress. The
latter, of course, proved in fact to be much the better theory in
its many applications to the problems of physics, mechanics,
and astronomy, and so we find that for some time after Newton's
death, whilst great strides were made in these subjects on the
Continent, in England there was little more than a marking
of time.

i68

9. Newton's Later Life

In 1669 Newton had succeeded Dr. Isaac Barrow to the
Lucasian Professorship of Mathematics at Cambridge University.
We may judge the high esteem in which he was held by his
countrymen from the fact that when, owing to the lapsing of
his fellowship, in 1675 he found himself faced with financial
anxieties, he was granted a special patent by the Crown authoriz-
ing him to retain the fellowship for as long as he held the
professorial chair.

So the years went on, Newton's time being fully taken up with
lectures, research, and the controversies arising therefrom, and
occasionally with a variation of the routine by theological studies.
His work was by no means confined to the subjects which we
•have already discussed. He was greatly interested in chemistry,
in chronological astronomy, and in thermometry. He was the
first to prove that change of physical state, i. e. freezing and
boiling, took place at a constant temperature. He was also
interested in geology, in magnetism, and electricity, and indeed
in almost every branch of natural philosophy.

By 1687 Newton had completed the three books which con-
stitute his great masterpiece, the Principia, and in that year
there developed an interesting conflict between Crown and
University in which Newton became involved. King James II
had issued an order to the authorities of the University of Cam-
bridge that one Father Francis, a Benedictine monk, should be
admitted to the degree of Master of Arts without taking the
oaths of allegiance and supremacy. The university regarded this
as an infringement of their rights and privileges, and they refused
to comply with the King's command. The Vice-Chancellor was
ordered to London to answer the charge of contempt for the
authority of the Crown, and he took with him a delegation of
nine to uphold the rights of the university in the High Courts.
One of these was Newton, and he played a prominent part in
the subsequent proceedings, with such success that the Crown
gave way. By way of reward, Newton was in 1688 elected to
parliament as a member for the university, though by a narrow

Later Life 169

majority. This parliament was dissolved in 1689, and he then
returned to Cambridge once more to pursue his professorial duties.

The strain of work, at all times heav5^ now began to tell on
him, and at the age of fifty, in 1692, he had a serious breakdown.
Usually quiet, shy, and reserved, he began to develop an irrita-
bility and a forgetfulness which a bad bout of insomnia only
served to accentuate. One morning he went to early service
leaving a lighted candle on his desk. On his return he found that
there had been a fire as a result of the upsetting of the candle,
caused, it is asserted, by his little dog ' Diamond ' . But whatever
the cause, several valuable papers which were the results of
considerable labour on his part were totally destroyed, and
Newton was much affected thereby. ' I am extremely troubled
at the embroilment I am in ' , wrote he to Mr. Pepys, ' and have
neither ate nor slept well this twelvemonth, nor have I my former
consistency of mind.' A period of melancholy followed. Some
assert his mind was affected, but this is highly improbable. There
is no doubt that his normal powers of concentration were tem-
porarily absent, but beyond this there was nothing other than the
irritability and nervous depression of a temporary breakdown
in health.

He soon regained his former health and elasticity of mind,
and in 1694 we find him engaged in a discussion with Flamsteed,
England's first astronomer royal, on certain problems connected
with the moon's motion.

In the same year, his former parliamentary friend, Mr. Montague,
afterwards Lord Halifax, became Chancellor of the Exchequer,
and in the course of his duties at this post he became interested
in the problem of the improvement of the coinage, at that time
in a debased condition. In this connexion Mr. Montague in
1695 offered Newton the position of Warden of the ]\Iint. As
the appointment carried with it a salary of some hundreds of
pounds a year, and the duties were such as not to interfere with
his university professorship, Newton accepted the offer. His
scientific knowledge enabled him to carry through the task of
recoinage with great skill, and as a rew^ard for his services he was
in 1697 promoted to the position of Master of the Mint with
a considerably increased salary, and shortly after this he received

lyo Sir Isaac Newton

the signal honour from France, in 1699, of having his name enrolled
as the first foreign Associate of the Academy of Sciences at Paris.

Newton was a conscientious man, and he soon realized that he
had now undertaken more duties than he could properly carry
out. We must remember that in addition to his professorship
at Cambridge and his Mastership of the Mint, he was at this time
embroiled in a bitter controversy respecting his theory of fluxions.
And so we find that in 1703 Newton resigned his chair at
Cambridge, thus terminating an honourable connexion with
Trinity College which had lasted since 1660, in which year he
had first become an undergraduate.

With this step, too, the main work of his life may be said to
have ended. The brilliant researches into so many branches of
scientific activity which had characterized the past twenty-five
years of his career were replaced by the steady labours attendant
upon his duties at the Mint, supplemented by an active interest
in the scientific w^ork of his contemporaries, and, as we have
already seen, an active defence of his own work in the past
against the attacks of his Continental traducers.

In 1703, the year in which he vacated his professorship, he
was elected President of the Royal Society, and in 1705 he received
the honour of knighthood from Queen Anne. His university,
too, had once more elected him as its representative in parliament,
and what with the Mint, the Parliament, and the Court (at which
he was now a great favourite), how different was the general
routine of his life as compared with the days of his lectures, his
experiments, and his calculations !

Yet he still remained a power of the first magnitude in the world
of science and mathematics. At this time there had developed
a system of international rivalry in mathematics which took
a very curious form. It consisted in the bandying about of
challenges. A man would develop a difficult problem the solution
of which would often involve some really original work, and he
would challenge the world to solve it. Presumably the challenger
himself would have a solution ready, and his object was to assert
his own superiority over his contemporaries. All the great
mathematicians of the day took part in these challenges : the
two Bemouillis, Huyghens, Leibnitz, de I'Hopital, and Newton.

Later Life 171

Newton was never beaten. For example, in 1697 John Ber-
nouilli proposed the problem of finding the nature of the line
other than a vertical straight line, along which a body must
descend from one point to another in the minimum of time.
Leibnitz spent six months in finding a solution and then trium-
phantly suggested sending the problem to Newton. Newton
gave a complete solution within twenty-four hours. He published
it anonymously, but Bemouilli at once recognized his hand,
exclaiming ' Ex ungue leonem ! ' (* Even as the lion is known
by his paw.') On another occasion, in 1716, Leibnitz proposed
another problem which Newton received one afternoon after
a fatiguing day's work. Nevertheless he solved the problem
within five hours.

Throughout his old age, as with his earlier years, we find in this
great man the same shyness, modesty, and sensitiveness of nature.
He seldom talked of personalities, of himself or of others. Yet with
it all he was ' candid and affable, and always put himself on a level
with his company ' . In appearance he was of medium height,
inclined to stoutness in later life, square-jawed, and sharp-
featured. His hair was grey from the age of thirty, and speedily
became silvery white, lending him a venerable appearance. He
had no recreation and took no exercise. Hard work and deep
meditation for anything up to eighteen hours per day were his
usual portion.

The stories of his absent-mindedness during the period of his
absorption in his problems are legion. Thus he was riding home
once and dismounted to walk his horse up a steep hill. When he
reached the top he emerged from a reverie to find that the horse
had slipped the bridle and gone away, leaving the bridle in his
hands. On another occasion he left his guests to get some more
wine, but forgot all about them and was found hard at work in
his study. Yet another story tells of how a friend. Dr. Stukeley,
called on him. Newton was out but his table was laid for dinner.
Dr. Stukeley lifted the cover and ate the dinner, and then replaced
the cover. When Newton appeared later he greeted Stukeley,
and sat down and lifted the cover. ' Dear me,' said he, ' I thought
I had not dined, but I see I have.' So the years went by. He was
always occupied with mental employment, and usually enjoyed

172 Sir Isaac Newton

an even state of health, until he was about eighty years of age.
He began to suffer from gout and other ailments, in the intervals
between which his mind remained unclouded. Much of his time
was now given up to study of divinity. On the 28th of February
1727 he rather unwisely attended a meeting of the Royal Society,
from the fatigue of which he never recovered. He became
insensible on the i8th of ]\Iarch and passed peacefully away on
the 20th, in the eighty-fifth year of his age.

The nation paid his memory all honour. For a week his body
lay in state, and on the 28th of March he was interred in West-
minster Abbey, and here a handsome monument was afterwards
erected to his memory.

Eulogies on his life and character exist by the score. One of
the most interesting is that attributed to Leibnitz. On being
asked by the Queen of Prussia what he thought of Newton, his
answer was, * Taking mathematicians from the beginning of the
world to the time when Newton lived, what he had done was
much the better half. The following eulogy from Playf air's
Dissertation is also worthy of mention :

' To his important inventions in pure mathematics Newton
added the greatest discoveries in the philosophy of nature ; and,
in passing through his hands, mechanics, optics, and astronomy
were not merely improved but renovated. No one ever left
knowledge in a state so different from that in which he found it.
Men were instructed not only in new truths, but in new methods
of discovering truth : they were made acquainted with the great
principle which connects together the most distant regions of
space, as well as the most remote periods of duration ; and which
was to lead to future discoveries, far beyond what the wisest
or most sanguine could anticipate.'

For, comparing scientific knowledge as he left it with the state
in which he found it, his work was in the real sense of the term
a revelation. His own view of it all is characteristically modest,
and fully worthy of record, and with it we conclude his biography.
* I know not ' , wrote he shortly before his death, * what the world
may think of my labours, but to myself it seems that I have been
but as a child playing on the sea-shore ; now finding some
prettier pebble or more beautiful shell than my companions,
while the unbounded ocean of truth lay undiscovered before me.*.

X

ROBERT BOYLE

I. Early Life

In comparison with the intellectual giant whose life and work
we have just studied, the achievements of the more normal type
of scientific pioneer must inevitably appear at a serious dis-
advantage. Nevertheless full
tribute must be paid to the
brilliant band of contem-
poraries who lived and worked
in Newton's days. This was
a period so rich in scientific
genius that it would be unjust
to study the work of any one
man without clearly pointing
out that he is chosen, not for
any outstanding merit above
his colleagues — Newton being,
of course, a notable exception
■ — but rather as a typical
representative of the genius
of his days.

With this understanding we
come to a brief study of the life of the Hon. Robert Boyle,
' saint and scientist '. He belongs to the earlier half of Newton's
days, but apart from the famous 'Boyle's Law', which has
brought him the notice of all schoolboys, his chief mission was
to teach, by the strong force of his lifelong example, the value
of experiment in research. That example was indeed necessary.
The original pioneers, Galileo and Gilbert, had been followed by
the Cartesian school of thinkers, who preferred synthesis and
theory to analysis and experiment. Francis Bacon, Lord Verulam,
had pleaded for an experimental basis for research, though not
himself a scientist. But what he preached Robert Boyle prac-
tised, and he did so with a patience and a persistence which,

Fig. 7:

THE HON. ROBERT
BOYLE

174 Robert Boyle

accompanied as it was by many successful contributions to
scientific knowledge, fully entitle him to be reckoned in the fore-
front of the world's great philosophers.

Robert Boyle was an Irishman, and was bom at Lismore in
Ulster on the 25th of January 1627. He was the seventh son of
Richard Boyle, Earl of Cork, a man who was able to trace his
descent back to Saxon times. According to the Domesday Book,
the family of Biuvile (as the name was then written) held land
in Herefordshire. The Boyle family were not, however, possessed
of much wealth when Richard Boyle went to Ireland. Indeed,
he tells us that when he arrived at Dublin in 1588 his total
fortune was twenty-seven pounds three shillings, a diamond ring,
a gold bracelet, personal clothing, a rapier, and a dagger. He
made good, however, and was able to buy from Sir Walter Raleigh
all his lands in Munster. He was created Earl of Cork in 1620.

Robert's mother, Catherine, only daughter of Sir Geoffrey
Fenton, the Irish Secretary of those days, died when he was but
three years old. His upbringing was therefore in the hands of
his father. The earl took his responsibility very seriously. He
had his 'views' on the subject of training a child. He was
genuinely fond of Robert, but he was no ' mollycoddler ' , and
with no wife to say him nay, he was able to carry out his theories
with probably much greater freedom than he might have done had
Robert' smother been still alive. ' He had ' , says one biographer,
' so great an aversion to the ill-judged fondness of some parents,
who will scarce let the sun shine, or the wind blow upon their
children, that he committed him to the care of a nurse in the
countr}^ with orders to bring him up hardy.' The simple life
and the healthy air no doubt benefited Robert greatly, but there
was one unforeseen result which a different theory of education
might have avoided. Among the country children with whom
Robert used to play were some who stuttered. Early childhood
is an age of imitation, and it was not long before young Boyle
stuttered too. The imitations first made in jest soon became
an unbreakable habit, and Boyle stuttered for the remainder of
his life.

When eight years old, he was sent to England to be educated

Early Life 175

with his brother at Eton under Sir Henry Wotton, an old friend
of his father's. Here Robert learned French and Latin rapidly,
and showed signs of coming scholarship of a high order. He was
the victim of a certain amount of favouritism, however, in the
sense that his master would often ' bestow upon him such balls
and tops and other implements of idleness as he had taken away
from others that had unduly used them '. He was unusually
introspective for a child. He studied himself and his mental
tendencies to a surprising degree, and he tells us that when he
found himself developing irregular mental habits he would
endeavour to cure himself by settling down to such humdrum
tasks as problems in square and cube roots. Certainly as a result
he became a clear thinker^' On one occasion the wall of his bed-
room fell in, and only the curtains of his bed saved him from
serious damage. The dust raised by the debris was, however,
so very thick that he would have been stifled but for the fact
that his quick brain prompted him to wrap his head in the sheet
and allow the air to strain through it.

After four years at Eton, Robert was withdrawn from school
by his father, and he spent the next few years with a private
tutor at Stalbridge. He now began writing verse, studying the
Scriptures, and recording the memoirs of his school-days.
This was surely remarkable in a lad of twelve years, and
inclines one to look for a tendency to scientific precociousness in
him, but there was no sign of this. He was evidently of a some-
what emotional disposition. He began to show an earnest desire
to study the Scriptures in their original languages. For this
purpose he was sent abroad in 1638, accompanied by an older
brother. Both were placed under the charge of M. Marcombe,
a French tutor, and they used their time abroad under his wise
guidance to the best advantage. They first went to Leyden, in
Holland, for a short course at the university ; thence into France,
staying for a while at Lyons, and later into Switzerland, where
for a time they settled at Geneva.

It was here that Robert Boyle suffered the great emotional
experience which, as he freely confesses, strongly inclined him
towards an earnestly religious life for the remainder of his days.

175 Robert Boyle

He was badly frightened by an unusually severe thunderstorm
in the middle of the night. To use his own words, written in
the third person,

' For at a time which (being in the very heat of summer)
promised nothing less, about the dead of night that adds most
terror to such accidents, [he] was suddenly waked in a fright with
such loud claps of thunder (which are oftentimes very terrible in
these hot climes and seasons), that he thought the earth would
owe an ague to the air, and every clap was both preceded and
attended with flashes of lightning, so frequent and so dazzling
that he began to imagine them the sallies of that fire that must
consume the world. The long continuance of that dismal tempest
where the winds were so loud as almost drowned the noise of the
very thunder, and the showers so hideous as almost quenched the
lightning ere it could reach his eyes, confirmed him in his appre-
hensions of the day of judgement being at hand. Whereupon
the consideration of his unpreparedness to welcome it, and the
hideousness of being surprised by it in an unfit condition, made
him resolve and vow that, if his fear were that night disappointed,
all his further additions to his life should be more religiously and
watchfully employed. The morning came, and a serene, cloudless
sky returned, when he ratified his determinations so solemnly,
that from that day he dated his conversion.'

The two Boyles left Geneva later for Italy, and amongst other
places they visited Florence. Here Robert made a study of
Galileo's writings, and they impressed him profoundly, and
doubtless his later love of experimental science must have been
largely inspired by this visit.

2. The Royal Society

In 1644 the two returned home. Their father had just died,
and Robert found himself the inheritor of the Stalbridge estates.
The country was in a turmoil owing to the war between the
Royalists and Parliament ; but in this conflict Boyle took no
part. He was essentially a student, and had no interest in
politics. Whatever the ruling authority, he was prepared to
abide peacefully by the laws of the land and to do his duty as
a citizen and a Christian.

There were others, too, who preferred study and philosophic

The Royal Society 177

discussion to partisanship and strife, and these people gravitated
instinctively towards each other. They constituted themselves
into an ' invisible college ', as they called themselves, and
their gatherings were important as being the foundation of
what became ultimately the Royal Society for the Advancement
of Learning.

Boyle derived much pleasure from these gatherings, and indeed
he found himself in a goodly company. The original idea of the
formation of this philosophical debating society appears to have
come from Dr. Theodore Hooke, a German scientist who had
settled in England, and who must not be confused with Robert
Hooke who was so persistent an opponent of Sir Isaac Newton.
These virtuosi, as Boyle called them, included such men as
Seth Ward, afterwards Bishop of Salisbury, Dr. Goddard,
Dr. Wallis, afterwards the Savilian Professor at Oxford,
Dr. Wilkins, Warden of Wadham College, Oxford, and later the
Master of Trinity, Cambridge, Dr. (afterwards Sir William) Petty,
Dr. Ralph Bathurst, and Christopher Wren. They met originally
in London, 1 their meetings dating from 1645. Their ' venue ' was
varied according to circumstances. When subjects connected
with the study of optics were under discussion, they would meet
at Dr. Goddard's lodgings, because that eminent philosopher
kept an assistant at work there, grinding lenses and constructing
optical instruments. At other times they would meet at Gresham
College. The range of the subjects discussed was very wide, and
the only topics that were forbidden were politics and religion.
It is well that we should ponder over the striking contrast of these
gatherings in the peaceful atmosphere of science to the surround-
ing conditions of strife, bloodshed, and political dissension.

For some years the gatherings continued in London. Boyle
attended whenever he could, but he was something of a wanderer
at this period, and much of his time was spent both on his Irish
estates and at Stalbridge. When in London he lived with a sister.
Lady Ranelagh, to whom he was devotedly attached. Boyle

^ Informal gatherings probably began at Oxford, but these were not
on the organized scale of those which were held in London, and which
probably mark the true beginnings of the ' invisible college '.
2613 M

178 Robert Boyle

was a life-long celibate, though when he was twenty he courted
the beautiful daughter of Cary, Earl of Monmouth. Although
he did not marry the lady, she was nevertheless the source of
much literary inspiration in him, and to her influence is attributed
a work Boyle wrote called Seraphic Love. He also wrote a Free
Discourse against Swearing much about this time.

On his return from Ireland in 1654, Robert Boyle definitely
settled in Oxford, and now began to take up scientific investiga-
tion in deep earnest. Being a comparatively wealthy man, he
had no difficulty in doing this. He equipped a laboratory in his
lodgings, and engaged Robert Hooke as his assistant, and these
two collaborated in many investigations of first-class importance.

By this time, too, a number of the original members of the
' invisible college ' had removed to Oxford. In order to maintain
proper continuity of discussions, and to avoid disbanding the
' college ', it was arranged for meetings to be held both at London
and Oxford. A proper intercourse was thus maintained between
the two ' branches ' so as to keep in touch with the problems upon
which each was engaged.

At Oxford, as in London, the ' venue ' was varied to suit the
circumstances of the occasion. Thus Dr. Petty 's lodgings were
at the house of an apothecary, and discussions which involved the
handling or inspection of drugs were, therefore, most conveniently
held there. But Boyle's lodgings and laboratory came in for the
larger share of the meetings at Oxford. The importance of this
unofficial organization soon became evident to everybody inter-
ested in philosophy, and those in authority began to realize that
a great national service would be done by extending to this band
of virtuosi the official recognition of the state. The return to
power of King Charles II, himself a dilettante student of science,
offered the opportunity, and in 1660, ' the invisible college ' was
finally incorporated by Royal Charter into the Royal Society,
and its members became Fellows. The Honourable Robert Boyle
was a member of the Council from the outset, and so important
has this institution become in the scientific scheme of this country
that a Fellowship of the Royal Society is nowadays regarded as
the greatest scientific distinction which a man can receive.

179

3- Researches on the Atmosphere prior to Boyle

The study of the physics of the atmosphere is one with which
must be honourably associated the names of Blaise Pascal
(1623-62) in France, Evangelista Torricelli (1608-47) ^.nd
Vincenzo Viviani (1622-1703), both pupils of the great Galileo,
in Italy, Otto von Guericke (1602-80) in Germany, and Robert
Boyle in England. What was the position when Boyle began to
take the matter up for experimental investigation ?

Prior to Galileo, very little was known about the atmosphere,
and from the days when Aristotle taught that there could be no
such thing as a vacuum, the general belief as expounded by
philosophers in general, even up to the time of Descartes, was in
the dictum that ' nature abhors a vacuum '. The ' horror vacui '
was an established institution, as though nature held its own views
on the subject, and had its own feelings in the matter.

The first doubts — and they were but vague — were held by
Galileo when he was told that a suction-pump having a very long
suction-pipe was unable to raise a greater ' head ' of water than
about thirty- three feet. We know now that this was simply
because such a head of water was a measure of the atmospheric
pressure, but Galileo, not knowing this, merely wondered if this
did not indicate a measurable limit to the force of the ' horror
vacui '. We may also say of Galileo that he knew that the air has
weight. This he showed by weighing a glass vessel filled with air,
and then forcing more air in under pressure and weighing again.

Galileo's friend and pupil, Torricelli, took the next important
step in this subject. Accepting the fact that the ' head ' of about
thirty-three feet of water was a measure of the resistance of a
vacuum, he argued that it could be better measured with a heavier
liquid. He chcse mercury and expected to get a column about
one-fourteenth of the height of the water column. The historic
experiment, always associated with his name, was actually
performed in 1643 by Viviani, pupil of both Galileo and Torricelli,
and was a thorough success. It was virtually the first barometer
in history. The full significance of this experiment was un-
doubtedly not lost upon- Torricelli. Although he never actually

M 2

i8o Robert Boyle

published his account, he wrote of it in detail to his friend Ricci;
in Rome, in the course of which he declared, ' the aim of my
investigation was not simply to produce a vacuum, but to make
an instrument which shows the mutations of the air, now heavier
and dense, and now lighter and thin '. He even realized the
expansion effect of the temperature as a disturbing factor in his
results, though it was not until 1704 that any proper temperature
corrections were applied to barometric readings.

The next great step was taken by Pascal. This young genius
— who established his fame as a mathematician when but sixteen
years old and died at thirty-nine — heard of the Torricelli experi-
ment indirectly from Father Mersenne (of whom we have already
heard in Chap. VIII as the intermediary between the great
mathematicians of those days), who had himself received an
account of the experiment from Ricci. Not all the details reached
Pascal, who therefore had to think out the lessons of the experi-
ment independently. He records as his conclusion ' that the
vacuum is not impossible in nature, and that she does not shun
it with so great a horror as many imagine '.

Pascal's next step was of profound importance. If, he argued,
Torricelli's mercury column was held up by the pressure of the
air only, then surely at a high altitude there is less air and, there-
fore, less pressure, and the mercury column would be shorter.
So he measured it at the top of a church steeple in Paris. The
difference was insufficient to be conclusive. He therefore asked
a brother-in-law in Auvergne to try this experiment by ascending
the mountain known as the Puy-de-D6me. One can imagine the
delight of the experimenter in finding that at the completion of
the ascent the mercury column had fallen three inches.

So ended the doctrine of the ' horror vacui ' in France and
Italy. Meanwhile in Germany Otto von Guericke was conducting
his experimental campaign to the same end. Some of his experi-
ments were both ingenious and theatrical, and were connected
with a study of ' suction '. He filled a wine cask with water,
tightly closed up the cask, and then tried to remove some of the
contents by means of a brass pump. But he only succeeded in
bursting the connexions between cask and pump. On strengthen-

1

Researches on Atmosphere prior to Boyle i8i

ing these connexions and trying again, it required three strong
men pulling at the piston to draw some water out, to the accom-
paniment of the hissing noise of air forcing its way in through
small leaks to replace the water. He
next replaced the leaky cask by a copper
sphere, and although water was drawn
out at first, the effect of the air pressure
outside was such as to cause the sphere
suddenly to collapse ' with a loud clap
and to the terror of all '.

The result of Guericke's experiments
was his invention of the air pump. It
was a crude affair whose chief merit lay
in the fact that it was the forerunner of
better things, but nevertheless it did
enable him to carry out experiments
with varied pressures. For example, he
found that ' a clock in a vacuum cannot
be heard to strike ; and a flame dies
out in it ; a bird opens its bill wide,
struggles for air, and dies ; fishes perish ;
grapes can be preserved six months in
vacuo, and so on.' Then there was his
famous experiment of the Magdeburg
hemispheres, i-2 feet in diameter. These
were held together by the atmospheric
pressure on exhausting the interior, and
in an impressive experiment before the
Emperor Ferdinand III and the Reichs-
tag in 1654, the hemispheres were pulled
apart only when teams of four pairs of horses were hitched to each.

Guericke's contributions to scientific investigations were many
and varied, and included a ' weather glass ' for predicting the
weather and an electrical machine based on the excitation of
a rotating ball of sulphur ; whilst in astronomy he interested
himself successfully in the periodicity and orbits of comets.
Guericke's researches were published in Experimenta Magde-
hurgica in 1672. He died in 1686.

Fig. 73. Boyle's pneu-
matic engine or air-pump.

l82

4. Boyle's Researches on the Atmosphere

Guericke's air-pump and experiments were first described in a
book by Kaspar Schott, called Mechanica hydraidico-pneumatica,
published in 1657. It was through this work that Robert Boyle
learnt these researches, and they stimulated him into taking up
the subject for himself. At this time
he was living at Oxford, where he had
set up a laboratory with Robert Hooke
as his chief assistant.

At the outset Boyle realized that for
efficient work, something less crude and
more workmanlike than Guericke's air-
pump would have to be devised. This
then was his first problem — the invention
of an efficient pump which would enable
him to experiment freely at pressures
both greater and less than that of the
atmosphere. The instrument which was
produced can, however, hardly be said
to be Boyle's, since Guericke supplied
the original idea, and Hooke supplied
the mechanical skill. Both Boyle and
Hooke freely collaborated to produce
the result, and accordingly they share

Fig. 74. Diagram illus-

tratinsr the principle of ^, ,
Boyle's air-pump. the honours

The principle of the instrument is
shown diagrammatically in Fig. 74. In the light of modern
air-pump practice it seems, of course, very crude. Never-
theless, it was a real advance on the pumps of those days,
and, as we shall see shortly, it was the means of achieving
much. The glass receiver R was spherical in shape and of
about three gallons capacity. It was closed at the top by
a brass plate fitting into a hole in which was a brass stopper S.
Dangling from S was a string and hook from which could be
suspended any article which it was required to subject to varying

Researches on the Atmosphere 183

pressure. The receiver R was made to communicate with the
vertical pump-barrel C by means of a pipe and stop-cock A.
There was a hole at the top of the barrel C which could be used
as an exhaust or kept closed by means of a brass plug B, as
desired. The piston P was made of wood, and was surrounded
by well-greased leather. It was solid and contained no valves,
such things being then unknown. The piston was actuated by
a rack and pinion arrangement D on the piston rod, the pinion
being worked by hand.

Suppose we wish to exhaust R. The procedure is as follows.
Open the stop-cock A, keeping B shut.
Draw P down. The air originally only
in R now also fills C. Hence the pressure
in R is somewhat reduced. Now close A
and open B, and move P up. The air in
C is driven out through B, and we are
now able to repeat as before, each cycle
of operations leaving the pressure in R
more and more diminished.

Suppose, on the other hand, it is required
to increase the pressure in R. The pro-
cedure described must be reversed. Keep-
ing A open and B closed, and starting with
P at the bottom, move P up, so driving the air from C into R.
Close A and open B, and move P down. More air is thereby
drawn into C from outside. Close B, reopen A, and repeat as
before, and it will be seen that each such cycle of operations leaves
the air in R at increased pressure.

This then was the apparatus with which Boyle equipped himself
in order to carry out his researches. What did he do ? One of
his first experiments was to measure the weight of a 'given sample
of air. His predecessors had contented themselves rather with
showing that the air has weight than with measuring what that
weight was. Boyle suspended a balance in the receiver R. From
the left pan dangled a bladder half-filled with water, and in the
right pan were weights to produce exact balance. On exhausting
the receiver the bladder and its contents of air and water were

Fig. 75. Boyle's deter-
mination of the weight of
the air.

184 Robert Boyle

now heavier. By a series of trials, the weights on the right hand
side were now adjusted so that exact balance was obtained not
before introducing into 7^, but after R was evacuated. The
difference between the two readings was then a measure of the
weight of the air in the bladder.

Boyle was able to demonstrate the degree of rarefaction
which his pump could produce by introducing into R a barometer
tube and reservoir (Fig. 76), and cementing the joint at ^. By
exhausting R he succeeded in getting down to less than one inch
of mercury. Boyle realized how this, of
which he speaks in his work The Spring oj
tlie Air as the nineteenth experiment, dis-
proved the theory of the ' horror vacui '.
For considering the evacuated space
above the liquid in the barometer tube,
he writes :

Fig. 76. Barometer
readings at reduced pres-
sure.

' And as for the care of the public good
of the universe ascribed to dead and stupid
bodies, we shall only demand why, in our
nineteenth experiment, upon the exsuc-
tion of the ambient air, the water deserted
the upper half of the glass tube, and did
not ascend to fill it up till the air was let
in upon it. Whereas, by its easy and
sudden rej oining that upper part of the
tube, it appeared both that there was then much space devoid of
air, and that the w^ater might, with small or no resistance, have
ascended into it, if it could have done so without the expulsion
of the re-admitted air ; which, it seems, was necessary to mind
the water of its former neglected duty to the universe.'

After which sarcasm he proceeded to the true explanation in
terms of the pressure of the air in R.

Another of his experiments was on the subject of suction.
Having exhausted R as far as possible, he closed the stop-cock 5
and removed the receiver from the pump. Immediately below
the pipe was placed a brass valve V (Fig. 77) to which was
attached a small scale pan P. On suddenly opening 5 the at-
tempted inrush of air into R created an upward thrust on the

Researches on the Atmosphere 185

under surface of V, forcing it up against the inlet pipe below R,
and automatically closing it. The force of suction here brought
into play could now be measured by putting weights in the pan
P until the valve was just forced away again. This Boyle refers
to in The Spring in the Air as his thirty-second experiment. He
wrote as follows :

' For, in the next place, our experiments seem to teach that the
supposed aversation of Nature to a vacuum is but accidental, or
in consequence, partly of the weight and fluidity, or at least the
fluxility of the bodies here below ; and
partly, and perhaps principally, of the
air, whose restless endeavour to expand
itself every way makes it either rush in
itself or compel the interposed bodies
into all spaces where it finds no greater
resistance than it can surmount. And
that in those motions which are made
" ob fugam vacui " (as the common phrase
is) bodies act without such generosity and
consideration as is wont to be ascribed to
them, is apparent enough in our thirty-
second experiment, where the torrent of
air, that seemed to strive to get into the
emptied receiver, did plainly prevent its
own design, by so impelling the valve as
to make it shut the only orifice the air
was to get in at. And if afterwards either
Nature or the internal air had a design the
external air should be attracted, they seemed to prosecute it
very universely by contriving to suck the valve so strongly, when
they found that by that suction the valve itself could not be
drawn in ; whereas, by forbearing to suck, the valve would, by
its own weight, have fallen down and suffered the excluding air
to return freely and to fill the exhausted vessel.'

There were many other experiments, not all connected with
hydrostatics, as for example, the suspending in the receiver of
a watch to show that sound will not travel in a vacuum, but
requires a medium for its propagation. The above, however,
are probably the most important of his first series of experiments.

Fig. 77. Bowie's Experi-
ment on Suction.

i86

5. Discovery of Boyh's Law

In 1660 Boyle published his results in a work called New
Experiments . . . touching the Spring of the Air, He illustrated
the pressure exerted by the air by calling to his aid a sort of
analogy in which he pictured the air particles as behaving as
though each was like a spherical spring. The effect of pressure
was to compress the spring and so to diminish the volume.

The book was on the whole a sound record of experimental
work. Nevertheless, it met with a certain amount of opposition,
particularly from Franciscus Linus, a Jesuit father of Liege.
Linus offered, by way of objection to Boyle's simple conten-
tions, the view that the air was of itself incapable of per-
forming ' such great matters as the counterpoising of a mercurial
cylinder of 29 inches ; he claimed to have found that the mercury
hangs by invisible threads {funiculi) from the upper end of the
tube, and to have felt them when he closed the upper end of the tube
with his finger '. In these days one is tempted to wonder that
Boyle should have troubled to reply to such utter nonsense, yet
he did, and on the whole it is well he did so. For as a consequence
of the further experiments which he now undertook by way of
reply to Linus, he discovered that great truth which we all speak
of to-day as Boyle's Law.

' We shall now endeavour ', wrote he,^ ' to manifest by experi-
ments purposely made, that the spring of the air is capable of
doing far more than it is necessary for us to ascribe to it, to solve
the phenomena of the Torricellian experiment. . . . We took then
a long glass tube, which by a dexterous hand and the help of
a lamp was in such a manner crooked at the bottom, that the
part turned up was almost parallel to the rest of the tube and,
the orifice of this shorter leg . . . being hermetically sealed, the
length of it was divided into inches (each of which was divided
into eight parts) by a straight list of paper, which, containing
those divisions, was carefully pasted all along it.'

A similar scale was pasted on the other limb, and mercury was

then introduced ' to fill the arch or bended part of the siphon ',

so that the level was the same on each side (Fig. 78 {a)). ' This

^ Boyle's Defence against Linus.

