UNIVERSITY OF CALIFORNIA LIBRARY 
 
LIBRARY 
 
 OF THE 
 
 UNIVERSITY OF CALIFORNIA. 
 
 Class 
 
ASTRONOMICAL ESSAYS 
 
 HISTORICAL AND DESCRIPTIVE 
 
 BY 
 
 J. ELLARD GORE, F.R.A.S. 
 
 MEMBER OF THE ROYAL IRISH ACADEMY 
 
 CORRESPONDING FELLOW OF THE ROYAL ASTRONOMICAL SOCIETY OF CANADA 
 HONORARY ASSOCIATE OF THE ASTRONOMICAL SOCIETY OF WALES, ETC. 
 
 AUTHOR OF " THE SCENERY OF THE HEAVENS," " THE VISIBLE UNIVERSE," 
 "THE WORLDS OF SPACE," "STUDIES IN ASTRONOMY," ETC. 
 
 WITH 6 ILLUSTRATIONS 
 
 LONDON 
 
 CHATTO 6f WINDUS 
 1907 
 
Ex umbris et imaginibus in veritatem 
 
 All rights reserved 
 
PREFACE 
 
 OF the essays included in this volume, the following 
 have appeared in Knowledge: "The Brightness of 
 Starlight," "Stellar Brightness and Density," "Holes 
 in the Heavens," "The Stellar Universe," "A Pos- 
 sible Celestial Catastrophe," and " The New Cosmo- 
 gony;" and the following in The Observatory: 
 " The Secular Variation of Stars," " The Number of 
 the Visible Stars," and "The Satellite of Sirius." 
 The rest have not been hitherto published. For 
 much of the information contained in the first 
 three essays, and in Nos. 7 and 8, I am indebted 
 to Houzeau and Lancaster's " Bibliographie Generate 
 de rAstronomie," vol. i., Introduction. For the 
 illustrations, my best thanks are due to Professor 
 Barnard, D.Sc., of the Yerkes Observatory (U.S.A.), 
 and to Dr. Max Wolf, of Heidelberg. 
 
 J. E. G. 
 
 April 1907. 
 
 221547 
 
CONTENTS 
 
 CHAPTER PAGE 
 
 I. PRIMITIVE ASTRONOMY... ... ... ... 1 
 
 II. EARLY ASTRONOMICAL OBSERVATIONS ... 26 
 
 III. EARLY ASTRONOMICAL THEORIES ... ... 36 
 
 IV. THE OLD GREEK ASTRONOMERS ... ... 57 
 
 v. PTOLEMY'S DESCRIPTION OF THE MILKY WAY ... 69 
 
 VI. THE NAMES OF THE STARS ... ... ... 78 
 
 VII. THE EVOLUTION OF ASTRONOMICAL INSTRUMENTS . . 88 
 
 VIII. MODERN THEORIES ... ... ... 99 
 
 ix. MICHELL'S ASTRONOMICAL VIEWS ... ... 112 
 
 x. SIR WILLIAM HERSCHEL'S ASTRONOMICAL THEORIES 
 
 AND OBSERVATIONS ... ... ... 124 
 
 XL THE BRIGHTNESS OF THE SUN ... ... ... 201 
 
 XII. THE SECULAR VARIATION OF STARS ... ... 204 
 
 Xin. THE BRIGHTNESS OF STARLIGHT... ... ... 215 
 
 XIV. THE NUMBER OF THE VISIBLE STARS ... 222 
 
 XV. STELLAR BRIGHTNESS AND DENSITY ... ... 226 
 
 XVI. THE SIZE OF STELLAR SYSTEMS ... ... 240 
 
 XVII. THE SATELLITE OF SIRIUS ... ... ... 245 
 
 XVTII. "HOLES IN THE HEAVENS " ... ... 249 
 
 vii 
 
ASTRONOMICAL ESSAYS 
 
 CHAPTER I 
 
 PRIMITIVE ASTRONOMY 
 
 IN the early infancy of the nations astronomy held 
 a much more important place in the daily life of the 
 people than it does in our time. Even educated people 
 in these days scarcely realize the necessity which the 
 ancients had of constantly referring to the motions 
 of the celestial bodies for a measure of time. Clocks 
 and watches have now become so common every- 
 where, we are liable to forget that even in the 
 present day they are regulated by the motions of 
 the stars, and that without astronomical observa- 
 tions navigation could not be carried on, and com- 
 merce could not have reached its present flourishing 
 condition. In ancient times, however, when a man 
 wanted to know the " time of day," or the hour of 
 the night, he was obliged to find it from the sky 
 itself ; and for this reason most people in those days 
 had some practical knowledge of the celestial motions. 
 In fact, man's attention was originally attracted to 
 the heavens, not by their beauty and mystery, but 
 by the ordinary requirements of everyday life. In 
 this way they came to know the heavens, and to 
 assist them in acquiring this knowledge they divided 
 
2 ASTRONOMICAL ESSAYS 
 
 the stars into groups or constellations, and, perhaps 
 naturally, gave these groups the figures and names 
 of men and animals. These names and figures are 
 still found useful for purposes of identification. 
 
 Probably the first thing which attracted the 
 attention of primitive man was the regular re- 
 currence of day and night. To him the day sym- 
 bolized life, and the night represented death. Some 
 of the ancient races counted the diurnal periods by 
 nights and the numbers of years by winters. Thus 
 the old Indians of North America, when asked their 
 age, used to say, " It is so many winters since I was 
 born." In the Scandinavian mythology the day was 
 supposed to be the daughter of the night. This fancy 
 probably originated from the idea of a primeval chaos, 
 in which there was no light, or, as it is described in 
 Genesis i. 2, " darkness was upon the face of the 
 deep." This method of counting the diurnal periods 
 by nights was in use for a long time in Europe. Our 
 "fortnight," a contraction of fourteen days, is an 
 example of this. 
 
 The division of the days and nights into shorter 
 periods now called hours was to the ancients a 
 more difficult matter. During the day it was com- 
 paratively easy to determine the time approximately 
 by observing the height of the sun and the length of 
 the shadows. But during the night this was not so 
 easy, and the constant change going on throughout 
 the year in the positions of the different constella- 
 tions, owing to the earth's motion round the sun, 
 must have considerably increased the difficulty. 
 From constant observation, however, the ancients 
 came to know at what time of the year certain 
 constellations or groups of stars like the Pleiades 
 
PRIMITIVE ASTRONOMY 3 
 
 or Hyades rose and set, and they could thus estimate 
 approximately the time which had elapsed since sun- 
 set. In the book of Genesis one of the oldest books 
 extant we find no mention of hours, but merely the 
 time of the day. Thus in chap. xix. 23, we read, 
 " The sun was risen upon the earth when Lot entered 
 into Zoar." And there are other similar passages. 
 It is the same in the poems of Homer and Hesiod. 
 The word " hours " is not mentioned by either Plato 
 or Zenophon. It occurs for the first time at the 
 end of the fourth century B.C. in the writings of 
 Menander, who uses the term hora, " hour," and 
 hemiorion, "half -hour." In the works of the great 
 Roman writers, such as Cicero, Caesar, Livy, Tacitus, 
 we find terms which were in use before the hour was 
 adopted. Among these may be mentioned ante lucem, 
 " before the day," ad lucem, " at the approach of day," 
 prima lux, " the beginning of day," etc. 
 
 Next to the succession of days and nights, perhaps 
 the most striking natural phenomenon to the ancients 
 would be the phases of the moon. The regularity of 
 their recurrence gives a very convenient division of 
 time. The complete disappearance of the moon (to 
 the naked eye) at the time of " new moon," or con- 
 junction with the sun, formed a well-marked epoch 
 for the ancient observers, and the reappearance of 
 the moon, as a crescent in the evening sky was wel- 
 comed by them with dances and fires. This custom 
 was continued down to the year 692 A.D., when it was 
 abolished at the third council of Constantinople. 
 
 The return of the lunar phases is comparatively 
 so rapid, and they occur with such regularity, that 
 even in primitive times the periodicity of the pheno- 
 menon must have been sufficiently obvious to every 
 
4 ASTRONOMICAL ESSAYS 
 
 one. The ancients recognized that the lunar revolu- 
 tion was divided into two parts, the " waxing " and 
 "waning" moon, as they are now called. Pliny speaks 
 of them as luna accedens and luna dbscedens. The 
 phases between the " quarters " and full moon were 
 called luna gibbosa by the Romans. Hence our modern 
 term " gibbous." The period of days constituting a 
 lunar month formed the first beginning of a calendar 
 among the ancients. This month consisted of 29 days, 
 corresponding to what is now called the synodical 
 month, or period from one " new moon " to the next. 
 This period is not an exact number of days, its actual 
 length being 29 d 12 h 44 m 2'86 S , but the round number 
 of 29 days was sufficiently close to satisfy the require- 
 ments of primitive peoples. 
 
 Among the ancients, imagination created various 
 forms supposed to be produced by the markings on 
 the moon's surface. Some saw the figure of a hare 
 or rabbit. The Chinese thought they could make 
 out a rabbit sitting on its hind quarters before a 
 mortar or basin, and holding in its fore paws a 
 pestle, with which it pounded rice ! A hare was also 
 imagined by the Hindoos, and also by the Indians 
 of North America. On the monuments of Central 
 America the moon is represented by a jug or spiral 
 shell, from which issues a hare. The ancients, Greeks 
 and Romans, saw the face of a girl. Others saw a 
 man. Shakespeare says 
 
 " This man with lanthorn, dog, and bush of thorn." 1 
 
 Next to the phases of the moon, and the lunar 
 month, the regular recurrence of the seasons and 
 
 1 Midsummer-Night's Dream, Act v. Sc. i. line 134. See also 
 The Tempest, Act n. Sc. ii. line 131. 
 
PRIMITIVE ASTRONOMY 5 
 
 the apparent annual course of the sun naturally 
 attracted the attention of primitive man. The 
 varying lengths of the shadows cast by the sun 
 at noon would have indicated the progress of the 
 annual cycle. When the shadows ceased to increase 
 or diminish, the ancients knew that the solstice had 
 arrived. The shortest shadows would mark the 
 summer solstice, or longest day, and the longest 
 shadows the shortest day, or winter solstice. But, 
 of course, the first measurements made of these 
 shadows were very rough. By marking the direc- 
 tion of the shadow at sunrise and sunset on a 
 certain day, and then in the following year noting 
 when the direction of the shadow was exactly the 
 same, the length of the year could be roughly deter- 
 mined. In ancient Egypt the heliacal 1 rising of a 
 star was used for this purpose, the brilliant star 
 Sirius being the one generally selected. 
 
 In high latitudes the phenomenon of the seasons 
 is very striking, but near the Equator the difference 
 is not so noticeable. The word " annual " is derived 
 from the word annus, which again comes from 
 annulus, " a ring," a word suggested by the apparent 
 circular motion of the sun in the course of a year. 
 The Greek word mairro?, " a cycle," has the same signi- 
 fication. The seasons were fairly well marked in 
 Egypt (about latitude 30), and here the institution 
 of the year was of great antiquity. At first the 
 length of the year was supposed to be 360 days, but 
 this was soon corrected to 365 days. This latter 
 period seems to have been known in Egypt so far 
 back as about 3000 B.C. This fact is known from 
 
 1 The rising of a star with the sun, or a little before sunrise, was 
 called the " heliacal rising" of the star. 
 
ASTRONOMICAL ESSAYS 
 
 inscriptions on the ancient monuments, the date of 
 which can be determined with considerable accuracy. 
 The more accurate value of 365J days seems to have 
 been known to the Chinese in the twenty-fourth 
 century B.C. 
 
 The ancients must have recognized at a very 
 early period that the stars always retained their 
 relative positions. Manillas (about A.D. 10) states 
 that in his day the constellations were the same as 
 at the time of Trojan war. The early observers 
 made their observations from the tops of hills. The 
 Chinese still point out the elevation from which 
 the emperor Tcheou-Kong observed the heavens in 
 the twelfth century B.C. In Egypt they observed 
 the stars and made their religious offerings on small 
 hills. 
 
 The first groups of stars noticed by the ancients 
 seem to have been the Pleiades and Hyades, the 
 Great Bear, Orion's belt, and the Southern Cross. 
 Owing to the precession of the equinoxes, the 
 Southern Cross was in ancient times visible in more 
 northern latitudes than it is at present. About 
 5000 years ago it was just visible in the latitude 
 of London when on the meridian. Although some 
 conspicuous groups were noticed in early times, the 
 division of the whole sky into constellations was not 
 accomplished until several centuries later. Homer 
 remarks that the Great Bear is the only constella- 
 tion which never sets. From this we may infer that 
 the constellations Draco, Cassiopeia, and Cepheus 
 had not been formed in his time. According to the 
 Chinese annals, it was in the reign of Yao, about 
 the twenty-fourth century B.C., that the stars were 
 formed into groups or constellations. At that time 
 
PRIMITIVE ASTRONOMY 7 
 
 the small star 10 (i) Draconis (near a Draconis) was 
 the pole star, and later on a Draconis was the star 
 nearest to the celestial pole. The pole star was 
 called tien-y by the ancient Chinese. In the sixth 
 century B.C., Confucius mentions some groups in the 
 work called the Chi-King, among which were stars 
 in Scorpio and Lyra. His commentators speak of 
 stars in Leo under the name of the Red Bird. This 
 probably refers to the red star a Hydra?, which 
 lies south of Leo. In Egypt some of the constella- 
 tions seem to have been known before the thirteenth 
 century B.C. In the tomb of Seti I. there is a lion 
 surrounded by stars, and near it a bull is depicted, 
 which probably represents Taurus. On the ceiling 
 of one of the rooms in the palace of Ramses Miamon 
 (the Greek Sesostris) figures of animals accompanied 
 by stars are shown in connection with the twelve 
 months of the year, showing that the zodiacal con- 
 stellations were then known. A further advance is 
 seen in the tomb of Ramses IV. at Thebes, thirteenth 
 century B.C. The zodiacal constellations were, how- 
 ever, formed at a much earlier date probably as 
 far back as the twentieth century B.C. Among the 
 Hindoos the oldest Vedas which date perhaps from 
 the eighteenth or twentieth century B.C. do not 
 mention any constellations except the Great Bear. 
 
 The ideas of the ancients with reference to the i 
 Milky Way are interesting. Some writers resemble \ 
 it to a road, and the Iroquois Indians called it " the 
 road of souls." Among the ancient Greeks and 
 Romans they supposed two doors, or places, in the 
 Milky Way where it intersected the Zodiac. By that 
 of Gemini they imagined that the souls entered into 
 the world, and by that of Sagittarius they departed 
 
ASTRONOMICAL ESSAYS 
 
 and returned to the gods ! The Chinese called the 
 Milky Way the celestial river, tien-ho. 
 
 Following the discovery of a pole star by the 
 ancient observers came the possibility of navigating 
 ships by its aid. According to Aratus and Ovid, the 
 Phenicians were the first to use the pole star for this 
 purpose. In the Middle Ages the Arabians, when 
 sailing in the southern seas, used the bright star 
 Canopus as a guide. 
 
 The primitive observers do not appear to have 
 had any clear idea of the immense distances of the 
 stars from the earth. Homer says that the moun- 
 tains of Greece reach far beyond the limits of the 
 atmosphere into the ethereal regions, and he seems 
 to have imagined that the starry heavens were not 
 very far beyond these mountain tops ! The ancients 
 thought the sky was a solid hemisphere resting on 
 the earth. 1 Other crystal spheres were afterwards 
 added, as w T e shall see in a subsequent chapter. The 
 earth itself was supposed to be flat, and surrounded 
 on all sides by water, but this idea was soon aban- 
 doned by the Greek astronomers. It seems, however, 
 to have survived in Western Europe down to the 
 time of the Crusades ; and even at the present day 
 there are a few ignorant people who retain the same 
 primitive idea. 
 
 It might be expected that the motions of the 
 planets among the stars would have attracted the 
 attention of the ancients at a very early period. It 
 is therefore very remarkable that for a long time 
 after the constellations were formed, the only planet 
 which seems to have been recognized was the 
 brilliant Venus. It is the only planet referred to 
 1 See Ps. civ. 3. 
 
PRIMITIVE ASTRONOMY 9 
 
 by Homer and Hesiod. This shows that the ancients 
 did not make a very careful examination of the 
 starry heavens, and did not accurately determine 
 the positions of even the brighter stars. Saturn 
 might possibly escape the notice of primitive races, 
 but it is not so easy to understand how Jupiter 
 and Mars which are sometimes very brilliant 
 could have eluded their observation. Although 
 Venus was known as Lucifer * when a morning star, 
 and Hesperus as an evening star, the identity of the 
 two objects was known to Pythagoras (sixth century 
 B.C.). This fact seems also to have been known 
 to the Egyptians at an early date. Pythagoras 
 appears to have known all the great planets (except, 
 of course, Uranus),' but he lived some three centuries 
 later than Hesiod. Venus was the only one of the 
 planets known in America when it was discovered 
 by Columbus. 
 
 The progress of astronomy in primitive times was 
 much retarded by the ignorance of writing. This 
 art began with hieroglyphics, as may be seen on the 
 Egyptian monuments. The Greeks appear to have 
 learned the art of writing by means of letters from 
 the Pheiiicians. The earliest Greek inscriptions seem 
 to date back to the end of the sixth century B.C. 
 Homer does not mention inscriptions, although he 
 refers to pictures and hieroglyphs. 
 
 With reference to the star sphere and its apparent 
 daily rotation round the earth, the idea of a meridian, 
 or great circle passing through the north and south 
 points of the horizon and the zenith, seems to have 
 been at first mentioned by Euclid in the fourth 
 century B.C. The colures are first referred to in 
 1 See Isa. xiv. 12. 
 
10 ASTRONOMICAL ESSAYS 
 
 the writings of Theon of Smyrna in the second 
 century B.C. Achilles Tatius (fourth century A.D.) fc 
 was the first to use the term " ecliptic " to designate 
 the 'sun's apparent path in the sky. The obliquity of 
 the sphere was a subject of wonder to the ancients. 
 Many of the old Greek philosophers, such as Anaxa- 
 goras, Empedocles, and Democritus, thought that the 
 celestial pole was originally in the zenith and that 
 the horizon was gradually raised from the north! 
 They supposed that at this time the sun's route, 
 which they thought was originally along the Equator, 
 had become oblique. In the twentieth to twenty- 
 third century B.C. the Accadians seem to have 
 divided the circle of the ecliptic into twelve parts, 
 corresponding to the present signs of the Zodiac. 
 The Chaldean astronomers observed the stars at their 
 settings and risings, that is to say, the last setting 
 visible in the evening and the first rising observable 
 in the morning sky. They constructed calendars 
 showing when these risings and settings would take 
 place, and they found groups of stars which rose and 
 set together. These groups were called paranatolai 
 by the Greeks. Hesiod speaks of the heliacal risings 
 and settings of the stars in various places in his works. 
 It was on the principle of these risings and settings 
 that the famous poem of Aratus was based. The 
 paranotellons were used by several of the old Greek 
 astronomers, including Eratosthenes, Hipparchus, 
 Hyginus, and Manilius. At the time of these so-called 
 heliacal risings and settings, the star was of course 
 at some distance from the sun's place. This distance 
 depended on the brightness of the star. From 
 Ptolemy's observations it seems that Sirius first 
 appeared in the morning sky when the sun was still 
 
PRIMITIVE ASTRONOMY 11 
 
 10 to 11 degrees below the horizon. In China similar 
 observations of the stars seem to have been made at 
 a very early period. In the calendar of Hia, which 
 dates from the twenty-second century B.C., the aspect 
 of the constellations at different times of the year is 
 given. 
 
