Pioneers of Science
by Sir Oliver Lodge · English · Gutenberg #28613 · 675,779 chars · public domain (US)
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Title: Pioneers of Science
Author: Sir Oliver Lodge
Release date: April 26, 2009 [eBook #28613]
Language: English
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Transcriber's Note
The punctuation and spelling from the original text have been faithfully
preserved. Only obvious typographical errors have been corrected.
There are several mathematical formulas within the text. They are
represented as follows:
Superscripts: x^3
Subscripts: x_3
Square Root: [square root] Greek Letters: [pi], [theta].
Greek star names are represented as [alpha], [gamma], for example.
PIONEERS OF SCIENCE
[Illustration]
[Illustration: NEWTON
_From the picture by Kneller, 1689, now at Cambridge_]
PIONEERS OF SCIENCE
BY
OLIVER LODGE, F.R.S.
PROFESSOR OF PHYSICS IN VICTORIA UNIVERSITY COLLEGE, LIVERPOOL
_WITH PORTRAITS AND OTHER ILLUSTRATIONS_
London
MACMILLAN AND CO.
AND NEW YORK
1893
RICHARD CLAY AND SONS, LIMITED,
LONDON AND BUNGAY.
PREFACE
This book takes its origin in a course of lectures on the history and
progress of Astronomy arranged for me in the year 1887 by three of my
colleagues (A.C.B., J.M., G.H.R.), one of whom gave the course its name.
The lectures having been found interesting, it was natural to write them
out in full and publish.
If I may claim for them any merit, I should say it consists in their
simple statement and explanation of scientific facts and laws. The
biographical details are compiled from all readily available sources,
there is no novelty or originality about them; though it is hoped that
there may be some vividness. I have simply tried to present a living
figure of each Pioneer in turn, and to trace his influence on the
progress of thought.
I am indebted to many biographers and writers, among others to Mr.
E.J.C. Morton, whose excellent set of lives published by the S.P.C.K.
saved me much trouble in the early part of the course.
As we approach recent times the subject grows more complex, and the men
more nearly contemporaries; hence the biographical aspect diminishes and
the scientific treatment becomes fuller, but in no case has it been
allowed to become technical and generally unreadable.
To the friends (C.C.C., F.W.H.M., E.F.R.) who with great kindness have
revised the proofs, and have indicated places where the facts could be
made more readily intelligible by a clearer statement, I express my
genuine gratitude.
UNIVERSITY COLLEGE, LIVERPOOL,
_November, 1892_.
CONTENTS
_PART I_
LECTURE I
PAGE
COPERNICUS AND THE MOTION OF THE EARTH 2
LECTURE II
TYCHO BRAHÉ AND THE EARLIEST OBSERVATORY 32
LECTURE III
KEPLER AND THE LAWS OF PLANETARY MOTION 56
LECTURE IV
GALILEO AND THE INVENTION OF THE TELESCOPE 80
LECTURE V
GALILEO AND THE INQUISITION 108
LECTURE VI
DESCARTES AND HIS THEORY OF VORTICES 136
LECTURE VII
SIR ISAAC NEWTON 159
LECTURE VIII
NEWTON AND THE LAW OF GRAVITATION 180
LECTURE IX
NEWTON'S "PRINCIPIA" 203
_PART II_
LECTURE X
ROEMER AND BRADLEY AND THE VELOCITY OF LIGHT 232
LECTURE XI
LAGRANGE AND LAPLACE--THE STABILITY OF THE SOLAR SYSTEM,
AND THE NEBULAR HYPOTHESIS 254
LECTURE XII
HERSCHEL AND THE MOTION OF THE FIXED STARS 273
LECTURE XIII
THE DISCOVERY OF THE ASTEROIDS 294
LECTURE XIV
BESSEL--THE DISTANCES OF THE STARS, AND THE DISCOVERY OF
STELLAR PLANETS 304
LECTURE XV
THE DISCOVERY OF NEPTUNE 317
LECTURE XVI
COMETS AND METEORS 331
LECTURE XVII
THE TIDES 353
LECTURE XVIII
THE TIDES, AND PLANETARY EVOLUTION 379
ILLUSTRATIONS
FIG. PAGE
1. ARCHIMEDES 8
2. LEONARDO DA VINCI 10
3. COPERNICUS 12
4. HOMERIC COSMOGONY 15
5. EGYPTIAN SYMBOL OF THE UNIVERSE 16
6. HINDOO EARTH 17
7. ORDER OF ANCIENT PLANETS CORRESPONDING TO THE DAYS OF
THE WEEK 19
8. PTOLEMAIC SYSTEM 20
9. SPECIMENS OF APPARENT PATHS OF VENUS AND OF MARS
AMONG THE STARS 21
10. APPARENT EPICYCLIC ORBITS OF JUPITER AND SATURN 22
11. EGYPTIAN SYSTEM 24
12. TRUE ORBITS OF EARTH AND JUPITER 25
13. ORBITS OF MERCURY AND EARTH 25
14. COPERNICAN SYSTEM AS FREQUENTLY REPRESENTED 26
15. SLOW MOVEMENT OF THE NORTH POLE IN A CIRCLE AMONG
THE STARS 29
16. TYCHONIC SYSTEM, SHOWING THE SUN WITH ALL THE PLANETS
REVOLVING ROUND THE EARTH 38
17. PORTRAIT OF TYCHO 41
18. EARLY OUT-DOOR QUADRANT OF TYCHO 43
19. MAP OF DENMARK, SHOWING THE ISLAND OF HUEN 45
20. URANIBURG 46
21. ASTROLABE 47
22. TYCHO'S LARGE SEXTANT 48
23. THE QUADRANT IN URANIBURG 49
24. TYCHO'S FORM OF TRANSIT CIRCLE 50
25. A MODERN TRANSIT CIRCLE 51
26. ORBITS OF SOME OF THE PLANETS DRAWN TO SCALE 60
27. MANY-SIDED POLYGON OR APPROXIMATE CIRCLE ENVELOPED
BY STRAIGHT LINES 61
28. KEPLER'S IDEA OF THE REGULAR SOLIDS 62
29. DIAGRAM OF EQUANT 67
30. EXCENTRIC CIRCLE SUPPOSED TO BE DIVIDED INTO EQUAL AREAS 68
31. MODE OF DRAWING AN ELLIPSE 70
32. KEPLER'S DIAGRAM PROVING EQUABLE DESCRIPTION OF AREAS
FOR AN ELLIPSE 71
33. DIAGRAM OF A PLANET'S VELOCITY IN DIFFERENT PARTS OF ITS ORBIT 72
34. PORTRAIT OF KEPLER 76
35. CURVE DESCRIBED BY A PROJECTILE 82
36. TWO FORMS OF PULSILOGY 87
37. TOWER OF PISA 91
38. VIEW OF THE HALF-MOON IN SMALL TELESCOPE 97
39. PORTION OF THE LUNAR SURFACE MORE HIGHLY MAGNIFIED 98
40. ANOTHER PORTION OF THE LUNAR SURFACE 99
41. LUNAR LANDSCAPE SHOWING EARTH 100
42. GALILEO'S METHOD OF ESTIMATING THE HEIGHT OF LUNAR MOUNTAIN 101
43. SOME CLUSTERS AND NEBULÆ 102
44. STAGES OF THE DISCOVERY OF JUPITER'S SATELLITES 103
45. ECLIPSES OF JUPITER'S SATELLITES 105
46. OLD DRAWINGS OF SATURN BY DIFFERENT OBSERVERS, WITH
THE IMPERFECT INSTRUMENTS OF THAT DAY 111
47. PHASES OF VENUS 112
48. SUNSPOTS AS SEEN WITH LOW POWER 113
49. A PORTION OF THE SUN'S DISK AS SEEN IN A POWERFUL MODERN
TELESCOPE 114
50. SATURN AND HIS RINGS 115
51. MAP OF ITALY 118
52. PORTRAIT OF GALILEO 126
53. PORTRAIT OF DESCARTES 148
54. DESCARTES'S EYE DIAGRAM 151
55. DESCARTES'S DIAGRAM OF VORTICES FROM HIS "PRINCIPIA" 152
56. MANOR-HOUSE OF WOOLSTHORPE 162
57. PROJECTILE DIAGRAM 170
58. } { 171
59. } DIAGRAMS ILLUSTRATIVE OF THOSE NEAR THE BEGINNING { 174
60. } OF NEWTON'S "PRINCIPIA" { 175
61-2. } { 175
63. PRISMATIC DISPERSION 182
64. A SINGLE CONSTITUENT OF WHITE LIGHT IS CAPABLE OF NO
MORE DISPERSION 183
65. PARALLEL BEAM PASSING THROUGH A LENS 184
66. NEWTON'S TELESCOPE 186
67. THE SEXTANT, AS NOW MADE 187
68. NEWTON WHEN YOUNG 196
69. SIR ISAAC NEWTON 200
70. ANOTHER "PRINCIPIA" DIAGRAM 207
71. WELL-KNOWN MODEL EXHIBITING THE OBLATE SPHEROIDAL
FORM AS A CONSEQUENCE OF SPINNING ABOUT A CENTRAL
AXIS 219
72. JUPITER 221
73. DIAGRAM OF EYE LOOKING AT A LIGHT REFLECTED IN A DISTANT
MIRROR THROUGH THE TEETH OF A REVOLVING WHEEL 238
74. FIZEAU'S WHEEL, SHOWING THE APPEARANCE OF DISTANT
IMAGE SEEN THROUGH ITS TEETH 239
75. ECLIPSES OF ONE OF JUPITER'S SATELLITES 241
76. A TRANSIT INSTRUMENT FOR THE BRITISH ASTRONOMICAL EXPEDITION,
1874 243
77. DIAGRAM OF EQUATORIALLY MOUNTED TELESCOPE 245
78. ABERRATION DIAGRAM 250
79. SHOWING THE THREE CONJUNCTION PLACES IN THE ORBITS OF
JUPITER AND SATURN 259
80. LORD ROSSE'S DRAWING OF THE SPIRAL NEBULA IN CANES
VENATICI 269
81. SATURN 271
82. PRINCIPLE OF NEWTONIAN REFLECTOR 278
83. HERSCHEL'S 40-FOOT TELESCOPE 283
84. WILLIAM HERSCHEL 285
85. CAROLINE HERSCHEL 287
86. DOUBLE STARS 288
87. OLD DRAWING OF THE CLUSTER IN HERCULES 290
88. OLD DRAWING OF THE ANDROMEDA NEBULA 291
89. THE GREAT NEBULA IN ORION 292
90. PLANETARY ORBITS TO SCALE 297
91. DIAGRAM ILLUSTRATING PARALLAX 307
92. THE KÖNIGSBERG HELIOMETER 312
93. PERTURBATIONS OF URANUS 320
94. URANUS' AND NEPTUNE'S RELATIVE POSITIONS 325
95. METEORITE 333
96. METEOR STREAM CROSSING FIELD OF TELESCOPE 334
97. DIAGRAM OF DIRECTION OF EARTH'S ORBITAL MOTION 335
98. PARABOLIC AND ELLIPTIC ORBITS 340
99. ORBIT OF HALLEY'S COMET 341
100. VARIOUS APPEARANCES OF HALLEY'S COMET WHEN LAST SEEN 342
101. HEAD OF DONATI'S COMET OF 1858 343
102. COMET 344
103. ENCKE'S COMET 345
104. BIELA'S COMET AS LAST SEEN IN TWO PORTIONS 346
105. RADIANT POINT PERSPECTIVE 348
106. PRESENT ORBIT OF NOVEMBER METEORS 349
107. ORBIT OF NOVEMBER METEORS BEFORE AND AFTER ENCOUNTER
WITH URANUS 351
108. THE MERSEY 355
109. CO-TIDAL LINES, SHOWING THE WAY THE TIDAL WAVE
REACHES THE BRITISH ISLES FROM THE ATLANTIC 359
110. WHIRLING EARTH MODEL 364
111. EARTH AND MOON MODEL 365
112. EARTH AND MOON (EARTH'S ROTATION NEGLECTED) 366
113. MAPS SHOWING HOW COMPARATIVELY FREE FROM LAND OBSTRUCTION
THE OCEAN IN THE SOUTHERN HEMISPHERE IS 369
114. SPRING AND NEAP TIDES 370
115. TIDAL CLOCK 371
116. SIR WILLIAM THOMSON (LORD KELVIN) 373
117. TIDE-GAUGE FOR RECORDING LOCAL TIDES 375
118. HARMONIC ANALYZER 375
119. TIDE-PREDICTER 376
120. WEEKLY SHEET OF CURVES 377
PIONEERS OF SCIENCE
PART I
_FROM DUSK TO DAYLIGHT_
DATES AND SUMMARY OF FACTS FOR LECTURE I
_Physical Science of the Ancients._ Thales 640 B.C., Anaximander 610
B.C., PYTHAGORAS 600 B.C., Anaxagoras 500 B.C., Eudoxus 400 B.C.,
ARISTOTLE 384 B.C., Aristarchus 300 B.C., ARCHIMEDES 287 B.C.,
Eratosthenes 276 B.C., HIPPARCHUS 160 B.C., Ptolemy 100 A.D.
_Science of the Middle Ages._ Cultivated only among the Arabs; largely
in the forms of astrology, alchemy, and algebra.
_Return of Science to Europe._ Roger Bacon 1240, Leonardo da Vinci 1480,
(Printing 1455), Columbus 1492, Copernicus 1543.
_A sketch of Copernik's life and work._ Born 1473 at Thorn in Poland.
Studied mathematics at Bologna. Became an ecclesiastic. Lived at
Frauenburg near mouth of Vistula. Substituted for the apparent motion of
the heavens the real motion of the earth. Published tables of planetary
motions. Motion still supposed to be in epicycles. Worked out his ideas
for 36 years, and finally dedicated his work to the Pope. Died just as
his book was printed, aged 72, a century before the birth of Newton. A
colossal statue by Thorwaldsen erected at Warsaw in 1830.
PIONEERS OF SCIENCE
LECTURE I
COPERNICUS AND THE MOTION OF THE EARTH
The ordinary run of men live among phenomena of which they know nothing
and care less. They see bodies fall to the earth, they hear sounds, they
kindle fires, they see the heavens roll above them, but of the causes
and inner working of the whole they are ignorant, and with their
ignorance they are content.
"Understand the structure of a soap-bubble?" said a cultivated literary
man whom I know; "I wouldn't cross the street to know it!"
And if this is a prevalent attitude now, what must have been the
attitude in ancient times, when mankind was emerging from savagery, and
when history seems composed of harassments by wars abroad and
revolutions at home? In the most violently disturbed times indeed, those
with which ordinary history is mainly occupied, science is quite
impossible. It needs as its condition, in order to flourish, a fairly
quiet, untroubled state, or else a cloister or university removed from
the din and bustle of the political and commercial world. In such places
it has taken its rise, and in such peaceful places and quiet times true
science will continue to be cultivated.
The great bulk of mankind must always remain, I suppose, more or less
careless of scientific research and scientific result, except in so far
as it affects their modes of locomotion, their health and pleasure, or
their purse.
But among a people hurried and busy and preoccupied, some in the pursuit
of riches, some in the pursuit of pleasure, and some, the majority, in
the struggle for existence, there arise in every generation, here and
there, one or two great souls--men who seem of another age and country,
who look upon the bustle and feverish activity and are not infected by
it, who watch others achieving prizes of riches and pleasure and are not
disturbed, who look on the world and the universe they are born in with
quite other eyes. To them it appears not as a bazaar to buy and to sell
in; not as a ladder to scramble up (or down) helter-skelter without
knowing whither or why; but as a fact--a great and mysterious fact--to
be pondered over, studied, and perchance in some small measure
understood. By the multitude these men were sneered at as eccentric or
feared as supernatural. Their calm, clear, contemplative attitude seemed
either insane or diabolic; and accordingly they have been pitied as
enthusiasts or killed as blasphemers. One of these great souls may have
been a prophet or preacher, and have called to his generation to bethink
them of why and what they were, to struggle less and meditate more, to
search for things of true value and not for dross. Another has been a
poet or musician, and has uttered in words or in song thoughts dimly
possible to many men, but by them unutterable and left inarticulate.
Another has been influenced still more _directly_ by the universe around
him, has felt at times overpowered by the mystery and solemnity of it
all, and has been impelled by a force stronger than himself to study it,
patiently, slowly, diligently; content if he could gather a few crumbs
of the great harvest of knowledge, happy if he could grasp some great
generalization or wide-embracing law, and so in some small measure enter
into the mind and thought of the Designer of all this wondrous frame of
things.
These last have been the men of science, the great and heaven-born men
of science; and they are few. In our own day, amid the throng of
inventions, there are a multitude of small men using the name of science
but working for their own ends, jostling and scrambling just as they
would jostle and scramble in any other trade or profession. These may be
workers, they may and do advance knowledge, but they are never pioneers.
Not to them is it given to open out great tracts of unexplored
territory, or to view the promised land as from a mountain-top. Of them
we shall not speak; we will concern ourselves only with the greatest,
the epoch-making men, to whose life and work we and all who come after
them owe so much. Such a man was Thales. Such was Archimedes,
Hipparchus, Copernicus. Such pre-eminently was Newton.
Now I am not going to attempt a history of science. Such a work in ten
lectures would be absurd. I intend to pick out a few salient names here
and there, and to study these in some detail, rather than by attempting
to deal with too many to lose individuality and distinctness.
We know so little of the great names of antiquity, that they are for
this purpose scarcely suitable. In some departments the science of the
Greeks was remarkable, though it is completely overshadowed by their
philosophy; yet it was largely based on what has proved to be a wrong
method of procedure, viz the introspective and conjectural, rather than
the inductive and experimental methods. They investigated Nature by
studying their own minds, by considering the meanings of words, rather
than by studying things and recording phenomena. This wrong (though by
no means, on the face of it, absurd) method was not pursued exclusively,
else would their science have been valueless, but the influence it had
was such as materially to detract from the value of their speculations
and discoveries. For when truth and falsehood are inextricably woven
into a statement, the truth is as hopelessly hidden as if it had never
been stated, for we have no criterion to distinguish the false from the
true.
[Illustration: FIG. 1.--Archimedes.]
Besides this, however, many of their discoveries were ultimately lost to
the world, some, as at Alexandria, by fire--the bigoted work of a
Mohammedan conqueror--some by irruption of barbarians; and all were
buried so long and so completely by the night of the dark ages, that
they had to be rediscovered almost as absolutely and completely as
though they had never been. Some of the names of antiquity we shall have
occasion to refer to; so I have arranged some of them in chronological
order on page 4, and as a representative one I may specially emphasize
Archimedes, one of the greatest men of science there has ever been, and
the father of physics.
The only effective link between the old and the new science is afforded
by the Arabs. The dark ages come as an utter gap in the scientific
history of Europe, and for more than a thousand years there was not a
scientific man of note except in Arabia; and with the Arabs knowledge
was so mixed up with magic and enchantment that one cannot contemplate
it with any degree of satisfaction, and little real progress was made.
In some of the _Waverley Novels_ you can realize the state of matters in
these times; and you know how the only approach to science is through
some Arab sorcerer or astrologer, maintained usually by a monarch, and
consulted upon all great occasions, as the oracles were of old.
In the thirteenth century, however, a really great scientific man
appeared, who may be said to herald the dawn of modern science in
Europe. This man was Roger Bacon. He cannot be said to do more than
herald it, however, for we must wait two hundred years for the next name
of great magnitude; moreover he was isolated, and so far in advance of
his time that he left no followers. His own work suffered from the
prevailing ignorance, for he was persecuted and imprisoned, not for the
commonplace and natural reason that he frightened the Church, but merely
because he was eccentric in his habits and knew too much.
The man I spoke of as coming two hundred years later is Leonardo da
Vinci. True he is best known as an artist, but if you read his works you
will come to the conclusion that he was the most scientific artist who
ever lived. He teaches the laws of perspective (then new), of light and
shade, of colour, of the equilibrium of bodies, and of a multitude of
other matters where science touches on art--not always quite correctly
according to modern ideas, but in beautiful and precise language. For
clear and conscious power, for wide-embracing knowledge and skill,
Leonardo is one of the most remarkable men that ever lived.