I
29'

Discovery of Boyle's Law 187

done, we began pouring quicksilver into the longer leg . . . till the
air in the shorter leg was by condensation reduced to take up but
half of the space it possessed ... we cast our eyes upon the longer
leg of the glass . . . and we observed not without delight and
satisfaction, that the quicksilver in that longer part of the tube
was 29 inches higher than the other.' He had in fact by applying
a pressure of two atmospheres ob-
tained half the original volume
(Fig. 78 {b)).

By this means Boyle obtained
a series of readings showing the
relation between pressure and
volume for pressures in excess of
that of the atmosphere. It now
remained for him to obtain a
further series for pressures less
than that of the atmosphere. For
this his first tube was of no use.
He now employed a long tube A
(Fig. 79), about 6 feet long, closed
at the lower end, and filled with
mercury. Into this was introduced
a warmed long narrow open tube
B, sealed at the top C with wax.
On cooling, the level of the mercury
rose in B above that of A , the differ-
ence in heights giving the excess of
atmospheric pressure over that of
the imprisoned air. By pushing the tube B farther in or out of A ,
a range of such pressures was obtained, and the corresponding
volumes as measured by the length of the air column were read.

By such methods Boyle was able to range his pressure readings
from as little as ij inches of mercury to ii7r% inches, and he
drew up a table of comparisons of his observed pressures with
the theoretical values he should have obtained ' according to the
h^^o thesis that supposes the pressures and expansions to be in
reciprocal proportion '.

78 79

Figs. 78 and 79. Experiments
on Boyle's Law.

1 88 Robert Boyle

His results, having regard to the difficulties with which he had
to contend, particularly in the second series of readings, were
excellent, and thoroughly established the law with which his
name is so familiarly associated.

In France, however, the law is not so known. Fourteen years
after Boyle's famous experiment, Edme Mariotte, a French
scientist of repute, published a book, Sur la nature de Vair, in
w^hich he described his own independent discovery of the law
* that air condenses in proportion to the weight by which it is
loaded '. It seems indeed curious that Mariotte should have been
unaware of Boyle's researches, yet so it was, and in all French
schools to-day they speak of i\Iariotte's Law just as we do of
Boyle's Law.

6. Further Scientific Work

It must not be supposed that Boyle's scientific interests lay
solely in the direction of the physics of the atmosphere, for
although it is with this subject that his fame is intimately bound
up, yet he has left behind him a solid record of work and specula-
tion in other branches of science.

The subject of heat, for example, engaged Boyle's attention
considerably. Much of this work is recorded in his New Experi-
ments and Observations touching Cold, published in 1665. He had,
for example, used his pump fairly successfully in an investigation
of the influence of pressure on the boiling-point, by introducing
into the receiver some water whose temperature was somewhat
lower than the normal boiling-point. On reducing the pressure
in the receiver he was able to reach a point at which the liquid
started to boil, so showing that reduction in pressure lowered the
boiling-point.

Another of his experiments in heat was to determine the
relative volumes of ice and water. He used for this purpose what
was then spoken of as a ' philosophical e^g ', i. e. a tube terminat-
ing with a bulb, the stem of which was graduated in terms of the
volume of the bulb. Into this he poured water and then im-
mersed the bulb in a freezing mixture (allowing the stem to
project above the freezing mixture in order to avoid bursting by

Further Scientific Work 189

allowing for expansion — a shrewd appreciation of the difficulties
of the experiment). He then measured the final position in the
stem after freezing had taken place. The result — uncorrected
for changes in the glass — gave an expansion of about ii per cent.
— rather a high value.

In these days it has become universally recognized that heat
is but a mode of motion. It is, however, a little startling to
realize that Robert Boyle and some of his contemporaries were
themselves exponents of this view 250 years ago, though their
ideas were somewhat vague and their experiments more so.
Nevertheless, Boyle for one was surprisingly accurate in man}^
of his conclusions. The small particles constituting bodies, he
tells us, are in rapid, haphazard motion in all directions, and this
motion is called heat. Cold is produced by a ' less vehement
agitation ' of the particles, and any means which could be
devised to increase this agitation would be found to produce heat.
To illustrate this view, he arranged for two spherical pieces of
brass so made that the concavity of the one could be placed in
intimate contact b\^ means of springs with the convexity of the
other. They were made to rotate in opposite directions in the
evacuated receiver of his pump. The vacuum was used so as to
meet the objection that the resistance to the air might be the
cause of the subsequent heat. He tells us that the heat produced
was so intense that he was unable to touch either of the brasses.
A further illustration of his as to the heat produced by arrested
motion was a hammer driving in a nail.

In dynamics it is interesting to record that Boyle verified
Galileo's famous ' Leaning Tower ' experiment by eliminating the
resistance of the atmosphere. He exhausted the receiver of his
pump, having first introduced therein a leaden bullet and a
piece of paper. The stop-cock was then closed and the receiver
(in the shape of a long tube) was detached and quickly inverted.
Both bodies were seen to arrive simultaneously at the bottom of
the tube.

Mention must also be made of Boyle's work in magnetism
and electricity. He was the first to show that magnetic forces
act through a vacuum by introducing both magnet and attracted

igo Robert Boyle

object into the evacuated vessel. He did a similar experiment
with regard to electrical attraction. He also records somewhat
amusingty how dry hair is easily electrified by friction. * That
false locks of hair brought to a certain degree of dryness, will
be attracted by the flesh of some persons, I had proof in two
beautiful ladies who wore them ; for at some times, I observed
that they could not keep them from flying to their cheeks, and
from striking these, tho' neither of them had occasion for or did
use paint.' He goes on to tell us of how one of the ladies ' gave
me leave to satisfy myself farther ; and desiring her to hold her
warm hand at a convenient distance from one of these locks taken
off and placed in the free air, as soon as she did this, the lower
end of the lock, which was free, applied itself presently to her
hand '.

7. Boyle's Later Life

Because of the evenness of his thoughts and his ideals the
remaining biographical details of Boyle's life are soon told.
Up to the time of his death he may be said to have devoted him-
self entirely to science and religion, and beyond these he had no
ambitions. But the sense in which he lived a religious life must
not be misunderstood. In 1600 the Earl of Clarendon tried to
persuade Boyle to take holy orders, pleading that the interests
of the Church called for this step. Such a plea would naturally
weigh strongly with Boyle ; nevertheless he refused.

' He reflected that, in the situation of life he was in, whatever
he wrote in support of religion would have as great weight as if
he was in the character of a clergyman. That he needed no
accession with respect to fortune, nor indeed any appetite for
greater, but, above all, according to his wonted modesty, he
frankly declared, that he had not felt any motion or tendency of
mind which he could safely esteem a call from the Holy Ghost ;
and so not venturing to take Holy Orders lest he should be found
to have lied into it.'

Nevertheless, as a layman, Boyle lived a deeply religious life.
He set up for himself a high moral standard, and he lived up to it.
Blessed with private means, he distributed his charity wisely.
The present-day Society for the Propagation of the Gospel in

Later Life iqi

Foreign Parts is an organization which developed from an earlier
one, of which Boyle was president, and amongst the charities
which interested him might be mentioned the care of widows
andiorphans, his distribution of about £i,ooo per annum for the
augmenting of the salaries of poorly paid clergy, and the founding
and endowing of an annual lecture ' in honour and defence of the
Christian religion '. Yet there were clergymen who did not
hesitate to declare 'that Robert Boyle's researches were destroying
religion and his experiments were undermining the universities '.
Boyle's own life stands as a sufficiently emphatic answer to such
an absurd charge.

He declined all honours. In 1665 he was invited to become
Provost of Eton but declined. Always a favourite with royalty,
he was on several occasions offered a peerage, but although four of
his brothers were peers,^ he persistently refused. He even declined
the high honour which he was offered on the 30th of November
1680, of becoming President of the Royal Society, though in this
case his refusal was his religious objection to taking the oath pre-
scribed for the President by the Society's charter of incorporation.

In appearance Boyle was ' tall but slender, and his countenance
pale and emaciated ; his constitution tender and delicate, and
was therefore very careful to observe and regulate himself,
according to the changes of the weather by his thermometer '.
We are also told that ' his health in the latter part of his life was
tender, and frequently interrupted, yet by observing an exact
regimen of diet, and never indulging in excess, he attained to the
sixty- fourth year of his age, and retained his sight to the last '.
His eyesight, however, gave him frequent trouble.

We have alread\^ pointed out how greatly attached he was to
his sister. Lady Ranelagh, and it is touching to note that thev
died almost together, she on the 23rd of December 1691, and he
on 30th December, a week later. Both bodies were interred in
the chancel of St. Martin's-in-the-Fields, in London.

The name of Robert Boyle will live in the annals of science,
firstly, because he opened up by his stimulating researches

^ It is amusing to note that Boyle has been referred to as ' the father
of modern chemistry, and brother of the Earl of Cork ' !

192 Robert Boyle

in aerostatics a scientific land of promise of which even these
days of aerodynamics and aerial locomotion have not exhausted
the possibilities, and secondly, because by the force of his own
precepts and life-long example, he brought about a welcome
reaction from the synthetical school of Descartes back to the
experimental school of Galileo and Gilbert. Practical investiga-
tion meant everything to Boyle. ' In my laborator\7 ', wrote
he, 'I find that water of Lethe which causes that I forget every-
thing but the joy of making experiments.' He is reported to have
said that he feared death only because after it he would know all
things, and no longer have the delight of making discoveries.

We may fittingly conclude this chapter by a quotation from
his book, The Christian Virtuoso, which reads : ' The book of
Nature is a fine and large piece of tapestr}^ rolled up, which we
are not able to see all at once, but must be content to wait for
the discovery of its beauty and symmetry, little by little, as it
gradually comes to be more unfolded or displayed.'

" -^^^f'F. 'vSSfSK^;:

Fig. 80. A chemicallaboratory in 1747.

XI

ANDRE A:\IPERE AND MAGNETIC
ELECTRICITY

I. Science after Newton

The remaining men of science whose lives we are to study
belong essentially to the modern school ; the science which they
helped to develop is the science taught to-day ; and the history
of this last period of our work is one of steady construction and
expansion along the solid paths of knowledge, pursued by great
men of all nations, collaborating in
friendly rivalry with a imity of purpose
the aim of which vvas the pursuit of truth.

Newton's theory of fluxions was not
so pliable as was the rival theor}^ in its
general applications to the problems
beyond those which Newton had him.-
self worked out m his Principia, and
consequently, whilst a rich harvest of
mathematical discovery was being reaped
on the Continent, the mathematical and
mechanical sciences lay stagnant in
England for many years. Yet the
coimtiy was not lacking in mathematical talent. Gregory Sander-
son, Waring, Emerson, T. Simpson, R. Simson, and others did
excellent work, but it was in the department of pure mathe-
matics alone ; whilst, on the Continent, Lagrange, Laplace,
DAlembert, Legendre, Lacroix, Cauchy, and a host of others
were achieving fame in the newer fields of the calculus and of its
applications to dynamics and astronomy.

In physical optics the period of stagnation following the
brilliant record of Newton and his illustrious rival Huyghens
was particularly marked, and hardly a fact of importance was
elicited or a theory advanced until the beginning of the nineteenth
century, when appeared Thomas Young's brilliant researches
on the subject of the interference of light. These inaugurated

2613 N

Fig. Si. ANDRE MARIE

amp£re

194 Andre Ampere

a wonderful recrudescence of research by ]\Ialus, Arago, and Biot
in France, and Wollaston, Brewster, and Herschell in England,
on the subject of polarized light. As a consequence, Huyghen's
wave theory at last came into its own, and a line of investigation
was opened up which has deeply affected all other branches of
physical science.

The long barren interval had produced a rashness of specula-
tion which, without the secure foundation of laboratory data,
had brought into being such futile theories as the ' caloric '
theory of heat, the ' phlogiston ' theory of combustion, the
* effluvia ' theory of magnets, and so on. All this was now
swept aside. Chemistry was caught in the forward' wave with
physical science. Combustion came to be properly under-
stood, the laws of conservation of mass and energy were estab-
lished, the emission theory of light was replaced by the wave
theory, and a wonderful advance was achieved in the study of
electricity and magnetism which not only welded these two
inseparably, but also linked up the study of electro-magnetism
with that of light and radiant energy.

Let us then turn to a brief summary of the advances in the
subject of electricity and magnetism, and see how it came about
that this study occupies its place to-day as the binding factor
of physics in general.

2. Electrostatics prior to Ampere

So far as the study of electricity and magnetism is con-
cerned, the eighteenth century was one of progress only in the
development of electrostatics. Current electricity was com-
pletely unknown, and prior to this period, very little more had
been established than the bare facts of electrification by friction.
Eighteenth-century research may be said to have started with
Stephen Gray, an Englishman, and Charles Francois de Cisternay
du Fay, a Frenchman. Gray established that different substances
possessed the property of electrical conductivity to varjdng
degrees, not through any physical differences such as colour,
hardness, &c., but merely through the differences in material,
so that, for example, metal wire conducts well, whilst silk does

Electrostatics prior to Ampere 195

not. So he developed a grouping of conductors and non-con-
ductors (insulators). It is also interesting to note that Gray-
showed the human body to be a conductor, and he electrified
a boy after suspending him by 'means of silk strings.

Du Fay went farther. It will be remembered that Gilbert had
classified substances as electrics and non-electrics, the former
being capable of electrification, and the latter incapable of
electrification by friction. Du Fay showed this to be an erroneous
view, since aU bodies could be electrified. Those which apparejttly
were ' non-electrics ' were merely such good conductors that they
were losing the charge to surrounding conductors as fast as they
were receiving it. The problem in such cases was therefore
merely one of sufficient insulation. Du Fay also succeeded in
establishing that there were two kinds of electricity, and he spoke
of them as ' vitreous ' and ' resinous ' electricity respectively.

The discovery of the Leyden jar in 1746 by Pieter van Musschen-
broek, a renowned Dutch physicist, was the next important
step. It was an accidental discovery, arising from an attempt
to electrify water in a bottle. Musschenbroek confessed to his
friend Reaumur (of thermometric fame) * that he would not take
another shock for the kingdom of France '. Per contra, Priestley
tells us that Professor Bose, of Wittenberg, was prepared to die by
the electric shock, in order that the account of his death ' might
furnish an article for the memoirs of the French Academy of
Sciences '.

Human nature being what it is, it is not surprising that the
violence of discharge of the Leyden jar attracted much public
attention. This was exploited to the full by itinerant ' per-
formers ', and when the discharge was combined with the human
body as a conductor of electricity, the exhibitions took an even
more elaborate turn. Nollet, ' in the King's presence, passed
the discharge through 180 guards. Later the Carthusian monks
at the Convent in Paris were formed into a line 900 feet long, by
means of iron wires between every two persons, and the whole
company, upon the discharge of the jar, gave a sudden spring
at the same instant. This behaviour of the austere monks must
have been ludicrous in the extreme.'

N 2

196 Andre Ampere

The illustrious American, Benjamin Franklin (1706-90), is
intimately associated with the progress in electrostatics which
now followed. He first drew attention in 1747 to the ' wonderful
effect of pointed bodies, both in drawing off and throwing off
the electrical fire '. In the same communication he enunciated
his now famous ' one-fluid ' theory of electricity (Du Fay had
hitherto taught a two-fluid theory). According to this all bodies
normally possess electricity and only exhibit electrical phenomena
when they acquire more than the normal amount (in which case
they exhibit ' plus ' or ' positive ' electricity) or lose some to

other bodies (in which case they
exhibit ' minus ' or ' negative '
electricity). This theory, which
^'ery simply explains all the or-
dinary elementary phenomena
of static electricity, gained early
acceptance, and successfully held
the field until very recent times.
Benj amin Franklin next turned
his attention to the subject of
atmospheric electricity, with
brilliant success. Thunderstorms
had hitherto been regarded as
due to the explosions of gases
in the upper atmosphere, but
Franklin had recorded a number
of important resemblances between the phenomena of light-
ning and those of the electrical discharge as he knew it from the
Ley den jar. These he set down in his note-book on the 7th of
November 1749 as follows : ' Electrical fluid agrees with hght-
ning in these particulars : (i) giving light ; (2) colour of the
light ; (3) crooked direction ; (4) swift motion ; (5) being con-
ducted by metals ; (6) crack or noise in exploding ; (7) sub-
sisting in water or ice ; (8) rending bodies it passes through ;
(9) destroying anhnals ; (10) melting metals ; (11) firing in-
flammable substances ; (12) sulphurous smell.' He determined
to apply the property of points in ' drawing off the electric fluid '

'IG.82. BENJAMIN FRANKLIN

Electrostatics prior to Ampere 197

to see if he could ' draw down ' the Hghtning, using a metal wire
attached to a kite for the purpose. His experiment, one of the
most famous in the history of science, was a complete success,
and led almost immediately to the installation of lightning
conductors on all large buildings.

As a consequence of the various qualitative researches to
which we have here referred, the way was now paved for giving
the subject a proper quantitative footing. Excellent work in
this field was done by Henry Cavendish (1731-1810) in England,
and Charles Augustin Coulomb (1736-1806) in France, the
former of whom carried out quantitative investigations on the
subject of the capacity of condensers, and even to some extent
anticipated Ohm's Law : whilst Coulomb, as a result of investiga-
tions on the torsional properties of hairs and wires, constructed
a torsion balance in 1777 and with it proved a number of funda-
mental theories in electrostatics and in magnetism. In particular
he showed that Newton's law of inverse squares was as true for
electric and magnetic attractions and repulsions as it was for
gravitation.

3. Current Electricity prior to Ampere

Let us turn now to the subject of current electricity, which
saw its beginnings towards the end of the eighteenth century.
Curiously enough, we owe the inception of this subject to the
researches of Luigi Galvani (1737-98), an Italian physician and
anatomist, on a totally different problem — that of the ability
of certain species of fish to give electric shocks, and from thence
to the study of animal electricity in general. The phenomenon
of the twitching and kicking exhibited by the leg of a dead frog
on being subjected to an electrical discharge was attributed by
Galvani as being due to a source of electricity in the nerve of
the leg. That the convulsions were not due to outside sources
of electricity he deduced from the fact that, for example, on
suspending the leg by copper hooks on the balcony of his house,
each time the wind blew the leg into contact with the iron
of the balcony rail, the twitching was observed, although there

198 Andre Ampere

was neither lightning nor electrical machine to supply the
charge.

Nevertheless, Alessandro Volta (1745-1827), a fellow country-
man, and Professor of Natural Philosophy at the University of
Pavia, challenged Galvani's conclusions, and the ensuing con-
troversy held the attention of the whole of the scientific world.
Although it was as a biologist that Volta was known, he had
yet closely interested himself in electrical science, and had
invented the electrophorus in 1775. Volta suspected that the
use of dissimilar metals, such as the iron and copper, in moistened
contact, was the vital factor in producing the electricity, and
that the nerve had no electricity of its own. He instanced such
phenomena as the metallic taste experienced when holding
a silver and a gold coin against the tongue, the coins being in
contact at one end, or joined by a wire. The reader can try it
by placing a strip of copper above the tongue and a strip of zinc
below, and then allowing the ends to touch.

Volta next discovered that acidulated water gives even better
results than moisture, and the evolution of what we speak of
to-day as the Voltaic cell was the logical outcome. In a letter
to the President of the Royal Society in 1800 he described both
his well-known voltaic pile and his ' crown of cups ' — a series of
cups containing brine or dilute acid, into each of which were
dipped strips of zinc and copper, joined * in series '.

Such then were the beginnings of the study of current elec-
tricity. Of how this subject was developed quantitatively by
Simon Ohm and others, and of how from it there grew up the
study of electro-chemistry, we shall have occasion to speak
later. But we now pass on to another development in the
direction of electro-magnetism of the greatest importance.

The honours of the initial discovery of the hitherto unsus-
pected relationship between electricity and magnetism go to
a Danish scientist, Hans Christian Oersted (1777-1857), a pro-
fessor in the University of Copenhagen, and he performed his
classic experiment which founded the science of electro-magnetism
in 18 19. There happened to be on his lecture-bench a magnetic
needle suppox'ted horizontally. Oersted was experimenting

Current Electricity prior to Ampere 199

with a galvanic battery at the time, and by a happy chance he
drew the magnetic needle towards the battery so that the wire
and the needle were parallel. He was amazed to see the needle,
hitherto peacefully pointing magnetic north and south, swing
round and set itself almost at right angles to its original direction.
He next reversed the direction of the current, and the needle
was again deflected, this time in the opposite direction. It was
a wonderful and a conclusive
discovery. In some way or
other, electricity and mag-
netism were intimately re-
lated to each other.

The experiment was de-
scribed by Oersted a year
later, and at once all Europe
was ringing with its signifi-
cance. A new field of re-
search was opened up. Oer-
sted himself did not contri-
bute anything further. He
had pointed the way, but of
the men who noted the road
and followed it, none did so with more brilliant success and
honour than he to whose biography we now proceed — Andre
Marie Ampere.

4. Andre Marie Ampere

This wonderful Frenchman was born at Lyons on the 22nd of
January 1775. His childhood was as remarkable as was his
later manhood. His father, Jacques Ampere, was a successful
merchant who retired, shortly after the birth of his only son,
to the privacy of a small estate he possessed in the village of
Polemieux.

Little Andre was a born mathematician, and practically
a self-taught one, for there was no school at Polemieux. He took
to arithmetic as a duck to water, and he would sit for hours
playing and calculating with pebbles or kidney beans. We are

Fig. 83. HANS CHRISTIAN
OERSTED

200 Andre Ampere

told that during a severe illness his mother took his pebbles
from him to prevent his exciting his brain with calculations.
She happened to leave him for a little while, and on her return
found that he had broken up a biscuit into little pieces, and
was working with these in the place of pebbles.

Andre's education was undertaken by his father, who first
taught him to read his own language and then proceeded to give
him lessons in Latin. But Andre was hungering for mathematics ;
Latin seemed purposeless to him, and he obviously disliked the
lessons. So his father abandoned them and permitted Andre to
devote his time to algebra and geometry.

In due course he had mastered the contents of such mathe-
matical books as were in his father's library, and he sought
more worlds to conquer. At Lyons there lived a friend of his
father, the Abbe Dubarron, and to him the two went. Little
Andre Ampere was but twelve years of age, yet he knew what
he wanted. He modestly asked for the loan of the mathematical
works of Euler and Bernoulli, two renowned mathematicians !
One can imagine the Abbe's amazement. ' But my little fellow,'
he explained, ' do you know that these books deal with the
differential calculus ? ' It sounded dreadful enough to the lad,
but he stood his ground. ' Well, no doubt I can learn all about
it,' he answered. ' Yes, my son,' said the Abbe, ' but they are
written in Latin ! ' This was a poser for the boy who had given
up the subject in dislike, but there was now a purpose in the
study which before did not exist. ' Then I must learn that too,'
he answered.

Such steadfastness of purpose greatly impressed Dubarron,
who resolved to help the lad. So whilst his father again turned
to teach him Latin, the Abbe took up the calculus with him,
and within a few months he was ready to read the coveted
books.

By the time Ampere was eighteen, he was at the height of his
mathematical knowledge, and as a culminating feat he had not
only read through Laplace's Mecanique celeste and Lagrange's
Mecanique analytiqiie, but had also worked out all the difficult
problems in the former. His reading, however, had not been

Andre Marie Ampere 201

confined to mathematics. He read every book that came within
reach, whatever the subject. Small wonder, therefore, that the
severe tax on his brain strained his health to the breaking-point.
The grief occasioned by the death of his father, who was
guillotined about this time, caused his complete breakdown.

Yet Ampere was young and full of vitality. Given the neces-
sary stimulus, the resilience of youth was bound to assert itself.
The stimulus appeared in the shape of a botanical work by
Jean Jacques Rousseau which chanced to fall into his hands.
The charm of the style, and the theme, so appropriate to the
beautiful surroundings of Polemieux, began to awake that chord
of sympathy for which his mind was waiting. He worked
through the book, he hunted for specimens, and gradually his
mental powers returned.

Another aid to his return to normality was supplied by a book
of Latin poems which fell into his hands about this time. The
poems pleased him, and he turned to others. Horace in particular
appealed to him very strongly, and he developed no mean
ability in the composition of Latin verse himself, and pages of
his note-books were filled with them.

At last restored to health. Ampere again threw himself whole-
heartedly into his life of study. Outdoor exercise was provided
by botanical hunts, and in the course of one of these expeditions,
when he was twenty-one years of age, he chanced to meet a lady
named Julie Carron, daughter of a resident in St. Germain,
a neighbouring village. With Andre it was a case of love at
first sight. The story is recorded in his diary under the title of
Amorum, and has been published, with his early correspondence,
by ]\Iadame Cheveux, an English translation of the work appear-
ing in 1873. In spite of the fact that his wooing was at times
a little mathematical, as when he tried to teach Julie how to
calculate the height of his village steeple, it met with success,
and he tells us that on the 3rd of July 1797 she consented to
become his wife.

This naturally brought into immediate prominence the problem
of his future. The question of an income wherewith to maintain
a home of his own had not hitherto troubled him. A family

202 Andre Ampere

council was held, at which his prospective parents-in-law urged
him to become a silk-mercer. But this hardly seemed to fit in
with his taste for mathematics and science, and Ampere decided
rather to take up teaching. He began giving private lessons
at Lyons, lodging there with a relative of Julie, and was married
on the 2nd of August 1799. Although not earning a large
income, they were very happy. In the August of the following
year his wife bore him a son, Jean Jacques Antoine, and he
now began to feel the necessity for doing something more lucra-
tive than these lessons. The persistent ill-health of his wife only
accentuated this necessity, and in December 1801 he succeeded
in obtaining the chair of physics and chemistry in the Central
School of the Department of Aisne. This, however, was but
a stepping-stone, and none too satisfactory a one at that, since
his wife was too unwell to join him.

In 1802 appeared a book called Considerations sitr la Theorie
mathematique du Jeu, the object of which was to show that in the
long run a persistent gambler must lose his money. Ampere's
object in writing this treatise was to gain publicity, and in this he
succeeded. Delambre, the famous mathematician, was impressed
by the obvious talent behind the book, and through his influence
Ampere was in 1803 offered an appointment as professor of
physics and chemistry in a newly formed school in his own town
of Lyons.

Overjoyed at the prospect of reunion with his beloved wif^
and chil(^, Ampere eagerly accepted. But alas, his happiness
was short-lived. His ailing wife grew worse, and on the 7th of
June 1804 all hope was abandoned of saving her. ' This day
has decided the rest of my life,' was his pathetic entry in his
diary. Six days later Julie was dead.

The blow to Ampere was overwhelming, and once again he
was a broken man. Life at Lyons became hateful to him. He
determined to leave it, and in 1805 he accepted an appointment
at the Polytechnic School of Paris. Here for some time he was
profoundly unhappy. Painful as his experiences of Lyons had
been, time had mellowed the acuteness of his sorrows, and he
bitterly regretted having left the place. His was a very peculiar

Andre Marie Ampere 203

frame of mind at this period. Here is his own description of it
in one of his letters :

' j\Iy life is a circle, with nothing to break its uniformity. . . .
I have but one pleasure, a very hollow, very artificial one, and
which I rarely enjoy, and that is to discuss metaphysical questions
with those who are engaged in this science at Paris, and who show
me more kindness than the mathematicians. But my position
obliges me to work at the pleasure of the latter, a circumstance
which does not contribute to my diversion, for I have no longer
any relish for mathematics. ... It is seldom, except on Sunday,
that I can see the metaphysicians, such as . . , M. de Tracy, with
whom I dine occasionally at Auteuil, where he resides. It is
almost the only place in Paris where the country reminds me of
. the banks of the Rhone.'

As the months went by, however. Ampere became less moody,
and more reconciled to his lot, and in July 1806 he married for
a second time. Things now went more smoothly. In 1808 he
was appointed Inspector-General to the University, and in 1809
he became Professor of Analytical Calculus and Mechanics at the
Polytechnic School of Paris, a post which he held till his death, and
here it was that his famous researches in electro-magnetism were
pursued.

5. Ampere's Researches

To the Institute of France there came on Monday, the nth of
September 1820, a member who had just returned from Geneva.
He brought with him an account of Oersted's great discovery,
and amongst the excited and interested auditors was Andre
Ampere. Ampere was profoundly impressed by the importance
of Oersted's experiment. He foresaw immense possibilities.
He went back to his laboratory, and repeated the experiment
for himself not only in its original simple form, but with every
conceivable variation.

Seven days later he appeared before the assembled Institute,
and gave a report of his week's labours, and showed how he had
amplified Oersted's work. He showed that if a current flow
along a wire from south to north, and a magnet be held under
the wire (Fig. 84 {a)), the northern point of the needle is deflected
westward, but if the magnet be held over the wire, then it is

204 Andre Ampere

(Fig. 84 {b)) deflected towards the east. He then proceeded
to generaUze still further, by showing in what way a magnetic
needle is deflected by an electric current, no matter what the
direction of the current may be. He pictured a swimmer —
a little mannikin, which came to be referred to as ' bonhomme
d' Ampere ' — swimming with the current so as to face the needle ;
that is to say, if the needle is above the wire, the mannikin
swims on his back, and if the needle is to the right of the wire,
the mannikin swims on his left side, and so on. Then in every

case the north pole of the needle is
deflected to the left of the mannikin,
and the south pole to the right. This is
nowadays spoken of as Ampere's Rule.
It may be re-stated thus : Imagine
yourself so placed that the current
enters by your feet and leaves by your
mouth ; then the north pole of the
magnet will always be deflected to
your left side.

Ampere's next step was of the
greatest importance. He argued that
since an electric current exerted on
the magnet an attraction across itself,
as it were, and since he could have got
the same effect if he had used another magnet instead of using
a wire carrying a current, he might reasonably expect to get
a similar effect by using another v/ire carrying a current instead
of the first magnet. In other words, he was naturally led to the
problem of the influence of two parallel electric currents on each
other. Ampere argued that two such currents ought to attract
or repel each other just as surely as would two magnetic poles.
He proceeded to put it to the test of experiment. He arranged
two wires side by side in such a way as to permit of their being
able to move freely, and he then sent an electric current in the
same direction through each. The wires at once moved towards
each other. He now reversed one current, and the wires at once
moved away from each other.

Fig. 84. Ampere's Experi-
ments, (a) Magnet under
cvirrent — deflexion west ;
(6) Magnet over current —
deflexion east.

Ampere's Researches 205

The paper in which these experiments were described was
entitled Un Memoire sur faction mutuelle de deux courants
electriqiies. Ampere's conclusions were at once attacked. His
critics asserted that what Ampere was showing them was not
a magnetic phenomenon at all, but purely electrical, and that
it was nothing more nor less than a case of simple electrical
attractions and repulsions. But there was a conclusive answer
to this, for where like electrical charges repel each other, and
unlike charges attract, yet in the case of parallel currents, like
currents (i.e. currents going in the same direction) attract each
other, whilst unlike currents repel. There are always those who
begrudge honour to those to whom it is due, and even when
it became evident that Ampere's conclusions were unassailable,
there were still those who tried to belittle him. There is a story
that one of these critics, in the presence of the famous Arago,
declared that since it was known that two currents acted upon one
and the same magnet, it was evident, to begin with, that tjiey would
act upon each other. Upon hearing this, Arago drew two keys out
of his pocket and replied, ' Each of these keys attracts a magnet,
do you believe that they, therefore, also attract each other ? '

Ampere carried his researches further, and succeeded in
showing that if the current strength of two such wires are C and
C', respectively, and if d is the distance between them, then the

CC

force of attraction or repulsion between them F = — -^, a result

d^

which prompted Clerk Maxwell to speak of Amipere as the
Newton of electricity.

Ampere's next experiment constituted yet another great
advance on the same road. It was obvious to him that there
was a magnetic ' field ' surrounding every electric current.
Indeed Schweigger had already invented the galvanometer,
based on the fact that in the case of a circular coil of wire, the
resultant magnetic force at the centre of the coil was at right
angles to the plane of the coil (Fig. 85). Schweigger saw that
if instead of one turn he had many turns of wire, the magnetic
effect at the centre would be correspondingly multiplied. Con-
sequently, if the coil be in the plane of the magnetic meridian,

2o6 Andre Ampere

and a magnetic needle be placed at the centre, then, on passing
a current round the coil the resulting magnetic force at the
centre was at right angles to this plane. Consequently there

were now two forces acting simul-
taneously on the magnetic needle,
(I) the force H (Fig. 86), due to the
natural tendency of the magnet to
point north, and (2) the force F at
right angles to it, due to the mag-
netic effect of the current in the coil.
As a result the needle was found to
swing into the position of the result-
ant R of these two forces, and since F
depends for its magnitude upon the
strength of the current C in the coil,
the angle 6 through which the needle
swung was a measure of the current
strength employed. This is the basis
of the whole theory of galvanometry.
Ampere also utilized the idea of
multiplying the magnetic effect at the centre of a coil carry-
ing a current by having a large number of turns, but instead
of arranging them into a coil as for a galvanometer, he arranged
them into a solenoid or long coil, as in Fig. %y. At the centre of

Fig. 85. Magnetic effect at
centre of coil.

^R

Plane of
coil.

id)

N

Fig. 86. Theory of Galvanometer.

Fig. 87. Theory of the Solenoid.

each turn is a magnetic force at right angles to the turn (Fig. 87 {a))
and therefore along the middle of the coil, and these collectively
make up a big magnetic force right along the length of the axis
of the coil, as in Fig. Sy (b)). Consequently such a coil behaves
magnetically like a bar magnet, and if freely suspended would set
itself facing magnetic north and south. Ampere found that the

Ampere's Researches 207

closer together the coils, the stronger was this magnetic force along
the axis of the coils, and he argued that since a bar of steel or
iron always became magnetized in a magnetic field, it should
also be possible to magnetize it by winding a coil round it, and
passing a current through the coil. He tried this with great
success. Steel of course is very retentive of magnetization,
and by this means he made bar magnets which could last a long
time. But soft iron is different, for it loses its magnetism imme-
diately on removal from the magnetic field in which it is placed,
and hence a soft iron bar placed in a solenoid becomes strongly
magnetized as soon as the current begins, and becomes immedi-
ately demagnetized on stopping the current. So we get the
electro-magnet, as Ampere called it, and arising from it have been
many practical inventions of first-class importance.