 The division of time into hours was in ancient 
 times different from that in use at present. The 
 time from sunrise to sunset was divided into a 
 number of divisions, and the nights into the same 
 number. Hence the hours of the night were not 
 equal to those of the day, and the length of both 
 varied with the seasons. These unequal hours were 
 used by the Greeks and were marked on their sun- 
 dials. Their clepsydras, or water clocks, were also 
 adapted to this system. Even the invention of 
 clocks did not at once lead to the modern system of 
 equal hours, and the long and short hours seem to 
 have survived down to even the fourteenth century 
 
 A.D. 
 
 The brightest stars are not scattered regularly 
 over the surface of the sky, and consequently their 
 risings could not give the ancient divisions of time 
 of equal length. In ancient Egypt a calendar found 
 on the ceiling of a royal tomb of the thirteenth 
 century B.C. shows the risings of the stars and con- 
 stellations for a whole year at Thebes. The Chinese 
 at a very early date seem to have used the method 
 of star culminations, that is, the passage of stars 
 across the meridian. For this purpose they used 
 the stars of the Plough and some stars in Lyra. 
 This method of culmination was also used by Hip- 
 parchus, who gives a list of stars suitable for the 
 purpose. 
 
12 ASTRONOMICAL ESSAYS 
 
 Although Venus was the only planet known in 
 very ancient times, all the night planets seem to 
 have been known in Egypt so far back as the 
 thirteenth century B.C., and long before they were 
 known to the Greeks. They were, however, known 
 to Pythagoras, as we have said, in the sixth century 
 B.C. ; and at the beginning of the Christian era their 
 movements were followed in all European countries. 
 Among the Assyrians Mercury was called Nebo. Its 
 image was sometimes represented with four wings, 
 referring, perhaps, to its apparently rapid movement 
 in the sky. Venus was called Istar or Astar. She 
 was supposed to be the mother of all beings. Mars 
 was called Nergal, and, as is well known, represented 
 the god of war. He was also called the god of hunt- 
 ing. Images of Mars are rare ; one represents him 
 with a sword in his hand and with the feet of a 
 cock. Jupiter was called Merodach, and among the 
 Greeks he was supposed to be the king of all the 
 gods. He was also represented with a sword in his 
 hand. Saturn was called Adar, and sometimes Ninip. 
 He was also called "the powerful," "the master of 
 force," "the destroyer of enemies," etc. He seems 
 to have been the Assyrian Hercules, but among the 
 Greeks he was the son of Uranus. The Hindoos 
 seem to have made an independent discovery of the 
 planets, but not till after the ninth century B.C. 
 The ancient Chinese also appear to have discovered 
 the planets independently. They connected them 
 with the five elements Mercury with water ; Venus, 
 metal ; Mars, fire (perhaps 011 account of its red 
 colour) ; and Saturn with earth. Venus seems to 
 have been the only planet which they named. They 
 called it Tai-pi, which means " very white." Among 
 
PRIMITIVE ASTRONOMY 13 
 
 the most ancient Chinese observations of the planets 
 is one of the position of Mars in Scorpio at the begin- 
 ning of the sixth century B.C. 
 
 In tropical regions the lunar month would have 
 been for the ancients the most important long 
 division of time, but in the temperate zones they 
 soon found that the year was of more importance. 
 An attempt was made to combine the lunar months 
 with the annual motion of the sun, but this was 
 found almost impossible, as the year does not con- 
 tain an even number of lunations. This difficulty 
 led to three kinds of calendar those exclusively 
 lunar, which are the most ancient ; those purely 
 solar ; and the luni-solar, which attempted to com- 
 bine the two systems. The principle of the lunar 
 calendar was to divide the year into 12 months, 
 these being alternately 29 and 30 days long, 
 which gave a year of 354 days. This being about 
 11 days too short, the seasons were gradually 
 displaced through all the months of the calendar 
 in the course of a few years. In fact, the period was 
 not a year, but a set of lunations. The solar calendar 
 appears to have been adopted at a very early period 
 by the ancient Egyptians. The regularity of the 
 annual rising of the Nile showed them the existence 
 of a period connected with the sun's annual motion. 
 The heliacal rising of Sirius seems to have been the 
 signal for the beginning of this inundation. The 
 Egyptian month was 30 days, divided into three 
 periods of ten days each, and five added days 
 brought the length of the year to 365 days, which 
 was an improvement, but still a little too short. 
 Some writers on Egyptology think that this Egyptian 
 year dates so far back as the twenty-third century 
 
14 ASTRONOMICAL ESSAYS 
 
 B.C. This year of 365 days being a little too short, 
 the heliacal rising of Sirius was disturbed in the 
 course of time, and came to occur in all months of 
 the year. It was also displaced by the precession of 
 the equinoxes. In the first century B.C. the year 
 of 365| days was adopted at Alexandria. 
 
 After the Egyptian calendar, the most ancient 
 seems to have been that of the Accadians. Their 
 year consisted of 360 days without any added days. 
 This was, of course, much too short, and this they 
 tried to correct by adding a thirteenth month every 
 six years. This gave a period of 366 days, which 
 was not so exact as the Egyptian year. 
 
 The solar calendar is the most practical of all, 
 and is the one at present in use. It was for a long 
 time based on the Alexandrian year. It was intro- 
 duced at Rome by Julius Caesar in the year 44 B.C., 
 and is hence known as the Julian year. ' Before the 
 time of Ceesar, the year was divided at Rome into 
 four parts Martius, the spring ; Aprilis, the 
 summer; Magus, the autumn; and Junius, the 
 winter. The name January was derived from 
 Janua, " a door," because it opened the year. The 
 Janua year of 365^ days is too long by nearly twelve 
 minutes. The Gregorian calendar corrected this by 
 repressing three days in every period of 400 years. 
 Thus the years 1700, 180,0, and 1900 were not leap 
 years, but 2000 will be a leap year, as it is divisible 
 by 400. 
 
 In ancient times some nations, while recognizing 
 the importance of the solar year, attempted to 
 reconcile it with the lunations. In Greece, down to 
 the time of Herodotus, they had twelve months of 
 thirty days; but when they found the summer 
 
PRIMITIVE ASTRONOMY 15 
 
 solstice inconveniently displaced, they added a thir- 
 teenth month to the year. The Arabians also added 
 occasionally a month to their year of 354 days ; but 
 these corrections were suppressed by Mahomet. 
 The Jews used a common measure of the motions 
 of the sun and moon, and thus formed a great year 
 of 600 years, or, more correctly, they found that 
 219,146 days were equal to 7421 lunations, which 
 is not far from the truth. In 329 B.C. Callippus 
 found that in 27,759 days, or about 76 years, there 
 were 940 synodic revolutions of the moon. This 
 cycle, combined with that of Meton, served to correct 
 the Grecian calendar. In this cycle of 76 years 
 there were 33 years of 354 days, 15 of 355 days, 
 and 28 of 384 days. This gave 499 months of 30 
 days, and 441 of 29 days a very complicated system. 
 One of the old Chinese astronomers, so far back 
 as the twenty-second century B.C., seems to have 
 noticed the cycle of 19 years, but in later times 
 about the second century B.C. they used a period 
 of 60 years, a cycle which seems to have been also 
 used in India. 
 
 The pyramids of Egypt seem to have been erected 
 partly as observatories, partly as temples, and partly 
 as tombs. Those of Sakkara and Dabschur seem to 
 be rather more ancient than those of Ghizeh. They 
 were built in layers of diminishing dimensions. 
 Those of Ghizeh are three in number, tne largest 
 that of Cheops (known as the Great Pyramid), that 
 of Chephron (brother of Cheops), and that of Meii- 
 kaura (son of Cheops) the Mycerinus of the Greeks. 
 From an astronomical observation found on a 
 papyrus, it appears that the pyramid of Menkaura 
 was built about 3009-3006 B.C. These pyramids are 
 
16 ASTRONOMICAL ESSAYS 
 
 oriented correctly to within a few minutes of arc. 
 In the Great Pyramid, the first inclined passage 
 (inclination about 26) would have pointed at the 
 time of its construction to the then pole star 
 a Draconis at its culmination below the pole. This 
 would fix its date at about 3050 B.C. In the Chal- 
 dean pyramids there were seven stages of different 
 colours, which represented the seven "planets." 
 Going from the base to the summit, Venus was repre- 
 sented by a white layer ; Saturn, black ; Jupiter, 
 purple ; Mercury, blue ; Mars, red ; the Moon, silver ; 
 and the Sun, gold. On the top of all was a small 
 temple, dedicated to the divinity in whose honour 
 the pyramid was built. In China they also built 
 pyramids, and the ruins of some of them still 
 remain. The ancient inhabitants of America also 
 constructed pyramids, which seem to have been used 
 both as observatories and temples. 
 
 tSome of the ancient writers thought that the 
 celestial bodies possessed souls, and were guided 
 by intelligence like human beings. This was the 
 opinion of Thales, Heraclitus, Aristotle, Cicero, 
 Seneca, and Socrates. Cicero says, "To refuse in- 
 telligence to the stars, whose order and perseverance 
 are so marvellous, and to which are entirely due the 
 preservation and the life of all beings, is to prove 
 one's self devoid of reason." x Even so late as the 
 fourteenth century A.D., Duns Scotus could hardly 
 believe that the stars were not animated. The gods 
 of the Greek mythology had perhaps their origin in 
 these ideas. The sun's apparent course in the sky 
 during the year particularly impressed the ancient 
 observers, and seemed to them to indicate the 
 1 De natura deorum, Bk. III. chap. 21. 
 
PRIMITIVE ASTRONOMY 17 
 
 existence of volition. Some, however, including 
 Anaximenes, Anaxagoras, and Herodotus, thought 
 that when the sun attained its greatest height 
 above the equator in summer he was driven back 
 by the winds and cold of the northern regions a 
 rather puerile idea, as it appears to us with our 
 wider knowledge. The ancients thought that at 
 sunset the sun descended into the sea, and that it 
 was carried back by the circular river, which sur- 
 rounded the earth, to the place where it should rise 
 the next morning. Joshua is supposed to have 
 stopped the sun in its course for some hours, and it 
 is related that in China, in the eleventh century B.C., 
 during a battle, the prince of the country of Lou 
 implored the sun to grant him a few more hours of 
 daylight, and that it actually went back about 40, 
 thus giving him about 2J hours more in which 
 to vanquish his enemies. Even in later times such 
 events are said to have occurred. It is stated by 
 contemporary historians that at the battle of Schmal- 
 kalde, fought by Charles V. on April 24, 1547, the 
 sun was arrested in its course for some time on the 
 horizon. But the historians of this event (?) must 
 have been in some way deceived. / 
 
 The religion of the Chaldeans was practically a 
 worship of the celestial bodies. They offered incense 
 to the sun, moon, the twelve signs of the zodiac, the 
 planets, and " all the host of heaven." l The Pleiades 
 were especial objects of adoration. Vast and splendid 
 temples were erected in honour of these sidereal 
 gods. At the time of Nimrod this form of worship 
 seems to have reached its zenith. 
 
 Tammuz, or Adonis, which is mentioned in the 
 1 Deut, iv. 19 ; and 2 Kings xxiii. 5. 
 
18 ASTRONOMICAL ESSAYS 
 
 Bible, 1 was the sun, which seemed to die each year 
 in winter, and rise again in the spring ; and most of 
 the other heathen gods were personifications of the 
 sun viewed under different aspects. The gods of the 
 ancient Egyptians had a similar origin. At noon 
 the sun was called Ra, and during the night Osiris, 
 and also Horus. It was the same among the Hindoos. 
 They worshipped the sun, the moon, the stars, the 
 aurora, lightning, etc. The god Mitra represented 
 the sun by day, and Varuna at night. They built 
 great temples in honour of the sun. One of the 
 largest of them is in Orissa. In later times Vishnu 
 represented the sun. He is the great hero of the 
 Sanscrit epic, the Mahabharata. Among European 
 nations, the Thor of the Scandinavians represented 
 the sun, but Odin was their supreme god. The feast 
 of Easter originally represented the resurrection or 
 rising of the sun (Astara) at the spring equinox. 
 The sun was also worshipped as a deity among the 
 ancient inhabitants of America and the islands of 
 the Pacific. 
 
 Connected with sun-worship was the worship of 
 the sacred fire. Primitive man naturally connected 
 the idea of fire with the solar heat. Among several 
 ancient nations a sacred fire was kept perpetually 
 burning in their temples. Even among the Jews 
 this custom was followed. 2 Vesta was the goddess 
 of fire at Rome, and the vestal virgins had charge 
 of the sacred fires. In Greece these sacred fires were 
 consecrated to Hestia, which was the Greek name of 
 Vesta. In other places in Italy, and also in Spain 
 and Russia, sacred fires were burnt in ancient times. 
 In Japan, and also in America, these fires formed 
 1 Ezek. viii. 14. 2 Lev. vi. 12, 13. 
 
PRIMITIVE ASTRONOMY 19 
 
 part of the ancient worship. The Greeks and Romans 
 derived the fire from the sun by means of mirrors 
 which acted like modern burning glasses. This was 
 usually done at the spring equinox. 
 
 Meteoric stones also formed objects of worship v 
 in primitive times. They were worshipped by the 
 Phenicians and others, and were placed in their 
 temples. It seems probable that the image referred 
 to in the Acts of the Apostles (xix. 35) as having 
 fallen " down from Jupiter " was carved from a 
 meteoric stone. 
 
 Falling stars or meteors were also worshipped 
 by the ancients. They are referred to by Aristotle, 
 Seneca, and Virgil. The Arabians thought they were 
 fiery stones thrown by angels 011 the heads of demons, 
 when the latter ventured too near the sky. This 
 idea is mentioned in the Koran, and is referred to by 
 the poet Moore in " Paradise and the Peri," where 
 he says 
 
 " Fleeter than the starry brands 
 Flung at night from angel hands 
 At those dark and daring sprites 
 Who would climb th' empyreal heights." 
 
 The formation of the constellations, although 
 commenced at a much earlier period, was not com- 
 pleted before the time of Eudoxus, who was a con- 
 temporary of Plato, about the fourth century B.C. 
 In this division of the stars into groups, some stars 
 were left outside and were not included in the 
 constellations. These were called by Ptolemy amor- 
 photoi, or without figure. All these are now included 
 in the modern constellations, the old boundaries 
 having been extended so as to enclose them. The 
 first star which seems to have been observed by the 
 
20 ASTRONOMICAL ESSAYS 
 
 ancients was the bright star Capella (a Aurigse), 
 which was called dilgan, " the foundation star." The 
 first observation of it probably dates back to about 
 2000 B.C. 
 
 The identity of some of the Egyptian constella- 
 tions with those of modern astronomy is doubtful. 
 Their most important constellation seems to have 
 been one called sahou, which appears to be identical 
 with our Orion. This was an important group in 
 Egypt, because it preceded and announced the ap- 
 proaching rise of Sirius, which again heralded the 
 annual inundation of the Nile. Aldebaran (a Tauri) 
 was called ary, and the Pleiades chooa, a word which 
 means "thousands." With reference to this latter 
 word, it is an interesting fact that photography has 
 revealed the existence of over two thousand stars in 
 this famous cluster. The Great Bear is referred to 
 in the Book of the Dead. 
 
 Among the ancient Hindoos the seven bright stars 
 of the Plough (Ursa Major) represented the seven 
 principal rich men or holy persons who were sup- 
 posed to live beyond Saturn. The bright star Pro- 
 cyon represented the monkey-god Hanumana, but it 
 is not easy to identify the other constellations of the 
 Hindoo sphere. 
 
 The ancient Chinese seem to have had about three 
 hundred groups or constellations. In the time of 
 Yao (about the twenty-fourth century B.C.) the sky 
 was divided into four quarters, and these were dis- 
 tinguished by different colours and animals. The 
 one containing the vernal or spring equinox was 
 represented by a white tiger, and the three others 
 by a red bird (the flamingo), a blue dragon, and a 
 black tortoise, or warrior. Among the stars show^n 
 
PRIMITIVE ASTRONOMY 21 
 
 we can identify the stars of the Plough, and a and ft 
 of the Little Bear. The Plough, or Great Bear, was 
 represented by a bushel or measure of corn, the tail 
 being the handle of the measure. The Chinese sphere 
 seems to have had an independent origin. 
 
 The ancient Arabians had their own sphere of %/ 
 imaginary animals among the stars. The Great and 
 Little Bears seem to have been their most important 
 constellations. 
 
 Why the constellations received the names they 
 bear it is not easy to see ; their nomenclature seems 
 to have been more a matter of caprice than anything \S 
 else. The origin of the name Coma Berenices is an 
 example of this. Hyginus relates that this constel- 
 lation was formed in the third century B.C., in the 
 following way : Berenice, wife of Ptolemy Euergetes 
 (son of Ptolemy Philadelphia), made a vow, when 
 her husband was about to leave her on a military 
 expedition, that if he returned in safety she would 
 cut off her hair and consecrate it in the temple of 
 Mars. Her husband returned, and she fulfilled her 
 vow, but on the following day the hair had dis- 
 appeared from the temple, and Conon, the mathe- 
 matician, showed Ptolemy seven stars near the 
 constellation of the Lion which did not belong to 
 any group of stars. These the poet Callimachus 
 formed into a constellation, and called it Coma 
 Berenices. This is referred to by Catullus in the 
 lines 
 
 " Idem me ille Conon coeleste numine vidit 
 E Bereneco vertice Csesariem." 
 
 Some of the names of the constellations have 
 been altered since ancient times. Thus the Lyre 
 
22 ASTRONOMICAL ESSAYS 
 
 formerly represented a sea tortoise, or turtle, with 
 its shell. 
 
 The following fable is related by the Persian 
 astronomer, Al-Sufi, in his " Description of the 
 Fixed Stars," written in the tenth century A.D. 
 Al-abur (Sirius) and Al-gumaisd (Procyon) were 
 two sisters of Suhail (Canopus). Canopus married 
 Al-djauza (Rigel), but having killed his new wife, 
 Canopus fled towards the South Pole, fearing the 
 anger of his sisters. Sirius followed him across the 
 Milky Way, but Procyon remained behind and wept 
 for Suhail till her eyes became weak. Al-Sufi says 
 that Sirius "is called Al-abur, because it has passed 
 across the Milky Way into the southern region." 1 
 Now, it seems to be a remarkable fact that the large 
 proper motion of Sirius would have carried it across 
 the Milky Way from the eastern to the western 
 border in a period of about 60,000 years. Possibly 
 the Arabian story may be based on a tradition of 
 Sirius having been seen on the opposite side of the 
 Milky Way by the men of the Stone Age. However 
 this may be, we know from the amount and direction 
 of the proper motion of Sirius, that it must have 
 passed across the Milky Way within the period 
 above stated. The Arabic name Al-abur is not 
 therefore, in this case, a fanciful one, but denotes an 
 actual fact. The proper motion of Procyon is very 
 similar, both in amount and direction, to that of 
 Sirius, and consequently it has been on the eastern 
 side of the Milky Way for ages past ; and this agrees 
 with the legend quoted above. 
 