About this time the tremendous invention of printing was achieved, and
Columbus unwittingly discovered the New World. The middle of the next
century must be taken as the real dawn of modern science; for the year
1543 marks the publication of the life-work of Copernicus.
[Illustration: FIG. 2.--Leonardo da Vinci.]
Nicolas Copernik was his proper name. Copernicus is merely the Latinized
form of it, according to the then prevailing fashion. He was born at
Thorn, in Polish Prussia, in 1473. His father is believed to have been a
German. He graduated at Cracow as doctor in arts and medicine, and was
destined for the ecclesiastical profession. The details of his life are
few; it seems to have been quiet and uneventful, and we know very little
about it. He was instructed in astronomy at Cracow, and learnt
mathematics at Bologna. Thence he went to Rome, where he was made
Professor of Mathematics; and soon afterwards he went into orders. On
his return home, he took charge of the principal church in his native
place, and became a canon. At Frauenburg, near the mouth of the Vistula,
he lived the remainder of his life. We find him reporting on coinage for
the Government, but otherwise he does not appear as having entered into
the life of the times.
He was a quiet, scholarly monk of studious habits, and with a reputation
which drew to him several earnest students, who received _vivâ voce_
instruction from him; so, in study and meditation, his life passed.
He compiled tables of the planetary motions which were far more correct
than any which had hitherto appeared, and which remained serviceable for
long afterwards. The Ptolemaic system of the heavens, which had been the
orthodox system all through the Christian era, he endeavoured to improve
and simplify by the hypothesis that the sun was the centre of the system
instead of the earth; and the first consequences of this change he
worked out for many years, producing in the end a great book: his one
life-work. This famous work, "De Revolutionibus Orbium Coelestium,"
embodied all his painstaking calculations, applied his new system to
each of the bodies in the solar system in succession, and treated
besides of much other recondite matter. Towards the close of his life it
was put into type. He can scarcely be said to have lived to see it
appear, for he was stricken with paralysis before its completion; but a
printed copy was brought to his bedside and put into his hands, so that
he might just feel it before he died.
[Illustration: FIG. 3.--Copernicus.]
That Copernicus was a giant in intellect or power--such as had lived in
the past, and were destined to live in the near future--I see no reason
whatever to believe. He was just a quiet, earnest, patient, and
God-fearing man, a deep student, an unbiassed thinker, although with no
specially brilliant or striking gifts; yet to him it was given to effect
such a revolution in the whole course of man's thoughts as is difficult
to parallel.
You know what the outcome of his work was. It proved--he did not merely
speculate, he proved--that the earth is a planet like the others, and
that it revolves round the sun.
Yes, it can be summed up in a sentence, but what a revelation it
contains. If you have never made an effort to grasp the full
significance of this discovery you will not appreciate it. The doctrine
is very familiar to us now, we have heard it, I suppose, since we were
four years old, but can you realize it? I know it was a long time before
I could. Think of the solid earth, with trees and houses, cities and
countries, mountains and seas--think of the vast tracts of land in Asia,
Africa, and America--and then picture the whole mass spinning like a
top, and rushing along its annual course round the sun at the rate of
nineteen miles every second.
Were we not accustomed to it, the idea would be staggering. No wonder it
was received with incredulity. But the difficulties of the conception
are not only physical, they are still more felt from the speculative and
theological points of view. With this last, indeed, the reconcilement
cannot be considered complete even yet. Theologians do not, indeed, now
_deny_ the fact of the earth's subordination in the scheme of the
universe, but many of them ignore it and pass it by. So soon as the
Church awoke to a perception of the tremendous and revolutionary import
of the new doctrines, it was bound to resist them or be false to its
traditions. For the whole tenor of men's thought must have been changed
had they accepted it. If the earth were not the central and
all-important body in the universe, if the sun and planets and stars
were not attendant and subsidiary lights, but were other worlds larger
and perhaps superior to ours, where was man's place in the universe?
and where were the doctrines they had maintained as irrefragable? I by
no means assert that the new doctrines were really utterly
irreconcilable with the more essential parts of the old dogmas, if only
theologians had had patience and genius enough to consider the matter
calmly. I suppose that in that case they might have reached the amount
of reconciliation at present attained, and not only have left scientific
truth in peace to spread as it could, but might perhaps themselves have
joined the band of earnest students and workers, as so many of the
higher Catholic clergy do at the present day.
But this was too much to expect. Such a revelation was not to be
accepted in a day or in a century--the easiest plan was to treat it as a
heresy, and try to crush it out.
Not in Copernik's life, however, did they perceive the dangerous
tendency of the doctrine--partly because it was buried in a ponderous
and learned treatise not likely to be easily understood; partly,
perhaps, because its propounder was himself an ecclesiastic; mainly
because he was a patient and judicious man, not given to loud or
intolerant assertion, but content to state his views in quiet
conversation, and to let them gently spread for thirty years before he
published them. And, when he did publish them, he used the happy device
of dedicating his great book to the Pope, and a cardinal bore the
expense of printing it. Thus did the Roman Church stand sponsor to a
system of truth against which it was destined in the next century to
hurl its anathemas, and to inflict on its conspicuous adherents torture,
imprisonment, and death.
To realize the change of thought, the utterly new view of the universe,
which the Copernican theory introduced, we must go back to preceding
ages, and try to recall the views which had been held as probable
concerning the form of the earth and the motion of the heavenly bodies.
[Illustration: FIG. 4.--Homeric Cosmogony.]
The earliest recorded notion of the earth is the very natural one that
it is a flat area floating in an illimitable ocean. The sun was a god
who drove his chariot across the heavens once a day; and Anaxagoras was
threatened with death and punished with banishment for teaching that the
sun was only a ball of fire, and that it might perhaps be as big as the
country of Greece. The obvious difficulty as to how the sun got back to
the east again every morning was got over--not by the conjecture that he
went back in the dark, nor by the idea that there was a fresh sun every
day; though, indeed, it was once believed that the moon was created once
a month, and periodically cut up into stars--but by the doctrine that in
the northern part of the earth was a high range of mountains, and that
the sun travelled round on the surface of the sea behind these.
Sometimes, indeed, you find a representation of the sun being rowed
round in a boat. Later on it was perceived to be necessary that the sun
should be able to travel beneath the earth, and so the earth was
supposed to be supported on pillars or on roots, or to be a dome-shaped
body floating in air--much like Dean Swift's island of Laputa. The
elephant and tortoise of the Hindu earth are, no doubt, emblematic or
typical, not literal.
[Illustration: FIG. 5.--Egyptian Symbol of the Universe.
The earth a figure with leaves, the heaven a figure with stars, the
principle of equilibrium and support, the boats of the rising and
setting sun.]
Aristotle, however, taught that the earth must be a sphere, and used all
the orthodox arguments of the present children's geography-books about
the way you see ships at sea, and about lunar eclipses.
To imagine a possible antipodes must, however, have been a tremendous
difficulty in the way of this conception of a sphere, and I scarcely
suppose that any one can at that time have contemplated the possibility
of such upside-down regions being inhabited. I find that intelligent
children invariably feel the greatest difficulty in realizing the
existence of inhabitants on the opposite side of the earth. Stupid
children, like stupid persons in general, will of course believe
anything they are told, and much good may the belief do them; but the
kind of difficulties felt by intelligent and thoughtful children are
most instructive, since it is quite certain that the early philosophers
must have encountered and overcome those very same difficulties by their
own genius.
[Illustration: FIG. 6.--Hindoo Earth.]
However, somehow or other the conception of a spherical earth was
gradually grasped, and the heavenly bodies were perceived all to revolve
round it: some moving regularly, as the stars, all fixed together into
one spherical shell or firmament; some moving irregularly and apparently
anomalously--these irregular bodies were therefore called planets [or
wanderers]. Seven of them were known, viz. Moon, Mercury, Venus, Sun,
Mars, Jupiter, Saturn, and there is little doubt that this number seven,
so suggested, is the origin of the seven days of the week.
The above order of the ancient planets is that of their supposed
distance from the earth. Not always, however, are they thus quoted
by the ancients: sometimes the sun is supposed nearer than Mercury
or Venus. It has always been known that the moon was the nearest of
the heavenly bodies; and some rough notion of its distance was
current. Mars, Jupiter, and Saturn were placed in that order
because that is the order of their apparent motions, and it was
natural to suppose that the slowest moving bodies were the furthest
off.
The order of the days of the week shows what astrologers considered
to be the order of the planets; on their system of each successive
hour of the day being ruled over by the successive planets taken in
order. The diagram (fig. 7) shows that if the Sun rule the first
hour of a certain day (thereby giving its name to the day) Venus
will rule the second hour, Mercury the third, and so on; the Sun
will thus be found to rule the eighth, fifteenth, and twenty-second
hour of that day, Venus the twenty-third, and Mercury the
twenty-fourth hour; so the Moon will rule the first hour of the
next day, which will therefore be Monday. On the same principle
(numbering round the hours successively, with the arrows) the first
hour of the next day will be found to be ruled by Mars, or by the
Saxon deity corresponding thereto; the first hour of the day after,
by Mercury (_Mercredi_), and so on (following the straight lines of
the pattern).
The order of the planets round the circle counter-clockwise, _i.e._
the direction of their proper motions, is that quoted above in the
text.
To explain the motion of the planets and reduce them to any sort of law
was a work of tremendous difficulty. The greatest astronomer of ancient
times was Hipparchus, and to him the system known as the Ptolemaic
system is no doubt largely due. But it was delivered to the world mainly
by Ptolemy, and goes by his name. This was a fine piece of work, and a
great advance on anything that had gone before; for although it is of
course saturated with error, still it is based on a large substratum of
truth. Its superiority to all the previously mentioned systems is
obvious. And it really did in its more developed form describe the
observed motions of the planets.
Each planet was, in the early stages of this system, as taught, say, by
Eudoxus, supposed to be set in a crystal sphere, which revolved so as to
carry the planet with it. The sphere had to be of crystal to account for
the visibility of other planets and the stars through it. Outside the
seven planetary spheres, arranged one inside the other, was a still
larger one in which were set the stars. This was believed to turn all
the others, and was called the _primum mobile_. The whole system was
supposed to produce, in its revolution, for the few privileged to hear
the music of the spheres, a sound as of some magnificent harmony.
[Illustration: FIG. 7.--Order of ancient planets corresponding to the
days of the week.]
The enthusiastic disciples of Pythagoras believed that their master was
privileged to hear this noble chant; and far be it from us to doubt
that the rapt and absorbing pleasure of contemplating the harmony of
nature, to a man so eminently great as Pythagoras, must be truly and
adequately represented by some such poetic conception.
[Illustration: FIG. 8.--Ptolemaic system.]
The precise kind of motion supposed to be communicated from the _primum
mobile_ to the other spheres so as to produce the observed motions of
the planets was modified and improved by various philosophers until it
developed into the epicyclic train of Hipparchus and of Ptolemy.
It is very instructive to observe a planet (say Mars or Jupiter) night
after night and plot down its place with reference to the fixed stars
on a celestial globe or star-map. Or, instead of direct observation by
alignment with known stars, it is easier to look out its right ascension
and declination in _Whitaker's Almanac_, and plot those down. If this be
done for a year or two, it will be found that the motion of the planet
is by no means regular, but that though on the whole it advances it
sometimes is stationary and sometimes goes back.[1]
[Illustration: FIG. 9.--Specimens of Apparent paths of Venus and of Mars
among the stars.]
[Illustration: FIG. 10.--Apparent epicyclic orbits of Jupiter and
Saturn; the Earth being supposed fixed at the centre, with the Sun
revolving in a small circle. A loop is made by each planet every year.]
These "stations" and "retrogressions" of the planets were well known to
the ancients. It was not to be supposed for a moment that the crystal
spheres were subject to any irregularity, neither was uniform circular
motion to be readily abandoned; so it was surmised that the main sphere
carried, not the planet itself, but the centre or axis of a subordinate
sphere, and that the planet was carried by this. The minor sphere could
be allowed to revolve at a different uniform pace from the main sphere,
and so a curve of some complexity could be obtained.
A curve described in space by a point of a circle or sphere, which
itself is carried along at the same time, is some kind of cycloid; if
the centre of the tracing circle travels along a straight line, we get
the ordinary cycloid, the curve traced in air by a nail on a
coach-wheel; but if the centre of the tracing circle be carried round
another circle the curve described is called an epicycloid. By such
curves the planetary stations and retrogressions could be explained. A
large sphere would have to revolve once for a "year" of the particular
planet, carrying with it a subsidiary sphere in which the planet was
fixed; this latter sphere revolving once for a "year" of the earth. The
actual looped curve thus described is depicted for Jupiter and Saturn in
the annexed diagram (fig. 10.)
It was long ago perceived that real material spheres were
unnecessary; such spheres indeed, though possibly transparent to
light, would be impermeable to comets: any other epicyclic gearing
would serve, and as a mere description of the motion it is simpler
to think of a system of jointed bars, one long arm carrying a
shorter arm, the two revolving at different rates, and the end of
the short one carrying the planet. This does all that is needful
for the first approximation to a planet's motion. In so far as the
motion cannot be thus truly stated, the short arm may be supposed
to carry another, and that another, and so on, so that the
resultant motion of the planet is compounded of a large number of
circular motions of different periods; by this device any required
amount of complexity could be attained. We shall return to this at
greater length in Lecture III.
The main features of the motion, as shown in the diagram, required
only two arms for their expression; one arm revolving with the
average motion of the planet, and the other revolving with the
apparent motion of the sun, and always pointing in the same
direction as the single arm supposed to carry the sun. This last
fact is of course because the motion to be represented does not
really belong to the planet at all, but to the earth, and so all
the main epicyclic motions for the superior planets were the same.
As for the inferior planets (Mercury and Venus) they only appear
to oscillate like the bob of a pendulum about the sun, and so it is
very obvious that they must be really revolving round it. An
ancient Egyptian system perceived this truth; but the Ptolemaic
system imagined them to revolve round the earth like the rest, with
an artificial system of epicycles to prevent their ever getting far
away from the neighbourhood of the sun.
It is easy now to see how the Copernican system explains the main
features of planetary motion, the stations and retrogressions,
quite naturally and without any complexity.
[Illustration: FIG. 11.--Egyptian system.]
Let the outer circle represent the orbit of Jupiter, and the inner
circle the orbit of the earth, which is moving faster than Jupiter
(since Jupiter takes 4332 days to make one revolution); then
remember that the apparent position of Jupiter is referred to the
infinitely distant fixed stars and refer to fig. 12.
Let E_1, E_2, &c., be successive positions of the earth; J_1,
J_2, &c., corresponding positions of Jupiter. Produce the lines
E_1 J_1, E_2 J_2, &c., to an enormously greater circle
outside, and it will be seen that the termination of these lines,
representing apparent positions of Jupiter among the stars,
advances while the earth goes from E_1 to E_3; is almost
stationary from somewhere about E_3 to E_4; and recedes from
E_4 to E_5; so that evidently the recessions of Jupiter are
only apparent, and are due to the orbital motion of the earth. The
apparent complications in the path of Jupiter, shown in Fig. 10,
are seen to be caused simply by the motion of the earth, and to be
thus completely and easily explained.
[Illustration: FIG. 12.--True orbits of Earth and Jupiter.]
The same thing for an inferior planet, say Mercury, is even still
more easily seen (_vide_ figure 13).
The motion of Mercury is direct from M'' to M''', retrograde from
M''' to M'', and stationary at M'' and M'''. It appears to
oscillate, taking 72·5 days for its direct swing, and 43·5 for its
return swing.
[Illustration: FIG. 13.--Orbit of Mercury and Earth.]
On this system no artificiality is required to prevent Mercury's
ever getting far from the sun: the radius of its orbit limits its
real and apparent excursions. Even if the earth were stationary,
the motions of Mercury and Venus would not be _essentially_
modified, but the stations and retrogressions of the superior
planets, Mars, Jupiter, &c., would wholly cease.
The complexity of the old mode of regarding apparent motion may be
illustrated by the case of a traveller in a railway train unaware
of his own motion. It is as though trees, hedges, distant objects,
were all flying past him and contorting themselves as you may see
the furrows of a ploughed field do when travelling, while you
yourself seem stationary amidst it all. How great a simplicity
would be introduced by the hypothesis that, after all, these things
might be stationary and one's self moving.
[Illustration: FIG. 14.--Copernican system as frequently represented.
But the cometary orbit is a much later addition, and no attempt is made
to show the relative distances of the planets.]
Now you are not to suppose that the system of Copernicus swept away the
entire doctrine of epicycles; that doctrine can hardly be said to be
swept away even now. As a description of a planet's motion it is not
incorrect, though it is geometrically cumbrous. If you describe the
motion of a railway train by stating that every point on the rim of each
wheel describes a cycloid with reference to the earth, and a circle with
reference to the train, and that the motion of the train is compounded
of these cycloidal and circular motions, you will not be saying what is
false, only what is cumbrous.
The Ptolemaic system demanded large epicycles, depending on the motion
of the earth, these are what Copernicus overthrew; but to express the
minuter details of the motion smaller epicycles remained, and grew more
and more complex as observations increased in accuracy, until a greater
man than either Copernicus or Ptolemy, viz. Kepler, replaced them all by
a simple ellipse.
One point I must not omit from this brief notice of the work of
Copernicus. Hipparchus had, by most sagacious interpretation of certain
observations of his, discovered a remarkable phenomenon called the
precession of the equinoxes. It was a discovery of the first magnitude,
and such as would raise to great fame the man who should have made it in
any period of the world's history, even the present. It is scarcely
expressible in popular language, and without some technical terms; but I
can try.
The plane of the earth's orbit produced into the sky gives the apparent
path of the sun throughout a year. This path is known as the ecliptic,
because eclipses only happen when the moon is in it. The sun keeps to it
accurately, but the planets wander somewhat above and below it (fig. 9),
and the moon wanders a good deal. It is manifest, however, in order that
there may be an eclipse of any kind, that a straight line must be able
to be drawn through earth and moon and sun (not necessarily through
their centres of course), and this is impossible unless some parts of
the three bodies are in one plane, viz. the ecliptic, or something very
near it. The ecliptic is a great circle of the sphere, and is usually
drawn on both celestial and terrestrial globes.
The earth's equator also produced into the sky, where it may still be
called the equator (sometimes it is awkwardly called "the equinoctial"),
gives another great circle inclined to the ecliptic and cutting it at
two opposite points, labelled respectively [Aries symbol] and [Libra
symbol], and together called "the equinoxes." The reason for the name is
that when the sun is in that part of the ecliptic it is temporarily also
on the equator, and hence is symmetrically situated with respect to the
earth's axis of rotation, and consequently day and night are equal all
over the earth.
Well, Hipparchus found, by plotting the position of the sun for a long
time,[2] that these points of intersection, or equinoxes, were not
stationary from century to century, but slowly moved among the stars,
moving as it were to meet the sun, so that he gets back to one of these
points again 20 minutes 23-1/4 seconds before it has really completed a
revolution, _i.e._ before the true year is fairly over. This slow
movement forward of the goal-post is called precession--the precession
of the equinoxes. (One result of it is to shorten our years by about 20
minutes each; for the shortened period has to be called a year, because
it is on the position of the sun with respect to the earth's axis that
our seasons depend.) Copernicus perceived that, assuming the motion of
the earth, a clearer account of this motion could be given. The ordinary
approximate statement concerning the earth's axis is that it remains
parallel to itself, _i.e._ has a fixed direction as the earth moves
round the sun. But if, instead of being thus fixed, it be supposed to
have a slow movement of revolution, so that it traces out a cone in the
course of about 26,000 years, then, since the equator of course goes
with it, the motion of its intersection with the fixed ecliptic is so
far accounted for. That is to say, the precession of the equinoxes is
seen to be dependent on, and caused by, a slow conical movement of the
earth's axis.