To Ampere also belongs the honour of the first suggestions of
the electric telegraph, although in the light of modern telegraphy
his suggestion was very crude. His idea was to have twenty-six
wires, one for each letter of the alphabet, and presumably
others for the numerals. Under each was then placed a magnetic
needle at the receiving end. At the sending end a current was
to be sent through each wire required according to the spelling
of the message, and the kicks in the corresponding magnetic
needle would enable the message to be read.

Finally, considerable thought over the whole range of electro-
magnetic phenomena which his industry and those of Arago
and others had succeeded in bringing to light led Ampere into
the realms of speculation. His theory was not so much an
attempt to explain electrical phenomena by magnetism as it
was the explanation of magnetic phenomena by electricity.
He considered each particle in a magnet as being encircled by
an equatorial current whose effect was to produce magnetic
poles, and he deduced that the fact that the earth was a giant
magnet was evidence of electric currents encircling the earth
from east to west. According to Ampere, the process of mag-
netizing a bar is essentially that of causing all the molecular electric
currents to flow in one direction. The theory was undoubtedly
ingenious, but is of historical interest only.

208

6. Ampere's Later Life

There is very little further of incident in the life of Andre
Ampere. He was associated with the Potytechnic School as
a teacher and with the University of Paris as inspector till the
time of his death, and on the whole he found his duties both
irksome and cramping to his intellect. The endless routine of
teaching hampered his research, and he felt this keenly. Yet it
was unavoidable, for he was dependent upon his salary. Almost
to the last he had to supplement his income by the giving of
private lessons to those who cared to pay for them.

Yet with it all he was remarkably indifferent to fame. Thus
he wrote and published a treatise on the differential and integral
calculus not only without attaching to it his name, but without
even a title.

As Ampere reached his fifties he developed a chronic affection
of the chest, but his periodic tours to the Mediterranean in
connexion with his inspectorship usually helped to restore his
health. In May 1836, however, he was seized with illness during
the journey to Marseilles, and in spite of every attention, he
died on the loth of June 1836, in his sixty-second year.

Throughout his life Ampere was a deeply religious Christian ;
though, like most philosophers, he had his periods of doubt and
scepticism. ' Doubt ', wrote he to a friend on one such occasion,
* is the greatest torment man can endure on earth.' Ampere
was possessed of many of those eccentricities often regarded as
characteristic of genius- His upbringing had kept him from the
contact of the world. He had never been to school or college,
and the conventional standards of the outside world were
foreign to him. As a consequence he developed what appeared
to be many absurdities of both dress and manners, and only
those privileged to come into intimate contact with him knew
what a warm-hearted, sincere man he was — of high ideals,
a devoted husband and father, and the truest of friends.

He was very excitable, and his son tells rather amusingly of
an occasion at Avignon when he was presented with a small bill

Ampere's Later Life 209

in connexion with the payment of a relay of post-horses. Some-
thing in the totalUng of the bill upset him. He lost his patience
and his temper to such an extent that he became quite inco-
herent, and when eventually he paid up, the postilion disdain-
fully remarked, ' There 's a " dog " that is not clever ! Where
did he learn to count ? '

Like so many other great men and deep thinkers, Ampere was
occasionally very absent-minded, and there are many amusing
anecdotes in illustration of this. Thus when he became
absorbed in demonstrations in the lecture-room, he would
sometimes, when heated, take out his pocket-handkerchief,
wipe the black-board with it, and then mop his forehead with
the duster. Another story tells how, whilst proceeding to the
school he was crossing a bridge over the Seine when he caught
sight of a coloured pebble. He picked it up and began examining
it carefully. Suddenly he realized that he was late. He pulled
out his watch, looked at it, threw it into the river, thrust the
stone in his pocket, and hurried away to his class.

Such, then, was the founder of Electro-magnetism, and when
in 188 1 there assembled in Paris an International Congress of
Electricians for the purpose of the adoption of universal units
for the fundamental quantities of electricity and magnetism
due homage was paid to his memory and to the influence his
researches had exerted on its labours, by naming after him the
practical unit of current — the ampere.

So his memory lives. It lives in the elementary text-books
on electricity and magnetism ; and it lives in the great electrical
inventions which have revolutionized modern comfort in almost
every branch of industrial activity ; it lives wherever, in fact,
the sciences of electricity and magnetism have been welded
together for the service of mankind.

2613

XII

SIR HUMPHRY DAVY

I. Early Days

Contemporary with the great pioneer of electro-magnetism
whose life we have just considered lived Sir Humphry Davy,
a man whose researches at this period on the relationship between
electricity and chemistry stand out as prominently as did

Ampere's in his particular
sphere of scientific activity.
Davy's versatile genius
found so many brilliant
outlets in the various
branches of physics, that,
although essentially a chem-
ist, we are bound to include
him amongst the eminent
band of physicists and
mathematicians of which
this book constitutes a
record.

Humphry Davy was born
at Penzance, in Cornwall,
on the 17th of December
1778, of old Cornish stock.
His father, Robert Davy,
was a wood-carver by trade, but had retired early from business
on inheriting a small income from Humphry's grandfather,
a successful builder. Davy's mother was Grace Millett, the
third and youngest daughter of a mercer of Penzance, and was
' remarkable for the placidity of her temper and the amiable
and benevolent tendency of her disposition '. There was
nothing particularly striking about Robert Davy. The fact
that, with but a small income, he was, even whilst a com-
paratively young man, content to do nothing to supplement it
speaks pretty much for itself.

Fig. 88. HUMPHRY DAVY

Early Days 211

Humphry was the eldest child of his parents, and was bright
and healthy from the outset. At the age of five his mother
sent him to his first school to learn to read and write. It was
a small private school. After a year here, Humphry was
passed on to the Grammar-school at Penzance. The head
master of this school was the Rev. J. Cory ton, an easy-going
man who was not very helpful to his pupils. Davy tells
us that he ' enjoyed much idleness at Mr. Coryton's school ',
and that on the whole it was a good thing for him that this
was so, since he was compelled to exert his own will and his own
intellect in making good the deficiencies of his master. ' What
I am, I have made myself ; I say this without vanity, and in
pure simplicity of heart,' wrote he on the same occasion.

That he was both sharp and witty as a boy is illustrated by
the following incident. Apparently Mr. Coryton's notion of
* applied discipline ' consisted in a habit of pulling the boys'
ears. Davy came in for a large share of this, and, apparently
having come to the conclusion that he must do something to
put an end to the practice, he appeared at school one morning
with his ears all plastered up. His master asked him what was
the matter, whereat Davy gravely explained that the plaster
was there to prevent mortification.

From his mother, Davy had developed a vivid imagination
and a love of poetry. He never tired of listening to both his
mother's and his grandmother's endless stocks of stories, or to
their readings from books of poems, and, being naturally quick-
minded, he soon developed a keen facility for story-telling
himself. Although he at all times easily mastered his lessons,
he was a natural boy and never devoted more time than
necessary to them. After school, this youngster, not yet nine,
would gather around him a willing audience of schoolmates,
to whom he would repeat story after story, some of which he
would invent for himself. He was as natural a leader amongst
his playmates then as he was a leader amongst men of science
in later life.

When he was nine years old his parents left Penzance and went
to live at Varfell, but in order not to interrupt Humphry's

o 2

212 Sir Humphry Davy

studies, such as they were, he was left behind, and lived with
Mr. John Tonkin, a local surgeon and apothecary. In view of
the great influence which this kindly man exerted on young
Davy's future, a word or two regarding him is advisable. This
kindly old man was held in high esteem locally, and chance had
decreed that he should have been lodging in the house of Mr.
and Mrs. Millett, the parents of Davy's mother, at the time of
their deaths (Mrs. Millett died within a week of her husband).
Mr. Tonkin befriended the orphan children as far as he was able.
A relative came to keep house for them, but Tonkin continued
in the occupation of his rooms, and he practically ' supplied the
place of a father to them '. He never ceased to take an affec-
tionate interest in them, and hence it is not surprising that
Humphry should stay with him when his parents left Penzance,
and when Humphry was fourteen' years of age, Mr. Tonkin sent
him at his own expense to the Truro Grammar-school for a year.

So far we may say of young Davy that while he showed
general ability, he displayed no special bent, except perhaps
that he was inordinately fond of lecturing. No audience was
necessary. He would just mount a chair in a room, and ' hold
forth ' to the four walls. Yet in a vague way he was ambitious,
and he would spend hours in solitude, dreaming, Dr. Paris tells
us in his biography, of fame.

In appearance there was little in him to suggest the embryo
genius. He was diminutive in stature, somewhat insignificant
in manner, round-shouldered, and his countenance * in its
natural state, was very far from comely '.

2. Youth

For a year after leaving Truro Davy spent his time somewhat
aimlessly, though perhaps not unintelligently. There was no
purpose in his movements and he gave no thought to the future.
But in December 1794 his father died unexpectedly, and
Humphry found himself suddenly forced to take stock of his
position. His father had left behind him a small income of
about £150 per year and a big debt of £1,300, and Humphry,
eldest of the five children, loved his mother dearly, and

Youth 213

quickly decided that the days of idling were over. What was he
to do ? His mother had returned to Penzance, and together
they sought the kmdly advice of Mr. Tonkin. As a result Davy
was apprenticed ui February 1795 to a Mr. Bingham Borlase,
who like Mr. Tonkin was a surgeon and apothecary.

Davy was very pleased with himself. He felt he had made
a move in the right direction, and he determined, by hard work
and deep study, to attain success. He was full of enthusiasm
and high spirits, and when alone would frequently give loud
vent to his innermost feelings. This habit of declaiming was
very strong in him, and we are told by Dr. John Davy, his
brother, that on one occasion, during his apprenticeship, he was
' on his way to visit a poor patient in the country, and in the
fervour of declamation, he threw out of his hand a phial of
medicine which he had to administer, and that when he arrived
at the bedside of the poor woman he was surprised at the loss
of it. The potion was found the next day in a hay field adjoining
the path '.

His note-book gives clear proof of the wonderful, though very
unbalanced, energy this youth displayed.

' It opens with " Hints towards the Investigation of Truth in
Religious and Political Opinions, composed as they occurred, to
be placed in a more regular manner hereafter ". His first essay
is "On the Immortality and Immateriality of the Soul " ; the
second bears the title of " Body, organized matter " ; and his
third is "On Governments ". Then there follows a variety of
essays on metaphysical and moral subjects . . . but besides these
there are some verses and the beginning of a romance, called
" An Idyll ", which is in the form of a dialogue, the characters
being " Trevelis, a warrior and friend of Prince Arthur", and
" :\Iorrobin, a Druid " ; the scene " A cliff at the Land's End in
Cornwall ".'

Throughout this period Mr. Tonkin was an invaluable friend,
adviser, and teacher to Humphry, and it was not very long before,
under his wise influence, superfluous subjects of study were
discarded, and gradually the lad's true bent became manifest.
In the years 1796 and 1797 he studied mathematics and chemistry,
his starting-point for the latter subject being Lavoisier's Elements

214 Sir Humphry Davy

of Chemistry, a book which deeply impressed him. He took to
experimenting, using the garret in Mr. Tonkin's house as his
laboratory, and soon his inventive genius asserted itself. Text-
book experiments were left behind, and he attempted others
of his own — his days of research had begun.

As luck would have it, Davy now began to make acquaintances
who were to be the means of providing for him the opportunities
to develop his talents. One of these was Gregory Watt, son
of the famous engineer, whom ill-health had brought to the
mild climes of Penzance. The two met, found much in
common, and became fast friends. Another was Davies Gilbert,
who was later a President of the Royal Society, and who
developed an interest in Davy through hearing that he was
* fond of chemical experiments '. Through the influence of
these two new-found friends Davy was offered a post as
laboratory assistant to Dr. Beddoes, founder and director of the
Pneumatic Institution at Clifton, Bristol, the function of which
was the curing of ailments by the administration of gases.
To Davy, with his chemical turn of mind, this seemed a splendid
opening. To old Mr. Tonkin, conservative in his medicine as
he was in everything else, it was a disastrous mistake. He was
all against it, and as a result was temporarily estranged from the
lad whom he loved, and whom he had so greatly befriended.

In spite of this Davy accepted the offer. Mr. Borlase, to
whom he had been apprenticed, kindly released him from his
indentures, and so in October 1798 he said farewell to his
mother and to his friends, and set out for Clifton.

3. Manhood

There was every encouragement at Clifton for Davy to make
good his ambition. The director. Dr. Beddoes, treated him
kindly, and with his wife made Davy's leisure hours sufficiently
pleasurable to afford him healthy stimulus for work. Here was
an institution whose functions called for a detailed study of
gases and their physical, chemical, and physiological properties,
and for this purpose there was a well-stocked laboratory. For
a keen experimentalist such as Davy it was a glorious opportunity.

Manhood 215

and he made the most of it. He had got over the ' speculation '
phase through which he had inevitably passed, and had come
to recognize that ' one good experiment is of more value than
the ingenuity of a brain like Newton's '.

Davy worked well and with success. His most important
researches in physics will be described more fully later, but it is
interesting to note that he instituted the study of anaesthesia
by his successful tests with nitrous-oxide, or laughing-gas, as it
is more popularly termed. A well-known physician of the time,
Dr. Mitchell, had declared this gas to be very poisonous, and
Davy was curious to try its effect for himself. He inhaled it
in small quantities, and satisfied himself that Dr. Mitchell's
statement was exaggerated. He now increased the dose, and
found himself able to breathe it for several minutes, till he
lost consciousness. He awoke without injury, and recorded
with delight his pleasant dreams during the period of uncon-
sciousness. The publication of these results aroused widespread
attention and Davy's name began to receive prominence. He
turned his attention to other gases, but with some of them he
was not quite so fortunate, and he became seriously ill through
inhaling nitric oxide and carburetted hydrogen.

For two and a half years Davy laboured on at Clifton, working
hard, achieving much, and winning the respect and admiration
of aU with whom he came into contact. Once again he was to
reap his reward, and take another, and this time much more
effective step, to that fame and honour which he had openly
proclaimed to be his aim.

One of the outstanding figures in the world of science at this
time was Benjamin Thompson, Count Rumford, soldier, states-
man, and scientist. Born in Massachusetts in 1753, he had, in
his early days, fought on the side of the English in the American
War of Independence. Later he had settled in Bavaria, where
he had been ennobled for his services, and in 1798 he was sent
to England as Minister Plenipotentiary of the Court of Bavaria.
As a British subject, however, he could not be received in this
capacity, but he resolved to stay on in England for a few years,
during the course of which he took a prominent part in the

2l6

Sir Humphry Davy

foundation of the Royal Institution. The scheme of this famous
institution was very extensive, and amongst its more prominent
features were the provision of a school of technical education
and an organized investigation into the management of fuel.
A lecture room and laboratory were to be built, and equipped
with the most up-to-date apparatus and appliances for the study
of ' all the mechanical arts as they apply to the various branches

of manufacture ', and
public lectures were to
be given. The institu-
tion was granted a Royal
Charter on the 13th of
January 1800, and Dr.
Garnett was appointed
the first Professor of
Physics and Chemistry.
But Count Rumford,
who was throughout the
moving spirit amongst
the managers, was un-
able to get on with him,
and as a result of a dis-
agreement over his pro-
posed syllabus of lectures,
he soon resigned his pro-
fessorship. He was succeeded by Thomas Young, the brilliant
physicist.

One of the posts created with the foundation of this Institu-
tion was that of Director of the Chemical Laboratory and
Assistant Editor of the Journals, and the question of this
appointment now came prominently to the fore. We shall
see shortly that one of Humphry Davy's most successful
research experiments of his Clifton days was by way of verifica-
tion of a theory of heat which had been advanced by Count
Ramford in opposition to the then current ' caloric ' theory,
and the publication of this had naturally given great satis-
faction to Count Rumford. Consequently, w^hen some friends

Fig. 89. THOMAS YOUNG

Manhood 217

urged upon him the advisabiUty of offering to Davy the vacant
appointment, he was well disposed to the suggestion, although
the two had never yet seen each other.

The managers met and it was resolved that Davy be appointed
to the post, and ' that he be allowed to occupy a room in the
house, and be furnished with coal and candles, and that he be
paid a salary of one hundred guineas per annum '. We can well
imagine with what delight Davy received the news, particularly
when he learnt that his duties would leave much leisure time for
research. He accepted the appointment, and on the nth of
^larch 1801 he entered upon his new duties. Rumford was at
first disappointed with him. Davy was, as has been before
mentioned, none too prepossessing in appearance, and he was
but twenty- two years old. ' Pert, smirking, and boyish ', the
interview had an irritating effect on Rumford, who would not
permit him to lecture in public until he had heard him in private.

Such a test was all that Davy needed. To one who had been
a lecturer since he was a child, even though his audience varied
from blank walls to a street-corner gathering of playmates, and
who was burning with the fire of ambition, the giving of a ' show '
lecture in private was no ordeal — it was a pleasure. Rumford
was at once won over, and in June 1801, two months after his
first appointment, he was promoted to be Lecturer in Chemistry,
and the entire resources of the Institution were placed at his
service.

Davy was a brilliant success from the outset. As a popular
lecturer he was unsurpassed, and his first course of lectures was
a series of triumphs in exposition and demonstration. Intellectual
and fashionable London flocked to hear him, and he achieved
both popularity and fame at a bound. His language was so
eloquent that Coleridge openly declared that he attended the
lectures ' to increase his stock of metaphors '. Davy's star was
truly in the ascendant.

But Davy's name has not been handed down to posterity on
the score of his success as a lecturer. His fame rests on his
achievements in chemical and physical research. It has been
pointed out that his duties left him much leisure time for his own

21 8 Sir Humphry Davy

experimental work, and this he employed with all the enthusiasm
of a mind dedicated wholly to the service of science in the
interests of mankind.

Two years after his appointment as Director of the Institution,
Thomas Young resigned. Brilliant man of science as he was,
he was no popular lecturer, and he felt his inability to ' get at '
a lay audience. Added to this he was a physician with a private
practice of a sort, and the public did not approve of a physician
taking duties outside his practice. So Yoimg gave up his post
and Davy was promoted in his stead.

Our young philosopher was now at the zenith of his power, and
the full force of his brilliant mind began to assert itself. He
lectured in his theatre, and he laboured in his laboratory, with
an apparently inexhaustible fund of energy, and the result was
seen in a brilliant series of researches extending over a wide
range of subjects.

What did he achieve ?

Fig. 90. One of Accum's Chemical Lectures.

219

4- Rtmford, Davy, and the Dynamical
Theory of Heat

The views universally accepted at the end of the eighteenth
centurj^ as to the nature of heat were embodied in what was
called the ' caloric ' theory. It was essentially a statement that
heat was something material, and it really arose as a result of
a theory of combustion which had been advanced by a famous
seventeenth-century chemist named Georg Ernst Stahl (1660-
1734) > of the University of Halle. This philosopher declared
that when a body bums it gives off a substance which he
called ' phlogiston '. Since burning and heat are ideas which
are necessarily related, it is not surprising that a corresponding
view developed with regard to heat, and that it, too, was con-
sidered to be a material substance. As to the properties of
' caloric ', as this material substance was called, there was much
vagueness. It was held to be highly elastic, and its particles
were supposed to repel each other. As afterwards developed
the property we speak of to-day as ' capacity for heat ' was
explained by the supposition that the heat particles attracted
ordinary matter, and that ' the heat was distributed amongst
bodies in quantities proportional to their mutual attractions ',
and hence to their capacities for heat.

It will be remembered that even as far back as the end of the
seventeenth century, Boyle, Bacon, and others had held views
on the nature of heat contrary to this, but the caloric theory
persisted nevertheless, and it is interesting to note that when in
1738 the French Academy of Sciences offered a prize for an essay
' on the nature of heat ', the three winners, one of whom was
the famous mathematician Euler, all favoured the materialistic
theory ; and strange to relate even as recently as 1850 the article
on ' Heat ' in the eighth edition of the Encyclopaedia Britannica
advanced the caloric theory in preference to the modern dyna-
mical theory.

For the starting-point of the overthrow of the caloric theory
we have to look to the researches of Count Rumford in 1798.
He had for many years been closely interested in the properties

220 Sir Humphry Davy

of heat (the study of fuel-economy, it will be recalled, was one
of the prime functions of the Royal Institution), and when in
the course of his duties, at Munich, he was engaged in the boring
of cannon in the military workshops, he was very much surprised
to notice the great heat which the grinding of the boring-tool
against his gun was producing. Whence, he asked himself, came
all this heat ?

Rumford began to consider the phenomenon in the light of the
caloric theory. A body giving out heat should be losing some of
its caloric. He therefore experimented with a view to ascertaining
if in fact the gun, the chips, or the borer had lost anything. But
of this he could find no sign. He next argued that if he went on
generating heat by boring long enough, there ought to come
a time when all the available caloric in the material he was using
must be exhausted, since there was never a suggestion that the
quantity of caloric in a body was inexhaustible. But experiment
showed him that there seemed no end to the heat which could
be produced ; he had merely to go on boring to get just as much
heat as he liked.

Did the heat, then, come from the air ? Rumford repeated
the experiment under water, and still the heat was produced,
making the water itself get warm. He now began strongly to
suspect that the caloric theory was all wrong, and he at once
recalled the theory of Bacon, Locke, Boyle, and others, that heat
is some form of manifestation of the setting up of vibrations in
a body, and if this were so, then, he argued, by sufficient friction
he should be able to create any quantity of heat he wished. He
was thus led to the experiment for which he i^ most famous.

Rumford fitted a blunt steel borer into the partially scooped-
out end of a cannon-shaped piece of brass, and he caused the
borer to press down on the brass by placing on it a weight of
ten thousand pounds. The whole was immersed in a box con-
taining about a gallon of water, into which also dipped a thermo-
meter. By suitable mechanism worked by two horses, he
arranged for the brass cylinder to rotate at a speed of thirty-two
revolutions per minute. As a consequence, the borer 'worked
its way violently ' into the brass. The initial temperature of the

The Dynamical Theory of Heat 221

water was 60° F., yet in one hour the temperature had risen to
107° F., and in one hour and a half it had reached 140° F., and
finally, after two hours and twenty minutes, the water actually
began to boil! 'It would be difficult', wrote Rumford, 'to
describe the surprise and astonishment expressed in the counten-
ances of the bystanders on seeing so large a quantity of cold water
heated, and actually made to boil, without any fire. Though
there was, in fact, nothing that could justly be considered as
surprising in this event, yet I acknowledge fairly that it afforded
me a degree of childish pleasure which, were I ambitious of the
reputation of a grave philosopher, I ought most certainly rather
to hide than to discover.'

Rumford's conclusion that heat was not material, but was
due to motion, was given in the following terms : ' It is hardly
necessary to add that anything which any insulated body, or
system of bodies, can continue to furnish without limitation
cannot possibly be a material substance ; and it appears to me to
be extremely difficult, if not quite impossible, to form any distinct
idea of anything capable of being excited and communicated in
the manner the heat was excited and communicated in these
experiments, except it be motion.' Writing to a friend later, he
said : ' I am persuaded that I shall live a sufficient long time to
have the satisfaction of seeing caloric interred with phlogiston
in the same tomb.*

This was the stage at which Davy took up the same subject.
Like Rumford, his work was essentially that of the production of
heat by friction. His materials and his experimental details,
however, were different. He began by taking two pieces of ice,
and by rubbing them together he was able to make them melt
even though all external warmth was excluded from them.
Three alternatives offered themselves by way of explanation.
Either the heat came from the ice, or it came from the air sur-
rounding the ice, or it came from the rubbing. There could be
no other alternative.

The first of these possibilities, Davy realized, could be at once
dismissed. The heat could not come from the ice, since ice is
cold, and, therefore, contains less heat than the water which the

222 Sir Humphry Davy

rubbing produced. So Davy turned his attention to the second
alternative. Did the heat come from the air surrounding the ice ?
Rumford had asked himself this question with regard to his
experiment, and it will be remembered he answered it by re-
peating the experiment under water. But this was not a complete
answer. It merely transferred the difficulty from the air to the
water. It was evident to Davy that to supply a complete answer
not only must the air be removed from the surroundings of the
experiment, but also nothing else must be substituted for it.
In other words, the experiment must be carried out in vacuo.

This was the crucial test, and Davy arranged his apparatus
accordingly. Two pieces of ice were introduced into the receiver
of an air-pump. The contact surface of one was concave, and
of the other convex. The rubbing movement was controlled by
clockwork. As a further aid to a conclusive decision, Davy kept
the temperature of the receiver itself below freezing-point, so
that there was absolutely nothing whatever in the surroundings
of the ice from which the heat could be derived. Nevertheless,
the ice steadily melted as the rubbing went on. Davy was
perfectly satisfied that there was only one possible source from
which the heat could come. It must have been derived from
* the rubbing '.

' Friction ', said Davy, ' causes vibration of the corpuscles
of bodies, and this vibration is heat.'

So, by the joint labours of Rumford and Davy, the first on-
slaughts on the caloric theory were made, and a new stage in the
world's knowledge of the subject of heat was begun. In 1807,
Thomas Young launched a trenchant attack on the caloric
theory in his Natural Philosophy, but it required another fifty
years for the final acceptance of the new doctrine.

5. Further Researches by Davy

Let us turn now to other directions in the realms of physics in
which the world is indebted to Davy's researches. We shall see
that in the main his work lies in the direction of electrical re-
searches, and particularly in those branches most associated with
chemistry ; for it must be borne in mind that Humphry Davy

Further Researches by Davy 223

was really one of the giant pioneers of chemical research, and
that in a book devoted to the history of chemistry his name
would find an even more important place than it does here.

Much of his work required that his apparatus should be
in vacuo, and since he found that the various forms of exhaust
pumps were unable to produce a sufficiently rarefied atmosphere
for his purposes, it is not surprising to find that Davy turned his
attention to the problem of high vacua, and that he solved it
in characteristic fashion. He employed chemical means as a
supplement to the ordinary type of exhaust pump. His method
was both ingenious and simple. Into the vessel to be exhausted
he introduced some caustic potash, and then filled it with carbonic
acid gas. He now placed the vessel on the receiver of the air-
pump, and exhausted it of as much of the gas as the pump would
permit. There was still, of course, some residual gas in the vessel.
All, however, that was now required was to seal the vessel and
to leave the caustic potash chemically to absorb the carbon
dioxide. Thus he obtained a highly rarefied atmosphere. A
modern alternative is to introduce copper filings into the vessel,
and then to fill with oxygen and exhaust. The copper combines
with the residual oxygen. By these means it is possible to
obtain vacua of less than a millionth of an atmosphere pressure.

Turning to Davy's researches in electricity, we may note by
way of introduction that there was available for his use at the
Royal Institution the most powerful battery then in existence.
It was made up of 200 porcelain cells, each containing ten double-
plates, virtually making a battery of 2,000 cells. With this
unique equipment Davy in 1801 made a far-reaching discovery
the results of which are seen in the electric lighting of to-day.

It is common knowledge that with almost any battery, on
causing the terminal wires to touch each other for an instant, and
so completing the electrical circuit, a spark is observed. Davy
had noticed this, and in the case of the powerful battery at the
Royal Institution, he further found that on drawing the terminal
wires apart after first contact, so as to leave a little air gap, the
sparking continued across the gap, forming a stream of fire from
one pole to the other. He noticed at the same time that the tips

224 Sir Humphry Davy

of the wires were intensely heated. This interested Davy very
much indeed, and he tried the effect of using different conductors,
and the effect was most marked when he used two pencils of
charcoal attached to the two terminal wires. When these were
brought together they sparked, and on drawing them apart,
a brilliant stream of light resulted across the air gap, and the
points of the carbon sticks became white hot. When the dis-
charge took place horizontally, the stream of light was seen to
bend upwards like a bow, owing, of course, to the rising of the
heated air, and because of this Davy spoke of the phenomenon as
the arc discharge.

He noticed that during the course of the discharge particles
of carbon are carried across from the positive stick to the negative
stick, causing the former to be used up at about twice the rate
of the latter, and causing a crater-like cup to form at the end of
the positive carbon. It was the interior of this crater which Davy
found to be the most intensely luminous, and the temperature
developed therein was without doubt the highest yet obtained
by artificial means. It was estimated to be about 3,000° C, and
in it platinum was found to melt and run like wax ; refractory
minerals such as sapphire, quartz, and magnesia were fused, and
bits of diamond seemed to evaporate. Thus was initiated the
electric lighting which forms so prominent a feature of twentieth-
century comfort.

An allied observation of Davy's which it is convenient for us
to notice here is concerned with the relative radiating powers of
a luminous body in air and in vacuo. ' I find ', he wrote in 1809,
' the radiation in vacuo from ignited (meaning incandescent)
platina is to that in air as three to one.'

We come now to Davy's greatest achievement : that of the
applications of electricity to chemical research. It had been
observed by Nicholson and Carlisle in 1800 that when the two
terminal wires of a battery were dipped in water, bubbles of gas
began to rise from them. Further examination and experiment
showed these two investigators that whilst the gas emanating
from the one wire extremity was oxygen, that from the other
was hydrogen. They were unable to say, however, whence came

Further Researches by Davy 225

these gases — whether from the electrical current, the battery, or
the water.

Further tests brought to light additional complications in the
phenomenon. Damp litmus paper applied at the positive pole
was seen to turn red, whilst at the negative pole it turned blue.
Clearly an acid was appearing at the positive end, and an alkali
at the negative end, at the same time as the oxygen and hydrogen
were being evolved. Now Cavendish had shown in 1784 that
pure water was composed of oxygen and hydrogen only, and it
therefore became evident that the passage of an electric current
through water was forming something in the water, and it became
important to find out what exactly was the effect of the current
on the water.

This was the problem which Davy took up and solved in 1806.
The patience and care exercised by him in these investigations
afford an excellent example of the reward which must inevitably
come to the worker who leaves nothing to chance.

It was necessary for him to be governed in his experimental
methods by some preliminary hypothesis. Davy did not believe
at first that the electric current produced anything in the water.
His idea was that both acid and alkali were being derived in
some way from the vessels which were being employed. His
plan, therefore, was to use apparatus which, on this hypothesis,
would prevent such formations from taking place. So he used
distilled water, placed in cups made of agate, only to find that
the cups were chemically affected by the current. He now re-
placed the agate cups with ones made from pure gold. But in
spite of all precautions, he still found acid appearing at the
positive end, and alkali at the negative end. Davy now decided
that the distilled water was unsatisfactory, since there was
always an element of possibility that in process of distillation
some salt was carried over with the water. He accordingly sub-
stituted for it water which had been evaporated very slowly, and
was pleased to find that the acid produced was weaker, although
the alkali was as strong as ever before. He began to feel that
he was moving in the right direction.

There was, however, a further possibility for which he had not

2613 p

226 Sir Humphry Davy

allowed. Might not the air surrounding the apparatus have
something to do with the effects produced ? So he placed the
gold cups in a vessel over the receiver of an air-pump, and com-
pletely exhausted the vessel, afterwards filling it with hydrogen
to ensure that no other gas could be left in. He was delighted
to find that he was now getting almost pure oxygen alone at
one pole, and almost pure hydrogen at the other.

It was a most important result. In the first place it confirmed
in a striking manner Cavendish's original discovery as to the
composition of water, but in addition to this the experiment
succeeded in establishing a totally new method of analysis of
substances, namely by decomposition by electrolysis.

Davy now proceeded to apply the lessons of the above experi-
ment. What, he asked, will be the effect of the passage of
electricity through other substances ? Potash and soda were, in
particular, two substances which had interested him for some
time. The current belief was that these were elements, and,
therefore, incapable of decomposition. Davy, however, had long
had his doubts. Here was a new means of testing the point.
He took some pure potash and heated it in a platinum spoon
till it was quite liquid. He now connected the two extremities
of the spoon by means of wires to the terminals of a battery
and so passed an electric current through the potash. Almost
immediately the liquid showed signs of agitation, and soon bubbles
began to form. Presently, beautiful silver globules came to the
surface, some of which burst into flame. ' Davy's delight when
he saw the minute shining globules like mercury burst through
the crust of potash and take fire as they reached the air, was so
great that he could not contain his joy — he actually bounded
about the room in ecstatic delight.' For the first time in history
pure potassium, as he named the new substance, had been isolated.
Owing to its strong affinity for oxygen, causing it so readily to
burst into flame, and to its extreme lightness (it floats in and
combines with water), Davy had great difficulty in collecting the
globules, but eventually he gathered some together and placed
them in naphtha, where he was able to examine them at his
leisure. In the same way he later separated out sodium. Thus

Further Researches by Davy 227

Davy was a pioneer in the study of electrolysis, a study which
has led to such present-day activities as copper, silver, and gold
refining, electroplating, electrotyping, and a hundred other com-
mercial processes of utility to mankind.

There are many other discoveries of first-class importance
which this brilliant man achieved, but most of them dealt with
chemistry, a subject outside the scope of this work. Neverthe-
less we cannot avoid mention of his classic of the
principle of the miner's safety-lamps.

We are told that, even as a bo}^ Davy was
touched at the tales of disaster due to the explosions
in mines, and as a young student he had made up
his mind that one day he would free the miner
from the terrors of these underground disasters.
Unfortunately, as the pit-workings in various
colliery undertakings reached a greater depth
below surface, these explosions were found to be
more frequent, and the trouble became so serious
that in 1813 there was formed a ' Society for the
Prevention of Accidents in Mines '. The society
very properly sought the assistance of men of
science ; at first, however, the suggestions which
came in were of little use.

