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+The Project Gutenberg EBook of History of Astronomy, by George Forbes
+
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+Title: History of Astronomy
+
+Author: George Forbes
+
+Release Date: May, 2005 [EBook #8172]
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+*** START OF THE PROJECT GUTENBERG EBOOK HISTORY OF ASTRONOMY ***
+
+
+
+
+Produced by Jonathan Ingram, Dave Maddock, Charles Franks
+and the Online Distributed Proofreading Team.
+
+
+
+
+
+
+[Illustration: SIR ISAAC NEWTON (From the bust by Roubiliac In Trinity
+College, Cambridge.)]
+
+HISTORY OF ASTRONOMY
+
+BY
+
+GEORGE FORBES,
+M.A., F.R.S., M. INST. C. E.,
+
+(FORMERLY PROFESSOR OF NATURAL PHILOSOPHY, ANDERSON'S COLLEGE, GLASGOW)
+
+AUTHOR OF "THE TRANSIT OF VENUS," RENDU'S "THEORY OF THE GLACIERS OF
+SAVOY," ETC., ETC.
+
+
+
+
+CONTENTS
+
+  PREFACE
+
+  BOOK I. THE GEOMETRICAL PERIOD
+
+     1. PRIMITIVE ASTRONOMY AND ASTROLOGY
+
+     2. ANCIENT ASTRONOMY--CHINESE AND CHALDAEANS
+
+     3. ANCIENT GREEK ASTRONOMY
+
+     4. THE REIGN OF EPICYCLES--FROM PTOLEMY TO COPERNICUS
+
+  BOOK II. THE DYNAMICAL PERIOD
+
+     5. DISCOVERY OF THE TRUE SOLAR SYSTEM--TYCHO BRAHE--KEPLER
+
+     6. GALILEO AND THE TELESCOPE--NOTIONS OF GRAVITY BY HORROCKS, ETC.
+
+     7. SIR ISAAC NEWTON--LAW OF UNIVERSAL GRAVITATION
+
+     8. NEWTON'S SUCCESSORS--HALLEY, EULER, LAGRANGE, LAPLACE, ETC.
+
+     9. DISCOVERY OF NEW PLANETS--HERSCHEL, PIAZZI, ADAMS, AND LE
+        VERRIER
+
+  BOOK III. OBSERVATION
+
+
+    10. INSTRUMENTS OF PRECISION--SIZE OF THE SOLAR SYSTEM
+
+    11. HISTORY OF THE TELESCOPE--SPECTROSCOPE
+
+  BOOK IV. THE PHYSICAL PERIOD
+
+    12. THE SUN
+
+    13. THE MOON AND PLANETS
+
+    14. COMETS AND METEORS
+
+    15. THE STARS AND NEBULAE
+
+  INDEX
+
+
+
+PREFACE
+
+
+An attempt has been made in these pages to trace the evolution of
+intellectual thought in the progress of astronomical discovery, and,
+by recognising the different points of view of the different ages, to
+give due credit even to the ancients. No one can expect, in a history
+of astronomy of limited size, to find a treatise on "practical" or on
+"theoretical astronomy," nor a complete "descriptive astronomy," and
+still less a book on "speculative astronomy." Something of each of
+these is essential, however, for tracing the progress of thought and
+knowledge which it is the object of this History to describe.
+
+The progress of human knowledge is measured by the increased habit of
+looking at facts from new points of view, as much as by the
+accumulation of facts. The mental capacity of one age does not seem to
+differ from that of other ages; but it is the imagination of new
+points of view that gives a wider scope to that capacity. And this is
+cumulative, and therefore progressive. Aristotle viewed the solar
+system as a geometrical problem; Kepler and Newton converted the point
+of view into a dynamical one. Aristotle's mental capacity to
+understand the meaning of facts or to criticise a train of reasoning
+may have been equal to that of Kepler or Newton, but the point of view
+was different.
+
+Then, again, new points of view are provided by the invention of new
+methods in that system of logic which we call mathematics. All that
+mathematics can do is to assure us that a statement A is equivalent to
+statements B, C, D, or is one of the facts expressed by the statements
+B, C, D; so that we may know, if B, C, and D are true, then A is true.
+To many people our inability to understand all that is contained in
+statements B, C, and D, without the cumbrous process of a mathematical
+demonstration, proves the feebleness of the human mind as a logical
+machine. For it required the new point of view imagined by Newton's
+analysis to enable people to see that, so far as planetary orbits are
+concerned, Kepler's three laws (B, C, D) were identical with Newton's
+law of gravitation (A). No one recognises more than the mathematical
+astronomer this feebleness of the human intellect, and no one is more
+conscious of the limitations of the logical process called
+mathematics, which even now has not solved directly the problem of
+only three bodies.
+
+These reflections, arising from the writing of this History, go to
+explain the invariable humility of the great mathematical astronomers.
+Newton's comparison of himself to the child on the seashore applies to
+them all. As each new discovery opens up, it may be, boundless oceans
+for investigation, for wonder, and for admiration, the great
+astronomers, refusing to accept mere hypotheses as true, have founded
+upon these discoveries a science as exact in its observation of facts
+as in theories. So it is that these men, who have built up the most
+sure and most solid of all the sciences, refuse to invite others to
+join them in vain speculation. The writer has, therefore, in this
+short History, tried to follow that great master, Airy, whose pupil he
+was, and the key to whose character was exactness and accuracy; and he
+recognises that Science is impotent except in her own limited sphere.
+
+It has been necessary to curtail many parts of the History in the
+attempt--perhaps a hopeless one--to lay before the reader in a limited
+space enough about each age to illustrate its tone and spirit, the
+ideals of the workers, the gradual addition of new points of view and
+of new means of investigation.
+
+It would, indeed, be a pleasure to entertain the hope that these pages
+might, among new recruits, arouse an interest in the greatest of all
+the sciences, or that those who have handled the theoretical or
+practical side might be led by them to read in the original some of
+the classics of astronomy. Many students have much compassion for the
+schoolboy of to-day, who is not allowed the luxury of learning the art
+of reasoning from him who still remains pre-eminently its greatest
+exponent, Euclid. These students pity also the man of to-morrow, who
+is not to be allowed to read, in the original Latin of the brilliant
+Kepler, how he was able--by observations taken from a moving platform,
+the earth, of the directions of a moving object, Mars--to deduce the
+exact shape of the path of each of these planets, and their actual
+positions on these paths at any time. Kepler's masterpiece is one of
+the most interesting books that was ever written, combining wit,
+imagination, ingenuity, and certainty.
+
+Lastly, it must be noted that, as a History of England cannot deal
+with the present Parliament, so also the unfinished researches and
+untested hypotheses of many well-known astronomers of to-day cannot be
+included among the records of the History of Astronomy. The writer
+regrets the necessity that thus arises of leaving without mention the
+names of many who are now making history in astronomical work.
+
+G. F.
+_August 1st, 1909._
+
+
+
+
+BOOK I. THE GEOMETRICAL PERIOD
+
+
+
+1. PRIMITIVE ASTRONOMY AND ASTROLOGY.
+
+
+The growth of intelligence in the human race has its counterpart in
+that of the individual, especially in the earliest stages.
+Intellectual activity and the development of reasoning powers are in
+both cases based upon the accumulation of experiences, and on the
+comparison, classification, arrangement, and nomenclature of these
+experiences. During the infancy of each the succession of events can
+be watched, but there can be no _a priori_ anticipations.
+Experience alone, in both cases, leads to the idea of cause and effect
+as a principle that seems to dominate our present universe, as a rule
+for predicting the course of events, and as a guide to the choice of a
+course of action. This idea of cause and effect is the most potent
+factor in developing the history of the human race, as of the
+individual.
+
+In no realm of nature is the principle of cause and effect more
+conspicuous than in astronomy; and we fall into the habit of thinking
+of its laws as not only being unchangeable in our universe, but
+necessary to the conception of any universe that might have been
+substituted in its place. The first inhabitants of the world were
+compelled to accommodate their acts to the daily and annual
+alternations of light and darkness and of heat and cold, as much as to
+the irregular changes of weather, attacks of disease, and the fortune
+of war. They soon came to regard the influence of the sun, in
+connection with light and heat, as a cause. This led to a search for
+other signs in the heavens. If the appearance of a comet was sometimes
+noted simultaneously with the death of a great ruler, or an eclipse
+with a scourge of plague, these might well be looked upon as causes in
+the same sense that the veering or backing of the wind is regarded as
+a cause of fine or foul weather.
+
+For these reasons we find that the earnest men of all ages have
+recorded the occurrence of comets, eclipses, new stars, meteor
+showers, and remarkable conjunctions of the planets, as well as
+plagues and famines, floods and droughts, wars and the deaths of great
+rulers. Sometimes they thought they could trace connections which
+might lead them to say that a comet presaged famine, or an eclipse
+war.
+
+Even if these men were sometimes led to evolve laws of cause and
+effect which now seem to us absurd, let us be tolerant, and gratefully
+acknowledge that these astrologers, when they suggested such "working
+hypotheses," were laying the foundations of observation and deduction.
+
+If the ancient Chaldaeans gave to the planetary conjunctions an
+influence over terrestrial events, let us remember that in our own
+time people have searched for connection between terrestrial
+conditions and periods of unusual prevalence of sun spots; while De la
+Rue, Loewy, and Balfour Stewart[1] thought they found a connection
+between sun-spot displays and the planetary positions. Thus we find
+scientific men, even in our own time, responsible for the belief that
+storms in the Indian Ocean, the fertility of German vines, famines in
+India, and high or low Nile-floods in Egypt follow the planetary
+positions.
+
+And, again, the desire to foretell the weather is so laudable that we
+cannot blame the ancient Greeks for announcing the influence of the
+moon with as much confidence as it is affirmed in Lord Wolseley's
+_Soldier's Pocket Book_.
+
+Even if the scientific spirit of observation and deduction (astronomy)
+has sometimes led to erroneous systems for predicting terrestrial
+events (astrology), we owe to the old astronomer and astrologer alike
+the deepest gratitude for their diligence in recording astronomical
+events. For, out of the scanty records which have survived the
+destructive acts of fire and flood, of monarchs and mobs, we have
+found much that has helped to a fuller knowledge of the heavenly
+motions than was possible without these records.
+
+So Hipparchus, about 150 B.C., and Ptolemy a little later, were able
+to use the observations of Chaldaean astrologers, as well as those of
+Alexandrian astronomers, and to make some discoveries which have
+helped the progress of astronomy in all ages. So, also, Mr. Cowell[2]
+has examined the marks made on the baked bricks used by the Chaldaeans
+for recording the eclipses of 1062 B.C. and 762 B.C.; and has thereby
+been enabled, in the last few years, to correct the lunar tables of
+Hansen, and to find a more accurate value for the secular acceleration
+of the moon's longitude and the node of her orbit than any that could
+be obtained from modern observations made with instruments of the
+highest precision.
+
+So again, Mr. Hind [3] was enabled to trace back the period during
+which Halley's comet has been a member of the solar system, and to
+identify it in the Chinese observations of comets as far back as 12
+B.C. Cowell and Cromellin extended the date to 240 B.C. In the same
+way the comet 1861.i. has been traced back in the Chinese records to
+617 A.D. [4]
+
+The theoretical views founded on Newton's great law of universal
+gravitation led to the conclusion that the inclination of the earth's
+equator to the plane of her orbit (the obliquity of the ecliptic) has
+been diminishing slowly since prehistoric times; and this fact has
+been confirmed by Egyptian and Chinese observations on the length of
+the shadow of a vertical pillar, made thousands of years before the
+Christian era, in summer and winter.
+
+There are other reasons why we must be tolerant of the crude notions
+of the ancients. The historian, wishing to give credit wherever it may
+be due, is met by two difficulties. Firstly, only a few records of
+very ancient astronomy are extant, and the authenticity of many of
+these is open to doubt. Secondly, it is very difficult to divest
+ourselves of present knowledge, and to appreciate the originality of
+thought required to make the first beginnings.
+
+With regard to the first point, we are generally dependent upon
+histories written long after the events. The astronomy of Egyptians,
+Babylonians, and Assyrians is known to us mainly through the Greek
+historians, and for information about the Chinese we rely upon the
+researches of travellers and missionaries in comparatively recent
+times. The testimony of the Greek writers has fortunately been
+confirmed, and we now have in addition a mass of facts translated from
+the original sculptures, papyri, and inscribed bricks, dating back
+thousands of years.
+
+In attempting to appraise the efforts of the beginners we must
+remember that it was natural to look upon the earth (as all the first
+astronomers did) as a circular plane, surrounded and bounded by the
+heaven, which was a solid vault, or hemisphere, with its concavity
+turned downwards. The stars seemed to be fixed on this vault; the
+moon, and later the planets, were seen to crawl over it. It was a
+great step to look on the vault as a hollow sphere carrying the sun
+too. It must have been difficult to believe that at midday the stars
+are shining as brightly in the blue sky as they do at night. It must
+have been difficult to explain how the sun, having set in the west,
+could get back to rise in the east without being seen _if_ it was
+always the same sun. It was a great step to suppose the earth to be
+spherical, and to ascribe the diurnal motions to its rotation.
+Probably the greatest step ever made in astronomical theory was the
+placing of the sun, moon, and planets at different distances from the
+earth instead of having them stuck on the vault of heaven. It was a
+transition from "flatland" to a space of three dimensions.
+
+Great progress was made when systematic observations began, such as
+following the motion of the moon and planets among the stars, and the
+inferred motion of the sun among the stars, by observing their
+_heliacal risings_--i.e., the times of year when a star
+would first be seen to rise at sunrise, and when it could last be seen
+to rise at sunset. The grouping of the stars into constellations and
+recording their places was a useful observation. The theoretical
+prediction of eclipses of the sun and moon, and of the motions of the
+planets among the stars, became later the highest goal in astronomy.
+
+To not one of the above important steps in the progress of astronomy
+can we assign the author with certainty. Probably many of them were
+independently taken by Chinese, Indian, Persian, Tartar, Egyptian,
+Babylonian, Assyrian, Phoenician, and Greek astronomers. And we have
+not a particle of information about the discoveries, which may have
+been great, by other peoples--by the Druids, the Mexicans, and the
+Peruvians, for example.
+
+We do know this, that all nations required to have a calendar. The
+solar year, the lunar month, and the day were the units, and it is
+owing to their incommensurability that we find so many calendars
+proposed and in use at different times. The only object to be attained
+by comparing the chronologies of ancient races is to fix the actual
+dates of observations recorded, and this is not a part of a history of
+astronomy.
+
+In conclusion, let us bear in mind the limited point of view of the
+ancients when we try to estimate their merit. Let us remember that the
+first astronomy was of two dimensions; the second astronomy was of
+three dimensions, but still purely geometrical. Since Kepler's day we
+have had a dynamical astronomy.
+
+
+FOOTNOTES:
+
+[1] Trans. R. S. E., xxiii. 1864, p. 499, _On Sun Spots_, etc., by
+B. Stewart. Also Trans. R. S. 1860-70. Also Prof. Ernest Brown, in
+_R. A. S. Monthly Notices_, 1900.
+
+[2] _R. A. S. Monthly Notices_, Sup.; 1905.
+
+[Illustration: CHALDAEAN BAKED BRICK OR TABLET, _Obverse and reverse
+sides_, Containing record of solar eclipse, 1062 B.C., used lately by
+Cowell for rendering the lunar theory more accurate than was possible
+by finest modern observations. (British Museum collection,
+No. 35908.)]
+
+[3] _R. A. S. Monthly Notices_, vol. x., p. 65.
+
+[4] R. S. E. Proc., vol. x., 1880.
+
+
+
+2. ANCIENT ASTRONOMY--THE CHINESE AND CHALDAEANS.
+
+
+The last section must have made clear the difficulties the way of
+assigning to the ancient nations their proper place in the development
+of primitive notions about astronomy. The fact that some alleged
+observations date back to a period before the Chinese had invented the
+art of writing leads immediately to the question how far tradition can
+be trusted.
+
+Our first detailed knowledge was gathered in the far East by
+travellers, and by the Jesuit priests, and was published in the
+eighteenth century. The Asiatic Society of Bengal contributed
+translations of Brahmin literature. The two principal sources of
+knowledge about Chinese astronomy were supplied, first by Father
+Souciet, who in 1729 published _Observations Astronomical,
+Geographical, Chronological, and Physical_, drawn from ancient
+Chinese books; and later by Father Moyriac-de-Mailla, who in 1777-1785
+published _Annals of the Chinese Empire, translated from
+Tong-Kien-Kang-Mou_.
+
+Bailly, in his _Astronomie Ancienne_ (1781), drew, from these and
+other sources, the conclusion that all we know of the astronomical
+learning of the Chinese, Indians, Chaldaeans, Assyrians, and Egyptians
+is but the remnant of a far more complete astronomy of which no trace
+can be found.
+
+Delambre, in his _Histoire de l'Astronomie Ancienne_ (1817),
+ridicules the opinion of Bailly, and considers that the progress made
+by all of these nations is insignificant.
+
+It will be well now to give an idea of some of the astronomy of the
+ancients not yet entirely discredited. China and Babylon may be taken
+as typical examples.
+
+_China_.--It would appear that Fohi, the first emperor, reigned
+about 2952 B.C., and shortly afterwards Yu-Chi made a sphere to
+represent the motions of the celestial bodies. It is also mentioned,
+in the book called Chu-King, supposed to have been written in 2205
+B.C., that a similar sphere was made in the time of Yao (2357
+B.C.).[1] It is said that the Emperor Chueni (2513 B.C.) saw five
+planets in conjunction the same day that the sun and moon were in
+conjunction. This is discussed by Father Martin (MSS. of De Lisle);
+also by M. Desvignolles (Mem. Acad. Berlin, vol. iii., p. 193), and by
+M. Kirsch (ditto, vol. v., p. 19), who both found that Mars, Jupiter,
+Saturn, and Mercury were all between the eleventh and eighteenth
+degrees of Pisces, all visible together in the evening on February
+28th 2446 B.C., while on the same day the sun and moon were in
+conjunction at 9 a.m., and that on March 1st the moon was in
+conjunction with the other four planets. But this needs confirmation.
+
+Yao, referred to above, gave instructions to his astronomers to
+determine the positions of the solstices and equinoxes, and they
+reported the names of the stars in the places occupied by the sun at
+these seasons, and in 2285 B.C. he gave them further orders. If this
+account be true, it shows a knowledge that the vault of heaven is a
+complete sphere, and that stars are shining at mid-day, although
+eclipsed by the sun's brightness.
+
+It is also asserted, in the book called _Chu-King_, that in the
+time of Yao the year was known to have 365-1/4 days, and that he
+adopted 365 days and added an intercalary day every four years (as in
+the Julian Calendar). This may be true or not, but the ancient Chinese
+certainly seem to have divided the circle into 365 degrees. To learn
+the length of the year needed only patient observation--a
+characteristic of the Chinese; but many younger nations got into a
+terrible mess with their calendar from ignorance of the year's length.
+
+It is stated that in 2159 B.C. the royal astronomers Hi and Ho failed
+to predict an eclipse. It probably created great terror, for they were
+executed in punishment for their neglect. If this account be true, it
+means that in the twenty-second century B.C. some rule for calculating
+eclipses was in use. Here, again, patient observation would easily
+lead to the detection of the eighteen-year cycle known to the
+Chaldeans as the _Saros_. It consists of 235 lunations, and in
+that time the pole of the moon's orbit revolves just once round the
+pole of the ecliptic, and for this reason the eclipses in one cycle
+are repeated with very slight modification in the next cycle, and so
+on for many centuries.
+
+It may be that the neglect of their duties by Hi and Ho, and their
+punishment, influenced Chinese astronomy; or that the succeeding
+records have not been available to later scholars; but the fact
+remains that--although at long intervals observations were made of
+eclipses, comets, and falling stars, and of the position of the
+solstices, and of the obliquity of the ecliptic--records become rare,
+until 776 B.C., when eclipses began to be recorded once more with some
+approach to continuity. Shortly afterwards notices of comets were
+added. Biot gave a list of these, and Mr. John Williams, in 1871,
+published _Observations of Comets from 611 B.C. to 1640 A.D.,
+Extracted from the Chinese Annals_.
+
+With regard to those centuries concerning which we have no
+astronomical Chinese records, it is fair to state that it is recorded
+that some centuries before the Christian era, in the reign of
+Tsin-Chi-Hoang, all the classical and scientific books that could be
+found were ordered to be destroyed. If true, our loss therefrom is as
+great as from the burning of the Alexandrian library by the Caliph
+Omar. He burnt all the books because he held that they must be either
+consistent or inconsistent with the Koran, and in the one case they
+were superfluous, in the other case objectionable.
+
+_Chaldaeans_.--Until the last half century historians were
+accustomed to look back upon the Greeks, who led the world from the
+fifth to the third century B.C., as the pioneers of art, literature,
+and science. But the excavations and researches of later years make us
+more ready to grant that in science as in art the Greeks only
+developed what they derived from the Egyptians, Babylonians, and
+Assyrians. The Greek historians said as much, in fact; and modern
+commentators used to attribute the assertion to undue modesty. Since,
+however, the records of the libraries have been unearthed it has been
+recognised that the Babylonians were in no way inferior in the matter
+of original scientific investigation to other races of the same era.
+
+The Chaldaeans, being the most ancient Babylonians, held the same
+station and dignity in the State as did the priests in Egypt, and
+spent all their time in the study of philosophy and astronomy, and the
+arts of divination and astrology. They held that the world of which we
+have a conception is an eternal world without any beginning or ending,
+in which all things are ordered by rules supported by a divine
+providence, and that the heavenly bodies do not move by chance, nor by
+their own will, but by the determinate will and appointment of the
+gods. They recorded these movements, but mainly in the hope of tracing
+the will of the gods in mundane affairs. Ptolemy (about 130 A.D.)
+made use of Babylonian eclipses in the eighth century B.C. for
+improving his solar and lunar tables.
+
+Fragments of a library at Agade have been preserved at Nineveh, from
+which we learn that the star-charts were even then divided into
+constellations, which were known by the names which they bear to this
+day, and that the signs of the zodiac were used for determining the
+courses of the sun, moon, and of the five planets Mercury, Venus,
+Mars, Jupiter, and Saturn.
+
+We have records of observations carried on under Asshurbanapal, who
+sent astronomers to different parts to study celestial phenomena. Here
+is one:--
+
+To the Director of Observations,--My Lord, his humble servant
+Nabushum-iddin, Great Astronomer of Nineveh, writes thus: "May Nabu
+and Marduk be propitious to the Director of these Observations, my
+Lord. The fifteenth day we observed the Node of the moon, and the moon
+was eclipsed."
+
+The Phoenicians are supposed to have used the stars for navigation,
+but there are no records. The Egyptian priests tried to keep such
+astronomical knowledge as they possessed to themselves. It is probable
+that they had arbitrary rules for predicting eclipses. All that was
+known to the Greeks about Egyptian science is to be found in the
+writings of Diodorus Siculus. But confirmatory and more authentic
+facts have been derived from late explorations. Thus we learn from
+E. B. Knobel[2] about the Jewish calendar dates, on records of land
+sales in Aramaic papyri at Assuan, translated by Professor A. H. Sayce
+and A. E. Cowley, (1) that the lunar cycle of nineteen years was used
+by the Jews in the fifth century B.C. [the present reformed Jewish
+calendar dating from the fourth century A.D.], a date a "little more
+than a century after the grandfathers and great-grandfathers of those
+whose business is recorded had fled into Egypt with Jeremiah" (Sayce);
+and (2) that the order of intercalation at that time was not
+dissimilar to that in use at the present day.
+
+Then again, Knobel reminds us of "the most interesting discovery a few
+years ago by Father Strassmeier of a Babylonian tablet recording a
+partial lunar eclipse at Babylon in the seventh year of Cambyses, on
+the fourteenth day of the Jewish month Tammuz." Ptolemy, in the
+Almagest (Suntaxis), says it occurred in the seventh year of Cambyses,
+on the night of the seventeenth and eighteenth of the Egyptian month
+Phamenoth. Pingre and Oppolzer fix the date July 16th, 533 B.C. Thus
+are the relations of the chronologies of Jews and Egyptians
+established by these explorations.
+
+
+FOOTNOTES:
+
+[1] These ancient dates are uncertain.
+
+[2] _R. A. S. Monthly Notices_, vol. lxviii., No. 5, March, 1908.
+
+
+
+3. ANCIENT GREEK ASTRONOMY.
+
+
+We have our information about the earliest Greek astronomy from
+Herodotus (born 480 B.C.). He put the traditions into writing. Thales
+(639-546 B.C.) is said to have predicted an eclipse, which caused much
+alarm, and ended the battle between the Medes and Lydians. Airy fixed
+the date May 28th, 585 B.C. But other modern astronomers give
+different dates. Thales went to Egypt to study science, and learnt
+from its priests the length of the year (which was kept a profound
+secret!), and the signs of the zodiac, and the positions of the
+solstices. He held that the sun, moon, and stars are not mere spots on
+the heavenly vault, but solids; that the moon derives her light from
+the sun, and that this fact explains her phases; that an eclipse of
+the moon happens when the earth cuts off the sun's light from her. He
+supposed the earth to be flat, and to float upon water. He determined
+the ratio of the sun's diameter to its orbit, and apparently made out
+the diameter correctly as half a degree. He left nothing in writing.
+
+His successors, Anaximander (610-547 B.C.) and Anaximenes (550-475
+B.C.), held absurd notions about the sun, moon, and stars, while
+Heraclitus (540-500 B.C.) supposed that the stars were lighted each
+night like lamps, and the sun each morning. Parmenides supposed the
+earth to be a sphere.
+
+Pythagoras (569-470 B.C.) visited Egypt to study science. He deduced
+his system, in which the earth revolves in an orbit, from fantastic
+first principles, of which the following are examples: "The circular
+motion is the most perfect motion," "Fire is more worthy than earth,"
+"Ten is the perfect number." He wrote nothing, but is supposed to have
+said that the earth, moon, five planets, and fixed stars all revolve
+round the sun, which itself revolves round an imaginary central fire
+called the Antichthon. Copernicus in the sixteenth century claimed
+Pythagoras as the founder of the system which he, Copernicus, revived.
+
+Anaxagoras (born 499 B.C.) studied astronomy in Egypt. He explained
+the return of the sun to the east each morning by its going under the
+flat earth in the night. He held that in a solar eclipse the moon
+hides the sun, and in a lunar eclipse the moon enters the earth's
+shadow--both excellent opinions. But he entertained absurd ideas of
+the vortical motion of the heavens whisking stones into the sky, there
+to be ignited by the fiery firmament to form stars. He was prosecuted
+for this unsettling opinion, and for maintaining that the moon is an
+inhabited earth. He was defended by Pericles (432 B.C.).
+
+Solon dabbled, like many others, in reforms of the calendar. The
+common year of the Greeks originally had 360 days--twelve months of
+thirty days. Solon's year was 354 days. It is obvious that these
+erroneous years would, before long, remove the summer to January and
+the winter to July. To prevent this it was customary at regular
+intervals to intercalate days or months. Meton (432 B.C.) introduced a
+reform based on the nineteen-year cycle. This is not the same as the
+Egyptian and Chaldean eclipse cycle called _Saros_ of 223
+lunations, or a little over eighteen years. The Metonic cycle is 235
+lunations or nineteen years, after which period the sun and moon
+occupy the same position relative to the stars. It is still used for
+fixing the date of Easter, the number of the year in Melon's cycle
+being the golden number of our prayer-books. Melon's system divided
+the 235 lunations into months of thirty days and omitted every
+sixty-third day. Of the nineteen years, twelve had twelve months and
+seven had thirteen months.
+
+Callippus (330 B.C.) used a cycle four times as long, 940 lunations,
+but one day short of Melon's seventy-six years. This was more correct.
+
+Eudoxus (406-350 B.C.) is said to have travelled with Plato in
+Egypt. He made astronomical observations in Asia Minor, Sicily, and
+Italy, and described the starry heavens divided into constellations.
+His name is connected with a planetary theory which as generally
+stated sounds most fanciful. He imagined the fixed stars to be on a
+vault of heaven; and the sun, moon, and planets to be upon similar
+vaults or spheres, twenty-six revolving spheres in all, the motion of
+each planet being resolved into its components, and a separate sphere
+being assigned for each component motion. Callippus (330 B.C.)
+increased the number to thirty-three. It is now generally accepted
+that the real existence of these spheres was not suggested, but the
+idea was only a mathematical conception to facilitate the construction
+of tables for predicting the places of the heavenly bodies.
+
+Aristotle (384-322 B.C.) summed up the state of astronomical knowledge
+in his time, and held the earth to be fixed in the centre of the
+world.
+
+Nicetas, Heraclides, and Ecphantes supposed the earth to revolve on
+its axis, but to have no orbital motion.
+
+The short epitome so far given illustrates the extraordinary deductive
+methods adopted by the ancient Greeks. But they went much farther in
+the same direction. They seem to have been in great difficulty to
+explain how the earth is supported, just as were those who invented
+the myth of Atlas, or the Indians with the tortoise. Thales thought
+that the flat earth floated on water. Anaxagoras thought that, being
+flat, it would be buoyed up and supported on the air like a kite.
+Democritus thought it remained fixed, like the donkey between two
+bundles of hay, because it was equidistant from all parts of the
+containing sphere, and there was no reason why it should incline one
+way rather than another. Empedocles attributed its state of rest to
+centrifugal force by the rapid circular movement of the heavens, as
+water is stationary in a pail when whirled round by a string.
+Democritus further supposed that the inclination of the flat earth to
+the ecliptic was due to the greater weight of the southern parts owing
+to the exuberant vegetation.
+
+For further references to similar efforts of imagination the reader is
+referred to Sir George Cornwall Lewis's _Historical Survey of the
+Astronomy of the Ancients_; London, 1862. His list of authorities
+is very complete, but some of his conclusions are doubtful. At p. 113
+of that work he records the real opinions of Socrates as set forth by
+Xenophon; and the reader will, perhaps, sympathise with Socrates in
+his views on contemporary astronomy:--
+
+With regard to astronomy he [Socrates] considered a knowledge of it
+desirable to the extent of determining the day of the year or month,
+and the hour of the night, ... but as to learning the courses of the
+stars, to be occupied with the planets, and to inquire about their
+distances from the earth, and their orbits, and the causes of their
+motions, he strongly objected to such a waste of valuable time. He
+dwelt on the contradictions and conflicting opinions of the physical
+philosophers, ... and, in fine, he held that the speculators on the
+universe and on the laws of the heavenly bodies were no better than
+madmen (_Xen. Mem_, i. 1, 11-15).
+
+Plato (born 429 B.C.), the pupil of Socrates, the fellow-student of
+Euclid, and a follower of Pythagoras, studied science in his travels
+in Egypt and elsewhere. He was held in so great reverence by all
+learned men that a problem which he set to the astronomers was the
+keynote to all astronomical investigation from this date till the time
+of Kepler in the sixteenth century. He proposed to astronomers _the
+problem of representing the courses of the planets by circular and
+uniform motions_.
+
+Systematic observation among the Greeks began with the rise of the
+Alexandrian school. Aristillus and Timocharis set up instruments and
+fixed the positions of the zodiacal stars, near to which all the
+planets in their orbits pass, thus facilitating the determination of
+planetary motions. Aristarchus (320-250 B.C.) showed that the sun must
+be at least nineteen times as far off as the moon, which is far short
+of the mark. He also found the sun's diameter, correctly, to be half a
+degree. Eratosthenes (276-196 B.C.) measured the inclination to the
+equator of the sun's apparent path in the heavens--i.e., he measured
+the obliquity of the ecliptic, making it 23 degrees 51', confirming
+our knowledge of its continuous diminution during historical times. He
+measured an arc of meridian, from Alexandria to Syene (Assuan), and
+found the difference of latitude by the length of a shadow at noon,
+summer solstice. He deduced the diameter of the earth, 250,000
+stadia. Unfortunately, we do not know the length of the stadium he
+used.
+
+Hipparchus (190-120 B.C.) may be regarded as the founder of
+observational astronomy. He measured the obliquity of the ecliptic,
+and agreed with Eratosthenes. He altered the length of the tropical
+year from 365 days, 6 hours to 365 days, 5 hours, 53 minutes--still
+four minutes too much. He measured the equation of time and the
+irregular motion of the sun; and allowed for this in his calculations
+by supposing that the centre, about which the sun moves uniformly, is
+situated a little distance from the fixed earth. He called this point
+the _excentric_. The line from the earth to the "excentric" was
+called the _line of apses_. A circle having this centre was
+called the _equant_, and he supposed that a radius drawn to the
+sun from the excentric passes over equal arcs on the equant in equal
+times. He then computed tables for predicting the place of the sun.
+
+He proceeded in the same way to compute Lunar tables. Making use of
+Chaldaean eclipses, he was able to get an accurate value of the moon's
+mean motion. [Halley, in 1693, compared this value with his own
+measurements, and so discovered the acceleration of the moon's mean
+motion. This was conclusively established, but could not be explained
+by the Newtonian theory for quite a long time.] He determined the
+plane of the moon's orbit and its inclination to the ecliptic. The
+motion of this plane round the pole of the ecliptic once in eighteen
+years complicated the problem. He located the moon's excentric as he
+had done the sun's. He also discovered some of the minor
+irregularities of the moon's motion, due, as Newton's theory proves,
+to the disturbing action of the sun's attraction.
+
+In the year 134 B.C. Hipparchus observed a new star. This upset every
+notion about the permanence of the fixed stars. He then set to work to
+catalogue all the principal stars so as to know if any others appeared
+or disappeared. Here his experiences resembled those of several later
+astronomers, who, when in search of some special object, have been
+rewarded by a discovery in a totally different direction. On comparing
+his star positions with those of Timocharis and Aristillus he found no
+stars that had appeared or disappeared in the interval of 150 years;
+but he found that all the stars seemed to have changed their places
+with reference to that point in the heavens where the ecliptic is 90
+degrees from the poles of the earth--i.e., the equinox. He found that
+this could be explained by a motion of the equinox in the direction of
+the apparent diurnal motion of the stars. This discovery of
+_precession of the equinoxes_, which takes place at the rate of 52".1
+every year, was necessary for the progress of accurate astronomical
+observations. It is due to a steady revolution of the earth's pole
+round the pole of the ecliptic once in 26,000 years in the opposite
+direction to the planetary revolutions.
+
+Hipparchus was also the inventor of trigonometry, both plane and
+spherical. He explained the method of using eclipses for determining
+the longitude.
+
+In connection with Hipparchus' great discovery it may be mentioned
+that modern astronomers have often attempted to fix dates in history
+by the effects of precession of the equinoxes. (1) At about the date
+when the Great Pyramid may have been built gamma Draconis was near to
+the pole, and must have been used as the pole-star. In the north face
+of the Great Pyramid is the entrance to an inclined passage, and six
+of the nine pyramids at Gizeh possess the same feature; all the
+passages being inclined at an angle between 26 degrees and 27 degrees
+to the horizon and in the plane of the meridian. It also appears that
+4,000 years ago--i.e., about 2100 B.C.--an observer at the lower end
+of the passage would be able to see gamma Draconis, the then
+pole-star, at its lower culmination.[1] It has been suggested that the
+passage was made for this purpose. On other grounds the date assigned
+to the Great Pyramid is 2123 B.C.
+
+(2) The Chaldaeans gave names to constellations now invisible from
+Babylon which would have been visible in 2000 B.C., at which date it
+is claimed that these people were studying astronomy.
+
+(3) In the Odyssey, Calypso directs Odysseus, in accordance with
+Phoenician rules for navigating the Mediterranean, to keep the Great
+Bear "ever on the left as he traversed the deep" when sailing from the
+pillars of Hercules (Gibraltar) to Corfu. Yet such a course taken now
+would land the traveller in Africa. Odysseus is said in his voyage in
+springtime to have seen the Pleiades and Arcturus setting late, which
+seemed to early commentators a proof of Homer's inaccuracy. Likewise
+Homer, both in the _Odyssey_ [2] (v. 272-5) and in the _Iliad_
+(xviii. 489), asserts that the Great Bear never set in those
+latitudes. Now it has been found that the precession of the equinoxes
+explains all these puzzles; shows that in springtime on the
+Mediterranean the Bear was just above the horizon, near the sea but
+not touching it, between 750 B.C. and 1000 B.C.; and fixes the date of
+the poems, thus confirming other evidence, and establishing Homer's
+character for accuracy. [3]
+
+(4) The orientation of Egyptian temples and Druidical stones is such
+that possibly they were so placed as to assist in the observation of
+the heliacal risings [4] of certain stars. If the star were known,
+this would give an approximate date. Up to the present the results of
+these investigations are far from being conclusive.
+
+Ptolemy (130 A.D.) wrote the Suntaxis, or Almagest, which includes a
+cyclopedia of astronomy, containing a summary of knowledge at that
+date. We have no evidence beyond his own statement that he was a
+practical observer. He theorised on the planetary motions, and held
+that the earth is fixed in the centre of the universe. He adopted the
+excentric and equant of Hipparchus to explain the unequal motions of
+the sun and moon. He adopted the epicycles and deferents which had
+been used by Apollonius and others to explain the retrograde motions
+of the planets. We, who know that the earth revolves round the sun
+once in a year, can understand that the apparent motion of a planet is
+only its motion relative to the earth. If, then, we suppose the earth
+fixed and the sun to revolve round it once a year, and the planets
+each in its own period, it is only necessary to impose upon each of
+these an additional _annual_ motion to enable us to represent truly
+the apparent motions. This way of looking at the apparent motions
+shows why each planet, when nearest to the earth, seems to move for a
+time in a retrograde direction. The attempts of Ptolemy and others of
+his time to explain the retrograde motion in this way were only
+approximate. Let us suppose each planet to have a bar with one end
+centred at the earth. If at the other end of the bar one end of a
+shorter bar is pivotted, having the planet at its other end, then the
+planet is given an annual motion in the secondary circle (the
+epicycle), whose centre revolves round the earth on the primary circle
+(the _deferent_), at a uniform rate round the excentric. Ptolemy
+supposed the centres of the epicycles of Mercury and Venus to be on a
+bar passing through the sun, and to be between the earth and the
+sun. The centres of the epicycles of Mars, Jupiter, and Saturn were
+supposed to be further away than the sun. Mercury and Venus were
+supposed to revolve in their epicycles in their own periodic times and
+in the deferent round the earth in a year. The major planets were
+supposed to revolve in the deferent round the earth in their own
+periodic times, and in their epicycles once in a year.
+
+It did not occur to Ptolemy to place the centres of the epicycles of
+Mercury and Venus at the sun, and to extend the same system to the
+major planets. Something of this sort had been proposed by the
+Egyptians (we are told by Cicero and others), and was accepted by
+Tycho Brahe; and was as true a representation of the relative motions
+in the solar system as when we suppose the sun to be fixed and the
+earth to revolve.
+
+The cumbrous system advocated by Ptolemy answered its purpose,
+enabling him to predict astronomical events approximately. He improved
+the lunar theory considerably, and discovered minor inequalities which
+could be allowed for by the addition of new epicycles. We may look
+upon these epicycles of Apollonius, and the excentric of Hipparchus,
+as the responses of these astronomers to the demand of Plato for
+uniform circular motions. Their use became more and more confirmed,
+until the seventeenth century, when the accurate observations of Tycho
+Brahe enabled Kepler to abolish these purely geometrical makeshifts,
+and to substitute a system in which the sun became physically its
+controller.
+
+
+FOOTNOTES:
+
+[1] _Phil. Mag_., vol. xxiv., pp. 481-4.
+
+[2]
+
+Plaeiadas t' esoronte kai ophe duonta bootaen
+'Arkton th' aen kai amaxan epiklaesin kaleousin,
+'Ae t' autou strephetai kai t' Oriona dokeuei,
+Oin d'ammoros esti loetron Okeanoio.
+
+"The Pleiades and Bootes that setteth late, and the Bear,
+which they likewise call the Wain, which turneth ever in one
+place, and keepeth watch upon Orion, and alone hath no part in
+the baths of the ocean."
+
+[3] See Pearson in the Camb. Phil. Soc. Proc., vol. iv., pt. ii., p.
+93, on whose authority the above statements are made.
+
+[4] See p. 6 for definition.
+
+
+
+4. THE REIGN OF EPICYCLES--FROM PTOLEMY TO COPERNICUS.
+
+
+After Ptolemy had published his book there seemed to be nothing more
+to do for the solar system except to go on observing and finding more
+and more accurate values for the constants involved--viz., the periods
+of revolution, the diameter of the deferent,[1] and its ratio to that
+of the epicycle,[2] the distance of the excentric[3] from the centre
+of the deferent, and the position of the line of apses,[4] besides the
+inclination and position of the plane of the planet's orbit. The only
+object ever aimed at in those days was to prepare tables for
+predicting the places of the planets. It was not a mechanical problem;
+there was no notion of a governing law of forces.
+
+From this time onwards all interest in astronomy seemed, in Europe at
+least, to sink to a low ebb. When the Caliph Omar, in the middle of
+the seventh century, burnt the library of Alexandria, which had been
+the centre of intellectual progress, that centre migrated to Baghdad,
+and the Arabs became the leaders of science and philosophy. In
+astronomy they made careful observations. In the middle of the ninth
+century Albategnius, a Syrian prince, improved the value of
+excentricity of the sun's orbit, observed the motion of the moon's
+apse, and thought he detected a smaller progression of the sun's
+apse. His tables were much more accurate than Ptolemy's. Abul Wefa, in
+the tenth century, seems to have discovered the moon's "variation."
+Meanwhile the Moors were leaders of science in the west, and Arzachel
+of Toledo improved the solar tables very much. Ulugh Begh, grandson of
+the great Tamerlane the Tartar, built a fine observatory at Samarcand
+in the fifteenth century, and made a great catalogue of stars, the
+first since the time of Hipparchus.
+
+At the close of the fifteenth century King Alphonso of Spain employed
+computers to produce the Alphonsine Tables (1488 A.D.), Purbach
+translated Ptolemy's book, and observations were carried out in
+Germany by Muller, known as Regiomontanus, and Waltherus.
+
+Nicolai Copernicus, a Sclav, was born in 1473 at Thorn, in Polish
+Prussia. He studied at Cracow and in Italy. He was a priest, and
+settled at Frauenberg. He did not undertake continuous observations,
+but devoted himself to simplifying the planetary systems and devising
+means for more accurately predicting the positions of the sun, moon,
+and planets. He had no idea of framing a solar system on a dynamical
+basis. His great object was to increase the accuracy of the
+calculations and the tables. The results of his cogitations were
+printed just before his death in an interesting book, _De
+Revolutionibus Orbium Celestium_. It is only by careful reading of
+this book that the true position of Copernicus can be realised. He
+noticed that Nicetas and others had ascribed the apparent diurnal
+rotation of the heavens to a real daily rotation of the earth about
+its axis, in the opposite direction to the apparent motion of the
+stars. Also in the writings of Martianus Capella he learnt that the
+Egyptians had supposed Mercury and Venus to revolve round the sun, and
+to be carried with him in his annual motion round the earth. He
+noticed that the same supposition, if extended to Mars, Jupiter, and
+Saturn, would explain easily why they, and especially Mars, seem so
+much brighter in opposition. For Mars would then be a great deal
+nearer to the earth than at other times. It would also explain the
+retrograde motion of planets when in opposition.
+
+We must here notice that at this stage Copernicus was actually
+confronted with the system accepted later by Tycho Brahe, with the
+earth fixed. But he now recalled and accepted the views of Pythagoras
+and others, according to which the sun is fixed and the earth
+revolves; and it must be noted that, geometrically, there is no
+difference of any sort between the Egyptian or Tychonic system and
+that of Pythagoras as revived by Copernicus, except that on the latter
+theory the stars ought to seem to move when the earth changes its
+position--a test which failed completely with the rough means of
+observation then available. The radical defect of all solar systems
+previous to the time of Kepler (1609 A.D.) was the slavish yielding to
+Plato's dictum demanding uniform circular motion for the planets, and
+the consequent evolution of the epicycle, which was fatal to any
+conception of a dynamical theory.
+
+Copernicus could not sever himself from this obnoxious tradition.[5]
+It is true that neither the Pythagorean nor the Egypto-Tychonic system
+required epicycles for explaining retrograde motion, as the Ptolemaic
+theory did. Furthermore, either system could use the excentric of
+Hipparchus to explain the irregular motion known as the equation of
+the centre. But Copernicus remarked that he could also use an
+epicycle for this purpose, or that he could use both an excentric and
+an epicycle for each planet, and so bring theory still closer into
+accord with observation. And this he proceeded to do.[6] Moreover,
+observers had found irregularities in the moon's motion, due, as we
+now know, to the disturbing attraction of the sun. To correct for
+these irregularities Copernicus introduced epicycle on epicycle in the
+lunar orbit.
+
+This is in its main features the system propounded by Copernicus. But
+attention must, to state the case fully, be drawn to two points to be
+found in his first and sixth books respectively. The first point
+relates to the seasons, and it shows a strange ignorance of the laws
+of rotating bodies. To use the words of Delambre,[7] in drawing
+attention to the strange conception,
+
+  he imagined that the earth, revolving round the sun, ought always to
+  show to it the same face; the contrary phenomena surprised him: to
+  explain them he invented a third motion, and added it to the two
+  real motions (rotation and orbital revolution). By this third motion
+  the earth, he held, made a revolution on itself and on the poles of
+  the ecliptic once a year.... Copernicus did not know that motion in
+  a straight line is the natural motion, and that motion in a curve is
+  the resultant of several movements. He believed, with Aristotle,
+  that circular motion was the natural one.
+
+Copernicus made this rotation of the earth's axis about the pole of
+the ecliptic retrograde (i.e., opposite to the orbital revolution),
+and by making it perform more than one complete revolution in a year,
+the added part being 1/26000 of the whole, he was able to include the
+precession of the equinoxes in his explanation of the seasons. His
+explanation of the seasons is given on leaf 10 of his book (the pages
+of this book are not all numbered, only alternate pages, or leaves).
+
+In his sixth book he discusses the inclination of the planetary orbits
+to the ecliptic. In regard to this the theory of Copernicus is unique;
+and it will be best to explain this in the words of Grant in his great
+work.[8] He says:--
+
+  Copernicus, as we have already remarked, did not attack the
+  principle of the epicyclical theory: he merely sought to make it
+  more simple by placing the centre of the earth's orbit in the centre
+  of the universe. This was the point to which the motions of the
+  planets were referred, for the planes of their orbits were made to
+  pass through it, and their points of least and greatest velocities
+  were also determined with reference to it.  By this arrangement the
+  sun was situate mathematically near the centre of the planetary
+  system, but he did not appear to have any physical connexion with
+  the planets as the centre of their motions.
+
+According to Copernicus' sixth book, the planes of the planetary
+orbits do not pass through the sun, and the lines of apses do not pass
+through to the sun.
+
+Such was the theory advanced by Copernicus: The earth moves in an
+epicycle, on a deferent whose centre is a little distance from the
+sun. The planets move in a similar way on epicycles, but their
+deferents have no geometrical or physical relation to the sun. The
+moon moves on an epicycle centred on a second epicycle, itself centred
+on a deferent, excentric to the earth. The earth's axis rotates about
+the pole of the ecliptic, making one revolution and a twenty-six
+thousandth part of a revolution in the sidereal year, in the opposite
+direction to its orbital motion.
+
+In view of this fanciful structure it must be noted, in fairness to
+Copernicus, that he repeatedly states that the reader is not obliged
+to accept his system as showing the real motions; that it does not
+matter whether they be true, even approximately, or not, so long as
+they enable us to compute tables from which the places of the planets
+among the stars can be predicted.[9] He says that whoever is not
+satisfied with this explanation must be contented by being told that
+"mathematics are for mathematicians" (Mathematicis mathematica
+scribuntur).
+
+At the same time he expresses his conviction over and over again that
+the earth is in motion. It is with him a pious belief, just as it was
+with Pythagoras and his school and with Aristarchus. "But" (as Dreyer
+says in his most interesting book, _Tycho Brahe_) "proofs of the
+physical truth of his system Copernicus had given none, and could give
+none," any more than Pythagoras or Aristarchus.
+
+There was nothing so startlingly simple in his system as to lead the
+cautious astronomer to accept it, as there was in the later Keplerian
+system; and the absence of parallax in the stars seemed to condemn his
+system, which had no physical basis to recommend it, and no
+simplification at all over the Egypto-Tychonic system, to which
+Copernicus himself drew attention. It has been necessary to devote
+perhaps undue space to the interesting work of Copernicus, because by
+a curious chance his name has become so widely known. He has been
+spoken of very generally as the founder of the solar system that is
+now accepted. This seems unfair, and on reading over what has been
+written about him at different times it will be noticed that the
+astronomers--those who have evidently read his great book--are very
+cautious in the words with which they eulogise him, and refrain from
+attributing to him the foundation of our solar system, which is
+entirely due to Kepler. It is only the more popular writers who give
+the idea that a revolution had been effected when Pythagoras' system
+was revived, and when Copernicus supported his view that the earth
+moves and is not fixed.
+
+It may be easy to explain the association of the name of Copernicus
+with the Keplerian system. But the time has long passed when the
+historian can support in any way this popular error, which was started
+not by astronomers acquainted with Kepler's work, but by those who
+desired to put the Church in the wrong by extolling Copernicus.
+
+Copernicus dreaded much the abuse he expected to receive from
+philosophers for opposing the authority of Aristotle, who had declared
+that the earth was fixed. So he sought and obtained the support of
+the Church, dedicating his great work to Pope Paul III. in a lengthy
+explanatory epistle. The Bishop of Cracow set up a memorial tablet in
+his honour.
+
+Copernicus was the most refined exponent, and almost the last
+representative, of the Epicyclical School. As has been already
+stated, his successor, Tycho Brahe, supported the same use of
+epicycles and excentrics as Copernicus, though he held the earth to be
+fixed. But Tycho Brahe was eminently a practical observer, and took
+little part in theory; and his observations formed so essential a
+portion of the system of Kepler that it is only fair to include his
+name among these who laid the foundations of the solar system which we
+accept to-day.
+
+In now taking leave of the system of epicycles let it be remarked that
+it has been held up to ridicule more than it deserves. On reading
+Airy's account of epicycles, in the beautifully clear language of his
+_Six Lectures on Astronomy_, the impression is made that the
+jointed bars there spoken of for describing the circles were supposed
+to be real. This is no more the case than that the spheres of Eudoxus
+and Callippus were supposed to be real. Both were introduced only to
+illustrate the mathematical conception upon which the solar,
+planetary, and lunar tables were constructed. The epicycles
+represented nothing more nor less than the first terms in the Fourier
+series, which in the last century has become a basis of such
+calculations, both in astronomy and physics generally.
+
+[Illustration: "QUADRANS MURALIS SIVE TICHONICUS." With portrait of
+Tycho Brahe, instruments, etc., painted on the wall; showing
+assistants using the sight, watching the clock, and recording. (From
+the author's copy of the _Astronomiae Instauratae Mechanica._)]
+
+
+FOOTNOTES:
+
+[1] For definition see p. 22.
+
+[2] _Ibid_.
+
+[3] For definition see p. 18.
+
+[4] For definition see p. 18.
+
+[5] In his great book Copernicus says: "The movement of the heavenly
+bodies is uniform, circular, perpetual, or else composed of circular
+movements." In this he proclaimed himself a follower of Pythagoras
+(see p. 14), as also when he says: "The world is spherical because the
+sphere is, of all figures, the most perfect" (Delambre,
+_Ast. Mod. Hist_., pp. 86, 87).
+
+[6] Kepler tells us that Tycho Brahe was pleased with this
+device, and adapted it to his own system.
+
+[7] _Hist. Ast._, vol. i., p. 354.
+
+[8] _Hist. of Phys. Ast._, p. vii.
+
+[9] "Est enim Astronomi proprium, historiam motuum coelestium
+diligenti et artificiosa observatione colligere. Deinde causas
+earundem, seu hypotheses, cum veras assequi nulla ratione possit
+... Neque enim necesse est, eas hypotheses esse veras, imo ne
+verisimiles quidem, sed sufficit hoc usum, si calculum observationibus
+congruentem exhibeant."
+
+
+
+
+BOOK II. THE DYNAMICAL PERIOD
+
+
+
+5. DISCOVERY OF THE TRUE SOLAR SYSTEM--TYCHO BRAHE--KEPLER.
+
+
+During the period of the intellectual and aesthetic revival, at the
+beginning of the sixteenth century, the "spirit of the age" was
+fostered by the invention of printing, by the downfall of the
+Byzantine Empire, and the scattering of Greek fugitives, carrying the
+treasures of literature through Western Europe, by the works of
+Raphael and Michael Angelo, by the Reformation, and by the extension
+of the known world through the voyages of Spaniards and Portuguese.
+During that period there came to the front the founder of accurate
+observational astronomy. Tycho Brahe, a Dane, born in 1546 of noble
+parents, was the most distinguished, diligent, and accurate observer
+of the heavens since the days of Hipparchus, 1,700 years before.
+
+Tycho was devoted entirely to his science from childhood, and the
+opposition of his parents only stimulated him in his efforts to
+overcome difficulties. He soon grasped the hopelessness of the old
+deductive methods of reasoning, and decided that no theories ought to
+be indulged in until preparations had been made by the accumulation of
+accurate observations. We may claim for him the title of founder of
+the inductive method.
+
+For a complete life of this great man the reader is referred to
+Dreyer's _Tycho Brahe_, Edinburgh, 1890, containing a complete
+bibliography. The present notice must be limited to noting the work
+done, and the qualities of character which enabled him to attain his
+scientific aims, and which have been conspicuous in many of his
+successors.
+
+He studied in Germany, but King Frederick of Denmark, appreciating his
+great talents, invited him to carry out his life's work in that
+country. He granted to him the island of Hveen, gave him a pension,
+and made him a canon of the Cathedral of Roskilde. On that island
+Tycho Brahe built the splendid observatory which he called Uraniborg,
+and, later, a second one for his assistants and students, called
+Stjerneborg. These he fitted up with the most perfect instruments, and
+never lost a chance of adding to his stock of careful observations.[1]
+
+The account of all these instruments and observations, printed at his
+own press on the island, was published by Tycho Brahe himself, and the
+admirable and numerous engravings bear witness to the excellence of
+design and the stability of his instruments.
+
+His mechanical skill was very great, and in his workmanship he was
+satisfied with nothing but the best. He recognised the importance of
+rigidity in the instruments, and, whereas these had generally been
+made of wood, he designed them in metal. His instruments included
+armillae like those which had been used in Alexandria, and other
+armillae designed by himself--sextants, mural quadrants, large
+celestial globes and various instruments for special purposes. He
+lived before the days of telescopes and accurate clocks. He invented
+the method of sub-dividing the degrees on the arc of an instrument by
+transversals somewhat in the way that Pedro Nunez had proposed.
+
+He originated the true system of observation and reduction of
+observations, recognising the fact that the best instrument in the
+world is not perfect; and with each of his instruments he set to work
+to find out the errors of graduation and the errors of mounting, the
+necessary correction being applied to each observation.
+
+When he wanted to point his instrument exactly to a star he was
+confronted with precisely the same difficulty as is met in gunnery and
+rifle-shooting. The sights and the object aimed at cannot be in focus
+together, and a great deal depends on the form of sight. Tycho Brahe
+invented, and applied to the pointers of his instruments, an
+aperture-sight of variable area, like the iris diaphragm used now in
+photography. This enabled him to get the best result with stars of
+different brightness. The telescope not having been invented, he
+could not use a telescopic-sight as we now do in gunnery. This not
+only removes the difficulty of focussing, but makes the minimum
+visible angle smaller. Helmholtz has defined the minimum angle
+measurable with the naked eye as being one minute of arc. In view of
+this it is simply marvellous that, when the positions of Tycho's
+standard stars are compared with the best modern catalogues, his
+probable error in right ascension is only +/- 24", 1, and in declination
+only +/- 25", 9.
+
+Clocks of a sort had been made, but Tycho Brahe found them so
+unreliable that he seldom used them, and many of his position-measurements
+were made by measuring the angular distances from known stars.
+
+Taking into consideration the absence of either a telescope or a
+clock, and reading his account of the labour he bestowed upon each
+observation, we must all agree that Kepler, who inherited these
+observations in MS., was justified, under the conditions then
+existing, in declaring that there was no hope of anyone ever improving
+upon them.
+
+In the year 1572, on November 11th, Tycho discovered in Cassiopeia a
+new star of great brilliance, and continued to observe it until the
+end of January, 1573. So incredible to him was such an event that he
+refused to believe his own eyes until he got others to confirm what he
+saw. He made accurate observations of its distance from the nine
+principal stars in Casseiopeia, and proved that it had no measurable
+parallax. Later he employed the same method with the comets of 1577,
+1580, 1582, 1585, 1590, 1593, and 1596, and proved that they too had
+no measurable parallax and must be very distant.
+
+The startling discovery that stars are not necessarily permanent, that
+new stars may appear, and possibly that old ones may disappear, had
+upon him exactly the same effect that a similar occurrence had upon
+Hipparchus 1,700 years before. He felt it his duty to catalogue all
+the principal stars, so that there should be no mistake in the
+future. During the construction of his catalogue of 1,000 stars he
+prepared and used accurate tables of refraction deduced from his own
+observations. Thus he eliminated (so far as naked eye observations
+required) the effect of atmospheric refraction which makes the
+altitude of a star seem greater than it really is.
+
+Tycho Brahe was able to correct the lunar theory by his observations.
+Copernicus had introduced two epicycles on the lunar orbit in the hope
+of obtaining a better accordance between theory and observation; and
+he was not too ambitious, as his desire was to get the tables accurate
+to ten minutes. Tycho Brahe found that the tables of Copernicus were
+in error as much as two degrees. He re-discovered the inequality
+called "variation" by observing the moon in all phases--a thing which
+had not been attended to. [It is remarkable that in the nineteenth
+century Sir George Airy established an altazimuth at Greenwich
+Observatory with this special object, to get observations of the moon
+in all phases.] He also discovered other lunar equalities, and wanted
+to add another epicycle to the moon's orbit, but he feared that these
+would soon become unmanageable if further observations showed more new
+inequalities.
+
+But, as it turned out, the most fruitful work of Tycho Brahe was on
+the motions of the planets, and especially of the planet Mars, for it
+was by an examination of these results that Kepler was led to the
+discovery of his immortal laws.
+
+After the death of King Frederick the observatories of Tycho Brahe
+were not supported. The gigantic power and industry displayed by this
+determined man were accompanied, as often happens, by an overbearing
+manner, intolerant of obstacles. This led to friction, and eventually
+the observatories were dismantled, and Tycho Brahe was received by the
+Emperor Rudolph II., who placed a house in Prague at his disposal.
+Here he worked for a few years, with Kepler as one of his assistants,
+and he died in the year 1601.
+
+It is an interesting fact that Tycho Brahe had a firm conviction that
+mundane events could be predicted by astrology, and that this belief
+was supported by his own predictions.
+
+It has already been stated that Tycho Brahe maintained that
+observation must precede theory. He did not accept the Copernican
+theory that the earth moves, but for a working hypothesis he used a
+modification of an old Egyptian theory, mathematically identical with
+that of Copernicus, but not involving a stellar parallax. He says
+(_De Mundi_, etc.) that
+
+  the Ptolemean system was too complicated, and the new one which that
+  great man Copernicus had proposed, following in the footsteps of
+  Aristarchus of Samos, though there was nothing in it contrary to
+  mathematical principles, was in opposition to those of physics, as
+  the heavy and sluggish earth is unfit to move, and the system is
+  even opposed to the authority of Scripture. The absence of annual
+  parallax further involves an incredible distance between the
+  outermost planet and the fixed stars.
+
+We are bound to admit that in the circumstances of the case, so long
+as there was no question of dynamical forces connecting the members of
+the solar system, his reasoning, as we should expect from such a man,
+is practical and sound. It is not surprising, then, that astronomers
+generally did not readily accept the views of Copernicus, that Luther
+(Luther's _Tischreden_, pp.  22, 60) derided him in his usual pithy
+manner, that Melancthon (_Initia doctrinae physicae_) said that
+Scripture, and also science, are against the earth's motion; and that
+the men of science whose opinion was asked for by the cardinals (who
+wished to know whether Galileo was right or wrong) looked upon
+Copernicus as a weaver of fanciful theories.
+
+Johann Kepler is the name of the man whose place, as is generally
+agreed, would have been the most difficult to fill among all those who
+have contributed to the advance of astronomical knowledge. He was born
+at Wiel, in the Duchy of Wurtemberg, in 1571. He held an appointment
+at Gratz, in Styria, and went to join Tycho Brahe in Prague, and to
+assist in reducing his observations. These came into his possession
+when Tycho Brahe died, the Emperor Rudolph entrusting to him the
+preparation of new tables (called the Rudolphine tables) founded on
+the new and accurate observations. He had the most profound respect
+for the knowledge, skill, determination, and perseverance of the man
+who had reaped such a harvest of most accurate data; and though Tycho
+hardly recognised the transcendent genius of the man who was working
+as his assistant, and although there were disagreements between them,
+Kepler held to his post, sustained by the conviction that, with these
+observations to test any theory, he would be in a position to settle
+for ever the problem of the solar system.
+
+[Illustration: PORTRAIT OF JOHANNES KEPLER.  By F. Wanderer, from
+Reitlinger's "Johannes Kepler" (original in Strassburg).]
+
+It has seemed to many that Plato's demand for uniform circular motion
+(linear or angular) was responsible for a loss to astronomy of good
+work during fifteen hundred years, for a hundred ill-considered
+speculative cosmogonies, for dissatisfaction, amounting to disgust,
+with these _a priori_ guesses, and for the relegation of the
+science to less intellectual races than Greeks and other Europeans.
+Nobody seemed to dare to depart from this fetish of uniform angular
+motion and circular orbits until the insight, boldness, and
+independence of Johann Kepler opened up a new world of thought and of
+intellectual delight.
+
+While at work on the Rudolphine tables he used the old epicycles and
+deferents and excentrics, but he could not make theory agree with
+observation. His instincts told him that these apologists for uniform
+motion were a fraud; and he proved it to himself by trying every
+possible variation of the elements and finding them fail.  The number
+of hypotheses which he examined and rejected was almost incredible
+(for example, that the planets turn round centres at a little distance
+from the sun, that the epicycles have centres at a little distance
+from the deferent, and so on). He says that, after using all these
+devices to make theory agree with Tycho's observations, he still found
+errors amounting to eight minutes of a degree. Then he said boldly
+that it was impossible that so good an observer as Tycho could have
+made a mistake of eight minutes, and added: "Out of these eight
+minutes we will construct a new theory that will explain the motions
+of all the planets." And he did it, with elliptic orbits having the
+sun in a focus of each.[2]
+
+It is often difficult to define the boundaries between fancies,
+imagination, hypothesis, and sound theory.  This extraordinary genius
+was a master in all these modes of attacking a problem. His analogy
+between the spaces occupied by the five regular solids and the
+distances of the planets from the sun, which filled him with so much
+delight, was a display of pure fancy. His demonstration of the three
+fundamental laws of planetary motion was the most strict and complete
+theory that had ever been attempted.
+
+It has been often suggested that the revival by Copernicus of the
+notion of a moving earth was a help to Kepler. No one who reads
+Kepler's great book could hold such an opinion for a moment. In fact,
+the excellence of Copernicus's book helped to prolong the life of the
+epicyclical theories in opposition to Kepler's teaching.
+
+All of the best theories were compared by him with observation. These
+were the Ptolemaic, the Copernican, and the Tychonic. The two latter
+placed all of the planetary orbits concentric with one another, the
+sun being placed a little away from their common centre, and having no
+apparent relation to them, and being actually outside the planes in
+which they move.  Kepler's first great discovery was that the planes
+of all the orbits pass through the sun; his second was that the line
+of apses of each planet passes through the sun; both were
+contradictory to the Copernican theory.
+
+He proceeds cautiously with his propositions until he arrives at his
+great laws, and he concludes his book by comparing observations of
+Mars, of all dates, with his theory.
+
+His first law states that the planets describe ellipses with the sun
+at a focus of each ellipse.
+
+His second law (a far more difficult one to prove) states that a line
+drawn from a planet to the sun sweeps over equal areas in equal
+times. These two laws were published in his great work, _Astronomia
+Nova, sen.  Physica Coelestis tradita commentariis de Motibus Stelloe;
+Martis_, Prague, 1609.
+
+It took him nine years more[3] to discover his third law, that the
+squares of the periodic times are proportional to the cubes of the
+mean distances from the sun.
+
+These three laws contain implicitly the law of universal
+gravitation. They are simply an alternative way of expressing that law
+in dealing with planets, not particles. Only, the power of the
+greatest human intellect is so utterly feeble that the meaning of the
+words in Kepler's three laws could not be understood until expounded
+by the logic of Newton's dynamics.
+
+The joy with which Kepler contemplated the final demonstration of
+these laws, the evolution of which had occupied twenty years, can
+hardly be imagined by us.  He has given some idea of it in a passage
+in his work on _Harmonics_, which is not now quoted, only lest
+someone might say it was egotistical--a term which is simply grotesque
+when applied to such a man with such a life's work accomplished.
+
+The whole book, _Astronomia Nova_, is a pleasure to read; the
+mass of observations that are used, and the ingenuity of the
+propositions, contrast strongly with the loose and imperfectly
+supported explanations of all his predecessors; and the indulgent
+reader will excuse the devotion of a few lines to an example of the
+ingenuity and beauty of his methods.
+
+It may seem a hopeless task to find out the true paths of Mars and the
+earth (at that time when their shape even was not known) from the
+observations giving only the relative direction from night to
+night. Now, Kepler had twenty years of observations of Mars to deal
+with. This enabled him to use a new method, to find the earth's
+orbit. Observe the date at any time when Mars is in opposition. The
+earth's position E at that date gives the longitude of Mars M. His
+period is 687 days. Now choose dates before and after the principal
+date at intervals of 687 days and its multiples.  Mars is in each case
+in the same position. Now for any date when Mars is at M and the earth
+at E3 the date of the year gives the angle E3SM. And the
+observation of Tycho gives the direction of Mars compared with the
+sun, SE3M. So all the angles of the triangle SEM in any of these
+positions of E are known, and also the ratios of SE1, SE2, SE3,
+SE4 to SM and to each other.
+
+For the orbit of Mars observations were chosen at intervals of a year,
+when the earth was always in the same place.
+
+[Illustration]
+
+But Kepler saw much farther than the geometrical facts. He realised
+that the orbits are followed owing to a force directed to the sun; and
+he guessed that this is the same force as the gravity that makes a
+stone fall. He saw the difficulty of gravitation acting through the
+void space.  He compared universal gravitation to magnetism, and
+speaks of the work of Gilbert of Colchester.  (Gilbert's book, _De
+Mundo Nostro Sublunari, Philosophia Nova_, Amstelodami, 1651,
+containing similar views, was published forty-eight years after
+Gilbert's death, and forty-two years after Kepler's book and
+reference.  His book _De Magnete_ was published in 1600.)
+
+A few of Kepler's views on gravitation, extracted from the
+Introduction to his _Astronomia Nova_, may now be mentioned:--
+
+1. Every body at rest remains at rest if outside the attractive power
+of other bodies.
+
+2. Gravity is a property of masses mutually attracting in such manner
+that the earth attracts a stone much more than a stone attracts the
+earth.
+
+3. Bodies are attracted to the earth's centre, not because it is the
+centre of the universe, but because it is the centre of the attracting
+particles of the earth.
+
+4. If the earth be not round (but spheroidal?), then bodies at
+different latitudes will not be attracted to its centre, but to
+different points in the neighbourhood of that centre.
+
+5. If the earth and moon were not retained in their orbits by vital
+force (_aut alia aligua aequipollenti_), the earth and moon would come
+together.
+
+6. If the earth were to cease to attract its waters, the oceans would
+all rise and flow to the moon.
+
+7. He attributes the tides to lunar attraction.  Kepler had been
+appointed Imperial Astronomer with a handsome salary (on paper), a
+fraction of which was doled out to him very irregularly. He was led to
+miserable makeshifts to earn enough to keep his family from
+starvation; and proceeded to Ratisbon in 1630 to represent his claims
+to the Diet. He arrived worn out and debilitated; he failed in his
+appeal, and died from fever, contracted under, and fed upon,
+disappointment and exhaustion. Those were not the days when men could
+adopt as a profession the "research of endowment."
+
+Before taking leave of Kepler, who was by no means a man of one idea,
+it ought to be here recorded that he was the first to suggest that a
+telescope made with both lenses convex (not a Galilean telescope) can
+have cross wires in the focus, for use as a pointer to fix accurately
+the positions of stars. An Englishman, Gascoigne, was the first to use
+this in practice.
+
+From the all too brief epitome here given of Kepler's greatest book,
+it must be obvious that he had at that time some inkling of the
+meaning of his laws--universal gravitation. From that moment the idea
+of universal gravitation was in the air, and hints and guesses were
+thrown out by many; and in time the law of gravitation would doubtless
+have been discovered, though probably not by the work of one man, even
+if Newton had not lived. But, if Kepler had not lived, who else could
+have discovered his laws?
+
+
+FOOTNOTES:
+
+[1] When the writer visited M. D'Arrest, the astronomer, at
+Copenhagen, in 1872, he was presented by D'Arrest with one of several
+bricks collected from the ruins of Uraniborg. This was one of his most
+cherished possessions until, on returning home after a prolonged
+absence on astronomical work, he found that his treasure had been
+tidied away from his study.
+
+[2] An ellipse is one of the plane, sections of a cone. It is an oval
+curve, which may be drawn by fixing two pins in a sheet of paper at S
+and H, fastening a string, SPH, to the two pins, and stretching it
+with a pencil point at P, and moving the pencil point, while the
+string is kept taut, to trace the oval ellipse, APB. S and H are the
+_foci_. Kepler found the sun to be in one focus, say S. AB is the
+_major axis_. DE is the _minor axis_. C is the _centre_. The direction
+of AB is the _line of apses_. The ratio of CS to CA is the
+_excentricity_. The position of the planet at A is the _perihelion_
+(nearest to the sun). The position of the planet at B is the
+_aphelion_ (farthest from the sun). The angle ASP is the _anomaly_
+when the planet is at P. CA or a line drawn from S to D is the _mean
+distance_ of the planet from the sun.
+
+[Illustration]
+
+[3] The ruled logarithmic paper we now use was not then to be had by
+going into a stationer's shop. Else he would have accomplished this in
+five minutes.
+
+
+
+6. GALILEO AND THE TELESCOPE--NOTIONS OF GRAVITY BY HORROCKS, ETC.
+
+
+It is now necessary to leave the subject of dynamical astronomy for a
+short time in order to give some account of work in a different
+direction originated by a contemporary of Kepler's, his senior in fact
+by seven years. Galileo Galilei was born at Pisa in 1564. The most
+scientific part of his work dealt with terrestrial dynamics; but one
+of those fortunate chances which happen only to really great men put
+him in the way of originating a new branch of astronomy.
+
+The laws of motion had not been correctly defined.  The only man of
+Galileo's time who seems to have worked successfully in the same
+direction as himself was that Admirable Crichton of the Italians,
+Leonardo da Vinci. Galileo cleared the ground. It had always been
+noticed that things tend to come to rest; a ball rolled on the ground,
+a boat moved on the water, a shot fired in the air. Galileo realised
+that in all of these cases a resisting force acts to stop the motion,
+and he was the first to arrive at the not very obvious law that the
+motion of a body will never stop, nor vary its speed, nor change its
+direction, except by the action of some force.
+
+It is not very obvious that a light body and a heavy one fall at the
+same speed (except for the resistance of the air). Galileo proved this
+on paper, but to convince the world he had to experiment from the
+leaning tower of Pisa.
+
+At an early age he discovered the principle of isochronism of the
+pendulum, which, in the hands of Huyghens in the middle of the
+seventeenth century, led to the invention of the pendulum clock,
+perhaps the most valuable astronomical instrument ever produced.
+
+These and other discoveries in dynamics may seem very obvious now; but
+it is often the most every-day matters which have been found to elude
+the inquiries of ordinary minds, and it required a high order of
+intellect to unravel the truth and discard the stupid maxims scattered
+through the works of Aristotle and accepted on his authority. A blind
+worship of scientific authorities has often delayed the progress of
+human knowledge, just as too much "instruction" of a youth often ruins
+his "education." Grant, in his history of Physical Astronomy, has well
+said that "the sagacity and skill which Galileo displays in resolving
+the phenomena of motion into their constituent elements, and hence
+deriving the original principles involved in them, will ever assure to
+him a distinguished place among those who have extended the domains of
+science."
+
+But it was work of a different kind that established Galileo's popular
+reputation. In 1609 Galileo heard that a Dutch spectacle-maker had
+combined a pair of lenses so as to magnify distant objects. Working on
+this hint, he solved the same problem, first on paper and then in
+practice. So he came to make one of the first telescopes ever used in
+astronomy. No sooner had he turned it on the heavenly bodies than he
+was rewarded by such a shower of startling discoveries as forthwith
+made his name the best known in Europe.  He found curious irregular
+black spots on the sun, revolving round it in twenty-seven days; hills
+and valleys on the moon; the planets showing discs of sensible size,
+not points like the fixed stars; Venus showing phases according to her
+position in relation to the sun; Jupiter accompanied by four moons;
+Saturn with appendages that he could not explain, but unlike the other
+planets; the Milky Way composed of a multitude of separate stars.
+
+His fame flew over Europe like magic, and his discoveries were much
+discussed--and there were many who refused to believe. Cosmo de Medici
+induced him to migrate to Florence to carry on his observations.  He
+was received by Paul V., the Pope, at Rome, to whom he explained his
+discoveries.
+
+He thought that these discoveries proved the truth of the Copernican
+theory of the Earth's motion; and he urged this view on friends and
+foes alike.  Although in frequent correspondence with Kepler, he never
+alluded to the New Astronomy, and wrote to him extolling the virtue of
+epicycles. He loved to argue, never shirked an encounter with any
+number of disputants, and laughed as he broke down their arguments.
+
+Through some strange course of events, not easy to follow, the
+Copernican theory, whose birth was welcomed by the Church, had now
+been taken up by certain anti-clerical agitators, and was opposed by
+the cardinals as well as by the dignitaries of the Reformed
+Church. Galileo--a good Catholic--got mixed up in these discussions,
+although on excellent terms with the Pope and his entourage. At last
+it came about that Galileo was summoned to appear at Rome, where he
+was charged with holding and teaching heretical opinions about the
+movement of the earth; and he then solemnly abjured these
+opinions. There has been much exaggeration and misstatement about his
+trial and punishment, and for a long time there was a great deal of
+bitterness shown on both sides. But the general verdict of the present
+day seems to be that, although Galileo himself was treated with
+consideration, the hostility of the Church to the views of Copernicus
+placed it in opposition also to the true Keplerian system, and this
+led to unprofitable controversies.  From the time of Galileo onwards,
+for some time, opponents of religion included the theory of the
+Earth's motion in their disputations, not so much for the love, or
+knowledge, of astronomy, as for the pleasure of putting the Church in
+the wrong. This created a great deal of bitterness and intolerance on
+both sides. Among the sufferers was Giordano Bruno, a learned
+speculative philosopher, who was condemned to be burnt at the stake.
+
+Galileo died on Christmas Day, 1642--the day of Newton's birth. The
+further consideration of the grand field of discovery opened out by
+Galileo with his telescopes must be now postponed, to avoid
+discontinuity in the history of the intellectual development of this
+period, which lay in the direction of dynamical, or physical,
+astronomy.
+
+Until the time of Kepler no one seems to have conceived the idea of
+universal physical forces controlling terrestrial phenomena, and
+equally applicable to the heavenly bodies. The grand discovery by
+Kepler of the true relationship of the Sun to the Planets, and the
+telescopic discoveries of Galileo and of those who followed him,
+spread a spirit of inquiry and philosophic thought throughout Europe,
+and once more did astronomy rise in estimation; and the irresistible
+logic of its mathematical process of reasoning soon placed it in the
+position it has ever since occupied as the foremost of the exact
+sciences.
+
+The practical application of this process of reasoning was enormously
+facilitated by the invention of logarithms by Napier. He was born at
+Merchistoun, near Edinburgh, in 1550, and died in 1617. By this system
+the tedious arithmetical operations necessary in astronomical
+calculations, especially those dealing with the trigonometrical
+functions of angles, were so much simplified that Laplace declared
+that by this invention the life-work of an astronomer was doubled.
+
+Jeremiah Horrocks (born 1619, died 1641) was an ardent admirer of
+Tycho Brahe and Kepler, and was able to improve the Rudolphine tables
+so much that he foretold a transit of Venus, in 1639, which these
+tables failed to indicate, and was the only observer of it. His life
+was short, but he accomplished a great deal, and rightly ascribed the
+lunar inequality called _evection_ to variations in the value of
+the eccentricity and in the direction of the line of apses, at the
+same time correctly assigning _the disturbing force of the Sun_
+as the cause. He discovered the errors in Jupiter's calculated place,
+due to what we now know as the long inequality of Jupiter and Saturn,
+and measured with considerable accuracy the acceleration at that date
+of Jupiter's mean motion, and indicated the retardation of Saturn's
+mean motion.
+
+Horrocks' investigations, so far as they could be collected, were
+published posthumously in 1672, and seldom, if ever, has a man who
+lived only twenty-two years originated so much scientific knowledge.
+
+At this period British science received a lasting impetus by the wise
+initiation of a much-abused man, Charles II., who founded the Royal
+Society of London, and also the Royal Observatory of Greeenwich, where
+he established Flamsteed as first Astronomer Royal, especially for
+lunar and stellar observations likely to be useful for navigation. At
+the same time the French Academy and the Paris Observatory were
+founded. All this within fourteen years, 1662-1675.
+
+Meanwhile gravitation in general terms was being discussed by Hooke,
+Wren, Halley, and many others.  All of these men felt a repugnance to
+accept the idea of a force acting across the empty void of space.
+Descartes (1596-1650) proposed an ethereal medium whirling round the
+sun with the planets, and having local whirls revolving with the
+satellites. As Delambre and Grant have said, this fiction only
+retarded the progress of pure science. It had no sort of relation to
+the more modern, but equally misleading, "nebular hypothesis." While
+many were talking and guessing, a giant mind was needed at this stage
+to make things clear.
+
+
+
+7. SIR ISAAC NEWTON--LAW OF UNIVERSAL GRAVITATION.
+
+
+We now reach the period which is the culminating point of interest in
+the history of dynamical astronomy.  Isaac Newton was born in
+1642. Pemberton states that Newton, having quitted Cambridge to avoid
+the plague, was residing at Wolsthorpe, in Lincolnshire, where he had
+been born; that he was sitting one day in the garden, reflecting upon
+the force which prevents a planet from flying off at a tangent and
+which draws it to the sun, and upon the force which draws the moon to
+the earth; and that he saw in the case of the planets that the sun's
+force must clearly be unequal at different distances, for the pull out
+of the tangential line in a minute is less for Jupiter than for
+Mars. He then saw that the pull of the earth on the moon would be less
+than for a nearer object. It is said that while thus meditating he saw
+an apple fall from a tree to the ground, and that this fact suggested
+the questions: Is the force that pulled that apple from the tree the
+same as the force which draws the moon to the earth?  Does the
+attraction for both of them follow the same law as to distance as is
+given by the planetary motions round the sun? It has been stated that
+in this way the first conception of universal gravitation arose.[1]
+
+Quite the most important event in the whole history of physical
+astronomy was the publication, in 1687, of Newton's _Principia
+(Philosophiae Naturalis Principia Mathematica)_. In this great work
+Newton started from the beginning of things, the laws of motion, and
+carried his argument, step by step, into every branch of physical
+astronomy; giving the physical meaning of Kepler's three laws, and
+explaining, or indicating the explanation of, all the known heavenly
+motions and their irregularities; showing that all of these were
+included in his simple statement about the law of universal
+gravitation; and proceeding to deduce from that law new irregularities
+in the motions of the moon which had never been noticed, and to
+discover the oblate figure of the earth and the cause of the
+tides. These investigations occupied the best part of his life; but he
+wrote the whole of his great book in fifteen months.
+
+Having developed and enunciated the true laws of motion, he was able
+to show that Kepler's second law (that equal areas are described by
+the line from the planet to the sun in equal times) was only another
+way of saying that the centripetal force on a planet is always
+directed to the sun. Also that Kepler's first law (elliptic orbits
+with the sun in one focus) was only another way of saying that the
+force urging a planet to the sun varies inversely as the square of the
+distance. Also (if these two be granted) it follows that Kepler's
+third law is only another way of saying that the sun's force on
+different planets (besides depending as above on distance) is
+proportional to their masses.
+
+Having further proved the, for that day, wonderful proposition that,
+with the law of inverse squares, the attraction by the separate
+particles of a sphere of uniform density (or one composed of
+concentric spherical shells, each of uniform density) acts as if the
+whole mass were collected at the centre, he was able to express the
+meaning of Kepler's laws in propositions which have been summarised as
+follows:--
+
+The law of universal gravitation.--_Every particle of matter in the
+universe attracts every other particle with a force varying inversely
+as the square of the distance between them, and directly as the
+product of the masses of the two particles_.[2]
+
+But Newton did not commit himself to the law until he had answered
+that question about the apple; and the above proposition now enabled
+him to deal with the Moon and the apple. Gravity makes a stone fall
+16.1 feet in a second. The moon is 60 times farther from the earth's
+centre than the stone, so it ought to be drawn out of a straight
+course through 16.1 feet in a minute. Newton found the distance
+through which she is actually drawn as a fraction of the earth's
+diameter.  But when he first examined this matter he proceeded to use
+a wrong diameter for the earth, and he found a serious discrepancy.
+This, for a time, seemed to condemn his theory, and regretfully he
+laid that part of his work aside. Fortunately, before Newton wrote the
+_Principia_ the French astronomer Picard made a new and correct
+measure of an arc of the meridian, from which he obtained an accurate
+value of the earth's diameter. Newton applied this value, and found,
+to his great joy, that when the distance of the moon is 60 times the
+radius of the earth she is attracted out of the straight course 16.1
+feet per minute, and that the force acting on a stone or an apple
+follows the same law as the force acting upon the heavenly bodies.[3]
+
+The universality claimed for the law--if not by Newton, at least by
+his commentators--was bold, and warranted only by the large number of
+cases in which Newton had found it to apply. Its universality has been
+under test ever since, and so far it has stood the test. There has
+often been a suspicion of a doubt, when some inequality of motion in
+the heavenly bodies has, for a time, foiled the astronomers in their
+attempts to explain it. But improved mathematical methods have always
+succeeded in the end, and so the seeming doubt has been converted into
+a surer conviction of the universality of the law.
+
+Having once established the law, Newton proceeded to trace some of its
+consequences. He saw that the figure of the earth depends partly on
+the mutual gravitation of its parts, and partly on the centrifugal
+tendency due to the earth's rotation, and that these should cause a
+flattening of the poles. He invented a mathematical method which he
+used for computing the ratio of the polar to the equatorial diameter.
+
+He then noticed that the consequent bulging of matter at the equator
+would be attracted by the moon unequally, the nearest parts being most
+attracted; and so the moon would tend to tilt the earth when in some
+parts of her orbit; and the sun would do this to a less extent,
+because of its great distance. Then he proved that the effect ought to
+be a rotation of the earth's axis over a conical surface in space,
+exactly as the axis of a top describes a cone, if the top has a sharp
+point, and is set spinning and displaced from the vertical. He
+actually calculated the amount; and so he explained the cause of the
+precession of the equinoxes discovered by Hipparchus about 150 B.C.
+
+One of his grandest discoveries was a method of weighing the heavenly
+bodies by their action on each other. By means of this principle he
+was able to compare the mass of the sun with the masses of those
+planets that have moons, and also to compare the mass of our moon with
+the mass of the earth.
+
+Thus Newton, after having established his great principle, devoted his
+splendid intellect to the calculation of its consequences. He proved
+that if a body be projected with any velocity in free space, subject
+only to a central force, varying inversely as the square of the
+distance, the body must revolve in a curve which may be any one of the
+sections of a cone--a circle, ellipse, parabola, or hyperbola; and he
+found that those comets of which he had observations move in parabolae
+round the Sun, and are thus subject to the universal law.
+
+Newton realised that, while planets and satellites are chiefly
+controlled by the central body about which they revolve, the new law
+must involve irregularities, due to their mutual action--such, in
+fact, as Horrocks had indicated. He determined to put this to a test
+in the case of the moon, and to calculate the sun's effect, from its
+mass compared with that of the earth, and from its distance. He proved
+that the average effect upon the plane of the orbit would be to cause
+the line in which it cuts the plane of the ecliptic (i.e., the line of
+nodes) to revolve in the ecliptic once in about nineteen years. This
+had been a known fact from the earliest ages. He also concluded that
+the line of apses would revolve in the plane of the lunar orbit also
+in about nineteen years; but the observed period is only ten
+years. For a long time this was the one weak point in the Newtonian
+theory. It was not till 1747 that Clairaut reconciled this with the
+theory, and showed why Newton's calculation was not exact.
+
+Newton proceeded to explain the other inequalities recognised by Tycho
+Brahe and older observers, and to calculate their maximum amounts as
+indicated by his theory. He further discovered from his calculations
+two new inequalities, one of the apogee, the other of the nodes, and
+assigned the maximum value. Grant has shown the values of some of
+these as given by observation in the tables of Meyer and more modern
+tables, and has compared them with the values assigned by Newton from
+his theory; and the comparison is very remarkable.
+
+                                     Newton.      Modern Tables.
+                                degrees '  "   degrees ' "
+Mean monthly motion of Apses         1.31.28         3.4.0
+Mean annual motion of nodes         19.18.1,23     19.21.22,50
+Mean value of "variation"              36.10          35.47
+Annual equation                        11.51          11.14
+Inequality of mean motion of apogee    19.43          22.17
+Inequality of mean motion of nodes      9.24           9.0
+
+The only serious discrepancy is the first, which has been already
+mentioned. Considering that some of these perturbations had never been
+discovered, that the cause of none of them had ever been known, and
+that he exhibited his results, if he did not also make the
+discoveries, by the synthetic methods of geometry, it is simply
+marvellous that he reached to such a degree of accuracy. He invented
+the infinitesimal calculus which is more suited for such calculations,
+but had he expressed his results in that language he would have been
+unintelligible to many.
+
+Newton's method of calculating the precession of the equinoxes,
+already referred to, is as beautiful as anything in the _Principia_.
+He had already proved the regression of the nodes of a satellite
+moving in an orbit inclined to the ecliptic. He now said that the
+nodes of a ring of satellites revolving round the earth's equator
+would consequently all regress. And if joined into a solid ring its
+node would regress; and it would do so, only more slowly, if
+encumbered by the spherical part of the earth's mass. Therefore the
+axis of the equatorial belt of the earth must revolve round the pole
+of the ecliptic. Then he set to work and found the amount due to the
+moon and that due to the sun, and so he solved the mystery of 2,000
+years.
+
+When Newton applied his law of gravitation to an explanation of the
+tides he started a new field for the application of mathematics to
+physical problems; and there can be little doubt that, if he could
+have been furnished with complete tidal observations from different
+parts of the world, his extraordinary powers of analysis would have
+enabled him to reach a satisfactory theory. He certainly opened up
+many mines full of intellectual gems; and his successors have never
+ceased in their explorations. This has led to improved mathematical
+methods, which, combined with the greater accuracy of observation,
+have rendered physical astronomy of to-day the most exact of the
+sciences.
+
+Laplace only expressed the universal opinion of posterity when he said
+that to the _Principia_ is assured "a pre-eminence above all the
+other productions of the human intellect."
+
+The name of Flamsteed, First Astronomer Royal, must here be mentioned
+as having supplied Newton with the accurate data required for
+completing the theory.
+
+The name of Edmund Halley, Second Astronomer Royal, must ever be held
+in repute, not only for his own discoveries, but for the part he
+played in urging Newton to commit to writing, and present to the Royal
+Society, the results of his investigations. But for his friendly
+insistence it is possible that the _Principia_ would never have
+been written; and but for his generosity in supplying the means the
+Royal Society could not have published the book.
+
+[Illustration: DEATH MASK OF SIR ISAAC NEWTON.
+Photographed specially for this work from the original, by kind
+permission of the Royal Society, London.]
+
+Sir Isaac Newton died in 1727, at the age of eighty-five. His body
+lay in state in the Jerusalem Chamber, and was buried in Westminster
+Abbey.
+
+
+FOOTNOTES:
+
+[1] The writer inherited from his father (Professor J. D. Forbes) a
+small box containing a bit of wood and a slip of paper, which had been
+presented to him by Sir David Brewster. On the paper Sir David had
+written these words: "If there be any truth in the story that Newton
+was led to the theory of gravitation by the fall of an apple, this bit
+of wood is probably a piece of the apple tree from which Newton saw
+the apple fall. When I was on a pilgrimage to the house in which
+Newton was born, I cut it off an ancient apple tree growing in his
+garden." When lecturing in Glasgow, about 1875, the writer showed it
+to his audience. The next morning, when removing his property from the
+lecture table, he found that his precious relic had been stolen. It
+would be interesting to know who has got it now!
+
+[2] It must be noted that these words, in which the laws of
+gravitation are always summarised in histories and text-books, do not
+appear in the _Principia_; but, though they must have been composed by
+some early commentator, it does not appear that their origin has been
+traced. Nor does it appear that Newton ever extended the law beyond
+the Solar System, and probably his caution would have led him to avoid
+any statement of the kind until it should be proved.
+
+With this exception the above statement of the law of universal
+gravitation contains nothing that is not to be found in the
+_Principia_; and the nearest approach to that statement occurs in the
+Seventh Proposition of Book III.:--
+
+Prop.: That gravitation occurs in all bodies, and that it is
+proportional to the quantity of matter in each.
+
+Cor. I.: The total attraction of gravitation on a planet arises, and
+is composed, out of the attraction on the separate parts.
+
+Cor. II.: The attraction on separate equal particles of a body is
+reciprocally as the square of the distance from the particles.
+
+[3] It is said that, when working out this final result, the
+probability of its confirming that part of his theory which he had
+reluctantly abandoned years before excited him so keenly that he was
+forced to hand over his calculations to a friend, to be completed by
+him.
+
+
+
+8. NEWTON'S SUCCESSORS--HALLEY, EULER, LAGRANGE, LAPLACE, ETC.
+
+
+Edmund Halley succeeded Flamsteed as Second Astronomer Royal in
+1721. Although he did not contribute directly to the mathematical
+proofs of Newton's theory, yet his name is closely associated with
+some of its greatest successes.
+
+He was the first to detect the acceleration of the moon's mean
+motion. Hipparchus, having compared his own observations with those of
+more ancient astronomers, supplied an accurate value of the moon's
+mean motion in his time. Halley similarly deduced a value for modern
+times, and found it sensibly greater. He announced this in 1693, but
+it was not until 1749 that Dunthorne used modern lunar tables to
+compute a lunar eclipse observed in Babylon 721 B.C., another at
+Alexandria 201 B.C., a solar eclipse observed by Theon 360 A.D., and
+two later ones up to the tenth century. He found that to explain
+these eclipses Halley's suggestion must be adopted, the acceleration
+being 10" in one century. In 1757 Lalande again fixed it at 10."
+
+The Paris Academy, in 1770, offered their prize for an investigation
+to see if this could be explained by the theory of gravitation. Euler
+won the prize, but failed to explain the effect, and said: "It appears
+to be established by indisputable evidence that the secular inequality
+of the moon's mean motion cannot be produced by the forces of
+gravitation."
+
+The same subject was again proposed for a prize which was shared by
+Lagrange [1] and Euler, neither finding a solution, while the latter
+asserted the existence of a resisting medium in space.
+
+Again, in 1774, the Academy submitted the same subject, a third time,
+for the prize; and again Lagrange failed to detect a cause in
+gravitation.
+
+Laplace [2] now took the matter in hand. He tried the effect of a
+non-instantaneous action of gravity, to no purpose. But in 1787 he
+gave the true explanation. The principal effect of the sun on the
+moon's orbit is to diminish the earth's influence, thus lengthening
+the period to a new value generally taken as constant. But Laplace's
+calculations showed the new value to depend upon the excentricity of
+the earth's orbit, which, according; to theory, has a periodical
+variation of enormous period, and has been continually diminishing for
+thousands of years. Thus the solar influence has been diminishing, and
+the moon's mean motion increased. Laplace computed the amount at 10"
+in one century, agreeing with observation. (Later on Adams showed that
+Laplace's calculation was wrong, and that the value he found was too
+large; so, part of the acceleration is now attributed by some
+astronomers to a lengthening of the day by tidal friction.)
+
+Another contribution by Halley to the verification of Newton's law was
+made when he went to St. Helena to catalogue the southern stars. He
+measured the change in length of the second's pendulum in different
+latitudes due to the changes in gravity foretold by Newton.
+
+Furthermore, he discovered the long inequality of Jupiter and Saturn,
+whose period is 929 years. For an investigation of this also the
+Academy of Sciences offered their prize. This led Euler to write a
+valuable essay disclosing a new method of computing perturbations,
+called the instantaneous ellipse with variable elements. The method
+was much developed by Lagrange.
+
+But again it was Laplace who solved the problem of the inequalities of
+Jupiter and Saturn by the theory of gravitation, reducing the errors
+of the tables from 20' down to 12", thus abolishing the use of
+empirical corrections to the planetary tables, and providing another
+glorious triumph for the law of gravitation. As Laplace justly said:
+"These inequalities appeared formerly to be inexplicable by the law of
+gravitation--they now form one of its most striking proofs."
+
+Let us take one more discovery of Halley, furnishing directly a new
+triumph for the theory. He noticed that Newton ascribed parabolic
+orbits to the comets which he studied, so that they come from
+infinity, sweep round the sun, and go off to infinity for ever, after
+having been visible a few weeks or months. He collected all the
+reliable observations of comets he could find, to the number of
+twenty-four, and computed their parabolic orbits by the rules laid
+down by Newton. His object was to find out if any of them really
+travelled in elongated ellipses, practically undistinguishable, in the
+visible part of their paths, from parabolae, in which case they would
+be seen more than once. He found two old comets whose orbits, in shape
+and position, resembled the orbit of a comet observed by himself in
+1682. Apian observed one in 1531; Kepler the other in 1607. The
+intervals between these appearances is seventy-five or seventy-six
+years. He then examined and found old records of similar appearance in
+1456, 1380, and 1305. It is true, he noticed, that the intervals
+varied by a year and a-half, and the inclination of the orbit to the
+ecliptic diminished with successive apparitions. But he knew from
+previous calculations that this might easily be due to planetary
+perturbations. Finally, he arrived at the conclusion that all of these
+comets were identical, travelling in an ellipse so elongated that the
+part where the comet was seen seemed to be part of a parabolic
+orbit. He then predicted its return at the end of 1758 or beginning of
+1759, when he should be dead; but, as he said, "if it should return,
+according to our prediction, about the year 1758, impartial posterity
+will not refuse to acknowledge that this was first discovered by an
+Englishman."[3] [_Synopsis Astronomiae Cometicae_, 1749.]
+
+Once again Halley's suggestion became an inspiration for the
+mathematical astronomer. Clairaut, assisted by Lalande, found that
+Saturn would retard the comet 100 days, Jupiter 518 days, and
+predicted its return to perihelion on April 13th, 1759. In his
+communication to the French Academy, he said that a comet travelling
+into such distant regions might be exposed to the influence of forces
+totally unknown, and "even of some planet too far removed from the sun
+to be ever perceived."
+
+The excitement of astronomers towards the end of 1758 became intense;
+and the honour of first catching sight of the traveller fell to an
+amateur in Saxony, George Palitsch, on Christmas Day, 1758. It reached
+perihelion on March 13th, 1759.
+
+This fact was a startling confirmation of the Newtonian theory,
+because it was a new kind of calculation of perturbations, and also it
+added a new member to the solar system, and gave a prospect of adding
+many more.
+
+When Halley's comet reappeared in 1835, Pontecoulant's computations
+for the date of perihelion passage were very exact, and afterwards he
+showed that, with more exact values of the masses of Jupiter and
+Saturn, his prediction was correct within two days, after an invisible
+voyage of seventy-five years!
+
+Hind afterwards searched out many old appearances of this comet, going
+back to 11 B.C., and most of these have been identified as being
+really Halley's comet by the calculations of Cowell and Cromellin[4]
+(of Greenwich Observatory), who have also predicted its next
+perihelion passage for April 8th to 16th, 1910, and have traced back
+its history still farther, to 240 B.C.
+
+Already, in November, 1907, the Astronomer Royal was trying to catch
+it by the aid of photography.
+
+
+FOOTNOTES:
+
+[1] Born 1736; died 1813.
+
+[2] Born 1749; died 1827.
+
+[3] This sentence does not appear in the original memoir communicated
+to the Royal Society, but was first published in a posthumous reprint.
+
+[4] _R. A. S. Monthly Notices_, 1907-8.
+
+
+
+9. DISCOVERY OF NEW PLANETS--HERSCHEL, PIAZZI, ADAMS, AND LE VERRIER.
+
+
+It would be very interesting, but quite impossible in these pages, to
+discuss all the exquisite researches of the mathematical astronomers,
+and to inspire a reverence for the names connected with these
+researches, which for two hundred years have been establishing the
+universality of Newton's law. The lunar and planetary theories, the
+beautiful theory of Jupiter's satellites, the figure of the earth, and
+the tides, were mathematically treated by Maclaurin, D'Alembert,
+Legendre, Clairaut, Euler, Lagrange, Laplace, Walmsley, Bailly,
+Lalande, Delambre, Mayer, Hansen, Burchardt, Binet, Damoiseau, Plana,
+Poisson, Gauss, Bessel, Bouvard, Airy, Ivory, Delaunay, Le Verrier,
+Adams, and others of later date.
+
+By passing over these important developments it is possible to trace
+some of the steps in the crowning triumph of the Newtonian theory, by
+which the planet Neptune was added to the known members of the solar
+system by the independent researches of Professor J.C. Adams and of
+M. Le Verrier, in 1846.
+
+It will be best to introduce this subject by relating how the
+eighteenth century increased the number of known planets, which was
+then only six, including the earth.
+
+On March 13th, 1781, Sir William Herschel was, as usual, engaged on
+examining some small stars, and, noticing that one of them appeared to
+be larger than the fixed stars, suspected that it might be a comet.
+To test this he increased his magnifying power from 227 to 460 and
+932, finding that, unlike the fixed stars near it, its definition was
+impaired and its size increased. This convinced him that the object
+was a comet, and he was not surprised to find on succeeding nights
+that the position was changed, the motion being in the ecliptic. He
+gave the observations of five weeks to the Royal Society without a
+suspicion that the object was a new planet.
+
+For a long time people could not compute a satisfactory orbit for the
+supposed comet, because it seemed to be near the perihelion, and no
+comet had ever been observed with a perihelion distance from the sun
+greater than four times the earth's distance. Lexell was the first to
+suspect that this was a new planet eighteen times as far from the sun
+as the earth is. In January, 1783, Laplace published the elliptic
+elements. The discoverer of a planet has a right to name it, so
+Herschel called it Georgium Sidus, after the king. But Lalande urged
+the adoption of the name Herschel. Bode suggested Uranus, and this
+was adopted. The new planet was found to rank in size next to Jupiter
+and Saturn, being 4.3 times the diameter of the earth.
+
+In 1787 Herschel discovered two satellites, both revolving in nearly
+the same plane, inclined 80 degrees to the ecliptic, and the motion of both
+was retrograde.
+
+In 1772, before Herschel's discovery, Bode[1] had discovered a curious
+arbitrary law of planetary distances. Opposite each planet's name
+write the figure 4; and, in succession, add the numbers 0, 3, 6, 12,
+24, 48, 96, etc., to the 4, always doubling the last numbers. You
+then get the planetary distances.
+
+  Mercury, dist.-- 4  4 +   0 =   4
+  Venus      "     7  4 +   3 =   7
+  Earth      "    10  4 +   6 =  10
+  Mars       "    15  4 +  12 =  16
+   --                 4 +  24 =  28
+  Jupiter  dist.  52  4 +  48 =  52
+  Saturn     "    95  4 +  96 = 100
+  (Uranus)   "   192  4 + 192 = 196
+   --                 4 + 384 = 388
+
+All the five planets, and the earth, fitted this rule, except that
+there was a blank between Mars and Jupiter. When Uranus was
+discovered, also fitting the rule, the conclusion was irresistible
+that there is probably a planet between Mars and Jupiter. An
+association of twenty-four astronomers was now formed in Germany to
+search for the planet. Almost immediately afterwards the planet was
+discovered, not by any member of the association, but by Piazzi, when
+engaged upon his great catalogue of stars. On January 1st, 1801, he
+observed a star which had changed its place the next night. Its motion
+was retrograde till January 11th, direct after the 13th. Piazzi fell
+ill before he had enough observations for computing the orbit with
+certainty, and the planet disappeared in the sun's rays. Gauss
+published an approximate ephemeris of probable positions when the
+planet should emerge from the sun's light. There was an exciting hunt,
+and on December 31st (the day before its birthday) De Zach captured
+the truant, and Piazzi christened it Ceres.
+
+
+The mean distance from the sun was found to be 2.767, agreeing with
+the 2.8 given by Bode's law. Its orbit was found to be inclined over
+10 degrees to the ecliptic, and its diameter was only 161 miles.
+
+On March 28th, 1802, Olbers discovered a new seventh magnitude star,
+which turned out to be a planet resembling Ceres. It was called
+Pallas. Gauss found its orbit to be inclined 35 degrees to the
+ecliptic, and to cut the orbit of Ceres; whence Olbers considered that
+these might be fragments of a broken-up planet. He then commenced a
+search for other fragments. In 1804 Harding discovered Juno, and in
+1807 Olbers found Vesta. The next one was not discovered until 1845,
+from which date asteroids, or minor planets (as these small planets
+are called), have been found almost every year. They now number about
+700.
+
+It is impossible to give any idea of the interest with which the first
+additions since prehistoric times to the planetary system were
+received. All of those who showered congratulations upon the
+discoverers regarded these discoveries in the light of rewards for
+patient and continuous labours, the very highest rewards that could be
+desired. And yet there remained still the most brilliant triumph of
+all, the addition of another planet like Uranus, before it had ever
+been seen, when the analysis of Adams and Le Verrier gave a final
+proof of the powers of Newton's great law to explain any planetary
+irregularity.
+
+After Sir William Herschel discovered Uranus, in 1781, it was found
+that astronomers had observed it on many previous occasions, mistaking
+it for a fixed star of the sixth or seventh magnitude. Altogether,
+nineteen observations of Uranus's position, from the time of
+Flamsteed, in 1690, had been recorded.
+
+In 1790 Delambre, using all these observations, prepared tables for
+computing its position. These worked well enough for a time, but at
+last the differences between the calculated and observed longitudes of
+the planet became serious. In 1821 Bouvard undertook a revision of the
+tables, but found it impossible to reconcile all the observations of
+130 years (the period of revolution of Uranus is eighty-four years).
+So he deliberately rejected the old ones, expressing the opinion that
+the discrepancies might depend upon "some foreign and unperceived
+cause which may have been acting upon the planet." In a few years the
+errors even of these tables became intolerable. In 1835 the error of
+longitude was 30"; in 1838, 50"; in 1841, 70"; and, by comparing the
+errors derived from observations made before and after opposition, a
+serious error of the distance (radius vector) became apparent.
+
+In 1843 John Couch Adams came out Senior Wrangler at Cambridge, and
+was free to undertake the research which as an undergraduate he had
+set himself--to see whether the disturbances of Uranus could be
+explained by assuming a certain orbit, and position in that orbit, of
+a hypothetical planet even more distant than Uranus. Such an
+explanation had been suggested, but until 1843 no one had the boldness
+to attack the problem. Bessel had intended to try, but a fatal
+illness overtook him.
+
+Adams first recalculated all known causes of disturbance, using the
+latest determinations of the planetary masses. Still the errors were
+nearly as great as ever. He could now, however, use these errors as
+being actually due to the perturbations produced by the unknown
+planet.
+
+In 1844, assuming a circular orbit, and a mean distance agreeing with
+Bode's law, he obtained a first approximation to the position of the
+supposed planet. He then asked Professor Challis, of Cambridge, to
+procure the latest observations of Uranus from Greenwich, which Airy
+immediately supplied. Then the whole work was recalculated from the
+beginning, with more exactness, and assuming a smaller mean distance.
+
+In September, 1845, he handed to Challis the elements of the
+hypothetical planet, its mass, and its apparent position for September
+30th, 1845. On September 22nd Challis wrote to Airy explaining the
+matter, and declaring his belief in Adams's capabilities. When Adams
+called on him Airy was away from home, but at the end of October,
+1845, he called again, and left a paper with full particulars of his
+results, which had, for the most part, reduced the discrepancies to
+about 1". As a matter of fact, it has since been found that the
+heliocentric place of the new planet then given was correct within
+about 2 degrees.
+
+Airy wrote expressing his interest, and asked for particulars about
+the radius vector. Adams did not then reply, as the answer to this
+question could be seen to be satisfactory by looking at the data
+already supplied. He was a most unassuming man, and would not push
+himself forward. He may have felt, after all the work he had done,
+that Airy's very natural inquiry showed no proportionate desire to
+search for the planet. Anyway, the matter lay in embryo for nine
+months.
+
+Meanwhile, one of the ablest French astronomers, Le Verrier,
+experienced in computing perturbations, was independently at work,
+knowing nothing about Adams. He applied to his calculations every
+possible refinement, and, considering the novelty of the problem, his
+calculation was one of the most brilliant in the records of
+astronomy. In criticism it has been said that these were exhibitions
+of skill rather than helps to a solution of the particular problem,
+and that, in claiming to find the elements of the orbit within certain
+limits, he was claiming what was, under the circumstances, impossible,
+as the result proved.
+
+In June, 1846, Le Verrier announced, in the _Comptes Rendus de
+l'Academie des Sciences_, that the longitude of the disturbing planet,
+for January 1st, 1847, was 325, and that the probable error did not
+exceed 10 degrees.
+
+This result agreed so well with Adams's (within 1 degrees) that Airy urged
+Challis to apply the splendid Northumberland equatoreal, at Cambridge,
+to the search. Challis, however, had already prepared an exhaustive
+plan of attack which must in time settle the point. His first work
+was to observe, and make a catalogue, or chart, of all stars near
+Adams's position.
+
+On August 31st, 1846, Le Verrier published the concluding
+part of his labours.
+
+On September 18th, 1846, Le Verrier communicated his results to the
+Astronomers at Berlin, and asked them to assist in searching for the
+planet. By good luck Dr. Bremiker had just completed a star-chart of
+the very part of the heavens including Le Verrier's position; thus
+eliminating all of Challis's preliminary work. The letter was received
+in Berlin on September 23rd; and the same evening Galle found the new
+planet, of the eighth magnitude, the size of its disc agreeing with Le
+Verrier's prediction, and the heliocentric longitude agreeing within
+57'. By this time Challis had recorded, without reduction, the
+observations of 3,150 stars, as a commencement for his search. On
+reducing these, he found a star, observed on August 12th, which was
+not in the same place on July 30th. This was the planet, and he had
+also observed it on August 4th.
+
+The feeling of wonder, admiration, and enthusiasm aroused by this
+intellectual triumph was overwhelming. In the world of astronomy
+reminders are met every day of the terrible limitations of human
+reasoning powers; and every success that enables the mind's eye to see
+a little more clearly the meaning of things has always been heartily
+welcomed by those who have themselves been engaged in like
+researches. But, since the publication of the _Principia_, in 1687,
+there is probably no analytical success which has raised among
+astronomers such a feeling of admiration and gratitude as when Adams
+and Le Verrier showed the inequalities in Uranus's motion to mean that
+an unknown planet was in a certain place in the heavens, where it was
+found.
+
+At the time there was an unpleasant display of international jealousy.
+The British people thought that the earlier date of Adams's work, and
+of the observation by Challis, entitled him to at least an equal share
+of credit with Le Verrier. The French, on the other hand, who, on the
+announcement of the discovery by Galle, glowed with pride in the new
+proof of the great powers of their astronomer, Le Verrier, whose life
+had a long record of successes in calculation, were incredulous on
+being told that it had all been already done by a young man whom they
+had never heard of.
+
+These displays of jealousy have long since passed away, and there is
+now universally an _entente cordiale_ that to each of these great men
+belongs equally the merit of having so thoroughly calculated this
+inverse problem of perturbations as to lead to the immediate discovery
+of the unknown planet, since called Neptune.
+
+It was soon found that the planet had been observed, and its position
+recorded as a fixed star by Lalande, on May 8th and 10th, 1795.
+
+Mr. Lassel, in the same year, 1846, with his two-feet reflector,
+discovered a satellite, with retrograde motion, which gave the mass of
+the planet about a twentieth of that of Jupiter.
+
+
+FOOTNOTES:
+
+[1] Bode's law, or something like it, had already been fore-shadowed
+by Kepler and others, especially Titius (see _Monatliche
+Correspondenz_, vol. vii., p. 72).
+
+
+
+
+BOOK III. OBSERVATION
+
+
+
+10. INSTRUMENTS OF PRECISION--STATE OF THE SOLAR SYSTEM.
+
+
+Having now traced the progress of physical astronomy up to the time
+when very striking proofs of the universality of the law of
+gravitation convinced the most sceptical, it must still be borne in
+mind that, while gravitation is certainly the principal force
+governing the motions of the heavenly bodies, there may yet be a
+resisting medium in space, and there may be electric and magnetic
+forces to deal with. There may, further, be cases where the effects of
+luminous radiative repulsion become apparent, and also Crookes'
+vacuum-effects described as "radiant matter." Nor is it quite certain
+that Laplace's proofs of the instantaneous propagation of gravity are
+final.
+
+And in the future, as in the past, Tycho Brahe's dictum must be
+maintained, that all theory shall be preceded by accurate
+observations. It is the pride of astronomers that their science stands
+above all others in the accuracy of the facts observed, as well as in
+the rigid logic of the mathematics used for interpreting these facts.
+
+It is interesting to trace historically the invention of those
+instruments of precision which have led to this result, and, without
+entering on the details required in a practical handbook, to note the
+guiding principles of construction in different ages.
+
+It is very probable that the Chaldeans may have made spheres, like the
+armillary sphere, for representing the poles of the heavens; and with
+rings to show the ecliptic and zodiac, as well as the equinoctial and
+solstitial colures; but we have no record. We only know that the tower
+of Belus, on an eminence, was their observatory. We have, however,
+distinct records of two such spheres used by the Chinese about 2500
+B.C. Gnomons, or some kind of sundial, were used by the Egyptians and
+others; and many of the ancient nations measured the obliquity of the
+ecliptic by the shadows of a vertical column in summer and winter. The
+natural horizon was the only instrument of precision used by those who
+determined star positions by the directions of their risings and
+settings; while in those days the clepsydra, or waterclock, was the
+best instrument for comparing their times of rising and setting.
+
+About 300 B.C. an observatory fitted with circular instruments for
+star positions was set up at Alexandria, the then centre of
+civilisation. We know almost nothing about the instruments used by
+Hipparchus in preparing his star catalogues and his lunar and solar
+tables; but the invention of the astrolabe is attributed to him.[1]
+
+In more modern times Nuremberg became a centre of astronomical
+culture. Waltherus, of that town, made really accurate observations of
+star altitudes, and of the distances between stars; and in 1484
+A.D. he used a kind of clock. Tycho Brahe tried these, but discarded
+them as being inaccurate.
+
+Tycho Brahe (1546-1601 A.D.) made great improvements in armillary
+spheres, quadrants, sextants, and large celestial globes. With these
+he measured the positions of stars, or the distance of a comet from
+several known stars. He has left us full descriptions of them,
+illustrated by excellent engravings. Previous to his time such
+instruments were made of wood. Tycho always used metal. He paid the
+greatest attention to the stability of mounting, to the orientation of
+his instruments, to the graduation of the arcs by the then new method
+of transversals, and to the aperture sight used upon his
+pointer. There were no telescopes in his day, and no pendulum
+clocks. He recognised the fact that there must be instrumental
+errors. He made these as small as was possible, measured their amount,
+and corrected his observations. His table of refractions enabled him
+to abolish the error due to our atmosphere so far as it could affect
+naked-eye observations. The azimuth circle of Tycho's largest quadrant
+had a diameter of nine feet, and the quadrant a radius of six feet. He
+introduced the mural quadrant for meridian observations.[2]
+
+[Illustration: ANCIENT CHINESE INSTRUMENTS, Including quadrant, celestial
+globe, and two armillae, in the Observatory at Peking. Photographed in
+Peking by the author in 1875, and stolen by the Germans when the
+Embassies were relieved by the allies in 1900.]
+
+The French Jesuits at Peking, in the seventeenth century, helped the
+Chinese in their astronomy. In 1875 the writer saw and photographed,
+on that part of the wall of Peking used by the Mandarins as an
+observatory, the six instruments handsomely designed by Father
+Verbiest, copied from the instruments of Tycho Brahe, and embellished
+with Chinese dragons and emblems cast on the supports. He also saw
+there two old instruments (which he was told were Arabic) of date
+1279, by Ko Show-King, astronomer to Koblai Khan, the grandson of
+Chenghis Khan. One of these last is nearly identical with the armillae
+of Tycho; and the other with his "armillae aequatoriae maximae," with
+which he observed the comet of 1585, besides fixed stars and
+planets.[3]
+
+The discovery by Galileo of the isochronism of the pendulum, followed
+by Huyghens's adaptation of that principle to clocks, has been one of
+the greatest aids to accurate observation. About the same time an
+equally beneficial step was the employment of the telescope as a
+pointer; not the Galilean with concave eye-piece, but with a
+magnifying glass to examine the focal image, at which also a fixed
+mark could be placed. Kepler was the first to suggest this. Gascoigne
+was the first to use it. Huyghens used a metal strip of variable width
+in the focus, as a micrometer to cover a planetary disc, and so to
+measure the width covered by the planet. The Marquis Malvasia, in
+1662, described the network of fine silver threads at right angles,
+which he used in the focus, much as we do now.
+
+In the hands of such a skilful man as Tycho Brahe, the old open
+sights, even without clocks, served their purpose sufficiently well to
+enable Kepler to discover the true theory of the solar system. But
+telescopic sights and clocks were required for proving some of
+Newton's theories of planetary perturbations. Picard's observations at
+Paris from 1667 onwards seem to embody the first use of the telescope
+as a pointer. He was also the first to introduce the use of Huyghens's
+clocks for observing the right ascension of stars. Olaus Romer was
+born at Copenhagen in 1644. In 1675, by careful study of the times of
+eclipses of Jupiter's satellites, he discovered that light took time
+to traverse space. Its velocity is 186,000 miles per second. In 1681
+he took up his duties as astronomer at Copenhagen, and built the first
+transit circle on a window-sill of his house. The iron axis was five
+feet long and one and a-half inches thick, and the telescope was fixed
+near one end with a counterpoise. The telescope-tube was a double
+cone, to prevent flexure. Three horizontal and three vertical wires
+were used in the focus. These were illuminated by a speculum, near the
+object-glass, reflecting the light from a lantern placed over the
+axis, the upper part of the telescope-tube being partly cut away to
+admit the light. A divided circle, with pointer and reading
+microscope, was provided for reading the declination. He realised the
+superiority of a circle with graduations over a much larger
+quadrant. The collimation error was found by reversing the instrument
+and using a terrestrial mark, the azimuth error by star observations.
+The time was expressed in fractions of a second. He also constructed a
+telescope with equatoreal mounting, to follow a star by one axial
+motion. In 1728 his instruments and observation records were destroyed
+by fire.
+
+Hevelius had introduced the vernier and tangent screw in his
+measurement of arc graduations. His observatory and records were burnt
+to the ground in 1679. Though an old man, he started afresh, and left
+behind him a catalogue of 1,500 stars.
+
+Flamsteed began his duties at Greenwich Observatory, as first
+Astronomer Royal, in 1676, with very poor instruments. In 1683 he put
+up a mural arc of 140 degrees, and in 1689 a better one, seventy-nine
+inches radius. He conducted his measurements with great skill, and
+introduced new methods to attain accuracy, using certain stars for
+determining the errors of his instruments; and he always reduced his
+observations to a form in which they could be readily used. He
+introduced new methods for determining the position of the equinox and
+the right ascension of a fundamental star. He produced a catalogue of
+2,935 stars. He supplied Sir Isaac Newton with results of observation
+required in his theoretical calculations. He died in 1719.
+
+Halley succeeded Flamsteed to find that the whole place had been
+gutted by the latter's executors. In 1721 he got a transit instrument,
+and in 1726 a mural quadrant by Graham. His successor in 1742,
+Bradley, replaced this by a fine brass quadrant, eight feet radius, by
+Bird; and Bradley's zenith sector was purchased for the observatory.
+An instrument like this, specially designed for zenith stars, is
+capable of greater rigidity than a more universal instrument; and
+there is no trouble with refraction in the zenith. For these reasons
+Bradley had set up this instrument at Kew, to attempt the proof of the
+earth's motion by observing the annual parallax of stars. He certainly
+found an annual variation of zenith distance, but not at the times of
+year required by the parallax. This led him to the discovery of the
+"aberration" of light and of nutation. Bradley has been described as
+the founder of the modern system of accurate observation. He died in
+1762, leaving behind him thirteen folio volumes of valuable but
+unreduced observations. Those relating to the stars were reduced by
+Bessel and published in 1818, at Konigsberg, in his well-known
+standard work, _Fundamenta Astronomiae_. In it are results showing the
+laws of refraction, with tables of its amount, the maximum value of
+aberration, and other constants.
+
+Bradley was succeeded by Bliss, and he by Maskelyne (1765), who
+carried on excellent work, and laid the foundations of the Nautical
+Almanac (1767). Just before his death he induced the Government to
+replace Bird's quadrant by a fine new mural _circle_, six feet in
+diameter, by Troughton, the divisions being read off by microscopes
+fixed on piers opposite to the divided circle. In this instrument the
+micrometer screw, with a divided circle for turning it, was applied
+for bringing the micrometer wire actually in line with a division on
+the circle--a plan which is still always adopted.