The prolongation of each end of the earth's axis into the sky, or the
celestial north and south poles, will thus slowly trace out an
approximate circle among the stars; and the course of the north pole
during historic time is exhibited in the annexed diagram.
It is now situated near one of the stars of the Lesser Bear, which we
therefore call the Pole star; but not always was it so, nor will it be
so in the future. The position of the north pole 4000 years ago is shown
in the figure; and a revolution will be completed in something like
26,000 years.[3]
[Illustration: FIG. 15.--Slow movement of the north pole in a circle
among the stars. (Copied from Sir R. Ball.)]
This perception of the conical motion of the earth's axis was a
beautiful generalization of Copernik's, whereby a multitude of facts
were grouped into a single phenomenon. Of course he did not explain the
motion of the axis itself. He stated the fact that it so moved, and I do
not suppose it ever struck him to seek for an explanation.
An explanation was given later, and that a most complete one; but the
idea even of seeking for it is a brilliant and striking one: the
achievement of the explanation by a single individual in the way it
actually was accomplished is one of the most astounding things in the
history of science; and were it not that the same individual
accomplished a dozen other things, equally and some still more
extraordinary, we should rank that man as one of the greatest
astronomers that ever lived.
As it is, he is Sir Isaac Newton.
We are to remember, then, as the life-work of Copernicus, that he placed
the sun in its true place as the centre of the solar system, instead of
the earth; that he greatly simplified the theory of planetary motion by
this step, and also by the simpler epicyclic chain which now sufficed,
and which he worked out mathematically; that he exhibited the precession
of the equinoxes (discovered by Hipparchus) as due to a conical motion
of the earth's axis; and that, by means of his simpler theory and more
exact planetary tables, he reduced to some sort of order the confused
chaos of the Ptolemaic system, whose accumulation of complexity and of
outstanding errors threatened to render astronomy impossible by the mere
burden of its detail.
There are many imperfections in his system, it is true; but his great
merit is that he dared to look at the facts of Nature with his own eyes,
unhampered by the prejudice of centuries. A system venerable with age,
and supported by great names, was universally believed, and had been
believed for centuries. To doubt this system, and to seek after another
and better one, at a time when all men's minds were governed by
tradition and authority, and when to doubt was sin--this required a
great mind and a high character. Such a mind and such a character had
this monk of Frauenburg. And it is interesting to notice that the
so-called religious scruples of smaller and less truly religious men did
not affect Copernicus; it was no dread of consequences to one form of
truth that led him to delay the publication of the other form of truth
specially revealed to him. In his dedication he says:--
"If there be some babblers who, though ignorant of all mathematics, take
upon them to judge of these things, and dare to blame and cavil at my
work, because of some passage of Scripture which they have wrested to
their own purpose, I regard them not, and will not scruple to hold their
judgment in contempt."
I will conclude with the words of one of his biographers (Mr. E.J.C.
Morton):--
"Copernicus cannot be said to have flooded with light the dark places of
nature--in the way that one stupendous mind subsequently did--but still,
as we look back through the long vista of the history of science, the
dim Titanic figure of the old monk seems to rear itself out of the dull
flats around it, pierces with its head the mists that overshadow them,
and catches the first gleam of the rising sun,
"'... like some iron peak, by the Creator
Fired with the red glow of the rushing morn.'"
DATES AND SUMMARY OF FACTS FOR LECTURE II
Copernicus lived from 1473 to 1543, and was contemporary with Paracelsus
and Raphael.
Tycho Brahé from 1546 to 1601.
Kepler from 1571 to 1630.
Galileo from 1564 to 1642.
Gilbert from 1540 to 1603.
Francis Bacon from 1561 to 1626.
Descartes from 1596 to 1650.
_A sketch of Tycho Brahé's life and work._ Tycho was a Danish noble,
born on his ancestral estate at Knudstorp, near Helsinborg, in 1546.
Adopted by his uncle, and sent to the University of Copenhagen to study
law. Attracted to astronomy by the occurrence of an eclipse on its
predicted day, August 21st, 1560. Began to construct astronomical
instruments, especially a quadrant and a sextant. Observed at Augsburg
and Wittenberg. Studied alchemy, but was recalled to astronomy by the
appearance of a new star. Overcame his aristocratic prejudices, and
delivered a course of lectures at Copenhagen, at the request of the
king. After this he married a peasant girl. Again travelled and observed
in Germany. In 1576 was sent for to Denmark by Frederick II., and
established in the island of Huen, with an endowment enabling him to
devote his life to astronomy. Built Uraniburg, furnished it with
splendid instruments, and became the founder of accurate instrumental
astronomy. His theories were poor, but his observations were admirable.
In 1592 Frederick died, and five years later, Tycho was impoverished and
practically banished. After wandering till 1599, he was invited to
Prague by the Emperor Rudolf, and there received John Kepler among other
pupils. But the sentence of exile was too severe, and he died in 1601,
aged 54 years.
A man of strong character, untiring energy, and devotion to accuracy,
his influence on astronomy has been immense.
LECTURE II
TYCHO BRAHÉ AND THE EARLIEST OBSERVATORY
We have seen how Copernicus placed the earth in its true position in the
solar system, making it merely one of a number of other worlds revolving
about a central luminary. And observe that there are two phenomena to be
thus accounted for and explained: first, the diurnal revolution of the
heavens; second, the annual motion of the sun among the stars.
The effect of the diurnal motion is conspicuous to every one, and
explains the rising, southing, and setting of the whole visible
firmament. The effect of the annual motion, _i.e._ of the apparent
annual motion, of the sun among the stars, is less obvious, but it may
be followed easily enough by observing the stars visible at any given
time of evening at different seasons of the year. At midnight, for
instance, the position of the sun is definite, viz. due north always,
but the constellation which at that time is due south or is rising or
setting varies with the time of year; an interval of one month producing
just the same effect on the appearance of the constellations as an
interval of two hours does (because the day contains twice as many hours
as the year contains months), _e.g._ the sky looks the same at midnight
on the 1st of October as it does at 10 p.m. on the 1st of November.
All these simple consequences of the geocentric as opposed to the
heliocentric point of view were pointed out by Copernicus, in addition
to his greater work of constructing improved planetary tables on the
basis of his theory. But it must be admitted that he himself felt the
hypothesis of the motion of the earth to be a difficulty. Its acceptance
is by no means such an easy and childish matter as we are apt now to
regard it, and the hostility to it is not at all surprising. The human
race, after having ridiculed and resisted the truth for a long time, is
apt to end in accepting it so blindly and unimaginatively as to fail to
recognize the real achievement of its first propounders, or the
difficulties which they had to overcome. The majority of men at the
present day have grown accustomed to hear the motion of the earth spoken
of: their acceptance of it means nothing: the attitude of the paradoxer
who denies it is more intelligent.
It is not to be supposed that the idea of thus explaining some of the
phenomena of the heavens, especially the daily motion of the entire
firmament, by a diurnal rotation of the earth had not struck any one. It
was often at this time referred to as the Pythagorean theory, and it had
been taught, I believe, by Aristarchus. But it was new to the modern
world, and it had the great weight of Aristotle against it.
Consequently, for long after Copernicus, only a few leading spirits
could be found to support it, and the long-established venerable
Ptolemaic system continued to be taught in all Universities.
The main objections to the motion of the earth were such as the
following:--
1. The motion is unfelt and difficult to imagine.
That it is unfelt is due to its uniformity, and can be explained
mechanically. That it is difficult to imagine is and remains true,
but a most important lesson we have to learn is that difficulty of
conception is no valid argument against reality.
2. That the stars do not alter their relative positions according to
the season of the year, but the constellations preserve always the same
aspect precisely, even to careful measurement.
This is indeed a difficulty, and a great one. In June the earth is
184 million miles away from where it was in December: how can we
see precisely the same fixed stars? It is not possible, unless they
are at a practically infinite distance. That is the only answer
that can be given. It was the tentative answer given by Copernicus.
It is the correct answer. Not only from every position of the
earth, but from every planet of the solar system, the same
constellations are visible, and the stars have the same aspect. The
whole immensity of the solar system shrinks to practically a point
when confronted with the distance of the stars.
Not, however, so entirely a speck as to resist the terrific
accuracy of the present century, and their microscopic relative
displacement with the season of the year has now at length been
detected, and the distance of many thereby measured.
3. That, if the earth revolved round the sun, Mercury and Venus ought to
show phases like the moon.
So they ought. Any globe must show phases if it live nearer the sun
than we do and if we go round it, for we shall see varying amounts
of its illuminated half. The only answer that Copernicus could give
to this was that they might be difficult to see without extra
powers of sight, but he ventured to predict that the phases would
be seen if ever our powers of vision should be enhanced.
4. That if the earth moved, or even revolved on its own axis, a stone or
other dropped body ought to be left far behind.
This difficulty is not a real one, like the two last, and it is
based on an ignorance of the laws of mechanics, which had not at
that time been formulated. We know now that a ball dropped from a
high tower, so far from lagging, drops a minute trifle _in front_
of the foot of a perpendicular, because the top of the tower is
moving a trace faster than the bottom, by reason of the diurnal
rotation. But, ignoring this, a stone dropped from the lamp of a
railway carriage drops in the centre of the floor, whether the
carriage be moving steadily or standing still; a slant direction of
fall could only be detected if the carriage were being accelerated
or if the brake were applied. A body dropped from a moving carriage
shares the motion of the carriage, and starts with that as its
initial velocity. A ball dropped from a moving balloon does not
simply drop, but starts off in whatever direction the car was
moving, its motion being immediately modified by gravity, precisely
in the same way as that of a thrown ball is modified. This is,
indeed, the whole philosophy of throwing--to drop a ball from a
moving carriage. The carriage is the hand, and, to throw far, a run
is taken and the body is jerked forward; the arm is also moved as
rapidly as possible on the shoulder as pivot. The fore-arm can be
moved still faster, and the wrist-joint gives yet another motion:
the art of throwing is to bring all these to bear at the same
instant, and then just as they have all attained their maximum
velocity to let the ball go. It starts off with the initial
velocity thus imparted, and is abandoned to gravity. If the vehicle
were able to continue its motion steadily, as a balloon does, the
ball when let go from it would appear to the occupant simply to
drop; and it would strike the ground at a spot vertically under the
moving vehicle, though by no means vertically below the place where
it started. The resistance of the air makes observations of this
kind inaccurate, except when performed inside a carriage so that
the air shares in the motion. Otherwise a person could toss and
catch a ball out of a train window just as well as if he were
stationary; though to a spectator outside he would seem to be using
great skill to throw the ball in the parabola adapted to bring it
back to his hand.
The same circumstance enhances the apparent difficulty of the
circus rider's jumping feats. All he has to do is to jump up and
down on the horse; the forward motion which carries him through
hoops belongs to him by virtue of the motion of the horse, without
effort on his part.
Thus, then, it happens that a stone dropped sixteen feet on the
earth appears to fall straight down, although its real path in
space is a very flat trajectory of nineteen miles base and sixteen
feet height; nineteen miles being the distance traversed by the
earth every second in the course of its annual journey round the
sun.
No wonder that it was thought that bodies must be left behind if
the earth was subject to such terrific speed as this. All that
Copernicus could suggest on this head was that perhaps the
atmosphere might help to carry things forward, and enable them to
keep pace with the earth.
There were thus several outstanding physical difficulties in the way of
the acceptance of the Copernican theory, besides the Biblical
difficulty.
It was quite natural that the idea of the earth's motion should be
repugnant, and take a long time to sink into the minds of men; and as
scientific progress was vastly slower then than it is now, we find not
only all priests but even some astronomers one hundred years afterwards
still imagining the earth to be at rest. And among them was a very
eminent one, Tycho Brahé.
It is interesting to note, moreover, that the argument about the motion
of the earth being contrary to Scripture appealed not only to
ecclesiastics in those days, but to scientific men also; and Tycho
Brahé, being a man of great piety, and highly superstitious also, was so
much influenced by it, that he endeavoured to devise some scheme by
which the chief practical advantages of the Copernican system could be
retained, and yet the earth be kept still at the centre of the whole.
This was done by making all the celestial sphere, with stars and
everything, rotate round the earth once a day, as in the Ptolemaic
scheme; and then besides this making all the planets revolve round the
sun, and this to revolve round the earth. Such is the Tychonic system.
So far as _relative_ motion is concerned it comes to the same thing;
just as when you drop a book you may say either that the earth rises to
meet the book, or that the book falls to meet the earth. Or when a fly
buzzes round your head, you may say that you are revolving round the
fly. But the absurdity of making the whole gigantic system of sun and
planets and stars revolve round our insignificant earth was too great to
be swallowed by other astronomers after they had once had a taste of the
Copernican theory; and accordingly the Tychonic system died a speedy and
an easy death at the same time as its inventor.
Wherein then lay the magnitude of the man?--not in his theories, which
were puerile, but in his observations, which were magnificent. He was
the first observational astronomer, the founder of the splendid system
of practical astronomy which has culminated in the present Greenwich
Observatory.
[Illustration: FIG. 16.--Tychonic system showing the sun with all the
planets revolving round the earth.]
Up to Tycho the only astronomical measurements had been of the rudest
kind. Copernicus even improved upon what had gone before, with measuring
rules made with his own hands. Ptolemy's observations could never be
trusted to half a degree. Tycho introduced accuracy before undreamed of,
and though his measurements, reckoned by modern ideas, are of course
almost ludicrously rough (remember no such thing as a telescope or
microscope was then dreamed of), yet, estimated by the era in which they
were made, they are marvels of accuracy, and not a single mistake due
to carelessness has ever been detected in them. In fact they may be
depended on almost to minutes of arc, _i.e._ to sixtieths of a degree.
For certain purposes connected with the proper motion of stars they are
still appealed to, and they served as the certain and trustworthy data
for succeeding generations of theorists to work upon. It was long,
indeed, after Tycho's death before observations approaching in accuracy
to his were again made.
In every sense, therefore, he was a pioneer: let us proceed to trace his
history.
Born the eldest son of a noble family--"as noble and ignorant as sixteen
undisputed quarterings could make them," as one of his biographers
says--in a period when, even more than at present, killing and hunting
were the only natural aristocratic pursuits, when all study was regarded
as something only fit for monks, and when science was looked at askance
as something unsavoury, useless, and semi-diabolic, there was little in
his introduction to the world urging him in the direction where his
genius lay. Of course he was destined for a soldier; but fortunately his
uncle, George Brahé, a more educated man than his father, having no son
of his own, was anxious to adopt him, and though not permitted to do so
for a time, succeeded in getting his way on the birth of a second son,
Steno--who, by the way, ultimately became Privy Councillor to the King
of Denmark.
Tycho's uncle gave him what he would never have got at home--a good
education; and ultimately put him to study law. At the age of thirteen
he entered the University of Copenhagen, and while there occurred the
determining influence of his life.
An eclipse of the sun in those days was not regarded with the
cold-blooded inquisitiveness or matter-of-fact apathy, according as
there is or is not anything to be learnt from it, with which such an
event is now regarded. Every occurrence in the heavens was then
believed to carry with it the destiny of nations and the fate of
individuals, and accordingly was of surpassing interest. Ever since the
time of Hipparchus it had been possible for some capable man here and
there to predict the occurrence of eclipses pretty closely. The thing is
not difficult. The prediction was not, indeed, to the minute and second,
as it is now; but the day could usually be hit upon pretty accurately
some time ahead, much as we now manage to hit upon the return of a
comet--barring accidents; and the hour could be predicted as the event
approached.
Well, the boy Tycho, among others, watched for this eclipse on August
21st, 1560; and when it appeared at its appointed time, every instinct
for the marvellous, dormant in his strong nature, awoke to strenuous
life, and he determined to understand for himself a science permitting
such wonderful possibilities of prediction. He was sent to Leipzig with
a tutor to go on with his study of law, but he seems to have done as
little law as possible: he spent all his money on books and instruments,
and sat up half the night studying and watching the stars.
In 1563 he observed a conjunction of Jupiter and Saturn, the precursor,
and _cause_ as he thought it, of the great plague. He found that the old
planetary tables were as much as a month in error in fixing this event,
and even the Copernican tables were several days out; so he formed the
resolve to devote his life to improving astronomical tables. This
resolve he executed with a vengeance. His first instrument was a jointed
ruler with sights for fixing the position of planets with respect to the
stars, and observing their stations and retrogressions. By thus
measuring the angles between a planet and two fixed stars, its position
can be plotted down on a celestial map or globe.
[Illustration: FIG. 17.--Portrait of Tycho.]
In 1565 his uncle George died, and made Tycho his heir. He returned to
Denmark, but met with nothing but ridicule and contempt for his absurd
drivelling away of time over useless pursuits. So he went back to
Germany--first to Wittenberg, thence, driven by the plague, to Rostock.
Here his fiery nature led him into an absurd though somewhat dangerous
adventure. A quarrel at some feast, on a mathematical point, with a
countryman, Manderupius, led to the fixing of a duel, and it was fought
with swords at 7 p.m. at the end of December, when, if there was any
light at all, it must have been of a flickering and unsatisfactory
nature. The result of this insane performance was that Tycho got his
nose cut clean off.
He managed however to construct an artificial one, some say of gold and
silver, some say of putty and brass; but whatever it was made of there
is no doubt that he wore it for the rest of his life, and it is a most
famous feature. It excited generally far more interest than his
astronomical researches. It is said, moreover, to have very fairly
resembled the original, but whether this remark was made by a friend or
by an enemy I cannot say. One account says that he used to carry about
with him a box of cement to apply whenever his nose came off, which it
periodically did.
About this time he visited Augsburg, met with some kindred and
enlightened spirits in that town, and with much enthusiasm and spirit
constructed a great quadrant. These early instruments were tremendous
affairs. A great number of workmen were employed upon this quadrant, and
it took twenty men to carry it to its place and erect it. It stood in
the open air for five years, and then was destroyed by a storm. With it
he made many observations.
[Illustration: FIG. 18.--Early out-door quadrant of Tycho; for
observing altitudes by help of the sights _D_, _L_ and the plumb line.]
On his return to Denmark in 1571, his fame preceded him, and he was
much better received; and in order to increase his power of constructing
instruments he took up the study of alchemy, and like the rest of the
persuasion tried to make gold. The precious metals were by many old
philosophers considered to be related in some way to the heavenly
bodies: silver to the moon, for instance--as we still see by the name
lunar caustic applied to nitrate of silver; gold to the sun, copper to
Mars, lead to Saturn. Hence astronomy and alchemy often went together.
Tycho all his life combined a little alchemy with his astronomical
labours, and he constructed a wonderful patent medicine to cure all
disorders, which had as wide a circulation in Europe in its time as
Holloway's pills; he gives a tremendous receipt for it, with liquid gold
and all manner of ingredients in it; among them, however, occurs a
little antimony--a well-known sudorific--and to this, no doubt, whatever
efficacy the medicine possessed was due.
So he might have gone on wasting his time, were it not that in November,
1572, a new star made its appearance, as they have done occasionally
before and since. On the average one may say that about every fifty
years a new star of fair magnitude makes its temporary appearance. They
are now known to be the result of some catastrophe or collision, whereby
immense masses of incandescent gas are produced. This one seen by Tycho
became as bright as Jupiter, and then died away in about a year and a
half. Tycho observed all its changes, and endeavoured to measure its
distance from the earth, with the result that it was proved to belong to
the region of the fixed stars, at an immeasurable distance, and was not
some nearer and more trivial phenomenon.
He was asked by the University of Copenhagen to give a course of
lectures on astronomy; but this was a step he felt some aristocratic
aversion to, until a little friendly pressure was brought to bear upon
him by a request from the king, and delivered they were.
He now seems to have finally thrown off his aristocratic prejudices, and
to have indulged himself in treading on the corns of nearly all the high
and mighty people he came into contact with. In short, he became what we
might now call a violent Radical; but he was a good-hearted man,
nevertheless, and many are the tales told of his visits to sick
peasants, of his consulting the stars as to their fate--all in perfect
good faith--and of the medicines which he concocted and prescribed for
them.