The autumn of the year 18 15 was an excep-
tionally bad one, and there was a series of heart-
rending disasters in the mines of the north. Davy
was in Scotland at the time, and to him the mine-
owners now appealed. He at once responded, and journeyed
to Newcastle for the purpose of obtaining samples of fire-damp.
For a fortnight he was busily employed studying the properties
of this gas. As a consequence he was able, on the 9th of Novem-
ber 1815, to present his safety lamp having a wire gauze surround-
ing the flame, a result of the principle he had discovered ' that
explosive mixtures of mine-damp will not pass through small
apertures or tubes ; and that if a lamp or lanthorn be made
air-tight at the sides, and furnished with apertures to admit the
air, it will not communicate flame to the outward atmosphere.'

p 2

Fig. 91. The
First Davy
Safety Lamp.

228

Sir Humphry Davy

There is, of course, an important physical principle involved
in this. Who is not familiar with the experiment in which a fine
wire gauze is held over a Bunsen burner ? Provided the gas be
Hghted below the gauze, there is no flame above it, and if the
gauze be raised or lowered, the flame rises and falls with it ;
whilst if the gas be lighted only above the gauze, there is no

Fig. 92. Davy and Stephenson Safety Lamps.

flame below it. Yet the fact remains that gas is coming through
the gauze, and can be ignited if a flame is applied.

What is the explanation ? It is all a question of conductivity.
The material of the gauze is so good a conductor, and the gauze
itself supplies such a large effective area of metal surface exposed
to the cold air, that the heat on the ' flame ' side is rapidly
conducted away in all directions over its surface, leaving
the temperature on the other side below the temperature of
ignition of the gas, and of course, it is only at temperatures

Further Researches by Davy 229

at or above the ignition temperature that a flame is at all
possible.

Hence Davy's idea was to have the flame from the oil-lamps
surrounded by gauze. The necessary air to maintain the flame
would then have to filter in through the gauze, and although the
inflammable fire-damp would pass through to the flame with
the air, and would of course ' catch fire ' inside the lamp, yet the
flame would be unable to strike back through the gauze again.

But note carefully how Davy's invention matured. He
studied his gas, discovered a principle, and devised his lamp as
a result of the principle. Almost at the same time George
Stephenson, of steam-engine fame, had also invented a safety-
lamp, using at first tubes instead of gauze to transmit the air,
and in his case the converse is true — namely, that he invented
the lamp and from it discovered the principle. It is a striking
illustration of the contrast between two lines of research of which
scientific history affords many other examples. There was much
controversy at the time as to which of these two could justly claim
priority for the invention, but there is no doubt that as far as
the principle underlying the invention is concerned the honours
go to Humphry Davy, and he fully merited the address of thanks
and the service of plate presented to him by the coal-owners of
Northumberland and Durham.

6. Further Biographical Details

Let us now return to further details of Davy's career. It will
be recalled that we referred to him as having succeeded
Thomas Young as Director of the Royal Institution. In this
capacity he was so far successful that he converted what had
been intended primarily as an institution for popular instruction
into an institution for research. Scarcely a week passed by with-
out Davy's being able to announce some fresh discovery. He
was working almost literally at fever heat.

All this time he was in high favour with everybody. Society
made much of him. Davy was young and, alas, was not proof
against the flattery and the vain compliments which showered

230 Sir Humphry Davy

on him. In his leisure hours he threw himself as energetically
into the life of fashion as he did into his work by day. Such
a life is bound to leave its mark, and Davy must have felt that
the freshness and the frankness of his nature were in jeopardy,
for in May 1803 he wrote thus :

' Be not alarmed, my dear friend, as to the effect of worldly
society on my mind : for the age of danger has passed away.
There are in the intellectual beings of all men paramount elements
— certain habits and passions that cannot change. I am a lover
of Nature, with an ungratified imagination. I shall continue to
search for untasted charms, for hidden beauties. My real, my
waking existence is amongst the objects of scientific research.
Common amusements and enjoyments are necessary to me only
as dreams, to interrupt the flow of thoughts too nearly analogous
to enlighten and vivify.'

Nevertheless he continued to burn the candle at both ends.
Often, we are told, he would leave himself so little time between
leaving his laboratory and going out to dinner that he would not
have time to change his clothing, and he would put a clean shirt
on over the soiled one, and similarly with his stockings. Such
a life could have but one result. Following on the hard work
entailed by his researches on the isolation of sodium and potas-
sium, he broke down, and for some weeks he lay seriously ill.
It was perhaps as well. For although on his recovery he
continued to work hard in his laboratory, he led a saner
social life.

Meanwhile he had been elected a Fellow of the Royal Society,
and by 1809 he was its secretary. A signal compliment was
paid to him, too, by France. These were Napoleonic days, and
England and France were anything but friendly. Yet in spite of
this fact Davy's contributions to scientific knowledge called forth
from the Institute of France the award of its gold medal. There
were those who did not hesitate to invite Davy to refuse the
award, and it is to Davy's infinite credit that he accepted the
offer. ' If the two countries or governments are at war/ he said,
' we men of science are not.'

At home, too, although, as we know, Davy never went to
a university, honorary degrees were conferred on him, and on

Further Biographical Details 231

the loth of April 1812 he was knighted. The honour came
most appropriately, for on the following day he was married.
His wife was a wealthy Scottish widow, whom Davy had first
met two years previously. They spent their honeymoon in
Scotland, and here Davy was able to indulge in his favourite
recreations of shooting and fishing.

In 1813, with his wife, he began a period of Continental travel,
his itinerary embracing France, Italy, Switzerland, Germany,
and home via Ostend. It was in many respects a tour of triumph,
for his reputation was now worldwide and he was everywhere
enthusiastically received. There is no doubt, however, that he was
a disappointment to those with whom he came into contact.
There was something in Davy's manner and bearing which
irritated — a mixture of flippancy, haughtiness, and no doubt
a want of appreciation of the foreign temperaments amongst
which he moved. Such instances as the admiring of a fine
alabaster statue as a remarkable specimen of stalactite when the
hearer was looking for an appreciation of the artistry of the thing
was hardly calculated to impress favourably. His biographer
assures us that in fact what looked like the swollen-headedness
of youthful success (Davy was but thirty-five at this time) was
in reality the outward concealment of an inward timidity and
nervousness ; and, indeed, it is but charitable so to regard it.

It was April 1815 when Sir Humphry Davy returned to
England, and as we have already seen, the latter portion of this
3^ear was busily spent by him in the problem of the safety-lamp.
Although he had solved the problem in principle by the end of
the year, he continued working at it with a view to effecting
practical improvements in the lamp, and this kept him well
occupied till 18 17, and in October of the following year, as areward
for his services to the nation in this connexion, he was created
a baronet. Finally, in November 1820, he was accorded the
highest honour it was in the power of his scientific colleagues to
confer on him, election to the office of President of the Royal
Society.

The next few years were busy ones for Davy, but in 1826 his
health began to fail. A life lived at top-speed as was his could not

232 Sir Humphry Davy

continue without some abrupt physical disaster, and towards the
end of the year he was seized with apoplexy, and although he
partially recovered, he knew himself to be a doomed man.
Acting on medical advice, he spent his winters in Rome, ' a ruin
amongst ruins ', and employed his enforced leisure in writing
The Consolations of Travel, and towards the end, when he was
unable to write, he dictated the passages to his brother, Dr. John
Davy, who was with him.

Davy faced death as he had faced life — courageously, confi-
dently, and hopefully. ' Behold me ', he wrote, ' on the couch
of death, my senses lost, my organs falling towards that state
in which they will be resolved into their primitive atoms ; still
is my mind unconquered, still all my passions, all my energies are
alive ; still are all my trains of thinking complete. Philosophy
has warmed me through life ; on the bed of death she does not
desert her disciple. ... I feel and believe that the genial warmth
of the sun of immortality which has shone through this frame
with feeble light shall be more permanent in the region of bliss.'

And so he felt to the very end. At his own desire, he was moved
from Rome to Geneva, where he died on the 29th of May 1829.

Scientists there have been whose memories are revered by
their colleagues for the work they have done. But Davy belongs
to the illustrious few whose names and memories are household
words for the service they have accorded to the whole of mankind.
Sir Humphry Davy's life stands as an example to the world of
the true spirit and service of science. The monetary value of
much that he achieved could have been enormous, but he
scorned so to use his talent, and no better tribute need we pay
to his memory than to conclude with his own pronouncement
to his friend, John Buddie, when the latter urged him to take
out a patent for his safety-lamp and so secure for himself an easy
five or ten thousand pounds per annum in royalties. ' No, my
good friend,' answered Davy, ' I never thought of such a thing.
My sole object was to serve the cause of humanity, and if I have
succeeded, I am amply rewarded on the gratifying reflection of
having done so.*

XIII

GEORG SIMON OHM AND HIS
FAMOUS LAW

I. Early Life and Progress

We have seen how the study of electrostatics began to develop
qualitatively under the stimulating researches of Franklin and
others, and quantitatively through the efforts of such men as
Coulomb and Cavendish : we
have also seen how Galvani
and Volta initiated the quali-
tative study of the electric
battery, of how Oersted and
Ampere carried the work far-
ther into the realms of elec-
tro-magnetism, and Davy into
the field of electro-chemistry.
We shall now see how Georg
Simon Ohm, struggling against
the almost overwhelming odds
of poverty, isolation, and lack
of recognition, discovered the
law with which his name is so
honourably associated, and so
laid a lasting foundation for the quantitative study of current
electricity.

Georg Simon Ohm was a German. He was born on the i6th of
March 1789, at Erlangen, in Bavaria, and was the elder of the
two sons of a master locksmith. Simon's father was a man of
common sense and understanding. It so chanced that when
a lad there had lodged in his house a young student of the
University of Erlangen. This student had given the lad who was
afterwards Simon's father lessons in mathematics in part pay-
ment of the rent, and these lessons had left in the mind of the
recipient a true appreciation of the value of learning.

Fig. 93. GEORG SIMON OHM

234 Georg Simon Ohm

Consequently, although it was his wish that his two sons,
Georg and Martin, should both in due course become locksmiths
like himself, he had no intention of denying them the privileges
of education. At first he sent them to the elementary school,
but from this he passed them on to the local secondary school,
or Gymnasium, as this type of school is called in Germany. Here
they were able to learn the rudiments of mathematics and science.
Both brothers displayed ability, the elder in science and the
younger in mathematics, and Charles de Langstorff, a man of
discernment and an eminent mathematician, who was in 1804
appointed to the chair of mathematics at the Gymnasium, pre-
dicted for the two brothers a brilliant future, and likened them
to the famous Bernouilli brothers.

In the face of such a pronouncement, Ohm felt himself unable to
insist on making locksmiths of his two boys, although as a matter
of fact, living at home as they did, they were rapidly picking up
the rudiments of their father's trade. Ohm was a poor man, but
with some friendly assistance he managed to give his sons three
terms each at the University of Erlangen. Three terms meant
an incomplete course, but the young men were thus enabled to
make for themselves an opportunity of completing their courses
later, and this is indeed what happened.

For a time Simon maintained himself as a private tutor in
Switzerland, and by 18 11 he had managed to save sufficient
money to return to Erlangen to finish his course and pass his
examinations at the University. He now obtained his first real
teaching appointment at a school in Bamberg. Being a teacher
by instinct, he settled down to what he regarded as a satisfactory
beginning to his career, and looked forward to the time when he
could repay his father, now growing old, for the love, care, and self-
sacrifice he had displayed in his endeavours to do well for his sons.

It was a hope doomed to disappointment ; for before very
long a series of difficulties caused the closing down of the school,
and the staff was dismissed. It was an unfortunate time. Europe
was in the throes of the Napoleonic wars, and Germany was
deeply committed. Ohm found himself unable to obtain another
scholastic appointment, and very dejectedly he returned to

Early Life and Progress 235

Erlangen. He had, however, no intention of being a drag on his
father, and so he helped him in the only way now possible — by
working at the vice in the locksmith's shop.

There can be no doubt that our future philosopher must have
found the work distasteful ; but there was nothing else for it.
Necessity and duty held him to his task, but he never lost hope
of returning to his beloved teaching. It was his ambition one day
to be a university professor, and he never doubted, through all
this trying time, but that one day he would achieve his aim.

At last his opportunity came. In 1817 he published an ' Essay
on Geometry ', ' written in a room without a lire ', and as a result
of the notice this received he was offered, and, as we may be well
sure, he eagerly accepted, the post of teacher of mathematics
and physics at the Jesuit High School in Cologne. Here he spent
nine and a half successful years as a teacher, and here it was that
he carried out those researches which made him known. As
a teacher he was an undoubted success. His lectures were
clearly thought out, well delivered, and popularly received, and
many of his students made their mark in after life, notably, for
example, Lejeune-Dirichlet, the mathematician.

Ohm's ambition, however, went beyond mere teaching. He
was deeply interested in problems of current electricity, and he
wanted to engage in research, but there were difficulties in the way.
His scholastic duties left him little time for experimental work,
and his slender purse rendered the acquirement of books and
apparatus an extremely slow process. Nevertheless, there were
two other factors which enabled him to triumph in spite of these
difficulties — his iron determination to carry through, and his
mechanical skill derived from his father's workshops. As a result
of the latter he was able to construct much of his apparatus for
himself ; and so, without hurry, quietly, but persistently, he
worked on in such spare time as he possessed, and gradually
built up an edifice of experimental work which enabled him by
1826 to set forth what he had done, and show a result which,
later, was to bring him and his country honour.

Let us consider briefly what was this series of experiments, and
whither it led.

236

2. Ohm' s Researches in Current Electricity

In 1822 Joseph Fourier published an epoch-making work
entitled La Theorie analytique de la Chaleur. It was an important
contribution to mathematical physics, and attracted the attention
of the whole of the scientific world. It was valuable not only for
the sake of the important matter which it contained, but also
for the marked stimulus it gave to experimental inquiry.

One of its chief features was its discussion of the subject of the
* heat conductivity ' of materials ; that is to say, the relative
abilities of different substances to transmit heat along themselves
when one extremity is subjected to higher temperatures than that
of the remainder ; and Fourier's conclusion was that the ' flux
of heat ', i. e. the total quantity of heat which flows in a given
time, is in direct proportion to the difference of temperatures
between its two ends.

This was a conc'usion which set Ohm thinking. He thought
he saw much that was similar between the problems of the flow
of heat along a metallic bar, and the flow of electricity along
a metallic conductor. He compared the idea of the flux of heat
with the idea of strength of current in electricity, and Fourier's
conclusion that the flux was proportional to the difference of
temperatures suggested to Ohm the corresponding idea of current
strength being proportional to the difference of potential at the
two terminals of a battery.

As a starting-point Ohm began to experiment on the effects of
using different conductors. He took a number of wires of different
materials but each of the same thickness, and beginning with
copper, he varied the lengths of the different conductors he used,
so as to get the same effect on the galvanometer in his circuit.
That is to say, he was experimenting on the effect of length on the
conductivities of the different materials.

His results are as follows. Taking the length of the copper
conductors as 1,000, the lengths of substances required to give
the same flow of current were :

Researches in Current Electricity 237

copper .

. 1,000

iron

gold

574

platinum

silver

. 356

tin

zinc

333

lead .

brass

280

174
171
168

97

and this gave Ohm an idea of the relative electrical conductivities
of these different substances. It is interesting to notice, however,
that his result for silver was very faulty, since it is actually a
better conductor than copper, although the above figures show
it to be poorer.

Later Ohm discovered the reason for the error. The trouble
arose from the fact that in the process of drawing the silver wire,
it had been covered wdth oily leather, as a result of which the wire
appeared to be greater in cross-section than it really was. Now
Ohm's next series of experiments was on the effect of varied
cross-sectional areas on the conductivity, and he found, using
wires of the same materials, that the conductivity was unaltered
if the cross-sectional area was kept proportional to the length.
This at once told him that his result for silver in the first series
of experiments must be wrong if the cross-section was too small,
and subsequent experiments with silver gave him a more correct
value.

The results of Ohm's researches thus far may be summarized
as follows. The conductivity of a given specimen of wire is
governed by three factors : (i) its length ; (2) its sectional area ;
and (3) the material of which it is composed. Looking at the
problem from the reciprocal point of view, the wire offers a
natural resistance to the passage of the electric current, and this
resistance, which we denote by the symbol R, is directly propor-
tional to the length /, inversely proportional to the cross-sectional
area a, and is also proportional to a constant p, the value of which
varies from material to material.

I
i. e. R = p-.
^a

It is not difficult to realize why the resistance of a wire to an
electric current is greater for a narrow than for a stout wire.
Although it is a very loose sort of comparison, we have a similar

238 Georg Simon Ohm

phenomenon in the case of a pipe conveying a current of water ;
a wide pipe offers Uttle resistance to the flow, whereas a narrow
pipe offers considerable resistance.

The symbol p in the above equation gives us what is called
the specific resistance, or more shortly, the resistivity of a given

material, and therefore the reciprocal - , usually denoted by k,

P
would give us the specific electrical conductivity of a given
material.

We now come to the second stage of Ohm's researches. It
should be mentioned that he had sent accounts of his observa-
tions to a scientific journal conducted by Schweigger, the famous
inventor of the galvanometer, and also to Poggendorf's ' Annalen ',

and in the course of these he

explained that he had been much

CoId<^ ^^ ^Hot troubled in his experiments by

^___ the vexatious variations in cur-

B/smuth j-ent which he experienced from

Fig. 94. The Thermo-Electric his batteries. To this Poggen-

^^^^^^^- dorf replied with the suggestion

that he should dispense with the batteries altogether, and

substitute for them a thermo-circuit.

This was a sound suggestion, and Ohm adopted it. Let us
consider briefly what is meant by a thermo-circuit. The ordinary
type of battery or electric cell is not the only means of producing
a current. In 182 1 Thomas Johann Seebeck, a Russian scientist
resident in Berlin, had discovered that if a strip of copper be
joined to a strip of bismuth so as to form a closed circuit, then,
if one junction be subjected to a higher temperature than the
other, a current of electricity at once flows round the circuit and
continues so to flow as long as the difference in temperature
between the two junctions exists. The presence of the current
is indicated by a deflexion in the needle of a galvanometer, G
(Fig. 94), introduced into the circuit. The strength of the current,
of course, is proportional to the temperature difference. This
phenomenon is true for any pair of metals, and in Seebeck's
original experiment the mere holding of one junction in the

Researches in Current Electricity 239

hand was sufficient to produce a current which he could
measure.

This was the principle which Simon Ohm employed in the place
of his troublesome batteries, and he did so with great success. He
was now at work upon the experiment which established his
famous law. His idea was to study the factors which affected the
strength of current in any given circuit. We have already seen
how Fourier's work on the flow of heat suggested to him the
influence of the potential difference between the two battery
terminals as one factor. The resistance offered by the circuit
to the passage of the current was, he realized, the other factor.
But he saw further. The resistance was made up of two portions.

Bismuth

Copper

\

Copper

^

f

J-L.

"\

t

[/

A

100"

I

steam

Connecting^ Wire__

( " \

Mercury — »-^^B
Fig. 95. Ohm's Apparatus

There was, first, the resistance of the conductor joining up the
battery terminals ; this he spoke of as the external resistance.
Secondly, there was the resistance of the battery itself ; this he
called the internal resistance. So long as Ohm used batteries
this internal resistance was a continual trouble, for it could not
be directly determined as could that of a wire conductor, that

/
is to say the formula R =p - could not be conveniently supplied.

Here, then, was an additional reason for discarding batteries,
and for using thermo- circuits instead ; for, besides being no
longer troubled by current variations in the battery, he was also
able to dispense with the consideration of internal resistances
other than those he could directly determine. Let us see how
Ohm set to work. He used a thermo- circuit of bismuth and
copper. One junction was maintained at a temperature of

240 Georg Simon Ohm

100° C. by immersion in a steam jacket ; the other junction at
0° C. by immersion in an ice-jacket. The copper was in two
disconnected portions, the extremity of each dipping into a cup
of mercury (Fig. 95), and Ohm could either ' make ' or ' break '
his circuit by introducing or withdrawing the ends of a connecting
wire between these two cups.

To measure the strength of the current produced, Ohm did not
use the ordinary form of galvanometer. Instead he used a torsion-
balance made by one of his assistants. This consisted of a magnetic
needle suspended from a graduated brass-head by means of a
flattened wire, five inches long. The circular brass-head was
radially divided into a hundred parts, and each ' centesimal ' of
a circle was further divided into quarters. The theory of the
galvanometer is applied in part. When the needle is placed under
the copper wire, and the circuit closed, the resulting current pro-
duces a deflexion of the magnetic needle, the magnitude of which
depends on the strength of the current. But, instead of measuring
this deflexion, the brass-head is rotated so as to bring back the
needle to its zero position, and it is the angle through which the head
is rotated which is observed. One advantage of this method is that
it reduces that ' bugbear ' of experimenters — the personal equation.

Ohm used in succession eight samples of copper wire, each of
equal thickness, but of lengths 2, 4, 6, 10, 18, 34, 66, and 130
inches. The following were the results he obtained in an experi-
ment he carried out on the 8th of January 1826 :

Restoring angle of

Length of copper torsion-head in

conductor {inches) centesimal divisions

2 326I

4 300I

6 277I

10 238^

18 190$

34 I34i

66 Ssi

130 48I

Ohm's conclusion was that ' the above numbers can be repre-
sented very satisfactorily by the equation

where X designates the intensity of the magnetic effect of the

Researches in Current Electricity 241

conductor whose length is x, a and h being constants depending
on the exciting force and the resistance of the remaining parts
of the circuit.'

Let us interpret his language in present-day terms. Ohm talks
of X as the intensity of the magnetic effect of the conductor, but
we know that the extent of this magnetic effect depends upon
the strength of the current, being essentially the ' Oersted ' effect
referred to in the last chapter. Hence X is replaced nowadays
by the symbol C, denoting the strength of the current in the
circuit. Again, Ohm says a is the constant ' depending on the
exciting force ' ; this exciting force is what to-day we call the
' electromotive force ', and it is that which sets up the difference
of potential, so causing the flow of the current. We denote
it by the symbol E. Finally, as to the denominator h +x, di very
little consideration will suffice to show that this expression really
gives a measure of the total resistance of the circuit to the passage
of the current ; for x is the length of the copper conductor, and,
as Ohm clearly showed in his first series of experiments on conduc-
tivity, the resistance of a conductor is directly proportional to
its length (see p. 236) ; and 6 is a constant ' depending on the
resistance of the remaining parts of the circuit '. A reference
to Fig. 95 will show to what portion of the circuit this refers,
namely, to the rod of bismuth, the two cups of mercury, and the
connecting wire ; these remained unchanged throughout the
whole series of experiments, and consequently Ohm was able to
assign to i a definite and a constant value. The quantity h -{-x
is therefore a measure of the total resistance of any given circuit,
and in the case of an ordinary battery circuit, using the nomen-
clature usual to-day, it consists of the external resistance R of
the wires, and the internal resistance r of the battery itself.

Hence we see that, substituting for every term in Ohm's original
expression the symbols of to-day, the expression reduces to

or, expressed in words, for any given electrical circuit,

„ ^ Electromotive Force

Current = — .„ ^ , -p. — ■. .

lotal Resistance

This relation is universally spoken of as Ohm's Law.
2613 Q

242 Georg Simon Ohm

Returning to the formula, X = -7 , Ohm assigned to the

exciting force a the value 7285, and to the external resistance & the
value 20J, and, using these values, his results were undoubtedly
excellent. Taking at random, for example, the length of the copper

conductor as 10 inches, X works out to -A. = - — ^ = 240-86,

2oi + 10 30J

whereas experiment gave 238^ ; or again, for x=6, the theoretical

value gives yY = 277-53, as compared with the experimental

result 277 1.

Ohm next consolidated his results by varying his -experimental
conditions, using brass instead of copper, and in another series
using thermo- junction temperatures of o°C. at one end and room
temperature at the other end. These, of course, altered both
current strength and electro-motive force, and also the internal
resistance, but his formula still held good.

So was established the famous law upon which all modern
electrical computations are based. Current electricity, as Ohm
found it, was a qualitative study to which numerical notions
were hardly applicable. As he left it, accurate definitions of
current strength, of electrical resistance, and of electro-motive
force, were clearly laid down, and the numerical relationship
between them conclusively established. It was a fine achieve-
ment, and, coming as it did from this quiet, unassuming German
scientist, it deserved the united acclamation of a grateful Germany
for the honour he brought his country.

Yet how, in fact, did his countrymen receive his work ?

3. How Ohm' s Results were received

Ohm had published occasional notices of his experimental
work in the scientific journals conducted in Germany by men
like Schweigger and Poggendorf. These notices had not attracted
much attention, but in 1827 Ohm had applied for, and had been
granted, leave of absence to go to Berlin, where library facilities
were so much better, to complete his experiments and publish
his results. Accordingly in that year there appeared his book
entitled The Galvanic Chain, M atliematically Worked Out. This

How his Results were received 243

work was in effect supplementary to his articles in that
it set forth a theoretical deduction of his law from ' first
principles '.

It is difficult to realize why it should be so, but the fact remains
that the book was badly received. ]\Iany who should have known
better simply ignored it altogether. To some extent the trouble
was due to the fact that very few people appeared to have noticed
his articles setting forth his experimental results, and conse-
quently, when they saw in the book what appeared to be a purely ■
theoretical argument unsupported by experiment, it was regarded
as the creation of a warped fancy. Ohm's theory, to quote one
critic, was ' a web of naked fancies ', which could never find
the semblance of support from even the most superficial observa-
tion of facts ; ' he who looks on the world ', proceeds the writer,
' with the eye of reverence must turn aside from this book as the
result of an incurable delusion, whose sole effort is to detract
from the dignity of nature '.

Ohm's disappointment was bitter and deep. For nine years
he had laboured at Cologne, building up a reputation as an
earnest teacher and a sincere seeker aftertruth. He had developed
legitimate aspirations. His ambition was to become a university
professor, and he had naturally thought that this work upon
which he had been engaged, based as it was on the irrefutable
logic of experimental fact, would win him his desired goal. Yet
now that it was completed, where he had looked for commenda-
tion he found at best complete indifference, and at worst open
abuse and derision.

More was yet to come. Amongst his critics was a certain
school official with whom in some administrative capacity Ohm
must have come into contact. This person was at all times an
opponent of the experimental school of thought, and, with this
initial bias against Ohm, he now became particularly hostile to
him. The influence of this opposition reached the Minister
of Education himself, and he, speaking officially, definitely
pronounced it as his opinion that ' a physicist who professed
such heresies was unworthy to teach science '.

This truly was a very severe blow, and in the depth of his

Q2

244 Georg Simon Ohm

misery Ohm took the only course consistent with his self-respect.
He resigned his appointment at Cologne.

It is inevitable to wonder why it was possible that in a country
so well represented in the world of science by men of eminence
and knowledge a series of investigations the searching character
of which could admit of no doubt, culminating in the discovery
of a law so obviously fraught with significance and importance,
should have been received with such shameful disregard and
with such obvious violation of the instincts of justice. The fact
remains that for the next six years this much-wronged man was
withdrawn from a useful activity which might have resulted in
further benefits to humanity, and was thrust into the obscurity
of casual coaching in Berlin, and during the whole of this time
the only certain source of income which he could ' enjoy ', apart
from such occasional private tuition as was asked of him, was
the giving of some three lessons a week in mathematics in a school
at a minute yearly salary.

4. Ohm's Later Career

Fortunately, the situation was so grotesquely illogical that it
could not persist. Ohm's work was sound and it existed in black
and white. It embraced a subject which was hound to receive
the attention of the world of science. Gradually it began to be
talked about. Ohm luckily was not entirely lost in obscurity.
During these six years of scientific exile, occasional articles
bearing his name found their way into Schweigger's periodical,
and although these were of minor importance, they at least
helped to set going rumours of a possible value in the work
which had brought him such unmerited disgrace.

It is no credit to Germany that first recognition of Ohm's work
was to come from abroad. Such great men as Lenz in Russia,
Wheatstone in England, and Joseph Henry in America, were all
at work on problems of current electricity, and sooner or later
it was inevitable that they should come up against the rumours
of Ohm's researches. In 1833 Henry asked Dr. Bache, ' Can you
give me any information about the theory of Ohm ? Where is

Later Career 245

it to be found ? ' Yet Dr. Bache could tell him nothing, and it
was only in 1837, when Henry was on a visit to England, that
he was able to get access to the information he sought.

In 1833 Ohm's luck changed. He obtained an appointment
under the Bavarian government at the Nuremberg Polytechnic
School, and in this position found himself better able to face the
future. Indeed his day was soon to come. Even in his own
country Poggendorf and Fechner were beginning to insist on the
high value of his work, but abroad, and particularly in England,
open admiration began to be expressed for his researches, which
now began to attain a wide publicity.

A culminating point came in 1841, in which year the Royal
Society of London conferred upon Ohm the award of the Copley
medal in recognition of his eminent services to science by the
discovery of his now famous law. This award, coveted by
scientists all the world over, and coming as it did from a foreign
country, deeply affected Ohm. It was a proud moment for
him, and it repaid him, no doubt, for all that he had suffered at
the hands of his own countrymen. It served, too, as a stimulus
to further effort, and he determined that he would carry on with
his researches with a renewed vigour and enthusiasm.

The next few years saw Ohm steadily at work, and although
most of what he did was outside the scope of electrical research,
it was none the less useful. His work on acoustics was especially
valuable, including as it did the theory of the siren and a dis-
sertation on the analysis of sounds by the ear. Some researches
which he seriously contemplated, and which he actually began,
in molecular ph3'sics, on a somewhat grandiose scale, in which
it was his intention to emulate Sir Isaac Newton in the
' parallel ' study of celestial mechanics, however, did not mature.
In 1849 he received the first real mark of recognition in his
own country in the shape of an appointment at the University
of Munich as professor, and the various duties which were
assigned to him in this capacity left him little time for his own
unofficial work.

This appointment was no ordinary incident in Ohm's life. It
. had been his great dream to become one day a university pro-

246 Georg Simon Ohm

fessor, and it was an ambition which had never left him. Now,
at the age of sixty years, his dream had come true. He had won
his place. His name was honoured throughout the world of
science. He had earned the respect of his colleagues and the love
of his students and he was content.

Duties multiplied : he had charge of the library and of the
museum : he became councillor of the telegraph administration.
What little spare time he had he devoted to the writing of a text-
book in physics.

Further recognition came in the shape of various orders, but
these in no wise spoilt him. Never a man of fashion, society,
rank, or pretence, he remained to the end the simple, quiet, truth-
loving man of science he always was. In appearance he was
somewhat short and plump and with a kindly, retiring look. He
seldom spoke except when addressed, and lived contentedly alone
and unmarried. To his colleagues and his critics he was always
the essence of courtesy and of generosity of thought. He died in
1854, continuing his official duties almost to the last.

We have already mentioned that in 1881 the International
Congress of Electricians at Paris paid homage to the memory
of Ampere by naming the practical unit of electrical current after
him. It was but fitting that the same congress should extend
similar honour to the memory of Georg Simon Ohm, after whom
they named the practical unit of electrical resistance.

In 1889, one hundred years after his birth, the Royal Bavarian
Academy of Sciences at Munich convened a special gathering
of scientists for the purpose of paying tribute to Ohm's
splendid services, and we cannot do better in conclusion than
quote the following fine passage from Professor E. von Lommel's
address :

' The deeds of a man of science are his scientific investigations.
Truth once discovered does not remain shut up in the study or
the laboratory. When the moment comes, it bursts its narrow
bonds and joins the quick pulse of life. That which has been
discovered in solitude, in the unselfish struggle for knowledge, in
pure love of science, is often fated to be the mighty lever to
advance the culture of our race. When, nearly a hundred years

Later Career

247

ago, Galvani saw the frog's legs twitch under the influence of two
metals touching, who could have suspected that the force of
Nature which caused those twitchings would transfer the thought
of man to far distant lands, with lightning speed, under the
waters of the ocean — would even render audible at a distance
the sound of the spoken word ? That this force of Nature —
after man by ceaseless investigation had learned vastly to
increase its strength — would illuminate our nights like the sun.
This enormous development of electro-technology could only
be accomplished upon the firm foundation of Ohm's law. For
only he can govern a force of Nature who has mastered its law.
Ohm, by wresting from Nature her long-concealed secret, has
placed the sceptre of this dominion in the hands of the present.' ^

1 From Sir R. Gregory's Discovery, p. 184.

) . c ^::^c

6ciifral3^rtrnrtfir jHfftii^ . ^ \

2t. m yr/Ci yOurcc^crd

Fig. 96. The first Membership Ticket of the British Association.

XIV

]\IICHAEL FARADAY

I. Early Life

There are two facts which make one marvel that Michael
Faraday should have made himself what he did. The first was
his parentage. The late Professor John Tyndall, an intimate
friend of Faraday, tells us :

' Believing, as I do, in the general truth of the doctrine of

hereditary transmission —
sharing the opinion of ^Ir.
Carlyle, that a really able
man never proceeded from
entirely stupid parents — I
used the privilege of my in-
timacy with Mr. Faraday to
ask him whether his parents
showed any signs of unusual
ability. He could remember
none.' ^

MICHAEL FARADAY

The other fact is that
throughout his career he
knew little or no mathe-
matics. He was not a mathe-
matician, and indeed he
once boasted that he never
made a mathematical calcu-
lation in his life except once
when he turned the handle of a Babbage calculating machine.