 Among the ancients the zodiacal constellations 
 
 1 The same story is told by Albufaragius (thirteenth century), 
 and is probably copied from Al-Sufi's work. 
 
PRIMITIVE ASTRONOMY 23 
 
 were naturally the most important, as they marked 
 the apparent course of the sun during the year. 
 According to Professor Sayce, these constellations 
 were probably formed by the Accadians in the 
 plains of Mesopotamia, some time between the 
 twentieth and the twenty -third century B.C. These 
 "signs of the zodiac" seem to have been very 
 similar to those known at present. On the Nineveh 
 tablets we find the ram, the bull, the twins, the 
 crab, the lion, the scorpion, an archer with a bow 
 (Sagittarius), a goat with a fish's tail (Capricornus), 
 and a deity pouring water out of a jar (Aquarius). 
 Virgo, the virgin, is not represented, however, nor 
 Libra, the balance. These seem to have been 
 formed in more modern times. In ancient times 
 Libra was included in Scorpio. When the zodiacal 
 signs were first formed, the constellations coincided 
 with the " signs," but, owing to the precession of 
 the equinoxes, these have gradually shifted. Thus 
 the sign "Aries" is now in Pisces, "Pisces" in 
 Aquarius, and so on. There seems to have been no 
 connection between the names of these " signs " and 
 the seasons of the year, or the labours of agricul- 
 ture. The nomenclature appears to have been quite 
 arbitrary. In the original zodiac of the Accadians, 
 each sign was subdivided into three parts, and as 
 a sign represented 30 of the circumference, each 
 of these subdivisions was 10. In each of these a 
 particular star was assigned, if a suitable one could 
 be found, and the appearance of this star on the 
 horizon announced the arrival of the corresponding 
 portion of the ecliptic. These subdivisions were 
 of considerable astrological importance in ancient 
 Egypt. In Persia and India they had somewhat 
 
24 ASTRONOMICAL ESSAYS 
 
 similar divisions. The signs of the zodiac were also 
 known in China at an early date, but they were 
 probably derived from the Western nations. 
 
 The principal constellations were drawn by Hip- 
 parchus on a solid globe. This was preserved at 
 Alexandria, and is referred to by Ptolemy, but it is 
 now unfortunately lost. Engraved stones represent- 
 ing Atlas supporting the heavens on his shoulders 
 have been found, but most of these were on too 
 small a scale to show the constellations satisfactorily. 
 There is one, however, in the Museum of Naples 
 on a large ball of marble. On this sphere the con- 
 stellations are shown, and many of them can be 
 identified. The date of this sphere is supposed to be 
 about 300 B.C. A similar sphere is preserved in the 
 Museum of Arolsen, and there is a marble plani- 
 sphere in the Vatican. On the latter may be re- 
 cognized the constellations Ursa Major and Minor, 
 Draco, the signs of the Zodiac, Canis Major, Hydra, 
 Centaurus, Lupus, and Aquila. Libra, the balance, 
 is shown, and the presence of this zodiacal sign 
 shows that the planisphere cannot date back much 
 farther than the beginning of the Christian era. 
 
 While some of the primitive nations had a solar 
 zodiac, others had a lunar one. These have been 
 found among the Arabians, the Hindoos, and the 
 Chinese. The moon's sidereal revolution round the 
 earth being between twenty-seven and twenty-eight 
 days, twenty-eight stars were selected along the 
 moon's apparent path in the sky, corresponding in 
 their intervals as nearly as possible to the moon's 
 motion in twenty-four hours. These spaces were 
 called the "lunar mansions." They probably origi- 
 nated in India. They are mentioned in the Rig-Veda, 
 
PRIMITIVE ASTRONOMY 25 
 
 one of the sacred books of the Hindoos, written 
 about the fourteenth century B.C. These divisions 
 had a great importance in the study of astrology. 
 The stars chosen to mark these " mansions " were 
 generally near the ecliptic, with the exception of 
 some, which were selected on account of their 
 brilliancy, such as Vega and Altair. Some, how- 
 ever, near the ecliptic, did not exceed the fourth 
 magnitude. The effect of precession has, of course, 
 much disturbed the positions of these " mansions " 
 in modern times, but they are now merely names, 
 even in India, and, like the signs of the zodiac, have 
 ceased to be of any practical importance. 
 
CHAPTER II 
 
 EARLY ASTRONOMICAL OBSERVATIONS 
 
 THE history of ancient astronomy is interesting as 
 showing the gradual development or evolution of 
 the " sublime science." The instruments used for 
 making observations in ancient times were crude 
 and not susceptible of any great accuracy. Still 
 much useful work was done, and many interesting 
 naked-eye observations are recorded in the ancient 
 annals. Some of these, however, seem to be mythi- 
 cal, or rather were calculated, not observed. Such is 
 the prehistoric conjunction of the sun, moon, and 
 the five (then) known planets north of the con- 
 stellation Orion referred to by the old Chinese 
 astronomers. Many observations were, however, 
 really made. Thus we learn from the Chinese 
 records that in the time of Yao, or about 2300 B.C., 
 there were astronomers officially appointed for the 
 determination of the equinoxes and solstices. For 
 finding the exact time of the solstices that is, when 
 the sun is at its greatest distance north or south 
 of the celestial equator they used a gnomon l and 
 style, and some of these were of considerable size. 
 The gnomon was also used in ancient Greece, and 
 survived in Europe down to the time of Gassendi. 
 
 1 The modern word "gnomon" is derived from the Greek word 
 a mark or token." 
 
 2G 
 
EARLY ASTRONOMICAL OBSERVATIONS 27 
 
 The oldest measure of the solstice of which we 
 have any record seems to have been one made by 
 the Chinese astronomer, Tcheou-Kong, about the 
 end of the twelfth century B.C., in the town of 
 Lo-yaiig, near the Yellow River. Some of these 
 old Chinese observations were used by Laplace for 
 the purpose of determining the diminution in the 
 obliquity of the ecliptic. It is mentioned by Plutarch 
 and Strabo that at the time of the summer solstice 
 (the " longest day ") the sun was in the zenith at 
 the town of Syene (now called Assouan) on the Nile, 
 and that it could then be seen at noon from the 
 bottom of wells. This must have occurred before 
 the tenth century B.C. 
 
 Astronomy seems to have slowly developed in 
 Greece, for it was not till 431 B.C. that we read of 
 the first reliable observation that of the summer 
 solstice made by Meton at Athens. 
 
 The observations above referred to were made, 
 as we have said, with a gnomon, but the Incas of 
 Peru used for the same purpose the shadows of two 
 poles cast by the rising or setting sun. They also 
 made observations on the passage of the sun through 
 the zenith towards the end of their summer, at which 
 time they held the greatest religious festival of the 
 year. The columns used for the purpose at Quito 
 were destroyed by order of the Spanish governor, 
 Sebastian Belalcacar. 
 
 With reference to eclipses, the most ancient on 
 record are those referred to in the Chinese annals. 
 There are six mentioned in the "Chou-king" of 
 Confucius, who lived in the sixth century B.C., and 
 thirty-six in his book called the " Chun-tsiou." The 
 most ancient of all is one mentioned in the former 
 
28 ASTRONOMICAL ESSAYS 
 
 book. It was an eclipse of the sun which took place 
 in that part of the heavens indicated by the stars 
 TT and cr Scorpii between which the ecliptic passes 
 on the first day of the third month of autumn, 
 a little after the Emperor Tchong-Kang began to 
 reign. According to chronology, which is, of course, 
 somewhat uncertain at such a distant date, this 
 emperor commenced his reign in the year 2158 B.C. 
 Some chronologists, however, think that this date is 
 about twenty years too far back, and astronomical 
 calculations confirm this opinion. Calculations made 
 by means of Oppolzer's tables show that the eclipse 
 probably occurred in the year 2136 B.C. From this 
 distant date down to the end of the seventeenth 
 century the Chinese annals record 460 eclipses of 
 the sun and some of the moon. A long series of 
 eclipses were also recorded by the Babylonians. 
 The Assyrians also registered eclipses, and those 
 of 929 B.C. and 808 B.C. are mentioned in connection 
 with historical events. These eclipses were used 
 by Ptolemy in forming his theory of the moon's 
 motions. Some of these eclipses were verified by 
 Laplace. A great eclipse of the sun is recorded in 
 which the zone of totality crossed Assyria. Oppolzer 
 has found the date of this eclipse as 762 B.C. The 
 Egyptians also recorded a large number of eclipses, 
 and their records go back to about 1600 B.C. In 
 the Indian work, the " Mahabharata," an eclipse 
 is recorded as having been seen in India, and 
 the date of this has been found by Oppolzer as 
 1409 B.C. 
 
 All the eclipses recorded by the Greeks are of 
 later date. The following are some of the most 
 famous of these eclipses. The eclipse of Thales, 
 
EARLY ASTRONOMICAL OBSERVATIONS 29 
 
 which put an end to the war between the Medes 
 and Lydians, about 584 B.C., but the date is rather 
 uncertain ; the eclipse of Larissa, when the Persians 
 besieged that town, about 556 B.C.; the eclipse of 
 Ennius, mentioned by Cicero, about 399 B.C. ; the 
 eclipse of Alexandria, about 364 B.C. ; and the eclipse 
 of Agathocles, which is well established as having 
 occurred on the morning of August 15, B.C. 309. 1 
 Plutarch mentions an eclipse as taking place about 
 374 B.C., which terrified the senate of Thebes and 
 the Theban army. 
 
 That regular observations were made by the 
 ancient astronomers is shown by the fact that on 
 tablets from Nineveh are found lists of planetary 
 and stellar observations and records of the phases 
 of the moon, etc. Observations have also been found 
 of the star a Draconis, which was in those times the 
 nearest bright star to the celestial pole. The Nineveh 
 tablets date back to the seventeenth century B.C. A 
 Chaldean tablet preserved in the British Museum 
 shows that the passage of the moon through its 
 nodes was carefully observed, indicating that the 
 inclination of the moon's orbit to the plane of the 
 ecliptic was known in those early times, and also 
 the cause of eclipses, which even in these enlight- 
 ened days seem to be a mystery to many so-called 
 1 educated " people. 
 
 It is known that astronomy was regularly studied 
 in China so far back as the twelfth century B.C. In 
 a book called the " Tcheou-li " details are given of 
 the organization for this purpose. There was a chief 
 astronomer, called foung-siang-chi, with a number of 
 assistants under him, whose duty it was to observe 
 1 Popular Astronomy, April, 1905. 
 
30 ASTRONOMICAL ESSAYS 
 
 the stars in their passage across the meridian, and 
 thus fix their places in the sky, as is done at 
 Greenwich Observatory in the present day. Another 
 astronomer, called pao-tchang-li, with a number of 
 assistants, discussed these observations and studied 
 the aspects of the planets, especially Jupiter, for 
 astrological purposes. They also predicted eclipses, 
 and reported them to the emperor. Meteorological 
 observations were also made. From the seventh 
 century B.C. the Chinese astronomers recorded the 
 appearance of comets and star-showers. In the great 
 work of Ma-touan-lin, consisting of 100 volumes, there 
 are 45 observations of sun-spots visible to the naked 
 eye. These observations were made between the 
 years A.D. 301 and A.D. 1205. Especially large sun- 
 spots were noted in the years 826 and 832. They 
 also recorded the "new" or "temporary stars" of 
 1572 (Tycho Brahe's) and 1604 (Kepler's), and also 
 that of B.C. 133, which is supposed to have led 
 Hipparchus to form his catalogue of stars. An 
 occultation of Mars by the moon is noted in the 
 year 68 P r?., and this is the earliest recorded oc- 
 cultatioii in the annals of astronomy. Between the 
 first century B.C. and the eleventh century A.D. the 
 Chinese astronomers recorded 37 observations of 
 Mercury ; and the general accuracy of these observa- 
 tions was verified by the great French astronomer, 
 Le Verrier. One of these observations records the 
 passage of the planet between the stars 77 and y 
 Virginis, which lie near the ecliptic, and calculation 
 shows that this actually occurred on September 19 
 and 20 in the year 155 A.D., thus confirming the 
 accuracy of the Chinese observations. Plutarch 
 relates that an occultation of the star Spica (a 
 
EARLY ASTRONOMICAL OBSERVATIONS 31 
 
 Virginis) was observed in the year 282 B.C., and this 
 observation was verified by Eiicke's calculations. 
 
 Almanacs seem to have had their origin among 
 the Assyrians, and later on we find reference to 
 " year books " in Hesiod, Ovid, Virgil, Pliny, and 
 other classical writers. To the usual astronomical 
 information the Chaldean astronomers added pre- 
 dictions of coming events, like " Zadkiel's Almanac " 
 of our own day. The Egyptian tablets examined by 
 Brugsch show the course of the planets in the years 
 105 to 133 A.D., predicting their exact places in the 
 sky, even when near the sun. In one of these 
 interesting tablets a conjunction of Jupiter and 
 Saturn is referred to in the constellation Aries. 
 This seems to have occurred in the year 120 A.D. 
 Even at the present day the Hindoo Brahmins 
 publish almanacs showing in advance eclipses and 
 the positions of the planets, which they calculate 
 by rules given in one of their ancient books. The 
 Mexicans prepared wheels for several years in advance 
 which answered the purpose of almanacs. 
 
 Before the invention of clocks and watches there 
 were various methods of measuring time. The first 
 that seems to have been used was the length of 
 shadows thrown by the sun. We learn from Aristo- 
 phanes that even in his day the time was measured 
 by the length of the shadow cast by a gnomon like 
 the style of a sundial. These gnomons were placed 
 on a pillar, and concentric circles were drawn round 
 the base of the pillar, thus indicating roughly the 
 hour of the day. This method was used by the 
 Chinese, who, as we have seen, used the gnomon 
 for observing the time of the solstices so far back 
 as the twelfth century B.C. In the seventeenth 
 
32 ASTRONOMICAL ESSAYS 
 
 century A.D. the people of Madagascar used this 
 method, which they learned from the Arabs, and 
 for a standard they employed the length of a 
 man's shadow. 
 
 According to Herodotus, the Chaldeans were the 
 first to make use of sundials, but they seem to have 
 been also used by the Egyptians in very early times. 
 In the third century B.C. the Chaldean priest Berosus 
 invented an instrument in which the shadow fell on 
 an inclined concave semicircle. One of these was dis- 
 covered in some ancient ruins near Rome. Another 
 was found in the ruins of Pompeii in the year 1854. 
 Some of these old sundials are preserved in the British 
 Museum, the Louvre, and the Museum at Naples. 
 The reference in the Bible to the shadow on " the 
 dial of Ahaz" shows that sundials were in use among 
 the Jews in ancient times. They were also used at 
 Athens so far back as 434 B.C., but they do not seem 
 to have been known in Rome until the year 292 B.C. 
 
 For the correct adjustment of these gnomons and 
 sundials it was, of course, necessary to draw a line 
 exactly due north and south a meridian line, as it 
 is now called. This the ancients seem to have been 
 able to do with remarkable accuracy. The Great 
 Pyramid of Ghizeh is oriented with great precision, 
 with an error of certainly less than a quarter of a 
 degree; and it is said that in the old pyramids of 
 Mexico and Yucatan, the error did not exceed 1. 
 The ancient Chinese attached great importance to 
 the observations of stars crossing the meridian, or 
 culminations as they are called, and seem to have 
 determined the direction of the meridian by measure- 
 ments of shadows at the rising and setting of the 
 sun. 
 
EARLY ASTRONOMICAL OBSERVATIONS 33 
 
 For measuring the hours the Greeks and others 
 used clepsydras, or water clocks. They were also 
 used by the Chinese at an early period, and are 
 described in their book the " Tcheou-li," which dates 
 back to the twelfth century B.C. This instrument 
 consisted of two vessels an upper one, in which 
 water was kept at a nearly constant level, and with 
 a hole in the bottom, through which the water ran 
 into a lower vessel. In this lower vessel was a 
 graduated vertical rod, the divisions on which repre- 
 sented about fourteen minutes of time. Another 
 form of clepsydra consisted of a metal cup with a 
 small hole in the bottom, floating in a vessel of 
 water. Some of these were regulated so as to fill 
 in about 22^ minutes. Clepsydras are still used in 
 some parts of Asia. They were also used in ancient 
 times in Egypt and Chaldea, probably so far back as 
 the sixteenth or seventeenth century in Egypt. One 
 made in Alexandria was constructed to go for a 
 year ! In more modern times we read of one being 
 sent to Charlemagne by the Persian caliph, Abdullah, 
 and one received by the Emperor Frederic II. from 
 the Sultan, of Egypt, Malek-al-Kamel. 
 
 The ancients found observations of the sun very 
 difficult, owing to its excessive brightness. Archi- 
 medes measured its diameter when rising. Seneca 
 speaks of the use of smoked glasses. He also 
 mentions that he observed the phases of a solar 
 eclipse by reflection in a surface of oil or pitch 
 A tub of water was for a long time used in Europe 
 for the same purpose. The old Chinese astronomers 
 measured the altitude of stars on the meridian by 
 means of a tube mounted on a movable axis. The 
 inclination of this tube to the horizon gave the 
 
 D 
 
34 ASTRONOMICAL ESSAYS 
 
 required altitude. This method was also used by 
 the ancient Hindoos, the tube being attached to the 
 style of a gnomon. 
 
 For the measurement of angles the Greeks divided 
 the circumference of the circle into 360, evidently 
 derived from the approximate number of days in 
 the year, and this division has survived to the 
 present day. The Chinese, however, divided the 
 circle into 365|, and this division is found in their 
 work the " Tcheou-pey," which was written about 
 the time of Hipparchus, a little before the beginning 
 of the Christian era. The " spheres " of Archimedes, 
 Hipparchus, and Ptolemy consisted of two rings, 
 having the same centre, but the plane of one at 
 right angles to the plane of the other. The inner 
 ring was fixed in the plane of the meridian, and the 
 other in the plane of the equator. The time of the 
 solstice was determined by the shadow of the upper 
 half of the equatorial ring falling on the lower half. 
 Sometimes movable circles were added for the ecliptic 
 and solstitial colure. The astrolabe of Hipparchus 
 represented in principle our modern equatorial tele- 
 scope. It had an hour-circle and a circle of declina- 
 tion. With these were connected two other circles, 
 one representing the ecliptic and the other the 
 solstitial colure. These circles were about eighteen 
 inches in diameter. This gave about one-sixth of an 
 inch to each degree, but, nevertheless, the longitudes 
 of Hipparchus are sometimes in error to the extent 
 of 2. One of Ptolemy's instruments was a regular 
 mural circle. Another was in the form of a right- 
 angled triangle, of which the sides were fixed one 
 horizontally and the other vertically, while the third 
 side, or hypotenuse, was movable, and could be pointed 
 
EARLY ASTRONOMICAL OBSERVATIONS 35 
 
 to the moon when on the meridian. The altitude 
 could then be found by measuring the horizontal 
 and vertical sides. Similar instruments seem to 
 have been used by the Chinese at the end of the 
 second century B.C. 
 
 For finding a level surface the ancient observers 
 used plumb-lines from a very early date. These are 
 depicted in the Egyptian hieroglyphics, and were 
 similar in shape to the modern triangles used by 
 masons. They are mentioned by Homer in the 
 Odyssey, and were used by the Grecian astronomers 
 and architects. 
 