+
+Pond succeeded Maskelyne in 1811, and was the first to use this
+instrument. From now onwards the places of stars were referred to the
+pole, not to the zenith; the zero being obtained from measures on
+circumpolar stars. Standard stars were used for giving the clock
+error. In 1816 a new transit instrument, by Troughton, was added, and
+from this date the Greenwich star places have maintained the very
+highest accuracy.
+
+George Biddell Airy, Seventh Astronomer Royal,[4] commenced his
+Greenwich labours in 1835. His first and greatest reformation in the
+work of the observatory was one he had already established at
+Cambridge, and is now universally adopted. He held that an observation
+is not completed until it has been reduced to a useful form; and in
+the case of the sun, moon, and planets these results were, in every
+case, compared with the tables, and the tabular error printed.
+
+Airy was firmly impressed with the object for which Charles II. had
+wisely founded the observatory in connection with navigation, and for
+observations of the moon. Whenever a meridian transit of the moon
+could be observed this was done. But, even so, there are periods in
+the month when the moon is too near the sun for a transit to be well
+observed. Also weather interferes with many meridian observations. To
+render the lunar observations more continuous, Airy employed
+Troughton's successor, James Simms, in conjunction with the engineers,
+Ransome and May, to construct an altazimuth with three-foot circles,
+and a five-foot telescope, in 1847. The result was that the number of
+lunar observations was immediately increased threefold, many of them
+being in a part of the moon's orbit which had previously been bare of
+observations. From that date the Greenwich lunar observations have
+been a model and a standard for the whole world.
+
+Airy also undertook to superintend the reduction of all Greenwich
+lunar observations from 1750 to 1830. The value of this laborious
+work, which was completed in 1848, cannot be over-estimated.
+
+The demands of astronomy, especially in regard to small minor planets,
+required a transit instrument and mural circle with a more powerful
+telescope. Airy combined the functions of both, and employed the same
+constructors as before to make a _transit-circle_ with a telescope of
+eleven and a-half feet focus and a circle of six-feet diameter, the
+object-glass being eight inches in diameter.
+
+Airy, like Bradley, was impressed with the advantage of employing
+stars in the zenith for determining the fundamental constants of
+astronomy. He devised a _reflex zenith tube_, in which the zenith
+point was determined by reflection from a surface of mercury. The
+design was so simple, and seemed so perfect, that great expectations
+were entertained. But unaccountable variations comparable with those
+of the transit circle appeared, and the instrument was put out of use
+until 1903, when the present Astronomer Royal noticed that the
+irregularities could be allowed for, being due to that remarkable
+variation in the position of the earth's axis included in circles of
+about six yards diameter at the north and south poles, discovered at
+the end of the nineteenth century. The instrument is now being used
+for investigating these variations; and in the year 1907 as many as
+1,545 observations of stars were made with the reflex zenith tube.
+
+In connection with zenith telescopes it must be stated that Respighi,
+at the Capitol Observatory at Rome, made use of a deep well with a
+level mercury surface at the bottom and a telescope at the top
+pointing downwards, which the writer saw in 1871. The reflection of
+the micrometer wires and of a star very near the zenith (but not quite
+in the zenith) can be observed together. His mercury trough was a
+circular plane surface with a shallow edge to retain the mercury. The
+surface quickly came to rest after disturbance by street traffic.
+
+Sir W. M. H. Christie, Eighth Astronomer Royal, took up his duties in
+that capacity in 1881. Besides a larger altazimuth that he erected in
+1898, he has widened the field of operations at Greenwich by the
+extensive use of photography and the establishment of large
+equatoreals. From the point of view of instruments of precision, one
+of the most important new features is the astrographic equatoreal, set
+up in 1892 and used for the Greenwich section of the great
+astrographic chart just completed. Photography has come to be of use,
+not only for depicting the sun and moon, comets and nebulae, but also
+to obtain accurate relative positions of neighbouring stars; to pick
+up objects that are invisible in any telescope; and, most of all
+perhaps, in fixing the positions of faint satellites. Thus Saturn's
+distant satellite, Phoebe, and the sixth and seventh satellites of
+Jupiter, have been followed regularly in their courses at Greenwich
+ever since their discovery with the thirty-inch reflector (erected in
+1897); and while doing so Mr. Melotte made, in 1908, the splendid
+discovery on some of the photographic plates of an eighth satellite of
+Jupiter, at an enormous distance from the planet. From observations in
+the early part of 1908, over a limited arc of its orbit, before
+Jupiter approached the sun, Mr. Cowell computed a retrograde orbit and
+calculated the future positions of this satellite, which enabled
+Mr. Melotte to find it again in the autumn--a great triumph both of
+calculation and of photographic observation. This satellite has never
+been seen, and has been photographed only at Greenwich, Heidelberg,
+and the Lick Observatory.
+
+Greenwich Observatory has been here selected for tracing the progress
+of accurate measurement. But there is one instrument of great value,
+the heliometer, which is not used at Greenwich. This serves the
+purpose of a double image micrometer, and is made by dividing the
+object-glass of a telescope along a diameter. Each half is mounted so
+as to slide a distance of several inches each way on an arc whose
+centre is the focus. The amount of the movement can be accurately
+read. Thus two fields of view overlap, and the adjustment is made to
+bring an image of one star over that of another star, and then to do
+the same by a displacement in the opposite direction. The total
+movement of the half-object glass is double the distance between the
+star images in the focal plane. Such an instrument has long been
+established at Oxford, and German astronomers have made great use of
+it. But in the hands of Sir David Gill (late His Majesty's Astronomer
+at the Cape of Good Hope), and especially in his great researches on
+Solar and on Stellar parallax, it has been recognised as an instrument
+of the very highest accuracy, measuring the distance between stars
+correctly to less than a tenth of a second of arc.
+
+The superiority of the heliometer over all other devices (except
+photography) for measuring small angles has been specially brought
+into prominence by Sir David Gill's researches on the distance of the
+sun--_i.e.,_ the scale of the solar system. A measurement of the
+distance of any planet fixes the scale, and, as Venus approaches the
+earth most nearly of all the planets, it used to be supposed that a
+Transit of Venus offered the best opportunity for such measurement,
+especially as it was thought that, as Venus entered on the solar disc,
+the sweep of light round the dark disc of Venus would enable a very
+precise observation to be made. The Transit of Venus in 1874, in
+which the present writer assisted, overthrew this delusion.
+
+In 1877 Sir David Gill used Lord Crawford's heliometer at the Island
+of Ascension to measure the parallax of Mars in opposition, and found
+the sun's distance 93,080,000 miles. He considered that, while the
+superiority of the heliometer had been proved, the results would be
+still better with the points of light shown by minor planets rather
+than with the disc of Mars.
+
+In 1888-9, at the Cape, he observed the minor planets Iris, Victoria,
+and Sappho, and secured the co-operation of four other heliometers.
+His final result was 92,870,000 miles, the parallax being 8",802
+(_Cape Obs_., Vol. VI.).
+
+So delicate were these measures that Gill detected a minute periodic
+error of theory of twenty-seven days, owing to a periodically
+erroneous position of the centre of gravity of the earth and moon to
+which the position of the observer was referred. This led him to
+correct the mass of the moon, and to fix its ratio to the earth's mass
+= 0.012240.
+
+Another method of getting the distance from the sun is to measure the
+velocity of the earth's orbital motion, giving the circumference
+traversed in a year, and so the radius of the orbit. This has been
+done by comparing observation and experiment. The aberration of light
+is an angle 20" 48, giving the ratio of the earth's velocity to the
+velocity of light. The velocity of light is 186,000 miles a second;
+whence the distance to the sun is 92,780,000 miles. There seems,
+however, to be some uncertainty about the true value of the
+aberration, any determination of which is subject to irregularities
+due to the "seasonal errors." The velocity of light was experimentally
+found, in 1862, by Fizeau and Foucault, each using an independent
+method. These methods have been developed, and new values found, by
+Cornu, Michaelson, Newcomb, and the present writer.
+
+Quite lately Halm, at the Cape of Good Hope, measured
+spectroscopically the velocity of the earth to and from a star by
+observations taken six months apart. Thence he obtained an accurate
+value of the sun's distance.[5]
+
+But the remarkably erratic minor planet, Eros, discovered by Witte in
+1898, approaches the earth within 15,000,000 miles at rare intervals,
+and, with the aid of photography, will certainly give us the best
+result. A large number of observatories combined to observe the
+opposition of 1900. Their results are not yet completely reduced, but
+the best value deduced so far for the parallax[6] is 8".807 +/-
+0".0028.[7]
+
+
+FOOTNOTES:
+
+[1] In 1480 Martin Behaim, of Nuremberg, produced his _astrolabe_ for
+measuring the latitude, by observation of the sun, at sea. It
+consisted of a graduated metal circle, suspended by a ring which was
+passed over the thumb, and hung vertically. A pointer was fixed to a
+pin at the centre. This arm, called the _alhidada_, worked round the
+graduated circle, and was pointed to the sun. The altitude of the sun
+was thus determined, and, by help of solar tables, the latitude could
+be found from observations made at apparent noon.
+
+[2] See illustration on p. 76.
+
+[3] See Dreyer's article on these instruments in _Copernicus_,
+Vol. I. They were stolen by the Germans after the relief of the
+Embassies, in 1900. The best description of these instruments is
+probably that contained in an interesting volume, which may be seen in
+the library of the R. A. S., entitled _Chinese Researches_, by
+Alexander Wyllie (Shanghai, 1897).
+
+[4] Sir George Airy was very jealous of this honourable title. He
+rightly held that there is only one Astronomer Royal at a time, as
+there is only one Mikado, one Dalai Lama. He said that His Majesty's
+Astronomer at the Cape of Good Hope, His Majesty's Astronomer for
+Scotland, and His Majesty's Astronomer for Ireland are not called
+Astronomers Royal.
+
+[5] _Annals of the Cape Observatory_, vol. x., part 3.
+
+[6] The parallax of the sun is the angle subtended by the earth's
+radius at the sun's distance.
+
+[7] A. R. Hinks, R.A.S.; _Monthly Notices_, June, 1909.
+
+
+
+11. HISTORY OF THE TELESCOPE
+
+
+Accounts of wonderful optical experiments by Roger Bacon (who died in
+1292), and in the sixteenth century by Digges, Baptista Porta, and
+Antonio de Dominis (Grant, _Hist. Ph. Ast_.), have led some to
+suppose that they invented the telescope. The writer considers that it
+is more likely that these notes refer to a kind of _camera
+obscura_, in which a lens throws an inverted image of a landscape
+on the wall.
+
+The first telescopes were made in Holland, the originator being either
+Henry Lipperhey,[1] Zacharias Jansen, or James Metius, and the date
+1608 or earlier.
+
+In 1609 Galileo, being in Venice, heard of the invention, went home
+and worked out the theory, and made a similar telescope. These
+telescopes were all made with a convex object-glass and a concave
+eye-lens, and this type is spoken of as the Galilean telescope. Its
+defects are that it has no real focus where cross-wires can be placed,
+and that the field of view is very small. Kepler suggested the convex
+eye-lens in 1611, and Scheiner claimed to have used one in 1617. But
+it was Huyghens who really introduced them. In the seventeenth century
+telescopes were made of great length, going up to 300 feet. Huyghens
+also invented the compound eye-piece that bears his name, made of two
+convex lenses to diminish spherical aberration.
+
+But the defects of colour remained, although their cause was unknown
+until Newton carried out his experiments on dispersion and the solar
+spectrum. To overcome the spherical aberration James Gregory,[2] of
+Aberdeen and Edinburgh, in 1663, in his _Optica Promota_,
+proposed a reflecting speculum of parabolic form. But it was Newton,
+about 1666, who first made a reflecting telescope; and he did it with
+the object of avoiding colour dispersion.
+
+Some time elapsed before reflectors were much used. Pound and Bradley
+used one presented to the Royal Society by Hadley in 1723. Hawksbee,
+Bradley, and Molyneaux made some. But James Short, of Edinburgh, made
+many excellent Gregorian reflectors from 1732 till his death in 1768.
+
+Newton's trouble with refractors, chromatic aberration, remained
+insurmountable until John Dollond (born 1706, died 1761), after many
+experiments, found out how to make an achromatic lens out of two
+lenses--one of crown glass, the other of flint glass--to destroy the
+colour, in a way originally suggested by Euler. He soon acquired a
+great reputation for his telescopes of moderate size; but there was a
+difficulty in making flint-glass lenses of large size. The first
+actual inventor and constructor of an achromatic telescope was Chester
+Moor Hall, who was not in trade, and did not patent it. Towards the
+close of the eighteenth century a Swiss named Guinand at last
+succeeded in producing larger flint-glass discs free from
+striae. Frauenhofer, of Munich, took him up in 1805, and soon
+produced, among others, Struve's Dorpat refractor of 9.9 inches
+diameter and 13.5 feet focal length, and another, of 12 inches
+diameter and 18 feet focal length, for Lamont, of Munich.
+
+In the nineteenth century gigantic _reflectors_ have been
+made. Lassel's 2-foot reflector, made by himself, did much good work,
+and discovered four new satellites. But Lord Rosse's 6-foot
+reflector, 54 feet focal length, constructed in 1845, is still the
+largest ever made. The imperfections of our atmosphere are against
+the use of such large apertures, unless it be on high mountains.
+During the last half century excellent specula have been made of
+silvered glass, and Dr. Common's 5-foot speculum (removed, since his
+death, to Harvard) has done excellent work. Then there are the 5-foot
+Yerkes reflector at Chicago, and the 4-foot by Grubb at Melbourne.
+
+Passing now from these large reflectors to refractors, further
+improvements have been made in the manufacture of glass by Chance, of
+Birmingham, Feil and Mantois, of Paris, and Schott, of Jena; while
+specialists in grinding lenses, like Alvan Clark, of the U.S.A., and
+others, have produced many large refractors.
+
+Cooke, of York, made an object-glass, 25-inch diameter, for Newall, of
+Gateshead, which has done splendid work at Cambridge. We have the
+Washington 26-inch by Clark, the Vienna 27-inch by Grubb, the Nice
+29-1/2-inch by Gautier, the Pulkowa 30-inch by Clark. Then there was
+the sensation of Clark's 36-inch for the Lick Observatory in
+California, and finally his _tour de force_, the Yerkes 40-inch
+refractor, for Chicago.
+
+At Greenwich there is the 28-inch photographic refractor, and the
+Thompson equatoreal by Grubb, carrying both the 26-inch photographic
+refractor and the 30-inch reflector. At the Cape of Good Hope we find
+Mr. Frank McClean's 24-inch refractor, with an object-glass prism for
+spectroscopic work.
+
+It would be out of place to describe here the practical adjuncts of a
+modern equatoreal--the adjustments for pointing it, the clock for
+driving it, the position-micrometer and various eye-pieces, the
+photographic and spectroscopic attachments, the revolving domes,
+observing seats, and rising floors and different forms of mounting,
+the siderostats and coelostats, and other convenient adjuncts, besides
+the registering chronograph and numerous facilities for aiding
+observation. On each of these a chapter might be written; but the
+most important part of the whole outfit is the man behind the
+telescope, and it is with him that a history is more especially
+concerned.
+
+
+SPECTROSCOPE.
+
+Since the invention of the telescope no discovery has given so great
+an impetus to astronomical physics as the spectroscope; and in giving
+us information about the systems of stars and their proper motions it
+rivals the telescope.
+
+Frauenhofer, at the beginning of the nineteenth century, while
+applying Dollond's discovery to make large achromatic telescopes,
+studied the dispersion of light by a prism. Admitting the light of the
+sun through a narrow slit in a window-shutter, an inverted image of
+the slit can be thrown, by a lens of suitable focal length, on the
+wall opposite. If a wedge or prism of glass be interposed, the image
+is deflected to one side; but, as Newton had shown, the images formed
+by the different colours of which white light is composed are
+deflected to different extents--the violet most, the red least. The
+number of colours forming images is so numerous as to form a
+continuous spectrum on the wall with all the colours--red, orange,
+yellow, green, blue, indigo, and violet. But Frauenhofer found with a
+narrow slit, well focussed by the lens, that some colours were missing
+in the white light of the sun, and these were shown by dark lines
+across the spectrum. These are the Frauenhofer lines, some of which
+he named by the letters of the alphabet. The D line is a very marked
+one in the yellow. These dark lines in the solar spectrum had already
+been observed by Wollaston. [3]
+
+On examining artificial lights it was found that incandescent solids
+and liquids (including the carbon glowing in a white gas flame) give
+continuous spectra; gases, except under enormous pressure, give bright
+lines. If sodium or common salt be thrown on the colourless flame of a
+spirit lamp, it gives it a yellow colour, and its spectrum is a bright
+yellow line agreeing in position with line D of the solar spectrum.
+
+In 1832 Sir David Brewster found some of the solar black lines
+increased in strength towards sunset, and attributed them to
+absorption in the earth's atmosphere. He suggested that the others
+were due to absorption in the sun's atmosphere. Thereupon Professor
+J. D. Forbes pointed out that during a nearly total eclipse the lines
+ought to be strengthened in the same way; as that part of the sun's
+light, coming from its edge, passes through a great distance in the
+sun's atmosphere. He tried this with the annular eclipse of 1836,
+with a negative result which has never been accounted for, and which
+seemed to condemn Brewster's view.
+
+In 1859 Kirchoff, on repeating Frauenhofer's experiment, found that,
+if a spirit lamp with salt in the flame were placed in the path of the
+light, the black D line is intensified. He also found that, if he used
+a limelight instead of the sunlight and passed it through the flame
+with salt, the spectrum showed the D line black; or the vapour of
+sodium absorbs the same light that it radiates. This proved to him the
+existence of sodium in the sun's atmosphere.[4] Iron, calcium, and
+other elements were soon detected in the same way.
+
+Extensive laboratory researches (still incomplete) have been carried
+out to catalogue (according to their wave-length on the undulatory
+theory of light) all the lines of each chemical element, under all
+conditions of temperature and pressure. At the same time, all the
+lines have been catalogued in the light of the sun and the brighter of
+the stars.
+
+Another method of obtaining spectra had long been known, by
+transmission through, or reflection from, a grating of equidistant
+lines ruled upon glass or metal. H. A. Rowland developed the art of
+constructing these gratings, which requires great technical skill, and
+for this astronomers owe him a debt of gratitude.
+
+In 1842 Doppler[5] proved that the colour of a luminous body, like the
+pitch or note of a sounding body, must be changed by velocity of
+approach or recession. Everyone has noticed on a railway that, on
+meeting a locomotive whistling, the note is lowered after the engine
+has passed. The pitch of a sound or the colour of a light depends on
+the number of waves striking the ear or eye in a second. This number
+is increased by approach and lowered by recession.
+
+Thus, by comparing the spectrum of a star alongside a spectrum of
+hydrogen, we may see all the lines, and be sure that there is hydrogen
+in the star; yet the lines in the star-spectrum may be all slightly
+displaced to one side of the lines of the comparison spectrum. If
+towards the violet end, it means mutual approach of the star and
+earth; if to the red end, it means recession. The displacement of
+lines does not tell us whether the motion is in the star, the earth,
+or both. The displacement of the lines being measured, we can
+calculate the rate of approach or recession in miles per second.
+
+In 1868 Huggins[6] succeeded in thus measuring the velocities of stars
+in the direction of the line of sight.
+
+In 1873 Vogel[7] compared the spectra of the sun's East (approaching)
+limb and West (receding) limb, and the displacement of lines endorsed
+the theory. This last observation was suggested by Zollner.
+
+
+FOOTNOTES:
+
+[1] In the _Encyclopaedia Britannica_, article "Telescope," and in
+Grant's _Physical Astronomy_, good reasons are given for awarding the
+honour to Lipperhey.
+
+[2] Will the indulgent reader excuse an anecdote which may encourage
+some workers who may have found their mathematics defective through
+want of use? James Gregory's nephew David had a heap of MS. notes by
+Newton. These descended to a Miss Gregory, of Edinburgh, who handed
+them to the present writer, when an undergraduate at Cambridge, to
+examine. After perusal, he lent them to his kindest of friends,
+J. C. Adams (the discoverer of Neptune), for his opinion. Adams's
+final verdict was: "I fear they are of no value. It is pretty evident
+that, when he wrote these notes, _Newton's mathematics were a little
+rusty_."
+
+[3] _R. S. Phil. Trans_.
+
+[4] The experiment had been made before by one who did not understand
+its meaning;. But Sir George G. Stokes had already given verbally the
+true explanation of Frauenhofer lines.
+
+[5] _Abh. d. Kon. Bohm. d. Wiss_., Bd. ii., 1841-42, p. 467. See
+also Fizeau in the _Ann. de Chem. et de Phys_., 1870, p. 211.
+
+[6] _R. S. Phil. Trans_., 1868.
+
+[7] _Ast. Nach_., No. 1, 864.
+
+
+
+
+BOOK IV. THE PHYSICAL PERIOD
+
+
+We have seen how the theory of the solar system was slowly developed
+by the constant efforts of the human mind to find out what are the
+rules of cause and effect by which our conception of the present
+universe and its development seems to be bound. In the primitive ages
+a mere record of events in the heavens and on the earth gave the only
+hope of detecting those uniform sequences from which to derive rules
+or laws of cause and effect upon which to rely. Then came the
+geometrical age, in which rules were sought by which to predict the
+movements of heavenly bodies. Later, when the relation of the sun to
+the courses of the planets was established, the sun came to be looked
+upon as a cause; and finally, early in the seventeenth century, for
+the first time in history, it began to be recognised that the laws of
+dynamics, exactly as they had been established for our own terrestrial
+world, hold good, with the same rigid invariability, at least as far
+as the limits of the solar system.
+
+Throughout this evolution of thought and conjecture there were two
+types of astronomers--those who supplied the facts, and those who
+supplied the interpretation through the logic of mathematics. So
+Ptolemy was dependent upon Hipparchus, Kepler on Tycho Brahe, and
+Newton in much of his work upon Flamsteed.
+
+When Galileo directed his telescope to the heavens, when Secchi and
+Huggins studied the chemistry of the stars by means of the
+spectroscope, and when Warren De la Rue set up a photoheliograph at
+Kew, we see that a progress in the same direction as before, in the
+evolution of our conception of the universe, was being made. Without
+definite expression at any particular date, it came to be an accepted
+fact that not only do earthly dynamics apply to the heavenly bodies,
+but that the laws we find established here, in geology, in chemistry,
+and in the laws of heat, may be extended with confidence to the
+heavenly bodies. Hence arose the branch of astronomy called
+astronomical physics, a science which claims a large portion of the
+work of the telescope, spectroscope, and photography. In this new
+development it is more than ever essential to follow the dictum of
+Tycho Brahe--not to make theories until all the necessary facts are
+obtained. The great astronomers of to-day still hold to Sir Isaac
+Newton's declaration, "Hypotheses non fingo." Each one may have his
+suspicions of a theory to guide him in a course of observation, and
+may call it a working hypothesis. But the cautious astronomer does
+not proclaim these to the world; and the historian is certainly not
+justified in including in his record those vague speculations founded
+on incomplete data which may be demolished to-morrow, and which,
+however attractive they may be, often do more harm than good to the
+progress of true science. Meanwhile the accumulation of facts has
+been prodigious, and the revelations of the telescope and spectroscope
+entrancing.
+
+
+
+12. THE SUN.
+
+
+One of Galileo's most striking discoveries, when he pointed his
+telescope to the heavenly bodies, was that of the irregularly shaped
+spots on the sun, with the dark central _umbra_ and the less
+dark, but more extensive, _penumbra_ surrounding it, sometimes
+with several umbrae in one penumbra. He has left us many drawings of
+these spots, and he fixed their period of rotation as a lunar month.
+
+[Illustration: SOLAR SURFACE, As Photographed at the Royal
+Observatory, Greenwich, showing sun-spots with umbrae, penumbrae, and
+faculae.]
+
+It is not certain whether Galileo, Fabricius, or Schemer was the first
+to see the spots. They all did good work. The spots were found to be
+ever varying in size and shape. Sometimes, when a spot disappears at
+the western limb of the sun, it is never seen again. In other cases,
+after a fortnight, it reappears at the eastern limb. The faculae, or
+bright areas, which are seen all over the sun's surface, but specially
+in the neighbourhood of spots, and most distinctly near the sun's
+edge, were discovered by Galileo. A high telescopic power resolves
+their structure into an appearance like willow-leaves, or rice-grains,
+fairly uniform in size, and more marked than on other parts of the
+sun's surface.
+
+Speculations as to the cause of sun-spots have never ceased from
+Galileo's time to ours. He supposed them to be clouds. Scheiner[1]
+said they were the indications of tumultuous movements occasionally
+agitating the ocean of liquid fire of which he supposed the sun to be
+composed.
+
+A. Wilson, of Glasgow, in 1769,[2] noticed a movement of the umbra
+relative to the penumbra in the transit of the spot over the sun's
+surface; exactly as if the spot were a hollow, with a black base and
+grey shelving sides. This was generally accepted, but later
+investigations have contradicted its universality. Regarding the cause
+of these hollows, Wilson said:--
+
+  Whether their first production and subsequent numberless changes
+  depend upon the eructation of elastic vapours from below, or upon
+  eddies or whirlpools commencing at the surface, or upon the
+  dissolving of the luminous matter in the solar atmosphere, as clouds
+  are melted and again given out by our air; or, if the reader
+  pleases, upon the annihilation and reproduction of parts of this
+  resplendent covering, is left for theory to guess at.[3]
+
+Ever since that date theory has been guessing at it. The solar
+astronomer is still applying all the instruments of modern research to
+find out which of these suppositions, or what modification of any of
+them, is nearest the truth. The obstacle--one that is perhaps fatal to
+a real theory--lies in the impossibility of reproducing comparative
+experiments in our laboratories or in our atmosphere.
+
+Sir William Herschel propounded an explanation of Wilson's observation
+which received much notice, but which, out of respect for his memory,
+is not now described, as it violated the elementary laws of heat.
+
+Sir John Herschel noticed that the spots are mostly confined to two
+zones extending to about 35 degrees on each side of the equator, and that a
+zone of equatoreal calms is free from spots. But it was
+R. C. Carrington[4] who, by his continuous observations at Redhill, in
+Surrey, established the remarkable fact that, while the rotation
+period in the highest latitudes, 50 degrees, where spots are seen, is
+twenty-seven-and-a-half days, near the equator the period is only
+twenty-five days. His splendid volume of observations of the sun led
+to much new information about the average distribution of spots at
+different epochs.
+
+Schwabe, of Dessau, began in 1826 to study the solar surface, and,
+after many years of work, arrived at a law of frequency which has been
+more fruitful of results than any discovery in solar physics.[5] In
+1843 he announced a decennial period of maxima and minima of sun-spot
+displays. In 1851 it was generally accepted, and, although a period of
+eleven years has been found to be more exact, all later observations,
+besides the earlier ones which have been hunted up for the purpose, go
+to establish a true periodicity in the number of sun-spots. But quite
+lately Schuster[6] has given reasons for admitting a number of
+co-existent periods, of which the eleven-year period was predominant
+in the nineteenth century.
+
+In 1851 Lament, a Scotchman at Munich, found a decennial period in the
+daily range of magnetic declination. In 1852 Sir Edward Sabine
+announced a similar period in the number of "magnetic storms"
+affecting all of the three magnetic elements--declination, dip, and
+intensity. Australian and Canadian observations both showed the
+decennial period in all three elements. Wolf, of Zurich, and Gauthier,
+of Geneva, each independently arrived at the same conclusion.
+
+It took many years before this coincidence was accepted as certainly
+more than an accident by the old-fashioned astronomers, who want rigid
+proof for every new theory. But the last doubts have long vanished,
+and a connection has been further traced between violent outbursts of
+solar activity and simultaneous magnetic storms.
+
+The frequency of the Aurora Borealis was found by Wolf to follow the
+same period. In fact, it is closely allied in its cause to terrestrial
+magnetism. Wolf also collected old observations tracing the
+periodicity of sun-spots back to about 1700 A.D.
+
+Spoerer deduced a law of dependence of the average latitude of
+sun-spots on the phase of the sun-spot period.
+
+All modern total solar eclipse observations seem to show that the
+shape of the luminous corona surrounding the moon at the moment of
+totality has a special distinct character during the time of a
+sun-spot maximum, and another, totally different, during a sun-spot
+minimum.
+
+A suspicion is entertained that the total quantity of heat received by
+the earth from the sun is subject to the same period. This would have
+far-reaching effects on storms, harvests, vintages, floods, and
+droughts; but it is not safe to draw conclusions of this kind except
+from a very long period of observations.
+
+Solar photography has deprived astronomers of the type of Carrington
+of the delight in devoting a life's work to collecting data. It has
+now become part of the routine work of an observatory.
+
+In 1845 Foucault and Fizeau took a daguerreotype photograph of the
+sun. In 1850 Bond produced one of the moon of great beauty, Draper
+having made some attempts at an even earlier date. But astronomical
+photography really owes its beginning to De la Rue, who used the
+collodion process for the moon in 1853, and constructed the Kew
+photoheliograph in 1857, from which date these instruments have been
+multiplied, and have given us an accurate record of the sun's surface.
+Gelatine dry plates were first used by Huggins in 1876.
+
+It is noteworthy that from the outset De la Rue recognised the value
+of stereoscopic vision, which is now known to be of supreme
+accuracy. In 1853 he combined pairs of photographs of the moon in the
+same phase, but under different conditions regarding libration,
+showing the moon from slightly different points of view. These in the
+stereoscope exhibited all the relief resulting from binocular vision,
+and looked like a solid globe. In 1860 he used successive photographs
+of the total solar eclipse stereoscopically, to prove that the red
+prominences belong to the sun, and not to the moon. In 1861 he
+similarly combined two photographs of a sun-spot, the perspective
+effect showing the umbra like a floor at the bottom of a hollow
+penumbra; and in one case the faculae were discovered to be sailing
+over a spot apparently at some considerable height. These appearances
+may be partly due to a proper motion; but, so far as it went, this was
+a beautiful confirmation of Wilson's discovery. Hewlett, however, in
+1894, after thirty years of work, showed that the spots are not always
+depressions, being very subject to disturbance.
+
+The Kew photographs [7] contributed a vast amount of information about
+sun-spots, and they showed that the faculae generally follow the spots
+in their rotation round the sun.
+
+The constitution of the sun's photosphere, the layer which is the
+principal light-source on the sun, has always been a subject of great
+interest; and much was done by men with exceptionally keen eyesight,
+like Mr. Dawes. But it was a difficult subject, owing to the rapidity
+of the changes in appearance of the so-called rice-grains, about 1" in
+diameter. The rapid transformations and circulations of these
+rice-grains, if thoroughly studied, might lead to a much better
+knowledge of solar physics. This seemed almost hopeless, as it was
+found impossible to identify any "rice-grain" in the turmoil after a
+few minutes. But M. Hansky, of Pulkowa (whose recent death is
+deplored), introduced successfully a scheme of photography, which
+might almost be called a solar cinematograph. He took photographs of
+the sun at intervals of fifteen or thirty seconds, and then enlarged
+selected portions of these two hundred times, giving a picture
+corresponding to a solar disc of six metres diameter. In these
+enlarged pictures he was able to trace the movements, and changes of
+shape and brightness, of individual rice-grains. Some granules become
+larger or smaller. Some seem to rise out of a mist, as it were, and to
+become clearer. Others grow feebler. Some are split in two. Some are
+rotated through a right angle in a minute or less, although each of
+the grains may be the size of Great Britain. Generally they move
+together in groups of very various velocities, up to forty kilometres
+a second. These movements seem to have definite relation to any
+sun-spots in the neighbourhood. From the results already obtained it
+seems certain that, if this method of observation be continued, it
+cannot fail to supply facts of the greatest importance.
+
+It is quite impossible to do justice here to the work of all those who
+are engaged on astronomical physics. The utmost that can be attempted
+is to give a fair idea of the directions of human thought and
+endeavour. During the last half-century America has made splendid
+progress, and an entirely new process of studying the photosphere has
+been independently perfected by Professor Hale at Chicago, and
+Deslandres at Paris.[8] They have succeeded in photographing the sun's
+surface in monochromatic light, such as the light given off as one of
+the bright lines of hydrogen or of calcium, by means of the
+"Spectroheliograph." The spectroscope is placed with its slit in the
+focus of an equatoreal telescope, pointed to the sun, so that the
+circular image of the sun falls on the slit. At the other end of the
+spectroscope is the photographic plate. Just in front of this plate
+there is another slit parallel to the first, in the position where the
+image of the first slit formed by the K line of calcium falls. Thus is
+obtained a photograph of the section of the sun, made by the first
+slit, only in K light. As the image of the sun passes over the first
+slit the photographic plate is moved at the same rate and in the same
+direction behind the second slit; and as successive sections of the
+sun's image in the equatoreal enter the apparatus, so are these
+sections successively thrown in their proper place on the photographic
+plate, always in K light. By using a high dispersion the faculae which
+give off K light can be correctly photographed, not only at the sun's
+edge, but all over his surface. The actual mechanical method of
+carrying out the observation is not quite so simple as what is here
+described.
+
+By choosing another line of the spectrum instead of calcium K--for
+example, the hydrogen line H(3)--we obtain two photographs, one
+showing the appearance of the calcium floculi, and the other of the
+hydrogen floculi, on the same part of the solar surface; and nothing
+is more astonishing than to note the total want of resemblance in the
+forms shown on the two. This mode of research promises to afford many
+new and useful data.
+
+The spectroscope has revealed the fact that, broadly speaking, the sun
+is composed of the same materials as the earth. Angstrom was the first
+to map out all of the lines to be found in the solar spectrum. But
+Rowland, of Baltimore, after having perfected the art of making true
+gratings with equidistant lines ruled on metal for producing spectra,
+then proceeded to make a map of the solar spectrum on a large scale.
+
+In 1866 Lockyer[9] threw an image of the sun upon the slit of a
+spectroscope, and was thus enabled to compare the spectrum of a spot
+with that of the general solar surface. The observation proved the
+darkness of a spot to be caused by increased absorption of light, not
+only in the dark lines, which are widened, but over the entire
+spectrum. In 1883 Young resolved this continuous obscurity into an
+infinite number of fine lines, which have all been traced in a shadowy
+way on to the general solar surface. Lockyer also detected
+displacements of the spectrum lines in the spots, such as would be
+produced by a rapid motion in the line of sight. It has been found
+that both uprushes and downrushes occur, but there is no marked
+predominance of either in a sun-spot. The velocity of motion thus
+indicated in the line of sight sometimes appears to amount to 320
+miles a second. But it must be remembered that pressure of a gas has
+some effect in displacing the spectral lines. So we must go on,
+collecting data, until a time comes when the meaning of all the facts
+can be made clear.
+
+_Total Solar Eclipses_.--During total solar eclipses the time is so
+short, and the circumstances so impressive, that drawings of the
+appearance could not always be trusted. The red prominences of jagged
+form that are seen round the moon's edge, and the corona with its
+streamers radiating or interlacing, have much detail that can hardly
+be recorded in a sketch. By the aid of photography a number of records
+can be taken during the progress of totality. From a study of these
+the extent of the corona is demonstrated in one case to extend to at
+least six diameters of the moon, though the eye has traced it
+farther. This corona is still one of the wonders of astronomy, and
+leads to many questions. What is its consistency, if it extends many
+million miles from the sun's surface? How is it that it opposed no
+resistance to the motion of comets which have almost grazed the sun's
+surface? Is this the origin of the zodiacal light? The character of
+the corona in photographic records has been shown to depend upon the
+phase of the sun-spot period. During the sun-spot maximum the corona
+seems most developed over the spot-zones--i.e., neither at the
+equator nor the poles. The four great sheaves of light give it a
+square appearance, and are made up of rays or plumes, delicate like
+the petals of a flower. During a minimum the nebulous ring seems to
+be made of tufts of fine hairs with aigrettes or radiations from both
+poles, and streamers from the equator.
+
+[Illustration: SOLAR ECLIPSE, 1882. From drawing by W. H. Wesley,
+Secretary R.A.S.; showing the prominences, the corona, and an unknown
+comet.]
+
+
+On September 19th, 1868, eclipse spectroscopy began with the Indian
+eclipse, in which all observers found that the red prominences showed
+a bright line spectrum, indicating the presence of hydrogen and other
+gases. So bright was it that Jansen exclaimed: "_Je verrai ces
+lignes-la en dehors des eclipses_." And the next day he observed the
+lines at the edge of the uneclipsed sun. Huggins had suggested this
+observation in February, 1868, his idea being to use prisms of such
+great dispersive power that the continuous spectrum reflected by our
+atmosphere should be greatly weakened, while a bright line would
+suffer no diminution by the high dispersion. On October 20th
+Lockyer,[10] having news of the eclipse, but not of Jansen's
+observations the day after, was able to see these lines. This was a
+splendid performance, for it enabled the prominences to be observed,
+not only during eclipses, but every day. Moreover, the next year
+Huggins was able, by using a wide slit, to see the whole of a
+prominence and note its shape. Prominences are classified, according
+to their form, into "flame" and "cloud" prominences, the spectrum of
+the latter showing calcium, hydrogen, and helium; that of the former
+including a number of metals.
+
+The D line of sodium is a double line, and in the same eclipse (1868)
+an orange line was noticed which was afterwards found to lie close to
+the two components of the D line. It did not correspond with any known
+terrestrial element, and the unknown element was called "helium." It
+was not until 1895 that Sir William Ramsay found this element as a gas
+in the mineral cleavite.
+
+The spectrum of the corona is partly continuous, indicating light
+reflected from the sun's body. But it also shows a green line
+corresponding with no known terrestrial element, and the name
+"coronium" has been given to the substance causing it.
+
+A vast number of facts have been added to our knowledge about the sun
+by photography and the spectroscope. Speculations and hypotheses in
+plenty have been offered, but it may be long before we have a complete
+theory evolved to explain all the phenomena of the storm-swept
+metallic atmosphere of the sun.
+
+The proceedings of scientific societies teem with such facts and
+"working hypotheses," and the best of them have been collected by Miss
+Clerke in her _History of Astronomy during the Nineteenth Century_. As
+to established facts, we learn from the spectroscopic researches (1)
+that the continuous spectrum is derived from the _photosphere_ or
+solar gaseous material compressed almost to liquid consistency; (2)
+that the _reversing layer_ surrounds it and gives rise to black
+lines in the spectrum; that the _chromosphere_ surrounds this, is
+composed mainly of hydrogen, and is the cause of the red prominences
+in eclipses; and that the gaseous _corona_ surrounds all of
+these, and extends to vast distances outside the sun's visible
+surface.
+
+
+FOOTNOTES:
+
+[1] _Rosa Ursina_, by C. Scheiner, _fol_.; Bracciani, 1630.
+
+[2] _R. S. Phil. Trans_., 1774.
+
+[3] _Ibid_, 1783.
+
+[4] _Observations on the Spots on the Sun, etc.,_ 4 degrees; London and
+Edinburgh, 1863.
+
+[5] _Periodicitat der Sonnenflecken. Astron. Nach. XXI._, 1844,
+P. 234.
+
+[6] _R.S. Phil. Trans._ (ser. A), 1906, p. 69-100.
+
+[7] "Researches on Solar Physics," by De la Rue, Stewart and Loewy;
+_R. S. Phil. Trans_., 1869, 1870.
+
+[8] "The Sun as Photographed on the K line"; _Knowledge_, London,
+1903, p. 229.
+
+[9] _R. S. Proc._, xv., 1867, p. 256.
+
+[10] _Acad. des Sc._, Paris; _C. R._, lxvii., 1868, p. 121.
+
+
+
+13. THE MOON AND PLANETS.
+
+
+_The Moon_.--Telescopic discoveries about the moon commence with
+Galileo's discovery that her surface has mountains and valleys, like
+the earth. He also found that, while she always turns the same face to
+us, there is periodically a slight twist to let us see a little round
+the eastern or western edge. This was called _libration_, and the
+explanation was clear when it was understood that in showing always
+the same face to us she makes one revolution a month on her axis
+_uniformly_, and that her revolution round the earth is not
+uniform.
+
+Galileo said that the mountains on the moon showed greater differences
+of level than those on the earth. Shroter supported this
+opinion. W. Herschel opposed it. But Beer and Madler measured the
+heights of lunar mountains by their shadows, and found four of them
+over 20,000 feet above the surrounding plains.
+
+Langrenus [1] was the first to do serious work on selenography, and
+named the lunar features after eminent men. Riccioli also made lunar
+charts. In 1692 Cassini made a chart of the full moon. Since then we
+have the charts of Schroter, Beer and Madler (1837), and of Schmidt,
+of Athens (1878); and, above all, the photographic atlas by Loewy and
+Puiseux.
+
+The details of the moon's surface require for their discussion a whole
+book, like that of Neison or the one by Nasmyth and Carpenter. Here a
+few words must suffice. Mountain ranges like our Andes or Himalayas
+are rare. Instead of that, we see an immense number of circular
+cavities, with rugged edges and flat interior, often with a cone in
+the centre, reminding one of instantaneous photographs of the splash
+of a drop of water falling into a pool. Many of these are fifty or
+sixty miles across, some more. They are generally spoken of as
+resembling craters of volcanoes, active or extinct, on the earth. But
+some of those who have most fully studied the shapes of craters deny
+altogether their resemblance to the circular objects on the moon.
+These so-called craters, in many parts, are seen to be closely
+grouped, especially in the snow-white parts of the moon. But there are
+great smooth dark spaces, like the clear black ice on a pond, more
+free from craters, to which the equally inappropriate name of seas has
+been given. The most conspicuous crater, _Tycho_, is near the south
+pole. At full moon there are seen to radiate from Tycho numerous
+streaks of light, or "rays," cutting through all the mountain
+formations, and extending over fully half the lunar disc, like the
+star-shaped cracks made on a sheet of ice by a blow. Similar cracks
+radiate from other large craters. It must be mentioned that these
+white rays are well seen only in full light of the sun at full moon,
+just as the white snow in the crevasses of a glacier is seen bright
+from a distance only when the sun is high, and disappears at
+sunset. Then there are deep, narrow, crooked "rills" which may have
+been water-courses; also "clefts" about half a mile wide, and often
+hundreds of miles long, like deep cracks in the surface going straight
+through mountain and valley.
+
+The moon shares with the sun the advantage of being a good subject for
+photography, though the planets are not. This is owing to her larger
+apparent size, and the abundance of illumination. The consequence is
+that the finest details of the moon, as seen in the largest telescope
+in the world, may be reproduced at a cost within the reach of all.
+
+No certain changes have ever been observed; but several suspicions
+have been expressed, especially as to the small crater _Linne_, in the
+_Mare Serenitatis_. It is now generally agreed that no certainty can
+be expected from drawings, and that for real evidence we must await
+the verdict of photography.
+
+No trace of water or of an atmosphere has been found on the moon. It
+is possible that the temperature is too low. In any case, no
+displacement of a star by atmospheric refraction at occultation has
+been surely recorded. The moon seems to be dead.
+
+The distance of the moon from the earth is just now the subject of
+re-measurement. The base line is from Greenwich to Cape of Good Hope,
+and the new feature introduced is the selection of a definite point on
+a crater (Mosting A), instead of the moon's edge, as the point whose
+distance is to be measured.
+
+_The Inferior Planets_.--When the telescope was invented, the phases
+of Venus attracted much attention; but the brightness of this planet,
+and her proximity to the sun, as with Mercury also, seemed to be a bar
+to the discovery of markings by which the axis and period of rotation
+could be fixed. Cassini gave the rotation as twenty-three hours, by
+observing a bright spot on her surface. Shroter made it 23h. 21m. 19s.
+This value was supported by others. In 1890 Schiaparelli[2] announced
+that Venus rotates, like our moon, once in one of her revolutions, and
+always directs the same face to the sun. This property has also been
+ascribed to Mercury; but in neither case has the evidence been
+generally accepted. Twenty-four hours is probably about the period of
+rotation for each of these planets.
+
+Several observers have claimed to have seen a planet within the orbit
+of Mercury, either in transit over the sun's surface or during an
+eclipse. It has even been named _Vulcan_. These announcements would
+have received little attention but for the fact that the motion of
+Mercury has irregularities which have not been accounted for by known
+planets; and Le Verrier[3] has stated that an intra-Mercurial planet
+or ring of asteroids would account for the unexplained part of the
+motion of the line of apses of Mercury's orbit amounting to 38" per
+century.
+
+_Mars_.--The first study of the appearance of Mars by Miraldi led him
+to believe that there were changes proceeding in the two white caps
+which are seen at the planet's poles. W. Herschel attributed these
+caps to ice and snow, and the dates of his observations indicated a
+melting of these ice-caps in the Martian summer.
+
+Schroter attributed the other markings on Mars to drifting clouds. But
+Beer and Madler, in 1830-39, identified the same dark spots as being
+always in the same place, though sometimes blurred by mist in the
+local winter. A spot sketched by Huyghens in 1672, one frequently seen
+by W. Herschel in 1783, another by Arago in 1813, and nearly all the
+markings recorded by Beer and Madler in 1830, were seen and drawn by
+F. Kaiser in Leyden during seventeen nights of the opposition of 1862
+(_Ast. Nacht._, No. 1,468), whence he deduced the period of rotation
+to be 24h. 37m. 22s.,62--or one-tenth of a second less than the period
+deduced by R. A. Proctor from a drawing by Hooke in 1666.
+
+It must be noted that, if the periods of rotation both of Mercury and
+Venus be about twenty-four hours, as seems probable, all the four
+planets nearest to the sun rotate in the same period, while the great
+planets rotate in about ten hours (Uranus and Neptune being still
+indeterminate).
+
+The general surface of Mars is a deep yellow; but there are dark grey
+or greenish patches. Sir John Herschel was the first to attribute the
+ruddy colour of Mars to its soil rather than to its atmosphere.
+
+The observations of that keen-sighted observer Dawes led to the first
+good map of Mars, in 1869. In the 1877 opposition Schiaparelli revived
+interest in the planet by the discovery of canals, uniformly about
+sixty miles wide, running generally on great circles, some of them
+being three or four thousand miles long. During the opposition of
+1881-2 the same observer re-observed the canals, and in twenty of them
+he found the canals duplicated,[4] the second canal being always 200
+to 400 miles distant from its fellow.
+
+The existence of these canals has been doubted. Mr. Lowell has now
+devoted years to the subject, has drawn them over and over again, and
+has photographed them; and accepts the explanation that they are
+artificial, and that vegetation grows on their banks. Thus is revived
+the old controversy between Whewell and Brewster as to the
+habitability of the planets. The new arguments are not yet generally
+accepted. Lowell believes he has, with the spectroscope, proved the
+existence of water on Mars.
+
+One of the most unexpected and interesting of all telescopic
+discoveries took place in the opposition of 1877, when Mars was
+unusually near to the earth. The Washington Observatory had acquired
+the fine 26-inch refractor, and Asaph Hall searched for satellites,
+concealing the planet's disc to avoid the glare. On August 11th he had
+a suspicion of a satellite. This was confirmed on the 16th, and on the
+following night a second one was added. They are exceedingly faint,
+and can be seen only by the most powerful telescopes, and only at the
+times of opposition. Their diameters are estimated at six or seven
+miles. It was soon found that the first, Deimos, completes its orbit
+in 30h. 18m. But the other, Phobos, at first was a puzzle, owing to
+its incredible velocity being unsuspected. Later it was found that the
+period of revolution was only 7h. 39m. 22s. Since the Martian day is
+twenty-four and a half hours, this leads to remarkable results.
+Obviously the easterly motion of the satellite overwhelms the diurnal
+rotation of the planet, and Phobos must appear to the inhabitants, if
+they exist, to rise in the west and set in the east, showing two or
+even three full moons in a day, so that, sufficiently well for the
+ordinary purposes of life, the hour of the day can be told by its
+phases.
+
+The discovery of these two satellites is, perhaps, the most
+interesting telescopic visual discovery made with the large telescopes
+of the last half century; photography having been the means of
+discovering all the other new satellites except Jupiter's fifth (in
+order of discovery).
+
+[Illustration: JUPITER. From a drawing by E. M. Antoniadi, showing
+transit of a satellite's shadow, the belts, and the "great red spot"
+(_Monthly Notices_, R. A. S., vol. lix., pl. x.).]
+
+_Jupiter._--Galileo's discovery of Jupiter's satellites was followed
+by the discovery of his belts. Zucchi and Torricelli seem to have seen
+them. Fontana, in 1633, reported three belts. In 1648 Grimaldi saw but
+two, and noticed that they lay parallel to the ecliptic. Dusky spots
+were also noticed as transient. Hooke[5] measured the motion of one in
+1664. In 1665 Cassini, with a fine telescope, 35-feet focal length,
+observed many spots moving from east to west, whence he concluded that
+Jupiter rotates on an axis like the earth. He watched an unusually
+permanent spot during twenty-nine rotations, and fixed the period at
+9h. 56m. Later he inferred that spots near the equator rotate quicker
+than those in higher latitudes (the same as Carrington found for the
+sun); and W. Herschel confirmed this in 1778-9.
+
+Jupiter's rapid rotation ought, according to Newton's theory, to be
+accompanied by a great flattening at the poles. Cassini had noted an
+oval form in 1691. This was confirmed by La Hire, Romer, and
+Picard. Pound measured the ellipticity = 1/(13.25).
+
+W. Herschel supposed the spots to be masses of cloud in the
+atmosphere--an opinion still accepted. Many of them were very
+permanent. Cassini's great spot vanished and reappeared nine times
+between 1665 and 1713. It was close to the northern margin of the
+southern belt. Herschel supposed the belts to be the body of the
+planet, and the lighter parts to be clouds confined to certain
+latitudes.
+
+In 1665 Cassini observed transits of the four satellites, and also saw
+their shadows on the planet, and worked out a lunar theory for
+Jupiter. Mathematical astronomers have taken great interest in the
+perturbations of the satellites, because their relative periods
+introduce peculiar effects. Airy, in his delightful book,
+_Gravitation_, has reduced these investigations to simple
+geometrical explanations.
+
+In 1707 and 1713 Miraldi noticed that the fourth satellite varies much
+in brightness. W. Herschel found this variation to depend upon its
+position in its orbit, and concluded that in the positions of
+feebleness it is always presenting to us a portion of its surface,
+which does not well reflect the sun's light; proving that it always
+turns the same face to Jupiter, as is the case with our moon. This
+fact had also been established for Saturn's fifth satellite, and may
+be true for all satellites.
+
+In 1826 Struve measured the diameters of the four satellites, and
+found them to be 2,429, 2,180, 3,561, and 3,046 miles.
+
+In modern times much interest has been taken in watching a rival to
+Cassini's famous spot. The "great red spot" was first observed by
+Niesten, Pritchett, and Tempel, in 1878, as a rosy cloud attached to a
+whitish zone beneath the dark southern equatorial band, shaped like
+the new war balloons, 30,000 miles long and 7,000 miles across. The
+next year it was brick-red. A white spot beside it completed a
+rotation in less time by 5-1/2 minutes than the red spot--a difference
+of 260 miles an hour. Thus they came together again every six weeks,
+but the motions did not continue uniform. The spot was feeble in
+1882-4, brightened in 1886, and, after many changes, is still visible.
+
+Galileo's great discovery of Jupiter's four moons was the last word in
+this connection until September 9th, 1892, when Barnard, using the
+36-inch refractor of the Lick Observatory, detected a tiny spot of
+light closely following the planet. This proved to be a new satellite
+(fifth), nearer to the planet than any other, and revolving round it
+in 11h. 57m. 23s. Between its rising and setting there must be an
+interval of 2-1/2 Jovian days, and two or three full moons. The sixth
+and seventh satellites were found by the examination of photographic
+plates at the Lick Observatory in 1905, since which time they have
+been continuously photographed, and their orbits traced, at Greenwich.
+On examining these plates in 1908 Mr. Melotte detected the eighth
+satellite, which seems to be revolving in a retrograde orbit three
+times as far from its planet as the next one (seventh), in these two
+points agreeing with the outermost of Saturn's satellites (Phoebe).
+
+_Saturn._--This planet, with its marvellous ring, was perhaps the most
+wonderful object of those first examined by Galileo's telescope. He
+was followed by Dominique Cassini, who detected bands like Jupiter's
+belts. Herschel established the rotation of the planet in 1775-94.
+From observations during one hundred rotations he found the period to
+be 10h. 16m. 0s., 44. Herschel also measured the ratio of the polar to
+the equatoreal diameter as 10:11.
+
+The ring was a complete puzzle to Galileo, most of all when the planet
+reached a position where the plane of the ring was in line with the
+earth, and the ring disappeared (December 4th, 1612). It was not until
+1656 that Huyghens, in his small pamphlet _De Saturni Luna Observatio
+Nova_, was able to suggest in a cypher the ring form; and in 1659, in
+his Systema Saturnium, he gave his reasons and translated the cypher:
+"The planet is surrounded by a slender flat ring, everywhere distinct
+from its surface, and inclined to the ecliptic." This theory explained
+all the phases of the ring which had puzzled others. This ring was
+then, and has remained ever since, a unique structure. We in this age
+have got accustomed to it. But Huyghens's discovery was received with
+amazement.
+
+In 1675 Cassini found the ring to be double, the concentric rings
+being separated by a black band--a fact which was placed beyond
+dispute by Herschel, who also found that the thickness of the ring
+subtends an angle less than 0".3. Shroter estimated its thickness at
+500 miles.
+
+Many speculations have been advanced to explain the origin and
+constitution of the ring. De Sejour said [6] that it was thrown off
+from Saturn's equator as a liquid ring, and afterwards solidified. He
+noticed that the outside would have a greater velocity, and be less
+attracted to the planet, than the inner parts, and that equilibrium
+would be impossible; so he supposed it to have solidified into a
+number of concentric rings, the exterior ones having the least
+velocity.
+
+Clerk Maxwell, in the Adams prize essay, gave a physico-mathematical
+demonstration that the rings must be composed of meteoritic matter
+like gravel. Even so, there must be collisions absorbing the energy of
+rotation, and tending to make the rings eventually fall into the
+planet. The slower motion of the external parts has been proved by the
+spectroscope in Keeler's hands, 1895.
+
+Saturn has perhaps received more than its share of attention owing to
+these rings. This led to other discoveries. Huyghens in 1655, and
+J. D. Cassini in 1671, discovered the sixth and eighth satellites
+(Titan and Japetus). Cassini lost his satellite, and in searching for
+it found Rhea (the fifth) in 1672, besides his old friend, whom he
+lost again. He added the third and fourth in 1684 (Tethys and
+Dione). The first and second (Mimas and Encelades) were added by
+Herschel in 1789, and the seventh (Hyperion) simultaneously by Lassel
+and Bond in 1848. The ninth (Phoebe) was found on photographs, by
+Pickering in 1898, with retrograde motion; and he has lately added a
+tenth.
+
+The occasional disappearance of Cassini's Japetus was found on
+investigation to be due to the same causes as that of Jupiter's fourth
+satellite, and proves that it always turns the same face to the
+planet.
+
+_Uranus and Neptune_.--The splendid discoveries of Uranus and two
+satellites by Sir William Herschel in 1787, and of Neptune by Adams
+and Le Verrier in 1846, have been already described. Lassel added two
+more satellites to Uranus in 1851, and found Neptune's satellite in
+1846. All of the satellites of Uranus have retrograde motion, and
+their orbits are inclined about 80 degrees to the ecliptic.
+
+The spectroscope has shown the existence of an absorbing atmosphere on
+Jupiter and Saturn, and there are suspicions that they partake
+something of the character of the sun, and emit some light besides
+reflecting solar light. On both planets some absorption lines seem to
+agree with the aqueous vapour lines of our own atmosphere; while one,
+which is a strong band in the red common to both planets, seems to
+agree with a line in the spectrum of some reddish stars.
+
+Uranus and Neptune are difficult to observe spectroscopically, but
+appear to have peculiar spectra agreeing together. Sometimes Uranus
+shows Frauenhofer lines, indicating reflected solar light. But
+generally these are not seen, and six broad bands of absorption
+appear. One is the F. of hydrogen; another is the red-star line of
+Jupiter and Saturn. Neptune is a very difficult object for the
+spectroscope.
+
+Quite lately [7] P. Lowell has announced that V. M. Slipher, at
+Flagstaff Observatory, succeeded in 1907 in rendering some plates
+sensitive far into the red. A reproduction is given of photographed
+spectra of the four outermost planets, showing (1) a great number of
+new lines and bands; (2) intensification of hydrogen F. and C. lines;
+(3) a steady increase of effects (1) and (2) as we pass from Jupiter
+and Saturn to Uranus, and a still greater increase in Neptune.
+
+_Asteroids_.--The discovery of these new planets has been
+described. At the beginning of the last century it was an immense
+triumph to catch a new one. Since photography was called into the
+service by Wolf, they have been caught every year in shoals. It is
+like the difference between sea fishing with the line and using a
+steam trawler. In the 1908 almanacs nearly seven hundred asteroids are
+included. The computation of their perturbations and ephemerides by
+Euler's and Lagrange's method of variable elements became so laborious
+that Encke devised a special process for these, which can be applied
+to many other disturbed orbits. [8]
+
+When a photograph is taken of a region of the heavens including an
+asteroid, the stars are photographed as points because the telescope
+is made to follow their motion; but the asteroids, by their proper
+motion, appear as short lines.
+
+The discovery of Eros and the photographic attack upon its path have
+been described in their relation to finding the sun's distance.
+
+A group of four asteroids has lately been found, with a mean distance
+and period equal to that of Jupiter. To three of these masculine names
+have been given--Hector, Patroclus, Achilles; the other has not yet
+been named.
+
+
+FOOTNOTES:
+
+[1] Langrenus (van Langren), F. Selenographia sive lumina austriae
+philippica; Bruxelles, 1645.
+
+[2] _Astr. Nach._, 2,944.
+
+[3] _Acad. des Sc._, Paris; _C.R._, lxxxiii., 1876.
+
+[4] _Mem. Spettr. Ital._, xi., p. 28.
+
+[5] _R. S. Phil. Trans_., No. 1.
+
+[6] Grant's _Hist. Ph. Ast_., p. 267.
+
+[7] _Nature_, November 12th, 1908.
+
+[8] _Ast. Nach_., Nos. 791, 792, 814, translated by G. B. Airy.
+_Naut. Alm_., Appendix, 1856.
+
+
+
+14. COMETS AND METEORS.
+
+
+Ever since Halley discovered that the comet of 1682 was a member of
+the solar system, these wonderful objects have had a new interest for
+astronomers; and a comparison of orbits has often identified the
+return of a comet, and led to the detection of an elliptic orbit where
+the difference from a parabola was imperceptible in the small portion
+of the orbit visible to us. A remarkable case in point was the comet
+of 1556, of whose identity with the comet of 1264 there could be
+little doubt. Hind wanted to compute the orbit more exactly than
+Halley had done. He knew that observations had been made, but they
+were lost. Having expressed his desire for a search, all the
+observations of Fabricius and of Heller, and also a map of the comet's
+path among the stars, were eventually unearthed in the most unlikely
+manner, after being lost nearly three hundred years. Hind and others
+were certain that this comet would return between 1844 and 1848, but
+it never appeared.
+
+When the spectroscope was first applied to finding the composition of
+the heavenly bodies, there was a great desire to find out what comets
+are made of. The first opportunity came in 1864, when Donati observed
+the spectrum of a comet, and saw three bright bands, thus proving that
+it was a gas and at least partly self-luminous. In 1868 Huggins
+compared the spectrum of Winnecke's comet with that of a Geissler tube
+containing olefiant gas, and found exact agreement. Nearly all comets
+have shown the same spectrum.[1] A very few comets have given bright
+band spectra differing from the normal type. Also a certain kind of
+continuous spectrum, as well as reflected solar light showing
+Frauenhofer lines, have been seen.
+
+[Illustration: COPY OF THE DRAWING MADE BY PAUL FABRICIUS. To define
+the path of comet 1556. After being lost for 300 years, this drawing
+was recovered by the prolonged efforts of Mr. Hind and Professor
+Littrow in 1856.]
+
+When Wells's comet, in 1882, approached very close indeed to the sun,
+the spectrum changed to a mono-chromatic yellow colour, due to sodium.
+
+For a full account of the wonders of the cometary world the reader is
+referred to books on descriptive astronomy, or to monographs on
+comets.[2] Nor can the very uncertain speculations about the structure
+of comets' tails be given here. A new explanation has been proposed
+almost every time that a great discovery has been made in the theory
+of light, heat, chemistry, or electricity.
+
+Halley's comet remained the only one of which a prediction of the
+return had been confirmed, until the orbit of the small, ill-defined
+comet found by Pons in 1819 was computed by Encke, and found to have a
+period of 3 1/3 years. It was predicted to return in 1822, and was
+recognised by him as identical with many previous comets. This comet,
+called after Encke, has showed in each of its returns an inexplicable
+reduction of mean distance, which led to the assertion of a resisting
+medium in space until a better explanation could be found.[3]
+
+Since that date fourteen comets have been found with elliptic orbits,
+whose aphelion distances are all about the same as Jupiter's mean
+distance; and six have an aphelion distance about ten per cent,
+greater than Neptune's mean distance. Other comets are similarly
+associated with the planets Saturn and Uranus.
+
+The physical transformations of comets are among the most wonderful of
+unexplained phenomena in the heavens. But, for physical astronomers,
+the greatest interest attaches to the reduction of radius vector of
+Encke's comet, the splitting of Biela's comet into two comets in 1846,
+and the somewhat similar behaviour of other comets. It must be noted,
+however, that comets have a sensible size, that all their parts cannot
+travel in exactly the same orbit under the sun's gravitation, and that
+their mass is not sufficient to retain the parts together very
+forcibly; also that the inevitable collision of particles, or else
+fluid friction, is absorbing energy, and so reducing the comet's
+velocity.
+
+In 1770 Lexell discovered a comet which, as was afterwards proved by
+investigations of Lexell, Burchardt, and Laplace, had in 1767 been
+deflected by Jupiter out of an orbit in which it was invisible from
+the earth into an orbit with a period of 5-1/2 years, enabling it to be
+seen. In 1779 it again approached Jupiter closer than some of his
+satellites, and was sent off in another orbit, never to be again
+recognised.
+
+But our interest in cometary orbits has been added to by the discovery
+that, owing to the causes just cited, a comet, if it does not separate
+into discrete parts like Biela's, must in time have its parts spread
+out so as to cover a sensible part of the orbit, and that, when the
+earth passes through such part of a comet's orbit, a meteor shower is
+the result.
+
+A magnificent meteor shower was seen in America on November 12th-13th,
+1833, when the paths of the meteors all seemed to radiate from a point
+in the constellation Leo. A similar display had been witnessed in
+Mexico by Humboldt and Bonpland on November 12th, 1799. H. A. Newton
+traced such records back to October 13th, A.D. 902. The orbital motion
+of a cloud or stream of small particles was indicated. The period
+favoured by H. A. Newton was 354-1/2 days; another suggestion was 375-1/2
+days, and another 33-1/4 years. He noticed that the advance of the date
+of the shower between 902 and 1833, at the rate of one day in seventy
+years, meant a progression of the node of the orbit. Adams undertook
+to calculate what the amount would be on all the five suppositions
+that had been made about the period. After a laborious work, he found
+that none gave one day in seventy years except the 33-1/4-year period,
+which did so exactly. H. A. Newton predicted a return of the shower on
+the night of November 13th-14th, 1866. He is now dead; but many of us
+are alive to recall the wonder and enthusiasm with which we saw this
+prediction being fulfilled by the grandest display of meteors ever
+seen by anyone now alive.
+
+The _progression_ of the nodes proved the path of the meteor
+stream to be retrograde. The _radiant_ had almost the exact
+longitude of the point towards which the earth was moving. This proved
+that the meteor cluster was at perihelion. The period being known, the
+eccentricity of the orbit was obtainable, also the orbital velocity of
+the meteors in perihelion; and, by comparing this with the earth's
+velocity, the latitude of the radiant enabled the inclination to be
+determined, while the longitude of the earth that night was the
+longitude of the node. In such a way Schiaparelli was able to find
+first the elements of the orbit of the August meteor shower
+(Perseids), and to show its identity with the orbit of Tuttle's comet
+1862.iii. Then, in January 1867, Le Verrier gave the elements of the
+November meteor shower (Leonids); and Peters, of Altona, identified
+these with Oppolzer's elements for Tempel's comet 1866--Schiaparelli
+having independently attained both of these results. Subsequently
+Weiss, of Vienna, identified the meteor shower of April 20th (Lyrids)
+with comet 1861. Finally, that indefatigable worker on meteors,
+A. S. Herschel, added to the number, and in 1878 gave a list of
+seventy-six coincidences between cometary and meteoric orbits.
+
+Cometary astronomy is now largely indebted to photography, not merely
+for accurate delineations of shape, but actually for the discovery of
+most of them. The art has also been applied to the observation of
+comets at distances from their perihelia so great as to prevent their
+visual observation. Thus has Wolf, of Heidelburg, found upon old
+plates the position of comet 1905.v., as a star of the 15.5 magnitude,
+783 days before the date of its discovery. From the point of view of
+the importance of finding out the divergence of a cometary orbit from
+a parabola, its period, and its aphelion distance, this increase of
+range attains the very highest value.
+
+The present Astronomer Royal, appreciating this possibility, has been
+searching by photography for Halley's comet since November, 1907,
+although its perihelion passage will not take place until April, 1910.
+
+
+FOOTNOTES:
+
+[1] In 1874, when the writer was crossing the Pacific Ocean in
+H.M.S. "Scout," Coggia's comet unexpectedly appeared, and (while
+Colonel Tupman got its positions with the sextant) he tried to use the
+prism out of a portable direct-vision spectroscope, without success
+until it was put in front of the object-glass of a binocular, when, to
+his great joy, the three band images were clearly seen.
+
+[2] Such as _The World of Comets_, by A. Guillemin; _History of
+Comets_, by G. R. Hind, London, 1859; _Theatrum Cometicum_, by S. de
+Lubienietz, 1667; _Cometographie_, by Pingre, Paris, 1783; _Donati's
+Comet_, by Bond.
+
+[3] The investigations by Von Asten (of St. Petersburg) seem to
+support, and later ones, especially those by Backlund (also of
+St. Petersburg), seem to discredit, the idea of a resisting medium.
+
+
+
+15. THE FIXED STARS AND NEBULAE.
+
+
+Passing now from our solar system, which appears to be subject to the
+action of the same forces as those we experience on our globe, there
+remains an innumerable host of fixed stars, nebulas, and nebulous
+clusters of stars. To these the attention of astronomers has been more
+earnestly directed since telescopes have been so much enlarged.
+Photography also has enabled a vast amount of work to be covered in a
+comparatively short period, and the spectroscope has given them the
+means, not only of studying the chemistry of the heavens, but also of
+detecting any motion in the line of sight from less than a mile a
+second and upwards in any star, however distant, provided it be bright
+enough.
+
+[Illustration: SIR WILLIAM HERSCHEL, F.R.S.--1738-1822. Painted by
+Lemuel F. Abbott; National Portrait Gallery, Room XX.]
+
+In the field of telescopic discovery beyond our solar system there is
+no one who has enlarged our knowledge so much as Sir William Herschel,
+to whom we owe the greatest discovery in dynamical astronomy among the
+stars--viz., that the law of gravitation extends to the most distant
+stars, and that many of them describe elliptic orbits about each
+other. W. Herschel was born at Hanover in 1738, came to England in
+1758 as a trained musician, and died in 1822. He studied science when
+he could, and hired a telescope, until he learnt to make his own
+specula and telescopes. He made 430 parabolic specula in twenty-one
+years. He discovered 2,500 nebulae and 806 double stars, counted the
+stars in 3,400 guage-fields, and compared the principal stars
+photometrically.
+
+Some of the things for which he is best known were results of those
+accidents that happen only to the indefatigable enthusiast. Such was
+the discovery of Uranus, which led to funds being provided for
+constructing his 40-feet telescope, after which, in 1786, he settled
+at Slough. In the same way, while trying to detect the annual parallax
+of the stars, he failed in that quest, but discovered binary systems
+of stars revolving in ellipses round each other; just as Bradley's
+attack on stellar parallax failed, but led to the discovery of
+aberration, nutation, and the true velocity of light.
+
+_Parallax_.--The absence of stellar parallax was the great
+objection to any theory of the earth's motion prior to Kepler's
+time. It is true that Kepler's theory itself could have been
+geometrically expressed equally well with the earth or any other point
+fixed. But in Kepler's case the obviously implied physical theory of
+the planetary motions, even before Newton explained the simplicity of
+conception involved, made astronomers quite ready to waive the claim
+for a rigid proof of the earth's motion by measurement of an annual
+parallax of stars, which they had insisted on in respect of
+Copernicus's revival of the idea of the earth's orbital motion.
+
+Still, the desire to measure this parallax was only intensified by the
+practical certainty of its existence, and by repeated failures. The
+attempts of Bradley failed. The attempts of Piazzi and Brinkley,[1]
+early in the nineteenth century, also failed. The first successes,
+afterwards confirmed, were by Bessel and Henderson. Both used stars
+whose proper motion had been found to be large, as this argued
+proximity. Henderson, at the Cape of Good Hope, observed alpha
+Centauri, whose annual proper motion he found to amount to 3".6, in
+1832-3; and a few years later deduced its parallax 1".16. His
+successor at the Cape, Maclear, reduced this to 0".92.
+
+In 1835 Struve assigned a doubtful parallax of 0".261 to Vega (alpha
+Lyrae). But Bessel's observations, between 1837 and 1840, of 61 Cygni,
+a star with the large proper motion of over 5", established its annual
+parallax to be 0".3483; and this was confirmed by Peters, who found
+the value 0".349.
+
+Later determinations for alpha2 Centauri, by Gill,[2] make its parallax
+0".75--This is the nearest known fixed star; and its light takes 4 1/3
+years to reach us. The light year is taken as the unit of measurement
+in the starry heavens, as the earth's mean distance is "the
+astronomical unit" for the solar system.[3] The proper motions and
+parallaxes combined tell us the velocity of the motion of these stars
+across the line of sight: alpha Centauri 14.4 miles a second=4.2
+astronomical units a year; 61 Cygni 37.9 miles a second=11.2
+astronomical units a year. These successes led to renewed zeal, and
+now the distances of many stars are known more or less accurately.
+
+Several of the brightest stars, which might be expected to be the
+nearest, have not shown a parallax amounting to a twentieth of a
+second of arc. Among these are Canopus, alpha Orionis, alpha Cygni, beta
+Centauri, and gamma Cassiopeia. Oudemans has published a list of
+parallaxes observed.[4]
+
+_Proper Motion._--In 1718 Halley[5] detected the proper motions
+of Arcturus and Sirius. In 1738 J. Cassinis[6] showed that the former
+had moved five minutes of arc since Tycho Brahe fixed its position. In
+1792 Piazzi noted the motion of 61 Cygni as given above. For a long
+time the greatest observed proper motion was that of a small star 1830
+Groombridge, nearly 7" a year; but others have since been found
+reaching as much as 10".
+
+Now the spectroscope enables the motion of stars to be detected at a
+single observation, but only that part of the motion that is in the
+line of sight. For a complete knowledge of a star's motion the proper
+motion and parallax must also be known.
+
+When Huggins first applied the Doppler principle to measure velocities
+in the line of sight,[7] the faintness of star spectra diminished the
+accuracy; but Vogel, in 1888, overcame this to a great extent by long
+exposures of photographic plates.
+
+It has often been noticed that stars which seem to belong to a group
+of nearly uniform magnitude have the same proper motion. The
+spectroscope has shown that these have also often the same velocity in
+the line of sight. Thus in the Great Bear, beta, gamma, delta,
+epsilon, zeta, all agree as to angular proper motion. delta was too
+faint for a spectroscopic measurement, but all the others have been
+shown to be approaching us at a rate of twelve to twenty miles a
+second. The same has been proved for proper motion, and line of sight
+motion, in the case of Pleiades and other groups.
+
+Maskelyne measured many proper motions of stars, from which W.
+Herschel[8] came to the conclusion that these apparent motions are for
+the most part due to a motion of the solar system in space towards a
+point in the constellation Hercules, R.A. 257 degrees; N. Decl. 25
+degrees. This grand discovery has been amply confirmed, and, though
+opinions differ as to the exact direction, it happens that the point
+first indicated by Herschel, from totally insufficient data, agrees
+well with modern estimates.
+
+Comparing the proper motions and parallaxes to get the actual velocity
+of each star relative to our system, C.L. Struve found the probable
+velocity of the solar system in space to be fifteen miles a second, or
+five astronomical units a year.
+
+The work of Herschel in this matter has been checked by comparing
+spectroscopic velocities in the line of sight which, so far as the
+sun's motion is concerned, would give a maximum rate of approach for
+stars near Hercules, a maximum rate of recession for stars in the
+opposite part of the heavens, and no effect for stars half-way
+between. In this way the spectroscope has confirmed generally
+Herschel's view of the direction, and makes the velocity eleven miles
+a second, or nearly four astronomical units a year.
+
+The average proper motion of a first magnitude star has been found to
+be 0".25 annually, and of a sixth magnitude star 0".04. But that all
+bright stars are nearer than all small stars, or that they show
+greater proper motion for that reason, is found to be far from the
+truth. Many statistical studies have been made in this connection, and
+interesting results may be expected from this treatment in the hands
+of Kapteyn of Groningen, and others.[9]
+
+On analysis of the directions of proper motions of stars in all parts
+of the heavens, Kapteyn has shown[10] that these indicate, besides the
+solar motion towards Hercules, two general drifts of stars in nearly
+opposite directions, which can be detected in any part of the
+heavens. This result has been confirmed from independent data by
+Eddington (_R.A.S., M.N._) and Dyson (_R.S.E. Proc._).
+
+Photography promises to assist in the measurement of parallax and
+proper motions. Herr Pulfrich, of the firm of Carl Zeiss, has vastly
+extended the applications of stereoscopic vision to astronomy--a
+subject which De la Rue took up in the early days of photography. He
+has made a stereo-comparator of great beauty and convenience for
+comparing stereoscopically two star photographs taken at different
+dates. Wolf of Heidelberg has used this for many purposes. His
+investigations depending on the solar motion in space are remarkable.
+He photographs stars in a direction at right angles to the line of the
+sun's motion. He has taken photographs of the same region fourteen
+years apart, the two positions of his camera being at the two ends of
+a base-line over 5,000,000,000 miles apart, or fifty-six astronomical
+units. On examining these stereoscopically, some of the stars rise out
+of the general plane of the stars, and seem to be much nearer. Many of
+the stars are thus seen to be suspended in space at different
+distances corresponding exactly to their real distances from our solar
+system, except when their proper motion interferes. The effect is most
+striking; the accuracy of measurement exceeds that of any other method
+of measuring such displacements, and it seems that with a long
+interval of time the advantage of the method increases.
+
+_Double Stars._--The large class of double stars has always been much
+studied by amateurs, partly for their beauty and colour, and partly as
+a test for telescopic definition. Among the many unexplained stellar
+problems there is one noticed in double stars that is thought by some
+to be likely to throw light on stellar evolution. It is this: There
+are many instances where one star of the pair is comparatively faint,
+and the two stars are contrasted in colour; and in every single case
+the general colour of the faint companion is invariably to be classed
+with colours more near to the blue end of the spectrum than that of
+the principal star.
+
+_Binary Stars._--Sir William Herschel began his observations of double
+stars in the hope of discovering an annual parallax of the stars. In
+this he was following a suggestion of Galileo's. The presumption is
+that, if there be no physical connection between the stars of a pair,
+the largest is the nearest, and has the greatest parallax. So, by
+noting the distance between the pair at different times of the year, a
+delicate test of parallax is provided, unaffected by major
+instrumental errors.
+
+Herschel did, indeed, discover changes of distance, but not of the
+character to indicate parallax. Following this by further observation,
+he found that the motions were not uniform nor rectilinear, and by a
+clear analysis of the movements he established the remarkable and
+wholly unexpected fact that in all these cases the motion is due to a
+revolution about their common centre of gravity.[11] He gave the
+approximate period of revolution of some of these: Castor, 342 years;
+delta Serpentis, 375 years; gamma Leonis, 1,200 years; epsilon Bootis,
+1,681 years.
+
+Twenty years later Sir John Herschel and Sir James South, after
+re-examination of these stars, confirmed[12] and extended the results,
+one pair of Coronae having in the interval completed more than a whole
+revolution.
+
+It is, then, to Sir William Herschel that we owe the extension of the
+law of gravitation, beyond the limits of the solar system, to the
+whole universe. His observations were confirmed by F.G.W. Struve (born
+1793, died 1864), who carried on the work at Dorpat. But it was first
+to Savary,[13] and later to Encke and Sir John Herschel, that we owe
+the computation of the elliptic elements of these stars; also the
+resulting identification of their law of force with Newton's force of
+gravitation applied to the solar system, and the force that makes an
+apple fall to the ground. As Grant well says in his _History_:
+"This may be justly asserted to be one of the most sublime truths
+which astronomical science has hitherto disclosed to the researches of
+the human mind."
+
+Latterly the best work on double stars has been done by
+S. W. Burnham,[14] at the Lick Observatory. The shortest period he
+found was eleven years (kappa Pegasi). In the case of some of
+these binaries the parallax has been measured, from which it appears
+that in four of the surest cases the orbits are about the size of the
+orbit of Uranus, these being probably among the smallest stellar
+orbits.
+
+The law of gravitation having been proved to extend to the stars, a
+discovery (like that of Neptune in its origin, though unlike it in the
+labour and originality involved in the calculation) that entrances the
+imagination became possible, and was realised by Bessel--the discovery
+of an unknown body by its gravitational disturbance on one that was
+visible. In 1834 and 1840 he began to suspect a want of uniformity in
+the proper motion of Sirius and Procyon respectively. In 1844, in a
+letter to Sir John Herschel,[15] he attributed these irregularities in
+each case to the attraction of an invisible companion, the period of
+revolution of Sirius being about half a century. Later he said: "I
+adhere to the conviction that Procyon and Sirius form real binary
+systems, consisting of a visible and an invisible star. There is no
+reason to suppose luminosity an essential quality of cosmical
+bodies. The visibility of countless stars is no argument against the
+invisibility of countless others." This grand conception led Peters to
+compute more accurately the orbit, and to assign the place of the
+invisible companion of Sirius. In 1862 Alvan G. Clark was testing a
+new 18-inch object-glass (now at Chicago) upon Sirius, and, knowing
+nothing of these predictions, actually found the companion in the very
+place assigned to it. In 1896 the companion of Procyon was discovered
+by Professor Schaeberle at the Lick Observatory.
+
+Now, by the refined parallax determinations of Gill at the Cape, we
+know that of Sirius to be 0".38. From this it has been calculated that
+the mass of Sirius equals two of our suns, and its intrinsic
+brightness equals twenty suns; but the companion, having a mass equal
+to our sun, has only a five-hundredth part of the sun's brightness.
+
+_Spectroscopic Binaries_.--On measuring the velocity of a star in the
+line of sight at frequent intervals, periodic variations have been
+found, leading to a belief in motion round an invisible
+companion. Vogel, in 1889, discovered this in the case of Spica (alpha
+Virginis), whose period is 4d. 0h. 19m., and the diameter of whose
+orbit is six million miles. Great numbers of binaries of this type
+have since then been discovered, all of short period.
+
+Also, in 1889, Pickering found that at regular intervals of fifty-two
+days the lines in the spectrum of zeta of the Great Bear are
+duplicated, indicating a relative velocity, equal to one hundred miles
+a second, of two components revolving round each other, of which that
+apparently single star must be composed.
+
+It would be interesting, no doubt, to follow in detail the
+accumulating knowledge about the distances, proper motions, and orbits
+of the stars; but this must be done elsewhere. Enough has been said to
+show how results are accumulating which must in time unfold to us the
+various stellar systems and their mutual relationships.
+
+_Variable Stars._--It has often happened in the history of different
+branches of physical science that observation and experiment were so
+far ahead of theory that hopeless confusion appeared to reign; and
+then one chance result has given a clue, and from that time all
+differences and difficulties in the previous researches have stood
+forth as natural consequences, explaining one another in a rational
+sequence. So we find parallax, proper motion, double stars, binary
+systems, variable stars, and new stars all bound together.
+
+The logical and necessary explanation given of the cause of ordinary
+spectroscopic binaries, and of irregular proper motions of Sirius and
+Procyon, leads to the inference that if ever the plane of such a
+binary orbit were edge-on to us there ought to be an eclipse of the
+luminous partner whenever the non-luminous one is interposed between
+us. This should give rise either to intermittence in the star's light
+or else to variability. It was by supposing the existence of a dark
+companion to Algol that its discoverer, Goodricke of York,[16] in
+1783, explained variable stars of this type. Algol (beta Persei)
+completes the period of variable brightness in 68.8 hours. It loses
+three-fifths of its light, and regains it in twelve hours. In 1889
+Vogel,[17] with the Potsdam spectrograph, actually found that the
+luminous star is receding before each eclipse, and approaching us
+after each eclipse; thus entirely supporting Goodricke's opinion.
+There are many variables of the Algol type, and information is
+steadily accumulating. But all variable stars do not suffer the sudden
+variations of Algol. There are many types, and the explanations of
+others have not proved so easy.
+
+The Harvard College photographs have disclosed the very great
+prevalence of variability, and this is certainly one of the lines in
+which modern discovery must progress.
+
+Roberts, in South Africa, has done splendid work on the periods of
+variables of the Algol type.
+
+_New Stars_.--Extreme instances of variable stars are the new stars
+such as those detected by Hipparchus, Tycho Brahe, and Kepler, of
+which many have been found in the last half-century. One of the latest
+great "Novae" was discovered in Auriga by a Scotsman, Dr. Anderson, on
+February 1st, 1892, and, with the modesty of his race, he communicated
+the fact to His Majesty's Astronomer for Scotland on an unsigned
+post-card.[18] Its spectrum was observed and photographed by Huggins
+and many others. It was full of bright lines of hydrogen, calcium,
+helium, and others not identified. The astounding fact was that lines
+were shown in pairs, bright and dark, on a faint continuous spectrum,
+indicating apparently that a dark body approaching us at the rate of
+550 miles a second[19] was traversing a cold nebulous atmosphere, and
+was heated to incandescence by friction, like a meteor in our
+atmosphere, leaving a luminous train behind it. It almost disappeared,
+and on April 26th it was of the sixteenth magnitude; but on August
+17th it brightened to the tenth, showing the principal nebular band in
+its spectrum, and no sign of approach or recession. It was as if it
+emerged from one part of the nebula, cooled down, and rushed through
+another part of the nebula, rendering the nebular gas more luminous
+than itself.[20]
+
+Since 1892 one Nova after another has shown a spectrum as described
+above, like a meteor rushing towards us and leaving a train behind,
+for this seems to be the obvious meaning of the spectra.
+
+The same may be said of the brilliant Nova Persei, brighter at its
+best than Capella, and discovered also by Dr. Anderson on February
+22nd, 1901. It increased in brightness as it reached the densest part
+of the nebula, then it varied for some weeks by a couple of
+magnitudes, up and down, as if passing through separate nebular
+condensations. In February, 1902, it could still be seen with an
+opera-glass. As with the other Novae, when it first dashed into the
+nebula it was vaporised and gave a continuous spectrum with dark lines
+of hydrogen and helium. It showed no bright lines paired with the dark
+ones to indicate a train left behind; but in the end its own
+luminosity died out, and the nebular spectrum predominated.
+
+The nebular illumination as seen in photographs, taken from August to
+November, seemed to spread out slowly in a gradually increasing circle
+at the rate of 90" in forty-eight days. Kapteyn put this down to the
+velocity of light, the original outburst sending its illumination to
+the nebulous gas and illuminating a spherical shell whose radius
+increased at the velocity of light. This supposition seems correct, in
+which case it can easily be shown from the above figures that the
+distance of this Nova was 300 light years.
+
+_Star Catalogues._--Since the days of very accurate observations
+numerous star-catalogues have been produced by individuals or by
+observatories. Bradley's monumental work may be said to head the list.
+Lacaille's, in the Southern hemisphere, was complementary. Then
+Piazzi, Lalande, Groombridge, and Bessel were followed by Argelander
+with his 324,000 stars, Rumker's Paramatta catalogue of the southern
+hemisphere, and the frequent catalogues of national observatories.
+Later the Astronomische Gesellschaft started their great catalogue,
+the combined work of many observatories. Other southern ones were
+Gould's at Cordova and Stone's at the Cape.
+
+After this we have a new departure. Gill at the Cape, having the comet
+1882.ii. all to himself in those latitudes, wished his friends in
+Europe to see it, and employed a local photographer to strap his
+camera to the observatory equatoreal, driven by clockwork, and
+adjusted on the comet by the eye. The result with half-an-hour's
+exposure was good, so he tried three hours. The result was such a
+display of sharp star images that he resolved on the Cape Photographic
+Durchmusterung, which after fourteen years, with Kapteyn's aid in
+reducing, was completed. Meanwhile the brothers Henry, of Paris, were
+engaged in going over Chacornac's zodiacal stars, and were about to
+catalogue the Milky Way portion, a serious labour, when they saw
+Gill's Comet photograph and conceived the idea of doing the rest of
+their work by photography. Gill had previously written to Admiral
+Mouchez, of the Paris Observatory, and explained to him his project
+for charting the heavens photographically, by combining the work of
+many observatories. This led Admiral Mouchez to support the brothers
+Henry in their scheme.[21] Gill, having got his own photographic work
+underway, suggested an international astrographic chart, the materials
+for different zones to be supplied by observatories of all nations,
+each equipped with similar photographic telescopes. At a conference in
+Paris, 1887, this was decided on, the stars on the charts going down
+to the fourteenth magnitude, and the catalogues to the eleventh.
+
+[Illustration: GREAT COMET, Nov. 14TH, 1882. (Exposure 2hrs. 20m.) By
+kind permission of Sir David Gill. From this photograph originated all
+stellar chart-photography.]
+
+This monumental work is nearing completion. The labour involved was
+immense, and the highest skill was required for devising instruments
+and methods to read off the star positions from the plates.
+
+Then we have the Harvard College collection of photographic plates,
+always being automatically added to; and their annex at Arequipa in
+Peru.
+
+Such catalogues vary in their degree of accuracy; and fundamental
+catalogues of standard stars have been compiled. These require
+extension, because the differential methods of the heliometer and the
+camera cannot otherwise be made absolute.
+
+The number of stars down to the fourteenth magnitude may be taken at
+about 30,000,000; and that of all the stars visible in the greatest
+modern telescopes is probably about 100,000,000.
+
+_Nebulae and Star-clusters._--Our knowledge of nebulae really dates from
+the time of W. Herschel. In his great sweeps of the heavens with his
+giant telescopes he opened in this direction a new branch of
+astronomy. At one time he held that all nebulae might be clusters of
+innumerable minute stars at a great distance. Then he recognised the
+different classes of nebulae, and became convinced that there is a
+widely-diffused "shining fluid" in space, though many so-called nebulae
+could be resolved by large telescopes into stars. He considered that
+the Milky Way is a great star cluster, whose form may be conjectured
+from numerous star-gaugings. He supposed that the compact "planetary
+nebulae" might show a stage of evolution from the diffuse nebulae, and
+that his classifications actually indicate various stages of
+development. Such speculations, like those of the ancients about the
+solar system, are apt to be harmful to true progress of knowledge
+unless in the hands of the ablest mathematical physicists; and
+Herschel violated their principles in other directions. But here his
+speculations have attracted a great deal of attention, and, with
+modifications, are accepted, at least as a working hypothesis, by a
+fair number of people.
+
+When Sir John Herschel had extended his father's researches into the
+Southern Hemisphere he was also led to the belief that some nebulae
+were a phosphorescent material spread through space like fog or mist.
+
+Then his views were changed by the revelations due to the great
+discoveries of Lord Rosse with his gigantic refractor,[22] when one
+nebula after another was resolved into a cluster of minute stars. At
+that time the opinion gained ground that with increase of telescopic
+power this would prove to be the case with all nebulae.
+
+In 1864 all doubt was dispelled by Huggins[23] in his first examination
+of the spectrum of a nebula, and the subsequent extension of this
+observation to other nebulae; thus providing a certain test which
+increase in the size of telescopes could never have given. In 1864
+Huggins found that all true nebulae give a spectrum of bright
+lines. Three are due to hydrogen; two (discovered by Copeland) are
+helium lines; others are unknown. Fifty-five lines have been
+photographed in the spectrum of the Orion nebula. It seems to be
+pretty certain that all true nebulae are gaseous, and show almost
+exactly the same spectrum.
+
+Other nebulae, and especially the white ones like that in Andromeda,
+which have not yet been resolved into stars, show a continuous
+spectrum; others are greenish and give no lines.
+
+A great deal has to be done by the chemist before the astronomer can
+be on sure ground in drawing conclusions from certain portions of his
+spectroscopic evidence.
+
+The light of the nebulas is remarkably actinic, so that photography
+has a specially fine field in revealing details imperceptible in the
+telescope. In 1885 the brothers Henry photographed, round the star
+Maia in the Pleiades, a spiral nebula 3' long, as bright on the plate
+as that star itself, but quite invisible in the telescope; and an
+exposure of four hours revealed other new nebula in the same
+district. That painstaking and most careful observer, Barnard, with
+10-1/4 hours' exposure, extended this nebulosity for several degrees,
+and discovered to the north of the Pleiades a huge diffuse nebulosity,
+in a region almost destitute of stars. By establishing a 10-inch
+instrument at an altitude of 6,000 feet, Barnard has revealed the wide
+distribution of nebular matter in the constellation Scorpio over a
+space of 4 degrees or 5 degrees square. Barnard asserts that the "nebular
+hypothesis" would have been killed at its birth by a knowledge of
+these photographs. Later he has used still more powerful instruments,
+and extended his discoveries.
+
+The association of stars with planetary nebulae, and the distribution
+of nebulae in the heavens, especially in relation to the Milky Way, are
+striking facts, which will certainly bear fruit when the time arrives
+for discarding vague speculations, and learning to read the true
+physical structure and history of the starry universe.
+
+_Stellar Spectra._--When the spectroscope was first available for
+stellar research, the leaders in this branch of astronomy were Huggins
+and Father Secchi,[24] of Rome. The former began by devoting years of
+work principally to the most accurate study of a few stars. The
+latter devoted the years from 1863 to 1867 to a general survey of the
+whole heavens, including 4,000 stars. He divided these into four
+principal classes, which have been of the greatest service. Half of
+his stars belonged to the first class, including Sirius, Vega,
+Regulus, Altair. The characteristic feature of their spectra is the
+strength and breadth of the hydrogen lines and the extreme faintness
+of the metallic lines. This class of star is white to the eye, and
+rich in ultra violet light.
+
+The second class includes about three-eighths of his stars, including
+Capella, Pollux, and Arcturus. These stars give a spectrum like that
+of our sun, and appear yellowish to the eye.
+
+The third class includes alpha Herculis, alpha Orionis (Betelgeux), Mira
+Ceti, and about 500 red and variable stars. The spectrum has fluted
+bands shaded from blue to red, and sharply defined at the more
+refrangible edge.
+
+The fourth class is a small one, containing no stars over fifth
+magnitude, of which 152 Schjellerup, in Canes Venatici, is a good
+example. This spectrum also has bands, but these are shaded on the
+violet side and sharp on the red side. They are due to carbon in some
+form. These stars are ruby red in the telescope.
+
+It would appear, then, that all stars are suns with continuous
+spectra, and the classes are differentiated by the character of the
+absorbent vapours of their atmospheres.
+
+It is very likely that, after the chemists have taught us how to
+interpret all the varieties of spectrum, it will be possible to
+ascribe the different spectrum-classes to different stages in the
+life-history of every star. Already there are plenty of people ready
+to lay down arbitrary assumptions about the lessons to be drawn from
+stellar spectra. Some say that they know with certainty that each star
+begins by being a nebula, and is condensed and heated by condensation
+until it begins to shine as a star; that it attains a climax of
+temperature, then cools down, and eventually becomes extinct. They go
+so far as to declare that they know what class of spectrum belongs to
+each stage of a star's life, and how to distinguish between one that
+is increasing and another that is decreasing in temperature.
+
+The more cautious astronomers believe that chemistry is not
+sufficiently advanced to justify all of these deductions; that, until
+chemists have settled the lately raised question of the transmutation
+of elements, no theory can be sure. It is also held that until they
+have explained, without room for doubt, the reasons for the presence
+of some lines, and the absence of others, of any element in a stellar
+spectrum; why the arc-spectrum of each element differs from its spark
+spectrum; what are all the various changes produced in the spectrum of
+a gas by all possible concomitant variations of pressure and
+temperature; also the meanings of all the flutings in the spectra of
+metalloids and compounds; and other equally pertinent matters--until
+that time arrives the part to be played by the astronomer is one of
+observation. By all means, they say, make use of "working hypotheses"
+to add an interest to years of laborious research, and to serve as a
+guide to the direction of further labours; but be sure not to fall
+into the error of calling any mere hypothesis a theory.
+
+_Nebular Hypothesis._--The Nebular Hypothesis, which was first, as it
+were, tentatively put forward by Laplace as a note in his _Systeme du
+Monde_, supposes the solar system to have been a flat, disk-shaped
+nebula at a high temperature in rapid rotation. In cooling it
+condensed, leaving revolving rings at different distances from the
+centre. These themselves were supposed to condense into the nucleus
+for a rotating planet, which might, in contracting, again throw off
+rings to form satellites. The speculation can be put in a really
+attractive form, but is in direct opposition to many of the actual
+facts; and so long as it is not favoured by those who wish to maintain
+the position of astronomy as the most exact of the sciences--exact in
+its facts, exact in its logic--this speculation must be recorded by
+the historian, only as he records the guesses of the ancient Greeks--as
+an interesting phase in the history of human thought.
+
+Other hypotheses, having the same end in view, are the meteoritic
+hypothesis of Lockyer and the planetesimal hypothesis that has been
+largely developed in the United States. These can best be read in the
+original papers to various journals, references to which may be found
+in the footnotes of Miss Clerke's _History of Astronomy during the
+Nineteenth Century_. The same can be said of Bredichin's hypothesis of
+comets' tails, Arrhenius's book on the applications of the theory of
+light repulsion, the speculations on radium, the origin of the sun's
+heat and the age of the earth, the electron hypothesis of terrestrial
+magnetism, and a host of similar speculations, all combining to throw
+an interesting light on the evolution of a modern train of thought
+that seems to delight in conjecture, while rebelling against that
+strict mathematical logic which has crowned astronomy as the queen of
+the sciences.
+
+
+FOOTNOTES:
+
+[1] _R. S. Phil Trans_., 1810 and 1817-24.
+
+[2] One of the most valuable contributions to our knowledge of stellar
+parallaxes is the result of Gill's work (_Cape Results_, vol. iii.,
+part ii., 1900).
+
+[3] Taking the velocity of light at 186,000 miles a second, and the
+earth's mean distance at 93,000,000 miles, 1 light year=5,865,696,000,000
+miles or 63,072 astronomical units; 1 astronomical unit a year=2.94
+miles a second; and the earth's orbital velocity=18.5 miles a second.
+
+[4] Ast. Nacht., 1889.
+
+[5] R. S. Phil. Trans., 1718.
+
+[6] Mem. Acad. des Sciences, 1738, p. 337.
+
+[7] R. S Phil. Trans., 1868.
+
+[8] _R.S. Phil Trans._, 1783.
+
+[9] See Kapteyn's address to the Royal Institution, 1908. Also Gill's
+presidential address to the British Association, 1907.
+
+[10] _Brit. Assoc. Rep._, 1905.
+
+[11] R. S. Phil. Trans., 1803, 1804.
+
+[12] Ibid, 1824.
+
+[13] Connaisance des Temps, 1830.
+
+[14] _R. A. S. Mem._, vol. xlvii., p. 178; _Ast. Nach._, No. 3,142;
+Catalogue published by Lick Observatory, 1901.
+
+[15] _R. A. S., M. N._, vol. vi.
+
+[16] _R. S. Phil. Trans._, vol. lxxiii., p. 484.
+
+[17] _Astr. Nach._, No. 2,947.
+
+[18] _R. S. E. Trans_., vol. xxvii. In 1901 Dr. Anderson discovered
+Nova Persei.
+
+[19] _Astr. Nach_., No. 3,079.
+
+[20] For a different explanation see Sir W. Huggins's lecture, Royal
+Institution, May 13th, 1892.
+
+[21] For the early history of the proposals for photographic
+cataloguing of stars, see the _Cape Photographic Durchmusterung_, 3
+vols. (_Ann. of the Cape Observatory_, vols. in., iv., and v.,
+Introduction.)
+
+[22] _R. S. Phil. Trans._, 1850, p. 499 _et seq._
+
+[23] _Ibid_, vol. cliv., p. 437.
+
+[24] _Brit. Assoc. Rep._, 1868, p. 165.
+
+
+
+INDEX
+
+
+Abul Wefa, 24
+Acceleration of moon's mean motion, 60
+Achromatic lens invented, 88
+Adams, J. C., 61, 65, 68, 69, 70, 87, 118, 124
+Airy, G. B., 13, 30, 37, 65, 69, 70, 80, 81, 114, 119
+Albetegnius, 24
+Alphonso, 24
+Altazimuth, 81
+Anaxagoras, 14, 16
+Anaximander, 14
+Anaximenes, 14
+Anderson, T. D., 137, 138
+Angstrom, A. J., 102
+Antoniadi, 113
+Apian, P., 63
+Apollonius, 22, 23
+Arago, 111
+Argelander, F. W. A., 139
+Aristarchus, 18, 29
+Aristillus, 17, 19
+Aristotle, 16, 30, 47
+Arrhenius, 146
+Arzachel, 24
+Asshurbanapal, 12
+Asteroids, discovery of, 67, 119
+Astrology, ancient and modern, 1-7, 38
+
+Backlund, 122
+Bacon, R., 86
+Bailly, 8, 65
+Barnard, E. E., 115, 143
+Beer and Madler, 107, 110, 111
+Behaim, 74
+Bessel, F.W., 65, 79, 128, 134, 139
+Biela, 123
+Binet, 65
+Biot, 10
+Bird, 79, 80
+Bliss, 80
+Bode, 66, 69
+Bond, G. P., 99, 117, 122
+Bouvard, A., 65, 68
+Bradley, J., 79, 80, 81, 87, 127, 128, 139
+Bredechin, 146
+Bremiker, 71
+Brewster, D., 52, 91, 112
+Brinkley, 128
+Bruno, G., 49
+Burchardt, 65, 123
+Burnham, S. W., 134
+
+Callippus, 15, 16, 31
+Carrington, R. C., 97, 99, 114
+Cassini, G. D., 107, 114, 115, 116, 117, 118
+Cassini, J., 109, 129
+Chacornac, 139
+Chaldaean astronomy, 11-13
+Challis, J., 69, 70, 71, 72
+Chance, 88
+Charles, II., 50, 81
+Chinese astronomy, 8-11
+Christie, W. M. H. (Ast. Roy.), 64, 82, 125
+Chueni, 9
+Clairaut, A. C., 56, 63, 65
+Clark, A. G., 89, 135
+Clerke, Miss, 106, 146
+Comets, 120
+Common, A. A., 88
+Cooke, 89
+Copeland, R., 142
+Copernicus, N., 14, 24-31, 37, 38, 41, 42, 49, 128
+Cornu, 85
+Cowell, P. H., 3, 5, 64, 83
+Crawford, Earl of, 84
+Cromellin, A. C., 5, 64
+
+D'Alembert, 65
+Damoiseau, 65
+D'Arrest, H. L., 34
+Dawes, W. R., 100, 111
+Delambre, J. B. J., 8, 27, 51, 65, 68
+De la Rue, W., 2, 94, 99, 100, 131
+Delaunay, 65
+Democritus, 16
+Descartes, 51
+De Sejour, 117
+Deslandres, II., 101
+Desvignolles, 9
+De Zach, 67
+Digges, L., 86
+Dollond, J., 87, 90
+Dominis, A. di., 86
+Donati, 120
+Doppler, 92, 129
+Draper, 99
+Dreyer, J. L. E., 29,77
+Dunthorne, 60
+Dyson, 131
+
+Eclipses, total solar, 103
+Ecphantes, 16
+Eddington, 131
+Ellipse, 41
+Empedocles, 16
+Encke, J. F., 119, 122, 123, 133
+Epicycles, 22
+Eratosthenes, 18
+Euclid, 17
+Eudoxus, 15, 31
+Euler, L., 60, 61, 62, 65, 88, 119
+
+Fabricius, D.,95, 120, 121
+Feil and Mantois, 88
+Fizeau, H. L., 85, 92, 99
+Flamsteed, J., 50, 58, 68, 78, 79, 93
+Fohi, 8
+Forbes, J. D., 52, 91
+Foucault, L., 85, 99
+Frauenhofer, J., 88, 90, 91
+
+Galilei, G., 38, 46-49, 77, 93, 94, 95, 96, 107, 113, 115, 116, 133
+Galle, 71, 72
+Gascoigne, W., 45, 77
+Gauss, C. F., 65, 67
+Gauthier, 98
+Gautier, 89
+Gilbert, 44
+Gill, D., 84, 85, 128, 135, 139, 140
+Goodricke, J., 136
+Gould, B. A., 139
+Grant, R., 27, 47, 51, 86, 134
+Graham, 79
+Greek astronomy, 8-11
+Gregory, J. and D., 87
+Grimaldi, 113
+Groombridge, S., 139
+Grubb, 88, 89
+Guillemin, 122
+Guinand, 88
+
+Hale, G. E., 101
+Hall, A., 112
+Hall, C. M., 88
+Halley, E., 19, 51, 58, 60, 61, 62, 63, 64, 79, 120, 122, 125, 129
+Halley's comet, 62-64
+Halm, 85
+Hansen, P. A., 3, 65
+Hansky, A. P., 100
+Harding, C. L., 67
+Heliometer, 83
+Heller, 120
+Helmholtz, H. L. F., 35
+Henderson, T., 128
+Henry, P. and P., 139, 140, 143
+Heraclides, 16
+Heraclitus, 14
+Herodotus, 13
+Herschel, W., 65, 68, 97, 107, 110, 114, 115, 116, 117, 118, 126, 127,
+  130, 131, 132, 141, 142
+Herschel, J., 97, 111, 133, 134, 142
+Herschel, A. S., 125
+Hevelius, J., 178
+Hind, J. R., 5, 64, 120, 121, 122
+Hipparchus, 3, 18, 19, 20, 22, 23, 24, 26, 36, 55, 60, 74, 93, 137
+Hooke, R., 51, 111, 114
+Horrocks, J., 50, 56
+Howlett, 100
+Huggins, W., 92, 93, 99, 106, 120, 129, 137, 138, 142, 144
+Humboldt and Bonpland, 124
+Huyghens, C., 47, 77, 87, 110, 116, 117
+
+Ivory, 65
+
+Jansen, P. J. C., 105, 106
+Jansen, Z., 86
+
+Kaiser, F., 111
+Kapteyn, J. C., 131, 138, 139
+Keeler, 117
+Kepler, J., 17, 23, 26, 29, 30, 36, 37, 38-46, 48, 49, 50, 52, 53, 63,
+  66, 77, 87, 93, 127, 137
+Kepler's laws, 42
+Kirchoff, G.R., 91
+Kirsch, 9
+Knobel, E.B., 12, 13
+Ko-Show-King, 76
+
+Lacaile, N.L., 139
+Lagrange, J.L., 61, 62, 65, 119
+La Hire, 114
+Lalande, J.J.L., 60, 63, 65, 66, 72, 139
+Lamont, J., 98
+Langrenus, 107
+Laplace, P.S. de, 50, 58, 61, 62, 65,66, 123, 146
+Lassel, 72, 88, 117, 118
+Law of universal gravitation, 53
+Legendre, 65
+Leonardo da Vinci, 46
+Lewis, G.C., 17
+Le Verrier, U.J.J., 65, 68, 70, 71,72, 110, 118, 125
+Lexell, 66, 123
+Light year, 128
+Lipperhey, H., 86
+Littrow, 121
+Lockyer, J.N., 103, 105, 146
+Logarithms invented, 50
+Loewy, 2, 100
+Long inequality of Jupiter and Saturn, 50, 62
+Lowell, P., 111, 112, 118
+Lubienietz, S. de, 122
+Luther, M., 38
+Lunar theory, 37, 50, 56, 64
+
+Maclaurin, 65
+Maclear, T., 128
+Malvasia, 77
+Martin, 9
+Maxwell, J. Clerk, 117
+Maskelyne, N., 80, 130
+McLean, F., 89
+Medici, Cosmo di, 48
+Melancthon, 38
+Melotte, 83, 116
+Meteors, 123
+Meton, 15
+Meyer, 57, 65
+Michaelson, 85
+Miraldi, 110, 114
+Molyneux, 87
+Moon, physical observations, 107
+Mouchez, 139
+Moyriac de Mailla, 8
+
+Napier, Lord, 50
+Nasmyth and Carpenter, 108
+Nebulae, 141, 146
+Neison, E., 108
+Neptune, discovery of, 68-72
+Newall, 89
+Newcomb, 85
+Newton, H.A., 124
+Newton, I., 5, 19, 43, 49, 51-60, 62, 64, 68, 77, 79, 87, 90, 93, 94,
+  114, 127, 133
+Nicetas, 16, 25
+Niesten, 115
+Nunez, P., 35
+
+Olbers, H.W.M., 67
+Omar, 11, 24
+Oppolzer, 13, 125
+Oudemans, 129
+
+Palitsch, G., 64
+Parallax, solar, 85, 86
+Parmenides, 14
+Paul III., 30
+Paul V., 48
+Pemberton, 51
+Peters, C.A.F., 125, 128, 135
+Photography, 99
+Piazzi, G., 67, 128, 129, 139
+Picard, 54, 77, 114
+Pickering, E.C., 118, 135
+Pingre, 13, 122
+Plana, 65
+Planets and satellites, physical observations, 109-119
+Plato, 17, 23, 26, 40
+Poisson, 65
+Pond, J., 80
+Pons, 122
+Porta, B., 86
+Pound, 87, 114
+Pontecoulant, 64
+Precession of the equinoxes, 19-21, 55, 57
+Proctor, R.A., 111
+Pritchett, 115
+Ptolemy, 11, 13, 21, 22, 23, 24, 93
+Puiseux and Loewy, 108
+Pulfrich, 131
+Purbach, G., 24
+Pythagoras, 14, 17, 25, 29
+
+Ramsay, W., 106
+Ransome and May, 81
+Reflecting telescopes invented, 87
+Regiomontanus (Muller), 24
+Respighi, 82
+Retrograde motion of planets, 22
+Riccioli, 107
+Roberts, 137
+Romer, O.,78, 114
+Rosse, Earl of, 88, 142
+Rowland, H. A., 92, 102
+Rudolph H.,37, 39
+Rumker, C., 139
+
+Sabine, E., 98
+Savary, 133
+Schaeberle, J. M., 135
+Schiaparelli, G. V., 110, 111, 124, 125
+Scheiner, C., 87, 95, 96
+Schmidt, 108
+Schott, 88
+Schroter, J. H., 107, 110, 111, 124, 125
+Schuster, 98
+Schwabe, G. H., 97
+Secchi, A., 93, 144
+Short, 87
+Simms, J., 81
+Slipher, V. M., 119
+Socrates, 17
+Solon, 15
+Souciet, 8
+South, J., 133
+Spectroscope, 89-92
+Spectroheliograph, 101
+Spoerer, G. F. W., 98
+Spots on the sun, 84;
+  periodicity of, 97
+Stars, Parallax, 127;
+  proper motion, 129;
+  double, 132;
+  binaries, 132, 135;
+  new, 19, 36, 137;
+  catalogues of, 19, 36, 139;
+  spectra of, 143
+Stewart, B., 2, 100
+Stokes, G. G., 91
+Stone, E. J., 139
+Struve, C. L., 130
+Struve, F. G. W,, 88, 115, 128, 133
+
+Telescopes invented, 47, 86;
+  large, 88
+Temple, 115, 125
+Thales, 13, 16
+Theon, 60
+Transit circle of Romer, 78
+Timocharis, 17, 19
+Titius, 66
+Torricelli, 113
+Troughton, E., 80
+Tupman, G. L., 120
+Tuttle, 125
+Tycho Brahe, 23, 25, 30, 33-38, 39, 40, 44, 50, 75, 77, 93, 94, 129, 137
+
+Ulugh Begh, 24
+Uranus, discovery of, 65
+
+Velocity of light, 86, 128;
+  of earth in orbit, 128
+Verbiest, 75
+Vogel, H. C., 92, 129, 135, 136
+Von Asten, 122
+
+Walmsley, 65
+Walterus, B., 24, 74
+Weiss, E., 125
+Wells, 122
+Wesley, 104
+Whewell, 112
+Williams, 10
+Wilson, A., 96, 100
+Winnecke, 120
+Witte, 86
+Wollaston, 90
+Wolf, M., 119, 125, 132
+Wolf, R., 98
+Wren, C., 51
+Wyllie, A., 77
+
+Yao, 9
+Young, C. A., 103
+Yu-Chi, 8
+
+Zenith telescopes, 79, 82
+Zollner, 92
+Zucchi, 113
+
+
+
+
+
+End of the Project Gutenberg EBook of History of Astronomy, by George Forbes
+
+*** END OF THE PROJECT GUTENBERG EBOOK HISTORY OF ASTRONOMY ***
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+The Project Gutenberg EBook of History of Astronomy, by George Forbes
+
+Copyright laws are changing all over the world. Be sure to check the
+copyright laws for your country before downloading or redistributing
+this or any other Project Gutenberg eBook.
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+*****These eBooks Were Prepared By Thousands of Volunteers!*****
+
+
+Title: History of Astronomy
+
+Author: George Forbes
+
+Release Date: May, 2005 [EBook #8172]
+[Yes, we are more than one year ahead of schedule]
+[This file was first posted on June 25, 2003]
+
+Edition: 10
+
+Language: English
+
+Character set encoding: ISO-8859-1
+
+*** START OF THE PROJECT GUTENBERG EBOOK HISTORY OF ASTRONOMY ***
+
+
+
+
+Produced by Jonathan Ingram, Dave Maddock, Charles Franks
+and the Online Distributed Proofreading Team.
+
+
+
+
+
+
+[Illustration: SIR ISAAC NEWTON (From the bust by Roubiliac In Trinity
+College, Cambridge.)]
+
+HISTORY OF ASTRONOMY
+
+BY
+
+GEORGE FORBES,
+M.A., F.R.S., M. INST. C. E.,
+
+(FORMERLY PROFESSOR OF NATURAL PHILOSOPHY, ANDERSON'S COLLEGE, GLASGOW)
+
+AUTHOR OF "THE TRANSIT OF VENUS," RENDU'S "THEORY OF THE GLACIERS OF
+SAVOY," ETC., ETC.
+
+
+
+
+CONTENTS
+
+  PREFACE
+
+  BOOK I. THE GEOMETRICAL PERIOD
+
+     1. PRIMITIVE ASTRONOMY AND ASTROLOGY
+
+     2. ANCIENT ASTRONOMY--CHINESE AND CHALD�ANS
+
+     3. ANCIENT GREEK ASTRONOMY
+
+     4. THE REIGN OF EPICYCLES--FROM PTOLEMY TO COPERNICUS
+
+  BOOK II. THE DYNAMICAL PERIOD
+
+     5. DISCOVERY OF THE TRUE SOLAR SYSTEM--TYCHO BRAHE--KEPLER
+
+     6. GALILEO AND THE TELESCOPE--NOTIONS OF GRAVITY BY HORROCKS, ETC.
+
+     7. SIR ISAAC NEWTON--LAW OF UNIVERSAL GRAVITATION
+
+     8. NEWTON'S SUCCESSORS--HALLEY, EULER, LAGRANGE, LAPLACE, ETC.
+
+     9. DISCOVERY OF NEW PLANETS--HERSCHEL, PIAZZI, ADAMS, AND LE
+        VERRIER
+
+  BOOK III. OBSERVATION
+
+
+    10. INSTRUMENTS OF PRECISION--SIZE OF THE SOLAR SYSTEM
+
+    11. HISTORY OF THE TELESCOPE--SPECTROSCOPE
+
+  BOOK IV. THE PHYSICAL PERIOD
+
+    12. THE SUN
+
+    13. THE MOON AND PLANETS
+
+    14. COMETS AND METEORS
+
+    15. THE STARS AND NEBUL�
+
+  INDEX
+
+
+
+PREFACE
+
+
+An attempt has been made in these pages to trace the evolution of
+intellectual thought in the progress of astronomical discovery, and,
+by recognising the different points of view of the different ages, to
+give due credit even to the ancients. No one can expect, in a history
+of astronomy of limited size, to find a treatise on "practical" or on
+"theoretical astronomy," nor a complete "descriptive astronomy," and
+still less a book on "speculative astronomy." Something of each of
+these is essential, however, for tracing the progress of thought and
+knowledge which it is the object of this History to describe.
+
+The progress of human knowledge is measured by the increased habit of
+looking at facts from new points of view, as much as by the
+accumulation of facts. The mental capacity of one age does not seem to
+differ from that of other ages; but it is the imagination of new
+points of view that gives a wider scope to that capacity. And this is
+cumulative, and therefore progressive. Aristotle viewed the solar
+system as a geometrical problem; Kepler and Newton converted the point
+of view into a dynamical one. Aristotle's mental capacity to
+understand the meaning of facts or to criticise a train of reasoning
+may have been equal to that of Kepler or Newton, but the point of view
+was different.
+
+Then, again, new points of view are provided by the invention of new
+methods in that system of logic which we call mathematics. All that
+mathematics can do is to assure us that a statement A is equivalent to
+statements B, C, D, or is one of the facts expressed by the statements
+B, C, D; so that we may know, if B, C, and D are true, then A is true.
+To many people our inability to understand all that is contained in
+statements B, C, and D, without the cumbrous process of a mathematical
+demonstration, proves the feebleness of the human mind as a logical
+machine. For it required the new point of view imagined by Newton's
+analysis to enable people to see that, so far as planetary orbits are
+concerned, Kepler's three laws (B, C, D) were identical with Newton's
+law of gravitation (A). No one recognises more than the mathematical
+astronomer this feebleness of the human intellect, and no one is more
+conscious of the limitations of the logical process called
+mathematics, which even now has not solved directly the problem of
+only three bodies.
+
+These reflections, arising from the writing of this History, go to
+explain the invariable humility of the great mathematical astronomers.
+Newton's comparison of himself to the child on the seashore applies to
+them all. As each new discovery opens up, it may be, boundless oceans
+for investigation, for wonder, and for admiration, the great
+astronomers, refusing to accept mere hypotheses as true, have founded
+upon these discoveries a science as exact in its observation of facts
+as in theories. So it is that these men, who have built up the most
+sure and most solid of all the sciences, refuse to invite others to
+join them in vain speculation. The writer has, therefore, in this
+short History, tried to follow that great master, Airy, whose pupil he
+was, and the key to whose character was exactness and accuracy; and he
+recognises that Science is impotent except in her own limited sphere.
+
+It has been necessary to curtail many parts of the History in the
+attempt--perhaps a hopeless one--to lay before the reader in a limited
+space enough about each age to illustrate its tone and spirit, the
+ideals of the workers, the gradual addition of new points of view and
+of new means of investigation.
+
+It would, indeed, be a pleasure to entertain the hope that these pages
+might, among new recruits, arouse an interest in the greatest of all
+the sciences, or that those who have handled the theoretical or
+practical side might be led by them to read in the original some of
+the classics of astronomy. Many students have much compassion for the
+schoolboy of to-day, who is not allowed the luxury of learning the art
+of reasoning from him who still remains pre-eminently its greatest
+exponent, Euclid. These students pity also the man of to-morrow, who
+is not to be allowed to read, in the original Latin of the brilliant
+Kepler, how he was able--by observations taken from a moving platform,
+the earth, of the directions of a moving object, Mars--to deduce the
+exact shape of the path of each of these planets, and their actual
+positions on these paths at any time. Kepler's masterpiece is one of
+the most interesting books that was ever written, combining wit,
+imagination, ingenuity, and certainty.
+
+Lastly, it must be noted that, as a History of England cannot deal
+with the present Parliament, so also the unfinished researches and
+untested hypotheses of many well-known astronomers of to-day cannot be
+included among the records of the History of Astronomy. The writer
+regrets the necessity that thus arises of leaving without mention the
+names of many who are now making history in astronomical work.
+
+G. F.
+_August 1st, 1909._
+
+
+
+
+BOOK I.  THE GEOMETRICAL PERIOD
+
+
+
+1. PRIMITIVE ASTRONOMY AND ASTROLOGY.
+
+
+The growth of intelligence in the human race has its counterpart in
+that of the individual, especially in the earliest stages.
+Intellectual activity and the development of reasoning powers are in
+both cases based upon the accumulation of experiences, and on the
+comparison, classification, arrangement, and nomenclature of these
+experiences. During the infancy of each the succession of events can
+be watched, but there can be no _� priori_ anticipations.
+Experience alone, in both cases, leads to the idea of cause and effect
+as a principle that seems to dominate our present universe, as a rule
+for predicting the course of events, and as a guide to the choice of a
+course of action. This idea of cause and effect is the most potent
+factor in developing the history of the human race, as of the
+individual.
+
+In no realm of nature is the principle of cause and effect more
+conspicuous than in astronomy; and we fall into the habit of thinking
+of its laws as not only being unchangeable in our universe, but
+necessary to the conception of any universe that might have been
+substituted in its place. The first inhabitants of the world were
+compelled to accommodate their acts to the daily and annual
+alternations of light and darkness and of heat and cold, as much as to
+the irregular changes of weather, attacks of disease, and the fortune
+of war.  They soon came to regard the influence of the sun, in
+connection with light and heat, as a cause. This led to a search for
+other signs in the heavens. If the appearance of a comet was sometimes
+noted simultaneously with the death of a great ruler, or an eclipse
+with a scourge of plague, these might well be looked upon as causes in
+the same sense that the veering or backing of the wind is regarded as
+a cause of fine or foul weather.