This latter was indeed a most remarkable fact, for there is no
doubt but that a mathematical equipment, even though of
a meagre kind, is a wonderful weapon of assistance to the
physicist. Yet such was Faraday's brilliance that his mind
was independent of this weapon. He was in the truest sense of
the term a master experimentalist. Experimentalists there have
been w^ho, looking to the mathematics for the basis of a theory,
have applied successfully the test of experiment to that theory :
1 Tyndall's Faraday as a Discoverer,

Early Life 249

others there have been, too, who, starting without either theory
or hypothesis, have by patient repetition of experiment built up
results the statistics of which have led them to great truths. But
Faraday belongs to neither of those groups. In him there was
that subtle sense which time after time suggested to him the
possibility of some physical truth, and he would at once proceed
to apply to it the test of the laboratory — and almost always with
astonishing success.

Michael was the son of James Faraday, a Yorkshireman ot
humble parentage, and a journeyman blacksmith by trade.
James had married in 1786 a farmer's daughter named Margaret
Hastwell, and shortly after, the couple migrated to London,
living for a time at Newington. Here four children were born
to them, of whom Michael, born on the 22nd of September 1791,
was the third. The mother was an almost illiterate woman, but
what she lacked in education she made up in neatness, frugality,
and love, and the children were accordingly as well cared for as
circumstances permitted.

On the whole they were poor circumstances indeed. When
Michael was five years old, the family moved from Newington
into some rooms over a coach-house in Jacob's Well Mews,
Charles Street, Manchester Square, and here the ill-health to
which James Faraday was repeatedly subject, together with the
severe industrial depression from which the country suffered at
the beginning of the nineteenth century, served to make the lot
of the Faraday family a hard and difficult one. Dr. Bence Jones,
Michael's chief biographer, tells us that in 1801, ' when the price
of corn rose above £g a quarter, the family obtained public relief,
and Michael's portion was a loaf, which had to serve him for
a week.'

This, then, was the atmosphere in which Michael was brought
up. It might, perhaps, have been worse, since at least he had
a roof over his head, and the Faradays were a united family. So
Michael lived the life of the average London street boy. ' My
education ', he writes, ' was of the most ordinary description,
consisting of little more than the rudiments of reading, writing,
and arithmetic, at a common day-school. My hours out of school

250 Michael Faraday

were passed at home and in the streets.' We know nothing in
particular, at this period of his Hfe, to suggest that there was in
this boy either special ambition or ability. He was merely
average, but without doubt this was only because the opportunity
was lacking.

The first taste of the world beyond his streets came at the age
of thirteen, when he was given a job by a Mr. George Riebau,
a bookseller and bookbinder, as errand boy. One of Mr. Riebau's
activities was the hiring out of papers of various kinds, and these
Michael used to deliver and collect. He gave his master such
satisfaction that after a year, in 1805, Mr. Riebau accepted him
as an apprentice to the bookbinding trade without a premium.
This brought Michael for the first time into intimate contact
with books, and, fortunately, he needed little encouragement to
make the most of his opportunity. There was innate common
sense in the lad, and Watts's Improvement of the Mind, which
he read as he bound the book, appealed to him. He then
read through Mrs. Marcet's Conversations on Chemistry, and the
article on ' Electricity ' in the Encyclopaedia Britannica, which
he was also binding, and he found himself irresistibly drawn to
a study of the facts of science.

He spent what few pence he could spare on odds and ends of
apparatus for a few home-made experiments, but he felt he must
get more information and instruction. Where was it to come
from ? Those were not the days of organized evening classes,
but to a small extent private enterprise supplied what public
spirit lacked. Wlien Faraday was nineteen he saw an ad-
vertisement in a shop window announcing that a ]\Ir. Tatum, of
Dorset Street, Fleet Street, was delivering a course of lectures
in Natural Philosophy at his private residence at eight o'clock on
certain evenings, admission one shilling per lecture. To Michael,
with his slender resources, it was a lot of money ; but with the
help of his elder brother Robert, by now a working blacksmith
like his father, he was able to raise the necessary amount, and so
he attended the lectures.

Another circumstance helped him considerably. Lodging at
Mr. Riebau's house was a French refugee, a M. Masquerier, an

Early Life 251

artist. This gentleman had noticed with some pleasure that
Michael had exhibited a taste for drawing, and he encouraged
him with hints and with the loan of Taylor's Perspective. As
a consequence, when he came to write out careful notes of
j\Ir. Tatum's lectures, he was able to illustrate them very fully,
and to bind them together into four volumes when they were
completed.

This course of lectures not only brought to Faraday some of
the joys of scientific knowledge, but it also brought him into
contact with people of similar taste. He thus made friend-
ships, but at the same time he began to develop a feeling of
unrest. The future of a routine of bookbinding which a year or
two before he had regarded as rosy with promise was now
becoming increasingly distasteful to him. The call of science
had begun.

2. Faraday and Davy

Then came that little circumstance which was to become the
turning-point in his life. One of Mr. Riebau's customers was
a i\Ir. Dance, a member of the Royal Institution. Various visits
to the bookshop had made this gentleman aware of Faraday's
liking for science, and he resolved to invite Michael to attend the
last four lectures of a course which Sir Humphry Davy was
concluding at the Royal Institution. The lectures were a revela-
tion of delight to Michael, and only served to increase his longing
to abandon trade and give himself up to the service of science.
But how ? He knew no one who might help him. Nevertheless
the period of his apprenticeship was nearly at an end, and he
felt that he must do something. In his ignorant helplessness he
wrote to the President of the Royal Society, and no doubt the
letter found its way fairly quickly to the presidential waste-paper
basket.

Our heavy-hearted, discontented Michael came to the end of
his apprenticeship. On the 8th of October 1812 he became
a full-fledged journeyman bookbinder, his age now being twenty-
one years. He was none too lucky in his employer, an ill-
tempered Frenchman, and the rather long hours of his employ

252 Michael Faraday

prevented him from devoting any leisure time to the science he
had come to love ; trade and the atmosphere of business were
becoming more and more hateful to him, and he felt he must
make one more effort to break away from his nauseating sur-
roundings.

Then came the happy thought which brought him ultimately
to the desired goal. Why not write to Sir Humphry Davy
himself ?

' My desire to escape from trade, which I thought vicious and
selfish, and to enter into the service of science, which I imagined
made its pursuers amiable and liberal, induced me at last to take
the bold and simple step of writing to Sir H. Davy, expressing my
wishes, and a hope that, if an opportunity came in his way, he
would favour my views ; at the same time I sent the notes I had
taken of his lectures.'

The letter clearly made some impression on Davy. The appeal
rang with sincerity, and the lecture notes showed ability. Davy
consulted the famous Mr. Pepys, a descendant of the great
diarist and 'one of the original managers of the London Institu-
tion. ' Pepys,' he said, ' what am I to do ? Here is a letter
from a young man named Faraday ; he has been attending my
lectures, and wants me to give him employment at the Royal
Institution — what can I do ? ' ' Do ? ' replied Pepys, ' put
him to wash bottles ; if he is good for anything he will do
it directly, if he refuses he is good for nothing.' ' No, no,' replied
Davy, ' we must try him with something better than that.'

So it was that our delighted Michael one day saw Davy's
carriage drive up to his home, and the following letter was handed
to him :

' Sir,

I am far from displeased with the proof you have given me of
your confidence, and which displays great zeal, power of memory,
and attention. I am obliged to go out of town, and shall not be
settled in town till the end of January ; I will then see you at any
time you wish. It would gratify me to be of any service to you.
I wish it may be in uiy power.
I am, sir.

Your obedient humble servant,

H. Davy.'

Faraday and Davy 253

As luck would have it, the situation of assistant in the labora-
tory of the Royal Institution fell vacant shortly after, and Davy
sent for Faraday. In the same letter to Dr. Paris, from which
we have just quoted, Faraday writes of this interview :

' At the same time that he thus gratified my desires as to
scientific employment, he still advised me not to give up the
prospects I had before me, telling me that science was a harsh
mistress, and, in a pecuniary point of view, but poorly rewarding
those who devoted themselves to her service. He smiled at my
notion of the superior moral feelings of philosophic men, and said
he would leave me to the experience of a few years to set me right
on that matter.'

As a result, at a meeting of the managers of the Royal Institu-
tion on the ist of March 1813 it was resolved ' that Michael
Faraday be engaged to fill the situation lately occupied by
Mr. Payne, on the same terms '.

Faraday's duties were of a very humble kind, but he was very
happy. He had got his chance. His main work was to assist the
lecturers and keep the apparatus and the laboratory clean. He
was provided with quarters at the top of the building, and he
received twenty-five shillings per week. He quickly showed
himself to be capable of better things, and it was not long before
he was assisting with minor experiments (at first mainly in
chemistry) and in acting as amanuensis to Davy. Further, he
became a regular member of the City Philosophical Society,
a weekly gathering which had developed from the private science
class of Mr. Tatum. Here he made a few friends, who constituted
themselves a sort of sub-society, meeting at Faraday's rooms
for discussion and mutual improvement.

Faraday rapidly established himself in the full favour of his
chief. Sir Humphry Davy, and when the latter set out, in October
1813, on his Continental tour, he invited Michael to accompany
him as amanuensis and general assistant (and incidentally, as it
turned out, owing to the last-minute defection of Davy's personal
servant, as unofficial valet), and although the intimate contact
between two such totally different minds and personalities gave
rise to various ' incidents ', it was for Faraday a wonderfully
helpful and educative tour. It brought him into new countries

254 Michael Faraday

and amongst new peoples, and above all he had the inestimable
privilege of meeting many of the great philosophers of Europe,
men who were afterwards to become his close and admiring
friends.

3. Further Career

The tour lasted till the spring of 1815, and on his return
Faraday was reinstated to his former position as laboratory
assistant at the Royal Institution, but at the augmented salary
of thirty shillings per week. The managers were justified in the
granting of the extra five shillings. Faraday was now beginning
to experiment in earnest, though still, of course, in quite an
elementary way, carrying out simple analyses. This was his
period of learning ; the days of creation had yet to come.

Meanwhile his attendance at the meetings of the City Philo-
sophical Society continued regularly, and on the 17th of January
he delivered to its members his first address, the subject being
on the general properties of matter. The same year, too, saw
the publication of his first paper, on an analysis of caustic lime,
in the Quarterly Journal of Science, the official organ of the Royal
Institution, and from this time onwards, for the next few years,
various papers of minor importance appeared at intervals.

We now come to 1820, in which year for the first time he
gained the ear of the Royal Society, by a paper ' on the new
compounds of chlorine and carbon, and on a new compound of
iodine, carbon, and hydrogen '. The paper was well received,
and seemed to provide a fitting starting-point for the life-long
series of researches vv'hich now followed. The year 1820 was
epoch-making in the history of electro-magnetism, for it saw
Oersted's great discovery of the magnetic effect of the electric
current, and Ampere's subsequent researches on the subject.
Dr. Wollaston took the subject up in England and unsuccessfully
attempted an experiment, to which we shall later refer, at the
Royal Institution. Faraday was present, and the proceedings
excited his interest profoundly. He very properly realized that
before attempting anything similar himself, he must first make
a careful study of what had been done, and so he began an

Further Career 255

intensive course of reading and experiment which culminated in
his pubUcation of A History of the Progress of Electro-Magnetism.

Finding himself now properly equipped with the facts of the
situation he set to work to achieve that which Wollaston had
failed to accomplish. The experiment was performed in December
182 1 and succeeded magnificently, and we are told that by way
of celebration the author of it treated himself to a visit to the
pit at Astley's Circus.

We now come to one of the happiest events in Faraday's long
life. He was a member of a small sect known as the Sandemanians,
and through his attendance at their place of worship he gained
an introduction to the family of Mr. John Barnard, one of the
elders, and a silversmith by trade. Faraday wooed, and won, the
third daughter of this gentleman, and he married Sarah Barnard
on the I2th of June 1821. It was, by his wish, the simplest of
ceremonies. He desired that the day should resemble any other
day as far as possible, and so he just married the lady and brought
her to his rooms at the Royal Institution. It was a happy union.
Twenty-five years after he recorded an entry in what was by then
a voluminous book of diplomas.

' 25th January, 1847.

Amongst these records and events, I here insert the date of
one which, as a source of honour and happiness, far exceeds all
the rest. We were married on June 12, 1821. M. Faraday.'

He had by this time been promoted to superintendent of the
laboratories, and his researches now began to assume first-class
importance. He carried out, in collaboration with Mr. Stodart,
some experiments on the alloys of steel, as a result of which ' he
was accustomed in after years to present to his friends razors
formed from them, and in 1823 he performed some important
experiments on the liquefaction of gases, through which he was
able to establish that all gases could be considered as the vapours
of their corresponding liquid, possessing very low boiling-points.
These experiments, involving as they did the subjection of glass
vessels to very high pressures, were not without risk to the
experimenter, and on one occasion an explosion caused no less
than thirteen pieces of glass to enter his eye.

256 Michael Faraday

Faraday had by now thoroughly estabHshed himself as a
scientist of high order, and on the 8th of February was elected,
unfortunately not without some jealous opposition from Sir
Humphry Davy, a Fellow of the RoyaL Society. The jealousy,
however, could only have been but a transient feeling on Davy's
part, since, through his influence and recommendation, Faraday
was in 1825 promoted to the position of Director of the Labora-
tories, at the same time as Mr. Brande was promoted from
Lecturer to Professor of Chemistry. One of Faraday's first acts
in his new capacity was to organize Friday evening gatherings
of those members who were interested in science, and these
quickly developed into those weekly discourses which became
so noted a feature of the activities of the institution.

The next few years saw our philosopher (he always had a leaning
towards that title, preferring it to either ' scientist ' or ' physicist ')
busily engaged on research on optical glass, and his services were
beginning to be increasingly in demand as consultant from
various outside sources. It brought him up against the big
moral fight of his life. What was his position ? As Director he
was in receipt of a salary of £100 per annum, plus lodgings, fuel,
and light. It was, of course, an absurdly small amount. Yet, in
1830, occasional consultations and various analyses brought in
something over a thousand pounds in fees, and in 183 1 it was
greater still. Here he was, then, at the parting of the ways. For
while on the one hand there was ahead of him the prospect of
a vast avenue of research with nothing in the shape of reward
other than the honour and glory of work nobly and unselfishly
done, he had on the other hand only to call a halt to research,
to have the whole of the commercial world at his feet, and so enjoy
in fees an almost unlimited income. ' \\Tiile once conversing
with Faraday on science, in its relation to commerce and litiga-
tion,' wrote Tyndall, ' he said to me, that at a certain period of his
career he was forced definitely to ask himself, and finally to
decide, whether he should make wealth or science the pursuit
of his life. He could not serve two masters, and he was therefore
compelled to choose between them.' His choice, like that of
Humphry Davy on a former occasion, leaves the world eternally

Further Career 257

grateful to his memory. The facts speak for themselves. In
183 1 his income derived from fees was £1,090 4s. ; in 1832 it fell
to ;fi55 9s. ; it was nil in 1838, and thence till 1845 it never
exceeded £22.

The cash value of research to the scientist is wellnigh nothing.
But to the general public, whom the research student serves, it
is wealth untold. Huxley once put the matter thus :

' I weigh my words when I say that if the nation could purchase
a potential Watt, or Davy, or Faraday, at the cost of a hundred
thousand pounds down, he would be dirt cheap at the money.
It is a mere common-place and everyday piece of knowledge that
what these men did has produced untold millions of wealth in the
narrowest economical sense of the word.'

Faraday died a poor man. ' But his was the glory of holding
aloft among the nations the scientific name of England for
a period of forty years.'

4. Faraday' s Researches in Electro-Magnetic Induction

The work which above all things has made Faraday famous
was his researches in electro-dynamics. We have already men-
tioned that in 1821, when the world of science was still ringing
with the news of Oersted's discovery of the magnetic effect of
an electric current, and of Ampere's further discoveries in the
same subject, Faraday succeeded in carrying the problem to
a further stage of solution by an experiment which had previously
been attempted, without success, by Wollaston at the Royal
Institution. What was this experiment ?

Oersted had shown that a magnetic needle in the neighbourhood
of a current tends to set itself at right angles to the conductor
conveying the current. This, as we know, is due to the fact
that a north pole tends to move along the ' lines of force ' in
a magnetic field in which it is placed. If we arrange a wire from
a battery B (Fig. 98) to be vertical, and to pass through the centre
of a horizontal piece of cardboard C, then, if we sprinkle iron
filings on the cardboard and gently tap the edge, the filings will
set themselves in lines which indicate the direction of the magnetic

2613 R

258

Michael Faraday

mm

\

/

fB

Fig. 98. Lines of
force round a wire
carrying a current.

force at any point. This is the direction along which a magnetic
pole would tend to move if free to do so. In this case we find that
the ' lines of force ', as these magnetic lines are caUed, are in
the shape of concentric circles round the
wire, and so it is that a north pole will
tend to rotate round the wire in a right-
hand direction, and a south pole in the
opposite direction.

Wollaston's view, with which Faraday
agreed, was that since action and reaction
are equal and opposite, if a magnetic pole
tends to rotate round a current, there must
be an equal tendency for a conductor carry-
ing a current to rotate round a magnetic
pole. It is all a question of which is free
to move, and which is fixed and so unable to move.

Faraday's experiment is shown diagrammatically in Fig. 99.
Placed in an electrical circuit are two mercury cups A and B.
Current enters A through the wire a, and leaves B through e.
A and B are connected by means of the wire c. m and m-^ are two

magnets, m in A being
free at one end and
pivoted at b, and in^
being rigidly held.
Dipping into B, how-
ever, there is a portion
of wire d suspended
from c at /. Hence
the left-hand half of
the apparatus was a
test of the rotation of
a movable pole m round a fixed conductor c, whilst the right-
hand half of the apparatus was a test of the rotation, in
the opposite direction, of a free conductor d round a fixed
magnet ntj^.

The experiment succeeded admirably, and we are told that
when Faraday saw the needle and wire revolve round each other.

Fig. 99. Faraday's experiment on mutual
rotations of magnet and wire carrying current.

Researches in Electro- Magnetic Induction 259

he danced about them with childlike delight, exclaiming, ' There
they go, there they go ! '

It was in 183 1 that Faraday's next and perhaps most far-
reaching discovery was made, whereby he was in effect able to
produce electricity from magnetism, and thus open up a new
branch of the subject, known to-day as electro-magnetic induc-
tion. It was the culminating result of some years of careful
thought and experiment.

Let us consider what was the general nature of the problem as
it presented itself to the mind of our philosopher. We have seen
that a current is surrounded by a magnetic field, as a result of
which it attracts a magnet. Further, Ampere showed that
a conductor carrying a current attracts or repels another con-
ductor carrying a current. It was also known that a body
carrying a static or stationary charge could induce a similar
charge in a conductor brought into its neighbourhood. Why,
thought Faraday, should it not be possible for a dynamic charge,
i, e. a current of electricity, to have a similar effect, and induce
a current in a conductor brought into its own neighbourhood ?
Looking at it from another angle, Faraday asked himself why it
should not be possible to produce or induce an electric current
from magnetism, seeing that Oersted and Ampere had produced
magnetic effects from a current of electricity.

Faraday first began thinking on these lines in 1824, and in
1825 he arranged a wire carrjang a current to lie alongside another
connected with a galvanometer, but he got no result. At this
time he was busy on researches on optical glass, and he was
unable to foUow up the subject of electricity, but in 1828, he
tried the experiment again, still without result.

It was not till another three years had elapsed that Faraday
met with success, but the year 1831 was probably for him the
most brilliant of his whole career. It will be recalled how Ampere
had shown that a solenoid carrying a current behaves as though
it were a magnet, and that a rod of iron placed in the solenoid
at once becomes magnetized by induction. Faraday hit on the
happy idea of utilizing this effect, and on the 29th of August
183 1 he took a soft wrought iron ring about six inches in diameter

R 2

26o Michael Faraday

and seven-eighths of an inch thick, and round each half of this
he wound coils X and Y (Fig. loo), X being connected to a battery
of ten cells B, and Y to a galvanometer G. On depressing the
key K to close the battery circuit round X, the galvanometer
needle swung completely round four or five times, and then came
to rest in its original position, and later, on disconnecting'/^, the
needle was again disturbed though in the opposite direction.

Faraday afterwards realized that the magnetism which was
produced in the iron ring by the current round X was the cause,
at the moments of starting and stopping the current only, of
a momentary electric current round Y, thus producing the

galvanometer ' kicks '.
But at the time he did
not fully realize the sig-
nificance of this. On the
23rd of September he
wrote as follows : ' I am
busy just now again on

T^ ^ I ~ T' ^-^ 7~^ ^ electro-magnetism, and

Fig. 100. Faraday s discovery 01 Jiiectro- °

Magnetic Induction. ^hmk I have got hold of

a good thing, but can't
say. It may be a weed instead of a fish that, after all my labour,
I may at last pull up.'

Thinking over the experiment we have just described, Faraday
felt that he must assure himself that this was definitely a case
of magnetism producing electricity. Accordingly he repeated
the experiment, substituting for the iron a ring of ' non-magnetic '
copper, and he was pleased to find that the effect was greatly
reduced.

His next experiment carried the results a stage farther. In-
stead of deriving his magnetism from an electric current, he went
direct to a magnet. He took a short cylinder B (Fig. loi) and
wound his wire round it, connecting the ends to a galvanometer.
He then took two bar magnets, in contact at one end A , and placed
B between the two opposite poles N and 5 of the other ends.
* Every time the magnetic contact A^ and S was made or broken,
there was magnetic motion at the indicating helix (i. e. at the

Researches in Electro- Magnetic Induction 261

galvanometer needle G), the effect being as in former cases, not
permanent, but a mere momentary push or pull. . . . Hence here
(was) distinct conversion of magnetism into electricity.' ^

Here, then, was the direct converse of Oersted's effect. Oersted
found a magnet to be excited by an electric current : Faraday
found an electric current which had been excited by a magnet.

It will be noticed that in all the experiments above described,

Faraday got a reading momentarily from his galvanometer only

at the instant of making contact, and at the instant of breaking

contact. During the normal passage of the current itself, or in

the last experiment during the normal ' flow ' of magnetism in

the magnetic circuit ANS, the galvanometer was perfectly steady,

showing no deflexion whatever.

It only registered a ' kick '

during the actual moment when

a change of conditions was

operating. This was a most

. , T- , .^1 Fig. 10 1. Faraday's experiments

important pomt. raraday, with -^, . ,^ ,. r -, ^■

t^ ir J > QQ Electro-Magnetic Induction.

that wonderful intuition which

was so powerful an asset to him in his experimental work, rightly

felt that it was, in fact, the governing factor.

On the ist of October 183 1 he proceeded to his next famous
experiment. Hitherto he had used some direct source of mag-
netism— first from an electro-magnetic iron ring, and then, as
we have just described, from an iron bar in contact with the
poles of two- magnets forming a magnetic current. He now
dispensed v.dth any such direct source of magnetism, and this
time wound his two reels of wire, each 203 feet long and of copper,
round a wooden rod or bobbin. As before the ends of one wire
were connected with a battery of ten ceUs, and of the other to
the terminals of a galvanometer. Again on making the circuit
there was a momentary kick of the needle of the galvanometer,
and on breaking, another kick on the opposite direction.

It was now quite clear to Faraday that the essential factor for
the production of an induced current in any given conductor is
that there must be a relative change of conditions between the
1 B. Jones, Life and Letters of Faraday.

262 Michael Faraday

primary, as he called the conductor connected to the battery, and
the secondary, or wire carrying the induced current ; and in the
case of electro-magnetic induction, here again the essential
factor is change, for regarding the source of magnetism as
being surrounded by a ' field of force ', the current will only
be induced in the conductor when it ' cuts ' the lines of force
in the magnetic field, i. e. when the conductor is in motion
relative to the field. Faraday obtained a striking verification of
this by taking a coil or solenoid of copper wire, and connecting
the ends to the terminals of a galvanometer. He used no battery
whatever in this case, but merely took a bar magnet and suddenly
plunged it into the coil. There was at once a kick of the galvano-
meter needle. On withdrawing the magnet he again got a transient
current through the coils, but this time in the opposite direction.

The evidence was practically complete. So much so, indeed,
that there was little more for other people to do than to develop
the practical applications of the new discoveries. Faraday's
researches had been very thorough. He realized, for example,
that since the earth is itself a big magnet, a coil in rapid rotation
would cut the earth's magnetic lines of force, and so induce
a current in the coil, and this phenomenon of earth inductance,
as it is called, he was also able to demonstrate.

Lenz, a Russian, supplemented what Faraday had done by
pointing out what has since been incorporated as part of the
law bearing his name, that in every case of induced current due
to a relative change in the magnetic conditions, the direction
of the induced current is always such as to tend to oppose the
change. It is, so to speak, Nature's natural remonstrance against
change, and is (in a very vague way, no doubt) somewhat
analogous to the idea of the principle of inertia in motion.

There is one other discovery by Faraday in connexion with
electro-magnetic induction to which we must refer, and which
did in fact indicate one very important direction along which
the practical application of his researches would go. On the
8th of February 1832 he succeeded in obtaining a spark from the
induced current. It is known that if an electrical current is
broken by a very small air-gap, then provided the difference

Researches in Electro- Magnetic Induction 263

of potential between the two ends of the broken wire producing
the gap is sufficiently great, the current will ' bridge ' the gap
with a spark. This is particularly the case when the circuit is
broken at the moment that the current is actually passing. In
this case the heat generated at the ends volatilizes the metal
and forms a medium of metaUic vapour, and this conveys the
current with sparking. Faraday's difficulty was to break the
circuit during the passing of the induced current, since it will
be remembered that the induced current is itself of but moment-
ary duration, once at the beginning, and once at the end, of the
passage of the current in the primary circuit. However, he got
over the difficulty by cutting the wire of his secondary circuit,
and arranging the cut ends to overlap lightly so that the slightest
shock would separate them. Instead of having a battery for
his primary, he had the secondary coil wound round a short rod
of iron the ends of which protruded beyond the coil. This rod
was held over the poles of a magnet, and was then released.
Its motion through the magnetic field between the poles generated
an induced current (due to the cutting of the magnetic lines of
force), but the slight shock of the impact of the rod on the magnet
at once separated the broken ends of the wire, and to Faraday's
delight, a spark at once appeared across the gap. It was an im-
portant discovery, upon which the modern system of electric
light is largely based. Faraday subsequently greatly improved
on the brightness of the sparking by using points of charcoal
on the wdres ; and thus Davy's original observations of the
electric arc were supplemented by a further discovery, and
the problem of electric lighting began to assume a practical
character.

Gladstone, great in statesmanship but somewhat narrow in
scientific vision, once asked Faraday, on seeing one of his famous
experiments terminate in an effect which, to the non-scientific
man, was very uninspiring, of what use his discovery could be.
' Why, sir,' answered Faraday, ' you will soon be able to tax it/
It is quite understandable that the mere momentary movement
of a galvanometer needle could not be of much significance to
the old lady who also innocently asked Faraday what good such

264 Michael Faraday

an experiment could be. Yet Faraday's reminder of Franklin's
answer to such a question, ' Madam, of what use is a new-born
child ? ' is full of significance. For out of the small galvanometer
deflexion which first showed Faraday the existence of electro-
magnetic induction, there has developed for the use and comfort
of mankind the electric light, the electric motor, the dynamo,
and the hosts of modern inventions which have followed in
their wake.

5. Further Researches in Electricity and Magnetism

We have by no means concluded the tale of Faraday's dis-
coveries, for his researches in electricity extended far beyond
the subject of electro-magnetism.

In 1835 Faraday interested himself in showing that the elec-
tricity derived from friction was identical with that derived from
the voltaic cell. Davy had opened up the subject of electrolysis,
or the analysis of compounds by the electric current. Faraday
showed that just as potassium iodide could be decomposed into
its constituents by the passage of a voltaic current, so he could
also obtain the same effect by using instead the current from
a frictional machine.

A further observation which confirmed him in his conclusions
as to the identity of these two sources of electricity was the fact
that the stream of electricity from his frictional machine was able
to produce a deflexion in his galvanometer identical with the
deflexion obtained from a battery current.

These experiments led Faraday naturally into a quantitative
investigation of the laws of electrolysis. He introduced termino-
logy in this connexion which is now universally adopted. He
called the ends or plates in the decomposing cell electrodes ; the
positive being called the anode and the negative the cathode ;
and he referred to the substance which the current was decom-
posing as the electrolyte. Faraday's method of work was as
follows. He determined to see under what varied conditions he
was able to electrolyse a given quantity of water. We speak
to-day of a cell in which two electrodes dip into an electrolyte
as a voltameter, and Faraday arranged a number of these volta-

Researches in Electricity and Magnetism 265

meters having platinum electrodes of varying size, from plates
to mere wires. On collecting the gas liberated on each separate
pair of electrodes, he found the same quantity in each case. His
conclusion was that ' when the same quantity of electricity is
passed through a series of cells containing acidulated water, the
electro-chemical action is independent of the size of the elec-
trodes '. This remained true, too, whether he used strong
currents or weak, or whether the acidulation of the water was
varied, and even when he used a stronger acid strength in one
voltameter than in another for the same current. He now felt
quite definitel}^ that the amount of chemical action produced
depended only upon the quantity of electricity passed. This is now
spoken of as Faraday's First Law of Electrolysis, and is a most
important result, for it gives us an additional and an accurate
means of measuring current which is totally independent of the
use of the magnetic effect. For if we know how much decomposi-
tion is produced by a unit amount of current per unit of time,
we have only to measure the actual decomposition obtained in
a given time to calculate exactly how many units of current
must have been employed. This method is frequently used
nowadays in standardizing or testing current-measuring instru-
ments of the magnetic type.

Faraday next proceeded to investigate the relationship between
the amounts of decomposition of different substances by the
same current, and he found that there imdoubtedly existed a
constant relation between the amounts of the several compounds
which are decomposed thereby. It works out to this, that for
example a current of one ampere always deposits in an hour
4-025 grm. of silver, whether the electrolyte is silver nitrate,
silver C3^anide, or any other silver compound. Similarly one
ampere will deposit in one hour i-i8i grm. of copper, 1-203 grm.
of zinc, and so on. These quantities, 4-025 for silver, 1-181 for
copper, 1-203 for zinc, &c., are proportional to what are known
as the electro-chemical equivalents of the various substances,
and without going into the exact significance of this term
(students of chemistry will of course be quite familiar with it),
it means in effect that by knowing how much of one substance

266 Michael Faraday

is deposited by a given current in unit time, we can at once
calculate, from a knowledge of these electro-chemical equivalents,
how much of any other substance would be deposited by the same
current in the same time. This then was another of Faraday's
many wonderful achievements, and his Laws of Electrolysis are
one of the commonplaces of every text-book on electricity to-day.

Following on this he next turned his attention to electrostatic
induction. Coulomb had developed a law of inverse squares as
between electrical charges, and in view of the similarity of this
to Newton's inverse square law for gravitational forces, he had
assumed that the attraction or repulsion between two charges
was also, like gravity, a case of ' action at a distance ' ; that is
to say, the intervening medium played no part in this. Faraday
felt that this was wrong, and that, on the contrary, the medium
played a vital part in the propagation or transmission of this
force. He spoke of the medium as a ' dielectric '. Action at
a distance presupposes the mutual attraction to take place along
the straight line joining the two charges, but Faraday's investiga-
tions showed that, as a matter of fact, the lines of induction are
curved, and these he called ' lines of force '. But v/hat is equally
important, he showed that the actual value of the force between
two charges differed according to the medium intervening be-
tween them, and so he discovered the property which he termed
* the dielectric constant ' of the medium, and which we nov/ speak
of as the ' specific inductive capacity '. Henry Cavendish, it
will be recalled, had discovered this long before, but his eccen-
tricity and the retiring, hermit-like life he led had not made for
publicity, and so Faraday, like most other people, knew nothing
of his work.

Faraday used in his experiments two concentric spheres, and
he filled the space between them with various media in succession.
He compared the electrical attraction or repulsion through them
with the results he obtained for air. He published his results in
1837. Taking air as unity, he got 2-26 for sulphur, 2-0 for shellac,
and 17 for glass.

We pass on now to the year 1845 for Faraday's next great
discovery. With his delicate vision and somewhat vivid imagina-

Researches in Electricity and Magnetism 267

tion, he had for a long time been feeling his way to a unification
of the various phenomena of nature, and in that year he succeeded
in showing by a beautiful experiment a definite relationship
between electricity and light. On the 24th of November 1845
he submitted to the Royal Society a memoir entitled, ' On the
Magnetization of Light, and the Illumination of Magnetic Lines
of Force '. It was a vivid title, and no one quite knows what w^^^
in his mind at the time. However the definite experiment which
it recorded, and the lesson it taught, were clear enough at any
rate. ' I have long ', wrote he, ' held an opinion, almost amount-
ing to conviction, in common, I believe, with many other lovers
of natural knowledge, that the various forms under which the
forces of matter are made manifest have one common origin ;
in other words are so directly related and mutually dependent,
that they are convertible, as it were, to one another, and possess
equivalents of power in their action. . . . This strong persuasion
extended to the power of light.'

Faraday's experiment was on the effect of magnets upon
a particular condition of light known as polarized light. In the
ordinary way light waves may be regarded as the ' passing on '
of ether vibrations much the same as water waves are the passing
on of water vibrations, but in the case of light the plane of
vibration is not restricted, and consequently a ray of light may
consist of waves in every conceivable plane. Fig. 102 may serve
to show the meaning of this a little more clearly. If we look
' edgewise ' behind a single wave, we merely see a short straight
line showing the extremes between which the vibration takes
place. In the figure, we are looking ' end on ' along a ' bunch '
of five light waves (the language employed here is unfortunately
very loose from the scientific point of view, but it will serve), and
the planes of their vibrations are seen to be all different — wave (i)
is vertical, wave (4) is horizontal, and the others are variously
inclined, but all are moving forward into the plane of the paper.