 The ancient observations in the library of Nineveh 
 were recorded on tablets of clay, on both sides, and 
 were numbered like the pages of a modern book. 
 These were afterwards baked in an oven to render 
 them durable. A number of these clay tablets were 
 collected by Layard, and are now preserved in the 
 British Museum. Plato wrote his works on sheets 
 of wax, and these were afterwards copied on parch- 
 ment by one of his pupils. Alexandria was for some 
 centuries before the Christian era the centre of in- 
 tellectual life. Its famous library contained a large 
 number of books collected by Aristotle and Theo- 
 phrastus, which were sold by Nebus to Ptolemy 
 Philadelphus. This wonderful library was destroyed 
 by fire in the fifth century B.C., and its destruction 
 was an irreparable loss to the history of astronomy. 
 
CHAPTER III 
 
 EARLY ASTRONOMICAL THEORIES 
 
 " When they come to model heaven 
 And calculate the stars, how they will wield 
 The mighty frame ; how build, unbuild, contrive 
 To save appearances ; how gird the sphere 
 With centric and eccentric scribbled o'er, 
 Cycle and epicycle, orb in orb." l 
 
 AT the time of the destruction of the Alexandrian 
 library, the Greek astronomers had arrived at certain 
 theories of more or less accuracy with reference to 
 the apparent motions of the heavenly bodies. These 
 theories were based on observations made during 
 several centuries by the Egyptians, Chaldeans, and 
 Chinese, and some account of these theories may 
 prove of interest to the general reader. 
 
 The cause of the moon's phases naturally excited 
 the curiosity of almost all ancient nations. These 
 phases were previously explained by the old astrono- 
 mers. The Babylonians at first explained them by 
 supposing that the moon had a bright side and a 
 dark side, that is, that one hemisphere was luminous 
 and the other dark, and these were presented to us 
 alternately by the effect of rotation. It seems 
 curious that they did not notice the fact which 
 now seems obvious that the phases depend on the 
 
 1 Milton's " Paradise Lost," viii. 79-85. 
 36 
 
EARLY ASTRONOMICAL THEORIES 37 
 
 position of the moon with reference to the sun. 
 The Greeks submitted the problem to a mathe- 
 matical investigation, and of course arrived at a 
 correct solution. From the form of the moon's 
 " terminator," or the boundary between the bright 
 and dark parts, Aristotle came to the conclusion 
 that our satellite is a dark body of spherical form ; 
 and the attempt made by Aristarchus to measure 
 the relative distances of the sun and moon show a 
 complete understanding of the laws of illumination 
 of a spherical body shining by reflected light. 
 
 An elongation of 15 from the sun was fixed by 
 the Horapolla 1 as necessary for first perceiving the 
 lunar crescent after conjunction with the sun, or 
 " new moon." The moon's " age " would then be 
 about 26 or 27 hours. Schmidt of Athens saw the 
 crescent moon, under the most favourable condi- 
 tions, between 25 and 26 hours after new moon, and 
 the close agreement of these ancient and modern 
 results is interesting. 
 
 More accurate observations of the lunar surface 
 soon abolished the purely imaginary figures which 
 the older astronomers fancied they saw in the moon. 
 Plutarch, in an interesting account of the moon's 
 appearance which was translated into Latin by 
 Kepler says that the most obvious spot on the 
 moon's surface is one which he calls the Gulf of 
 Hecate. This seems to be identical with the dark 
 spot now known as Mare Crisium, which is the most 
 conspicuous marking visible during the daytime 
 when the moon is at some distance from the sun. 
 
 1 The Horapolla was a work on hieroglyphics. It is a Greek 
 translation from the Egyptian by Phillipus. The writer probably 
 lived about the beginning of the fifth century A.D. 
 
38 ASTRONOMICAL ESSAYS 
 
 Two other spots are referred to by Plutarch, but it 
 is difficult or impossible to identify them. Some of 
 the ancients thought that the spots were due to the 
 reflection of features on the earth from a surface 
 resembling a badly polished mirror. This theory 
 was maintained by Clearchus among the Greeks, 
 and, according to Humboldt, is still believed in by 
 the modern Persians. Plutarch, however, seems to 
 have thought the spots were really inherent in the 
 moon. 
 
 The "earth-shine" visible on the dark part of 
 the moon when in the crescent phase seems to have 
 greatly puzzled the ancient astronomers. Posidonius 
 thought that it might be due to sunshine passing 
 through the body of the moon, which, according to 
 this theory, would be semi-transparent. The correct 
 explanation was not arrived at until the fifteenth 
 century. 
 
 The study of the moon's path in the sky of 
 course led the Greeks not only to an explanation of 
 the phases, but also to that of eclipses. But the 
 earlier writers held some absurd theories with refer- 
 ence to eclipses. For example, Anaximander thought 
 that the light from the sun and moon came through 
 a hole, and that when an eclipse occurred this hole 
 was temporarily closed. Others thought that, when 
 eclipsed, the sun and moon left the sky for a little 
 and descended to the earth a still more ridiculous 
 idea. It was with reference to this latter idea that 
 the Greeks called eclipses KaOaLpeo-is (a pulling down). 
 We first meet the word eKXciTrcris in Thucydides' history 
 of the Peloponnesiaii war. It seems, however, that 
 in very early times the Assyrians, Chinese, and 
 Hindoos understood the cause of eclipses, and they 
 
EARLY ASTRONOMICAL THEORIES 39 
 
 were even predicted by the Hindoos and Egyptians 
 with some approach to accuracy. This prediction 
 was accomplished by the Greeks by means of the 
 cycle known as the Saros, a period of about eighteen 
 years. The observations of a long series of eclipses 
 led to the discovery that at the end of 223 lunar 
 months, or about 6585| days, eclipses of the moon 
 return in the same order, and nearly of the same 
 magnitude ; but a small difference between the true 
 period and the assumed one somewhat disturbed the 
 accuracy of the predictions. The same remark 
 applies to eclipses of the sun, but the Babylonian \ 
 astronomers only attempted to predict lunar eclipses. 
 The Chinese also recognized a certain law in the 
 recurrence of eclipses, but sometimes failed in their 
 prediction. For these failures the official astrono- 
 mers were punished. It is related that in the 
 twenty- second century B.C. the Chinese astronomers 
 Hi and Ho were executed because they failed to 
 announce a great eclipse of the sun which occurred 
 about that time. A period triple the length of the 
 Saros, or 19,756 days, was called by the ancients 
 exeligmos, but according to Hipparchus, it would be 
 necessary for greater accuracy to extend the period 
 to 126,007 days, or about 345 years. This contains 
 4267 lunar months. In the Assyrian inscriptions 
 there is a reference to a cycle of 1805 years. This 
 was probably arrived at, not from observations, but 
 from a knowledge of the periods of revolution of the 
 earth and moon. This long period has been recently 
 referred to by Mr. A. C. D. Crommelin, who suggests 
 for it the name of Megalosaros. He says it "gives 
 surprisingly accurate results as regards duration of 
 totality, and also as regards the latitude of the 
 
40 ASTRONOMICAL ESSAYS 
 
 track, while the shift in longitude follows a fairly 
 regular law." l 
 
 Eclipses of the sun have been at all times more 
 easily understood by ordinary people than eclipses 
 of the moon. The darkening of the sun's light by 
 the interposition of the moon's body seems more 
 obvious than the passing of the moon through the 
 earth's shadow. The uncertainty connected with the 
 prediction of solar eclipses in ancient times is shown 
 by the fact that the prediction of one in the fourth 
 century B.C. by Helicon of Cyzichus, which duly took 
 place, was looked upon as a great achievement in 
 those days. Eudemus predicted another ; but even 
 in the time of Alexander the Great these eclipses 
 could not be predicted with any certainty. 
 
 The Romans were still more backward in their 
 knowledge of eclipses. The prediction of an eclipse 
 by Sulpicius Gallus in the second century B.C. as 
 related by Livy seems to be of doubtful historical 
 accuracy. However, in the time of the Emperor 
 Claudius, the Roman astronomers, having acquired 
 more accurate knowledge from the Alexandrian 
 school, attained some skill in the prediction of these 
 phenomena. 
 
 One of the greatest difficulties experienced by the 
 ancients in accepting the theory that solar eclipses 
 were caused by the interposition of the moon, was 
 that an eclipse of the sun did not occur at every 
 new moon. This was at last explained when they 
 discovered that the moon's orbit was inclined to the 
 ecliptic. Another phenomenon which puzzled them 
 greatly was the fact that the moon is sometimes 
 although rarely seen to be totally eclipsed when 
 1 The Observatory, October, 1901, p. 382. 
 
EARLY ASTRONOMICAL THEORIES 41 
 
 the sun is still above the horizon near sunset. Pliny 
 (first century A.D.) describes an eclipse of this sort 
 which he speaks of as a prodigy. Cleomenes (second 
 century) doubted the truth of the observation, but 
 suggested that it might be due to refraction, a theory 
 which we now know to be the true one. 
 
 The ancients noticed that the moon is not wholly 
 obscured by the earth's shadow during total eclipses, 
 and Plutarch remarked that the darkening was less 
 the farther the moon was from the earth at the time 
 of eclipse. 
 
 Total eclipses of the sun produced a deep impres- 
 sion among the ancients, especially before their cause 
 was discovered. Plutarch remarked that even during 
 totality there was no absolute darkness, but that a 
 light remained comparable with twilight. He noticed 
 that there was a light round the sun which prevented 
 the darkness from becoming complete. 1 The same 
 phenomenon was previously mentioned by Philo- 
 stratus in his "Life of Apollonius of Tyana," and 
 this latter notice is probably the earliest reference 
 to the solar corona. 
 
 The first ideas of the ancient astronomers with 
 reference to the apparent motions of the celestial 
 bodies were very primitive. At least, so they seem 
 to us with our wider knowledge. They imagined 
 that each celestial motion had a sphere of its own 
 that is, a crystal sphere and that each of these 
 spheres rotated separately round the earth. They 
 supposed that the sun, moon, and each of the five 
 planets then known namely, Mercury, Venus, Mars, 
 Jupiter, and Saturn had each its separate crystal 
 sphere, to which it was attached! For the fixed 
 1 " De facie in orbae Lunse," chap. 19, 37-40. 
 
42 ASTRONOMICAL ESSAYS 
 
 stars, they imagined an eighth sphere, and they 
 thought that in their case one was sufficient, because 
 these bodies appeared to move in unison, and did 
 not change their relative positions. These spheres 
 they arranged in order of the velocity of the ap- 
 parent motions. It was a very natural conclusion 
 that the more rapidly a celestial body moved, the 
 nearer it is to the earth. Even now this principle 
 is applied in estimating the distances of the stars ; 
 those having large proper motions being considered 
 as probably nearer to us than those with smaller 
 motions. On this hypothesis they arranged the 
 distances in the following order, Mercury, Venus, .the 
 Sun, Mars, Jupiter, Saturn, and the fixed stars. But 
 when they came to observe the occasional retrograde 
 motions of the planets, and the inclination of the 
 lunar orbit to the ecliptic, these motions no longer 
 seemed so simple as they at first imagined, and to 
 explain the apparent irregularities they were obliged 
 to add further spheres for each body. This, of course, 
 made the system a very complicated one. 
 
 Eudoxus of Cnidus, a friend of Plato, seems to 
 have been the first to fix the necessary number of 
 these concentric spheres. To the moon he assigned 
 three, and to the sun three more. For each of the 
 planets he thought four spheres were necessary, but 
 for the fixed stars he considered that one would 
 suffice. This made a total of 27 spheres. But even 
 this number failed to represent all the observed 
 motions, and Callippus, who came after Eudoxus, 
 found it necessary to add seven spheres more two 
 for the sun, two for the moon, and one for each of 
 the planets Mercury, Venus, and Mars, thus raising 
 the total to 34 spheres. But again this large number 
 
EARLY ASTRONOMICAL THEORIES 43 
 
 of imaginary spheres was not sufficient to account 
 for motions afterwards detected by further obser- 
 vations, and Aristotle was obliged to increase the 
 number to 55. 
 
 A grave objection to these crystal spheres might 
 have occurred to these old astronomers, and that is 
 that the distances of the sun, moon, and planets 
 from the earth were subject to change. In the case 
 of the sun and moon this is evident from the fact 
 that eclipses of the sun are sometimes total, and 
 sometimes annular. The planets also vary much in 
 their apparent brilliancy, a fact which might have 
 suggested, one would think, that their distances 
 from the earth also varied. But these objections 
 were overlooked. Sosigenes l seems to have been 
 the first to realize the force of these objections. 
 
 A curious result of this theory of crystal spheres 
 was the idea of the ancients about the " harmony 
 of the spheres." They fancied that the rotation of 
 these spheres might produce a sound or musical note. 
 This idea seems to have been held by Pythagoras at 
 the time when only eight spheres were supposed 
 necessary. The musical diatonic scale contains eight 
 notes in its gamut. There should therefore, he] sup- 
 posed, be eight notes emitted by the bodies of the 
 planetary system. Pythagoras thought that the 
 more rapid the motion the higher the note, and since 
 all the spheres were supposed to rotate round the 
 earth in 24 hours, the farthest bodies had the 
 greatest velocity, and the nearest the least. Hence, 
 in the planetary system, Saturn would give the 
 highest note, and the moon the lowest. The fixed 
 
 1 This was the astronomer employed by Julius Csesar to arrange 
 the correction of the calendar, 46 B.C. 
 
44 ASTRONOMICAL ESSAYS 
 
 stars would, of course, give a higher note still. It 
 has not been accurately determined what note 
 Pythagoras attributed to each body. The Chinese 
 book, the " Koue-yu," mentioned these supposed 
 musical notes ; and Job says, " When the morning 
 stars sang together, and all the sons of God shouted 
 for joy" (xxxviii. 7), but this is probably allegorical. 
 They are also referred to in the old legends of 
 India. The fact that these musical notes are in- 
 audible to us was explained by the ancients by sup- 
 posing that, owing to habit, our ears have become 
 insensible to them. They thought, however, that in 
 moments of absolute silence it might be possible to 
 hear them. These fanciful ideas have now vanished 
 with the crystal spheres on which they were based. 
 
 The idea of spheres to which the celestial bodies 
 were attached necessitated the conclusion that these 
 motions were uniform. But further observations 
 showed that this was not so. The difference in the 
 length of the four quarters of the year formed 
 by the sun's passage through the equinoxes and 
 solstices was known to Eudoxus, Democritus, Eucte- 
 mon, Callippus, Geminus, and Hipparchus. They 
 found that these quarters varied in length from 88J 
 to 94^ days. From this irregularity Ptolemy recog- 
 nized the necessity of distinguishing between mean 
 time and the time shown by a sundial. They found 
 the same irregularity in the case of the moon. The 
 Egyptians and Chaldeans seem to have noticed the 
 movements of the apsides and nodes of the lunar 
 orbit, and from them the Greeks appear to have 
 derived their knowledge on this subject. 
 
 Down to the second century B.C. the knowledge 
 of the Chinese with reference to the celestial motions 
 
EARLY ASTRONOMICAL THEORIES 45 
 
 seems to have been inferior to that of Hipparchus 
 and Ptolemy, but in the third century A.D. we learn 
 from a Chinese work called " Kien-siaiig " that they 
 knew that the length of the year was slightly less 
 than 365J days, and that the moon's motion is not 
 uniform. The irregularity in the sun's apparent 
 motion was not discovered by the Chinese until the 
 end of the fifth century A.D. The discovery was 
 made by a hermit named Tchang-tse-sin, and was the 
 result of thirty years' study of the sky. It has been 
 stated, however, that so early as the sixth century 
 B.C. the Chinese had some knowledge of the synodic 
 periods of the planets, but this knowledge was not 
 ascertained scientifically until a thousand years 
 later. \> 
 
 The astronomical tables used in India in ancient ,v 
 times were zealously guarded by the priests, and 
 could not be obtained for many years. The tables 
 of the " Suriya-siddhanta " seem to have been cor- 
 rected in the thirteenth century. Laplace thought 
 that the earlier tables were subsequent to the time 
 of Ptolemy. 
 
 From allusions made by Ovid, Claudianus, and 
 Martianus Capella, it seems that Archimedes con- 
 structed a sort of planetarium in the third century 
 B.C. to represent the motions of the celestial bodies. 
 This was a hollow glass globe, on which the stars 
 were represented by small discs. The sun, moon, 
 and planets were carried on movable supports, and 
 the movements were produced by means of gearing. 
 These motions showed the phases of the moon, 
 eclipses, etc. It w^as probably driven by water- 
 power. A similar instrument was afterwards con- 
 structed by Posidonius, and in the Talmud (about 
 
46 ASTRONOMICAL ESSAYS 
 
 30 A.D.) an instrument for representing the phases 
 of the moon is mentioned. 
 
 Finding that the hypothesis of crystal spheres 
 did not satisfactorily account for all the observed 
 movements of the celestial bodies, the ancient 
 astronomers had recourse to the theory of eccen- 
 trics. Thus, in the case of the sun, they supposed 
 that the centre of the apparent solar motion was 
 not in the earth, but at some distance from it. But 
 they considered the orbit to be a circle, not an 
 ellipse. In this way they rather ingeniously ac- 
 counted for the variation in the sun's distance 
 and velocity. For the moon, however, the case is 
 different, and to account for its motion they 
 imagined it revolving in a small circle, called an 
 Epicycle, the centre of which moved on a larger 
 circle, called the Deferent, the centre of the deferent 
 being at the earth. In the epicycle the motion was 
 supposed to be retrograde that is, in the direction 
 of the hands of a clock and in the deferent direct, 
 or planetary motion. The period of revolution in 
 each of these circles was the same. This hypothesis 
 of epicycles and deferents was introduced in the 
 fourth century B.C. In the third century B.C. 
 Apollonius of Perga was the great authority on 
 the subject, and the hypothesis was further elabor- 
 ated by Hipparchus and Ptolemy. From the 
 observed inequalities in the lengths of the quarters 
 of the year, Hipparchus deduced from this theory 
 the eccentricity of the earth's orbit and found it , 
 or 0*041. Its real value is now known to be 0*01077, 
 or ^ nearly. The moon, however, presented further 
 difficulties. To explain the variation known as the 
 " equation of the centre," an epicycle was found to 
 
EARLY ASTRONOMICAL THEORIES 47 
 
 be sufficient, but Ptolemy, finding that the position 
 of the perigee of the lunar orbit was not a fixed 
 point, turned the deferent into another eccentric, 
 the centre of which, placed near the earth, revolved 
 slowly round our globe with the velocity of the 
 lunar apsides. The corresponding epicycle was sup- 
 posed to make its revolution in a time equal to the 
 moon's anomalistic period. In this way the observed 
 motions were represented to a certain degree of 
 approximation. To explain the oscillation of the 
 perigee, Ptolemy supposed that the epicycle was 
 subject to an oscillation of about 13. This he 
 called the prosneusis of the epicycle. Ptolemy, how- 
 ever, does not seem to have thoroughly understood 
 the law which rules this inequality. His attempts 
 at explaining other inequalities, such as the evec- 
 tion, were not very satisfactory, and he seems to 
 have finally abandoned the attempt to explain all the 
 irregularities in the moon's motion. In fact, ancient 
 astronomy added but little to the theory of the lunar 
 motions, and these motions have become thoroughly 
 understood only in comparatively modern times. 
 