The daughter of one of these peasants he married, and very happy the
marriage seems to have been.
[Illustration: FIG. 19.--Map of Denmark, showing the island of Huen.
_Walker & Boutallse._]
Now comes the crowning episode in Tycho's life. Frederick II., realizing
how eminent a man they had among them, and how much he could do if only
he had the means--for we must understand that Tycho, though of good
family and well off, was by no means what we would call a wealthy
man--Frederick II. made him a splendid and enlightened offer. The offer
was this: that if Tycho would agree to settle down and make his
astronomical observations in Denmark, he should have an estate in Norway
settled upon him, a pension of £400 a year for life, a site for a large
observatory, and £20,000 to build it with.
[Illustration: FIG. 20.--Uraniburg.]
[Illustration: FIG. 21.--Astrolabe. An old instrument with sights for
marking the positions of the celestial bodies roughly. A sort of
skeleton celestial globe.]
[Illustration:
SEXTANS ASTRONOMICVS
TRIGONICVS PRO DISTANTIIS
rimandis.
FIG. 22.--Tycho's large sextant; for measuring the angular distance
between two bodies by direct sighting.]
Well, if ever money was well spent, this was. By its means Denmark
before long headed the nations of Europe in the matter of science--a
thing it has not done before or since. The site granted was the island
of Huen, between Copenhagen and Elsinore; and here the most magnificent
observatory ever built was raised, and called Uraniburg--the castle of
the heavens. It was built on a hill in the centre of the island, and
included gardens, printing shops, laboratory, dwelling-houses, and four
observatories--all furnished with the most splendid instruments that
Tycho could devise, and that could then be constructed. It was decorated
with pictures and sculptures of eminent men, and altogether was a most
gorgeous place. £20,000 no doubt went far in those days, but the
original grant was supplemented by Tycho himself, who is said to have
spent another equal sum out of his own pocket on the place.
[Illustration: QVADRANS MAXIMVS CHALIBEUS QUADRATO INCLUSUS, ET
Horizonti Azimuthali chalybeo insistens.
FIG. 23.--The Quadrant in Uraniburg; or altitude and azimuth
instrument.]
For twenty years this great temple of science was continually worked in
by him, and he soon became the foremost scientific man in Europe.
Philosophers, statesmen, and occasionally kings, came to visit the great
astronomer, and to inspect his curiosities.
[Illustration:
QVADRANS MVRALIS
SIVE TICHONICUS.
FIG. 24.--Tycho's form of transit circle.
The method of utilising the extremely uniform rotation of the earth by
watching the planets and stars as they cross the meridian, and recording
their times of transit; observing also at the same time their meridian
altitudes (see observer _F_), was the invention of Tycho, and
constitutes his greatest achievement. His method is followed to this day
in all observatories.]
[Illustration: FIG. 25.--A modern transit circle, showing essentially
the same parts as in Tycho's instrument, viz. the observer watching the
transit, the clock, the recorder of the observation, and the graduated
circle; the latter to be read by a second observer.]
And very wholesome for some of these great personages must have been the
treatment they met with. For Tycho was no respecter of persons. His
humbly-born wife sat at the head of the table, whoever was there; and he
would snub and contradict a chancellor just as soon as he would a serf.
Whatever form his pride may have taken when a youth, in his maturity it
impelled him to ignore differences of rank not substantially justified,
and he seemed to take a delight in exposing the ignorance of shallow
titled persons, to whom contradiction and exposure were most unusual
experiences.
For sick peasants he would take no end of trouble, and went about
doctoring them for nothing, till he set all the professional doctors
against him; so that when his day of misfortune came, as come it did,
their influence was not wanting to help to ruin one who spoilt their
practice, and whom they derided as a quack.
But some of the great ignorant folk who came to visit his temple of
science, and to inspect its curiosities, felt themselves insulted--not
always without reason. He kept a tame maniac in the house, named Lep,
and he used to regard the sayings of this personage as oracular,
presaging future events, and far better worth listening to than ordinary
conversation. Consequently he used to have him at his banquets and feed
him himself; and whenever Lep opened his mouth to speak, every one else
was peremptorily ordered to hold his tongue, so that Lep's words might
be written down. In fact it was something like an exaggerated edition of
Betsy Trotwood and Mr. Dick.
"It must have been an odd dinner party" (says Prof. Stuart), "with this
strange, wild, terribly clever man, with his red hair and brazen nose,
sometimes flashing with wit and knowledge, sometimes making the whole
company, princes and servants alike, hold their peace and listen humbly
to the ravings of a poor imbecile."
To people he despised he did not show his serious instruments. He had
other attractions, in the shape of a lot of toy machinery, little
windmills, and queer doors, and golden globes, and all manner of
ingenious tricks and automata, many of which he had made himself, and
these he used to show them instead; and no doubt they were well enough
pleased with them. Those of the visitors, however, who really cared to
see and understand his instruments, went away enchanted with his genius
and hospitality.
I may, perhaps, be producing an unfair impression of imperiousness and
insolence. Tycho was fiery, no doubt, but I think we should wrong him
if we considered him insolent. Most of the nobles of his day were
haughty persons, accustomed to deal with serfs, and very likely to sneer
at and trample on any meek man of science whom they could easily
despise. So Tycho was not meek; he stood up for the honour of his
science, and paid them back in their own coin, with perhaps a little
interest. That this behaviour was not worldly-wise is true enough, but I
know of no commandment enjoining us to be worldly-wise.
If we knew more about his so-called imbecile _protégé_ we should
probably find some reason for the interest which Tycho took in him.
Whether he was what is now called a "clairvoyant" or not, Tycho
evidently regarded his utterances as oracular, and of course when one is
receiving what may be a revelation from heaven it is natural to suppress
ordinary conversation.
Among the noble visitors whom he received and entertained, it is
interesting to notice James I. of England, who spent eight days at
Uraniburg on the occasion of his marriage with Anne of Denmark in 1590,
and seems to have been deeply impressed by his visit.
Among other gifts, James presented Tycho with a dog (depicted in Fig.
24), and this same animal was subsequently the cause of trouble. For it
seems that one day the Chancellor of Denmark, Walchendorf, brutally
kicked the poor beast; and Tycho, who was very fond of animals, gave him
a piece of his mind in no measured language. Walchendorf went home
determined to ruin him. King Frederick, however, remained his true
friend, doubtless partly influenced thereto by his Queen Sophia, an
enlightened woman who paid many visits to Uraniburg, and knew Tycho
well. But unfortunately Frederick died; and his son, a mere boy, came to
the throne.
Now was the time for the people whom Tycho had offended, for those who
were jealous of his great fame and importance, as well as for those who
cast longing eyes on his estate and endowments. The boy-king, too,
unfortunately paid a visit to Tycho, and, venturing upon a decided
opinion on some recondite subject, received a quiet setting down which
he ill relished.
Letters written by Tycho about this time are full of foreboding. He
greatly dreads having to leave Uraniburg, with which his whole life has
for twenty years been bound up. He tries to comfort himself with the
thought that, wherever he is sent, he will have the same heavens and the
same stars over his head.
Gradually his Norwegian estate and his pension were taken away, and in
five years poverty compelled him to abandon his magnificent temple, and
to take a small house in Copenhagen.
Not content with this, Walchendorf got a Royal Commission appointed to
inquire into the value of his astronomical labours. This sapient body
reported that his work was not only useless, but noxious; and soon after
he was attacked by the populace in the public street.
Nothing was left for him now but to leave the country, and he went into
Germany, leaving his wife and instruments to follow him whenever he
could find a home for them.
His wanderings in this dark time--some two years--are not quite clear;
but at last the enlightened Emperor of Bohemia, Rudolph II., invited him
to settle in Prague. Thither he repaired, a castle was given him as an
observatory, a house in the city, and 3000 crowns a year for life. So
his instruments were set up once more, students flocked to hear him and
to receive work at his hands--among them a poor youth, John Kepler, to
whom he was very kind, and who became, as you know, a still greater man
than his master.
But the spirit of Tycho was broken, and though some good work was done
at Prague--more observations made, and the Rudolphine tables begun--yet
the hand of death was upon him. A painful disease seized him, attended
with sleeplessness and temporary delirium, during the paroxysms of
which he frequently exclaimed, _Ne frustra vixisse videar_. ("Oh that it
may not appear that I have lived in vain!")
Quietly, however, at last, and surrounded by his friends and relatives,
this fierce, passionate soul passed away, on the 24th of October, 1601.
His beloved instruments, which were almost a part of himself, were
stored by Rudolph in a museum with scrupulous care, until the taking of
Prague by the Elector Palatine's troops. In this disturbed time they got
smashed, dispersed, and converted to other purposes. One thing only was
saved--the great brass globe, which some thirty years after was
recognized by a later king of Denmark as having belonged to Tycho, and
deposited in the Library of the Academy of Sciences at Copenhagen, where
I believe it is to this day.
The island of Huen was overrun by the Danish nobility, and nothing now
remains of Uraniburg but a mound of earth and two pits.
As to the real work of Tycho, that has become immortal enough,--chiefly
through the labours of his friend and scholar whose life we shall
consider in the next lecture.
SUMMARY OF FACTS FOR LECTURE III
_Life and work of Kepler._ Kepler was born in December, 1571, at Weil in
Würtemberg. Father an officer in the duke's army, mother something of a
virago, both very poor. Kepler was utilized as a tavern pot-boy, but
ultimately sent to a charity school, and thence to the University of
Tübingen. Health extremely delicate; he was liable to violent attacks
all his life. Studied mathematics, and accepted an astronomical
lectureship at Graz as the first post which offered. Endeavoured to
discover some connection between the number of the planets, their times
of revolution, and their distances from the sun. Ultimately hit upon his
fanciful regular-solid hypothesis, and published his first book in 1597.
In 1599 was invited by Tycho to Prague, and there appointed Imperial
mathematician, at a handsome but seldom paid salary. Observed the new
star of 1604. Endeavoured to find the law of refraction of light from
Vitellio's measurements, but failed. Analyzed Tycho's observations to
find the true law of motion of Mars. After incredible labour, through
innumerable wrong guesses, and six years of almost incessant
calculation, he at length emerged in his two "laws"--discoveries which
swept away all epicycles, deferents, equants, and other remnants of the
Greek system, and ushered in the dawn of modern astronomy.
LAW I. _Planets move in ellipses, with the Sun in one focus._
LAW II. _The radius vector (or line joining sun and planet) sweeps out
equal areas in equal times._
Published his second book containing these laws in 1609. Death of
Rudolph in 1612, and subsequent increased misery and misfortune of
Kepler. Ultimately discovered the connection between the times and
distances of the planets for which he had been groping all his mature
life, and announced it in 1618:--
LAW III. _The square of the time of revolution (or year) of each planet
is proportional to the cube of its mean distance from the sun._
The book in which this law was published ("On Celestial Harmonies") was
dedicated to James of England. In 1620 had to intervene to protect his
mother from being tortured for witchcraft. Accepted a professorship at
Linz. Published the Rudolphine tables in 1627, embodying Tycho's
observations and his own theory. Made a last effort to overcome his
poverty by getting the arrears of his salary paid at Prague, but was
unsuccessful, and, contracting brain fever on the journey, died in
November, 1630, aged 59.
A man of keen imagination, indomitable perseverance, and uncompromising
love of truth, Kepler overcame ill-health, poverty, and misfortune, and
placed himself in the very highest rank of scientific men. His laws, so
extraordinarily discovered, introduced order and simplicity into what
else would have been a chaos of detailed observations; and they served
as a secure basis for the splendid erection made on them by Newton.
_Seven planets of the Ptolemaic system--_
Moon, Mercury, Venus, Sun, Mars, Jupiter, Saturn.
_Six planets of the Copernican system--_
Mercury, Venus, Earth, Mars, Jupiter, Saturn.
_The five regular solids, in appropriate order--_
Octahedron, Icosahedron, Dodecahedron, Tetrahedron, Cube.
_Table illustrating Kepler's third law._
+---------+---------------+-----------+---------------+----------------+
| | Mean distance | Length | Cube of the | Square of the |
| Planet. | from Sun. | of Year. | Distance. | Time. |
| | D | T | D^3 | T^2 |
+---------+---------------+-----------+---------------+----------------+
| Mercury | ·3871 | ·24084 | ·05801 | ·05801 |
| Venus | ·7233 | ·61519 | ·37845 | ·37846 |
| Earth | 1·0000 | 1·0000 | 1·0000 | 1·0000 |
| Mars | 1·5237 | 1·8808 | 3·5375 | 3·5375 |
| Jupiter | 5·2028 | 11·862 | 140·83 | 140·70 |
| Saturn | 9·5388 | 29·457 | 867·92 | 867·70 |
+---------+---------------+-----------+---------------+----------------+
The length of the earth's year is 365·256 days; its mean distance from
the sun, taken above as unity, is 92,000,000 miles.
LECTURE III
KEPLER AND THE LAWS OF PLANETARY MOTION
It is difficult to imagine a stronger contrast between two men engaged
in the same branch of science than exists between Tycho Brahé, the
subject of last lecture, and Kepler, our subject on the present
occasion.
The one, rich, noble, vigorous, passionate, strong in mechanical
ingenuity and experimental skill, but not above the average in
theoretical and mathematical power.
The other, poor, sickly, devoid of experimental gifts, and unfitted by
nature for accurate observation, but strong almost beyond competition in
speculative subtlety and innate mathematical perception.
The one is the complement of the other; and from the fact of their
following each other so closely arose the most surprising benefits to
science.
The outward life of Kepler is to a large extent a mere record of poverty
and misfortune. I shall only sketch in its broad features, so that we
may have more time to attend to his work.
He was born (so his biographer assures us) in longitude 29° 7', latitude
48° 54', on the 21st of December, 1571. His parents seem to have been of
fair condition, but by reason, it is said, of his becoming surety for a
friend, the father lost all his slender income, and was reduced to
keeping a tavern. Young John Kepler was thereupon taken from school,
and employed as pot-boy between the ages of nine and twelve. He was a
sickly lad, subject to violent illnesses from the cradle, so that his
life was frequently despaired of. Ultimately he was sent to a monastic
school and thence to the University of Tübingen, where he graduated
second on the list. Meanwhile home affairs had gone to rack and ruin.
His father abandoned the home, and later died abroad. The mother
quarrelled with all her relations, including her son John; who was
therefore glad to get away as soon as possible.
All his connection with astronomy up to this time had been the hearing
the Copernican theory expounded in University lectures, and defending it
in a college debating society.
An astronomical lectureship at Graz happening to offer itself, he was
urged to take it, and agreed to do so, though stipulating that it should
not debar him from some more brilliant profession when there was a
chance.
For astronomy in those days seems to have ranked as a minor science,
like mineralogy or meteorology now. It had little of the special dignity
with which the labours of Kepler himself were destined so greatly to aid
in endowing it.
Well, he speedily became a thorough Copernican, and as he had a most
singularly restless and inquisitive mind, full of appreciation of
everything relating to number and magnitude--was a born speculator and
thinker just as Mozart was a born musician, or Bidder a born
calculator--he was agitated by questions such as these: Why are there
exactly six planets? Is there any connection between their orbital
distances, or between their orbits and the times of describing them?
These things tormented him, and he thought about them day and night. It
is characteristic of the spirit of the times--this questioning why there
should be six planets. Nowadays, we should simply record the fact and
look out for a seventh. Then, some occult property of the number six was
groped for, such as that it was equal to 1 + 2 + 3 and likewise equal to
1 × 2 × 3, and so on. Many fine reasons had been given for the seven
planets of the Ptolemaic system (see, for instance, p. 106), but for
the six planets of the Copernican system the reasons were not so cogent.
Again, with respect to their successive distances from the sun, some law
would seem to regulate their distance, but it was not known.
(Parenthetically I may remark that it is not known even now: a crude
empirical statement known as Bode's law--see page 294--is all that has
been discovered.)
Once more, the further the planet the slower it moved; there seemed to
be some law connecting speed and distance. This also Kepler made
continual attempts to discover.
[Illustration: FIG. 26.--Orbits of some of the planets drawn to scale:
showing the gap between Mars and Jupiter.]
One of his ideas concerning the law of the successive distances was
based on the inscription of a triangle in a circle. If you inscribe in a
circle a large number of equilateral triangles, they envelop another
circle bearing a definite ratio to the first: these might do for the
orbits of two planets (see Fig. 27). Then try inscribing and
circumscribing squares, hexagons, and other figures, and see if the
circles thus defined would correspond to the several planetary orbits.
But they would not give any satisfactory result. Brooding over this
disappointment, the idea of trying solid figures suddenly strikes him.
"What have plane figures to do with the celestial orbits?" he cries out;
"inscribe the regular solids." And then--brilliant idea--he remembers
that there are but five. Euclid had shown that there could be only five
regular solids.[4] The number evidently corresponds to the gaps between
the six planets. The reason of there being only six seems to be
attained. This coincidence assures him he is on the right track, and
with great enthusiasm and hope he "represents the earth's orbit by a
sphere as the norm and measure of all"; round it he circumscribes a
dodecahedron, and puts another sphere round that, which is approximately
the orbit of Mars; round that, again, a tetrahedron, the corners of
which mark the sphere of the orbit of Jupiter; round that sphere, again,
he places a cube, which roughly gives the orbit of Saturn.
[Illustration: FIG. 27.--Many-sided polygon or approximate circle
enveloped by straight lines, as for instance by a number of equilateral
triangles.]
On the other hand, he inscribes in the sphere of the earth's orbit an
icosahedron; and inside the sphere determined by that, an octahedron;
which figures he takes to inclose the spheres of Venus and of Mercury
respectively.
The imagined discovery is purely fictitious and accidental. First of
all, eight planets are now known; and secondly, their real distances
agree only very approximately with Kepler's hypothesis.
[Illustration: FIG. 28.--Frameworks with inscribed and circumscribed
spheres, representing the five regular solids distributed as Kepler
supposed them to be among the planetary orbits. (See "Summary" at
beginning of this lecture, p. 57.)]
Nevertheless, the idea gave him great delight. He says:--"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 calculation, until I could
see whether my hypothesis would agree with the orbits of Copernicus, or
whether my joy was to vanish into air."
He then went on to speculate as to the cause of the planets' motion.
The old idea was that they were carried round by angels or celestial
intelligences. Kepler tried to establish some propelling force emanating
from the sun, like the spokes of a windmill.
This first book of his brought him into notice, and served as an
introduction to Tycho and to Galileo.
Tycho Brahé was at this time at Prague under the patronage of the
Emperor Rudolph; and as he was known to have by far the best planetary
observations of any man living, Kepler wrote to him to know if he might
come and examine them so as to perfect his theory.
Tycho immediately replied, "Come, not as a stranger, but as a very
welcome friend; come and share in my observations with such instruments
as I have with me, and as a dearly beloved associate." After this visit,
Tycho wrote again, offering him the post of mathematical assistant,
which after hesitation was accepted. Part of the hesitation Kepler
expresses by saying that "for observations his sight was dull, and for
mechanical operations his hand was awkward. He suffered much from weak
eyes, and dare not expose himself to night air." In all this he was, of
course, the antipodes of Tycho, but in mathematical skill he was greatly
his superior.
On his way to Prague he was seized with one of his periodical illnesses,
and all his means were exhausted by the time he could set forward again,
so that he had to apply for help to Tycho.
It is clear, indeed, that for some time now he subsisted entirely on the
bounty of Tycho, and he expresses himself most deeply grateful for all
the kindness he received from that noble and distinguished man, the head
of the scientific world at that date.
To illustrate Tycho's kindness and generosity, I must read you a letter
written to him by Kepler. It seems that Kepler, on one of his absences
from Prague, driven half mad with poverty and trouble, fell foul of
Tycho, whom he thought to be behaving badly in money matters to him and
his family, and wrote him a violent letter full of reproaches and
insults. Tycho's secretary replied quietly enough, pointing out the
groundlessness and ingratitude of the accusation.