+
+For these reasons we find that the earnest men of all ages have
+recorded the occurrence of comets, eclipses, new stars, meteor
+showers, and remarkable conjunctions of the planets, as well as
+plagues and famines, floods and droughts, wars and the deaths of great
+rulers. Sometimes they thought they could trace connections which
+might lead them to say that a comet presaged famine, or an eclipse
+war.
+
+Even if these men were sometimes led to evolve laws of cause and
+effect which now seem to us absurd, let us be tolerant, and gratefully
+acknowledge that these astrologers, when they suggested such "working
+hypotheses," were laying the foundations of observation and deduction.
+
+If the ancient Chald�ans gave to the planetary conjunctions an
+influence over terrestrial events, let us remember that in our own
+time people have searched for connection between terrestrial
+conditions and periods of unusual prevalence of sun spots; while De la
+Rue, Loewy, and Balfour Stewart[1] thought they found a connection
+between sun-spot displays and the planetary positions. Thus we find
+scientific men, even in our own time, responsible for the belief that
+storms in the Indian Ocean, the fertility of German vines, famines in
+India, and high or low Nile-floods in Egypt follow the planetary
+positions.
+
+And, again, the desire to foretell the weather is so laudable that we
+cannot blame the ancient Greeks for announcing the influence of the
+moon with as much confidence as it is affirmed in Lord Wolseley's
+_Soldier's Pocket Book_.
+
+Even if the scientific spirit of observation and deduction (astronomy)
+has sometimes led to erroneous systems for predicting terrestrial
+events (astrology), we owe to the old astronomer and astrologer alike
+the deepest gratitude for their diligence in recording astronomical
+events. For, out of the scanty records which have survived the
+destructive acts of fire and flood, of monarchs and mobs, we have
+found much that has helped to a fuller knowledge of the heavenly
+motions than was possible without these records.
+
+So Hipparchus, about 150 B.C., and Ptolemy a little later, were able
+to use the observations of Chald�an astrologers, as well as those of
+Alexandrian astronomers, and to make some discoveries which have
+helped the progress of astronomy in all ages.  So, also, Mr. Cowell[2]
+has examined the marks made on the baked bricks used by the Chald�ans
+for recording the eclipses of 1062 B.C. and 762 B.C.; and has thereby
+been enabled, in the last few years, to correct the lunar tables of
+Hansen, and to find a more accurate value for the secular acceleration
+of the moon's longitude and the node of her orbit than any that could
+be obtained from modern observations made with instruments of the
+highest precision.
+
+So again, Mr. Hind [3] was enabled to trace back the period during
+which Halley's comet has been a member of the solar system, and to
+identify it in the Chinese observations of comets as far back as 12
+B.C. Cowell and Cromellin extended the date to 240 B.C. In the same
+way the comet 1861.i. has been traced back in the Chinese records to
+617 A.D. [4]
+
+The theoretical views founded on Newton's great law of universal
+gravitation led to the conclusion that the inclination of the earth's
+equator to the plane of her orbit (the obliquity of the ecliptic) has
+been diminishing slowly since prehistoric times; and this fact has
+been confirmed by Egyptian and Chinese observations on the length of
+the shadow of a vertical pillar, made thousands of years before the
+Christian era, in summer and winter.
+
+There are other reasons why we must be tolerant of the crude notions
+of the ancients. The historian, wishing to give credit wherever it may
+be due, is met by two difficulties. Firstly, only a few records of
+very ancient astronomy are extant, and the authenticity of many of
+these is open to doubt. Secondly, it is very difficult to divest
+ourselves of present knowledge, and to appreciate the originality of
+thought required to make the first beginnings.
+
+With regard to the first point, we are generally dependent upon
+histories written long after the events.  The astronomy of Egyptians,
+Babylonians, and Assyrians is known to us mainly through the Greek
+historians, and for information about the Chinese we rely upon the
+researches of travellers and missionaries in comparatively recent
+times. The testimony of the Greek writers has fortunately been
+confirmed, and we now have in addition a mass of facts translated from
+the original sculptures, papyri, and inscribed bricks, dating back
+thousands of years.
+
+In attempting to appraise the efforts of the beginners we must
+remember that it was natural to look upon the earth (as all the first
+astronomers did) as a circular plane, surrounded and bounded by the
+heaven, which was a solid vault, or hemisphere, with its concavity
+turned downwards. The stars seemed to be fixed on this vault; the
+moon, and later the planets, were seen to crawl over it. It was a
+great step to look on the vault as a hollow sphere carrying the sun
+too. It must have been difficult to believe that at midday the stars
+are shining as brightly in the blue sky as they do at night. It must
+have been difficult to explain how the sun, having set in the west,
+could get back to rise in the east without being seen _if_ it was
+always the same sun. It was a great step to suppose the earth to be
+spherical, and to ascribe the diurnal motions to its rotation.
+Probably the greatest step ever made in astronomical theory was the
+placing of the sun, moon, and planets at different distances from the
+earth instead of having them stuck on the vault of heaven. It was a
+transition from "flatland" to a space of three dimensions.
+
+Great progress was made when systematic observations began, such as
+following the motion of the moon and planets among the stars, and the
+inferred motion of the sun among the stars, by observing their
+_heliacal risings_--i.e., the times of year when a star
+would first be seen to rise at sunrise, and when it could last be seen
+to rise at sunset. The grouping of the stars into constellations and
+recording their places was a useful observation. The theoretical
+prediction of eclipses of the sun and moon, and of the motions of the
+planets among the stars, became later the highest goal in astronomy.
+
+To not one of the above important steps in the progress of astronomy
+can we assign the author with certainty. Probably many of them were
+independently taken by Chinese, Indian, Persian, Tartar, Egyptian,
+Babylonian, Assyrian, Phoenician, and Greek astronomers.  And we have
+not a particle of information about the discoveries, which may have
+been great, by other peoples--by the Druids, the Mexicans, and the
+Peruvians, for example.
+
+We do know this, that all nations required to have a calendar. The
+solar year, the lunar month, and the day were the units, and it is
+owing to their incommensurability that we find so many calendars
+proposed and in use at different times. The only object to be attained
+by comparing the chronologies of ancient races is to fix the actual
+dates of observations recorded, and this is not a part of a history of
+astronomy.
+
+In conclusion, let us bear in mind the limited point of view of the
+ancients when we try to estimate their merit. Let us remember that the
+first astronomy was of two dimensions; the second astronomy was of
+three dimensions, but still purely geometrical. Since Kepler's day we
+have had a dynamical astronomy.
+
+
+FOOTNOTES:
+
+[1] Trans. R. S. E., xxiii. 1864, p. 499, _On Sun Spots_, etc., by
+B. Stewart. Also Trans. R. S. 1860-70. Also Prof. Ernest Brown, in
+_R. A. S. Monthly Notices_, 1900.
+
+[2] _R. A. S. Monthly Notices_, Sup.; 1905.
+
+[Illustration: CHALD�AN BAKED BRICK OR TABLET, _Obverse and reverse
+sides_, Containing record of solar eclipse, 1062 B.C., used lately by
+Cowell for rendering the lunar theory more accurate than was possible
+by finest modern observations. (British Museum collection,
+No. 35908.)]
+
+[3] _R. A. S. Monthly Notices_, vol. x., p. 65.
+
+[4] R. S. E. Proc., vol. x., 1880.
+
+
+
+2. ANCIENT ASTRONOMY--THE CHINESE AND CHALD�ANS.
+
+
+The last section must have made clear the difficulties the way of
+assigning to the ancient nations their proper place in the development
+of primitive notions about astronomy. The fact that some alleged
+observations date back to a period before the Chinese had invented the
+art of writing leads immediately to the question how far tradition can
+be trusted.
+
+Our first detailed knowledge was gathered in the far East by
+travellers, and by the Jesuit priests, and was published in the
+eighteenth century. The Asiatic Society of Bengal contributed
+translations of Brahmin literature. The two principal sources of
+knowledge about Chinese astronomy were supplied, first by Father
+Souciet, who in 1729 published _Observations Astronomical,
+Geographical, Chronological, and Physical_, drawn from ancient
+Chinese books; and later by Father Moyriac-de-Mailla, who in 1777-1785
+published _Annals of the Chinese Empire, translated from
+Tong-Kien-Kang-Mou_.
+
+Bailly, in his _Astronomie Ancienne_ (1781), drew, from these and
+other sources, the conclusion that all we know of the astronomical
+learning of the Chinese, Indians, Chald�ans, Assyrians, and Egyptians
+is but the remnant of a far more complete astronomy of which no trace
+can be found.
+
+Delambre, in his _Histoire de l'Astronomie Ancienne_ (1817),
+ridicules the opinion of Bailly, and considers that the progress made
+by all of these nations is insignificant.
+
+It will be well now to give an idea of some of the astronomy of the
+ancients not yet entirely discredited.  China and Babylon may be taken
+as typical examples.
+
+_China_.--It would appear that Fohi, the first emperor, reigned
+about 2952 B.C., and shortly afterwards Yu-Chi made a sphere to
+represent the motions of the celestial bodies. It is also mentioned,
+in the book called Chu-King, supposed to have been written in 2205
+B.C., that a similar sphere was made in the time of Yao (2357
+B.C.).[1] It is said that the Emperor Chueni (2513 B.C.) saw five
+planets in conjunction the same day that the sun and moon were in
+conjunction. This is discussed by Father Martin (MSS. of De Lisle);
+also by M. Desvignolles (Mem. Acad. Berlin, vol. iii., p. 193), and by
+M. Kirsch (ditto, vol. v., p. 19), who both found that Mars, Jupiter,
+Saturn, and Mercury were all between the eleventh and eighteenth
+degrees of Pisces, all visible together in the evening on February
+28th 2446 B.C., while on the same day the sun and moon were in
+conjunction at 9 a.m., and that on March 1st the moon was in
+conjunction with the other four planets. But this needs confirmation.
+
+Yao, referred to above, gave instructions to his astronomers to
+determine the positions of the solstices and equinoxes, and they
+reported the names of the stars in the places occupied by the sun at
+these seasons, and in 2285 B.C. he gave them further orders. If this
+account be true, it shows a knowledge that the vault of heaven is a
+complete sphere, and that stars are shining at mid-day, although
+eclipsed by the sun's brightness.
+
+It is also asserted, in the book called _Chu-King_, that in the
+time of Yao the year was known to have 3651/4 days, and that he
+adopted 365 days and added an intercalary day every four years (as in
+the Julian Calendar). This may be true or not, but the ancient Chinese
+certainly seem to have divided the circle into 365 degrees. To learn
+the length of the year needed only patient observation--a
+characteristic of the Chinese; but many younger nations got into a
+terrible mess with their calendar from ignorance of the year's length.
+
+It is stated that in 2159 B.C. the royal astronomers Hi and Ho failed
+to predict an eclipse. It probably created great terror, for they were
+executed in punishment for their neglect. If this account be true, it
+means that in the twenty-second century B.C. some rule for calculating
+eclipses was in use. Here, again, patient observation would easily
+lead to the detection of the eighteen-year cycle known to the
+Chaldeans as the _Saros_. It consists of 235 lunations, and in
+that time the pole of the moon's orbit revolves just once round the
+pole of the ecliptic, and for this reason the eclipses in one cycle
+are repeated with very slight modification in the next cycle, and so
+on for many centuries.
+
+It may be that the neglect of their duties by Hi and Ho, and their
+punishment, influenced Chinese astronomy; or that the succeeding
+records have not been available to later scholars; but the fact
+remains that--although at long intervals observations were made of
+eclipses, comets, and falling stars, and of the position of the
+solstices, and of the obliquity of the ecliptic--records become rare,
+until 776 B.C., when eclipses began to be recorded once more with some
+approach to continuity. Shortly afterwards notices of comets were
+added. Biot gave a list of these, and Mr. John Williams, in 1871,
+published _Observations of Comets from 611 B.C. to 1640 A.D.,
+Extracted from the Chinese Annals_.
+
+With regard to those centuries concerning which we have no
+astronomical Chinese records, it is fair to state that it is recorded
+that some centuries before the Christian era, in the reign of
+Tsin-Chi-Hoang, all the classical and scientific books that could be
+found were ordered to be destroyed. If true, our loss therefrom is as
+great as from the burning of the Alexandrian library by the Caliph
+Omar. He burnt all the books because he held that they must be either
+consistent or inconsistent with the Koran, and in the one case they
+were superfluous, in the other case objectionable.
+
+_Chald�ans_.--Until the last half century historians were
+accustomed to look back upon the Greeks, who led the world from the
+fifth to the third century B.C., as the pioneers of art, literature,
+and science. But the excavations and researches of later years make us
+more ready to grant that in science as in art the Greeks only
+developed what they derived from the Egyptians, Babylonians, and
+Assyrians. The Greek historians said as much, in fact; and modern
+commentators used to attribute the assertion to undue modesty. Since,
+however, the records of the libraries have been unearthed it has been
+recognised that the Babylonians were in no way inferior in the matter
+of original scientific investigation to other races of the same era.
+
+The Chald�ans, being the most ancient Babylonians, held the same
+station and dignity in the State as did the priests in Egypt, and
+spent all their time in the study of philosophy and astronomy, and the
+arts of divination and astrology. They held that the world of which we
+have a conception is an eternal world without any beginning or ending,
+in which all things are ordered by rules supported by a divine
+providence, and that the heavenly bodies do not move by chance, nor by
+their own will, but by the determinate will and appointment of the
+gods. They recorded these movements, but mainly in the hope of tracing
+the will of the gods in mundane affairs. Ptolemy (about 130 A.D.)
+made use of Babylonian eclipses in the eighth century B.C. for
+improving his solar and lunar tables.
+
+Fragments of a library at Agade have been preserved at Nineveh, from
+which we learn that the star-charts were even then divided into
+constellations, which were known by the names which they bear to this
+day, and that the signs of the zodiac were used for determining the
+courses of the sun, moon, and of the five planets Mercury, Venus,
+Mars, Jupiter, and Saturn.
+
+We have records of observations carried on under Asshurbanapal, who
+sent astronomers to different parts to study celestial phenomena. Here
+is one:--
+
+To the Director of Observations,--My Lord, his humble servant
+Nabushum-iddin, Great Astronomer of Nineveh, writes thus: "May Nabu
+and Marduk be propitious to the Director of these Observations, my
+Lord. The fifteenth day we observed the Node of the moon, and the moon
+was eclipsed."
+
+The Phoenicians are supposed to have used the stars for navigation,
+but there are no records. The Egyptian priests tried to keep such
+astronomical knowledge as they possessed to themselves. It is probable
+that they had arbitrary rules for predicting eclipses. All that was
+known to the Greeks about Egyptian science is to be found in the
+writings of Diodorus Siculus. But confirmatory and more authentic
+facts have been derived from late explorations. Thus we learn from
+E. B. Knobel[2] about the Jewish calendar dates, on records of land
+sales in Aramaic papyri at Assuan, translated by Professor A. H. Sayce
+and A. E. Cowley, (1) that the lunar cycle of nineteen years was used
+by the Jews in the fifth century B.C. [the present reformed Jewish
+calendar dating from the fourth century A.D.], a date a "little more
+than a century after the grandfathers and great-grandfathers of those
+whose business is recorded had fled into Egypt with Jeremiah" (Sayce);
+and (2) that the order of intercalation at that time was not
+dissimilar to that in use at the present day.
+
+Then again, Knobel reminds us of "the most interesting discovery a few
+years ago by Father Strassmeier of a Babylonian tablet recording a
+partial lunar eclipse at Babylon in the seventh year of Cambyses, on
+the fourteenth day of the Jewish month Tammuz."  Ptolemy, in the
+Almagest (Suntaxis), says it occurred in the seventh year of Cambyses,
+on the night of the seventeenth and eighteenth of the Egyptian month
+Phamenoth.  Pingr� and Oppolzer fix the date July 16th, 533 B.C. Thus
+are the relations of the chronologies of Jews and Egyptians
+established by these explorations.
+
+
+FOOTNOTES:
+
+[1] These ancient dates are uncertain.
+
+[2] _R. A. S. Monthly Notices_, vol. lxviii., No. 5, March, 1908.
+
+
+
+3. ANCIENT GREEK ASTRONOMY.
+
+
+We have our information about the earliest Greek astronomy from
+Herodotus (born 480 B.C.). He put the traditions into writing. Thales
+(639-546 B.C.) is said to have predicted an eclipse, which caused much
+alarm, and ended the battle between the Medes and Lydians. Airy fixed
+the date May 28th, 585 B.C. But other modern astronomers give
+different dates. Thales went to Egypt to study science, and learnt
+from its priests the length of the year (which was kept a profound
+secret!), and the signs of the zodiac, and the positions of the
+solstices. He held that the sun, moon, and stars are not mere spots on
+the heavenly vault, but solids; that the moon derives her light from
+the sun, and that this fact explains her phases; that an eclipse of
+the moon happens when the earth cuts off the sun's light from her. He
+supposed the earth to be flat, and to float upon water. He determined
+the ratio of the sun's diameter to its orbit, and apparently made out
+the diameter correctly as half a degree. He left nothing in writing.
+
+His successors, Anaximander (610-547 B.C.) and Anaximenes (550-475
+B.C.), held absurd notions about the sun, moon, and stars, while
+Heraclitus (540-500 B.C.)  supposed that the stars were lighted each
+night like lamps, and the sun each morning. Parmenides supposed the
+earth to be a sphere.
+
+Pythagoras (569-470 B.C.) visited Egypt to study science. He deduced
+his system, in which the earth revolves in an orbit, from fantastic
+first principles, of which the following are examples: "The circular
+motion is the most perfect motion," "Fire is more worthy than earth,"
+"Ten is the perfect number." He wrote nothing, but is supposed to have
+said that the earth, moon, five planets, and fixed stars all revolve
+round the sun, which itself revolves round an imaginary central fire
+called the Antichthon. Copernicus in the sixteenth century claimed
+Pythagoras as the founder of the system which he, Copernicus, revived.
+
+Anaxagoras (born 499 B.C.) studied astronomy in Egypt. He explained
+the return of the sun to the east each morning by its going under the
+flat earth in the night. He held that in a solar eclipse the moon
+hides the sun, and in a lunar eclipse the moon enters the earth's
+shadow--both excellent opinions. But he entertained absurd ideas of
+the vortical motion of the heavens whisking stones into the sky, there
+to be ignited by the fiery firmament to form stars. He was prosecuted
+for this unsettling opinion, and for maintaining that the moon is an
+inhabited earth. He was defended by Pericles (432 B.C.).
+
+Solon dabbled, like many others, in reforms of the calendar. The
+common year of the Greeks originally had 360 days--twelve months of
+thirty days. Solon's year was 354 days. It is obvious that these
+erroneous years would, before long, remove the summer to January and
+the winter to July. To prevent this it was customary at regular
+intervals to intercalate days or months. Meton (432 B.C.) introduced a
+reform based on the nineteen-year cycle. This is not the same as the
+Egyptian and Chaldean eclipse cycle called _Saros_ of 223
+lunations, or a little over eighteen years.  The Metonic cycle is 235
+lunations or nineteen years, after which period the sun and moon
+occupy the same position relative to the stars. It is still used for
+fixing the date of Easter, the number of the year in Melon's cycle
+being the golden number of our prayer-books.  Melon's system divided
+the 235 lunations into months of thirty days and omitted every
+sixty-third day. Of the nineteen years, twelve had twelve months and
+seven had thirteen months.
+
+Callippus (330 B.C.) used a cycle four times as long, 940 lunations,
+but one day short of Melon's seventy-six years. This was more correct.
+
+Eudoxus (406-350 B.C.) is said to have travelled with Plato in
+Egypt. He made astronomical observations in Asia Minor, Sicily, and
+Italy, and described the starry heavens divided into constellations.
+His name is connected with a planetary theory which as generally
+stated sounds most fanciful. He imagined the fixed stars to be on a
+vault of heaven; and the sun, moon, and planets to be upon similar
+vaults or spheres, twenty-six revolving spheres in all, the motion of
+each planet being resolved into its components, and a separate sphere
+being assigned for each component motion. Callippus (330 B.C.)
+increased the number to thirty-three. It is now generally accepted
+that the real existence of these spheres was not suggested, but the
+idea was only a mathematical conception to facilitate the construction
+of tables for predicting the places of the heavenly bodies.
+
+Aristotle (384-322 B.C.) summed up the state of astronomical knowledge
+in his time, and held the earth to be fixed in the centre of the
+world.
+
+Nicetas, Heraclides, and Ecphantes supposed the earth to revolve on
+its axis, but to have no orbital motion.
+
+The short epitome so far given illustrates the extraordinary deductive
+methods adopted by the ancient Greeks. But they went much farther in
+the same direction. They seem to have been in great difficulty to
+explain how the earth is supported, just as were those who invented
+the myth of Atlas, or the Indians with the tortoise. Thales thought
+that the flat earth floated on water. Anaxagoras thought that, being
+flat, it would be buoyed up and supported on the air like a kite.
+Democritus thought it remained fixed, like the donkey between two
+bundles of hay, because it was equidistant from all parts of the
+containing sphere, and there was no reason why it should incline one
+way rather than another. Empedocles attributed its state of rest to
+centrifugal force by the rapid circular movement of the heavens, as
+water is stationary in a pail when whirled round by a string.
+Democritus further supposed that the inclination of the flat earth to
+the ecliptic was due to the greater weight of the southern parts owing
+to the exuberant vegetation.
+
+For further references to similar efforts of imagination the reader is
+referred to Sir George Cornwall Lewis's _Historical Survey of the
+Astronomy of the Ancients_; London, 1862. His list of authorities
+is very complete, but some of his conclusions are doubtful.  At p. 113
+of that work he records the real opinions of Socrates as set forth by
+Xenophon; and the reader will, perhaps, sympathise with Socrates in
+his views on contemporary astronomy:--
+
+With regard to astronomy he [Socrates] considered a knowledge of it
+desirable to the extent of determining the day of the year or month,
+and the hour of the night, ... but as to learning the courses of the
+stars, to be occupied with the planets, and to inquire about their
+distances from the earth, and their orbits, and the causes of their
+motions, he strongly objected to such a waste of valuable time. He
+dwelt on the contradictions and conflicting opinions of the physical
+philosophers, ... and, in fine, he held that the speculators on the
+universe and on the laws of the heavenly bodies were no better than
+madmen (_Xen. Mem_, i. 1, 11-15).
+
+Plato (born 429 B.C.), the pupil of Socrates, the fellow-student of
+Euclid, and a follower of Pythagoras, studied science in his travels
+in Egypt and elsewhere.  He was held in so great reverence by all
+learned men that a problem which he set to the astronomers was the
+keynote to all astronomical investigation from this date till the time
+of Kepler in the sixteenth century. He proposed to astronomers _the
+problem of representing the courses of the planets by circular and
+uniform motions_.
+
+Systematic observation among the Greeks began with the rise of the
+Alexandrian school. Aristillus and Timocharis set up instruments and
+fixed the positions of the zodiacal stars, near to which all the
+planets in their orbits pass, thus facilitating the determination of
+planetary motions. Aristarchus (320-250 B.C.) showed that the sun must
+be at least nineteen times as far off as the moon, which is far short
+of the mark. He also found the sun's diameter, correctly, to be half a
+degree.  Eratosthenes (276-196 B.C.) measured the inclination to the
+equator of the sun's apparent path in the heavens--i.e., he
+measured the obliquity of the ecliptic, making it 23� 51', confirming
+our knowledge of its continuous diminution during historical times. He
+measured an arc of meridian, from Alexandria to Syene (Assuan), and
+found the difference of latitude by the length of a shadow at noon,
+summer solstice. He deduced the diameter of the earth, 250,000
+stadia. Unfortunately, we do not know the length of the stadium he
+used.
+
+Hipparchus (190-120 B.C.) may be regarded as the founder of
+observational astronomy. He measured the obliquity of the ecliptic,
+and agreed with Eratosthenes.  He altered the length of the tropical
+year from 365 days, 6 hours to 365 days, 5 hours, 53 minutes--still
+four minutes too much. He measured the equation of time and the
+irregular motion of the sun; and allowed for this in his calculations
+by supposing that the centre, about which the sun moves uniformly, is
+situated a little distance from the fixed earth. He called this point
+the _excentric_. The line from the earth to the "excentric" was
+called the _line of apses_. A circle having this centre was
+called the _equant_, and he supposed that a radius drawn to the
+sun from the excentric passes over equal arcs on the equant in equal
+times. He then computed tables for predicting the place of the sun.
+
+He proceeded in the same way to compute Lunar tables. Making use of
+Chald�an eclipses, he was able to get an accurate value of the moon's
+mean motion.  [Halley, in 1693, compared this value with his own
+measurements, and so discovered the acceleration of the moon's mean
+motion. This was conclusively established, but could not be explained
+by the Newtonian theory for quite a long time.] He determined the
+plane of the moon's orbit and its inclination to the ecliptic. The
+motion of this plane round the pole of the ecliptic once in eighteen
+years complicated the problem. He located the moon's excentric as he
+had done the sun's.  He also discovered some of the minor
+irregularities of the moon's motion, due, as Newton's theory proves,
+to the disturbing action of the sun's attraction.
+
+In the year 134 B.C. Hipparchus observed a new star.  This upset every
+notion about the permanence of the fixed stars. He then set to work to
+catalogue all the principal stars so as to know if any others appeared
+or disappeared. Here his experiences resembled those of several later
+astronomers, who, when in search of some special object, have been
+rewarded by a discovery in a totally different direction. On comparing
+his star positions with those of Timocharis and Aristillus he found no
+stars that had appeared or disappeared in the interval of 150 years;
+but he found that all the stars seemed to have changed their places
+with reference to that point in the heavens where the ecliptic is 90�
+from the poles of the earth--i.e., the equinox. He found that this
+could be explained by a motion of the equinox in the direction of the
+apparent diurnal motion of the stars. This discovery of _precession of
+the equinoxes_, which takes place at the rate of 52".1 every year, was
+necessary for the progress of accurate astronomical observations. It
+is due to a steady revolution of the earth's pole round the pole of
+the ecliptic once in 26,000 years in the opposite direction to the
+planetary revolutions.
+
+Hipparchus was also the inventor of trigonometry, both plane and
+spherical. He explained the method of using eclipses for determining
+the longitude.
+
+In connection with Hipparchus' great discovery it may be mentioned
+that modern astronomers have often attempted to fix dates in history
+by the effects of precession of the equinoxes. (1) At about the date
+when the Great Pyramid may have been built gamma Draconis was near to the
+pole, and must have been used as the pole-star. In the north face of
+the Great Pyramid is the entrance to an inclined passage, and six of
+the nine pyramids at Gizeh possess the same feature; all the passages
+being inclined at an angle between 26� and 27� to the horizon and in
+the plane of the meridian. It also appears that 4,000 years
+ago--i.e., about 2100 B.C.--an observer at the lower end of the
+passage would be able to see gamma Draconis, the then pole-star, at its
+lower culmination.[1] It has been suggested that the passage was made
+for this purpose. On other grounds the date assigned to the Great
+Pyramid is 2123 B.C.
+
+(2) The Chald�ans gave names to constellations now invisible from
+Babylon which would have been visible in 2000 B.C., at which date it
+is claimed that these people were studying astronomy.
+
+(3) In the Odyssey, Calypso directs Odysseus, in accordance with
+Phoenician rules for navigating the Mediterranean, to keep the Great
+Bear "ever on the left as he traversed the deep" when sailing from the
+pillars of Hercules (Gibraltar) to Corfu. Yet such a course taken now
+would land the traveller in Africa.  Odysseus is said in his voyage in
+springtime to have seen the Pleiades and Arcturus setting late, which
+seemed to early commentators a proof of Homer's inaccuracy.  Likewise
+Homer, both in the _Odyssey_ [2] (v. 272-5) and in the _Iliad_
+(xviii. 489), asserts that the Great Bear never set in those
+latitudes. Now it has been found that the precession of the equinoxes
+explains all these puzzles; shows that in springtime on the
+Mediterranean the Bear was just above the horizon, near the sea but
+not touching it, between 750 B.C. and 1000 B.C.; and fixes the date of
+the poems, thus confirming other evidence, and establishing Homer's
+character for accuracy. [3]
+
+(4) The orientation of Egyptian temples and Druidical stones is such
+that possibly they were so placed as to assist in the observation of
+the heliacal risings [4] of certain stars. If the star were known,
+this would give an approximate date. Up to the present the results of
+these investigations are far from being conclusive.
+
+Ptolemy (130 A.D.) wrote the Suntaxis, or Almagest, which includes a
+cyclopedia of astronomy, containing a summary of knowledge at that
+date. We have no evidence beyond his own statement that he was a
+practical observer. He theorised on the planetary motions, and held
+that the earth is fixed in the centre of the universe. He adopted the
+excentric and equant of Hipparchus to explain the unequal motions of
+the sun and moon. He adopted the epicycles and deferents which had
+been used by Apollonius and others to explain the retrograde motions
+of the planets. We, who know that the earth revolves round the sun
+once in a year, can understand that the apparent motion of a planet is
+only its motion relative to the earth. If, then, we suppose the earth
+fixed and the sun to revolve round it once a year, and the planets
+each in its own period, it is only necessary to impose upon each of
+these an additional _annual_ motion to enable us to represent truly
+the apparent motions. This way of looking at the apparent motions
+shows why each planet, when nearest to the earth, seems to move for a
+time in a retrograde direction. The attempts of Ptolemy and others of
+his time to explain the retrograde motion in this way were only
+approximate. Let us suppose each planet to have a bar with one end
+centred at the earth.  If at the other end of the bar one end of a
+shorter bar is pivotted, having the planet at its other end, then the
+planet is given an annual motion in the secondary circle (the
+epicycle), whose centre revolves round the earth on the primary circle
+(the _deferent_), at a uniform rate round the excentric. Ptolemy
+supposed the centres of the epicycles of Mercury and Venus to be on a
+bar passing through the sun, and to be between the earth and the
+sun. The centres of the epicycles of Mars, Jupiter, and Saturn were
+supposed to be further away than the sun.  Mercury and Venus were
+supposed to revolve in their epicycles in their own periodic times and
+in the deferent round the earth in a year. The major planets were
+supposed to revolve in the deferent round the earth in their own
+periodic times, and in their epicycles once in a year.
+
+It did not occur to Ptolemy to place the centres of the epicycles of
+Mercury and Venus at the sun, and to extend the same system to the
+major planets. Something of this sort had been proposed by the
+Egyptians (we are told by Cicero and others), and was accepted by
+Tycho Brahe; and was as true a representation of the relative motions
+in the solar system as when we suppose the sun to be fixed and the
+earth to revolve.
+
+The cumbrous system advocated by Ptolemy answered its purpose,
+enabling him to predict astronomical events approximately. He improved
+the lunar theory considerably, and discovered minor inequalities which
+could be allowed for by the addition of new epicycles.  We may look
+upon these epicycles of Apollonius, and the excentric of Hipparchus,
+as the responses of these astronomers to the demand of Plato for
+uniform circular motions. Their use became more and more confirmed,
+until the seventeenth century, when the accurate observations of Tycho
+Brahe enabled Kepler to abolish these purely geometrical makeshifts,
+and to substitute a system in which the sun became physically its
+controller.
+
+
+FOOTNOTES:
+
+[1] _Phil. Mag_., vol. xxiv., pp. 481-4.
+
+[2]
+
+Plaeiadas t' esoronte kai opse duonta bootaen
+'Arkton th' aen kai amaxan epiklaesin kaleousin,
+'Ae t' autou strephetai kai t' Oriona dokeuei,
+Oin d'ammoros esti loetron Okeanoio.
+
+"The Pleiades and Bo�tes that setteth late, and the Bear,
+which they likewise call the Wain, which turneth ever in one
+place, and keepeth watch upon Orion, and alone hath no part in
+the baths of the ocean."
+
+[3] See Pearson in the Camb. Phil. Soc. Proc., vol. iv., pt. ii., p.
+93, on whose authority the above statements are made.
+
+[4] See p. 6 for definition.
+
+
+
+4. THE REIGN OF EPICYCLES--FROM PTOLEMY TO COPERNICUS.
+
+
+After Ptolemy had published his book there seemed to be nothing more
+to do for the solar system except to go on observing and finding more
+and more accurate values for the constants involved--viz., the periods
+of revolution, the diameter of the deferent,[1] and its ratio to that
+of the epicycle,[2] the distance of the excentric[3] from the centre
+of the deferent, and the position of the line of apses,[4] besides the
+inclination and position of the plane of the planet's orbit. The only
+object ever aimed at in those days was to prepare tables for
+predicting the places of the planets. It was not a mechanical problem;
+there was no notion of a governing law of forces.
+
+From this time onwards all interest in astronomy seemed, in Europe at
+least, to sink to a low ebb.  When the Caliph Omar, in the middle of
+the seventh century, burnt the library of Alexandria, which had been
+the centre of intellectual progress, that centre migrated to Baghdad,
+and the Arabs became the leaders of science and philosophy. In
+astronomy they made careful observations. In the middle of the ninth
+century Albategnius, a Syrian prince, improved the value of
+excentricity of the sun's orbit, observed the motion of the moon's
+apse, and thought he detected a smaller progression of the sun's
+apse. His tables were much more accurate than Ptolemy's. Abul Wefa, in
+the tenth century, seems to have discovered the moon's "variation."
+Meanwhile the Moors were leaders of science in the west, and Arzachel
+of Toledo improved the solar tables very much. Ulugh Begh, grandson of
+the great Tamerlane the Tartar, built a fine observatory at Samarcand
+in the fifteenth century, and made a great catalogue of stars, the
+first since the time of Hipparchus.
+
+At the close of the fifteenth century King Alphonso of Spain employed
+computers to produce the Alphonsine Tables (1488 A.D.), Purbach
+translated Ptolemy's book, and observations were carried out in
+Germany by M�ller, known as Regiomontanus, and Waltherus.
+
+Nicolai Copernicus, a Sclav, was born in 1473 at Thorn, in Polish
+Prussia. He studied at Cracow and in Italy. He was a priest, and
+settled at Frauenberg.  He did not undertake continuous observations,
+but devoted himself to simplifying the planetary systems and devising
+means for more accurately predicting the positions of the sun, moon,
+and planets. He had no idea of framing a solar system on a dynamical
+basis.  His great object was to increase the accuracy of the
+calculations and the tables. The results of his cogitations were
+printed just before his death in an interesting book, _De
+Revolutionibus Orbium Celestium_. It is only by careful reading of
+this book that the true position of Copernicus can be realised. He
+noticed that Nicetas and others had ascribed the apparent diurnal
+rotation of the heavens to a real daily rotation of the earth about
+its axis, in the opposite direction to the apparent motion of the
+stars. Also in the writings of Martianus Capella he learnt that the
+Egyptians had supposed Mercury and Venus to revolve round the sun, and
+to be carried with him in his annual motion round the earth. He
+noticed that the same supposition, if extended to Mars, Jupiter, and
+Saturn, would explain easily why they, and especially Mars, seem so
+much brighter in opposition.  For Mars would then be a great deal
+nearer to the earth than at other times. It would also explain the
+retrograde motion of planets when in opposition.
+
+We must here notice that at this stage Copernicus was actually
+confronted with the system accepted later by Tycho Brahe, with the
+earth fixed. But he now recalled and accepted the views of Pythagoras
+and others, according to which the sun is fixed and the earth
+revolves; and it must be noted that, geometrically, there is no
+difference of any sort between the Egyptian or Tychonic system and
+that of Pythagoras as revived by Copernicus, except that on the latter
+theory the stars ought to seem to move when the earth changes its
+position--a test which failed completely with the rough means of
+observation then available. The radical defect of all solar systems
+previous to the time of Kepler (1609 A.D.) was the slavish yielding to
+Plato's dictum demanding uniform circular motion for the planets, and
+the consequent evolution of the epicycle, which was fatal to any
+conception of a dynamical theory.
+
+Copernicus could not sever himself from this obnoxious tradition.[5]
+It is true that neither the Pythagorean nor the Egypto-Tychonic system
+required epicycles for explaining retrograde motion, as the Ptolemaic
+theory did. Furthermore, either system could use the excentric of
+Hipparchus to explain the irregular motion known as the equation of
+the centre.  But Copernicus remarked that he could also use an
+epicycle for this purpose, or that he could use both an excentric and
+an epicycle for each planet, and so bring theory still closer into
+accord with observation. And this he proceeded to do.[6] Moreover,
+observers had found irregularities in the moon's motion, due, as we
+now know, to the disturbing attraction of the sun.  To correct for
+these irregularities Copernicus introduced epicycle on epicycle in the
+lunar orbit.
+
+This is in its main features the system propounded by Copernicus. But
+attention must, to state the case fully, be drawn to two points to be
+found in his first and sixth books respectively. The first point
+relates to the seasons, and it shows a strange ignorance of the laws
+of rotating bodies. To use the words of Delambre,[7] in drawing
+attention to the strange conception,
+
+  he imagined that the earth, revolving round the sun, ought always to
+  show to it the same face; the contrary phenomena surprised him: to
+  explain them he invented a third motion, and added it to the two
+  real motions (rotation and orbital revolution). By this third motion
+  the earth, he held, made a revolution on itself and on the poles of
+  the ecliptic once a year ... Copernicus did not know that motion in
+  a straight line is the natural motion, and that motion in a curve is
+  the resultant of several movements. He believed, with Aristotle,
+  that circular motion was the natural one.
+
+Copernicus made this rotation of the earth's axis about the pole of
+the ecliptic retrograde (i.e., opposite to the orbital revolution),
+and by making it perform more than one complete revolution in a year,
+the added part being 1/26000 of the whole, he was able to include the
+precession of the equinoxes in his explanation of the seasons. His
+explanation of the seasons is given on leaf 10 of his book (the pages
+of this book are not all numbered, only alternate pages, or leaves).
+
+In his sixth book he discusses the inclination of the planetary orbits
+to the ecliptic. In regard to this the theory of Copernicus is unique;
+and it will be best to explain this in the words of Grant in his great
+work.[8] He says:--
+
+  Copernicus, as we have already remarked, did not attack the
+  principle of the epicyclical theory: he merely sought to make it
+  more simple by placing the centre of the earth's orbit in the centre
+  of the universe. This was the point to which the motions of the
+  planets were referred, for the planes of their orbits were made to
+  pass through it, and their points of least and greatest velocities
+  were also determined with reference to it.  By this arrangement the
+  sun was situate mathematically near the centre of the planetary
+  system, but he did not appear to have any physical connexion with
+  the planets as the centre of their motions.
+
+According to Copernicus' sixth book, the planes of the planetary
+orbits do not pass through the sun, and the lines of apses do not pass
+through to the sun.
+
+Such was the theory advanced by Copernicus: The earth moves in an
+epicycle, on a deferent whose centre is a little distance from the
+sun. The planets move in a similar way on epicycles, but their
+deferents have no geometrical or physical relation to the sun. The
+moon moves on an epicycle centred on a second epicycle, itself centred
+on a deferent, excentric to the earth.  The earth's axis rotates about
+the pole of the ecliptic, making one revolution and a twenty-six
+thousandth part of a revolution in the sidereal year, in the opposite
+direction to its orbital motion.
+
+In view of this fanciful structure it must be noted, in fairness to
+Copernicus, that he repeatedly states that the reader is not obliged
+to accept his system as showing the real motions; that it does not
+matter whether they be true, even approximately, or not, so long as
+they enable us to compute tables from which the places of the planets
+among the stars can be predicted.[9] He says that whoever is not
+satisfied with this explanation must be contented by being told that
+"mathematics are for mathematicians" (Mathematicis mathematica
+scribuntur).
+
+At the same time he expresses his conviction over and over again that
+the earth is in motion. It is with him a pious belief, just as it was
+with Pythagoras and his school and with Aristarchus. "But" (as Dreyer
+says in his most interesting book, _Tycho Brahe_) "proofs of the
+physical truth of his system Copernicus had given none, and could give
+none," any more than Pythagoras or Aristarchus.
+
+There was nothing so startlingly simple in his system as to lead the
+cautious astronomer to accept it, as there was in the later Keplerian
+system; and the absence of parallax in the stars seemed to condemn his
+system, which had no physical basis to recommend it, and no
+simplification at all over the Egypto-Tychonic system, to which
+Copernicus himself drew attention. It has been necessary to devote
+perhaps undue space to the interesting work of Copernicus, because by
+a curious chance his name has become so widely known. He has been
+spoken of very generally as the founder of the solar system that is
+now accepted. This seems unfair, and on reading over what has been
+written about him at different times it will be noticed that the
+astronomers--those who have evidently read his great book--are very
+cautious in the words with which they eulogise him, and refrain from
+attributing to him the foundation of our solar system, which is
+entirely due to Kepler.  It is only the more popular writers who give
+the idea that a revolution had been effected when Pythagoras' system
+was revived, and when Copernicus supported his view that the earth
+moves and is not fixed.
+
+It may be easy to explain the association of the name of Copernicus
+with the Keplerian system. But the time has long passed when the
+historian can support in any way this popular error, which was started
+not by astronomers acquainted with Kepler's work, but by those who
+desired to put the Church in the wrong by extolling Copernicus.
+
+Copernicus dreaded much the abuse he expected to receive from
+philosophers for opposing the authority of Aristotle, who had declared
+that the earth was fixed.  So he sought and obtained the support of
+the Church, dedicating his great work to Pope Paul III. in a lengthy
+explanatory epistle. The Bishop of Cracow set up a memorial tablet in
+his honour.
+
+Copernicus was the most refined exponent, and almost the last
+representative, of the Epicyclical School.  As has been already
+stated, his successor, Tycho Brahe, supported the same use of
+epicycles and excentrics as Copernicus, though he held the earth to be
+fixed. But Tycho Brahe was eminently a practical observer, and took
+little part in theory; and his observations formed so essential a
+portion of the system of Kepler that it is only fair to include his
+name among these who laid the foundations of the solar system which we
+accept to-day.
+
+In now taking leave of the system of epicycles let it be remarked that
+it has been held up to ridicule more than it deserves. On reading
+Airy's account of epicycles, in the beautifully clear language of his
+_Six Lectures on Astronomy_, the impression is made that the
+jointed bars there spoken of for describing the circles were supposed
+to be real. This is no more the case than that the spheres of Eudoxus
+and Callippus were supposed to be real. Both were introduced only to
+illustrate the mathematical conception upon which the solar,
+planetary, and lunar tables were constructed.  The epicycles
+represented nothing more nor less than the first terms in the Fourier
+series, which in the last century has become a basis of such
+calculations, both in astronomy and physics generally.
+
+[Illustration: "QUADRANS MURALIS SIVE TICHONICUS."  With portrait of
+Tycho Brahe, instruments, etc., painted on the wall; showing
+assistants using the sight, watching the clock, and recording.  (From
+the author's copy of the _Astronomi� Instaurat� Mechanica._)]
+
+
+FOOTNOTES:
+
+[1] For definition see p. 22.
+
+[2] _Ibid_.
+
+[3] For definition see p. 18.
+
+[4] For definition see p. 18.
+
+[5] In his great book Copernicus says: "The movement of the heavenly
+bodies is uniform, circular, perpetual, or else composed of circular
+movements." In this he proclaimed himself a follower of Pythagoras
+(see p. 14), as also when he says: "The world is spherical because the
+sphere is, of all figures, the most perfect" (Delambre,
+_Ast. Mod. Hist_., pp. 86, 87).
+
+[6] Kepler tells us that Tycho Brahe was pleased with this
+device, and adapted it to his own system.
+
+[7] _Hist. Ast._, vol. i., p. 354.
+
+[8] _Hist. of Phys. Ast._, p. vii.
+
+[9] "Est enim Astronomi proprium, historiam motuum coelestium
+diligenti et artificiosa observatione colligere. Deinde causas
+earundem, seu hypotheses, cum veras assequi nulla ratione possit
+... Neque enim necesse est, eas hypotheses esse veras, imo ne
+verisimiles quidem, sed sufficit hoc usum, si calculum observationibus
+congruentem exhibeant."
+
+
+
+
+BOOK II. THE DYNAMICAL PERIOD
+
+
+
+5. DISCOVERY OF THE TRUE SOLAR SYSTEM--TYCHO BRAHE--KEPLER.
+
+
+During the period of the intellectual and aesthetic revival, at the
+beginning of the sixteenth century, the "spirit of the age" was
+fostered by the invention of printing, by the downfall of the
+Byzantine Empire, and the scattering of Greek fugitives, carrying the
+treasures of literature through Western Europe, by the works of
+Raphael and Michael Angelo, by the Reformation, and by the extension
+of the known world through the voyages of Spaniards and Portuguese.
+During that period there came to the front the founder of accurate
+observational astronomy. Tycho Brahe, a Dane, born in 1546 of noble
+parents, was the most distinguished, diligent, and accurate observer
+of the heavens since the days of Hipparchus, 1,700 years before.
+
+Tycho was devoted entirely to his science from childhood, and the
+opposition of his parents only stimulated him in his efforts to
+overcome difficulties.  He soon grasped the hopelessness of the old
+deductive methods of reasoning, and decided that no theories ought to
+be indulged in until preparations had been made by the accumulation of
+accurate observations.  We may claim for him the title of founder of
+the inductive method.
+
+For a complete life of this great man the reader is referred to
+Dreyer's _Tycho Brahe_, Edinburgh, 1890, containing a complete
+bibliography. The present notice must be limited to noting the work
+done, and the qualities of character which enabled him to attain his
+scientific aims, and which have been conspicuous in many of his
+successors.
+
+He studied in Germany, but King Frederick of Denmark, appreciating his
+great talents, invited him to carry out his life's work in that
+country. He granted to him the island of Hveen, gave him a pension,
+and made him a canon of the Cathedral of Roskilde. On that island
+Tycho Brahe built the splendid observatory which he called Uraniborg,
+and, later, a second one for his assistants and students, called
+Stjerneborg. These he fitted up with the most perfect instruments, and
+never lost a chance of adding to his stock of careful observations.[1]
+
+The account of all these instruments and observations, printed at his
+own press on the island, was published by Tycho Brahe himself, and the
+admirable and numerous engravings bear witness to the excellence of
+design and the stability of his instruments.
+
+His mechanical skill was very great, and in his workmanship he was
+satisfied with nothing but the best. He recognised the importance of
+rigidity in the instruments, and, whereas these had generally been
+made of wood, he designed them in metal. His instruments included
+armillae like those which had been used in Alexandria, and other
+armillae designed by himself--sextants, mural quadrants, large
+celestial globes and various instruments for special purposes. He
+lived before the days of telescopes and accurate clocks. He invented
+the method of sub-dividing the degrees on the arc of an instrument by
+transversals somewhat in the way that Pedro Nunez had proposed.
+
+He originated the true system of observation and reduction of
+observations, recognising the fact that the best instrument in the
+world is not perfect; and with each of his instruments he set to work
+to find out the errors of graduation and the errors of mounting, the
+necessary correction being applied to each observation.
+
+When he wanted to point his instrument exactly to a star he was
+confronted with precisely the same difficulty as is met in gunnery and
+rifle-shooting. The sights and the object aimed at cannot be in focus
+together, and a great deal depends on the form of sight. Tycho Brahe
+invented, and applied to the pointers of his instruments, an
+aperture-sight of variable area, like the iris diaphragm used now in
+photography. This enabled him to get the best result with stars of
+different brightness.  The telescope not having been invented, he
+could not use a telescopic-sight as we now do in gunnery.  This not
+only removes the difficulty of focussing, but makes the minimum
+visible angle smaller. Helmholtz has defined the minimum angle
+measurable with the naked eye as being one minute of arc. In view of
+this it is simply marvellous that, when the positions of Tycho's
+standard stars are compared with the best modern catalogues, his
+probable error in right ascension is only � 24", 1, and in declination
+only � 25", 9.
+
+Clocks of a sort had been made, but Tycho Brahe found them so
+unreliable that he seldom used them, and many of his position-measurements
+were made by measuring the angular distances from known stars.
+
+Taking into consideration the absence of either a telescope or a
+clock, and reading his account of the labour he bestowed upon each
+observation, we must all agree that Kepler, who inherited these
+observations in MS., was justified, under the conditions then
+existing, in declaring that there was no hope of anyone ever improving
+upon them.
+
+In the year 1572, on November 11th, Tycho discovered in Cassiopeia a
+new star of great brilliance, and continued to observe it until the
+end of January, 1573. So incredible to him was such an event that he
+refused to believe his own eyes until he got others to confirm what he
+saw. He made accurate observations of its distance from the nine
+principal stars in Casseiopeia, and proved that it had no measurable
+parallax. Later he employed the same method with the comets of 1577,
+1580, 1582, 1585, 1590, 1593, and 1596, and proved that they too had
+no measurable parallax and must be very distant.
+
+The startling discovery that stars are not necessarily permanent, that
+new stars may appear, and possibly that old ones may disappear, had
+upon him exactly the same effect that a similar occurrence had upon
+Hipparchus 1,700 years before. He felt it his duty to catalogue all
+the principal stars, so that there should be no mistake in the
+future. During the construction of his catalogue of 1,000 stars he
+prepared and used accurate tables of refraction deduced from his own
+observations. Thus he eliminated (so far as naked eye observations
+required) the effect of atmospheric refraction which makes the
+altitude of a star seem greater than it really is.
+
+Tycho Brahe was able to correct the lunar theory by his observations.
+Copernicus had introduced two epicycles on the lunar orbit in the hope
+of obtaining a better accordance between theory and observation; and
+he was not too ambitious, as his desire was to get the tables accurate
+to ten minutes. Tycho Brahe found that the tables of Copernicus were
+in error as much as two degrees. He re-discovered the inequality
+called "variation" by observing the moon in all phases--a thing which
+had not been attended to. [It is remarkable that in the nineteenth
+century Sir George Airy established an altazimuth at Greenwich
+Observatory with this special object, to get observations of the moon
+in all phases.] He also discovered other lunar equalities, and wanted
+to add another epicycle to the moon's orbit, but he feared that these
+would soon become unmanageable if further observations showed more new
+inequalities.
+
+But, as it turned out, the most fruitful work of Tycho Brahe was on
+the motions of the planets, and especially of the planet Mars, for it
+was by an examination of these results that Kepler was led to the
+discovery of his immortal laws.
+
+After the death of King Frederick the observatories of Tycho Brahe
+were not supported. The gigantic power and industry displayed by this
+determined man were accompanied, as often happens, by an overbearing
+manner, intolerant of obstacles. This led to friction, and eventually
+the observatories were dismantled, and Tycho Brahe was received by the
+Emperor Rudolph II., who placed a house in Prague at his disposal.
+Here he worked for a few years, with Kepler as one of his assistants,
+and he died in the year 1601.
+
+It is an interesting fact that Tycho Brahe had a firm conviction that
+mundane events could be predicted by astrology, and that this belief
+was supported by his own predictions.
+
+It has already been stated that Tycho Brahe maintained that
+observation must precede theory. He did not accept the Copernican
+theory that the earth moves, but for a working hypothesis he used a
+modification of an old Egyptian theory, mathematically identical with
+that of Copernicus, but not involving a stellar parallax.  He says
+(_De Mundi_, etc.) that
+
+  the Ptolemean system was too complicated, and the new one which that
+  great man Copernicus had proposed, following in the footsteps of
+  Aristarchus of Samos, though there was nothing in it contrary to
+  mathematical principles, was in opposition to those of physics, as
+  the heavy and sluggish earth is unfit to move, and the system is
+  even opposed to the authority of Scripture. The absence of annual
+  parallax further involves an incredible distance between the
+  outermost planet and the fixed stars.
+
+We are bound to admit that in the circumstances of the case, so long
+as there was no question of dynamical forces connecting the members of
+the solar system, his reasoning, as we should expect from such a man,
+is practical and sound. It is not surprising, then, that astronomers
+generally did not readily accept the views of Copernicus, that Luther
+(Luther's _Tischreden_, pp.  22, 60) derided him in his usual pithy
+manner, that Melancthon (_Initia doctrinae physicae_) said that
+Scripture, and also science, are against the earth's motion; and that
+the men of science whose opinion was asked for by the cardinals (who
+wished to know whether Galileo was right or wrong) looked upon
+Copernicus as a weaver of fanciful theories.
+
+Johann Kepler is the name of the man whose place, as is generally
+agreed, would have been the most difficult to fill among all those who
+have contributed to the advance of astronomical knowledge. He was born
+at Wiel, in the Duchy of Wurtemberg, in 1571. He held an appointment
+at Gratz, in Styria, and went to join Tycho Brahe in Prague, and to
+assist in reducing his observations. These came into his possession
+when Tycho Brahe died, the Emperor Rudolph entrusting to him the
+preparation of new tables (called the Rudolphine tables) founded on
+the new and accurate observations. He had the most profound respect
+for the knowledge, skill, determination, and perseverance of the man
+who had reaped such a harvest of most accurate data; and though Tycho
+hardly recognised the transcendent genius of the man who was working
+as his assistant, and although there were disagreements between them,
+Kepler held to his post, sustained by the conviction that, with these
+observations to test any theory, he would be in a position to settle
+for ever the problem of the solar system.
+
+[Illustration: PORTRAIT OF JOHANNES KEPLER.  By F. Wanderer, from
+Reitlinger's "Johannes Kepler" (original in Strassburg).]
+
+It has seemed to many that Plato's demand for uniform circular motion
+(linear or angular) was responsible for a loss to astronomy of good
+work during fifteen hundred years, for a hundred ill-considered
+speculative cosmogonies, for dissatisfaction, amounting to disgust,
+with these _� priori_ guesses, and for the relegation of the
+science to less intellectual races than Greeks and other Europeans.
+Nobody seemed to dare to depart from this fetish of uniform angular
+motion and circular orbits until the insight, boldness, and
+independence of Johann Kepler opened up a new world of thought and of
+intellectual delight.
+
+While at work on the Rudolphine tables he used the old epicycles and
+deferents and excentrics, but he could not make theory agree with
+observation. His instincts told him that these apologists for uniform
+motion were a fraud; and he proved it to himself by trying every
+possible variation of the elements and finding them fail.  The number
+of hypotheses which he examined and rejected was almost incredible
+(for example, that the planets turn round centres at a little distance
+from the sun, that the epicycles have centres at a little distance
+from the deferent, and so on). He says that, after using all these
+devices to make theory agree with Tycho's observations, he still found
+errors amounting to eight minutes of a degree. Then he said boldly
+that it was impossible that so good an observer as Tycho could have
+made a mistake of eight minutes, and added: "Out of these eight
+minutes we will construct a new theory that will explain the motions
+of all the planets." And he did it, with elliptic orbits having the
+sun in a focus of each.[2]
+
+It is often difficult to define the boundaries between fancies,
+imagination, hypothesis, and sound theory.  This extraordinary genius
+was a master in all these modes of attacking a problem. His analogy
+between the spaces occupied by the five regular solids and the
+distances of the planets from the sun, which filled him with so much
+delight, was a display of pure fancy. His demonstration of the three
+fundamental laws of planetary motion was the most strict and complete
+theory that had ever been attempted.
+
+It has been often suggested that the revival by Copernicus of the
+notion of a moving earth was a help to Kepler. No one who reads
+Kepler's great book could hold such an opinion for a moment. In fact,
+the excellence of Copernicus's book helped to prolong the life of the
+epicyclical theories in opposition to Kepler's teaching.
+
+All of the best theories were compared by him with observation. These
+were the Ptolemaic, the Copernican, and the Tychonic. The two latter
+placed all of the planetary orbits concentric with one another, the
+sun being placed a little away from their common centre, and having no
+apparent relation to them, and being actually outside the planes in
+which they move.  Kepler's first great discovery was that the planes
+of all the orbits pass through the sun; his second was that the line
+of apses of each planet passes through the sun; both were
+contradictory to the Copernican theory.
+
+He proceeds cautiously with his propositions until he arrives at his
+great laws, and he concludes his book by comparing observations of
+Mars, of all dates, with his theory.
+
+His first law states that the planets describe ellipses with the sun
+at a focus of each ellipse.
+
+His second law (a far more difficult one to prove) states that a line
+drawn from a planet to the sun sweeps over equal areas in equal
+times. These two laws were published in his great work, _Astronomia
+Nova, sen.  Physica Coelestis tradita commentariis de Motibus Stelloe;
+Martis_, Prague, 1609.
+
+It took him nine years more[3] to discover his third law, that the
+squares of the periodic times are proportional to the cubes of the
+mean distances from the sun.
+
+These three laws contain implicitly the law of universal
+gravitation. They are simply an alternative way of expressing that law
+in dealing with planets, not particles. Only, the power of the
+greatest human intellect is so utterly feeble that the meaning of the
+words in Kepler's three laws could not be understood until expounded
+by the logic of Newton's dynamics.
+
+The joy with which Kepler contemplated the final demonstration of
+these laws, the evolution of which had occupied twenty years, can
+hardly be imagined by us.  He has given some idea of it in a passage
+in his work on _Harmonics_, which is not now quoted, only lest
+someone might say it was egotistical--a term which is simply grotesque
+when applied to such a man with such a life's work accomplished.
+
+The whole book, _Astronomia Nova_, is a pleasure to read; the
+mass of observations that are used, and the ingenuity of the
+propositions, contrast strongly with the loose and imperfectly
+supported explanations of all his predecessors; and the indulgent
+reader will excuse the devotion of a few lines to an example of the
+ingenuity and beauty of his methods.
+
+It may seem a hopeless task to find out the true paths of Mars and the
+earth (at that time when their shape even was not known) from the
+observations giving only the relative direction from night to
+night. Now, Kepler had twenty years of observations of Mars to deal
+with. This enabled him to use a new method, to find the earth's
+orbit. Observe the date at any time when Mars is in opposition. The
+earth's position E at that date gives the longitude of Mars M. His
+period is 687 days. Now choose dates before and after the principal
+date at intervals of 687 days and its multiples.  Mars is in each case
+in the same position. Now for any date when Mars is at M and the earth
+at E3 the date of the year gives the angle E3SM. And the
+observation of Tycho gives the direction of Mars compared with the
+sun, SE3M. So all the angles of the triangle SEM in any of these
+positions of E are known, and also the ratios of SE1, SE2, SE3,
+SE4 to SM and to each other.
+
+For the orbit of Mars observations were chosen at intervals of a year,
+when the earth was always in the same place.
+
+[Illustration]
+
+But Kepler saw much farther than the geometrical facts. He realised
+that the orbits are followed owing to a force directed to the sun; and
+he guessed that this is the same force as the gravity that makes a
+stone fall. He saw the difficulty of gravitation acting through the
+void space.  He compared universal gravitation to magnetism, and
+speaks of the work of Gilbert of Colchester.  (Gilbert's book, _De
+Mundo Nostro Sublunari, Philosophia Nova_, Amstelodami, 1651,
+containing similar views, was published forty-eight years after
+Gilbert's death, and forty-two years after Kepler's book and
+reference.  His book _De Magnete_ was published in 1600.)
+
+A few of Kepler's views on gravitation, extracted from the
+Introduction to his _Astronomia Nova_, may now be mentioned:--
+
+1. Every body at rest remains at rest if outside the attractive power
+of other bodies.
+
+2. Gravity is a property of masses mutually attracting in such manner
+that the earth attracts a stone much more than a stone attracts the
+earth.
+
+3. Bodies are attracted to the earth's centre, not because it is the
+centre of the universe, but because it is the centre of the attracting
+particles of the earth.
+
+4. If the earth be not round (but spheroidal?), then bodies at
+different latitudes will not be attracted to its centre, but to
+different points in the neighbourhood of that centre.
+
+5. If the earth and moon were not retained in their orbits by vital
+force (_aut alia aligua aequipollenti_), the earth and moon would come
+together.
+
+6. If the earth were to cease to attract its waters, the oceans would
+all rise and flow to the moon.
+
+7. He attributes the tides to lunar attraction.  Kepler had been
+appointed Imperial Astronomer with a handsome salary (on paper), a
+fraction of which was doled out to him very irregularly. He was led to
+miserable makeshifts to earn enough to keep his family from
+starvation; and proceeded to Ratisbon in 1630 to represent his claims
+to the Diet. He arrived worn out and debilitated; he failed in his
+appeal, and died from fever, contracted under, and fed upon,
+disappointment and exhaustion. Those were not the days when men could
+adopt as a profession the "research of endowment."
+
+Before taking leave of Kepler, who was by no means a man of one idea,
+it ought to be here recorded that he was the first to suggest that a
+telescope made with both lenses convex (not a Galilean telescope) can
+have cross wires in the focus, for use as a pointer to fix accurately
+the positions of stars. An Englishman, Gascoigne, was the first to use
+this in practice.
+
+From the all too brief epitome here given of Kepler's greatest book,
+it must be obvious that he had at that time some inkling of the
+meaning of his laws--universal gravitation. From that moment the idea
+of universal gravitation was in the air, and hints and guesses were
+thrown out by many; and in time the law of gravitation would doubtless
+have been discovered, though probably not by the work of one man, even
+if Newton had not lived. But, if Kepler had not lived, who else could
+have discovered his laws?
+
+
+FOOTNOTES:
+
+[1] When the writer visited M. D'Arrest, the astronomer, at
+Copenhagen, in 1872, he was presented by D'Arrest with one of several
+bricks collected from the ruins of Uraniborg. This was one of his most
+cherished possessions until, on returning home after a prolonged
+absence on astronomical work, he found that his treasure had been
+tidied away from his study.
+
+[2] An ellipse is one of the plane, sections of a cone. It is an oval
+curve, which may be drawn by fixing two pins in a sheet of paper at S
+and H, fastening a string, SPH, to the two pins, and stretching it
+with a pencil point at P, and moving the pencil point, while the
+string is kept taut, to trace the oval ellipse, APB. S and H are the
+_foci_. Kepler found the sun to be in one focus, say S. AB is the
+_major axis_. DE is the _minor axis_. C is the _centre_. The direction
+of AB is the _line of apses_. The ratio of CS to CA is the
+_excentricity_. The position of the planet at A is the _perihelion_
+(nearest to the sun). The position of the planet at B is the
+_aphelion_ (farthest from the sun). The angle ASP is the _anomaly_
+when the planet is at P. CA or a line drawn from S to D is the _mean
+distance_ of the planet from the sun.
+
+[Illustration]
+
+[3] The ruled logarithmic paper we now use was not then to be had by
+going into a stationer's shop. Else he would have accomplished this in
+five minutes.
+
+
+
+6. GALILEO AND THE TELESCOPE--NOTIONS OF GRAVITY BY HORROCKS, ETC.
+
+
+It is now necessary to leave the subject of dynamical astronomy for a
+short time in order to give some account of work in a different
+direction originated by a contemporary of Kepler's, his senior in fact
+by seven years. Galileo Galilei was born at Pisa in 1564. The most
+scientific part of his work dealt with terrestrial dynamics; but one
+of those fortunate chances which happen only to really great men put
+him in the way of originating a new branch of astronomy.
+
+The laws of motion had not been correctly defined.  The only man of
+Galileo's time who seems to have worked successfully in the same
+direction as himself was that Admirable Crichton of the Italians,
+Leonardo da Vinci. Galileo cleared the ground. It had always been
+noticed that things tend to come to rest; a ball rolled on the ground,
+a boat moved on the water, a shot fired in the air. Galileo realised
+that in all of these cases a resisting force acts to stop the motion,
+and he was the first to arrive at the not very obvious law that the
+motion of a body will never stop, nor vary its speed, nor change its
+direction, except by the action of some force.
+
+It is not very obvious that a light body and a heavy one fall at the
+same speed (except for the resistance of the air). Galileo proved this
+on paper, but to convince the world he had to experiment from the
+leaning tower of Pisa.
+
+At an early age he discovered the principle of isochronism of the
+pendulum, which, in the hands of Huyghens in the middle of the
+seventeenth century, led to the invention of the pendulum clock,
+perhaps the most valuable astronomical instrument ever produced.
+
+These and other discoveries in dynamics may seem very obvious now; but
+it is often the most every-day matters which have been found to elude
+the inquiries of ordinary minds, and it required a high order of
+intellect to unravel the truth and discard the stupid maxims scattered
+through the works of Aristotle and accepted on his authority. A blind
+worship of scientific authorities has often delayed the progress of
+human knowledge, just as too much "instruction" of a youth often ruins
+his "education." Grant, in his history of Physical Astronomy, has well
+said that "the sagacity and skill which Galileo displays in resolving
+the phenomena of motion into their constituent elements, and hence
+deriving the original principles involved in them, will ever assure to
+him a distinguished place among those who have extended the domains of
+science."
+
+But it was work of a different kind that established Galileo's popular
+reputation. In 1609 Galileo heard that a Dutch spectacle-maker had
+combined a pair of lenses so as to magnify distant objects. Working on
+this hint, he solved the same problem, first on paper and then in
+practice. So he came to make one of the first telescopes ever used in
+astronomy. No sooner had he turned it on the heavenly bodies than he
+was rewarded by such a shower of startling discoveries as forthwith
+made his name the best known in Europe.  He found curious irregular
+black spots on the sun, revolving round it in twenty-seven days; hills
+and valleys on the moon; the planets showing discs of sensible size,
+not points like the fixed stars; Venus showing phases according to her
+position in relation to the sun; Jupiter accompanied by four moons;
+Saturn with appendages that he could not explain, but unlike the other
+planets; the Milky Way composed of a multitude of separate stars.
+
+His fame flew over Europe like magic, and his discoveries were much
+discussed--and there were many who refused to believe. Cosmo de Medici
+induced him to migrate to Florence to carry on his observations.  He
+was received by Paul V., the Pope, at Rome, to whom he explained his
+discoveries.
+
+He thought that these discoveries proved the truth of the Copernican
+theory of the Earth's motion; and he urged this view on friends and
+foes alike.  Although in frequent correspondence with Kepler, he never
+alluded to the New Astronomy, and wrote to him extolling the virtue of
+epicycles. He loved to argue, never shirked an encounter with any
+number of disputants, and laughed as he broke down their arguments.
+
+Through some strange course of events, not easy to follow, the
+Copernican theory, whose birth was welcomed by the Church, had now
+been taken up by certain anti-clerical agitators, and was opposed by
+the cardinals as well as by the dignitaries of the Reformed
+Church. Galileo--a good Catholic--got mixed up in these discussions,
+although on excellent terms with the Pope and his entourage. At last
+it came about that Galileo was summoned to appear at Rome, where he
+was charged with holding and teaching heretical opinions about the
+movement of the earth; and he then solemnly abjured these
+opinions. There has been much exaggeration and misstatement about his
+trial and punishment, and for a long time there was a great deal of
+bitterness shown on both sides. But the general verdict of the present
+day seems to be that, although Galileo himself was treated with
+consideration, the hostility of the Church to the views of Copernicus
+placed it in opposition also to the true Keplerian system, and this
+led to unprofitable controversies.  From the time of Galileo onwards,
+for some time, opponents of religion included the theory of the
+Earth's motion in their disputations, not so much for the love, or
+knowledge, of astronomy, as for the pleasure of putting the Church in
+the wrong. This created a great deal of bitterness and intolerance on
+both sides. Among the sufferers was Giordano Bruno, a learned
+speculative philosopher, who was condemned to be burnt at the stake.
+
+Galileo died on Christmas Day, 1642--the day of Newton's birth. The
+further consideration of the grand field of discovery opened out by
+Galileo with his telescopes must be now postponed, to avoid
+discontinuity in the history of the intellectual development of this
+period, which lay in the direction of dynamical, or physical,
+astronomy.
+
+Until the time of Kepler no one seems to have conceived the idea of
+universal physical forces controlling terrestrial phenomena, and
+equally applicable to the heavenly bodies. The grand discovery by
+Kepler of the true relationship of the Sun to the Planets, and the
+telescopic discoveries of Galileo and of those who followed him,
+spread a spirit of inquiry and philosophic thought throughout Europe,
+and once more did astronomy rise in estimation; and the irresistible
+logic of its mathematical process of reasoning soon placed it in the
+position it has ever since occupied as the foremost of the exact
+sciences.
+
+The practical application of this process of reasoning was enormously
+facilitated by the invention of logarithms by Napier. He was born at
+Merchistoun, near Edinburgh, in 1550, and died in 1617. By this system
+the tedious arithmetical operations necessary in astronomical
+calculations, especially those dealing with the trigonometrical
+functions of angles, were so much simplified that Laplace declared
+that by this invention the life-work of an astronomer was doubled.
+
+Jeremiah Horrocks (born 1619, died 1641) was an ardent admirer of
+Tycho Brahe and Kepler, and was able to improve the Rudolphine tables
+so much that he foretold a transit of Venus, in 1639, which these
+tables failed to indicate, and was the only observer of it. His life
+was short, but he accomplished a great deal, and rightly ascribed the
+lunar inequality called _evection_ to variations in the value of
+the eccentricity and in the direction of the line of apses, at the
+same time correctly assigning _the disturbing force of the Sun_
+as the cause. He discovered the errors in Jupiter's calculated place,
+due to what we now know as the long inequality of Jupiter and Saturn,
+and measured with considerable accuracy the acceleration at that date
+of Jupiter's mean motion, and indicated the retardation of Saturn's
+mean motion.
+
+Horrocks' investigations, so far as they could be collected, were
+published posthumously in 1672, and seldom, if ever, has a man who
+lived only twenty-two years originated so much scientific knowledge.
+
+At this period British science received a lasting impetus by the wise
+initiation of a much-abused man, Charles II., who founded the Royal
+Society of London, and also the Royal Observatory of Greeenwich, where
+he established Flamsteed as first Astronomer Royal, especially for
+lunar and stellar observations likely to be useful for navigation. At
+the same time the French Academy and the Paris Observatory were
+founded. All this within fourteen years, 1662-1675.
+
+Meanwhile gravitation in general terms was being discussed by Hooke,
+Wren, Halley, and many others.  All of these men felt a repugnance to
+accept the idea of a force acting across the empty void of space.
+Descartes (1596-1650) proposed an ethereal medium whirling round the
+sun with the planets, and having local whirls revolving with the
+satellites. As Delambre and Grant have said, this fiction only
+retarded the progress of pure science. It had no sort of relation to
+the more modern, but equally misleading, "nebular hypothesis." While
+many were talking and guessing, a giant mind was needed at this stage
+to make things clear.
+
+
+
+7. SIR ISAAC NEWTON--LAW OF UNIVERSAL GRAVITATION.
+
+
+We now reach the period which is the culminating point of interest in
+the history of dynamical astronomy.  Isaac Newton was born in
+1642. Pemberton states that Newton, having quitted Cambridge to avoid
+the plague, was residing at Wolsthorpe, in Lincolnshire, where he had
+been born; that he was sitting one day in the garden, reflecting upon
+the force which prevents a planet from flying off at a tangent and
+which draws it to the sun, and upon the force which draws the moon to
+the earth; and that he saw in the case of the planets that the sun's
+force must clearly be unequal at different distances, for the pull out
+of the tangential line in a minute is less for Jupiter than for
+Mars. He then saw that the pull of the earth on the moon would be less
+than for a nearer object. It is said that while thus meditating he saw
+an apple fall from a tree to the ground, and that this fact suggested
+the questions: Is the force that pulled that apple from the tree the
+same as the force which draws the moon to the earth?  Does the
+attraction for both of them follow the same law as to distance as is
+given by the planetary motions round the sun? It has been stated that
+in this way the first conception of universal gravitation arose.[1]
+
+Quite the most important event in the whole history of physical
+astronomy was the publication, in 1687, of Newton's _Principia
+(Philosophiae Naturalis Principia Mathematica)_. In this great work
+Newton started from the beginning of things, the laws of motion, and
+carried his argument, step by step, into every branch of physical
+astronomy; giving the physical meaning of Kepler's three laws, and
+explaining, or indicating the explanation of, all the known heavenly
+motions and their irregularities; showing that all of these were
+included in his simple statement about the law of universal
+gravitation; and proceeding to deduce from that law new irregularities
+in the motions of the moon which had never been noticed, and to
+discover the oblate figure of the earth and the cause of the
+tides. These investigations occupied the best part of his life; but he
+wrote the whole of his great book in fifteen months.
+
+Having developed and enunciated the true laws of motion, he was able
+to show that Kepler's second law (that equal areas are described by
+the line from the planet to the sun in equal times) was only another
+way of saying that the centripetal force on a planet is always
+directed to the sun. Also that Kepler's first law (elliptic orbits
+with the sun in one focus) was only another way of saying that the
+force urging a planet to the sun varies inversely as the square of the
+distance. Also (if these two be granted) it follows that Kepler's
+third law is only another way of saying that the sun's force on
+different planets (besides depending as above on distance) is
+proportional to their masses.
+
+Having further proved the, for that day, wonderful proposition that,
+with the law of inverse squares, the attraction by the separate
+particles of a sphere of uniform density (or one composed of
+concentric spherical shells, each of uniform density) acts as if the
+whole mass were collected at the centre, he was able to express the
+meaning of Kepler's laws in propositions which have been summarised as
+follows:--
+
+The law of universal gravitation.--_Every particle of matter in the
+universe attracts every other particle with a force varying inversely
+as the square of the distance between them, and directly as the
+product of the masses of the two particles_.[2]
+
+But Newton did not commit himself to the law until he had answered
+that question about the apple; and the above proposition now enabled
+him to deal with the Moon and the apple. Gravity makes a stone fall
+16.1 feet in a second. The moon is 60 times farther from the earth's
+centre than the stone, so it ought to be drawn out of a straight
+course through 16.1 feet in a minute. Newton found the distance
+through which she is actually drawn as a fraction of the earth's
+diameter.  But when he first examined this matter he proceeded to use
+a wrong diameter for the earth, and he found a serious discrepancy.
+This, for a time, seemed to condemn his theory, and regretfully he
+laid that part of his work aside. Fortunately, before Newton wrote the
+_Principia_ the French astronomer Picard made a new and correct
+measure of an arc of the meridian, from which he obtained an accurate
+value of the earth's diameter. Newton applied this value, and found,
+to his great joy, that when the distance of the moon is 60 times the
+radius of the earth she is attracted out of the straight course 16.1
+feet per minute, and that the force acting on a stone or an apple
+follows the same law as the force acting upon the heavenly bodies.[3]
+
+The universality claimed for the law--if not by Newton, at least by
+his commentators--was bold, and warranted only by the large number of
+cases in which Newton had found it to apply. Its universality has been
+under test ever since, and so far it has stood the test. There has
+often been a suspicion of a doubt, when some inequality of motion in
+the heavenly bodies has, for a time, foiled the astronomers in their
+attempts to explain it. But improved mathematical methods have always
+succeeded in the end, and so the seeming doubt has been converted into
+a surer conviction of the universality of the law.
+
+Having once established the law, Newton proceeded to trace some of its
+consequences. He saw that the figure of the earth depends partly on
+the mutual gravitation of its parts, and partly on the centrifugal
+tendency due to the earth's rotation, and that these should cause a
+flattening of the poles. He invented a mathematical method which he
+used for computing the ratio of the polar to the equatorial diameter.
+
+He then noticed that the consequent bulging of matter at the equator
+would be attracted by the moon unequally, the nearest parts being most
+attracted; and so the moon would tend to tilt the earth when in some
+parts of her orbit; and the sun would do this to a less extent,
+because of its great distance. Then he proved that the effect ought to
+be a rotation of the earth's axis over a conical surface in space,
+exactly as the axis of a top describes a cone, if the top has a sharp
+point, and is set spinning and displaced from the vertical. He
+actually calculated the amount; and so he explained the cause of the
+precession of the equinoxes discovered by Hipparchus about 150 B.C.
+
+One of his grandest discoveries was a method of weighing the heavenly
+bodies by their action on each other. By means of this principle he
+was able to compare the mass of the sun with the masses of those
+planets that have moons, and also to compare the mass of our moon with
+the mass of the earth.
+
+Thus Newton, after having established his great principle, devoted his
+splendid intellect to the calculation of its consequences. He proved
+that if a body be projected with any velocity in free space, subject
+only to a central force, varying inversely as the square of the
+distance, the body must revolve in a curve which may be any one of the
+sections of a cone--a circle, ellipse, parabola, or hyperbola; and he
+found that those comets of which he had observations move in parabolae
+round the Sun, and are thus subject to the universal law.
+
+Newton realised that, while planets and satellites are chiefly
+controlled by the central body about which they revolve, the new law
+must involve irregularities, due to their mutual action--such, in
+fact, as Horrocks had indicated. He determined to put this to a test
+in the case of the moon, and to calculate the sun's effect, from its
+mass compared with that of the earth, and from its distance. He proved
+that the average effect upon the plane of the orbit would be to cause
+the line in which it cuts the plane of the ecliptic (i.e., the line of
+nodes) to revolve in the ecliptic once in about nineteen years. This
+had been a known fact from the earliest ages. He also concluded that
+the line of apses would revolve in the plane of the lunar orbit also
+in about nineteen years; but the observed period is only ten
+years. For a long time this was the one weak point in the Newtonian
+theory. It was not till 1747 that Clairaut reconciled this with the
+theory, and showed why Newton's calculation was not exact.
+
+Newton proceeded to explain the other inequalities recognised by Tycho
+Brahe and older observers, and to calculate their maximum amounts as
+indicated by his theory. He further discovered from his calculations
+two new inequalities, one of the apogee, the other of the nodes, and
+assigned the maximum value. Grant has shown the values of some of
+these as given by observation in the tables of Meyer and more modern
+tables, and has compared them with the values assigned by Newton from
+his theory; and the comparison is very remarkable.
+
+                                     Newton.      Modern Tables.
+                                      � '  "         � ' "
+Mean monthly motion of Apses         1.31.28         3.4.0
+Mean annual motion of nodes         19.18.1,23     19.21.22,50
+Mean value of "variation"              36.10          35.47
+Annual equation                        11.51          11.14
+Inequality of mean motion of apogee    19.43          22.17
+Inequality of mean motion of nodes      9.24           9.0
+
+The only serious discrepancy is the first, which has been already
+mentioned. Considering that some of these perturbations had never been
+discovered, that the cause of none of them had ever been known, and
+that he exhibited his results, if he did not also make the
+discoveries, by the synthetic methods of geometry, it is simply
+marvellous that he reached to such a degree of accuracy. He invented
+the infinitesimal calculus which is more suited for such calculations,
+but had he expressed his results in that language he would have been
+unintelligible to many.
+
+Newton's method of calculating the precession of the equinoxes,
+already referred to, is as beautiful as anything in the _Principia_.
+He had already proved the regression of the nodes of a satellite
+moving in an orbit inclined to the ecliptic. He now said that the
+nodes of a ring of satellites revolving round the earth's equator
+would consequently all regress. And if joined into a solid ring its
+node would regress; and it would do so, only more slowly, if
+encumbered by the spherical part of the earth's mass. Therefore the
+axis of the equatorial belt of the earth must revolve round the pole
+of the ecliptic. Then he set to work and found the amount due to the
+moon and that due to the sun, and so he solved the mystery of 2,000
+years.
+
+When Newton applied his law of gravitation to an explanation of the
+tides he started a new field for the application of mathematics to
+physical problems; and there can be little doubt that, if he could
+have been furnished with complete tidal observations from different
+parts of the world, his extraordinary powers of analysis would have
+enabled him to reach a satisfactory theory.  He certainly opened up
+many mines full of intellectual gems; and his successors have never
+ceased in their explorations. This has led to improved mathematical
+methods, which, combined with the greater accuracy of observation,
+have rendered physical astronomy of to-day the most exact of the
+sciences.
+
+Laplace only expressed the universal opinion of posterity when he said
+that to the _Principia_ is assured "a pre-eminence above all the
+other productions of the human intellect."
+
+The name of Flamsteed, First Astronomer Royal, must here be mentioned
+as having supplied Newton with the accurate data required for
+completing the theory.
+
+The name of Edmund Halley, Second Astronomer Royal, must ever be held
+in repute, not only for his own discoveries, but for the part he
+played in urging Newton to commit to writing, and present to the Royal
+Society, the results of his investigations. But for his friendly
+insistence it is possible that the _Principia_ would never have
+been written; and but for his generosity in supplying the means the
+Royal Society could not have published the book.
+
+[Illustration: DEATH MASK OF SIR ISAAC NEWTON.
+Photographed specially for this work from the original, by kind
+permission of the Royal Society, London.]
+
+Sir Isaac Newton died in 1727, at the age of eighty-five.  His body
+lay in state in the Jerusalem Chamber, and was buried in Westminster
+Abbey.
+
+
+FOOTNOTES:
+
+[1] The writer inherited from his father (Professor J. D. Forbes) a
+small box containing a bit of wood and a slip of paper, which had been
+presented to him by Sir David Brewster. On the paper Sir David had
+written these words: "If there be any truth in the story that Newton
+was led to the theory of gravitation by the fall of an apple, this bit
+of wood is probably a piece of the apple tree from which Newton saw
+the apple fall. When I was on a pilgrimage to the house in which
+Newton was born, I cut it off an ancient apple tree growing in his
+garden." When lecturing in Glasgow, about 1875, the writer showed it
+to his audience. The next morning, when removing his property from the
+lecture table, he found that his precious relic had been stolen. It
+would be interesting to know who has got it now!
+
+[2] It must be noted that these words, in which the laws of
+gravitation are always summarised in histories and text-books, do not
+appear in the _Principia_; but, though they must have been composed by
+some early commentator, it does not appear that their origin has been
+traced. Nor does it appear that Newton ever extended the law beyond
+the Solar System, and probably his caution would have led him to avoid
+any statement of the kind until it should be proved.
+
+With this exception the above statement of the law of universal
+gravitation contains nothing that is not to be found in the
+_Principia_; and the nearest approach to that statement occurs in the
+Seventh Proposition of Book III.:--
+
+Prop.: That gravitation occurs in all bodies, and that it is
+proportional to the quantity of matter in each.
+
+Cor. I.: The total attraction of gravitation on a planet arises, and
+is composed, out of the attraction on the separate parts.
+
+Cor. II.: The attraction on separate equal particles of a body is
+reciprocally as the square of the distance from the particles.
+
+[3] It is said that, when working out this final result, the
+probability of its confirming that part of his theory which he had
+reluctantly abandoned years before excited him so keenly that he was
+forced to hand over his calculations to a friend, to be completed by
+him.
+
+
+
+8. NEWTON'S SUCCESSORS--HALLEY, EULER, LAGRANGE, LAPLACE, ETC.
+
+
+Edmund Halley succeeded Flamsteed as Second Astronomer Royal in
+1721. Although he did not contribute directly to the mathematical
+proofs of Newton's theory, yet his name is closely associated with
+some of its greatest successes.
+
+He was the first to detect the acceleration of the moon's mean
+motion. Hipparchus, having compared his own observations with those of
+more ancient astronomers, supplied an accurate value of the moon's
+mean motion in his time. Halley similarly deduced a value for modern
+times, and found it sensibly greater.  He announced this in 1693, but
+it was not until 1749 that Dunthorne used modern lunar tables to
+compute a lunar eclipse observed in Babylon 721 B.C., another at
+Alexandria 201 B.C., a solar eclipse observed by Theon 360 A.D., and
+two later ones up to the tenth century.  He found that to explain
+these eclipses Halley's suggestion must be adopted, the acceleration
+being 10" in one century. In 1757 Lalande again fixed it at 10."
+
+The Paris Academy, in 1770, offered their prize for an investigation
+to see if this could be explained by the theory of gravitation. Euler
+won the prize, but failed to explain the effect, and said: "It appears
+to be established by indisputable evidence that the secular inequality
+of the moon's mean motion cannot be produced by the forces of
+gravitation."
+
+The same subject was again proposed for a prize which was shared by
+Lagrange [1] and Euler, neither finding a solution, while the latter
+asserted the existence of a resisting medium in space.
+
+Again, in 1774, the Academy submitted the same subject, a third time,
+for the prize; and again Lagrange failed to detect a cause in
+gravitation.
+
+Laplace [2] now took the matter in hand. He tried the effect of a
+non-instantaneous action of gravity, to no purpose. But in 1787 he
+gave the true explanation.  The principal effect of the sun on the
+moon's orbit is to diminish the earth's influence, thus lengthening
+the period to a new value generally taken as constant. But Laplace's
+calculations showed the new value to depend upon the excentricity of
+the earth's orbit, which, according; to theory, has a periodical
+variation of enormous period, and has been continually diminishing for
+thousands of years. Thus the solar influence has been diminishing, and
+the moon's mean motion increased. Laplace computed the amount at 10"
+in one century, agreeing with observation. (Later on Adams showed that
+Laplace's calculation was wrong, and that the value he found was too
+large; so, part of the acceleration is now attributed by some
+astronomers to a lengthening of the day by tidal friction.)
+
+Another contribution by Halley to the verification of Newton's law was
+made when he went to St. Helena to catalogue the southern stars. He
+measured the change in length of the second's pendulum in different
+latitudes due to the changes in gravity foretold by Newton.
+
+Furthermore, he discovered the long inequality of Jupiter and Saturn,
+whose period is 929 years. For an investigation of this also the
+Academy of Sciences offered their prize. This led Euler to write a
+valuable essay disclosing a new method of computing perturbations,
+called the instantaneous ellipse with variable elements. The method
+was much developed by Lagrange.
+
+But again it was Laplace who solved the problem of the inequalities of
+Jupiter and Saturn by the theory of gravitation, reducing the errors
+of the tables from 20' down to 12", thus abolishing the use of
+empirical corrections to the planetary tables, and providing another
+glorious triumph for the law of gravitation.  As Laplace justly said:
+"These inequalities appeared formerly to be inexplicable by the law of
+gravitation--they now form one of its most striking proofs."
+
+Let us take one more discovery of Halley, furnishing directly a new
+triumph for the theory. He noticed that Newton ascribed parabolic
+orbits to the comets which he studied, so that they come from
+infinity, sweep round the sun, and go off to infinity for ever, after
+having been visible a few weeks or months. He collected all the
+reliable observations of comets he could find, to the number of
+twenty-four, and computed their parabolic orbits by the rules laid
+down by Newton. His object was to find out if any of them really
+travelled in elongated ellipses, practically undistinguishable, in the
+visible part of their paths, from parabol�, in which case they would
+be seen more than once. He found two old comets whose orbits, in shape
+and position, resembled the orbit of a comet observed by himself in
+1682.  Apian observed one in 1531; Kepler the other in 1607.  The
+intervals between these appearances is seventy-five or seventy-six
+years. He then examined and found old records of similar appearance in
+1456, 1380, and 1305. It is true, he noticed, that the intervals
+varied by a year and a-half, and the inclination of the orbit to the
+ecliptic diminished with successive apparitions.  But he knew from
+previous calculations that this might easily be due to planetary
+perturbations. Finally, he arrived at the conclusion that all of these
+comets were identical, travelling in an ellipse so elongated that the
+part where the comet was seen seemed to be part of a parabolic
+orbit. He then predicted its return at the end of 1758 or beginning of
+1759, when he should be dead; but, as he said, "if it should return,
+according to our prediction, about the year 1758, impartial posterity
+will not refuse to acknowledge that this was first discovered by an
+Englishman."[3] [_Synopsis Astronomiae Cometicae_, 1749.]
+
+Once again Halley's suggestion became an inspiration for the
+mathematical astronomer. Clairaut, assisted by Lalande, found that
+Saturn would retard the comet 100 days, Jupiter 518 days, and
+predicted its return to perihelion on April 13th, 1759. In his
+communication to the French Academy, he said that a comet travelling
+into such distant regions might be exposed to the influence of forces
+totally unknown, and "even of some planet too far removed from the sun
+to be ever perceived."
+
+The excitement of astronomers towards the end of 1758 became intense;
+and the honour of first catching sight of the traveller fell to an
+amateur in Saxony, George Palitsch, on Christmas Day, 1758. It reached
+perihelion on March 13th, 1759.
+
+This fact was a startling confirmation of the Newtonian theory,
+because it was a new kind of calculation of perturbations, and also it
+added a new member to the solar system, and gave a prospect of adding
+many more.
+
+When Halley's comet reappeared in 1835, Pontecoulant's computations
+for the date of perihelion passage were very exact, and afterwards he
+showed that, with more exact values of the masses of Jupiter and
+Saturn, his prediction was correct within two days, after an invisible
+voyage of seventy-five years!
+
+Hind afterwards searched out many old appearances of this comet, going
+back to 11 B.C., and most of these have been identified as being
+really Halley's comet by the calculations of Cowell and Cromellin[4]
+(of Greenwich Observatory), who have also predicted its next
+perihelion passage for April 8th to 16th, 1910, and have traced back
+its history still farther, to 240 B.C.
+
+Already, in November, 1907, the Astronomer Royal was trying to catch
+it by the aid of photography.
+
+
+FOOTNOTES:
+
+[1] Born 1736; died 1813.
+
+[2] Born 1749; died 1827.
+
+[3] This sentence does not appear in the original memoir communicated
+to the Royal Society, but was first published in a posthumous reprint.
+
+[4] _R. A. S. Monthly Notices_, 1907-8.
+
+
+
+9. DISCOVERY OF NEW PLANETS--HERSCHEL, PIAZZI, ADAMS, AND LE VERRIER.
+
+
+It would be very interesting, but quite impossible in these pages, to
+discuss all the exquisite researches of the mathematical astronomers,
+and to inspire a reverence for the names connected with these
+researches, which for two hundred years have been establishing the
+universality of Newton's law. The lunar and planetary theories, the
+beautiful theory of Jupiter's satellites, the figure of the earth, and
+the tides, were mathematically treated by Maclaurin, D'Alembert,
+Legendre, Clairaut, Euler, Lagrange, Laplace, Walmsley, Bailly,
+Lalande, Delambre, Mayer, Hansen, Burchardt, Binet, Damoiseau, Plana,
+Poisson, Gauss, Bessel, Bouvard, Airy, Ivory, Delaunay, Le Verrier,
+Adams, and others of later date.
+
+By passing over these important developments it is possible to trace
+some of the steps in the crowning triumph of the Newtonian theory, by
+which the planet Neptune was added to the known members of the solar
+system by the independent researches of Professor J.C. Adams and of
+M. Le Verrier, in 1846.
+
+It will be best to introduce this subject by relating how the
+eighteenth century increased the number of known planets, which was
+then only six, including the earth.
+
+On March 13th, 1781, Sir William Herschel was, as usual, engaged on
+examining some small stars, and, noticing that one of them appeared to
+be larger than the fixed stars, suspected that it might be a comet.
+To test this he increased his magnifying power from 227 to 460 and
+932, finding that, unlike the fixed stars near it, its definition was
+impaired and its size increased.  This convinced him that the object
+was a comet, and he was not surprised to find on succeeding nights
+that the position was changed, the motion being in the ecliptic. He
+gave the observations of five weeks to the Royal Society without a
+suspicion that the object was a new planet.
+
+For a long time people could not compute a satisfactory orbit for the
+supposed comet, because it seemed to be near the perihelion, and no
+comet had ever been observed with a perihelion distance from the sun
+greater than four times the earth's distance. Lexell was the first to
+suspect that this was a new planet eighteen times as far from the sun
+as the earth is. In January, 1783, Laplace published the elliptic
+elements. The discoverer of a planet has a right to name it, so
+Herschel called it Georgium Sidus, after the king.  But Lalande urged
+the adoption of the name Herschel.  Bode suggested Uranus, and this
+was adopted. The new planet was found to rank in size next to Jupiter
+and Saturn, being 4.3 times the diameter of the earth.
+
+In 1787 Herschel discovered two satellites, both revolving in nearly
+the same plane, inclined 80� to the ecliptic, and the motion of both
+was retrograde.
+
+In 1772, before Herschel's discovery, Bode[1] had discovered a curious
+arbitrary law of planetary distances.  Opposite each planet's name
+write the figure 4; and, in succession, add the numbers 0, 3, 6, 12,
+24, 48, 96, etc., to the 4, always doubling the last numbers.  You
+then get the planetary distances.
+
+  Mercury, dist.-- 4  4 +   0 =   4
+  Venus      "     7  4 +   3 =   7
+  Earth      "    10  4 +   6 =  10
+  Mars       "    15  4 +  12 =  16
+   --                 4 +  24 =  28
+  Jupiter  dist.  52  4 +  48 =  52
+  Saturn     "    95  4 +  96 = 100
+  (Uranus)   "   192  4 + 192 = 196
+   --                 4 + 384 = 388
+
+All the five planets, and the earth, fitted this rule, except that
+there was a blank between Mars and Jupiter. When Uranus was
+discovered, also fitting the rule, the conclusion was irresistible
+that there is probably a planet between Mars and Jupiter. An
+association of twenty-four astronomers was now formed in Germany to
+search for the planet. Almost immediately afterwards the planet was
+discovered, not by any member of the association, but by Piazzi, when
+engaged upon his great catalogue of stars. On January 1st, 1801, he
+observed a star which had changed its place the next night. Its motion
+was retrograde till January 11th, direct after the 13th.  Piazzi fell
+ill before he had enough observations for computing the orbit with
+certainty, and the planet disappeared in the sun's rays. Gauss
+published an approximate ephemeris of probable positions when the
+planet should emerge from the sun's light. There was an exciting hunt,
+and on December 31st (the day before its birthday) De Zach captured
+the truant, and Piazzi christened it Ceres.
+
+
+The mean distance from the sun was found to be 2.767, agreeing with
+the 2.8 given by Bode's law. Its orbit was found to be inclined over
+10� to the ecliptic, and its diameter was only 161 miles.
+
+On March 28th, 1802, Olbers discovered a new seventh magnitude star,
+which turned out to be a planet resembling Ceres. It was called
+Pallas. Gauss found its orbit to be inclined 35� to the ecliptic, and
+to cut the orbit of Ceres; whence Olbers considered that these might
+be fragments of a broken-up planet. He then commenced a search for
+other fragments. In 1804 Harding discovered Juno, and in 1807 Olbers
+found Vesta. The next one was not discovered until 1845, from which
+date asteroids, or minor planets (as these small planets are called),
+have been found almost every year. They now number about 700.
+
+It is impossible to give any idea of the interest with which the first
+additions since prehistoric times to the planetary system were
+received. All of those who showered congratulations upon the
+discoverers regarded these discoveries in the light of rewards for
+patient and continuous labours, the very highest rewards that could be
+desired. And yet there remained still the most brilliant triumph of
+all, the addition of another planet like Uranus, before it had ever
+been seen, when the analysis of Adams and Le Verrier gave a final
+proof of the powers of Newton's great law to explain any planetary
+irregularity.
+
+After Sir William Herschel discovered Uranus, in 1781, it was found
+that astronomers had observed it on many previous occasions, mistaking
+it for a fixed star of the sixth or seventh magnitude. Altogether,
+nineteen observations of Uranus's position, from the time of
+Flamsteed, in 1690, had been recorded.
+
+In 1790 Delambre, using all these observations, prepared tables for
+computing its position. These worked well enough for a time, but at
+last the differences between the calculated and observed longitudes of
+the planet became serious. In 1821 Bouvard undertook a revision of the
+tables, but found it impossible to reconcile all the observations of
+130 years (the period of revolution of Uranus is eighty-four years).
+So he deliberately rejected the old ones, expressing the opinion that
+the discrepancies might depend upon "some foreign and unperceived
+cause which may have been acting upon the planet." In a few years the
+errors even of these tables became intolerable. In 1835 the error of
+longitude was 30"; in 1838, 50"; in 1841, 70"; and, by comparing the
+errors derived from observations made before and after opposition, a
+serious error of the distance (radius vector) became apparent.
+
+In 1843 John Couch Adams came out Senior Wrangler at Cambridge, and
+was free to undertake the research which as an undergraduate he had
+set himself--to see whether the disturbances of Uranus could be
+explained by assuming a certain orbit, and position in that orbit, of
+a hypothetical planet even more distant than Uranus.  Such an
+explanation had been suggested, but until 1843 no one had the boldness
+to attack the problem.  Bessel had intended to try, but a fatal
+illness overtook him.
+
+Adams first recalculated all known causes of disturbance, using the
+latest determinations of the planetary masses. Still the errors were
+nearly as great as ever.  He could now, however, use these errors as
+being actually due to the perturbations produced by the unknown
+planet.
+
+In 1844, assuming a circular orbit, and a mean distance agreeing with
+Bode's law, he obtained a first approximation to the position of the
+supposed planet.  He then asked Professor Challis, of Cambridge, to
+procure the latest observations of Uranus from Greenwich, which Airy
+immediately supplied. Then the whole work was recalculated from the
+beginning, with more exactness, and assuming a smaller mean distance.
+
+In September, 1845, he handed to Challis the elements of the
+hypothetical planet, its mass, and its apparent position for September
+30th, 1845. On September 22nd Challis wrote to Airy explaining the
+matter, and declaring his belief in Adams's capabilities. When Adams
+called on him Airy was away from home, but at the end of October,
+1845, he called again, and left a paper with full particulars of his
+results, which had, for the most part, reduced the discrepancies to
+about 1". As a matter of fact, it has since been found that the
+heliocentric place of the new planet then given was correct within
+about 2�.
+
+Airy wrote expressing his interest, and asked for particulars about
+the radius vector. Adams did not then reply, as the answer to this
+question could be seen to be satisfactory by looking at the data
+already supplied.  He was a most unassuming man, and would not push
+himself forward. He may have felt, after all the work he had done,
+that Airy's very natural inquiry showed no proportionate desire to
+search for the planet.  Anyway, the matter lay in embryo for nine
+months.
+
+Meanwhile, one of the ablest French astronomers, Le Verrier,
+experienced in computing perturbations, was independently at work,
+knowing nothing about Adams. He applied to his calculations every
+possible refinement, and, considering the novelty of the problem, his
+calculation was one of the most brilliant in the records of
+astronomy. In criticism it has been said that these were exhibitions
+of skill rather than helps to a solution of the particular problem,
+and that, in claiming to find the elements of the orbit within certain
+limits, he was claiming what was, under the circumstances, impossible,
+as the result proved.
+
+In June, 1846, Le Verrier announced, in the _Comptes Rendus de
+l'Academie des Sciences_, that the longitude of the disturbing planet,
+for January 1st, 1847, was 325, and that the probable error did not
+exceed 10�.
+
+This result agreed so well with Adams's (within 1�) that Airy urged
+Challis to apply the splendid Northumberland equatoreal, at Cambridge,
+to the search.  Challis, however, had already prepared an exhaustive
+plan of attack which must in time settle the point.  His first work
+was to observe, and make a catalogue, or chart, of all stars near
+Adams's position.
+
+On August 31st, 1846, Le Verrier published the concluding
+part of his labours.
+
+On September 18th, 1846, Le Verrier communicated his results to the
+Astronomers at Berlin, and asked them to assist in searching for the
+planet. By good luck Dr. Bremiker had just completed a star-chart of
+the very part of the heavens including Le Verrier's position; thus
+eliminating all of Challis's preliminary work. The letter was received
+in Berlin on September 23rd; and the same evening Galle found the new
+planet, of the eighth magnitude, the size of its disc agreeing with Le
+Verrier's prediction, and the heliocentric longitude agreeing within
+57'. By this time Challis had recorded, without reduction, the
+observations of 3,150 stars, as a commencement for his search.  On
+reducing these, he found a star, observed on August 12th, which was
+not in the same place on July 30th. This was the planet, and he had
+also observed it on August 4th.
+
+The feeling of wonder, admiration, and enthusiasm aroused by this
+intellectual triumph was overwhelming.  In the world of astronomy
+reminders are met every day of the terrible limitations of human
+reasoning powers; and every success that enables the mind's eye to see
+a little more clearly the meaning of things has always been heartily
+welcomed by those who have themselves been engaged in like
+researches. But, since the publication of the _Principia_, in 1687,
+there is probably no analytical success which has raised among
+astronomers such a feeling of admiration and gratitude as when Adams
+and Le Verrier showed the inequalities in Uranus's motion to mean that
+an unknown planet was in a certain place in the heavens, where it was
+found.
+
+At the time there was an unpleasant display of international jealousy.
+The British people thought that the earlier date of Adams's work, and
+of the observation by Challis, entitled him to at least an equal share
+of credit with Le Verrier. The French, on the other hand, who, on the
+announcement of the discovery by Galle, glowed with pride in the new
+proof of the great powers of their astronomer, Le Verrier, whose life
+had a long record of successes in calculation, were incredulous on
+being told that it had all been already done by a young man whom they
+had never heard of.
+
+These displays of jealousy have long since passed away, and there is
+now universally an _entente cordiale_ that to each of these great men
+belongs equally the merit of having so thoroughly calculated this
+inverse problem of perturbations as to lead to the immediate discovery
+of the unknown planet, since called Neptune.
+
+It was soon found that the planet had been observed, and its position
+recorded as a fixed star by Lalande, on May 8th and 10th, 1795.
+
+Mr. Lassel, in the same year, 1846, with his two-feet reflector,
+discovered a satellite, with retrograde motion, which gave the mass of
+the planet about a twentieth of that of Jupiter.
+
+
+FOOTNOTES:
+
+[1] Bode's law, or something like it, had already been fore-shadowed
+by Kepler and others, especially Titius (see _Monatliche
+Correspondenz_, vol. vii., p. 72).
+
+
+
+
+BOOK III. OBSERVATION
+
+
+
+10. INSTRUMENTS OF PRECISION--STATE OF THE SOLAR SYSTEM.
+
+
+Having now traced the progress of physical astronomy up to the time
+when very striking proofs of the universality of the law of
+gravitation convinced the most sceptical, it must still be borne in
+mind that, while gravitation is certainly the principal force
+governing the motions of the heavenly bodies, there may yet be a
+resisting medium in space, and there may be electric and magnetic
+forces to deal with. There may, further, be cases where the effects of
+luminous radiative repulsion become apparent, and also Crookes'
+vacuum-effects described as "radiant matter." Nor is it quite certain
+that Laplace's proofs of the instantaneous propagation of gravity are
+final.
+
+And in the future, as in the past, Tycho Brahe's dictum must be
+maintained, that all theory shall be preceded by accurate
+observations. It is the pride of astronomers that their science stands
+above all others in the accuracy of the facts observed, as well as in
+the rigid logic of the mathematics used for interpreting these facts.
+
+It is interesting to trace historically the invention of those
+instruments of precision which have led to this result, and, without
+entering on the details required in a practical handbook, to note the
+guiding principles of construction in different ages.
+
+It is very probable that the Chaldeans may have made spheres, like the
+armillary sphere, for representing the poles of the heavens; and with
+rings to show the ecliptic and zodiac, as well as the equinoctial and
+solstitial colures; but we have no record. We only know that the tower
+of Belus, on an eminence, was their observatory.  We have, however,
+distinct records of two such spheres used by the Chinese about 2500
+B.C.  Gnomons, or some kind of sundial, were used by the Egyptians and
+others; and many of the ancient nations measured the obliquity of the
+ecliptic by the shadows of a vertical column in summer and winter. The
+natural horizon was the only instrument of precision used by those who
+determined star positions by the directions of their risings and
+settings; while in those days the clepsydra, or waterclock, was the
+best instrument for comparing their times of rising and setting.
+
+About 300 B.C. an observatory fitted with circular instruments for
+star positions was set up at Alexandria, the then centre of
+civilisation. We know almost nothing about the instruments used by
+Hipparchus in preparing his star catalogues and his lunar and solar
+tables; but the invention of the astrolabe is attributed to him.[1]
+
+In more modern times Nuremberg became a centre of astronomical
+culture. Waltherus, of that town, made really accurate observations of
+star altitudes, and of the distances between stars; and in 1484
+A.D. he used a kind of clock. Tycho Brahe tried these, but discarded
+them as being inaccurate.
+
+Tycho Brahe (1546-1601 A.D.) made great improvements in armillary
+spheres, quadrants, sextants, and large celestial globes. With these
+he measured the positions of stars, or the distance of a comet from
+several known stars. He has left us full descriptions of them,
+illustrated by excellent engravings. Previous to his time such
+instruments were made of wood.  Tycho always used metal. He paid the
+greatest attention to the stability of mounting, to the orientation of
+his instruments, to the graduation of the arcs by the then new method
+of transversals, and to the aperture sight used upon his
+pointer. There were no telescopes in his day, and no pendulum
+clocks. He recognised the fact that there must be instrumental
+errors. He made these as small as was possible, measured their amount,
+and corrected his observations.  His table of refractions enabled him
+to abolish the error due to our atmosphere so far as it could affect
+naked-eye observations. The azimuth circle of Tycho's largest quadrant
+had a diameter of nine feet, and the quadrant a radius of six feet. He
+introduced the mural quadrant for meridian observations.[2]
+
+[Illustration: ANCIENT CHINESE INSTRUMENTS, Including quadrant, celestial
+globe, and two armillae, in the Observatory at Peking. Photographed in
+Peking by the author in 1875, and stolen by the Germans when the
+Embassies were relieved by the allies in 1900.]
+
+The French Jesuits at Peking, in the seventeenth century, helped the
+Chinese in their astronomy. In 1875 the writer saw and photographed,
+on that part of the wall of Peking used by the Mandarins as an
+observatory, the six instruments handsomely designed by Father
+Verbiest, copied from the instruments of Tycho Brahe, and embellished
+with Chinese dragons and emblems cast on the supports. He also saw
+there two old instruments (which he was told were Arabic) of date
+1279, by Ko Show-King, astronomer to Koblai Khan, the grandson of
+Chenghis Khan. One of these last is nearly identical with the armillae
+of Tycho; and the other with his "armillae �quatori� maxim�," with
+which he observed the comet of 1585, besides fixed stars and
+planets.[3]
+
+The discovery by Galileo of the isochronism of the pendulum, followed
+by Huyghens's adaptation of that principle to clocks, has been one of
+the greatest aids to accurate observation. About the same time an
+equally beneficial step was the employment of the telescope as a
+pointer; not the Galilean with concave eye-piece, but with a
+magnifying glass to examine the focal image, at which also a fixed
+mark could be placed.  Kepler was the first to suggest this. Gascoigne
+was the first to use it. Huyghens used a metal strip of variable width
+in the focus, as a micrometer to cover a planetary disc, and so to
+measure the width covered by the planet. The Marquis Malvasia, in
+1662, described the network of fine silver threads at right angles,
+which he used in the focus, much as we do now.
+
+In the hands of such a skilful man as Tycho Brahe, the old open
+sights, even without clocks, served their purpose sufficiently well to
+enable Kepler to discover the true theory of the solar system. But
+telescopic sights and clocks were required for proving some of
+Newton's theories of planetary perturbations. Picard's observations at
+Paris from 1667 onwards seem to embody the first use of the telescope
+as a pointer. He was also the first to introduce the use of Huyghens's
+clocks for observing the right ascension of stars.  Olaus Romer was
+born at Copenhagen in 1644. In 1675, by careful study of the times of
+eclipses of Jupiter's satellites, he discovered that light took time
+to traverse space. Its velocity is 186,000 miles per second. In 1681
+he took up his duties as astronomer at Copenhagen, and built the first
+transit circle on a window-sill of his house. The iron axis was five
+feet long and one and a-half inches thick, and the telescope was fixed
+near one end with a counterpoise. The telescope-tube was a double
+cone, to prevent flexure. Three horizontal and three vertical wires
+were used in the focus. These were illuminated by a speculum, near the
+object-glass, reflecting the light from a lantern placed over the
+axis, the upper part of the telescope-tube being partly cut away to
+admit the light. A divided circle, with pointer and reading
+microscope, was provided for reading the declination. He realised the
+superiority of a circle with graduations over a much larger
+quadrant. The collimation error was found by reversing the instrument
+and using a terrestrial mark, the azimuth error by star observations.
+The time was expressed in fractions of a second. He also constructed a
+telescope with equatoreal mounting, to follow a star by one axial
+motion. In 1728 his instruments and observation records were destroyed
+by fire.
+
+Hevelius had introduced the vernier and tangent screw in his
+measurement of arc graduations. His observatory and records were burnt
+to the ground in 1679. Though an old man, he started afresh, and left
+behind him a catalogue of 1,500 stars.
+
+Flamsteed began his duties at Greenwich Observatory, as first
+Astronomer Royal, in 1676, with very poor instruments. In 1683 he put
+up a mural arc of 140�, and in 1689 a better one, seventy-nine inches
+radius.  He conducted his measurements with great skill, and
+introduced new methods to attain accuracy, using certain stars for
+determining the errors of his instruments; and he always reduced his
+observations to a form in which they could be readily used. He
+introduced new methods for determining the position of the equinox and
+the right ascension of a fundamental star.  He produced a catalogue of
+2,935 stars. He supplied Sir Isaac Newton with results of observation
+required in his theoretical calculations. He died in 1719.
+
+Halley succeeded Flamsteed to find that the whole place had been
+gutted by the latter's executors. In 1721 he got a transit instrument,
+and in 1726 a mural quadrant by Graham. His successor in 1742,
+Bradley, replaced this by a fine brass quadrant, eight feet radius, by
+Bird; and Bradley's zenith sector was purchased for the observatory.
+An instrument like this, specially designed for zenith stars, is
+capable of greater rigidity than a more universal instrument; and
+there is no trouble with refraction in the zenith. For these reasons
+Bradley had set up this instrument at Kew, to attempt the proof of the
+earth's motion by observing the annual parallax of stars. He certainly
+found an annual variation of zenith distance, but not at the times of
+year required by the parallax. This led him to the discovery of the
+"aberration" of light and of nutation. Bradley has been described as
+the founder of the modern system of accurate observation. He died in
+1762, leaving behind him thirteen folio volumes of valuable but
+unreduced observations. Those relating to the stars were reduced by
+Bessel and published in 1818, at K�nigsberg, in his well-known
+standard work, _Fundamenta Astronomiae_. In it are results showing the
+laws of refraction, with tables of its amount, the maximum value of
+aberration, and other constants.
+
+Bradley was succeeded by Bliss, and he by Maskelyne (1765), who
+carried on excellent work, and laid the foundations of the Nautical
+Almanac (1767).  Just before his death he induced the Government to
+replace Bird's quadrant by a fine new mural _circle_, six feet in
+diameter, by Troughton, the divisions being read off by microscopes
+fixed on piers opposite to the divided circle. In this instrument the
+micrometer screw, with a divided circle for turning it, was applied
+for bringing the micrometer wire actually in line with a division on
+the circle--a plan which is still always adopted.
+
+Pond succeeded Maskelyne in 1811, and was the first to use this
+instrument. From now onwards the places of stars were referred to the
+pole, not to the zenith; the zero being obtained from measures on
+circumpolar stars. Standard stars were used for giving the clock
+error. In 1816 a new transit instrument, by Troughton, was added, and
+from this date the Greenwich star places have maintained the very
+highest accuracy.
+
+George Biddell Airy, Seventh Astronomer Royal,[4] commenced his
+Greenwich labours in 1835. His first and greatest reformation in the
+work of the observatory was one he had already established at
+Cambridge, and is now universally adopted. He held that an observation
+is not completed until it has been reduced to a useful form; and in
+the case of the sun, moon, and planets these results were, in every
+case, compared with the tables, and the tabular error printed.
+
+Airy was firmly impressed with the object for which Charles II. had
+wisely founded the observatory in connection with navigation, and for
+observations of the moon. Whenever a meridian transit of the moon
+could be observed this was done. But, even so, there are periods in
+the month when the moon is too near the sun for a transit to be well
+observed. Also weather interferes with many meridian observations. To
+render the lunar observations more continuous, Airy employed
+Troughton's successor, James Simms, in conjunction with the engineers,
+Ransome and May, to construct an altazimuth with three-foot circles,
+and a five-foot telescope, in 1847. The result was that the number of
+lunar observations was immediately increased threefold, many of them
+being in a part of the moon's orbit which had previously been bare of
+observations. From that date the Greenwich lunar observations have
+been a model and a standard for the whole world.
+
+Airy also undertook to superintend the reduction of all Greenwich
+lunar observations from 1750 to 1830.  The value of this laborious
+work, which was completed in 1848, cannot be over-estimated.
+
+The demands of astronomy, especially in regard to small minor planets,
+required a transit instrument and mural circle with a more powerful
+telescope. Airy combined the functions of both, and employed the same
+constructors as before to make a _transit-circle_ with a telescope of
+eleven and a-half feet focus and a circle of six-feet diameter, the
+object-glass being eight inches in diameter.
+
+Airy, like Bradley, was impressed with the advantage of employing
+stars in the zenith for determining the fundamental constants of
+astronomy. He devised a _reflex zenith tube_, in which the zenith
+point was determined by reflection from a surface of mercury. The
+design was so simple, and seemed so perfect, that great expectations
+were entertained. But unaccountable variations comparable with those
+of the transit circle appeared, and the instrument was put out of use
+until 1903, when the present Astronomer Royal noticed that the
+irregularities could be allowed for, being due to that remarkable
+variation in the position of the earth's axis included in circles of
+about six yards diameter at the north and south poles, discovered at
+the end of the nineteenth century. The instrument is now being used
+for investigating these variations; and in the year 1907 as many as
+1,545 observations of stars were made with the reflex zenith tube.
+
+In connection with zenith telescopes it must be stated that Respighi,
+at the Capitol Observatory at Rome, made use of a deep well with a
+level mercury surface at the bottom and a telescope at the top
+pointing downwards, which the writer saw in 1871. The reflection of
+the micrometer wires and of a star very near the zenith (but not quite
+in the zenith) can be observed together.  His mercury trough was a
+circular plane surface with a shallow edge to retain the mercury. The
+surface quickly came to rest after disturbance by street traffic.
+
+Sir W. M. H. Christie, Eighth Astronomer Royal, took up his duties in
+that capacity in 1881. Besides a larger altazimuth that he erected in
+1898, he has widened the field of operations at Greenwich by the
+extensive use of photography and the establishment of large
+equatoreals.  From the point of view of instruments of precision, one
+of the most important new features is the astrographic equatoreal, set
+up in 1892 and used for the Greenwich section of the great
+astrographic chart just completed. Photography has come to be of use,
+not only for depicting the sun and moon, comets and nebulae, but also
+to obtain accurate relative positions of neighbouring stars; to pick
+up objects that are invisible in any telescope; and, most of all
+perhaps, in fixing the positions of faint satellites. Thus Saturn's
+distant satellite, Phoebe, and the sixth and seventh satellites of
+Jupiter, have been followed regularly in their courses at Greenwich
+ever since their discovery with the thirty-inch reflector (erected in
+1897); and while doing so Mr. Melotte made, in 1908, the splendid
+discovery on some of the photographic plates of an eighth satellite of
+Jupiter, at an enormous distance from the planet. From observations in
+the early part of 1908, over a limited arc of its orbit, before
+Jupiter approached the sun, Mr. Cowell computed a retrograde orbit and
+calculated the future positions of this satellite, which enabled
+Mr. Melotte to find it again in the autumn--a great triumph both of
+calculation and of photographic observation. This satellite has never
+been seen, and has been photographed only at Greenwich, Heidelberg,
+and the Lick Observatory.
+
+Greenwich Observatory has been here selected for tracing the progress
+of accurate measurement. But there is one instrument of great value,
+the heliometer, which is not used at Greenwich. This serves the
+purpose of a double image micrometer, and is made by dividing the
+object-glass of a telescope along a diameter. Each half is mounted so
+as to slide a distance of several inches each way on an arc whose
+centre is the focus. The amount of the movement can be accurately
+read. Thus two fields of view overlap, and the adjustment is made to
+bring an image of one star over that of another star, and then to do
+the same by a displacement in the opposite direction. The total
+movement of the half-object glass is double the distance between the
+star images in the focal plane. Such an instrument has long been
+established at Oxford, and German astronomers have made great use of
+it. But in the hands of Sir David Gill (late His Majesty's Astronomer
+at the Cape of Good Hope), and especially in his great researches on
+Solar and on Stellar parallax, it has been recognised as an instrument
+of the very highest accuracy, measuring the distance between stars
+correctly to less than a tenth of a second of arc.
+
+The superiority of the heliometer over all other devices (except
+photography) for measuring small angles has been specially brought
+into prominence by Sir David Gill's researches on the distance of the
+sun--_i.e.,_ the scale of the solar system. A measurement of the
+distance of any planet fixes the scale, and, as Venus approaches the
+earth most nearly of all the planets, it used to be supposed that a
+Transit of Venus offered the best opportunity for such measurement,
+especially as it was thought that, as Venus entered on the solar disc,
+the sweep of light round the dark disc of Venus would enable a very
+precise observation to be made.  The Transit of Venus in 1874, in
+which the present writer assisted, overthrew this delusion.
+
+In 1877 Sir David Gill used Lord Crawford's heliometer at the Island
+of Ascension to measure the parallax of Mars in opposition, and found
+the sun's distance 93,080,000 miles. He considered that, while the
+superiority of the heliometer had been proved, the results would be
+still better with the points of light shown by minor planets rather
+than with the disc of Mars.
+
+In 1888-9, at the Cape, he observed the minor planets Iris, Victoria,
+and Sappho, and secured the co-operation of four other heliometers.
+His final result was 92,870,000 miles, the parallax being 8",802
+(_Cape Obs_., Vol. VI.).
+
+So delicate were these measures that Gill detected a minute periodic
+error of theory of twenty-seven days, owing to a periodically
+erroneous position of the centre of gravity of the earth and moon to
+which the position of the observer was referred. This led him to
+correct the mass of the moon, and to fix its ratio to the earth's mass
+= 0.012240.
+
+Another method of getting the distance from the sun is to measure the
+velocity of the earth's orbital motion, giving the circumference
+traversed in a year, and so the radius of the orbit. This has been
+done by comparing observation and experiment. The aberration of light
+is an angle 20" 48, giving the ratio of the earth's velocity to the
+velocity of light. The velocity of light is 186,000 miles a second;
+whence the distance to the sun is 92,780,000 miles. There seems,
+however, to be some uncertainty about the true value of the
+aberration, any determination of which is subject to irregularities
+due to the "seasonal errors." The velocity of light was experimentally
+found, in 1862, by Fizeau and Foucault, each using an independent
+method. These methods have been developed, and new values found, by
+Cornu, Michaelson, Newcomb, and the present writer.
+
+Quite lately Halm, at the Cape of Good Hope, measured
+spectroscopically the velocity of the earth to and from a star by
+observations taken six months apart.  Thence he obtained an accurate
+value of the sun's distance.[5]
+
+But the remarkably erratic minor planet, Eros, discovered by Witte in
+1898, approaches the earth within 15,000,000 miles at rare intervals,
+and, with the aid of photography, will certainly give us the best
+result. A large number of observatories combined to observe the
+opposition of 1900. Their results are not yet completely reduced, but
+the best value deduced so far for the parallax[6] is 8".807 �
+0".0028.[7]
+
+
+FOOTNOTES:
+
+[1] In 1480 Martin Behaim, of Nuremberg, produced his _astrolabe_ for
+measuring the latitude, by observation of the sun, at sea. It
+consisted of a graduated metal circle, suspended by a ring which was
+passed over the thumb, and hung vertically. A pointer was fixed to a
+pin at the centre. This arm, called the _alhidada_, worked round the
+graduated circle, and was pointed to the sun.  The altitude of the sun
+was thus determined, and, by help of solar tables, the latitude could
+be found from observations made at apparent noon.