 The discovery of the inequality in the moon's 
 motion, known as the "variation," is sometimes 
 attributed to the Arabian astronomer, Abul Wefa, 
 but this claim cannot be sustained, and the dis- 
 covery seems to have been made by Tycho Brahe 
 in 1601. To explain the variation another circle 
 had to be added. Although the Arabians did not 
 know of the " variation," they did not fail to notice 
 that the moon's latitude is not constant. This fact 
 seems to have been discovered in the tenth century 
 by Hussan-Ali ben Amadjour, but he did not find 
 the law which governed it. 
 
48 ASTRONOMICAL ESSAYS 
 
 Although the hypothesis of epicycles and de- 
 ferents represented roughly the moon's position in 
 the sky at a given time, it failed to indicate satis- 
 factorily the varying distances of the moon from 
 the earth. In fact, it made the distance at apogee 
 nearly double the distance at perigee. This, of 
 course, did not agree with the apparent diameters. 
 Albategnius, in the ninth century A.D., computed 
 from eclipses that the diameters varied only from 
 29J' to 35^'. And even this was a greater difference 
 than it is in reality. Copernicus recognized this 
 discrepancy between theory and observation, and 
 tried to correct it by adding more circles, but without 
 success. Tycho Brahe also attempted a reconcilia- 
 tion, and with somewhat better success; but the 
 necessary arrangement of circles became at last so 
 complicated and unwieldy that Kepler preferred to 
 abandon the hypothesis, and trust to observations 
 for empirical values of the necessary corrections. 
 
 The motions of the planets were also represented 
 by epicycles and eccentrics. Ptolemy used a first 
 eccentric, which was called by his successors the 
 " equant." This was a circle supposed to be de- 
 scribed by the centre of the deferent. Heraclides 
 of Pontus, who lived long previous to Hipparchus, 
 seems to have had clear ideas of the motions of 
 Mercury and Venus round the sun. According to 
 his views, the sun was carried on an epicycle, the 
 centre of which corresponded to what is now known 
 as the "mean sun." Round this point the two 
 inferior planets described circles or epicyles which 
 the sun carried with it. Seneca thought that the 
 retrograde motions of the superior planets were not 
 real, but merely apparent. 
 
EARLY ASTRONOMICAL THEORIES 49 
 
 The approximations obtained by Ptolemy were 
 nearly as exact as observations could be made by 
 the instruments of his day. They would not, how- 
 ever, have agreed with modern measures of preci- 
 sion. Ptolemy thought that the lines of apsides 
 of the planets were invariable, but the old Indian 
 astronomers were aware of the displacement of 
 both the apsides and nodes of the planetary orbits, 
 and the reality of these motions was established 
 by the Arabian astronomers. The latter also knew 
 of the slow diminution in the obliquity of the 
 ecliptic. 
 
 Notwithstanding, however, the discoveries they 
 made, the Arabians continued to use the epicycles 
 of Ptolemy, and in fact this was the only practical 
 system in use down to the time of Kepler. It was 
 used as a guide to the motions of the planetary 
 system for about 1500 years. A single exception has, 
 however, been recorded. Alpetragus, an Arabian 
 astronomer who lived in the twelfth century A.D., 
 proposed to replace the epicycles by spirals. But 
 the attempt was not very successful, and was soon 
 abandoned. 
 
 The Egyptians and Chaldeans, who were able to 
 predict eclipses, must have had some methods of 
 calculation, but these were probably very rough, 
 and had they been of any real value, the Greeks 
 would most probably have preserved and improved 
 them. The Hindoos and Chinese, who were outside 
 the influence of Greek civilization, seem to have been 
 the only people among the ancients who had indepen- 
 dent methods of calculating the celestial motions. 
 Correctly speaking, however, the Chinese had no 
 astronomical theory. Their methods of calculation 
 
 E 
 
50 ASTRONOMICAL ESSAYS 
 
 were empirical, that is, they were founded on observa- 
 tion, and not on theory. They did not trouble them- 
 selves as to ivhy the planets move as they do, but 
 merely observed the motions, and then formed tables 
 for each planet to enable them to predict their posi- 
 tions in the future. These motions were supposed to 
 be uniform. As the planets have a retrograde motion 
 for some time when near opposition, discrepancies 
 occurred between the predicted and observed places, 
 and this difficulty they could not overcome. Beyond 
 this point they never advanced, and so they remain 
 to the present day. 
 
 The most important of the Hindoo books on our 
 present subject is the " Suriya-siddhanta," the author 
 of which is unknown. It is in verse, and is a collec- 
 tion of rules without any theory. By these rules 
 the pundits predicted eclipses and the positions of 
 the planets. But apparently they did not know the 
 reason of these rules, which were expressed in words, 
 and not in the form of equations, as in modern calcu- 
 lations. Even the numbers used were expressed in 
 words, and not by figures, as at present. This added 
 to the obscurity of the method, and made it unin- 
 telligible, except to the initiated. Although the 
 methods of the " Suriya-siddhanta " are inferior to 
 those of Ptolemy, they were somewhat more advanced 
 in one point, namely, in the use of sines instead of the 
 chords of arcs. Cosines are also mentioned in this 
 work. The author determined the value of the pre- 
 cession more accurately than Ptolemy did, but he 
 seems not to have known of the displacement of the 
 earth's apogee. He places the equinox near Piscium, 
 which fixes the date of the work at 572 A.D., and this 
 is confirmed by other considerations. 
 
EARLY ASTRONOMICAL THEORIES 51 
 
 With reference to the real distances of the sun, 
 moon, and planets from the earth, the early astrono- 
 mers did not arrive at any very definite conclusion. 
 In the third century B.C. Aristarchus of Samos 
 attempted to determine the relative distances of the 
 sun and moon by observations of the moon when in 
 quadrature with the sun, that is, at " half moon." 
 The principle of this method is easily understood. 
 When the moon is in quadrature, the " terminator," 
 or boundary line between the dark and bright parts, 
 should be a straight line passing through the centre 
 of the moon's disc. When in this position the sun 
 and earth, as seen from the moon, subtend a right 
 angle ; and then measuring the angle between the sun 
 and moon, we have all the angles of a right-angled 
 triangle, and hence the ratio of the sides. The method 
 is an ingenious one, but is not possible in practice, 
 owing to the difficulty in determining the moment 
 when the moon is exactly half full, due to the irregu- 
 larities of its surface. By this method Aristarchus 
 found the distance of the sun to be only nineteen 
 times that of the moon. Further observations, how- 
 ever, led Aristarchus to suspect that the sun's distance 
 is much greater, and we now know that the real dis- 
 tance is nearly 400 times the distance of the moon. 
 
 Hipparchus thought he might be able to find the 
 distance of the moon by means of lunar eclipses. 
 If, he argued, the sun may be considered at a very 
 great distance compared with the distance of the 
 moon, then its apparent diameter, as seen from the 
 moon when in opposition, would not differ much 
 from the diameter as seen from the earth at the 
 same moment. And this assumption is not far from 
 the truth. We can then find the length of the 
 
52 ASTRONOMICAL ESSAYS 
 
 earth's shadow, and its observed diameter at any 
 time would give the distance of the point on the axis 
 of the cone at which the shadow would have this 
 diameter. Now, the time occupied by the moon in 
 passing through the shadow, when a lunar eclipse is 
 a central one, gives the diameter of the shadow, and 
 hence we can infer the moon's distance. By this 
 method Hipparchus found the distance of the moon 
 to be 72 radii of the earth. This number is about 
 20 per cent, too great, but his attempt shows clearly 
 his genius and originality. Ptolemy having instru- 
 ments superior to those who preceded him, attempted 
 a direct measurement of the moon's distance. This 
 he tried to do by measuring the moon's altitude 
 above the horizon in different lunations. But he 
 did not allow for the effect of refraction, and so his 
 result was not so accurate as it might have been. 
 Having obtained a value for the moon's distance, 
 Ptolemy thought he might proceed to determine 
 the distance of the sun from the diameter of the 
 earth's shadow. But his observations were not 
 sufficiently delicate for the purpose, and the parallax 
 he found was much too large. Knowing the distances 
 of the sun and moon, their apparent diameters would 
 give, of course, their real dimensions. The ancients 
 estimated the apparent diameters very ingeniously 
 by noting the time taken by the sun and moon in 
 rising or setting. They measured the time by a 
 clepsydra, or water clock, and with the same instru- 
 ment they measured the length of the day or night, 
 or the time taken by the earth in making one rotation 
 on its axis ; or, what comes to the same thing, the 
 time of one revolution of the star-sphere round the 
 earth. Then the ratio between the time occupied 
 
EARLY ASTRONOMICAL THEORIES 53 
 
 by the sun in rising or setting and the total length 
 of the diurnal rotation gave a fraction which repre- 
 sented the apparent diameter of the sun with 
 reference to 360, the number of degrees in a circle. 
 Thus, if the time taken by the sun in rising or setting 
 is found to be two minutes, then its apparent diameter 
 would be 24^6o or yfo ^ a complete circle, and ff =J 
 a degree, which is roughly the apparent diameter. 
 This method was used by the Egyptians, and was 
 repeated in Greece by Aristarchus ; but it was justly 
 criticized by Hipparchus, who pointed out that the 
 measurement was affected by the angle at which 
 the sun rose above the horizon. 
 
 The early astronomers seem to have been much 
 surprised at finding from the lunar parallax that 
 the moon's real diameter was at least one-fourth of 
 the earth's diameter. From this result they saw 
 that the sun, which is so very much farther away, 
 must be enormously larger than the earth. This 
 discovery must have caused quite a revolution in 
 their ideas of the size of the universe. 
 
 As to the sun's real size, opinions differed widely 
 among the ancients, as they had no means of 
 accurately measuring its distance. Anaxagoras 
 (about 500 B.C.) thought it might be a fiery stone 
 perhaps about equal in size to the Peloponnesus ; l 
 but this was objected to on religious grounds as 
 being an insult to the god Apollo, and Anaxagoras' 
 life was only saved through the influence of Pericles. 
 That the sun is considerably larger than the earth 
 was admitted by Archimedes, Aristarchus, Hippar- 
 chus, Posidonius, and Ptolemy, but they did not 
 agree as to the probable size. 
 
 1 The southern portion of Greece, now called the Morea. 
 
54 ASTRONOMICAL ESSAYS 
 
 Comets were a source of much wonder to the 
 ancients, and they failed to account for them by 
 the laws of planetary motion. They were, however, 
 carefully observed. The course of the comet of 370 
 B.C. was described by Aristotle with such accuracy 
 that Pingre was enabled to compute an orbit. 
 Meteors were for a long time considered as having 
 their origin in the earth's atmosphere. 
 
 Among the Greeks, Orpheus is said to have been 
 the first to consider the probability of life in other 
 worlds. Heraclides, and all the followers of Pytha- 
 goras, considered each star as the centre of a planetary 
 system. The plurality of inhabited worlds was also 
 taught by Democritus and Epicurus, and Plutarch 
 thought it a reasonable hypothesis. Holding these 
 views, they naturally believed that the moon was 
 inhabited, and they thought that probably its 
 animals were larger and its plants more beautiful 
 than ours. 
 
 The early astronomers seem to have had some 
 idea of the precession of the equinoxes, but the fact 
 was first definitely established by Hipparchus in 
 127 B.C. The motion was first indicated by the 
 displacement of the pole star in the course of ages. 
 In the time of Yao (twenty-fourth ceutury B.C.) the 
 star a Draconis was only 2^ from the pole, and the 
 small star near it, 10 (i) Draconis, was only 1 46'. 
 This latter star although only of the 5th magnitude 
 was considered as the pole star by the ancient 
 Chinese, and they called it tien-y. a Draconis was 
 the pole star of the ancient Assyrians. In the time 
 of Hipparchus, the celestial pole formed, he says, a 
 quadrilateral with three other stars. These stars 
 were possibly 31 (Hevelius) Camelopardali, and two 
 
EARLY ASTRONOMICAL THEORIES 55 
 
 others of the 6th magnitude. Delambre, however, 
 preferred a and /3 UrssB Minoris and K Draconis, but 
 these, although brighter, are much farther off. But 
 it was not by these changes of the pole star that 
 the precession was discovered, but by the change in 
 the position of the equinoctial points. Hipparchus, 
 comparing the position of the star Spica (a Virginis) 
 in his time with its recorded position in the time of 
 Timocharis, found that the equinoxes retrograded 
 along the equator, and with wonderful genius con- 
 cluded that this motion took place round the poles 
 of the ecliptic, and not round the poles of the equator, 
 and that this movement was not a motion of the 
 stars themselves, but a displacement of the sun's 
 path. This was perhaps the nlost remarkable dis- 
 covery made by the ancient astronomers. The 
 truth of the discovery was not, however, at first 
 universally admitted. Germinus, Theon of Smyrna, 
 and Cleomedes ignored it, and Proclus actually 
 rejected it as fanciful, because the Egyptians and 
 Chaldeans had not discovered it. Others misunder- 
 stood it, and, without any good foundation for 
 their opinion, thought it was an oscillatory motion. 
 According to Theon of Alexandria (father of 
 Hypatia), this oscillation amounted to 8 011 each 
 side of a mean position, with a period of 2560 years. 
 The Hindoos, however, believed that the oscillation 
 amounted to 27. The Arabian astronomers also 
 fell into the same error, and even in the thirteenth 
 century A.D. they believed in a circular motion of 
 the equinoctial points with a radius of 4 19', and 
 with an oscillation in longitude of 10 45' in 
 a period of 4000 years. Even Copernicus believed 
 in something of this sort, but the oscillatory 
 
56 ASTRONOMICAL ESSAYS 
 
 motion was finally rejected by Tycho Brahe. In 
 China the discovery of the precession was not made 
 until long after the time of Hipparchus. The 
 Assyrian astronomers concluded that the period of 
 precession was about 43,200 years, which is nearly 
 double its real value. The precession is referred to 
 by Virgil in the "Eclogues," and by Dante in the 
 " Inferno." The ancients considered it as a period of 
 restitution in the life of the universe. 
 
 With reference to the planetary motions, the 
 Hindoos imagined that at the creation the seven 
 planets were assembled at the zero of Aries, and 
 that at the end of time they will all again be collected 
 in the same spot. This idea seems to have been the 
 origin of the Hindoo maha-yuga, or great age of 
 4,320,000 years. This is 100 times the Assyrian 
 period of precession mentioned above. In China 
 this was called the chang-yuen. 
 
CHAPTER IV 
 
 THE OLD GREEK ASTRONOMERS 
 
 " At non ingenio qusesitum nomen ab sevo 
 Excidet ; ingenio stat sine morte decus." * 
 
 IN the last chapter reference was made to several of 
 the ancient Greek astronomers. The following is a 
 short account of the most famous of these old founders 
 of Greek astronomy. They are given as nearly as 
 possible in order of time. 
 
 THALES of Miletus was born about 640 B.C., and 
 died about 562 B.C. He is generally supposed to have v 
 been the founder of Greek astronomy. He thought 
 that the stars are fire, that the moon shines by 
 reflected light from the sun, and that at new moon 
 it becomes invisible because its dark side is turned 
 towards the earth. Like most of the ancients, how- 
 ever, he thought that the earth was the centre of 
 the universe a natural idea, perhaps, in the infancy 
 of science, but an hypothesis long since exploded. 
 He divided the year into 365 days. He calculated 
 the height of the pyramids of Egypt by measuring 
 the length of their shadows. The pyramids were, 
 of course, ancient monuments even in the time of 
 Thales. According to Herodotus, Thales predicted 
 an eclipse of the sun, a phenomenon which duly 
 
 1 Propertius, Eligies, iv. 1, 63 (iii. 1, 2). 
 57 
 
58 ASTRONOMICAL ESSAYS 
 
 occurred, and which put an end to the war between 
 the Medes and Lydians ; but that this prediction was 
 really made seems doubtful. It also seems dubious 
 whether the eclipse referred to was really a total 
 one, and even the year in which it happened is some- 
 what uncertain. Thales is also said to have measured 
 the sun's apparent diameter, but his result has not 
 been recorded. 
 
 ANAXIMANDEB, also of Miletus, was born 610 B.C., 
 and died in 547 B.C., so that he was a contemporary 
 of Thales, and indeed a disciple of his. It seems 
 doubtful what his astronomical views really were. 
 According to Diogenes Laertes, he believed the earth 
 to be a sphere ; but this seems doubtful, as it is not 
 referred to by Aristotle. According to Plutarch, he 
 thought the earth was shaped like a cylinder or 
 column, and that the sun was about equal in size 
 to the earth. Plutarch also states that he constructed 
 a sphere and horoscope and invented the gnomon ; 
 but this account does not seem to be reliable. 
 
 PYTHAGORAS of Samos was born about 580 B.C., 
 and died about 500 B.C. He studied among the 
 Egyptians, Persians, and Chaldeans. He seems to 
 have known that the earth is spherical. He con- 
 sidered the question of the musical notes supposed 
 to be produced by the planets and constituting the 
 " harmony of the spheres " referred to in the last 
 chapter. Pythagoras recognized that the " evening 
 star" and the "morning star" were one and the 
 same planet, Venus, as we now call it, but in ancient 
 times known as Hesperus when an evening star, and 
 Phosphorus or Lucifer when visible in the morning 
 sky. Pythagoras is said to have died of hunger in 
 his old age. 
 
THE OLD GREEK ASTRONOMERS 59 
 
 PHILOLAUS of Croton was a pupil of Pythagoras 
 and a contemporary of Socrates. He thought that 
 the sun was a glass disc, which reflected the light of 
 the universe ! He taught, however, that the earth 
 revolved round the sun, like Venus and Mercury. 
 According to Plutarch, the views of Philolaus were 
 adopted by Plato in his old age. Philolaus found 
 the length of the lunar month to be 29J days, the 
 lunar year 351 days, and the solar year 364J days. 
 
 ANAXIMBNES, also of Miletus, was born about 
 530 B.C. According to Pliny, he erected the first 
 sundial in Lacedomonia; and according to Theon 
 of Smyrna, he thought the moon shone by light 
 reflected from the sun, and knew the cause of 
 eclipses of the moon. He was succeeded by his 
 pupil, 
 
 ANAXAGOBAS, who was born about 500 B.C., and 
 died in 428 B.C. As stated in the last chapter, he 
 thought that the sun was a fiery stone about the 
 size of the Peloponnesus. Like many of the early 
 Greek astronomers, his views were merely based on 
 theory, and not tested by any appeal to observations. 
 He was the first to explain the phases of the moon, 
 and her motion round the earth. Among his pupils 
 were Euripides, Pericles, and Socrates. 
 
 DEMOCBITUS. Born about 460 B.C., and died about 
 361 B.C. He taught that the earth was a globe sus- 
 pended in space, that the moon had mountains like 
 the earth, that the Milky Way was an immense 
 multitude of stars, and that there is an infinite 
 number of worlds in space. He believed that matter 
 consists of atoms, an hypothesis which agrees with 
 modern theories. 
 
 EMPEDOCLES (about 450 B.C.) knew the cause of 
 
60 ASTRONOMICAL ESSAYS 
 
 solar eclipses, and that the planets were beyond the 
 moon's orbit. He thought, however, that the sun's 
 distance was only three times that of the moon. 
 