Kepler repents instantly, and replies:--
"MOST NOBLE TYCHO," (these are the words of his letter), "how shall
I enumerate or rightly estimate your benefits conferred on me? For
two months you have liberally and gratuitously maintained me, and
my whole family; you have provided for all my wishes; you have done
me every possible kindness; you have communicated to me everything
you hold most dear; no one, by word or deed, has intentionally
injured me in anything; in short, not to your children, your wife,
or yourself have you shown more indulgence than to me. This being
so, as I am anxious to put on record, I cannot reflect without
consternation that I should have been so given up by God to my own
intemperance as to shut my eyes on all these benefits; that,
instead of modest and respectful gratitude, I should indulge for
three weeks in continual moroseness towards all your family, in
headlong passion and the utmost insolence towards yourself, who
possess so many claims on my veneration, from your noble family,
your extraordinary learning, and distinguished reputation. Whatever
I have said or written against the person, the fame, the honour,
and the learning of your excellency; or whatever, in any other way,
I have injuriously spoken or written (if they admit no other more
favourable interpretation), as, to my grief, I have spoken and
written many things, and more than I can remember; all and
everything I recant, and freely and honestly declare and profess to
be groundless, false, and incapable of proof."
Tycho accepted the apology thus heartily rendered, and the temporary
breach was permanently healed.
In 1601, Kepler was appointed "Imperial mathematician," to assist Tycho
in his calculations.
The Emperor Rudolph did a good piece of work in thus maintaining these
two eminent men, but it is quite clear that it was as astrologers that
he valued them; and all he cared for in the planetary motions was
limited to their supposed effect on his own and his kingdom's destiny.
He seems to have been politically a weak and superstitious prince, who
was letting his kingdom get into hopeless confusion, and entangling
himself in all manner of political complications. While Bohemia
suffered, however, the world has benefited at his hands; and the tables
upon which Tycho was now engaged are well called the Rudolphine tables.
These tables of planetary motion Tycho had always regarded as the main
work of his life; but he died before they were finished, and on his
death-bed he intrusted the completion of them to Kepler, who loyally
undertook their charge.
The Imperial funds were by this time, however, so taxed by wars and
other difficulties that the tables could only be proceeded with very
slowly, a staff of calculators being out of the question. In fact,
Kepler could not get even his own salary paid: he got orders, and
promises, and drafts on estates for it; but when the time came for them
to be honoured they were worthless, and he had no power to enforce his
claims.
So everything but brooding had to be abandoned as too expensive, and he
proceeded to study optics. He gave a very accurate explanation of the
action of the human eye, and made many hypotheses, some of them shrewd
and close to the mark, concerning the law of refraction of light in
dense media: but though several minor points of interest turned up,
nothing of the first magnitude came out of this long research.
The true law of refraction was discovered some years after by a Dutch
professor, Willebrod Snell.
We must now devote a little time to the main work of Kepler's life. All
the time he had been at Prague he had been making a severe study of the
motion of the planet Mars, analyzing minutely Tycho's books of
observations, in order to find out, if possible, the true theory of his
motion. Aristotle had taught that circular motion was the only perfect
and natural motion, and that the heavenly bodies therefore necessarily
moved in circles.
So firmly had this idea become rooted in men's minds, that no one ever
seems to have contemplated the possibility of its being false or
meaningless.
When Hipparchus and others found that, as a matter of fact, the planets
did _not_ revolve in simple circles, they did not try other curves, as
we should at once do now, but they tried combinations of circles, as we
saw in Lecture I. The small circle carried by a bigger one was called an
Epicycle. The carrying circle was called the Deferent. If for any reason
the earth had to be placed out of the centre, the main planetary orbit
was called an Excentric, and so on.
But although the planetary paths might be roughly represented by a
combination of circles, their speeds could not, on the hypothesis of
uniform motion in each circle round the earth as a fixed body. Hence was
introduced the idea of an Equant, _i.e._ an arbitrary point, not the
earth, about which the speed might be uniform. Copernicus, by making the
sun the centre, had been able to simplify a good deal of this, and to
abolish the equant.
But now that Kepler had the accurate observations of Tycho to refer to,
he found immense difficulty in obtaining the true positions of the
planets for long together on any such theory.
He specially attacked the motion of the planet Mars, because that was
sufficiently rapid in its changes for a considerable collection of data
to have accumulated with respect to it. He tried all manner of circular
orbits for the earth and for Mars, placing them in all sorts of aspects
with respect to the sun. The problem to be solved was to choose such an
orbit and such a law of speed, for both the earth and Mars, that a line
joining them, produced out to the stars, should always mark correctly
the apparent position of Mars as seen from the earth. He had to arrange
the size of the orbits that suited best, then the positions of their
centres, both being supposed excentric with respect to the sun; but he
could not get any such arrangement to work with uniform motion about the
sun. So he reintroduced the equant, and thus had another variable at his
disposal--in fact, two, for he had an equant for the earth and another
for Mars, getting a pattern of the kind suggested in Fig. 29.
The equants might divide the line in any arbitrary ratio. All sorts of
combinations had to be tried, the relative positions of the earth and
Mars to be worked out for each, and compared with Tycho's recorded
observations. It was easy to get them to agree for a short time, but
sooner or later a discrepancy showed itself.
[Illustration: FIG. 29.--_S_ represents the sun; _EC_, the centre of the
earth's orbit, to be placed as best suited; _MC_, the same for Mars;
_EE_, the earth's equant, or point about which the earth uniformly
revolved (_i.e._ the point determining the law of speed about the sun),
likewise to be placed anywhere, but supposed to be in the line joining
_S_ to _EC_; _ME_, the same thing for Mars; with _?ME_ for an
alternative hypothesis that perhaps Mars' equant was on line joining
_EC_ with _MC_.]
I need not say that all these attempts and gropings, thus briefly
summarized, entailed enormous labour, and required not only great
pertinacity, but a most singularly constituted mind, that could thus
continue groping in the dark without a possible ray of theory to
illuminate its search. Grope he did, however, with unexampled diligence.
At length he hit upon a point that seemed nearly right. He thought he
had found the truth; but no, before long the position of the planet, as
calculated, and as recorded by Tycho, differed by eight minutes of arc,
or about one-eighth of a degree. Could the observation be wrong by this
small amount? No, he had known Tycho, and knew that he was never wrong
eight minutes in an observation.
So he set out the whole weary way again, and said that with those eight
minutes he would yet find out the law of the universe. He proceeded to
see if by making the planet librate, or the plane of its orbit tilt up
and down, anything could be done. He was rewarded by finding that at any
rate the plane of the orbit did not tilt up and down: it was fixed, and
this was a simplification on Copernicus's theory. It is not an absolute
fixture, but the changes are very small (see Laplace, page 266).
[Illustration: FIG. 30.--Excentric circle supposed to be divided into
equal areas. The sun, _S_, being placed at a selected point, it was
possible to represent the varying speed of a planet by saying that it
moved from _A_ to _B_, from _B_ to _C_, and so on, in equal times.]
At last he thought of giving up the idea of _uniform_ circular motion,
and of trying _varying_ circular motion, say inversely as its distance
from the sun. To simplify calculation, he divided the orbit into
triangles, and tried if making the triangles equal would do. A great
piece of luck, they did beautifully: the rate of description of areas
(not arcs) is uniform. Over this discovery he greatly rejoices. He feels
as though he had been carrying on a war against the planet and had
triumphed; but his gratulation was premature. Before long fresh little
errors appeared, and grew in importance. Thus he announces it himself:--
"While thus triumphing over Mars, and preparing for him, as for one
already vanquished, tabular prisons and equated excentric fetters, it is
buzzed here and there that the victory is vain, and that the war is
raging anew as violently as before. For the enemy left at home a
despised captive has burst all the chains of the equations, and broken
forth from the prisons of the tables."
Still, a part of the truth had been gained, and was not to be abandoned
any more. The law of speed was fixed: that which is now known as his
second law. But what about the shape of the orbit--Was it after all
possible that Aristotle, and every philosopher since Aristotle, had been
wrong? that circular motion was not the perfect and natural motion, but
that planets might move in some other closed curve?
Suppose he tried an oval. Well, there are a great variety of ovals, and
several were tried: with the result that they could be made to answer
better than a circle, but still were not right.
Now, however, the geometrical and mathematical difficulties of
calculation, which before had been tedious and oppressive, threatened to
become overwhelming; and it is with a rising sense of despondency that
Kepler sees his six years' unremitting labour leading deeper and deeper
into complication.
One most disheartening circumstance appeared, viz. that when he made the
circuit oval his law of equable description of areas broke down. That
seemed to require the circular orbit, and yet no circular orbit was
quite accurate.
While thinking and pondering for weeks and months over this new dilemma
and complication of difficulties, till his brain reeled, an accidental
ray of light broke upon him in a way not now intelligible, or barely
intelligible. Half the extreme breadth intercepted between the circle
and oval was 429/100,000 of the radius, and he remembered that the
"optical inequality" of Mars was also about 429/100,000. This
coincidence, in his own words, woke him out of sleep; and for some
reason or other impelled him instantly to try making the planet
oscillate in the diameter of its epicycle instead of revolve round it--a
singular idea, but Copernicus had had a similar one to explain the
motions of Mercury.
[Illustration: FIG. 31.--Mode of drawing an ellipse. The two pins _F_
are the foci.]
Away he started through his calculations again. A long course of work
night and day was rewarded by finding that he was now able to hit off
the motions better than before; but what a singularly complicated motion
it was. Could it be expressed no more simply? Yes, the curve so
described by the planet is a comparatively simple one: it is a special
kind of oval--the ellipse. Strange that he had not thought of it before.
It was a famous curve, for the Greek geometers had studied it as one of
the sections of a cone, but it was not so well known in Kepler's time.
The fact that the planets move in it has raised it to the first
importance, and it is familiar enough to us now. But did it satisfy the
law of speed? Could the rate of description of areas be uniform with
it? Well, he tried the ellipse, and to his inexpressible delight he
found that it did satisfy the condition of equable description of areas,
if the sun was in one focus. So, moving the planet in a selected
ellipse, with the sun in one focus, at a speed given by the equable area
description, its position agreed with Tycho's observations within the
limits of the error of experiment. Mars was finally conquered, and
remains in his prison-house to this day. The orbit was found.
[Illustration: FIG. 32.]
In a paroxysm of delight Kepler celebrates his victory by a triumphant
figure, sketched actually on his geometrical diagram--the diagram which
proves that the law of equable description of areas can hold good with
an ellipse. The above is a tracing of it.
Such is a crude and bald sketch of the steps by which Kepler rose to his
great generalizations--the two laws which have immortalized his name.
All the complications of epicycle, equant, deferent, excentric, and the
like, were swept at once away, and an orbit of striking and beautiful
properties substituted. Well might he be called, as he was, "the
legislator," or law interpreter, "of the heavens."
[Illustration: FIG. 33.--If _S_ is the sun, a planet or comet moves from
_P_ to _P_1_, from _P_2_ to _P_3_, and from _P_4_ to _P_5_ in
the same time; if the shaded areas are equal.]
He concludes his book on the motions of Mars with a half comic appeal to
the Emperor to provide him with the sinews of war for an attack on
Mars's relations--father Jupiter, brother Mercury, and the rest--but the
death of his unhappy patron in 1612 put an end to all these schemes, and
reduced Kepler to the utmost misery. While at Prague his salary was in
continual arrear, and it was with difficulty that he could provide
sustenance for his family. He had been there eleven years, but they had
been hard years of poverty, and he could leave without regret were it
not that he should have to leave Tycho's instruments and observations
behind him. While he was hesitating what best to do, and reduced to the
verge of despair, his wife, who had long been suffering from low spirits
and despondency, and his three children, were taken ill; one of the sons
died of small-pox, and the wife eleven days after of low fever and
epilepsy. No money could be got at Prague, so after a short time he
accepted a professorship at Linz, and withdrew with his two quite young
remaining children.
He provided for himself now partly by publishing a prophesying almanack,
a sort of Zadkiel arrangement--a thing which he despised, but the
support of which he could not afford to do without. He is continually
attacking and throwing sarcasm at astrology, but it was the only thing
for which people would pay him, and on it after a fashion he lived. We
do not find that his circumstances were ever prosperous, and though
8,000 crowns were due to him from Bohemia he could not manage to get
them paid.
About this time occurred a singular interruption to his work. His old
mother, of whose fierce temper something has already been indicated, had
been engaged in a law-suit for some years near their old home in
Würtemberg. A change of judge having in process of time occurred, the
defendant saw his way to turn the tables on the old lady by accusing her
of sorcery. She was sent to prison, and condemned to the torture, with
the usual intelligent idea of extracting a "voluntary" confession.
Kepler had to hurry from Linz to interpose. He succeeded in saving her
from the torture, but she remained in prison for a year or so. Her
spirit, however, was unbroken, for no sooner was she released than she
commenced a fresh action against her accuser. But fresh trouble was
averted by the death of the poor old dame at the age of nearly eighty.
This narration renders the unflagging energy shown by her son in his
mathematical wrestlings less surprising.
Interspersed with these domestic troubles, and with harassing and
unsuccessful attempts to get his rights, he still brooded over his old
problem of some possible connection between the distances of the planets
from the sun and their times of revolution, _i.e._ the length of their
years.
It might well have been that there was no connection, that it was purely
imaginary, like his old idea of the law of the successive distances of
the planets, and like so many others of the guesses and fancies which
he entertained and spent his energies in probing. But fortunately this
time there was a connection, and he lived to have the joy of discovering
it.
The connection is this, that if one compares the distance of the
different planets from the sun with the length of time they take to go
round him, the cube of the respective distances is proportional to the
square of the corresponding times. In other words, the ratio of r^3
to T^2 for every planet is the same. Or, again, the length of a
planet's year depends on the 3/2th power of its distance from the sun.
Or, once more, the speed of each planet in its orbit is as the inverse
square-root of its distance from the sun. The product of the distance
into the square of the speed is the same for each planet.
This (however stated) is called Kepler's third law. It welds the planets
together, and shows them to be one system. His rapture on detecting the
law was unbounded, and he breaks out into an exulting rhapsody:--
"What I prophesied two-and-twenty years ago, as soon as I discovered the
five solids among the heavenly orbits--what I firmly believed long
before I had seen Ptolemy's _Harmonies_--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 Tycho Brahé, for which I settled in Prague, for which
I have devoted the best part of my life to astronomical contemplations,
at length I have brought to light, and recognized its truth beyond my
most sanguine expectations. It is not eighteen months since I got the
first glimpse of light, three months since the dawn, very few days since
the unveiled sun, most admirable to gaze upon, burst upon me. Nothing
holds me; I will indulge 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 six thousand years for an observer."
Soon after this great work his third book appeared: it was an epitome of
the Copernican theory, a clear and fairly popular exposition of it,
which had the honour of being at once suppressed and placed on the list
of books prohibited by the Church, side by side with the work of
Copernicus himself, _De Revolutionibus Orbium Coelestium_.
This honour, however, gave Kepler no satisfaction--it rather occasioned
him dismay, especially as it deprived him of all pecuniary benefit, and
made it almost impossible for him to get a publisher to undertake
another book.
Still he worked on at the Rudolphine tables of Tycho, and ultimately,
with some small help from Vienna, completed them; but he could not get
the means to print them. He applied to the Court till he was sick of
applying: they lay idle four years. At last he determined to pay for the
type himself. What he paid it with, God knows, but he did pay it, and he
did bring out the tables, and so was faithful to the behest of his
friend.
This great publication marks an era in astronomy. They were the first
really accurate tables which navigators ever possessed; they were the
precursors of our present _Nautical Almanack_.
After this, the Grand Duke of Tuscany sent Kepler a golden chain, which
is interesting inasmuch as it must really have come from Galileo, who
was in high favour at the Italian Court at this time.
Once more Kepler made a determined attempt to get his arrears of salary
paid, and rescue himself and family from their bitter poverty. He
travelled to Prague on purpose, attended the imperial meeting, and
pleaded his own cause, but it was all fruitless; and exhausted by the
journey, weakened by over-study, and disheartened by the failure, he
caught a fever, and died in his fifty-ninth year. His body was buried at
Ratisbon, and 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 a stone.
[Illustration: FIG. 34.--Portrait of Kepler, older.]
The contiguity of the lives of Kepler and Tycho furnishes a moral too
obvious to need pointing out. What Kepler might have achieved had he
been relieved of those ghastly struggles for subsistence one cannot
tell, but this much is clear, that had Tycho been subjected to the same
misfortune, instead of being born rich and being assisted by generous
and enlightened patrons, he could have accomplished very little. His
instruments, his observatory--the tools by which he did his work--would
have been impossible for him. Frederick and Sophia of Denmark, and
Rudolph of Bohemia, are therefore to be remembered as co-workers with
him.
Kepler, with his ill-health and inferior physical energy, was unable to
command the like advantages. Much, nevertheless, he did; more one cannot
but feel he might have done had he been properly helped. Besides, the
world would have been free from the reproach of accepting the fruits of
his bright genius while condemning the worker to a life of misery,
relieved only by the beauty of his own thoughts and the ecstasy awakened
in him by the harmony and precision of Nature.
Concerning the method of Kepler, the mode by which he made his
discoveries, we must remember that he gives us an account of all the
steps, unsuccessful as well as successful, by which he travelled. He
maps out his route like a traveller. In fact he compares himself to
Columbus or Magellan, voyaging into unknown lands, and recording his
wandering route. This being remembered, it will be found that his
methods do not differ so utterly from those used by other philosophers
in like case. His imagination was perhaps more luxuriant and was allowed
freer play than most men's, but it was nevertheless always controlled by
rigid examination and comparison of hypotheses with fact.
Brewster says of him:--"Ardent, restless, burning to distinguish
himself by discovery, he attempted everything; and once having obtained
a glimpse of a clue, no labour was too hard in following or verifying
it. A few of his attempts succeeded--a multitude failed. Those which
failed seem to us now fanciful, those which succeeded appear to us
sublime. But his methods were the same. When in search of what really
existed he sometimes found it; when in pursuit of a chimæra he could not
but fail; but in either case he displayed the same great qualities, and
that obstinate perseverance which must conquer all difficulties except
those really insurmountable."
To realize what he did for astronomy, it is necessary for us now to
consider some science still in its infancy. Astronomy is so clear and so
thoroughly explored now, that it is difficult to put oneself into a
contemporary attitude. But take some other science still barely
developed: meteorology, for instance. The science of the weather, the
succession of winds and rain, sunshine and frost, clouds and fog, is now
very much in the condition of astronomy before Kepler.
We have passed through the stage of ascribing atmospheric
disturbances--thunderstorms, cyclones, earthquakes, and the like--to
supernatural agency; we have had our Copernican era: not perhaps brought
about by a single individual, but still achieved. Something of the laws
of cyclone and anticyclone are known, and rude weather predictions
across the Atlantic are roughly possible. Barometers and thermometers
and anemometers, and all their tribe, represent the astronomical
instruments in the island of Huen; and our numerous meteorological
observatories, with their continual record of events, represent the work
of Tycho Brahé.
Observation is heaped on observation; tables are compiled; volumes are
filled with data; the hours of sunshine are recorded, the fall of rain,
the moisture in the air, the kind of clouds, the temperature--millions
of facts; but where is the Kepler to study and brood over them? Where
is the man to spend his life in evolving the beginnings of law and order
from the midst of all this chaos?
Perhaps as a man he may not come, but his era will come. Through this
stage the science must pass, ere it is ready for the commanding
intellect of a Newton.
But what a work it will be for the man, whoever he be that undertakes
it--a fearful monotonous grind of calculation, hypothesis, hypothesis,
calculation, a desperate and groping endeavour to reconcile theories
with facts.
A life of such labour, crowned by three brilliant discoveries, the world
owes (and too late recognizes its obligation) to the harshly treated
German genius, Kepler.