+
+[2] See illustration on p. 76.
+
+[3] See Dreyer's article on these instruments in _Copernicus_,
+Vol. I. They were stolen by the Germans after the relief of the
+Embassies, in 1900. The best description of these instruments is
+probably that contained in an interesting volume, which may be seen in
+the library of the R. A. S., entitled _Chinese Researches_, by
+Alexander Wyllie (Shanghai, 1897).
+
+[4] Sir George Airy was very jealous of this honourable title. He
+rightly held that there is only one Astronomer Royal at a time, as
+there is only one Mikado, one Dalai Lama. He said that His Majesty's
+Astronomer at the Cape of Good Hope, His Majesty's Astronomer for
+Scotland, and His Majesty's Astronomer for Ireland are not called
+Astronomers Royal.
+
+[5] _Annals of the Cape Observatory_, vol. x., part 3.
+
+[6] The parallax of the sun is the angle subtended by the earth's
+radius at the sun's distance.
+
+[7] A. R. Hinks, R.A.S.; _Monthly Notices_, June, 1909.
+
+
+
+11. HISTORY OF THE TELESCOPE
+
+
+Accounts of wonderful optical experiments by Roger Bacon (who died in
+1292), and in the sixteenth century by Digges, Baptista Porta, and
+Antonio de Dominis (Grant, _Hist. Ph. Ast_.), have led some to
+suppose that they invented the telescope. The writer considers that it
+is more likely that these notes refer to a kind of _camera
+obscura_, in which a lens throws an inverted image of a landscape
+on the wall.
+
+The first telescopes were made in Holland, the originator being either
+Henry Lipperhey,[1] Zacharias Jansen, or James Metius, and the date
+1608 or earlier.
+
+In 1609 Galileo, being in Venice, heard of the invention, went home
+and worked out the theory, and made a similar telescope. These
+telescopes were all made with a convex object-glass and a concave
+eye-lens, and this type is spoken of as the Galilean telescope. Its
+defects are that it has no real focus where cross-wires can be placed,
+and that the field of view is very small.  Kepler suggested the convex
+eye-lens in 1611, and Scheiner claimed to have used one in 1617. But
+it was Huyghens who really introduced them. In the seventeenth century
+telescopes were made of great length, going up to 300 feet. Huyghens
+also invented the compound eye-piece that bears his name, made of two
+convex lenses to diminish spherical aberration.
+
+But the defects of colour remained, although their cause was unknown
+until Newton carried out his experiments on dispersion and the solar
+spectrum. To overcome the spherical aberration James Gregory,[2] of
+Aberdeen and Edinburgh, in 1663, in his _Optica Promota_,
+proposed a reflecting speculum of parabolic form. But it was Newton,
+about 1666, who first made a reflecting telescope; and he did it with
+the object of avoiding colour dispersion.
+
+Some time elapsed before reflectors were much used.  Pound and Bradley
+used one presented to the Royal Society by Hadley in 1723. Hawksbee,
+Bradley, and Molyneaux made some. But James Short, of Edinburgh, made
+many excellent Gregorian reflectors from 1732 till his death in 1768.
+
+Newton's trouble with refractors, chromatic aberration, remained
+insurmountable until John Dollond (born 1706, died 1761), after many
+experiments, found out how to make an achromatic lens out of two
+lenses--one of crown glass, the other of flint glass--to destroy the
+colour, in a way originally suggested by Euler. He soon acquired a
+great reputation for his telescopes of moderate size; but there was a
+difficulty in making flint-glass lenses of large size. The first
+actual inventor and constructor of an achromatic telescope was Chester
+Moor Hall, who was not in trade, and did not patent it.  Towards the
+close of the eighteenth century a Swiss named Guinand at last
+succeeded in producing larger flint-glass discs free from
+striae. Frauenhofer, of Munich, took him up in 1805, and soon
+produced, among others, Struve's Dorpat refractor of 9.9 inches
+diameter and 13.5 feet focal length, and another, of 12 inches
+diameter and 18 feet focal length, for Lamont, of Munich.
+
+In the nineteenth century gigantic _reflectors_ have been
+made. Lassel's 2-foot reflector, made by himself, did much good work,
+and discovered four new satellites.  But Lord Rosse's 6-foot
+reflector, 54 feet focal length, constructed in 1845, is still the
+largest ever made.  The imperfections of our atmosphere are against
+the use of such large apertures, unless it be on high mountains.
+During the last half century excellent specula have been made of
+silvered glass, and Dr.  Common's 5-foot speculum (removed, since his
+death, to Harvard) has done excellent work. Then there are the 5-foot
+Yerkes reflector at Chicago, and the 4-foot by Grubb at Melbourne.
+
+Passing now from these large reflectors to refractors, further
+improvements have been made in the manufacture of glass by Chance, of
+Birmingham, Feil and Mantois, of Paris, and Schott, of Jena; while
+specialists in grinding lenses, like Alvan Clark, of the U.S.A., and
+others, have produced many large refractors.
+
+Cooke, of York, made an object-glass, 25-inch diameter, for Newall, of
+Gateshead, which has done splendid work at Cambridge. We have the
+Washington 26-inch by Clark, the Vienna 27-inch by Grubb, the Nice
+291/2-inch by Gautier, the Pulkowa 30-inch by Clark. Then there was
+the sensation of Clark's 36-inch for the Lick Observatory in
+California, and finally his _tour de force_, the Yerkes 40-inch
+refractor, for Chicago.
+
+At Greenwich there is the 28-inch photographic refractor, and the
+Thompson equatoreal by Grubb, carrying both the 26-inch photographic
+refractor and the 30-inch reflector. At the Cape of Good Hope we find
+Mr. Frank McClean's 24-inch refractor, with an object-glass prism for
+spectroscopic work.
+
+It would be out of place to describe here the practical adjuncts of a
+modern equatoreal--the adjustments for pointing it, the clock for
+driving it, the position-micrometer and various eye-pieces, the
+photographic and spectroscopic attachments, the revolving domes,
+observing seats, and rising floors and different forms of mounting,
+the siderostats and coelostats, and other convenient adjuncts, besides
+the registering chronograph and numerous facilities for aiding
+observation.  On each of these a chapter might be written; but the
+most important part of the whole outfit is the man behind the
+telescope, and it is with him that a history is more especially
+concerned.
+
+
+SPECTROSCOPE.
+
+Since the invention of the telescope no discovery has given so great
+an impetus to astronomical physics as the spectroscope; and in giving
+us information about the systems of stars and their proper motions it
+rivals the telescope.
+
+Frauenhofer, at the beginning of the nineteenth century, while
+applying Dollond's discovery to make large achromatic telescopes,
+studied the dispersion of light by a prism. Admitting the light of the
+sun through a narrow slit in a window-shutter, an inverted image of
+the slit can be thrown, by a lens of suitable focal length, on the
+wall opposite. If a wedge or prism of glass be interposed, the image
+is deflected to one side; but, as Newton had shown, the images formed
+by the different colours of which white light is composed are
+deflected to different extents--the violet most, the red least. The
+number of colours forming images is so numerous as to form a
+continuous spectrum on the wall with all the colours--red, orange,
+yellow, green, blue, indigo, and violet. But Frauenhofer found with a
+narrow slit, well focussed by the lens, that some colours were missing
+in the white light of the sun, and these were shown by dark lines
+across the spectrum.  These are the Frauenhofer lines, some of which
+he named by the letters of the alphabet. The D line is a very marked
+one in the yellow. These dark lines in the solar spectrum had already
+been observed by Wollaston. [3]
+
+On examining artificial lights it was found that incandescent solids
+and liquids (including the carbon glowing in a white gas flame) give
+continuous spectra; gases, except under enormous pressure, give bright
+lines. If sodium or common salt be thrown on the colourless flame of a
+spirit lamp, it gives it a yellow colour, and its spectrum is a bright
+yellow line agreeing in position with line D of the solar spectrum.
+
+In 1832 Sir David Brewster found some of the solar black lines
+increased in strength towards sunset, and attributed them to
+absorption in the earth's atmosphere.  He suggested that the others
+were due to absorption in the sun's atmosphere. Thereupon Professor
+J. D.  Forbes pointed out that during a nearly total eclipse the lines
+ought to be strengthened in the same way; as that part of the sun's
+light, coming from its edge, passes through a great distance in the
+sun's atmosphere.  He tried this with the annular eclipse of 1836,
+with a negative result which has never been accounted for, and which
+seemed to condemn Brewster's view.
+
+In 1859 Kirchoff, on repeating Frauenhofer's experiment, found that,
+if a spirit lamp with salt in the flame were placed in the path of the
+light, the black D line is intensified. He also found that, if he used
+a limelight instead of the sunlight and passed it through the flame
+with salt, the spectrum showed the D line black; or the vapour of
+sodium absorbs the same light that it radiates. This proved to him the
+existence of sodium in the sun's atmosphere.[4] Iron, calcium, and
+other elements were soon detected in the same way.
+
+Extensive laboratory researches (still incomplete) have been carried
+out to catalogue (according to their wave-length on the undulatory
+theory of light) all the lines of each chemical element, under all
+conditions of temperature and pressure. At the same time, all the
+lines have been catalogued in the light of the sun and the brighter of
+the stars.
+
+Another method of obtaining spectra had long been known, by
+transmission through, or reflection from, a grating of equidistant
+lines ruled upon glass or metal.  H. A. Rowland developed the art of
+constructing these gratings, which requires great technical skill, and
+for this astronomers owe him a debt of gratitude.
+
+In 1842 Doppler[5] proved that the colour of a luminous body, like the
+pitch or note of a sounding body, must be changed by velocity of
+approach or recession. Everyone has noticed on a railway that, on
+meeting a locomotive whistling, the note is lowered after the engine
+has passed. The pitch of a sound or the colour of a light depends on
+the number of waves striking the ear or eye in a second. This number
+is increased by approach and lowered by recession.
+
+Thus, by comparing the spectrum of a star alongside a spectrum of
+hydrogen, we may see all the lines, and be sure that there is hydrogen
+in the star; yet the lines in the star-spectrum may be all slightly
+displaced to one side of the lines of the comparison spectrum. If
+towards the violet end, it means mutual approach of the star and
+earth; if to the red end, it means recession. The displacement of
+lines does not tell us whether the motion is in the star, the earth,
+or both.  The displacement of the lines being measured, we can
+calculate the rate of approach or recession in miles per second.
+
+In 1868 Huggins[6] succeeded in thus measuring the velocities of stars
+in the direction of the line of sight.
+
+In 1873 Vogel[7] compared the spectra of the sun's East (approaching)
+limb and West (receding) limb, and the displacement of lines endorsed
+the theory. This last observation was suggested by Z�llner.
+
+
+FOOTNOTES:
+
+[1] In the _Encyclopaedia Britannica_, article "Telescope," and in
+Grant's _Physical Astronomy_, good reasons are given for awarding the
+honour to Lipperhey.
+
+[2] Will the indulgent reader excuse an anecdote which may encourage
+some workers who may have found their mathematics defective through
+want of use? James Gregory's nephew David had a heap of MS. notes by
+Newton. These descended to a Miss Gregory, of Edinburgh, who handed
+them to the present writer, when an undergraduate at Cambridge, to
+examine. After perusal, he lent them to his kindest of friends,
+J. C. Adams (the discoverer of Neptune), for his opinion. Adams's
+final verdict was: "I fear they are of no value. It is pretty evident
+that, when he wrote these notes, _Newton's mathematics were a little
+rusty_."
+
+[3] _R. S. Phil. Trans_.
+
+[4] The experiment had been made before by one who did not understand
+its meaning;. But Sir George G. Stokes had already given verbally the
+true explanation of Frauenhofer lines.
+
+[5] _Abh. d. K�n. B�hm. d. Wiss_., Bd. ii., 1841-42, p. 467. See
+also Fizeau in the _Ann. de Chem. et de Phys_., 1870, p. 211.
+
+[6] _R. S. Phil. Trans_., 1868.
+
+[7] _Ast. Nach_., No. 1, 864.
+
+
+
+
+BOOK IV. THE PHYSICAL PERIOD
+
+
+We have seen how the theory of the solar system was slowly developed
+by the constant efforts of the human mind to find out what are the
+rules of cause and effect by which our conception of the present
+universe and its development seems to be bound. In the primitive ages
+a mere record of events in the heavens and on the earth gave the only
+hope of detecting those uniform sequences from which to derive rules
+or laws of cause and effect upon which to rely. Then came the
+geometrical age, in which rules were sought by which to predict the
+movements of heavenly bodies. Later, when the relation of the sun to
+the courses of the planets was established, the sun came to be looked
+upon as a cause; and finally, early in the seventeenth century, for
+the first time in history, it began to be recognised that the laws of
+dynamics, exactly as they had been established for our own terrestrial
+world, hold good, with the same rigid invariability, at least as far
+as the limits of the solar system.
+
+Throughout this evolution of thought and conjecture there were two
+types of astronomers--those who supplied the facts, and those who
+supplied the interpretation through the logic of mathematics. So
+Ptolemy was dependent upon Hipparchus, Kepler on Tycho Brahe, and
+Newton in much of his work upon Flamsteed.
+
+When Galileo directed his telescope to the heavens, when Secchi and
+Huggins studied the chemistry of the stars by means of the
+spectroscope, and when Warren De la Rue set up a photoheliograph at
+Kew, we see that a progress in the same direction as before, in the
+evolution of our conception of the universe, was being made. Without
+definite expression at any particular date, it came to be an accepted
+fact that not only do earthly dynamics apply to the heavenly bodies,
+but that the laws we find established here, in geology, in chemistry,
+and in the laws of heat, may be extended with confidence to the
+heavenly bodies. Hence arose the branch of astronomy called
+astronomical physics, a science which claims a large portion of the
+work of the telescope, spectroscope, and photography. In this new
+development it is more than ever essential to follow the dictum of
+Tycho Brahe--not to make theories until all the necessary facts are
+obtained. The great astronomers of to-day still hold to Sir Isaac
+Newton's declaration, "Hypotheses non fingo." Each one may have his
+suspicions of a theory to guide him in a course of observation, and
+may call it a working hypothesis.  But the cautious astronomer does
+not proclaim these to the world; and the historian is certainly not
+justified in including in his record those vague speculations founded
+on incomplete data which may be demolished to-morrow, and which,
+however attractive they may be, often do more harm than good to the
+progress of true science.  Meanwhile the accumulation of facts has
+been prodigious, and the revelations of the telescope and spectroscope
+entrancing.
+
+
+
+12. THE SUN.
+
+
+One of Galileo's most striking discoveries, when he pointed his
+telescope to the heavenly bodies, was that of the irregularly shaped
+spots on the sun, with the dark central _umbra_ and the less
+dark, but more extensive, _penumbra_ surrounding it, sometimes
+with several umbrae in one penumbra. He has left us many drawings of
+these spots, and he fixed their period of rotation as a lunar month.
+
+[Illustration: SOLAR SURFACE, As Photographed at the Royal
+Observatory, Greenwich, showing sun-spots with umbrae, penumbrae, and
+faculae.]
+
+It is not certain whether Galileo, Fabricius, or Schemer was the first
+to see the spots. They all did good work. The spots were found to be
+ever varying in size and shape. Sometimes, when a spot disappears at
+the western limb of the sun, it is never seen again.  In other cases,
+after a fortnight, it reappears at the eastern limb. The faculae, or
+bright areas, which are seen all over the sun's surface, but specially
+in the neighbourhood of spots, and most distinctly near the sun's
+edge, were discovered by Galileo. A high telescopic power resolves
+their structure into an appearance like willow-leaves, or rice-grains,
+fairly uniform in size, and more marked than on other parts of the
+sun's surface.
+
+Speculations as to the cause of sun-spots have never ceased from
+Galileo's time to ours. He supposed them to be clouds. Scheiner[1]
+said they were the indications of tumultuous movements occasionally
+agitating the ocean of liquid fire of which he supposed the sun to be
+composed.
+
+A. Wilson, of Glasgow, in 1769,[2] noticed a movement of the umbra
+relative to the penumbra in the transit of the spot over the sun's
+surface; exactly as if the spot were a hollow, with a black base and
+grey shelving sides. This was generally accepted, but later
+investigations have contradicted its universality. Regarding the cause
+of these hollows, Wilson said:--
+
+  Whether their first production and subsequent numberless changes
+  depend upon the eructation of elastic vapours from below, or upon
+  eddies or whirlpools commencing at the surface, or upon the
+  dissolving of the luminous matter in the solar atmosphere, as clouds
+  are melted and again given out by our air; or, if the reader
+  pleases, upon the annihilation and reproduction of parts of this
+  resplendent covering, is left for theory to guess at.[3]
+
+Ever since that date theory has been guessing at it.  The solar
+astronomer is still applying all the instruments of modern research to
+find out which of these suppositions, or what modification of any of
+them, is nearest the truth. The obstacle--one that is perhaps fatal to
+a real theory--lies in the impossibility of reproducing comparative
+experiments in our laboratories or in our atmosphere.
+
+Sir William Herschel propounded an explanation of Wilson's observation
+which received much notice, but which, out of respect for his memory,
+is not now described, as it violated the elementary laws of heat.
+
+Sir John Herschel noticed that the spots are mostly confined to two
+zones extending to about 35� on each side of the equator, and that a
+zone of equatoreal calms is free from spots. But it was
+R. C. Carrington[4] who, by his continuous observations at Redhill, in
+Surrey, established the remarkable fact that, while the rotation
+period in the highest latitudes, 50�, where spots are seen, is
+twenty-seven-and-a-half days, near the equator the period is only
+twenty-five days. His splendid volume of observations of the sun led
+to much new information about the average distribution of spots at
+different epochs.
+
+Schwabe, of Dessau, began in 1826 to study the solar surface, and,
+after many years of work, arrived at a law of frequency which has been
+more fruitful of results than any discovery in solar physics.[5] In
+1843 he announced a decennial period of maxima and minima of sun-spot
+displays. In 1851 it was generally accepted, and, although a period of
+eleven years has been found to be more exact, all later observations,
+besides the earlier ones which have been hunted up for the purpose, go
+to establish a true periodicity in the number of sun-spots. But quite
+lately Schuster[6] has given reasons for admitting a number of
+co-existent periods, of which the eleven-year period was predominant
+in the nineteenth century.
+
+In 1851 Lament, a Scotchman at Munich, found a decennial period in the
+daily range of magnetic declination.  In 1852 Sir Edward Sabine
+announced a similar period in the number of "magnetic storms"
+affecting all of the three magnetic elements--declination, dip, and
+intensity. Australian and Canadian observations both showed the
+decennial period in all three elements. Wolf, of Zurich, and Gauthier,
+of Geneva, each independently arrived at the same conclusion.
+
+It took many years before this coincidence was accepted as certainly
+more than an accident by the old-fashioned astronomers, who want rigid
+proof for every new theory. But the last doubts have long vanished,
+and a connection has been further traced between violent outbursts of
+solar activity and simultaneous magnetic storms.
+
+The frequency of the Aurora Borealis was found by Wolf to follow the
+same period. In fact, it is closely allied in its cause to terrestrial
+magnetism. Wolf also collected old observations tracing the
+periodicity of sun-spots back to about 1700 A.D.
+
+Spoerer deduced a law of dependence of the average latitude of
+sun-spots on the phase of the sun-spot period.
+
+All modern total solar eclipse observations seem to show that the
+shape of the luminous corona surrounding the moon at the moment of
+totality has a special distinct character during the time of a
+sun-spot maximum, and another, totally different, during a sun-spot
+minimum.
+
+A suspicion is entertained that the total quantity of heat received by
+the earth from the sun is subject to the same period. This would have
+far-reaching effects on storms, harvests, vintages, floods, and
+droughts; but it is not safe to draw conclusions of this kind except
+from a very long period of observations.
+
+Solar photography has deprived astronomers of the type of Carrington
+of the delight in devoting a life's work to collecting data. It has
+now become part of the routine work of an observatory.
+
+In 1845 Foucault and Fizeau took a daguerreotype photograph of the
+sun. In 1850 Bond produced one of the moon of great beauty, Draper
+having made some attempts at an even earlier date. But astronomical
+photography really owes its beginning to De la Rue, who used the
+collodion process for the moon in 1853, and constructed the Kew
+photoheliograph in 1857, from which date these instruments have been
+multiplied, and have given us an accurate record of the sun's surface.
+Gelatine dry plates were first used by Huggins in 1876.
+
+It is noteworthy that from the outset De la Rue recognised the value
+of stereoscopic vision, which is now known to be of supreme
+accuracy. In 1853 he combined pairs of photographs of the moon in the
+same phase, but under different conditions regarding libration,
+showing the moon from slightly different points of view.  These in the
+stereoscope exhibited all the relief resulting from binocular vision,
+and looked like a solid globe.  In 1860 he used successive photographs
+of the total solar eclipse stereoscopically, to prove that the red
+prominences belong to the sun, and not to the moon.  In 1861 he
+similarly combined two photographs of a sun-spot, the perspective
+effect showing the umbra like a floor at the bottom of a hollow
+penumbra; and in one case the facul� were discovered to be sailing
+over a spot apparently at some considerable height.  These appearances
+may be partly due to a proper motion; but, so far as it went, this was
+a beautiful confirmation of Wilson's discovery. Hewlett, however, in
+1894, after thirty years of work, showed that the spots are not always
+depressions, being very subject to disturbance.
+
+The Kew photographs [7] contributed a vast amount of information about
+sun-spots, and they showed that the facul� generally follow the spots
+in their rotation round the sun.
+
+The constitution of the sun's photosphere, the layer which is the
+principal light-source on the sun, has always been a subject of great
+interest; and much was done by men with exceptionally keen eyesight,
+like Mr. Dawes. But it was a difficult subject, owing to the rapidity
+of the changes in appearance of the so-called rice-grains, about 1" in
+diameter. The rapid transformations and circulations of these
+rice-grains, if thoroughly studied, might lead to a much better
+knowledge of solar physics. This seemed almost hopeless, as it was
+found impossible to identify any "rice-grain" in the turmoil after a
+few minutes. But M.  Hansky, of Pulkowa (whose recent death is
+deplored), introduced successfully a scheme of photography, which
+might almost be called a solar cinematograph. He took photographs of
+the sun at intervals of fifteen or thirty seconds, and then enlarged
+selected portions of these two hundred times, giving a picture
+corresponding to a solar disc of six metres diameter. In these
+enlarged pictures he was able to trace the movements, and changes of
+shape and brightness, of individual rice-grains. Some granules become
+larger or smaller. Some seem to rise out of a mist, as it were, and to
+become clearer.  Others grow feebler. Some are split in two. Some are
+rotated through a right angle in a minute or less, although each of
+the grains may be the size of Great Britain. Generally they move
+together in groups of very various velocities, up to forty kilometres
+a second.  These movements seem to have definite relation to any
+sun-spots in the neighbourhood. From the results already obtained it
+seems certain that, if this method of observation be continued, it
+cannot fail to supply facts of the greatest importance.
+
+It is quite impossible to do justice here to the work of all those who
+are engaged on astronomical physics.  The utmost that can be attempted
+is to give a fair idea of the directions of human thought and
+endeavour.  During the last half-century America has made splendid
+progress, and an entirely new process of studying the photosphere has
+been independently perfected by Professor Hale at Chicago, and
+Deslandres at Paris.[8] They have succeeded in photographing the sun's
+surface in monochromatic light, such as the light given off as one of
+the bright lines of hydrogen or of calcium, by means of the
+"Spectroheliograph." The spectroscope is placed with its slit in the
+focus of an equatoreal telescope, pointed to the sun, so that the
+circular image of the sun falls on the slit. At the other end of the
+spectroscope is the photographic plate. Just in front of this plate
+there is another slit parallel to the first, in the position where the
+image of the first slit formed by the K line of calcium falls. Thus is
+obtained a photograph of the section of the sun, made by the first
+slit, only in K light. As the image of the sun passes over the first
+slit the photographic plate is moved at the same rate and in the same
+direction behind the second slit; and as successive sections of the
+sun's image in the equatoreal enter the apparatus, so are these
+sections successively thrown in their proper place on the photographic
+plate, always in K light. By using a high dispersion the facul� which
+give off K light can be correctly photographed, not only at the sun's
+edge, but all over his surface. The actual mechanical method of
+carrying out the observation is not quite so simple as what is here
+described.
+
+By choosing another line of the spectrum instead of calcium K--for
+example, the hydrogen line H(3)--we obtain two photographs, one
+showing the appearance of the calcium floculi, and the other of the
+hydrogen floculi, on the same part of the solar surface; and nothing
+is more astonishing than to note the total want of resemblance in the
+forms shown on the two. This mode of research promises to afford many
+new and useful data.
+
+The spectroscope has revealed the fact that, broadly speaking, the sun
+is composed of the same materials as the earth. �ngstrom was the first
+to map out all of the lines to be found in the solar spectrum. But
+Rowland, of Baltimore, after having perfected the art of making true
+gratings with equidistant lines ruled on metal for producing spectra,
+then proceeded to make a map of the solar spectrum on a large scale.
+
+In 1866 Lockyer[9] threw an image of the sun upon the slit of a
+spectroscope, and was thus enabled to compare the spectrum of a spot
+with that of the general solar surface. The observation proved the
+darkness of a spot to be caused by increased absorption of light, not
+only in the dark lines, which are widened, but over the entire
+spectrum. In 1883 Young resolved this continuous obscurity into an
+infinite number of fine lines, which have all been traced in a shadowy
+way on to the general solar surface. Lockyer also detected
+displacements of the spectrum lines in the spots, such as would be
+produced by a rapid motion in the line of sight. It has been found
+that both uprushes and downrushes occur, but there is no marked
+predominance of either in a sun-spot. The velocity of motion thus
+indicated in the line of sight sometimes appears to amount to 320
+miles a second. But it must be remembered that pressure of a gas has
+some effect in displacing the spectral lines.  So we must go on,
+collecting data, until a time comes when the meaning of all the facts
+can be made clear.
+
+_Total Solar Eclipses_.--During total solar eclipses the time is so
+short, and the circumstances so impressive, that drawings of the
+appearance could not always be trusted. The red prominences of jagged
+form that are seen round the moon's edge, and the corona with its
+streamers radiating or interlacing, have much detail that can hardly
+be recorded in a sketch. By the aid of photography a number of records
+can be taken during the progress of totality. From a study of these
+the extent of the corona is demonstrated in one case to extend to at
+least six diameters of the moon, though the eye has traced it
+farther. This corona is still one of the wonders of astronomy, and
+leads to many questions. What is its consistency, if it extends many
+million miles from the sun's surface? How is it that it opposed no
+resistance to the motion of comets which have almost grazed the sun's
+surface? Is this the origin of the zodiacal light?  The character of
+the corona in photographic records has been shown to depend upon the
+phase of the sun-spot period. During the sun-spot maximum the corona
+seems most developed over the spot-zones--i.e., neither at the
+equator nor the poles. The four great sheaves of light give it a
+square appearance, and are made up of rays or plumes, delicate like
+the petals of a flower.  During a minimum the nebulous ring seems to
+be made of tufts of fine hairs with aigrettes or radiations from both
+poles, and streamers from the equator.
+
+[Illustration: SOLAR ECLIPSE, 1882.  From drawing by W. H. Wesley,
+Secretary R.A.S.; showing the prominences, the corona, and an unknown
+comet.]
+
+
+On September 19th, 1868, eclipse spectroscopy began with the Indian
+eclipse, in which all observers found that the red prominences showed
+a bright line spectrum, indicating the presence of hydrogen and other
+gases.  So bright was it that Jansen exclaimed: "_Je verrai ces
+lignes-l� en dehors des �clipses_." And the next day he observed the
+lines at the edge of the uneclipsed sun.  Huggins had suggested this
+observation in February, 1868, his idea being to use prisms of such
+great dispersive power that the continuous spectrum reflected by our
+atmosphere should be greatly weakened, while a bright line would
+suffer no diminution by the high dispersion.  On October 20th
+Lockyer,[10] having news of the eclipse, but not of Jansen's
+observations the day after, was able to see these lines. This was a
+splendid performance, for it enabled the prominences to be observed,
+not only during eclipses, but every day. Moreover, the next year
+Huggins was able, by using a wide slit, to see the whole of a
+prominence and note its shape.  Prominences are classified, according
+to their form, into "flame" and "cloud" prominences, the spectrum of
+the latter showing calcium, hydrogen, and helium; that of the former
+including a number of metals.
+
+The D line of sodium is a double line, and in the same eclipse (1868)
+an orange line was noticed which was afterwards found to lie close to
+the two components of the D line. It did not correspond with any known
+terrestrial element, and the unknown element was called "helium." It
+was not until 1895 that Sir William Ramsay found this element as a gas
+in the mineral cleavite.
+
+The spectrum of the corona is partly continuous, indicating light
+reflected from the sun's body. But it also shows a green line
+corresponding with no known terrestrial element, and the name
+"coronium" has been given to the substance causing it.
+
+A vast number of facts have been added to our knowledge about the sun
+by photography and the spectroscope. Speculations and hypotheses in
+plenty have been offered, but it may be long before we have a complete
+theory evolved to explain all the phenomena of the storm-swept
+metallic atmosphere of the sun.
+
+The proceedings of scientific societies teem with such facts and
+"working hypotheses," and the best of them have been collected by Miss
+Clerke in her _History of Astronomy during the Nineteenth Century_. As
+to established facts, we learn from the spectroscopic researches (1)
+that the continuous spectrum is derived from the _photosphere_ or
+solar gaseous material compressed almost to liquid consistency; (2)
+that the _reversing layer_ surrounds it and gives rise to black
+lines in the spectrum; that the _chromosphere_ surrounds this, is
+composed mainly of hydrogen, and is the cause of the red prominences
+in eclipses; and that the gaseous _corona_ surrounds all of
+these, and extends to vast distances outside the sun's visible
+surface.
+
+
+FOOTNOTES:
+
+[1] _Rosa Ursina_, by C. Scheiner, _fol_.; Bracciani, 1630.
+
+[2] _R. S. Phil. Trans_., 1774.
+
+[3] _Ibid_, 1783.
+
+[4] _Observations on the Spots on the Sun, etc.,_ 4�; London and
+Edinburgh, 1863.
+
+[5] _Periodicit�t der Sonnenflecken. Astron. Nach. XXI._, 1844,
+P. 234.
+
+[6] _R.S. Phil. Trans._ (ser. A), 1906, p. 69-100.
+
+[7] "Researches on Solar Physics," by De la Rue, Stewart and Loewy;
+_R. S. Phil. Trans_., 1869, 1870.
+
+[8] "The Sun as Photographed on the K line"; _Knowledge_, London,
+1903, p. 229.
+
+[9] _R. S. Proc._, xv., 1867, p. 256.
+
+[10] _Acad. des Sc._, Paris; _C. R._, lxvii., 1868, p. 121.
+
+
+
+13. THE MOON AND PLANETS.
+
+
+_The Moon_.--Telescopic discoveries about the moon commence with
+Galileo's discovery that her surface has mountains and valleys, like
+the earth. He also found that, while she always turns the same face to
+us, there is periodically a slight twist to let us see a little round
+the eastern or western edge. This was called _libration_, and the
+explanation was clear when it was understood that in showing always
+the same face to us she makes one revolution a month on her axis
+_uniformly_, and that her revolution round the earth is not
+uniform.
+
+Galileo said that the mountains on the moon showed greater differences
+of level than those on the earth.  Shr�ter supported this
+opinion. W. Herschel opposed it. But Beer and M�dler measured the
+heights of lunar mountains by their shadows, and found four of them
+over 20,000 feet above the surrounding plains.
+
+Langrenus [1] was the first to do serious work on selenography, and
+named the lunar features after eminent men. Riccioli also made lunar
+charts. In 1692 Cassini made a chart of the full moon. Since then we
+have the charts of Schr�ter, Beer and M�dler (1837), and of Schmidt,
+of Athens (1878); and, above all, the photographic atlas by Loewy and
+Puiseux.
+
+The details of the moon's surface require for their discussion a whole
+book, like that of Neison or the one by Nasmyth and Carpenter. Here a
+few words must suffice. Mountain ranges like our Andes or Himalayas
+are rare. Instead of that, we see an immense number of circular
+cavities, with rugged edges and flat interior, often with a cone in
+the centre, reminding one of instantaneous photographs of the splash
+of a drop of water falling into a pool. Many of these are fifty or
+sixty miles across, some more. They are generally spoken of as
+resembling craters of volcanoes, active or extinct, on the earth. But
+some of those who have most fully studied the shapes of craters deny
+altogether their resemblance to the circular objects on the moon.
+These so-called craters, in many parts, are seen to be closely
+grouped, especially in the snow-white parts of the moon. But there are
+great smooth dark spaces, like the clear black ice on a pond, more
+free from craters, to which the equally inappropriate name of seas has
+been given. The most conspicuous crater, _Tycho_, is near the south
+pole. At full moon there are seen to radiate from Tycho numerous
+streaks of light, or "rays," cutting through all the mountain
+formations, and extending over fully half the lunar disc, like the
+star-shaped cracks made on a sheet of ice by a blow.  Similar cracks
+radiate from other large craters. It must be mentioned that these
+white rays are well seen only in full light of the sun at full moon,
+just as the white snow in the crevasses of a glacier is seen bright
+from a distance only when the sun is high, and disappears at
+sunset. Then there are deep, narrow, crooked "rills" which may have
+been water-courses; also "clefts" about half a mile wide, and often
+hundreds of miles long, like deep cracks in the surface going straight
+through mountain and valley.
+
+The moon shares with the sun the advantage of being a good subject for
+photography, though the planets are not. This is owing to her larger
+apparent size, and the abundance of illumination. The consequence is
+that the finest details of the moon, as seen in the largest telescope
+in the world, may be reproduced at a cost within the reach of all.
+
+No certain changes have ever been observed; but several suspicions
+have been expressed, especially as to the small crater _Linn�_, in the
+_Mare Serenitatis_. It is now generally agreed that no certainty can
+be expected from drawings, and that for real evidence we must await
+the verdict of photography.
+
+No trace of water or of an atmosphere has been found on the moon. It
+is possible that the temperature is too low. In any case, no
+displacement of a star by atmospheric refraction at occultation has
+been surely recorded. The moon seems to be dead.
+
+The distance of the moon from the earth is just now the subject of
+re-measurement. The base line is from Greenwich to Cape of Good Hope,
+and the new feature introduced is the selection of a definite point on
+a crater (M�sting A), instead of the moon's edge, as the point whose
+distance is to be measured.
+
+_The Inferior Planets_.--When the telescope was invented, the phases
+of Venus attracted much attention; but the brightness of this planet,
+and her proximity to the sun, as with Mercury also, seemed to be a bar
+to the discovery of markings by which the axis and period of rotation
+could be fixed. Cassini gave the rotation as twenty-three hours, by
+observing a bright spot on her surface. Shr�ter made it 23h. 21m. 19s.
+This value was supported by others. In 1890 Schiaparelli[2] announced
+that Venus rotates, like our moon, once in one of her revolutions, and
+always directs the same face to the sun. This property has also been
+ascribed to Mercury; but in neither case has the evidence been
+generally accepted. Twenty-four hours is probably about the period of
+rotation for each of these planets.
+
+Several observers have claimed to have seen a planet within the orbit
+of Mercury, either in transit over the sun's surface or during an
+eclipse. It has even been named _Vulcan_. These announcements would
+have received little attention but for the fact that the motion of
+Mercury has irregularities which have not been accounted for by known
+planets; and Le Verrier[3] has stated that an intra-Mercurial planet
+or ring of asteroids would account for the unexplained part of the
+motion of the line of apses of Mercury's orbit amounting to 38" per
+century.
+
+_Mars_.--The first study of the appearance of Mars by Miraldi led him
+to believe that there were changes proceeding in the two white caps
+which are seen at the planet's poles. W. Herschel attributed these
+caps to ice and snow, and the dates of his observations indicated a
+melting of these ice-caps in the Martian summer.
+
+Schroter attributed the other markings on Mars to drifting clouds. But
+Beer and M�dler, in 1830-39, identified the same dark spots as being
+always in the same place, though sometimes blurred by mist in the
+local winter. A spot sketched by Huyghens in 1672, one frequently seen
+by W. Herschel in 1783, another by Arago in 1813, and nearly all the
+markings recorded by Beer and M�dler in 1830, were seen and drawn by
+F. Kaiser in Leyden during seventeen nights of the opposition of 1862
+(_Ast. Nacht._, No. 1,468), whence he deduced the period of rotation
+to be 24h. 37m. 22s.,62--or one-tenth of a second less than the period
+deduced by R. A. Proctor from a drawing by Hooke in 1666.
+
+It must be noted that, if the periods of rotation both of Mercury and
+Venus be about twenty-four hours, as seems probable, all the four
+planets nearest to the sun rotate in the same period, while the great
+planets rotate in about ten hours (Uranus and Neptune being still
+indeterminate).
+
+The general surface of Mars is a deep yellow; but there are dark grey
+or greenish patches. Sir John Herschel was the first to attribute the
+ruddy colour of Mars to its soil rather than to its atmosphere.
+
+The observations of that keen-sighted observer Dawes led to the first
+good map of Mars, in 1869. In the 1877 opposition Schiaparelli revived
+interest in the planet by the discovery of canals, uniformly about
+sixty miles wide, running generally on great circles, some of them
+being three or four thousand miles long. During the opposition of
+1881-2 the same observer re-observed the canals, and in twenty of them
+he found the canals duplicated,[4] the second canal being always 200
+to 400 miles distant from its fellow.
+
+The existence of these canals has been doubted.  Mr. Lowell has now
+devoted years to the subject, has drawn them over and over again, and
+has photographed them; and accepts the explanation that they are
+artificial, and that vegetation grows on their banks.  Thus is revived
+the old controversy between Whewell and Brewster as to the
+habitability of the planets. The new arguments are not yet generally
+accepted. Lowell believes he has, with the spectroscope, proved the
+existence of water on Mars.
+
+One of the most unexpected and interesting of all telescopic
+discoveries took place in the opposition of 1877, when Mars was
+unusually near to the earth. The Washington Observatory had acquired
+the fine 26-inch refractor, and Asaph Hall searched for satellites,
+concealing the planet's disc to avoid the glare. On August 11th he had
+a suspicion of a satellite. This was confirmed on the 16th, and on the
+following night a second one was added. They are exceedingly faint,
+and can be seen only by the most powerful telescopes, and only at the
+times of opposition. Their diameters are estimated at six or seven
+miles. It was soon found that the first, Deimos, completes its orbit
+in 30h. 18m.  But the other, Phobos, at first was a puzzle, owing to
+its incredible velocity being unsuspected. Later it was found that the
+period of revolution was only 7h. 39m. 22s. Since the Martian day is
+twenty-four and a half hours, this leads to remarkable results.
+Obviously the easterly motion of the satellite overwhelms the diurnal
+rotation of the planet, and Phobos must appear to the inhabitants, if
+they exist, to rise in the west and set in the east, showing two or
+even three full moons in a day, so that, sufficiently well for the
+ordinary purposes of life, the hour of the day can be told by its
+phases.
+
+The discovery of these two satellites is, perhaps, the most
+interesting telescopic visual discovery made with the large telescopes
+of the last half century; photography having been the means of
+discovering all the other new satellites except Jupiter's fifth (in
+order of discovery).
+
+[Illustration: JUPITER.  From a drawing by E. M. Antoniadi, showing
+transit of a satellite's shadow, the belts, and the "great red spot"
+(_Monthly Notices_, R. A. S., vol. lix., pl. x.).]
+
+_Jupiter._--Galileo's discovery of Jupiter's satellites was followed
+by the discovery of his belts. Zucchi and Torricelli seem to have seen
+them. Fontana, in 1633, reported three belts. In 1648 Grimaldi saw but
+two, and noticed that they lay parallel to the ecliptic. Dusky spots
+were also noticed as transient. Hooke[5] measured the motion of one in
+1664. In 1665 Cassini, with a fine telescope, 35-feet focal length,
+observed many spots moving from east to west, whence he concluded that
+Jupiter rotates on an axis like the earth. He watched an unusually
+permanent spot during twenty-nine rotations, and fixed the period at
+9h. 56m. Later he inferred that spots near the equator rotate quicker
+than those in higher latitudes (the same as Carrington found for the
+sun); and W. Herschel confirmed this in 1778-9.
+
+Jupiter's rapid rotation ought, according to Newton's theory, to be
+accompanied by a great flattening at the poles. Cassini had noted an
+oval form in 1691. This was confirmed by La Hire, R�mer, and
+Picard. Pound measured the ellipticity = 1/(13.25).
+
+W. Herschel supposed the spots to be masses of cloud in the
+atmosphere--an opinion still accepted.  Many of them were very
+permanent. Cassini's great spot vanished and reappeared nine times
+between 1665 and 1713. It was close to the northern margin of the
+southern belt. Herschel supposed the belts to be the body of the
+planet, and the lighter parts to be clouds confined to certain
+latitudes.
+
+In 1665 Cassini observed transits of the four satellites, and also saw
+their shadows on the planet, and worked out a lunar theory for
+Jupiter. Mathematical astronomers have taken great interest in the
+perturbations of the satellites, because their relative periods
+introduce peculiar effects. Airy, in his delightful book,
+_Gravitation_, has reduced these investigations to simple
+geometrical explanations.
+
+In 1707 and 1713 Miraldi noticed that the fourth satellite varies much
+in brightness. W. Herschel found this variation to depend upon its
+position in its orbit, and concluded that in the positions of
+feebleness it is always presenting to us a portion of its surface,
+which does not well reflect the sun's light; proving that it always
+turns the same face to Jupiter, as is the case with our moon. This
+fact had also been established for Saturn's fifth satellite, and may
+be true for all satellites.
+
+In 1826 Struve measured the diameters of the four satellites, and
+found them to be 2,429, 2,180, 3,561, and 3,046 miles.
+
+In modern times much interest has been taken in watching a rival to
+Cassini's famous spot. The "great red spot" was first observed by
+Niesten, Pritchett, and Tempel, in 1878, as a rosy cloud attached to a
+whitish zone beneath the dark southern equatorial band, shaped like
+the new war balloons, 30,000 miles long and 7,000 miles across. The
+next year it was brick-red. A white spot beside it completed a
+rotation in less time by 51/2 minutes than the red spot--a difference
+of 260 miles an hour. Thus they came together again every six weeks,
+but the motions did not continue uniform.  The spot was feeble in
+1882-4, brightened in 1886, and, after many changes, is still visible.
+
+Galileo's great discovery of Jupiter's four moons was the last word in
+this connection until September 9th, 1892, when Barnard, using the
+36-inch refractor of the Lick Observatory, detected a tiny spot of
+light closely following the planet. This proved to be a new satellite
+(fifth), nearer to the planet than any other, and revolving round it
+in 11h. 57m. 23s. Between its rising and setting there must be an
+interval of 21/2 Jovian days, and two or three full moons. The sixth
+and seventh satellites were found by the examination of photographic
+plates at the Lick Observatory in 1905, since which time they have
+been continuously photographed, and their orbits traced, at Greenwich.
+On examining these plates in 1908 Mr. Melotte detected the eighth
+satellite, which seems to be revolving in a retrograde orbit three
+times as far from its planet as the next one (seventh), in these two
+points agreeing with the outermost of Saturn's satellites (Phoebe).
+
+_Saturn._--This planet, with its marvellous ring, was perhaps the most
+wonderful object of those first examined by Galileo's telescope. He
+was followed by Dominique Cassini, who detected bands like Jupiter's
+belts. Herschel established the rotation of the planet in 1775-94.
+From observations during one hundred rotations he found the period to
+be 10h. 16m. 0s., 44. Herschel also measured the ratio of the polar to
+the equatoreal diameter as 10:11.
+
+The ring was a complete puzzle to Galileo, most of all when the planet
+reached a position where the plane of the ring was in line with the
+earth, and the ring disappeared (December 4th, 1612). It was not until
+1656 that Huyghens, in his small pamphlet _De Saturni Luna Observatio
+Nova_, was able to suggest in a cypher the ring form; and in 1659, in
+his Systema Saturnium, he gave his reasons and translated the cypher:
+"The planet is surrounded by a slender flat ring, everywhere distinct
+from its surface, and inclined to the ecliptic." This theory explained
+all the phases of the ring which had puzzled others. This ring was
+then, and has remained ever since, a unique structure.  We in this age
+have got accustomed to it. But Huyghens's discovery was received with
+amazement.
+
+In 1675 Cassini found the ring to be double, the concentric rings
+being separated by a black band--a fact which was placed beyond
+dispute by Herschel, who also found that the thickness of the ring
+subtends an angle less than 0".3. Shr�ter estimated its thickness at
+500 miles.
+
+Many speculations have been advanced to explain the origin and
+constitution of the ring. De Sejour said [6] that it was thrown off
+from Saturn's equator as a liquid ring, and afterwards solidified. He
+noticed that the outside would have a greater velocity, and be less
+attracted to the planet, than the inner parts, and that equilibrium
+would be impossible; so he supposed it to have solidified into a
+number of concentric rings, the exterior ones having the least
+velocity.
+
+Clerk Maxwell, in the Adams prize essay, gave a physico-mathematical
+demonstration that the rings must be composed of meteoritic matter
+like gravel. Even so, there must be collisions absorbing the energy of
+rotation, and tending to make the rings eventually fall into the
+planet. The slower motion of the external parts has been proved by the
+spectroscope in Keeler's hands, 1895.
+
+Saturn has perhaps received more than its share of attention owing to
+these rings. This led to other discoveries. Huyghens in 1655, and
+J. D. Cassini in 1671, discovered the sixth and eighth satellites
+(Titan and Japetus). Cassini lost his satellite, and in searching for
+it found Rhea (the fifth) in 1672, besides his old friend, whom he
+lost again. He added the third and fourth in 1684 (Tethys and
+Dione). The first and second (Mimas and Encelades) were added by
+Herschel in 1789, and the seventh (Hyperion) simultaneously by Lassel
+and Bond in 1848. The ninth (Phoebe) was found on photographs, by
+Pickering in 1898, with retrograde motion; and he has lately added a
+tenth.
+
+The occasional disappearance of Cassini's Japetus was found on
+investigation to be due to the same causes as that of Jupiter's fourth
+satellite, and proves that it always turns the same face to the
+planet.
+
+_Uranus and Neptune_.--The splendid discoveries of Uranus and two
+satellites by Sir William Herschel in 1787, and of Neptune by Adams
+and Le Verrier in 1846, have been already described. Lassel added two
+more satellites to Uranus in 1851, and found Neptune's satellite in
+1846. All of the satellites of Uranus have retrograde motion, and
+their orbits are inclined about 80� to the ecliptic.
+
+The spectroscope has shown the existence of an absorbing atmosphere on
+Jupiter and Saturn, and there are suspicions that they partake
+something of the character of the sun, and emit some light besides
+reflecting solar light. On both planets some absorption lines seem to
+agree with the aqueous vapour lines of our own atmosphere; while one,
+which is a strong band in the red common to both planets, seems to
+agree with a line in the spectrum of some reddish stars.
+
+Uranus and Neptune are difficult to observe spectroscopically, but
+appear to have peculiar spectra agreeing together. Sometimes Uranus
+shows Frauenhofer lines, indicating reflected solar light. But
+generally these are not seen, and six broad bands of absorption
+appear.  One is the F. of hydrogen; another is the red-star line of
+Jupiter and Saturn. Neptune is a very difficult object for the
+spectroscope.
+
+Quite lately [7] P. Lowell has announced that V. M.  Slipher, at
+Flagstaff Observatory, succeeded in 1907 in rendering some plates
+sensitive far into the red. A reproduction is given of photographed
+spectra of the four outermost planets, showing (1) a great number of
+new lines and bands; (2) intensification of hydrogen F.  and C. lines;
+(3) a steady increase of effects (1) and (2) as we pass from Jupiter
+and Saturn to Uranus, and a still greater increase in Neptune.
+
+_Asteroids_.--The discovery of these new planets has been
+described. At the beginning of the last century it was an immense
+triumph to catch a new one. Since photography was called into the
+service by Wolf, they have been caught every year in shoals. It is
+like the difference between sea fishing with the line and using a
+steam trawler. In the 1908 almanacs nearly seven hundred asteroids are
+included. The computation of their perturbations and ephemerides by
+Euler's and Lagrange's method of variable elements became so laborious
+that Encke devised a special process for these, which can be applied
+to many other disturbed orbits. [8]
+
+When a photograph is taken of a region of the heavens including an
+asteroid, the stars are photographed as points because the telescope
+is made to follow their motion; but the asteroids, by their proper
+motion, appear as short lines.
+
+The discovery of Eros and the photographic attack upon its path have
+been described in their relation to finding the sun's distance.
+
+A group of four asteroids has lately been found, with a mean distance
+and period equal to that of Jupiter. To three of these masculine names
+have been given--Hector, Patroclus, Achilles; the other has not yet
+been named.
+
+
+FOOTNOTES:
+
+[1] Langrenus (van Langren), F. Selenographia sive lumina austriae
+philippica; Bruxelles, 1645.
+
+[2] _Astr. Nach._, 2,944.
+
+[3] _Acad. des Sc._, Paris; _C.R._, lxxxiii., 1876.
+
+[4] _Mem. Spettr. Ital._, xi., p. 28.
+
+[5] _R. S. Phil. Trans_., No. 1.
+
+[6] Grant's _Hist. Ph. Ast_., p. 267.
+
+[7] _Nature_, November 12th, 1908.
+
+[8] _Ast. Nach_., Nos. 791, 792, 814, translated by G. B. Airy.
+_Naut. Alm_., Appendix, 1856.
+
+
+
+14. COMETS AND METEORS.
+
+
+Ever since Halley discovered that the comet of 1682 was a member of
+the solar system, these wonderful objects have had a new interest for
+astronomers; and a comparison of orbits has often identified the
+return of a comet, and led to the detection of an elliptic orbit where
+the difference from a parabola was imperceptible in the small portion
+of the orbit visible to us. A remarkable case in point was the comet
+of 1556, of whose identity with the comet of 1264 there could be
+little doubt.  Hind wanted to compute the orbit more exactly than
+Halley had done. He knew that observations had been made, but they
+were lost. Having expressed his desire for a search, all the
+observations of Fabricius and of Heller, and also a map of the comet's
+path among the stars, were eventually unearthed in the most unlikely
+manner, after being lost nearly three hundred years.  Hind and others
+were certain that this comet would return between 1844 and 1848, but
+it never appeared.
+
+When the spectroscope was first applied to finding the composition of
+the heavenly bodies, there was a great desire to find out what comets
+are made of. The first opportunity came in 1864, when Donati observed
+the spectrum of a comet, and saw three bright bands, thus proving that
+it was a gas and at least partly self-luminous.  In 1868 Huggins
+compared the spectrum of Winnecke's comet with that of a Geissler tube
+containing olefiant gas, and found exact agreement. Nearly all comets
+have shown the same spectrum.[1] A very few comets have given bright
+band spectra differing from the normal type. Also a certain kind of
+continuous spectrum, as well as reflected solar light showing
+Frauenhofer lines, have been seen.
+
+[Illustration: COPY OF THE DRAWING MADE BY PAUL FABRICIUS.  To define
+the path of comet 1556. After being lost for 300 years, this drawing
+was recovered by the prolonged efforts of Mr. Hind and Professor
+Littrow in 1856.]
+
+When Wells's comet, in 1882, approached very close indeed to the sun,
+the spectrum changed to a mono-chromatic yellow colour, due to sodium.
+
+For a full account of the wonders of the cometary world the reader is
+referred to books on descriptive astronomy, or to monographs on
+comets.[2] Nor can the very uncertain speculations about the structure
+of comets' tails be given here. A new explanation has been proposed
+almost every time that a great discovery has been made in the theory
+of light, heat, chemistry, or electricity.
+
+Halley's comet remained the only one of which a prediction of the
+return had been confirmed, until the orbit of the small, ill-defined
+comet found by Pons in 1819 was computed by Encke, and found to have a
+period of 3 1/3 years. It was predicted to return in 1822, and was
+recognised by him as identical with many previous comets. This comet,
+called after Encke, has showed in each of its returns an inexplicable
+reduction of mean distance, which led to the assertion of a resisting
+medium in space until a better explanation could be found.[3]
+
+Since that date fourteen comets have been found with elliptic orbits,
+whose aphelion distances are all about the same as Jupiter's mean
+distance; and six have an aphelion distance about ten per cent,
+greater than Neptune's mean distance. Other comets are similarly
+associated with the planets Saturn and Uranus.
+
+The physical transformations of comets are among the most wonderful of
+unexplained phenomena in the heavens. But, for physical astronomers,
+the greatest interest attaches to the reduction of radius vector of
+Encke's comet, the splitting of Biela's comet into two comets in 1846,
+and the somewhat similar behaviour of other comets. It must be noted,
+however, that comets have a sensible size, that all their parts cannot
+travel in exactly the same orbit under the sun's gravitation, and that
+their mass is not sufficient to retain the parts together very
+forcibly; also that the inevitable collision of particles, or else
+fluid friction, is absorbing energy, and so reducing the comet's
+velocity.
+
+In 1770 Lexell discovered a comet which, as was afterwards proved by
+investigations of Lexell, Burchardt, and Laplace, had in 1767 been
+deflected by Jupiter out of an orbit in which it was invisible from
+the earth into an orbit with a period of 51/2 years, enabling it to be
+seen. In 1779 it again approached Jupiter closer than some of his
+satellites, and was sent off in another orbit, never to be again
+recognised.
+
+But our interest in cometary orbits has been added to by the discovery
+that, owing to the causes just cited, a comet, if it does not separate
+into discrete parts like Biela's, must in time have its parts spread
+out so as to cover a sensible part of the orbit, and that, when the
+earth passes through such part of a comet's orbit, a meteor shower is
+the result.
+
+A magnificent meteor shower was seen in America on November 12th-13th,
+1833, when the paths of the meteors all seemed to radiate from a point
+in the constellation Leo. A similar display had been witnessed in
+Mexico by Humboldt and Bonpland on November 12th, 1799. H. A. Newton
+traced such records back to October 13th, A.D. 902. The orbital motion
+of a cloud or stream of small particles was indicated. The period
+favoured by H. A. Newton was 3541/2 days; another suggestion was 3751/2
+days, and another 331/4 years.  He noticed that the advance of the date
+of the shower between 902 and 1833, at the rate of one day in seventy
+years, meant a progression of the node of the orbit.  Adams undertook
+to calculate what the amount would be on all the five suppositions
+that had been made about the period. After a laborious work, he found
+that none gave one day in seventy years except the 331/4-year period,
+which did so exactly. H. A. Newton predicted a return of the shower on
+the night of November 13th-14th, 1866. He is now dead; but many of us
+are alive to recall the wonder and enthusiasm with which we saw this
+prediction being fulfilled by the grandest display of meteors ever
+seen by anyone now alive.
+
+The _progression_ of the nodes proved the path of the meteor
+stream to be retrograde. The _radiant_ had almost the exact
+longitude of the point towards which the earth was moving. This proved
+that the meteor cluster was at perihelion. The period being known, the
+eccentricity of the orbit was obtainable, also the orbital velocity of
+the meteors in perihelion; and, by comparing this with the earth's
+velocity, the latitude of the radiant enabled the inclination to be
+determined, while the longitude of the earth that night was the
+longitude of the node. In such a way Schiaparelli was able to find
+first the elements of the orbit of the August meteor shower
+(Perseids), and to show its identity with the orbit of Tuttle's comet
+1862.iii. Then, in January 1867, Le Verrier gave the elements of the
+November meteor shower (Leonids); and Peters, of Altona, identified
+these with Oppolzer's elements for Tempel's comet 1866--Schiaparelli
+having independently attained both of these results. Subsequently
+Weiss, of Vienna, identified the meteor shower of April 20th (Lyrids)
+with comet 1861. Finally, that indefatigable worker on meteors,
+A. S. Herschel, added to the number, and in 1878 gave a list of
+seventy-six coincidences between cometary and meteoric orbits.
+
+Cometary astronomy is now largely indebted to photography, not merely
+for accurate delineations of shape, but actually for the discovery of
+most of them.  The art has also been applied to the observation of
+comets at distances from their perihelia so great as to prevent their
+visual observation. Thus has Wolf, of Heidelburg, found upon old
+plates the position of comet 1905.v., as a star of the 15.5 magnitude,
+783 days before the date of its discovery. From the point of view of
+the importance of finding out the divergence of a cometary orbit from
+a parabola, its period, and its aphelion distance, this increase of
+range attains the very highest value.
+
+The present Astronomer Royal, appreciating this possibility, has been
+searching by photography for Halley's comet since November, 1907,
+although its perihelion passage will not take place until April, 1910.
+
+
+FOOTNOTES:
+
+[1] In 1874, when the writer was crossing the Pacific Ocean in
+H.M.S. "Scout," Coggia's comet unexpectedly appeared, and (while
+Colonel Tupman got its positions with the sextant) he tried to use the
+prism out of a portable direct-vision spectroscope, without success
+until it was put in front of the object-glass of a binocular, when, to
+his great joy, the three band images were clearly seen.
+
+[2] Such as _The World of Comets_, by A. Guillemin; _History of
+Comets_, by G. R. Hind, London, 1859; _Theatrum Cometicum_, by S. de
+Lubienietz, 1667; _Cometographie_, by Pingr�, Paris, 1783; _Donati's
+Comet_, by Bond.
+
+[3] The investigations by Von Asten (of St. Petersburg) seem to
+support, and later ones, especially those by Backlund (also of
+St. Petersburg), seem to discredit, the idea of a resisting medium.
+
+
+
+15. THE FIXED STARS AND NEBUL�.
+
+
+Passing now from our solar system, which appears to be subject to the
+action of the same forces as those we experience on our globe, there
+remains an innumerable host of fixed stars, nebulas, and nebulous
+clusters of stars. To these the attention of astronomers has been more
+earnestly directed since telescopes have been so much enlarged.
+Photography also has enabled a vast amount of work to be covered in a
+comparatively short period, and the spectroscope has given them the
+means, not only of studying the chemistry of the heavens, but also of
+detecting any motion in the line of sight from less than a mile a
+second and upwards in any star, however distant, provided it be bright
+enough.
+
+[Illustration: SIR WILLIAM HERSCHEL, F.R.S.--1738-1822.  Painted by
+Lemuel F. Abbott; National Portrait Gallery, Room XX.]
+
+In the field of telescopic discovery beyond our solar system there is
+no one who has enlarged our knowledge so much as Sir William Herschel,
+to whom we owe the greatest discovery in dynamical astronomy among the
+stars--viz., that the law of gravitation extends to the most distant
+stars, and that many of them describe elliptic orbits about each
+other. W. Herschel was born at Hanover in 1738, came to England in
+1758 as a trained musician, and died in 1822. He studied science when
+he could, and hired a telescope, until he learnt to make his own
+specula and telescopes. He made 430 parabolic specula in twenty-one
+years. He discovered 2,500 nebul� and 806 double stars, counted the
+stars in 3,400 guage-fields, and compared the principal stars
+photometrically.
+
+Some of the things for which he is best known were results of those
+accidents that happen only to the indefatigable enthusiast. Such was
+the discovery of Uranus, which led to funds being provided for
+constructing his 40-feet telescope, after which, in 1786, he settled
+at Slough. In the same way, while trying to detect the annual parallax
+of the stars, he failed in that quest, but discovered binary systems
+of stars revolving in ellipses round each other; just as Bradley's
+attack on stellar parallax failed, but led to the discovery of
+aberration, nutation, and the true velocity of light.
+
+_Parallax_.--The absence of stellar parallax was the great
+objection to any theory of the earth's motion prior to Kepler's
+time. It is true that Kepler's theory itself could have been
+geometrically expressed equally well with the earth or any other point
+fixed. But in Kepler's case the obviously implied physical theory of
+the planetary motions, even before Newton explained the simplicity of
+conception involved, made astronomers quite ready to waive the claim
+for a rigid proof of the earth's motion by measurement of an annual
+parallax of stars, which they had insisted on in respect of
+Copernicus's revival of the idea of the earth's orbital motion.
+
+Still, the desire to measure this parallax was only intensified by the
+practical certainty of its existence, and by repeated failures. The
+attempts of Bradley failed. The attempts of Piazzi and Brinkley,[1]
+early in the nineteenth century, also failed. The first successes,
+afterwards confirmed, were by Bessel and Henderson.  Both used stars
+whose proper motion had been found to be large, as this argued
+proximity. Henderson, at the Cape of Good Hope, observed alpha
+Centauri, whose annual proper motion he found to amount to 3".6, in
+1832-3; and a few years later deduced its parallax 1".16.  His
+successor at the Cape, Maclear, reduced this to 0".92.
+
+In 1835 Struve assigned a doubtful parallax of 0".261 to Vega (alpha
+Lyr�). But Bessel's observations, between 1837 and 1840, of 61 Cygni,
+a star with the large proper motion of over 5", established its annual
+parallax to be 0".3483; and this was confirmed by Peters, who found
+the value 0".349.
+
+Later determinations for alpha2 Centauri, by Gill,[2] make its parallax
+0".75--This is the nearest known fixed star; and its light takes 4 1/3
+years to reach us. The light year is taken as the unit of measurement
+in the starry heavens, as the earth's mean distance is "the
+astronomical unit" for the solar system.[3] The proper motions and
+parallaxes combined tell us the velocity of the motion of these stars
+across the line of sight: alpha Centauri 14.4 miles a second=4.2
+astronomical units a year; 61 Cygni 37.9 miles a second=11.2
+astronomical units a year. These successes led to renewed zeal, and
+now the distances of many stars are known more or less accurately.
+
+Several of the brightest stars, which might be expected to be the
+nearest, have not shown a parallax amounting to a twentieth of a
+second of arc. Among these are Canopus, alpha Orionis, alpha Cygni, beta
+Centauri, and gamma Cassiopeia. Oudemans has published a list of
+parallaxes observed.[4]
+
+_Proper Motion._--In 1718 Halley[5] detected the proper motions
+of Arcturus and Sirius. In 1738 J. Cassinis[6] showed that the former
+had moved five minutes of arc since Tycho Brahe fixed its position. In
+1792 Piazzi noted the motion of 61 Cygni as given above. For a long
+time the greatest observed proper motion was that of a small star 1830
+Groombridge, nearly 7" a year; but others have since been found
+reaching as much as 10".
+
+Now the spectroscope enables the motion of stars to be detected at a
+single observation, but only that part of the motion that is in the
+line of sight. For a complete knowledge of a star's motion the proper
+motion and parallax must also be known.
+
+When Huggins first applied the Doppler principle to measure velocities
+in the line of sight,[7] the faintness of star spectra diminished the
+accuracy; but V�gel, in 1888, overcame this to a great extent by long
+exposures of photographic plates.
+
+It has often been noticed that stars which seem to belong to a group
+of nearly uniform magnitude have the same proper motion. The
+spectroscope has shown that these have also often the same velocity in
+the line of sight. Thus in the Great Bear, beta, gamma, delta,
+epsilon, zeta, all agree as to angular proper motion. delta was too
+faint for a spectroscopic measurement, but all the others have been
+shown to be approaching us at a rate of twelve to twenty miles a
+second. The same has been proved for proper motion, and line of sight
+motion, in the case of Pleiades and other groups.
+
+Maskelyne measured many proper motions of stars, from which W.
+Herschel[8] came to the conclusion that these apparent motions are for
+the most part due to a motion of the solar system in space towards a
+point in the constellation Hercules, R.A. 257�; N. Decl. 25�.  This
+grand discovery has been amply confirmed, and, though opinions differ
+as to the exact direction, it happens that the point first indicated
+by Herschel, from totally insufficient data, agrees well with modern
+estimates.
+
+Comparing the proper motions and parallaxes to get the actual velocity
+of each star relative to our system, C.L. Struve found the probable
+velocity of the solar system in space to be fifteen miles a second, or
+five astronomical units a year.
+
+The work of Herschel in this matter has been checked by comparing
+spectroscopic velocities in the line of sight which, so far as the
+sun's motion is concerned, would give a maximum rate of approach for
+stars near Hercules, a maximum rate of recession for stars in the
+opposite part of the heavens, and no effect for stars half-way
+between. In this way the spectroscope has confirmed generally
+Herschel's view of the direction, and makes the velocity eleven miles
+a second, or nearly four astronomical units a year.
+
+The average proper motion of a first magnitude star has been found to
+be 0".25 annually, and of a sixth magnitude star 0".04. But that all
+bright stars are nearer than all small stars, or that they show
+greater proper motion for that reason, is found to be far from the
+truth. Many statistical studies have been made in this connection, and
+interesting results may be expected from this treatment in the hands
+of Kapteyn of Groningen, and others.[9]
+
+On analysis of the directions of proper motions of stars in all parts
+of the heavens, Kapteyn has shown[10] that these indicate, besides the
+solar motion towards Hercules, two general drifts of stars in nearly
+opposite directions, which can be detected in any part of the
+heavens. This result has been confirmed from independent data by
+Eddington (_R.A.S., M.N._) and Dyson (_R.S.E. Proc._).
+
+Photography promises to assist in the measurement of parallax and
+proper motions. Herr Pulfrich, of the firm of Carl Zeiss, has vastly
+extended the applications of stereoscopic vision to astronomy--a
+subject which De la Rue took up in the early days of photography.  He
+has made a stereo-comparator of great beauty and convenience for
+comparing stereoscopically two star photographs taken at different
+dates. Wolf of Heidelberg has used this for many purposes. His
+investigations depending on the solar motion in space are remarkable.
+He photographs stars in a direction at right angles to the line of the
+sun's motion. He has taken photographs of the same region fourteen
+years apart, the two positions of his camera being at the two ends of
+a base-line over 5,000,000,000 miles apart, or fifty-six astronomical
+units. On examining these stereoscopically, some of the stars rise out
+of the general plane of the stars, and seem to be much nearer. Many of
+the stars are thus seen to be suspended in space at different
+distances corresponding exactly to their real distances from our solar
+system, except when their proper motion interferes. The effect is most
+striking; the accuracy of measurement exceeds that of any other method
+of measuring such displacements, and it seems that with a long
+interval of time the advantage of the method increases.
+
+_Double Stars._--The large class of double stars has always been much
+studied by amateurs, partly for their beauty and colour, and partly as
+a test for telescopic definition. Among the many unexplained stellar
+problems there is one noticed in double stars that is thought by some
+to be likely to throw light on stellar evolution. It is this: There
+are many instances where one star of the pair is comparatively faint,
+and the two stars are contrasted in colour; and in every single case
+the general colour of the faint companion is invariably to be classed
+with colours more near to the blue end of the spectrum than that of
+the principal star.
+
+_Binary Stars._--Sir William Herschel began his observations of double
+stars in the hope of discovering an annual parallax of the stars. In
+this he was following a suggestion of Galileo's. The presumption is
+that, if there be no physical connection between the stars of a pair,
+the largest is the nearest, and has the greatest parallax. So, by
+noting the distance between the pair at different times of the year, a
+delicate test of parallax is provided, unaffected by major
+instrumental errors.
+
+Herschel did, indeed, discover changes of distance, but not of the
+character to indicate parallax. Following this by further observation,
+he found that the motions were not uniform nor rectilinear, and by a
+clear analysis of the movements he established the remarkable and
+wholly unexpected fact that in all these cases the motion is due to a
+revolution about their common centre of gravity.[11] He gave the
+approximate period of revolution of some of these: Castor, 342 years;
+delta Serpentis, 375 years; gamma Leonis, 1,200 years; epsilon Bootis,
+1,681 years.
+
+Twenty years later Sir John Herschel and Sir James South, after
+re-examination of these stars, confirmed[12] and extended the results,
+one pair of Coron� having in the interval completed more than a whole
+revolution.
+
+It is, then, to Sir William Herschel that we owe the extension of the
+law of gravitation, beyond the limits of the solar system, to the
+whole universe. His observations were confirmed by F.G.W. Struve (born
+1793, died 1864), who carried on the work at Dorpat. But it was first
+to Savary,[13] and later to Encke and Sir John Herschel, that we owe
+the computation of the elliptic elements of these stars; also the
+resulting identification of their law of force with Newton's force of
+gravitation applied to the solar system, and the force that makes an
+apple fall to the ground. As Grant well says in his _History_:
+"This may be justly asserted to be one of the most sublime truths
+which astronomical science has hitherto disclosed to the researches of
+the human mind."
+
+Latterly the best work on double stars has been done by
+S. W. Burnham,[14] at the Lick Observatory. The shortest period he
+found was eleven years (kappa Pegasi).  In the case of some of
+these binaries the parallax has been measured, from which it appears
+that in four of the surest cases the orbits are about the size of the
+orbit of Uranus, these being probably among the smallest stellar
+orbits.
+
+The law of gravitation having been proved to extend to the stars, a
+discovery (like that of Neptune in its origin, though unlike it in the
+labour and originality involved in the calculation) that entrances the
+imagination became possible, and was realised by Bessel--the discovery
+of an unknown body by its gravitational disturbance on one that was
+visible. In 1834 and 1840 he began to suspect a want of uniformity in
+the proper motion of Sirius and Procyon respectively. In 1844, in a
+letter to Sir John Herschel,[15] he attributed these irregularities in
+each case to the attraction of an invisible companion, the period of
+revolution of Sirius being about half a century. Later he said: "I
+adhere to the conviction that Procyon and Sirius form real binary
+systems, consisting of a visible and an invisible star.  There is no
+reason to suppose luminosity an essential quality of cosmical
+bodies. The visibility of countless stars is no argument against the
+invisibility of countless others." This grand conception led Peters to
+compute more accurately the orbit, and to assign the place of the
+invisible companion of Sirius. In 1862 Alvan G. Clark was testing a
+new 18-inch object-glass (now at Chicago) upon Sirius, and, knowing
+nothing of these predictions, actually found the companion in the very
+place assigned to it. In 1896 the companion of Procyon was discovered
+by Professor Schaeberle at the Lick Observatory.
+
+Now, by the refined parallax determinations of Gill at the Cape, we
+know that of Sirius to be 0".38. From this it has been calculated that
+the mass of Sirius equals two of our suns, and its intrinsic
+brightness equals twenty suns; but the companion, having a mass equal
+to our sun, has only a five-hundredth part of the sun's brightness.
+
+_Spectroscopic Binaries_.--On measuring the velocity of a star in the
+line of sight at frequent intervals, periodic variations have been
+found, leading to a belief in motion round an invisible
+companion. Vogel, in 1889, discovered this in the case of Spica (alpha
+Virginis), whose period is 4d. 0h. 19m., and the diameter of whose
+orbit is six million miles. Great numbers of binaries of this type
+have since then been discovered, all of short period.
+
+Also, in 1889, Pickering found that at regular intervals of fifty-two
+days the lines in the spectrum of zeta of the Great Bear are
+duplicated, indicating a relative velocity, equal to one hundred miles
+a second, of two components revolving round each other, of which that
+apparently single star must be composed.
+
+It would be interesting, no doubt, to follow in detail the
+accumulating knowledge about the distances, proper motions, and orbits
+of the stars; but this must be done elsewhere. Enough has been said to
+show how results are accumulating which must in time unfold to us the
+various stellar systems and their mutual relationships.
+
+_Variable Stars._--It has often happened in the history of different
+branches of physical science that observation and experiment were so
+far ahead of theory that hopeless confusion appeared to reign; and
+then one chance result has given a clue, and from that time all
+differences and difficulties in the previous researches have stood
+forth as natural consequences, explaining one another in a rational
+sequence. So we find parallax, proper motion, double stars, binary
+systems, variable stars, and new stars all bound together.
+
+The logical and necessary explanation given of the cause of ordinary
+spectroscopic binaries, and of irregular proper motions of Sirius and
+Procyon, leads to the inference that if ever the plane of such a
+binary orbit were edge-on to us there ought to be an eclipse of the
+luminous partner whenever the non-luminous one is interposed between
+us. This should give rise either to intermittence in the star's light
+or else to variability.  It was by supposing the existence of a dark
+companion to Algol that its discoverer, Goodricke of York,[16] in
+1783, explained variable stars of this type. Algol (beta Persei)
+completes the period of variable brightness in 68.8 hours. It loses
+three-fifths of its light, and regains it in twelve hours. In 1889
+Vogel,[17] with the Potsdam spectrograph, actually found that the
+luminous star is receding before each eclipse, and approaching us
+after each eclipse; thus entirely supporting Goodricke's opinion.
+There are many variables of the Algol type, and information is
+steadily accumulating. But all variable stars do not suffer the sudden
+variations of Algol. There are many types, and the explanations of
+others have not proved so easy.
+
+The Harvard College photographs have disclosed the very great
+prevalence of variability, and this is certainly one of the lines in
+which modern discovery must progress.
+
+Roberts, in South Africa, has done splendid work on the periods of
+variables of the Algol type.
+
+_New Stars_.--Extreme instances of variable stars are the new stars
+such as those detected by Hipparchus, Tycho Brahe, and Kepler, of
+which many have been found in the last half-century. One of the latest
+great "Nov�" was discovered in Auriga by a Scotsman, Dr. Anderson, on
+February 1st, 1892, and, with the modesty of his race, he communicated
+the fact to His Majesty's Astronomer for Scotland on an unsigned
+post-card.[18] Its spectrum was observed and photographed by Huggins
+and many others. It was full of bright lines of hydrogen, calcium,
+helium, and others not identified. The astounding fact was that lines
+were shown in pairs, bright and dark, on a faint continuous spectrum,
+indicating apparently that a dark body approaching us at the rate of
+550 miles a second[19] was traversing a cold nebulous atmosphere, and
+was heated to incandescence by friction, like a meteor in our
+atmosphere, leaving a luminous train behind it. It almost disappeared,
+and on April 26th it was of the sixteenth magnitude; but on August
+17th it brightened to the tenth, showing the principal nebular band in
+its spectrum, and no sign of approach or recession.  It was as if it
+emerged from one part of the nebula, cooled down, and rushed through
+another part of the nebula, rendering the nebular gas more luminous
+than itself.[20]
+
+Since 1892 one Nova after another has shown a spectrum as described
+above, like a meteor rushing towards us and leaving a train behind,
+for this seems to be the obvious meaning of the spectra.
+
+The same may be said of the brilliant Nova Persei, brighter at its
+best than Capella, and discovered also by Dr. Anderson on February
+22nd, 1901. It increased in brightness as it reached the densest part
+of the nebula, then it varied for some weeks by a couple of
+magnitudes, up and down, as if passing through separate nebular
+condensations. In February, 1902, it could still be seen with an
+opera-glass. As with the other Nov�, when it first dashed into the
+nebula it was vaporised and gave a continuous spectrum with dark lines
+of hydrogen and helium. It showed no bright lines paired with the dark
+ones to indicate a train left behind; but in the end its own
+luminosity died out, and the nebular spectrum predominated.
+
+The nebular illumination as seen in photographs, taken from August to
+November, seemed to spread out slowly in a gradually increasing circle
+at the rate of 90" in forty-eight days. Kapteyn put this down to the
+velocity of light, the original outburst sending its illumination to
+the nebulous gas and illuminating a spherical shell whose radius
+increased at the velocity of light. This supposition seems correct, in
+which case it can easily be shown from the above figures that the
+distance of this Nova was 300 light years.
+
+_Star Catalogues._--Since the days of very accurate observations
+numerous star-catalogues have been produced by individuals or by
+observatories. Bradley's monumental work may be said to head the list.
+Lacaille's, in the Southern hemisphere, was complementary.  Then
+Piazzi, Lalande, Groombridge, and Bessel were followed by Argelander
+with his 324,000 stars, Rumker's Paramatta catalogue of the southern
+hemisphere, and the frequent catalogues of national observatories.
+Later the Astronomische Gesellschaft started their great catalogue,
+the combined work of many observatories. Other southern ones were
+Gould's at Cordova and Stone's at the Cape.
+
+After this we have a new departure. Gill at the Cape, having the comet
+1882.ii. all to himself in those latitudes, wished his friends in
+Europe to see it, and employed a local photographer to strap his
+camera to the observatory equatoreal, driven by clockwork, and
+adjusted on the comet by the eye. The result with half-an-hour's
+exposure was good, so he tried three hours. The result was such a
+display of sharp star images that he resolved on the Cape Photographic
+Durchmusterung, which after fourteen years, with Kapteyn's aid in
+reducing, was completed. Meanwhile the brothers Henry, of Paris, were
+engaged in going over Chacornac's zodiacal stars, and were about to
+catalogue the Milky Way portion, a serious labour, when they saw
+Gill's Comet photograph and conceived the idea of doing the rest of
+their work by photography.  Gill had previously written to Admiral
+Mouchez, of the Paris Observatory, and explained to him his project
+for charting the heavens photographically, by combining the work of
+many observatories. This led Admiral Mouchez to support the brothers
+Henry in their scheme.[21] Gill, having got his own photographic work
+underway, suggested an international astrographic chart, the materials
+for different zones to be supplied by observatories of all nations,
+each equipped with similar photographic telescopes. At a conference in
+Paris, 1887, this was decided on, the stars on the charts going down
+to the fourteenth magnitude, and the catalogues to the eleventh.
+
+[Illustration: GREAT COMET, Nov. 14TH, 1882. (Exposure 2hrs. 20m.)  By
+kind permission of Sir David Gill. From this photograph originated all
+stellar chart-photography.]
+
+This monumental work is nearing completion. The labour involved was
+immense, and the highest skill was required for devising instruments
+and methods to read off the star positions from the plates.
+
+Then we have the Harvard College collection of photographic plates,
+always being automatically added to; and their annex at Arequipa in
+Peru.
+
+Such catalogues vary in their degree of accuracy; and fundamental
+catalogues of standard stars have been compiled. These require
+extension, because the differential methods of the heliometer and the
+camera cannot otherwise be made absolute.
+
+The number of stars down to the fourteenth magnitude may be taken at
+about 30,000,000; and that of all the stars visible in the greatest
+modern telescopes is probably about 100,000,000.
+
+_Nebul� and Star-clusters._--Our knowledge of nebul� really dates from
+the time of W. Herschel. In his great sweeps of the heavens with his
+giant telescopes he opened in this direction a new branch of
+astronomy.  At one time he held that all nebul� might be clusters of
+innumerable minute stars at a great distance. Then he recognised the
+different classes of nebul�, and became convinced that there is a
+widely-diffused "shining fluid" in space, though many so-called nebul�
+could be resolved by large telescopes into stars.  He considered that
+the Milky Way is a great star cluster, whose form may be conjectured
+from numerous star-gaugings. He supposed that the compact "planetary
+nebul�" might show a stage of evolution from the diffuse nebul�, and
+that his classifications actually indicate various stages of
+development. Such speculations, like those of the ancients about the
+solar system, are apt to be harmful to true progress of knowledge
+unless in the hands of the ablest mathematical physicists; and
+Herschel violated their principles in other directions. But here his
+speculations have attracted a great deal of attention, and, with
+modifications, are accepted, at least as a working hypothesis, by a
+fair number of people.
+
+When Sir John Herschel had extended his father's researches into the
+Southern Hemisphere he was also led to the belief that some nebulae
+were a phosphorescent material spread through space like fog or mist.
+
+Then his views were changed by the revelations due to the great
+discoveries of Lord Rosse with his gigantic refractor,[22] when one
+nebula after another was resolved into a cluster of minute stars. At
+that time the opinion gained ground that with increase of telescopic
+power this would prove to be the case with all nebul�.
+
+In 1864 all doubt was dispelled by Huggins[23] in his first examination
+of the spectrum of a nebula, and the subsequent extension of this
+observation to other nebul�; thus providing a certain test which
+increase in the size of telescopes could never have given. In 1864
+Huggins found that all true nebulae give a spectrum of bright
+lines. Three are due to hydrogen; two (discovered by Copeland) are
+helium lines; others are unknown. Fifty-five lines have been
+photographed in the spectrum of the Orion nebula. It seems to be
+pretty certain that all true nebulae are gaseous, and show almost
+exactly the same spectrum.
+
+Other nebul�, and especially the white ones like that in Andromeda,
+which have not yet been resolved into stars, show a continuous
+spectrum; others are greenish and give no lines.
+
+A great deal has to be done by the chemist before the astronomer can
+be on sure ground in drawing conclusions from certain portions of his
+spectroscopic evidence.
+
+The light of the nebulas is remarkably actinic, so that photography
+has a specially fine field in revealing details imperceptible in the
+telescope. In 1885 the brothers Henry photographed, round the star
+Maia in the Pleiades, a spiral nebula 3' long, as bright on the plate
+as that star itself, but quite invisible in the telescope; and an
+exposure of four hours revealed other new nebula in the same
+district. That painstaking and most careful observer, Barnard, with
+101/4 hours' exposure, extended this nebulosity for several degrees,
+and discovered to the north of the Pleiades a huge diffuse nebulosity,
+in a region almost destitute of stars. By establishing a 10-inch
+instrument at an altitude of 6,000 feet, Barnard has revealed the wide
+distribution of nebular matter in the constellation Scorpio over a
+space of 4� or 5� square.  Barnard asserts that the "nebular
+hypothesis" would have been killed at its birth by a knowledge of
+these photographs. Later he has used still more powerful instruments,
+and extended his discoveries.
+
+The association of stars with planetary nebul�, and the distribution
+of nebul� in the heavens, especially in relation to the Milky Way, are
+striking facts, which will certainly bear fruit when the time arrives
+for discarding vague speculations, and learning to read the true
+physical structure and history of the starry universe.
+
+_Stellar Spectra._--When the spectroscope was first available for
+stellar research, the leaders in this branch of astronomy were Huggins
+and Father Secchi,[24] of Rome. The former began by devoting years of
+work principally to the most accurate study of a few stars.  The
+latter devoted the years from 1863 to 1867 to a general survey of the
+whole heavens, including 4,000 stars. He divided these into four
+principal classes, which have been of the greatest service. Half of
+his stars belonged to the first class, including Sirius, Vega,
+Regulus, Altair. The characteristic feature of their spectra is the
+strength and breadth of the hydrogen lines and the extreme faintness
+of the metallic lines. This class of star is white to the eye, and
+rich in ultra violet light.
+
+The second class includes about three-eighths of his stars, including
+Capella, Pollux, and Arcturus. These stars give a spectrum like that
+of our sun, and appear yellowish to the eye.
+
+The third class includes alpha Herculis, alpha Orionis (Betelgeux), Mira
+Ceti, and about 500 red and variable stars.  The spectrum has fluted
+bands shaded from blue to red, and sharply defined at the more
+refrangible edge.
+
+The fourth class is a small one, containing no stars over fifth
+magnitude, of which 152 Schjellerup, in Canes Venatici, is a good
+example. This spectrum also has bands, but these are shaded on the
+violet side and sharp on the red side. They are due to carbon in some
+form.  These stars are ruby red in the telescope.
+
+It would appear, then, that all stars are suns with continuous
+spectra, and the classes are differentiated by the character of the
+absorbent vapours of their atmospheres.
+
+It is very likely that, after the chemists have taught us how to
+interpret all the varieties of spectrum, it will be possible to
+ascribe the different spectrum-classes to different stages in the
+life-history of every star.  Already there are plenty of people ready
+to lay down arbitrary assumptions about the lessons to be drawn from
+stellar spectra. Some say that they know with certainty that each star
+begins by being a nebula, and is condensed and heated by condensation
+until it begins to shine as a star; that it attains a climax of
+temperature, then cools down, and eventually becomes extinct.  They go
+so far as to declare that they know what class of spectrum belongs to
+each stage of a star's life, and how to distinguish between one that
+is increasing and another that is decreasing in temperature.
+
+The more cautious astronomers believe that chemistry is not
+sufficiently advanced to justify all of these deductions; that, until
+chemists have settled the lately raised question of the transmutation
+of elements, no theory can be sure. It is also held that until they
+have explained, without room for doubt, the reasons for the presence
+of some lines, and the absence of others, of any element in a stellar
+spectrum; why the arc-spectrum of each element differs from its spark
+spectrum; what are all the various changes produced in the spectrum of
+a gas by all possible concomitant variations of pressure and
+temperature; also the meanings of all the flutings in the spectra of
+metalloids and compounds; and other equally pertinent matters--until
+that time arrives the part to be played by the astronomer is one of
+observation. By all means, they say, make use of "working hypotheses"
+to add an interest to years of laborious research, and to serve as a
+guide to the direction of further labours; but be sure not to fall
+into the error of calling any mere hypothesis a theory.
+
+_Nebular Hypothesis._--The Nebular Hypothesis, which was first, as it
+were, tentatively put forward by Laplace as a note in his _Syst�me du
+Monde_, supposes the solar system to have been a flat, disk-shaped
+nebula at a high temperature in rapid rotation. In cooling it
+condensed, leaving revolving rings at different distances from the
+centre. These themselves were supposed to condense into the nucleus
+for a rotating planet, which might, in contracting, again throw off
+rings to form satellites.  The speculation can be put in a really
+attractive form, but is in direct opposition to many of the actual
+facts; and so long as it is not favoured by those who wish to maintain
+the position of astronomy as the most exact of the sciences--exact in
+its facts, exact in its logic--this speculation must be recorded by
+the historian, only as he records the guesses of the ancient Greeks--as
+an interesting phase in the history of human thought.
+
+Other hypotheses, having the same end in view, are the meteoritic
+hypothesis of Lockyer and the planetesimal hypothesis that has been
+largely developed in the United States. These can best be read in the
+original papers to various journals, references to which may be found
+in the footnotes of Miss Clerke's _History of Astronomy during the
+Nineteenth Century_. The same can be said of Bredichin's hypothesis of
+comets' tails, Arrhenius's book on the applications of the theory of
+light repulsion, the speculations on radium, the origin of the sun's
+heat and the age of the earth, the electron hypothesis of terrestrial
+magnetism, and a host of similar speculations, all combining to throw
+an interesting light on the evolution of a modern train of thought
+that seems to delight in conjecture, while rebelling against that
+strict mathematical logic which has crowned astronomy as the queen of
+the sciences.
+
+
+FOOTNOTES:
+
+[1] _R. S. Phil Trans_., 1810 and 1817-24.
+
+[2] One of the most valuable contributions to our knowledge of stellar
+parallaxes is the result of Gill's work (_Cape Results_, vol. iii.,
+part ii., 1900).
+
+[3] Taking the velocity of light at 186,000 miles a second, and the
+earth's mean distance at 93,000,000 miles, 1 light year=5,865,696,000,000
+miles or 63,072 astronomical units; 1 astronomical unit a year=2.94
+miles a second; and the earth's orbital velocity=18.5 miles a second.
+
+[4] Ast. Nacht., 1889.
+
+[5] R. S. Phil. Trans., 1718.
+
+[6] Mem. Acad. des Sciences, 1738, p. 337.
+
+[7] R. S Phil. Trans., 1868.
+
+[8] _R.S. Phil Trans._, 1783.
+
+[9] See Kapteyn's address to the Royal Institution, 1908. Also Gill's
+presidential address to the British Association, 1907.
+
+[10] _Brit. Assoc. Rep._, 1905.
+
+[11] R. S. Phil. Trans., 1803, 1804.
+
+[12] Ibid, 1824.
+
+[13] Connaisance des Temps, 1830.
+
+[14] _R. A. S. Mem._, vol. xlvii., p. 178; _Ast. Nach._, No. 3,142;
+Catalogue published by Lick Observatory, 1901.
+
+[15] _R. A. S., M. N._, vol. vi.
+
+[16] _R. S. Phil. Trans._, vol. lxxiii., p. 484.
+
+[17] _Astr. Nach._, No. 2,947.
+
+[18] _R. S. E. Trans_., vol. xxvii. In 1901 Dr. Anderson discovered
+Nova Persei.
+
+[19] _Astr. Nach_., No. 3,079.
+
+[20] For a different explanation see Sir W. Huggins's lecture, Royal
+Institution, May 13th, 1892.
+
+[21] For the early history of the proposals for photographic
+cataloguing of stars, see the _Cape Photographic Durchmusterung_, 3
+vols. (_Ann. of the Cape Observatory_, vols. in., iv., and v.,
+Introduction.)
+
+[22] _R. S. Phil. Trans._, 1850, p. 499 _et seq._
+
+[23] _Ibid_, vol. cliv., p. 437.
+
+[24] _Brit. Assoc. Rep._, 1868, p. 165.
+
+
+
+INDEX
+
+
+Abul Wefa, 24
+Acceleration of moon's mean motion, 60
+Achromatic lens invented, 88
+Adams, J. C., 61, 65, 68, 69, 70, 87, 118, 124
+Airy, G. B., 13, 30, 37, 65, 69, 70, 80, 81, 114, 119
+Albetegnius, 24
+Alphonso, 24
+Altazimuth, 81
+Anaxagoras, 14, 16
+Anaximander, 14
+Anaximenes, 14
+Anderson, T. D., 137, 138
+�ngstrom, A. J., 102
+Antoniadi, 113
+Apian, P., 63
+Apollonius, 22, 23
+Arago, 111
+Argelander, F. W. A., 139
+Aristarchus, 18, 29
+Aristillus, 17, 19
+Aristotle, 16, 30, 47
+Arrhenius, 146
+Arzachel, 24
+Asshurbanapal, 12
+Asteroids, discovery of, 67, 119
+Astrology, ancient and modern, 1-7, 38
+
+Backlund, 122
+Bacon, R., 86
+Bailly, 8, 65
+Barnard, E. E., 115, 143
+Beer and M�dler, 107, 110, 111
+Behaim, 74
+Bessel, F.W., 65, 79, 128, 134, 139
+Biela, 123
+Binet, 65
+Biot, 10
+Bird, 79, 80
+Bliss, 80
+Bode, 66, 69
+Bond, G. P., 99, 117, 122
+Bouvard, A., 65, 68
+Bradley, J., 79, 80, 81, 87, 127, 128, 139
+Bredechin, 146
+Bremiker, 71
+Brewster, D., 52, 91, 112
+Brinkley, 128
+Bruno, G., 49
+Burchardt, 65, 123
+Burnham, S. W., 134
+
+Callippus, 15, 16, 31
+Carrington, R. C., 97, 99, 114
+Cassini, G. D., 107, 114, 115, 116, 117, 118
+Cassini, J., 109, 129
+Chacornac, 139
+Chald�an astronomy, 11-13
+Challis, J., 69, 70, 71, 72
+Chance, 88
+Charles, II., 50, 81
+Chinese astronomy, 8-11
+Christie, W. M. H. (Ast. Roy.), 64, 82, 125
+Chueni, 9
+Clairaut, A. C., 56, 63, 65
+Clark, A. G., 89, 135
+Clerke, Miss, 106, 146
+Comets, 120
+Common, A. A., 88
+Cooke, 89
+Copeland, R., 142
+Copernicus, N., 14, 24-31, 37, 38, 41, 42, 49, 128
+Cornu, 85
+Cowell, P. H., 3, 5, 64, 83
+Crawford, Earl of, 84
+Cromellin, A. C., 5, 64
+
+D'Alembert, 65
+Damoiseau, 65
+D'Arrest, H. L., 34
+Dawes, W. R., 100, 111
+Delambre, J. B. J., 8, 27, 51, 65, 68
+De la Rue, W., 2, 94, 99, 100, 131
+Delaunay, 65
+Democritus, 16
+Descartes, 51
+De Sejour, 117
+Deslandres, II., 101
+Desvignolles, 9
+De Zach, 67
+Digges, L., 86
+Dollond, J., 87, 90
+Dominis, A. di., 86
+Donati, 120
+Doppler, 92, 129
+Draper, 99
+Dreyer, J. L. E., 29,77
+Dunthorne, 60
+Dyson, 131
+
+Eclipses, total solar, 103
+Ecphantes, 16
+Eddington, 131
+Ellipse, 41
+Empedocles, 16
+Encke, J. F., 119, 122, 123, 133
+Epicycles, 22
+Eratosthenes, 18
+Euclid, 17
+Eudoxus, 15, 31
+Euler, L., 60, 61, 62, 65, 88, 119
+
+Fabricius, D.,95, 120, 121
+Feil and Mantois, 88
+Fizeau, H. L., 85, 92, 99
+Flamsteed, J., 50, 58, 68, 78, 79, 93
+Fohi, 8
+Forbes, J. D., 52, 91
+Foucault, L., 85, 99
+Frauenhofer, J., 88, 90, 91
+
+Galilei, G., 38, 46-49, 77, 93, 94, 95, 96, 107, 113, 115, 116, 133
+Galle, 71, 72
+Gascoigne, W., 45, 77
+Gauss, C. F., 65, 67
+Gauthier, 98
+Gautier, 89
+Gilbert, 44
+Gill, D., 84, 85, 128, 135, 139, 140
+Goodricke, J., 136
+Gould, B. A., 139
+Grant, R., 27, 47, 51, 86, 134
+Graham, 79
+Greek astronomy, 8-11
+Gregory, J. and D., 87
+Grimaldi, 113
+Groombridge, S., 139
+Grubb, 88, 89
+Guillemin, 122
+Guinand, 88
+
+Hale, G. E., 101
+Hall, A., 112
+Hall, C. M., 88
+Halley, E., 19, 51, 58, 60, 61, 62, 63, 64, 79, 120, 122, 125, 129
+Halley's comet, 62-64
+Halm, 85
+Hansen, P. A., 3, 65
+Hansky, A. P., 100
+Harding, C. L., 67
+Heliometer, 83
+Heller, 120
+Helmholtz, H. L. F., 35
+Henderson, T., 128
+Henry, P. and P., 139, 140, 143
+Heraclides, 16
+Heraclitus, 14
+Herodotus, 13
+Herschel, W., 65, 68, 97, 107, 110, 114, 115, 116, 117, 118, 126, 127,
+  130, 131, 132, 141, 142
+Herschel, J., 97, 111, 133, 134, 142
+Herschel, A. S., 125
+Hevelius, J., 178
+Hind, J. R., 5, 64, 120, 121, 122
+Hipparchus, 3, 18, 19, 20, 22, 23, 24, 26, 36, 55, 60, 74, 93, 137
+Hooke, R., 51, 111, 114
+Horrocks, J., 50, 56
+Howlett, 100
+Huggins, W., 92, 93, 99, 106, 120, 129, 137, 138, 142, 144
+Humboldt and Bonpland, 124
+Huyghens, C., 47, 77, 87, 110, 116, 117
+
+Ivory, 65
+
+Jansen, P. J. C., 105, 106
+Jansen, Z., 86
+
+Kaiser, F., 111
+Kapteyn, J. C., 131, 138, 139
+Keeler, 117
+Kepler, J., 17, 23, 26, 29, 30, 36, 37, 38-46, 48, 49, 50, 52, 53, 63,
+  66, 77, 87, 93, 127, 137
+Kepler's laws, 42
+Kirchoff, G.R., 91
+Kirsch, 9
+Knobel, E.B., 12, 13
+Ko-Show-King, 76
+
+Lacaile, N.L., 139
+Lagrange, J.L., 61, 62, 65, 119
+La Hire, 114
+Lalande, J.J.L., 60, 63, 65, 66, 72, 139
+Lamont, J., 98
+Langrenus, 107
+Laplace, P.S. de, 50, 58, 61, 62, 65,66, 123, 146
+Lassel, 72, 88, 117, 118
+Law of universal gravitation, 53
+Legendre, 65
+Leonardo da Vinci, 46
+Lewis, G.C., 17
+Le Verrier, U.J.J., 65, 68, 70, 71,72, 110, 118, 125
+Lexell, 66, 123
+Light year, 128
+Lipperhey, H., 86
+Littrow, 121
+Lockyer, J.N., 103, 105, 146
+Logarithms invented, 50
+Loewy, 2, 100
+Long inequality of Jupiter and Saturn, 50, 62
+Lowell, P., 111, 112, 118
+Lubienietz, S. de, 122
+Luther, M., 38
+Lunar theory, 37, 50, 56, 64
+
+Maclaurin, 65
+Maclear, T., 128
+Malvasia, 77
+Martin, 9
+Maxwell, J. Clerk, 117
+Maskelyne, N., 80, 130
+McLean, F., 89
+Medici, Cosmo di, 48
+Melancthon, 38
+Melotte, 83, 116
+Meteors, 123
+Meton, 15
+Meyer, 57, 65
+Michaelson, 85
+Miraldi, 110, 114
+Molyneux, 87
+Moon, physical observations, 107
+Mouchez, 139
+Moyriac de Mailla, 8
+
+Napier, Lord, 50
+Nasmyth and Carpenter, 108
+Nebulae, 141, 146
+Neison, E., 108
+Neptune, discovery of, 68-72
+Newall, 89
+Newcomb, 85
+Newton, H.A., 124
+Newton, I., 5, 19, 43, 49, 51-60, 62, 64, 68, 77, 79, 87, 90, 93, 94,
+  114, 127, 133
+Nicetas, 16, 25
+Niesten, 115
+Nunez, P., 35
+
+Olbers, H.W.M., 67
+Omar, 11, 24
+Oppolzer, 13, 125
+Oudemans, 129
+
+Palitsch, G., 64
+Parallax, solar, 85, 86
+Parmenides, 14
+Paul III., 30
+Paul V., 48
+Pemberton, 51
+Peters, C.A.F., 125, 128, 135
+Photography, 99
+Piazzi, G., 67, 128, 129, 139
+Picard, 54, 77, 114
+Pickering, E.C., 118, 135
+Pingr�, 13, 122
+Plana, 65
+Planets and satellites, physical observations, 109-119
+Plato, 17, 23, 26, 40
+Poisson, 65
+Pond, J., 80
+Pons, 122
+Porta, B., 86
+Pound, 87, 114
+Pontecoulant, 64
+Precession of the equinoxes, 19-21, 55, 57
+Proctor, R.A., 111
+Pritchett, 115
+Ptolemy, 11, 13, 21, 22, 23, 24, 93
+Puiseux and Loewy, 108
+Pulfrich, 131
+Purbach, G., 24
+Pythagoras, 14, 17, 25, 29
+
+Ramsay, W., 106
+Ransome and May, 81
+Reflecting telescopes invented, 87
+Regiomontanus (M�ller), 24
+Respighi, 82
+Retrograde motion of planets, 22
+Riccioli, 107
+Roberts, 137
+R�mer, O.,78, 114
+Rosse, Earl of, 88, 142
+Rowland, H. A., 92, 102
+Rudolph H.,37, 39
+Rumker, C., 139
+
+Sabine, E., 98
+Savary, 133
+Schaeberle, J. M., 135
+Schiaparelli, G. V., 110, 111, 124, 125
+Scheiner, C., 87, 95, 96
+Schmidt, 108
+Schott, 88
+Schr�ter, J. H., 107, 110, 111, 124, 125
+Schuster, 98
+Schwabe, G. H., 97
+Secchi, A., 93, 144
+Short, 87
+Simms, J., 81
+Slipher, V. M., 119
+Socrates, 17
+Solon, 15
+Souciet, 8
+South, J., 133
+Spectroscope, 89-92
+Spectroheliograph, 101
+Spoerer, G. F. W., 98
+Spots on the sun, 84;
+  periodicity of, 97
+Stars, Parallax, 127;
+  proper motion, 129;
+  double, 132;
+  binaries, 132, 135;
+  new, 19, 36, 137;
+  catalogues of, 19, 36, 139;
+  spectra of, 143
+Stewart, B., 2, 100
+Stokes, G. G., 91
+Stone, E. J., 139
+Struve, C. L., 130
+Struve, F. G. W,, 88, 115, 128, 133
+
+Telescopes invented, 47, 86;
+  large, 88
+Temple, 115, 125
+Thales, 13, 16
+Theon, 60
+Transit circle of R�mer, 78
+Timocharis, 17, 19
+Titius, 66
+Torricelli, 113
+Troughton, E., 80
+Tupman, G. L., 120
+Tuttle, 125
+Tycho Brahe, 23, 25, 30, 33-38, 39, 40, 44, 50, 75, 77, 93, 94, 129, 137
+
+Ulugh Begh, 24
+Uranus, discovery of, 65
+
+Velocity of light, 86, 128;
+  of earth in orbit, 128
+Verbiest, 75
+Vogel, H. C., 92, 129, 135, 136
+Von Asten, 122
+
+Walmsley, 65
+Walterus, B., 24, 74
+Weiss, E., 125
+Wells, 122
+Wesley, 104
+Whewell, 112
+Williams, 10
+Wilson, A., 96, 100
+Winnecke, 120
+Witte, 86
+Wollaston, 90
+Wolf, M., 119, 125, 132
+Wolf, R., 98
+Wren, C., 51
+Wyllie, A., 77
+
+Yao, 9
+Young, C. A., 103
+Yu-Chi, 8
+
+Zenith telescopes, 79, 82
+Z�llner, 92
+Zucchi, 113
+
+
+
+
+
+End of the Project Gutenberg EBook of History of Astronomy, by George Forbes
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+Author: George Forbes
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+*** START OF THE PROJECT GUTENBERG EBOOK HISTORY OF ASTRONOMY ***
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+
+
+<p align="center"><img src="001.jpg" alt="[Illustration: SIR ISAAC NEWTON (From the bust by Roubiliac In Trinity College, Cambridge.)]" /></p>
+
+<div align="center">
+<h1>HISTORY OF ASTRONOMY</h1>
+
+<h2>BY</h2>
+
+<h2>GEORGE FORBES,<br />
+M.A., F.R.S., M. INST. C. E.,</h2>
+
+<p><b>(FORMERLY PROFESSOR OF NATURAL PHILOSOPHY, ANDERSON&#8217;S
+COLLEGE, GLASGOW)</b></p>
+
+<p>AUTHOR OF &#8220;THE TRANSIT OF VENUS,&#8221; RENDU&#8217;S
+&#8220;THEORY OF THE GLACIERS OF SAVOY,&#8221; ETC., ETC.</p>
+</div>
+
+<p><br /><br /></p>
+
+<h1>CONTENTS</h1>
+
+<blockquote>
+<p><a href="#preface">PREFACE</a></p>
+</blockquote>
+
+<h2>BOOK I. THE GEOMETRICAL PERIOD</h2>
+
+<blockquote>
+<p><a href="#1">1. PRIMITIVE ASTRONOMY AND ASTROLOGY</a></p>
+
+<p><a href="#2">2. ANCIENT ASTRONOMY&#8212;CHINESE
+AND CHALD&#198;ANS</a></p>
+
+<p><a href="#3">3. ANCIENT GREEK ASTRONOMY</a></p>
+
+<p><a href="#4">4. THE REIGN OF EPICYCLES&#8212;FROM PTOLEMY TO COPERNICUS</a></p>
+</blockquote>
+
+<h2>BOOK II. THE DYNAMICAL PERIOD</h2>
+
+<blockquote>
+<p><a href="#5">5. DISCOVERY OF THE TRUE SOLAR SYSTEM&#8212;TYCHO BRAHE&#8212;KEPLER</a></p>
+
+<p><a href="#6">6. GALILEO AND THE TELESCOPE&#8212;NOTIONS OF GRAVITY BY HORROCKS, ETC.</a></p>
+
+<p><a href="#7">7. SIR ISAAC NEWTON&#8212;LAW OF UNIVERSAL GRAVITATION</a></p>
+
+<p><a href="#8">8. NEWTON&#8217;S SUCCESSORS&#8212;HALLEY, EULER, LAGRANGE, LAPLACE, ETC.</a></p>
+
+<p><a href="#9">9. DISCOVERY OF NEW PLANETS&#8212;HERSCHEL, PIAZZI, ADAMS, AND
+LE VERRIER</a></p>
+</blockquote>
+
+<h2>BOOK III. OBSERVATION</h2>
+
+<blockquote>
+
+<p><a href="#10">10. INSTRUMENTS OF PRECISION&#8212;SIZE
+OF THE SOLAR SYSTEM</a></p>
+
+<p><a href="#11">11. HISTORY OF THE TELESCOPE&#8212;SPECTROSCOPE</a></p>
+</blockquote>
+
+<h2>BOOK IV. THE PHYSICAL PERIOD</h2>
+
+<blockquote>
+<p><a href="#12">12. THE SUN</a></p>
+
+<p><a href="#13">13. THE MOON AND PLANETS</a></p>
+
+<p><a href="#14">14. COMETS AND METEORS</a></p>
+
+<p><a href="#15">15. THE STARS AND NEBUL&#198;</a></p>
+
+<p><a href="#index">INDEX</a></p>
+</blockquote>
+
+<hr width="75%" size="1" align="center" />
+
+<p><br /><br /></p>
+
+<a name="preface"></a>
+<h1>PREFACE</h1>
+
+<p>An attempt has been made in these pages to trace the
+evolution of intellectual thought in the progress
+of astronomical discovery, and, by recognising the
+different points of view of the different ages, to
+give due credit even to the ancients. No one can
+expect, in a history of astronomy of limited size,
+to find a treatise on &#8220;practical&#8221; or on
+&#8220;theoretical astronomy,&#8221; nor a complete
+&#8220;descriptive astronomy,&#8221; and still less
+a book on &#8220;speculative astronomy.&#8221;
+Something of each of these is essential, however,
+for tracing the progress of thought and knowledge
+which it is the object of this History to describe.</p>
+
+<p>The progress of human knowledge is measured by the
+increased habit of looking at facts from new points
+of view, as much as by the accumulation of facts.
+The mental capacity of one age does not seem to differ
+from that of other ages; but it is the imagination
+of new points of view that gives a wider scope to
+that capacity. And this is cumulative, and therefore
+progressive. Aristotle viewed the solar system
+as a geometrical problem; Kepler and Newton converted
+the point of view into a dynamical one. Aristotle&#8217;s
+mental capacity to understand the meaning of facts
+or to criticise a train of reasoning may have been
+equal to that of Kepler or Newton, but the point of
+view was different.</p>
+
+<p>Then, again, new points of view are provided by the
+invention of new methods in that system of logic which
+we call mathematics. All that mathematics can
+do is to assure us that a statement A is equivalent
+to statements B, C, D, or is one of the facts expressed
+by the statements B, C, D; so that we may know, if
+B, C, and D are true, then A is true. To many
+people our inability to understand all that is contained
+in statements B, C, and D, without the cumbrous process
+of a mathematical demonstration, proves the feebleness
+of the human mind as a logical machine. For it
+required the new point of view imagined by Newton&#8217;s
+analysis to enable people to see that, so far as planetary
+orbits are concerned, Kepler&#8217;s three laws (B,
+C, D) were identical with Newton&#8217;s law of gravitation
+(A). No one recognises more than the mathematical
+astronomer this feebleness of the human intellect,
+and no one is more conscious of the limitations of
+the logical process called mathematics, which even
+now has not solved directly the problem of only three
+bodies.</p>
+
+<p>These reflections, arising from the writing of this
+History, go to explain the invariable humility of
+the great mathematical astronomers. Newton&#8217;s
+comparison of himself to the child on the seashore
+applies to them all. As each new discovery opens
+up, it may be, boundless oceans for investigation,
+for wonder, and for admiration, the great astronomers,
+refusing to accept mere hypotheses as true, have founded
+upon these discoveries a science as exact in its observation
+of facts as in theories. So it is that these
+men, who have built up the most sure and most solid
+of all the sciences, refuse to invite others to join
+them in vain speculation. The writer has, therefore,
+in this short History, tried to follow that great
+master, Airy, whose pupil he was, and the key to whose
+character was exactness and accuracy; and he recognises
+that Science is impotent except in her own limited
+sphere.</p>
+
+<p>It has been necessary to curtail many parts of the
+History in the attempt&#8212;perhaps a hopeless
+one&#8212;to lay before the reader in a limited
+space enough about each age to illustrate its tone
+and spirit, the ideals of the workers, the gradual
+addition of new points of view and of new means of
+investigation.</p>
+
+<p>It would, indeed, be a pleasure to entertain the hope
+that these pages might, among new recruits, arouse
+an interest in the greatest of all the sciences, or
+that those who have handled the theoretical or practical
+side might be led by them to read in the original some
+of the classics of astronomy. Many students have
+much compassion for the schoolboy of to-day, who is
+not allowed the luxury of learning the art of reasoning
+from him who still remains pre-eminently its greatest
+exponent, Euclid. These students pity also the
+man of to-morrow, who is not to be allowed to read,
+in the original Latin of the brilliant Kepler, how
+he was able&#8212;by observations taken from a
+moving platform, the earth, of the directions of a
+moving object, Mars&#8212;to deduce the exact
+shape of the path of each of these planets, and their
+actual positions on these paths at any time.
+Kepler&#8217;s masterpiece is one of the most interesting
+books that was ever written, combining wit, imagination,
+ingenuity, and certainty.</p>
+
+<p>Lastly, it must be noted that, as a History of England
+cannot deal with the present Parliament, so also the
+unfinished researches and untested hypotheses of many
+well-known astronomers of to-day cannot be included
+among the records of the History of Astronomy.
+The writer regrets the necessity that thus arises
+of leaving without mention the names of many who are
+now making history in astronomical work.</p>
+
+<p>G. F.<br />
+<i>August 1st, 1909.</i></p>
+
+<p><br /><br /></p>
+
+<h1>BOOK I.  THE GEOMETRICAL PERIOD</h1>
+
+<p><br /><br /></p>
+
+<a name="1"></a>
+<h2>1. PRIMITIVE ASTRONOMY AND ASTROLOGY.</h2>
+
+<p>The growth of intelligence in the human race has its
+counterpart in that of the individual, especially
+in the earliest stages. Intellectual activity
+and the development of reasoning powers are in both
+cases based upon the accumulation of experiences, and
+on the comparison, classification, arrangement, and
+nomenclature of these experiences. During the
+infancy of each the succession of events can be watched,
+but there can be no <i>&#224; priori</i> anticipations.
+Experience alone, in both cases, leads to the idea
+of cause and effect as a principle that seems to dominate
+our present universe, as a rule for predicting the
+course of events, and as a guide to the choice of a
+course of action. This idea of cause and effect
+is the most potent factor in developing the history
+of the human race, as of the individual.</p>
+
+<p>In no realm of nature is the principle of cause and
+effect more conspicuous than in astronomy; and we
+fall into the habit of thinking of its laws as not
+only being unchangeable in our universe, but necessary
+to the conception of any universe that might have been
+substituted in its place. The first inhabitants
+of the world were compelled to accommodate their acts
+to the daily and annual alternations of light and
+darkness and of heat and cold, as much as to the irregular
+changes of weather, attacks of disease, and the fortune
+of war.  They soon came to regard the influence
+of the sun, in connection with light and heat, as
+a cause. This led to a search for other signs
+in the heavens. If the appearance of a comet was
+sometimes noted simultaneously with the death of a
+great ruler, or an eclipse with a scourge of plague,
+these might well be looked upon as causes in the same
+sense that the veering or backing of the wind is regarded
+as a cause of fine or foul weather.</p>
+
+<p>For these reasons we find that the earnest men of
+all ages have recorded the occurrence of comets, eclipses,
+new stars, meteor showers, and remarkable conjunctions
+of the planets, as well as plagues and famines, floods
+and droughts, wars and the deaths of great rulers.
+Sometimes they thought they could trace connections
+which might lead them to say that a comet presaged
+famine, or an eclipse war.</p>
+
+<p>Even if these men were sometimes led to evolve laws
+of cause and effect which now seem to us absurd, let
+us be tolerant, and gratefully acknowledge that these
+astrologers, when they suggested such &#8220;working
+hypotheses,&#8221; were laying the foundations of observation
+and deduction.</p>
+
+<p>If the ancient Chald&#230;ans gave to the planetary conjunctions
+an influence over terrestrial events, let us remember
+that in our own time people have searched for connection
+between terrestrial conditions and periods of unusual
+prevalence of sun spots; while De la Rue, Loewy, and
+Balfour Stewart<a href="#fn1_1">[1]</a> thought they found a connection
+between sun-spot displays and the planetary positions.
+Thus we find scientific men, even in our own time,
+responsible for the belief that storms in the Indian
+Ocean, the fertility of German vines, famines in India,
+and high or low Nile-floods in Egypt follow the planetary
+positions.</p>
+
+<p>And, again, the desire to foretell the weather is
+so laudable that we cannot blame the ancient Greeks
+for announcing the influence of the moon with as much
+confidence as it is affirmed in Lord Wolseley&#8217;s
+<i>Soldier&#8217;s Pocket Book</i>.</p>
+
+<p>Even if the scientific spirit of observation and deduction
+(astronomy) has sometimes led to erroneous systems
+for predicting terrestrial events (astrology), we
+owe to the old astronomer and astrologer alike the
+deepest gratitude for their diligence in recording
+astronomical events. For, out of the scanty records
+which have survived the destructive acts of fire and
+flood, of monarchs and mobs, we have found much that
+has helped to a fuller knowledge of the heavenly motions
+than was possible without these records.</p>
+
+<p>So Hipparchus, about 150 B.C., and Ptolemy a little
+later, were able to use the observations of Chald&#230;an
+astrologers, as well as those of Alexandrian astronomers,
+and to make some discoveries which have helped the
+progress of astronomy in all ages.  So, also,
+Mr. Cowell<a href="#fn1_2">[2]</a> has examined the marks made on the baked
+bricks used by the Chald&#230;ans for recording the eclipses
+of 1062 B.C. and 762 B.C.; and has thereby been enabled,
+in the last few years, to correct the lunar tables
+of Hansen, and to find a more accurate value for the
+secular acceleration of the moon&#8217;s longitude
+and the node of her orbit than any that could be obtained
+from modern observations made with instruments of the
+highest precision.</p>
+
+<p>So again, Mr. Hind <a href="#fn1_3">[3]</a> was enabled to trace back the
+period during which Halley&#8217;s comet has been
+a member of the solar system, and to identify it in
+the Chinese observations of comets as far back as 12
+B.C. Cowell and Cromellin extended the date to
+240 B.C. In the same way the comet 1861.i. has
+been traced back in the Chinese records to 617 A.D.
+<a href="#fn1_4">[4]</a></p>
+
+<p>The theoretical views founded on Newton&#8217;s great
+law of universal gravitation led to the conclusion
+that the inclination of the earth&#8217;s equator
+to the plane of her orbit (the obliquity of the ecliptic)
+has been diminishing slowly since prehistoric times;
+and this fact has been confirmed by Egyptian and Chinese
+observations on the length of the shadow of a vertical
+pillar, made thousands of years before the Christian
+era, in summer and winter.</p>
+
+<p>There are other reasons why we must be tolerant of
+the crude notions of the ancients. The historian,
+wishing to give credit wherever it may be due, is
+met by two difficulties. Firstly, only a few records
+of very ancient astronomy are extant, and the authenticity
+of many of these is open to doubt. Secondly,
+it is very difficult to divest ourselves of present
+knowledge, and to appreciate the originality of thought
+required to make the first beginnings.</p>
+
+<p>With regard to the first point, we are generally dependent
+upon histories written long after the events.
+ The astronomy of Egyptians, Babylonians, and Assyrians
+is known to us mainly through the Greek historians,
+and for information about the Chinese we rely upon
+the researches of travellers and missionaries in comparatively
+recent times. The testimony of the Greek writers
+has fortunately been confirmed, and we now have in
+addition a mass of facts translated from the original
+sculptures, papyri, and inscribed bricks, dating back
+thousands of years.</p>
+
+<p>In attempting to appraise the efforts of the beginners
+we must remember that it was natural to look upon
+the earth (as all the first astronomers did) as a
+circular plane, surrounded and bounded by the heaven,
+which was a solid vault, or hemisphere, with its concavity
+turned downwards. The stars seemed to be fixed
+on this vault; the moon, and later the planets, were
+seen to crawl over it. It was a great step to
+look on the vault as a hollow sphere carrying the sun
+too. It must have been difficult to believe that
+at midday the stars are shining as brightly in the
+blue sky as they do at night. It must have been
+difficult to explain how the sun, having set in the
+west, could get back to rise in the east without being
+seen <i>if</i> it was always the same sun. It
+was a great step to suppose the earth to be spherical,
+and to ascribe the diurnal motions to its rotation.
+Probably the greatest step ever made in astronomical
+theory was the placing of the sun, moon, and planets
+at different distances from the earth instead of having
+them stuck on the vault of heaven. It was a transition
+from &#8220;flatland&#8221; to a space of three dimensions.</p>
+
+<p>Great progress was made when systematic observations
+began, such as following the motion of the moon and
+planets among the stars, and the inferred motion of
+the sun among the stars, by observing their <i>heliacal
+risings</i>&#8212;i.e., the times of year when
+a star would first be seen to rise at sunrise, and
+when it could last be seen to rise at sunset.
+The grouping of the stars into constellations and
+recording their places was a useful observation.
+The theoretical prediction of eclipses of the sun
+and moon, and of the motions of the planets among
+the stars, became later the highest goal in astronomy.</p>
+
+<p>To not one of the above important steps in the progress
+of astronomy can we assign the author with certainty.
+Probably many of them were independently taken by
+Chinese, Indian, Persian, Tartar, Egyptian, Babylonian,
+Assyrian, Phoenician, and Greek astronomers.
+And we have not a particle of information about the
+discoveries, which may have been great, by other peoples&#8212;by
+the Druids, the Mexicans, and the Peruvians, for example.</p>
+
+<p>We do know this, that all nations required to have
+a calendar. The solar year, the lunar month,
+and the day were the units, and it is owing to their
+incommensurability that we find so many calendars
+proposed and in use at different times. The only
+object to be attained by comparing the chronologies
+of ancient races is to fix the actual dates of observations
+recorded, and this is not a part of a history of astronomy.</p>
+
+<p>In conclusion, let us bear in mind the limited point
+of view of the ancients when we try to estimate their
+merit. Let us remember that the first astronomy
+was of two dimensions; the second astronomy was of
+three dimensions, but still purely geometrical.