 METON (about 465-385 B.C.) discovered the 
 " metonic cycle " in conjunction with EUCTEMON. 
 
 PLATO was born at Athens in 429 B.C., the year 
 in which Pericles died, and he lived till 347 B.C. He 
 was really a geometer, but deserves to be considered 
 as one of the earlier promoters of astronomy, as he 
 proposed to the mathematicians the problem of repre- 
 senting the apparent celestial motions by means of 
 circles. Over the door of his house is said to have 
 been written the motto, " Let no one ignorant of 
 geometry enter here." 
 
 EUDOXUS of Cnidus, son of Eschiiius, was born 
 about 408 B.C., and died about 355 B.C. He was a 
 pupil of Archytas, and probably Plato. He was an 
 astrologer, geometer, physician, and legislator. He 
 had also a great reputation as an astronomer. He 
 made various observations in Sicily and in Asia. 
 He found the length of the year to be 365J days. 
 According to Archimedes, he estimated the sun's 
 diameter to be only nine times that of the moon- 
 He seems to have written works, which are now lost, 
 on the " Period," the " Contour of the Earth," the 
 " Phenomena," and the " Mirror." A poetical version 
 of the " Phenomena," written by Aratus, is, however, 
 extant. 
 
 ARISTOTLE was born in 384 B.C. at Stagira, and 
 was hence called " the Stagirite." He wrote a work 
 on astronomy, which is now lost, but his work on 
 the sky (-Trepl ovpavov) contains some observations. It 
 chiefly consists, however, of theories on the motions 
 of the celestial bodies. A commentary on this work 
 
THE OLD GREEK ASTRONOMERS 61 
 
 was written by Simplicius in the fifth century A.D. 
 Aristotle was for some time tutor to Alexander the 
 Great. In his later years he was persecuted on a 
 charge of impiety and condemned to death, but he 
 fled to Chalcis, and died there in 322 B.C. He is said to 
 have observed an occultation of Mars by the moon, 
 and also one of a star by Jupiter, about 357 B.C. 
 
 EUDEMUS of Rhodes was a disciple of Aristotle. 
 He wrote a history of astronomy, of which only a 
 fragment remains. He found the obliquity of the 
 ecliptic to be 24, which was a close approximation 
 to the value it had in his time. 
 
 CALLIPPUS of Cyzicus was a pupil of Eudoxus and 
 a contemporary of Aristotle. He formed a lunar 
 period of four metonic cycles diminished by one day. 
 This was called a "callippic," and began 330 B.C. 
 He also wrote a work on the heliacal risings of the 
 planets. 
 
 HEBACLIDES of Pontus (about 373 B.C.) was a con- 
 temporary of Plato. He wrote several works which 
 are now lost. According to Simplicius, he believed 
 that the earth moved in a circle, while the heavens 
 were at rest. 
 
 AUTOLYCUS (about 340 B.C.). He wrote two 
 books ; one on the moving sphere (Ilcpt Kwovpevrjs 
 cr^at/aas), and the other on the risings and settings of 
 the stars (Ilepi eTrtroXcov Kat Svcrecov). These are the 
 most ancient of the Greek works on astronomy 
 which have been preserved. 
 
 PYTHEAS of Marseilles one of the Greek colonies 
 lived in the reign of Alexander the Great, about 
 330 B.C. He used the gnomon to find the altitude 
 of the sun at the summer solstice (longest day) by 
 means of its shadow. He is said to have observed 
 
62 ASTRONOMICAL ESSAYS 
 
 at Marseilles that on the longest day the height of 
 the gnomon was to the length of its shadow in the 
 proportion of 600 to 209. Allowing for the change 
 in the obliquity of the ecliptic in 2230 years (about 
 17' 23"), 1 I find that this observation would make 
 the latitude of Marseilles about 42 56^. The correct 
 latitude is 43 17' 50", so that Pytheas' observation 
 was not far from the truth. 
 
 EUCLID, the famous geometer, was born about 
 330 B.C., and died about 275 B.C. He is chiefly known 
 by his " Elements of Geometry," familiar to every 
 schoolboy; but he also wrote a book called the 
 "Phenomena" (tfrawofjiwa), which treats of the risings 
 and settings of the stars. He recognized that the 
 earth is a sphere. He also wrote a work on optics. 
 
 TIMOCHABIS and ABISTYLLUS (about 300 B.C.) made 
 some important observations of the positions of 
 stars, which were afterwards used by Hipparchus 
 in establishing his great discovery of the precession 
 of the equinoxes. 
 
 ABISTABCHUS of Samos (about 310-250 B.C.). 
 He wrote a work on " Sizes and Distances." He 
 taught that the moon shines by reflected light from 
 the sun, and that the earth rotates on an axis. His 
 attempt to measure the sun's distance from the earth 
 is described in the preceding chapter. According to 
 Plutarch, Aristarchus believed that the sun was im- 
 movable, and that the earth revolved round it ; but 
 in those times it was dangerous to hold such views, 
 and, like Anaxagoras, he was accused of impiety. 
 
 1 The obliquity of the ecliptic in 1900 was, according to Stock- 
 well, 23 27' 8-26", and diminishing at the rate of 0-468" per 
 annum. Hence the obliquity in the time of Pytheas would be 
 about 23 27' 8" + 17' 23", or 23 44' 31". 
 
THE OLD GREEK ASTRONOMERS 63 
 
 ARATUS was a contemporary of Aristarchus. He 
 wrote works entitled the " Phenomena," the " Diose- 
 mia " (Signs and Prognostics), and the " Mirror." He 
 can hardly be called an astronomer, as he seems to have 
 made no observations, and merely versified the work 
 of Eudoxus. In the " Phenomena " he gives a descrip- 
 tion of the constellations (after Eudoxus). Some of 
 his statements are curious. For example, he says 
 that Lyra only contains small stars, but at present its 
 principal star, Vega, is one of the highest stars in the 
 heavens. He also says that Cygnus contains stars 
 neither large 'nor small, but one of them, a Cygni, is 
 now but little below the first magnitude, and e and S 
 are above the third magnitude. Commentaries were 
 written on the work of Aratus by Cicero, Caesar 
 Germanicus, and Festus Avienus. 
 
 ARCHIMEDES of Syracuse was born 287 B.C., and 
 was killed by the Roman soldiers at the capture of 
 Syracuse in 212 B.C. He was a contemporary of 
 Eratosthenes. Although chiefly known as a mathe- 
 matician and one of the greatest that ever lived 
 he also wrote jn astronomy. He went to Egypt to 
 instruct the priests of that country, and at Alexandria 
 made the acquaintance of Conon, the geometer, to 
 whom we owe the formation of the constellation 
 Coma Berenices. Archimedes supposed that the 
 sun's diameter was about 300 times that of the 
 moon. This would make it about 648,000 miles. 
 The real value is 866,000 miles, so that Archimedes' 
 estimate was not very wide of the mark. He 
 attempted to measure the sun's apparent diameter, 
 and found it less than 32' 56", and more than 27' 0". 
 But Archimedes was evidently ignorant of trigo- 
 nometry, and could not calculate the angle at the 
 
64 ASTRONOMICAL ESSAYS 
 
 vertex of an isosceles triangle when he knew the 
 sides and the base. This ignorance of trigonometry 
 was common to all the ancient astronomers and 
 mathematicians down to the time of Hipparchus. 
 Archimedes is said to have constructed a sort of 
 " orrery " for representing the motions of the 
 celestial bodies. 
 
 ERATOSTHENES of Gyrene was born in 276 B.C. 
 He was appointed librarian of the Alexandrian 
 library by Ptolemy Euergetes. He was the first to 
 measure the size of the earth, and employed the 
 method used at present. He constructed large 
 "armillas," or fixed circular instruments, for making 
 astronomical observations. Most of his writings are 
 lost, with the exception of some fragments. A book 
 called the " Catasterisms " (KaTao-Tpto-/xot), or constel- 
 lations, is ascribed to him, but the authorship seems 
 doubtful. It contains a list of 44 constellations and 
 475 stars, but with no accurate positions given. 
 Eratosthenes was also a poet, grammarian, philoso- 
 pher, geometer, and geographer. Having become 
 blind in his old age, he committed suicide by volun- 
 tary starvation in 196 B.C. 
 
 APOLLONIUS of Perga in Pamphylia, and hence 
 called Pergseus. He was one of the greatest mathe- 
 maticians of antiquity. He lived about 250-220 B.C. 
 He wrote a work on conic sections. He seems to 
 have held the theory that the planets revolve round 
 the sun. 
 
 HIPPABCHUS, born about 166 B.C., at Nicsea in 
 Bithynia. He was the greatest astronomer of an- 
 tiquity, and has been called the Father of Astro- 
 nomy. Most of his observations seem to have been 
 made at Rhodes. Some say that he also observed 
 
THE OLD GREEK ASTRONOMERS 65 
 
 at Alexandria, but others deny this. He wrote a 
 commentary on Aratus, and this is the only one of 
 his works which has been preserved. He formed a 
 catalogue of the fixed stars, which was afterwards 
 revised by Ptolemy. He discovered the precession 
 of the equinoxes, and investigated the motions of 
 the moon's nodes and apogee, her parallax, eccen- 
 tricity, equation of the centre, and the inclination of 
 her orbit. He calculated eclipses. He deduced the 
 eccentricity of the earth's orbit, and found the 
 length of the tropical year to within 4J minutes of 
 the correct value. He was the first to use methods 
 of calculation analogous to modern plane and 
 spherical astronomy, and made a better approxi- 
 mation to the sun's distance than had been previously 
 obtained. Professor de Morgan says of him, " If 
 Hipparchus had possessed the pendulum and tele- 
 scope, fifty years might have enabled his successors 
 to place astronomy in the state in which it stood at 
 the birth of Newton." 
 
 POSIDONIUS, a Stoic philosopher, was born about 
 135 B.C., and died about 50 B.C. He observed at 
 Rhodes, and constructed a planetary machine, or 
 " orrery." He computed the earth's circumference 
 to be 180,000 stadia. Only fragments of his writings 
 have been preserved. 
 
 CLEOMBDES lived in the reign of the Roman 
 emperor Augustus, first century B.C. He wrote a 
 book with the title " Circular Theory of the Celestial 
 Phenomena" (/cu/cAiK?/? #eo/otas TWI/ /xerewpcov). This is, 
 correctly speaking, a work on cosmography, but 
 contains some astronomical researches. He proves 
 that the earth is a sphere, but, like most of the 
 ancients, he thought it was the centre of the 
 
 p 
 
66 ASTRONOMICAL ESSAYS 
 
 universe. He attempted a measurement of the 
 earth's circumference, and gives details. He found 
 from astronomical observations that the distance 
 from Rhodes to Alexandria is about ^ of the earth's 
 circumference, and taking the actual distance as 
 5000 stadia, the circumference would be 240,000 
 stadia. The exact length of a " stadium " is not 
 very certain, but assuming it to be about 157*5 
 metres, or 516'73 feet, 1 this would make the earth's 
 circumference about 23,480 miles, which is a fairly 
 close approximation. 
 
 GEMINUS of Rhodes is supposed to have lived in 
 the time of Cicero, about 70 B.C. He wrote a work 
 entitled "An Introduction to the Phenomena" 
 (ao-ayuyr) ts TO, ^ati/o/xeva). It contains no reference to 
 the "Phenomena" of Aratus, and seems to have 
 been an introduction to astronomy. He mentions 
 the stars which have proper names, such as the 
 Pleiades, Hyades, the Manger and Asses (Cancer), 
 Regulus, Spica, the Fishes, Arcturus, Procyon, Sirius, 
 Canopus, etc. He also gives the names of the 
 northern and southern constellations. From this 
 list we learn that the little constellation Equuleus 
 (LTTTTOV Trporo/xTJ) was formed by Hipparchus. A note 
 added to the work by an anonymous writer gives 
 the following list of first magnitude stars : Capella, 
 Vega, Arcturus, /3 Leonis, Aldebaran, Procyon, Betel- 
 geuse, Spica, Rigel, Sirius, Fomalhaut, Eridani (the 
 last of the river), Canopus, and Centauri fourteen 
 in all. Curiously enough, he omits Altair and 
 Regulus, and includes {3 Leonis. This latter star 
 was also rated first magnitude by Ptolemy, and by 
 Al-Sufi in the tenth century A.D., but it is now a 
 1 Dreyer, " Planetary Systems," p. 175. 
 
THE OLD GREEK ASTRONOMERS 67 
 
 little below the second magnitude ; and Altair is 
 fully first magnitude. 
 
 MANILIUS lived about A.D. 10. He wrote a poem 
 with the title 'Acrrpovo/uKojy. 
 
 MENELAUS wrote a book 011 the sphere, and made 
 some astronomical observations at Rome about the 
 year 98 A.D., in the reign of the emperor Trajan. 
 He suggested that the Milky Way is a collection of 
 faint stars. 
 
 PTOLEMY. His correct name was Claudius Ptole- 
 mseus Pelusiniensis. He was an astronomer, mathe- 
 matician, and geographer. Little is known of his 
 life, but it seems certain that he observed at Alex- 
 andria in the years 127 to 151 A.D., during the reigns 
 of the Roman emperors Hadrian and Antoninus Pius, 
 and as he survived Antoninus," he must have been 
 alive in A.D. 161. According to an Arabic tradition, 
 he lived to the age of 78. He wrote several works, 
 including a large one on geography, but his greatest 
 work is the famous one known as the " Almagest." 
 The correct title of this work is MeyoA^ 2wraas r^s 
 'Ao-rpoi/o/uas. The name Almagest is a compound of 
 the Arabic al (the) and the Greek /xeyi'o-rt (greatest), 
 meaning his greatest work. It was translated from 
 the Greek into Arabic about the year 827 A.D., 
 by Ishak Ibn Houain, by order of the caliph Al 
 Mamun, who then reigned at Bagdad. The em- 
 peror Frederick II. had it translated into Latin 
 about the year 1230, and about the year 1350 
 Girardus of Cremona made a translation of it at 
 Toledo. A translation by Liechtenstein was printed 
 at Venice in 1515. The Greek text was printed 
 at Basle in 1528, accompanied by a commentary 
 on it by Theon of Alexandria (fourth century), 
 
68 ASTRONOMICAL ESSAYS 
 
 father of the famous Hypatia. This edition was 
 edited by Simon Grymnseus. A Latin translation 
 from the Greek was made by Trapezimtius (George 
 of Trebizond), and printed at Venice in 1527, and in 
 Basle in 1541 and 1551. A Greek edition, corrected 
 by Halley, was printed at Oxford in 1712. Another 
 Greek edition with a French translation was pub- 
 lished by Halma in 1816. This edition was chiefly 
 derived from a ninth or tenth century Greek manu- 
 script preserved in the Bibliotheque du Roi, Paris. 
 Ptolemy's observations were based on those of Hip- 
 parchus. But he seems to have made some observa- 
 tions himself, as his description of the Milky Way 
 appears to be original, and also his alignments of 
 certain stars. The inequality in the moon's motion 
 known as the evection was discovered by Ptolemy. 
 This is the largest of the lunar inequalities, and is 
 due to the alternate increase and decrease of the 
 eccentricity of its orbit. 
 
CHAPTER V 
 
 PTOLEMY'S DESCRIPTION OF THE MILKY WAY 
 
 IN the second chapter of the eighth book of his 
 famous work the "Almagest," Ptolemy gives a de- 
 scription of the Milky Way as he saw it in the 
 second century of the Christian era. As this descrip- 
 tion is not, I think, generally known, I give his 
 account translated from Halma's French translation 
 of the "Almagest" (from the original Greek), pub- 
 lished in 1816 (Tome Second, p. 84). I have identi- 
 fied the stars mentioned by Ptolemy, and give my 
 identification in square brackets. When the mean- 
 ing of a word seems doubtful, I give the original 
 Greek word used by Ptolemy. Ptolemy says 
 
 " Such is the order according to which we have 
 been able to place the stars. We will add to this 
 description what it is possible to say on the situation 
 of the milky zone, as we have observed in each of 
 its parts, in trying to describe the different appear- 
 ances. 
 
 " In the first place, the Milky Way is not a circle, 
 but a zone, which is almost everywhere as white as 
 milk, and this has given it the name it bears. Now, 
 this zone is neither equal nor regular everywhere, 
 but varies as much in width as in shade of colour, 
 as well as in the number of stars in its parts, and 
 
 69 
 
70 ASTRONOMICAL ESSAYS 
 
 by the diversity of its positions ; and also because 
 that in some places it is divided into two branches, 
 as it is easy to see if we examine it with a little 
 attention. The following are the most remarkable 
 details we have found, and those most worthy of 
 observation. 
 
 " The double portion of this zone has one of its 
 points of junction near the altar [Ara], and another 
 near the bird [Cygnus] ; and of these two branches, 
 the more western or preceding one does not touch 
 the other. For they separate at the points of the 
 altar and the bird (the hen) [or Cygnus]. But the 
 following branch touches the rest of the milky zone 
 and forms but a single zone, through the middle 
 of which we can describe a great circle. We will 
 speak of this zone, beginning with the more southern 
 portions. 
 
 " These are at the feet of the centaur, but less 
 dense (apatorcpa) and darker (d/x-avporepa). The portion 
 which is in the joint of the right hind foot is a little 
 more southern than the northern line of the milky 
 zone, as well as that which is in the left fore knee, 
 and that which is on the right hind ankle [of the 
 centaur]. But that of the shank of the left fore leg 
 is in the middle of the milky part. While that of 
 the same hoof, and that of the right fore hoof [a 
 Centauri] are distant, towards the bear, from the 
 southern curve, about two of the 360 of a great 
 circle. They are denser at the hind feet. Then the 
 northern curve of the milky zone is about 1J from 
 the loins of this animal, and the southern occupies 
 the hearth of the altar and touches the more northern 
 of the two stars which are in the hearth [/3 and y 
 Arse], and the more southern of the two at the 
 
PTOLEMY ON THE MILKY WAY 71 
 
 base [0 Arse]. And the northern star of the hearth 
 [e Arss], with that which is in the middle, is in the 
 same milky zone, and these parts are much more 
 transparent [apatorc/>a]. Its northern part includes 
 the three joints placed immediately before the sting 
 of the scorpion [6, t, K Scorpii], and the nebulous 
 cluster [557 Dunlop], which is behind the sting [A., v 
 Scorpii]. The apsis or southern curve touches the 
 right hind heel of the archer [Sagittarius] and 
 includes the star of the right hand. That of the 
 southern portion of Sagittarius is outside the milky 
 zone, and that of the point of the arrow [y Sagit- 
 tarii] is in the middle. The stars of the northern 
 portion of Sagittarius are also in the milky zone, 
 deviating from each other, and from the apsides or 
 curves, by a little more than 1, the southern from 
 that of the south; and the northern from the 
 opposite. All which surrounds these three joints is 
 a little thicker [^pe/ta iruKvorepa], but that which 
 surrounds the point of the arrow is very dense, and 
 appears like a smoke. The following portions are a 
 little more transparent, and extend up to the eagle 
 [Aquila], preserving the same width. The star at 
 the extremity of the tail of the serpent [0 Ophiuchi ?], 
 which is held by the serpent bearer [Ophiuchus], 
 placed in pure air [icei/Ao/os ae/ot], is distant by a little 
 more than 1 from the preceding curve of the milky 
 zone. But of the bright stars which are below, 
 the two preceding are in the same zone, the more 
 southern being at 1, and the more northern at 2 
 distant from the following curve. The following 
 star of those which are in the right shoulder of 
 the eagle [<r Aquilse] touches the same curve, and 
 the preceding [/x, Aquilse] is included, as well as the 
 
72 ASTRONOMICAL ESSAYS 
 
 preceding bright one of those which are in the left 
 wing [7 Aquilse]. But the bright one of the back 
 [a Aquilse ?], and the two which are in a straight line 
 with it, almost touch the same curve. After this 
 the whole of the arrow [Sagitta] is in the milky zone, 
 and the star at its point [y Sagittse] is 1 from the 
 curve towards the east, while that of the notch 
 [a Sagittse] is distant 2 towards the west. The 
 portions round the eagle are a little more loaded 
 [VvKi/oTepa], and the others are a little brighter. 
 The zone then passes over the hen [Cygnus], and the 
 apsis of the side of the bars and the west is limited 
 by the star of the southern shoulder of the hen 
 [y Cygni ?], and by the star of the same wing, and by 
 the two of the southern foot. 1 The curve towards 
 the east and south is terminated by the star at the 
 extremity of the southern tarsus [ Cygni], and in- 
 cludes the two unformed (d/xo/a^wTous) [r and or Cygni], 
 which are under the same wing, and are distant 
 about 2 ; and the portions which surround this wing 
 are rather full. Those which follow them belong to 
 this zone, and are much denser. They appear to 
 commence another part, for they bend towards the 
 extremity of the other, but leaving a space between 
 them. On their southern side they touch the zone, 
 which we will now describe, and which is very 
 bright at this place of contact. But after this inter- 
 ruption of density, which is near the other part, 
 it commences from the bright star which is in the 
 tail of the bird [a Cygni], and from the nebulous 
 cluster of the northern knee [o 1 , o 2 , Cygni]. Then 
 these portions curve a little up to the star of the 
 southern knee [<o Cygni ?], preserving their density, 
 1 The description here is somewhat obscure. J. E. G. 
 