SUMMARY OF FACTS FOR LECTURES IV AND V
In 1564, Michael Angelo died and Galileo was born; in 1642, Galileo died
and Newton was born. Milton lived from 1608 to 1674.
For teaching the plurality of worlds, with other heterodox doctrines,
and refusing to recant, Bruno, after six years' imprisonment in Rome,
was burnt at the stake on the 16th of February, 1600 A.D. A "natural"
death in the dungeons of the Inquisition saved Antonio de Dominis, the
explainer of the rainbow, from the same fate, but his body and books
were publicly burned at Rome in 1624.
The persecution of Galileo began in 1615, became intense in 1632, and so
lasted till his death and after.
* * * * *
Galileo Galilei, eldest son of Vincenzo de Bonajuti de Galilei, a noble
Florentine, was born at Pisa, 18th of February, 1564. At the age of 17
was sent to the University of Pisa to study medicine. Observed the swing
of a pendulum and applied it to count pulse-beats. Read Euclid and
Archimedes, and could be kept at medicine no more. At 26 was appointed
Lecturer in Mathematics at Pisa. Read Bruno and became smitten with the
Copernican theory. Controverted the Aristotelians concerning falling
bodies, at Pisa. Hence became unpopular and accepted a chair at Padua,
1592. Invented a thermometer. Wrote on astronomy, adopting the Ptolemaic
system provisionally, and so opened up a correspondence with Kepler,
with whom he formed a friendship. Lectured on the new star of 1604, and
publicly renounced the old systems of astronomy. Invented a calculating
compass or "Gunter's scale." In 1609 invented a telescope, after hearing
of a Dutch optician's discovery. Invented the microscope soon after.
Rapidly completed a better telescope and began a survey of the heavens.
On the 8th of January, 1610, discovered Jupiter's satellites. Observed
the mountains in the moon, and roughly measured their height. Explained
the visibility of the new moon by _earth-shine_. Was invited to the
Grand Ducal Court of Tuscany by Cosmo de Medici, and appointed
philosopher to that personage. Discovered innumerable new stars, and the
nebulæ. Observed a triple appearance of Saturn. Discovered the phases
of Venus predicted by Copernicus, and spots on the sun. Wrote on
floating bodies. Tried to get his satellites utilized for determining
longitude at sea.
Went to Rome to defend the Copernican system, then under official
discussion, and as a result was formally forbidden ever to teach it. On
the accession of Pope Urban VIII. in 1623, Galileo again visited Rome to
pay his respects, and was well received. In 1632 appeared his
"Dialogues" on the Ptolemaic and Copernican systems. Summoned to Rome,
practically imprisoned, and "rigorously questioned." Was made to recant
22nd of June, 1633. Forbidden evermore to publish anything, or to teach,
or receive friends. Retired to Arcetri in broken down health. Death of
his favourite daughter, Sister Maria Celeste. Wrote and meditated on the
laws of motion. Discovered the moon's libration. In 1637 he became
blind. The rigour was then slightly relaxed and many visited him: among
them John Milton. Died 8th of January, 1642, aged 78. As a prisoner of
the Inquisition his right to make a will or to be buried in consecrated
ground was disputed. Many of his manuscripts were destroyed.
Galileo, besides being a singularly clear-headed thinker and
experimental genius, was also something of a musician, a poet, and an
artist. He was full of humour as well as of solid common-sense, and his
literary style is brilliant. Of his scientific achievements those now
reckoned most weighty, are the discovery of the Laws of Motion, and the
laying of the foundations of Mechanics.
_Particulars of Jupiter's Satellites,
Illustrating their obedience to Kepler's third law._
--------------------------------------------------------------------------
| | | Distance| | | T^2
| | Time of | from | | | ----
Satellite.|Diameter revolution | Jupiter, | T^2 | d^3 | d^3
| miles.| in hours. |in Jovian | | | which is
| miles | (T) | radii. | | |practically
| | | (d) | | | constant.
----------|-------|------------|----------|---------|---------|-----------
No. 1. | 2437 | 42·47 | 6·049 | 1803·7 | 221·44 | 8·149
No. 2. | 2188 | 85·23 | 9·623 | 7264·1 | 891·11 | 8·152
No. 3. | 3575 | 177·72 | 15·350 | 29488· | 3916·8 | 8·153
No. 4. | 3059 | 400·53 | 26·998 |160426· |19679· | 8·152
--------------------------------------------------------------------------
The diameter of Jupiter is 85,823 miles.
_Falling Bodies._
Since all bodies fall at the same rate, except for the disturbing effect
of the resistance of the air, a statement of their rates of fall is of
interest. In one second a freely falling body near the earth is found to
drop 16 feet. In two seconds it drops 64 feet altogether, viz. 16 feet
in the first, and 48 feet in the next second; because at the beginning
of every second after the first it has the accumulated velocity of
preceding seconds. The height fallen by a dropped body is not
proportional to the time simply, but to what is rather absurdly called
the square of the time, _i.e._ the time multiplied by itself.
For instance, in 3 seconds it drops 9 × 16 = 144 feet; in 4 seconds 16 ×
16, or 256 feet, and so on. The distances travelled in 1, 2, 3, 4, &c.,
seconds by a body dropped from rest and not appreciably resisted by the
air, are 1, 4, 9, 16, 25, &c., respectively, each multiplied by the
constant 16 feet.
Another way of stating the law is to say that the heights travelled in
successive seconds proceed in the proportion 1, 3, 5, 7, 9, &c.; again
multiplied by 16 feet in each case.
[Illustration: FIG. 35.--Curve described by a projectile, showing how it
drops from the line of fire, _O D_, in successive seconds, the same
distances _AP_, _BQ_, _CR_, &c., as are stated above for a dropped
body.]
All this was experimentally established by Galileo.
A body takes half a second to drop 4 feet; and a quarter of a second to
drop 1 foot. The easiest way of estimating a quarter of a second with
some accuracy is to drop a bullet one foot.
A bullet thrown or shot in any direction falls just as much as if merely
dropped; but instead of falling from the starting-point it drops
vertically from the line of fire. (See fig. 35).
The rate of fall depends on the intensity of gravity; if it could be
doubled, a body would fall twice as far in the same time; but to make it
fall a given distance in half the time the intensity of gravity would
have to be quadrupled. At a place where the intensity of gravity is
1/3600 of what it is here, a body would fall as far in a minute as it
now falls in a second. Such a place occurs at about the distance of the
moon (_cf._ page 177).
The fact that the height fallen through is proportional to the square
of the time proves that the attraction of the earth or the intensity of
gravity is sensibly constant throughout ordinary small ranges. Over
great distances of fall, gravity cannot be considered constant; so for
things falling through great spaces the Galilean law of the square of
the time does not hold.
The fact that things near the earth fall 16 feet in the first second
proves that the intensity of ordinary terrestrial gravity is 32 British
units of force per pound of matter.
The fact that all bodies fall at the same rate (when the resistance of
the air is eliminated), proves that weight is proportional to mass; or
more explicitly, that the gravitative attraction of the earth on matter
near its surface depends on the amount of that matter, as estimated by
its inertia, and on nothing else.
LECTURE IV
GALILEO AND THE INVENTION OF THE TELESCOPE
Contemporary with the life of Kepler, but overlapping it at both ends,
comes the great and eventful life of Galileo Galilei,[5] a man whose
influence on the development of human thought has been greater than that
of any man whom we have yet considered, and upon whom, therefore, it is
necessary for us, in order to carry out the plan of these lectures, to
bestow much time. A man of great and wide culture, a so-called universal
genius, it is as an experimental philosopher that he takes the first
rank. In this capacity he must be placed alongside of Archimedes, and it
is pretty certain that between the two there was no man of magnitude
equal to either in experimental philosophy. It is perhaps too bold a
speculation, but I venture to doubt whether in succeeding generations we
find his equal in the domain of purely experimental science until we
come to Faraday. Faraday was no doubt his superior, but I know of no
other of whom the like can unhesitatingly be said. In mathematical and
deductive science, of course, it is quite otherwise. Kepler, for
instance, and many men before and since, have far excelled Galileo in
mathematical skill and power, though at the same time his achievements
in this department are by no means to be despised.
Born at Pisa three centuries ago, on the very day that Michael Angelo
lay dying in Rome, he inherited from his father a noble name, cultivated
tastes, a keen love of truth, and an impoverished patrimony. Vincenzo de
Galilei, a descendant of the important Bonajuti family, was himself a
mathematician and a musician, and in a book of his still extant he
declares himself in favour of free and open inquiry into scientific
matters, unrestrained by the weight of authority and tradition.
In all probability the son imbibed these precepts: certainly he acted on
them.
Vincenzo, having himself experienced the unremunerative character of
scientific work, had a horror of his son's taking to it, especially as
in his boyhood he was always constructing ingenious mechanical toys, and
exhibiting other marks of precocity. So the son was destined for
business--to be, in fact, a cloth-dealer. But he was to receive a good
education first, and was sent to an excellent convent school.
Here he made rapid progress, and soon excelled in all branches of
classics and literature. He delighted in poetry, and in later years
wrote several essays on Dante, Tasso, and Ariosto, besides composing
some tolerable poems himself. He played skilfully on several musical
instruments, especially on the lute, of which indeed he became a master,
and on which he solaced himself when quite an old man. Besides this he
seems to have had some skill as an artist, which was useful afterwards
in illustrating his discoveries, and to have had a fine sensibility as
an art critic, for we find several eminent painters of that day
acknowledging the value of the opinion of the young Galileo.
Perceiving all this display of ability, the father wisely came to the
conclusion that the selling of woollen stuffs would hardly satisfy his
aspirations for long, and that it was worth a sacrifice to send him to
the University. So to the University of his native town he went, with
the avowed object of studying medicine, that career seeming the most
likely to be profitable. Old Vincenzo's horror of mathematics or science
as a means of obtaining a livelihood is justified by the fact that while
the University Professor of Medicine received 2,000 scudi a year, the
Professor of Mathematics had only 60, that is £13 a year, or 7-1/2_d._ a
day.
So the son had been kept properly ignorant of such poverty-stricken
subjects, and to study medicine he went.
But his natural bent showed itself even here. For praying one day in the
Cathedral, like a good Catholic as he was all his life, his attention
was arrested by the great lamp which, after lighting it, the verger had
left swinging to and fro. Galileo proceeded to time its swings by the
only watch he possessed--viz., his own pulse. He noticed that the time
of swing remained as near as he could tell the same, notwithstanding the
fact that the swings were getting smaller and smaller.
By subsequent experiment he verified the law, and the isochronism of the
pendulum was discovered. An immensely important practical discovery
this, for upon it all modern clocks are based; and Huyghens soon applied
it to the astronomical clock, which up to that time had been a crude and
quite untrustworthy instrument.
The best clock which Tycho Brahé could get for his observatory was
inferior to one that may now be purchased for a few shillings; and this
change is owing to the discovery of the pendulum by Galileo. Not that he
applied it to clocks; he was not thinking of astronomy, he was thinking
of medicine, and wanted to count people's pulses. The pendulum served;
and "pulsilogies," as they were called, were thus introduced to and used
by medical practitioners.
The Tuscan Court came to Pisa for the summer months, for it was then a
seaside place, and among the suite was Ostillio Ricci, a distinguished
mathematician and old friend of the Galileo family. The youth visited
him, and one day, it is said, heard a lesson in Euclid being given by
Ricci to the pages while he stood outside the door entranced. Anyhow he
implored Ricci to help him into some knowledge of mathematics, and the
old man willingly consented. So he mastered Euclid and passed on to
Archimedes, for whom he acquired a great veneration.
His father soon heard of this obnoxious proclivity, and did what he
could to divert him back to medicine again. But it was no use.
Underneath his Galen and Hippocrates were secreted copies of Euclid and
Archimedes, to be studied at every available opportunity. Old Vincenzo
perceived the bent of genius to be too strong for him, and at last gave
way.
[Illustration: FIG. 36.--Two forms of pulsilogy. The string is wound up
till the swinging weight keeps time with the pulse, and the position of
a bead or of an index connected with the string is then read on a scale
or dial.]
With prodigious rapidity the released philosopher now assimilated the
elements of mathematics and physics, and at twenty-six we find him
appointed for three years to the University Chair of Mathematics, and
enjoying the paternally dreaded stipend of 7-1/2_d._ a day.
Now it was that he pondered over the laws of falling bodies. He
verified, by experiment, the fact that the velocity acquired by falling
down any slope of given height was independent of the angle of slope.
Also, that the height fallen through was proportional to the square of
the time.
Another thing he found experimentally was that all bodies, heavy and
light, fell at the same rate, striking the ground at the same time.[6]
Now this was clean contrary to what he had been taught. The physics of
those days were a simple reproduction of statements in old books.
Aristotle had asserted certain things to be true, and these were
universally believed. No one thought of trying the thing to see if it
really were so. The idea of making an experiment would have savoured of
impiety, because it seemed to tend towards scepticism, and cast a doubt
on a reverend authority.
Young Galileo, with all the energy and imprudence of youth (what a
blessing that youth has a little imprudence and disregard of
consequences in pursuing a high ideal!), as soon as he perceived that
his instructors were wrong on the subject of falling bodies, instantly
informed them of the fact. Whether he expected them to be pleased or not
is a question. Anyhow, they were not pleased, but were much annoyed by
his impertinent arrogance.
It is, perhaps, difficult for us now to appreciate precisely their
position. These doctrines of antiquity, which had come down hoary with
age, and the discovery of which had reawakened learning and quickened
intellectual life, were accepted less as a science or a philosophy, than
as a religion. Had they regarded Aristotle as a verbally inspired
writer, they could not have received his statements with more
unhesitating conviction. In any dispute as to a question of fact, such
as the one before us concerning the laws of falling bodies, their method
was not to make an experiment, but to turn over the pages of Aristotle;
and he who could quote chapter and verse of this great writer was held
to settle the question and raise it above the reach of controversy.
It is very necessary for us to realize this state of things clearly,
because otherwise the attitude of the learned of those days towards
every new discovery seems stupid and almost insane. They had a
crystallized system of truth, perfect, symmetrical--it wanted no
novelty, no additions; every addition or growth was an imperfection, an
excrescence, a deformity. Progress was unnecessary and undesired. The
Church had a rigid system of dogma, which must be accepted in its
entirety on pain of being treated as a heretic. Philosophers had a
cast-iron system of truth to match--a system founded upon Aristotle--and
so interwoven with the great theological dogmas that to question one was
almost equivalent to casting doubt upon the other.
In such an atmosphere true science was impossible. The life-blood of
science is growth, expansion, freedom, development. Before it could
appear it must throw off these old shackles of centuries. It must burst
its old skin, and emerge, worn with the struggle, weakly and
unprotected, but free and able to grow and to expand. The conflict was
inevitable, and it was severe. Is it over yet? I fear not quite, though
so nearly as to disturb science hardly at all. Then it was different; it
was terrible. Honour to the men who bore the first shock of the battle!
Now Aristotle had said that bodies fell at rates depending on their
weight.
A 5 lb. weight would fall five times as quick as a 1 lb. weight; a 50
lb. weight fifty times as quick, and so on.
Why he said so nobody knows. He cannot have tried. He was not above
trying experiments, like his smaller disciples; but probably it never
occurred to him to doubt the fact. It seems so natural that a heavy body
should fall quicker than a light one; and perhaps he thought of a stone
and a feather, and was satisfied.
Galileo, however, asserted that the weight did not matter a bit, that
everything fell at the same rate (even a stone and a feather, but for
the resistance of the air), and would reach the ground in the same time.
And he was not content to be pooh-poohed and snubbed. He knew he was
right, and he was determined to make every one see the facts as he saw
them. So one morning, before the assembled University, he ascended the
famous leaning tower, taking with him a 100 lb. shot and a 1 lb. shot.
He balanced them on the edge of the tower, and let them drop together.
Together they fell, and together they struck the ground.
The simultaneous clang of those two weights sounded the death-knell of
the old system of philosophy, and heralded the birth of the new.
But was the change sudden? Were his opponents convinced? Not a jot.
Though they had seen with their eyes, and heard with their ears, the
full light of heaven shining upon them, they went back muttering and
discontented to their musty old volumes and their garrets, there to
invent occult reasons for denying the validity of the observation, and
for referring it to some unknown disturbing cause.
They saw that if they gave way on this one point they would be letting
go their anchorage, and henceforward would be liable to drift along with
the tide, not knowing whither. They dared not do this. No; they _must_
cling to the old traditions; they could not cast away their rotting
ropes and sail out on to the free ocean of God's truth in a spirit of
fearless faith.
[Illustration: FIG. 37.--Tower of Pisa.]
Yet they had received a shock: as by a breath of fresh salt breeze and
a dash of spray in their faces, they had been awakened out of their
comfortable lethargy. They felt the approach of a new era.
Yes, it was a shock; and they hated the young Galileo for giving it
them--hated him with the sullen hatred of men who fight for a lost and
dying cause.
We need scarcely blame these men; at least we need not blame them
overmuch. To say that they acted as they did is to say that they were
human, were narrow-minded, and were the apostles of a lost cause. But
_they_ could not know this; _they_ had no experience of the past to
guide them; the conditions under which they found themselves were novel,
and had to be met for the first time. Conduct which was excusable then
would be unpardonable now, in the light of all this experience to guide
us. Are there any now who practically repeat their error, and resist new
truth? who cling to any old anchorage of dogma, and refuse to rise with
the tide of advancing knowledge? There may be some even now.
Well, the unpopularity of Galileo smouldered for a time, until, by
another noble imprudence, he managed to offend a semi-royal personage,
Giovanni de Medici, by giving his real opinion, when consulted, about a
machine which de Medici had invented for cleaning out the harbour of
Leghorn. He said it was as useless as it in fact turned out to be.
Through the influence of the mortified inventor he lost favour at Court;
and his enemies took advantage of the fact to render his chair
untenable. He resigned before his three years were up, and retired to
Florence.
His father at this time died, and the family were left in narrow
circumstances. He had a brother and three sisters to provide for.
He was offered a professorship at Padua for six years by the Senate of
Venice, and willingly accepted it.
Now began a very successful career. His introductory address was marked
by brilliant eloquence, and his lectures soon acquired fame. He wrote
for his pupils on the laws of motion, on fortifications, on sundials, on
mechanics, and on the celestial globe: some of these papers are now
lost, others have been printed during the present century.
Kepler sent him a copy of his new book, _Mysterium Cosmographicum_, and
Galileo in thanking him for it writes him the following letter:--[7]
"I count myself happy, in the search after truth, to have so great
an ally as yourself, and one who is so great a friend of the truth
itself. It is really pitiful that there are so few who seek truth,
and who do not pursue a perverse method of philosophising. But this
is not the place to mourn over the miseries of our times, but to
congratulate you on your splendid discoveries in confirmation of
truth. I shall read your book to the end, sure of finding much that
is excellent in it. I shall do so with the more pleasure, because
_I have been for many years 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. _I have collected many arguments for the purpose of
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 become an
object of ridicule and scorn. I should certainly venture to publish
my speculations if there were more people like you. But this not
being the case, I refrain from such an undertaking."
Kepler urged him to publish his arguments in favour of the Copernican
theory, but he hesitated for the present, knowing that his declaration
would be received with ridicule and opposition, and thinking it wiser to
get rather more firmly seated in his chair before encountering the
storm of controversy.
The six years passed away, and the Venetian Senate, anxious not to lose
so bright an ornament, renewed his appointment for another six years at
a largely increased salary.
Soon after this appeared a new star, the stella nova of 1604, not the
one Tycho had seen--that was in 1572--but the same that Kepler was so
much interested in.
Galileo gave a course of three lectures upon it to a great audience. At
the first the theatre was over-crowded, so he had to adjourn to a hall
holding 1000 persons. At the next he had to lecture in the open air.
He took occasion to rebuke his hearers for thronging to hear about an
ephemeral novelty, while for the much more wonderful and important
truths about the permanent stars and facts of nature they had but deaf
ears.