+Since Kepler&#8217;s day we have had a dynamical astronomy.</p>
+
+<p><br /><br /></p>
+
+<p><b>FOOTNOTES:</b></p>
+
+<p><a name="fn1_1">[1]</a> Trans. R. S. E., xxiii. 1864, p. 499, <i>On
+Sun Spots</i>, <i>etc</i>., by B. Stewart. Also
+Trans. R. S. 1860-70. Also Prof. Ernest
+Brown, in <i>R. A. S. Monthly Notices</i>, 1900.</p>
+
+<p><a name="fn1_2">[2]</a> <i>R. A. S. Monthly Notices</i>, Sup.; 1905.</p>
+
+<p align="center"><img src="002.jpg" alt="[Illustration: CHALD&#198;AN BAKED BRICK OR TABLET, <i>Obverse and reverse sides</i>,
+Containing record of solar eclipse, 1062 B.C., used
+lately by Cowell for rendering the lunar theory more
+accurate than was possible by finest modern observations.
+(British Museum collection, No. 35908.)]" /></p>
+
+<p><a name="fn1_3">[3]</a> <i>R. A. S. Monthly Notices</i>, vol. x.,
+p. 65.</p>
+
+<p><a name="fn1_4">[4]</a> R. S. E. Proc., vol. x., 1880.</p>
+
+<p><br /><br /></p>
+
+<a name="2"></a>
+<h2>2. ANCIENT ASTRONOMY&#8212;THE CHINESE AND CHALD&#198;ANS.</h2>
+
+<p>The last section must have made clear the difficulties
+the way of assigning to the ancient nations their
+proper place in the development of primitive notions
+about astronomy. The fact that some alleged observations
+date back to a period before the Chinese had invented
+the art of writing leads immediately to the question
+how far tradition can be trusted.</p>
+
+<p>Our first detailed knowledge was gathered in the far
+East by travellers, and by the Jesuit priests, and
+was published in the eighteenth century. The
+Asiatic Society of Bengal contributed translations
+of Brahmin literature. The two principal sources
+of knowledge about Chinese astronomy were supplied,
+first by Father Souciet, who in 1729 published <i>Observations
+Astronomical, Geographical, Chronological, and Physical</i>,
+drawn from ancient Chinese books; and later by Father
+Moyriac-de-Mailla, who in 1777-1785 published <i>Annals
+of the Chinese Empire, translated from Tong-Kien-Kang-Mou</i>.</p>
+
+<p>Bailly, in his <i>Astronomie Ancienne</i> (1781),
+drew, from these and other sources, the conclusion
+that all we know of the astronomical learning of the
+Chinese, Indians, Chald&#230;ans, Assyrians, and Egyptians
+is but the remnant of a far more complete astronomy
+of which no trace can be found.</p>
+
+<p>Delambre, in his <i>Histoire de l&#8217;Astronomie
+Ancienne</i> (1817), ridicules the opinion of Bailly,
+and considers that the progress made by all of these
+nations is insignificant.</p>
+
+<p>It will be well now to give an idea of some of the
+astronomy of the ancients not yet entirely discredited.
+ China and Babylon may be taken as typical examples.</p>
+
+<p><i>China</i>.&#8212;It would appear that Fohi,
+the first emperor, reigned about 2952 B.C., and shortly
+afterwards Yu-Chi made a sphere to represent the motions
+of the celestial bodies. It is also mentioned,
+in the book called Chu-King, supposed to have been
+written in 2205 B.C., that a similar sphere was made
+in the time of Yao (2357 B.C.).<a href="#fn2_1">[1]</a> It is said that
+the Emperor Chueni (2513 B.C.) saw five planets in
+conjunction the same day that the sun and moon were
+in conjunction. This is discussed by Father Martin
+(MSS. of De Lisle); also by M. Desvignolles (Mem.
+Acad. Berlin, vol. iii., p. 193), and by M. Kirsch
+(ditto, vol. v., p. 19), who both found that Mars,
+Jupiter, Saturn, and Mercury were all between the
+eleventh and eighteenth degrees of Pisces, all visible
+together in the evening on February 28th 2446 B.C.,
+while on the same day the sun and moon were in conjunction
+at 9 a.m., and that on March 1st the moon was in conjunction
+with the other four planets. But this needs confirmation.</p>
+
+<p>Yao, referred to above, gave instructions to his astronomers
+to determine the positions of the solstices and equinoxes,
+and they reported the names of the stars in the places
+occupied by the sun at these seasons, and in 2285
+B.C. he gave them further orders. If this account
+be true, it shows a knowledge that the vault of heaven
+is a complete sphere, and that stars are shining at
+mid-day, although eclipsed by the sun&#8217;s brightness.</p>
+
+<p>It is also asserted, in the book called <i>Chu-King</i>,
+that in the time of Yao the year was known to have
+365&#188; days, and that he adopted 365 days and added
+an intercalary day every four years (as in the Julian
+Calendar). This may be true or not, but the ancient
+Chinese certainly seem to have divided the circle
+into 365 degrees. To learn the length of the
+year needed only patient observation&#8212;a
+characteristic of the Chinese; but many younger nations
+got into a terrible mess with their calendar from
+ignorance of the year&#8217;s length.</p>
+
+<p>It is stated that in 2159 B.C. the royal astronomers
+Hi and Ho failed to predict an eclipse. It probably
+created great terror, for they were executed in punishment
+for their neglect. If this account be true, it
+means that in the twenty-second century B.C. some rule
+for calculating eclipses was in use. Here, again,
+patient observation would easily lead to the detection
+of the eighteen-year cycle known to the Chaldeans
+as the <i>Saros</i>. It consists of 235 lunations,
+and in that time the pole of the moon&#8217;s orbit
+revolves just once round the pole of the ecliptic,
+and for this reason the eclipses in one cycle are
+repeated with very slight modification in the next
+cycle, and so on for many centuries.</p>
+
+<p>It may be that the neglect of their duties by Hi and
+Ho, and their punishment, influenced Chinese astronomy;
+or that the succeeding records have not been available
+to later scholars; but the fact remains that&#8212;although
+at long intervals observations were made of eclipses,
+comets, and falling stars, and of the position of the
+solstices, and of the obliquity of the ecliptic&#8212;records
+become rare, until 776 B.C., when eclipses began to
+be recorded once more with some approach to continuity.
+Shortly afterwards notices of comets were added.
+Biot gave a list of these, and Mr. John Williams, in
+1871, published <i>Observations of Comets from 611
+B.C. to 1640 A.D., Extracted from the Chinese Annals</i>.</p>
+
+<p>With regard to those centuries concerning which we
+have no astronomical Chinese records, it is fair to
+state that it is recorded that some centuries before
+the Christian era, in the reign of Tsin-Chi-Hoang,
+all the classical and scientific books that could be
+found were ordered to be destroyed. If true, our
+loss therefrom is as great as from the burning of
+the Alexandrian library by the Caliph Omar. He
+burnt all the books because he held that they must
+be either consistent or inconsistent with the Koran,
+and in the one case they were superfluous, in the
+other case objectionable.</p>
+
+<p><i>Chald&#230;ans</i>.&#8212;Until the last half century
+historians were accustomed to look back upon the Greeks,
+who led the world from the fifth to the third century
+B.C., as the pioneers of art, literature, and science.
+But the excavations and researches of later years make
+us more ready to grant that in science as in art the
+Greeks only developed what they derived from the Egyptians,
+Babylonians, and Assyrians. The Greek historians
+said as much, in fact; and modern commentators used
+to attribute the assertion to undue modesty. Since,
+however, the records of the libraries have been unearthed
+it has been recognised that the Babylonians were in
+no way inferior in the matter of original scientific
+investigation to other races of the same era.</p>
+
+<p>The Chald&#230;ans, being the most ancient Babylonians,
+held the same station and dignity in the State as
+did the priests in Egypt, and spent all their time
+in the study of philosophy and astronomy, and the
+arts of divination and astrology. They held that
+the world of which we have a conception is an eternal
+world without any beginning or ending, in which all
+things are ordered by rules supported by a divine
+providence, and that the heavenly bodies do not move
+by chance, nor by their own will, but by the determinate
+will and appointment of the gods. They recorded
+these movements, but mainly in the hope of tracing
+the will of the gods in mundane affairs. Ptolemy
+(about 130 A.D.) made use of Babylonian eclipses in
+the eighth century B.C. for improving his solar and
+lunar tables.</p>
+
+<p>Fragments of a library at Agade have been preserved
+at Nineveh, from which we learn that the star-charts
+were even then divided into constellations, which
+were known by the names which they bear to this day,
+and that the signs of the zodiac were used for determining
+the courses of the sun, moon, and of the five planets
+Mercury, Venus, Mars, Jupiter, and Saturn.</p>
+
+<p>We have records of observations carried on under Asshurbanapal,
+who sent astronomers to different parts to study celestial
+phenomena. Here is one:&#8212;</p>
+
+<p>To the Director of Observations,&#8212;My Lord,
+his humble servant Nabushum-iddin, Great Astronomer
+of Nineveh, writes thus: &#8220;May Nabu and
+Marduk be propitious to the Director of these Observations,
+my Lord. The fifteenth day we observed the Node
+of the moon, and the moon was eclipsed.&#8221;</p>
+
+<p>The Phoenicians are supposed to have used the stars
+for navigation, but there are no records. The
+Egyptian priests tried to keep such astronomical knowledge
+as they possessed to themselves. It is probable
+that they had arbitrary rules for predicting eclipses.
+All that was known to the Greeks about Egyptian science
+is to be found in the writings of Diodorus Siculus.
+But confirmatory and more authentic facts have been
+derived from late explorations. Thus we learn
+from E. B. Knobel<a href="#fn2_2">[2]</a> about the Jewish calendar dates,
+on records of land sales in Aramaic papyri at Assuan,
+translated by Professor A. H. Sayce and A. E. Cowley,
+(1) that the lunar cycle of nineteen years was used
+by the Jews in the fifth century B.C. [the present
+reformed Jewish calendar dating from the fourth century
+A.D.], a date a &#8220;little more than a century
+after the grandfathers and great-grandfathers of those
+whose business is recorded had fled into Egypt with
+Jeremiah&#8221; (Sayce); and (2) that the order of
+intercalation at that time was not dissimilar to that
+in use at the present day.</p>
+
+<p>Then again, Knobel reminds us of &#8220;the most interesting
+discovery a few years ago by Father Strassmeier of
+a Babylonian tablet recording a partial lunar eclipse
+at Babylon in the seventh year of Cambyses, on the
+fourteenth day of the Jewish month Tammuz.&#8221;
+ Ptolemy, in the Almagest (Suntaxis), says it occurred
+in the seventh year of Cambyses, on the night of the
+seventeenth and eighteenth of the Egyptian month Phamenoth.
+ Pingr&#233; and Oppolzer fix the date July 16th, 533 B.C.
+Thus are the relations of the chronologies of Jews
+and Egyptians established by these explorations.</p>
+
+<p><br /><br /></p>
+
+<p><b>FOOTNOTES:</b></p>
+
+<p><a name="fn2_1">[1]</a> These ancient dates are uncertain.</p>
+
+<p><a name="fn2_2">[2]</a> <i>R. A. S. Monthly Notices</i>, vol. lxviii.,
+No. 5, March, 1908.</p>
+
+<p><br /><br /></p>
+
+<a name="3"></a>
+<h2>3. ANCIENT GREEK ASTRONOMY.</h2>
+
+<p>We have our information about the earliest Greek astronomy
+from Herodotus (born 480 B.C.). He put the traditions
+into writing. Thales (639-546 B.C.) is said to
+have predicted an eclipse, which caused much alarm,
+and ended the battle between the Medes and Lydians.
+Airy fixed the date May 28th, 585 B.C. But other
+modern astronomers give different dates. Thales
+went to Egypt to study science, and learnt from its
+priests the length of the year (which was kept a profound
+secret!), and the signs of the zodiac, and the positions
+of the solstices. He held that the sun, moon,
+and stars are not mere spots on the heavenly vault,
+but solids; that the moon derives her light from the
+sun, and that this fact explains her phases; that an
+eclipse of the moon happens when the earth cuts off
+the sun&#8217;s light from her. He supposed the
+earth to be flat, and to float upon water. He
+determined the ratio of the sun&#8217;s diameter to
+its orbit, and apparently made out the diameter correctly
+as half a degree. He left nothing in writing.</p>
+
+<p>His successors, Anaximander (610-547 B.C.) and Anaximenes
+(550-475 B.C.), held absurd notions about the sun,
+moon, and stars, while Heraclitus (540-500 B.C.)
+supposed that the stars were lighted each night like
+lamps, and the sun each morning. Parmenides supposed
+the earth to be a sphere.</p>
+
+<p>Pythagoras (569-470 B.C.) visited Egypt to study science.
+He deduced his system, in which the earth revolves
+in an orbit, from fantastic first principles, of which
+the following are examples: &#8220;The circular
+motion is the most perfect motion,&#8221; &#8220;Fire
+is more worthy than earth,&#8221; &#8220;Ten is the
+perfect number.&#8221; He wrote nothing, but is
+supposed to have said that the earth, moon, five planets,
+and fixed stars all revolve round the sun, which itself
+revolves round an imaginary central fire called the
+Antichthon. Copernicus in the sixteenth century
+claimed Pythagoras as the founder of the system which
+he, Copernicus, revived.</p>
+
+<p>Anaxagoras (born 499 B.C.) studied astronomy in Egypt.
+He explained the return of the sun to the east each
+morning by its going under the flat earth in the night.
+He held that in a solar eclipse the moon hides the
+sun, and in a lunar eclipse the moon enters the earth&#8217;s
+shadow&#8212;both excellent opinions. But
+he entertained absurd ideas of the vortical motion
+of the heavens whisking stones into the sky, there
+to be ignited by the fiery firmament to form stars.
+He was prosecuted for this unsettling opinion, and
+for maintaining that the moon is an inhabited earth.
+He was defended by Pericles (432 B.C.).</p>
+
+<p>Solon dabbled, like many others, in reforms of the
+calendar. The common year of the Greeks originally
+had 360 days&#8212;twelve months of thirty days.
+Solon&#8217;s year was 354 days. It is obvious
+that these erroneous years would, before long, remove
+the summer to January and the winter to July.
+To prevent this it was customary at regular intervals
+to intercalate days or months. Meton (432 B.C.)
+introduced a reform based on the nineteen-year cycle.
+This is not the same as the Egyptian and Chaldean
+eclipse cycle called <i>Saros</i> of 223 lunations,
+or a little over eighteen years.  The Metonic
+cycle is 235 lunations or nineteen years, after which
+period the sun and moon occupy the same position relative
+to the stars. It is still used for fixing the
+date of Easter, the number of the year in Melon&#8217;s
+cycle being the golden number of our prayer-books.
+ Melon&#8217;s system divided the 235 lunations into
+months of thirty days and omitted every sixty-third
+day. Of the nineteen years, twelve had twelve months
+and seven had thirteen months.</p>
+
+<p>Callippus (330 B.C.) used a cycle four times as long,
+940 lunations, but one day short of Melon&#8217;s
+seventy-six years. This was more correct.</p>
+
+<p>Eudoxus (406-350 B.C.) is said to have travelled with
+Plato in Egypt. He made astronomical observations
+in Asia Minor, Sicily, and Italy, and described the
+starry heavens divided into constellations. His
+name is connected with a planetary theory which as
+generally stated sounds most fanciful. He imagined
+the fixed stars to be on a vault of heaven; and the
+sun, moon, and planets to be upon similar vaults or
+spheres, twenty-six revolving spheres in all, the motion
+of each planet being resolved into its components,
+and a separate sphere being assigned for each component
+motion. Callippus (330 B.C.) increased the number
+to thirty-three. It is now generally accepted
+that the real existence of these spheres was not suggested,
+but the idea was only a mathematical conception to
+facilitate the construction of tables for predicting
+the places of the heavenly bodies.</p>
+
+<p>Aristotle (384-322 B.C.) summed up the state of astronomical
+knowledge in his time, and held the earth to be fixed
+in the centre of the world.</p>
+
+<p>Nicetas, Heraclides, and Ecphantes supposed the earth
+to revolve on its axis, but to have no orbital motion.</p>
+
+<p>The short epitome so far given illustrates the extraordinary
+deductive methods adopted by the ancient Greeks.
+But they went much farther in the same direction.
+They seem to have been in great difficulty to explain
+how the earth is supported, just as were those who
+invented the myth of Atlas, or the Indians with the
+tortoise. Thales thought that the flat earth
+floated on water. Anaxagoras thought that, being
+flat, it would be buoyed up and supported on the air
+like a kite. Democritus thought it remained fixed,
+like the donkey between two bundles of hay, because
+it was equidistant from all parts of the containing
+sphere, and there was no reason why it should incline
+one way rather than another. Empedocles attributed
+its state of rest to centrifugal force by the rapid
+circular movement of the heavens, as water is stationary
+in a pail when whirled round by a string. Democritus
+further supposed that the inclination of the flat earth
+to the ecliptic was due to the greater weight of the
+southern parts owing to the exuberant vegetation.</p>
+
+<p>For further references to similar efforts of imagination
+the reader is referred to Sir George Cornwall Lewis&#8217;s
+<i>Historical Survey of the Astronomy of the Ancients</i>;
+London, 1862. His list of authorities is very
+complete, but some of his conclusions are doubtful.
+ At p. 113 of that work he records the real opinions
+of Socrates as set forth by Xenophon; and the reader
+will, perhaps, sympathise with Socrates in his views
+on contemporary astronomy:&#8212;</p>
+
+<p>With regard to astronomy he [Socrates] considered
+a knowledge of it desirable to the extent of determining
+the day of the year or month, and the hour of the
+night, ... but as to learning the courses of the stars,
+to be occupied with the planets, and to inquire about
+their distances from the earth, and their orbits,
+and the causes of their motions, he strongly objected
+to such a waste of valuable time. He dwelt on
+the contradictions and conflicting opinions of the
+physical philosophers, ... and, in fine, he held that
+the speculators on the universe and on the laws of
+the heavenly bodies were no better than madmen (<i>Xen.
+Mem</i>, i. 1, 11-15).</p>
+
+<p>Plato (born 429 B.C.), the pupil of Socrates, the
+fellow-student of Euclid, and a follower of Pythagoras,
+studied science in his travels in Egypt and elsewhere.
+ He was held in so great reverence by all learned
+men that a problem which he set to the astronomers
+was the keynote to all astronomical investigation
+from this date till the time of Kepler in the sixteenth
+century. He proposed to astronomers <i>the problem
+of representing the courses of the planets by circular
+and uniform motions</i>.</p>
+
+<p>Systematic observation among the Greeks began with
+the rise of the Alexandrian school. Aristillus
+and Timocharis set up instruments and fixed the positions
+of the zodiacal stars, near to which all the planets
+in their orbits pass, thus facilitating the determination
+of planetary motions. Aristarchus (320-250 B.C.)
+showed that the sun must be at least nineteen times
+as far off as the moon, which is far short of the
+mark. He also found the sun&#8217;s diameter,
+correctly, to be half a degree.  Eratosthenes
+(276-196 B.C.) measured the inclination to the equator
+of the sun&#8217;s apparent path in the heavens&#8212;i.e.,
+he measured the obliquity of the ecliptic, making
+it 23&#176; 51&#8217;, confirming our knowledge of its
+continuous diminution during historical times.
+He measured an arc of meridian, from Alexandria to
+Syene (Assuan), and found the difference of latitude
+by the length of a shadow at noon, summer solstice.
+He deduced the diameter of the earth, 250,000 stadia.
+Unfortunately, we do not know the length of the stadium
+he used.</p>
+
+<p>Hipparchus (190-120 B.C.) may be regarded as the founder
+of observational astronomy. He measured the obliquity
+of the ecliptic, and agreed with Eratosthenes.
+ He altered the length of the tropical year from 365
+days, 6 hours to 365 days, 5 hours, 53 minutes&#8212;still
+four minutes too much. He measured the equation
+of time and the irregular motion of the sun; and allowed
+for this in his calculations by supposing that the
+centre, about which the sun moves uniformly, is situated
+a little distance from the fixed earth. He called
+this point the <i>excentric</i>. The line from
+the earth to the &#8220;excentric&#8221; was called
+the <i>line of apses</i>. A circle having this
+centre was called the <i>equant</i>, and he supposed
+that a radius drawn to the sun from the excentric
+passes over equal arcs on the equant in equal times.
+He then computed tables for predicting the place of
+the sun.</p>
+
+<p>He proceeded in the same way to compute Lunar tables.
+Making use of Chald&#230;an eclipses, he was able to get
+an accurate value of the moon&#8217;s mean motion.
+ [Halley, in 1693, compared this value with his own
+measurements, and so discovered the acceleration of
+the moon&#8217;s mean motion. This was conclusively
+established, but could not be explained by the Newtonian
+theory for quite a long time.] He determined the plane
+of the moon&#8217;s orbit and its inclination to the
+ecliptic. The motion of this plane round the
+pole of the ecliptic once in eighteen years complicated
+the problem. He located the moon&#8217;s excentric
+as he had done the sun&#8217;s.  He also discovered
+some of the minor irregularities of the moon&#8217;s
+motion, due, as Newton&#8217;s theory proves, to the
+disturbing action of the sun&#8217;s attraction.</p>
+
+<p>In the year 134 B.C. Hipparchus observed a new
+star.  This upset every notion about the permanence
+of the fixed stars. He then set to work to catalogue
+all the principal stars so as to know if any others
+appeared or disappeared. Here his experiences
+resembled those of several later astronomers, who,
+when in search of some special object, have been rewarded
+by a discovery in a totally different direction.
+On comparing his star positions with those of Timocharis
+and Aristillus he found no stars that had appeared
+or disappeared in the interval of 150 years; but he
+found that all the stars seemed to have changed their
+places with reference to that point in the heavens
+where the ecliptic is 90&#176; from the poles of the earth&#8212;i.e.,
+the equinox. He found that this could be explained
+by a motion of the equinox in the direction of the
+apparent diurnal motion of the stars. This discovery
+of <i>precession of the equinoxes</i>, which takes
+place at the rate of 52".1 every year, was necessary
+for the progress of accurate astronomical observations.
+It is due to a steady revolution of the earth&#8217;s
+pole round the pole of the ecliptic once in 26,000
+years in the opposite direction to the planetary revolutions.</p>
+
+<p>Hipparchus was also the inventor of trigonometry,
+both plane and spherical. He explained the method
+of using eclipses for determining the longitude.</p>
+
+<p>In connection with Hipparchus&#8217; great discovery
+it may be mentioned that modern astronomers have often
+attempted to fix dates in history by the effects of
+precession of the equinoxes. (1) At about the date
+when the Great Pyramid may have been built &#947; Draconis
+was near to the pole, and must have been used as the
+pole-star. In the north face of the Great Pyramid
+is the entrance to an inclined passage, and six of
+the nine pyramids at Gizeh possess the same feature;
+all the passages being inclined at an angle between
+26&#176; and 27&#176; to the horizon and in the plane of the
+meridian. It also appears that 4,000 years ago&#8212;i.e.,
+about 2100 B.C.&#8212;an observer at the lower
+end of the passage would be able to see &#947; Draconis,
+the then pole-star, at its lower culmination.<a href="#fn3_1">[1]</a> It
+has been suggested that the passage was made for this
+purpose. On other grounds the date assigned to
+the Great Pyramid is 2123 B.C.</p>
+
+<p>(2) The Chald&#230;ans gave names to constellations now
+invisible from Babylon which would have been visible
+in 2000 B.C., at which date it is claimed that these
+people were studying astronomy.</p>
+
+<p>(3) In the Odyssey, Calypso directs Odysseus, in accordance
+with Phoenician rules for navigating the Mediterranean,
+to keep the Great Bear &#8220;ever on the left as
+he traversed the deep&#8221; when sailing from the
+pillars of Hercules (Gibraltar) to Corfu. Yet
+such a course taken now would land the traveller in
+Africa.  Odysseus is said in his voyage in springtime
+to have seen the Pleiades and Arcturus setting late,
+which seemed to early commentators a proof of Homer&#8217;s
+inaccuracy.  Likewise Homer, both in the <i>Odyssey</i>
+<a href="#fn3_2">[2]</a> (v. 272-5) and in the <i>Iliad</i> (xviii. 489),
+asserts that the Great Bear never set in those latitudes.
+Now it has been found that the precession of the equinoxes
+explains all these puzzles; shows that in springtime
+on the Mediterranean the Bear was just above the horizon,
+near the sea but not touching it, between 750 B.C.
+and 1000 B.C.; and fixes the date of the poems, thus
+confirming other evidence, and establishing Homer&#8217;s
+character for accuracy. <a href="#fn3_3">[3]</a></p>
+
+<p>(4) The orientation of Egyptian temples and Druidical
+stones is such that possibly they were so placed as
+to assist in the observation of the heliacal risings
+<a href="#fn3_4">[4]</a> of certain stars. If the star were known,
+this would give an approximate date. Up to the
+present the results of these investigations are far
+from being conclusive.</p>
+
+<p>Ptolemy (130 A.D.) wrote the Suntaxis, or Almagest,
+which includes a cyclopedia of astronomy, containing
+a summary of knowledge at that date. We have
+no evidence beyond his own statement that he was a
+practical observer. He theorised on the planetary
+motions, and held that the earth is fixed in the centre
+of the universe. He adopted the excentric and
+equant of Hipparchus to explain the unequal motions
+of the sun and moon. He adopted the epicycles
+and deferents which had been used by Apollonius and
+others to explain the retrograde motions of the planets.
+We, who know that the earth revolves round the sun
+once in a year, can understand that the apparent motion
+of a planet is only its motion relative to the earth.
+If, then, we suppose the earth fixed and the sun to
+revolve round it once a year, and the planets each
+in its own period, it is only necessary to impose upon
+each of these an additional <i>annual</i> motion to
+enable us to represent truly the apparent motions.
+This way of looking at the apparent motions shows
+why each planet, when nearest to the earth, seems to
+move for a time in a retrograde direction. The
+attempts of Ptolemy and others of his time to explain
+the retrograde motion in this way were only approximate.
+Let us suppose each planet to have a bar with one end
+centred at the earth.  If at the other end of
+the bar one end of a shorter bar is pivotted, having
+the planet at its other end, then the planet is given
+an annual motion in the secondary circle (the epicycle),
+whose centre revolves round the earth on the primary
+circle (the <i>deferent</i>), at a uniform rate round
+the excentric. Ptolemy supposed the centres of
+the epicycles of Mercury and Venus to be on a bar
+passing through the sun, and to be between the earth
+and the sun. The centres of the epicycles of
+Mars, Jupiter, and Saturn were supposed to be further
+away than the sun.  Mercury and Venus were supposed
+to revolve in their epicycles in their own periodic
+times and in the deferent round the earth in a year.
+The major planets were supposed to revolve in the
+deferent round the earth in their own periodic times,
+and in their epicycles once in a year.</p>
+
+<p>It did not occur to Ptolemy to place the centres of
+the epicycles of Mercury and Venus at the sun, and
+to extend the same system to the major planets.
+Something of this sort had been proposed by the Egyptians
+(we are told by Cicero and others), and was accepted
+by Tycho Brahe; and was as true a representation of
+the relative motions in the solar system as when we
+suppose the sun to be fixed and the earth to revolve.</p>
+
+<p>The cumbrous system advocated by Ptolemy answered
+its purpose, enabling him to predict astronomical
+events approximately. He improved the lunar theory
+considerably, and discovered minor inequalities which
+could be allowed for by the addition of new epicycles.
+ We may look upon these epicycles of Apollonius, and
+the excentric of Hipparchus, as the responses of these
+astronomers to the demand of Plato for uniform circular
+motions. Their use became more and more confirmed,
+until the seventeenth century, when the accurate observations
+of Tycho Brahe enabled Kepler to abolish these purely
+geometrical makeshifts, and to substitute a system
+in which the sun became physically its controller.</p>
+
+<p><br /><br /></p>
+
+<p><b>FOOTNOTES:</b></p>
+
+<p><a name="fn3_1">[1]</a> <i>Phil. Mag</i>., vol. xxiv., pp. 481-4.</p>
+
+<p><a name="fn3_2">[2]</a></p>
+
+<p>Plaeiadas t&#8217; esoronte kai opse duonta bootaen<br />
+&#8216;Arkton th&#8217; aen kai amaxan epiklaesin
+kaleousin,<br />
+&#8216;Ae t&#8217; autou strephetai kai t&#8217; Oriona
+dokeuei,<br />
+Oin d&#8217;ammoros esti loetron Okeanoio.</p>
+
+<p>&#8220;The Pleiades and Bo&#246;tes that setteth late,
+and the Bear, which they likewise call the Wain, which
+turneth ever in one place, and keepeth watch upon
+Orion, and alone hath no part in the baths of the
+ocean.&#8221;</p>
+
+<p><a name="fn3_3">[3]</a> See Pearson in the Camb. Phil. Soc.
+Proc., vol. iv., pt. ii., p. 93, on whose authority
+the above statements are made.</p>
+
+<p><a name="fn3_4">[4]</a> See p. 6 for definition.</p>
+
+<p><br /><br /></p>
+
+<a name="4"></a>
+<h2>4. THE REIGN OF EPICYCLES&#8212;FROM PTOLEMY
+TO COPERNICUS.</h2>
+
+<p>After Ptolemy had published his book there seemed
+to be nothing more to do for the solar system except
+to go on observing and finding more and more accurate
+values for the constants involved--viz., the periods
+of revolution, the diameter of the deferent,<a href="#fn4_1">[1]</a> and
+its ratio to that of the epicycle,<a href="#fn4_2">[2]</a> the distance
+of the excentric<a href="#fn4_3">[3]</a> from the centre of the deferent,
+and the position of the line of apses,<a href="#fn4_4">[4]</a> besides the
+inclination and position of the plane of the planet&#8217;s
+orbit. The only object ever aimed at in those
+days was to prepare tables for predicting the places
+of the planets. It was not a mechanical problem;
+there was no notion of a governing law of forces.</p>
+
+<p>From this time onwards all interest in astronomy seemed,
+in Europe at least, to sink to a low ebb.  When
+the Caliph Omar, in the middle of the seventh century,
+burnt the library of Alexandria, which had been the
+centre of intellectual progress, that centre migrated
+to Baghdad, and the Arabs became the leaders of science
+and philosophy. In astronomy they made careful
+observations. In the middle of the ninth century
+Albategnius, a Syrian prince, improved the value of
+excentricity of the sun&#8217;s orbit, observed the
+motion of the moon&#8217;s apse, and thought he detected
+a smaller progression of the sun&#8217;s apse.
+His tables were much more accurate than Ptolemy&#8217;s.
+Abul Wefa, in the tenth century, seems to have discovered
+the moon&#8217;s &#8220;variation.&#8221; Meanwhile
+the Moors were leaders of science in the west, and
+Arzachel of Toledo improved the solar tables very
+much. Ulugh Begh, grandson of the great Tamerlane
+the Tartar, built a fine observatory at Samarcand
+in the fifteenth century, and made a great catalogue
+of stars, the first since the time of Hipparchus.</p>
+
+<p>At the close of the fifteenth century King Alphonso
+of Spain employed computers to produce the Alphonsine
+Tables (1488 A.D.), Purbach translated Ptolemy&#8217;s
+book, and observations were carried out in Germany
+by M&#252;ller, known as Regiomontanus, and Waltherus.</p>
+
+<p>Nicolai Copernicus, a Sclav, was born in 1473 at Thorn,
+in Polish Prussia. He studied at Cracow and in
+Italy. He was a priest, and settled at Frauenberg.
+ He did not undertake continuous observations, but
+devoted himself to simplifying the planetary systems
+and devising means for more accurately predicting
+the positions of the sun, moon, and planets.
+He had no idea of framing a solar system on a dynamical
+basis.  His great object was to increase the accuracy
+of the calculations and the tables. The results
+of his cogitations were printed just before his death
+in an interesting book, <i>De Revolutionibus Orbium
+Celestium</i>. It is only by careful reading of
+this book that the true position of Copernicus can
+be realised. He noticed that Nicetas and others
+had ascribed the apparent diurnal rotation of the
+heavens to a real daily rotation of the earth about
+its axis, in the opposite direction to the apparent
+motion of the stars. Also in the writings of
+Martianus Capella he learnt that the Egyptians had
+supposed Mercury and Venus to revolve round the sun,
+and to be carried with him in his annual motion round
+the earth. He noticed that the same supposition,
+if extended to Mars, Jupiter, and Saturn, would explain
+easily why they, and especially Mars, seem so much
+brighter in opposition.  For Mars would then be
+a great deal nearer to the earth than at other times.
+It would also explain the retrograde motion of planets
+when in opposition.</p>
+
+<p>We must here notice that at this stage Copernicus
+was actually confronted with the system accepted later
+by Tycho Brahe, with the earth fixed. But he
+now recalled and accepted the views of Pythagoras
+and others, according to which the sun is fixed and
+the earth revolves; and it must be noted that, geometrically,
+there is no difference of any sort between the Egyptian
+or Tychonic system and that of Pythagoras as revived
+by Copernicus, except that on the latter theory the
+stars ought to seem to move when the earth changes
+its position&#8212;a test which failed completely
+with the rough means of observation then available.
+The radical defect of all solar systems previous to
+the time of Kepler (1609 A.D.) was the slavish yielding
+to Plato&#8217;s dictum demanding uniform circular
+motion for the planets, and the consequent evolution
+of the epicycle, which was fatal to any conception
+of a dynamical theory.</p>
+
+<p>Copernicus could not sever himself from this obnoxious
+tradition.<a href="#fn4_5">[5]</a> It is true that neither the Pythagorean
+nor the Egypto-Tychonic system required epicycles
+for explaining retrograde motion, as the Ptolemaic
+theory did. Furthermore, either system could use
+the excentric of Hipparchus to explain the irregular
+motion known as the equation of the centre.
+But Copernicus remarked that he could also use an
+epicycle for this purpose, or that he could use both
+an excentric and an epicycle for each planet, and
+so bring theory still closer into accord with observation.
+And this he proceeded to do.<a href="#fn4_6">[6]</a> Moreover, observers
+had found irregularities in the moon&#8217;s motion,
+due, as we now know, to the disturbing attraction
+of the sun.  To correct for these irregularities
+Copernicus introduced epicycle on epicycle in the
+lunar orbit.</p>
+
+<p>This is in its main features the system propounded
+by Copernicus. But attention must, to state the
+case fully, be drawn to two points to be found in
+his first and sixth books respectively. The first
+point relates to the seasons, and it shows a strange
+ignorance of the laws of rotating bodies. To
+use the words of Delambre,<a href="#fn4_7">[7]</a> in drawing attention
+to the strange conception,</p>
+
+<blockquote>he imagined that the earth, revolving
+round the sun, ought always to show to it the same
+face; the contrary phenomena surprised him: to
+explain them he invented a third motion, and added
+it to the two real motions (rotation and orbital
+revolution). By this third motion the earth,
+he held, made a revolution on itself and on the poles
+of the ecliptic once a year ... Copernicus
+did not know that motion in a straight line is the
+natural motion, and that motion in a curve is the
+resultant of several movements. He believed, with
+Aristotle, that circular motion was the natural
+one.</blockquote>
+
+<p>Copernicus made this rotation of the earth&#8217;s
+axis about the pole of the ecliptic retrograde (i.e.,
+opposite to the orbital revolution), and by making
+it perform more than one complete revolution in a year,
+the added part being 1/26000 of the whole, he was able
+to include the precession of the equinoxes in his
+explanation of the seasons. His explanation of
+the seasons is given on leaf 10 of his book (the pages
+of this book are not all numbered, only alternate pages,
+or leaves).</p>
+
+<p>In his sixth book he discusses the inclination of
+the planetary orbits to the ecliptic. In regard
+to this the theory of Copernicus is unique; and it
+will be best to explain this in the words of Grant
+in his great work.<a href="#fn4_8">[8]</a> He says:&#8212;</p>
+
+<blockquote>Copernicus, as we have already remarked,
+did not attack the principle of the epicyclical
+theory: he merely sought to make it more simple
+by placing the centre of the earth&#8217;s orbit in
+the centre of the universe. This was the point
+to which the motions of the planets were referred,
+for the planes of their orbits were made to pass
+through it, and their points of least and greatest
+velocities were also determined with reference to
+it.  By this arrangement the sun was situate
+mathematically near the centre of the planetary system,
+but he did not appear to have any physical connexion
+with the planets as the centre of their motions.</blockquote>
+
+<p>According to Copernicus&#8217; sixth book, the planes
+of the planetary orbits do not pass through the sun,
+and the lines of apses do not pass through to the
+sun.</p>
+
+<p>Such was the theory advanced by Copernicus: The
+earth moves in an epicycle, on a deferent whose centre
+is a little distance from the sun. The planets
+move in a similar way on epicycles, but their deferents
+have no geometrical or physical relation to the sun.
+The moon moves on an epicycle centred on a second
+epicycle, itself centred on a deferent, excentric
+to the earth.  The earth&#8217;s axis rotates
+about the pole of the ecliptic, making one revolution
+and a twenty-six thousandth part of a revolution in
+the sidereal year, in the opposite direction to its
+orbital motion.</p>
+
+<p>In view of this fanciful structure it must be noted,
+in fairness to Copernicus, that he repeatedly states
+that the reader is not obliged to accept his system
+as showing the real motions; that it does not matter
+whether they be true, even approximately, or not, so
+long as they enable us to compute tables from which
+the places of the planets among the stars can be predicted.<a href="#fn4_9">[9]</a>
+He says that whoever is not satisfied with this explanation
+must be contented by being told that &#8220;mathematics
+are for mathematicians&#8221; (Mathematicis mathematica
+scribuntur).</p>
+
+<p>At the same time he expresses his conviction over
+and over again that the earth is in motion. It
+is with him a pious belief, just as it was with Pythagoras
+and his school and with Aristarchus. &#8220;But&#8221;
+(as Dreyer says in his most interesting book, <i>Tycho
+Brahe</i>) &#8220;proofs of the physical truth of
+his system Copernicus had given none, and could give
+none,&#8221; any more than Pythagoras or Aristarchus.</p>
+
+<p>There was nothing so startlingly simple in his system
+as to lead the cautious astronomer to accept it, as
+there was in the later Keplerian system; and the absence
+of parallax in the stars seemed to condemn his system,
+which had no physical basis to recommend it, and no
+simplification at all over the Egypto-Tychonic system,
+to which Copernicus himself drew attention. It
+has been necessary to devote perhaps undue space to
+the interesting work of Copernicus, because by a curious
+chance his name has become so widely known. He
+has been spoken of very generally as the founder of
+the solar system that is now accepted. This seems
+unfair, and on reading over what has been written
+about him at different times it will be noticed that
+the astronomers&#8212;those who have evidently
+read his great book&#8212;are very cautious in
+the words with which they eulogise him, and refrain
+from attributing to him the foundation of our solar
+system, which is entirely due to Kepler.  It
+is only the more popular writers who give the idea
+that a revolution had been effected when Pythagoras&#8217;
+system was revived, and when Copernicus supported
+his view that the earth moves and is not fixed.</p>
+
+<p>It may be easy to explain the association of the name
+of Copernicus with the Keplerian system. But
+the time has long passed when the historian can support
+in any way this popular error, which was started not
+by astronomers acquainted with Kepler&#8217;s work,
+but by those who desired to put the Church in the
+wrong by extolling Copernicus.</p>
+
+<p>Copernicus dreaded much the abuse he expected to receive
+from philosophers for opposing the authority of Aristotle,
+who had declared that the earth was fixed.  So
+he sought and obtained the support of the Church,
+dedicating his great work to Pope Paul III. in a lengthy
+explanatory epistle. The Bishop of Cracow set
+up a memorial tablet in his honour.</p>
+
+<p>Copernicus was the most refined exponent, and almost
+the last representative, of the Epicyclical School.
+ As has been already stated, his successor, Tycho
+Brahe, supported the same use of epicycles and excentrics
+as Copernicus, though he held the earth to be fixed.
+But Tycho Brahe was eminently a practical observer,
+and took little part in theory; and his observations
+formed so essential a portion of the system of Kepler
+that it is only fair to include his name among these
+who laid the foundations of the solar system which
+we accept to-day.</p>
+
+<p>In now taking leave of the system of epicycles let
+it be remarked that it has been held up to ridicule
+more than it deserves. On reading Airy&#8217;s
+account of epicycles, in the beautifully clear language
+of his <i>Six Lectures on Astronomy</i>, the impression
+is made that the jointed bars there spoken of for
+describing the circles were supposed to be real.
+This is no more the case than that the spheres of Eudoxus
+and Callippus were supposed to be real. Both were
+introduced only to illustrate the mathematical conception
+upon which the solar, planetary, and lunar tables
+were constructed.  The epicycles represented
+nothing more nor less than the first terms in the Fourier
+series, which in the last century has become a basis
+of such calculations, both in astronomy and physics
+generally.</p>
+
+<p align="center"><img src="003.jpg" alt="[Illustration: &#8220;QUADRANS MURALIS SIVE TICHONICUS.&#8221;
+ With portrait of Tycho Brahe, instruments, <i>etc</i>.,
+painted on the wall; showing assistants using the
+sight, watching the clock, and recording.  (From the
+author&#8217;s copy of the <i>Astronomi&#230; Instaurat&#230;
+Mechanica.</i>)]" /></p>
+
+<p><br /><br /></p>
+
+<p><b>FOOTNOTES:</b></p>
+
+<p><a name="fn4_1">[1]</a> For definition see p. 22.</p>
+
+<p><a name="fn4_2">[2]</a> <i>Ibid</i>.</p>
+
+<p><a name="fn4_3">[3]</a> For definition see p. 18.</p>
+
+<p><a name="fn4_4">[4]</a> For definition see p. 18.</p>
+
+<p><a name="fn4_5">[5]</a> In his great book Copernicus says: &#8220;The
+movement of the heavenly bodies is uniform, circular,
+perpetual, or else composed of circular movements.&#8221;
+In this he proclaimed himself a follower of Pythagoras
+(see p. 14), as also when he says: &#8220;The
+world is spherical because the sphere is, of all figures,
+the most perfect&#8221; (Delambre, <i>Ast. Mod.
+Hist</i>., pp. 86, 87).</p>
+
+<p><a name="fn4_6">[6]</a> Kepler tells us that Tycho Brahe was pleased with
+this device, and adapted it to his own system.</p>
+
+<p><a name="fn4_7">[7]</a> <i>Hist. Ast.</i>, vol. i., p. 354.</p>
+
+<p><a name="fn4_8">[8]</a> <i>Hist. of Phys. Ast.</i>, p. vii.</p>
+
+<p><a name="fn4_9">[9]</a> &#8220;Est enim Astronomi proprium, historiam
+motuum coelestium diligenti et artificiosa observatione
+colligere. Deinde causas earundem, seu hypotheses,
+cum veras assequi nulla ratione possit ... Neque
+enim necesse est, eas hypotheses esse veras, imo ne
+verisimiles quidem, sed sufficit hoc usum, si calculum
+observationibus congruentem exhibeant.&#8221;</p>
+
+<p><br /><br /></p>
+
+<h1>BOOK II. THE DYNAMICAL PERIOD</h1>
+
+<p><br /><br /></p>
+
+<a name="5"></a>
+<h2>5. DISCOVERY OF THE TRUE SOLAR SYSTEM&#8212;TYCHO BRAHE&#8212;KEPLER.</h2>
+
+<p>During the period of the intellectual and aesthetic
+revival, at the beginning of the sixteenth century,
+the &#8220;spirit of the age&#8221; was fostered by
+the invention of printing, by the downfall of the
+Byzantine Empire, and the scattering of Greek fugitives,
+carrying the treasures of literature through Western
+Europe, by the works of Raphael and Michael Angelo,
+by the Reformation, and by the extension of the known
+world through the voyages of Spaniards and Portuguese.
+During that period there came to the front the founder
+of accurate observational astronomy. Tycho Brahe,
+a Dane, born in 1546 of noble parents, was the most
+distinguished, diligent, and accurate observer of
+the heavens since the days of Hipparchus, 1,700 years
+before.</p>
+
+<p>Tycho was devoted entirely to his science from childhood,
+and the opposition of his parents only stimulated
+him in his efforts to overcome difficulties.
+ He soon grasped the hopelessness of the old deductive
+methods of reasoning, and decided that no theories
+ought to be indulged in until preparations had been
+made by the accumulation of accurate observations.
+ We may claim for him the title of founder of the
+inductive method.</p>
+
+<p>For a complete life of this great man the reader is
+referred to Dreyer&#8217;s <i>Tycho Brahe</i>, Edinburgh,
+1890, containing a complete bibliography. The
+present notice must be limited to noting the work
+done, and the qualities of character which enabled
+him to attain his scientific aims, and which have
+been conspicuous in many of his successors.</p>
+
+<p>He studied in Germany, but King Frederick of Denmark,
+appreciating his great talents, invited him to carry
+out his life&#8217;s work in that country. He
+granted to him the island of Hveen, gave him a pension,
+and made him a canon of the Cathedral of Roskilde.
+On that island Tycho Brahe built the splendid observatory
+which he called Uraniborg, and, later, a second one
+for his assistants and students, called Stjerneborg.
+These he fitted up with the most perfect instruments,
+and never lost a chance of adding to his stock of
+careful observations.<a href="#fn5_1">[1]</a></p>
+
+<p>The account of all these instruments and observations,
+printed at his own press on the island, was published
+by Tycho Brahe himself, and the admirable and numerous
+engravings bear witness to the excellence of design
+and the stability of his instruments.</p>
+
+<p>His mechanical skill was very great, and in his workmanship
+he was satisfied with nothing but the best. He
+recognised the importance of rigidity in the instruments,
+and, whereas these had generally been made of wood,
+he designed them in metal. His instruments included
+armillae like those which had been used in Alexandria,
+and other armillae designed by himself&#8212;sextants,
+mural quadrants, large celestial globes and various
+instruments for special purposes. He lived before
+the days of telescopes and accurate clocks. He
+invented the method of sub-dividing the degrees on
+the arc of an instrument by transversals somewhat
+in the way that Pedro Nunez had proposed.</p>
+
+<p>He originated the true system of observation and reduction
+of observations, recognising the fact that the best
+instrument in the world is not perfect; and with each
+of his instruments he set to work to find out the
+errors of graduation and the errors of mounting, the
+necessary correction being applied to each observation.</p>
+
+<p>When he wanted to point his instrument exactly to
+a star he was confronted with precisely the same difficulty
+as is met in gunnery and rifle-shooting. The
+sights and the object aimed at cannot be in focus
+together, and a great deal depends on the form of sight.
+Tycho Brahe invented, and applied to the pointers
+of his instruments, an aperture-sight of variable
+area, like the iris diaphragm used now in photography.
+This enabled him to get the best result with stars
+of different brightness.  The telescope not having
+been invented, he could not use a telescopic-sight
+as we now do in gunnery.  This not only removes
+the difficulty of focussing, but makes the minimum
+visible angle smaller. Helmholtz has defined the
+minimum angle measurable with the naked eye as being
+one minute of arc. In view of this it is simply
+marvellous that, when the positions of Tycho&#8217;s
+standard stars are compared with the best modern catalogues,
+his probable error in right ascension is only &#177; 24&#8221;,
+1, and in declination only &#177; 25&#8221;, 9.</p>
+
+<p>Clocks of a sort had been made, but Tycho Brahe found
+them so unreliable that he seldom used them, and many
+of his position-measurements were made by measuring
+the angular distances from known stars.</p>
+
+<p>Taking into consideration the absence of either a
+telescope or a clock, and reading his account of the
+labour he bestowed upon each observation, we must
+all agree that Kepler, who inherited these observations
+in MS., was justified, under the conditions then existing,
+in declaring that there was no hope of anyone ever
+improving upon them.</p>
+
+<p>In the year 1572, on November 11th, Tycho discovered
+in Cassiopeia a new star of great brilliance, and
+continued to observe it until the end of January,
+1573. So incredible to him was such an event that
+he refused to believe his own eyes until he got others
+to confirm what he saw. He made accurate observations
+of its distance from the nine principal stars in Casseiopeia,
+and proved that it had no measurable parallax.
+Later he employed the same method with the comets of
+1577, 1580, 1582, 1585, 1590, 1593, and 1596, and
+proved that they too had no measurable parallax and
+must be very distant.</p>
+
+<p>The startling discovery that stars are not necessarily
+permanent, that new stars may appear, and possibly
+that old ones may disappear, had upon him exactly
+the same effect that a similar occurrence had upon
+Hipparchus 1,700 years before. He felt it his
+duty to catalogue all the principal stars, so that
+there should be no mistake in the future. During
+the construction of his catalogue of 1,000 stars he
+prepared and used accurate tables of refraction deduced
+from his own observations. Thus he eliminated
+(so far as naked eye observations required) the effect
+of atmospheric refraction which makes the altitude
+of a star seem greater than it really is.</p>
+
+<p>Tycho Brahe was able to correct the lunar theory by
+his observations. Copernicus had introduced two
+epicycles on the lunar orbit in the hope of obtaining
+a better accordance between theory and observation;
+and he was not too ambitious, as his desire was to
+get the tables accurate to ten minutes. Tycho
+Brahe found that the tables of Copernicus were in
+error as much as two degrees. He re-discovered
+the inequality called &#8220;variation&#8221; by observing
+the moon in all phases&#8212;a thing which had
+not been attended to. [It is remarkable that in the
+nineteenth century Sir George Airy established an
+altazimuth at Greenwich Observatory with this special
+object, to get observations of the moon in all phases.]
+He also discovered other lunar equalities, and wanted
+to add another epicycle to the moon&#8217;s orbit,
+but he feared that these would soon become unmanageable
+if further observations showed more new inequalities.</p>
+
+<p>But, as it turned out, the most fruitful work of Tycho
+Brahe was on the motions of the planets, and especially
+of the planet Mars, for it was by an examination of
+these results that Kepler was led to the discovery
+of his immortal laws.</p>
+
+<p>After the death of King Frederick the observatories
+of Tycho Brahe were not supported. The gigantic
+power and industry displayed by this determined man
+were accompanied, as often happens, by an overbearing
+manner, intolerant of obstacles. This led to friction,
+and eventually the observatories were dismantled,
+and Tycho Brahe was received by the Emperor Rudolph
+II., who placed a house in Prague at his disposal.
+Here he worked for a few years, with Kepler as one
+of his assistants, and he died in the year 1601.</p>
+
+<p>It is an interesting fact that Tycho Brahe had a firm
+conviction that mundane events could be predicted
+by astrology, and that this belief was supported by
+his own predictions.</p>
+
+<p>It has already been stated that Tycho Brahe maintained
+that observation must precede theory. He did
+not accept the Copernican theory that the earth moves,
+but for a working hypothesis he used a modification
+of an old Egyptian theory, mathematically identical
+with that of Copernicus, but not involving a stellar
+parallax.  He says (<i>De Mundi</i>, <i>etc</i>.)
+that</p>
+
+<blockquote>the Ptolemean system was too complicated,
+and the new one which that great man Copernicus
+had proposed, following in the footsteps of Aristarchus
+of Samos, though there was nothing in it contrary to
+mathematical principles, was in opposition to those
+of physics, as the heavy and sluggish earth is unfit
+to move, and the system is even opposed to the authority
+of Scripture. The absence of annual parallax
+further involves an incredible distance between the
+outermost planet and the fixed stars.</blockquote>
+
+<p>We are bound to admit that in the circumstances of
+the case, so long as there was no question of dynamical
+forces connecting the members of the solar system,
+his reasoning, as we should expect from such a man,
+is practical and sound. It is not surprising,
+then, that astronomers generally did not readily accept
+the views of Copernicus, that Luther (Luther&#8217;s
+<i>Tischreden</i>, pp.  22, 60) derided him in his
+usual pithy manner, that Melancthon (<i>Initia doctrinae
+physicae</i>) said that Scripture, and also science,
+are against the earth&#8217;s motion; and that the
+men of science whose opinion was asked for by the cardinals
+(who wished to know whether Galileo was right or wrong)
+looked upon Copernicus as a weaver of fanciful theories.</p>
+
+<p>Johann Kepler is the name of the man whose place,
+as is generally agreed, would have been the most difficult
+to fill among all those who have contributed to the
+advance of astronomical knowledge. He was born
+at Wiel, in the Duchy of Wurtemberg, in 1571.
+He held an appointment at Gratz, in Styria, and went
+to join Tycho Brahe in Prague, and to assist in reducing
+his observations. These came into his possession
+when Tycho Brahe died, the Emperor Rudolph entrusting
+to him the preparation of new tables (called the Rudolphine
+tables) founded on the new and accurate observations.
+He had the most profound respect for the knowledge,
+skill, determination, and perseverance of the man
+who had reaped such a harvest of most accurate data;
+and though Tycho hardly recognised the transcendent
+genius of the man who was working as his assistant,
+and although there were disagreements between them,
+Kepler held to his post, sustained by the conviction
+that, with these observations to test any theory,
+he would be in a position to settle for ever the problem
+of the solar system.</p>
+
+<img src="004.jpg" alt="[Illustration: PORTRAIT OF JOHANNES KEPLER.
+ By F. Wanderer, from Reitlinger&#8217;s &#8220;Johannes
+Kepler&#8221; (original in Strassburg).]" align="right" />
+
+<p>It has seemed to many that Plato&#8217;s demand for
+uniform circular motion (linear or angular) was responsible
+for a loss to astronomy of good work during fifteen
+hundred years, for a hundred ill-considered speculative
+cosmogonies, for dissatisfaction, amounting to disgust,
+with these <i>&#224; priori</i> guesses, and for the relegation
+of the science to less intellectual races than Greeks
+and other Europeans. Nobody seemed to dare to
+depart from this fetish of uniform angular motion
+and circular orbits until the insight, boldness, and
+independence of Johann Kepler opened up a new world
+of thought and of intellectual delight.</p>
+
+<p>While at work on the Rudolphine tables he used the
+old epicycles and deferents and excentrics, but he
+could not make theory agree with observation.
+His instincts told him that these apologists for uniform
+motion were a fraud; and he proved it to himself by
+trying every possible variation of the elements and
+finding them fail.  The number of hypotheses
+which he examined and rejected was almost incredible
+(for example, that the planets turn round centres at
+a little distance from the sun, that the epicycles
+have centres at a little distance from the deferent,
+and so on). He says that, after using all these
+devices to make theory agree with Tycho&#8217;s observations,
+he still found errors amounting to eight minutes of
+a degree. Then he said boldly that it was impossible
+that so good an observer as Tycho could have made
+a mistake of eight minutes, and added: &#8220;Out
+of these eight minutes we will construct a new theory
+that will explain the motions of all the planets.&#8221;
+And he did it, with elliptic orbits having the sun
+in a focus of each.<a href="#fn5_2">[2]</a></p>
+
+<p>It is often difficult to define the boundaries between
+fancies, imagination, hypothesis, and sound theory.
+ This extraordinary genius was a master in all these
+modes of attacking a problem. His analogy between
+the spaces occupied by the five regular solids and
+the distances of the planets from the sun, which filled
+him with so much delight, was a display of pure fancy.
+His demonstration of the three fundamental laws of
+planetary motion was the most strict and complete
+theory that had ever been attempted.</p>
+
+<p>It has been often suggested that the revival by Copernicus
+of the notion of a moving earth was a help to Kepler.
+No one who reads Kepler&#8217;s great book could hold
+such an opinion for a moment. In fact, the excellence
+of Copernicus&#8217;s book helped to prolong the life
+of the epicyclical theories in opposition to Kepler&#8217;s
+teaching.</p>
+
+<p>All of the best theories were compared by him with
+observation. These were the Ptolemaic, the Copernican,
+and the Tychonic. The two latter placed all of
+the planetary orbits concentric with one another, the
+sun being placed a little away from their common centre,
+and having no apparent relation to them, and being
+actually outside the planes in which they move.
+ Kepler&#8217;s first great discovery was that the
+planes of all the orbits pass through the sun; his
+second was that the line of apses of each planet passes
+through the sun; both were contradictory to the Copernican
+theory.</p>
+
+<p>He proceeds cautiously with his propositions until
+he arrives at his great laws, and he concludes his
+book by comparing observations of Mars, of all dates,
+with his theory.</p>
+
+<p>His first law states that the planets describe ellipses
+with the sun at a focus of each ellipse.</p>
+
+<p>His second law (a far more difficult one to prove)
+states that a line drawn from a planet to the sun
+sweeps over equal areas in equal times. These
+two laws were published in his great work, <i>Astronomia
+Nova, sen.  Physica Coelestis tradita commentariis
+de Motibus Stelloe; Martis</i>, Prague, 1609.</p>
+
+<p>It took him nine years more<a href="#fn5_3">[3]</a> to discover his third
+law, that the squares of the periodic times are proportional
+to the cubes of the mean distances from the sun.</p>
+
+<p>These three laws contain implicitly the law of universal
+gravitation. They are simply an alternative way
+of expressing that law in dealing with planets, not
+particles. Only, the power of the greatest human
+intellect is so utterly feeble that the meaning of
+the words in Kepler&#8217;s three laws could not be
+understood until expounded by the logic of Newton&#8217;s
+dynamics.</p>
+
+<p>The joy with which Kepler contemplated the final demonstration
+of these laws, the evolution of which had occupied
+twenty years, can hardly be imagined by us.
+He has given some idea of it in a passage in his work
+on <i>Harmonics</i>, which is not now quoted, only
+lest someone might say it was egotistical&#8212;a
+term which is simply grotesque when applied to such
+a man with such a life&#8217;s work accomplished.</p>
+
+<p>The whole book, <i>Astronomia Nova</i>, is a pleasure
+to read; the mass of observations that are used, and
+the ingenuity of the propositions, contrast strongly
+with the loose and imperfectly supported explanations
+of all his predecessors; and the indulgent reader
+will excuse the devotion of a few lines to an example
+of the ingenuity and beauty of his methods.</p>
+
+<img src="006.png" alt="" align="right" />
+
+<p>It may seem a hopeless task to find out the true paths
+of Mars and the earth (at that time when their shape
+even was not known) from the observations giving only
+the relative direction from night to night. Now,
+Kepler had twenty years of observations of Mars to
+deal with. This enabled him to use a new method,
+to find the earth&#8217;s orbit. Observe the
+date at any time when Mars is in opposition. The
+earth&#8217;s position E at that date gives the longitude
+of Mars M. His period is 687 days. Now choose
+dates before and after the principal date at intervals
+of 687 days and its multiples.  Mars is in each
+case in the same position. Now for any date when
+Mars is at M and the earth at E<sub>3</sub> the date of the year
+gives the angle E<sub>3</sub>SM. And the observation of
+Tycho gives the direction of Mars compared with the
+sun, SE<sub>3</sub>M. So all the angles of the triangle SEM
+in any of these positions of E are known, and also
+the ratios of SE<sub>1</sub>, SE<sub>2</sub>, SE<sub>3</sub>, SE<sub>4</sub> to SM and to each
+other.</p>
+
+<p>For the orbit of Mars observations were chosen at
+intervals of a year, when the earth was always in
+the same place.</p>
+
+<p>But Kepler saw much farther than the geometrical facts.
+He realised that the orbits are followed owing to
+a force directed to the sun; and he guessed that this
+is the same force as the gravity that makes a stone
+fall. He saw the difficulty of gravitation acting
+through the void space.  He compared universal
+gravitation to magnetism, and speaks of the work of
+Gilbert of Colchester.  (Gilbert&#8217;s book, <i>De
+Mundo Nostro Sublunari, Philosophia Nova</i>, Amstelodami,
+1651, containing similar views, was published forty-eight
+years after Gilbert&#8217;s death, and forty-two years
+after Kepler&#8217;s book and reference.  His
+book <i>De Magnete</i> was published in 1600.)</p>
+
+<p>A few of Kepler&#8217;s views on gravitation, extracted
+from the Introduction to his <i>Astronomia Nova</i>,
+may now be mentioned:&#8212;</p>
+
+<p>1. Every body at rest remains at rest if outside
+the attractive power of other bodies.</p>
+
+<p>2. Gravity is a property of masses mutually attracting
+in such manner that the earth attracts a stone much
+more than a stone attracts the earth.</p>
+
+<p>3. Bodies are attracted to the earth&#8217;s
+centre, not because it is the centre of the universe,
+but because it is the centre of the attracting particles
+of the earth.</p>
+
+<p>4. If the earth be not round (but spheroidal?),
+then bodies at different latitudes will not be attracted
+to its centre, but to different points in the neighbourhood
+of that centre.</p>
+
+<p>5. If the earth and moon were not retained in
+their orbits by vital force (<i>aut alia aligua aequipollenti</i>),
+the earth and moon would come together.</p>
+
+<p>6. If the earth were to cease to attract its
+waters, the oceans would all rise and flow to the
+moon.</p>
+
+<p>7. He attributes the tides to lunar attraction.
+ Kepler had been appointed Imperial Astronomer with
+a handsome salary (on paper), a fraction of which
+was doled out to him very irregularly. He was
+led to miserable makeshifts to earn enough to keep
+his family from starvation; and proceeded to Ratisbon
+in 1630 to represent his claims to the Diet.
+He arrived worn out and debilitated; he failed in his
+appeal, and died from fever, contracted under, and
+fed upon, disappointment and exhaustion. Those
+were not the days when men could adopt as a profession
+the &#8220;research of endowment.&#8221;</p>
+
+<p>Before taking leave of Kepler, who was by no means
+a man of one idea, it ought to be here recorded that
+he was the first to suggest that a telescope made
+with both lenses convex (not a Galilean telescope)
+can have cross wires in the focus, for use as a pointer
+to fix accurately the positions of stars. An
+Englishman, Gascoigne, was the first to use this in
+practice.</p>
+
+<p>From the all too brief epitome here given of Kepler&#8217;s
+greatest book, it must be obvious that he had at that
+time some inkling of the meaning of his laws&#8212;universal
+gravitation. From that moment the idea of universal
+gravitation was in the air, and hints and guesses were
+thrown out by many; and in time the law of gravitation
+would doubtless have been discovered, though probably
+not by the work of one man, even if Newton had not
+lived. But, if Kepler had not lived, who else
+could have discovered his laws?</p>
+
+<p><br /><br /></p>
+
+<p><b>FOOTNOTES:</b></p>
+
+<p><a name="fn5_1">[1]</a> When the writer visited M. D&#8217;Arrest, the
+astronomer, at Copenhagen, in 1872, he was presented
+by D&#8217;Arrest with one of several bricks collected
+from the ruins of Uraniborg. This was one of his
+most cherished possessions until, on returning home
+after a prolonged absence on astronomical work, he
+found that his treasure had been tidied away from
+his study.</p>
+
+<img src="005.png" alt="" align="right" />
+
+<p><a name="fn5_2">[2]</a> An ellipse is one of the plane, sections of a
+cone. It is an oval curve, which may be drawn
+by fixing two pins in a sheet of paper at S and H,
+fastening a string, SPH, to the two pins, and stretching
+it with a pencil point at P, and moving the pencil
+point, while the string is kept taut, to trace the
+oval ellipse, APB. S and H are the <i>foci</i>.
+Kepler found the sun to be in one focus, say S. AB
+is the <i>major axis</i>. DE is the <i>minor
+axis</i>. C is the <i>centre</i>. The direction
+of AB is the <i>line of apses</i>. The ratio of
+CS to CA is the <i>excentricity</i>. The position
+of the planet at A is the <i>perihelion</i> (nearest
+to the sun). The position of the planet at B is
+the <i>aphelion</i> (farthest from the sun).
+The angle ASP is the <i>anomaly</i> when the planet
+is at P. CA or a line drawn from S to D is the <i>mean
+distance</i> of the planet from the sun.</p>
+
+<p><a name="fn5_3">[3]</a> The ruled logarithmic paper we now use was not
+then to be had by going into a stationer&#8217;s shop.
+Else he would have accomplished this in five minutes.</p>
+
+<p><br /><br /></p>
+
+<a name="6"></a>
+<h2>6. GALILEO AND THE TELESCOPE&#8212;NOTIONS OF GRAVITY BY HORROCKS, ETC.</h2>
+
+<p>It is now necessary to leave the subject of dynamical
+astronomy for a short time in order to give some account
+of work in a different direction originated by a contemporary
+of Kepler&#8217;s, his senior in fact by seven years.
+Galileo Galilei was born at Pisa in 1564. The
+most scientific part of his work dealt with terrestrial
+dynamics; but one of those fortunate chances which
+happen only to really great men put him in the way
+of originating a new branch of astronomy.</p>
+
+<p>The laws of motion had not been correctly defined.
+ The only man of Galileo&#8217;s time who seems to
+have worked successfully in the same direction as
+himself was that Admirable Crichton of the Italians,
+Leonardo da Vinci. Galileo cleared the ground.
+It had always been noticed that things tend to come
+to rest; a ball rolled on the ground, a boat moved
+on the water, a shot fired in the air. Galileo
+realised that in all of these cases a resisting force
+acts to stop the motion, and he was the first to arrive
+at the not very obvious law that the motion of a body
+will never stop, nor vary its speed, nor change its
+direction, except by the action of some force.</p>
+
+<p>It is not very obvious that a light body and a heavy
+one fall at the same speed (except for the resistance
+of the air). Galileo proved this on paper, but
+to convince the world he had to experiment from the
+leaning tower of Pisa.</p>
+
+<p>At an early age he discovered the principle of isochronism
+of the pendulum, which, in the hands of Huyghens in
+the middle of the seventeenth century, led to the
+invention of the pendulum clock, perhaps the most
+valuable astronomical instrument ever produced.</p>
+
+<p>These and other discoveries in dynamics may seem very
+obvious now; but it is often the most every-day matters
+which have been found to elude the inquiries of ordinary
+minds, and it required a high order of intellect to
+unravel the truth and discard the stupid maxims scattered
+through the works of Aristotle and accepted on his
+authority. A blind worship of scientific authorities
+has often delayed the progress of human knowledge,
+just as too much &#8220;instruction&#8221; of a youth
+often ruins his &#8220;education.&#8221; Grant,
+in his history of Physical Astronomy, has well said
+that &#8220;the sagacity and skill which Galileo displays
+in resolving the phenomena of motion into their constituent
+elements, and hence deriving the original principles
+involved in them, will ever assure to him a distinguished
+place among those who have extended the domains of
+science.&#8221;</p>
+
+<p>But it was work of a different kind that established
+Galileo&#8217;s popular reputation. In 1609 Galileo
+heard that a Dutch spectacle-maker had combined a
+pair of lenses so as to magnify distant objects.
+Working on this hint, he solved the same problem,
+first on paper and then in practice. So he came
+to make one of the first telescopes ever used in astronomy.
+No sooner had he turned it on the heavenly bodies than
+he was rewarded by such a shower of startling discoveries
+as forthwith made his name the best known in Europe.
+ He found curious irregular black spots on the sun,
+revolving round it in twenty-seven days; hills and
+valleys on the moon; the planets showing discs of sensible
+size, not points like the fixed stars; Venus showing
+phases according to her position in relation to the
+sun; Jupiter accompanied by four moons; Saturn with
+appendages that he could not explain, but unlike the
+other planets; the Milky Way composed of a multitude
+of separate stars.</p>
+
+<p>His fame flew over Europe like magic, and his discoveries
+were much discussed&#8212;and there were many
+who refused to believe. Cosmo de Medici induced
+him to migrate to Florence to carry on his observations.
+ He was received by Paul V., the Pope, at Rome, to
+whom he explained his discoveries.</p>
+
+<p>He thought that these discoveries proved the truth
+of the Copernican theory of the Earth&#8217;s motion;
+and he urged this view on friends and foes alike.
+ Although in frequent correspondence with Kepler, he
+never alluded to the New Astronomy, and wrote to him
+extolling the virtue of epicycles. He loved to
+argue, never shirked an encounter with any number
+of disputants, and laughed as he broke down their arguments.</p>
+
+<p>Through some strange course of events, not easy to
+follow, the Copernican theory, whose birth was welcomed
+by the Church, had now been taken up by certain anti-clerical
+agitators, and was opposed by the cardinals as well
+as by the dignitaries of the Reformed Church.
+Galileo&#8212;a good Catholic&#8212;got mixed
+up in these discussions, although on excellent terms
+with the Pope and his entourage. At last it came
+about that Galileo was summoned to appear at Rome,
+where he was charged with holding and teaching heretical
+opinions about the movement of the earth; and he then
+solemnly abjured these opinions. There has been
+much exaggeration and misstatement about his trial
+and punishment, and for a long time there was a great
+deal of bitterness shown on both sides. But the
+general verdict of the present day seems to be that,
+although Galileo himself was treated with consideration,
+the hostility of the Church to the views of Copernicus
+placed it in opposition also to the true Keplerian
+system, and this led to unprofitable controversies.
+ From the time of Galileo onwards, for some time,
+opponents of religion included the theory of the Earth&#8217;s
+motion in their disputations, not so much for the love,
+or knowledge, of astronomy, as for the pleasure of
+putting the Church in the wrong. This created
+a great deal of bitterness and intolerance on both
+sides. Among the sufferers was Giordano Bruno,
+a learned speculative philosopher, who was condemned
+to be burnt at the stake.</p>
+
+<p>Galileo died on Christmas Day, 1642&#8212;the
+day of Newton&#8217;s birth. The further consideration
+of the grand field of discovery opened out by Galileo
+with his telescopes must be now postponed, to avoid
+discontinuity in the history of the intellectual development
+of this period, which lay in the direction of dynamical,
+or physical, astronomy.</p>
+
+<p>Until the time of Kepler no one seems to have conceived
+the idea of universal physical forces controlling
+terrestrial phenomena, and equally applicable to the
+heavenly bodies. The grand discovery by Kepler
+of the true relationship of the Sun to the Planets,
+and the telescopic discoveries of Galileo and of those
+who followed him, spread a spirit of inquiry and philosophic
+thought throughout Europe, and once more did astronomy
+rise in estimation; and the irresistible logic of
+its mathematical process of reasoning soon placed it
+in the position it has ever since occupied as the
+foremost of the exact sciences.</p>
+
+<p>The practical application of this process of reasoning
+was enormously facilitated by the invention of logarithms
+by Napier. He was born at Merchistoun, near Edinburgh,
+in 1550, and died in 1617. By this system the
+tedious arithmetical operations necessary in astronomical
+calculations, especially those dealing with the trigonometrical
+functions of angles, were so much simplified that Laplace
+declared that by this invention the life-work of an
+astronomer was doubled.</p>
+
+<p>Jeremiah Horrocks (born 1619, died 1641) was an ardent
+admirer of Tycho Brahe and Kepler, and was able to
+improve the Rudolphine tables so much that he foretold
+a transit of Venus, in 1639, which these tables failed
+to indicate, and was the only observer of it.
+His life was short, but he accomplished a great deal,
+and rightly ascribed the lunar inequality called <i>evection</i>
+to variations in the value of the eccentricity and
+in the direction of the line of apses, at the same
+time correctly assigning <i>the disturbing force of
+the Sun</i> as the cause. He discovered the errors
+in Jupiter&#8217;s calculated place, due to what we
+now know as the long inequality of Jupiter and Saturn,
+and measured with considerable accuracy the acceleration
+at that date of Jupiter&#8217;s mean motion, and indicated
+the retardation of Saturn&#8217;s mean motion.</p>
+
+<p>Horrocks&#8217; investigations, so far as they could
+be collected, were published posthumously in 1672,
+and seldom, if ever, has a man who lived only twenty-two
+years originated so much scientific knowledge.</p>
+
+<p>At this period British science received a lasting
+impetus by the wise initiation of a much-abused man,
+Charles II., who founded the Royal Society of London,
+and also the Royal Observatory of Greeenwich, where
+he established Flamsteed as first Astronomer Royal,
+especially for lunar and stellar observations likely
+to be useful for navigation. At the same time
+the French Academy and the Paris Observatory were
+founded. All this within fourteen years, 1662-1675.</p>
+
+<p>Meanwhile gravitation in general terms was being discussed
+by Hooke, Wren, Halley, and many others.  All
+of these men felt a repugnance to accept the idea
+of a force acting across the empty void of space.
+Descartes (1596-1650) proposed an ethereal medium whirling
+round the sun with the planets, and having local whirls
+revolving with the satellites. As Delambre and
+Grant have said, this fiction only retarded the progress
+of pure science. It had no sort of relation to
+the more modern, but equally misleading, &#8220;nebular
+hypothesis.&#8221; While many were talking and
+guessing, a giant mind was needed at this stage to
+make things clear.</p>
+
+<p><br /><br /></p>
+
+<a name="7"></a>
+<h2>7. SIR ISAAC NEWTON&#8212;LAW OF UNIVERSAL
+GRAVITATION.</h2>
+
+<p>We now reach the period which is the culminating point
+of interest in the history of dynamical astronomy.
+ Isaac Newton was born in 1642. Pemberton states
+that Newton, having quitted Cambridge to avoid the
+plague, was residing at Wolsthorpe, in Lincolnshire,
+where he had been born; that he was sitting one day
+in the garden, reflecting upon the force which prevents
+a planet from flying off at a tangent and which draws
+it to the sun, and upon the force which draws the moon
+to the earth; and that he saw in the case of the planets
+that the sun&#8217;s force must clearly be unequal
+at different distances, for the pull out of the tangential
+line in a minute is less for Jupiter than for Mars.
+He then saw that the pull of the earth on the moon
+would be less than for a nearer object. It is
+said that while thus meditating he saw an apple fall
+from a tree to the ground, and that this fact suggested
+the questions: Is the force that pulled that apple
+from the tree the same as the force which draws the
+moon to the earth?  Does the attraction for both
+of them follow the same law as to distance as is given
+by the planetary motions round the sun? It has
+been stated that in this way the first conception
+of universal gravitation arose.<a href="#fn7_1">[1]</a></p>
+
+<p>Quite the most important event in the whole history
+of physical astronomy was the publication, in 1687,
+of Newton&#8217;s <i>Principia (Philosophiae Naturalis
+Principia Mathematica)</i>. In this great work
+Newton started from the beginning of things, the laws
+of motion, and carried his argument, step by step,
+into every branch of physical astronomy; giving the
+physical meaning of Kepler&#8217;s three laws, and
+explaining, or indicating the explanation of, all the
+known heavenly motions and their irregularities; showing
+that all of these were included in his simple statement
+about the law of universal gravitation; and proceeding
+to deduce from that law new irregularities in the
+motions of the moon which had never been noticed, and
+to discover the oblate figure of the earth and the
+cause of the tides. These investigations occupied
+the best part of his life; but he wrote the whole
+of his great book in fifteen months.</p>
+
+<p>Having developed and enunciated the true laws of motion,
+he was able to show that Kepler&#8217;s second law
+(that equal areas are described by the line from the
+planet to the sun in equal times) was only another
+way of saying that the centripetal force on a planet
+is always directed to the sun. Also that Kepler&#8217;s
+first law (elliptic orbits with the sun in one focus)
+was only another way of saying that the force urging
+a planet to the sun varies inversely as the square
+of the distance. Also (if these two be granted)
+it follows that Kepler&#8217;s third law is only another
+way of saying that the sun&#8217;s force on different
+planets (besides depending as above on distance) is
+proportional to their masses.</p>
+
+<p>Having further proved the, for that day, wonderful
+proposition that, with the law of inverse squares,
+the attraction by the separate particles of a sphere
+of uniform density (or one composed of concentric
+spherical shells, each of uniform density) acts as
+if the whole mass were collected at the centre, he
+was able to express the meaning of Kepler&#8217;s
+laws in propositions which have been summarised as
+follows:&#8212;</p>
+
+<p>The law of universal gravitation.&#8212;<i>Every
+particle of matter in the universe attracts every
+other particle with a force varying inversely as the
+square of the distance between them, and directly as
+the product of the masses of the two particles</i>.<a href="#fn7_2">[2]</a></p>
+
+<p>But Newton did not commit himself to the law until
+he had answered that question about the apple; and
+the above proposition now enabled him to deal with
+the Moon and the apple. Gravity makes a stone
+fall 16.1 feet in a second. The moon is 60 times
+farther from the earth&#8217;s centre than the stone,
+so it ought to be drawn out of a straight course through
+16.1 feet in a minute. Newton found the distance
+through which she is actually drawn as a fraction of
+the earth&#8217;s diameter.  But when he first
+examined this matter he proceeded to use a wrong diameter
+for the earth, and he found a serious discrepancy.
+This, for a time, seemed to condemn his theory, and
+regretfully he laid that part of his work aside.
+Fortunately, before Newton wrote the <i>Principia</i>
+the French astronomer Picard made a new and correct
+measure of an arc of the meridian, from which he obtained
+an accurate value of the earth&#8217;s diameter.
+Newton applied this value, and found, to his great
+joy, that when the distance of the moon is 60 times
+the radius of the earth she is attracted out of the
+straight course 16.1 feet per minute, and that the
+force acting on a stone or an apple follows the same
+law as the force acting upon the heavenly bodies.<a href="#fn7_3">[3]</a></p>
+
+<p>The universality claimed for the law&#8212;if
+not by Newton, at least by his commentators&#8212;was
+bold, and warranted only by the large number of cases
+in which Newton had found it to apply. Its universality
+has been under test ever since, and so far it has
+stood the test. There has often been a suspicion
+of a doubt, when some inequality of motion in the
+heavenly bodies has, for a time, foiled the astronomers
+in their attempts to explain it. But improved
+mathematical methods have always succeeded in the
+end, and so the seeming doubt has been converted into
+a surer conviction of the universality of the law.</p>
+
+<p>Having once established the law, Newton proceeded
+to trace some of its consequences. He saw that
+the figure of the earth depends partly on the mutual
+gravitation of its parts, and partly on the centrifugal
+tendency due to the earth&#8217;s rotation, and that
+these should cause a flattening of the poles.
+He invented a mathematical method which he used for
+computing the ratio of the polar to the equatorial
+diameter.</p>
+
+<p>He then noticed that the consequent bulging of matter
+at the equator would be attracted by the moon unequally,
+the nearest parts being most attracted; and so the
+moon would tend to tilt the earth when in some parts
+of her orbit; and the sun would do this to a less extent,
+because of its great distance. Then he proved
+that the effect ought to be a rotation of the earth&#8217;s
+axis over a conical surface in space, exactly as the
+axis of a top describes a cone, if the top has a sharp
+point, and is set spinning and displaced from the vertical.
+He actually calculated the amount; and so he explained
+the cause of the precession of the equinoxes discovered
+by Hipparchus about 150 B.C.</p>
+
+<p>One of his grandest discoveries was a method of weighing
+the heavenly bodies by their action on each other.
+By means of this principle he was able to compare
+the mass of the sun with the masses of those planets
+that have moons, and also to compare the mass of our
+moon with the mass of the earth.</p>
+
+<p>Thus Newton, after having established his great principle,
+devoted his splendid intellect to the calculation
+of its consequences. He proved that if a body
+be projected with any velocity in free space, subject
+only to a central force, varying inversely as the square
+of the distance, the body must revolve in a curve
+which may be any one of the sections of a cone&#8212;a
+circle, ellipse, parabola, or hyperbola; and he found
+that those comets of which he had observations move
+in parabolae round the Sun, and are thus subject to
+the universal law.</p>
+
+<p>Newton realised that, while planets and satellites
+are chiefly controlled by the central body about which
+they revolve, the new law must involve irregularities,
+due to their mutual action&#8212;such, in fact,
+as Horrocks had indicated. He determined to put
+this to a test in the case of the moon, and to calculate
+the sun&#8217;s effect, from its mass compared with
+that of the earth, and from its distance. He proved
+that the average effect upon the plane of the orbit
+would be to cause the line in which it cuts the plane
+of the ecliptic (i.e., the line of nodes) to revolve
+in the ecliptic once in about nineteen years.
+This had been a known fact from the earliest ages.
+He also concluded that the line of apses would revolve
+in the plane of the lunar orbit also in about nineteen
+years; but the observed period is only ten years.
+For a long time this was the one weak point in the
+Newtonian theory. It was not till 1747 that Clairaut
+reconciled this with the theory, and showed why Newton&#8217;s
+calculation was not exact.</p>
+
+<p>Newton proceeded to explain the other inequalities
+recognised by Tycho Brahe and older observers, and
+to calculate their maximum amounts as indicated by
+his theory. He further discovered from his calculations
+two new inequalities, one of the apogee, the other
+of the nodes, and assigned the maximum value.
+Grant has shown the values of some of these as given
+by observation in the tables of Meyer and more modern
+tables, and has compared them with the values assigned
+by Newton from his theory; and the comparison is very
+remarkable.</p>
+
+<pre>Newton.      Modern Tables.
+&#176; &#8217;  "         &#176; &#8217; "
+Mean monthly motion of Apses         1.31.28         3.4.0
+Mean annual motion of nodes         19.18.1,23     19.21.22,50
+Mean value of &#8220;variation&#8221;              36.10          35.47
+Annual equation                        11.51          11.14
+Inequality of mean motion of apogee    19.43          22.17
+Inequality of mean motion of nodes      9.24           9.0</pre>
+
+<p>The only serious discrepancy is the first, which has
+been already mentioned. Considering that some
+of these perturbations had never been discovered,
+that the cause of none of them had ever been known,
+and that he exhibited his results, if he did not also
+make the discoveries, by the synthetic methods of
+geometry, it is simply marvellous that he reached
+to such a degree of accuracy. He invented the
+infinitesimal calculus which is more suited for such
+calculations, but had he expressed his results in
+that language he would have been unintelligible to
+many.</p>
+
+<p>Newton&#8217;s method of calculating the precession
+of the equinoxes, already referred to, is as beautiful
+as anything in the <i>Principia</i>. He had already
+proved the regression of the nodes of a satellite
+moving in an orbit inclined to the ecliptic. He
+now said that the nodes of a ring of satellites revolving
+round the earth&#8217;s equator would consequently
+all regress. And if joined into a solid ring its
+node would regress; and it would do so, only more slowly,
+if encumbered by the spherical part of the earth&#8217;s
+mass. Therefore the axis of the equatorial belt
+of the earth must revolve round the pole of the ecliptic.
+Then he set to work and found the amount due to the
+moon and that due to the sun, and so he solved the
+mystery of 2,000 years.</p>
+
+<p>When Newton applied his law of gravitation to an explanation
+of the tides he started a new field for the application
+of mathematics to physical problems; and there can
+be little doubt that, if he could have been furnished
+with complete tidal observations from different parts
+of the world, his extraordinary powers of analysis
+would have enabled him to reach a satisfactory theory.
+ He certainly opened up many mines full of intellectual
+gems; and his successors have never ceased in their
+explorations. This has led to improved mathematical
+methods, which, combined with the greater accuracy
+of observation, have rendered physical astronomy of
+to-day the most exact of the sciences.</p>
+
+<p>Laplace only expressed the universal opinion of posterity
+when he said that to the <i>Principia</i> is assured
+&#8220;a pre-eminence above all the other productions
+of the human intellect.&#8221;</p>
+
+<p>The name of Flamsteed, First Astronomer Royal, must
+here be mentioned as having supplied Newton with the
+accurate data required for completing the theory.</p>
+
+<p>The name of Edmund Halley, Second Astronomer Royal,
+must ever be held in repute, not only for his own
+discoveries, but for the part he played in urging
+Newton to commit to writing, and present to the Royal
+Society, the results of his investigations. But
+for his friendly insistence it is possible that the
+<i>Principia</i> would never have been written; and
+but for his generosity in supplying the means the
+Royal Society could not have published the book.</p>
+
+<p align="center"><img src="007.jpg" alt="[Illustration: DEATH MASK OF SIR ISAAC NEWTON.
+Photographed specially for this work from the original,
+by kind permission of the Royal Society, London.]" /></p>
+
+<p>Sir Isaac Newton died in 1727, at the age of eighty-five.
+ His body lay in state in the Jerusalem Chamber, and
+was buried in Westminster Abbey.</p>
+
+<p><br /><br /></p>
+
+<p><b>FOOTNOTES:</b></p>
+
+<p><a name="fn7_1">[1]</a> The writer inherited from his father (Professor
+J. D. Forbes) a small box containing a bit of wood
+and a slip of paper, which had been presented to him
+by Sir David Brewster. On the paper Sir David
+had written these words: &#8220;If there be any
+truth in the story that Newton was led to the theory
+of gravitation by the fall of an apple, this bit of
+wood is probably a piece of the apple tree from which
+Newton saw the apple fall. When I was on a pilgrimage
+to the house in which Newton was born, I cut it off
+an ancient apple tree growing in his garden.&#8221;
+When lecturing in Glasgow, about 1875, the writer showed
+it to his audience. The next morning, when removing
+his property from the lecture table, he found that
+his precious relic had been stolen. It would
+be interesting to know who has got it now!</p>
+
+<p><a name="fn7_2">[2]</a> It must be noted that these words, in which the
+laws of gravitation are always summarised in histories
+and text-books, do not appear in the <i>Principia</i>;
+but, though they must have been composed by some early
+commentator, it does not appear that their origin has
+been traced. Nor does it appear that Newton ever
+extended the law beyond the Solar System, and probably
+his caution would have led him to avoid any statement
+of the kind until it should be proved.</p>
+
+<p>With this exception the above statement of the law
+of universal gravitation contains nothing that is
+not to be found in the <i>Principia</i>; and the nearest
+approach to that statement occurs in the Seventh Proposition
+of Book III.:&#8212;</p>
+
+<p>Prop.: That gravitation occurs in all bodies,
+and that it is proportional to the quantity of matter
+in each.</p>
+
+<p>Cor. I.: The total attraction of gravitation
+on a planet arises, and is composed, out of the attraction
+on the separate parts.</p>
+
+<p>Cor. II.: The attraction on separate equal
+particles of a body is reciprocally as the square
+of the distance from the particles.</p>
+
+<p><a name="fn7_3">[3]</a> It is said that, when working out this final result,
+the probability of its confirming that part of his
+theory which he had reluctantly abandoned years before
+excited him so keenly that he was forced to hand over
+his calculations to a friend, to be completed by him.</p>
+
+<p><br /><br /></p>
+
+<a name="8"></a>
+<h2>8. NEWTON&#8217;S SUCCESSORS&#8212;HALLEY,
+EULER, LAGRANGE, LAPLACE, ETC.</h2>
+
+<p>Edmund Halley succeeded Flamsteed as Second Astronomer
+Royal in 1721. Although he did not contribute
+directly to the mathematical proofs of Newton&#8217;s
+theory, yet his name is closely associated with some
+of its greatest successes.</p>
+
+<p>He was the first to detect the acceleration of the
+moon&#8217;s mean motion. Hipparchus, having
+compared his own observations with those of more ancient
+astronomers, supplied an accurate value of the moon&#8217;s
+mean motion in his time. Halley similarly deduced
+a value for modern times, and found it sensibly greater.
+ He announced this in 1693, but it was not until 1749
+that Dunthorne used modern lunar tables to compute
+a lunar eclipse observed in Babylon 721 B.C., another
+at Alexandria 201 B.C., a solar eclipse observed by
+Theon 360 A.D., and two later ones up to the tenth
+century.  He found that to explain these eclipses
+Halley&#8217;s suggestion must be adopted, the acceleration
+being 10&#8221; in one century. In 1757 Lalande
+again fixed it at 10.&#8221;</p>
+
+<p>The Paris Academy, in 1770, offered their prize for
+an investigation to see if this could be explained
+by the theory of gravitation. Euler won the prize,
+but failed to explain the effect, and said: &#8220;It
+appears to be established by indisputable evidence
+that the secular inequality of the moon&#8217;s mean
+motion cannot be produced by the forces of gravitation.&#8221;</p>
+
+<p>The same subject was again proposed for a prize which
+was shared by Lagrange <a href="#fn8_1">[1]</a> and Euler, neither finding
+a solution, while the latter asserted the existence
+of a resisting medium in space.</p>
+
+<p>Again, in 1774, the Academy submitted the same subject,
+a third time, for the prize; and again Lagrange failed
+to detect a cause in gravitation.</p>
+
+<p>Laplace <a href="#fn8_2">[2]</a> now took the matter in hand. He tried
+the effect of a non-instantaneous action of gravity,
+to no purpose. But in 1787 he gave the true explanation.
+ The principal effect of the sun on the moon&#8217;s
+orbit is to diminish the earth&#8217;s influence, thus
+lengthening the period to a new value generally taken
+as constant. But Laplace&#8217;s calculations
+showed the new value to depend upon the excentricity
+of the earth&#8217;s orbit, which, according; to theory,
+has a periodical variation of enormous period, and
+has been continually diminishing for thousands of
+years. Thus the solar influence has been diminishing,
+and the moon&#8217;s mean motion increased. Laplace
+computed the amount at 10&#8221; in one century, agreeing
+with observation. (Later on Adams showed that Laplace&#8217;s
+calculation was wrong, and that the value he found
+was too large; so, part of the acceleration is now
+attributed by some astronomers to a lengthening of
+the day by tidal friction.)</p>
+
+<p>Another contribution by Halley to the verification
+of Newton&#8217;s law was made when he went to St.
+Helena to catalogue the southern stars. He measured
+the change in length of the second&#8217;s pendulum
+in different latitudes due to the changes in gravity
+foretold by Newton.</p>
+
+<p>Furthermore, he discovered the long inequality of
+Jupiter and Saturn, whose period is 929 years.
+For an investigation of this also the Academy of Sciences
+offered their prize. This led Euler to write a
+valuable essay disclosing a new method of computing
+perturbations, called the instantaneous ellipse with
+variable elements. The method was much developed
+by Lagrange.</p>
+
+<p>But again it was Laplace who solved the problem of
+the inequalities of Jupiter and Saturn by the theory
+of gravitation, reducing the errors of the tables
+from 20&#8217; down to 12&#8221;, thus abolishing the
+use of empirical corrections to the planetary tables,
+and providing another glorious triumph for the law
+of gravitation.  As Laplace justly said:
+&#8220;These inequalities appeared formerly to be inexplicable
+by the law of gravitation&#8212;they now form
+one of its most striking proofs.&#8221;</p>
+
+<p>Let us take one more discovery of Halley, furnishing
+directly a new triumph for the theory. He noticed
+that Newton ascribed parabolic orbits to the comets
+which he studied, so that they come from infinity,
+sweep round the sun, and go off to infinity for ever,
+after having been visible a few weeks or months.
+He collected all the reliable observations of comets
+he could find, to the number of twenty-four, and computed
+their parabolic orbits by the rules laid down by Newton.
+His object was to find out if any of them really travelled
+in elongated ellipses, practically undistinguishable,
+in the visible part of their paths, from parabol&#230;,
+in which case they would be seen more than once.
+He found two old comets whose orbits, in shape and
+position, resembled the orbit of a comet observed by
+himself in 1682.  Apian observed one in 1531;
+Kepler the other in 1607.  The intervals between
+these appearances is seventy-five or seventy-six years.
+He then examined and found old records of similar appearance
+in 1456, 1380, and 1305. It is true, he noticed,
+that the intervals varied by a year and a-half, and
+the inclination of the orbit to the ecliptic diminished
+with successive apparitions.  But he knew from
+previous calculations that this might easily be due
+to planetary perturbations. Finally, he arrived
+at the conclusion that all of these comets were identical,
+travelling in an ellipse so elongated that the part
+where the comet was seen seemed to be part of a parabolic
+orbit. He then predicted its return at the end
+of 1758 or beginning of 1759, when he should be dead;
+but, as he said, &#8220;if it should return, according
+to our prediction, about the year 1758, impartial posterity
+will not refuse to acknowledge that this was first
+discovered by an Englishman."<a href="#fn8_3">[3]</a> [<i>Synopsis Astronomiae
+Cometicae</i>, 1749.]</p>
+
+<p>Once again Halley&#8217;s suggestion became an inspiration
+for the mathematical astronomer. Clairaut, assisted
+by Lalande, found that Saturn would retard the comet
+100 days, Jupiter 518 days, and predicted its return
+to perihelion on April 13th, 1759. In his communication
+to the French Academy, he said that a comet travelling
+into such distant regions might be exposed to the influence
+of forces totally unknown, and &#8220;even of some
+planet too far removed from the sun to be ever perceived.&#8221;</p>
+
+<p>The excitement of astronomers towards the end of 1758
+became intense; and the honour of first catching sight
+of the traveller fell to an amateur in Saxony, George
+Palitsch, on Christmas Day, 1758. It reached
+perihelion on March 13th, 1759.</p>
+
+<p>This fact was a startling confirmation of the Newtonian
+theory, because it was a new kind of calculation of
+perturbations, and also it added a new member to the
+solar system, and gave a prospect of adding many more.</p>
+
+<p>When Halley&#8217;s comet reappeared in 1835, Pontecoulant&#8217;s
+computations for the date of perihelion passage were
+very exact, and afterwards he showed that, with more
+exact values of the masses of Jupiter and Saturn,
+his prediction was correct within two days, after an
+invisible voyage of seventy-five years!</p>
+
+<p>Hind afterwards searched out many old appearances
+of this comet, going back to 11 B.C., and most of
+these have been identified as being really Halley&#8217;s
+comet by the calculations of Cowell and Cromellin<a href="#fn8_4">[4]</a>
+(of Greenwich Observatory), who have also predicted
+its next perihelion passage for April 8th to 16th,
+1910, and have traced back its history still farther,
+to 240 B.C.</p>
+
+<p>Already, in November, 1907, the Astronomer Royal was
+trying to catch it by the aid of photography.</p>
+
+<p><br /><br /></p>
+
+<p><b>FOOTNOTES:</b></p>
+
+<p><a name="fn8_1">[1]</a> Born 1736; died 1813.</p>
+
+<p><a name="fn8_2">[2]</a> Born 1749; died 1827.</p>
+
+<p><a name="fn8_3">[3]</a> This sentence does not appear in the original
+memoir communicated to the Royal Society, but was
+first published in a posthumous reprint.</p>
+
+<p><a name="fn8_4">[4]</a> <i>R. A. S. Monthly Notices</i>, 1907-8.</p>
+
+<p><br /><br /></p>
+
+<a name="9"></a>
+<h2>9. DISCOVERY OF NEW PLANETS&#8212;HERSCHEL,
+PIAZZI, ADAMS, AND LE VERRIER.</h2>
+
+<p>It would be very interesting, but quite impossible
+in these pages, to discuss all the exquisite researches
+of the mathematical astronomers, and to inspire a
+reverence for the names connected with these researches,
+which for two hundred years have been establishing
+the universality of Newton&#8217;s law. The lunar
+and planetary theories, the beautiful theory of Jupiter&#8217;s
+satellites, the figure of the earth, and the tides,
+were mathematically treated by Maclaurin, D&#8217;Alembert,
+Legendre, Clairaut, Euler, Lagrange, Laplace, Walmsley,
+Bailly, Lalande, Delambre, Mayer, Hansen, Burchardt,
+Binet, Damoiseau, Plana, Poisson, Gauss, Bessel, Bouvard,
+Airy, Ivory, Delaunay, Le Verrier, Adams, and others
+of later date.</p>
+
+<p>By passing over these important developments it is
+possible to trace some of the steps in the crowning
+triumph of the Newtonian theory, by which the planet
+Neptune was added to the known members of the solar
+system by the independent researches of Professor J.C.
+Adams and of M. Le Verrier, in 1846.</p>
+
+<p>It will be best to introduce this subject by relating
+how the eighteenth century increased the number of
+known planets, which was then only six, including
+the earth.</p>
+
+<p>On March 13th, 1781, Sir William Herschel was, as
+usual, engaged on examining some small stars, and,
+noticing that one of them appeared to be larger than
+the fixed stars, suspected that it might be a comet.
+To test this he increased his magnifying power from
+227 to 460 and 932, finding that, unlike the fixed
+stars near it, its definition was impaired and its
+size increased.  This convinced him that the object
+was a comet, and he was not surprised to find on succeeding
+nights that the position was changed, the motion being
+in the ecliptic. He gave the observations of
+five weeks to the Royal Society without a suspicion
+that the object was a new planet.</p>
+
+<p>For a long time people could not compute a satisfactory
+orbit for the supposed comet, because it seemed to
+be near the perihelion, and no comet had ever been
+observed with a perihelion distance from the sun greater
+than four times the earth&#8217;s distance. Lexell
+was the first to suspect that this was a new planet
+eighteen times as far from the sun as the earth is.
+In January, 1783, Laplace published the elliptic elements.
+The discoverer of a planet has a right to name it,
+so Herschel called it Georgium Sidus, after the king.
+ But Lalande urged the adoption of the name Herschel.
+ Bode suggested Uranus, and this was adopted.
+The new planet was found to rank in size next to Jupiter
+and Saturn, being 4.3 times the diameter of the earth.</p>
+
+<p>In 1787 Herschel discovered two satellites, both revolving
+in nearly the same plane, inclined 80&#176; to the ecliptic,
+and the motion of both was retrograde.</p>
+
+<p>In 1772, before Herschel&#8217;s discovery, Bode<a href="#fn9_1">[1]</a>
+had discovered a curious arbitrary law of planetary
+distances.  Opposite each planet&#8217;s name
+write the figure 4; and, in succession, add the numbers
+0, 3, 6, 12, 24, 48, 96, <i>etc</i>., to the 4, always
+doubling the last numbers.  You then get the
+planetary distances.</p>
+
+<pre>
+  Mercury, dist.-- 4  4 +   0 =   4
+  Venus      "     7  4 +   3 =   7
+  Earth      "    10  4 +   6 =  10
+  Mars       "    15  4 +  12 =  16
+   --                 4 +  24 =  28
+  Jupiter  dist.  52  4 +  48 =  52
+  Saturn     "    95  4 +  96 = 100
+  (Uranus)   "   192  4 + 192 = 196
+   --                 4 + 384 = 388
+</pre>
+
+<p>All the five planets, and the earth, fitted this rule,
+except that there was a blank between Mars and Jupiter.
+When Uranus was discovered, also fitting the rule,
+the conclusion was irresistible that there is probably
+a planet between Mars and Jupiter. An association
+of twenty-four astronomers was now formed in Germany
+to search for the planet. Almost immediately
+afterwards the planet was discovered, not by any member
+of the association, but by Piazzi, when engaged upon
+his great catalogue of stars. On January 1st,
+1801, he observed a star which had changed its place
+the next night. Its motion was retrograde till
+January 11th, direct after the 13th.  Piazzi fell
+ill before he had enough observations for computing
+the orbit with certainty, and the planet disappeared
+in the sun&#8217;s rays. Gauss published an approximate
+ephemeris of probable positions when the planet should
+emerge from the sun&#8217;s light. There was an
+exciting hunt, and on December 31st (the day before
+its birthday) De Zach captured the truant, and Piazzi
+christened it Ceres.</p>
+
+<p>The mean distance from the sun was found to be 2.767,
+agreeing with the 2.8 given by Bode&#8217;s law.
+Its orbit was found to be inclined over 10&#176; to the
+ecliptic, and its diameter was only 161 miles.</p>
+
+<p>On March 28th, 1802, Olbers discovered a new seventh
+magnitude star, which turned out to be a planet resembling
+Ceres. It was called Pallas. Gauss found
+its orbit to be inclined 35&#176; to the ecliptic, and
+to cut the orbit of Ceres; whence Olbers considered
+that these might be fragments of a broken-up planet.
+He then commenced a search for other fragments.
+In 1804 Harding discovered Juno, and in 1807 Olbers
+found Vesta. The next one was not discovered until
+1845, from which date asteroids, or minor planets
+(as these small planets are called), have been found
+almost every year. They now number about 700.</p>
+
+<p>It is impossible to give any idea of the interest
+with which the first additions since prehistoric times
+to the planetary system were received. All of
+those who showered congratulations upon the discoverers
+regarded these discoveries in the light of rewards
+for patient and continuous labours, the very highest
+rewards that could be desired. And yet there
+remained still the most brilliant triumph of all,
+the addition of another planet like Uranus, before
+it had ever been seen, when the analysis of Adams
+and Le Verrier gave a final proof of the powers of
+Newton&#8217;s great law to explain any planetary
+irregularity.</p>
+
+<p>After Sir William Herschel discovered Uranus, in 1781,
+it was found that astronomers had observed it on many
+previous occasions, mistaking it for a fixed star
+of the sixth or seventh magnitude. Altogether,
+nineteen observations of Uranus&#8217;s position, from
+the time of Flamsteed, in 1690, had been recorded.</p>
+
+<p>In 1790 Delambre, using all these observations, prepared
+tables for computing its position. These worked
+well enough for a time, but at last the differences
+between the calculated and observed longitudes of
+the planet became serious. In 1821 Bouvard undertook
+a revision of the tables, but found it impossible
+to reconcile all the observations of 130 years (the
+period of revolution of Uranus is eighty-four years).
+So he deliberately rejected the old ones, expressing
+the opinion that the discrepancies might depend upon
+&#8220;some foreign and unperceived cause which may
+have been acting upon the planet.&#8221; In a
+few years the errors even of these tables became intolerable.
+In 1835 the error of longitude was 30&#8221;; in 1838,
+50&#8221;; in 1841, 70&#8221;; and, by comparing the
+errors derived from observations made before and after
+opposition, a serious error of the distance (radius
+vector) became apparent.</p>
+
+<p>In 1843 John Couch Adams came out Senior Wrangler
+at Cambridge, and was free to undertake the research
+which as an undergraduate he had set himself&#8212;to
+see whether the disturbances of Uranus could be explained
+by assuming a certain orbit, and position in that orbit,
+of a hypothetical planet even more distant than Uranus.
+ Such an explanation had been suggested, but until
+1843 no one had the boldness to attack the problem.
+ Bessel had intended to try, but a fatal illness overtook
+him.</p>
+
+<p>Adams first recalculated all known causes of disturbance,
+using the latest determinations of the planetary masses.
+Still the errors were nearly as great as ever.
+ He could now, however, use these errors as being
+actually due to the perturbations produced by the unknown
+planet.</p>
+
+<p>In 1844, assuming a circular orbit, and a mean distance
+agreeing with Bode&#8217;s law, he obtained a first
+approximation to the position of the supposed planet.
+ He then asked Professor Challis, of Cambridge, to
+procure the latest observations of Uranus from Greenwich,
+which Airy immediately supplied. Then the whole
+work was recalculated from the beginning, with more
+exactness, and assuming a smaller mean distance.</p>
+
+<p>In September, 1845, he handed to Challis the elements
+of the hypothetical planet, its mass, and its apparent
+position for September 30th, 1845. On September
+22nd Challis wrote to Airy explaining the matter,
+and declaring his belief in Adams&#8217;s capabilities.
+When Adams called on him Airy was away from home,
+but at the end of October, 1845, he called again,
+and left a paper with full particulars of his results,
+which had, for the most part, reduced the discrepancies
+to about 1&#8221;. As a matter of fact, it has
+since been found that the heliocentric place of the
+new planet then given was correct within about 2&#176;.</p>
+
+<p>Airy wrote expressing his interest, and asked for
+particulars about the radius vector. Adams did
+not then reply, as the answer to this question could
+be seen to be satisfactory by looking at the data
+already supplied.  He was a most unassuming man,
+and would not push himself forward. He may have
+felt, after all the work he had done, that Airy&#8217;s
+very natural inquiry showed no proportionate desire
+to search for the planet.  Anyway, the matter
+lay in embryo for nine months.</p>
+
+<p>Meanwhile, one of the ablest French astronomers, Le
+Verrier, experienced in computing perturbations, was
+independently at work, knowing nothing about Adams.
+He applied to his calculations every possible refinement,
+and, considering the novelty of the problem, his calculation
+was one of the most brilliant in the records of astronomy.
+In criticism it has been said that these were exhibitions
+of skill rather than helps to a solution of the particular
+problem, and that, in claiming to find the elements
+of the orbit within certain limits, he was claiming
+what was, under the circumstances, impossible, as
+the result proved.</p>
+
+<p>In June, 1846, Le Verrier announced, in the <i>Comptes
+Rendus de l&#8217;Academie des Sciences</i>, that
+the longitude of the disturbing planet, for January
+1st, 1847, was 325, and that the probable error did
+not exceed 10&#176;.</p>
+
+<p>This result agreed so well with Adams&#8217;s (within
+1&#176;) that Airy urged Challis to apply the splendid
+Northumberland equatoreal, at Cambridge, to the search.
+ Challis, however, had already prepared an exhaustive
+plan of attack which must in time settle the point.
+ His first work was to observe, and make a catalogue,
+or chart, of all stars near Adams&#8217;s position.</p>
+
+<p>On August 31st, 1846, Le Verrier published the concluding
+part of his labours.</p>
+
+<p>On September 18th, 1846, Le Verrier communicated his
+results to the Astronomers at Berlin, and asked them
+to assist in searching for the planet. By good
+luck Dr. Bremiker had just completed a star-chart of
+the very part of the heavens including Le Verrier&#8217;s
+position; thus eliminating all of Challis&#8217;s
+preliminary work. The letter was received in
+Berlin on September 23rd; and the same evening Galle
+found the new planet, of the eighth magnitude, the
+size of its disc agreeing with Le Verrier&#8217;s
+prediction, and the heliocentric longitude agreeing
+within 57&#8217;. By this time Challis had recorded,
+without reduction, the observations of 3,150 stars,
+as a commencement for his search.  On reducing
+these, he found a star, observed on August 12th, which
+was not in the same place on July 30th. This
+was the planet, and he had also observed it on August
+4th.</p>
+
+<p>The feeling of wonder, admiration, and enthusiasm
+aroused by this intellectual triumph was overwhelming.
+ In the world of astronomy reminders are met every
+day of the terrible limitations of human reasoning
+powers; and every success that enables the mind&#8217;s
+eye to see a little more clearly the meaning of things
+has always been heartily welcomed by those who have
+themselves been engaged in like researches. But,
+since the publication of the <i>Principia</i>, in 1687,
+there is probably no analytical success which has raised
+among astronomers such a feeling of admiration and
+gratitude as when Adams and Le Verrier showed the
+inequalities in Uranus&#8217;s motion to mean that
+an unknown planet was in a certain place in the heavens,
+where it was found.</p>
+
+<p>At the time there was an unpleasant display of international
+jealousy. The British people thought that the
+earlier date of Adams&#8217;s work, and of the observation
+by Challis, entitled him to at least an equal share
+of credit with Le Verrier. The French, on the
+other hand, who, on the announcement of the discovery
+by Galle, glowed with pride in the new proof of the
+great powers of their astronomer, Le Verrier, whose
+life had a long record of successes in calculation,
+were incredulous on being told that it had all been
+already done by a young man whom they had never heard
+of.</p>
+
+<p>These displays of jealousy have long since passed
+away, and there is now universally an <i>entente cordiale</i>
+that to each of these great men belongs equally the
+merit of having so thoroughly calculated this inverse
+problem of perturbations as to lead to the immediate
+discovery of the unknown planet, since called Neptune.</p>
+
+<p>It was soon found that the planet had been observed,
+and its position recorded as a fixed star by Lalande,
+on May 8th and 10th, 1795.</p>
+
+<p>Mr. Lassel, in the same year, 1846, with his two-feet
+reflector, discovered a satellite, with retrograde
+motion, which gave the mass of the planet about a
+twentieth of that of Jupiter.</p>
+
+<p><br /><br /></p>
+
+<p><b>FOOTNOTES:</b></p>
+
+<p><a name="fn9_1">[1]</a> Bode&#8217;s law, or something like it, had already
+been fore-shadowed by Kepler and others, especially
+Titius (see <i>Monatliche Correspondenz</i>, vol.
+vii., p. 72).</p>
+
+<p><br /><br /></p>
+
+<h1>BOOK III. OBSERVATION</h1>
+
+<p><br /><br /></p>
+
+<a name="10"></a>
+<h2>10. INSTRUMENTS OF PRECISION&#8212;STATE
+OF THE SOLAR SYSTEM.</h2>
+
+<p>Having now traced the progress of physical astronomy
+up to the time when very striking proofs of the universality
+of the law of gravitation convinced the most sceptical,
+it must still be borne in mind that, while gravitation
+is certainly the principal force governing the motions
+of the heavenly bodies, there may yet be a resisting
+medium in space, and there may be electric and magnetic
+forces to deal with. There may, further, be cases
+where the effects of luminous radiative repulsion
+become apparent, and also Crookes&#8217; vacuum-effects
+described as &#8220;radiant matter.&#8221; Nor
+is it quite certain that Laplace&#8217;s proofs of
+the instantaneous propagation of gravity are final.</p>
+
+<p>And in the future, as in the past, Tycho Brahe&#8217;s
+dictum must be maintained, that all theory shall be
+preceded by accurate observations. It is the
+pride of astronomers that their science stands above
+all others in the accuracy of the facts observed, as
+well as in the rigid logic of the mathematics used
+for interpreting these facts.</p>
+
+<p>It is interesting to trace historically the invention
+of those instruments of precision which have led to
+this result, and, without entering on the details
+required in a practical handbook, to note the guiding
+principles of construction in different ages.</p>
+
+<p>It is very probable that the Chaldeans may have made
+spheres, like the armillary sphere, for representing
+the poles of the heavens; and with rings to show the
+ecliptic and zodiac, as well as the equinoctial and
+solstitial colures; but we have no record. We
+only know that the tower of Belus, on an eminence,
+was their observatory.  We have, however, distinct
+records of two such spheres used by the Chinese about
+2500 B.C.  Gnomons, or some kind of sundial,
+were used by the Egyptians and others; and many of
+the ancient nations measured the obliquity of the
+ecliptic by the shadows of a vertical column in summer
+and winter. The natural horizon was the only
+instrument of precision used by those who determined
+star positions by the directions of their risings and
+settings; while in those days the clepsydra, or waterclock,
+was the best instrument for comparing their times
+of rising and setting.</p>
+
+<p>About 300 B.C. an observatory fitted with circular
+instruments for star positions was set up at Alexandria,
+the then centre of civilisation. We know almost
+nothing about the instruments used by Hipparchus in
+preparing his star catalogues and his lunar and solar
+tables; but the invention of the astrolabe is attributed
+to him.<a href="#fn10_1">[1]</a></p>
+
+<p>In more modern times Nuremberg became a centre of
+astronomical culture. Waltherus, of that town,
+made really accurate observations of star altitudes,
+and of the distances between stars; and in 1484 A.D.
+he used a kind of clock. Tycho Brahe tried these,
+but discarded them as being inaccurate.</p>
+
+<p>Tycho Brahe (1546-1601 A.D.) made great improvements
+in armillary spheres, quadrants, sextants, and large
+celestial globes. With these he measured the
+positions of stars, or the distance of a comet from
+several known stars. He has left us full descriptions
+of them, illustrated by excellent engravings.
+Previous to his time such instruments were made of
+wood.  Tycho always used metal. He paid the
+greatest attention to the stability of mounting, to
+the orientation of his instruments, to the graduation
+of the arcs by the then new method of transversals,
+and to the aperture sight used upon his pointer.
+There were no telescopes in his day, and no pendulum
+clocks. He recognised the fact that there must
+be instrumental errors. He made these as small
+as was possible, measured their amount, and corrected
+his observations.  His table of refractions enabled
+him to abolish the error due to our atmosphere so
+far as it could affect naked-eye observations.
+The azimuth circle of Tycho&#8217;s largest quadrant
+had a diameter of nine feet, and the quadrant a radius
+of six feet. He introduced the mural quadrant
+for meridian observations.<a href="#fn10_2">[2]</a></p>
+
+<p align="center"><img src="008.jpg" alt="[Illustration: ANCIENT CHINESE INSTRUMENTS, Including
+quadrant, celestial globe, and two armillae, in the
+Observatory at Peking. Photographed in Peking
+by the author in 1875, and stolen by the Germans when
+the Embassies were relieved by the allies in 1900.]" /></p>
+
+<p>The French Jesuits at Peking, in the seventeenth century,
+helped the Chinese in their astronomy. In 1875
+the writer saw and photographed, on that part of the
+wall of Peking used by the Mandarins as an observatory,
+the six instruments handsomely designed by Father
+Verbiest, copied from the instruments of Tycho Brahe,
+and embellished with Chinese dragons and emblems cast
+on the supports. He also saw there two old instruments
+(which he was told were Arabic) of date 1279, by Ko
+Show-King, astronomer to Koblai Khan, the grandson
+of Chenghis Khan. One of these last is nearly
+identical with the armillae of Tycho; and the other
+with his &#8220;armillae &#230;quatori&#230; maxim&#230;,&#8221; with
+which he observed the comet of 1585, besides fixed
+stars and planets.<a href="#fn10_3">[3]</a></p>
+
+<p>The discovery by Galileo of the isochronism of the
+pendulum, followed by Huyghens&#8217;s adaptation
+of that principle to clocks, has been one of the greatest
+aids to accurate observation. About the same time
+an equally beneficial step was the employment of the
+telescope as a pointer; not the Galilean with concave
+eye-piece, but with a magnifying glass to examine
+the focal image, at which also a fixed mark could
+be placed.  Kepler was the first to suggest this.
+Gascoigne was the first to use it. Huyghens used
+a metal strip of variable width in the focus, as a
+micrometer to cover a planetary disc, and so to measure
+the width covered by the planet. The Marquis Malvasia,
+in 1662, described the network of fine silver threads
+at right angles, which he used in the focus, much
+as we do now.</p>
+
+<p>In the hands of such a skilful man as Tycho Brahe,
+the old open sights, even without clocks, served their
+purpose sufficiently well to enable Kepler to discover
+the true theory of the solar system. But telescopic
+sights and clocks were required for proving some of
+Newton&#8217;s theories of planetary perturbations.
+Picard&#8217;s observations at Paris from 1667 onwards
+seem to embody the first use of the telescope as a
+pointer. He was also the first to introduce the
+use of Huyghens&#8217;s clocks for observing the right
+ascension of stars.  Olaus Romer was born at
+Copenhagen in 1644. In 1675, by careful study
+of the times of eclipses of Jupiter&#8217;s satellites,
+he discovered that light took time to traverse space.
+Its velocity is 186,000 miles per second. In 1681
+he took up his duties as astronomer at Copenhagen,
+and built the first transit circle on a window-sill
+of his house. The iron axis was five feet long
+and one and a-half inches thick, and the telescope
+was fixed near one end with a counterpoise. The
+telescope-tube was a double cone, to prevent flexure.
+Three horizontal and three vertical wires were used
+in the focus. These were illuminated by a speculum,
+near the object-glass, reflecting the light from a
+lantern placed over the axis, the upper part of the
+telescope-tube being partly cut away to admit the
+light. A divided circle, with pointer and reading
+microscope, was provided for reading the declination.
+He realised the superiority of a circle with graduations
+over a much larger quadrant. The collimation
+error was found by reversing the instrument and using
+a terrestrial mark, the azimuth error by star observations.
+The time was expressed in fractions of a second.
+He also constructed a telescope with equatoreal mounting,
+to follow a star by one axial motion. In 1728
+his instruments and observation records were destroyed
+by fire.</p>
+
+<p>Hevelius had introduced the vernier and tangent screw
+in his measurement of arc graduations. His observatory
+and records were burnt to the ground in 1679.
+Though an old man, he started afresh, and left behind
+him a catalogue of 1,500 stars.</p>
+
+<p>Flamsteed began his duties at Greenwich Observatory,
+as first Astronomer Royal, in 1676, with very poor
+instruments. In 1683 he put up a mural arc of
+140&#176;, and in 1689 a better one, seventy-nine inches
+radius.  He conducted his measurements with great
+skill, and introduced new methods to attain accuracy,
+using certain stars for determining the errors of
+his instruments; and he always reduced his observations
+to a form in which they could be readily used.
+He introduced new methods for determining the position
+of the equinox and the right ascension of a fundamental
+star.  He produced a catalogue of 2,935 stars.
+He supplied Sir Isaac Newton with results of observation
+required in his theoretical calculations. He died
+in 1719.</p>
+
+<p>Halley succeeded Flamsteed to find that the whole
+place had been gutted by the latter&#8217;s executors.
+In 1721 he got a transit instrument, and in 1726 a
+mural quadrant by Graham. His successor in 1742,
+Bradley, replaced this by a fine brass quadrant, eight
+feet radius, by Bird; and Bradley&#8217;s zenith sector
+was purchased for the observatory. An instrument
+like this, specially designed for zenith stars, is
+capable of greater rigidity than a more universal instrument;
+and there is no trouble with refraction in the zenith.
+For these reasons Bradley had set up this instrument
+at Kew, to attempt the proof of the earth&#8217;s
+motion by observing the annual parallax of stars.
+He certainly found an annual variation of zenith distance,
+but not at the times of year required by the parallax.
+This led him to the discovery of the &#8220;aberration&#8221;
+of light and of nutation. Bradley has been described
+as the founder of the modern system of accurate observation.
+He died in 1762, leaving behind him thirteen folio
+volumes of valuable but unreduced observations.
+Those relating to the stars were reduced by Bessel
+and published in 1818, at K&#246;nigsberg, in his well-known
+standard work, <i>Fundamenta Astronomiae</i>.
+In it are results showing the laws of refraction,
+with tables of its amount, the maximum value of aberration,
+and other constants.</p>
+
+<p>Bradley was succeeded by Bliss, and he by Maskelyne
+(1765), who carried on excellent work, and laid the
+foundations of the Nautical Almanac (1767).
+Just before his death he induced the Government to
+replace Bird&#8217;s quadrant by a fine new mural <i>circle</i>,
+six feet in diameter, by Troughton, the divisions
+being read off by microscopes fixed on piers opposite
+to the divided circle. In this instrument the
+micrometer screw, with a divided circle for turning
+it, was applied for bringing the micrometer wire actually
+in line with a division on the circle&#8212;a
+plan which is still always adopted.</p>
+
+<p>Pond succeeded Maskelyne in 1811, and was the first
+to use this instrument. From now onwards the
+places of stars were referred to the pole, not to
+the zenith; the zero being obtained from measures on
+circumpolar stars. Standard stars were used for
+giving the clock error. In 1816 a new transit
+instrument, by Troughton, was added, and from this
+date the Greenwich star places have maintained the
+very highest accuracy.</p>
+
+<p>George Biddell Airy, Seventh Astronomer Royal,<a href="#fn10_4">[4]</a>
+commenced his Greenwich labours in 1835. His
+first and greatest reformation in the work of the
+observatory was one he had already established at
+Cambridge, and is now universally adopted. He
+held that an observation is not completed until it
+has been reduced to a useful form; and in the case
+of the sun, moon, and planets these results were, in
+every case, compared with the tables, and the tabular
+error printed.</p>
+
+<p>Airy was firmly impressed with the object for which
+Charles II. had wisely founded the observatory in
+connection with navigation, and for observations of
+the moon. Whenever a meridian transit of the moon
+could be observed this was done. But, even so,
+there are periods in the month when the moon is too
+near the sun for a transit to be well observed.