Now there are certain transparent or partially transparent
substances which have a remarkable effect on such a bunch of
waves when their surfaces are exposed to light. When the bunch
of waves impinges on the surface, all are stopped except the waves

268 Michael Faraday

of one plane only, so that the Hght which emerges— of considerably
less intensity, of course, than that which enters the medium— is
such that there is one, and only one plane of vibration. It is
just as though the interposing medium were a set of railings,
shown dotted in the figure, parallel to the plane of vibration
of any ray (2) in the bunch. All the other rays will be stopped
by the obstacle, but ray (2) will pass on between the rails quite
easily. Such emergent light is spoken of as plane-polarized light,
and many substances will have the effect of polarizing the light

which passes through them,
tourmaline being a notable
example.

We are now in a position
to be able to appreciate the
nature of Faraday's experi-
ment. He employed as his
polarizing medium a piece of
heavy glass known as silico-
borate of lead. The light
which entered this glass was
unpolarized ; but that which
emerged from it was polar-
ized, and the direction of the
plane of polarization was
carefully noted by means of
a ' Nicol prism ' — a split piece of calcite which could be rotated,
and which accordingly acted just like rotating a second set of the
railings already mentioned ; that is to say, since the light was
already polarized by the glass, until the direction of ' the rails '
coincided with the plane of polarization, no light could penetrate
the Nicol prism at all, but at a certain point in the rotation,
the ' rails ' now coinciding with the plane of polarization, the
light bursts through the prism suddenly, and the angle at which
this occurs can be noted.

Having done this, Faraday now placed the arrangement
between the poles of a powerful magnet, so that the magnetic
lines of force were in the same direction as that in which the

Fig. 102. Unpolarized Light-waves,
showing various indinations of the
plane of vibration.

Researches in Electricity and Magnetism 269

light was travelling through the heavy glass medium. The
immediate effect was that where before the polarized light was
passing through the Nicol prism, it suddenly ceased to do so,
until the nicol was rotated to a different position, when the
light again burst through. This clearly proved that the effect
of the magnetic field was to rotate the plane of polarization of the
light, and as soon as the magnetic field was removed, the light
was restored to its original plane of polarization. Faraday
subsequently obtained similar results by substituting for the
magnet a coil of wire carrying the current, with the glass medium
at the centre.

So for the first time in history there was established a definite
connexion between light and electricity, and the problem of the
ultimate meaning of all forces was notably advanced. Tyndall
refers to it as the 'jewel in the casket', and adds, 'I should
liken (it) to the Weisshorn among mountains — high, beautiful,
and alone ' .

But Faraday's scientific record is not complete without refer-
ence to one further discovery, a consequence of the experiment
we have just described. He gave his discovery in a paper before
the Royal Society on the i8th of December 1845, entitled ' On
the Magnetic Condition of All Matter ' . He had long been struck
with, as he thought it, the incongruity of the existence of only
two magnetic substances, iron and nickel. He began to suspect
that other substances ought to exhibit magnetic phenomena under
suitable conditions. So he set to work testing various substances,
and before long he was able to add cobalt to iron and nickel.
But on the 4th of November 1845 he suspended from a silk thread
a bar of heavy glass, and this he placed between the poles of
a powerful electro-magnet. Now if the bar had been of iron, we
know that on account of its permeability to magnetism it would
have set itself parallel to the lines of force, that is to say, in the
direction of the line joining the north and the south poles of the
magnet. Imagine Faraday's surprise, therefore, when he found
that his rod of glass set itself at right angles to the magnetic
lines of force joining north and south poles and therefore indicat-
ing a magnetic repulsion instead of a magnetic attraction, ihis

270 Michael Faraday

phenomenon Faraday called diamagnetism, and the reason why-
he had not discovered it before was because his magnets had not
been sufficiently powerful. He extended his observations and
satisfied himself that all substances are either para-magnetic or
dia-magnetic, and that examples of the latter group are sulphur,
india-rubber, asbestos, and human tissue. Referring to this
last substance he says : * If a man could be in the magnetic
field, like Mohammed's coffin, he would turn until across the
magnetic line.'

' 6. Faraday's Later Life

So much for the scientist. Meanwhile what of the man ?
Wonderful as a thinker, his private life was simplicity itself. He
had no children of his own, but for ten years from 1830 to 1840
his niece. Miss Jane Barnard, came to live with Faraday and his
wife, and from her we get the following interesting story of the
philosopher's daily routine :

' We often found him hard at work on experiments connected
with his researches, his apron full of holes. If very busy he would
merely give a nod, and aunt would sit down quietly at a distance,
till presently he would make a note on his slate and turn round
to us for a talk ; or perhaps he would agree to come upstairs to
finish the evening with a game at bagatelle, stipulating for
half-an-hour's quiet work first to finish his experiment. He was
fond of all ingenious games, and he always excelled in them. For
a time he took up the Chinese puzzle. . . . Another time, when he
had been unwell, he amused himself with papyroplastics, and
with his dexterous fingers made a chest of drawers and pigeon-
house, &c. When dull and dispirited, as sometimes he was to
an extreme degree, my aunt used to carry him off to Brighton,
or somewhere, for a few days, and they generally came back
refreshed and invigorated. Once they had very wet weather
in some out-of-the-way place, and there was a want of amusement,
so he ruled a sheet of paper, and made a neat draught board,
on which they played games with pink and white lozenges for
draughts. . . .

' Often of an evening they would go to the Zoological Gardens
and find interest in the animals, especially the new arrivals,
though he was always much diverted by the tricks of the monkeys.
We have seen him laugh till the tears ran down his cheeks as he

Later Life 271

watched them. He never missed seeing the wonderful sights of
the acrobats and tumblers, giants and dwarfs; even Punch and
Judy was an unfailing source of delight.' ^

Faraday was at all times neat and punctual in his habits. In
his laboratory everything not only had its place, but had to
be in that place. He breakfasted at eight, spent his mornings in
the laboratory, dined at half-past two, and retired to his study
in the afternoons to write his papers and to prepare for his next
day's work. Like his predecessor. Sir Humphry Davy, he was
a most successful and fascinating lecturer, and his discourses
were always delivered to a crowded and a delighted audience.
He himself always enjoyed lecturing, particularly when he was
addressing a juvenile audience, for he always loved children.

The strain of his work began to tell very seriously on his health,
and between the years 1838 and 1841 he repeatedly broke down,
but the loving care of his devoted wife saved him, though for
a period of two years he had to abandon completely even the
reading of science. In 1841 his wife took him to Switzerland,
and they were accompanied by her brother, George Barnard,
an artist. During this period he was in a very low condition,
and even conversation was painful to him, but he rallied, and
returned to England fit and well in 1843.

Meanwhile learned societies all the world over were electing
him to their fellowships, the Royal Society awarded him every
medal it was in its power to confer, including the Copley Medal
twice over, the universities showered honorary degrees on him,
and foreign monarchs conferred various orders. In 1844 France
awarded him the 'blue riband' of international science by
electing him one of the eight foreign Associates of the Academy
of Sciences. Yet he sought not a single honour. In fact, when
the Presidency of the Royal Society fell vacant, and the council
of the Society unanimously invited him to succeed to this, the
highest scientific position in England, Faraday refused. ' Tyn-
dall,' said he to his old friend and pupil, ' I must remain plain
Michael Faraday to the last.'

* B. Jones, Life and Letters, vol. ii, p. 114.

272 Michael Faraday

An incident which occurred in 1835 is well worthy of note. It
will be recalled that Faraday, owing to his renunciation of
pecuniary benefits which his work could earn for him, was a poor
man. Sir Robert Peel, then in power, wished to confer on the
great philosopher a state pension of £300 per annum as a mark
of the gratitude of the nation for his work. Faraday's first
impulse was to decline this, but his friends persuaded him other-
wise, pointing out to him that the pension was not a charity,
but a reward, and in the nature of a compliment to science.

Before, however, the matter could be settled further Peel left
office, and was succeeded by Lord Melbourne, who, taking the
subject up as a matter of form (his scientific outlook was very
different from that of his predecessor), sent for Faraday. The
interview was a very unfortunate one. Melbourne ' in utter
ignorance of the man ' , used such tenns as ' humbug ' , and
P araday, deeply hurt, left him and wrote declining to have any-
thing to do with the proposal, stating that he had manifestly
mistaken his Lordship's intention of honouring science in his
person. The good-humoured nobleman at first considered the
matter a capital joke ; but he was afterwards led to look at it
more seriously. An excellent lady, who was a friend to both
Faraday and the Minister, tried to arrange matters between
them ; but she found Faraday very difficult to move from the
position he had assumed. After many fruitless efforts, she at
length begged him to state what he would require of Lord
]\Ielbourne to induce him to change his mind. He replied,
' " I should require from his lordship what I have no right or
reason to expect that he would grant — a written apology for
the words he permitted himself to use to me." The required
apology came, frank and full, creditable alike to the prime
minister and the philosopher,' ^ and so eventually Faraday
accepted the proffered pension.

White-haired, grey-eyed, kindly of face, and gentle of manner,

Faraday was nevertheless by nature very excitable. Says

Tyndall, ' Underneath his sweetness and gentleness was the heat

of a volcano. He was a man of excitable and fiery nature ;

^ Tyndall's Faraday as a Discoverer, p. 199.

Later Life 273

but through high self-discipHne he had converted the fire into
a central glow and motive power of life, instead of permitting
it to waste itself in useless passion/ ^

The last years of this great philosopher were years of peace.
In 1862 he began to feel his declining powers somewhat keenly,
and he told his audience at the Royal Institution that he had
been before them too long. He was over seventy years old, and
both his brain and body were tired ; so he gave himself over to
the loving care of his wife and niece, and they, with the willing
assistance of a host of affectionate friends, made his last years
a period of tranquillity and patient resignation for the end.

Towards the close of the year 1865 he had an attack of illness
from which he never recovered, and slowly an advancing though
painless paralysis gained on him. Much of his time was passed
in sleep, but his waking hours were always peaceful. He rarely
saw any one, though inquiries were legion. ' Tyndall,' he had
once said, ' the sweetest reward of my work is the sympathy
and goodwill which it has caused to flow in upon me from all
quarters of the world.' So it had been during the period of his
scientific activity, and so it continued when he lay dying. The
end came on the 25th of August 1867. ' Slowly and peacefully
he sank towards his final rest, and when it came, his death was
a falling asleep. In the fullness of his honours and of his age he
quitted us ; the good fight was fought, the work of duty — shall
I not say of glory — done.' ^

^ Ihid., p. 45. 2 Ibid., p. 203.

2613

APPLIED

XV
LORD KELVIN AND

SCIENCE

I. Early Record

The scientific pre-eminence of Lord Kelvin in the latter half
of the nineteenth century is beyond dispute. The number and

importance of his contribu-
lions to original research and
discovery are truly remark-
able. Yet on most of these
we must needs be silent. For
Kelvin was a brilliant mathe-
matician, and the abstruse
nature of most of his re-
searches, bound up as they
are with the arguments de-
rived from higher mathema-
tics, places them far beyond
the reach of most people,
-^uch readers must therefore
ontent themselves with an
aspect of Kelvin's career
vvhich, even though it repre-
sents but a portion of his
eminent services to mankind,
nevertheless suffices to mark
applied

physicist ' — that is to say, as one who taught and practised with
consistency that the best performance of the everyday occupa-
tions of mankind are those to which the principles of science are
rigidly applied. It was Kelvin's great influence which assured to
the world for all time that the best type of engineer, for example,
is at the same time a true man of science.

William Thomson was born at Belfast on the 20th of June
1824. He was the second son of James Thomson, Professor of

Tig . 1 03 . WILLIAM THOMSON, after-
wards Lord Kelvin, 30 April 1856

out a unique position for him : we refer to his work as an

Early Record 275

IMathematics at the Royal Academical Institute at Belfast, who
had risen to this position from relatively humble beginnings by
sheer hard work and determination. William's mother was
a Miss Gardiner, the daughter of a Glasgow merchant, so taking
into account the fact that the Thomsons were original emigrants
from Scotland escaping religious persecution in the days of the
Covenant, it is not surprising that, with all the natural pride of
Irish birth which both William and his father possessed, there
was much of the Scotsman in them, and as such they are proudly
regarded by all men bom north of the Tweed.

Certainly, the proverbial seriousness of outlook and hardiness
of development typical of the average Scots family was present
in the Thomsons. There were four sons and three daughters, and
unfortunately, whilst all were still young, Mrs. Thomson died,
and the professor accordingly had the main responsibility for
their upbringing. He threw himself into the task, and combined
keen affection with stem discipline with such success that all his
sons eventually achieved distinction in their respective spheres
of activity.

In 1832, when William was but eight years old, his father was
offered the post of Professor of Mathematics at Glagsow Univer-
sity, and so the whole family migrated to Scotland. Thus began
an association with Glasgow which lasted, in one form and another,
until William's death in 1907. It is amusing to note that at his
new post Professor James found himself one of many professors
of the name of Thomson. There was Thomas Thomson the
chemist ; William Thomson of Materia Medica ; Allen Thomson
of Anatomy . . . Dr. James Thomson of Mathematics, &c., and
the university was not infrequently referred to as the ' Thomsonian
University ' .

Life during this period was for William and his elder brother
James a stern round of hard study varied by long family holidays
during the vacations. Both showed early signs of unusual
ability, and, remarkable to relate, when William was but ten
years old they passed their matriculation examination at the
Glasgow University. Further, the two brothers more than held
their own amongst their fellow students, it being quite usual for

s 2

276 Lord Kelvin

William to come out top and James a close second. Nor must it
be thought that the course of study was in any sense easy.
Lagrange's Theory of Functions in mathematics, Newton's
Principia, and Laplace's Mecaniqiie celeste in natural philosophy,
and commensurate studies in logic, Latin, Greek, moral philo-
sophy, and chemistry were all included in the course. In all of
these both brothers did well in spite of the competition of such
men as John Caird, afterwards to become the Principal of the
University.

In the summer of 1840 the professor took his two sons for
a holiday tour in Germany. He wanted the boys to study the
German language, but William had come into the possession of
a copy of Fourier's famous Theorie analytique de la Chaleur, that
same book which had so inspired Simon Ohm in his electrical
researches in 1826 (see p. 236). The originality of the mathe-
matical methods employed in this book greatly fascinated William,
and he spent far more time on the book than he did on the study
of German, and indeed his first paper, a defence of Fourier
against the criticisms of a Professor Kelland on some of the
conclusions of the book, was actually begun at Frankfort in
July 1840, and was completed in Glasgow in the following year.
The reading of Fourier's book was a distinct event in William
Thomson's life, for the whole of his later career shows very
definitely how his work was constantly influenced by Fourier's
methods.

In October 1841 Thomson was admitted a student at St. Peter's
College, Cambridge. His father realized fully that, however
useful the course at Glasgow might be, the best road to an
academic career was via the Cambridge Mathematical Tripos.
The person who came out top in the Tripos lists was known as
the Senior Wrangler (the lists are only published alphabetically
nowadays), and it was not long before Thomson's name became
freely mentioned as both the prospective Senior Wrangler and
as the coming Smith's Prizeman — another of the highest of the
mathematical honours of the university. There seemed just
grounds for this belief. He worked under WilUam Hopkins,
most renowned of tutors : he contributed a series of able and

Early Record 277

original papers to the Cambridge Mathematical Journal ; and
he obviously outshone the majority of his fellow students. By
way of diversion from work, he kept himself physically fit by
walking, rowing, and swimming ; and mentally fresh by the
devotion of occasional hours to music, for he was, indeed, an
active member and later President of the University Musical
Society.

There is no doubt that as the date of the Tripos Examinations
drew near, William Thomson became a little anxious. He knew
how very keen was his father on his success, and he was most
anxious not to disappoint him. Professor Thomson was ambitious
for his son. There was to be a vacancy shortly at the University
of Glasgow in the professorship of natural philosophy, and
James Thomson felt that if William could but do well enough
at Cambridge, his chance of obtaining the appointment at Glas-
gow was probably very good. On the other hand, the peculiar
requirements of the examiners involved William in much irk-
some drudgery of a kind that would be of little use to him in
after life, and his studies were somewhat distasteful to him on
this account.

In due course the examination results were published, and it
was seen that William Thomson came second. He was beaten
by Parkinson of St. John's. Shortly after, these two were again
rivals for the Smith's Prize, and this time it was Thomson who
was first, and Parkinson second. As to the actual merits of our
Smith's Prizeman and Second Wrangler, it must surely suffice
to note the comment which one of the examiners is reported to
have made to the other, ' You and I are just about fit to mend
his pen.'

Following on these examinations in the early part of 1845,
Thomson went to London and met Faraday, and subsequently
passed on to Paris to study physics under the famous Regnault,
then at work on his wonderful series of experiments for the
determination of the various constants in the theory of heat.

In May 1846 the aged Dr. Meikleham, Professor of Natural
Philosophy at Glasgow University, died. The Faculty met on
the nth of September and, ' having deUberated on the respective

278 Lord Kelvin

qualifications of the various candidates, unanimously appointed
Mr. William Thomson, B.A., Fellow of St. Peter's College,
Cambridge', to the vacant professorship. He was twenty- two
years of age, and from now onwards began a professional career
which lasted for over sixty years, and which brought him world-
homage.

2. Early Researches in Electricity

Professor William Thomson's inaugural lecture was delivered
in November 1846. It was ' a carefully prepared introductory
lecture on the scope and methods of physical science '. The
delivery suffered somewhat from the lecturer's nervousness : but
he soon got over this. There was never, however, much of the
natural teacher about him. He was too deeply steeped in prob-
lems of research. Many of his students were Arts students for
whom attendance at the natural philosophy class was com-
pulsory, and on these much of what Thomson had to say was
lost. Nevertheless it was both fascinating and inspiring to all
to watch him digress as he frequently did, to develop an idea
which his remarks might suddenly bring to his mind, and he
would then completely forget his class, and fill the board time
after time with what was in fact a real exhibition of ' research
in the making '. A somewhat extreme example of the abstruse
nature of his lectures is that of a student who once remarked,
* Well, I listened to the lectures on the pendulum for a month,
and all I know about the pendulum yet is that it wags'. Yet
from the outset Thomson was the practical physicist seeking for
a clear physical meaning, where the stereotyped text-book gave
only a mathematical statement. Thus Dr. A. Russell, the
Principal of Faraday House, tells us that when he was asked by

dx
Professor Thomson the meaning of the symbol — , he said

dt

' with much complacency, that it was the limiting value of the

ratio of the increment of x to the increment of t when the latter

increment was indefinitely diminished '. This was of course,

the stock mathematical meaning, but it did not satisfy Thomson.

Early Researches in Electricity 279

' That 's what Todhunter ^ would say/ said he. ' Does nobody
know that it represents a velocity ? '

The session of a Scottish University of those days lasted only
six months, and this left Thomson much leisure for research.
His earlier activities were in the direction of statical electricity.
Coulomb's well-known laws of electrostatic attraction had been
challenged by W. Snow Harris, an experimentalist of high
repute, and Thomson boldly attacked Harris in defence of
Coulomb. The outcome of this controversy was that Thomson
successfully developed a new method for the investigation of this
class of problem, known as the 'method of electrical images '.
We do not propose to go into this method and into his many
ingenious applications of it, but it will suffice here to point out
that as a consequence Thomson was able triumphantly to
vindicate Coulomb's theory. Another of Thomson's achieve-
ments was the ' absolute ' determination, by mechanical methods
which have now become mere commonplaces of a laboratory
course, of the volt and ampere. These are respectively the
practical units of potential difference (i. e. of electromotive force)
and of electrical current. We are all familiar with the gold leaf
electroscope. There is a difference of potential and therefore
a force of attraction between the leaves and the inner walls of
the electroscope and as a consequence the gold leaves fly apart.
Between any two plates or surfaces, in fact, which are at different
electrical potentials will there be a natural force of attraction,
and Thomson first worked out the value of this attraction in
terms of the size of the two surfaces, and of their distances apart.
If for any given set of conditions there corresponds a definite
force of attraction to a given difference of potential, then by
measuring this force the corresponding difference of potential,
or voltage, is at once found.

The devising of the necessary experimental details was but
a step from this, and Thomson developed two forms — the
' attracted disk ' form and the ' quadrant electrometer '. In the
former there are two parallel plates. The lower one is charged

1 Todhunter was the universally-read author of the mathematical
text-books of those days.

28o

Lord Kelvin

up to a voltage which it is required to measure, and it attracts
the upper Ught disk (connected to the earth to bring its potential
to zero, since we regard the earth's potential as zero) with a force
which is directly measured by springs or counter-weights such
that they just counteract the electrical force between the plates.
In the quadrant electrometer the attraction between the plates
of different potentials is made to produce rotation the extent of
which is proportional to the potential difference. This is
arranged for by having two fiat boxes, A and B, shaped as

the two opposite quadrants of a
circle (Fig. 104). In place of the
remaining quadrants C and D,
there is a figure-of-eight-shaped
plate of thin aluminium, sus-
pended horizontally from a gradu-
ated head by means of a torsion
fibre in such a way that on setting
up a potential difference between
the plate and boxes, the oblique
attraction swings D into B and C
into A. The angle of swing is
measured by the graduated head,
and from it the necessary poten-
tial difference can be calculated.
The great advantage of this lies
in the fact that the value of the volt as so obtained depends only
upon a measured mechanical force and upon the linear dimensions
of the apparatus. That is to say, it makes the volt independent
of any other electrical quantities, and so gives us what is known
as an absolute determination of the volt. This is invaluable, and
Thomson extended the idea further in finding in a similar manner
an absolute determination of the unit of current — the ampere.
This he accomplished by using the fact that between two coils
of wire carrying a current there is a mechanical attraction or
repulsion. He arranged for the same current to flow through
each coil, and literally weighed the attraction between them.
Finally, to obtain the standard ohm, it was only necessary

Fig. 104. The principle of the
Quadrant Electrometer.

Early Researches in Electricity 281

for Thomson to apply to his absolute measurements of the volt
and the ampere the consequences of Ohm's Law. He so adjusted
a coil of wire as to carry a current of one ampere with a difference
of potential between its ends of one volt. Then it followed from
Ohm's Law that the resistance of this coil was one ohm.

One other important piece of work amongst Thomson's
earlier researches in electricity must not be omitted from our
record, since it shows him to have been an unconscious pioneer
of that most dramatic of all discoveries of twentieth-century
science — viz., wireless telegraphy.
In 1847, Hermann von Helmholtz,
a brilliant physicist, had drawn
attention to some puzzling observa-
tions by Riess in connexion with
the discharge of a Leyden j ar. Riess
had wound a wire round a knitting-
needle, and he arranged for the cur-
rent of discharge of a Leyden jar to
pass round this wire. He expected
of course to find his needle mag-
netized as a result, but what he
did not expect to find, yet what
nevertheless proved to be the case,
was that through a course of experi-
ments sometimes one end of the
needle became the north-seeking

pole, and sometimes it was the other end which was so left.
This was very puzzling, as was also a corresponding observation
by Wollaston, who on using the current of discharge from a Leyden
jar to decompose the water by electrolysis found that instead
of getting his oxygen at one electrode and his hydrogen at the
other he obtained instead a mixture of both gases at each
electrode.

Helmholtz, with characteristic brilliance of vision, suggested
that these observations could be explained by the assumption
that the Leyden jar discharge was oscillatory in character, and
in 1853 Thomson took up this point in a paper ' On the Oscil-

FiG. 105. HERMANN von
HELMHOLTZ

282 Lord Kelvin

latory Discharge of a Leyden Jar ' which he communicated to
the Glasgow Philosophical Society, in the course of which he
not only proved mathematically that this was so, but he also
developed a formula for determining the rapidity with which the
oscillations were taking place.

The discharge of a Leyden jar may be likened in some respects
to the ' letting go ' of a pendulum ball which has been pulled
to one side. As the ball swings down to its lowest position it
gains in kinetic energy at the expense of the store of potential
energy which had been supplied to it by the hand which drew
it to one side, and this kinetic energy gives to the ball a speed
which carries it past its lowest position, and the ball sweeps
upwards on the other (and shall we say the negative) side, once
more losing its kinetic energy and regaining its potential energy.
The ball now repeats its oscillatory journey, this time from the
negative side to the positive, again surging past its lowest
position ; but gradually the resistance of the air reduces the
swing, till the ball eventually comes to rest at its lowest position ;
and the denser the medium in which the ball is swinging, the
quicker does it come to rest, and indeed if the medium were
sufficiently viscous, the ball would probably never get past the
lowest position on its first journey downward. Similarly, in
a sense, with a Leyden jar, which, it will be remembered, consists
essentially of a glass jar coated inside and outside with layers
of tinfoil. To charge up, we connect the inner coating to the
positive terminal and the outer coating to the negative terminal
of an electrical machine, and so induce on each charges which
are equal but opposite in sign. To discharge we bring a wire
from the inner coating up to a wire from the outer coating, and
so great is the potential difference between the two that the
discharge begins before the wires touch, a spark leaping across
the intervening air-gap with a loud noise or snap. The whole
thing appears to be instantaneous, but in fact it is not so, but
takes a minute fraction of time. Not only so, but as with the
pendulum, the current of one sign surges from, say, the inside
of the jar to the wires and so on to the outside of the jar, thus
momentarily re-charging the jar in the opposite way, and then

Early Researches in Electricity 283

the charge surges back again along the wire, and then forward
again, each time with diminished energy owing to the resistance
of the wire and the heating at the tips, until it dies away, leaving
insufficient energy ultimately to carry the current across the
air-gap. In the best of cases this all takes but a fraction of
a second, but frequently the resistance and the heat generated
suffice even to prevent
a single complete os-
cillation.

We owe the knowledge
of all this to William
Thomson, and the ulti-
mate results were beyond
even his wildest dreams.
For working on this far-
ther. Clerk Maxwell,
another brilliant con-
temporary of Thomson,
showed in an epoch-
making piece of research
that if these oscillations
are sufficiently rapid,
much of the energy
stored in the Ley den jar

can be radiated out into space in the form of electro-magnetic
waves : and Hertz, following on this, not only produced such
waves, but devised a means of detecting or receiving them, and
so wireless telegraphy became a scientific possibility : and, in
the hands of such men as Sir Oliver Lodge, Signor Marconi,
and Professor Fleming, has now become one of the normal
adjuncts of civilization.

Fig. 106. JAMES CLERK MAXWELL

284

3- Researches in Heat

We turn now to another important subject upon which the
future Lord Kelvin turned the Hght of his genius — the subject
of the dynamical theory of heat, or thermodynamics.

We have mentioned at some length the researches of Count
Rumford and Sir Humphry Davy in showing the relation between
heat and mechanical work, and it will be recalled that these
men attacked the caloric theory of heat, which had hitherto
been universally accepted and remained in possession of the
field right through the first half of the eighteenth century.

In 1824, impetus was given to the study of thermodynamics
by the publication, by Nicolas Leonard Sadi-Carnot, of a work
called Reflexions sur la puissance motrice du feu. In this work
Carnot tried to determine mathematically how much mechanical
work could be performed by a steam engine, and from this he
went to the more purely theoretical consideration of the amount
of work which could be performed by an ideal heat-engine.
Carnot introduced the idea of a complete cycle of operations
and of the principle of reversibility. Starting with a source of
heat maintained at a high temperature (i. e. a boiler), he takes
heat from this source and utilizes it by converting part of it into
mechanical work, restoring the remainder of it to a condenser
kept at a low temperature. Then (arguing theoretically of
course), taking the reverse cycle, by performing on the engine
an equal amount of work to that previously performed by the
engine, he is able to extract the heat again from the condenser,
and restore it to the original boiler or source. In effect, Carnot
realized that not only was it possible to convert mechanical
work into heat but also that the reverse was possible, namely,
to convert heat into mechanical work ; and also that to a given
amount of mechanical work there corresponds a definite amount
of heat. He did not, however, actually measure the amount of
this ' mechanical equivalent of heat ', as it is now called, and for
many years the extreme importance of Carnot's work was not
recognized, until William Thomson drew the attention of the
scientific world to it in a paper which he published in 1849,

Researches in Heat 285

entitled * An account of Camot's Theory of the Motive Power
of Heat, and Numerical Results from Regnault's Experiments
on Steam '.

IMeanwhile various workers were attempting to establish the
doctrine of the conservation of energy, namely, that the total
energy in the universe is constant, and that when energy dis-
appears in one form, e. g.
heat, it must reappear in
another form, e. g. mechani-
cal energy. No such specu-
lations could have any final
value until the actual
mechanical equivalent of
heat had been determined,
and for this we are indebted
to James Prescott Joule, a
young Manchester brewer
and scientific amateur. This
remarkable young man had
spent years in studying
the relations between the
various forms of energy, his
researches culminating in
that famous experiment in
which he converted the
mechanical energy of a fall-
ing weight into the heat
produced by the rotation
of a baffle-plate in a vessel of water, giving him a result of 778
foot-pounds of work as the mechanical equivalent of the pound-
degree Fahrenheit.

Yet no one would listen to Joule. In April 1847 he gave
a popular lecture on the subject in Manchester. Most of the
newspapers ignored it, the Manchester Guardian being a notable
exception ; as in the case of Carnot, it again remained for
William Thomson to force recognition for Joule from a reluctant
world of science. Joule was due to read a paper on the subject

Fig. 107. J. P. JOULE

286 Lord Kelvin

of his experiments before the British Association at Oxford
in June 1847, ^^t the Chairman, to whom the paper seemed
unimportant, asked him to be brief. ' I can never forget ', said
Thomson, when as Lord Kelvin he was unveiling a statue of
Joule in Manchester in 1893, ' the British Association at Oxford
in 1847, when ... I heard a paper read by a very unassuming
young man, wlio betrayed no consciousness in his manner that
he had a great idea to unfold. I was tremendously struck with
the paper. . . .' As to what happened on the conclusion of his
reading, we may turn to Joule's own account. ' Discussion not
being invited, the communication would have passed without
comment if a young man had not risen in the section, and by
his intelligent observations created a lively interest in the new
theory. The young man was William Thomson.'

In the light of the researches of both Carnot and Joule, William
Thomson was now able to make an important contribution to
the subject of thermometry. No thermometer can be perfectly
reliable as an absolute measurer of temperature which is depen-
dent upon the behaviour of a substance. For example, no two
specimens of glass expand in precisely the same way. So in the
case of mercury-in-glass thermometers, which depend for their
reading upon the physical property of the expansion of both
glass and mercury, the probability is that there are as many
scales as there are thermometers, since there can be no absolute
uniformity ; similarly with gas thermometers, in which tem-
perature changes follow the physical properties of pressure and
volume changes ; so also with electrical thermometers, which
depend upon the physical property of the variation of electrical
resistance with temperature. In fact, no thermometer can be
absolutely reliable unless it is totally independent of the physical
properties of any substance whatever, and Thomson saw in
Carnot's cycle of operations with the ideal engine a means of
obtaining a scale of temperatures which would be independent
of all physical properties.

We have seen that a steam engine may be regarded as a heat
engine which takes in heat at boiler temperature and converts
sotne of this heat into work by utilizing the expansion of the

Researches in Heat 287

steam in the cylinder to move a piston to and fro. The
diminished heat of the cooled steana is now passed to the con-
denser and is changed into liquid form. Consequently the
heat which has been converted into work is the difference
between the heat taken from the boiler and the heat returned
to the condenser.

It is not necessary for us to regard steam as the onty substance
for such a cycle of operations. Carnot taught that theoretically,
in the ideal engine, any substance may be made to do mechanical
work by expansion so long as we regard it as passing between
a source of heat (like the boiler) and a receiver (like the con-
denser). Now Thomson pointed out that the amount of work
which can be done by such an engine depends upon two things —
firstly upon the difference of temperatures between source and
receiver (that is to say, if the boiler temperature is 150 degrees
higher than the condenser temperature, more mechanical work
could be done than if the difference were only 100 degrees),
and secondly, upon the absolute values of these temperatures.
Thus the mechanical work which would be done between the
temperatures of 200° C. and 100° C. is not the same as
would be done between 150° C. and 50° C, or between 100° C.
and 0° C.

So far as the first of these conditions is concerned we may
say that if a quantity of heat Q^ be put in at the higher tempera-
ture Tj, and if a quantity of heat Q^ be put out at the lower
temperature Tg then the ratio of these temperatures is fixed by
the relation

Keeping the boiler heat fixed, that is to say, keeping T^ and
(2i constant, suppose we utilize the whole of this heat Q^, and
convert it all into mechanical work. Then Q<y becomes nil,
and therefore Tg becomes nil too. This fixes in fact a zero of
temperature on this new scale of temperature measurement,
namely, that condenser temperature at which all the heat from
the boiler is converted into work. It is impossible to conceive of
a greater degree of cold than this, and so Thomson spoke of it as

288 Lord Kelvin

the absolute zero of temperature, and he denoted it by o° Absolute,
or 0° A.

As to the value of this absolute zero on the ordinary thermo-
meter scales of daily use, we must turn to the second of the
conditions above referred to. Here Thomson showed that,
working between boiler temperature of ioo° C. (the temperature
of boiling water) and condenser temperature of o^ C. (i. e. of
freezing water), for every 373 parts of heat put in at 100° C, the
engine will return 273 parts into the receiver, converting 100 parts

into mechanical work. This means that ^^ = ^^ and therefore

Q2 273
the ratio of temperatures on the absolute scale will also be

yA = — To make an easy comparison with the Centigrade

scale, Thomson next decided that the length of the degree on
his new scale would be arranged so that there should be 100 of
them between the melting-point of ice and the boiling-point of
water. He had in fact to determine T^, and T^, such that

T, — T„^ 100, and -^ = ^^^-^ , and a simple calculation shows
T. 273 ^

that this gives 273° A. as corresponding to 0° C, and 373° A. as
corresponding to 100° C, and 0° A. as corresponding to —273° C.
Thus his scale was complete, and it is now universally known as
Thomson's absolute thermodynamic scale. It is solely concerned
with the work done by the thermometric substance employed,
and it is totally independent of all its physical properties ; and
so it is without exception the most satisfactory scale of tem-
perature known. In addition it is very simply related to all the
other temperature scales in daily use.