But the main point he brought out concerning the new star was that it
upset the received Aristotelian doctrine of the immutability of the
heavens. According to that doctrine the heavens were unchangeable,
perfect, subject neither to growth nor to decay. Here was a body, not a
meteor but a real distant star, which had not been visible and which
would shortly fade away again, but which meanwhile was brighter than
Jupiter.
The staff of petrified professorial wisdom were annoyed at the
appearance of the star, still more at Galileo's calling public attention
to it; and controversy began at Padua. However, he accepted it; and now
boldly threw down the gauntlet in favour of the Copernican theory,
utterly repudiating the old Ptolemaic system which up to that time he
had taught in the schools according to established custom.
The earth no longer the only world to which all else in the firmament
were obsequious attendants, but a mere insignificant speck among the
host of heaven! Man no longer the centre and cynosure of creation, but,
as it were, an insect crawling on the surface of this little speck! All
this not set down in crabbed Latin in dry folios for a few learned
monks, as in Copernicus's time, but promulgated and argued in rich
Italian, illustrated by analogy, by experiment, and with cultured wit;
taught not to a few scholars here and there in musty libraries, but
proclaimed in the vernacular to the whole populace with all the energy
and enthusiasm of a recent convert and a master of language! Had a
bombshell been exploded among the fossilized professors it had been less
disturbing.
But there was worse in store for them.
A Dutch optician, Hans Lippershey by name, of Middleburg, had in his
shop a curious toy, rigged up, it is said, by an apprentice, and made
out of a couple of spectacle lenses, whereby, if one looked through it,
the weather-cock of a neighbouring church spire was seen nearer and
upside down.
The tale goes that the Marquis Spinola, happening to call at the shop,
was struck with the toy and bought it. He showed it to Prince Maurice of
Nassau, who thought of using it for military reconnoitring. All this is
trivial. What is important is that some faint and inaccurate echo of
this news found its way to Padua, and into the ears of Galileo.
The seed fell on good soil. All that night he sat up and pondered. He
knew about lenses and magnifying glasses. He had read Kepler's theory of
the eye, and had himself lectured on optics. Could he not hit on the
device and make an instrument capable of bringing the heavenly bodies
nearer? Who knew what marvels he might not so perceive! By morning he
had some schemes ready to try, and one of them was successful.
Singularly enough it was not the same plan as the Dutch optician's, it
was another mode of achieving the same end.
He took an old small organ pipe, jammed a suitably chosen spectacle
glass into either end, one convex the other concave, and behold, he had
the half of a wretchedly bad opera glass capable of magnifying three
times. It was better than the Dutchman's, however; it did not invert.
It is easy to understand the general principle of a telescope. A
general knowledge of the common magnifying glass may be assumed.
Roger Bacon knew about lenses; and the ancients often refer to
them, though usually as burning glasses. The magnifying power of
globes of water must have been noticed soon after the discovery of
glass and the art of working it.
A magnifying glass is most simply thought of as an additional lens
to the eye. The eye has a lens by which ordinary vision is
accomplished, an extra glass lens strengthens it and enables
objects to be seen nearer and therefore apparently bigger. But to
apply a magnifying glass to distant objects is impossible. In order
to magnify distant objects, another function of lenses has also to
be employed, viz., their power of forming real images, the power on
which their use as burning-glasses depends: for the best focus is
an image of the sun. Although the object itself is inaccessible,
the image of it is by no means so, and to the image a magnifier can
be applied. This is exactly what is done in the telescope; the
object glass or large lens forms an image, which is then looked at
through a magnifying glass or eye-piece.
Of course the image is nothing like so big as the object. For
astronomical objects it is almost infinitely less; still it is an
exact representation at an accessible place, and no one expects a
telescope to show distant bodies as big as they really are. All it
does is to show them bigger than they could be seen without it.
But if the objects are not distant, the same principle may still be
applied, and two lenses may be used, one to form an image, the
other to magnify it; only if the object can be put where we please,
we can easily place it so that its image is already much bigger
than the object even before magnification by the eye lens. This is
the compound microscope, the invention of which soon followed the
telescope. In fact the two instruments shade off into one another,
so that the reading telescope or reading microscope of a laboratory
(for reading thermometers, and small divisions generally) goes by
either name at random.
The arrangement so far described depicts things on the retina the
unaccustomed way up. By using a concave glass instead of a convex,
and placing it so as to prevent any image being formed, except on
the retina direct, this inconvenience is avoided.
[Illustration: FIG. 38.--View of the half-moon in small telescope. The
darker regions, or plains, used to be called "seas."]
Such a thing as Galileo made may now be bought at a toy-shop for I
suppose half a crown, and yet what a potentiality lay in that "glazed
optic tube," as Milton called it. Away he went with it to Venice and
showed it to the Signoria, to their great astonishment. "Many noblemen
and senators," says Galileo, "though of advanced age, mounted to the top
of one of the highest towers to watch the ships, which were visible
through my glass two hours before they were seen entering the harbour,
for it makes a thing fifty miles off as near and clear as if it were
only five." Among the people too the instrument excited the greatest
astonishment and interest, so that he was nearly mobbed. The Senate
hinted to him that a present of the instrument would not be
unacceptable, so Galileo took the hint and made another for them.
[Illustration: FIG. 39.--Portion of the lunar surface more highly
magnified, showing the shadows of a mountain range, deep pits, and other
details.]
They immediately doubled his salary at Padua, making it 1000 florins,
and confirmed him in the enjoyment of it for life.
He now eagerly began the construction of a larger and better instrument.
Grinding the lenses with his own hands with consummate skill, he
succeeded in making a telescope magnifying thirty times. Thus equipped
he was ready to begin a survey of the heavens.
[Illustration: FIG. 40.--Another portion of the lunar surface, showing a
so-called crater or vast lava pool and other evidences of ancient heat
unmodified by water.]
The first object he carefully examined was naturally the moon. He found
there everything at first sight very like the earth, mountains and
valleys, craters and plains, rocks, and apparently seas. You may imagine
the hostility excited among the Aristotelian philosophers, especially no
doubt those he had left behind at Pisa, on the ground of his spoiling
the pure, smooth, crystalline, celestial face of the moon as they had
thought it, and making it harsh and rugged and like so vile and ignoble
a body as the earth.
[Illustration: FIG. 41.--Lunar landscape showing earth. The earth would
be a stationary object in the moon's sky: its only apparent motion being
a slow oscillation as of a pendulum (the result of the moon's
libration).]
He went further, however, into heterodoxy than this--he not only made
the moon like the earth, but he made the earth shine like the moon. The
visibility of "the old moon in the new moon's arms" he explained by
earth-shine. Leonardo had given the same explanation a century before.
Now one of the many stock arguments against Copernican theory of the
earth being a planet like the rest was that the earth was dull and dark
and did not shine. Galileo argued that it shone just as much as the moon
does, and in fact rather more--especially if it be covered with clouds.
One reason of the peculiar brilliancy of Venus is that she is a very
cloudy planet.[8] Seen from the moon the earth would look exactly as the
moon does to us, only a little brighter and sixteen times as big (four
times the diameter).
[Illustration: FIG. 42.--Galileo's method of estimating the height of
lunar mountain.
_AB'BC_ is the illuminated half of the moon. _SA_ is a solar ray just
catching the peak of the mountain _M_. Then by geometry, as _MN_ is to
_MA_, so is _MA_ to _MB'_; whence the height of the mountain, _MN_, can
be determined. The earth and spectator are supposed to be somewhere in
the direction _BA_ produced, _i.e._ towards the top of the page.]
Galileo made a very good estimate of the height of lunar mountains,
of which many are five miles high and some as much as seven. He did
this simply by measuring from the half-moon's straight edge the
distance at which their peaks caught the rising or setting sun. The
above simple diagram shows that as this distance is to the diameter
of the moon, so is the height of the sun-tipped mountain to the
aforesaid distance.
Wherever Galileo turned his telescope new stars appeared. The Milky Way,
which had so puzzled the ancients, was found to be composed of stars.
Stars that appeared single to the eye were some of them found to be
double; and at intervals were found hazy nebulous wisps, some of which
seemed to be star clusters, while others seemed only a fleecy cloud.
[Illustration: FIG. 43.--Some clusters and nebulæ.]
[Illustration: FIG. 44.--Jupiter's satellites, showing the stages of
their discovery.]
Now we come to his most brilliant, at least his most sensational,
discovery. Examining Jupiter minutely on January 7, 1610, he noticed
three little stars near it, which he noted down as fixing its then
position. On the following night Jupiter had moved to the other side of
the three stars. This was natural enough, but was it moving the right
way? On examination it appeared not. Was it possible the tables were
wrong? The next evening was cloudy, and he had to curb his feverish
impatience. On the 10th there were only two, and those on the other
side. On the 11th two again, but one bigger than the other. On the 12th
the three re-appeared, and on the 13th there were four. No more
appeared.
Jupiter then had moons like the earth, four of them in fact, and they
revolved round him in periods which were soon determined.
The reason why they were not all visible at first, and why their
visibility so rapidly changes, is because they revolve round him
almost in the plane of our vision, so that sometimes they are in
front and sometimes behind him, while again at other times they
plunge into his shadow and are thus eclipsed from the light of the
sun which enables us to see them. A large modern telescope will
show the moons when in front of Jupiter, but small telescopes will
only show them when clear of the disk and shadow. Often all four
can be thus seen, but three or two is a very common amount of
visibility. Quite a small telescope, such as a ship's telescope, if
held steadily, suffices to show the satellites of Jupiter, and very
interesting objects they are. They are of habitable size, and may
be important worlds for all we know to the contrary.
The news of the discovery soon spread and excited the greatest interest
and astonishment. Many of course refused to believe it. Some there were
who having been shown them refused to believe their eyes, and asserted
that although the telescope acted well enough for terrestrial objects,
it was altogether false and illusory when applied to the heavens. Others
took the safer ground of refusing to look through the glass. One of
these who would not look at the satellites happened to die soon
afterwards. "I hope," says Galileo, "that he saw them on his way to
heaven."
The way in which Kepler received the news is characteristic, though by
adding four to the supposed number of planets it might have seemed to
upset his notions about the five regular solids.
He says,[9] "I was sitting idle at home thinking of you, most
excellent Galileo, and your letters, when the news was brought me
of the discovery of four planets by the help of the double
eye-glass. Wachenfels stopped his carriage at my door to tell me,
when such a fit of wonder seized me at a report which seemed so
very absurd, and I was thrown into such agitation at seeing an old
dispute between us decided in this way, that between his joy, my
colouring, and the laughter of us both, confounded as we were by
such a novelty, we were hardly capable, he of speaking, or I of
listening....
"On our separating, I immediately fell to thinking how there could
be any addition to the number of planets without overturning my
_Mysterium Cosmographicon_, published thirteen years ago, according
to which Euclid's five regular solids do not allow more than six
planets round the sun.
"But I am so far from disbelieving the existence of the four
circumjovial planets that I long for a telescope to anticipate you
if possible in discovering two round Mars (as the proportion seems
to me to require) six or eight round Saturn, and one each round
Mercury and Venus."
[Illustration: FIG. 45.--Eclipses of Jupiter's satellites. The diagram
shows the first (_i.e._ the nearest) moon in Jupiter's shadow, the
second as passing between earth and Jupiter, and appearing to transit
his disk, the third as on the verge of entering his shadow, and the
fourth quite plainly and separately visible.]
As an illustration of the opposite school, I will take the following
extract from Francesco Sizzi, a Florentine astronomer, who argues
against the discovery thus:--
"There are seven windows in the head, two nostrils, two eyes, two
ears, and a mouth; so in the heavens there are two favourable
stars, two unpropitious, two luminaries, and Mercury alone
undecided and indifferent. From which and many other similar
phenomena of nature, such as the seven metals, &c., which it were
tedious to enumerate, we gather that the number of planets is
necessarily seven.
"Moreover, the satellites are invisible to the naked eye, and
therefore can have no influence on the earth, and therefore would
be useless, and therefore do not exist.
"Besides, the Jews and other ancient nations as well as modern
Europeans have adopted the division of the week into seven days,
and have named them from the seven planets: now if we increase the
number of the planets this whole system falls to the ground."
To these arguments Galileo replied that whatever their force might be as
a reason for believing beforehand that no more than seven planets would
be discovered, they hardly seemed of sufficient weight to destroy the
new ones when actually seen.
Writing to Kepler at this time, Galileo ejaculates:
"Oh, my dear Kepler, how I wish that we could have one hearty laugh
together! Here, at Padua, is the 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."
A young German _protégé_ of Kepler, Martin Horkey, was travelling in
Italy, and meeting Galileo at Bologna was favoured with a view through
his telescope. But supposing that Kepler must necessarily be jealous of
such great discoveries, and thinking to please him, he writes, "I cannot
tell what to think about these observations. They are stupendous, they
are wonderful, but whether they are true or false I cannot tell." He
concludes, "I will never concede his four new planets to that Italian
from Padua though I die for it." So he published a pamphlet asserting
that reflected rays and optical illusions were the sole cause of the
appearance, and that the only use of the imaginary planets was to
gratify Galileo's thirst for gold and notoriety.
When after this performance he paid a visit to his old instructor
Kepler, he got a reception which astonished him. However, he pleaded so
hard to be forgiven that Kepler restored him to partial favour, on this
condition, that he was to look again at the satellites, and this time to
see them and own that they were there.
By degrees the enemies of Galileo were compelled to confess to the truth
of the discovery, and the next step was to outdo him. Scheiner counted
five, Rheiter nine, and others went as high as twelve. Some of these
were imaginary, some were fixed stars, and four satellites only are
known to this day.[10]
Here, close to the summit of his greatness, we must leave him for a
time. A few steps more and he will be on the brow of the hill; a short
piece of table-land, and then the descent begins.
LECTURE V
GALILEO AND THE INQUISITION
One sinister event occurred while Galileo was at Padua, some time before
the era we have now arrived at, before the invention of the
telescope--two years indeed after he had first gone to Padua; an event
not directly concerning Galileo, but which I must mention because it
must have shadowed his life both at the time and long afterwards. It was
the execution of Giordano Bruno for heresy. This eminent philosopher had
travelled largely, had lived some time in England, had acquired new and
heterodox views on a variety of subjects, and did not hesitate to
propound them even after he had returned to Italy.
The Copernican doctrine of the motion of the earth was one of his
obnoxious heresies. Being persecuted to some extent by the Church, Bruno
took refuge in Venice--a free republic almost independent of the
Papacy--where he felt himself safe. Galileo was at Padua hard by: the
University of Padua was under the government of the Senate of Venice:
the two men must in all probability have met.
Well, the Inquisition at Rome sent messengers to Venice with a demand
for the extradition of Bruno--they wanted him at Rome to try him for
heresy.
In a moment of miserable weakness the Venetian republic gave him up, and
Bruno was taken to Rome. There he was tried, and cast into the dungeons
for six years, and because he entirely refused to recant, was at length
delivered over to the secular arm and burned at the stake on 16th
February, Anno Domini 1600.
This event could not but have cast a gloom over the mind of lovers and
expounders of truth, and the lesson probably sank deep into Galileo's
soul.
In dealing with these historic events will you allow me to repudiate
once for all the slightest sectarian bias or meaning. I have nothing to
do with Catholic or Protestant as such. I have nothing to do with the
Church of Rome as such. I am dealing with the history of science. But
historically at one period science and the Church came into conflict. It
was not specially one Church rather than another--it was the Church in
general, the only one that then existed in those countries.
Historically, I say, they came into conflict, and historically the
Church was the conqueror. It got its way; and science, in the persons of
Bruno, Galileo, and several others, was vanquished.
Such being the facts, there is no help but to mention them in dealing
with the history of science.
Doubtless _now_ the Church regards it as an unhappy victory, and gladly
would ignore this painful struggle. This, however, is impossible. With
their creed the Churchmen of that day could act in no other way. They
were bound to prosecute heresy, and they were bound to conquer in the
struggle or be themselves shattered.
But let me insist on the fact that no one accuses the ecclesiastical
courts of crime or evil motives. They attacked heresy after their
manner, as the civil courts attacked witchcraft after _their_ manner.
Both erred grievously, but both acted with the best intentions.
We must remember, moreover, that his doctrines were scientifically
heterodox, and the University Professors of that day were probably quite
as ready to condemn them as the Church was. To realise the position we
must think of some subjects which _to-day_ are scientifically
heterodox, and of the customary attitude adopted towards them by
persons of widely differing creeds.
If it be contended now, as it is, that the ecclesiastics treated Galileo
well, I admit it freely: they treated him as well as they possibly
could. They overcame him, and he recanted; but if he had not recanted,
if he had persisted in his heresy, they would--well, they would still
have treated his soul well, but they would have set fire to his body.
Their mistake consisted not in cruelty, but in supposing themselves the
arbiters of eternal truth; and by no amount of slurring and glossing
over facts can they evade the responsibility assumed by them on account
of this mistaken attitude.
I am not here attacking the dogma of Papal Infallibility: it is
historically, I believe, quite unaffected by the controversy respecting
the motion of the earth, no Papal edict _ex cathedrâ_ having been
promulgated on the subject.
We left Galileo standing at his telescope and beginning his survey of
the heavens. We followed him indeed through a few of his first great
discoveries--the discovery of the mountains and other variety of surface
in the moon, of the nebulæ and a multitude of faint stars, and lastly of
the four satellites of Jupiter.
This latter discovery made an immense sensation, and contributed its
share to his removal from Padua, which quickly followed it, as I shall
shortly narrate; but first I think it will be best to continue our
survey of his astronomical discoveries without regard to the place
whence they were made.
Before the end of the year Galileo had made another discovery--this time
on Saturn. But to guard against the host of plagiarists and impostors,
he published it in the form of an anagram, which, at the request of the
Emperor Rudolph (a request probably inspired by Kepler), he interpreted;
it ran thus: The furthest planet is triple.
Very soon after he found that Venus was changing from a full moon to a
half moon appearance. He announced this also by an anagram, and waited
till it should become a crescent, which it did.
This was a dreadful blow to the anti-Copernicans, for it removed the
last lingering difficulty to the reception of the Copernican doctrine.
[Illustration: FIG. 46.--Old drawings of Saturn by different observers,
with the imperfect instruments of that day. The first is Galileo's idea
of what he saw.]
Copernicus had predicted, indeed, a hundred years before, that, if ever
our powers of sight were sufficiently enhanced, Venus and Mercury would
be seen to have phases like the moon. And now Galileo with his
telescope verifies the prediction to the letter.
Here was a triumph for the grand old monk, and a bitter morsel for his
opponents.
Castelli writes: "This must now convince the most obstinate." But
Galileo, with more experience, replies:--"You almost make me laugh
by saying that these clear observations are sufficient to convince
the most obstinate; it seems you have yet to learn that long ago
the observations were enough to convince those who are capable of
reasoning, and those who wish to learn the truth; but that to
convince the obstinate, and those who care for nothing beyond the
vain applause of the senseless vulgar, not even the testimony of
the stars would suffice, were they to descend on earth to speak for
themselves. Let us, then, endeavour to procure some knowledge for
ourselves, and rest contented with this sole satisfaction; but of
advancing in popular opinion, or of gaining the assent of the
book-philosophers, let us abandon both the hope and the desire."
[Illustration: FIG. 47.--Phases of Venus. Showing also its apparent
variations in size by reason of its varying distance from the earth.
When fully illuminated it is necessarily most distant. It looks
brightest to us when a broad crescent.]
What a year's work it had been!
In twelve months observational astronomy had made such a bound as it has
never made before or since.
Why did not others make any of these observations? Because no one could
make telescopes like Galileo.
He gathered pupils round him however, and taught them how to work the
lenses, so that gradually these instruments penetrated Europe, and
astronomers everywhere verified his splendid discoveries.
But still he worked on, and by March in the very next year, he saw
something still more hateful to the Aristotelian philosophers, viz.
spots on the sun.
[Illustration: FIG. 48.]
If anything was pure and perfect it was the sun, they said. Was this
impostor going to blacken its face too?
Well, there they were. They slowly formed and changed, and by moving all
together showed him that the sun rotated about once a month.