+Also weather interferes with many meridian observations.
+To render the lunar observations more continuous,
+Airy employed Troughton&#8217;s successor, James Simms,
+in conjunction with the engineers, Ransome and May,
+to construct an altazimuth with three-foot circles,
+and a five-foot telescope, in 1847. The result
+was that the number of lunar observations was immediately
+increased threefold, many of them being in a part
+of the moon&#8217;s orbit which had previously been
+bare of observations. From that date the Greenwich
+lunar observations have been a model and a standard
+for the whole world.</p>
+
+<p>Airy also undertook to superintend the reduction of
+all Greenwich lunar observations from 1750 to 1830.
+ The value of this laborious work, which was completed
+in 1848, cannot be over-estimated.</p>
+
+<p>The demands of astronomy, especially in regard to
+small minor planets, required a transit instrument
+and mural circle with a more powerful telescope.
+Airy combined the functions of both, and employed the
+same constructors as before to make a <i>transit-circle</i>
+with a telescope of eleven and a-half feet focus and
+a circle of six-feet diameter, the object-glass being
+eight inches in diameter.</p>
+
+<p>Airy, like Bradley, was impressed with the advantage
+of employing stars in the zenith for determining the
+fundamental constants of astronomy. He devised
+a <i>reflex zenith tube</i>, in which the zenith point
+was determined by reflection from a surface of mercury.
+The design was so simple, and seemed so perfect, that
+great expectations were entertained. But unaccountable
+variations comparable with those of the transit circle
+appeared, and the instrument was put out of use until
+1903, when the present Astronomer Royal noticed that
+the irregularities could be allowed for, being due
+to that remarkable variation in the position of the
+earth&#8217;s axis included in circles of about six
+yards diameter at the north and south poles, discovered
+at the end of the nineteenth century. The instrument
+is now being used for investigating these variations;
+and in the year 1907 as many as 1,545 observations
+of stars were made with the reflex zenith tube.</p>
+
+<p>In connection with zenith telescopes it must be stated
+that Respighi, at the Capitol Observatory at Rome,
+made use of a deep well with a level mercury surface
+at the bottom and a telescope at the top pointing
+downwards, which the writer saw in 1871. The reflection
+of the micrometer wires and of a star very near the
+zenith (but not quite in the zenith) can be observed
+together.  His mercury trough was a circular
+plane surface with a shallow edge to retain the mercury.
+The surface quickly came to rest after disturbance
+by street traffic.</p>
+
+<p>Sir W. M. H. Christie, Eighth Astronomer Royal, took
+up his duties in that capacity in 1881. Besides
+a larger altazimuth that he erected in 1898, he has
+widened the field of operations at Greenwich by the
+extensive use of photography and the establishment
+of large equatoreals.  From the point of view
+of instruments of precision, one of the most important
+new features is the astrographic equatoreal, set up
+in 1892 and used for the Greenwich section of the great
+astrographic chart just completed. Photography
+has come to be of use, not only for depicting the
+sun and moon, comets and nebulae, but also to obtain
+accurate relative positions of neighbouring stars;
+to pick up objects that are invisible in any telescope;
+and, most of all perhaps, in fixing the positions
+of faint satellites. Thus Saturn&#8217;s distant
+satellite, Phoebe, and the sixth and seventh satellites
+of Jupiter, have been followed regularly in their
+courses at Greenwich ever since their discovery with
+the thirty-inch reflector (erected in 1897); and while
+doing so Mr. Melotte made, in 1908, the splendid discovery
+on some of the photographic plates of an eighth satellite
+of Jupiter, at an enormous distance from the planet.
+From observations in the early part of 1908, over
+a limited arc of its orbit, before Jupiter approached
+the sun, Mr. Cowell computed a retrograde orbit and
+calculated the future positions of this satellite,
+which enabled Mr. Melotte to find it again in the
+autumn&#8212;a great triumph both of calculation
+and of photographic observation. This satellite
+has never been seen, and has been photographed only
+at Greenwich, Heidelberg, and the Lick Observatory.</p>
+
+<p>Greenwich Observatory has been here selected for tracing
+the progress of accurate measurement. But there
+is one instrument of great value, the heliometer,
+which is not used at Greenwich. This serves the
+purpose of a double image micrometer, and is made by
+dividing the object-glass of a telescope along a diameter.
+Each half is mounted so as to slide a distance of
+several inches each way on an arc whose centre is
+the focus. The amount of the movement can be accurately
+read. Thus two fields of view overlap, and the
+adjustment is made to bring an image of one star over
+that of another star, and then to do the same by a
+displacement in the opposite direction. The total
+movement of the half-object glass is double the distance
+between the star images in the focal plane. Such
+an instrument has long been established at Oxford,
+and German astronomers have made great use of it.
+But in the hands of Sir David Gill (late His Majesty&#8217;s
+Astronomer at the Cape of Good Hope), and especially
+in his great researches on Solar and on Stellar parallax,
+it has been recognised as an instrument of the very
+highest accuracy, measuring the distance between stars
+correctly to less than a tenth of a second of arc.</p>
+
+<p>The superiority of the heliometer over all other devices
+(except photography) for measuring small angles has
+been specially brought into prominence by Sir David
+Gill&#8217;s researches on the distance of the sun&#8212;<i>i.e.,</i>
+the scale of the solar system. A measurement of
+the distance of any planet fixes the scale, and, as
+Venus approaches the earth most nearly of all the
+planets, it used to be supposed that a Transit of
+Venus offered the best opportunity for such measurement,
+especially as it was thought that, as Venus entered
+on the solar disc, the sweep of light round the dark
+disc of Venus would enable a very precise observation
+to be made.  The Transit of Venus in 1874, in
+which the present writer assisted, overthrew this delusion.</p>
+
+<p>In 1877 Sir David Gill used Lord Crawford&#8217;s
+heliometer at the Island of Ascension to measure the
+parallax of Mars in opposition, and found the sun&#8217;s
+distance 93,080,000 miles. He considered that,
+while the superiority of the heliometer had been proved,
+the results would be still better with the points
+of light shown by minor planets rather than with the
+disc of Mars.</p>
+
+<p>In 1888-9, at the Cape, he observed the minor planets
+Iris, Victoria, and Sappho, and secured the co-operation
+of four other heliometers. His final result was
+92,870,000 miles, the parallax being 8",802 (<i>Cape
+Obs</i>., Vol. VI.).</p>
+
+<p>So delicate were these measures that Gill detected
+a minute periodic error of theory of twenty-seven
+days, owing to a periodically erroneous position of
+the centre of gravity of the earth and moon to which
+the position of the observer was referred. This
+led him to correct the mass of the moon, and to fix
+its ratio to the earth&#8217;s mass = 0.012240.</p>
+
+<p>Another method of getting the distance from the sun
+is to measure the velocity of the earth&#8217;s orbital
+motion, giving the circumference traversed in a year,
+and so the radius of the orbit. This has been
+done by comparing observation and experiment.
+The aberration of light is an angle 20&#8221; 48,
+giving the ratio of the earth&#8217;s velocity to the
+velocity of light. The velocity of light is 186,000
+miles a second; whence the distance to the sun is
+92,780,000 miles. There seems, however, to be
+some uncertainty about the true value of the aberration,
+any determination of which is subject to irregularities
+due to the &#8220;seasonal errors.&#8221; The
+velocity of light was experimentally found, in 1862,
+by Fizeau and Foucault, each using an independent
+method. These methods have been developed, and
+new values found, by Cornu, Michaelson, Newcomb, and
+the present writer.</p>
+
+<p>Quite lately Halm, at the Cape of Good Hope, measured
+spectroscopically the velocity of the earth to and
+from a star by observations taken six months apart.
+ Thence he obtained an accurate value of the sun&#8217;s
+distance.<a href="#fn10_5">[5]</a></p>
+
+<p>But the remarkably erratic minor planet, Eros, discovered
+by Witte in 1898, approaches the earth within 15,000,000
+miles at rare intervals, and, with the aid of photography,
+will certainly give us the best result. A large
+number of observatories combined to observe the opposition
+of 1900. Their results are not yet completely
+reduced, but the best value deduced so far for the
+parallax<a href="#fn10_6">[6]</a> is 8".807 &#177; 0".0028.<a href="#fn10_7">[7]</a></p>
+
+<p><br /><br /></p>
+
+<p><b>FOOTNOTES:</b></p>
+
+<p><a name="fn10_1">[1]</a> In 1480 Martin Behaim, of Nuremberg, produced
+his <i>astrolabe</i> for measuring the latitude, by
+observation of the sun, at sea. It consisted
+of a graduated metal circle, suspended by a ring which
+was passed over the thumb, and hung vertically.
+A pointer was fixed to a pin at the centre. This
+arm, called the <i>alhidada</i>, worked round the
+graduated circle, and was pointed to the sun.
+ The altitude of the sun was thus determined, and,
+by help of solar tables, the latitude could be found
+from observations made at apparent noon.</p>
+
+<p><a name="fn10_2">[2]</a> See illustration on p. 76.</p>
+
+<p><a name="fn10_3">[3]</a> See Dreyer&#8217;s article on these instruments
+in <i>Copernicus</i>, Vol. I. They were stolen
+by the Germans after the relief of the Embassies,
+in 1900. The best description of these instruments
+is probably that contained in an interesting volume,
+which may be seen in the library of the R. A. S.,
+entitled <i>Chinese Researches</i>, by Alexander Wyllie
+(Shanghai, 1897).</p>
+
+<p><a name="fn10_4">[4]</a> Sir George Airy was very jealous of this honourable
+title. He rightly held that there is only one
+Astronomer Royal at a time, as there is only one Mikado,
+one Dalai Lama. He said that His Majesty&#8217;s
+Astronomer at the Cape of Good Hope, His Majesty&#8217;s
+Astronomer for Scotland, and His Majesty&#8217;s Astronomer
+for Ireland are not called Astronomers Royal.</p>
+
+<p><a name="fn10_5">[5]</a> <i>Annals of the Cape Observatory</i>, vol. x.,
+part 3.</p>
+
+<p><a name="fn10_6">[6]</a> The parallax of the sun is the angle subtended
+by the earth&#8217;s radius at the sun&#8217;s distance.</p>
+
+<p><a name="fn10_7">[7]</a> A. R. Hinks, R.A.S.; <i>Monthly Notices</i>, June,
+1909.</p>
+
+<p><br /><br /></p>
+
+<a name="11"></a>
+<h2>11. HISTORY OF THE TELESCOPE</h2>
+
+<p>Accounts of wonderful optical experiments by Roger
+Bacon (who died in 1292), and in the sixteenth century
+by Digges, Baptista Porta, and Antonio de Dominis
+(Grant, <i>Hist. Ph. Ast</i>.), have led
+some to suppose that they invented the telescope.
+The writer considers that it is more likely that these
+notes refer to a kind of <i>camera obscura</i>, in
+which a lens throws an inverted image of a landscape
+on the wall.</p>
+
+<p>The first telescopes were made in Holland, the originator
+being either Henry Lipperhey,<a href="#fn11_1">[1]</a> Zacharias Jansen,
+or James Metius, and the date 1608 or earlier.</p>
+
+<p>In 1609 Galileo, being in Venice, heard of the invention,
+went home and worked out the theory, and made a similar
+telescope. These telescopes were all made with
+a convex object-glass and a concave eye-lens, and
+this type is spoken of as the Galilean telescope.
+Its defects are that it has no real focus where cross-wires
+can be placed, and that the field of view is very
+small.  Kepler suggested the convex eye-lens
+in 1611, and Scheiner claimed to have used one in 1617.
+But it was Huyghens who really introduced them.
+In the seventeenth century telescopes were made of
+great length, going up to 300 feet. Huyghens
+also invented the compound eye-piece that bears his
+name, made of two convex lenses to diminish spherical
+aberration.</p>
+
+<p>But the defects of colour remained, although their
+cause was unknown until Newton carried out his experiments
+on dispersion and the solar spectrum. To overcome
+the spherical aberration James Gregory,<a href="#fn11_2">[2]</a> of Aberdeen
+and Edinburgh, in 1663, in his <i>Optica Promota</i>,
+proposed a reflecting speculum of parabolic form.
+But it was Newton, about 1666, who first made a reflecting
+telescope; and he did it with the object of avoiding
+colour dispersion.</p>
+
+<p>Some time elapsed before reflectors were much used.
+ Pound and Bradley used one presented to the Royal
+Society by Hadley in 1723. Hawksbee, Bradley,
+and Molyneaux made some. But James Short, of Edinburgh,
+made many excellent Gregorian reflectors from 1732
+till his death in 1768.</p>
+
+<p>Newton&#8217;s trouble with refractors, chromatic
+aberration, remained insurmountable until John Dollond
+(born 1706, died 1761), after many experiments, found
+out how to make an achromatic lens out of two lenses&#8212;one
+of crown glass, the other of flint glass&#8212;to
+destroy the colour, in a way originally suggested
+by Euler. He soon acquired a great reputation
+for his telescopes of moderate size; but there was
+a difficulty in making flint-glass lenses of large
+size. The first actual inventor and constructor
+of an achromatic telescope was Chester Moor Hall,
+who was not in trade, and did not patent it.
+Towards the close of the eighteenth century a Swiss
+named Guinand at last succeeded in producing larger
+flint-glass discs free from striae. Frauenhofer,
+of Munich, took him up in 1805, and soon produced,
+among others, Struve&#8217;s Dorpat refractor of 9.9
+inches diameter and 13.5 feet focal length, and another,
+of 12 inches diameter and 18 feet focal length, for
+Lamont, of Munich.</p>
+
+<p>In the nineteenth century gigantic <i>reflectors</i>
+have been made. Lassel&#8217;s 2-foot reflector,
+made by himself, did much good work, and discovered
+four new satellites.  But Lord Rosse&#8217;s 6-foot
+reflector, 54 feet focal length, constructed in 1845,
+is still the largest ever made.  The imperfections
+of our atmosphere are against the use of such large
+apertures, unless it be on high mountains. During
+the last half century excellent specula have been made
+of silvered glass, and Dr.  Common&#8217;s 5-foot
+speculum (removed, since his death, to Harvard) has
+done excellent work. Then there are the 5-foot
+Yerkes reflector at Chicago, and the 4-foot by Grubb
+at Melbourne.</p>
+
+<p>Passing now from these large reflectors to refractors,
+further improvements have been made in the manufacture
+of glass by Chance, of Birmingham, Feil and Mantois,
+of Paris, and Schott, of Jena; while specialists in
+grinding lenses, like Alvan Clark, of the U.S.A., and
+others, have produced many large refractors.</p>
+
+<p>Cooke, of York, made an object-glass, 25-inch diameter,
+for Newall, of Gateshead, which has done splendid
+work at Cambridge. We have the Washington 26-inch
+by Clark, the Vienna 27-inch by Grubb, the Nice 29&#189;-inch
+by Gautier, the Pulkowa 30-inch by Clark. Then
+there was the sensation of Clark&#8217;s 36-inch for
+the Lick Observatory in California, and finally his
+<i>tour de force</i>, the Yerkes 40-inch refractor,
+for Chicago.</p>
+
+<p>At Greenwich there is the 28-inch photographic refractor,
+and the Thompson equatoreal by Grubb, carrying both
+the 26-inch photographic refractor and the 30-inch
+reflector. At the Cape of Good Hope we find Mr.
+Frank McClean&#8217;s 24-inch refractor, with an object-glass
+prism for spectroscopic work.</p>
+
+<p>It would be out of place to describe here the practical
+adjuncts of a modern equatoreal&#8212;the adjustments
+for pointing it, the clock for driving it, the position-micrometer
+and various eye-pieces, the photographic and spectroscopic
+attachments, the revolving domes, observing seats,
+and rising floors and different forms of mounting,
+the siderostats and coelostats, and other convenient
+adjuncts, besides the registering chronograph and
+numerous facilities for aiding observation.
+On each of these a chapter might be written; but the
+most important part of the whole outfit is the man
+behind the telescope, and it is with him that a history
+is more especially concerned.</p>
+
+<p><b>SPECTROSCOPE.</b></p>
+
+<p>Since the invention of the telescope no discovery
+has given so great an impetus to astronomical physics
+as the spectroscope; and in giving us information
+about the systems of stars and their proper motions
+it rivals the telescope.</p>
+
+<p>Frauenhofer, at the beginning of the nineteenth century,
+while applying Dollond&#8217;s discovery to make large
+achromatic telescopes, studied the dispersion of light
+by a prism. Admitting the light of the sun through
+a narrow slit in a window-shutter, an inverted image
+of the slit can be thrown, by a lens of suitable focal
+length, on the wall opposite. If a wedge or prism
+of glass be interposed, the image is deflected to
+one side; but, as Newton had shown, the images formed
+by the different colours of which white light is composed
+are deflected to different extents&#8212;the
+violet most, the red least. The number of colours
+forming images is so numerous as to form a continuous
+spectrum on the wall with all the colours&#8212;red,
+orange, yellow, green, blue, indigo, and violet.
+But Frauenhofer found with a narrow slit, well focussed
+by the lens, that some colours were missing in the
+white light of the sun, and these were shown by dark
+lines across the spectrum.  These are the Frauenhofer
+lines, some of which he named by the letters of the
+alphabet. The D line is a very marked one in
+the yellow. These dark lines in the solar spectrum
+had already been observed by Wollaston. <a href="#fn11_3">[3]</a></p>
+
+<p>On examining artificial lights it was found that incandescent
+solids and liquids (including the carbon glowing in
+a white gas flame) give continuous spectra; gases,
+except under enormous pressure, give bright lines.
+If sodium or common salt be thrown on the colourless
+flame of a spirit lamp, it gives it a yellow colour,
+and its spectrum is a bright yellow line agreeing
+in position with line D of the solar spectrum.</p>
+
+<p>In 1832 Sir David Brewster found some of the solar
+black lines increased in strength towards sunset,
+and attributed them to absorption in the earth&#8217;s
+atmosphere.  He suggested that the others were
+due to absorption in the sun&#8217;s atmosphere.
+Thereupon Professor J. D.  Forbes pointed out that
+during a nearly total eclipse the lines ought to be
+strengthened in the same way; as that part of the sun&#8217;s
+light, coming from its edge, passes through a great
+distance in the sun&#8217;s atmosphere.  He tried
+this with the annular eclipse of 1836, with a negative
+result which has never been accounted for, and which
+seemed to condemn Brewster&#8217;s view.</p>
+
+<p>In 1859 Kirchoff, on repeating Frauenhofer&#8217;s
+experiment, found that, if a spirit lamp with salt
+in the flame were placed in the path of the light,
+the black D line is intensified. He also found
+that, if he used a limelight instead of the sunlight
+and passed it through the flame with salt, the spectrum
+showed the D line black; or the vapour of sodium absorbs
+the same light that it radiates. This proved to
+him the existence of sodium in the sun&#8217;s atmosphere.<a href="#fn11_4">[4]</a>
+Iron, calcium, and other elements were soon detected
+in the same way.</p>
+
+<p>Extensive laboratory researches (still incomplete)
+have been carried out to catalogue (according to their
+wave-length on the undulatory theory of light) all
+the lines of each chemical element, under all conditions
+of temperature and pressure. At the same time,
+all the lines have been catalogued in the light of
+the sun and the brighter of the stars.</p>
+
+<p>Another method of obtaining spectra had long been
+known, by transmission through, or reflection from,
+a grating of equidistant lines ruled upon glass or
+metal.  H. A. Rowland developed the art of constructing
+these gratings, which requires great technical skill,
+and for this astronomers owe him a debt of gratitude.</p>
+
+<p>In 1842 Doppler<a href="#fn11_5">[5]</a> proved that the colour of a luminous
+body, like the pitch or note of a sounding body, must
+be changed by velocity of approach or recession.
+Everyone has noticed on a railway that, on meeting
+a locomotive whistling, the note is lowered after the
+engine has passed. The pitch of a sound or the
+colour of a light depends on the number of waves striking
+the ear or eye in a second. This number is increased
+by approach and lowered by recession.</p>
+
+<p>Thus, by comparing the spectrum of a star alongside
+a spectrum of hydrogen, we may see all the lines,
+and be sure that there is hydrogen in the star; yet
+the lines in the star-spectrum may be all slightly
+displaced to one side of the lines of the comparison
+spectrum. If towards the violet end, it means
+mutual approach of the star and earth; if to the red
+end, it means recession. The displacement of
+lines does not tell us whether the motion is in the
+star, the earth, or both.  The displacement of
+the lines being measured, we can calculate the rate
+of approach or recession in miles per second.</p>
+
+<p>In 1868 Huggins<a href="#fn11_6">[6]</a> succeeded in thus measuring the
+velocities of stars in the direction of the line of
+sight.</p>
+
+<p>In 1873 Vogel<a href="#fn11_7">[7]</a> compared the spectra of the sun&#8217;s
+East (approaching) limb and West (receding) limb,
+and the displacement of lines endorsed the theory.
+This last observation was suggested by Z&#246;llner.</p>
+
+<p><br /><br /></p>
+
+<p><b>FOOTNOTES:</b></p>
+
+<p><a name="fn11_1">[1]</a> In the <i>Encyclopaedia Britannica</i>, article
+&#8220;Telescope,&#8221; and in Grant&#8217;s <i>Physical
+Astronomy</i>, good reasons are given for awarding
+the honour to Lipperhey.</p>
+
+<p><a name="fn11_2">[2]</a> Will the indulgent reader excuse an anecdote which
+may encourage some workers who may have found their
+mathematics defective through want of use? James
+Gregory&#8217;s nephew David had a heap of MS. notes
+by Newton. These descended to a Miss Gregory,
+of Edinburgh, who handed them to the present writer,
+when an undergraduate at Cambridge, to examine.
+After perusal, he lent them to his kindest of friends,
+J. C. Adams (the discoverer of Neptune), for his opinion.
+Adams&#8217;s final verdict was: &#8220;I fear
+they are of no value. It is pretty evident that,
+when he wrote these notes, <i>Newton&#8217;s mathematics
+were a little rusty</i>.&#8221;</p>
+
+<p><a name="fn11_3">[3]</a> <i>R. S. Phil. Trans</i>.</p>
+
+<p><a name="fn11_4">[4]</a> The experiment had been made before by one who
+did not understand its meaning;. But Sir George
+G. Stokes had already given verbally the true explanation
+of Frauenhofer lines.</p>
+
+<p><a name="fn11_5">[5]</a> <i>Abh. d. K&#246;n. B&#246;hm. d. Wiss</i>.,
+Bd. ii., 1841-42, p. 467. See also Fizeau in
+the <i>Ann. de Chem. et de Phys</i>., 1870, p. 211.</p>
+
+<p><a name="fn11_6">[6]</a> <i>R. S. Phil. Trans</i>., 1868.</p>
+
+<p><a name="fn11_7">[7]</a> <i>Ast. Nach</i>., No. 1, 864.</p>
+
+<p><br /><br /></p>
+
+<h1>BOOK IV. THE PHYSICAL PERIOD</h1>
+
+<p>We have seen how the theory of the solar system was
+slowly developed by the constant efforts of the human
+mind to find out what are the rules of cause and effect
+by which our conception of the present universe and
+its development seems to be bound. In the primitive
+ages a mere record of events in the heavens and on
+the earth gave the only hope of detecting those uniform
+sequences from which to derive rules or laws of cause
+and effect upon which to rely. Then came the
+geometrical age, in which rules were sought by which
+to predict the movements of heavenly bodies.
+Later, when the relation of the sun to the courses
+of the planets was established, the sun came to be
+looked upon as a cause; and finally, early in the
+seventeenth century, for the first time in history,
+it began to be recognised that the laws of dynamics,
+exactly as they had been established for our own terrestrial
+world, hold good, with the same rigid invariability,
+at least as far as the limits of the solar system.</p>
+
+<p>Throughout this evolution of thought and conjecture
+there were two types of astronomers&#8212;those
+who supplied the facts, and those who supplied the
+interpretation through the logic of mathematics.
+So Ptolemy was dependent upon Hipparchus, Kepler on
+Tycho Brahe, and Newton in much of his work upon Flamsteed.</p>
+
+<p>When Galileo directed his telescope to the heavens,
+when Secchi and Huggins studied the chemistry of the
+stars by means of the spectroscope, and when Warren
+De la Rue set up a photoheliograph at Kew, we see
+that a progress in the same direction as before, in
+the evolution of our conception of the universe, was
+being made. Without definite expression at any
+particular date, it came to be an accepted fact that
+not only do earthly dynamics apply to the heavenly
+bodies, but that the laws we find established here,
+in geology, in chemistry, and in the laws of heat,
+may be extended with confidence to the heavenly bodies.
+Hence arose the branch of astronomy called astronomical
+physics, a science which claims a large portion of
+the work of the telescope, spectroscope, and photography.
+In this new development it is more than ever essential
+to follow the dictum of Tycho Brahe&#8212;not
+to make theories until all the necessary facts are
+obtained. The great astronomers of to-day still
+hold to Sir Isaac Newton&#8217;s declaration, &#8220;Hypotheses
+non fingo.&#8221; Each one may have his suspicions
+of a theory to guide him in a course of observation,
+and may call it a working hypothesis.  But the
+cautious astronomer does not proclaim these to the
+world; and the historian is certainly not justified
+in including in his record those vague speculations
+founded on incomplete data which may be demolished
+to-morrow, and which, however attractive they may
+be, often do more harm than good to the progress of
+true science.  Meanwhile the accumulation of facts
+has been prodigious, and the revelations of the telescope
+and spectroscope entrancing.</p>
+
+<p><br /><br /></p>
+
+<a name="12"></a>
+<h2>12. THE SUN.</h2>
+
+<p>One of Galileo&#8217;s most striking discoveries,
+when he pointed his telescope to the heavenly bodies,
+was that of the irregularly shaped spots on the sun,
+with the dark central <i>umbra</i> and the less dark,
+but more extensive, <i>penumbra</i> surrounding it,
+sometimes with several umbrae in one penumbra.
+He has left us many drawings of these spots, and he
+fixed their period of rotation as a lunar month.</p>
+
+<p align="center"><img src="009.jpg" alt="[Illustration: SOLAR SURFACE, As Photographed
+at the Royal Observatory, Greenwich, showing sun-spots
+with umbrae, penumbrae, and faculae.]" /></p>
+
+<p>It is not certain whether Galileo, Fabricius, or Schemer
+was the first to see the spots. They all did
+good work. The spots were found to be ever varying
+in size and shape. Sometimes, when a spot disappears
+at the western limb of the sun, it is never seen again.
+ In other cases, after a fortnight, it reappears at
+the eastern limb. The faculae, or bright areas,
+which are seen all over the sun&#8217;s surface, but
+specially in the neighbourhood of spots, and most
+distinctly near the sun&#8217;s edge, were discovered
+by Galileo. A high telescopic power resolves
+their structure into an appearance like willow-leaves,
+or rice-grains, fairly uniform in size, and more marked
+than on other parts of the sun&#8217;s surface.</p>
+
+<p>Speculations as to the cause of sun-spots have never
+ceased from Galileo&#8217;s time to ours. He
+supposed them to be clouds. Scheiner<a href="#fn12_1">[1]</a> said
+they were the indications of tumultuous movements occasionally
+agitating the ocean of liquid fire of which he supposed
+the sun to be composed.</p>
+
+<p>A. Wilson, of Glasgow, in 1769,<a href="#fn12_2">[2]</a> noticed a movement
+of the umbra relative to the penumbra in the transit
+of the spot over the sun&#8217;s surface; exactly
+as if the spot were a hollow, with a black base and
+grey shelving sides. This was generally accepted,
+but later investigations have contradicted its universality.
+Regarding the cause of these hollows, Wilson said:&#8212;</p>
+
+<blockquote>Whether their first production and subsequent
+numberless changes depend upon the eructation of
+elastic vapours from below, or upon eddies or whirlpools
+commencing at the surface, or upon the dissolving
+of the luminous matter in the solar atmosphere, as
+clouds are melted and again given out by our air;
+or, if the reader pleases, upon the annihilation
+and reproduction of parts of this resplendent covering,
+is left for theory to guess at.<a href="#fn12_3">[3]</a></blockquote>
+
+<p>Ever since that date theory has been guessing at it.
+ The solar astronomer is still applying all the instruments
+of modern research to find out which of these suppositions,
+or what modification of any of them, is nearest the
+truth. The obstacle&#8212;one that is perhaps
+fatal to a real theory&#8212;lies in the impossibility
+of reproducing comparative experiments in our laboratories
+or in our atmosphere.</p>
+
+<p>Sir William Herschel propounded an explanation of
+Wilson&#8217;s observation which received much notice,
+but which, out of respect for his memory, is not now
+described, as it violated the elementary laws of heat.</p>
+
+<p>Sir John Herschel noticed that the spots are mostly
+confined to two zones extending to about 35&#176; on each
+side of the equator, and that a zone of equatoreal
+calms is free from spots. But it was R. C. Carrington<a href="#fn12_4">[4]</a>
+who, by his continuous observations at Redhill, in
+Surrey, established the remarkable fact that, while
+the rotation period in the highest latitudes, 50&#176;,
+where spots are seen, is twenty-seven-and-a-half days,
+near the equator the period is only twenty-five days.
+His splendid volume of observations of the sun led
+to much new information about the average distribution
+of spots at different epochs.</p>
+
+<p>Schwabe, of Dessau, began in 1826 to study the solar
+surface, and, after many years of work, arrived at
+a law of frequency which has been more fruitful of
+results than any discovery in solar physics.<a href="#fn12_5">[5]</a> In
+1843 he announced a decennial period of maxima and
+minima of sun-spot displays. In 1851 it was generally
+accepted, and, although a period of eleven years has
+been found to be more exact, all later observations,
+besides the earlier ones which have been hunted up
+for the purpose, go to establish a true periodicity
+in the number of sun-spots. But quite lately
+Schuster<a href="#fn12_6">[6]</a> has given reasons for admitting a number
+of co-existent periods, of which the eleven-year period
+was predominant in the nineteenth century.</p>
+
+<p>In 1851 Lament, a Scotchman at Munich, found a decennial
+period in the daily range of magnetic declination.
+ In 1852 Sir Edward Sabine announced a similar period
+in the number of &#8220;magnetic storms&#8221; affecting
+all of the three magnetic elements&#8212;declination,
+dip, and intensity. Australian and Canadian observations
+both showed the decennial period in all three elements.
+Wolf, of Zurich, and Gauthier, of Geneva, each independently
+arrived at the same conclusion.</p>
+
+<p>It took many years before this coincidence was accepted
+as certainly more than an accident by the old-fashioned
+astronomers, who want rigid proof for every new theory.
+But the last doubts have long vanished, and a connection
+has been further traced between violent outbursts of
+solar activity and simultaneous magnetic storms.</p>
+
+<p>The frequency of the Aurora Borealis was found by
+Wolf to follow the same period. In fact, it is
+closely allied in its cause to terrestrial magnetism.
+Wolf also collected old observations tracing the periodicity
+of sun-spots back to about 1700 A.D.</p>
+
+<p>Spoerer deduced a law of dependence of the average
+latitude of sun-spots on the phase of the sun-spot
+period.</p>
+
+<p>All modern total solar eclipse observations seem to
+show that the shape of the luminous corona surrounding
+the moon at the moment of totality has a special distinct
+character during the time of a sun-spot maximum, and
+another, totally different, during a sun-spot minimum.</p>
+
+<p>A suspicion is entertained that the total quantity
+of heat received by the earth from the sun is subject
+to the same period. This would have far-reaching
+effects on storms, harvests, vintages, floods, and
+droughts; but it is not safe to draw conclusions of
+this kind except from a very long period of observations.</p>
+
+<p>Solar photography has deprived astronomers of the
+type of Carrington of the delight in devoting a life&#8217;s
+work to collecting data. It has now become part
+of the routine work of an observatory.</p>
+
+<p>In 1845 Foucault and Fizeau took a daguerreotype photograph
+of the sun. In 1850 Bond produced one of the
+moon of great beauty, Draper having made some attempts
+at an even earlier date. But astronomical photography
+really owes its beginning to De la Rue, who used the
+collodion process for the moon in 1853, and constructed
+the Kew photoheliograph in 1857, from which date these
+instruments have been multiplied, and have given us
+an accurate record of the sun&#8217;s surface.
+Gelatine dry plates were first used by Huggins in 1876.</p>
+
+<p>It is noteworthy that from the outset De la Rue recognised
+the value of stereoscopic vision, which is now known
+to be of supreme accuracy. In 1853 he combined
+pairs of photographs of the moon in the same phase,
+but under different conditions regarding libration,
+showing the moon from slightly different points of
+view.  These in the stereoscope exhibited all
+the relief resulting from binocular vision, and looked
+like a solid globe.  In 1860 he used successive
+photographs of the total solar eclipse stereoscopically,
+to prove that the red prominences belong to the sun,
+and not to the moon.  In 1861 he similarly combined
+two photographs of a sun-spot, the perspective effect
+showing the umbra like a floor at the bottom of a hollow
+penumbra; and in one case the facul&#230; were discovered
+to be sailing over a spot apparently at some considerable
+height.  These appearances may be partly due
+to a proper motion; but, so far as it went, this was
+a beautiful confirmation of Wilson&#8217;s discovery.
+Hewlett, however, in 1894, after thirty years of work,
+showed that the spots are not always depressions,
+being very subject to disturbance.</p>
+
+<p>The Kew photographs <a href="#fn12_7">[7]</a> contributed a vast amount
+of information about sun-spots, and they showed that
+the facul&#230; generally follow the spots in their rotation
+round the sun.</p>
+
+<p>The constitution of the sun&#8217;s photosphere, the
+layer which is the principal light-source on the sun,
+has always been a subject of great interest; and much
+was done by men with exceptionally keen eyesight,
+like Mr. Dawes. But it was a difficult subject,
+owing to the rapidity of the changes in appearance
+of the so-called rice-grains, about 1&#8221; in diameter.
+The rapid transformations and circulations of these
+rice-grains, if thoroughly studied, might lead to a
+much better knowledge of solar physics. This
+seemed almost hopeless, as it was found impossible
+to identify any &#8220;rice-grain&#8221; in the turmoil
+after a few minutes. But M.  Hansky, of Pulkowa
+(whose recent death is deplored), introduced successfully
+a scheme of photography, which might almost be called
+a solar cinematograph. He took photographs of
+the sun at intervals of fifteen or thirty seconds,
+and then enlarged selected portions of these two hundred
+times, giving a picture corresponding to a solar disc
+of six metres diameter. In these enlarged pictures
+he was able to trace the movements, and changes of
+shape and brightness, of individual rice-grains.
+Some granules become larger or smaller. Some
+seem to rise out of a mist, as it were, and to become
+clearer.  Others grow feebler. Some are split
+in two. Some are rotated through a right angle
+in a minute or less, although each of the grains may
+be the size of Great Britain. Generally they move
+together in groups of very various velocities, up to
+forty kilometres a second.  These movements seem
+to have definite relation to any sun-spots in the
+neighbourhood. From the results already obtained
+it seems certain that, if this method of observation
+be continued, it cannot fail to supply facts of the
+greatest importance.</p>
+
+<p>It is quite impossible to do justice here to the work
+of all those who are engaged on astronomical physics.
+ The utmost that can be attempted is to give a fair
+idea of the directions of human thought and endeavour.
+ During the last half-century America has made splendid
+progress, and an entirely new process of studying the
+photosphere has been independently perfected by Professor
+Hale at Chicago, and Deslandres at Paris.<a href="#fn12_8">[8]</a> They
+have succeeded in photographing the sun&#8217;s surface
+in monochromatic light, such as the light given off
+as one of the bright lines of hydrogen or of calcium,
+by means of the &#8220;Spectroheliograph.&#8221;
+The spectroscope is placed with its slit in the focus
+of an equatoreal telescope, pointed to the sun, so
+that the circular image of the sun falls on the slit.
+At the other end of the spectroscope is the photographic
+plate. Just in front of this plate there is another
+slit parallel to the first, in the position where the
+image of the first slit formed by the K line of calcium
+falls. Thus is obtained a photograph of the section
+of the sun, made by the first slit, only in K light.
+As the image of the sun passes over the first slit
+the photographic plate is moved at the same rate and
+in the same direction behind the second slit; and
+as successive sections of the sun&#8217;s image in
+the equatoreal enter the apparatus, so are these sections
+successively thrown in their proper place on the photographic
+plate, always in K light. By using a high dispersion
+the facul&#230; which give off K light can be correctly
+photographed, not only at the sun&#8217;s edge, but
+all over his surface. The actual mechanical method
+of carrying out the observation is not quite so simple
+as what is here described.</p>
+
+<p>By choosing another line of the spectrum instead of
+calcium K&#8212;for example, the hydrogen line
+H<sub>(3)</sub>&#8212;we obtain two photographs, one showing
+the appearance of the calcium floculi, and the other
+of the hydrogen floculi, on the same part of the solar
+surface; and nothing is more astonishing than to note
+the total want of resemblance in the forms shown on
+the two. This mode of research promises to afford
+many new and useful data.</p>
+
+<p>The spectroscope has revealed the fact that, broadly
+speaking, the sun is composed of the same materials
+as the earth. &#197;ngstrom was the first to map out all
+of the lines to be found in the solar spectrum.
+But Rowland, of Baltimore, after having perfected
+the art of making true gratings with equidistant lines
+ruled on metal for producing spectra, then proceeded
+to make a map of the solar spectrum on a large scale.</p>
+
+<p>In 1866 Lockyer<a href="#fn12_9">[9]</a> threw an image of the sun upon
+the slit of a spectroscope, and was thus enabled to
+compare the spectrum of a spot with that of the general
+solar surface. The observation proved the darkness
+of a spot to be caused by increased absorption of light,
+not only in the dark lines, which are widened, but
+over the entire spectrum. In 1883 Young resolved
+this continuous obscurity into an infinite number
+of fine lines, which have all been traced in a shadowy
+way on to the general solar surface. Lockyer also
+detected displacements of the spectrum lines in the
+spots, such as would be produced by a rapid motion
+in the line of sight. It has been found that
+both uprushes and downrushes occur, but there is no
+marked predominance of either in a sun-spot.
+The velocity of motion thus indicated in the line
+of sight sometimes appears to amount to 320 miles
+a second. But it must be remembered that pressure
+of a gas has some effect in displacing the spectral
+lines.  So we must go on, collecting data, until
+a time comes when the meaning of all the facts can
+be made clear.</p>
+
+<p><i>Total Solar Eclipses</i>.&#8212;During total
+solar eclipses the time is so short, and the circumstances
+so impressive, that drawings of the appearance could
+not always be trusted. The red prominences of
+jagged form that are seen round the moon&#8217;s edge,
+and the corona with its streamers radiating or interlacing,
+have much detail that can hardly be recorded in a
+sketch. By the aid of photography a number of
+records can be taken during the progress of totality.
+From a study of these the extent of the corona is
+demonstrated in one case to extend to at least six
+diameters of the moon, though the eye has traced it
+farther. This corona is still one of the wonders
+of astronomy, and leads to many questions. What
+is its consistency, if it extends many million miles
+from the sun&#8217;s surface? How is it that it
+opposed no resistance to the motion of comets which
+have almost grazed the sun&#8217;s surface? Is
+this the origin of the zodiacal light?  The character
+of the corona in photographic records has been shown
+to depend upon the phase of the sun-spot period.
+During the sun-spot maximum the corona seems most
+developed over the spot-zones&#8212;i.e., neither
+at the equator nor the poles. The four great
+sheaves of light give it a square appearance, and
+are made up of rays or plumes, delicate like the petals
+of a flower.  During a minimum the nebulous ring
+seems to be made of tufts of fine hairs with aigrettes
+or radiations from both poles, and streamers from
+the equator.</p>
+
+<p align="center"><img src="010.jpg" alt="[Illustration: SOLAR ECLIPSE, 1882.  From
+drawing by W. H. Wesley, Secretary R.A.S.; showing
+the prominences, the corona, and an unknown comet.]" /></p>
+
+<p>On September 19th, 1868, eclipse spectroscopy began
+with the Indian eclipse, in which all observers found
+that the red prominences showed a bright line spectrum,
+indicating the presence of hydrogen and other gases.
+ So bright was it that Jansen exclaimed: &#8220;<i>Je
+verrai ces lignes-l&#224; en dehors des &#233;clipses</i>.&#8221;
+And the next day he observed the lines at the edge
+of the uneclipsed sun.  Huggins had suggested
+this observation in February, 1868, his idea being
+to use prisms of such great dispersive power that
+the continuous spectrum reflected by our atmosphere
+should be greatly weakened, while a bright line would
+suffer no diminution by the high dispersion.
+On October 20th Lockyer,<a href="#fn12_10">[10]</a> having news of the eclipse,
+but not of Jansen&#8217;s observations the day after,
+was able to see these lines. This was a splendid
+performance, for it enabled the prominences to be observed,
+not only during eclipses, but every day. Moreover,
+the next year Huggins was able, by using a wide slit,
+to see the whole of a prominence and note its shape.
+ Prominences are classified, according to their form,
+into &#8220;flame&#8221; and &#8220;cloud&#8221; prominences,
+the spectrum of the latter showing calcium, hydrogen,
+and helium; that of the former including a number
+of metals.</p>
+
+<p>The D line of sodium is a double line, and in the
+same eclipse (1868) an orange line was noticed which
+was afterwards found to lie close to the two components
+of the D line. It did not correspond with any
+known terrestrial element, and the unknown element
+was called &#8220;helium.&#8221; It was not until
+1895 that Sir William Ramsay found this element as
+a gas in the mineral cleavite.</p>
+
+<p>The spectrum of the corona is partly continuous, indicating
+light reflected from the sun&#8217;s body. But
+it also shows a green line corresponding with no known
+terrestrial element, and the name &#8220;coronium&#8221;
+has been given to the substance causing it.</p>
+
+<p>A vast number of facts have been added to our knowledge
+about the sun by photography and the spectroscope.
+Speculations and hypotheses in plenty have been offered,
+but it may be long before we have a complete theory
+evolved to explain all the phenomena of the storm-swept
+metallic atmosphere of the sun.</p>
+
+<p>The proceedings of scientific societies teem with
+such facts and &#8220;working hypotheses,&#8221; and
+the best of them have been collected by Miss Clerke
+in her <i>History of Astronomy during the Nineteenth
+Century</i>. As to established facts, we learn
+from the spectroscopic researches (1) that the continuous
+spectrum is derived from the <i>photosphere</i> or
+solar gaseous material compressed almost to liquid
+consistency; (2) that the <i>reversing layer</i> surrounds
+it and gives rise to black lines in the spectrum;
+that the <i>chromosphere</i> surrounds this, is composed
+mainly of hydrogen, and is the cause of the red prominences
+in eclipses; and that the gaseous <i>corona</i> surrounds
+all of these, and extends to vast distances outside
+the sun&#8217;s visible surface.</p>
+
+<p><br /><br /></p>
+
+<p><b>FOOTNOTES:</b></p>
+
+<p><a name="fn12_1">[1]</a> <i>Rosa Ursina</i>, by C. Scheiner, <i>fol</i>.;
+Bracciani, 1630.</p>
+
+<p><a name="fn12_2">[2]</a> <i>R. S. Phil. Trans</i>., 1774.</p>
+
+<p><a name="fn12_3">[3]</a> <i>Ibid</i>, 1783.</p>
+
+<p><a name="fn12_4">[4]</a> <i>Observations on the Spots on the Sun, etc.,</i>
+4&#176;; London and Edinburgh, 1863.</p>
+
+<p><a name="fn12_5">[5]</a> <i>Periodicit&#228;t der Sonnenflecken. Astron.
+Nach. XXI.</i>, 1844, P. 234.</p>
+
+<p><a name="fn12_6">[6]</a> <i>R.S. Phil. Trans.</i> (ser.
+A), 1906, p. 69-100.</p>
+
+<p><a name="fn12_7">[7]</a> &#8220;Researches on Solar Physics,&#8221; by
+De la Rue, Stewart and Loewy; <i>R. S. Phil.
+Trans</i>., 1869, 1870.</p>
+
+<p><a name="fn12_8">[8]</a> &#8220;The Sun as Photographed on the K line&#8221;;
+<i>Knowledge</i>, London, 1903, p. 229.</p>
+
+<p><a name="fn12_9">[9]</a> <i>R. S. Proc.</i>, xv., 1867, p. 256.</p>
+
+<p><a name="fn12_10">[10]</a> <i>Acad. des Sc.</i>, Paris; <i>C. R.</i>,
+lxvii., 1868, p. 121.</p>
+
+<p><br /><br /></p>
+
+<a name="13"></a>
+<h2>13. THE MOON AND PLANETS.</h2>
+
+<p><i>The Moon</i>.&#8212;Telescopic discoveries
+about the moon commence with Galileo&#8217;s discovery
+that her surface has mountains and valleys, like the
+earth. He also found that, while she always turns
+the same face to us, there is periodically a slight
+twist to let us see a little round the eastern or
+western edge. This was called <i>libration</i>,
+and the explanation was clear when it was understood
+that in showing always the same face to us she makes
+one revolution a month on her axis <i>uniformly</i>,
+and that her revolution round the earth is not uniform.</p>
+
+<p>Galileo said that the mountains on the moon showed
+greater differences of level than those on the earth.
+ Shr&#246;ter supported this opinion. W. Herschel
+opposed it. But Beer and M&#228;dler measured the
+heights of lunar mountains by their shadows, and found
+four of them over 20,000 feet above the surrounding
+plains.</p>
+
+<p>Langrenus <a href="#fn13_1">[1]</a> was the first to do serious work on
+selenography, and named the lunar features after eminent
+men. Riccioli also made lunar charts. In
+1692 Cassini made a chart of the full moon. Since
+then we have the charts of Schr&#246;ter, Beer and M&#228;dler
+(1837), and of Schmidt, of Athens (1878); and, above
+all, the photographic atlas by Loewy and Puiseux.</p>
+
+<p>The details of the moon&#8217;s surface require for
+their discussion a whole book, like that of Neison
+or the one by Nasmyth and Carpenter. Here a few
+words must suffice. Mountain ranges like our Andes
+or Himalayas are rare. Instead of that, we see
+an immense number of circular cavities, with rugged
+edges and flat interior, often with a cone in the
+centre, reminding one of instantaneous photographs
+of the splash of a drop of water falling into a pool.
+Many of these are fifty or sixty miles across, some
+more. They are generally spoken of as resembling
+craters of volcanoes, active or extinct, on the earth.
+But some of those who have most fully studied the
+shapes of craters deny altogether their resemblance
+to the circular objects on the moon. These so-called
+craters, in many parts, are seen to be closely grouped,
+especially in the snow-white parts of the moon.
+But there are great smooth dark spaces, like the clear
+black ice on a pond, more free from craters, to which
+the equally inappropriate name of seas has been given.
+The most conspicuous crater, <i>Tycho</i>, is near
+the south pole. At full moon there are seen to
+radiate from Tycho numerous streaks of light, or &#8220;rays,&#8221;
+cutting through all the mountain formations, and extending
+over fully half the lunar disc, like the star-shaped
+cracks made on a sheet of ice by a blow.  Similar
+cracks radiate from other large craters. It must
+be mentioned that these white rays are well seen only
+in full light of the sun at full moon, just as the
+white snow in the crevasses of a glacier is seen bright
+from a distance only when the sun is high, and disappears
+at sunset. Then there are deep, narrow, crooked
+&#8220;rills&#8221; which may have been water-courses;
+also &#8220;clefts&#8221; about half a mile wide, and
+often hundreds of miles long, like deep cracks in
+the surface going straight through mountain and valley.</p>
+
+<p>The moon shares with the sun the advantage of being
+a good subject for photography, though the planets
+are not. This is owing to her larger apparent
+size, and the abundance of illumination. The consequence
+is that the finest details of the moon, as seen in
+the largest telescope in the world, may be reproduced
+at a cost within the reach of all.</p>
+
+<p>No certain changes have ever been observed; but several
+suspicions have been expressed, especially as to the
+small crater <i>Linn&#233;</i>, in the <i>Mare Serenitatis</i>.
+It is now generally agreed that no certainty can be
+expected from drawings, and that for real evidence
+we must await the verdict of photography.</p>
+
+<p>No trace of water or of an atmosphere has been found
+on the moon. It is possible that the temperature
+is too low. In any case, no displacement of a
+star by atmospheric refraction at occultation has
+been surely recorded. The moon seems to be dead.</p>
+
+<p>The distance of the moon from the earth is just now
+the subject of re-measurement. The base line
+is from Greenwich to Cape of Good Hope, and the new
+feature introduced is the selection of a definite point
+on a crater (M&#246;sting A), instead of the moon&#8217;s
+edge, as the point whose distance is to be measured.</p>
+
+<p><i>The Inferior Planets</i>.&#8212;When the telescope
+was invented, the phases of Venus attracted much attention;
+but the brightness of this planet, and her proximity
+to the sun, as with Mercury also, seemed to be a bar
+to the discovery of markings by which the axis and
+period of rotation could be fixed. Cassini gave
+the rotation as twenty-three hours, by observing a
+bright spot on her surface. Shr&#246;ter made it 23h.
+21m. 19s. This value was supported by others.
+In 1890 Schiaparelli<a href="#fn13_2">[2]</a> announced that Venus rotates,
+like our moon, once in one of her revolutions, and
+always directs the same face to the sun. This
+property has also been ascribed to Mercury; but in
+neither case has the evidence been generally accepted.
+Twenty-four hours is probably about the period of
+rotation for each of these planets.</p>
+
+<p>Several observers have claimed to have seen a planet
+within the orbit of Mercury, either in transit over
+the sun&#8217;s surface or during an eclipse.
+It has even been named <i>Vulcan</i>. These announcements
+would have received little attention but for the fact
+that the motion of Mercury has irregularities which
+have not been accounted for by known planets; and
+Le Verrier<a href="#fn13_3">[3]</a> has stated that an intra-Mercurial planet
+or ring of asteroids would account for the unexplained
+part of the motion of the line of apses of Mercury&#8217;s
+orbit amounting to 38&#8221; per century.</p>
+
+<p><i>Mars</i>.&#8212;The first study of the appearance
+of Mars by Miraldi led him to believe that there were
+changes proceeding in the two white caps which are
+seen at the planet&#8217;s poles. W. Herschel
+attributed these caps to ice and snow, and the dates
+of his observations indicated a melting of these ice-caps
+in the Martian summer.</p>
+
+<p>Schroter attributed the other markings on Mars to drifting
+clouds. But Beer and M&#228;dler, in 1830-39, identified
+the same dark spots as being always in the same place,
+though sometimes blurred by mist in the local winter.
+A spot sketched by Huyghens in 1672, one frequently
+seen by W. Herschel in 1783, another by Arago in 1813,
+and nearly all the markings recorded by Beer and M&#228;dler
+in 1830, were seen and drawn by F. Kaiser in Leyden
+during seventeen nights of the opposition of 1862
+(<i>Ast. Nacht.</i>, No. 1,468), whence he deduced
+the period of rotation to be 24h. 37m. 22s.,62&#8212;or
+one-tenth of a second less than the period deduced
+by R. A. Proctor from a drawing by Hooke in 1666.</p>
+
+<p>It must be noted that, if the periods of rotation
+both of Mercury and Venus be about twenty-four hours,
+as seems probable, all the four planets nearest to
+the sun rotate in the same period, while the great
+planets rotate in about ten hours (Uranus and Neptune
+being still indeterminate).</p>
+
+<p>The general surface of Mars is a deep yellow; but
+there are dark grey or greenish patches. Sir
+John Herschel was the first to attribute the ruddy
+colour of Mars to its soil rather than to its atmosphere.</p>
+
+<p>The observations of that keen-sighted observer Dawes
+led to the first good map of Mars, in 1869. In
+the 1877 opposition Schiaparelli revived interest
+in the planet by the discovery of canals, uniformly
+about sixty miles wide, running generally on great
+circles, some of them being three or four thousand
+miles long. During the opposition of 1881-2 the
+same observer re-observed the canals, and in twenty
+of them he found the canals duplicated,<a href="#fn13_4">[4]</a> the second
+canal being always 200 to 400 miles distant from its
+fellow.</p>
+
+<p>The existence of these canals has been doubted.
+ Mr. Lowell has now devoted years to the subject,
+has drawn them over and over again, and has photographed
+them; and accepts the explanation that they are artificial,
+and that vegetation grows on their banks.  Thus
+is revived the old controversy between Whewell and
+Brewster as to the habitability of the planets.
+The new arguments are not yet generally accepted.
+Lowell believes he has, with the spectroscope, proved
+the existence of water on Mars.</p>
+
+<p>One of the most unexpected and interesting of all
+telescopic discoveries took place in the opposition
+of 1877, when Mars was unusually near to the earth.
+The Washington Observatory had acquired the fine 26-inch
+refractor, and Asaph Hall searched for satellites,
+concealing the planet&#8217;s disc to avoid the glare.
+On August 11th he had a suspicion of a satellite.
+This was confirmed on the 16th, and on the following
+night a second one was added. They are exceedingly
+faint, and can be seen only by the most powerful telescopes,
+and only at the times of opposition. Their diameters
+are estimated at six or seven miles. It was soon
+found that the first, Deimos, completes its orbit
+in 30h. 18m.  But the other, Phobos, at first
+was a puzzle, owing to its incredible velocity being
+unsuspected. Later it was found that the period
+of revolution was only 7h. 39m. 22s. Since the
+Martian day is twenty-four and a half hours, this
+leads to remarkable results. Obviously the easterly
+motion of the satellite overwhelms the diurnal rotation
+of the planet, and Phobos must appear to the inhabitants,
+if they exist, to rise in the west and set in the
+east, showing two or even three full moons in a day,
+so that, sufficiently well for the ordinary purposes
+of life, the hour of the day can be told by its phases.</p>
+
+<p>The discovery of these two satellites is, perhaps,
+the most interesting telescopic visual discovery made
+with the large telescopes of the last half century;
+photography having been the means of discovering all
+the other new satellites except Jupiter&#8217;s fifth
+(in order of discovery).</p>
+
+<p align="center"><img src="011.jpg" alt="[Illustration: JUPITER.  From a drawing
+by E. M. Antoniadi, showing transit of a satellite&#8217;s
+shadow, the belts, and the &#8220;great red spot&#8221;
+(<i>Monthly Notices</i>, R. A. S., vol. lix., pl. x.).]" /></p>
+
+<p><i>Jupiter.</i>&#8212;Galileo&#8217;s discovery
+of Jupiter&#8217;s satellites was followed by the
+discovery of his belts. Zucchi and Torricelli
+seem to have seen them. Fontana, in 1633, reported
+three belts. In 1648 Grimaldi saw but two, and
+noticed that they lay parallel to the ecliptic.
+Dusky spots were also noticed as transient. Hooke<a href="#fn13_5">[5]</a>
+measured the motion of one in 1664. In 1665 Cassini,
+with a fine telescope, 35-feet focal length, observed
+many spots moving from east to west, whence he concluded
+that Jupiter rotates on an axis like the earth.
+He watched an unusually permanent spot during twenty-nine
+rotations, and fixed the period at 9h. 56m. Later
+he inferred that spots near the equator rotate quicker
+than those in higher latitudes (the same as Carrington
+found for the sun); and W. Herschel confirmed this
+in 1778-9.</p>
+
+<p>Jupiter&#8217;s rapid rotation ought, according to
+Newton&#8217;s theory, to be accompanied by a great
+flattening at the poles. Cassini had noted an
+oval form in 1691. This was confirmed by La Hire,
+R&#246;mer, and Picard. Pound measured the ellipticity
+= 1/(13.25).</p>
+
+<p>W. Herschel supposed the spots to be masses of cloud
+in the atmosphere&#8212;an opinion still accepted.
+ Many of them were very permanent. Cassini&#8217;s
+great spot vanished and reappeared nine times between
+1665 and 1713. It was close to the northern margin
+of the southern belt. Herschel supposed the belts
+to be the body of the planet, and the lighter parts
+to be clouds confined to certain latitudes.</p>
+
+<p>In 1665 Cassini observed transits of the four satellites,
+and also saw their shadows on the planet, and worked
+out a lunar theory for Jupiter. Mathematical
+astronomers have taken great interest in the perturbations
+of the satellites, because their relative periods
+introduce peculiar effects. Airy, in his delightful
+book, <i>Gravitation</i>, has reduced these investigations
+to simple geometrical explanations.</p>
+
+<p>In 1707 and 1713 Miraldi noticed that the fourth satellite
+varies much in brightness. W. Herschel found
+this variation to depend upon its position in its
+orbit, and concluded that in the positions of feebleness
+it is always presenting to us a portion of its surface,
+which does not well reflect the sun&#8217;s light;
+proving that it always turns the same face to Jupiter,
+as is the case with our moon. This fact had also
+been established for Saturn&#8217;s fifth satellite,
+and may be true for all satellites.</p>
+
+<p>In 1826 Struve measured the diameters of the four
+satellites, and found them to be 2,429, 2,180, 3,561,
+and 3,046 miles.</p>
+
+<p>In modern times much interest has been taken in watching
+a rival to Cassini&#8217;s famous spot. The &#8220;great
+red spot&#8221; was first observed by Niesten, Pritchett,
+and Tempel, in 1878, as a rosy cloud attached to a
+whitish zone beneath the dark southern equatorial band,
+shaped like the new war balloons, 30,000 miles long
+and 7,000 miles across. The next year it was
+brick-red. A white spot beside it completed a
+rotation in less time by 5&#189; minutes than the red spot&#8212;a
+difference of 260 miles an hour. Thus they came
+together again every six weeks, but the motions did
+not continue uniform.  The spot was feeble in
+1882-4, brightened in 1886, and, after many changes,
+is still visible.</p>
+
+<p>Galileo&#8217;s great discovery of Jupiter&#8217;s
+four moons was the last word in this connection until
+September 9th, 1892, when Barnard, using the 36-inch
+refractor of the Lick Observatory, detected a tiny
+spot of light closely following the planet. This
+proved to be a new satellite (fifth), nearer to the
+planet than any other, and revolving round it in 11h.
+57m. 23s. Between its rising and setting there
+must be an interval of 2&#189; Jovian days, and two or
+three full moons. The sixth and seventh satellites
+were found by the examination of photographic plates
+at the Lick Observatory in 1905, since which time they
+have been continuously photographed, and their orbits
+traced, at Greenwich. On examining these plates
+in 1908 Mr. Melotte detected the eighth satellite,
+which seems to be revolving in a retrograde orbit three
+times as far from its planet as the next one (seventh),
+in these two points agreeing with the outermost of
+Saturn&#8217;s satellites (Phoebe).</p>
+
+<p><i>Saturn.</i>&#8212;This planet, with its marvellous
+ring, was perhaps the most wonderful object of those
+first examined by Galileo&#8217;s telescope. He
+was followed by Dominique Cassini, who detected bands
+like Jupiter&#8217;s belts. Herschel established
+the rotation of the planet in 1775-94. From observations
+during one hundred rotations he found the period to
+be 10h. 16m. 0s., 44. Herschel also measured the
+ratio of the polar to the equatoreal diameter as 10:11.</p>
+
+<p>The ring was a complete puzzle to Galileo, most of
+all when the planet reached a position where the plane
+of the ring was in line with the earth, and the ring
+disappeared (December 4th, 1612). It was not until
+1656 that Huyghens, in his small pamphlet <i>De Saturni
+Luna Observatio Nova</i>, was able to suggest in a
+cypher the ring form; and in 1659, in his Systema
+Saturnium, he gave his reasons and translated the cypher:
+&#8220;The planet is surrounded by a slender flat ring,
+everywhere distinct from its surface, and inclined
+to the ecliptic.&#8221; This theory explained
+all the phases of the ring which had puzzled others.
+This ring was then, and has remained ever since, a
+unique structure.  We in this age have got accustomed
+to it. But Huyghens&#8217;s discovery was received
+with amazement.</p>
+
+<p>In 1675 Cassini found the ring to be double, the concentric
+rings being separated by a black band&#8212;a
+fact which was placed beyond dispute by Herschel,
+who also found that the thickness of the ring subtends
+an angle less than 0".3. Shr&#246;ter estimated its
+thickness at 500 miles.</p>
+
+<p>Many speculations have been advanced to explain the
+origin and constitution of the ring. De Sejour
+said <a href="#fn13_6">[6]</a> that it was thrown off from Saturn&#8217;s
+equator as a liquid ring, and afterwards solidified.
+He noticed that the outside would have a greater velocity,
+and be less attracted to the planet, than the inner
+parts, and that equilibrium would be impossible; so
+he supposed it to have solidified into a number of
+concentric rings, the exterior ones having the least
+velocity.</p>
+
+<p>Clerk Maxwell, in the Adams prize essay, gave a physico-mathematical
+demonstration that the rings must be composed of meteoritic
+matter like gravel. Even so, there must be collisions
+absorbing the energy of rotation, and tending to make
+the rings eventually fall into the planet. The
+slower motion of the external parts has been proved
+by the spectroscope in Keeler&#8217;s hands, 1895.</p>
+
+<p>Saturn has perhaps received more than its share of
+attention owing to these rings. This led to other
+discoveries. Huyghens in 1655, and J. D. Cassini
+in 1671, discovered the sixth and eighth satellites
+(Titan and Japetus). Cassini lost his satellite,
+and in searching for it found Rhea (the fifth) in
+1672, besides his old friend, whom he lost again.
+He added the third and fourth in 1684 (Tethys and
+Dione). The first and second (Mimas and Encelades)
+were added by Herschel in 1789, and the seventh (Hyperion)
+simultaneously by Lassel and Bond in 1848. The
+ninth (Phoebe) was found on photographs, by Pickering
+in 1898, with retrograde motion; and he has lately
+added a tenth.</p>
+
+<p>The occasional disappearance of Cassini&#8217;s Japetus
+was found on investigation to be due to the same causes
+as that of Jupiter&#8217;s fourth satellite, and proves
+that it always turns the same face to the planet.</p>
+
+<p><i>Uranus and Neptune</i>.&#8212;The splendid
+discoveries of Uranus and two satellites by Sir William
+Herschel in 1787, and of Neptune by Adams and Le Verrier
+in 1846, have been already described. Lassel added
+two more satellites to Uranus in 1851, and found Neptune&#8217;s
+satellite in 1846. All of the satellites of Uranus
+have retrograde motion, and their orbits are inclined
+about 80&#176; to the ecliptic.</p>
+
+<p>The spectroscope has shown the existence of an absorbing
+atmosphere on Jupiter and Saturn, and there are suspicions
+that they partake something of the character of the
+sun, and emit some light besides reflecting solar
+light. On both planets some absorption lines seem
+to agree with the aqueous vapour lines of our own
+atmosphere; while one, which is a strong band in the
+red common to both planets, seems to agree with a
+line in the spectrum of some reddish stars.</p>
+
+<p>Uranus and Neptune are difficult to observe spectroscopically,
+but appear to have peculiar spectra agreeing together.
+Sometimes Uranus shows Frauenhofer lines, indicating
+reflected solar light. But generally these are
+not seen, and six broad bands of absorption appear.
+ One is the F. of hydrogen; another is the red-star
+line of Jupiter and Saturn. Neptune is a very
+difficult object for the spectroscope.</p>
+
+<p>Quite lately <a href="#fn13_7">[7]</a> P. Lowell has announced that V. M.
+ Slipher, at Flagstaff Observatory, succeeded in 1907
+in rendering some plates sensitive far into the red.
+A reproduction is given of photographed spectra of
+the four outermost planets, showing (1) a great number
+of new lines and bands; (2) intensification of hydrogen
+F.  and C. lines; (3) a steady increase of effects
+(1) and (2) as we pass from Jupiter and Saturn to
+Uranus, and a still greater increase in Neptune.</p>
+
+<p><i>Asteroids</i>.&#8212;The discovery of these
+new planets has been described. At the beginning
+of the last century it was an immense triumph to catch
+a new one. Since photography was called into the
+service by Wolf, they have been caught every year in
+shoals. It is like the difference between sea
+fishing with the line and using a steam trawler.
+In the 1908 almanacs nearly seven hundred asteroids
+are included. The computation of their perturbations
+and ephemerides by Euler&#8217;s and Lagrange&#8217;s
+method of variable elements became so laborious that
+Encke devised a special process for these, which can
+be applied to many other disturbed orbits. <a href="#fn13_8">[8]</a></p>
+
+<p>When a photograph is taken of a region of the heavens
+including an asteroid, the stars are photographed
+as points because the telescope is made to follow
+their motion; but the asteroids, by their proper motion,
+appear as short lines.</p>
+
+<p>The discovery of Eros and the photographic attack
+upon its path have been described in their relation
+to finding the sun&#8217;s distance.</p>
+
+<p>A group of four asteroids has lately been found, with
+a mean distance and period equal to that of Jupiter.
+To three of these masculine names have been given&#8212;Hector,
+Patroclus, Achilles; the other has not yet been named.</p>
+
+<p><br /><br /></p>
+
+<p><b>FOOTNOTES:</b></p>
+
+<p><a name="fn13_1">[1]</a> Langrenus (van Langren), F. Selenographia sive
+lumina austriae philippica; Bruxelles, 1645.</p>
+
+<p><a name="fn13_2">[2]</a> <i>Astr. Nach.</i>, 2,944.</p>
+
+<p><a name="fn13_3">[3]</a> <i>Acad. des Sc.</i>, Paris; <i>C.R.</i>, lxxxiii.,
+1876.</p>
+
+<p><a name="fn13_4">[4]</a> <i>Mem. Spettr. Ital.</i>, xi., p. 28.</p>
+
+<p><a name="fn13_5">[5]</a> <i>R. S. Phil. Trans</i>., No. 1.</p>
+
+<p><a name="fn13_6">[6]</a> Grant&#8217;s <i>Hist. Ph. Ast</i>.,
+p. 267.</p>
+
+<p><a name="fn13_7">[7]</a> <i>Nature</i>, November 12th, 1908.</p>
+
+<p><a name="fn13_8">[8]</a> <i>Ast. Nach</i>., Nos. 791, 792, 814, translated
+by G. B. Airy. <i>Naut. Alm</i>., Appendix, 1856.</p>
+
+<p><br /><br /></p>
+
+<a name="14"></a>
+<h2>14. COMETS AND METEORS.</h2>
+
+<p>Ever since Halley discovered that the comet of 1682
+was a member of the solar system, these wonderful
+objects have had a new interest for astronomers; and
+a comparison of orbits has often identified the return
+of a comet, and led to the detection of an elliptic
+orbit where the difference from a parabola was imperceptible
+in the small portion of the orbit visible to us.
+A remarkable case in point was the comet of 1556,
+of whose identity with the comet of 1264 there could
+be little doubt.  Hind wanted to compute the
+orbit more exactly than Halley had done. He knew
+that observations had been made, but they were lost.
+Having expressed his desire for a search, all the
+observations of Fabricius and of Heller, and also a
+map of the comet&#8217;s path among the stars, were
+eventually unearthed in the most unlikely manner,
+after being lost nearly three hundred years.
+Hind and others were certain that this comet would
+return between 1844 and 1848, but it never appeared.</p>
+
+<p>When the spectroscope was first applied to finding
+the composition of the heavenly bodies, there was
+a great desire to find out what comets are made of.
+The first opportunity came in 1864, when Donati observed
+the spectrum of a comet, and saw three bright bands,
+thus proving that it was a gas and at least partly
+self-luminous.  In 1868 Huggins compared the spectrum
+of Winnecke&#8217;s comet with that of a Geissler tube
+containing olefiant gas, and found exact agreement.
+Nearly all comets have shown the same spectrum.<a href="#fn14_1">[1]</a>
+A very few comets have given bright band spectra differing
+from the normal type. Also a certain kind of
+continuous spectrum, as well as reflected solar light
+showing Frauenhofer lines, have been seen.</p>
+
+<p align="center"><img src="012.jpg" alt="[Illustration: COPY OF THE DRAWING MADE BY PAUL
+FABRICIUS.  To define the path of comet 1556.
+After being lost for 300 years, this drawing was recovered
+by the prolonged efforts of Mr. Hind and Professor
+Littrow in 1856.]" /></p>
+
+<p>When Wells&#8217;s comet, in 1882, approached very
+close indeed to the sun, the spectrum changed to a
+mono-chromatic yellow colour, due to sodium.</p>
+
+<p>For a full account of the wonders of the cometary
+world the reader is referred to books on descriptive
+astronomy, or to monographs on comets.<a href="#fn14_2">[2]</a> Nor can
+the very uncertain speculations about the structure
+of comets&#8217; tails be given here. A new explanation
+has been proposed almost every time that a great discovery
+has been made in the theory of light, heat, chemistry,
+or electricity.</p>
+
+<p>Halley&#8217;s comet remained the only one of which
+a prediction of the return had been confirmed, until
+the orbit of the small, ill-defined comet found by
+Pons in 1819 was computed by Encke, and found to have
+a period of 3 1/3 years. It was predicted to
+return in 1822, and was recognised by him as identical
+with many previous comets. This comet, called
+after Encke, has showed in each of its returns an inexplicable
+reduction of mean distance, which led to the assertion
+of a resisting medium in space until a better explanation
+could be found.<a href="#fn14_3">[3]</a></p>
+
+<p>Since that date fourteen comets have been found with
+elliptic orbits, whose aphelion distances are all
+about the same as Jupiter&#8217;s mean distance; and
+six have an aphelion distance about ten per cent,
+greater than Neptune&#8217;s mean distance. Other
+comets are similarly associated with the planets Saturn
+and Uranus.</p>
+
+<p>The physical transformations of comets are among the
+most wonderful of unexplained phenomena in the heavens.
+But, for physical astronomers, the greatest interest
+attaches to the reduction of radius vector of Encke&#8217;s
+comet, the splitting of Biela&#8217;s comet into two
+comets in 1846, and the somewhat similar behaviour
+of other comets. It must be noted, however, that
+comets have a sensible size, that all their parts cannot
+travel in exactly the same orbit under the sun&#8217;s
+gravitation, and that their mass is not sufficient
+to retain the parts together very forcibly; also that
+the inevitable collision of particles, or else fluid
+friction, is absorbing energy, and so reducing the
+comet&#8217;s velocity.</p>
+
+<p>In 1770 Lexell discovered a comet which, as was afterwards
+proved by investigations of Lexell, Burchardt, and
+Laplace, had in 1767 been deflected by Jupiter out
+of an orbit in which it was invisible from the earth
+into an orbit with a period of 5&#189; years, enabling it
+to be seen. In 1779 it again approached Jupiter
+closer than some of his satellites, and was sent off
+in another orbit, never to be again recognised.</p>
+
+<p>But our interest in cometary orbits has been added
+to by the discovery that, owing to the causes just
+cited, a comet, if it does not separate into discrete
+parts like Biela&#8217;s, must in time have its parts
+spread out so as to cover a sensible part of the orbit,
+and that, when the earth passes through such part
+of a comet&#8217;s orbit, a meteor shower is the result.</p>
+
+<p>A magnificent meteor shower was seen in America on
+November 12th-13th, 1833, when the paths of the meteors
+all seemed to radiate from a point in the constellation
+Leo. A similar display had been witnessed in
+Mexico by Humboldt and Bonpland on November 12th, 1799.
+H. A. Newton traced such records back to October 13th,
+A.D. 902. The orbital motion of a cloud or stream
+of small particles was indicated. The period
+favoured by H. A. Newton was 354&#189; days; another suggestion
+was 375&#189; days, and another 33&#188; years.  He noticed
+that the advance of the date of the shower between
+902 and 1833, at the rate of one day in seventy years,
+meant a progression of the node of the orbit.
+ Adams undertook to calculate what the amount would
+be on all the five suppositions that had been made
+about the period. After a laborious work, he found
+that none gave one day in seventy years except the
+33&#188;-year period, which did so exactly. H. A.
+Newton predicted a return of the shower on the night
+of November 13th-14th, 1866. He is now dead; but
+many of us are alive to recall the wonder and enthusiasm
+with which we saw this prediction being fulfilled
+by the grandest display of meteors ever seen by anyone
+now alive.</p>
+
+<p>The <i>progression</i> of the nodes proved the path
+of the meteor stream to be retrograde. The <i>radiant</i>
+had almost the exact longitude of the point towards
+which the earth was moving. This proved that
+the meteor cluster was at perihelion. The period
+being known, the eccentricity of the orbit was obtainable,
+also the orbital velocity of the meteors in perihelion;
+and, by comparing this with the earth&#8217;s velocity,
+the latitude of the radiant enabled the inclination
+to be determined, while the longitude of the earth
+that night was the longitude of the node. In
+such a way Schiaparelli was able to find first the
+elements of the orbit of the August meteor shower
+(Perseids), and to show its identity with the orbit
+of Tuttle&#8217;s comet 1862.iii. Then, in January
+1867, Le Verrier gave the elements of the November
+meteor shower (Leonids); and Peters, of Altona, identified
+these with Oppolzer&#8217;s elements for Tempel&#8217;s
+comet 1866&#8212;Schiaparelli having independently
+attained both of these results. Subsequently
+Weiss, of Vienna, identified the meteor shower of April
+20th (Lyrids) with comet 1861. Finally, that
+indefatigable worker on meteors, A. S. Herschel, added
+to the number, and in 1878 gave a list of seventy-six
+coincidences between cometary and meteoric orbits.</p>
+
+<p>Cometary astronomy is now largely indebted to photography,
+not merely for accurate delineations of shape, but
+actually for the discovery of most of them.
+The art has also been applied to the observation of
+comets at distances from their perihelia so great as
+to prevent their visual observation. Thus has
+Wolf, of Heidelburg, found upon old plates the position
+of comet 1905.v., as a star of the 15.5 magnitude,
+783 days before the date of its discovery. From
+the point of view of the importance of finding out
+the divergence of a cometary orbit from a parabola,
+its period, and its aphelion distance, this increase
+of range attains the very highest value.</p>
+
+<p>The present Astronomer Royal, appreciating this possibility,
+has been searching by photography for Halley&#8217;s
+comet since November, 1907, although its perihelion
+passage will not take place until April, 1910.</p>
+
+<p><br /><br /></p>
+
+<p><b>FOOTNOTES:</b></p>
+
+<p><a name="fn14_1">[1]</a> In 1874, when the writer was crossing the Pacific
+Ocean in H.M.S. &#8220;Scout,&#8221; Coggia&#8217;s
+comet unexpectedly appeared, and (while Colonel Tupman
+got its positions with the sextant) he tried to use
+the prism out of a portable direct-vision spectroscope,
+without success until it was put in front of the object-glass
+of a binocular, when, to his great joy, the three
+band images were clearly seen.</p>
+
+<p><a name="fn14_2">[2]</a> Such as <i>The World of Comets</i>, by A. Guillemin;
+<i>History of Comets</i>, by G. R. Hind, London, 1859;
+<i>Theatrum Cometicum</i>, by S. de Lubienietz, 1667;
+<i>Cometographie</i>, by Pingr&#233;, Paris, 1783; <i>Donati&#8217;s
+Comet</i>, by Bond.</p>
+
+<p><a name="fn14_3">[3]</a> The investigations by Von Asten (of St. Petersburg)
+seem to support, and later ones, especially those
+by Backlund (also of St. Petersburg), seem to discredit,
+the idea of a resisting medium.</p>
+
+<p><br /><br /></p>
+
+<a name="15"></a>
+<h2>15. THE FIXED STARS AND NEBUL&#198;.</h2>
+
+<p>Passing now from our solar system, which appears to
+be subject to the action of the same forces as those
+we experience on our globe, there remains an innumerable
+host of fixed stars, nebulas, and nebulous clusters
+of stars. To these the attention of astronomers
+has been more earnestly directed since telescopes
+have been so much enlarged. Photography also
+has enabled a vast amount of work to be covered in
+a comparatively short period, and the spectroscope
+has given them the means, not only of studying the
+chemistry of the heavens, but also of detecting any
+motion in the line of sight from less than a mile a
+second and upwards in any star, however distant, provided
+it be bright enough.</p>
+
+<img src="013.jpg" alt="[Illustration: SIR WILLIAM HERSCHEL, F.R.S.&#8212;1738-1822.
+ Painted by Lemuel F. Abbott; National Portrait Gallery,
+Room XX.]" align="right" />
+
+<p>In the field of telescopic discovery beyond our solar
+system there is no one who has enlarged our knowledge
+so much as Sir William Herschel, to whom we owe the
+greatest discovery in dynamical astronomy among the
+stars&#8212;viz., that the law of gravitation
+extends to the most distant stars, and that many of
+them describe elliptic orbits about each other.
+W. Herschel was born at Hanover in 1738, came to England
+in 1758 as a trained musician, and died in 1822.
+He studied science when he could, and hired a telescope,
+until he learnt to make his own specula and telescopes.
+He made 430 parabolic specula in twenty-one years.
+He discovered 2,500 nebul&#230; and 806 double stars, counted
+the stars in 3,400 guage-fields, and compared the
+principal stars photometrically.</p>
+
+<p>Some of the things for which he is best known were
+results of those accidents that happen only to the
+indefatigable enthusiast. Such was the discovery
+of Uranus, which led to funds being provided for constructing
+his 40-feet telescope, after which, in 1786, he settled
+at Slough. In the same way, while trying to detect
+the annual parallax of the stars, he failed in that
+quest, but discovered binary systems of stars revolving
+in ellipses round each other; just as Bradley&#8217;s
+attack on stellar parallax failed, but led to the discovery
+of aberration, nutation, and the true velocity of
+light.</p>
+
+<p><i>Parallax</i>.&#8212;The absence of stellar
+parallax was the great objection to any theory of
+the earth&#8217;s motion prior to Kepler&#8217;s time.
+It is true that Kepler&#8217;s theory itself could
+have been geometrically expressed equally well with
+the earth or any other point fixed. But in Kepler&#8217;s
+case the obviously implied physical theory of the
+planetary motions, even before Newton explained the
+simplicity of conception involved, made astronomers
+quite ready to waive the claim for a rigid proof of
+the earth&#8217;s motion by measurement of an annual
+parallax of stars, which they had insisted on in respect
+of Copernicus&#8217;s revival of the idea of the earth&#8217;s
+orbital motion.</p>
+
+<p>Still, the desire to measure this parallax was only
+intensified by the practical certainty of its existence,
+and by repeated failures. The attempts of Bradley
+failed. The attempts of Piazzi and Brinkley,<a href="#fn15_1">[1]</a>
+early in the nineteenth century, also failed.
+The first successes, afterwards confirmed, were by
+Bessel and Henderson.  Both used stars whose
+proper motion had been found to be large, as this argued
+proximity. Henderson, at the Cape of Good Hope,
+observed &#945; Centauri, whose annual proper motion
+he found to amount to 3".6, in 1832-3; and a few years
+later deduced its parallax 1".16.  His successor
+at the Cape, Maclear, reduced this to 0".92.</p>
+
+<p>In 1835 Struve assigned a doubtful parallax of 0".261
+to Vega (&#945; Lyr&#230;). But Bessel&#8217;s observations,
+between 1837 and 1840, of 61 Cygni, a star with the
+large proper motion of over 5&#8221;, established its
+annual parallax to be 0".3483; and this was confirmed
+by Peters, who found the value 0".349.</p>
+
+<p>Later determinations for &#945;<sub>2</sub> Centauri, by Gill,<a href="#fn15_2">[2]</a>
+make its parallax 0".75&#8212;This is the nearest
+known fixed star; and its light takes 4 1/3 years
+to reach us. The lightyear is taken as the unit
+of measurement in the starry heavens, as the earth&#8217;s
+mean distance is &#8220;the astronomical unit&#8221;
+for the solar system.<a href="#fn15_3">[3]</a> The proper motions and parallaxes
+combined tell us the velocity of the motion of these
+stars across the line of sight: &#945; Centauri
+14.4 miles a second=4.2 astronomical units a year;
+61 Cygni 37.9 miles a second=11.2 astronomical units
+a year. These successes led to renewed zeal, and
+now the distances of many stars are known more or less
+accurately.</p>
+
+<p>Several of the brightest stars, which might be expected
+to be the nearest, have not shown a parallax amounting
+to a twentieth of a second of arc. Among these
+are Canopus, &#945; Orionis, &#945; Cygni, &#946; Centauri,
+and &#947; Cassiopeia. Oudemans has published a
+list of parallaxes observed.<a href="#fn15_4">[4]</a></p>
+
+<p><i>Proper Motion.</i>&#8212;In 1718 Halley<a href="#fn15_5">[5]</a>
+detected the proper motions of Arcturus and Sirius.
+In 1738 J. Cassinis<a href="#fn15_6">[6]</a> showed that the former had
+moved five minutes of arc since Tycho Brahe fixed its
+position. In 1792 Piazzi noted the motion of
+61 Cygni as given above. For a long time the
+greatest observed proper motion was that of a small
+star 1830 Groombridge, nearly 7&#8221; a year; but
+others have since been found reaching as much as 10&#8221;.</p>
+
+<p>Now the spectroscope enables the motion of stars to
+be detected at a single observation, but only that
+part of the motion that is in the line of sight.
+For a complete knowledge of a star&#8217;s motion the
+proper motion and parallax must also be known.</p>
+
+<p>When Huggins first applied the Doppler principle to
+measure velocities in the line of sight,<a href="#fn15_7">[7]</a> the faintness
+of star spectra diminished the accuracy; but V&#246;gel,
+in 1888, overcame this to a great extent by long exposures
+of photographic plates.</p>
+
+<p>It has often been noticed that stars which seem to
+belong to a group of nearly uniform magnitude have
+the same proper motion. The spectroscope has
+shown that these have also often the same velocity
+in the line of sight. Thus in the Great Bear,
+&#946;, &#947;, &#948;, &#949;, &#950;, all agree as to
+angular proper motion. &#948; was too faint for a spectroscopic
+measurement, but all the others have been shown to
+be approaching us at a rate of twelve to twenty miles
+a second. The same has been proved for proper
+motion, and line of sight motion, in the case of Pleiades
+and other groups.</p>
+
+<p>Maskelyne measured many proper motions of stars, from
+which W. Herschel<a href="#fn15_8">[8]</a> came to the conclusion that these
+apparent motions are for the most part due to a motion
+of the solar system in space towards a point in the
+constellation Hercules, R.A. 257&#176;; N. Decl. 25&#176;.
+ This grand discovery has been amply confirmed, and,
+though opinions differ as to the exact direction,
+it happens that the point first indicated by Herschel,
+from totally insufficient data, agrees well with modern
+estimates.</p>
+
+<p>Comparing the proper motions and parallaxes to get
+the actual velocity of each star relative to our system,
+C.L. Struve found the probable velocity of the
+solar system in space to be fifteen miles a second,
+or five astronomical units a year.</p>
+
+<p>The work of Herschel in this matter has been checked
+by comparing spectroscopic velocities in the line
+of sight which, so far as the sun&#8217;s motion is
+concerned, would give a maximum rate of approach for
+stars near Hercules, a maximum rate of recession for
+stars in the opposite part of the heavens, and no
+effect for stars half-way between. In this way
+the spectroscope has confirmed generally Herschel&#8217;s
+view of the direction, and makes the velocity eleven
+miles a second, or nearly four astronomical units
+a year.</p>
+
+<p>The average proper motion of a first magnitude star
+has been found to be 0".25 annually, and of a sixth
+magnitude star 0".04. But that all bright stars
+are nearer than all small stars, or that they show
+greater proper motion for that reason, is found to
+be far from the truth. Many statistical studies
+have been made in this connection, and interesting
+results may be expected from this treatment in the
+hands of Kapteyn of Groningen, and others.<a href="#fn15_9">[9]</a></p>
+
+<p>On analysis of the directions of proper motions of
+stars in all parts of the heavens, Kapteyn has shown<a href="#fn15_10">[10]</a>
+that these indicate, besides the solar motion towards
+Hercules, two general drifts of stars in nearly opposite
+directions, which can be detected in any part of the
+heavens. This result has been confirmed from independent
+data by Eddington (<i>R.A.S., M.N.</i>) and Dyson
+(<i>R.S.E. Proc.</i>).</p>
+
+<p>Photography promises to assist in the measurement
+of parallax and proper motions. Herr Pulfrich,
+of the firm of Carl Zeiss, has vastly extended the
+applications of stereoscopic vision to astronomy&#8212;a
+subject which De la Rue took up in the early days of
+photography.  He has made a stereo-comparator
+of great beauty and convenience for comparing stereoscopically
+two star photographs taken at different dates.
+Wolf of Heidelberg has used this for many purposes.
+His investigations depending on the solar motion in
+space are remarkable. He photographs stars in
+a direction at right angles to the line of the sun&#8217;s
+motion. He has taken photographs of the same region
+fourteen years apart, the two positions of his camera
+being at the two ends of a base-line over 5,000,000,000
+miles apart, or fifty-six astronomical units.
+On examining these stereoscopically, some of the stars
+rise out of the general plane of the stars, and seem
+to be much nearer. Many of the stars are thus
+seen to be suspended in space at different distances
+corresponding exactly to their real distances from
+our solar system, except when their proper motion
+interferes. The effect is most striking; the
+accuracy of measurement exceeds that of any other method
+of measuring such displacements, and it seems that
+with a long interval of time the advantage of the
+method increases.</p>
+
+<p><i>Double Stars.</i>&#8212;The large class of
+double stars has always been much studied by amateurs,
+partly for their beauty and colour, and partly as
+a test for telescopic definition. Among the many
+unexplained stellar problems there is one noticed
+in double stars that is thought by some to be likely
+to throw light on stellar evolution. It is this:
+There are many instances where one star of the pair
+is comparatively faint, and the two stars are contrasted
+in colour; and in every single case the general colour
+of the faint companion is invariably to be classed
+with colours more near to the blue end of the spectrum
+than that of the principal star.</p>
+
+<p><i>Binary Stars.</i>&#8212;Sir William Herschel
+began his observations of double stars in the hope
+of discovering an annual parallax of the stars.
+In this he was following a suggestion of Galileo&#8217;s.
+The presumption is that, if there be no physical connection
+between the stars of a pair, the largest is the nearest,
+and has the greatest parallax. So, by noting
+the distance between the pair at different times of
+the year, a delicate test of parallax is provided,
+unaffected by major instrumental errors.</p>
+
+<p>Herschel did, indeed, discover changes of distance,
+but not of the character to indicate parallax.
+Following this by further observation, he found that
+the motions were not uniform nor rectilinear, and by
+a clear analysis of the movements he established the
+remarkable and wholly unexpected fact that in all
+these cases the motion is due to a revolution about
+their common centre of gravity.<a href="#fn15_11">[11]</a> He gave the approximate
+period of revolution of some of these: Castor,
+342 years; &#948; Serpentis, 375 years; &#947; Leonis, 1,200
+years; &#949; Bootis, 1,681 years.</p>
+
+<p>Twenty years later Sir John Herschel and Sir James
+South, after re-examination of these stars, confirmed<a href="#fn15_12">[12]</a>
+and extended the results, one pair of Coron&#230; having
+in the interval completed more than a whole revolution.</p>
+
+<p>It is, then, to Sir William Herschel that we owe the
+extension of the law of gravitation, beyond the limits
+of the solar system, to the whole universe. His
+observations were confirmed by F.G.W. Struve (born
+1793, died 1864), who carried on the work at Dorpat.
+But it was first to Savary,<a href="#fn15_13">[13]</a> and later to Encke
+and Sir John Herschel, that we owe the computation
+of the elliptic elements of these stars; also the
+resulting identification of their law of force with
+Newton&#8217;s force of gravitation applied to the
+solar system, and the force that makes an apple fall
+to the ground. As Grant well says in his <i>History</i>:
+&#8220;This may be justly asserted to be one of the
+most sublime truths which astronomical science has
+hitherto disclosed to the researches of the human
+mind.&#8221;</p>
+
+<p>Latterly the best work on double stars has been done
+by S. W. Burnham,<a href="#fn15_14">[14]</a> at the Lick Observatory.
+The shortest period he found was eleven years (&#954;
+Pegasi).  In the case of some of these binaries
+the parallax has been measured, from which it appears
+that in four of the surest cases the orbits are about
+the size of the orbit of Uranus, these being probably
+among the smallest stellar orbits.</p>
+
+<p>The law of gravitation having been proved to extend
+to the stars, a discovery (like that of Neptune in
+its origin, though unlike it in the labour and originality
+involved in the calculation) that entrances the imagination
+became possible, and was realised by Bessel&#8212;the
+discovery of an unknown body by its gravitational
+disturbance on one that was visible. In 1834
+and 1840 he began to suspect a want of uniformity in
+the proper motion of Sirius and Procyon respectively.
+In 1844, in a letter to Sir John Herschel,<a href="#fn15_15">[15]</a> he
+attributed these irregularities in each case to the
+attraction of an invisible companion, the period of
+revolution of Sirius being about half a century.
+Later he said: &#8220;I adhere to the conviction
+that Procyon and Sirius form real binary systems,
+consisting of a visible and an invisible star.
+ There is no reason to suppose luminosity an essential
+quality of cosmical bodies. The visibility of
+countless stars is no argument against the invisibility
+of countless others.&#8221; This grand conception
+led Peters to compute more accurately the orbit, and
+to assign the place of the invisible companion of
+Sirius. In 1862 Alvan G. Clark was testing a
+new 18-inch object-glass (now at Chicago) upon Sirius,
+and, knowing nothing of these predictions, actually
+found the companion in the very place assigned to
+it. In 1896 the companion of Procyon was discovered
+by Professor Schaeberle at the Lick Observatory.</p>
+
+<p>Now, by the refined parallax determinations of Gill
+at the Cape, we know that of Sirius to be 0".38.
+From this it has been calculated that the mass of
+Sirius equals two of our suns, and its intrinsic brightness
+equals twenty suns; but the companion, having a mass
+equal to our sun, has only a five-hundredth part of
+the sun&#8217;s brightness.</p>
+
+<p><i>Spectroscopic Binaries</i>.&#8212;On measuring
+the velocity of a star in the line of sight at frequent
+intervals, periodic variations have been found, leading
+to a belief in motion round an invisible companion.
+Vogel, in 1889, discovered this in the case of Spica
+(&#945; Virginis), whose period is 4d. 0h. 19m., and
+the diameter of whose orbit is six million miles.
+Great numbers of binaries of this type have since
+then been discovered, all of short period.</p>
+
+<p>Also, in 1889, Pickering found that at regular intervals
+of fifty-two days the lines in the spectrum of &#950;
+of the Great Bear are duplicated, indicating a relative
+velocity, equal to one hundred miles a second, of
+two components revolving round each other, of which
+that apparently single star must be composed.</p>
+
+<p>It would be interesting, no doubt, to follow in detail
+the accumulating knowledge about the distances, proper
+motions, and orbits of the stars; but this must be
+done elsewhere. Enough has been said to show
+how results are accumulating which must in time unfold
+to us the various stellar systems and their mutual
+relationships.</p>
+
+<p><i>Variable Stars.</i>&#8212;It has often happened
+in the history of different branches of physical science
+that observation and experiment were so far ahead
+of theory that hopeless confusion appeared to reign;
+and then one chance result has given a clue, and from
+that time all differences and difficulties in the
+previous researches have stood forth as natural consequences,
+explaining one another in a rational sequence.
+So we find parallax, proper motion, double stars, binary
+systems, variable stars, and new stars all bound together.</p>
+
+<p>The logical and necessary explanation given of the
+cause of ordinary spectroscopic binaries, and of irregular
+proper motions of Sirius and Procyon, leads to the
+inference that if ever the plane of such a binary
+orbit were edge-on to us there ought to be an eclipse
+of the luminous partner whenever the non-luminous
+one is interposed between us. This should give
+rise either to intermittence in the star&#8217;s light
+or else to variability.  It was by supposing the
+existence of a dark companion to Algol that its discoverer,
+Goodricke of York,<a href="#fn15_16">[16]</a> in 1783, explained variable
+stars of this type. Algol (&#946; Persei) completes
+the period of variable brightness in 68.8 hours.
+It loses three-fifths of its light, and regains it
+in twelve hours. In 1889 Vogel,<a href="#fn15_17">[17]</a> with the
+Potsdam spectrograph, actually found that the luminous
+star is receding before each eclipse, and approaching
+us after each eclipse; thus entirely supporting Goodricke&#8217;s
+opinion. There are many variables of the Algol
+type, and information is steadily accumulating.
+But all variable stars do not suffer the sudden variations
+of Algol. There are many types, and the explanations
+of others have not proved so easy.</p>
+
+<p>The Harvard College photographs have disclosed the
+very great prevalence of variability, and this is
+certainly one of the lines in which modern discovery
+must progress.</p>
+
+<p>Roberts, in South Africa, has done splendid work on
+the periods of variables of the Algol type.</p>
+
+<p><i>New Stars</i>.&#8212;Extreme instances of
+variable stars are the new stars such as those detected
+by Hipparchus, Tycho Brahe, and Kepler, of which many
+have been found in the last half-century. One
+of the latest great &#8220;Nov&#230;&#8221; was discovered
+in Auriga by a Scotsman, Dr. Anderson, on February
+1st, 1892, and, with the modesty of his race, he communicated
+the fact to His Majesty&#8217;s Astronomer for Scotland
+on an unsigned post-card.<a href="#fn15_18">[18]</a> Its spectrum was observed
+and photographed by Huggins and many others.
+It was full of bright lines of hydrogen, calcium,
+helium, and others not identified. The astounding
+fact was that lines were shown in pairs, bright and
+dark, on a faint continuous spectrum, indicating apparently
+that a dark body approaching us at the rate of 550
+miles a second<a href="#fn15_19">[19]</a> was traversing a cold nebulous atmosphere,
+and was heated to incandescence by friction, like
+a meteor in our atmosphere, leaving a luminous train
+behind it. It almost disappeared, and on April
+26th it was of the sixteenth magnitude; but on August
+17th it brightened to the tenth, showing the principal
+nebular band in its spectrum, and no sign of approach
+or recession.  It was as if it emerged from one
+part of the nebula, cooled down, and rushed through
+another part of the nebula, rendering the nebular gas
+more luminous than itself.<a href="#fn15_20">[20]</a></p>
+
+<p>Since 1892 one Nova after another has shown a spectrum
+as described above, like a meteor rushing towards
+us and leaving a train behind, for this seems to be
+the obvious meaning of the spectra.</p>
+
+<p>The same may be said of the brilliant Nova Persei,
+brighter at its best than Capella, and discovered
+also by Dr. Anderson on February 22nd, 1901.
+It increased in brightness as it reached the densest
+part of the nebula, then it varied for some weeks
+by a couple of magnitudes, up and down, as if passing
+through separate nebular condensations. In February,
+1902, it could still be seen with an opera-glass.
+As with the other Nov&#230;, when it first dashed into the
+nebula it was vaporised and gave a continuous spectrum
+with dark lines of hydrogen and helium. It showed
+no bright lines paired with the dark ones to indicate
+a train left behind; but in the end its own luminosity
+died out, and the nebular spectrum predominated.</p>
+
+<p>The nebular illumination as seen in photographs, taken
+from August to November, seemed to spread out slowly
+in a gradually increasing circle at the rate of 90&#8221;
+in forty-eight days. Kapteyn put this down to
+the velocity of light, the original outburst sending
+its illumination to the nebulous gas and illuminating
+a spherical shell whose radius increased at the velocity
+of light. This supposition seems correct, in
+which case it can easily be shown from the above figures
+that the distance of this Nova was 300 light years.</p>
+
+<p><i>Star Catalogues.</i>&#8212;Since the days
+of very accurate observations numerous star-catalogues
+have been produced by individuals or by observatories.
+Bradley&#8217;s monumental work may be said to head
+the list. Lacaille&#8217;s, in the Southern hemisphere,
+was complementary.  Then Piazzi, Lalande, Groombridge,
+and Bessel were followed by Argelander with his 324,000
+stars, Rumker&#8217;s Paramatta catalogue of the southern
+hemisphere, and the frequent catalogues of national
+observatories. Later the Astronomische Gesellschaft
+started their great catalogue, the combined work of
+many observatories. Other southern ones were
+Gould&#8217;s at Cordova and Stone&#8217;s at the Cape.</p>
+
+<p>After this we have a new departure. Gill at the
+Cape, having the comet 1882.ii. all to himself in
+those latitudes, wished his friends in Europe to see
+it, and employed a local photographer to strap his
+camera to the observatory equatoreal, driven by clockwork,
+and adjusted on the comet by the eye. The result
+with half-an-hour&#8217;s exposure was good, so he
+tried three hours. The result was such a display
+of sharp star images that he resolved on the Cape Photographic
+Durchmusterung, which after fourteen years, with Kapteyn&#8217;s
+aid in reducing, was completed. Meanwhile the
+brothers Henry, of Paris, were engaged in going over
+Chacornac&#8217;s zodiacal stars, and were about to
+catalogue the Milky Way portion, a serious labour,
+when they saw Gill&#8217;s Comet photograph and conceived
+the idea of doing the rest of their work by photography.
+ Gill had previously written to Admiral Mouchez, of
+the Paris Observatory, and explained to him his project
+for charting the heavens photographically, by combining
+the work of many observatories. This led Admiral
+Mouchez to support the brothers Henry in their scheme.<a href="#fn15_21">[21]</a>
+Gill, having got his own photographic work underway,
+suggested an international astrographic chart, the
+materials for different zones to be supplied by observatories
+of all nations, each equipped with similar photographic
+telescopes. At a conference in Paris, 1887, this
+was decided on, the stars on the charts going down
+to the fourteenth magnitude, and the catalogues to
+the eleventh.</p>
+
+<p align="center"><img src="014.jpg" alt="[Illustration: GREAT COMET, Nov. 14TH, 1882.
+(Exposure 2hrs. 20m.)  By kind permission of Sir David
+Gill. From this photograph originated all stellar
+chart-photography.]" /></p>
+
+<p>This monumental work is nearing completion. The
+labour involved was immense, and the highest skill
+was required for devising instruments and methods
+to read off the star positions from the plates.</p>
+
+<p>Then we have the Harvard College collection of photographic
+plates, always being automatically added to; and their
+annex at Arequipa in Peru.</p>
+
+<p>Such catalogues vary in their degree of accuracy;
+and fundamental catalogues of standard stars have
+been compiled. These require extension, because
+the differential methods of the heliometer and the
+camera cannot otherwise be made absolute.</p>
+
+<p>The number of stars down to the fourteenth magnitude
+may be taken at about 30,000,000; and that of all
+the stars visible in the greatest modern telescopes
+is probably about 100,000,000.</p>
+
+<p><i>Nebul&#230; and Star-clusters.</i>&#8212;Our knowledge
+of nebul&#230; really dates from the time of W. Herschel.
+In his great sweeps of the heavens with his giant
+telescopes he opened in this direction a new branch
+of astronomy.  At one time he held that all nebul&#230;
+might be clusters of innumerable minute stars at a
+great distance. Then he recognised the different
+classes of nebul&#230;, and became convinced that there
+is a widely-diffused &#8220;shining fluid&#8221; in
+space, though many so-called nebul&#230; could be resolved
+by large telescopes into stars.  He considered
+that the Milky Way is a great star cluster, whose
+form may be conjectured from numerous star-gaugings.
+He supposed that the compact &#8220;planetary nebul&#230;&#8221;
+might show a stage of evolution from the diffuse nebul&#230;,
+and that his classifications actually indicate various
+stages of development. Such speculations, like
+those of the ancients about the solar system, are
+apt to be harmful to true progress of knowledge unless
+in the hands of the ablest mathematical physicists;
+and Herschel violated their principles in other directions.
+But here his speculations have attracted a great deal
+of attention, and, with modifications, are accepted,
+at least as a working hypothesis, by a fair number
+of people.</p>
+
+<p>When Sir John Herschel had extended his father&#8217;s
+researches into the Southern Hemisphere he was also
+led to the belief that some nebulae were a phosphorescent
+material spread through space like fog or mist.</p>
+
+<p>Then his views were changed by the revelations due
+to the great discoveries of Lord Rosse with his gigantic
+refractor,<a href="#fn15_22">[22]</a> when one nebula after another was resolved
+into a cluster of minute stars. At that time
+the opinion gained ground that with increase of telescopic
+power this would prove to be the case with all nebul&#230;.</p>
+
+<p>In 1864 all doubt was dispelled by Huggins<a href="#fn15_23">[23]</a> in
+his first examination of the spectrum of a nebula,
+and the subsequent extension of this observation to
+other nebul&#230;; thus providing a certain test which
+increase in the size of telescopes could never have
+given. In 1864 Huggins found that all true nebulae
+give a spectrum of bright lines. Three are due
+to hydrogen; two (discovered by Copeland) are helium
+lines; others are unknown. Fifty-five lines have
+been photographed in the spectrum of the Orion nebula.
+It seems to be pretty certain that all true nebulae
+are gaseous, and show almost exactly the same spectrum.</p>
+
+<p>Other nebul&#230;, and especially the white ones like that
+in Andromeda, which have not yet been resolved into
+stars, show a continuous spectrum; others are greenish
+and give no lines.</p>
+
+<p>A great deal has to be done by the chemist before
+the astronomer can be on sure ground in drawing conclusions
+from certain portions of his spectroscopic evidence.</p>
+
+<p>The light of the nebulas is remarkably actinic, so
+that photography has a specially fine field in revealing
+details imperceptible in the telescope. In 1885
+the brothers Henry photographed, round the star Maia
+in the Pleiades, a spiral nebula 3&#8217; long, as
+bright on the plate as that star itself, but quite
+invisible in the telescope; and an exposure of four
+hours revealed other new nebula in the same district.
+That painstaking and most careful observer, Barnard,
+with 10&#188; hours&#8217; exposure, extended this nebulosity
+for several degrees, and discovered to the north of
+the Pleiades a huge diffuse nebulosity, in a region
+almost destitute of stars. By establishing a 10-inch
+instrument at an altitude of 6,000 feet, Barnard has
+revealed the wide distribution of nebular matter in
+the constellation Scorpio over a space of 4&#176; or 5&#176;
+square.  Barnard asserts that the &#8220;nebular
+hypothesis&#8221; would have been killed at its birth
+by a knowledge of these photographs. Later he
+has used still more powerful instruments, and extended
+his discoveries.</p>
+
+<p>The association of stars with planetary nebul&#230;, and
+the distribution of nebul&#230; in the heavens, especially
+in relation to the Milky Way, are striking facts,
+which will certainly bear fruit when the time arrives
+for discarding vague speculations, and learning to
+read the true physical structure and history of the
+starry universe.</p>
+
+<p><i>Stellar Spectra.</i>&#8212;When the spectroscope
+was first available for stellar research, the leaders
+in this branch of astronomy were Huggins and Father
+Secchi,<a href="#fn15_24">[24]</a> of Rome. The former began by devoting
+years of work principally to the most accurate study
+of a few stars.  The latter devoted the years
+from 1863 to 1867 to a general survey of the whole
+heavens, including 4,000 stars. He divided these
+into four principal classes, which have been of the
+greatest service. Half of his stars belonged
+to the first class, including Sirius, Vega, Regulus,
+Altair. The characteristic feature of their spectra
+is the strength and breadth of the hydrogen lines
+and the extreme faintness of the metallic lines.
+This class of star is white to the eye, and rich in
+ultra violet light.</p>
+
+<p>The second class includes about three-eighths of his
+stars, including Capella, Pollux, and Arcturus.
+These stars give a spectrum like that of our sun,
+and appear yellowish to the eye.</p>
+
+<p>The third class includes &#945; Herculis, &#945; Orionis
+(Betelgeux), Mira Ceti, and about 500 red and variable
+stars.  The spectrum has fluted bands shaded
+from blue to red, and sharply defined at the more
+refrangible edge.</p>
+
+<p>The fourth class is a small one, containing no stars
+over fifth magnitude, of which 152 Schjellerup, in
+Canes Venatici, is a good example. This spectrum
+also has bands, but these are shaded on the violet
+side and sharp on the red side. They are due to
+carbon in some form.  These stars are ruby red
+in the telescope.</p>
+
+<p>It would appear, then, that all stars are suns with
+continuous spectra, and the classes are differentiated
+by the character of the absorbent vapours of their
+atmospheres.</p>
+
+<p>It is very likely that, after the chemists have taught
+us how to interpret all the varieties of spectrum,
+it will be possible to ascribe the different spectrum-classes
+to different stages in the life-history of every star.
+ Already there are plenty of people ready to lay down
+arbitrary assumptions about the lessons to be drawn
+from stellar spectra. Some say that they know
+with certainty that each star begins by being a nebula,
+and is condensed and heated by condensation until
+it begins to shine as a star; that it attains a climax
+of temperature, then cools down, and eventually becomes
+extinct.  They go so far as to declare that they
+know what class of spectrum belongs to each stage
+of a star&#8217;s life, and how to distinguish between
+one that is increasing and another that is decreasing
+in temperature.</p>
+
+<p>The more cautious astronomers believe that chemistry
+is not sufficiently advanced to justify all of these
+deductions; that, until chemists have settled the
+lately raised question of the transmutation of elements,
+no theory can be sure. It is also held that until
+they have explained, without room for doubt, the reasons
+for the presence of some lines, and the absence of
+others, of any element in a stellar spectrum; why
+the arc-spectrum of each element differs from its spark
+spectrum; what are all the various changes produced
+in the spectrum of a gas by all possible concomitant
+variations of pressure and temperature; also the meanings
+of all the flutings in the spectra of metalloids and
+compounds; and other equally pertinent matters&#8212;until
+that time arrives the part to be played by the astronomer
+is one of observation. By all means, they say,
+make use of &#8220;working hypotheses&#8221; to add
+an interest to years of laborious research, and to
+serve as a guide to the direction of further labours;
+but be sure not to fall into the error of calling
+any mere hypothesis a theory.</p>
+
+<p><i>Nebular Hypothesis.</i>&#8212;The Nebular
+Hypothesis, which was first, as it were, tentatively
+put forward by Laplace as a note in his <i>Syst&#232;me
+du Monde</i>, supposes the solar system to have been
+a flat, disk-shaped nebula at a high temperature in
+rapid rotation. In cooling it condensed, leaving
+revolving rings at different distances from the centre.
+These themselves were supposed to condense into the
+nucleus for a rotating planet, which might, in contracting,
+again throw off rings to form satellites.  The
+speculation can be put in a really attractive form,
+but is in direct opposition to many of the actual
+facts; and so long as it is not favoured by those who
+wish to maintain the position of astronomy as the
+most exact of the sciences&#8212;exact in its
+facts, exact in its logic&#8212;this speculation
+must be recorded by the historian, only as he records
+the guesses of the ancient Greeks--as an interesting
+phase in the history of human thought.</p>
+
+<p>Other hypotheses, having the same end in view, are
+the meteoritic hypothesis of Lockyer and the planetesimal
+hypothesis that has been largely developed in the
+United States. These can best be read in the
+original papers to various journals, references to
+which may be found in the footnotes of Miss Clerke&#8217;s
+<i>History of Astronomy during the Nineteenth Century</i>.
+The same can be said of Bredichin&#8217;s hypothesis
+of comets&#8217; tails, Arrhenius&#8217;s book on
+the applications of the theory of light repulsion,
+the speculations on radium, the origin of the sun&#8217;s
+heat and the age of the earth, the electron hypothesis
+of terrestrial magnetism, and a host of similar speculations,
+all combining to throw an interesting light on the
+evolution of a modern train of thought that seems
+to delight in conjecture, while rebelling against that
+strict mathematical logic which has crowned astronomy
+as the queen of the sciences.</p>
+
+<p><br /><br /></p>
+
+<p><b>FOOTNOTES:</b></p>
+
+<p><a name="fn15_1">[1]</a> <i>R. S. Phil Trans</i>., 1810 and 1817-24.</p>
+
+<p><a name="fn15_2">[2]</a> One of the most valuable contributions to our
+knowledge of stellar parallaxes is the result of Gill&#8217;s
+work (<i>Cape Results</i>, vol. iii., part ii., 1900).</p>
+
+<p><a name="fn15_3">[3]</a> Taking the velocity of light at 186,000 miles
+a second, and the earth&#8217;s mean distance at 93,000,000
+miles, 1 light-year=5,865,696,000,000 miles or 63,072
+astronomical units; 1 astronomical unit a year=2.94
+miles a second; and the earth&#8217;s orbital velocity=18.5
+miles a second.</p>
+
+<p><a name="fn15_4">[4]</a> Ast. Nacht., 1889.</p>
+
+<p><a name="fn15_5">[5]</a> R. S. Phil. Trans., 1718.</p>
+
+<p><a name="fn15_6">[6]</a> Mem. Acad. des Sciences, 1738, p. 337.</p>
+
+<p><a name="fn15_7">[7]</a> R. S Phil. Trans., 1868.</p>
+
+<p><a name="fn15_8">[8]</a> <i>R.S. Phil Trans.</i>, 1783.</p>
+
+<p><a name="fn15_9">[9]</a> See Kapteyn&#8217;s address to the Royal Institution,
+1908. Also Gill&#8217;s presidential address
+to the British Association, 1907.</p>
+
+<p><a name="fn15_10">[10]</a> <i>Brit. Assoc. Rep.</i>, 1905.</p>
+
+<p><a name="fn15_11">[11]</a> R. S. Phil. Trans., 1803, 1804.</p>
+
+<p><a name="fn15_12">[12]</a> Ibid, 1824.</p>
+
+<p><a name="fn15_13">[13]</a> Connaisance des Temps, 1830.</p>
+
+<p><a name="fn15_14">[14]</a> <i>R. A. S. Mem.</i>, vol. xlvii., p. 178;
+<i>Ast. Nach.</i>, No. 3,142; Catalogue published
+by Lick Observatory, 1901.</p>
+
+<p><a name="fn15_15">[15]</a> <i>R. A. S., M. N.</i>, vol. vi.</p>
+
+<p><a name="fn15_16">[16]</a> <i>R. S. Phil. Trans.</i>, vol. lxxiii.,
+p. 484.</p>
+
+<p><a name="fn15_17">[17]</a> <i>Astr. Nach.</i>, No. 2,947.</p>
+
+<p><a name="fn15_18">[18]</a> <i>R. S. E. Trans</i>., vol. xxvii.
+In 1901 Dr. Anderson discovered Nova Persei.</p>
+
+<p><a name="fn15_19">[19]</a> <i>Astr. Nach</i>., No. 3,079.</p>
+
+<p><a name="fn15_20">[20]</a> For a different explanation see Sir W. Huggins&#8217;s
+lecture, Royal Institution, May 13th, 1892.</p>
+
+<p><a name="fn15_21">[21]</a> For the early history of the proposals for photographic
+cataloguing of stars, see the <i>Cape Photographic
+Durchmusterung</i>, 3 vols. (<i>Ann. of the Cape Observatory</i>,
+vols. in., iv., and v., Introduction.)</p>
+
+<p><a name="fn15_22">[22]</a> <i>R. S. Phil. Trans.</i>, 1850, p.
+499 <i>et seq.</i></p>
+
+<p><a name="fn15_23">[23]</a> <i>Ibid</i>, vol. cliv., p. 437.</p>
+
+<p><a name="fn15_24">[24]</a> <i>Brit. Assoc. Rep.</i>, 1868, p.
