  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: CHALDÆAN BAKED BRICK OR TABLET, 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: 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 γ 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 γ 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 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:
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. “QUADRANS MURALIS SIVE TICHONICUS.” FOOTNOTES: |
|