Before taking leave of Galileo's astronomical researches, I must
mention an observation made at the end of 1612, that the apparent
triplicity of Saturn (Fig. 46) had vanished.
[Illustration: FIG. 49.--A portion of the sun's disk as seen in a
powerful modern telescope.]
"Looking on Saturn within these few days, I found it solitary,
without the assistance of its accustomed stars, and in short
perfectly round and defined, like Jupiter, and such it still
remains. Now what can be said of so strange a metamorphosis? Are
perhaps the two smaller stars consumed like spots on the sun? Have
they suddenly vanished and fled? Or has Saturn devoured his own
children? Or was the appearance indeed fraud and illusion, with
which the glasses have so long time mocked me and so many others
who have so often observed with me? Now perhaps the time is come to
revive the withering hopes of those, who, guided by more profound
contemplations, have fathomed all the fallacies of the new
observations and recognized their impossibility! I cannot resolve
what to say in a chance so strange, so new, so unexpected. The
shortness of time, the unexampled occurrence, the weakness of my
intellect, the terror of being mistaken, have greatly confounded
me."
However, he plucked up courage, and conjectured that the two attendants
would reappear, by revolving round the planet.
[Illustration: FIG. 50.--Saturn and his rings, as seen under the most
favourable circumstances.]
The real reason of their disappearance is well known to us now. The
plane of Saturn's rings oscillates slowly about our line of sight, and
so we sometimes see them edgeways and sometimes with a moderate amount
of obliquity. The rings are so thin that, when turned precisely
edgeways, they become invisible. The two imaginary attendants were the
most conspicuous portions of the ring, subsequently called _ansæ_.
I have thought it better not to interrupt this catalogue of brilliant
discoveries by any biographical details; but we must now retrace our
steps to the years 1609 and 1610, the era of the invention of the
telescope.
By this time Galileo had been eighteen years at Padua, and like many
another man in like case, was getting rather tired of continual
lecturing. Moreover, he felt so full of ideas that he longed to have a
better opportunity of following them up, and more time for thinking them
out.
Now in the holidays he had been accustomed to return to his family home
at Pisa, and there to come a good deal into contact with the Grand-Ducal
House of Tuscany. Young Cosmo di Medici became in fact his pupil, and
arrived at man's estate with the highest opinion of the philosopher.
This young man had now come to the throne as Cosmo II., and to him
Galileo wrote saying how much he should like more time and leisure, how
full he was of discoveries if he only had the chance of a reasonable
income without the necessity of consuming so large a portion of his time
in elementary teaching, and practically asking to be removed to some
position in the Court. Nothing was done for a time, but negotiations
proceeded, and soon after the discovery of Jupiter's satellites Cosmo
wrote making a generous offer, which Galileo gladly and enthusiastically
accepted, and at once left Padua for Florence. All his subsequent
discoveries date from Florence.
Thus closed his brilliant and happy career as a professor at the
University of Padua. He had been treated well: his pay had become larger
than that of any Professor of Mathematics up to that time; and, as you
know, immediately after his invention of the telescope the Venetian
Senate, in a fit of enthusiasm, had doubled it and secured it to him for
life wherever he was. To throw up his chair and leave the place the very
next year scarcely seems a strictly honourable procedure. It was legal
enough no doubt, and it is easy for small men to criticize a great one,
but nevertheless I think we must admit that it is a step such as a man
with a keen sense of honour would hardly have taken.
One quite feels and sympathizes with the temptation. Not emolument, but
leisure; freedom from harassing engagements and constant teaching, and
liberty to prosecute his studies day and night without interference:
this was the golden prospect before him. He yielded, but one cannot help
wishing he had not.
As it turned out it was a false step--the first false step of his public
career. When made it was irretrievable, and it led to great misery.
At first it seemed brilliant enough. The great philosopher of the Tuscan
Court was courted and flattered by princes and nobles, he enjoyed a
world-wide reputation, lived as luxuriously as he cared for, had his
time all to himself, and lectured but very seldom, on great occasions or
to a few crowned heads.
His position was in fact analogous to that of Tycho Brahé in his island
of Huen.
Misfortune overtook both. In Tycho's case it arose mainly from the death
of his patron. In Galileo's it was due to a more insidious cause, to
understand which cause aright we must remember the political divisions
of Italy at that date.
Tuscany was a Papal State, and thought there was by no means free.
Venice was a free republic, and was even hostile to the Papacy. In 1606
the Pope had placed it under an interdict. In reply it had ejected every
Jesuit.
Out of this atmosphere of comparative enlightenment and freedom into
that hotbed of mediævalism and superstition went Galileo with his eyes
open. Keen was the regret of his Paduan and Venetian friends; bitter
were their remonstrances and exhortations. But he was determined to go,
and, not without turning some of his old friends into enemies, he went.
Seldom has such a man made so great a mistake: never, I suppose, has one
been so cruelly punished for it.
[Illustration: FIG. 51.--Map of Italy.]
We must remember, however, that Galileo, though by no means a saint, was
yet a really religious man, a devout Catholic and thorough adherent of
the Church, so that he would have no dislike to place himself under her
sway. Moreover, he had been born a Tuscan, his family had lived at
Florence or Pisa, and it felt like going home. His theological attitude
is worthy of notice, for he was not in the least a sceptic. He quite
acquiesces in the authority of the Bible, especially in all matters
concerning faith and conduct; as to its statements in scientific
matters, he argues that we are so liable to misinterpret their meaning
that it is really easier to examine Nature for truth in scientific
matters, and that when direct observation and Scripture seem to clash,
it is because of our fallacious interpretation of one or both of them.
He is, in fact, what one now calls a "reconciler."
It is curious to find such a man prosecuted for heresy, when to-day his
opinions are those of the orthodox among the orthodox. But so it ever
is, and the heresy of one generation becomes the commonplace of the
next.
He accepts Joshua's miracle, for instance, not as a striking poem, but
as a literal fact; and he points out how much more simply it could be
done on the Copernican system by stopping the earth's rotation for a
short time, than by stopping the sun and moon and all the host of heaven
as on the old Ptolemaic system, or again by stopping only the sun and
not any of the other bodies, and so throwing astronomy all wrong.
This reads to us like satire, but no doubt it was his genuine opinion.
These Scriptural reconciliations of his, however, angered the religious
authorities still more. They said it was bad enough for this heretic to
try and upset old _scientific_ beliefs, and to spoil the face of
_Nature_ with his infidel discoveries, but at least he might leave the
Bible alone; and they addressed an indignant remonstrance to Rome, to
protect it from the hands of ignorant laymen.
Thus, wherever he turned he encountered hostility. Of course he had many
friends--some of them powerful like Cosmo, all of them faithful and
sincere. But against the power of Rome what could they do? Cosmo dared
no more than remonstrate, and ultimately his successor had to refrain
from even this, so enchained and bound was the spirit of the rulers of
those days; and so when his day of tribulation came he stood alone and
helpless in the midst of his enemies.
You may wonder, perhaps, why this man should excite so much more
hostility than many another man who was suffered to believe and teach
much the same doctrines unmolested. But no other man had made such
brilliant and exciting discoveries. No man stood so prominently forward
in the eyes of all Christendom as the champion of the new doctrines. No
other man stated them so clearly and forcibly, nor drove them home with
such brilliant and telling illustrations.
And again, there was the memory of his early conflict with the
Aristotelians at Pisa, of his scornful and successful refutation of
their absurdities. All this made him specially obnoxious to the
Aristotelian Jesuits in their double capacity both of priests and of
philosophers, and they singled him out for relentless official
persecution.
Not yet, however, is he much troubled by them. The chief men at Rome
have not yet moved. Messages, however, keep going up from Tuscany to
Rome respecting the teachings of this man, and of the harm he is doing
by his pertinacious preaching of the Copernican doctrine that the earth
moves.
At length, in 1615, Pope Paul V. wrote requesting him to come to Rome to
explain his views. He went, was well received, made a special friend of
Cardinal Barberino--an accomplished man in high position, who became in
fact the next Pope. Galileo showed cardinals and others his telescope,
and to as many as would look through it he showed Jupiter's satellites
and his other discoveries. He had a most successful visit. He talked, he
harangued, he held forth in the midst of fifteen or twenty disputants at
once, confounding his opponents and putting them to shame.
His method was to let the opposite arguments be stated as fully and
completely as possible, himself aiding, and often adducing the most
forcible and plausible arguments against his own views; and then, all
having been well stated, he would proceed to utterly undermine and
demolish the whole fabric, and bring out the truth in such a way as to
convince all honest minds. It was this habit that made him such a
formidable antagonist. He never shrank from meeting an opposing
argument, never sought to ignore it, or cloak it in a cloud of words.
Every hostile argument he seemed to delight in, as a foe to be crushed,
and the better and stronger they sounded the more he liked them. He knew
many of them well, he invented a number more, and had he chosen could
have out-argued the stoutest Aristotelian on his own grounds. Thus did
he lead his adversaries on, almost like Socrates, only to ultimately
overwhelm them in a more hopeless rout. All this in Rome too, in the
heart of the Catholic world. Had he been worldly-wise, he would
certainly have kept silent and unobtrusive till he had leave to go away
again. But he felt like an apostle of the new doctrines, whose mission
it was to proclaim them even in this centre of the world and of the
Church.
Well, he had an audience with the Pope--a chat an hour long--and the two
parted good friends, mutually pleased with each other.
He writes that he is all right now, and might return home when he liked.
But the question began to be agitated whether the whole system of
Copernicus ought not to be condemned as impious and heretical. This view
was persistently urged upon the Pope and College of Cardinals, and it
was soon to be decided upon.
Had Galileo been unfaithful to the Church he could have left them to
stultify themselves in any way they thought proper, and himself have
gone; but he felt supremely interested in the result, and he stayed. He
writes:--
"So far as concerns the clearing of my own character, I might
return home immediately; but although this new question regards me
no more than all those who for the last eighty years have supported
those opinions both in public and private, yet, as perhaps I may be
of some assistance in that part of the discussion which depends on
the knowledge of truths ascertained by means of the sciences which
I profess, I, as a zealous and Catholic Christian, neither can nor
ought to withhold that assistance which my knowledge affords, and
this business keeps me sufficiently employed."
It is possible that his stay was the worst thing for the cause he had at
heart. Anyhow, the result was that the system was condemned, and both
the book of Copernicus and the epitome of it by Kepler were placed on
the forbidden list,[11] and Galileo himself was formally ordered never
to teach or to believe the motion of the earth.
He quitted Rome in disgust, which before long broke out in satire. The
only way in which he could safely speak of these views now was as if
they were hypothetical and uncertain, and so we find him writing to the
Archduke Leopold, with a presentation copy of his book on the tides, the
following:--
"This theory occurred to me when in Rome whilst the theologians
were debating on the prohibition of Copernicus's book, and of the
opinion maintained in it of the motion of the earth, which I at
that time believed: until it pleased those gentlemen to suspend the
book, and declare the opinion false and repugnant to the Holy
Scriptures. Now, as I know how well it becomes me to obey and
believe the decisions of my superiors, which proceed out of more
knowledge than the weakness of my intellect can attain to, this
theory which I send you, which is founded on the motion of the
earth, I now look upon as a fiction and a dream, and beg your
highness to receive it as such. But as poets often learn to prize
the creations of their fancy, so in like manner do I set some value
on this absurdity of mine. It is true that when I sketched this
little work I did hope that Copernicus would not, after eighty
years, be convicted of error; and I had intended to develop and
amplify it further, but a voice from heaven suddenly awakened me,
and at once annihilated all my confused and entangled fancies."
This sarcasm, if it had been in print, would probably have been
dangerous. It was safe in a private letter, but it shows us his real
feelings.
However, he was left comparatively quiet for a time. He was getting an
old man now, and passed the time studiously enough, partly at his house
in Florence, partly at his villa in Arcetri, a mile or so out of the
town.
Here was a convent, and in it his two daughters were nuns. One of them,
who passed under the name of Sister Maria Celeste, seems to have been a
woman of considerable capacity--certainly she was of a most affectionate
disposition--and loved and honoured her father in the most dutiful way.
This was a quiet period of his life, spoiled only by occasional fits of
illness and severe rheumatic pains, to which the old man was always
liable. Many little circumstances are known of this peaceful time. For
instance, the convent clock won't go, and Galileo mends it for them. He
is always doing little things for them, and sending presents to the Lady
Superior and his two daughters.
He was occupied now with problems in hydrostatics, and on other matters
unconnected with astronomy: a large piece of work which I must pass
over. Most interesting and acute it is, however.
In 1623, when the old Pope died, there was elected to the Papal throne,
as Urban VIII., Cardinal Barberino, a man of very considerable
enlightenment, and a personal friend of Galileo's, so that both he and
his daughters rejoice greatly, and hope that things will come all right,
and the forbidding edict be withdrawn.
The year after this election he manages to make another journey to Rome
to compliment his friend on his elevation to the Pontifical chair. He
had many talks with Urban, and made himself very agreeable.
Urban wrote to the Grand Duke Ferdinand, son of Cosmo:--
"For We find in him not only literary distinction but also love of
piety, and he is strong in those qualities by which Pontifical good
will is easily obtainable. 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 recalls 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."
Encouraged, doubtless, by these marks of approbation, and reposing too
much confidence in the individual good will of the Pope, without heeding
the crowd of half-declared enemies who were seeking to undermine his
reputation, he set about, after his return to Florence, his greatest
literary and most popular work, _Dialogues on the Ptolemaic and
Copernican Systems_. This purports to be a series of four conversations
between three characters: Salviati, a Copernican philosopher; Sagredo, a
wit and scholar, not specially learned, but keen and critical, and who
lightens the talk with chaff; Simplicio, an Aristotelian philosopher,
who propounds the stock absurdities which served instead of arguments to
the majority of men.
The conversations are something between Plato's _Dialogues_ and Sir
Arthur Helps's _Friends in Council_. The whole is conducted with great
good temper and fairness; and, discreetly enough, no definite conclusion
is arrived at, the whole being left in abeyance as if for a fifth and
decisive dialogue, which, however, was never written, and perhaps was
only intended in case the reception was favourable.
The preface also sets forth that the object of the writer is to show
that the Roman edict forbidding the Copernican doctrine was not issued
in ignorance of the facts of the case, as had been maliciously reported,
and that he wishes to show how well and clearly it was all known
beforehand. So he says the dialogue on the Copernican side takes up the
question purely as a mathematical hypothesis or speculative figment, and
gives it every artificial advantage of which the theory is capable.
This piece of caution was insufficient to blind the eyes of the
Cardinals; for in it the arguments in favour of the earth's motion are
so cogent and unanswerable, and are so popularly stated, as to do more
in a few years to undermine the old system than all that he had written
and spoken before. He could not get it printed for two years after he
had written it, and then only got consent through a piece of
carelessness or laziness on the part of the ecclesiastical censor
through whose hands the manuscript passed--for which he was afterwards
dismissed.
However, it did appear, and was eagerly read; the more, perhaps, as the
Church at once sought to suppress it.
The Aristotelians were furious, and represented to the Pope that he
himself was the character intended by Simplicio, the philosopher whose
opinions get alternately refuted and ridiculed by the other two, till he
is reduced to an abject state of impotence.
The idea that Galileo had thus cast ridicule upon his friend and patron
is no doubt a gratuitous and insulting libel: there is no telling
whether or not Urban believed it, but certainly his countenance changed
to Galileo henceforward, and whether overruled by his Cardinals, or
actuated by some other motive, his favour was completely withdrawn.
The infirm old man was instantly summoned to Rome. His friends pleaded
his age--he was now seventy--his ill-health, the time of year, the state
of the roads, the quarantine existing on account of the plague. It was
all of no avail, to Rome he must go, and on the 14th of February he
arrived.
[Illustration: FIG. 52.--Portrait of Galileo.]
His daughter at Arcetri was in despair; and anxiety and fastings and
penances self-inflicted on his account, dangerously reduced her health.
At Rome he was not imprisoned, but he was told to keep indoors, and show
himself as little as possible. He was allowed, however, to stay at the
house of the Tuscan Ambassador instead of in gaol.
By April he was removed to the chambers of the Inquisition, and examined
several times. Here, however, the anxiety was too much, and his health
began to give way seriously; so, before long, he was allowed to return
to the Ambassador's house; and, after application had been made, was
allowed to drive in the public garden in a half-closed carriage. Thus in
every way the Inquisition dealt with him as leniently as they could. He
was now their prisoner, and they might have cast him into their
dungeons, as many another had been cast. By whatever they were
influenced--perhaps the Pope's old friendship, perhaps his advanced age
and infirmities--he was not so cruelly used.
Still, they had their rules; he _must_ be made to recant and abjure his
heresy; and, if necessary, torture must be applied. This he knew well
enough, and his daughter knew it, and her distress may be imagined.
Moreover, it is not as if they had really been heretics, as if they
hated or despised the Church of Rome. On the contrary, they loved and
honoured the Church. They were sincere and devout worshippers, and only
on a few scientific matters did Galileo presume to differ from his
ecclesiastical superiors: his disagreement with them occasioned him real
sorrow; and his dearest hope was that they could be brought to his way
of thinking and embrace the truth.
Every time he was sent for by the Inquisition he was in danger of
torture unless he recanted. All his friends urged him repeatedly to
submit. They said resistance was hopeless and fatal. Within the memory
of men still young, Giordano Bruno had been burnt alive for a similar
heresy. This had happened while Galileo was at Padua. Venice was full of
it. And since that, only eight years ago indeed, Antonio de Dominis,
Archbishop of Salpetria, had been sentenced to the same fate: "to be
handed over to the secular arm to be dealt with as mercifully as
possible without the shedding of blood." So ran the hideous formula
condemning a man to the stake. After his sentence, this unfortunate man
died in the dungeons in which he had been incarcerated six years--died
what is called a "natural" death; but the sentence was carried out,
notwithstanding, on his lifeless body and his writings. His writings for
which he had been willing to die!
These were the tender mercies of the Inquisition; and this was the kind
of meaning lurking behind many of their well-sounding and merciful
phrases. For instance, what they call "rigorous examination," we call
"torture." Let us, however, remember in our horror at this mode of
compelling a prisoner to say anything they wished, that they were a
legally constituted tribunal; that they acted with well established
rules, and not in passion; and that torture was a recognized mode of
extracting evidence, not only in ecclesiastical but in civil courts, at
that date.
All this, however, was but poor solace to the pitiable old philosopher,
thus ruthlessly haled up and down, questioned and threatened, threatened
and questioned, receiving agonizing letters from his daughter week by
week, and trying to keep up a little spirit to reply as happily and
hopefully as he could.
This condition of things could not go on. From February to June the
suspense lasted. On the 20th of June he was summoned again, and told he
would be wanted all next day for a rigorous examination. Early in the
morning of the 21st he repaired thither, and the doors were shut. Out of
those chambers of horror he did not reappear till the 24th. What went on
all those three days no one knows. He himself was bound to secrecy. No
outsider was present. The records of the Inquisition are jealously
guarded. That he was technically tortured is certain; that he actually
underwent the torment of the rack is doubtful. Much learning has been
expended upon the question, especially in Germany. Several eminent
scholars have held the fact of actual torture to be indisputable
(geometrically certain, one says), and they confirm it by the hernia
from which he afterwards suffered, this being a well-known and frequent
consequence.
Other equally learned commentators, however, deny that the last stage
was reached. For there are five stages all laid down in the rules of the
Inquisition, and steadily adhered to in a rigorous examination, at each
stage an opportunity being given for recantation, every utterance,
groan, or sigh being strictly recorded. The recantation so given has to
be confirmed a day or two later, under pain of a precisely similar
ordeal.
The five stages are:--1st. The official threat in the court. 2nd. The
taking to the door of the torture chamber and renewing the official
threat. 3rd. The taking inside and showing the instruments. 4th.
Undressing and binding upon the rack. 5th. _Territio realis._
Through how many of these ghastly acts Galileo passed I do not know. I
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