+165.</p>
+
+<p><br /><br /></p>
+
+<h1>INDEX</h1>
+
+<p>Abul Wefa, 24<br />
+Acceleration of moon&#8217;s mean motion, 60<br />
+Achromatic lens invented, 88<br />
+Adams, J. C., 61, 65, 68, 69, 70, 87, 118, 124<br />
+Airy, G. B., 13, 30, 37, 65, 69, 70, 80, 81, 114,
+119<br />
+Albetegnius, 24<br />
+Alphonso, 24<br />
+Altazimuth, 81<br />
+Anaxagoras, 14, 16<br />
+Anaximander, 14<br />
+Anaximenes, 14<br />
+Anderson, T. D., 137, 138<br />
+&#197;ngstrom, A. J., 102<br />
+Antoniadi, 113<br />
+Apian, P., 63<br />
+Apollonius, 22, 23<br />
+Arago, 111<br />
+Argelander, F. W. A., 139<br />
+Aristarchus, 18, 29<br />
+Aristillus, 17, 19<br />
+Aristotle, 16, 30, 47<br />
+Arrhenius, 146<br />
+Arzachel, 24<br />
+Asshurbanapal, 12<br />
+Asteroids, discovery of, 67, 119<br />
+Astrology, ancient and modern, 1-7, 38</p>
+
+<p>Backlund, 122<br />
+Bacon, R., 86<br />
+Bailly, 8, 65<br />
+Barnard, E. E., 115, 143<br />
+Beer and M&#228;dler, 107, 110, 111<br />
+Behaim, 74<br />
+Bessel, F.W., 65, 79, 128, 134, 139<br />
+Biela, 123<br />
+Binet, 65<br />
+Biot, 10<br />
+Bird, 79, 80<br />
+Bliss, 80<br />
+Bode, 66, 69<br />
+Bond, G. P., 99, 117, 122<br />
+Bouvard, A., 65, 68<br />
+Bradley, J., 79, 80, 81, 87, 127, 128, 139<br />
+Bredechin, 146<br />
+Bremiker, 71<br />
+Brewster, D., 52, 91, 112<br />
+Brinkley, 128<br />
+Bruno, G., 49<br />
+Burchardt, 65, 123<br />
+Burnham, S. W., 134</p>
+
+<p>Callippus, 15, 16, 31<br />
+Carrington, R. C., 97, 99, 114<br />
+Cassini, G. D., 107, 114, 115, 116, 117, 118<br />
+Cassini, J., 109, 129<br />
+Chacornac, 139<br />
+Chald&#230;an astronomy, 11-13<br />
+Challis, J., 69, 70, 71, 72<br />
+Chance, 88<br />
+Charles, II., 50, 81<br />
+Chinese astronomy, 8-11<br />
+Christie, W. M. H. (Ast. Roy.), 64, 82, 125<br />
+Chueni, 9<br />
+Clairaut, A. C., 56, 63, 65<br />
+Clark, A. G., 89, 135<br />
+Clerke, Miss, 106, 146<br />
+Comets, 120<br />
+Common, A. A., 88<br />
+Cooke, 89<br />
+Copeland, R., 142<br />
+Copernicus, N., 14, 24-31, 37, 38, 41, 42, 49, 128<br />
+Cornu, 85<br />
+Cowell, P. H., 3, 5, 64, 83<br />
+Crawford, Earl of, 84<br />
+Cromellin, A. C., 5, 64</p>
+
+<p>D&#8217;Alembert, 65<br />
+Damoiseau, 65<br />
+D&#8217;Arrest, H. L., 34<br />
+Dawes, W. R., 100, 111<br />
+Delambre, J. B. J., 8, 27, 51, 65, 68<br />
+De la Rue, W., 2, 94, 99, 100, 131<br />
+Delaunay, 65<br />
+Democritus, 16<br />
+Descartes, 51<br />
+De Sejour, 117<br />
+Deslandres, II., 101<br />
+Desvignolles, 9<br />
+De Zach, 67<br />
+Digges, L., 86<br />
+Dollond, J., 87, 90<br />
+Dominis, A. di., 86<br />
+Donati, 120<br />
+Doppler, 92, 129<br />
+Draper, 99<br />
+Dreyer, J. L. E., 29,77<br />
+Dunthorne, 60<br />
+Dyson, 131</p>
+
+<p>Eclipses, total solar, 103<br />
+Ecphantes, 16<br />
+Eddington, 131<br />
+Ellipse, 41<br />
+Empedocles, 16<br />
+Encke, J. F., 119, 122, 123, 133<br />
+Epicycles, 22<br />
+Eratosthenes, 18<br />
+Euclid, 17<br />
+Eudoxus, 15, 31<br />
+Euler, L., 60, 61, 62, 65, 88, 119</p>
+
+<p>Fabricius, D.,95, 120, 121<br />
+Feil and Mantois, 88<br />
+Fizeau, H. L., 85, 92, 99<br />
+Flamsteed, J., 50, 58, 68, 78, 79, 93<br />
+Fohi, 8<br />
+Forbes, J. D., 52, 91<br />
+Foucault, L., 85, 99<br />
+Frauenhofer, J., 88, 90, 91</p>
+
+<p>Galilei, G., 38, 46-49, 77, 93, 94, 95, 96, 107, 113,
+115, 116, 133<br />
+Galle, 71, 72<br />
+Gascoigne, W., 45, 77<br />
+Gauss, C. F., 65, 67<br />
+Gauthier, 98<br />
+Gautier, 89<br />
+Gilbert, 44<br />
+Gill, D., 84, 85, 128, 135, 139, 140<br />
+Goodricke, J., 136<br />
+Gould, B. A., 139<br />
+Grant, R., 27, 47, 51, 86, 134<br />
+Graham, 79<br />
+Greek astronomy, 8-11<br />
+Gregory, J. and D., 87<br />
+Grimaldi, 113<br />
+Groombridge, S., 139<br />
+Grubb, 88, 89<br />
+Guillemin, 122<br />
+Guinand, 88</p>
+
+<p>Hale, G. E., 101<br />
+Hall, A., 112<br />
+Hall, C. M., 88<br />
+Halley, E., 19, 51, 58, 60, 61, 62, 63, 64, 79, 120,
+122, 125, 129<br />
+Halley&#8217;s comet, 62-64<br />
+Halm, 85<br />
+Hansen, P. A., 3, 65<br />
+Hansky, A. P., 100<br />
+Harding, C. L., 67<br />
+Heliometer, 83<br />
+Heller, 120<br />
+Helmholtz, H. L. F., 35<br />
+Henderson, T., 128<br />
+Henry, P. and P., 139, 140, 143<br />
+Heraclides, 16<br />
+Heraclitus, 14<br />
+Herodotus, 13<br />
+Herschel, W., 65, 68, 97, 107, 110, 114, 115, 116,
+117, 118, 126, 127,<br />
+130, 131, 132, 141, 142<br />
+Herschel, J., 97, 111, 133, 134, 142<br />
+Herschel, A. S., 125<br />
+Hevelius, J., 178<br />
+Hind, J. R., 5, 64, 120, 121, 122<br />
+Hipparchus, 3, 18, 19, 20, 22, 23, 24, 26, 36, 55,
+60, 74, 93, 137<br />
+Hooke, R., 51, 111, 114<br />
+Horrocks, J., 50, 56<br />
+Howlett, 100<br />
+Huggins, W., 92, 93, 99, 106, 120, 129, 137, 138,
+142, 144<br />
+Humboldt and Bonpland, 124<br />
+Huyghens, C., 47, 77, 87, 110, 116, 117</p>
+
+<p>Ivory, 65</p>
+
+<p>Jansen, P. J. C., 105, 106<br />
+Jansen, Z., 86</p>
+
+<p>Kaiser, F., 111<br />
+Kapteyn, J. C., 131, 138, 139<br />
+Keeler, 117<br />
+Kepler, J., 17, 23, 26, 29, 30, 36, 37, 38-46, 48,
+49, 50, 52, 53, 63,<br />
+66, 77, 87, 93, 127, 137<br />
+Kepler&#8217;s laws, 42<br />
+Kirchoff, G.R., 91<br />
+Kirsch, 9<br />
+Knobel, E.B., 12, 13<br />
+Ko-Show-King, 76</p>
+
+<p>Lacaile, N.L., 139<br />
+Lagrange, J.L., 61, 62, 65, 119<br />
+La Hire, 114<br />
+Lalande, J.J.L., 60, 63, 65, 66, 72, 139<br />
+Lamont, J., 98<br />
+Langrenus, 107<br />
+Laplace, P.S. de, 50, 58, 61, 62, 65,66, 123, 146<br />
+Lassel, 72, 88, 117, 118<br />
+Law of universal gravitation, 53<br />
+Legendre, 65<br />
+Leonardo da Vinci, 46<br />
+Lewis, G.C., 17<br />
+Le Verrier, U.J.J., 65, 68, 70, 71,72, 110, 118, 125<br />
+Lexell, 66, 123<br />
+Light year, 128<br />
+Lipperhey, H., 86<br />
+Littrow, 121<br />
+Lockyer, J.N., 103, 105, 146<br />
+Logarithms invented, 50<br />
+Loewy, 2, 100<br />
+Long inequality of Jupiter and Saturn, 50, 62<br />
+Lowell, P., 111, 112, 118<br />
+Lubienietz, S. de, 122<br />
+Luther, M., 38<br />
+Lunar theory, 37, 50, 56, 64</p>
+
+<p>Maclaurin, 65<br />
+Maclear, T., 128<br />
+Malvasia, 77<br />
+Martin, 9<br />
+Maxwell, J. Clerk, 117<br />
+Maskelyne, N., 80, 130<br />
+McLean, F., 89<br />
+Medici, Cosmo di, 48<br />
+Melancthon, 38<br />
+Melotte, 83, 116<br />
+Meteors, 123<br />
+Meton, 15<br />
+Meyer, 57, 65<br />
+Michaelson, 85<br />
+Miraldi, 110, 114<br />
+Molyneux, 87<br />
+Moon, physical observations, 107<br />
+Mouchez, 139<br />
+Moyriac de Mailla, 8</p>
+
+<p>Napier, Lord, 50<br />
+Nasmyth and Carpenter, 108<br />
+Nebulae, 141, 146<br />
+Neison, E., 108<br />
+Neptune, discovery of, 68-72<br />
+Newall, 89<br />
+Newcomb, 85<br />
+Newton, H.A., 124<br />
+Newton, I., 5, 19, 43, 49, 51-60, 62, 64, 68, 77,
+79, 87, 90, 93, 94,<br />
+114, 127, 133<br />
+Nicetas, 16, 25<br />
+Niesten, 115<br />
+Nunez, P., 35</p>
+
+<p>Olbers, H.W.M., 67<br />
+Omar, 11, 24<br />
+Oppolzer, 13, 125<br />
+Oudemans, 129</p>
+
+<p>Palitsch, G., 64<br />
+Parallax, solar, 85, 86<br />
+Parmenides, 14<br />
+Paul III., 30<br />
+Paul V., 48<br />
+Pemberton, 51<br />
+Peters, C.A.F., 125, 128, 135<br />
+Photography, 99<br />
+Piazzi, G., 67, 128, 129, 139<br />
+Picard, 54, 77, 114<br />
+Pickering, E.C., 118, 135<br />
+Pingr&#233;, 13, 122<br />
+Plana, 65<br />
+Planets and satellites, physical observations, 109-119<br />
+Plato, 17, 23, 26, 40<br />
+Poisson, 65<br />
+Pond, J., 80<br />
+Pons, 122<br />
+Porta, B., 86<br />
+Pound, 87, 114<br />
+Pontecoulant, 64<br />
+Precession of the equinoxes, 19-21, 55, 57<br />
+Proctor, R.A., 111<br />
+Pritchett, 115<br />
+Ptolemy, 11, 13, 21, 22, 23, 24, 93<br />
+Puiseux and Loewy, 108<br />
+Pulfrich, 131<br />
+Purbach, G., 24<br />
+Pythagoras, 14, 17, 25, 29</p>
+
+<p>Ramsay, W., 106<br />
+Ransome and May, 81<br />
+Reflecting telescopes invented, 87<br />
+Regiomontanus (M&#252;ller), 24<br />
+Respighi, 82<br />
+Retrograde motion of planets, 22<br />
+Riccioli, 107<br />
+Roberts, 137<br />
+R&#246;mer, O.,78, 114<br />
+Rosse, Earl of, 88, 142<br />
+Rowland, H. A., 92, 102<br />
+Rudolph H.,37, 39<br />
+Rumker, C., 139</p>
+
+<p>Sabine, E., 98<br />
+Savary, 133<br />
+Schaeberle, J. M., 135<br />
+Schiaparelli, G. V., 110, 111, 124, 125<br />
+Scheiner, C., 87, 95, 96<br />
+Schmidt, 108<br />
+Schott, 88<br />
+Schr&#246;ter, J. H., 107, 110, 111, 124, 125<br />
+Schuster, 98<br />
+Schwabe, G. H., 97<br />
+Secchi, A., 93, 144<br />
+Short, 87<br />
+Simms, J., 81<br />
+Slipher, V. M., 119<br />
+Socrates, 17<br />
+Solon, 15<br />
+Souciet, 8<br />
+South, J., 133<br />
+Spectroscope, 89-92<br />
+Spectroheliograph, 101<br />
+Spoerer, G. F. W., 98<br />
+Spots on the sun, 84;<br />
+periodicity of, 97<br />
+Stars, Parallax, 127;<br />
+proper motion, 129;<br />
+double, 132;<br />
+binaries, 132, 135;<br />
+new, 19, 36, 137;<br />
+catalogues of, 19, 36, 139;<br />
+spectra of, 143<br />
+Stewart, B., 2, 100<br />
+Stokes, G. G., 91<br />
+Stone, E. J., 139<br />
+Struve, C. L., 130<br />
+Struve, F. G. W,, 88, 115, 128, 133</p>
+
+<p>Telescopes invented, 47, 86;<br />
+large, 88<br />
+Temple, 115, 125<br />
+Thales, 13, 16<br />
+Theon, 60<br />
+Transit circle of R&#246;mer, 78<br />
+Timocharis, 17, 19<br />
+Titius, 66<br />
+Torricelli, 113<br />
+Troughton, E., 80<br />
+Tupman, G. L., 120<br />
+Tuttle, 125<br />
+Tycho Brahe, 23, 25, 30, 33-38, 39, 40, 44, 50, 75,
+77, 93, 94, 129, 137</p>
+
+<p>Ulugh Begh, 24<br />
+Uranus, discovery of, 65</p>
+
+<p>Velocity of light, 86, 128;<br />
+of earth in orbit, 128<br />
+Verbiest, 75<br />
+Vogel, H. C., 92, 129, 135, 136<br />
+Von Asten, 122</p>
+
+<p>Walmsley, 65<br />
+Walterus, B., 24, 74<br />
+Weiss, E., 125<br />
+Wells, 122<br />
+Wesley, 104<br />
+Whewell, 112<br />
+Williams, 10<br />
+Wilson, A., 96, 100<br />
+Winnecke, 120<br />
+Witte, 86<br />
+Wollaston, 90<br />
+Wolf, M., 119, 125, 132<br />
+Wolf, R., 98<br />
+Wren, C., 51<br />
+Wyllie, A., 77</p>
+
+<p>Yao, 9<br />
+Young, C. A., 103<br />
+Yu-Chi, 8</p>
+
+<p>Zenith telescopes, 79, 82<br />
+Z&#246;llner, 92<br />
+Zucchi, 113 </p>
+
+
+
+
+
+
+
+
+<pre>
+
+
+
+
+
+End of the Project Gutenberg EBook of History of Astronomy, by George Forbes
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+The Project Gutenberg EBook of History of Astronomy, by George Forbes
+
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+*****These eBooks Were Prepared By Thousands of Volunteers!*****
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+Title: History of Astronomy
+
+Author: George Forbes
+
+Release Date: May, 2005 [EBook #8172]
+[Yes, we are more than one year ahead of schedule]
+[This file was first posted on June 25, 2003]
+
+Edition: 10
+
+Language: English
+
+Character set encoding: Unicode UTF-8
+
+*** START OF THE PROJECT GUTENBERG EBOOK HISTORY OF ASTRONOMY ***
+
+
+
+
+Produced by Jonathan Ingram, Dave Maddock, Charles Franks
+and the Online Distributed Proofreading Team.
+
+
+
+
+
+
+[Illustration: SIR ISAAC NEWTON (From the bust by Roubiliac In Trinity
+College, Cambridge.)]
+
+HISTORY OF ASTRONOMY
+
+BY
+
+GEORGE FORBES,
+M.A., F.R.S., M. INST. C. E.,
+
+(FORMERLY PROFESSOR OF NATURAL PHILOSOPHY, ANDERSON'S COLLEGE, GLASGOW)
+
+AUTHOR OF "THE TRANSIT OF VENUS," RENDU'S "THEORY OF THE GLACIERS OF
+SAVOY," ETC., ETC.
+
+
+
+
+CONTENTS
+
+  PREFACE
+
+  BOOK I. THE GEOMETRICAL PERIOD
+
+     1. PRIMITIVE ASTRONOMY AND ASTROLOGY
+
+     2. ANCIENT ASTRONOMY--CHINESE AND CHALDÆANS
+
+     3. ANCIENT GREEK ASTRONOMY
+
+     4. THE REIGN OF EPICYCLES--FROM PTOLEMY TO COPERNICUS
+
+  BOOK II. THE DYNAMICAL PERIOD
+
+     5. DISCOVERY OF THE TRUE SOLAR SYSTEM--TYCHO BRAHE--KEPLER
+
+     6. GALILEO AND THE TELESCOPE--NOTIONS OF GRAVITY BY HORROCKS, ETC.
+
+     7. SIR ISAAC NEWTON--LAW OF UNIVERSAL GRAVITATION
+
+     8. NEWTON'S SUCCESSORS--HALLEY, EULER, LAGRANGE, LAPLACE, ETC.
+
+     9. DISCOVERY OF NEW PLANETS--HERSCHEL, PIAZZI, ADAMS, AND LE
+        VERRIER
+
+  BOOK III. OBSERVATION
+
+
+    10. INSTRUMENTS OF PRECISION--SIZE OF THE SOLAR SYSTEM
+
+    11. HISTORY OF THE TELESCOPE--SPECTROSCOPE
+
+  BOOK IV. THE PHYSICAL PERIOD
+
+    12. THE SUN
+
+    13. THE MOON AND PLANETS
+
+    14. COMETS AND METEORS
+
+    15. THE STARS AND NEBULÆ
+
+  INDEX
+
+
+
+PREFACE
+
+
+An attempt has been made in these pages to trace the evolution of
+intellectual thought in the progress of astronomical discovery, and,
+by recognising the different points of view of the different ages, to
+give due credit even to the ancients. No one can expect, in a history
+of astronomy of limited size, to find a treatise on "practical" or on
+"theoretical astronomy," nor a complete "descriptive astronomy," and
+still less a book on "speculative astronomy." Something of each of
+these is essential, however, for tracing the progress of thought and
+knowledge which it is the object of this History to describe.
+
+The progress of human knowledge is measured by the increased habit of
+looking at facts from new points of view, as much as by the
+accumulation of facts. The mental capacity of one age does not seem to
+differ from that of other ages; but it is the imagination of new
+points of view that gives a wider scope to that capacity. And this is
+cumulative, and therefore progressive. Aristotle viewed the solar
+system as a geometrical problem; Kepler and Newton converted the point
+of view into a dynamical one. Aristotle's mental capacity to
+understand the meaning of facts or to criticise a train of reasoning
+may have been equal to that of Kepler or Newton, but the point of view
+was different.
+
+Then, again, new points of view are provided by the invention of new
+methods in that system of logic which we call mathematics. All that
+mathematics can do is to assure us that a statement A is equivalent to
+statements B, C, D, or is one of the facts expressed by the statements
+B, C, D; so that we may know, if B, C, and D are true, then A is true.
+To many people our inability to understand all that is contained in
+statements B, C, and D, without the cumbrous process of a mathematical
+demonstration, proves the feebleness of the human mind as a logical
+machine. For it required the new point of view imagined by Newton's
+analysis to enable people to see that, so far as planetary orbits are
+concerned, Kepler's three laws (B, C, D) were identical with Newton's
+law of gravitation (A). No one recognises more than the mathematical
+astronomer this feebleness of the human intellect, and no one is more
+conscious of the limitations of the logical process called
+mathematics, which even now has not solved directly the problem of
+only three bodies.
+
+These reflections, arising from the writing of this History, go to
+explain the invariable humility of the great mathematical astronomers.
+Newton's comparison of himself to the child on the seashore applies to
+them all. As each new discovery opens up, it may be, boundless oceans
+for investigation, for wonder, and for admiration, the great
+astronomers, refusing to accept mere hypotheses as true, have founded
+upon these discoveries a science as exact in its observation of facts
+as in theories. So it is that these men, who have built up the most
+sure and most solid of all the sciences, refuse to invite others to
+join them in vain speculation. The writer has, therefore, in this
+short History, tried to follow that great master, Airy, whose pupil he
+was, and the key to whose character was exactness and accuracy; and he
+recognises that Science is impotent except in her own limited sphere.
+
+It has been necessary to curtail many parts of the History in the
+attempt--perhaps a hopeless one--to lay before the reader in a limited
+space enough about each age to illustrate its tone and spirit, the
+ideals of the workers, the gradual addition of new points of view and
+of new means of investigation.
+
+It would, indeed, be a pleasure to entertain the hope that these pages
+might, among new recruits, arouse an interest in the greatest of all
+the sciences, or that those who have handled the theoretical or
+practical side might be led by them to read in the original some of
+the classics of astronomy. Many students have much compassion for the
+schoolboy of to-day, who is not allowed the luxury of learning the art
+of reasoning from him who still remains pre-eminently its greatest
+exponent, Euclid. These students pity also the man of to-morrow, who
+is not to be allowed to read, in the original Latin of the brilliant
+Kepler, how he was able--by observations taken from a moving platform,
+the earth, of the directions of a moving object, Mars--to deduce the
+exact shape of the path of each of these planets, and their actual
+positions on these paths at any time. Kepler's masterpiece is one of
+the most interesting books that was ever written, combining wit,
+imagination, ingenuity, and certainty.
+
+Lastly, it must be noted that, as a History of England cannot deal
+with the present Parliament, so also the unfinished researches and
+untested hypotheses of many well-known astronomers of to-day cannot be
+included among the records of the History of Astronomy. The writer
+regrets the necessity that thus arises of leaving without mention the
+names of many who are now making history in astronomical work.
+
+G. F.
+_August 1st, 1909._
+
+
+
+
+BOOK I.  THE GEOMETRICAL PERIOD
+
+
+
+1. PRIMITIVE ASTRONOMY AND ASTROLOGY.
+
+
+The growth of intelligence in the human race has its counterpart in
+that of the individual, especially in the earliest stages.
+Intellectual activity and the development of reasoning powers are in
+both cases based upon the accumulation of experiences, and on the
+comparison, classification, arrangement, and nomenclature of these
+experiences. During the infancy of each the succession of events can
+be watched, but there can be no _à priori_ anticipations.
+Experience alone, in both cases, leads to the idea of cause and effect
+as a principle that seems to dominate our present universe, as a rule
+for predicting the course of events, and as a guide to the choice of a
+course of action. This idea of cause and effect is the most potent
+factor in developing the history of the human race, as of the
+individual.
+
+In no realm of nature is the principle of cause and effect more
+conspicuous than in astronomy; and we fall into the habit of thinking
+of its laws as not only being unchangeable in our universe, but
+necessary to the conception of any universe that might have been
+substituted in its place. The first inhabitants of the world were
+compelled to accommodate their acts to the daily and annual
+alternations of light and darkness and of heat and cold, as much as to
+the irregular changes of weather, attacks of disease, and the fortune
+of war.  They soon came to regard the influence of the sun, in
+connection with light and heat, as a cause. This led to a search for
+other signs in the heavens. If the appearance of a comet was sometimes
+noted simultaneously with the death of a great ruler, or an eclipse
+with a scourge of plague, these might well be looked upon as causes in
+the same sense that the veering or backing of the wind is regarded as
+a cause of fine or foul weather.
+
+For these reasons we find that the earnest men of all ages have
+recorded the occurrence of comets, eclipses, new stars, meteor
+showers, and remarkable conjunctions of the planets, as well as
+plagues and famines, floods and droughts, wars and the deaths of great
+rulers. Sometimes they thought they could trace connections which
+might lead them to say that a comet presaged famine, or an eclipse
+war.
+
+Even if these men were sometimes led to evolve laws of cause and
+effect which now seem to us absurd, let us be tolerant, and gratefully
+acknowledge that these astrologers, when they suggested such "working
+hypotheses," were laying the foundations of observation and deduction.
+
+If the ancient Chaldæans gave to the planetary conjunctions an
+influence over terrestrial events, let us remember that in our own
+time people have searched for connection between terrestrial
+conditions and periods of unusual prevalence of sun spots; while De la
+Rue, Loewy, and Balfour Stewart[1] thought they found a connection
+between sun-spot displays and the planetary positions. Thus we find
+scientific men, even in our own time, responsible for the belief that
+storms in the Indian Ocean, the fertility of German vines, famines in
+India, and high or low Nile-floods in Egypt follow the planetary
+positions.
+
+And, again, the desire to foretell the weather is so laudable that we
+cannot blame the ancient Greeks for announcing the influence of the
+moon with as much confidence as it is affirmed in Lord Wolseley's
+_Soldier's Pocket Book_.
+
+Even if the scientific spirit of observation and deduction (astronomy)
+has sometimes led to erroneous systems for predicting terrestrial
+events (astrology), we owe to the old astronomer and astrologer alike
+the deepest gratitude for their diligence in recording astronomical
+events. For, out of the scanty records which have survived the
+destructive acts of fire and flood, of monarchs and mobs, we have
+found much that has helped to a fuller knowledge of the heavenly
+motions than was possible without these records.
+
+So Hipparchus, about 150 B.C., and Ptolemy a little later, were able
+to use the observations of Chaldæan astrologers, as well as those of
+Alexandrian astronomers, and to make some discoveries which have
+helped the progress of astronomy in all ages.  So, also, Mr. Cowell[2]
+has examined the marks made on the baked bricks used by the Chaldæans
+for recording the eclipses of 1062 B.C. and 762 B.C.; and has thereby
+been enabled, in the last few years, to correct the lunar tables of
+Hansen, and to find a more accurate value for the secular acceleration
+of the moon's longitude and the node of her orbit than any that could
+be obtained from modern observations made with instruments of the
+highest precision.
+
+So again, Mr. Hind [3] was enabled to trace back the period during
+which Halley's comet has been a member of the solar system, and to
+identify it in the Chinese observations of comets as far back as 12
+B.C. Cowell and Cromellin extended the date to 240 B.C. In the same
+way the comet 1861.i. has been traced back in the Chinese records to
+617 A.D. [4]
+
+The theoretical views founded on Newton's great law of universal
+gravitation led to the conclusion that the inclination of the earth's
+equator to the plane of her orbit (the obliquity of the ecliptic) has
+been diminishing slowly since prehistoric times; and this fact has
+been confirmed by Egyptian and Chinese observations on the length of
+the shadow of a vertical pillar, made thousands of years before the
+Christian era, in summer and winter.
+
+There are other reasons why we must be tolerant of the crude notions
+of the ancients. The historian, wishing to give credit wherever it may
+be due, is met by two difficulties. Firstly, only a few records of
+very ancient astronomy are extant, and the authenticity of many of
+these is open to doubt. Secondly, it is very difficult to divest
+ourselves of present knowledge, and to appreciate the originality of
+thought required to make the first beginnings.
+
+With regard to the first point, we are generally dependent upon
+histories written long after the events.  The astronomy of Egyptians,
+Babylonians, and Assyrians is known to us mainly through the Greek
+historians, and for information about the Chinese we rely upon the
+researches of travellers and missionaries in comparatively recent
+times. The testimony of the Greek writers has fortunately been
+confirmed, and we now have in addition a mass of facts translated from
+the original sculptures, papyri, and inscribed bricks, dating back
+thousands of years.
+
+In attempting to appraise the efforts of the beginners we must
+remember that it was natural to look upon the earth (as all the first
+astronomers did) as a circular plane, surrounded and bounded by the
+heaven, which was a solid vault, or hemisphere, with its concavity
+turned downwards. The stars seemed to be fixed on this vault; the
+moon, and later the planets, were seen to crawl over it. It was a
+great step to look on the vault as a hollow sphere carrying the sun
+too. It must have been difficult to believe that at midday the stars
+are shining as brightly in the blue sky as they do at night. It must
+have been difficult to explain how the sun, having set in the west,
+could get back to rise in the east without being seen _if_ it was
+always the same sun. It was a great step to suppose the earth to be
+spherical, and to ascribe the diurnal motions to its rotation.
+Probably the greatest step ever made in astronomical theory was the
+placing of the sun, moon, and planets at different distances from the
+earth instead of having them stuck on the vault of heaven. It was a
+transition from "flatland" to a space of three dimensions.
+
+Great progress was made when systematic observations began, such as
+following the motion of the moon and planets among the stars, and the
+inferred motion of the sun among the stars, by observing their
+_heliacal risings_--i.e., the times of year when a star
+would first be seen to rise at sunrise, and when it could last be seen
+to rise at sunset. The grouping of the stars into constellations and
+recording their places was a useful observation. The theoretical
+prediction of eclipses of the sun and moon, and of the motions of the
+planets among the stars, became later the highest goal in astronomy.
+
+To not one of the above important steps in the progress of astronomy
+can we assign the author with certainty. Probably many of them were
+independently taken by Chinese, Indian, Persian, Tartar, Egyptian,
+Babylonian, Assyrian, Phoenician, and Greek astronomers.  And we have
+not a particle of information about the discoveries, which may have
+been great, by other peoples--by the Druids, the Mexicans, and the
+Peruvians, for example.
+
+We do know this, that all nations required to have a calendar. The
+solar year, the lunar month, and the day were the units, and it is
+owing to their incommensurability that we find so many calendars
+proposed and in use at different times. The only object to be attained
+by comparing the chronologies of ancient races is to fix the actual
+dates of observations recorded, and this is not a part of a history of
+astronomy.
+
+In conclusion, let us bear in mind the limited point of view of the
+ancients when we try to estimate their merit. Let us remember that the
+first astronomy was of two dimensions; the second astronomy was of
+three dimensions, but still purely geometrical. Since Kepler's day we
+have had a dynamical astronomy.
+
+
+FOOTNOTES:
+
+[1] Trans. R. S. E., xxiii. 1864, p. 499, _On Sun Spots_, etc., by
+B. Stewart. Also Trans. R. S. 1860-70. Also Prof. Ernest Brown, in
+_R. A. S. Monthly Notices_, 1900.
+
+[2] _R. A. S. Monthly Notices_, Sup.; 1905.
+
+[Illustration: CHALDÆAN BAKED BRICK OR TABLET, _Obverse and reverse
+sides_, Containing record of solar eclipse, 1062 B.C., used lately by
+Cowell for rendering the lunar theory more accurate than was possible
+by finest modern observations. (British Museum collection,
+No. 35908.)]
+
+[3] _R. A. S. Monthly Notices_, vol. x., p. 65.
+
+[4] R. S. E. Proc., vol. x., 1880.
+
+
+
+2. ANCIENT ASTRONOMY--THE CHINESE AND CHALDÆANS.
+
+
+The last section must have made clear the difficulties the way of
+assigning to the ancient nations their proper place in the development
+of primitive notions about astronomy. The fact that some alleged
+observations date back to a period before the Chinese had invented the
+art of writing leads immediately to the question how far tradition can
+be trusted.
+
+Our first detailed knowledge was gathered in the far East by
+travellers, and by the Jesuit priests, and was published in the
+eighteenth century. The Asiatic Society of Bengal contributed
+translations of Brahmin literature. The two principal sources of
+knowledge about Chinese astronomy were supplied, first by Father
+Souciet, who in 1729 published _Observations Astronomical,
+Geographical, Chronological, and Physical_, drawn from ancient
+Chinese books; and later by Father Moyriac-de-Mailla, who in 1777-1785
+published _Annals of the Chinese Empire, translated from
+Tong-Kien-Kang-Mou_.
+
+Bailly, in his _Astronomie Ancienne_ (1781), drew, from these and
+other sources, the conclusion that all we know of the astronomical
+learning of the Chinese, Indians, Chaldæans, Assyrians, and Egyptians
+is but the remnant of a far more complete astronomy of which no trace
+can be found.
+
+Delambre, in his _Histoire de l'Astronomie Ancienne_ (1817),
+ridicules the opinion of Bailly, and considers that the progress made
+by all of these nations is insignificant.
+
+It will be well now to give an idea of some of the astronomy of the
+ancients not yet entirely discredited.  China and Babylon may be taken
+as typical examples.
+
+_China_.--It would appear that Fohi, the first emperor, reigned
+about 2952 B.C., and shortly afterwards Yu-Chi made a sphere to
+represent the motions of the celestial bodies. It is also mentioned,
+in the book called Chu-King, supposed to have been written in 2205
+B.C., that a similar sphere was made in the time of Yao (2357
+B.C.).[1] It is said that the Emperor Chueni (2513 B.C.) saw five
+planets in conjunction the same day that the sun and moon were in
+conjunction. This is discussed by Father Martin (MSS. of De Lisle);
+also by M. Desvignolles (Mem. Acad. Berlin, vol. iii., p. 193), and by
+M. Kirsch (ditto, vol. v., p. 19), who both found that Mars, Jupiter,
+Saturn, and Mercury were all between the eleventh and eighteenth
+degrees of Pisces, all visible together in the evening on February
+28th 2446 B.C., while on the same day the sun and moon were in
+conjunction at 9 a.m., and that on March 1st the moon was in
+conjunction with the other four planets. But this needs confirmation.
+
+Yao, referred to above, gave instructions to his astronomers to
+determine the positions of the solstices and equinoxes, and they
+reported the names of the stars in the places occupied by the sun at
+these seasons, and in 2285 B.C. he gave them further orders. If this
+account be true, it shows a knowledge that the vault of heaven is a
+complete sphere, and that stars are shining at mid-day, although
+eclipsed by the sun's brightness.
+
+It is also asserted, in the book called _Chu-King_, that in the
+time of Yao the year was known to have 365¼ days, and that he
+adopted 365 days and added an intercalary day every four years (as in
+the Julian Calendar). This may be true or not, but the ancient Chinese
+certainly seem to have divided the circle into 365 degrees. To learn
+the length of the year needed only patient observation--a
+characteristic of the Chinese; but many younger nations got into a
+terrible mess with their calendar from ignorance of the year's length.
+
+It is stated that in 2159 B.C. the royal astronomers Hi and Ho failed
+to predict an eclipse. It probably created great terror, for they were
+executed in punishment for their neglect. If this account be true, it
+means that in the twenty-second century B.C. some rule for calculating
+eclipses was in use. Here, again, patient observation would easily
+lead to the detection of the eighteen-year cycle known to the
+Chaldeans as the _Saros_. It consists of 235 lunations, and in
+that time the pole of the moon's orbit revolves just once round the
+pole of the ecliptic, and for this reason the eclipses in one cycle
+are repeated with very slight modification in the next cycle, and so
+on for many centuries.
+
+It may be that the neglect of their duties by Hi and Ho, and their
+punishment, influenced Chinese astronomy; or that the succeeding
+records have not been available to later scholars; but the fact
+remains that--although at long intervals observations were made of
+eclipses, comets, and falling stars, and of the position of the
+solstices, and of the obliquity of the ecliptic--records become rare,
+until 776 B.C., when eclipses began to be recorded once more with some
+approach to continuity. Shortly afterwards notices of comets were
+added. Biot gave a list of these, and Mr. John Williams, in 1871,
+published _Observations of Comets from 611 B.C. to 1640 A.D.,
+Extracted from the Chinese Annals_.
+
+With regard to those centuries concerning which we have no
+astronomical Chinese records, it is fair to state that it is recorded
+that some centuries before the Christian era, in the reign of
+Tsin-Chi-Hoang, all the classical and scientific books that could be
+found were ordered to be destroyed. If true, our loss therefrom is as
+great as from the burning of the Alexandrian library by the Caliph
+Omar. He burnt all the books because he held that they must be either
+consistent or inconsistent with the Koran, and in the one case they
+were superfluous, in the other case objectionable.
+
+_Chaldæans_.--Until the last half century historians were
+accustomed to look back upon the Greeks, who led the world from the
+fifth to the third century B.C., as the pioneers of art, literature,
+and science. But the excavations and researches of later years make us
+more ready to grant that in science as in art the Greeks only
+developed what they derived from the Egyptians, Babylonians, and
+Assyrians. The Greek historians said as much, in fact; and modern
+commentators used to attribute the assertion to undue modesty. Since,
+however, the records of the libraries have been unearthed it has been
+recognised that the Babylonians were in no way inferior in the matter
+of original scientific investigation to other races of the same era.
+
+The Chaldæans, being the most ancient Babylonians, held the same
+station and dignity in the State as did the priests in Egypt, and
+spent all their time in the study of philosophy and astronomy, and the
+arts of divination and astrology. They held that the world of which we
+have a conception is an eternal world without any beginning or ending,
+in which all things are ordered by rules supported by a divine
+providence, and that the heavenly bodies do not move by chance, nor by
+their own will, but by the determinate will and appointment of the
+gods. They recorded these movements, but mainly in the hope of tracing
+the will of the gods in mundane affairs. Ptolemy (about 130 A.D.)
+made use of Babylonian eclipses in the eighth century B.C. for
+improving his solar and lunar tables.
+
+Fragments of a library at Agade have been preserved at Nineveh, from
+which we learn that the star-charts were even then divided into
+constellations, which were known by the names which they bear to this
+day, and that the signs of the zodiac were used for determining the
+courses of the sun, moon, and of the five planets Mercury, Venus,
+Mars, Jupiter, and Saturn.
+
+We have records of observations carried on under Asshurbanapal, who
+sent astronomers to different parts to study celestial phenomena. Here
+is one:--
+
+To the Director of Observations,--My Lord, his humble servant
+Nabushum-iddin, Great Astronomer of Nineveh, writes thus: "May Nabu
+and Marduk be propitious to the Director of these Observations, my
+Lord. The fifteenth day we observed the Node of the moon, and the moon
+was eclipsed."
+
+The Phoenicians are supposed to have used the stars for navigation,
+but there are no records. The Egyptian priests tried to keep such
+astronomical knowledge as they possessed to themselves. It is probable
+that they had arbitrary rules for predicting eclipses. All that was
+known to the Greeks about Egyptian science is to be found in the
+writings of Diodorus Siculus. But confirmatory and more authentic
+facts have been derived from late explorations. Thus we learn from
+E. B. Knobel[2] about the Jewish calendar dates, on records of land
+sales in Aramaic papyri at Assuan, translated by Professor A. H. Sayce
+and A. E. Cowley, (1) that the lunar cycle of nineteen years was used
+by the Jews in the fifth century B.C. [the present reformed Jewish
+calendar dating from the fourth century A.D.], a date a "little more
+than a century after the grandfathers and great-grandfathers of those
+whose business is recorded had fled into Egypt with Jeremiah" (Sayce);
+and (2) that the order of intercalation at that time was not
+dissimilar to that in use at the present day.
+
+Then again, Knobel reminds us of "the most interesting discovery a few
+years ago by Father Strassmeier of a Babylonian tablet recording a
+partial lunar eclipse at Babylon in the seventh year of Cambyses, on
+the fourteenth day of the Jewish month Tammuz."  Ptolemy, in the
+Almagest (Suntaxis), says it occurred in the seventh year of Cambyses,
+on the night of the seventeenth and eighteenth of the Egyptian month
+Phamenoth.  Pingré and Oppolzer fix the date July 16th, 533 B.C. Thus
+are the relations of the chronologies of Jews and Egyptians
+established by these explorations.
+
+
+FOOTNOTES:
+
+[1] These ancient dates are uncertain.
+
+[2] _R. A. S. Monthly Notices_, vol. lxviii., No. 5, March, 1908.
+
+
+
+3. ANCIENT GREEK ASTRONOMY.
+
+
+We have our information about the earliest Greek astronomy from
+Herodotus (born 480 B.C.). He put the traditions into writing. Thales
+(639-546 B.C.) is said to have predicted an eclipse, which caused much
+alarm, and ended the battle between the Medes and Lydians. Airy fixed
+the date May 28th, 585 B.C. But other modern astronomers give
+different dates. Thales went to Egypt to study science, and learnt
+from its priests the length of the year (which was kept a profound
+secret!), and the signs of the zodiac, and the positions of the
+solstices. He held that the sun, moon, and stars are not mere spots on
+the heavenly vault, but solids; that the moon derives her light from
+the sun, and that this fact explains her phases; that an eclipse of
+the moon happens when the earth cuts off the sun's light from her. He
+supposed the earth to be flat, and to float upon water. He determined
+the ratio of the sun's diameter to its orbit, and apparently made out
+the diameter correctly as half a degree. He left nothing in writing.
+
+His successors, Anaximander (610-547 B.C.) and Anaximenes (550-475
+B.C.), held absurd notions about the sun, moon, and stars, while
+Heraclitus (540-500 B.C.)  supposed that the stars were lighted each
+night like lamps, and the sun each morning. Parmenides supposed the
+earth to be a sphere.
+
+Pythagoras (569-470 B.C.) visited Egypt to study science. He deduced
+his system, in which the earth revolves in an orbit, from fantastic
+first principles, of which the following are examples: "The circular
+motion is the most perfect motion," "Fire is more worthy than earth,"
+"Ten is the perfect number." He wrote nothing, but is supposed to have
+said that the earth, moon, five planets, and fixed stars all revolve
+round the sun, which itself revolves round an imaginary central fire
+called the Antichthon. Copernicus in the sixteenth century claimed
+Pythagoras as the founder of the system which he, Copernicus, revived.
+
+Anaxagoras (born 499 B.C.) studied astronomy in Egypt. He explained
+the return of the sun to the east each morning by its going under the
+flat earth in the night. He held that in a solar eclipse the moon
+hides the sun, and in a lunar eclipse the moon enters the earth's
+shadow--both excellent opinions. But he entertained absurd ideas of
+the vortical motion of the heavens whisking stones into the sky, there
+to be ignited by the fiery firmament to form stars. He was prosecuted
+for this unsettling opinion, and for maintaining that the moon is an
+inhabited earth. He was defended by Pericles (432 B.C.).
+
+Solon dabbled, like many others, in reforms of the calendar. The
+common year of the Greeks originally had 360 days--twelve months of
+thirty days. Solon's year was 354 days. It is obvious that these
+erroneous years would, before long, remove the summer to January and
+the winter to July. To prevent this it was customary at regular
+intervals to intercalate days or months. Meton (432 B.C.) introduced a
+reform based on the nineteen-year cycle. This is not the same as the
+Egyptian and Chaldean eclipse cycle called _Saros_ of 223
+lunations, or a little over eighteen years.  The Metonic cycle is 235
+lunations or nineteen years, after which period the sun and moon
+occupy the same position relative to the stars. It is still used for
+fixing the date of Easter, the number of the year in Melon's cycle
+being the golden number of our prayer-books.  Melon's system divided
+the 235 lunations into months of thirty days and omitted every
+sixty-third day. Of the nineteen years, twelve had twelve months and
+seven had thirteen months.
+
+Callippus (330 B.C.) used a cycle four times as long, 940 lunations,
+but one day short of Melon's seventy-six years. This was more correct.
+
+Eudoxus (406-350 B.C.) is said to have travelled with Plato in
+Egypt. He made astronomical observations in Asia Minor, Sicily, and
+Italy, and described the starry heavens divided into constellations.
+His name is connected with a planetary theory which as generally
+stated sounds most fanciful. He imagined the fixed stars to be on a
+vault of heaven; and the sun, moon, and planets to be upon similar
+vaults or spheres, twenty-six revolving spheres in all, the motion of
+each planet being resolved into its components, and a separate sphere
+being assigned for each component motion. Callippus (330 B.C.)
+increased the number to thirty-three. It is now generally accepted
+that the real existence of these spheres was not suggested, but the
+idea was only a mathematical conception to facilitate the construction
+of tables for predicting the places of the heavenly bodies.
+
+Aristotle (384-322 B.C.) summed up the state of astronomical knowledge
+in his time, and held the earth to be fixed in the centre of the
+world.
+
+Nicetas, Heraclides, and Ecphantes supposed the earth to revolve on
+its axis, but to have no orbital motion.
+
+The short epitome so far given illustrates the extraordinary deductive
+methods adopted by the ancient Greeks. But they went much farther in
+the same direction. They seem to have been in great difficulty to
+explain how the earth is supported, just as were those who invented
+the myth of Atlas, or the Indians with the tortoise. Thales thought
+that the flat earth floated on water. Anaxagoras thought that, being
+flat, it would be buoyed up and supported on the air like a kite.
+Democritus thought it remained fixed, like the donkey between two
+bundles of hay, because it was equidistant from all parts of the
+containing sphere, and there was no reason why it should incline one
+way rather than another. Empedocles attributed its state of rest to
+centrifugal force by the rapid circular movement of the heavens, as
+water is stationary in a pail when whirled round by a string.
+Democritus further supposed that the inclination of the flat earth to
+the ecliptic was due to the greater weight of the southern parts owing
+to the exuberant vegetation.
+
+For further references to similar efforts of imagination the reader is
+referred to Sir George Cornwall Lewis's _Historical Survey of the
+Astronomy of the Ancients_; London, 1862. His list of authorities
+is very complete, but some of his conclusions are doubtful.  At p. 113
+of that work he records the real opinions of Socrates as set forth by
+Xenophon; and the reader will, perhaps, sympathise with Socrates in
+his views on contemporary astronomy:--
+
+With regard to astronomy he [Socrates] considered a knowledge of it
+desirable to the extent of determining the day of the year or month,
+and the hour of the night, ... but as to learning the courses of the
+stars, to be occupied with the planets, and to inquire about their
+distances from the earth, and their orbits, and the causes of their
+motions, he strongly objected to such a waste of valuable time. He
+dwelt on the contradictions and conflicting opinions of the physical
+philosophers, ... and, in fine, he held that the speculators on the
+universe and on the laws of the heavenly bodies were no better than
+madmen (_Xen_.  _Mem_, i. 1, 11-15).
+
+Plato (born 429 B.C.), the pupil of Socrates, the fellow-student of
+Euclid, and a follower of Pythagoras, studied science in his travels
+in Egypt and elsewhere.  He was held in so great reverence by all
+learned men that a problem which he set to the astronomers was the
+keynote to all astronomical investigation from this date till the time
+of Kepler in the sixteenth century. He proposed to astronomers _the
+problem of representing the courses of the planets by circular and
+uniform motions_.
+
+Systematic observation among the Greeks began with the rise of the
+Alexandrian school. Aristillus and Timocharis set up instruments and
+fixed the positions of the zodiacal stars, near to which all the
+planets in their orbits pass, thus facilitating the determination of
+planetary motions. Aristarchus (320-250 B.C.) showed that the sun must
+be at least nineteen times as far off as the moon, which is far short
+of the mark. He also found the sun's diameter, correctly, to be half a
+degree.  Eratosthenes (276-196 B.C.) measured the inclination to the
+equator of the sun's apparent path in the heavens--i.e., he
+measured the obliquity of the ecliptic, making it 23° 51', confirming
+our knowledge of its continuous diminution during historical times. He
+measured an arc of meridian, from Alexandria to Syene (Assuan), and
+found the difference of latitude by the length of a shadow at noon,
+summer solstice. He deduced the diameter of the earth, 250,000
+stadia. Unfortunately, we do not know the length of the stadium he
+used.
+
+Hipparchus (190-120 B.C.) may be regarded as the founder of
+observational astronomy. He measured the obliquity of the ecliptic,
+and agreed with Eratosthenes.  He altered the length of the tropical
+year from 365 days, 6 hours to 365 days, 5 hours, 53 minutes--still
+four minutes too much. He measured the equation of time and the
+irregular motion of the sun; and allowed for this in his calculations
+by supposing that the centre, about which the sun moves uniformly, is
+situated a little distance from the fixed earth. He called this point
+the _excentric_. The line from the earth to the "excentric" was
+called the _line of apses_. A circle having this centre was
+called the _equant_, and he supposed that a radius drawn to the
+sun from the excentric passes over equal arcs on the equant in equal
+times. He then computed tables for predicting the place of the sun.
+
+He proceeded in the same way to compute Lunar tables. Making use of
+Chaldæan eclipses, he was able to get an accurate value of the moon's
+mean motion.  [Halley, in 1693, compared this value with his own
+measurements, and so discovered the acceleration of the moon's mean
+motion. This was conclusively established, but could not be explained
+by the Newtonian theory for quite a long time.] He determined the
+plane of the moon's orbit and its inclination to the ecliptic. The
+motion of this plane round the pole of the ecliptic once in eighteen
+years complicated the problem. He located the moon's excentric as he
+had done the sun's.  He also discovered some of the minor
+irregularities of the moon's motion, due, as Newton's theory proves,
+to the disturbing action of the sun's attraction.
+
+In the year 134 B.C. Hipparchus observed a new star.  This upset every
+notion about the permanence of the fixed stars. He then set to work to
+catalogue all the principal stars so as to know if any others appeared
+or disappeared. Here his experiences resembled those of several later
+astronomers, who, when in search of some special object, have been
+rewarded by a discovery in a totally different direction. On comparing
+his star positions with those of Timocharis and Aristillus he found no
+stars that had appeared or disappeared in the interval of 150 years;
+but he found that all the stars seemed to have changed their places
+with reference to that point in the heavens where the ecliptic is 90°
+from the poles of the earth--i.e., the equinox. He found that this
+could be explained by a motion of the equinox in the direction of the
+apparent diurnal motion of the stars. This discovery of _precession of
+the equinoxes_, which takes place at the rate of 52".1 every year, was
+necessary for the progress of accurate astronomical observations. It
+is due to a steady revolution of the earth's pole round the pole of
+the ecliptic once in 26,000 years in the opposite direction to the
+planetary revolutions.
+
+Hipparchus was also the inventor of trigonometry, both plane and
+spherical. He explained the method of using eclipses for determining
+the longitude.
+
+In connection with Hipparchus' great discovery it may be mentioned
+that modern astronomers have often attempted to fix dates in history
+by the effects of precession of the equinoxes. (1) At about the date
+when the Great Pyramid may have been built γDraconis was near to the
+pole, and must have been used as the pole-star. In the north face of
+the Great Pyramid is the entrance to an inclined passage, and six of
+the nine pyramids at Gizeh possess the same feature; all the passages
+being inclined at an angle between 26° and 27° to the horizon and in
+the plane of the meridian. It also appears that 4,000 years
+ago--i.e., about 2100 B.C.--an observer at the lower end of the
+passage would be able to see γDraconis, the then pole-star, at its
+lower culmination.[1] It has been suggested that the passage was made
+for this purpose. On other grounds the date assigned to the Great
+Pyramid is 2123 B.C.
+
+(2) The Chaldæans gave names to constellations now invisible from
+Babylon which would have been visible in 2000 B.C., at which date it
+is claimed that these people were studying astronomy.
+
+(3) In the Odyssey, Calypso directs Odysseus, in accordance with
+Phoenician rules for navigating the Mediterranean, to keep the Great
+Bear "ever on the left as he traversed the deep" when sailing from the
+pillars of Hercules (Gibraltar) to Corfu. Yet such a course taken now
+would land the traveller in Africa.  Odysseus is said in his voyage in
+springtime to have seen the Pleiades and Arcturus setting late, which
+seemed to early commentators a proof of Homer's inaccuracy.  Likewise
+Homer, both in the _Odyssey_ [2] (v. 272-5) and in the _Iliad_
+(xviii. 489), asserts that the Great Bear never set in those
+latitudes. Now it has been found that the precession of the equinoxes
+explains all these puzzles; shows that in springtime on the
+Mediterranean the Bear was just above the horizon, near the sea but
+not touching it, between 750 B.C. and 1000 B.C.; and fixes the date of
+the poems, thus confirming other evidence, and establishing Homer's
+character for accuracy. [3]
+
+(4) The orientation of Egyptian temples and Druidical stones is such
+that possibly they were so placed as to assist in the observation of
+the heliacal risings [4] of certain stars. If the star were known,
+this would give an approximate date. Up to the present the results of
+these investigations are far from being conclusive.
+
+Ptolemy (130 A.D.) wrote the Suntaxis, or Almagest, which includes a
+cyclopedia of astronomy, containing a summary of knowledge at that
+date. We have no evidence beyond his own statement that he was a
+practical observer. He theorised on the planetary motions, and held
+that the earth is fixed in the centre of the universe. He adopted the
+excentric and equant of Hipparchus to explain the unequal motions of
+the sun and moon. He adopted the epicycles and deferents which had
+been used by Apollonius and others to explain the retrograde motions
+of the planets. We, who know that the earth revolves round the sun
+once in a year, can understand that the apparent motion of a planet is
+only its motion relative to the earth. If, then, we suppose the earth
+fixed and the sun to revolve round it once a year, and the planets
+each in its own period, it is only necessary to impose upon each of
+these an additional _annual_ motion to enable us to represent truly
+the apparent motions. This way of looking at the apparent motions
+shows why each planet, when nearest to the earth, seems to move for a
+time in a retrograde direction. The attempts of Ptolemy and others of
+his time to explain the retrograde motion in this way were only
+approximate. Let us suppose each planet to have a bar with one end
+centred at the earth.  If at the other end of the bar one end of a
+shorter bar is pivotted, having the planet at its other end, then the
+planet is given an annual motion in the secondary circle (the
+epicycle), whose centre revolves round the earth on the primary circle
+(the _deferent_), at a uniform rate round the excentric. Ptolemy
+supposed the centres of the epicycles of Mercury and Venus to be on a
+bar passing through the sun, and to be between the earth and the
+sun. The centres of the epicycles of Mars, Jupiter, and Saturn were
+supposed to be further away than the sun.  Mercury and Venus were
+supposed to revolve in their epicycles in their own periodic times and
+in the deferent round the earth in a year. The major planets were
+supposed to revolve in the deferent round the earth in their own
+periodic times, and in their epicycles once in a year.
+
+It did not occur to Ptolemy to place the centres of the epicycles of
+Mercury and Venus at the sun, and to extend the same system to the
+major planets. Something of this sort had been proposed by the
+Egyptians (we are told by Cicero and others), and was accepted by
+Tycho Brahe; and was as true a representation of the relative motions
+in the solar system as when we suppose the sun to be fixed and the
+earth to revolve.
+
+The cumbrous system advocated by Ptolemy answered its purpose,
+enabling him to predict astronomical events approximately. He improved
+the lunar theory considerably, and discovered minor inequalities which
+could be allowed for by the addition of new epicycles.  We may look
+upon these epicycles of Apollonius, and the excentric of Hipparchus,
+as the responses of these astronomers to the demand of Plato for
+uniform circular motions. Their use became more and more confirmed,
+until the seventeenth century, when the accurate observations of Tycho
+Brahe enabled Kepler to abolish these purely geometrical makeshifts,
+and to substitute a system in which the sun became physically its
+controller.
+
+
+FOOTNOTES:
+
+[1] _Phil. Mag_., vol. xxiv., pp. 481-4.
+
+[2]
+
+Πληιάδας τʽ ἐσορω̑ντε καὶ ὀψὲ δύοντα βοώτην
+ʼΆρκτον θ̕, ἣν καὶ ἅμαξαν ἐπίκλησιν καλέουσιν,
+ʽΉ τ̕ αὐτου̑ στρέφεται καὶ τ̕ ʼΩρίωνα δοκεύει,
+Οἴη δ̕ἄμμορος ἐστι λοετρων ʽΩκεανοι̑ο.
+
+"The Pleiades and Boötes that setteth late, and the Bear,
+which they likewise call the Wain, which turneth ever in one
+place, and keepeth watch upon Orion, and alone hath no part in
+the baths of the ocean."
+
+[3] See Pearson in the Camb. Phil. Soc. Proc., vol. iv., pt. ii., p.
+93, on whose authority the above statements are made.
+
+[4] See p. 6 for definition.
+
+
+
+4. THE REIGN OF EPICYCLES--FROM PTOLEMY TO COPERNICUS.
+
+
+After Ptolemy had published his book there seemed to be nothing more
+to do for the solar system except to go on observing and finding more
+and more accurate values for the constants involved--viz., the periods
+of revolution, the diameter of the deferent,[1] and its ratio to that
+of the epicycle,[2] the distance of the excentric[3] from the centre
+of the deferent, and the position of the line of apses,[4] besides the
+inclination and position of the plane of the planet's orbit. The only
+object ever aimed at in those days was to prepare tables for
+predicting the places of the planets. It was not a mechanical problem;
+there was no notion of a governing law of forces.
+
+From this time onwards all interest in astronomy seemed, in Europe at
+least, to sink to a low ebb.  When the Caliph Omar, in the middle of
+the seventh century, burnt the library of Alexandria, which had been
+the centre of intellectual progress, that centre migrated to Baghdad,
+and the Arabs became the leaders of science and philosophy. In
+astronomy they made careful observations. In the middle of the ninth
+century Albategnius, a Syrian prince, improved the value of
+excentricity of the sun's orbit, observed the motion of the moon's
+apse, and thought he detected a smaller progression of the sun's
+apse. His tables were much more accurate than Ptolemy's. Abul Wefa, in
+the tenth century, seems to have discovered the moon's "variation."
+Meanwhile the Moors were leaders of science in the west, and Arzachel
+of Toledo improved the solar tables very much. Ulugh Begh, grandson of
+the great Tamerlane the Tartar, built a fine observatory at Samarcand
+in the fifteenth century, and made a great catalogue of stars, the
+first since the time of Hipparchus.
+
+At the close of the fifteenth century King Alphonso of Spain employed
+computers to produce the Alphonsine Tables (1488 A.D.), Purbach
+translated Ptolemy's book, and observations were carried out in
+Germany by Müller, known as Regiomontanus, and Waltherus.
+
+Nicolai Copernicus, a Sclav, was born in 1473 at Thorn, in Polish
+Prussia. He studied at Cracow and in Italy. He was a priest, and
+settled at Frauenberg.  He did not undertake continuous observations,
+but devoted himself to simplifying the planetary systems and devising
+means for more accurately predicting the positions of the sun, moon,
+and planets. He had no idea of framing a solar system on a dynamical
+basis.  His great object was to increase the accuracy of the
+calculations and the tables. The results of his cogitations were
+printed just before his death in an interesting book, _De
+Revolutionibus Orbium Celestium_. It is only by careful reading of
+this book that the true position of Copernicus can be realised. He
+noticed that Nicetas and others had ascribed the apparent diurnal
+rotation of the heavens to a real daily rotation of the earth about
+its axis, in the opposite direction to the apparent motion of the
+stars. Also in the writings of Martianus Capella he learnt that the
+Egyptians had supposed Mercury and Venus to revolve round the sun, and
+to be carried with him in his annual motion round the earth. He
+noticed that the same supposition, if extended to Mars, Jupiter, and
+Saturn, would explain easily why they, and especially Mars, seem so
+much brighter in opposition.  For Mars would then be a great deal
+nearer to the earth than at other times. It would also explain the
+retrograde motion of planets when in opposition.
+
+We must here notice that at this stage Copernicus was actually
+confronted with the system accepted later by Tycho Brahe, with the
+earth fixed. But he now recalled and accepted the views of Pythagoras
+and others, according to which the sun is fixed and the earth
+revolves; and it must be noted that, geometrically, there is no
+difference of any sort between the Egyptian or Tychonic system and
+that of Pythagoras as revived by Copernicus, except that on the latter
+theory the stars ought to seem to move when the earth changes its
+position--a test which failed completely with the rough means of
+observation then available. The radical defect of all solar systems
+previous to the time of Kepler (1609 A.D.) was the slavish yielding to
+Plato's dictum demanding uniform circular motion for the planets, and
+the consequent evolution of the epicycle, which was fatal to any
+conception of a dynamical theory.
+
+Copernicus could not sever himself from this obnoxious tradition.[5]
+It is true that neither the Pythagorean nor the Egypto-Tychonic system
+required epicycles for explaining retrograde motion, as the Ptolemaic
+theory did. Furthermore, either system could use the excentric of
+Hipparchus to explain the irregular motion known as the equation of
+the centre.  But Copernicus remarked that he could also use an
+epicycle for this purpose, or that he could use both an excentric and
+an epicycle for each planet, and so bring theory still closer into
+accord with observation. And this he proceeded to do.[6] Moreover,
+observers had found irregularities in the moon's motion, due, as we
+now know, to the disturbing attraction of the sun.  To correct for
+these irregularities Copernicus introduced epicycle on epicycle in the
+lunar orbit.
+
+This is in its main features the system propounded by Copernicus. But
+attention must, to state the case fully, be drawn to two points to be
+found in his first and sixth books respectively. The first point
+relates to the seasons, and it shows a strange ignorance of the laws
+of rotating bodies. To use the words of Delambre,[7] in drawing
+attention to the strange conception,
+
+  he imagined that the earth, revolving round the sun, ought always to
+  show to it the same face; the contrary phenomena surprised him: to
+  explain them he invented a third motion, and added it to the two
+  real motions (rotation and orbital revolution). By this third motion
+  the earth, he held, made a revolution on itself and on the poles of
+  the ecliptic once a year ... Copernicus did not know that motion in
+  a straight line is the natural motion, and that motion in a curve is
+  the resultant of several movements. He believed, with Aristotle,
+  that circular motion was the natural one.
+
+Copernicus made this rotation of the earth's axis about the pole of
+the ecliptic retrograde (i.e., opposite to the orbital revolution),
+and by making it perform more than one complete revolution in a year,
+the added part being 1/26000 of the whole, he was able to include the
+precession of the equinoxes in his explanation of the seasons. His
+explanation of the seasons is given on leaf 10 of his book (the pages
+of this book are not all numbered, only alternate pages, or leaves).
+
+In his sixth book he discusses the inclination of the planetary orbits
+to the ecliptic. In regard to this the theory of Copernicus is unique;
+and it will be best to explain this in the words of Grant in his great
+work.[8] He says:--
+
+  Copernicus, as we have already remarked, did not attack the
+  principle of the epicyclical theory: he merely sought to make it
+  more simple by placing the centre of the earth's orbit in the centre
+  of the universe. This was the point to which the motions of the
+  planets were referred, for the planes of their orbits were made to
+  pass through it, and their points of least and greatest velocities
+  were also determined with reference to it.  By this arrangement the
+  sun was situate mathematically near the centre of the planetary
+  system, but he did not appear to have any physical connexion with
+  the planets as the centre of their motions.
+
+According to Copernicus' sixth book, the planes of the planetary
+orbits do not pass through the sun, and the lines of apses do not pass
+through to the sun.
+
+Such was the theory advanced by Copernicus: The earth moves in an
+epicycle, on a deferent whose centre is a little distance from the
+sun. The planets move in a similar way on epicycles, but their
+deferents have no geometrical or physical relation to the sun. The
+moon moves on an epicycle centred on a second epicycle, itself centred
+on a deferent, excentric to the earth.  The earth's axis rotates about
+the pole of the ecliptic, making one revolution and a twenty-six
+thousandth part of a revolution in the sidereal year, in the opposite
+direction to its orbital motion.
+
+In view of this fanciful structure it must be noted, in fairness to
+Copernicus, that he repeatedly states that the reader is not obliged
+to accept his system as showing the real motions; that it does not
+matter whether they be true, even approximately, or not, so long as
+they enable us to compute tables from which the places of the planets
+among the stars can be predicted.[9] He says that whoever is not
+satisfied with this explanation must be contented by being told that
+"mathematics are for mathematicians" (Mathematicis mathematica
+scribuntur).
+
+At the same time he expresses his conviction over and over again that
+the earth is in motion. It is with him a pious belief, just as it was
+with Pythagoras and his school and with Aristarchus. "But" (as Dreyer
+says in his most interesting book, _Tycho Brahe_) "proofs of the
+physical truth of his system Copernicus had given none, and could give
+none," any more than Pythagoras or Aristarchus.
+
+There was nothing so startlingly simple in his system as to lead the
+cautious astronomer to accept it, as there was in the later Keplerian
+system; and the absence of parallax in the stars seemed to condemn his
+system, which had no physical basis to recommend it, and no
+simplification at all over the Egypto-Tychonic system, to which
+Copernicus himself drew attention. It has been necessary to devote
+perhaps undue space to the interesting work of Copernicus, because by
+a curious chance his name has become so widely known. He has been
+spoken of very generally as the founder of the solar system that is
+now accepted. This seems unfair, and on reading over what has been
+written about him at different times it will be noticed that the
+astronomers--those who have evidently read his great book--are very
+cautious in the words with which they eulogise him, and refrain from
+attributing to him the foundation of our solar system, which is
+entirely due to Kepler.  It is only the more popular writers who give
+the idea that a revolution had been effected when Pythagoras' system
+was revived, and when Copernicus supported his view that the earth
+moves and is not fixed.
+
+It may be easy to explain the association of the name of Copernicus
+with the Keplerian system. But the time has long passed when the
+historian can support in any way this popular error, which was started
+not by astronomers acquainted with Kepler's work, but by those who
+desired to put the Church in the wrong by extolling Copernicus.
+
+Copernicus dreaded much the abuse he expected to receive from
+philosophers for opposing the authority of Aristotle, who had declared
+that the earth was fixed.  So he sought and obtained the support of
+the Church, dedicating his great work to Pope Paul III. in a lengthy
+explanatory epistle. The Bishop of Cracow set up a memorial tablet in
+his honour.
+
+Copernicus was the most refined exponent, and almost the last
+representative, of the Epicyclical School.  As has been already
+stated, his successor, Tycho Brahe, supported the same use of
+epicycles and excentrics as Copernicus, though he held the earth to be
+fixed. But Tycho Brahe was eminently a practical observer, and took
+little part in theory; and his observations formed so essential a
+portion of the system of Kepler that it is only fair to include his
+name among these who laid the foundations of the solar system which we
+accept to-day.
+
+In now taking leave of the system of epicycles let it be remarked that
+it has been held up to ridicule more than it deserves. On reading
+Airy's account of epicycles, in the beautifully clear language of his
+_Six Lectures on Astronomy_, the impression is made that the
+jointed bars there spoken of for describing the circles were supposed
+to be real. This is no more the case than that the spheres of Eudoxus
+and Callippus were supposed to be real. Both were introduced only to
+illustrate the mathematical conception upon which the solar,
+planetary, and lunar tables were constructed.  The epicycles
+represented nothing more nor less than the first terms in the Fourier
+series, which in the last century has become a basis of such
+calculations, both in astronomy and physics generally.
+
+[Illustration: "QUADRANS MURALIS SIVE TICHONICUS."  With portrait of
+Tycho Brahe, instruments, etc., painted on the wall; showing
+assistants using the sight, watching the clock, and recording.  (From
+the author's copy of the _Astronomiæ Instauratæ Mechanica._)]
+
+
+FOOTNOTES:
+
+[1] For definition see p. 22.
+
+[2] _Ibid_.
+
+[3] For definition see p. 18.
+
+[4] For definition see p. 18.
+
+[5] In his great book Copernicus says: "The movement of the heavenly
+bodies is uniform, circular, perpetual, or else composed of circular
+movements." In this he proclaimed himself a follower of Pythagoras
+(see p. 14), as also when he says: "The world is spherical because the
+sphere is, of all figures, the most perfect" (Delambre,
+_Ast. Mod. Hist_., pp. 86, 87).
+
+[6] Kepler tells us that Tycho Brahe was pleased with this
+device, and adapted it to his own system.
+
+[7] _Hist. Ast._, vol. i., p. 354.
+
+[8] _Hist. of Phys. Ast._, p. vii.
+
+[9] "Est enim Astronomi proprium, historiam motuum coelestium
+diligenti et artificiosa observatione colligere. Deinde causas
+earundem, seu hypotheses, cum veras assequi nulla ratione possit
+... Neque enim necesse est, eas hypotheses esse veras, imo ne
+verisimiles quidem, sed sufficit hoc usum, si calculum observationibus
+congruentem exhibeant."
+
+
+
+
+BOOK II. THE DYNAMICAL PERIOD
+
+
+
+5. DISCOVERY OF THE TRUE SOLAR SYSTEM--TYCHO BRAHE--KEPLER.
+
+
+During the period of the intellectual and aesthetic revival, at the
+beginning of the sixteenth century, the "spirit of the age" was
+fostered by the invention of printing, by the downfall of the
+Byzantine Empire, and the scattering of Greek fugitives, carrying the
+treasures of literature through Western Europe, by the works of
+Raphael and Michael Angelo, by the Reformation, and by the extension
+of the known world through the voyages of Spaniards and Portuguese.
+During that period there came to the front the founder of accurate
+observational astronomy. Tycho Brahe, a Dane, born in 1546 of noble
+parents, was the most distinguished, diligent, and accurate observer
+of the heavens since the days of Hipparchus, 1,700 years before.
+
+Tycho was devoted entirely to his science from childhood, and the
+opposition of his parents only stimulated him in his efforts to
+overcome difficulties.  He soon grasped the hopelessness of the old
+deductive methods of reasoning, and decided that no theories ought to
+be indulged in until preparations had been made by the accumulation of
+accurate observations.  We may claim for him the title of founder of
+the inductive method.
+
+For a complete life of this great man the reader is referred to
+Dreyer's _Tycho Brahe_, Edinburgh, 1890, containing a complete
+bibliography. The present notice must be limited to noting the work
+done, and the qualities of character which enabled him to attain his
+scientific aims, and which have been conspicuous in many of his
+successors.
+
+He studied in Germany, but King Frederick of Denmark, appreciating his
+great talents, invited him to carry out his life's work in that
+country. He granted to him the island of Hveen, gave him a pension,
+and made him a canon of the Cathedral of Roskilde. On that island
+Tycho Brahe built the splendid observatory which he called Uraniborg,
+and, later, a second one for his assistants and students, called
+Stjerneborg. These he fitted up with the most perfect instruments, and
+never lost a chance of adding to his stock of careful observations.[1]
+
+The account of all these instruments and observations, printed at his
+own press on the island, was published by Tycho Brahe himself, and the
+admirable and numerous engravings bear witness to the excellence of
+design and the stability of his instruments.
+
+His mechanical skill was very great, and in his workmanship he was
+satisfied with nothing but the best. He recognised the importance of
+rigidity in the instruments, and, whereas these had generally been
+made of wood, he designed them in metal. His instruments included
+armillae like those which had been used in Alexandria, and other
+armillae designed by himself--sextants, mural quadrants, large
+celestial globes and various instruments for special purposes. He
+lived before the days of telescopes and accurate clocks. He invented
+the method of sub-dividing the degrees on the arc of an instrument by
+transversals somewhat in the way that Pedro Nunez had proposed.
+
+He originated the true system of observation and reduction of
+observations, recognising the fact that the best instrument in the
+world is not perfect; and with each of his instruments he set to work
+to find out the errors of graduation and the errors of mounting, the
+necessary correction being applied to each observation.
+
+When he wanted to point his instrument exactly to a star he was
+confronted with precisely the same difficulty as is met in gunnery and
+rifle-shooting. The sights and the object aimed at cannot be in focus
+together, and a great deal depends on the form of sight. Tycho Brahe
+invented, and applied to the pointers of his instruments, an
+aperture-sight of variable area, like the iris diaphragm used now in
+photography. This enabled him to get the best result with stars of
+different brightness.  The telescope not having been invented, he
+could not use a telescopic-sight as we now do in gunnery.  This not
+only removes the difficulty of focussing, but makes the minimum
+visible angle smaller. Helmholtz has defined the minimum angle
+measurable with the naked eye as being one minute of arc. In view of
+this it is simply marvellous that, when the positions of Tycho's
+standard stars are compared with the best modern catalogues, his
+probable error in right ascension is only ± 24", 1, and in declination
+only ± 25", 9.
+
+Clocks of a sort had been made, but Tycho Brahe found them so
+unreliable that he seldom used them, and many of his position-measurements
+were made by measuring the angular distances from known stars.
+
+Taking into consideration the absence of either a telescope or a
+clock, and reading his account of the labour he bestowed upon each
+observation, we must all agree that Kepler, who inherited these
+observations in MS., was justified, under the conditions then
+existing, in declaring that there was no hope of anyone ever improving
+upon them.
+
+In the year 1572, on November 11th, Tycho discovered in Cassiopeia a
+new star of great brilliance, and continued to observe it until the
+end of January, 1573. So incredible to him was such an event that he
+refused to believe his own eyes until he got others to confirm what he
+saw. He made accurate observations of its distance from the nine
+principal stars in Casseiopeia, and proved that it had no measurable
+parallax. Later he employed the same method with the comets of 1577,
+1580, 1582, 1585, 1590, 1593, and 1596, and proved that they too had
+no measurable parallax and must be very distant.
+
+The startling discovery that stars are not necessarily permanent, that
+new stars may appear, and possibly that old ones may disappear, had
+upon him exactly the same effect that a similar occurrence had upon
+Hipparchus 1,700 years before. He felt it his duty to catalogue all
+the principal stars, so that there should be no mistake in the
+future. During the construction of his catalogue of 1,000 stars he
+prepared and used accurate tables of refraction deduced from his own
+observations. Thus he eliminated (so far as naked eye observations
+required) the effect of atmospheric refraction which makes the
+altitude of a star seem greater than it really is.
+
+Tycho Brahe was able to correct the lunar theory by his observations.
+Copernicus had introduced two epicycles on the lunar orbit in the hope
+of obtaining a better accordance between theory and observation; and
+he was not too ambitious, as his desire was to get the tables accurate
+to ten minutes. Tycho Brahe found that the tables of Copernicus were
+in error as much as two degrees. He re-discovered the inequality
+called "variation" by observing the moon in all phases--a thing which
+had not been attended to. [It is remarkable that in the nineteenth
+century Sir George Airy established an altazimuth at Greenwich
+Observatory with this special object, to get observations of the moon
+in all phases.] He also discovered other lunar equalities, and wanted
+to add another epicycle to the moon's orbit, but he feared that these
+would soon become unmanageable if further observations showed more new
+inequalities.
+
+But, as it turned out, the most fruitful work of Tycho Brahe was on
+the motions of the planets, and especially of the planet Mars, for it
+was by an examination of these results that Kepler was led to the
+discovery of his immortal laws.
+
+After the death of King Frederick the observatories of Tycho Brahe
+were not supported. The gigantic power and industry displayed by this
+determined man were accompanied, as often happens, by an overbearing
+manner, intolerant of obstacles. This led to friction, and eventually
+the observatories were dismantled, and Tycho Brahe was received by the
+Emperor Rudolph II., who placed a house in Prague at his disposal.
+Here he worked for a few years, with Kepler as one of his assistants,
+and he died in the year 1601.
+
+It is an interesting fact that Tycho Brahe had a firm conviction that
+mundane events could be predicted by astrology, and that this belief
+was supported by his own predictions.
+
+It has already been stated that Tycho Brahe maintained that
+observation must precede theory. He did not accept the Copernican
+theory that the earth moves, but for a working hypothesis he used a
+modification of an old Egyptian theory, mathematically identical with
+that of Copernicus, but not involving a stellar parallax.  He says
+(_De Mundi_, etc.) that
+
+  the Ptolemean system was too complicated, and the new one which that
+  great man Copernicus had proposed, following in the footsteps of
+  Aristarchus of Samos, though there was nothing in it contrary to
+  mathematical principles, was in opposition to those of physics, as
+  the heavy and sluggish earth is unfit to move, and the system is
+  even opposed to the authority of Scripture. The absence of annual
+  parallax further involves an incredible distance between the
+  outermost planet and the fixed stars.
+
+We are bound to admit that in the circumstances of the case, so long
+as there was no question of dynamical forces connecting the members of
+the solar system, his reasoning, as we should expect from such a man,
+is practical and sound. It is not surprising, then, that astronomers
+generally did not readily accept the views of Copernicus, that Luther
+(Luther's _Tischreden_, pp.  22, 60) derided him in his usual pithy
+manner, that Melancthon (_Initia doctrinae physicae_) said that
+Scripture, and also science, are against the earth's motion; and that
+the men of science whose opinion was asked for by the cardinals (who
+wished to know whether Galileo was right or wrong) looked upon
+Copernicus as a weaver of fanciful theories.
+
+Johann Kepler is the name of the man whose place, as is generally
+agreed, would have been the most difficult to fill among all those who
+have contributed to the advance of astronomical knowledge. He was born
+at Wiel, in the Duchy of Wurtemberg, in 1571. He held an appointment
+at Gratz, in Styria, and went to join Tycho Brahe in Prague, and to
+assist in reducing his observations. These came into his possession
+when Tycho Brahe died, the Emperor Rudolph entrusting to him the
+preparation of new tables (called the Rudolphine tables) founded on
+the new and accurate observations. He had the most profound respect
+for the knowledge, skill, determination, and perseverance of the man
+who had reaped such a harvest of most accurate data; and though Tycho
+hardly recognised the transcendent genius of the man who was working
+as his assistant, and although there were disagreements between them,
+Kepler held to his post, sustained by the conviction that, with these
+observations to test any theory, he would be in a position to settle
+for ever the problem of the solar system.
+
+[Illustration: PORTRAIT OF JOHANNES KEPLER.  By F. Wanderer, from
+Reitlinger's "Johannes Kepler" (original in Strassburg).]
+
+It has seemed to many that Plato's demand for uniform circular motion
+(linear or angular) was responsible for a loss to astronomy of good
+work during fifteen hundred years, for a hundred ill-considered
+speculative cosmogonies, for dissatisfaction, amounting to disgust,
+with these _à priori_ guesses, and for the relegation of the
+science to less intellectual races than Greeks and other Europeans.
+Nobody seemed to dare to depart from this fetish of uniform angular
+motion and circular orbits until the insight, boldness, and
+independence of Johann Kepler opened up a new world of thought and of
+intellectual delight.
+
+While at work on the Rudolphine tables he used the old epicycles and
+deferents and excentrics, but he could not make theory agree with
+observation. His instincts told him that these apologists for uniform
+motion were a fraud; and he proved it to himself by trying every
+possible variation of the elements and finding them fail.  The number
+of hypotheses which he examined and rejected was almost incredible
+(for example, that the planets turn round centres at a little distance
+from the sun, that the epicycles have centres at a little distance
+from the deferent, and so on). He says that, after using all these
+devices to make theory agree with Tycho's observations, he still found
+errors amounting to eight minutes of a degree. Then he said boldly
+that it was impossible that so good an observer as Tycho could have
+made a mistake of eight minutes, and added: "Out of these eight
+minutes we will construct a new theory that will explain the motions
+of all the planets." And he did it, with elliptic orbits having the
+sun in a focus of each.[2]
+
+It is often difficult to define the boundaries between fancies,
+imagination, hypothesis, and sound theory.  This extraordinary genius
+was a master in all these modes of attacking a problem. His analogy
+between the spaces occupied by the five regular solids and the
+distances of the planets from the sun, which filled him with so much
+delight, was a display of pure fancy. His demonstration of the three
+fundamental laws of planetary motion was the most strict and complete
+theory that had ever been attempted.
+
+It has been often suggested that the revival by Copernicus of the
+notion of a moving earth was a help to Kepler. No one who reads
+Kepler's great book could hold such an opinion for a moment. In fact,
+the excellence of Copernicus's book helped to prolong the life of the
+epicyclical theories in opposition to Kepler's teaching.
+
+All of the best theories were compared by him with observation. These
+were the Ptolemaic, the Copernican, and the Tychonic. The two latter
+placed all of the planetary orbits concentric with one another, the
+sun being placed a little away from their common centre, and having no
+apparent relation to them, and being actually outside the planes in
+which they move.  Kepler's first great discovery was that the planes
+of all the orbits pass through the sun; his second was that the line
+of apses of each planet passes through the sun; both were
+contradictory to the Copernican theory.
+
+He proceeds cautiously with his propositions until he arrives at his
+great laws, and he concludes his book by comparing observations of
+Mars, of all dates, with his theory.
+
+His first law states that the planets describe ellipses with the sun
+at a focus of each ellipse.
+
+His second law (a far more difficult one to prove) states that a line
+drawn from a planet to the sun sweeps over equal areas in equal
+times. These two laws were published in his great work, _Astronomia
+Nova, sen.  Physica Coelestis tradita commentariis de Motibus Stelloe;
+Martis_, Prague, 1609.
+
+It took him nine years more[3] to discover his third law, that the
+squares of the periodic times are proportional to the cubes of the
+mean distances from the sun.
+
+These three laws contain implicitly the law of universal
+gravitation. They are simply an alternative way of expressing that law
+in dealing with planets, not particles. Only, the power of the
+greatest human intellect is so utterly feeble that the meaning of the
+words in Kepler's three laws could not be understood until expounded
+by the logic of Newton's dynamics.
+
+The joy with which Kepler contemplated the final demonstration of
+these laws, the evolution of which had occupied twenty years, can
+hardly be imagined by us.  He has given some idea of it in a passage
+in his work on _Harmonics_, which is not now quoted, only lest
+someone might say it was egotistical--a term which is simply grotesque
+when applied to such a man with such a life's work accomplished.
+
+The whole book, _Astronomia Nova_, is a pleasure to read; the
+mass of observations that are used, and the ingenuity of the
+propositions, contrast strongly with the loose and imperfectly
+supported explanations of all his predecessors; and the indulgent
+reader will excuse the devotion of a few lines to an example of the
+ingenuity and beauty of his methods.
+
+It may seem a hopeless task to find out the true paths of Mars and the
+earth (at that time when their shape even was not known) from the
+observations giving only the relative direction from night to
+night. Now, Kepler had twenty years of observations of Mars to deal
+with. This enabled him to use a new method, to find the earth's
+orbit. Observe the date at any time when Mars is in opposition. The
+earth's position E at that date gives the longitude of Mars M. His
+period is 687 days. Now choose dates before and after the principal
+date at intervals of 687 days and its multiples.  Mars is in each case
+in the same position. Now for any date when Mars is at M and the earth
+at E₃ the date of the year gives the angle E₃SM. And the
+observation of Tycho gives the direction of Mars compared with the
+sun, SE₃M. So all the angles of the triangle SEM in any of these
+positions of E are known, and also the ratios of SE₁, SE₂, SE₃,
+SE₄ to SM and to each other.
+
+For the orbit of Mars observations were chosen at intervals of a year,
+when the earth was always in the same place.
+
+[Illustration]
+
+But Kepler saw much farther than the geometrical facts. He realised
+that the orbits are followed owing to a force directed to the sun; and
+he guessed that this is the same force as the gravity that makes a
+stone fall. He saw the difficulty of gravitation acting through the
+void space.  He compared universal gravitation to magnetism, and
+speaks of the work of Gilbert of Colchester.  (Gilbert's book, _De
+Mundo Nostro Sublunari, Philosophia Nova_, Amstelodami, 1651,
+containing similar views, was published forty-eight years after
+Gilbert's death, and forty-two years after Kepler's book and
+reference.  His book _De Magnete_ was published in 1600.)
+
+A few of Kepler's views on gravitation, extracted from the
+Introduction to his _Astronomia Nova_, may now be mentioned:--
+
+1. Every body at rest remains at rest if outside the attractive power
+of other bodies.
+
+2. Gravity is a property of masses mutually attracting in such manner
+that the earth attracts a stone much more than a stone attracts the
+earth.
+
+3. Bodies are attracted to the earth's centre, not because it is the
+centre of the universe, but because it is the centre of the attracting
+particles of the earth.
+
+4. If the earth be not round (but spheroidal?), then bodies at
+different latitudes will not be attracted to its centre, but to
+different points in the neighbourhood of that centre.
+
+5. If the earth and moon were not retained in their orbits by vital
+force (_aut alia aligua aequipollenti_), the earth and moon would come
+together.
+
+6. If the earth were to cease to attract its waters, the oceans would
+all rise and flow to the moon.
+
+7. He attributes the tides to lunar attraction.  Kepler had been
+appointed Imperial Astronomer with a handsome salary (on paper), a
+fraction of which was doled out to him very irregularly. He was led to
+miserable makeshifts to earn enough to keep his family from
+starvation; and proceeded to Ratisbon in 1630 to represent his claims
+to the Diet. He arrived worn out and debilitated; he failed in his
+appeal, and died from fever, contracted under, and fed upon,
+disappointment and exhaustion. Those were not the days when men could
+adopt as a profession the "research of endowment."
+
+Before taking leave of Kepler, who was by no means a man of one idea,
+it ought to be here recorded that he was the first to suggest that a
+telescope made with both lenses convex (not a Galilean telescope) can
+have cross wires in the focus, for use as a pointer to fix accurately
+the positions of stars. An Englishman, Gascoigne, was the first to use
+this in practice.
+
+From the all too brief epitome here given of Kepler's greatest book,
+it must be obvious that he had at that time some inkling of the
+meaning of his laws--universal gravitation. From that moment the idea
+of universal gravitation was in the air, and hints and guesses were
+thrown out by many; and in time the law of gravitation would doubtless
+have been discovered, though probably not by the work of one man, even
+if Newton had not lived. But, if Kepler had not lived, who else could
+have discovered his laws?
+
+
+FOOTNOTES:
+
+[1] When the writer visited M. D'Arrest, the astronomer, at
+Copenhagen, in 1872, he was presented by D'Arrest with one of several
+bricks collected from the ruins of Uraniborg. This was one of his most
+cherished possessions until, on returning home after a prolonged
+absence on astronomical work, he found that his treasure had been
+tidied away from his study.
+
+[2] An ellipse is one of the plane, sections of a cone. It is an oval
+curve, which may be drawn by fixing two pins in a sheet of paper at S
+and H, fastening a string, SPH, to the two pins, and stretching it
+with a pencil point at P, and moving the pencil point, while the
+string is kept taut, to trace the oval ellipse, APB. S and H are the
+_foci_. Kepler found the sun to be in one focus, say S. AB is the
+_major axis_. DE is the _minor axis_. C is the _centre_. The direction
+of AB is the _line of apses_. The ratio of CS to CA is the
+_excentricity_. The position of the planet at A is the _perihelion_
+(nearest to the sun). The position of the planet at B is the
+_aphelion_ (farthest from the sun). The angle ASP is the _anomaly_
+when the planet is at P. CA or a line drawn from S to D is the _mean
+distance_ of the planet from the sun.
+
+[Illustration]
+
+[3] The ruled logarithmic paper we now use was not then to be had by
+going into a stationer's shop. Else he would have accomplished this in
+five minutes.
+
+
+
+6. GALILEO AND THE TELESCOPE--NOTIONS OF GRAVITY BY HORROCKS, ETC.
+
+
+It is now necessary to leave the subject of dynamical astronomy for a
+short time in order to give some account of work in a different
+direction originated by a contemporary of Kepler's, his senior in fact
+by seven years. Galileo Galilei was born at Pisa in 1564. The most
+scientific part of his work dealt with terrestrial dynamics; but one
+of those fortunate chances which happen only to really great men put
+him in the way of originating a new branch of astronomy.
+
+The laws of motion had not been correctly defined.  The only man of
+Galileo's time who seems to have worked successfully in the same
+direction as himself was that Admirable Crichton of the Italians,
+Leonardo da Vinci. Galileo cleared the ground. It had always been
+noticed that things tend to come to rest; a ball rolled on the ground,
+a boat moved on the water, a shot fired in the air. Galileo realised
+that in all of these cases a resisting force acts to stop the motion,
+and he was the first to arrive at the not very obvious law that the
+motion of a body will never stop, nor vary its speed, nor change its
+direction, except by the action of some force.
+
+It is not very obvious that a light body and a heavy one fall at the
+same speed (except for the resistance of the air). Galileo proved this
+on paper, but to convince the world he had to experiment from the
+leaning tower of Pisa.
+
+At an early age he discovered the principle of isochronism of the
+pendulum, which, in the hands of Huyghens in the middle of the
+seventeenth century, led to the invention of the pendulum clock,
+perhaps the most valuable astronomical instrument ever produced.
+
+These and other discoveries in dynamics may seem very obvious now; but
+it is often the most every-day matters which have been found to elude
+the inquiries of ordinary minds, and it required a high order of
+intellect to unravel the truth and discard the stupid maxims scattered
+through the works of Aristotle and accepted on his authority. A blind
+worship of scientific authorities has often delayed the progress of
+human knowledge, just as too much "instruction" of a youth often ruins
+his "education." Grant, in his history of Physical Astronomy, has well
+said that "the sagacity and skill which Galileo displays in resolving
+the phenomena of motion into their constituent elements, and hence
+deriving the original principles involved in them, will ever assure to
+him a distinguished place among those who have extended the domains of
+science."
+
+But it was work of a different kind that established Galileo's popular
+reputation. In 1609 Galileo heard that a Dutch spectacle-maker had
+combined a pair of lenses so as to magnify distant objects. Working on
+this hint, he solved the same problem, first on paper and then in
+practice. So he came to make one of the first telescopes ever used in
+astronomy. No sooner had he turned it on the heavenly bodies than he
+was rewarded by such a shower of startling discoveries as forthwith
+made his name the best known in Europe.  He found curious irregular
+black spots on the sun, revolving round it in twenty-seven days; hills
+and valleys on the moon; the planets showing discs of sensible size,
+not points like the fixed stars; Venus showing phases according to her
+position in relation to the sun; Jupiter accompanied by four moons;
+Saturn with appendages that he could not explain, but unlike the other
+planets; the Milky Way composed of a multitude of separate stars.
+
+His fame flew over Europe like magic, and his discoveries were much
+discussed--and there were many who refused to believe. Cosmo de Medici
+induced him to migrate to Florence to carry on his observations.  He
+was received by Paul V., the Pope, at Rome, to whom he explained his
+discoveries.
+
+He thought that these discoveries proved the truth of the Copernican
+theory of the Earth's motion; and he urged this view on friends and
+foes alike.  Although in frequent correspondence with Kepler, he never
+alluded to the New Astronomy, and wrote to him extolling the virtue of
+epicycles. He loved to argue, never shirked an encounter with any
+number of disputants, and laughed as he broke down their arguments.
+
+Through some strange course of events, not easy to follow, the
+Copernican theory, whose birth was welcomed by the Church, had now
+been taken up by certain anti-clerical agitators, and was opposed by
+the cardinals as well as by the dignitaries of the Reformed
+Church. Galileo--a good Catholic--got mixed up in these discussions,
+although on excellent terms with the Pope and his entourage. At last
+it came about that Galileo was summoned to appear at Rome, where he
+was charged with holding and teaching heretical opinions about the
+movement of the earth; and he then solemnly abjured these
+opinions. There has been much exaggeration and misstatement about his
+trial and punishment, and for a long time there was a great deal of
+bitterness shown on both sides. But the general verdict of the present
+day seems to be that, although Galileo himself was treated with
+consideration, the hostility of the Church to the views of Copernicus
+placed it in opposition also to the true Keplerian system, and this
+led to unprofitable controversies.  From the time of Galileo onwards,
+for some time, opponents of religion included the theory of the
+Earth's motion in their disputations, not so much for the love, or
+knowledge, of astronomy, as for the pleasure of putting the Church in
+the wrong. This created a great deal of bitterness and intolerance on
+both sides. Among the sufferers was Giordano Bruno, a learned
+speculative philosopher, who was condemned to be burnt at the stake.
+
+Galileo died on Christmas Day, 1642--the day of Newton's birth. The
+further consideration of the grand field of discovery opened out by
+Galileo with his telescopes must be now postponed, to avoid
+discontinuity in the history of the intellectual development of this
+period, which lay in the direction of dynamical, or physical,
+astronomy.
+
+Until the time of Kepler no one seems to have conceived the idea of
+universal physical forces controlling terrestrial phenomena, and
+equally applicable to the heavenly bodies. The grand discovery by
+Kepler of the true relationship of the Sun to the Planets, and the
+telescopic discoveries of Galileo and of those who followed him,
+spread a spirit of inquiry and philosophic thought throughout Europe,
+and once more did astronomy rise in estimation; and the irresistible
+logic of its mathematical process of reasoning soon placed it in the
+position it has ever since occupied as the foremost of the exact
+sciences.
+
+The practical application of this process of reasoning was enormously
+facilitated by the invention of logarithms by Napier. He was born at
+Merchistoun, near Edinburgh, in 1550, and died in 1617. By this system
+the tedious arithmetical operations necessary in astronomical
+calculations, especially those dealing with the trigonometrical
+functions of angles, were so much simplified that Laplace declared
+that by this invention the life-work of an astronomer was doubled.
+
+Jeremiah Horrocks (born 1619, died 1641) was an ardent admirer of
+Tycho Brahe and Kepler, and was able to improve the Rudolphine tables
+so much that he foretold a transit of Venus, in 1639, which these
+tables failed to indicate, and was the only observer of it. His life
+was short, but he accomplished a great deal, and rightly ascribed the
+lunar inequality called _evection_ to variations in the value of
+the eccentricity and in the direction of the line of apses, at the
+same time correctly assigning _the disturbing force of the Sun_
+as the cause. He discovered the errors in Jupiter's calculated place,
+due to what we now know as the long inequality of Jupiter and Saturn,
+and measured with considerable accuracy the acceleration at that date
+of Jupiter's mean motion, and indicated the retardation of Saturn's
+mean motion.
+
+Horrocks' investigations, so far as they could be collected, were
+published posthumously in 1672, and seldom, if ever, has a man who
+lived only twenty-two years originated so much scientific knowledge.
+
+At this period British science received a lasting impetus by the wise
+initiation of a much-abused man, Charles II., who founded the Royal
+Society of London, and also the Royal Observatory of Greeenwich, where
+he established Flamsteed as first Astronomer Royal, especially for
+lunar and stellar observations likely to be useful for navigation. At
+the same time the French Academy and the Paris Observatory were
+founded. All this within fourteen years, 1662-1675.
+
+Meanwhile gravitation in general terms was being discussed by Hooke,
+Wren, Halley, and many others.  All of these men felt a repugnance to
+accept the idea of a force acting across the empty void of space.
+Descartes (1596-1650) proposed an ethereal medium whirling round the
+sun with the planets, and having local whirls revolving with the
+satellites. As Delambre and Grant have said, this fiction only
+retarded the progress of pure science. It had no sort of relation to
+the more modern, but equally misleading, "nebular hypothesis." While
+many were talking and guessing, a giant mind was needed at this stage
+to make things clear.
+
+
+
+7. SIR ISAAC NEWTON--LAW OF UNIVERSAL GRAVITATION.
+
+
+We now reach the period which is the culminating point of interest in
+the history of dynamical astronomy.  Isaac Newton was born in
+1642. Pemberton states that Newton, having quitted Cambridge to avoid
+the plague, was residing at Wolsthorpe, in Lincolnshire, where he had
+been born; that he was sitting one day in the garden, reflecting upon
+the force which prevents a planet from flying off at a tangent and
+which draws it to the sun, and upon the force which draws the moon to
+the earth; and that he saw in the case of the planets that the sun's
+force must clearly be unequal at different distances, for the pull out
+of the tangential line in a minute is less for Jupiter than for
+Mars. He then saw that the pull of the earth on the moon would be less
+than for a nearer object. It is said that while thus meditating he saw
+an apple fall from a tree to the ground, and that this fact suggested
+the questions: Is the force that pulled that apple from the tree the
+same as the force which draws the moon to the earth?  Does the
+attraction for both of them follow the same law as to distance as is
+given by the planetary motions round the sun? It has been stated that
+in this way the first conception of universal gravitation arose.[1]
+
+Quite the most important event in the whole history of physical
+astronomy was the publication, in 1687, of Newton's _Principia
+(Philosophiae Naturalis Principia Mathematica)_. In this great work
+Newton started from the beginning of things, the laws of motion, and
+carried his argument, step by step, into every branch of physical
+astronomy; giving the physical meaning of Kepler's three laws, and
+explaining, or indicating the explanation of, all the known heavenly
+motions and their irregularities; showing that all of these were
+included in his simple statement about the law of universal
+gravitation; and proceeding to deduce from that law new irregularities
+in the motions of the moon which had never been noticed, and to
+discover the oblate figure of the earth and the cause of the
+tides. These investigations occupied the best part of his life; but he
+wrote the whole of his great book in fifteen months.
+
+Having developed and enunciated the true laws of motion, he was able
+to show that Kepler's second law (that equal areas are described by
+the line from the planet to the sun in equal times) was only another
+way of saying that the centripetal force on a planet is always
+directed to the sun. Also that Kepler's first law (elliptic orbits
+with the sun in one focus) was only another way of saying that the
+force urging a planet to the sun varies inversely as the square of the
+distance. Also (if these two be granted) it follows that Kepler's
+third law is only another way of saying that the sun's force on
+different planets (besides depending as above on distance) is
+proportional to their masses.
+
+Having further proved the, for that day, wonderful proposition that,
+with the law of inverse squares, the attraction by the separate
+particles of a sphere of uniform density (or one composed of
+concentric spherical shells, each of uniform density) acts as if the
+whole mass were collected at the centre, he was able to express the
+meaning of Kepler's laws in propositions which have been summarised as
+follows:--
+
+The law of universal gravitation.--_Every particle of matter in the
+universe attracts every other particle with a force varying inversely
+as the square of the distance between them, and directly as the
+product of the masses of the two particles_.[2]
+
+But Newton did not commit himself to the law until he had answered
+that question about the apple; and the above proposition now enabled
+him to deal with the Moon and the apple. Gravity makes a stone fall
+16.1 feet in a second. The moon is 60 times farther from the earth's
+centre than the stone, so it ought to be drawn out of a straight
+course through 16.1 feet in a minute. Newton found the distance
+through which she is actually drawn as a fraction of the earth's
+diameter.  But when he first examined this matter he proceeded to use
+a wrong diameter for the earth, and he found a serious discrepancy.
+This, for a time, seemed to condemn his theory, and regretfully he
+laid that part of his work aside. Fortunately, before Newton wrote the
+_Principia_ the French astronomer Picard made a new and correct
+measure of an arc of the meridian, from which he obtained an accurate
+value of the earth's diameter. Newton applied this value, and found,
+to his great joy, that when the distance of the moon is 60 times the
+radius of the earth she is attracted out of the straight course 16.1
+feet per minute, and that the force acting on a stone or an apple
+follows the same law as the force acting upon the heavenly bodies.[3]
+
+The universality claimed for the law--if not by Newton, at least by
+his commentators--was bold, and warranted only by the large number of
+cases in which Newton had found it to apply. Its universality has been
+under test ever since, and so far it has stood the test. There has
+often been a suspicion of a doubt, when some inequality of motion in
+the heavenly bodies has, for a time, foiled the astronomers in their
+attempts to explain it. But improved mathematical methods have always
+succeeded in the end, and so the seeming doubt has been converted into
+a surer conviction of the universality of the law.
+
+Having once established the law, Newton proceeded to trace some of its
+consequences. He saw that the figure of the earth depends partly on
+the mutual gravitation of its parts, and partly on the centrifugal
+tendency due to the earth's rotation, and that these should cause a
+flattening of the poles. He invented a mathematical method which he
+used for computing the ratio of the polar to the equatorial diameter.
+
+He then noticed that the consequent bulging of matter at the equator
+would be attracted by the moon unequally, the nearest parts being most
+attracted; and so the moon would tend to tilt the earth when in some
+parts of her orbit; and the sun would do this to a less extent,
+because of its great distance. Then he proved that the effect ought to
+be a rotation of the earth's axis over a conical surface in space,
+exactly as the axis of a top describes a cone, if the top has a sharp
+point, and is set spinning and displaced from the vertical. He
+actually calculated the amount; and so he explained the cause of the
+precession of the equinoxes discovered by Hipparchus about 150 B.C.
+
+One of his grandest discoveries was a method of weighing the heavenly
+bodies by their action on each other. By means of this principle he
+was able to compare the mass of the sun with the masses of those
+planets that have moons, and also to compare the mass of our moon with
+the mass of the earth.
+
+Thus Newton, after having established his great principle, devoted his
+splendid intellect to the calculation of its consequences. He proved
+that if a body be projected with any velocity in free space, subject
+only to a central force, varying inversely as the square of the
+distance, the body must revolve in a curve which may be any one of the
+sections of a cone--a circle, ellipse, parabola, or hyperbola; and he
+found that those comets of which he had observations move in parabolae
+round the Sun, and are thus subject to the universal law.
+
+Newton realised that, while planets and satellites are chiefly
+controlled by the central body about which they revolve, the new law
+must involve irregularities, due to their mutual action--such, in
+fact, as Horrocks had indicated. He determined to put this to a test
+in the case of the moon, and to calculate the sun's effect, from its
+mass compared with that of the earth, and from its distance. He proved
+that the average effect upon the plane of the orbit would be to cause
+the line in which it cuts the plane of the ecliptic (i.e., the line of
+nodes) to revolve in the ecliptic once in about nineteen years. This
+had been a known fact from the earliest ages. He also concluded that
+the line of apses would revolve in the plane of the lunar orbit also
+in about nineteen years; but the observed period is only ten
+years. For a long time this was the one weak point in the Newtonian
+theory. It was not till 1747 that Clairaut reconciled this with the
+theory, and showed why Newton's calculation was not exact.
+
+Newton proceeded to explain the other inequalities recognised by Tycho
+Brahe and older observers, and to calculate their maximum amounts as
+indicated by his theory. He further discovered from his calculations
+two new inequalities, one of the apogee, the other of the nodes, and
+assigned the maximum value. Grant has shown the values of some of
+these as given by observation in the tables of Meyer and more modern
+tables, and has compared them with the values assigned by Newton from
+his theory; and the comparison is very remarkable.
+
+                                     Newton.      Modern Tables.
+                                      ° '  "         ° ' "
+Mean monthly motion of Apses         1.31.28         3.4.0
+Mean annual motion of nodes         19.18.1,23     19.21.22,50
+Mean value of "variation"              36.10          35.47
+Annual equation                        11.51          11.14
+Inequality of mean motion of apogee    19.43          22.17
+Inequality of mean motion of nodes      9.24           9.0
+
+The only serious discrepancy is the first, which has been already
+mentioned. Considering that some of these perturbations had never been
+discovered, that the cause of none of them had ever been known, and
+that he exhibited his results, if he did not also make the
+discoveries, by the synthetic methods of geometry, it is simply
+marvellous that he reached to such a degree of accuracy. He invented
+the infinitesimal calculus which is more suited for such calculations,
+but had he expressed his results in that language he would have been
+unintelligible to many.
+
+Newton's method of calculating the precession of the equinoxes,
+already referred to, is as beautiful as anything in the _Principia_.
+He had already proved the regression of the nodes of a satellite
+moving in an orbit inclined to the ecliptic. He now said that the
+nodes of a ring of satellites revolving round the earth's equator
+would consequently all regress. And if joined into a solid ring its
+node would regress; and it would do so, only more slowly, if
+encumbered by the spherical part of the earth's mass. Therefore the
+axis of the equatorial belt of the earth must revolve round the pole
+of the ecliptic. Then he set to work and found the amount due to the
+moon and that due to the sun, and so he solved the mystery of 2,000
+years.
+
+When Newton applied his law of gravitation to an explanation of the
+tides he started a new field for the application of mathematics to
+physical problems; and there can be little doubt that, if he could
+have been furnished with complete tidal observations from different
+parts of the world, his extraordinary powers of analysis would have
+enabled him to reach a satisfactory theory.  He certainly opened up
+many mines full of intellectual gems; and his successors have never
+ceased in their explorations. This has led to improved mathematical
+methods, which, combined with the greater accuracy of observation,
+have rendered physical astronomy of to-day the most exact of the
+sciences.
+
+Laplace only expressed the universal opinion of posterity when he said
+that to the _Principia_ is assured "a pre-eminence above all the
+other productions of the human intellect."
+
+The name of Flamsteed, First Astronomer Royal, must here be mentioned
+as having supplied Newton with the accurate data required for
+completing the theory.
+
+The name of Edmund Halley, Second Astronomer Royal, must ever be held
+in repute, not only for his own discoveries, but for the part he
+played in urging Newton to commit to writing, and present to the Royal
+Society, the results of his investigations. But for his friendly
+insistence it is possible that the _Principia_ would never have
+been written; and but for his generosity in supplying the means the
+Royal Society could not have published the book.
+
+[Illustration: DEATH MASK OF SIR ISAAC NEWTON.
+Photographed specially for this work from the original, by kind
+permission of the Royal Society, London.]
+
+Sir Isaac Newton died in 1727, at the age of eighty-five.  His body
+lay in state in the Jerusalem Chamber, and was buried in Westminster
+Abbey.
+
+
+FOOTNOTES:
+
+[1] The writer inherited from his father (Professor J. D. Forbes) a
+small box containing a bit of wood and a slip of paper, which had been
+presented to him by Sir David Brewster. On the paper Sir David had
+written these words: "If there be any truth in the story that Newton
+was led to the theory of gravitation by the fall of an apple, this bit
+of wood is probably a piece of the apple tree from which Newton saw
+the apple fall. When I was on a pilgrimage to the house in which
+Newton was born, I cut it off an ancient apple tree growing in his
+garden." When lecturing in Glasgow, about 1875, the writer showed it
+to his audience. The next morning, when removing his property from the
+lecture table, he found that his precious relic had been stolen. It
+would be interesting to know who has got it now!
+
+[2] It must be noted that these words, in which the laws of
+gravitation are always summarised in histories and text-books, do not
+appear in the _Principia_; but, though they must have been composed by
+some early commentator, it does not appear that their origin has been
+traced. Nor does it appear that Newton ever extended the law beyond
+the Solar System, and probably his caution would have led him to avoid
+any statement of the kind until it should be proved.
+
+With this exception the above statement of the law of universal
+gravitation contains nothing that is not to be found in the
+_Principia_; and the nearest approach to that statement occurs in the
+Seventh Proposition of Book III.:--
+
+Prop.: That gravitation occurs in all bodies, and that it is
+proportional to the quantity of matter in each.
+
+Cor. I.: The total attraction of gravitation on a planet arises, and
+is composed, out of the attraction on the separate parts.
+
+Cor. II.: The attraction on separate equal particles of a body is
+reciprocally as the square of the distance from the particles.
+
+[3] It is said that, when working out this final result, the
+probability of its confirming that part of his theory which he had
+reluctantly abandoned years before excited him so keenly that he was
+forced to hand over his calculations to a friend, to be completed by
+him.
+
+
+
+8. NEWTON'S SUCCESSORS--HALLEY, EULER, LAGRANGE, LAPLACE, ETC.
+
+
+Edmund Halley succeeded Flamsteed as Second Astronomer Royal in
+1721. Although he did not contribute directly to the mathematical
+proofs of Newton's theory, yet his name is closely associated with
+some of its greatest successes.
+
+He was the first to detect the acceleration of the moon's mean
+motion. Hipparchus, having compared his own observations with those of
+more ancient astronomers, supplied an accurate value of the moon's
+mean motion in his time. Halley similarly deduced a value for modern
+times, and found it sensibly greater.  He announced this in 1693, but
+it was not until 1749 that Dunthorne used modern lunar tables to
+compute a lunar eclipse observed in Babylon 721 B.C., another at
+Alexandria 201 B.C., a solar eclipse observed by Theon 360 A.D., and
+two later ones up to the tenth century.  He found that to explain
+these eclipses Halley's suggestion must be adopted, the acceleration
+being 10" in one century. In 1757 Lalande again fixed it at 10."
+
+The Paris Academy, in 1770, offered their prize for an investigation
+to see if this could be explained by the theory of gravitation. Euler
+won the prize, but failed to explain the effect, and said: "It appears
+to be established by indisputable evidence that the secular inequality
+of the moon's mean motion cannot be produced by the forces of
+gravitation."
+
+The same subject was again proposed for a prize which was shared by
+Lagrange [1] and Euler, neither finding a solution, while the latter
+asserted the existence of a resisting medium in space.
+
+Again, in 1774, the Academy submitted the same subject, a third time,
+for the prize; and again Lagrange failed to detect a cause in
+gravitation.
+
+Laplace [2] now took the matter in hand. He tried the effect of a
+non-instantaneous action of gravity, to no purpose. But in 1787 he
+gave the true explanation.  The principal effect of the sun on the
+moon's orbit is to diminish the earth's influence, thus lengthening
+the period to a new value generally taken as constant. But Laplace's
+calculations showed the new value to depend upon the excentricity of
+the earth's orbit, which, according; to theory, has a periodical
+variation of enormous period, and has been continually diminishing for
+thousands of years. Thus the solar influence has been diminishing, and
+the moon's mean motion increased. Laplace computed the amount at 10"
+in one century, agreeing with observation. (Later on Adams showed that
+Laplace's calculation was wrong, and that the value he found was too
+large; so, part of the acceleration is now attributed by some
+astronomers to a lengthening of the day by tidal friction.)
+
+Another contribution by Halley to the verification of Newton's law was
+made when he went to St. Helena to catalogue the southern stars. He
+measured the change in length of the second's pendulum in different
+latitudes due to the changes in gravity foretold by Newton.
+
+Furthermore, he discovered the long inequality of Jupiter and Saturn,
+whose period is 929 years. For an investigation of this also the
+Academy of Sciences offered their prize. This led Euler to write a
+valuable essay disclosing a new method of computing perturbations,
+called the instantaneous ellipse with variable elements. The method
+was much developed by Lagrange.
+
+But again it was Laplace who solved the problem of the inequalities of
+Jupiter and Saturn by the theory of gravitation, reducing the errors
+of the tables from 20' down to 12", thus abolishing the use of
+empirical corrections to the planetary tables, and providing another
+glorious triumph for the law of gravitation.  As Laplace justly said:
+"These inequalities appeared formerly to be inexplicable by the law of
+gravitation--they now form one of its most striking proofs."
+
+Let us take one more discovery of Halley, furnishing directly a new
+triumph for the theory. He noticed that Newton ascribed parabolic
+orbits to the comets which he studied, so that they come from
+infinity, sweep round the sun, and go off to infinity for ever, after
+having been visible a few weeks or months. He collected all the
+reliable observations of comets he could find, to the number of
+twenty-four, and computed their parabolic orbits by the rules laid
+down by Newton. His object was to find out if any of them really
+travelled in elongated ellipses, practically undistinguishable, in the
+visible part of their paths, from parabolæ, in which case they would
+be seen more than once. He found two old comets whose orbits, in shape
+and position, resembled the orbit of a comet observed by himself in
+1682.  Apian observed one in 1531; Kepler the other in 1607.  The
+intervals between these appearances is seventy-five or seventy-six
+years. He then examined and found old records of similar appearance in
+1456, 1380, and 1305. It is true, he noticed, that the intervals
+varied by a year and a-half, and the inclination of the orbit to the
+ecliptic diminished with successive apparitions.  But he knew from
+previous calculations that this might easily be due to planetary
+perturbations. Finally, he arrived at the conclusion that all of these
+comets were identical, travelling in an ellipse so elongated that the
+part where the comet was seen seemed to be part of a parabolic
+orbit. He then predicted its return at the end of 1758 or beginning of
+1759, when he should be dead; but, as he said, "if it should return,
+according to our prediction, about the year 1758, impartial posterity
+will not refuse to acknowledge that this was first discovered by an
+Englishman."[3] [_Synopsis Astronomiae Cometicae_, 1749.]
+
+Once again Halley's suggestion became an inspiration for the
+mathematical astronomer. Clairaut, assisted by Lalande, found that
+Saturn would retard the comet 100 days, Jupiter 518 days, and
+predicted its return to perihelion on April 13th, 1759. In his
+communication to the French Academy, he said that a comet travelling
+into such distant regions might be exposed to the influence of forces
+totally unknown, and "even of some planet too far removed from the sun
+to be ever perceived."
+
+The excitement of astronomers towards the end of 1758 became intense;
+and the honour of first catching sight of the traveller fell to an
+amateur in Saxony, George Palitsch, on Christmas Day, 1758. It reached
+perihelion on March 13th, 1759.
+
+This fact was a startling confirmation of the Newtonian theory,
+because it was a new kind of calculation of perturbations, and also it
+added a new member to the solar system, and gave a prospect of adding
+many more.
+
+When Halley's comet reappeared in 1835, Pontecoulant's computations
+for the date of perihelion passage were very exact, and afterwards he
+showed that, with more exact values of the masses of Jupiter and
+Saturn, his prediction was correct within two days, after an invisible
+voyage of seventy-five years!
+
+Hind afterwards searched out many old appearances of this comet, going
+back to 11 B.C., and most of these have been identified as being
+really Halley's comet by the calculations of Cowell and Cromellin[4]
+(of Greenwich Observatory), who have also predicted its next
+perihelion passage for April 8th to 16th, 1910, and have traced back
+its history still farther, to 240 B.C.
+
+Already, in November, 1907, the Astronomer Royal was trying to catch
+it by the aid of photography.
+
+
+FOOTNOTES:
+
+[1] Born 1736; died 1813.
+
+[2] Born 1749; died 1827.
+
+[3] This sentence does not appear in the original memoir communicated
+to the Royal Society, but was first published in a posthumous reprint.
+
+[4] _R. A. S. Monthly Notices_, 1907-8.
+
+
+
+9. DISCOVERY OF NEW PLANETS--HERSCHEL, PIAZZI, ADAMS, AND LE VERRIER.
+
+
+It would be very interesting, but quite impossible in these pages, to
+discuss all the exquisite researches of the mathematical astronomers,
+and to inspire a reverence for the names connected with these
+researches, which for two hundred years have been establishing the
+universality of Newton's law. The lunar and planetary theories, the
+beautiful theory of Jupiter's satellites, the figure of the earth, and
+the tides, were mathematically treated by Maclaurin, D'Alembert,
+Legendre, Clairaut, Euler, Lagrange, Laplace, Walmsley, Bailly,
+Lalande, Delambre, Mayer, Hansen, Burchardt, Binet, Damoiseau, Plana,
+Poisson, Gauss, Bessel, Bouvard, Airy, Ivory, Delaunay, Le Verrier,
+Adams, and others of later date.
+
+By passing over these important developments it is possible to trace
+some of the steps in the crowning triumph of the Newtonian theory, by
+which the planet Neptune was added to the known members of the solar
+system by the independent researches of Professor J.C. Adams and of
+M. Le Verrier, in 1846.
+
+It will be best to introduce this subject by relating how the
+eighteenth century increased the number of known planets, which was
+then only six, including the earth.
+
+On March 13th, 1781, Sir William Herschel was, as usual, engaged on
+examining some small stars, and, noticing that one of them appeared to
+be larger than the fixed stars, suspected that it might be a comet.
+To test this he increased his magnifying power from 227 to 460 and
+932, finding that, unlike the fixed stars near it, its definition was
+impaired and its size increased.  This convinced him that the object
+was a comet, and he was not surprised to find on succeeding nights
+that the position was changed, the motion being in the ecliptic. He
+gave the observations of five weeks to the Royal Society without a
+suspicion that the object was a new planet.
+
+For a long time people could not compute a satisfactory orbit for the
+supposed comet, because it seemed to be near the perihelion, and no
+comet had ever been observed with a perihelion distance from the sun
+greater than four times the earth's distance. Lexell was the first to
+suspect that this was a new planet eighteen times as far from the sun
+as the earth is. In January, 1783, Laplace published the elliptic
+elements. The discoverer of a planet has a right to name it, so
+Herschel called it Georgium Sidus, after the king.  But Lalande urged
+the adoption of the name Herschel.  Bode suggested Uranus, and this
+was adopted. The new planet was found to rank in size next to Jupiter
+and Saturn, being 4.3 times the diameter of the earth.
+
+In 1787 Herschel discovered two satellites, both revolving in nearly
+the same plane, inclined 80° to the ecliptic, and the motion of both
+was retrograde.
+
+In 1772, before Herschel's discovery, Bode[1] had discovered a curious
+arbitrary law of planetary distances.  Opposite each planet's name
+write the figure 4; and, in succession, add the numbers 0, 3, 6, 12,
+24, 48, 96, etc., to the 4, always doubling the last numbers.  You
+then get the planetary distances.
+
+  Mercury, dist.-- 4  4 +   0 =   4
+  Venus      "     7  4 +   3 =   7
+  Earth      "    10  4 +   6 =  10
+  Mars       "    15  4 +  12 =  16
+   --                 4 +  24 =  28
+  Jupiter  dist.  52  4 +  48 =  52
+  Saturn     "    95  4 +  96 = 100
+  (Uranus)   "   192  4 + 192 = 196
+   --                 4 + 384 = 388
+
+All the five planets, and the earth, fitted this rule, except that
+there was a blank between Mars and Jupiter. When Uranus was
+discovered, also fitting the rule, the conclusion was irresistible
+that there is probably a planet between Mars and Jupiter. An
+association of twenty-four astronomers was now formed in Germany to
+search for the planet. Almost immediately afterwards the planet was
+discovered, not by any member of the association, but by Piazzi, when
+engaged upon his great catalogue of stars. On January 1st, 1801, he
+observed a star which had changed its place the next night. Its motion
+was retrograde till January 11th, direct after the 13th.  Piazzi fell
+ill before he had enough observations for computing the orbit with
+certainty, and the planet disappeared in the sun's rays. Gauss
+published an approximate ephemeris of probable positions when the
+planet should emerge from the sun's light. There was an exciting hunt,
+and on December 31st (the day before its birthday) De Zach captured
+the truant, and Piazzi christened it Ceres.
+
+
+The mean distance from the sun was found to be 2.767, agreeing with
+the 2.8 given by Bode's law. Its orbit was found to be inclined over
+10° to the ecliptic, and its diameter was only 161 miles.
+
+On March 28th, 1802, Olbers discovered a new seventh magnitude star,
+which turned out to be a planet resembling Ceres. It was called
+Pallas. Gauss found its orbit to be inclined 35° to the ecliptic, and
+to cut the orbit of Ceres; whence Olbers considered that these might
+be fragments of a broken-up planet. He then commenced a search for
+other fragments. In 1804 Harding discovered Juno, and in 1807 Olbers
+found Vesta. The next one was not discovered until 1845, from which
+date asteroids, or minor planets (as these small planets are called),
+have been found almost every year. They now number about 700.
+
+It is impossible to give any idea of the interest with which the first
+additions since prehistoric times to the planetary system were
+received. All of those who showered congratulations upon the
+discoverers regarded these discoveries in the light of rewards for
+patient and continuous labours, the very highest rewards that could be
+desired. And yet there remained still the most brilliant triumph of
+all, the addition of another planet like Uranus, before it had ever
+been seen, when the analysis of Adams and Le Verrier gave a final
+proof of the powers of Newton's great law to explain any planetary
+irregularity.
+
+After Sir William Herschel discovered Uranus, in 1781, it was found
+that astronomers had observed it on many previous occasions, mistaking
+it for a fixed star of the sixth or seventh magnitude. Altogether,
+nineteen observations of Uranus's position, from the time of
+Flamsteed, in 1690, had been recorded.
+
+In 1790 Delambre, using all these observations, prepared tables for
+computing its position. These worked well enough for a time, but at
+last the differences between the calculated and observed longitudes of
+the planet became serious. In 1821 Bouvard undertook a revision of the
+tables, but found it impossible to reconcile all the observations of
+130 years (the period of revolution of Uranus is eighty-four years).
+So he deliberately rejected the old ones, expressing the opinion that
+the discrepancies might depend upon "some foreign and unperceived
+cause which may have been acting upon the planet." In a few years the
+errors even of these tables became intolerable. In 1835 the error of
+longitude was 30"; in 1838, 50"; in 1841, 70"; and, by comparing the
+errors derived from observations made before and after opposition, a
+serious error of the distance (radius vector) became apparent.
+
+In 1843 John Couch Adams came out Senior Wrangler at Cambridge, and
+was free to undertake the research which as an undergraduate he had
+set himself--to see whether the disturbances of Uranus could be
+explained by assuming a certain orbit, and position in that orbit, of
+a hypothetical planet even more distant than Uranus.  Such an
+explanation had been suggested, but until 1843 no one had the boldness
+to attack the problem.  Bessel had intended to try, but a fatal
+illness overtook him.
+
+Adams first recalculated all known causes of disturbance, using the
+latest determinations of the planetary masses. Still the errors were
+nearly as great as ever.  He could now, however, use these errors as
+being actually due to the perturbations produced by the unknown
+planet.
+
+In 1844, assuming a circular orbit, and a mean distance agreeing with
+Bode's law, he obtained a first approximation to the position of the
+supposed planet.  He then asked Professor Challis, of Cambridge, to
+procure the latest observations of Uranus from Greenwich, which Airy
+immediately supplied. Then the whole work was recalculated from the
+beginning, with more exactness, and assuming a smaller mean distance.
+
+In September, 1845, he handed to Challis the elements of the
+hypothetical planet, its mass, and its apparent position for September
+30th, 1845. On September 22nd Challis wrote to Airy explaining the
+matter, and declaring his belief in Adams's capabilities. When Adams
+called on him Airy was away from home, but at the end of October,
+1845, he called again, and left a paper with full particulars of his
+results, which had, for the most part, reduced the discrepancies to
+about 1". As a matter of fact, it has since been found that the
+heliocentric place of the new planet then given was correct within
+about 2°.
+
+Airy wrote expressing his interest, and asked for particulars about
+the radius vector. Adams did not then reply, as the answer to this
+question could be seen to be satisfactory by looking at the data
+already supplied.  He was a most unassuming man, and would not push
+himself forward. He may have felt, after all the work he had done,
+that Airy's very natural inquiry showed no proportionate desire to
+search for the planet.  Anyway, the matter lay in embryo for nine
+months.
+
+Meanwhile, one of the ablest French astronomers, Le Verrier,
+experienced in computing perturbations, was independently at work,
+knowing nothing about Adams. He applied to his calculations every
+possible refinement, and, considering the novelty of the problem, his
+calculation was one of the most brilliant in the records of
+astronomy. In criticism it has been said that these were exhibitions
+of skill rather than helps to a solution of the particular problem,
+and that, in claiming to find the elements of the orbit within certain
+limits, he was claiming what was, under the circumstances, impossible,
+as the result proved.
+
+In June, 1846, Le Verrier announced, in the _Comptes Rendus de
+l'Academie des Sciences_, that the longitude of the disturbing planet,
+for January 1st, 1847, was 325, and that the probable error did not
+exceed 10°.
+
+This result agreed so well with Adams's (within 1°) that Airy urged
+Challis to apply the splendid Northumberland equatoreal, at Cambridge,
+to the search.  Challis, however, had already prepared an exhaustive
+plan of attack which must in time settle the point.  His first work
+was to observe, and make a catalogue, or chart, of all stars near
+Adams's position.
+
+On August 31st, 1846, Le Verrier published the concluding
+part of his labours.
+
+On September 18th, 1846, Le Verrier communicated his results to the
+Astronomers at Berlin, and asked them to assist in searching for the
+planet. By good luck Dr. Bremiker had just completed a star-chart of
+the very part of the heavens including Le Verrier's position; thus
+eliminating all of Challis's preliminary work. The letter was received
+in Berlin on September 23rd; and the same evening Galle found the new
+planet, of the eighth magnitude, the size of its disc agreeing with Le
+Verrier's prediction, and the heliocentric longitude agreeing within
+57'. By this time Challis had recorded, without reduction, the
+observations of 3,150 stars, as a commencement for his search.  On
+reducing these, he found a star, observed on August 12th, which was
+not in the same place on July 30th. This was the planet, and he had
+also observed it on August 4th.
+
+The feeling of wonder, admiration, and enthusiasm aroused by this
+intellectual triumph was overwhelming.  In the world of astronomy
+reminders are met every day of the terrible limitations of human
+reasoning powers; and every success that enables the mind's eye to see
+a little more clearly the meaning of things has always been heartily
+welcomed by those who have themselves been engaged in like
+researches. But, since the publication of the _Principia_, in 1687,
+there is probably no analytical success which has raised among
+astronomers such a feeling of admiration and gratitude as when Adams
+and Le Verrier showed the inequalities in Uranus's motion to mean that
+an unknown planet was in a certain place in the heavens, where it was
+found.
+
+At the time there was an unpleasant display of international jealousy.
+The British people thought that the earlier date of Adams's work, and
+of the observation by Challis, entitled him to at least an equal share
+of credit with Le Verrier. The French, on the other hand, who, on the
+announcement of the discovery by Galle, glowed with pride in the new
+proof of the great powers of their astronomer, Le Verrier, whose life
+had a long record of successes in calculation, were incredulous on
+being told that it had all been already done by a young man whom they
+had never heard of.
+
+These displays of jealousy have long since passed away, and there is
+now universally an _entente cordiale_ that to each of these great men
+belongs equally the merit of having so thoroughly calculated this
+inverse problem of perturbations as to lead to the immediate discovery
+of the unknown planet, since called Neptune.
+
+It was soon found that the planet had been observed, and its position
+recorded as a fixed star by Lalande, on May 8th and 10th, 1795.
+
+Mr. Lassel, in the same year, 1846, with his two-feet reflector,
+discovered a satellite, with retrograde motion, which gave the mass of
+the planet about a twentieth of that of Jupiter.
+
+
+FOOTNOTES:
+
+[1] Bode's law, or something like it, had already been fore-shadowed
+by Kepler and others, especially Titius (see _Monatliche
+Correspondenz_, vol. vii., p. 72).
+
+
+
+
+BOOK III. OBSERVATION
+
+
+
+10. INSTRUMENTS OF PRECISION--STATE OF THE SOLAR SYSTEM.