PTOLEMY ON THE MILKY WAY 73 
 
 which diminishes by degrees to the crown of Cepheus. 
 And the side which faces the bear ends at the 
 southern star of the three in the crown [e Cephei], and 
 at the following of these three [8 Cephei], at which it 
 forms twT) elevations (eoxas), one towards the bear 
 and the east, the other towards the south and east. 
 After which the Milky Way entirely embraces Cassio- 
 peia, except the star at the extremity of the foot 
 [t Cassiopeiae]. The southern curve goes up to the 
 star in the head of Cassiopeia [] ; and the northern 
 to that which is under the foot of the chair [8?], 
 and that on the leg of Cassiopeia [e]. The other stars 
 which surround it are all within the Milky Way, of 
 which the neighbouring portions of the curves form 
 a more rarefied current, and those of the middle of 
 Cassiopeia show a very extended density. Then 
 the right portion of Perseus is included in the milky 
 zone. The solitary star outside the right knee of 
 Perseus limits the northern side, which is more 
 rarefied ; but the southern [side], which is more dense, 
 is limited by the bright star which is in the right 
 knee [A?], and by the two following of the three 
 southern. 1 The nebulous cluster, which is in the hilt 
 of the sword [x], the star of the head [r], that of the 
 right shoulder [7], and that of the right elbow [77], 
 are included. The quadrilateral of the right [knee], 
 and of the calf of same leg [d], is in the middle of the 
 milky zone, but the star of the right heel [e] is a 
 little inside the southern side. Then comes the belt 
 of the coachman [Auriga], which appears of less 
 density. The star called the she-goat [Capella] 011 
 his left shoulder, and the two on his right arm 
 [y and 6 Aurigse], almost touch the northern and 
 1 Here the description is again obscure. J. E. G. 
 
7 ASTRONOMICAL ESSAYS 
 
 eastern border of the milky zone. The little star 
 which is above and near the left foot [2 or 4 ?] limits 
 the western and southern side, and that which is 
 half a degree above the right foot [* or x> Al-Sufi] is 
 within the same side. The two close stars of the 
 left arm, called the kids [rj and Aurigae], are in the 
 middle of the zone, of which the milk then passes 
 through the feet of the twins [Gemini], showing itself 
 rather dense and rather extended round the stars 
 which are at the extremities of the feet. The follow- 
 ing [26 Aurigse?] of the three stars in a straight 
 line, which are on the right foot of the coachman, 
 and the following of the two on the club of Orion 
 [x 3 Orionis], with the northern of the four at the 
 extremity of his hand [f l and / 2 ], limit the preceding 
 extremity of the milky zone. The bright one of the 
 right hand of the coachman [6 Aurigse], and that of 
 the following extremity of the foot of the following 
 twin [y, Geminorum], are about 1 within the follow- 
 ing border. The others at the extremities of the 
 feet, 77, /A, v, are in the middle of the milky zone. 
 Beyond this, it passes by the little and great dog, 
 leaving the little one [Procyon] rather far to the 
 east, and the great one [Sirius] almost quite outside 
 the milky white, towards the west, for it goes like a 
 cloud which touches the star on the back of that 
 [dog], and also the three following on the neck 
 [0, p., y ?]. The solitary star which is above the head 
 of this dog, outside and further off, is nearly 2J 
 inside the curve towards the east ; the milky current 
 is rather rare ; it goes then through the ship Argo ; 
 the northern and preceding star [], among those 
 which form the armour [damSio-Ki] of the poop, limits 
 the western curve of the zone. That of the middle 
 
PTOLEMY ON THE MILKY WAY 75 
 
 of this armour [x], and the close ones below, as well 
 as the bright one of the deck near the rudder, and 
 the middle one of the three on the keel, touch, or 
 nearly so, the same side. The northern of the 
 three at the foot of the mast limits the curve to- 
 wards the east. The bright one at the extremity of 
 the gallery is 1 inside the same side. The bright 
 one below the armour in the rudder is 1 outside the 
 same side. The southern of the two bright ones in 
 the middle of the mast [S?] touches the same side. 
 The two bright ones of the same section of the keel 
 [7 and x?] are about 2 inside the preceding curve. 
 At this place the milky current joins the zone which 
 passes through the feet of the centaur. Its course is 
 rather bright in the ship Argo, but that which 
 surrounds the armour is rather dull, as well as that 
 which surrounds the foot of the mast and the section 
 of the keel. 
 
 " Now, the zone of which we have just spoken, 
 forming, as we have said, an interruption near 
 that which clusters round the altar, from which 
 it recommences, includes the first three contiguous 
 joints in the body of the scorpion, and leaves towards 
 the west by a degree outside the curved border, the 
 following star [r Scorpio] of three which are in the 
 body, but the star which is in the fourth joint 
 [rj Scorpii] is found in the open space between the 
 two zones, at a distance nearly equal one from the 
 other, and a little more than one degree. 
 
 " Then the preceding zone proceeds, turning 
 towards the east, by a degree of the circle, similarly, 
 and terminates the preceding side of the white or 
 milky part by the star of the right knee of ser- 
 pentarius [^ Ophiuchi], and the following side by 
 
76 ASTRONOMICAL ESSAYS 
 
 the star before the same leg. But the western of 
 those at the extremity of the same foot [36 (A) 
 Ophiuchi] touches the same side. Then the western 
 curve is limited by the star of the right elbow of 
 serpentarius [/x, Ophiuchi] and the eastern side by 
 the preceding of two which are at the extremity 
 of the same hand [v Ophiuchi]. From this place 
 there is a considerable interval (StaAeija/xa), caused 
 by the ethereal span, in which are the two stars 
 of the serpent's tail [ and 77 Serpentis] following 
 those of the extremity. All the tortuous and thin 
 part of this zone is a rare and almost ethereal 
 current, except that which includes the three 
 points, which is rather dense. 
 
 " After this interruption the Milky Way recom- 
 mences at the four stars which follow the right 
 shoulder of serpentarius [66, 67, 68, and 70 Ophiuchi] ; 
 and the bright solitary one placed near the tail of 
 the eagle [ Aquilse] terminates, in touching it, 
 the curved eastern extremity of this zone, but the 
 opposite curve is terminated by the more distant 
 of the four just mentioned 011 the side of the bear. 
 From this point the zone becomes brighter and 
 contracts in the preceding portions of the beak 
 of the bird [Cygnus], almost having the appearance 
 of an interruption. But the rest from this beak 
 [ft Cygni] up to the breast [7 Cygni] is wider and 
 denser, and the star on the neck [17 Cygni] is in 
 the middle of this density. But a rarer portion 
 rises towards the bears from the breast to the star 
 on the shoulder of the right wing [S Cygni], as well 
 as from the two close stars in the right foot [o 1 and 
 o 2 Cygni]. Thus, as we have said, there is a total 
 interruption between the two zones from the stars 
 
PTOLEMY ON THE MILKY WAY 77 
 
 of the bird above named to the bright star of its 
 tail " [a Cygni]. 
 
 As the ancients had probably very keen eyesight, 
 Ptolemy's description of the Milky Way is valuable 
 for comparison with modern observations. 
 
CHAPTER VI 
 
 THE NAMES OF THE STARS 
 
 THE names by which the brighter stars are known 
 as least most of them have come down to us from 
 a remote antiquity. But the original names have 
 been more or less altered to suit the requirements 
 of our English tongue. Some of the ancient Arabic 
 names were long and difficult to pronounce, and 
 these have been curtailed and otherwise modified. 
 An examination of these old names and the changes 
 which they have undergone in modern times may 
 prove of interest to the general reader. 
 
 We will first consider the brightest stars in order 
 of brilliancy, beginning with the brilliant Sirius, 
 the brightest of the stellar hosts. The name Sirius 
 is supposed to be derived from the Greek word 
 o-etp605 (seirios), which signifies brightness and heat. 
 Professor Max Mliller thought that the Greek word 
 might be traced to the Sanscrit svar or suonasira^<,. 
 Sirius seems to have been worshipped by the ancient 
 Egyptians under the names of Sothis and Osiris, and 
 the latter name without the initial " O " very much 
 resembles our modern name. The Arabic name for 
 the star was al-shira al-jamdnija, the bright star of 
 Yemen, or Arabia Felix. Perhaps the word shira 
 might, in the course of time, be corrupted into Sirius. 
 It was also known as the " dog-star," from the fact 
 
 78 
 
THE NAMES OF THE STARS 79 
 
 of its rising in ancient times with the sun at the 
 time when the so-called dog-days commenced. The 
 Hebrew name was Sihor. Sirius is supposed to re- 
 present the three-headed dog Cerberus, who guarded 
 the entrance to Hades in the Greek mythology. It 
 is first mentioned by Hesiod. The French word 
 soleil, "the sun," is supposed to be derived from 
 Syr-ceil^ " the eye of Sirius." 
 
 Next to Sirius in brightness is the bright southern 
 star Canopus (a Argus), which does not rise above the 
 English horizon. The Arabic name was kdnupus, or, 
 in Greek, /cavw/?os. It was also called by the Arabian 
 astronomers suha/il from the root sahala " that 
 which traverses a plain," referring probably to its 
 low altitude in the Arabian sky, where it would 
 appear to move along the southern horizon. After 
 Canopus, in order of brightness, comes a Centauri, 
 but, so far as I know, this star bears 110 specific 
 name. 
 
 Next to Sirius the brightest star visible in the 
 Northern hemisphere is perhaps Arcturus, although 
 it is closely rivalled by Capella and Vega. The name 
 Arcturus is derived from the Greek words O/OKTOS and 
 ov/aa, which signify a bear's tail, so called apparently 
 because it lies nearly in the continuation of the Great 
 Bear's tail. The Arabic name for the star was al- 
 simak-al~ramih, " the simak armed with a lance." 
 According to the Persian astronomer Al-Sufi, who 
 wrote a "Description of the Fixed Stars" in the 
 tenth century, the word simak means "elevated," 
 referring to the high altitude the star attains above 
 the horizon. Schjellerup, however, thought that the 
 word refers to the brilliancy of the star, and not to 
 its altitude. 
 
80 ASTRONOMICAL ESSAYS 
 
 The bright star Capella (a Aurigse) derives its 
 name from the goat or kid which is represented in 
 the arms of Auriga, the waggoner or " charioteer " 
 on the ancient globes and maps. The Arabic name 
 for the star was al-aijuk, the meaning of which is 
 doubtful. Schjellerup thought it to be the same as 
 the Greek word a'i, " a goat." The Arabians called it 
 " the Guardian of the Pleiades." It was also called 
 Dilgan by the ancients. 
 
 The name of the bright star Vega (a Lyrse) seems 
 to have had its origin in the Arabic word vdki, or 
 al-nasr al-vdki, " the falling eagle," the wings of the 
 bird being represented by the stars c and Lyrae, 
 which form with Vega a little triangle, called by the 
 Arabians al-atsafi, " the trivet." But what relation 
 exists between a " falling eagle " and the musical 
 instrument known as a lyre (Persian al-lura) is 
 not very clear. Possibly, however, as Schjellerup 
 suggests, the Arabic word al-schaljdk (a goose) 
 also applied to the constellation Lyra refers to the 
 resemblance in shape between a plucked goose and 
 a Greek lyre. The Greek called the constellation x*'Avs, 
 " a tortoise," which also somewhat resembles a lyre in 
 shape. 
 
 We next come to Rigel, the brilliant white star 
 in the left foot of Orion. The name is clearly derived 
 from the first word of the compound Arabic name 
 ridjl-al-djauzd, " the leg of the giant " (Orion). It 
 may be here mentioned that the three well-known 
 stars, 8, c, and Orionis, forming " Orion's belt," were 
 called by the Arabian astronomers mintakat al- 
 djauzd, "the belt of the giant," and the stars 
 forming the " sword " al-lakat, " the gleaned ears 
 of corn," and also saif al-djabbar, "the sword of 
 
THE NAMES OF THE STARS 81 
 
 the giant." Perhaps the latter word is the origin 
 of the name Algebar, formerly applied to Rigel. 
 Manilius says 
 
 " Orion's beams ! Orion's beams 1 
 His star-gemmed belt and shining blade, 
 His isles of light, his silvery stream, 
 And gloomy gulf of mystic shade." 
 
 Following Rigel in order of brightness, the bright 
 star Procyoii (a Canis Minoris) may be placed. This 
 name is derived from the Greek irpoKvuv, which means 
 the "advanced dog," or the dog which goes before 
 Sirius, the " dog-star," because it rises or appears 
 before Sirius in the morning sky. It was called by 
 the Arabians al-schird al-schdmia, or "the Syrian 
 Sirius," because it set in the direction of Syria. It 
 was also called al-schird al-gumaisd, " the blear-eyed 
 Sirius," the sister of suhail, or Canopus. 
 
 After Procyon in order of brightness comes the 
 southern star Achernar (a Eridani). This name is 
 derived from the Arabic dchir al-nahr, "the end 
 of the river." But the " Last in the River," the 
 eo-xaros rov Trora/xoG of Ptolemy, is certainly the star 
 6 Eridani, as the description of Ptolemy's star by 
 Al-Sufi clearly shows. was rated first magnitude 
 by Ptolemy and Al-Sufi, but it has now faded to the 
 third magnitude. 
 
 The red star Betelgeuse is variable to some extent, 
 but at its normal brightness it is not much inferior 
 to Procyon. The name Betelgeuse seems to be derived 
 from the Arabic ibt al-djauzd. It was also called 
 viankib al-djauzd, " the shoulder of the giant." 
 
 We next come to Altair (a Aquilse), a name which 
 is clearly derived from the Arabic al-nasr al-tdir, 
 
 G 
 
82 ASTRONOMICAL ESSAYS 
 
 "the flying vulture," a name also applied by the 
 ancients to the whole constellation, of which the 
 Latin name is Aquila, " the eagle." 
 
 The red star Aldebaran (a Tauri) derives its 
 name from the Arabic al-dabaran, "the attendant 
 or follower," because it follows the Pleiades in the 
 diurnal motion. It was also called din al-tsaur, " the 
 eye of the bull." It was also known by several other 
 Arabic names, such as al-fanik, "the great camel," 
 the other stars, or Hyades, being called al-kilas, " the 
 young camels." 
 
 Pollux (ft Geminorum) is the southern of the two 
 bright stars Castor and Pollux in the constellation 
 Gemini, "the twins." They derive their names from 
 the famous brothers in Greek mythology. Castor (a 
 Geminorum) was called by the Arabians mukaddam 
 al-dzira/in and ras al tandm, " the head of the twin." 
 To the two stars they applied the term al-dzira al- 
 mdbsutat, " the outstretched arm." Pollux is a little 
 brighter than Castor. 
 
 Spica (a Virginis) a word meaning "an ear of 
 corn " (French 6pi\ held in the hand of the Virgin. 
 The Arabic name was al-simdk al-azal, " the unarmed 
 simak," the meaning of which is not clear. 
 
 Antares (a Scorpii) is said to be derived from 
 the Greek dvrapes, meaning " redder than Mars." The 
 Arabic name was al-kalb, " the heart of the scorpion.'' 
 Hence the Latin name Cor Scorpionis. 
 
 Fomalhaut (a Piscis Australis). Derived from the 
 Arabic fum-al-hut al-djantibi, " the mouth of the 
 southern fish." 
 
 Deneb (a Cygni). This name is derived from the 
 first part of the Arabic name dzanab al-dadjddja, 
 " the tail of the hen," referring to its position in the 
 
THE NAMES OF THE STARS 83 
 
 ancient figure which represented a hen or swan 
 flying towards the south. 
 
 Regulus (a Leonis). This name seems to have been 
 first used by Copernicus as the diminutive of rex, " a 
 king." Ptolemy called it /foo-i'Ato-Kos. It was named by 
 the Arabians al-maliki, " the royal star," and kalb al- 
 asad, " the heart of the lion," whence the Latin name 
 Cor Leonis. This star, with 77 and y in the well-known 
 " Sickle," the Arabians called al-dhafirat, " the tress 
 of hair," and the whole " Sickle " they resembled to 
 the raised tail of a lion. In the figure of Leo, how- 
 ever, given in Heis' Atlas, the sickle forms the head 
 and shoulders of the lion. 
 
 Bellatrix (y Orionis) means "the female warrior." 
 Its Arabic name was al-nddjid, and also al-mirzam. 
 
 e Orionis, called Alnilam, from the Arabic al- 
 nizhdm, " the string of pearls," evidently an allusion 
 to the three stars 8, e, in " the belt of Orion." 
 
 Orionis, called Alnitak, from the Arabic nitdk 
 al-djauzd, " the girdle of the giant." 
 
