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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
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 BRAHE 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 NEBULAE 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 KOeNIGSBERG 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.
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.
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 viva 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.
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.
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.
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.
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.
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.
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]
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.
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 E1, E2, &c., be successive positions of the earth; J1, J2, &c., corresponding positions of Jupiter. Produce the lines E1 J1, E2 J2, &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 E1 to E3; is almost stationary from somewhere about E3 to E4; and recedes from E4 to E5; 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.
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.
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.
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]
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 Brahe 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 Brahe'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 BRAHE 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 Brahe.
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 Brahe, 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.
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 Brahe, 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.
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.
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.
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 L400 a year for life, a site for a large observatory, and L20,000 to build it with.
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. L20,000 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.
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.
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 protege 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 Wuertemberg. 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 Tuebingen. 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 Brahe, 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 deg. 7', latitude 48 deg. 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 Tuebingen, 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 x 2 x 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.
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.
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.
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 Brahe 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." |
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