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.
| 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 of Newton's "Principia" | 174 | ||
| 60. | 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 |
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.
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 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 Cœlestium," 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 ♈ and ♎, 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 23¼ 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.'"
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.
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.