+
+
+Having now traced the progress of physical astronomy up to the time
+when very striking proofs of the universality of the law of
+gravitation convinced the most sceptical, it must still be borne in
+mind that, while gravitation is certainly the principal force
+governing the motions of the heavenly bodies, there may yet be a
+resisting medium in space, and there may be electric and magnetic
+forces to deal with. There may, further, be cases where the effects of
+luminous radiative repulsion become apparent, and also Crookes'
+vacuum-effects described as "radiant matter." Nor is it quite certain
+that Laplace's proofs of the instantaneous propagation of gravity are
+final.
+
+And in the future, as in the past, Tycho Brahe's dictum must be
+maintained, that all theory shall be preceded by accurate
+observations. It is the pride of astronomers that their science stands
+above all others in the accuracy of the facts observed, as well as in
+the rigid logic of the mathematics used for interpreting these facts.
+
+It is interesting to trace historically the invention of those
+instruments of precision which have led to this result, and, without
+entering on the details required in a practical handbook, to note the
+guiding principles of construction in different ages.
+
+It is very probable that the Chaldeans may have made spheres, like the
+armillary sphere, for representing the poles of the heavens; and with
+rings to show the ecliptic and zodiac, as well as the equinoctial and
+solstitial colures; but we have no record. We only know that the tower
+of Belus, on an eminence, was their observatory.  We have, however,
+distinct records of two such spheres used by the Chinese about 2500
+B.C.  Gnomons, or some kind of sundial, were used by the Egyptians and
+others; and many of the ancient nations measured the obliquity of the
+ecliptic by the shadows of a vertical column in summer and winter. The
+natural horizon was the only instrument of precision used by those who
+determined star positions by the directions of their risings and
+settings; while in those days the clepsydra, or waterclock, was the
+best instrument for comparing their times of rising and setting.
+
+About 300 B.C. an observatory fitted with circular instruments for
+star positions was set up at Alexandria, the then centre of
+civilisation. We know almost nothing about the instruments used by
+Hipparchus in preparing his star catalogues and his lunar and solar
+tables; but the invention of the astrolabe is attributed to him.[1]
+
+In more modern times Nuremberg became a centre of astronomical
+culture. Waltherus, of that town, made really accurate observations of
+star altitudes, and of the distances between stars; and in 1484
+A.D. he used a kind of clock. Tycho Brahe tried these, but discarded
+them as being inaccurate.
+
+Tycho Brahe (1546-1601 A.D.) made great improvements in armillary
+spheres, quadrants, sextants, and large celestial globes. With these
+he measured the positions of stars, or the distance of a comet from
+several known stars. He has left us full descriptions of them,
+illustrated by excellent engravings. Previous to his time such
+instruments were made of wood.  Tycho always used metal. He paid the
+greatest attention to the stability of mounting, to the orientation of
+his instruments, to the graduation of the arcs by the then new method
+of transversals, and to the aperture sight used upon his
+pointer. There were no telescopes in his day, and no pendulum
+clocks. He recognised the fact that there must be instrumental
+errors. He made these as small as was possible, measured their amount,
+and corrected his observations.  His table of refractions enabled him
+to abolish the error due to our atmosphere so far as it could affect
+naked-eye observations. The azimuth circle of Tycho's largest quadrant
+had a diameter of nine feet, and the quadrant a radius of six feet. He
+introduced the mural quadrant for meridian observations.[2]
+
+[Illustration: ANCIENT CHINESE INSTRUMENTS, Including quadrant, celestial
+globe, and two armillae, in the Observatory at Peking. Photographed in
+Peking by the author in 1875, and stolen by the Germans when the
+Embassies were relieved by the allies in 1900.]
+
+The French Jesuits at Peking, in the seventeenth century, helped the
+Chinese in their astronomy. In 1875 the writer saw and photographed,
+on that part of the wall of Peking used by the Mandarins as an
+observatory, the six instruments handsomely designed by Father
+Verbiest, copied from the instruments of Tycho Brahe, and embellished
+with Chinese dragons and emblems cast on the supports. He also saw
+there two old instruments (which he was told were Arabic) of date
+1279, by Ko Show-King, astronomer to Koblai Khan, the grandson of
+Chenghis Khan. One of these last is nearly identical with the armillae
+of Tycho; and the other with his "armillae æquatoriæ maximæ," with
+which he observed the comet of 1585, besides fixed stars and
+planets.[3]
+
+The discovery by Galileo of the isochronism of the pendulum, followed
+by Huyghens's adaptation of that principle to clocks, has been one of
+the greatest aids to accurate observation. About the same time an
+equally beneficial step was the employment of the telescope as a
+pointer; not the Galilean with concave eye-piece, but with a
+magnifying glass to examine the focal image, at which also a fixed
+mark could be placed.  Kepler was the first to suggest this. Gascoigne
+was the first to use it. Huyghens used a metal strip of variable width
+in the focus, as a micrometer to cover a planetary disc, and so to
+measure the width covered by the planet. The Marquis Malvasia, in
+1662, described the network of fine silver threads at right angles,
+which he used in the focus, much as we do now.
+
+In the hands of such a skilful man as Tycho Brahe, the old open
+sights, even without clocks, served their purpose sufficiently well to
+enable Kepler to discover the true theory of the solar system. But
+telescopic sights and clocks were required for proving some of
+Newton's theories of planetary perturbations. Picard's observations at
+Paris from 1667 onwards seem to embody the first use of the telescope
+as a pointer. He was also the first to introduce the use of Huyghens's
+clocks for observing the right ascension of stars.  Olaus Romer was
+born at Copenhagen in 1644. In 1675, by careful study of the times of
+eclipses of Jupiter's satellites, he discovered that light took time
+to traverse space. Its velocity is 186,000 miles per second. In 1681
+he took up his duties as astronomer at Copenhagen, and built the first
+transit circle on a window-sill of his house. The iron axis was five
+feet long and one and a-half inches thick, and the telescope was fixed
+near one end with a counterpoise. The telescope-tube was a double
+cone, to prevent flexure. Three horizontal and three vertical wires
+were used in the focus. These were illuminated by a speculum, near the
+object-glass, reflecting the light from a lantern placed over the
+axis, the upper part of the telescope-tube being partly cut away to
+admit the light. A divided circle, with pointer and reading
+microscope, was provided for reading the declination. He realised the
+superiority of a circle with graduations over a much larger
+quadrant. The collimation error was found by reversing the instrument
+and using a terrestrial mark, the azimuth error by star observations.
+The time was expressed in fractions of a second. He also constructed a
+telescope with equatoreal mounting, to follow a star by one axial
+motion. In 1728 his instruments and observation records were destroyed
+by fire.
+
+Hevelius had introduced the vernier and tangent screw in his
+measurement of arc graduations. His observatory and records were burnt
+to the ground in 1679. Though an old man, he started afresh, and left
+behind him a catalogue of 1,500 stars.
+
+Flamsteed began his duties at Greenwich Observatory, as first
+Astronomer Royal, in 1676, with very poor instruments. In 1683 he put
+up a mural arc of 140°, and in 1689 a better one, seventy-nine inches
+radius.  He conducted his measurements with great skill, and
+introduced new methods to attain accuracy, using certain stars for
+determining the errors of his instruments; and he always reduced his
+observations to a form in which they could be readily used. He
+introduced new methods for determining the position of the equinox and
+the right ascension of a fundamental star.  He produced a catalogue of
+2,935 stars. He supplied Sir Isaac Newton with results of observation
+required in his theoretical calculations. He died in 1719.
+
+Halley succeeded Flamsteed to find that the whole place had been
+gutted by the latter's executors. In 1721 he got a transit instrument,
+and in 1726 a mural quadrant by Graham. His successor in 1742,
+Bradley, replaced this by a fine brass quadrant, eight feet radius, by
+Bird; and Bradley's zenith sector was purchased for the observatory.
+An instrument like this, specially designed for zenith stars, is
+capable of greater rigidity than a more universal instrument; and
+there is no trouble with refraction in the zenith. For these reasons
+Bradley had set up this instrument at Kew, to attempt the proof of the
+earth's motion by observing the annual parallax of stars. He certainly
+found an annual variation of zenith distance, but not at the times of
+year required by the parallax. This led him to the discovery of the
+"aberration" of light and of nutation. Bradley has been described as
+the founder of the modern system of accurate observation. He died in
+1762, leaving behind him thirteen folio volumes of valuable but
+unreduced observations. Those relating to the stars were reduced by
+Bessel and published in 1818, at Königsberg, in his well-known
+standard work, _Fundamenta Astronomiae_. In it are results showing the
+laws of refraction, with tables of its amount, the maximum value of
+aberration, and other constants.
+
+Bradley was succeeded by Bliss, and he by Maskelyne (1765), who
+carried on excellent work, and laid the foundations of the Nautical
+Almanac (1767).  Just before his death he induced the Government to
+replace Bird's quadrant by a fine new mural _circle_, six feet in
+diameter, by Troughton, the divisions being read off by microscopes
+fixed on piers opposite to the divided circle. In this instrument the
+micrometer screw, with a divided circle for turning it, was applied
+for bringing the micrometer wire actually in line with a division on
+the circle--a plan which is still always adopted.
+
+Pond succeeded Maskelyne in 1811, and was the first to use this
+instrument. From now onwards the places of stars were referred to the
+pole, not to the zenith; the zero being obtained from measures on
+circumpolar stars. Standard stars were used for giving the clock
+error. In 1816 a new transit instrument, by Troughton, was added, and
+from this date the Greenwich star places have maintained the very
+highest accuracy.
+
+George Biddell Airy, Seventh Astronomer Royal,[4] commenced his
+Greenwich labours in 1835. His first and greatest reformation in the
+work of the observatory was one he had already established at
+Cambridge, and is now universally adopted. He held that an observation
+is not completed until it has been reduced to a useful form; and in
+the case of the sun, moon, and planets these results were, in every
+case, compared with the tables, and the tabular error printed.
+
+Airy was firmly impressed with the object for which Charles II. had
+wisely founded the observatory in connection with navigation, and for
+observations of the moon. Whenever a meridian transit of the moon
+could be observed this was done. But, even so, there are periods in
+the month when the moon is too near the sun for a transit to be well
+observed. Also weather interferes with many meridian observations. To
+render the lunar observations more continuous, Airy employed
+Troughton's successor, James Simms, in conjunction with the engineers,
+Ransome and May, to construct an altazimuth with three-foot circles,
+and a five-foot telescope, in 1847. The result was that the number of
+lunar observations was immediately increased threefold, many of them
+being in a part of the moon's orbit which had previously been bare of
+observations. From that date the Greenwich lunar observations have
+been a model and a standard for the whole world.
+
+Airy also undertook to superintend the reduction of all Greenwich
+lunar observations from 1750 to 1830.  The value of this laborious
+work, which was completed in 1848, cannot be over-estimated.
+
+The demands of astronomy, especially in regard to small minor planets,
+required a transit instrument and mural circle with a more powerful
+telescope. Airy combined the functions of both, and employed the same
+constructors as before to make a _transit-circle_ with a telescope of
+eleven and a-half feet focus and a circle of six-feet diameter, the
+object-glass being eight inches in diameter.
+
+Airy, like Bradley, was impressed with the advantage of employing
+stars in the zenith for determining the fundamental constants of
+astronomy. He devised a _reflex zenith tube_, in which the zenith
+point was determined by reflection from a surface of mercury. The
+design was so simple, and seemed so perfect, that great expectations
+were entertained. But unaccountable variations comparable with those
+of the transit circle appeared, and the instrument was put out of use
+until 1903, when the present Astronomer Royal noticed that the
+irregularities could be allowed for, being due to that remarkable
+variation in the position of the earth's axis included in circles of
+about six yards diameter at the north and south poles, discovered at
+the end of the nineteenth century. The instrument is now being used
+for investigating these variations; and in the year 1907 as many as
+1,545 observations of stars were made with the reflex zenith tube.
+
+In connection with zenith telescopes it must be stated that Respighi,
+at the Capitol Observatory at Rome, made use of a deep well with a
+level mercury surface at the bottom and a telescope at the top
+pointing downwards, which the writer saw in 1871. The reflection of
+the micrometer wires and of a star very near the zenith (but not quite
+in the zenith) can be observed together.  His mercury trough was a
+circular plane surface with a shallow edge to retain the mercury. The
+surface quickly came to rest after disturbance by street traffic.
+
+Sir W. M. H. Christie, Eighth Astronomer Royal, took up his duties in
+that capacity in 1881. Besides a larger altazimuth that he erected in
+1898, he has widened the field of operations at Greenwich by the
+extensive use of photography and the establishment of large
+equatoreals.  From the point of view of instruments of precision, one
+of the most important new features is the astrographic equatoreal, set
+up in 1892 and used for the Greenwich section of the great
+astrographic chart just completed. Photography has come to be of use,
+not only for depicting the sun and moon, comets and nebulae, but also
+to obtain accurate relative positions of neighbouring stars; to pick
+up objects that are invisible in any telescope; and, most of all
+perhaps, in fixing the positions of faint satellites. Thus Saturn's
+distant satellite, Phoebe, and the sixth and seventh satellites of
+Jupiter, have been followed regularly in their courses at Greenwich
+ever since their discovery with the thirty-inch reflector (erected in
+1897); and while doing so Mr. Melotte made, in 1908, the splendid
+discovery on some of the photographic plates of an eighth satellite of
+Jupiter, at an enormous distance from the planet. From observations in
+the early part of 1908, over a limited arc of its orbit, before
+Jupiter approached the sun, Mr. Cowell computed a retrograde orbit and
+calculated the future positions of this satellite, which enabled
+Mr. Melotte to find it again in the autumn--a great triumph both of
+calculation and of photographic observation. This satellite has never
+been seen, and has been photographed only at Greenwich, Heidelberg,
+and the Lick Observatory.
+
+Greenwich Observatory has been here selected for tracing the progress
+of accurate measurement. But there is one instrument of great value,
+the heliometer, which is not used at Greenwich. This serves the
+purpose of a double image micrometer, and is made by dividing the
+object-glass of a telescope along a diameter. Each half is mounted so
+as to slide a distance of several inches each way on an arc whose
+centre is the focus. The amount of the movement can be accurately
+read. Thus two fields of view overlap, and the adjustment is made to
+bring an image of one star over that of another star, and then to do
+the same by a displacement in the opposite direction. The total
+movement of the half-object glass is double the distance between the
+star images in the focal plane. Such an instrument has long been
+established at Oxford, and German astronomers have made great use of
+it. But in the hands of Sir David Gill (late His Majesty's Astronomer
+at the Cape of Good Hope), and especially in his great researches on
+Solar and on Stellar parallax, it has been recognised as an instrument
+of the very highest accuracy, measuring the distance between stars
+correctly to less than a tenth of a second of arc.
+
+The superiority of the heliometer over all other devices (except
+photography) for measuring small angles has been specially brought
+into prominence by Sir David Gill's researches on the distance of the
+sun--_i.e.,_ the scale of the solar system. A measurement of the
+distance of any planet fixes the scale, and, as Venus approaches the
+earth most nearly of all the planets, it used to be supposed that a
+Transit of Venus offered the best opportunity for such measurement,
+especially as it was thought that, as Venus entered on the solar disc,
+the sweep of light round the dark disc of Venus would enable a very
+precise observation to be made.  The Transit of Venus in 1874, in
+which the present writer assisted, overthrew this delusion.
+
+In 1877 Sir David Gill used Lord Crawford's heliometer at the Island
+of Ascension to measure the parallax of Mars in opposition, and found
+the sun's distance 93,080,000 miles. He considered that, while the
+superiority of the heliometer had been proved, the results would be
+still better with the points of light shown by minor planets rather
+than with the disc of Mars.
+
+In 1888-9, at the Cape, he observed the minor planets Iris, Victoria,
+and Sappho, and secured the co-operation of four other heliometers.
+His final result was 92,870,000 miles, the parallax being 8",802
+(_Cape Obs_., Vol. VI.).
+
+So delicate were these measures that Gill detected a minute periodic
+error of theory of twenty-seven days, owing to a periodically
+erroneous position of the centre of gravity of the earth and moon to
+which the position of the observer was referred. This led him to
+correct the mass of the moon, and to fix its ratio to the earth's mass
+= 0.012240.
+
+Another method of getting the distance from the sun is to measure the
+velocity of the earth's orbital motion, giving the circumference
+traversed in a year, and so the radius of the orbit. This has been
+done by comparing observation and experiment. The aberration of light
+is an angle 20" 48, giving the ratio of the earth's velocity to the
+velocity of light. The velocity of light is 186,000 miles a second;
+whence the distance to the sun is 92,780,000 miles. There seems,
+however, to be some uncertainty about the true value of the
+aberration, any determination of which is subject to irregularities
+due to the "seasonal errors." The velocity of light was experimentally
+found, in 1862, by Fizeau and Foucault, each using an independent
+method. These methods have been developed, and new values found, by
+Cornu, Michaelson, Newcomb, and the present writer.
+
+Quite lately Halm, at the Cape of Good Hope, measured
+spectroscopically the velocity of the earth to and from a star by
+observations taken six months apart.  Thence he obtained an accurate
+value of the sun's distance.[5]
+
+But the remarkably erratic minor planet, Eros, discovered by Witte in
+1898, approaches the earth within 15,000,000 miles at rare intervals,
+and, with the aid of photography, will certainly give us the best
+result. A large number of observatories combined to observe the
+opposition of 1900. Their results are not yet completely reduced, but
+the best value deduced so far for the parallax[6] is 8".807 ±
+0".0028.[7]
+
+
+FOOTNOTES:
+
+[1] In 1480 Martin Behaim, of Nuremberg, produced his _astrolabe_ for
+measuring the latitude, by observation of the sun, at sea. It
+consisted of a graduated metal circle, suspended by a ring which was
+passed over the thumb, and hung vertically. A pointer was fixed to a
+pin at the centre. This arm, called the _alhidada_, worked round the
+graduated circle, and was pointed to the sun.  The altitude of the sun
+was thus determined, and, by help of solar tables, the latitude could
+be found from observations made at apparent noon.
+
+[2] See illustration on p. 76.
+
+[3] See Dreyer's article on these instruments in _Copernicus_,
+Vol. I. They were stolen by the Germans after the relief of the
+Embassies, in 1900. The best description of these instruments is
+probably that contained in an interesting volume, which may be seen in
+the library of the R. A. S., entitled _Chinese Researches_, by
+Alexander Wyllie (Shanghai, 1897).
+
+[4] Sir George Airy was very jealous of this honourable title. He
+rightly held that there is only one Astronomer Royal at a time, as
+there is only one Mikado, one Dalai Lama. He said that His Majesty's
+Astronomer at the Cape of Good Hope, His Majesty's Astronomer for
+Scotland, and His Majesty's Astronomer for Ireland are not called
+Astronomers Royal.
+
+[5] _Annals of the Cape Observatory_, vol. x., part 3.
+
+[6] The parallax of the sun is the angle subtended by the earth's
+radius at the sun's distance.
+
+[7] A. R. Hinks, R.A.S.; _Monthly Notices_, June, 1909.
+
+
+
+11. HISTORY OF THE TELESCOPE
+
+
+Accounts of wonderful optical experiments by Roger Bacon (who died in
+1292), and in the sixteenth century by Digges, Baptista Porta, and
+Antonio de Dominis (Grant, _Hist. Ph. Ast_.), have led some to
+suppose that they invented the telescope. The writer considers that it
+is more likely that these notes refer to a kind of _camera
+obscura_, in which a lens throws an inverted image of a landscape
+on the wall.
+
+The first telescopes were made in Holland, the originator being either
+Henry Lipperhey,[1] Zacharias Jansen, or James Metius, and the date
+1608 or earlier.
+
+In 1609 Galileo, being in Venice, heard of the invention, went home
+and worked out the theory, and made a similar telescope. These
+telescopes were all made with a convex object-glass and a concave
+eye-lens, and this type is spoken of as the Galilean telescope. Its
+defects are that it has no real focus where cross-wires can be placed,
+and that the field of view is very small.  Kepler suggested the convex
+eye-lens in 1611, and Scheiner claimed to have used one in 1617. But
+it was Huyghens who really introduced them. In the seventeenth century
+telescopes were made of great length, going up to 300 feet. Huyghens
+also invented the compound eye-piece that bears his name, made of two
+convex lenses to diminish spherical aberration.
+
+But the defects of colour remained, although their cause was unknown
+until Newton carried out his experiments on dispersion and the solar
+spectrum. To overcome the spherical aberration James Gregory,[2] of
+Aberdeen and Edinburgh, in 1663, in his _Optica Promota_,
+proposed a reflecting speculum of parabolic form. But it was Newton,
+about 1666, who first made a reflecting telescope; and he did it with
+the object of avoiding colour dispersion.
+
+Some time elapsed before reflectors were much used.  Pound and Bradley
+used one presented to the Royal Society by Hadley in 1723. Hawksbee,
+Bradley, and Molyneaux made some. But James Short, of Edinburgh, made
+many excellent Gregorian reflectors from 1732 till his death in 1768.
+
+Newton's trouble with refractors, chromatic aberration, remained
+insurmountable until John Dollond (born 1706, died 1761), after many
+experiments, found out how to make an achromatic lens out of two
+lenses--one of crown glass, the other of flint glass--to destroy the
+colour, in a way originally suggested by Euler. He soon acquired a
+great reputation for his telescopes of moderate size; but there was a
+difficulty in making flint-glass lenses of large size. The first
+actual inventor and constructor of an achromatic telescope was Chester
+Moor Hall, who was not in trade, and did not patent it.  Towards the
+close of the eighteenth century a Swiss named Guinand at last
+succeeded in producing larger flint-glass discs free from
+striae. Frauenhofer, of Munich, took him up in 1805, and soon
+produced, among others, Struve's Dorpat refractor of 9.9 inches
+diameter and 13.5 feet focal length, and another, of 12 inches
+diameter and 18 feet focal length, for Lamont, of Munich.
+
+In the nineteenth century gigantic _reflectors_ have been
+made. Lassel's 2-foot reflector, made by himself, did much good work,
+and discovered four new satellites.  But Lord Rosse's 6-foot
+reflector, 54 feet focal length, constructed in 1845, is still the
+largest ever made.  The imperfections of our atmosphere are against
+the use of such large apertures, unless it be on high mountains.
+During the last half century excellent specula have been made of
+silvered glass, and Dr.  Common's 5-foot speculum (removed, since his
+death, to Harvard) has done excellent work. Then there are the 5-foot
+Yerkes reflector at Chicago, and the 4-foot by Grubb at Melbourne.
+
+Passing now from these large reflectors to refractors, further
+improvements have been made in the manufacture of glass by Chance, of
+Birmingham, Feil and Mantois, of Paris, and Schott, of Jena; while
+specialists in grinding lenses, like Alvan Clark, of the U.S.A., and
+others, have produced many large refractors.
+
+Cooke, of York, made an object-glass, 25-inch diameter, for Newall, of
+Gateshead, which has done splendid work at Cambridge. We have the
+Washington 26-inch by Clark, the Vienna 27-inch by Grubb, the Nice
+29½-inch by Gautier, the Pulkowa 30-inch by Clark. Then there was
+the sensation of Clark's 36-inch for the Lick Observatory in
+California, and finally his _tour de force_, the Yerkes 40-inch
+refractor, for Chicago.
+
+At Greenwich there is the 28-inch photographic refractor, and the
+Thompson equatoreal by Grubb, carrying both the 26-inch photographic
+refractor and the 30-inch reflector. At the Cape of Good Hope we find
+Mr. Frank McClean's 24-inch refractor, with an object-glass prism for
+spectroscopic work.
+
+It would be out of place to describe here the practical adjuncts of a
+modern equatoreal--the adjustments for pointing it, the clock for
+driving it, the position-micrometer and various eye-pieces, the
+photographic and spectroscopic attachments, the revolving domes,
+observing seats, and rising floors and different forms of mounting,
+the siderostats and coelostats, and other convenient adjuncts, besides
+the registering chronograph and numerous facilities for aiding
+observation.  On each of these a chapter might be written; but the
+most important part of the whole outfit is the man behind the
+telescope, and it is with him that a history is more especially
+concerned.
+
+
+SPECTROSCOPE.
+
+Since the invention of the telescope no discovery has given so great
+an impetus to astronomical physics as the spectroscope; and in giving
+us information about the systems of stars and their proper motions it
+rivals the telescope.
+
+Frauenhofer, at the beginning of the nineteenth century, while
+applying Dollond's discovery to make large achromatic telescopes,
+studied the dispersion of light by a prism. Admitting the light of the
+sun through a narrow slit in a window-shutter, an inverted image of
+the slit can be thrown, by a lens of suitable focal length, on the
+wall opposite. If a wedge or prism of glass be interposed, the image
+is deflected to one side; but, as Newton had shown, the images formed
+by the different colours of which white light is composed are
+deflected to different extents--the violet most, the red least. The
+number of colours forming images is so numerous as to form a
+continuous spectrum on the wall with all the colours--red, orange,
+yellow, green, blue, indigo, and violet. But Frauenhofer found with a
+narrow slit, well focussed by the lens, that some colours were missing
+in the white light of the sun, and these were shown by dark lines
+across the spectrum.  These are the Frauenhofer lines, some of which
+he named by the letters of the alphabet. The D line is a very marked
+one in the yellow. These dark lines in the solar spectrum had already
+been observed by Wollaston. [3]
+
+On examining artificial lights it was found that incandescent solids
+and liquids (including the carbon glowing in a white gas flame) give
+continuous spectra; gases, except under enormous pressure, give bright
+lines. If sodium or common salt be thrown on the colourless flame of a
+spirit lamp, it gives it a yellow colour, and its spectrum is a bright
+yellow line agreeing in position with line D of the solar spectrum.
+
+In 1832 Sir David Brewster found some of the solar black lines
+increased in strength towards sunset, and attributed them to
+absorption in the earth's atmosphere.  He suggested that the others
+were due to absorption in the sun's atmosphere. Thereupon Professor
+J. D.  Forbes pointed out that during a nearly total eclipse the lines
+ought to be strengthened in the same way; as that part of the sun's
+light, coming from its edge, passes through a great distance in the
+sun's atmosphere.  He tried this with the annular eclipse of 1836,
+with a negative result which has never been accounted for, and which
+seemed to condemn Brewster's view.
+
+In 1859 Kirchoff, on repeating Frauenhofer's experiment, found that,
+if a spirit lamp with salt in the flame were placed in the path of the
+light, the black D line is intensified. He also found that, if he used
+a limelight instead of the sunlight and passed it through the flame
+with salt, the spectrum showed the D line black; or the vapour of
+sodium absorbs the same light that it radiates. This proved to him the
+existence of sodium in the sun's atmosphere.[4] Iron, calcium, and
+other elements were soon detected in the same way.
+
+Extensive laboratory researches (still incomplete) have been carried
+out to catalogue (according to their wave-length on the undulatory
+theory of light) all the lines of each chemical element, under all
+conditions of temperature and pressure. At the same time, all the
+lines have been catalogued in the light of the sun and the brighter of
+the stars.
+
+Another method of obtaining spectra had long been known, by
+transmission through, or reflection from, a grating of equidistant
+lines ruled upon glass or metal.  H. A. Rowland developed the art of
+constructing these gratings, which requires great technical skill, and
+for this astronomers owe him a debt of gratitude.
+
+In 1842 Doppler[5] proved that the colour of a luminous body, like the
+pitch or note of a sounding body, must be changed by velocity of
+approach or recession. Everyone has noticed on a railway that, on
+meeting a locomotive whistling, the note is lowered after the engine
+has passed. The pitch of a sound or the colour of a light depends on
+the number of waves striking the ear or eye in a second. This number
+is increased by approach and lowered by recession.
+
+Thus, by comparing the spectrum of a star alongside a spectrum of
+hydrogen, we may see all the lines, and be sure that there is hydrogen
+in the star; yet the lines in the star-spectrum may be all slightly
+displaced to one side of the lines of the comparison spectrum. If
+towards the violet end, it means mutual approach of the star and
+earth; if to the red end, it means recession. The displacement of
+lines does not tell us whether the motion is in the star, the earth,
+or both.  The displacement of the lines being measured, we can
+calculate the rate of approach or recession in miles per second.
+
+In 1868 Huggins[6] succeeded in thus measuring the velocities of stars
+in the direction of the line of sight.
+
+In 1873 Vogel[7] compared the spectra of the sun's East (approaching)
+limb and West (receding) limb, and the displacement of lines endorsed
+the theory. This last observation was suggested by Zöllner.
+
+
+FOOTNOTES:
+
+[1] In the _Encyclopaedia Britannica_, article "Telescope," and in
+Grant's _Physical Astronomy_, good reasons are given for awarding the
+honour to Lipperhey.
+
+[2] Will the indulgent reader excuse an anecdote which may encourage
+some workers who may have found their mathematics defective through
+want of use? James Gregory's nephew David had a heap of MS. notes by
+Newton. These descended to a Miss Gregory, of Edinburgh, who handed
+them to the present writer, when an undergraduate at Cambridge, to
+examine. After perusal, he lent them to his kindest of friends,
+J. C. Adams (the discoverer of Neptune), for his opinion. Adams's
+final verdict was: "I fear they are of no value. It is pretty evident
+that, when he wrote these notes, _Newton's mathematics were a little
+rusty_."
+
+[3] _R. S. Phil. Trans_.
+
+[4] The experiment had been made before by one who did not understand
+its meaning;. But Sir George G. Stokes had already given verbally the
+true explanation of Frauenhofer lines.
+
+[5] _Abh. d. Kön. Böhm. d. Wiss_., Bd. ii., 1841-42, p. 467. See
+also Fizeau in the _Ann. de Chem. et de Phys_., 1870, p. 211.
+
+[6] _R. S. Phil. Trans_., 1868.
+
+[7] _Ast. Nach_., No. 1, 864.
+
+
+
+
+BOOK IV. THE PHYSICAL PERIOD
+
+
+We have seen how the theory of the solar system was slowly developed
+by the constant efforts of the human mind to find out what are the
+rules of cause and effect by which our conception of the present
+universe and its development seems to be bound. In the primitive ages
+a mere record of events in the heavens and on the earth gave the only
+hope of detecting those uniform sequences from which to derive rules
+or laws of cause and effect upon which to rely. Then came the
+geometrical age, in which rules were sought by which to predict the
+movements of heavenly bodies. Later, when the relation of the sun to
+the courses of the planets was established, the sun came to be looked
+upon as a cause; and finally, early in the seventeenth century, for
+the first time in history, it began to be recognised that the laws of
+dynamics, exactly as they had been established for our own terrestrial
+world, hold good, with the same rigid invariability, at least as far
+as the limits of the solar system.
+
+Throughout this evolution of thought and conjecture there were two
+types of astronomers--those who supplied the facts, and those who
+supplied the interpretation through the logic of mathematics. So
+Ptolemy was dependent upon Hipparchus, Kepler on Tycho Brahe, and
+Newton in much of his work upon Flamsteed.
+
+When Galileo directed his telescope to the heavens, when Secchi and
+Huggins studied the chemistry of the stars by means of the
+spectroscope, and when Warren De la Rue set up a photoheliograph at
+Kew, we see that a progress in the same direction as before, in the
+evolution of our conception of the universe, was being made. Without
+definite expression at any particular date, it came to be an accepted
+fact that not only do earthly dynamics apply to the heavenly bodies,
+but that the laws we find established here, in geology, in chemistry,
+and in the laws of heat, may be extended with confidence to the
+heavenly bodies. Hence arose the branch of astronomy called
+astronomical physics, a science which claims a large portion of the
+work of the telescope, spectroscope, and photography. In this new
+development it is more than ever essential to follow the dictum of
+Tycho Brahe--not to make theories until all the necessary facts are
+obtained. The great astronomers of to-day still hold to Sir Isaac
+Newton's declaration, "Hypotheses non fingo." Each one may have his
+suspicions of a theory to guide him in a course of observation, and
+may call it a working hypothesis.  But the cautious astronomer does
+not proclaim these to the world; and the historian is certainly not
+justified in including in his record those vague speculations founded
+on incomplete data which may be demolished to-morrow, and which,
+however attractive they may be, often do more harm than good to the
+progress of true science.  Meanwhile the accumulation of facts has
+been prodigious, and the revelations of the telescope and spectroscope
+entrancing.
+
+
+
+12. THE SUN.
+
+
+One of Galileo's most striking discoveries, when he pointed his
+telescope to the heavenly bodies, was that of the irregularly shaped
+spots on the sun, with the dark central _umbra_ and the less
+dark, but more extensive, _penumbra_ surrounding it, sometimes
+with several umbrae in one penumbra. He has left us many drawings of
+these spots, and he fixed their period of rotation as a lunar month.
+
+[Illustration: SOLAR SURFACE, As Photographed at the Royal
+Observatory, Greenwich, showing sun-spots with umbrae, penumbrae, and
+faculae.]
+
+It is not certain whether Galileo, Fabricius, or Schemer was the first
+to see the spots. They all did good work. The spots were found to be
+ever varying in size and shape. Sometimes, when a spot disappears at
+the western limb of the sun, it is never seen again.  In other cases,
+after a fortnight, it reappears at the eastern limb. The faculae, or
+bright areas, which are seen all over the sun's surface, but specially
+in the neighbourhood of spots, and most distinctly near the sun's
+edge, were discovered by Galileo. A high telescopic power resolves
+their structure into an appearance like willow-leaves, or rice-grains,
+fairly uniform in size, and more marked than on other parts of the
+sun's surface.
+
+Speculations as to the cause of sun-spots have never ceased from
+Galileo's time to ours. He supposed them to be clouds. Scheiner[1]
+said they were the indications of tumultuous movements occasionally
+agitating the ocean of liquid fire of which he supposed the sun to be
+composed.
+
+A. Wilson, of Glasgow, in 1769,[2] noticed a movement of the umbra
+relative to the penumbra in the transit of the spot over the sun's
+surface; exactly as if the spot were a hollow, with a black base and
+grey shelving sides. This was generally accepted, but later
+investigations have contradicted its universality. Regarding the cause
+of these hollows, Wilson said:--
+
+  Whether their first production and subsequent numberless changes
+  depend upon the eructation of elastic vapours from below, or upon
+  eddies or whirlpools commencing at the surface, or upon the
+  dissolving of the luminous matter in the solar atmosphere, as clouds
+  are melted and again given out by our air; or, if the reader
+  pleases, upon the annihilation and reproduction of parts of this
+  resplendent covering, is left for theory to guess at.[3]
+
+Ever since that date theory has been guessing at it.  The solar
+astronomer is still applying all the instruments of modern research to
+find out which of these suppositions, or what modification of any of
+them, is nearest the truth. The obstacle--one that is perhaps fatal to
+a real theory--lies in the impossibility of reproducing comparative
+experiments in our laboratories or in our atmosphere.
+
+Sir William Herschel propounded an explanation of Wilson's observation
+which received much notice, but which, out of respect for his memory,
+is not now described, as it violated the elementary laws of heat.
+
+Sir John Herschel noticed that the spots are mostly confined to two
+zones extending to about 35° on each side of the equator, and that a
+zone of equatoreal calms is free from spots. But it was
+R. C. Carrington[4] who, by his continuous observations at Redhill, in
+Surrey, established the remarkable fact that, while the rotation
+period in the highest latitudes, 50°, where spots are seen, is
+twenty-seven-and-a-half days, near the equator the period is only
+twenty-five days. His splendid volume of observations of the sun led
+to much new information about the average distribution of spots at
+different epochs.
+
+Schwabe, of Dessau, began in 1826 to study the solar surface, and,
+after many years of work, arrived at a law of frequency which has been
+more fruitful of results than any discovery in solar physics.[5] In
+1843 he announced a decennial period of maxima and minima of sun-spot
+displays. In 1851 it was generally accepted, and, although a period of
+eleven years has been found to be more exact, all later observations,
+besides the earlier ones which have been hunted up for the purpose, go
+to establish a true periodicity in the number of sun-spots. But quite
+lately Schuster[6] has given reasons for admitting a number of
+co-existent periods, of which the eleven-year period was predominant
+in the nineteenth century.
+
+In 1851 Lament, a Scotchman at Munich, found a decennial period in the
+daily range of magnetic declination.  In 1852 Sir Edward Sabine
+announced a similar period in the number of "magnetic storms"
+affecting all of the three magnetic elements--declination, dip, and
+intensity. Australian and Canadian observations both showed the
+decennial period in all three elements. Wolf, of Zurich, and Gauthier,
+of Geneva, each independently arrived at the same conclusion.
+
+It took many years before this coincidence was accepted as certainly
+more than an accident by the old-fashioned astronomers, who want rigid
+proof for every new theory. But the last doubts have long vanished,
+and a connection has been further traced between violent outbursts of
+solar activity and simultaneous magnetic storms.
+
+The frequency of the Aurora Borealis was found by Wolf to follow the
+same period. In fact, it is closely allied in its cause to terrestrial
+magnetism. Wolf also collected old observations tracing the
+periodicity of sun-spots back to about 1700 A.D.
+
+Spoerer deduced a law of dependence of the average latitude of
+sun-spots on the phase of the sun-spot period.
+
+All modern total solar eclipse observations seem to show that the
+shape of the luminous corona surrounding the moon at the moment of
+totality has a special distinct character during the time of a
+sun-spot maximum, and another, totally different, during a sun-spot
+minimum.
+
+A suspicion is entertained that the total quantity of heat received by
+the earth from the sun is subject to the same period. This would have
+far-reaching effects on storms, harvests, vintages, floods, and
+droughts; but it is not safe to draw conclusions of this kind except
+from a very long period of observations.
+
+Solar photography has deprived astronomers of the type of Carrington
+of the delight in devoting a life's work to collecting data. It has
+now become part of the routine work of an observatory.
+
+In 1845 Foucault and Fizeau took a daguerreotype photograph of the
+sun. In 1850 Bond produced one of the moon of great beauty, Draper
+having made some attempts at an even earlier date. But astronomical
+photography really owes its beginning to De la Rue, who used the
+collodion process for the moon in 1853, and constructed the Kew
+photoheliograph in 1857, from which date these instruments have been
+multiplied, and have given us an accurate record of the sun's surface.
+Gelatine dry plates were first used by Huggins in 1876.
+
+It is noteworthy that from the outset De la Rue recognised the value
+of stereoscopic vision, which is now known to be of supreme
+accuracy. In 1853 he combined pairs of photographs of the moon in the
+same phase, but under different conditions regarding libration,
+showing the moon from slightly different points of view.  These in the
+stereoscope exhibited all the relief resulting from binocular vision,
+and looked like a solid globe.  In 1860 he used successive photographs
+of the total solar eclipse stereoscopically, to prove that the red
+prominences belong to the sun, and not to the moon.  In 1861 he
+similarly combined two photographs of a sun-spot, the perspective
+effect showing the umbra like a floor at the bottom of a hollow
+penumbra; and in one case the faculæ were discovered to be sailing
+over a spot apparently at some considerable height.  These appearances
+may be partly due to a proper motion; but, so far as it went, this was
+a beautiful confirmation of Wilson's discovery. Hewlett, however, in
+1894, after thirty years of work, showed that the spots are not always
+depressions, being very subject to disturbance.
+
+The Kew photographs [7] contributed a vast amount of information about
+sun-spots, and they showed that the faculæ generally follow the spots
+in their rotation round the sun.
+
+The constitution of the sun's photosphere, the layer which is the
+principal light-source on the sun, has always been a subject of great
+interest; and much was done by men with exceptionally keen eyesight,
+like Mr. Dawes. But it was a difficult subject, owing to the rapidity
+of the changes in appearance of the so-called rice-grains, about 1" in
+diameter. The rapid transformations and circulations of these
+rice-grains, if thoroughly studied, might lead to a much better
+knowledge of solar physics. This seemed almost hopeless, as it was
+found impossible to identify any "rice-grain" in the turmoil after a
+few minutes. But M.  Hansky, of Pulkowa (whose recent death is
+deplored), introduced successfully a scheme of photography, which
+might almost be called a solar cinematograph. He took photographs of
+the sun at intervals of fifteen or thirty seconds, and then enlarged
+selected portions of these two hundred times, giving a picture
+corresponding to a solar disc of six metres diameter. In these
+enlarged pictures he was able to trace the movements, and changes of
+shape and brightness, of individual rice-grains. Some granules become
+larger or smaller. Some seem to rise out of a mist, as it were, and to
+become clearer.  Others grow feebler. Some are split in two. Some are
+rotated through a right angle in a minute or less, although each of
+the grains may be the size of Great Britain. Generally they move
+together in groups of very various velocities, up to forty kilometres
+a second.  These movements seem to have definite relation to any
+sun-spots in the neighbourhood. From the results already obtained it
+seems certain that, if this method of observation be continued, it
+cannot fail to supply facts of the greatest importance.
+
+It is quite impossible to do justice here to the work of all those who
+are engaged on astronomical physics.  The utmost that can be attempted
+is to give a fair idea of the directions of human thought and
+endeavour.  During the last half-century America has made splendid
+progress, and an entirely new process of studying the photosphere has
+been independently perfected by Professor Hale at Chicago, and
+Deslandres at Paris.[8] They have succeeded in photographing the sun's
+surface in monochromatic light, such as the light given off as one of
+the bright lines of hydrogen or of calcium, by means of the
+"Spectroheliograph." The spectroscope is placed with its slit in the
+focus of an equatoreal telescope, pointed to the sun, so that the
+circular image of the sun falls on the slit. At the other end of the
+spectroscope is the photographic plate. Just in front of this plate
+there is another slit parallel to the first, in the position where the
+image of the first slit formed by the K line of calcium falls. Thus is
+obtained a photograph of the section of the sun, made by the first
+slit, only in K light. As the image of the sun passes over the first
+slit the photographic plate is moved at the same rate and in the same
+direction behind the second slit; and as successive sections of the
+sun's image in the equatoreal enter the apparatus, so are these
+sections successively thrown in their proper place on the photographic
+plate, always in K light. By using a high dispersion the faculæ which
+give off K light can be correctly photographed, not only at the sun's
+edge, but all over his surface. The actual mechanical method of
+carrying out the observation is not quite so simple as what is here
+described.
+
+By choosing another line of the spectrum instead of calcium K--for
+example, the hydrogen line H₍₃₎--we obtain two photographs, one
+showing the appearance of the calcium floculi, and the other of the
+hydrogen floculi, on the same part of the solar surface; and nothing
+is more astonishing than to note the total want of resemblance in the
+forms shown on the two. This mode of research promises to afford many
+new and useful data.
+
+The spectroscope has revealed the fact that, broadly speaking, the sun
+is composed of the same materials as the earth. Ångstrom was the first
+to map out all of the lines to be found in the solar spectrum. But
+Rowland, of Baltimore, after having perfected the art of making true
+gratings with equidistant lines ruled on metal for producing spectra,
+then proceeded to make a map of the solar spectrum on a large scale.
+
+In 1866 Lockyer[9] threw an image of the sun upon the slit of a
+spectroscope, and was thus enabled to compare the spectrum of a spot
+with that of the general solar surface. The observation proved the
+darkness of a spot to be caused by increased absorption of light, not
+only in the dark lines, which are widened, but over the entire
+spectrum. In 1883 Young resolved this continuous obscurity into an
+infinite number of fine lines, which have all been traced in a shadowy
+way on to the general solar surface. Lockyer also detected
+displacements of the spectrum lines in the spots, such as would be
+produced by a rapid motion in the line of sight. It has been found
+that both uprushes and downrushes occur, but there is no marked
+predominance of either in a sun-spot. The velocity of motion thus
+indicated in the line of sight sometimes appears to amount to 320
+miles a second. But it must be remembered that pressure of a gas has
+some effect in displacing the spectral lines.  So we must go on,
+collecting data, until a time comes when the meaning of all the facts
+can be made clear.
+
+_Total Solar Eclipses_.--During total solar eclipses the time is so
+short, and the circumstances so impressive, that drawings of the
+appearance could not always be trusted. The red prominences of jagged
+form that are seen round the moon's edge, and the corona with its
+streamers radiating or interlacing, have much detail that can hardly
+be recorded in a sketch. By the aid of photography a number of records
+can be taken during the progress of totality. From a study of these
+the extent of the corona is demonstrated in one case to extend to at
+least six diameters of the moon, though the eye has traced it
+farther. This corona is still one of the wonders of astronomy, and
+leads to many questions. What is its consistency, if it extends many
+million miles from the sun's surface? How is it that it opposed no
+resistance to the motion of comets which have almost grazed the sun's
+surface? Is this the origin of the zodiacal light?  The character of
+the corona in photographic records has been shown to depend upon the
+phase of the sun-spot period. During the sun-spot maximum the corona
+seems most developed over the spot-zones--i.e., neither at the
+equator nor the poles. The four great sheaves of light give it a
+square appearance, and are made up of rays or plumes, delicate like
+the petals of a flower.  During a minimum the nebulous ring seems to
+be made of tufts of fine hairs with aigrettes or radiations from both
+poles, and streamers from the equator.
+
+[Illustration: SOLAR ECLIPSE, 1882.  From drawing by W. H. Wesley,
+Secretary R.A.S.; showing the prominences, the corona, and an unknown
+comet.]
+
+
+On September 19th, 1868, eclipse spectroscopy began with the Indian
+eclipse, in which all observers found that the red prominences showed
+a bright line spectrum, indicating the presence of hydrogen and other
+gases.  So bright was it that Jansen exclaimed: "_Je verrai ces
+lignes-là en dehors des éclipses_." And the next day he observed the
+lines at the edge of the uneclipsed sun.  Huggins had suggested this
+observation in February, 1868, his idea being to use prisms of such
+great dispersive power that the continuous spectrum reflected by our
+atmosphere should be greatly weakened, while a bright line would
+suffer no diminution by the high dispersion.  On October 20th
+Lockyer,[10] having news of the eclipse, but not of Jansen's
+observations the day after, was able to see these lines. This was a
+splendid performance, for it enabled the prominences to be observed,
+not only during eclipses, but every day. Moreover, the next year
+Huggins was able, by using a wide slit, to see the whole of a
+prominence and note its shape.  Prominences are classified, according
+to their form, into "flame" and "cloud" prominences, the spectrum of
+the latter showing calcium, hydrogen, and helium; that of the former
+including a number of metals.
+
+The D line of sodium is a double line, and in the same eclipse (1868)
+an orange line was noticed which was afterwards found to lie close to
+the two components of the D line. It did not correspond with any known
+terrestrial element, and the unknown element was called "helium." It
+was not until 1895 that Sir William Ramsay found this element as a gas
+in the mineral cleavite.
+
+The spectrum of the corona is partly continuous, indicating light
+reflected from the sun's body. But it also shows a green line
+corresponding with no known terrestrial element, and the name
+"coronium" has been given to the substance causing it.
+
+A vast number of facts have been added to our knowledge about the sun
+by photography and the spectroscope. Speculations and hypotheses in
+plenty have been offered, but it may be long before we have a complete
+theory evolved to explain all the phenomena of the storm-swept
+metallic atmosphere of the sun.
+
+The proceedings of scientific societies teem with such facts and
+"working hypotheses," and the best of them have been collected by Miss
+Clerke in her _History of Astronomy during the Nineteenth Century_. As
+to established facts, we learn from the spectroscopic researches (1)
+that the continuous spectrum is derived from the _photosphere_ or
+solar gaseous material compressed almost to liquid consistency; (2)
+that the _reversing layer_ surrounds it and gives rise to black
+lines in the spectrum; that the _chromosphere_ surrounds this, is
+composed mainly of hydrogen, and is the cause of the red prominences
+in eclipses; and that the gaseous _corona_ surrounds all of
+these, and extends to vast distances outside the sun's visible
+surface.
+
+
+FOOTNOTES:
+
+[1] _Rosa Ursina_, by C. Scheiner, _fol_.; Bracciani, 1630.
+
+[2] _R. S. Phil. Trans_., 1774.
+
+[3] _Ibid_, 1783.
+
+[4] _Observations on the Spots on the Sun, etc.,_ 4°; London and
+Edinburgh, 1863.
+
+[5] _Periodicität der Sonnenflecken. Astron. Nach. XXI._, 1844,
+P. 234.
+
+[6] _R.S. Phil. Trans._ (ser. A), 1906, p. 69-100.
+
+[7] "Researches on Solar Physics," by De la Rue, Stewart and Loewy;
+_R. S. Phil. Trans_., 1869, 1870.
+
+[8] "The Sun as Photographed on the K line"; _Knowledge_, London,
+1903, p. 229.
+
+[9] _R. S. Proc._, xv., 1867, p. 256.
+
+[10] _Acad. des Sc._, Paris; _C. R._, lxvii., 1868, p. 121.
+
+
+
+13. THE MOON AND PLANETS.
+
+
+_The Moon_.--Telescopic discoveries about the moon commence with
+Galileo's discovery that her surface has mountains and valleys, like
+the earth. He also found that, while she always turns the same face to
+us, there is periodically a slight twist to let us see a little round
+the eastern or western edge. This was called _libration_, and the
+explanation was clear when it was understood that in showing always
+the same face to us she makes one revolution a month on her axis
+_uniformly_, and that her revolution round the earth is not
+uniform.
+
+Galileo said that the mountains on the moon showed greater differences
+of level than those on the earth.  Shröter supported this
+opinion. W. Herschel opposed it. But Beer and Mädler measured the
+heights of lunar mountains by their shadows, and found four of them
+over 20,000 feet above the surrounding plains.
+
+Langrenus [1] was the first to do serious work on selenography, and
+named the lunar features after eminent men. Riccioli also made lunar
+charts. In 1692 Cassini made a chart of the full moon. Since then we
+have the charts of Schröter, Beer and Mädler (1837), and of Schmidt,
+of Athens (1878); and, above all, the photographic atlas by Loewy and
+Puiseux.
+
+The details of the moon's surface require for their discussion a whole
+book, like that of Neison or the one by Nasmyth and Carpenter. Here a
+few words must suffice. Mountain ranges like our Andes or Himalayas
+are rare. Instead of that, we see an immense number of circular
+cavities, with rugged edges and flat interior, often with a cone in
+the centre, reminding one of instantaneous photographs of the splash
+of a drop of water falling into a pool. Many of these are fifty or
+sixty miles across, some more. They are generally spoken of as
+resembling craters of volcanoes, active or extinct, on the earth. But
+some of those who have most fully studied the shapes of craters deny
+altogether their resemblance to the circular objects on the moon.
+These so-called craters, in many parts, are seen to be closely
+grouped, especially in the snow-white parts of the moon. But there are
+great smooth dark spaces, like the clear black ice on a pond, more
+free from craters, to which the equally inappropriate name of seas has
+been given. The most conspicuous crater, _Tycho_, is near the south
+pole. At full moon there are seen to radiate from Tycho numerous
+streaks of light, or "rays," cutting through all the mountain
+formations, and extending over fully half the lunar disc, like the
+star-shaped cracks made on a sheet of ice by a blow.  Similar cracks
+radiate from other large craters. It must be mentioned that these
+white rays are well seen only in full light of the sun at full moon,
+just as the white snow in the crevasses of a glacier is seen bright
+from a distance only when the sun is high, and disappears at
+sunset. Then there are deep, narrow, crooked "rills" which may have
+been water-courses; also "clefts" about half a mile wide, and often
+hundreds of miles long, like deep cracks in the surface going straight
+through mountain and valley.
+
+The moon shares with the sun the advantage of being a good subject for
+photography, though the planets are not. This is owing to her larger
+apparent size, and the abundance of illumination. The consequence is
+that the finest details of the moon, as seen in the largest telescope
+in the world, may be reproduced at a cost within the reach of all.
+
+No certain changes have ever been observed; but several suspicions
+have been expressed, especially as to the small crater _Linné_, in the
+_Mare Serenitatis_. It is now generally agreed that no certainty can
+be expected from drawings, and that for real evidence we must await
+the verdict of photography.
+
+No trace of water or of an atmosphere has been found on the moon. It
+is possible that the temperature is too low. In any case, no
+displacement of a star by atmospheric refraction at occultation has
+been surely recorded. The moon seems to be dead.
+
+The distance of the moon from the earth is just now the subject of
+re-measurement. The base line is from Greenwich to Cape of Good Hope,
+and the new feature introduced is the selection of a definite point on
+a crater (Mösting A), instead of the moon's edge, as the point whose
+distance is to be measured.
+
+_The Inferior Planets_.--When the telescope was invented, the phases
+of Venus attracted much attention; but the brightness of this planet,
+and her proximity to the sun, as with Mercury also, seemed to be a bar
+to the discovery of markings by which the axis and period of rotation
+could be fixed. Cassini gave the rotation as twenty-three hours, by
+observing a bright spot on her surface. Shröter made it 23h. 21m. 19s.
+This value was supported by others. In 1890 Schiaparelli[2] announced
+that Venus rotates, like our moon, once in one of her revolutions, and
+always directs the same face to the sun. This property has also been
+ascribed to Mercury; but in neither case has the evidence been
+generally accepted. Twenty-four hours is probably about the period of
+rotation for each of these planets.
+
+Several observers have claimed to have seen a planet within the orbit
+of Mercury, either in transit over the sun's surface or during an
+eclipse. It has even been named _Vulcan_. These announcements would
+have received little attention but for the fact that the motion of
+Mercury has irregularities which have not been accounted for by known
+planets; and Le Verrier[3] has stated that an intra-Mercurial planet
+or ring of asteroids would account for the unexplained part of the
+motion of the line of apses of Mercury's orbit amounting to 38" per
+century.
+
+_Mars_.--The first study of the appearance of Mars by Miraldi led him
+to believe that there were changes proceeding in the two white caps
+which are seen at the planet's poles. W. Herschel attributed these
+caps to ice and snow, and the dates of his observations indicated a
+melting of these ice-caps in the Martian summer.
+
+Schröter attributed the other markings on Mars to drifting clouds. But
+Beer and Mädler, in 1830-39, identified the same dark spots as being
+always in the same place, though sometimes blurred by mist in the
+local winter. A spot sketched by Huyghens in 1672, one frequently seen
+by W. Herschel in 1783, another by Arago in 1813, and nearly all the
+markings recorded by Beer and Mädler in 1830, were seen and drawn by
+F. Kaiser in Leyden during seventeen nights of the opposition of 1862
+(_Ast. Nacht._, No. 1,468), whence he deduced the period of rotation
+to be 24h. 37m. 22s.,62--or one-tenth of a second less than the period
+deduced by R. A. Proctor from a drawing by Hooke in 1666.
+
+It must be noted that, if the periods of rotation both of Mercury and
+Venus be about twenty-four hours, as seems probable, all the four
+planets nearest to the sun rotate in the same period, while the great
+planets rotate in about ten hours (Uranus and Neptune being still
+indeterminate).
+
+The general surface of Mars is a deep yellow; but there are dark grey
+or greenish patches. Sir John Herschel was the first to attribute the
+ruddy colour of Mars to its soil rather than to its atmosphere.
+
+The observations of that keen-sighted observer Dawes led to the first
+good map of Mars, in 1869. In the 1877 opposition Schiaparelli revived
+interest in the planet by the discovery of canals, uniformly about
+sixty miles wide, running generally on great circles, some of them
+being three or four thousand miles long. During the opposition of
+1881-2 the same observer re-observed the canals, and in twenty of them
+he found the canals duplicated,[4] the second canal being always 200
+to 400 miles distant from its fellow.
+
+The existence of these canals has been doubted.  Mr. Lowell has now
+devoted years to the subject, has drawn them over and over again, and
+has photographed them; and accepts the explanation that they are
+artificial, and that vegetation grows on their banks.  Thus is revived
+the old controversy between Whewell and Brewster as to the
+habitability of the planets. The new arguments are not yet generally
+accepted. Lowell believes he has, with the spectroscope, proved the
+existence of water on Mars.
+
+One of the most unexpected and interesting of all telescopic
+discoveries took place in the opposition of 1877, when Mars was
+unusually near to the earth. The Washington Observatory had acquired
+the fine 26-inch refractor, and Asaph Hall searched for satellites,
+concealing the planet's disc to avoid the glare. On August 11th he had
+a suspicion of a satellite. This was confirmed on the 16th, and on the
+following night a second one was added. They are exceedingly faint,
+and can be seen only by the most powerful telescopes, and only at the
+times of opposition. Their diameters are estimated at six or seven
+miles. It was soon found that the first, Deimos, completes its orbit
+in 30h. 18m.  But the other, Phobos, at first was a puzzle, owing to
+its incredible velocity being unsuspected. Later it was found that the
+period of revolution was only 7h. 39m. 22s. Since the Martian day is
+twenty-four and a half hours, this leads to remarkable results.
+Obviously the easterly motion of the satellite overwhelms the diurnal
+rotation of the planet, and Phobos must appear to the inhabitants, if
+they exist, to rise in the west and set in the east, showing two or
+even three full moons in a day, so that, sufficiently well for the
+ordinary purposes of life, the hour of the day can be told by its
+phases.
+
+The discovery of these two satellites is, perhaps, the most
+interesting telescopic visual discovery made with the large telescopes
+of the last half century; photography having been the means of
+discovering all the other new satellites except Jupiter's fifth (in
+order of discovery).
+
+[Illustration: JUPITER.  From a drawing by E. M. Antoniadi, showing
+transit of a satellite's shadow, the belts, and the "great red spot"
+(_Monthly Notices_, R. A. S., vol. lix., pl. x.).]
+
+_Jupiter._--Galileo's discovery of Jupiter's satellites was followed
+by the discovery of his belts. Zucchi and Torricelli seem to have seen
+them. Fontana, in 1633, reported three belts. In 1648 Grimaldi saw but
+two, and noticed that they lay parallel to the ecliptic. Dusky spots
+were also noticed as transient. Hooke[5] measured the motion of one in
+1664. In 1665 Cassini, with a fine telescope, 35-feet focal length,
+observed many spots moving from east to west, whence he concluded that
+Jupiter rotates on an axis like the earth. He watched an unusually
+permanent spot during twenty-nine rotations, and fixed the period at
+9h. 56m. Later he inferred that spots near the equator rotate quicker
+than those in higher latitudes (the same as Carrington found for the
+sun); and W. Herschel confirmed this in 1778-9.
+
+Jupiter's rapid rotation ought, according to Newton's theory, to be
+accompanied by a great flattening at the poles. Cassini had noted an
+oval form in 1691. This was confirmed by La Hire, Römer, and
+Picard. Pound measured the ellipticity = 1/(13.25).
+
+W. Herschel supposed the spots to be masses of cloud in the
+atmosphere--an opinion still accepted.  Many of them were very
+permanent. Cassini's great spot vanished and reappeared nine times
+between 1665 and 1713. It was close to the northern margin of the
+southern belt. Herschel supposed the belts to be the body of the
+planet, and the lighter parts to be clouds confined to certain
+latitudes.
+
+In 1665 Cassini observed transits of the four satellites, and also saw
+their shadows on the planet, and worked out a lunar theory for
+Jupiter. Mathematical astronomers have taken great interest in the
+perturbations of the satellites, because their relative periods
+introduce peculiar effects. Airy, in his delightful book,
+_Gravitation_, has reduced these investigations to simple
+geometrical explanations.
+
+In 1707 and 1713 Miraldi noticed that the fourth satellite varies much
+in brightness. W. Herschel found this variation to depend upon its
+position in its orbit, and concluded that in the positions of
+feebleness it is always presenting to us a portion of its surface,
+which does not well reflect the sun's light; proving that it always
+turns the same face to Jupiter, as is the case with our moon. This
+fact had also been established for Saturn's fifth satellite, and may
+be true for all satellites.
+
+In 1826 Struve measured the diameters of the four satellites, and
+found them to be 2,429, 2,180, 3,561, and 3,046 miles.
+
+In modern times much interest has been taken in watching a rival to
+Cassini's famous spot. The "great red spot" was first observed by
+Niesten, Pritchett, and Tempel, in 1878, as a rosy cloud attached to a
+whitish zone beneath the dark southern equatorial band, shaped like
+the new war balloons, 30,000 miles long and 7,000 miles across. The
+next year it was brick-red. A white spot beside it completed a
+rotation in less time by 5½ minutes than the red spot--a difference
+of 260 miles an hour. Thus they came together again every six weeks,
+but the motions did not continue uniform.  The spot was feeble in
+1882-4, brightened in 1886, and, after many changes, is still visible.
+
+Galileo's great discovery of Jupiter's four moons was the last word in
+this connection until September 9th, 1892, when Barnard, using the
+36-inch refractor of the Lick Observatory, detected a tiny spot of
+light closely following the planet. This proved to be a new satellite
+(fifth), nearer to the planet than any other, and revolving round it
+in 11h. 57m. 23s. Between its rising and setting there must be an
+interval of 2½ Jovian days, and two or three full moons. The sixth
+and seventh satellites were found by the examination of photographic
+plates at the Lick Observatory in 1905, since which time they have
+been continuously photographed, and their orbits traced, at Greenwich.
+On examining these plates in 1908 Mr. Melotte detected the eighth
+satellite, which seems to be revolving in a retrograde orbit three
+times as far from its planet as the next one (seventh), in these two
+points agreeing with the outermost of Saturn's satellites (Phoebe).
+
+_Saturn._--This planet, with its marvellous ring, was perhaps the most
+wonderful object of those first examined by Galileo's telescope. He
+was followed by Dominique Cassini, who detected bands like Jupiter's
+belts. Herschel established the rotation of the planet in 1775-94.
+From observations during one hundred rotations he found the period to
+be 10h. 16m. 0s., 44. Herschel also measured the ratio of the polar to
+the equatoreal diameter as 10:11.
+
+The ring was a complete puzzle to Galileo, most of all when the planet
+reached a position where the plane of the ring was in line with the
+earth, and the ring disappeared (December 4th, 1612). It was not until
+1656 that Huyghens, in his small pamphlet _De Saturni Luna Observatio
+Nova_, was able to suggest in a cypher the ring form; and in 1659, in
+his Systema Saturnium, he gave his reasons and translated the cypher:
+"The planet is surrounded by a slender flat ring, everywhere distinct
+from its surface, and inclined to the ecliptic." This theory explained
+all the phases of the ring which had puzzled others. This ring was
+then, and has remained ever since, a unique structure.  We in this age
+have got accustomed to it. But Huyghens's discovery was received with
+amazement.
+
+In 1675 Cassini found the ring to be double, the concentric rings
+being separated by a black band--a fact which was placed beyond
+dispute by Herschel, who also found that the thickness of the ring
+subtends an angle less than 0".3. Shröter estimated its thickness at
+500 miles.
+
+Many speculations have been advanced to explain the origin and
+constitution of the ring. De Sejour said [6] that it was thrown off
+from Saturn's equator as a liquid ring, and afterwards solidified. He
+noticed that the outside would have a greater velocity, and be less
+attracted to the planet, than the inner parts, and that equilibrium
+would be impossible; so he supposed it to have solidified into a
+number of concentric rings, the exterior ones having the least
+velocity.
+
+Clerk Maxwell, in the Adams prize essay, gave a physico-mathematical
+demonstration that the rings must be composed of meteoritic matter
+like gravel. Even so, there must be collisions absorbing the energy of
+rotation, and tending to make the rings eventually fall into the
+planet. The slower motion of the external parts has been proved by the
+spectroscope in Keeler's hands, 1895.
+
+Saturn has perhaps received more than its share of attention owing to
+these rings. This led to other discoveries. Huyghens in 1655, and
+J. D. Cassini in 1671, discovered the sixth and eighth satellites
+(Titan and Japetus). Cassini lost his satellite, and in searching for
+it found Rhea (the fifth) in 1672, besides his old friend, whom he
+lost again. He added the third and fourth in 1684 (Tethys and
+Dione). The first and second (Mimas and Encelades) were added by
+Herschel in 1789, and the seventh (Hyperion) simultaneously by Lassel
+and Bond in 1848. The ninth (Phoebe) was found on photographs, by
+Pickering in 1898, with retrograde motion; and he has lately added a
+tenth.
+
+The occasional disappearance of Cassini's Japetus was found on
+investigation to be due to the same causes as that of Jupiter's fourth
+satellite, and proves that it always turns the same face to the
+planet.
+
+_Uranus and Neptune_.--The splendid discoveries of Uranus and two
+satellites by Sir William Herschel in 1787, and of Neptune by Adams
+and Le Verrier in 1846, have been already described. Lassel added two
+more satellites to Uranus in 1851, and found Neptune's satellite in
+1846. All of the satellites of Uranus have retrograde motion, and
+their orbits are inclined about 80° to the ecliptic.
+
+The spectroscope has shown the existence of an absorbing atmosphere on
+Jupiter and Saturn, and there are suspicions that they partake
+something of the character of the sun, and emit some light besides
+reflecting solar light. On both planets some absorption lines seem to
+agree with the aqueous vapour lines of our own atmosphere; while one,
+which is a strong band in the red common to both planets, seems to
+agree with a line in the spectrum of some reddish stars.
+
+Uranus and Neptune are difficult to observe spectroscopically, but
+appear to have peculiar spectra agreeing together. Sometimes Uranus
+shows Frauenhofer lines, indicating reflected solar light. But
+generally these are not seen, and six broad bands of absorption
+appear.  One is the F. of hydrogen; another is the red-star line of
+Jupiter and Saturn. Neptune is a very difficult object for the
+spectroscope.
+
+Quite lately [7] P. Lowell has announced that V. M.  Slipher, at
+Flagstaff Observatory, succeeded in 1907 in rendering some plates
+sensitive far into the red. A reproduction is given of photographed
+spectra of the four outermost planets, showing (1) a great number of
+new lines and bands; (2) intensification of hydrogen F.  and C. lines;
+(3) a steady increase of effects (1) and (2) as we pass from Jupiter
+and Saturn to Uranus, and a still greater increase in Neptune.
+
+_Asteroids_.--The discovery of these new planets has been
+described. At the beginning of the last century it was an immense
+triumph to catch a new one. Since photography was called into the
+service by Wolf, they have been caught every year in shoals. It is
+like the difference between sea fishing with the line and using a
+steam trawler. In the 1908 almanacs nearly seven hundred asteroids are
+included. The computation of their perturbations and ephemerides by
+Euler's and Lagrange's method of variable elements became so laborious
+that Encke devised a special process for these, which can be applied
+to many other disturbed orbits. [8]
+
+When a photograph is taken of a region of the heavens including an
+asteroid, the stars are photographed as points because the telescope
+is made to follow their motion; but the asteroids, by their proper
+motion, appear as short lines.
+
+The discovery of Eros and the photographic attack upon its path have
+been described in their relation to finding the sun's distance.
+
+A group of four asteroids has lately been found, with a mean distance
+and period equal to that of Jupiter. To three of these masculine names
+have been given--Hector, Patroclus, Achilles; the other has not yet
+been named.
+
+
+FOOTNOTES:
+
+[1] Langrenus (van Langren), F. Selenographia sive lumina austriae
+philippica; Bruxelles, 1645.
+
+[2] _Astr. Nach._, 2,944.
+
+[3] _Acad. des Sc._, Paris; _C.R._, lxxxiii., 1876.
+
+[4] _Mem. Spettr. Ital._, xi., p. 28.
+
+[5] _R. S. Phil. Trans_., No. 1.
+
+[6] Grant's _Hist. Ph. Ast_., p. 267.
+
+[7] _Nature_, November 12th, 1908.
+
+[8] _Ast. Nach_., Nos. 791, 792, 814, translated by G. B. Airy.
+_Naut. Alm_., Appendix, 1856.
+
+
+
+14. COMETS AND METEORS.
+
+
+Ever since Halley discovered that the comet of 1682 was a member of
+the solar system, these wonderful objects have had a new interest for
+astronomers; and a comparison of orbits has often identified the
+return of a comet, and led to the detection of an elliptic orbit where
+the difference from a parabola was imperceptible in the small portion
+of the orbit visible to us. A remarkable case in point was the comet
+of 1556, of whose identity with the comet of 1264 there could be
+little doubt.  Hind wanted to compute the orbit more exactly than
+Halley had done. He knew that observations had been made, but they
+were lost. Having expressed his desire for a search, all the
+observations of Fabricius and of Heller, and also a map of the comet's
+path among the stars, were eventually unearthed in the most unlikely
+manner, after being lost nearly three hundred years.  Hind and others
+were certain that this comet would return between 1844 and 1848, but
+it never appeared.
+
+When the spectroscope was first applied to finding the composition of
+the heavenly bodies, there was a great desire to find out what comets
+are made of. The first opportunity came in 1864, when Donati observed
+the spectrum of a comet, and saw three bright bands, thus proving that
+it was a gas and at least partly self-luminous.  In 1868 Huggins
+compared the spectrum of Winnecke's comet with that of a Geissler tube
+containing olefiant gas, and found exact agreement. Nearly all comets
+have shown the same spectrum.[1] A very few comets have given bright
+band spectra differing from the normal type. Also a certain kind of
+continuous spectrum, as well as reflected solar light showing
+Frauenhofer lines, have been seen.
+
+[Illustration: COPY OF THE DRAWING MADE BY PAUL FABRICIUS.  To define
+the path of comet 1556. After being lost for 300 years, this drawing
+was recovered by the prolonged efforts of Mr. Hind and Professor
+Littrow in 1856.]
+
+When Wells's comet, in 1882, approached very close indeed to the sun,
+the spectrum changed to a mono-chromatic yellow colour, due to sodium.
+
+For a full account of the wonders of the cometary world the reader is
+referred to books on descriptive astronomy, or to monographs on
+comets.[2] Nor can the very uncertain speculations about the structure
+of comets' tails be given here. A new explanation has been proposed
+almost every time that a great discovery has been made in the theory
+of light, heat, chemistry, or electricity.
+
+Halley's comet remained the only one of which a prediction of the
+return had been confirmed, until the orbit of the small, ill-defined
+comet found by Pons in 1819 was computed by Encke, and found to have a
+period of 3⅓ years. It was predicted to return in 1822, and was
+recognised by him as identical with many previous comets. This comet,
+called after Encke, has showed in each of its returns an inexplicable
+reduction of mean distance, which led to the assertion of a resisting
+medium in space until a better explanation could be found.[3]
+
+Since that date fourteen comets have been found with elliptic orbits,
+whose aphelion distances are all about the same as Jupiter's mean
+distance; and six have an aphelion distance about ten per cent,
+greater than Neptune's mean distance. Other comets are similarly
+associated with the planets Saturn and Uranus.
+
+The physical transformations of comets are among the most wonderful of
+unexplained phenomena in the heavens. But, for physical astronomers,
+the greatest interest attaches to the reduction of radius vector of
+Encke's comet, the splitting of Biela's comet into two comets in 1846,
+and the somewhat similar behaviour of other comets. It must be noted,
+however, that comets have a sensible size, that all their parts cannot
+travel in exactly the same orbit under the sun's gravitation, and that
+their mass is not sufficient to retain the parts together very
+forcibly; also that the inevitable collision of particles, or else
+fluid friction, is absorbing energy, and so reducing the comet's
+velocity.
+
+In 1770 Lexell discovered a comet which, as was afterwards proved by
+investigations of Lexell, Burchardt, and Laplace, had in 1767 been
+deflected by Jupiter out of an orbit in which it was invisible from
+the earth into an orbit with a period of 5½ years, enabling it to be
+seen. In 1779 it again approached Jupiter closer than some of his
+satellites, and was sent off in another orbit, never to be again
+recognised.
+
+But our interest in cometary orbits has been added to by the discovery
+that, owing to the causes just cited, a comet, if it does not separate
+into discrete parts like Biela's, must in time have its parts spread
+out so as to cover a sensible part of the orbit, and that, when the
+earth passes through such part of a comet's orbit, a meteor shower is
+the result.
+
+A magnificent meteor shower was seen in America on November 12th-13th,
+1833, when the paths of the meteors all seemed to radiate from a point
+in the constellation Leo. A similar display had been witnessed in
+Mexico by Humboldt and Bonpland on November 12th, 1799. H. A. Newton
+traced such records back to October 13th, A.D. 902. The orbital motion
+of a cloud or stream of small particles was indicated. The period
+favoured by H. A. Newton was 354½ days; another suggestion was 375½
+days, and another 33¼ years.  He noticed that the advance of the date
+of the shower between 902 and 1833, at the rate of one day in seventy
+years, meant a progression of the node of the orbit.  Adams undertook
+to calculate what the amount would be on all the five suppositions
+that had been made about the period. After a laborious work, he found
+that none gave one day in seventy years except the 33¼-year period,
+which did so exactly. H. A. Newton predicted a return of the shower on
+the night of November 13th-14th, 1866. He is now dead; but many of us
+are alive to recall the wonder and enthusiasm with which we saw this
+prediction being fulfilled by the grandest display of meteors ever
+seen by anyone now alive.
+
+The _progression_ of the nodes proved the path of the meteor
+stream to be retrograde. The _radiant_ had almost the exact
+longitude of the point towards which the earth was moving. This proved
+that the meteor cluster was at perihelion. The period being known, the
+eccentricity of the orbit was obtainable, also the orbital velocity of
+the meteors in perihelion; and, by comparing this with the earth's
+velocity, the latitude of the radiant enabled the inclination to be
+determined, while the longitude of the earth that night was the
+longitude of the node. In such a way Schiaparelli was able to find
+first the elements of the orbit of the August meteor shower
+(Perseids), and to show its identity with the orbit of Tuttle's comet
+1862.iii. Then, in January 1867, Le Verrier gave the elements of the
+November meteor shower (Leonids); and Peters, of Altona, identified
+these with Oppolzer's elements for Tempel's comet 1866--Schiaparelli
+having independently attained both of these results. Subsequently
+Weiss, of Vienna, identified the meteor shower of April 20th (Lyrids)
+with comet 1861. Finally, that indefatigable worker on meteors,
+A. S. Herschel, added to the number, and in 1878 gave a list of
+seventy-six coincidences between cometary and meteoric orbits.
+
+Cometary astronomy is now largely indebted to photography, not merely
+for accurate delineations of shape, but actually for the discovery of
+most of them.  The art has also been applied to the observation of
+comets at distances from their perihelia so great as to prevent their
+visual observation. Thus has Wolf, of Heidelburg, found upon old
+plates the position of comet 1905.v., as a star of the 15.5 magnitude,
+783 days before the date of its discovery. From the point of view of
+the importance of finding out the divergence of a cometary orbit from
+a parabola, its period, and its aphelion distance, this increase of
+range attains the very highest value.
+
+The present Astronomer Royal, appreciating this possibility, has been
+searching by photography for Halley's comet since November, 1907,
+although its perihelion passage will not take place until April, 1910.
+
+
+FOOTNOTES:
+
+[1] In 1874, when the writer was crossing the Pacific Ocean in
+H.M.S. "Scout," Coggia's comet unexpectedly appeared, and (while
+Colonel Tupman got its positions with the sextant) he tried to use the
+prism out of a portable direct-vision spectroscope, without success
+until it was put in front of the object-glass of a binocular, when, to
+his great joy, the three band images were clearly seen.
+
+[2] Such as _The World of Comets_, by A. Guillemin; _History of
+Comets_, by G. R. Hind, London, 1859; _Theatrum Cometicum_, by S. de
+Lubienietz, 1667; _Cometographie_, by Pingré, Paris, 1783; _Donati's
+Comet_, by Bond.
+
+[3] The investigations by Von Asten (of St. Petersburg) seem to
+support, and later ones, especially those by Backlund (also of
+St. Petersburg), seem to discredit, the idea of a resisting medium.
+
+
+
+15. THE FIXED STARS AND NEBUL.
+
+
+Passing now from our solar system, which appears to be subject to the
+action of the same forces as those we experience on our globe, there
+remains an innumerable host of fixed stars, nebulas, and nebulous
+clusters of stars. To these the attention of astronomers has been more
+earnestly directed since telescopes have been so much enlarged.
+Photography also has enabled a vast amount of work to be covered in a
+comparatively short period, and the spectroscope has given them the
+means, not only of studying the chemistry of the heavens, but also of
+detecting any motion in the line of sight from less than a mile a
+second and upwards in any star, however distant, provided it be bright
+enough.
+
+[Illustration: SIR WILLIAM HERSCHEL, F.R.S.--1738-1822.  Painted by
+Lemuel F. Abbott; National Portrait Gallery, Room XX.]
+
+In the field of telescopic discovery beyond our solar system there is
+no one who has enlarged our knowledge so much as Sir William Herschel,
+to whom we owe the greatest discovery in dynamical astronomy among the
+stars--viz., that the law of gravitation extends to the most distant
+stars, and that many of them describe elliptic orbits about each
+other. W. Herschel was born at Hanover in 1738, came to England in
+1758 as a trained musician, and died in 1822. He studied science when
+he could, and hired a telescope, until he learnt to make his own
+specula and telescopes. He made 430 parabolic specula in twenty-one
+years. He discovered 2,500 nebulæ and 806 double stars, counted the
+stars in 3,400 guage-fields, and compared the principal stars
+photometrically.
+
+Some of the things for which he is best known were results of those
+accidents that happen only to the indefatigable enthusiast. Such was
+the discovery of Uranus, which led to funds being provided for
+constructing his 40-feet telescope, after which, in 1786, he settled
+at Slough. In the same way, while trying to detect the annual parallax
+of the stars, he failed in that quest, but discovered binary systems
+of stars revolving in ellipses round each other; just as Bradley's
+attack on stellar parallax failed, but led to the discovery of
+aberration, nutation, and the true velocity of light.
+
+_Parallax_.--The absence of stellar parallax was the great
+objection to any theory of the earth's motion prior to Kepler's
+time. It is true that Kepler's theory itself could have been
+geometrically expressed equally well with the earth or any other point
+fixed. But in Kepler's case the obviously implied physical theory of
+the planetary motions, even before Newton explained the simplicity of
+conception involved, made astronomers quite ready to waive the claim
+for a rigid proof of the earth's motion by measurement of an annual
+parallax of stars, which they had insisted on in respect of
+Copernicus's revival of the idea of the earth's orbital motion.
+
+Still, the desire to measure this parallax was only intensified by the
+practical certainty of its existence, and by repeated failures. The
+attempts of Bradley failed. The attempts of Piazzi and Brinkley,[1]
+early in the nineteenth century, also failed. The first successes,
+afterwards confirmed, were by Bessel and Henderson.  Both used stars
+whose proper motion had been found to be large, as this argued
+proximity. Henderson, at the Cape of Good Hope, observed α
+Centauri, whose annual proper motion he found to amount to 3".6, in
+1832-3; and a few years later deduced its parallax 1".16.  His
+successor at the Cape, Maclear, reduced this to 0".92.
+
+In 1835 Struve assigned a doubtful parallax of 0".261 to Vega (α
+Lyræ). But Bessel's observations, between 1837 and 1840, of 61 Cygni,
+a star with the large proper motion of over 5", established its annual
+parallax to be 0".3483; and this was confirmed by Peters, who found
+the value 0".349.
+
+Later determinations for α₂ Centauri, by Gill,[2] make its parallax
+0".75--This is the nearest known fixed star; and its light takes 4⅓
+years to reach us. The light year is taken as the unit of measurement
+in the starry heavens, as the earth's mean distance is "the
+astronomical unit" for the solar system.[3] The proper motions and
+parallaxes combined tell us the velocity of the motion of these stars
+across the line of sight: α Centauri 14.4 miles a second=4.2
+astronomical units a year; 61 Cygni 37.9 miles a second=11.2
+astronomical units a year. These successes led to renewed zeal, and
+now the distances of many stars are known more or less accurately.
+
+Several of the brightest stars, which might be expected to be the
+nearest, have not shown a parallax amounting to a twentieth of a
+second of arc. Among these are Canopus, α Orionis, α Cygni, β
+Centauri, and γ Cassiopeia. Oudemans has published a list of
+parallaxes observed.[4]
+
+_Proper Motion._--In 1718 Halley[5] detected the proper motions
+of Arcturus and Sirius. In 1738 J. Cassinis[6] showed that the former
+had moved five minutes of arc since Tycho Brahe fixed its position. In
+1792 Piazzi noted the motion of 61 Cygni as given above. For a long
+time the greatest observed proper motion was that of a small star 1830
+Groombridge, nearly 7" a year; but others have since been found
+reaching as much as 10".
+
+Now the spectroscope enables the motion of stars to be detected at a
+single observation, but only that part of the motion that is in the
+line of sight. For a complete knowledge of a star's motion the proper
+motion and parallax must also be known.
+
+When Huggins first applied the Doppler principle to measure velocities
+in the line of sight,[7] the faintness of star spectra diminished the
+accuracy; but Vögel, in 1888, overcame this to a great extent by long
+exposures of photographic plates.
+
+It has often been noticed that stars which seem to belong to a group
+of nearly uniform magnitude have the same proper motion. The
+spectroscope has shown that these have also often the same velocity in
+the line of sight. Thus in the Great Bear, β, γ, δ, ε, ζ, all
+agree as to angular proper motion. δ was too faint for a
+spectroscopic measurement, but all the others have been shown to be
+approaching us at a rate of twelve to twenty miles a second. The same
+has been proved for proper motion, and line of sight motion, in the
+case of Pleiades and other groups.
+
+Maskelyne measured many proper motions of stars, from which W.
+Herschel[8] came to the conclusion that these apparent motions are for
+the most part due to a motion of the solar system in space towards a
+point in the constellation Hercules, R.A. 257°; N. Decl. 25°.  This
+grand discovery has been amply confirmed, and, though opinions differ
+as to the exact direction, it happens that the point first indicated
+by Herschel, from totally insufficient data, agrees well with modern
+estimates.
+
+Comparing the proper motions and parallaxes to get the actual velocity
+of each star relative to our system, C.L. Struve found the probable
+velocity of the solar system in space to be fifteen miles a second, or
+five astronomical units a year.
+
+The work of Herschel in this matter has been checked by comparing
+spectroscopic velocities in the line of sight which, so far as the
+sun's motion is concerned, would give a maximum rate of approach for
+stars near Hercules, a maximum rate of recession for stars in the
+opposite part of the heavens, and no effect for stars half-way
+between. In this way the spectroscope has confirmed generally
+Herschel's view of the direction, and makes the velocity eleven miles
+a second, or nearly four astronomical units a year.
+
+The average proper motion of a first magnitude star has been found to
+be 0".25 annually, and of a sixth magnitude star 0".04. But that all
+bright stars are nearer than all small stars, or that they show
+greater proper motion for that reason, is found to be far from the
+truth. Many statistical studies have been made in this connection, and
+interesting results may be expected from this treatment in the hands
+of Kapteyn of Groningen, and others.[9]
+
+On analysis of the directions of proper motions of stars in all parts
+of the heavens, Kapteyn has shown[10] that these indicate, besides the
+solar motion towards Hercules, two general drifts of stars in nearly
+opposite directions, which can be detected in any part of the
+heavens. This result has been confirmed from independent data by
+Eddington (_R.A.S., M.N._) and Dyson (_R.S.E. Proc._).
+
+Photography promises to assist in the measurement of parallax and
+proper motions. Herr Pulfrich, of the firm of Carl Zeiss, has vastly
+extended the applications of stereoscopic vision to astronomy--a
+subject which De la Rue took up in the early days of photography.  He
+has made a stereo-comparator of great beauty and convenience for
+comparing stereoscopically two star photographs taken at different
+dates. Wolf of Heidelberg has used this for many purposes. His
+investigations depending on the solar motion in space are remarkable.
+He photographs stars in a direction at right angles to the line of the
+sun's motion. He has taken photographs of the same region fourteen
+years apart, the two positions of his camera being at the two ends of
+a base-line over 5,000,000,000 miles apart, or fifty-six astronomical
+units. On examining these stereoscopically, some of the stars rise out
+of the general plane of the stars, and seem to be much nearer. Many of
+the stars are thus seen to be suspended in space at different
+distances corresponding exactly to their real distances from our solar
+system, except when their proper motion interferes. The effect is most
+striking; the accuracy of measurement exceeds that of any other method
+of measuring such displacements, and it seems that with a long
+interval of time the advantage of the method increases.
+
+_Double Stars._--The large class of double stars has always been much
+studied by amateurs, partly for their beauty and colour, and partly as
+a test for telescopic definition. Among the many unexplained stellar
+problems there is one noticed in double stars that is thought by some
+to be likely to throw light on stellar evolution. It is this: There
+are many instances where one star of the pair is comparatively faint,
+and the two stars are contrasted in colour; and in every single case
+the general colour of the faint companion is invariably to be classed
+with colours more near to the blue end of the spectrum than that of
+the principal star.
+
+_Binary Stars._--Sir William Herschel began his observations of double
+stars in the hope of discovering an annual parallax of the stars. In
+this he was following a suggestion of Galileo's. The presumption is
+that, if there be no physical connection between the stars of a pair,
+the largest is the nearest, and has the greatest parallax. So, by
+noting the distance between the pair at different times of the year, a
+delicate test of parallax is provided, unaffected by major
+instrumental errors.
+
+Herschel did, indeed, discover changes of distance, but not of the
+character to indicate parallax. Following this by further observation,
+he found that the motions were not uniform nor rectilinear, and by a
+clear analysis of the movements he established the remarkable and
+wholly unexpected fact that in all these cases the motion is due to a
+revolution about their common centre of gravity.[11] He gave the
+approximate period of revolution of some of these: Castor, 342 years;
+δ Serpentis, 375 years; γ Leonis, 1,200 years; ε Bootis, 1,681 years.
+
+Twenty years later Sir John Herschel and Sir James South, after
+re-examination of these stars, confirmed[12] and extended the results,
+one pair of Coronæ having in the interval completed more than a whole
+revolution.
+
+It is, then, to Sir William Herschel that we owe the extension of the
+law of gravitation, beyond the limits of the solar system, to the
+whole universe. His observations were confirmed by F.G.W. Struve (born
+1793, died 1864), who carried on the work at Dorpat. But it was first
+to Savary,[13] and later to Encke and Sir John Herschel, that we owe
+the computation of the elliptic elements of these stars; also the
+resulting identification of their law of force with Newton's force of
+gravitation applied to the solar system, and the force that makes an
+apple fall to the ground. As Grant well says in his _History_:
+"This may be justly asserted to be one of the most sublime truths
+which astronomical science has hitherto disclosed to the researches of
+the human mind."
+
+Latterly the best work on double stars has been done by
+S. W. Burnham,[14] at the Lick Observatory. The shortest period he
+found was eleven years (κ Pegasi).  In the case of some of
+these binaries the parallax has been measured, from which it appears
+that in four of the surest cases the orbits are about the size of the
+orbit of Uranus, these being probably among the smallest stellar
+orbits.
+
+The law of gravitation having been proved to extend to the stars, a
+discovery (like that of Neptune in its origin, though unlike it in the
+labour and originality involved in the calculation) that entrances the
+imagination became possible, and was realised by Bessel--the discovery
+of an unknown body by its gravitational disturbance on one that was
+visible. In 1834 and 1840 he began to suspect a want of uniformity in
+the proper motion of Sirius and Procyon respectively. In 1844, in a
+letter to Sir John Herschel,[15] he attributed these irregularities in
+each case to the attraction of an invisible companion, the period of
+revolution of Sirius being about half a century. Later he said: "I
+adhere to the conviction that Procyon and Sirius form real binary
+systems, consisting of a visible and an invisible star.  There is no
+reason to suppose luminosity an essential quality of cosmical
+bodies. The visibility of countless stars is no argument against the
+invisibility of countless others." This grand conception led Peters to
+compute more accurately the orbit, and to assign the place of the
+invisible companion of Sirius. In 1862 Alvan G. Clark was testing a
+new 18-inch object-glass (now at Chicago) upon Sirius, and, knowing
+nothing of these predictions, actually found the companion in the very
+place assigned to it. In 1896 the companion of Procyon was discovered
+by Professor Schaeberle at the Lick Observatory.
+
+Now, by the refined parallax determinations of Gill at the Cape, we
+know that of Sirius to be 0".38. From this it has been calculated that
+the mass of Sirius equals two of our suns, and its intrinsic
+brightness equals twenty suns; but the companion, having a mass equal
+to our sun, has only a five-hundredth part of the sun's brightness.
+
+_Spectroscopic Binaries_.--On measuring the velocity of a star in the
+line of sight at frequent intervals, periodic variations have been
+found, leading to a belief in motion round an invisible
+companion. Vogel, in 1889, discovered this in the case of Spica (α
+Virginis), whose period is 4d. 0h. 19m., and the diameter of whose
+orbit is six million miles. Great numbers of binaries of this type
+have since then been discovered, all of short period.
+
+Also, in 1889, Pickering found that at regular intervals of fifty-two
+days the lines in the spectrum of ζ of the Great Bear are
+duplicated, indicating a relative velocity, equal to one hundred miles
+a second, of two components revolving round each other, of which that
+apparently single star must be composed.
+
+It would be interesting, no doubt, to follow in detail the
+accumulating knowledge about the distances, proper motions, and orbits
+of the stars; but this must be done elsewhere. Enough has been said to
+show how results are accumulating which must in time unfold to us the
+various stellar systems and their mutual relationships.
+
+_Variable Stars._--It has often happened in the history of different
+branches of physical science that observation and experiment were so
+far ahead of theory that hopeless confusion appeared to reign; and
+then one chance result has given a clue, and from that time all
+differences and difficulties in the previous researches have stood
+forth as natural consequences, explaining one another in a rational
+sequence. So we find parallax, proper motion, double stars, binary
+systems, variable stars, and new stars all bound together.
+
+The logical and necessary explanation given of the cause of ordinary
+spectroscopic binaries, and of irregular proper motions of Sirius and
+Procyon, leads to the inference that if ever the plane of such a
+binary orbit were edge-on to us there ought to be an eclipse of the
+luminous partner whenever the non-luminous one is interposed between
+us. This should give rise either to intermittence in the star's light
+or else to variability.  It was by supposing the existence of a dark
+companion to Algol that its discoverer, Goodricke of York,[16] in
+1783, explained variable stars of this type. Algol (β Persei)
+completes the period of variable brightness in 68.8 hours. It loses
+three-fifths of its light, and regains it in twelve hours. In 1889
+Vogel,[17] with the Potsdam spectrograph, actually found that the
+luminous star is receding before each eclipse, and approaching us
+after each eclipse; thus entirely supporting Goodricke's opinion.
+There are many variables of the Algol type, and information is
+steadily accumulating. But all variable stars do not suffer the sudden
+variations of Algol. There are many types, and the explanations of
+others have not proved so easy.
+
+The Harvard College photographs have disclosed the very great
+prevalence of variability, and this is certainly one of the lines in
+which modern discovery must progress.
+
+Roberts, in South Africa, has done splendid work on the periods of
+variables of the Algol type.
+
+_New Stars_.--Extreme instances of variable stars are the new stars
+such as those detected by Hipparchus, Tycho Brahe, and Kepler, of
+which many have been found in the last half-century. One of the latest
+great "Novæ" was discovered in Auriga by a Scotsman, Dr. Anderson, on
+February 1st, 1892, and, with the modesty of his race, he communicated
+the fact to His Majesty's Astronomer for Scotland on an unsigned
+post-card.[18] Its spectrum was observed and photographed by Huggins
+and many others. It was full of bright lines of hydrogen, calcium,
+helium, and others not identified. The astounding fact was that lines
+were shown in pairs, bright and dark, on a faint continuous spectrum,
+indicating apparently that a dark body approaching us at the rate of
+550 miles a second[19] was traversing a cold nebulous atmosphere, and
+was heated to incandescence by friction, like a meteor in our
+atmosphere, leaving a luminous train behind it. It almost disappeared,
+and on April 26th it was of the sixteenth magnitude; but on August
+17th it brightened to the tenth, showing the principal nebular band in
+its spectrum, and no sign of approach or recession.  It was as if it
+emerged from one part of the nebula, cooled down, and rushed through
+another part of the nebula, rendering the nebular gas more luminous
+than itself.[20]
+
+Since 1892 one Nova after another has shown a spectrum as described
+above, like a meteor rushing towards us and leaving a train behind,
+for this seems to be the obvious meaning of the spectra.
+
+The same may be said of the brilliant Nova Persei, brighter at its
+best than Capella, and discovered also by Dr. Anderson on February
+22nd, 1901. It increased in brightness as it reached the densest part
+of the nebula, then it varied for some weeks by a couple of
+magnitudes, up and down, as if passing through separate nebular
+condensations. In February, 1902, it could still be seen with an
+opera-glass. As with the other Novæ, when it first dashed into the
+nebula it was vaporised and gave a continuous spectrum with dark lines
+of hydrogen and helium. It showed no bright lines paired with the dark
+ones to indicate a train left behind; but in the end its own
+luminosity died out, and the nebular spectrum predominated.
+
+The nebular illumination as seen in photographs, taken from August to
+November, seemed to spread out slowly in a gradually increasing circle
+at the rate of 90" in forty-eight days. Kapteyn put this down to the
+velocity of light, the original outburst sending its illumination to
+the nebulous gas and illuminating a spherical shell whose radius
+increased at the velocity of light. This supposition seems correct, in
+which case it can easily be shown from the above figures that the
+distance of this Nova was 300 light years.
+
+_Star Catalogues._--Since the days of very accurate observations
+numerous star-catalogues have been produced by individuals or by
+observatories. Bradley's monumental work may be said to head the list.
+Lacaille's, in the Southern hemisphere, was complementary.  Then
+Piazzi, Lalande, Groombridge, and Bessel were followed by Argelander
+with his 324,000 stars, Rumker's Paramatta catalogue of the southern
+hemisphere, and the frequent catalogues of national observatories.
+Later the Astronomische Gesellschaft started their great catalogue,
+the combined work of many observatories. Other southern ones were
+Gould's at Cordova and Stone's at the Cape.
+
+After this we have a new departure. Gill at the Cape, having the comet
+1882.ii. all to himself in those latitudes, wished his friends in
+Europe to see it, and employed a local photographer to strap his
+camera to the observatory equatoreal, driven by clockwork, and
+adjusted on the comet by the eye. The result with half-an-hour's
+exposure was good, so he tried three hours. The result was such a
+display of sharp star images that he resolved on the Cape Photographic
+Durchmusterung, which after fourteen years, with Kapteyn's aid in
+reducing, was completed. Meanwhile the brothers Henry, of Paris, were
+engaged in going over Chacornac's zodiacal stars, and were about to
+catalogue the Milky Way portion, a serious labour, when they saw
+Gill's Comet photograph and conceived the idea of doing the rest of
+their work by photography.  Gill had previously written to Admiral
+Mouchez, of the Paris Observatory, and explained to him his project
+for charting the heavens photographically, by combining the work of
+many observatories. This led Admiral Mouchez to support the brothers
+Henry in their scheme.[21] Gill, having got his own photographic work
+underway, suggested an international astrographic chart, the materials
+for different zones to be supplied by observatories of all nations,
+each equipped with similar photographic telescopes. At a conference in
+Paris, 1887, this was decided on, the stars on the charts going down
+to the fourteenth magnitude, and the catalogues to the eleventh.
+
+[Illustration: GREAT COMET, Nov. 14TH, 1882. (Exposure 2hrs. 20m.)  By
+kind permission of Sir David Gill. From this photograph originated all
+stellar chart-photography.]
+
+This monumental work is nearing completion. The labour involved was
+immense, and the highest skill was required for devising instruments
+and methods to read off the star positions from the plates.
+
+Then we have the Harvard College collection of photographic plates,
+always being automatically added to; and their annex at Arequipa in
+Peru.
+
+Such catalogues vary in their degree of accuracy; and fundamental
+catalogues of standard stars have been compiled. These require
+extension, because the differential methods of the heliometer and the
+camera cannot otherwise be made absolute.
+
+The number of stars down to the fourteenth magnitude may be taken at
+about 30,000,000; and that of all the stars visible in the greatest
+modern telescopes is probably about 100,000,000.
+
+_Nebulæ and Star-clusters._--Our knowledge of nebulæ really dates from
+the time of W. Herschel. In his great sweeps of the heavens with his
+giant telescopes he opened in this direction a new branch of
+astronomy.  At one time he held that all nebulæ might be clusters of
+innumerable minute stars at a great distance. Then he recognised the
+different classes of nebulæ, and became convinced that there is a
+widely-diffused "shining fluid" in space, though many so-called nebulæ
+could be resolved by large telescopes into stars.  He considered that
+the Milky Way is a great star cluster, whose form may be conjectured
+from numerous star-gaugings. He supposed that the compact "planetary
+nebulæ" might show a stage of evolution from the diffuse nebulæ, and
+that his classifications actually indicate various stages of
+development. Such speculations, like those of the ancients about the
+solar system, are apt to be harmful to true progress of knowledge
+unless in the hands of the ablest mathematical physicists; and
+Herschel violated their principles in other directions. But here his
+speculations have attracted a great deal of attention, and, with
+modifications, are accepted, at least as a working hypothesis, by a
+fair number of people.
+
+When Sir John Herschel had extended his father's researches into the
+Southern Hemisphere he was also led to the belief that some nebulae
+were a phosphorescent material spread through space like fog or mist.
+
+Then his views were changed by the revelations due to the great
+discoveries of Lord Rosse with his gigantic refractor,[22] when one
+nebula after another was resolved into a cluster of minute stars. At
+that time the opinion gained ground that with increase of telescopic
+power this would prove to be the case with all nebulæ.
+
+In 1864 all doubt was dispelled by Huggins[23] in his first examination
+of the spectrum of a nebula, and the subsequent extension of this
+observation to other nebulæ; thus providing a certain test which
+increase in the size of telescopes could never have given. In 1864
+Huggins found that all true nebulae give a spectrum of bright
+lines. Three are due to hydrogen; two (discovered by Copeland) are
+helium lines; others are unknown. Fifty-five lines have been
+photographed in the spectrum of the Orion nebula. It seems to be
+pretty certain that all true nebulae are gaseous, and show almost
+exactly the same spectrum.
+
+Other nebulæ, and especially the white ones like that in Andromeda,
+which have not yet been resolved into stars, show a continuous
+spectrum; others are greenish and give no lines.
+
+A great deal has to be done by the chemist before the astronomer can
+be on sure ground in drawing conclusions from certain portions of his
+spectroscopic evidence.
+
+The light of the nebulas is remarkably actinic, so that photography
+has a specially fine field in revealing details imperceptible in the
+telescope. In 1885 the brothers Henry photographed, round the star
+Maia in the Pleiades, a spiral nebula 3' long, as bright on the plate
+as that star itself, but quite invisible in the telescope; and an
+exposure of four hours revealed other new nebula in the same
+district. That painstaking and most careful observer, Barnard, with
+10¼ hours' exposure, extended this nebulosity for several degrees,
+and discovered to the north of the Pleiades a huge diffuse nebulosity,
+in a region almost destitute of stars. By establishing a 10-inch
+instrument at an altitude of 6,000 feet, Barnard has revealed the wide
+distribution of nebular matter in the constellation Scorpio over a
+space of 4° or 5° square.  Barnard asserts that the "nebular
+hypothesis" would have been killed at its birth by a knowledge of
+these photographs. Later he has used still more powerful instruments,
+and extended his discoveries.
+
+The association of stars with planetary nebulæ, and the distribution
+of nebulæ in the heavens, especially in relation to the Milky Way, are
+striking facts, which will certainly bear fruit when the time arrives
+for discarding vague speculations, and learning to read the true
+physical structure and history of the starry universe.
+
+_Stellar Spectra._--When the spectroscope was first available for
+stellar research, the leaders in this branch of astronomy were Huggins
+and Father Secchi,[24] of Rome. The former began by devoting years of
+work principally to the most accurate study of a few stars.  The
+latter devoted the years from 1863 to 1867 to a general survey of the
+whole heavens, including 4,000 stars. He divided these into four
+principal classes, which have been of the greatest service. Half of
+his stars belonged to the first class, including Sirius, Vega,
+Regulus, Altair. The characteristic feature of their spectra is the
+strength and breadth of the hydrogen lines and the extreme faintness
+of the metallic lines. This class of star is white to the eye, and
+rich in ultra violet light.
+
+The second class includes about three-eighths of his stars, including
+Capella, Pollux, and Arcturus. These stars give a spectrum like that
+of our sun, and appear yellowish to the eye.
+
+The third class includes α Herculis, α Orionis (Betelgeux), Mira
+Ceti, and about 500 red and variable stars.  The spectrum has fluted
+bands shaded from blue to red, and sharply defined at the more
+refrangible edge.
+
+The fourth class is a small one, containing no stars over fifth
+magnitude, of which 152 Schjellerup, in Canes Venatici, is a good
+example. This spectrum also has bands, but these are shaded on the
+violet side and sharp on the red side. They are due to carbon in some
+form.  These stars are ruby red in the telescope.
+
+It would appear, then, that all stars are suns with continuous
+spectra, and the classes are differentiated by the character of the
+absorbent vapours of their atmospheres.
+
+It is very likely that, after the chemists have taught us how to
+interpret all the varieties of spectrum, it will be possible to
+ascribe the different spectrum-classes to different stages in the
+life-history of every star.  Already there are plenty of people ready
+to lay down arbitrary assumptions about the lessons to be drawn from
+stellar spectra. Some say that they know with certainty that each star
+begins by being a nebula, and is condensed and heated by condensation
+until it begins to shine as a star; that it attains a climax of
+temperature, then cools down, and eventually becomes extinct.  They go
+so far as to declare that they know what class of spectrum belongs to
+each stage of a star's life, and how to distinguish between one that
+is increasing and another that is decreasing in temperature.
+
+The more cautious astronomers believe that chemistry is not
+sufficiently advanced to justify all of these deductions; that, until
+chemists have settled the lately raised question of the transmutation
+of elements, no theory can be sure. It is also held that until they
+have explained, without room for doubt, the reasons for the presence
+of some lines, and the absence of others, of any element in a stellar
+spectrum; why the arc-spectrum of each element differs from its spark
+spectrum; what are all the various changes produced in the spectrum of
+a gas by all possible concomitant variations of pressure and
+temperature; also the meanings of all the flutings in the spectra of
+metalloids and compounds; and other equally pertinent matters--until
+that time arrives the part to be played by the astronomer is one of
+observation. By all means, they say, make use of "working hypotheses"
+to add an interest to years of laborious research, and to serve as a
+guide to the direction of further labours; but be sure not to fall
+into the error of calling any mere hypothesis a theory.
+
+_Nebular Hypothesis._--The Nebular Hypothesis, which was first, as it
+were, tentatively put forward by Laplace as a note in his _Système du
+Monde_, supposes the solar system to have been a flat, disk-shaped
+nebula at a high temperature in rapid rotation. In cooling it
+condensed, leaving revolving rings at different distances from the
+centre. These themselves were supposed to condense into the nucleus
+for a rotating planet, which might, in contracting, again throw off
+rings to form satellites.  The speculation can be put in a really
+attractive form, but is in direct opposition to many of the actual
+facts; and so long as it is not favoured by those who wish to maintain
+the position of astronomy as the most exact of the sciences--exact in
+its facts, exact in its logic--this speculation must be recorded by
+the historian, only as he records the guesses of the ancient Greeks--as
+an interesting phase in the history of human thought.
+
+Other hypotheses, having the same end in view, are the meteoritic
+hypothesis of Lockyer and the planetesimal hypothesis that has been
+largely developed in the United States. These can best be read in the
+original papers to various journals, references to which may be found
+in the footnotes of Miss Clerke's _History of Astronomy during the
+Nineteenth Century_. The same can be said of Bredichin's hypothesis of
+comets' tails, Arrhenius's book on the applications of the theory of
+light repulsion, the speculations on radium, the origin of the sun's
+heat and the age of the earth, the electron hypothesis of terrestrial
+magnetism, and a host of similar speculations, all combining to throw
+an interesting light on the evolution of a modern train of thought
+that seems to delight in conjecture, while rebelling against that
+strict mathematical logic which has crowned astronomy as the queen of
+the sciences.
+
+
+FOOTNOTES:
+
+[1] _R. S. Phil Trans_., 1810 and 1817-24.
+
+[2] One of the most valuable contributions to our knowledge of stellar
+parallaxes is the result of Gill's work (_Cape Results_, vol. iii.,
+part ii., 1900.)
+
+[3] Taking the velocity of light at 186,000 miles a second, and the
+earth's mean distance at 93,000,000 miles, 1 light year=5,865,696,000,000
+miles or 63,072 astronomical units; 1 astronomical unit a year=2.94
+miles a second; and the earth's orbital velocity=18.5 miles a second.
+
+[4] Ast. Nacht., 1889.
+
+[5] R. S. Phil. Trans., 1718.
+
+[6] Mem. Acad. des Sciences, 1738, p. 337.
+
+[7] R. S Phil. Trans., 1868.
+
+[8] _R.S. Phil Trans._, 1783.
+
+[9] See Kapteyn's address to the Royal Institution, 1908. Also Gill's
+presidential address to the British Association, 1907.
+
+[10] _Brit. Assoc. Rep._, 1905.
+
+[11] R. S. Phil. Trans., 1803, 1804.
+
+[12] Ibid, 1824.
+
+[13] Connaisance des Temps, 1830.
+
+[14] _R. A. S. Mem._, vol. xlvii., p. 178; _Ast. Nach._, No. 3,142;
+Catalogue published by Lick Observatory, 1901.
+
+[15] _R. A. S., M. N._, vol. vi.
+
+[16] _R. S. Phil. Trans._, vol. lxxiii., p. 484.
+
+[17] _Astr. Nach._, No. 2,947.
+
+[18] _R. S. E. Trans_., vol. xxvii. In 1901 Dr. Anderson discovered
+Nova Persei.
+
+[19] _Astr. Nach_., No. 3,079.
+
+[20] For a different explanation see Sir W. Huggins's lecture, Royal
+Institution, May 13th, 1892.
+
+[21] For the early history of the proposals for photographic
+cataloguing of stars, see the _Cape Photographic Durchmusterung_, 3
+vols. (_Ann. of the Cape Observatory_, vols. in., iv., and v.,
+Introduction.)
+
+[22] _R. S. Phil. Trans._, 1850, p. 499 _et seq._
+
+[23] _Ibid_, vol. cliv., p. 437.
+
+[24] _Brit. Assoc. Rep._, 1868, p. 165.
+
+
+
+INDEX
+
+
+Abul Wefa, 24
+Acceleration of moon's mean motion, 60
+Achromatic lens invented, 88
+Adams, J. C., 61, 65, 68, 69, 70, 87, 118, 124
+Airy, G. B., 13, 30, 37, 65, 69, 70, 80, 81, 114, 119
+Albetegnius, 24
+Alphonso, 24
+Altazimuth, 81
+Anaxagoras, 14, 16
+Anaximander, 14
+Anaximenes, 14
+Anderson, T. D., 137, 138
+Ångstrom, A. J., 102
+Antoniadi, 113
+Apian, P., 63
+Apollonius, 22, 23
+Arago, 111
+Argelander, F. W. A., 139
+Aristarchus, 18, 29
+Aristillus, 17, 19
+Aristotle, 16, 30, 47
+Arrhenius, 146
+Arzachel, 24
+Asshurbanapal, 12
+Asteroids, discovery of, 67, 119
+Astrology, ancient and modern, 1-7, 38
+
+Backlund, 122
+Bacon, R., 86
+Bailly, 8, 65
+Barnard, E. E., 115, 143
+Beer and Mädler, 107, 110, 111
+Behaim, 74
+Bessel, F.W., 65, 79, 128, 134, 139
+Biela, 123
+Binet, 65
+Biot, 10
+Bird, 79, 80
+Bliss, 80
+Bode, 66, 69
+Bond, G. P., 99, 117, 122
+Bouvard, A., 65, 68
+Bradley, J., 79, 80, 81, 87, 127, 128, 139
+Bredechin, 146
+Bremiker, 71
+Brewster, D., 52, 91, 112
+Brinkley, 128
+Bruno, G., 49
+Burchardt, 65, 123
+Burnham, S. W., 134
+
+Callippus, 15, 16, 31
+Carrington, R. C., 97, 99, 114
+Cassini, G. D., 107, 114, 115, 116, 117, 118
+Cassini, J., 109, 129
+Chacornac, 139
+Chaldæan astronomy, 11-13
+Challis, J., 69, 70, 71, 72
+Chance, 88
+Charles, II., 50, 81
+Chinese astronomy, 8-11
+Christie, W. M. H. (Ast. Roy.), 64, 82, 125
+Chueni, 9
+Clairaut, A. C., 56, 63, 65
+Clark, A. G., 89, 135
+Clerke, Miss, 106, 146
+Comets, 120
+Common, A. A., 88
+Cooke, 89
+Copeland, R., 142
+Copernicus, N., 14, 24-31, 37, 38, 41, 42, 49, 128
+Cornu, 85
+Cowell, P. H., 3, 5, 64, 83
+Crawford, Earl of, 84
+Cromellin, A. C., 5, 64
+
+D'Alembert, 65
+Damoiseau, 65
+D'Arrest, H. L., 34
+Dawes, W. R., 100, 111
+Delambre, J. B. J., 8, 27, 51, 65, 68
+De la Rue, W., 2, 94, 99, 100, 131
+Delaunay, 65
+Democritus, 16
+Descartes, 51
+De Sejour, 117
+Deslandres, II., 101
+Desvignolles, 9
+De Zach, 67
+Digges, L., 86
+Dollond, J., 87, 90
+Dominis, A. di., 86
+Donati, 120
+Doppler, 92, 129
+Draper, 99
+Dreyer, J. L. E., 29,77
+Dunthorne, 60
+Dyson, 131
+
+Eclipses, total solar, 103
+Ecphantes, 16
+Eddington, 131
+Ellipse, 41
+Empedocles, 16
+Encke, J. F., 119, 122, 123, 133
+Epicycles, 22
+Eratosthenes, 18
+Euclid, 17
+Eudoxus, 15, 31
+Euler, L., 60, 61, 62, 65, 88, 119
+
+Fabricius, D.,95, 120, 121
+Feil and Mantois, 88
+Fizeau, H. L., 85, 92, 99
+Flamsteed, J., 50, 58, 68, 78, 79, 93
+Fohi, 8
+Forbes, J. D., 52, 91
+Foucault, L., 85, 99
+Frauenhofer, J., 88, 90, 91
+
+Galilei, G., 38, 46-49, 77, 93, 94, 95, 96, 107, 113, 115, 116, 133
+Galle, 71, 72
+Gascoigne, W., 45, 77
+Gauss, C. F., 65, 67
+Gauthier, 98
+Gautier, 89
+Gilbert, 44
+Gill, D., 84, 85, 128, 135, 139, 140
+Goodricke, J., 136
+Gould, B. A., 139
+Grant, R., 27, 47, 51, 86, 134
+Graham, 79
+Greek astronomy, 8-11
+Gregory, J. and D., 87
+Grimaldi, 113
+Groombridge, S., 139
+Grubb, 88, 89
+Guillemin, 122
+Guinand, 88
+
+Hale, G. E., 101
+Hall, A., 112
+Hall, C. M., 88
+Halley, E., 19, 51, 58, 60, 61, 62, 63, 64, 79, 120, 122, 125, 129
+Halley's comet, 62-64
+Halm, 85
+Hansen, P. A., 3, 65
+Hansky, A. P., 100
+Harding, C. L., 67
+Heliometer, 83
+Heller, 120
+Helmholtz, H. L. F., 35
+Henderson, T., 128
+Henry, P. and P., 139, 140, 143
+Heraclides, 16
+Heraclitus, 14
+Herodotus, 13
+Herschel, W., 65, 68, 97, 107, 110, 114, 115, 116, 117, 118, 126, 127,
+  130, 131, 132, 141, 142
+Herschel, J., 97, 111, 133, 134, 142
+Herschel, A. S., 125
+Hevelius, J., 178
+Hind, J. R., 5, 64, 120, 121, 122
+Hipparchus, 3, 18, 19, 20, 22, 23, 24, 26, 36, 55, 60, 74, 93, 137
+Hooke, R., 51, 111, 114
+Horrocks, J., 50, 56
+Howlett, 100
+Huggins, W., 92, 93, 99, 106, 120, 129, 137, 138, 142, 144
+Humboldt and Bonpland, 124
+Huyghens, C., 47, 77, 87, 110, 116, 117
+
+Ivory, 65
+
+Jansen, P. J. C., 105, 106
+Jansen, Z., 86
+
+Kaiser, F., 111
+Kapteyn, J. C., 131, 138, 139
+Keeler, 117
+Kepler, J., 17, 23, 26, 29, 30, 36, 37, 38-46, 48, 49, 50, 52, 53, 63,
+  66, 77, 87, 93, 127, 137
+Kepler's laws, 42
+Kirchoff, G.R., 91
+Kirsch, 9
+Knobel, E.B., 12, 13
+Ko-Show-King, 76
+
+Lacaile, N.L., 139
+Lagrange, J.L., 61, 62, 65, 119
+La Hire, 114
+Lalande, J.J.L., 60, 63, 65, 66, 72, 139
+Lamont, J., 98
+Langrenus, 107
+Laplace, P.S. de, 50, 58, 61, 62, 65,66, 123, 146
+Lassel, 72, 88, 117, 118
+Law of universal gravitation, 53
+Legendre, 65
+Leonardo da Vinci, 46
+Lewis, G.C., 17
+Le Verrier, U.J.J., 65, 68, 70, 71,72, 110, 118, 125
+Lexell, 66, 123
+Light year, 128
+Lipperhey, H., 86
+Littrow, 121
+Lockyer, J.N., 103, 105, 146
+Logarithms invented, 50
+Loewy, 2, 100
+Long inequality of Jupiter and Saturn, 50, 62
+Lowell, P., 111, 112, 118
+Lubienietz, S. de, 122
+Luther, M., 38
+Lunar theory, 37, 50, 56, 64
+
+Maclaurin, 65
+Maclear, T., 128
+Malvasia, 77
+Martin, 9
+Maxwell, J. Clerk, 117
+Maskelyne, N., 80, 130
+McLean, F., 89
+Medici, Cosmo di, 48
+Melancthon, 38
+Melotte, 83, 116
+Meteors, 123
+Meton, 15
+Meyer, 57, 65
+Michaelson, 85
+Miraldi, 110, 114
+Molyneux, 87
+Moon, physical observations, 107
+Mouchez, 139
+Moyriac de Mailla, 8
+
+Napier, Lord, 50
+Nasmyth and Carpenter, 108
+Nebulae, 141, 146
+Neison, E., 108
+Neptune, discovery of, 68-72
+Newall, 89
+Newcomb, 85
+Newton, H.A., 124
+Newton, I., 5, 19, 43, 49, 51-60, 62, 64, 68, 77, 79, 87, 90, 93, 94,
+  114, 127, 133
+Nicetas, 16, 25
+Niesten, 115
+Nunez, P., 35
+
+Olbers, H.W.M., 67
+Omar, 11, 24
+Oppolzer, 13, 125
+Oudemans, 129
+
+Palitsch, G., 64
+Parallax, solar, 85, 86
+Parmenides, 14
+Paul III., 30
+Paul V., 48
+Pemberton, 51
+Peters, C.A.F., 125, 128, 135
+Photography, 99
+Piazzi, G., 67, 128, 129, 139
+Picard, 54, 77, 114
+Pickering, E.C., 118, 135
+Pingré, 13, 122
+Plana, 65
+Planets and satellites, physical observations, 109-119
+Plato, 17, 23, 26, 40
+Poisson, 65
+Pond, J., 80
+Pons, 122
+Porta, B., 86
+Pound, 87, 114
+Pontecoulant, 64
+Precession of the equinoxes, 19-21, 55, 57
+Proctor, R.A., 111
+Pritchett, 115
+Ptolemy, 11, 13, 21, 22, 23, 24, 93
+Puiseux and Loewy, 108
+Pulfrich, 131
+Purbach, G., 24
+Pythagoras, 14, 17, 25, 29
+
+Ramsay, W., 106
+Ransome and May, 81
+Reflecting telescopes invented, 87
+Regiomontanus (Müller), 24
+Respighi, 82
+Retrograde motion of planets, 22
+Riccioli, 107
+Roberts, 137
+Römer, O.,78, 114
+Rosse, Earl of, 88, 142
+Rowland, H. A., 92, 102
+Rudolph H.,37, 39
+Rumker, C., 139
+
+Sabine, E., 98
+Savary, 133
+Schaeberle, J. M., 135
+Schiaparelli, G. V., 110, 111, 124, 125
+Scheiner, C., 87, 95, 96
+Schmidt, 108
+Schott, 88
+Schröter, J. H., 107, 110, 111, 124, 125
+Schuster, 98
+Schwabe, G. H., 97
+Secchi, A., 93, 144
+Short, 87
+Simms, J., 81
+Slipher, V. M., 119
+Socrates, 17
+Solon, 15
+Souciet, 8
+South, J., 133
+Spectroscope, 89-92
+Spectroheliograph, 101
+Spoerer, G. F. W., 98
+Spots on the sun, 84;
+  periodicity of, 97
+Stars, Parallax, 127;
+  proper motion, 129;
+  double, 132;
+  binaries, 132, 135;
+  new, 19, 36, 137;
+  catalogues of, 19, 36, 139;
+  spectra of, 143
+Stewart, B., 2, 100
+Stokes, G. G., 91
+Stone, E. J., 139
+Struve, C. L., 130
+Struve, F. G. W,, 88, 115, 128, 133
+
+Telescopes invented, 47, 86;
+  large, 88
+Temple, 115, 125
+Thales, 13, 16
+Theon, 60
+Transit circle of Römer, 78
+Timocharis, 17, 19
+Titius, 66
+Torricelli, 113
+Troughton, E., 80
+Tupman, G. L., 120
+Tuttle, 125
+Tycho Brahe, 23, 25, 30, 33-38, 39, 40, 44, 50, 75, 77, 93, 94, 129, 137
+
+Ulugh Begh, 24
+Uranus, discovery of, 65
+
+Velocity of light, 86, 128;
+  of earth in orbit, 128
+Verbiest, 75
+Vogel, H. C., 92, 129, 135, 136
+Von Asten, 122
+
+Walmsley, 65
+Walterus, B., 24, 74
+Weiss, E., 125
+Wells, 122
+Wesley, 104
+Whewell, 112
+Williams, 10
+Wilson, A., 96, 100
+Winnecke, 120
+Witte, 86
+Wollaston, 90
+Wolf, M., 119, 125, 132
+Wolf, R., 98
+Wren, C., 51
+Wyllie, A., 77
+
+Yao, 9
+Young, C. A., 103
+Yu-Chi, 8
+
+Zenith telescopes, 79, 82
+Zöllner, 92
+Zucchi, 113
+
+
+
+
+
+End of the Project Gutenberg EBook of History of Astronomy, by George Forbes
+
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