4. Ocean Telegraphy

Let us now consider one of the many examples of Thomson's
service to mankind in the role of applied physicist and consulting
engineer — the laying of the Atlantic cable. We have already
seen how the researches of Oersted, Ampere, Arago, and others
had paved the way to the invention of the electric telegraph by

Ocean Telegraphy 289

Cooke, Wheatstone, and Morse, and by the end of 1S40 com-
mercial telegraphic undertakings were in operation in both
England and America. By 1850, improvements had been so
generally perfected that telegraphy by land was possible over
hundreds of miles, and the problem of submarine telegraphy
emerged from the realms of discussion into the reality of a Dover
to Calais line success- _

fully laid by Cramp -
ton, and followed
soon after by other
short lines connecting
England with Ireland,
and with Holland.

The natural ambi-
tion of all telegraph
engineers was, how-
ever, the establishing
of telegraphic com-
munication between
England and America.
Why was this re-
garded as such a for-
midable undertaking ?
When, in August of
1850, the Dover to
Calais line was first
laid, the cable used
was a copper wire
surrounded by gutta-
percha insulation, and it was at once noticed that the signals
received were ' extraordinarily sluggish ' as compared with the
clear signals usual to overland telegraphy. Two hours later
the hue was severed by the anchor of a fishing-smack. So
far as the latter of these troubles was concerned the remedy
was obviously the strengthening of the cable, but so far as the
question of sluggish signalling was concerned the remedy was
not so immediately obvious.

2613 T

Fig. 108, Five-needled instrument patented by-
Messrs. Cooke and Wheatstone in 1837.

290 Lord Kelvin

PYom a general discussion, however, the fact soon emerged
that such a cable was really in effect an elongated Leyden jar
of great capacity, the copper acting as the inner lining, the salt
water as the outer lining, and the gutta-percha as the ' glass '
of the jar ; and when a battery is connected up to one end of
the core, the 'Leyden jar' gradually gets charged up, first at
the battery end, and gradually farther and farther along the
wire, and so to the other end ; and similarly when the battery
is withdrawn (or the circuit broken), the discharge is equally
gradual.

In May 1855, William Thomson took up the discussion in
a paper communicated to the Royal Society, entitled ' On the

Fig. 109. Sections of the second and third Atlantic Cables.

Theory of the Electric Telegraph ' , in the course of which he
established a most important law governing the retardation of
the electrical impulse along a cable. He showed the retardation
to be proportional to (a) the ' capacity ' and (b) the ' resistance *
of the cable. Now each of these quantities is proportional to
the length, and so it follows that the time retardation of a signal
is proportional to the square of the length. Thus ' if a cable
200 miles long showed a retardation of i-gth second, one 2,000
miles of similar thickness would have a retardation 100 times
as great, or 10 seconds ' .^ The enormous difficulty of a trans-
Atlantic cable is therefore very evident, and it now remained
for Thomson to show how this could be overcome.

Essentially he recommended two things — the employment of
a copper cable of as low a resistance (and therefore of as high
^ S. P. Thompson's Life of Lord Kelvin, vol. i, p. 329.

Ocean Telegraphy 291

a conductivity) as possible, and the use of as thick a cross-section
as possible.

Considerable opposition was offered to Thomson's theory,
but ultimately his view prevailed, and in 1858 the newly-formed
Atlantic Telegraph Company, of which William Thomson was
a director, successfully laid its first cable. The signals from
such a long cable were, however, so weak that ordinary methods
of receiving messages were of no avail, and so Thomson invented
the famous mirror galvanometer, now regarded as part of the
normal equipment of all scientific laboratories. In this the
magnet at the centre of the coil of the ordinary galvanometer
is attached to a vertically suspended small spherical mirror
which of course swings with the magnet whenever a current
passes round the coil. A spot of light from a lamp is reflected
from this mirror on to a distant scale, and provided the scale is
sufficiently far away, a very small movement on the part of the
magnet and mirror will cause a big swing of the spot along the
scale and so the mirror galvanometer is very sensitive to small
current changes. By this means the feeble currents received
at the receiver of the cable were successfully recorded. Alas,
after a few weeks' precarious work, the messages ceased, and
the cable would not work. Nevertheless, inasmuch as during
these few weeks no less than 732 messages, some of them of
first-class importance, had been sent through, the project could
not altogether be regarded as a failure.

It was decided to try again, and Thomson busied himself
with the plans for the new venture forthwith. A cable ship, the
Great Eastern, was designed to take the whole length of cable
required, and to have the necessary freedom of manoeuvring
which the difficulties of laying required, and in 1866, after two
attempts, not only was the Hne successfully laid, but the original
line was once more rendered serviceable. As electrical engineer
to the expedition, William Thomson was knighted, and on his
return was presented with the freedom of the city of Glasgow.

Shortly after he replaced his mirror galvanometer by his still
more sensitive siphon recorder, in which a ' small and delicate
pen was formed by a piece of very fine glass tube in the form of

T 2

Ocean Telegraphy

293

a siphon, of which the shorter end dipped in an ink bottle, while
the other end wrote the message in little zig-zag notches on
a ribbon of paper drawn past it by machinery. The siphon was
moved to and fro by the signalling currents which flowed in
a small coil hung between the poles of an electromagnet, excited
by a local battery, and the ink was spurted in a succession of
fine drops from the pen to the paper. This was accomplished by
electrifying the ink-bottle and
ink by a local electrical machine,
and keeping the paper in con-
tact with an uninsulated metal
roller. Electric attraction be-
tween the electrified ink and the
unelectrified paper thus drew
out the ink drops, and the pen,
which never touched paper, was
quite unretarded by friction ' .^
The siphon recorder is in use to
this day.

It was probably his activities
in this direction that caused
Thomson to turn his attention Fig. m. Lord Kelvin's Early
to the many other applications Siphori-recorder.

of science to the problems of engineering. He definitely took
up the commercial side by entering into partnership with Mr.
C. F. Varley and Professor Fleeming Jenkin, and the firm of
Thomson, Varley and Jenkin took up all phases of telegraphic
engineering with great success, and to them are due most of the
up-to-date inventions which have made submarine telegraphy
the pronounced success which it is to-day.

^ Gray's Lord Kelvin, p. 270.

294

5- Research in Navigation

Thomson's years of research on ocean cables brought him
naturally into intimate contact with some of the urgent problems
awaiting solution in the science of navigation. It is therefore
a matter for Uttle surprise that here, too, he achieved wonders.

There was, for example, his invention of the sounding-machine.
One of the first requisites in the organization of the laying of
the Atlantic cable was a proper charting of the ocean bed, and
the method which he found in vogue was somewhat primitive
and very laborious. A sinker was lowered attached to an inch-
and-a-half-thick rope. This required many hands and in deep
water the ship had to be stopped for the operation. As a first
measure, Thomson suggested the use of pianoforte wires as being of
great tensile strength, but the problem which required solution
was to find a means whereby, with a minimum of both labour and
time, a weight could be lowered and kept vertical, and a measure
of the depth obtained. Accordingly he invented a winding-
machine fitted with a brake to prevent both kinking and the
too rapid running out of the wire. Only two men were needed
to handle the apparatus. One of the sinkers was in the form of
a cylinder containing a long, narrow, glass tube the inside of
which was lined with chromate of silver. The deeper this sinks,
the further up the tube does the sea-water penetrate, and in so
doing it reacts chemically on the chromate of silver, producing
a discoloration. On rewinding, the length of discoloured tube
is at once a measure of the depth. The usual length of cable
used to-day is 300 fathoms, the wire being of steel and made
up of seven strands.

In this connexion it is related that Joule once found Sir
William surrounded by coils of pianoforte wire, and he inquired
what they were for. He was told they were for sounding. ' For
sounding what note ? ' inquired Joule. ' The deep C,' was
Sir William's reply.

As to its value to seamen, Admiral Sir W. R. Kennedy once
wrote thus :

' Some years ago I left a port on the coast of Patagonia in the

Research in Navigation 295

Ruhy, We shaped a course for Golfo Nuevo for the night. At
8 p.m. the navigation officer came to my cabin and showed me
the position of the ship, well clear of the land and lOO fathoms

no bottom, marked on the chart. " All right ", I said.

" Throw Thomson overboard." The navigator looked at me

to see if I was joking. " Why, there 's no bottom at loo fathoms,
sir." " Well, heave Thomson over." He left the cabin, and
presently I heard the whirr of the wire suddenly stop. I rushed
on deck. Fifteen fathoms ! " Stop her, hard-a-port, leadsmen on

both chains ! " Sure enough, 15 fathoms. I hove to all night,

but had we continued on our course we should have been ashore

before daylight. The coast line was not correctly charted. No

wonder that we sailors bless the name of Lord Kelvin.' ^

We turn next to Sir William's invention of the modern mariner's
compass — probably his most popularly- known achievement.
In 1870 something prompted him to choose the subject of the
mariner's compass for a magazine article, and he discovered
that he knew very little about it. So he set himself to study the
matter. He quickly realized how unsatisfactory were the forms
then in use. The needles were heavy and long (as much as
fifteen inches in some cases), and were mounted on large cards
for steadiness, but in fact the action was sluggish in fine weather
(if the compass did not stick altogether), whilst in stormy
weather the instrument was practically useless.

Excellent pioneer work on the theory of compass deviation
had been done by Archibald Smith, who was, indeed, the original
source of Thomson's inspirations. Working on from Smith's
standpoint, Thomson showed that, contrary to the prevailing
practice, steadiness of the compass in stormy weather could
best be obtained by short needles mounted on a light card.
He clearly saw the necessity for a slow horizontal swing to
avoid unsteadiness, and for very little friction to prevent sticking.
He paid much attention, too, to the problem of shielding his
compass from the magnetism due to the ship's ironwork.

As a result of all this, Thomson's marine compass takes the
following form. The ' card ' consists of an extremely light (less
than -|th of an ounce) graduated paper ring, kept circular by

1 Sir R. Gregory's Discovery, p. 270,

296 Lord Kelvin

a light ring of aluminium. Threads of silk extend radially from
the rim to an aluminium centre, on the cap of which is a sapphire
bearing resting on an iridium point which projects upward from
the compass bowl. The ' compass needle ' is built up of eight
thin magnets of glass-hard steel from 3 J inches to 2 inches long,
strung together ' like the steps of a rope ladder ' on two silk
threads attached to the radial threads. The weight is distributed
at a distance from the axis, giving a long period of free vibration

Fig. 112. Thomson's (Lord Kelvin's) Compass,
(i) Frame and Needles. (2) Section of Compass Bowl.

The Compass Card consists of a broad ring of paper marked with
degrees and points, attached to a frame like that in (i) above, where
an aluminium ring, A, A, is connected by 32 radial silk threads to a central
disk of aluminium, in the centre of which is a round hole designed to
receive an aluminium cap with a highly polished sapphire centre worked
to the form of an open cone. To direct the card eight short light needles,
N, N, are suspended by silk threads from the outer ring. The section
shows the mounting of the card on its pivot.

(an important essential for steadiness of action), and the friction
at the point of support is very little indeed.

With regard to the question of compass errors due to the
ship's magnetism, Thomson's design was based on the fact that
part of the ship's magnetism is permanent and due to the per-
manent iron structures (it does, however, change ver}^ slowly,
requiring periodic adjustment) and part is 'induced', and
alters with change of course and position. The former, which
may affect the ' needle ' by as much as 20° in ordinary iron
vessels, and 30° in war-ships, is corrected for by two sets of
steel magnets placed at right angles to each other, with their

Research in Navigation 297

centres under the binnacle needle, one directed fore and aft,
and the other set directed athwartship. The error due to the
induced magnetism, which may amount to from 5° to 10°, is
corrected for by placing tvv^o soft iron spheres one on each side
of the compass with their centre line at right angles to the ship's
length. This keeps the induced magnetism annulled, since as its
value changes, so also does the in-
duced magnetism of the spheres.

It took Sir William many years
to overcome the conservatism of
the Xavy, but eventually he had
the satisfaction of seeing the almost
universal use of his compass not
only in our own Navy, but through-
out the merchant service, and in
most foreign Navies, though to-
day it is beginning to be replaced
by the more recent gyro-compass.

The achievements of the sound-
ing-machine and the mariner's
compass are wonderful enough, but
they by no means exhaust the tale
of Thomson's magnificent services
to those who ' go down to the sea
in ships ' . Space only permits of
their bare mention. There is his
work on the furnishing of light-

houses with distinctive lights to

Fig. 113. Standard INlariner's
Compass,

distinguish one from the other, his
work on tides and his invention of the tide-predicting machine,
his mathematical investigations on waves in general, and his
work on the design of ships. Smah wonder, therefore, is it that
we read in the standard biography of this great man ^ the tribute
of the sailor in the distant seas of the East, ' I don't know who
this Thomson may be, but every sailor ought to pray for him
every night.*

1 S. P. Thompson's Life of Lord Kelvin.

298

6. Further Biographical Details

Of the scores of further contributions in almost every direction
of scientific activity nothing more can here be said than that
it is hoped that the interested reader will seek them out in the
standard biographies which have been written, and well written,
by men who were brought into intimate contact with their subject.

Reference might have been made to the famous collaboration

Jl

P

^w^fm^^^^

y^^^2

Fig. 114. Lord Kelvin on board the Lalla RookJi, 23 September 1885.

which produced Thomson and Tait's Natural Philosophy, and
which set a new and high standard in the text-book presentation
of the principles of scientific inquiry ; to Thomson's fascinating
investigations on the age of the earth and on the age of the
sun's heat, developed from a consideration of the laws of cooling —
investigations which profoundly stirred the scientific world at
the time he made them, though the discovery of radium subse-
quently considerably modified the value of his results in both
these investigations ; and to the famous Baltimore lectures,
delivered by invitation to ' professional students in physical

Further Biographical Details 299

science ' in 1884 at the Johns Hopkins University, in which he
dealt exhaustively with the wave theory of Hght. Our intention,
however, has been rather to lay stress on those portions of his
work which served to link up the scientific investigator with the
activities of the engineer, and to leave his more purely abstract
researches for the further reading of the interested students.

In 1852 William Thomson, then a young professor of twenty-
eight, married Miss Crum, a daughter of Walter Crum, a first
cousin of his father's. It was a happy union, but Lady Thomson
was constantly in delicate health and died in 1870. Four years
later he married again. He had visited I\Iadeira the previous
summer as consulting engineer for the W^estern and Brazilian
Cable Company, and a fault in the cable had kept him there for
sixteen days, during the course of which he met Miss Frances
Anna Blandy, daughter of a prominent Madeira citizen. He
was drawn to her at first by the promptitude with which she
had picked up ' dot and dash ' practice, and he returned to the
island in the succeeding summer, and the two were married at
the British Consular Chapel, Funchal Bay, Madeira. They were
devotedly attached to each other to the end.

In 1 85 1 Thomson had been elected a Fellow of the Royal
Society. In 1890 he was elected its President, and remained so for
five years. It is impossible, however, to record the full number
of the honours he received from all the world over. The Royal
Society of Edinburgh, of which he was for many years President,
awarded him both the Keith Medal and the Victoria Jubilee
I\Iedal, and the Royal Society of London the Copley Medal and
the Royal Medal : the Institute of France elected him one of
their Foreign Associates, the French President made him a Grand
Officer of the Legion of Honour, and Prussia a Knight of the
Order ' Pour le ]\Ierite ' .

In England, apart from the honours bestowed upon him by
the brotherhood of science, further recognition came to him at
the hands of Queen Victoria, who on New Year's day of 1892
conferred upon him a peerage. He took the title of Baron Kelvin
of Netherall, Largs, the name being taken from the Kelvin river,
in close proximity to the new University buildings at Glasgow.

300 Lord Kelvin

The year 1896, however, saw a most remarkable demonstration,
world-wide in its character and extraordinary in its sincerity,
in his honour. For this was the year of Kelvin' s completion of
a half-century of illustrious service to Glasgow as the Professor of
N atural Philosophy at its University. A great gathering assembled
— scientific colleagues of international fame from England,

Ireland, the Co-
lonies, and from
every civilized
foreign country,
representatives of
kings, princes, col-
leges, and scien-
tific societies and
institutions.

In 1899 Lord
Kelvin resigned
his professorship.
He was now
seventy- five years
old, and he felt
that the time had
come when this
step was neces-
sary. He was suc-
ceeded by Andrew
Gray, a former
student and as-
sistant, and later
author of an able biography of his great master. Yet Kelvin
could not altogether sever his long connexion with the University,
and with characteristic grace he inscribed his name on the rolls
of the University as a research student.

Retirement from his professional duties by no means meant
a withdrawal from his scientific activities, and these continued
if anything with a renewed vigour and freshness which astonished
all his friends. Old as he was, except for occasional bouts of

Further Biographical Details 301

facial neuralgia, his health continued good. He died peacefully
on the i8th of December 1907. His grave is alongside that of
Sir Isaac Newton. He was buried on the 23rd of December
with a stately simplicity which worthily lifted the occasion.
' There he sleeps well who toiled during a long life for the
cause of natural knowledge, and served nobly, as a hero of
peace, his country and the
world.' 1

In this short record we have
said very little of the man him.-
self; of his wonderful vitality,
and of the remarkable influ-
ence his very presence exerted
on both students and col-
leagues. It is worthy to note
that of all the illustrious men
some record of whose lives has
been given in this volume,
Lord Kelvin is the only one
of whom it can be said that
there are men alive to-day
who came under his personal
influence as either pupil or
colleague. Thus Dr. Russell,
in his short volume on Lord
Kelvin, tells us :

Fi(

T16. A Centra! Tclcplio^ic
Exchange to-day.

' Even in his introductory
lectures Thomson soared to heights which made many of his
class feel giddy and helpless. He would say, for example, that
all motion is relative motion. . . . Having thus unsettled the
ideas of his class and awakened their interest, he would point
out how easy it is to get the relative motion. . . . Towards
the end of the session, owing to the very comprehensive pro-
gramme that had to be got through, the pace had to be
quickened. The last day was always an eventful one, the pro-
fessor sometimes lecturing ... to those of the class who could
remain, long after the hour was up. The writer was one of those

^ Cray's Lord Kelvin, p. 304.

302 Lord Kelvin

who remained to the end — a period of over four hours — in 1878. . . .
But even the most enthusiastic of us were beginning to be fagged
before the professor gave any signs of concluding. The memory
of that last lecture is a treasured possession ' ; and again, ' All
old students look back on their attendance at Kelvin's lectures
as something never to be forgotten and to be treasured deep in
their hearts. . . .' ' Kelvin had a powerful imagination, a strong
inductive faculty, and a power of realizing his conceptions in
practice which has only been equalled by the greatest inventors.
The possession of three such faculties by the same man is probably
unique. His deductions were not of such world-wide importance
as those of Sir Isaac Newton. It is very difficult to make a
comparison between these two intellectual giants, as the ages in
which they lived are so far apart. Newton was more painstaking
and thorough. He published little that was open to criticism.
Kelvin, on the other hand, could hardly wait until his experiments
were finished. There was so much to do and such short time to
do it in. Whatever his hand found to do he did with all his
might.'

From Andrew Gray at Glasgow, we get the following tribute :

' Genius has been said to be the power of taking infinite pains :
it is that indeed, but it is also far more. Genius means ideas,
intuition, a faculty of seizing by thought the hidden relation of
things, and withal the power of proceeding step by step to their
clear and full expression, whether in the language of mathematical
analysis or in the direction of dail}^ life. Such was the genius of
Lord Kelvin ; it was lofty and it was practical. He understood —
for he had felt — the fascination of knowledge apart from its
application to mechanical devices ; he did not disdain to devote
his great powers to the service of mankind. His objects of daily
contemplation were the play of forces, the actions of bodies in all
their varied manifestations, or, as he preferred to sum up the
realm of physics, the observation and discussion of properties
of matter. But his eyes were ever open to the hearing of all that
he saw or discovered on the improvement of industrial appliances,
to the possibility of using it to increase the comfort and safety
of men, and so to augment the sum total of human happiness.'

On the 4th of May 192 1 there assembled a gathering of
scientists. The occasion was the first award by the Institute of
Civil Engineers of a newly-created Kelvin IMedal. The meeting
was presided over by the great philosopher and politician.
Lord Balfour, and in the course of his address he said •

Further Biographical Details 303

' Lord Kelvin had in a manner hardly, and perhaps never,
equalled before, except by Archimedes, the power of theorizing
on the darkest, most obscure, and most intimate secrets of Nature,
and at the same time, and almost in the same breath, carrying
out effectively and practically some engineering feat, or carrying
to a successful issue some engineering invention. He was one of
the leaders in the movement which had compelled all modern
engineers worthy of the name to be themselves men not merely
of practice, but of theory, to carry out engineering undertakings
in the spirit of true scientific inquiry and with an eye fixed on the
rapidly growing knowledge of the mechanics of Nature, which
can only be acquired by the patient work of physicists and
mathematicians in their laboratories and studies/

Fig. 117. Buoys and Grapnels used in recovering the
Atlantic Telegraph Cable of 1^65.

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n^wr

T^T—^-m>.

1

Fig. 1 1 8. The Growth of Aviation. An early French print (1798)
contemplating Napoleon's descent on England through the air.

XVI

SCIENCE TO-DAY AND TO-MORROW

I. Retrospect and Prospect

In these pages we have passed the progress of knowledge in
review, century by century. The story has been one of steady
progress. Truth after truth has been brought to light, law after
law has been unearthed, fallacy after fallacy and misconception
after misconception have been removed. Gradually there has
emerged a glimpse of a grand c'osmical scheme of order, law, and
method which commands our respect and compels our awe.

Of late the pace has quickened. Discoveries of first-class
importance have brqught with them inventions of equal import.
Wonderful as was once overland and submarine telegraphy to
a world accustomed only to postal communication, even wireless
telegraphy is to-day regarded as one of the commonplaces of
everyday life, and wireless telephony no longer surprises us.

Yet we are still on the threshold of knowledge. Only one small
corner of nature's veil of truth has been lifted to the understand-
ing of mankind. Newton, it will be remembered, once wrote :
' 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, whilst the great ocean of truth lay all undiscovered
before me.' We have advanced far since Newton's day, yet at
best we can say that a few more pebbles have been rounded, and
a few more shells exposed. The infinite ocean of discoverable
truth still lies before us.

To-day, with barely a quarter of the century gone, we are
already far beyond the point at which Lord Kelvin and his
nineteenth-century contemporaries stopped. In more directions
than one, events are stirring in the world of science, and already
vast possibilities of rapid future development are opening up.

2613 u

3o6

2. Applied Physics

What is the general trend of scientific research to-day ? Apart
from the normal development of the applications of the already
discovered laws of physics in the direction of utility (two of the
latest examples of which are the perfecting of wireless telephony
and wireless telephotography), in the world of applied physics
one of the main features of the twentieth century has undoubtedly
been the conquest of the air. So far as the ' lighter than air '
machines are concerned, the fundamental scientific problems
have not been very great, though they are by no means to be
dismissed.

The problem of the heavier-than-air machine, or aeroplane, has,
however, been a much more formidable one. To some extent,

it was the influence of Newton
himself which retarded progress,
for he worked out a theory
which taught that the resistance
to a rapidly moving object in
119. Illustrating heavier- the air w^ould be SO great that
than-air flight. ^^i^ mechanical power required

to maintain such motion was enormous and prohibitive. Pioneer
work by Professor Langley, of America, from 1887 onwards
cleared away this misconception. He showed that, contrary to
Newton's deductions, the more rapid is the motion in horizontal
flight of a given plane, the less will be the power required to
support it. The problem was further developed on the theoretical
side by such men as Bryan, Bairstow, and Lanchester, and on
the practical side by such pioneers as the brothers Wilbur and
Orville Wright.

Some very slight insight into the fundamental problems involved
in the theory of ' heavier-than-air ' flight may perhaps be realized
by the following. Imagine a plane AB (Fig. 119), inclined to the
horizontal by a small angle. Its weight W acts vertically down-
wards, and to sustain this weight there must be an equal and
upward force. Now suppose that by means of engines and pro-
pellers a ' fore and aft ' force F is produced along the length AB,

Fig.

Applied Physics 307

causing the plane to move forwards (on wheels — ' taxi-ing ', as it is
called in aeroplane language). This sets up a horizontal windage
pressure P (against the direction of motion) on the under side
of the surface, and at the same time creates a partial vacuum
on the upper surface of AB, and as a combined result there is
developed an upward force or reaction W-^, which increases with
the speed of the motion, and which, when it becomes greater
than W, will cau'^e the machine to rise at the same time as it is
moving forward with the speed due to F, and it then becomes
a question of maintaining this speed to preserve this upward
thrust. The whole argument is, it will be noticed, independent
of the lateral compass direction taken, and so the provision o^
steering accommodation will thus make directive locomotion
possible, while the controlling of the angle AB to the horizontal
will enable the necessary variations in the value of W-^ to be made
to lift the machine higher or to bring ic lower down as desired. No
mention has been made, of course, of the hundred and one modify-
ing considerations which are really involved, such as shape,
surface area, skin friction, drag, and so on.

3. Pure Physics

Turning now to the sphere of pure physics, the feature of
present-day research is the investigation of the structure of the
atom. It is well over a hundred years since Dalton first enunciated
his atomic theory, according to which the atom was the ' last
word ' in the subdivision of matter. To-day we know that the
atom is an exceedingly complicated structure.

The start in this direction may be said to date from 1878, in
which year Sir William Crookes, when studying the discharge of
electricity through a highly rarefied tube, discovered the ' cathode
rays ', a stream of minute electrified particles to which the name
of ' electrons ' was afterwards given. Hertz, of wireless tele-
graphy fame, showed in 1893 that these rays could penetrate
thin sheets of certain metals (including aluminium) placed inside
the vacuum tubes, and following this up, Lenard, in 1894, suc-
ceeded in passing these cathode rays out into the air by having

u 2

3o8 Science To-day and To-morrow

the end of the vacuum tube of aluminium, thus acting as a window
to the rays, which remained luminous in the air, and which were
found also to affect a photographic plate.

It may be mentioned in passing that a year later, in 1895,
Rontgen, in repeating Lenard's work, discovered almost by
accident the existence of X-rays, and worked out their remarkable
properties, to the great benefit of mankind in the many subsequent
applications to medicine and surgery.

Returning, however, to our main theme, we come to Henri
Becquerel's discovery, in 1896, of radio-activity in uranium and
its compounds — that is to say, these substances were phos-
phorescent on exposure to sunlight, and emitted rays which
could penetrate materials opaque to light, and would affect
a photographic plate.

In 1903 radium itself was isolated by Professor and Madame
Curie, and the problem of its remarkable store of energy began
to agitate the world of science ; for radium gives out heat and
light continuously without evident chemical change, and even
radium-salts maintain a temperature of 3° Fahrenheit above
that of their surroundings.

Whence comes this apparently inexhaustible store of energy ?
According to the Disintegration Theory of Rutherford and Soddy,
the rays emitted by a radio-active substance are evidences of the
breaking up of its atomic structure, and according to calculation
one grain of radium would reduce to half a grain in 1,760 years.
Similarly ' radium emanation ', a gas emitted by radium, and
much more ' active ' than the radium itself, reduces to one-half in
four days. Sir WiUiam Ramsay computed that the energy in a ton
of radium is equivalent to that of a million and a half tons of coal.

As a development from aU this, and from the detailed researches
of Sir J. J. Thomson and others on the subject of the electron,
there has developed in the past few years a conception of the
structure of matter widely different from that which held the
field in the nineteenth century. According to the present-day
view, instead of the atom being regarded as a single indivisible
something, it is considered to be made up of a minute nucleus
of positively electrified matter (positive and negative electricity

Pure Physics 309

' slumped together ' with a preponderance of the former) sur-
rounded by a number (anything up to 92) of exceedingly minute
negative electrons, probably revolving round the nucleus at vary-
ing distances much as do the planets round the sun. The mass
of the atom is concentrated at the nucleus, the negative electron
weighing only about 1/1830 of the weight of the positive nucleus.

In the normal atom, the amount of positive electricity on the
nucleus is exactly equal to the number of negative electrons
surrounding it, but this number varies from element to element.
It is known as the Atomic Number. Its value for lead is 82, for
mercury 80, for gold 79, for oxygen 8, for helium 2, and for
hydrogen i. The physical and chemical properties of the element
depend upon this number, and so there arises a vastly important
problem for the future — one of those fascinating problems which
link up the distant past with the years to come. It is no less
a problem than that of the transmutation of the elements.

Mercury has an atomic number of 80 and gold of 79, and all
that has to be done is to reduce the charge in the nucleus by
one — there is no doubt that an accommodating negative electron
would at once also depart — and the thiijg is done. And about
the only way to do it is to bombard the nucleus with a suitably
light projectile — a helium atom or a hydrogen atom, for example
■ — which would have to be small enough to escape collision with
the surrounding negative electrons. In a million such shots,
thousands will so collide, thousands more will go clean through
the space between the electrons and emerge on the other side,
thousands more will so nearly but not quite hit the nucleus that
they will be deflected round it like a comet round the sun, and
perhaps only one will actually hit the elusive nucleus, and then
it is a question whether it will do this with sufficient energy to
produce the necessary disruption. And finally, millions of such
successes would be required to get a sufficient amount of trans-
mutation to be appreciable.

Yet it has actually been done, recently, by Professor Ruther-
ford, of Cambridge. His attack was on atoms of nitrogen
(atomic number 7), and his ' bombs ' were atoms of helium (in
the form of high speed particles emitted radio-actively by what

310 Science To-day and To-morrow

is known as radium — C, with a speed of 12,000 miles per second).
Rutherford showed that from a small percentage of these atoms
of nitrogen he succeeded in producing atoms of hydrogen (atomic
number i), and so we get the first really authentic case of artificial
transmutation of an element on record.

4. Einstein and Relativity

We turn finally to the much-talked-of theory of relativity
which is at present holding the attention of all physicists and

mathematicians and with
which is associated the name
of Albert Einstein. Born
in Switzerland, of Jewish
parentage, some forty-three
\-ears ago, he succeeded Van
't Hoff as an ' akademischer '
professor at the University
of Berlin. Gifted with a
wonderful creative imagina-
^tt^^ X^jJHlBP tion, a profound knowledge

^^^W ^l^r^ of mathematics and physics,

and all the delicate sym-
pathy of a master musician
(he is almost as brilliant a
violinist as he is a philo-
sopher), he has come to the world with a mission of whose
import we have not heard the like since the time of Newton.

We have seen how Huyghens, in opposition to Newton,
developed a wave theory of light, as a result of which there grew
up a conception of a medium pervading all space, whose function
it was to transmit the light waves. This medium is spoken of
as the ether, and much controversy and discussion has centred
round the problem of its properties. It has proved most elusive.
It can be neither felt nor seen, and every attempt to show its
actual presence has failed. Clerk Maxwell, one of the most
brilliant of the nineteenth-century mathematical physicists,
developed his famous electro-magnetic theory of light (after

Fig. 120. ALBERT EINSTEIN

Einstein and Relativity 311

having shown that the same ether which was necessary for the
propagation of light waves at a speed of 186,000 miles per second,
was also necessary for transmission of electro-magnetic dis-
turbances at the same speed), according to which light was itself
electro-magnetic in origin, the sensation of light being in fact due
to the passage of electric waves through the ether.

Hertz, we know, strikingly verified the relation between light
and electricity by showing that the oscillations of the discharge
of a Ley den jar set up ether waves at a speed of 186,000 miles
a second, and we also saw how Faraday showed a relation
between light and magnetism. Zeeman, too, discovered sucli
relationship. A spectrum of sodium light shows two bright
yellow lines ; but place the incandescent sodium between the
poles of a powerful magnet and the two yellow lines at once give
place to ten such lines.

The electronic theory of matter, to which we have already
referred, developed naturally from all this. The unit of elec-
tricity is the electron and a stream of electrons produces an
electric current. But at the same time the electronic particle
is the ultimate unit of matter, and the vibrations of the negative
electrons around the positive nucleus give rise to the phenomenon
of light. Now comes one of Einstein's strong contentions. If
matter is derived from the electron, and if light is also derived
from the electron, then since the former is affected by gravitation,
why not the latter also ?

Einstein argued that just as a body shooting past another body
must be deflected out of its course by the gravitational influence
of the latter, so a ray of light shooting past a body would be
deflected out of its course also. With the huge speed of 186,000
miles per second, it would no doubt require a huge body to
produce a small deflexion, but Einstein predicted a definite
value for \Vz case of a ray of light shooting past the sun. This
could be calculated from Newton's law of gravitation, but it is
part of the new theory that Newton's law requires some modifica-
tion ; and working on his own formula, Einstein prophesied
a deflexion practically double that which he derived from
Newton's formula.

312 Science To-day and To-morrow

Here was a fitting opportunity, not only to test Einstein's
theory — but also to test it against Newton's. One can stud}^ the
passage of a light-ray past the sun only when there is a total
eclipse, as then the sun is blotted out and the stars suddenly
appear ; and of course those stars whose ' lines of sight ' just
skim past the sun can be photographed, and a careful study
should show a slight displacement of their position in the skies
from that which they normally occupy when the sun is elsewhere.

The story constitutes one of the romances of science. Einstein,
a German-Swiss professor in a recently hostile country, made his
prophecy. But ' genius knows no frontier '. England, while
the late war was still in progress, arranged the eclipse expedition
to Sobral, in South America, and to Principe, off West Africa, to
put the matter to the test. The result is well known. It was
a triumphant vindication of Einstein's theory.

No longer can we, then, with absolute truth, say of light that it
travels in straight lines. No longer can we say convincingly that
parallel lines never meet ; nor that the straight line joining two
points is the shortest distance between them.

For the exact expressions of the laws of nature which it is the
business of the scientist to discover we seek the language of
mathematics, for this we regard as being both exact and universal.
But unfortunately, as Einstein points out, the mathematical
language employed hitherto has not been absolutely universal,
and accordingly could not be regarded as exact. Why is this ?
It is because the observer who framed the laws has omitted to
allow for his own motion.

All the constituent portions of the universe are in motion in one
way or another, and the relative effects are different to observers
in different parts of the universe. We on the earth are not
moving in quite the same way as are the observers on, say, the
star Sirius, and as a consequence the facts of nature seem different
to the two sets of observers. The scientist on the earth builds
up his series of formulae and equations, to express the laws of
nature as he sees them, and the scientist on Sirius does likewise.
But on comparing them (assuming we could), we find the sets of
formulae and equations are different. Einstein says that so long

Einstein and Relativity 313

as this is so the laws cannot be regarded as absolute, but only as
relative. So we say that the underlying doctrine of Einstein is
that the mathematical expression of the laws of nature shall be
independent of the state of motion of the observer who frames
them.

As a matter of history, assuming that the ether of space really
existed, a number of attempts were made by various people by
various means to detect the motion of the earth through this
ether, and so to allow for its effect on the laws of nature. These
attempts all failed, and Einstein boldly asserted that such a
motion was, in the nature of things, incapable of detection, and
from this view he began to develop his theory, which demands
from us a totally different scheme of perception from that to
which we have been accustomed.

Where we have regarded matter, space, and time as completely
separate conceptions, Einstein asserts that these are, on the
contrary, intimately bound up with each other, and that there
is only one fundamental fact of experience — a happening or an
event. Space and time are inseparable. Events do not occur
at a certain point at a certain time — they simply ' are ', and for
the full representation of events we must replace the old scheme
of three axes of reference at right angles by four axes at right
angles, the fourth being a time-axis. On the ' three- a^^es^' scheme,
ten different observers, having of course their different motions,
and, therefore, their different outlooks, would give ten different
representations of any one event. But on the four-dimensional
* continuum ', as it is called, one event gives one representation,
provided the axes of reference are the same for all.

Relativity of space is of course by no means a new conception ;
but the time factor in relativity is undoubtedly a new thing. Let
us now sfee in what fundamental respects Einstein differs from
Newton. Newton taught that perfectly free matter moves in
straight lines, and to explain curved motion he brought in the
idea of force — in the case of the moon moving round the earth,
for example, the force of gravitation. Einstein, too, says that
perfectly free matter moves in straight lines, but his contention
is that the moon is moving in a straight line, only to us it appears

314 Science To-day and To-morrow

not to be so, owing to the fact that * space in the neighbourhood
of matter is modified in such a way that a straight Hne in it
appears to an observer who is unaware of the modification to be
curved '. We remarked before that on the new philosophy
a straight Hne is no longer the shortest distance between two
points. This might be said to be an Einsteinian fact expressed in
Euclidean language. To express it in Einsteinian language, it
would be more correct to say that ' a straight line is the shortest
distance between two points, but the ' distance ' must be taken
m the ' four-dimensional continuum ' and not in that relatively
selected portion of it which we call space, and which we represent
on our old-fashioned three-dimensional framework of reference.

A word of caution is here necessary. The modern theory of
relativity has in no sense dethroned Newton. The equations
which develop from Einstein's theory show a law of gravitation
which so far agrees with Newton's law that we may say that
for the ordinary speeds with which we are concerned in most of
the problems which confront us the two are practically identical.
They begin to differ, however, as the velocities increase, and for
those speeds comparable with that of light the divergence
becomes very great.

In June 1921 Albert Einstein visited this country to deliver
a lecture at King's College, London, and after the lecture he was
the guest of honour at a dinner attended by the most eminent
English philosophers. Toasting the health of the guest, the
Principal, Mr. Ernest Barker, used these fine words :

' We welcome you twice, for discovering a new truth which has
added to the knowledge of the universe, and for coming to us from
a country that was lately our enemy to knit the broken threads
of international science. If at your command the straight lines
have been banished from our universe, there is yet one straight
line which will always remain — the straight line of right and
justice. May both our nations follow this straight line side by
side in a parallel movement, which, in spite of Euclid, will yet
bring them together in friendship with one another and friendship
with the other nations of the world.'

BIBLIOGRAPHY

The object of this bibliography is to draw the attention of the reader
to the general literature in scientific history rather than to the biographies
of the scientists.

Scientific Method and General Scientific History.

J. A. Thomson. Introduction to Science. Home University Library

(Williams & Norgate). 191 1. 2S. M. net.
F. W. Westaway. Scientific Method, its Philosophy and its Practice,

(Blackie & Son.) 2nd Edition. 1919. los. 6d. net.
Henri Poincare. Science and Method, translated by Hon. Bertrand

Russell. (Nelson & Sons.) 1914. 6s. net.
Norman Campbell. What is Science ? (Methuen.) 1921. 5s. net.
Charles Singer. Studies in the History and Method of Science. Oxford

(Clarendon Press). First Series, out of print. Second Scries, 1920,

48s. net.
Karl Pearson. The Grammar of Science. (A. & C. Black.) 3rd Edition.

Part I, Physical. 191 1. los. net.
Sir R. A. Gregory. Discovery, the Spirit and Service of Science. (Mac-

millan.) loth Edition, 1921. 7s. 6d. net.
F. S. Marvin. The Living Past. Oxford (Clarendon Press). 1920.

5s. ()d. net.
W. W. Rouse Ball. A Short History of Mathematics. (Macmillan.)

6th Edition. 12s. 6d. net.
F. Cajori. A History of Elementary Mathematics. (Macmillan.) 125.net.

A History of Physics. (Macmillan.) 14s. net.

E. Mach. The Science of Mechanics (with Supplementary Volume).

(Open Court Publishing Company.) 1907. 95. 6d. net. Supple-
mentary volume, 2s. 6d. net.
Sir O. Lodge. Pioneers of Science. (Macmillan.) 75. 6d. net. Mainly

astronomical.

Ancient Science.

J. L. Heiberg. Science and Mathematics in Classical Antiquity. Oxford

(Clarendon Press). 1922. 25. 6d. net.
R. W. Livingstone and others. The Legacy of Greece. Oxford (Clarendon

Press). 192 1. 7s. 6^;. net. (Chapters on Science and Mathematics by

Sir T. Heath, Dr. Charles Singer, and Professor D' Arcy W. Thompson.)
C\Til Bailey and others. The Legacy of Rome. Oxford (Clarendon

Press). 1923. (Chapter on Roman Science by Dr. Charles Singer.)
Sir T. L. Heath. Greek Mathematics (2 vols.). Oxford (Clarendon

Press). 192 1. 50s. net.

3i6 Bibliography

A ristotle.

Charles Singer. Greek Biology and Greek Medicine. Oxford (Clarendon
Press), 1922. 2s. (>d. net.

Euclid.

Sir T. L. Heath. Euclid in Greek. (Cambridge University Press.) 1920.
IDS. net. Very interesting notes.

The Thirteen Books of Euclid's Elements. (Cambridge University

Press.) 1905. 52s. 6d. net.

Archimedes.

Sir T. L. Heath. The Works of Archimedes. (Cambridge University
Press.) 1907. 17s. 6d. net.

Science in the Middle Ages.

Hearnshaw. Mediaeval Contributions to Modern Civilization. (Harrap
& Sons.) 1921. 7s. 6d. net. The Chapter on 'Science' by Dr. C.
Singer gives an excellent survey of mediaeval science.

A. G. Little. Roger Bacon Essays. Oxford (Clarendon Press). 1914.
i6s. net.

J. L. E. Dreyer. History of Planetary Systems from Thales to Kepler.
(Cambridge University Press). 1905. 12s. ()d. net.

Charles Singer. Studies in the History and Method of Science. Oxford
(Clarendon Press). In vol. i, 'The Scientific Views and Visions of
Saint Hildegarde ', by C. Singer, ably depicts twelfth-century science.
In vol. ii are: 'Mediaeval Astronomy', by J. L. E. Dreyer;
' Science in the Thirteenth Century ', by R. Steele ; ' The Scientific
Works of Galileo ', by J. J. Fahie ; ' Science and the Unity of Man-
kind ', by F. S. Marvin ; ' Steps leading to the Invention of the
First Optical Apparatus ', by C. Singer.

The Modern Period.

A. D. Lindsay. A Discourse on Method by Rene Descartes. (J. M. Dent.)

Everyman. 1912. 25. net.
J. A. Thomson. Progress of Science (Nineteenth Century Series).

(Chambers.) ^s. net.
A. MacFarlane. Ten British Mathematicians. (Chapman & Hall.)

85. dd. net.
— — Ten British Physicists. (Chapman & Hall.) Ss. 6d. net.

INDEX

Aberration, spherical, 145;

chromatic, 146, 148
Absolute scale of temperature,

286 et seq.
Absolute zero, 287, 288
Academy, Plato's, 23, 27
Accademiadel Cimento, 139
Aeroplane, 306, 307
Air, conquest of, '306, 307 ; weight

of, 179, 183, 184
Air-oTin, 50
Alchemy, 53, 54
d'Alembert, 193

Alexander the Great, 26, 27, 28, 33
Alexander of Hales, 57
Alexandria, School of, 33 et seq.
Alo^ebra, beginnings of, 51
Alhazen, 53

Almagest, Ptolemy's, 47. 52, 78
Ampere, A. M., 193, 199 et seq.,

210, 254, 257, 259, 288
Ampere's Rule, 204
Ampere, the, 209
Amyntas III, 25
Anaesthesia, Davy on, 215
Angle of Dip, 100, loi
Analytical geometry, 125, 129,

132 et seq.
Anaximander, 21
Anaximenes, 21
Animal electricity, 197
Anne, Queen, 170
Anode, 264
Antoninus, Marcus Aurelius, 46,

Antonio de Dominis, 1^3, 137
Apollo Lycacus, temple of, 26
ApoUonius of Perga, 34, 50
Aquinas, St. Thomas, ^7
Arabian philosophy, rise of, 52, 53
Arago, 194, 205, 207, 288
Arc discharge. 224, 263
Archimedes, 34, 39 et seq., 50, 85,

105, 303 ; principle of, 42, 43
Arcliytas of Tarentum, 35
Aristarchus of Samos, 49, 72
Aristotle, 7, 24, 25 et seq., 47, 53,

54, 55. 58, 73, 74,75, 93, 103, 106,

III, 115, 132, 138, 179
Arithmetic, beginning of, 20, 36
Astrology, 5s, 56, 57, 86
Astronomy, beginnings of, 20
Athens, 23, 25
Atlantic cable, 288
Atmosphere, researches on, 179

et seq.
Atmospheric electricity, 196, 197;

refraction, 50, 84
Atom, structure of, ^07 et seq.
Atomic nature of Matter, 7
Atomic number, 309
Attracted disk electrometer, 279
Bache, Dr., 244, 245
Bacon, Francis, 139, 173, 219, 220
Bacon, Roger, 52 et seq., 94, 112

Bairstow, 306

Baltimore lectures. Kelvin's, 298

Barberini, Cardinal M., 119

Barlowe, \V., 96

Barometer, history of, 179 et seq.

Barrow, Dr. I., 144, 145, 165, 168

Bathurst, Dr. R., 177

Becquerel, H., 308

Heddoes, Dr., 214

Beeckman, Isaac, 128

Bellarmine, Cardinal, ti8

Bernouilli Brothers, 170, 171, 234

Bmomial Theorem, 163

Hiot, 194

Boetliius, 51

Boiling-point and pressure, 188

Bonaventiira, the Seraphic, 60

Bose, IQ5

Bossard, 102

Houcher de Perthes. 8

Boyle, Richard, 174

Boyle, Hon. R., 6, 140, 173 et seq.,

219, 220; researches on atmo-
sphere, 182 et seq.
Boyle's Law, 186 et seq.
Brewster, 194

Bruno, G, no, iii, 117, 121
Bryant, 306
Burning glasses, 44
Byrhtferth, s6
Cable, Atlantic, 288
Cables, insulation of, 289
Caird, J., 276
Calculus, invention of, 85, 144,

163 et seq.; Leibnitz's Differ-
ential, 165 et seq.
Caliisthenes, 26
Caloric, theory of, 194, 216, 219

et seq., 284
Capacity, 266 ; of condensers,

197: specific inductive, 266
Cardan, 102

Cariiot, Sadi, 284, 285, 286
Cartesian mathematics. 132 et

seq., 162, 163

Cartesian School, 163, 173
Cassini, 140
Cathode, 264
Cathode rays, 307
Cauchy, 193

Cavendish, H., 197, 226, 233, 266
Centrifugal force, 131
Crsi, Marchese Federigo, 139
Lhaicis, 28
Chaldea, 19, 20
Challenges in mathematics, 128,

170. 171

Charles II, 139, 178

Charlet, Father, !26

China, 19, 49

Christina, Queen of Sweden, 136,

137

Chromatic aberration, 146, 148

Circle, 24, 35, 36, 85, 86

Circle-dip, 101

riaudian, 44

Clement IV, Pope, 60, 61

Clepsydra, 50

College, Invisible, 177, 17S

Collins, J., 167

Combustion, theories of, 104

Comets, orbits and periodicity of,

181
Compass, mariner's, 100, 295

et seq.

Condensers, capacity of, 197
Conductivity, electrical, JOO, 194,

236. 237 ; heat, 236
Conductors, electrical, 195
Cone, 24

Conic Sections, 24, 35
Conservation of energy, 194, 285 ;

of mass, 194

Contiiiuit}', principle of, 84, 85
Cooke, 289
Co-ordinate geometry, 125, 129,

132 et seq.
Copernican System, 71 et seq., 88,

102, no, 112, 118
Copernicus, N., 6, 49, 67 et seq.,

81, no, 112,- 118, 138
Corpuscular theory of light. 153
Cortesiu^, Martinus, 102
("osimo II of Tuscany, 117
Coulomb, C. A., 197, 233, 266, 279
Craig, 166

Crookes, SirW., 307
Crown of cups, 198
Ctesibus, 50
Cube, doubling the, 35
Curie, M. et Mme., 308
Current electricity, 194, 197 et

seq., 263 et seq.
Cycloidal pendulum, 152

Dalton, 7, 307

Dannemann, F., 11

Dark Age, 53, 54

Darwin, 8

Davy, Sir H., 7. 210 et seq., 233,
251, 252, 253, 256, 257, 263. 271,
284

'De Magnete', 94, 95, 96, 97, 98
et seq.

' De revolutionibus orbium caeles-
tium ', 75 et seq., 138

Delambre, 202

Descartes, Rene, 102, 125 et seq.,
138, 139, 144, 162, 163, "179, 192

Descartes, Joachim, 125, 126, 127

Deviation of Light, 146

' Dialogues ', Galileo's, 120

Diamagnetism, 269, 270

Dielectric, 266; constant, 266

Digges, Thos., 107

Diogenes Laertius, 25

Diophantus, 45, 51

Dip Circle, loi

Dip, Magnetic, 100, lOl

Dirichlet, Lejeune-, 235

' Discourse on Method ', 132, 139

3i8

Index

Disintecration theory, .^08

Dispersion of Liplit/148

Dominis, Father, 133, 137

Doubliro; the Cube^ 35

Dubarron, Abbe, 200

Dynamo, 264

Earth, age of, 298 ; as a magnet,
100, lOI

Effluvia theory of magnets, 194

Egypt. 19, 21, 23

Ehrenberg. 8

Einstein, A., 310 at seq.

EI-Mamoun, 52

El-Mansour, 52

Electric lighting, 223, 224, 262,
263, 264 ; telegraph, 207

Electrical conducti\ity, 100;
images, 279 ; machine, 181 ;
resistance, 237, 238

Electricity : animal. 197 ; atmo-
spheric, 196, 197; current, 194,
197 et seq. ; induction of, 266

Electrics, 100

Electrification by friction, 21, 99,
190, 194, 19.S

Electrochemistry, 198, 224 et
-seq., 264 et seq.; magnet, 207,
269 ; magnetism, 194, igS, 203
et seq., 254, 257 et seq.; induction
of, 257 et seq.; motor, 264;
statics, 194 et seq., 279 et seq.;
static induction, 266

Electrode, 264

Electrolysis, 224 et seq., 264 et
seq., 281

Electrolyte, 264

Electrometer, Kelvin's, 279, 280

Electron, 99, 307 et seq , 311

Electrophorus, 198

Electroscope, 279

Klements, Aristotelian, 29, 30, 56

Elizabeth, Queen, 96, 97

Ellipse, 24. 85

Hmerson, 193

Emission theory of Light, 153,

Energy, conservation of, 194,

285 ; radiant, 194
Eratosthenes, 34, 49
Ermeiand, Bishop of, 69
Ether, the, 152, 310, 311, 313
Euclid, 21, 34 et seq., 39, 85, 104,

14^
Eudoxus, 35, 37
Euler, 219
Evaluation of tt, 41
Exhaustion, proof by, 35, 37
Experimental Science, founding

of, 93 et seq., 103 et seq.
Falling bodies, 30. 107
Faraday, M., 7, 248 et seq., 257,277
du Fay, C. F. de (J., 194, 195, 190
Fechner, 245

Ferdinand dei Medici, 105
Ferdinand of Tuscany, 119, 120
Flamsteed, 169
Fleming, Prof, 283
Florentine School of Physicists,

139
Fluent, 164

Fluxions, Newton's theory of, 163
et seq., 170.

Focus of Lens, 132, n3, 145

Force, centrifugal, 131 ; doctrine
of, 32 ; lines of, 266

Forces, parallelogram of, 32

Forcing pump, 50

Foucault, J. L , 154

Four Primary Elements, 29

Fourier, J., 236, 23Q, 276

Francis, Father, 168

Franciscans, ^j^ 60

Franklin, B., 197, 233, 264

Frauenhofer, 7

Frederick II, King, 82

Freind. ]., 64

Friction and Heat, 219 et seq.

Frictional electricity, 264

Fuller, Thos., 97

Galilei, Galileo, 6, 29, 93, 94, 97,
103 et seq., 138. 139, 151, 155, 173,
176, 179, 189, 192

Galilei, Vincenzo, 103, 104

Gallus, 51

Galvanometer, 205, 206, 238, 291

Galvini, L., 197, 233

Garnett, Dr., 216

Gases, liquefaction of, 255

Gauricus, 50

Geometrical analysis, 24

Geometr}', of three dimensions,
35; beginnings of, 19; co-ordin-
ate, 125, 129. I32etseq.; Euclid's,
34, ^5 ; proof by exhaustion, 35

Gerbert, 54

Gilbert Club, 102

Gilbert, Davies, 214

Gilbert, William, 93 et seq., 130,
138, 173, 192

Giovanni dei Medici, 109

Gladstone, 263

Gnomonic numbers, 22

Goddard, Dr., 177

Gold-leaf electroscope, 281

Gravity, Aristotle's theory of, 30 ;
Newton's theory of, 144, 154 et
seq. ; Plato's theory of, 30 '

Gray, Andrew, 302

Gray, Stephen, 194, IQ5

Greek language, 7, 57, 58;
peoples, 19, 20; science, last
days of, 50, 51

Greenwich Observatory, founda-
tion of, 140

Gregory, J., 149

Grosseteste, Robert, e,-j^ 58. 59

Guericke, O., 140, 179, 180, "181,
182

Guido Ubaldi, 105

Gunnery, early writers on, 107

Gunpowder, invention of, 63

Guy de Foulques, 60

Gyro-compass, 297

Halifax, Lord, i6q

Halley, E., 140, 161, 163

Haroun El-Raschid, 52

Harris, W. Snow, 279

Hartmann, G., 100

Heat, conductivity, 236; mechani-
cal equivalent of, 284, 285; nature

of, iSg, 216, 219 et seq., 2846

seq.

Heath, Sir T. L., 35
Heavens, immutability of, 29, m
Helmholtz, H. von, 281
Henle, 8

Henry, J., 244. 245
Hermeias, 26
Hero of Alexandria, 50
Herpyllis, 28
Herschell, 194
Hertz, 283, 307, 311
Hiero, Kmg, 39, 42
Hipparchus, 47
Hippocrates of Chios, 35
Hippocrates of Cos, 35
Hooke, R., 140, 150, 161, 162, 177,

178, 182
Hooke, Theodore, 177
de THopital, 170
Hopkins, W., 276
Huxley, 257
Huyghens, 140, 151, 152, 153,

154, 156. 170, 193, "194. 3'0
Hydrostatics, 40, 42, 43, 117
Hypatia, -i
Hyperbola, 24
Hypsicles, 36
Ice, density of, 188
Images, electrical, 279
Immutability of the heavens, 29,

III
India, 19, 49
Inductance, earth, 262
Induction, electro-magnetic, 257

et seq.
Industrial revolution, 7
Infinitesimals, 85
Innocent IV, Pope, 60
Inquisition, iii, 119 et seq., 130
Institute of Bologna, 139
Insulation of cables, 289
Insulators, 100, 195
Interference of light, 193
Inverse square law , for electricitv,

266; of gravitation, 144, 155 et

seq., 197

Invisible College, 177, 178
Ionia, 23
lonians, 21

Isochronism, principle of, 104
James I, 97
James II, 168
Jerome de Esculo, 61
Jews, 52
Joule, J. P., 8, 285, 286

Jupiter, III

■59

Kelland, Prof., 276

Kelvin, Lord, 274 et seq., 305;
researches in electricity, 278 et
seq. ; in heat, 284 et seq. ; ocean-
telegraphy, 288 et seq. ; naviga-
tion, 294 et seq.

Kepler, J., 6 7s, 79 et seq., 115,
118, 132, 138, 143, 154

Kepler's Laws of planetary mo-
tion, 87, 89 et seq. ; Newton on,
154 et seq.

Kepler's Principle of Continuity -
84, 85

Index

319

rCppler's ' Sterp.ometria \ 85

Kolliker, 8

Lacroix, 193

Lag^range, 193, 200, 276

Lanchester, 306

Laiigstorff. C. dp, aix

Laplace, 193, 200, 276

Latin, use of, 54

Latitude and longitude, 49

Lavoisier, 213

Laws of Motion, Newton's, 123

Learned societies, foundation of,

Leeuwenhoek, 8

Legend re, 193

Leibnitz, 85, 140, 150, 165, 166,
167, 170, 171, 172

Lenard, 307, 308

Lenses, 53, 83, 112 et seq., 132,
133, 145, 146. 177

Lenz, 244, 262

Le\er, principle of, 41

Leyden jar, 195, 197, 281, 282; |
oscillatory discharge of, 281,
282,311 1

Librationofmoon, 118

Light, electric, 223, 224, 262, 263, :
264 ; Euclid on, 50 ; interference
of, 193; magnetization of, 267; |
polarized, 194, 267 et seq. ; Pto- |
lemv on, 50; speed of, 311; j
theories of, 151 et seq., 194, 311
et seq.

Liglitning, 196, 197

Limits, theory of. 37, 38, 40, 85

Lines of Force, 266

l^iims, Franciscus, 186

Lippershey, Hans, 112

Liquefaction of gases. 255

Loadstone, 98, 99, 100, 101

Locke, 220

Lodge, Sir O., 283

Lommel, E. von. 246
.Longitude, determination of, T17

Lyceum, the, 26

Lyncean Society, 139

Macrocosm and Microcosm, doc-
trine of, <;^

Maestlin.'M., 80

Magdeburg hemispheres, i8i

Magnetic dip, 100; meridian, too

Magnetism, early studies, 98 et
seq., 189, 194

Malus, 194

Marcellus, 45

Marconi, 283

Marcus Aurelius Antoninus, 46,

Mariner's compass, 100, 295 et

seq

Mariotte, E., 188
Mass, conservation of, 194
Mathematical challenges, 128,

170, 171
Maurice, Count of Nassau, 113
Maxwell, J, Clerk, 205, 283, 310
Mechanical equivalcrit of heat,

2.S4. 285
Mechanical powers, Galileo on,

108

Mechanics, Archimedes', 40 ;
Aristotelian, 30, 31,32, 4ietseq.,
10.^ ; Galileo's, lo.s et seq., 123

Meikleham, Dr., 277

Melbourne, Lord, 272

Menaechmus, 24, 35, 50

Mensuration, 85

Mersenne, M., 127, 130, iSo

Meridian, magnetic, 100

Milton, J., 115, 123

Mirror galvanometer, 291

Mitchell, Dr., 215

Mitscherlich, 7

Moon, attraction of, 159, 160;
irregularities on, 29 ; libration
of, n8. 169

Moors, 52

Morse, 289

Motion, Aristotle's theory of, 29,
30, 105 ; Newton's Laws of, 123,
"155. 156

Motor, electric, 264

Miiller, J , 68

Multiplier, Schweigger's, 205

Music, 51

Musschenbroek, P. van, 195

Mvdorge, Claude, 127

' Mysterium Cosmographicum \
82

Nautical Almanac, 88

Navigation, Kelvin's researches
in, 294 et seq.

Nestorians, 52

Newton, Sir L, 6, 45, 85, 123, 138
et seq., 173, 177, 193," 197, 245,
301,30.^,310, 311, 312, 313; his
Law of gravitation, 154 et seq.,
311, 312; his Laws of motion,
123, 155, 156; his mathematical
researches, 163 et seq.; Newton's
^^ing^s, 151 ; his theory of light,
153

Nichomachus, 2^

Nicol prism, 268, 269

Nile flooding.s, 19

Nitrous-oxide, 215

Nollet, 195

Non-electrics, 106

Norman, R., loi

Novae, 1 11

' Novum organum ', 139

Numbers, gnomonic, 22 ; square,
22

Ocean Telegraphy, 288 et seq.

Oersted, H. C, i()8, 199, 203, 254,

257, 2.:;9, 260, 288

Ohm, G. S., 198, 233 et seq., 276

Ohm, the, 246, 280

Ohm's Law, 197, 236 et seq., 280

Oldenburgh, 150, 166, 167

Opera glass, 113

Optics, Alhazenon, 53 ; R. Bacon
on, 6=;, 66 ; Descartes on, 132,
133,145; Galileo on, 112 et seq. ;
Kepler on, 83, 84; Newton on,
14.^ et seq. ; Physical, 193 ; Pio-
lemy on, 50

'Opus Maius, Minus, and Ter-
tium ', 61

Oscillations, times of. 104

tr, evaluation of, 41

Padua, Universitv of, 70

Pappus, 34, 47, 5'i

Parabola, 24, 40, 108

' Paralipomena in Vitellionem '.

83

Paramagnetism, 269, 270
Paris Observatory, 140
Parkinson, 277
Pascal, B., 140, 179, 180
Paul III, Pooe, 76
Paul IV, Pope, ii8
Peel. Sir R., 272
Pelletier, 7

Pendulum, 104, 151, 152
Pepys, 8., 169
Peregrinus, Peter, 100, 102
Peripatetic School, 26 et seq., 47,

10:;, 106, III, US, 118, 138, 162
Petty, Sir VV., 177, 178
Philip of Macedon, 26
Philoiaus, 24
Phlogiston, 194, 21Q
Physicians, Royal College of, 96,

97
Pi card, 160
Pile, voltaic, 98
Pisa, leaning tower, experiment,

106
Planetary motion, laws of, 87, 8g

et seq., 154 et seq.
Plato, 7, 23, 24, 2^=^, 26, 30, 3.S, 37,

.so, 5«;, i.H

Plato's Academy, 23, 27
Plin}-, 51, 53

Poggendorf, 238, 242, 245
Polarity, magnetic, 98, loi
Polariz d light, 194, 267 et seq.
Porta, Giovaimi B., 98
Posidonius, 50
Priestley. 195
'Principia', Newton's, i^S- 162,

168,193
Principle of Continuity, 84, 85
Prism, Nicol, 268, 269
Proclus, 24, 34, 37
Projectile, path of, 107, 108
Proof by exhaustion, 35, 37
Proxenus of Atarneus, 25
Ptolemaic System, 47 etseq., 72,

110
Ptolemy, Claude, 34, 46 et seq.,

68, 73. 74, 91
Ptolemy, Lagus, 33, 34
Ptolemy. Philadelphus, 34
I'ulsilogiuin, 104
Pump, invention of, 181, 182
I'urbach, 68
Pythagoras and his followers, 21,

22, 23, 34, 72, 73; theorem of,

21. 22, 37
Pythias, 26, 28

Quadrant electrometer, 279, 2S0
Radio-activity, 308
Rainbow, 133, 137
Raleigh, Sir \V., 174
Ramsay. Sir W., 308
Ranelagh, Lady, 177
Reaumur, 195
Recombination of light, 147

320

Refraction, atmosphpric, 50; of

light. 50, 83, 132, 146
Regiomuntanus, 68, 69
Regnault, 27J
Relativity 3ioetseq.
Resistance, electrical, 237, 238
Revi\ al of scientific inquiry, 67
Rheticus, 71. 78
Ricci, O . 104, 180
Rich. Edmund, 58
Riess, Prof., 281
Rings, Newton's, 151 ; Saturn's,

I '7. '52
Roge' Bacon, 52etseq., 112; his

scientific prophecies, 03
Rontgen, 308
Rotation ot plane of polarization,

269
Rotation of sun, 116
Rousseau, J. J., 201
Royal Acadt-my of Sciences, 139
Royal College of Physicians, 90,

97
Royal Institution, 216, 217, 220,

223, 251, 252, 253, 254, 256, 257,

273
Royal Society, 139, 150, 160, 161,

166, 167, 170, 172. ijCf et seq.,

igi. iq8. 2:^0, 2|5, 267, 271
Rudolph II 82. (SO
Rudolphine Tables, 83, 87
Rumfoid, Count, 215, 216, 219 et

seq , 284

Russell, A., 278, 301
Rutherford, 308, 309, 310
Safety lamps. 227 et seq.
Sagredus, J. F., 96
Sanderson, G., ig3
Saturn's Rings, 1 17, 152
Schemer, 1 16
Schleiden, 8
Schott, Kaspar, 182
Schwann, 8

Schweigger, 205, 238, 242, 244
Schweigger's multiplier, 205
Screw ot Aichimedes, 44
Sea-depth recorder, 294, 29^
Seebeck, T. J., 238
Seneca, 51

Serirs, mathematical, 40
Sdvester II, 54
Simpson, 1., "193
Simson, R., 193
Siphon-fountain, 50
Siphon recorder, 291, 292
Siren, the, 245

Index

Sizzi, 115

Sneli's Law of refraction, 83, 132

Socrates, 23

Soddy, 308

Solareclipse, first prediction of, 2i

Solenoid, theory of, 206, 259

Sound, 23, 152, 245

Sounding ma\jhine, 294, 295

Specific inductive capacity, 266

Spectrum analysis, 8, 145, 146

Sp-ed of light, 153, 154

Speusippus, 26

Spherical aberration, 145

Spiral of Archimedes, 41

Square numbers, 22

Squaring the circle, 35, 36

Stahl, G. E., 21Q

Stars, variability of, 29. in

State, change of physical, 168

Statical electricity, 264, 279 et

seq.
Statics, Archimedes on, 41
'Stereometria ', Kepler's, 85
Stevenson, G., 229
Stevinus, io8
Strabo, 51
Stukelev, Dr., 171
Sun, rotation of, 116; spots, 29,

1 16
Syrians, 52
System, Copernican, 71 et seq.,

88, 102, no, 112, 118; Ptolemaic,

47 et seq., 72, no
Tatum, Mr, 250, 253
Telegraph}', 207; ocean, 288 et

seq ; wireless, 281, 282, 283
Telephony, wireless, 306
Telescope, 79, 83, 84, n2etseq.,

145. '4Q
Temporary stars, in
Terrella, loi

Thales of ]Miletus, 21, 35, 99
Theatetus, 35
Theodolite, 50
Theon of Alexandria, 51
Thermo-circuit, 238
Thermodynamics, 284 et seq.;

absolute scale of temperature,

287 et seq.
Thermometry, 109, 168, 286etseq.
Thompson, B., 215, 216, 219 et

seq.
Thompson, Sylvanus P , 102
Thomson, J., 274, 275, 277
Thomson, J. J., 308
Tides, 50

' Timaeus '. Plato's, 55
Time, measurement of, 104
Timon of Athens, 24
Todhunter, 279
Tonkin, J , 212, 213, 214
Torricelli, E, 139. 140, 179, 180
Torsion bal nee, 197
Trigonometry, C pernicus "n, 7J
Tycho Brahe, 78, 82, 83, 87, 89,

i.';4
T yndall, J., 248, 256, 272, 273
Ubaldi G., 105

Unduiatory theory, i52etseq., 194
Universe, Kepler's early theors

of, 81

Universities, beginning of, ^4
Urban VIII. Pope, 119
Vacuum, Aristotle on, 30, 179:

Boyle on, 185 ; Davy on, 223

Galileo on, 179
Van't Hoff, 310
Vesalius, 6
Vienna Universit}^ 68
Virchow, 8
V.tello, 83
Viviani. 139
Volt, absolute determination o

279, 280
Volta. A., 198, 233
Voltaic pile, 198
Voltaire, 162
Voltameter, 264

Vortex theory, 129 et seq., 136, 13'
Wallis, Dr., 177
Ward, Seth., 177
Waring, 193
Water-clock, 50
Watzelrode, L., 69, 70
Wave theory of light, 152 et seq.

194, 310
Waves, electro-magnetic, 28

310, 3"
Wheatstone, 244, 289
Wilkins, Dr., 177
Wireless telegraphy, 281, 28:

283 ; telephony, 306 «

Wollaston, 7, 194, 254, 257, 25^

281
Wotton, Sir H., 87
Wren, Sir C., 161, 162, 177
WVight Brothers, 306
X-rays, 308
Xenocrates, 26
Young, T., 10, 193, 216, 218, 223,

229
Zeeman, 311

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