 77 Ursse Majoris. This star, which is at the end of 
 the Great Bear's tail, or handle of the Plough, is some- 
 times called Alkaid or Benetnasch, names derived 
 from the Arabic al-kaid, " the Governor," and the 
 name applied to the four stars a, /?, y, and S, sarir 
 bandtnasch, " the coach of the children of the litter." J 
 c Ursse is called Alirth, probably a corruption of the 
 Arabic al-djun, " the gulf." Ursse Majoris is called 
 Mizar, of which the origin is doubtful. Its Arabic 
 name was al-andk, " the little she-goat." Close to 
 Mizar is a small star now called Alcor, but named 
 by the Arabians al-suhd, " the neglected small star," 
 
 1 Litter means " a bier." o, j3, 7, and 8 formed the bier, and e, 
 and 7j the mourners following the coffin. 
 
84 ASTRONOMICAL ESSAYS 
 
 and also al-schitd, " winter," and al-nuaisch, "the little 
 litter." With reference to this little star the Arabians 
 had a proverb, " I show him al-suhd, and he shows 
 me the moon," which seems to imply that it could be 
 easily seen by the ancient astronomers, and was not, 
 as some have supposed, a test of keen eyesight in 
 those days. 
 
 |8 Tauri (formerly y Aurigae) is called Nath, a 
 word apparently derived from the Arabic al-natih, 
 "the butting," referring to its position on the tip 
 of the bull's horn. Admiral Smyth suggested that 
 this might be the origin of the saying, " Not knowing 
 B from a bull's foot." 
 
 Mirfak (a Persei) is derived from the Arabic 
 al-marfik, " the elbow," referring perhaps to its 
 position in the well-known curved line of stars in 
 Perseus. 
 
 Alhena (y Geminorum). Perhaps derived from 
 the Arabic al-hamat, "a mark made with a hot 
 iron on the neck of a camel, " a term applied to 
 the stars y and Geminorum. These were also 
 called al-ma'isdn, " the star which shines with a 
 sharp light." 
 
 8 Canis Majoris is sometimes called Wezea, from 
 the Arabic al-wezu, "weight," because it does not 
 rise much above the southern horizon in northern 
 latitudes, as if weighed down. 
 
 Menkalinan (/? Aurigse). Derived, according to 
 Admiral Smyth, from the Arabic menkib-dhi-l'inan ; 
 but this name is not mentioned by Al-Sufi, who calls 
 it tavdbi al-aij'Cik. 
 
 Polaris (the pole star), called in the Alphonsine 
 Tables " Abrucaba," the origin of which is uncertain. 
 The Arabic name was al-djuda'i, " the kid." 
 
THE NAMES OF THE STARS 85 
 
 a Ophiuchi, Ras al-agne. Evidently derived from 
 the Arabic rds al-hauvd, " the head of Peylle, the 
 serpent-bearer." 
 
 Alpheratz (a Andromeda). A name derived from 
 the Arabic surrat al-f arras, " the navel of the horse." 
 It was also called rds al-musalsalat, " the head of the 
 chained lady." a Andromedae was included in Pegasus 
 by Ptolemy. 
 
 Alphard (a Hydrse). From the Arabic al-fard, 
 " the solitary one," because there is no other bright 
 star near it. It is also called Cor Hydrae. It is a 
 well-known red star, and is so described by Al-Sufi. 
 The ancient Chinese observers called it "the Red 
 Bird." 
 
 Almach (7 Andromedse). A name perhaps derived 
 from the Arabic andk al-ardh, " the panther." 
 
 Hamal (a Arietis), " a sheep." The Arabic name 
 was al ndtih. ft and y Arietis were called al-scha- 
 ratain, " the two marks," because they were near 
 the moon's place at certain times. 
 
 Denebola (ft Leonis) is a name derived from the 
 Arabic dzanab al-dsad, " the tail of the lion." This 
 star seems to have been considerably brighter in 
 former times than at present, for Al-Sufi (tenth 
 century) speaks of it as " the brilliant and great star 
 of the first magnitude which is found on the tail," 
 similar words being used with reference to Regulus. 
 Denebola was also rated first magnitude by Ptolemy. 
 But it is now about one magnitude fainter than 
 Regulus, and below the second magnitude. The 
 Arabians called it al-sarfa, " the vicissitude," perhaps 
 with reference to variation in its light. 
 
 y Leonis was called Algeiba, from the Arabic al- 
 djcibha al-asad, " the front of the lion." 
 
86 ASTRONOMICAL ESSAYS 
 
 Algol (/? Persei). The famous variable star. The 
 fluctuations in its light were possibly known to the 
 ancient astronomers, as they called it al-gul, " the 
 demon," which suggests that the old observers of 
 celestial phenomena may have noticed some pecu- 
 liarity in the light of the star. 
 
 ft Ceti was called Diphda, from the Arabic al- 
 dhifda al-tsdni, " the second frog " ; the " first frog " 
 being al-dhifda al-auval, or Fomalhaut (a Piscis 
 Australis). These old Arabic names seem very 
 fanciful. 
 
 Alphecca (a Coronse Borealis) is a name derived 
 from the Arabic al-munei min al-fakka, " the brilliant 
 of the crown," or " the gem of the coronet," as it 
 has been called by recent writers. 
 
 fi Andromedse is called Mizar and Mirach. Mizar 
 means " a girdle," and mirach " a mantle or apron," 
 both names having reference to the old figure of 
 Andromeda, " the chained lady." 
 
 Etanin (y Draconis) is supposed to be derived from 
 the Arabic ras al-tannin, "the dragon's kead," A but 
 this word is not given by Al-Sufi. 
 
 Schedir (a Cassiopeise) is perhaps a corruption of 
 the Arabic al-sadr, " the heart." The star is slightly 
 variable in its light. 
 
 Enif (e Pegasi). From the Arabic auf, " the nose " 
 of the horse. It was also called fum al-faras, " the 
 mouth of the horse." 
 
 c Bootis, called Tzar, Mizar, and Mirse. The 
 Arabic names were tabi al-simdk, rajat al-simdk, and 
 rdjat al-facca. The modern names are all probably 
 derived from the Arabic word mizar, " an apron." 
 It is a fine double star, and the elder Struve called it 
 " Pulcherrima " on account of its beauty. 
 
THE NAMES OF THE STARS 87 
 
 Alderamiu (a Cephir) is evidently derived from 
 the Arabic al-dzira al-jamin, " the right arm " (of 
 the monarch Cepheus). 
 
 Scheat (/? Pegasi) is perhaps a corruption of the 
 Arabic said, " an arm." 
 
 Algenib (y Pegasi) is probably a corruption of the 
 Arabic name djandh al-faras, "the wing of the horse." 
 
 j3 Eridani was called Cursa, from the Arabic kursi 
 al-djauza al-mukaddam, " the anterior throne of the 
 giant" (Orion), a name given to the stars A, ft, \l/ 
 Eridani, and r Orionis, which form a trapezium close 
 to Rigel, and supposed to form a throne or footstool 
 for Orion. 
 
 Chaph (ft Cassiopeise) is derived from the Arabic 
 al-kaff al-chahib, " the tinted hand " (of " the lady 
 in the chair"). 
 
 Alwaid (ft Dracoiiis) is derived from the Arabic 
 al-avaidz, " the old camels," a term applied to the 
 stars v, ft, , and y in the head of the dragon. 
 
 Vindemiatrix (e Virginis) comes from Provindemia- 
 tor, a name given to this star " because it rises in the 
 morning just before the vintage." The Arabic name 
 was al-auva, "the crier," perhaps because it an- 
 nounced the coming vintage. 
 
 Albirev (ft Cygni) is a name of doubtful origin. 
 The Arabic name was minkar al dadjudja, "the 
 beak of the hen " (or swan). 
 
 There are some other stars which have names 
 derived from the Arabic, but those mentioned above 
 are the most important ; and even some of those are 
 fast becoming obsolete. The names of the brighter 
 stars, however, such as Sirius, Canopus, Arcturus, 
 Capella, Vega, Rigel, Procyon, Aldebaran, Spica, 
 Altair, Betelgeuse, etc., will probably live for all time. 
 
CHAPTER VII 
 
 THE EVOLUTION OF ASTRONOMICAL INSTRUMENTS 
 
 WITH the view of rendering their observations more 
 exact, the Arabian astronomers increased the size of 
 their instruments and built large observatories to 
 aid them in their labours. In the ninth century A.D. 
 one was founded by Albategnius, otherwise called 
 Al-Battani, in the palace of Aractus, or Rakkah, to 
 the north-west of Bagdad. The " Alphonsine Tables " 
 of the moon's motion were based on observations 
 made by Albategnius. A little later another was 
 erected by Ibn Tunis on the hill of Mokatim, near 
 Cairo. It was here that they first attempted to 
 measure time by counting the beats of a pendulum, 
 and of observing the sun by reflection from water. 
 Towards the end of the tenth century Abul Wefa 
 founded an observatory near Bagdad, and followed 
 the planets in their orbits round the sun. In this 
 observatory there was a quadrant of about 20 feet 
 radius, and a stone sextant of 56 feet radius, which 
 was used for observing the meridian altitudes of 
 the sun. 
 
 In the twelfth century Gabir ben Aflah, known 
 as Geber, a Spanish Moor, erected an observatory at 
 Giraldi, in Spain. This was the first observatory 
 built in Europe. Later on, about A.D. 1259, a mag- 
 nificent observatory was founded by Ilskhan-Olagon, 
 
 88 
 
ASTRONOMICAL INSTRUMENTS 89 
 
 grandson of Genghis Khan, at Meragah, near Taurus, 
 and this was the seat of the labours of Nasir-Eddin, 
 who published Astronomical Tables, editions of 
 Euclid's "Elements," and the "Spherics" of Theo- 
 dosius and Menelaus. In this observatory there 
 were some enormous instuments, and among them 
 a gnomon. 
 
 In the fifteenth century the famous astronomer, 
 Ulugh Beigh, founded an observatory at Samarcand. 
 This remarkable man, whose real name was Moham- 
 med Taragai Ibn Shah-rokh Ibn-Timur, was the 
 grandson of the celebrated conqueror Timur-len 
 (Timer the lame) the Tamerlane of modern stories. 
 The name Ulugh Beigh means " the great lord." * 
 Shortly after this the Mongol emperors of India 
 established large astronomical instruments in the 
 principal towns of their empire. These instruments 
 differed but little from those used by Tycho Brahe 
 at the end of the sixteenth century. Tycho Brahe 
 had in his observatory at Uraniburgh four enormous 
 circles, which were as highly ornamental as they 
 were geometrically accurate. 
 
 For six or seven centuries all scientific work 
 seems to have been confined to the Arabian astrono- 
 mers. Little or nothing was done at Rome or 
 Constantinople, and these times have been well 
 called the Dark Ages. On the revival of learning 
 in the period known as the Renaissance Europe 
 acquired all its knowledge from the Arabians, and 
 imitated them in their observations as well as in 
 other scientific matters. But if Europeans were the 
 disciples of the Arabians in the twelfth to the 
 
 1 Ulugh Beigh was assassinated by order of his son, Abdallatif, in 
 the year 1449. 
 
90 ASTRONOMICAL ESSAYS 
 
 fifteenth centuries, they soon went far beyond 
 their teachers. 
 
 At first came the invention of clocks with weights 
 and wheel-work, which replaced the clepsydras, or 
 water clocks, of the ancients. It is often stated that 
 the introduction of clocks was due to Wallingfort in 
 the beginning of the fourteenth century, but this is 
 a mistake. Clocks with wheels and weights are 
 mentioned as having been used in the abbey of 
 Citeaux in the first half of the twelfth century. 1 
 A clock was erected in Westminster Hall in 1288, 
 and a little after that date clocks were constructed 
 in many places in England. Dante, who died in 
 1321, alludes to clocks, and Maratori tells us that 
 in the fourteenth century there were clocks in all 
 the chief towns in Italy. In these the hours were 
 sounded from 1 to 24. In. Milan there was a clock in 
 the Church of St. Gothard before 1339. Padua had 
 one in 1344. This showed the course of the sun and 
 planets. The clock of Charles V. in Paris dates from 
 1364, and that of Strasburgh from 1368. A mechanical 
 contrivance for regulating the motions of clocks with 
 weights is said to have been invented by Gerbert, 
 afterwards Pope Sylvestre II. It was somewhat 
 similar in principle to the modern escapement of 
 clocks and watches. One of these old clocks is pre- 
 served in the South Kensington Museum, London. 
 Watches are referred to by an Italian poet, Gaspar 
 Vesconte, in one of his poems written towards the 
 close of the fifteenth century. Like all the clocks of 
 those days, they had at first only hour-hands. 
 
 For portable clocks and watches it was of course 
 necessary to replace the weights by some other 
 1 Calmet, " Commentaire Litteraire, etc.," vol. i. p. 279. 
 
ASTRONOMICAL INSTRUMENTS 91 
 
 motor-power, and in the year 1674 the spiral spring 
 was introduced by Robert Hooke. In the sixteenth 
 century hour-glasses were used. One of these ran 
 for 24 hours, and lead powder was used instead of 
 sand. 
 
 Walther was the first to use clocks in an astrono- 
 mical observatory. This was in 1484. Tycho Brahe 
 used four, and took an average. Hevelius succeeded 
 in obtaining the time accurately to about twenty 
 seconds. 
 
 The idea of using a pendulum in clocks regulated 
 by an escapement is due to Huygeiis, who published 
 an account of his invention in the year 1658. This 
 new departure in clock-making met with a warm 
 reception, and after Huygens' invention became 
 known, Hevelius was the first to use it in astrono- 
 mical observations. The combination of pendulum 
 clocks with telescopes has led to the great accuracy 
 of modern observations. 
 
 The ancients seem to have had some idea of 
 optical instruments. A lens used as a reading-glass 
 would naturally be the first thing to be thought of. 
 In the tumulus of Birs-Nimroud ivory tablets have 
 been found engraved with mathematical figures of 
 such delicacy and minute accuracy that it seems 
 impossible to suppose that they could have been 
 executed with the naked eye. And this suspicion 
 has been confirmed by the actual discovery of a 
 quartz lens in the same ruins. For similar purposes 
 the Romans used hollow globes of glass filled with 
 water, which acted as magnifying glasses. The 
 emperor Nero is said to have used a concave lens 
 formed from an emerald to correct his short sight, 
 but it seems more probable that he used it on 
 
92 ASTRONOMICAL ESSAYS 
 
 account of the green colour being good for the eye- 
 sight than from any optical advantage it possessed. 
 
 The use of lenses made slow progress, but specta- 
 cles seem to have been used towards the end of the 
 twelfth century. Combinations of lenses to increase 
 the magnifying power were, however, unknown at 
 this period. These seem to have been proposed by 
 the Italian Fracastor in the first half of the sixteenth 
 century, and about the year 1590 the same inventor 
 hit upon the idea of the compound microscope. 
 
 Although the ancients had no knowledge of the 
 principle of telescopes formed by a combination of 
 lenses, they used mirrors for the purpose of divina- 
 tion in their temples, and it is related that in the 
 ancient lighthouse at Alexandria there was a metal 
 mirror in which ships at a distance could be seen 
 more distinctly than with the naked eye on the 
 same principle as the " front view " reflecting tele- 
 scope of Sir William Herschel. This mirror is said 
 to have been over a yard in diameter, thus exceed- 
 ing in size the mirror of Lord Rosse's smaller tele- 
 scope. A similar mirror is said to have existed at 
 Ragusa in Austria. It does not appear, however, 
 that these mirrors were ever used for astronomical 
 purposes. 
 
 Before the invention of the telescope, simple 
 tubes blackened 011 the inside were used to cut off 
 extraneous light and concentrate the view on 
 distant objects. The advantage of these tubes 
 seems to have been known to Aristotle and Strabo. 
 A tube of this kind is said to have been actually 
 used by Julius Caesar before his invasion of Britain 
 for examining the coast of England from the 
 heights of Cape Gris Nez. They are also mentioned 
 
ASTRONOMICAL INSTRUMENTS 98 
 
 in the Talmud, written in the first or second cen- 
 tury. The ancient inhabitants of America also seem 
 to have used tubes for the same purpose, for they 
 have been found in the old graves of that country. 
 The first of these was found in 1842 in a tumulus at 
 Elisabethtown in West Virginia, and others have 
 since been discovered. They were made of steatite, 
 which is soft and easily worked. These tubes varied 
 from eight to twelve inches in length. The diameter 
 or "aperture," as it is called in modern telescopes 
 was about half an inch, and they were contracted 
 near the eye-end to about one-fifth of an inch. That 
 these tubes were used for the purpose mentioned is 
 proved by the fact that a small statuette found in 
 an Indian grave in Bolivia has a tube of this sort in 
 its hand and applied to its eye. These tubes could 
 not have had lenses in them, as glass was quite 
 unknown in America when it \vas discovered by 
 Columbus. 
 
 The principle of the modern telescope seems to 
 have been known for a long time before it was 
 actually applied in practice. Roger Bacon, writing 
 in 1265, describes very clearly the course of luminous 
 rays through lenses, and indicates the arrangement 
 necessary for seeing distant objects magnified. The 
 real invention of the telescope was probably due to 
 some amateur. Glorioso, who succeeded Galileo at 
 the University of Padua, states that^ Pope Leo X. 
 who died in 1521 had in his possession a telescope 
 which magnified distant objects. Several attempts 
 to show how telescopes might be constructed were 
 made in the sixteenth century. Among those who 
 wrote on the subject may be mentioned Porta in 
 1509, John Dee in 1570, and Thomas Digges in 1591. 
 
94 ASTRONOMICAL ESSAYS 
 
 On October 2, 1608, Lippershay or Laprey, a 
 spectacle-maker of Middleburgh, Holland, petitioned 
 the States-General to grant him a patent for an 
 instrument for magnifying distant objects. Before 
 granting his request,* the States-General asked him 
 to construct an instrument which could be used with 
 both eyes, and in reply he sent them a binocular, 
 probably one similar in construction to our modern 
 opera-glasses. Meanwhile, on October 17, 1608, a 
 man named Jacob Metius otherwise known as Adri- 
 anzoon son of Adrian Metius, Inspector-General 
 of Fortifications, and a well-known mathematician, 
 claimed priority in the invention, and stated that 
 his first attempt was made ten years previously. 
 On February 13, 1609, the States-General considered 
 the claims of these rival inventors, and declined to 
 grant a patent to Lippershay on the grounds that he 
 was not the only one to construct the new instru- 
 ment. They were, in fact, already being sold by 
 Zeeland opticians. In December, 1608, the French 
 envoy in Holland wrote to Sully that he had made 
 an arrangement with Lippershay to obtain a tele- 
 scope for King Henry IV., and early in 1609 they 
 were being sold by a goldsmith in Brussels. 
 
 In May, 1609, Galileo, being at Venice, heard of 
 the new invention, and from details sent to him by 
 Badovere from Paris, he constructed a telescope. He 
 placed his lenses at the extremities of an organ pipe, 
 and from the tower of St. Mark he showed his 
 friends the powers of the new instrument. Turning 
 his telescope to the sky, he found himself in the 
 presence of wonders of which he had previously no 
 conception. His observations created much interest 
 and astonishment in Europe, and the news of his 
 
ASTRONOMICAL INSTRUMENTS 95 
 
 discoveries spread with wonderful rapidity. The 
 first revelations made by Galileo's instrument were 
 the mountains of the moon, the spots on the sun, the 
 satellites of Jupiter, and the starry nature of the 
 Milky Way. In fact, a new universe was revealed 
 to his astonished vision. His telescopes were made 
 on the principle of the modern opera-glass, namely, 
 with a convex object-glass and concave eyepiece, 
 both being single lens. His largest instrument only 
 magnified about thirty times. Galileo foresaw that 
 his modest instrument would soon be improved on, 
 and that there was practically no limit to the future 
 observations of astronomers. 
 
 The invention of the telescope did not at once 
 lead to the improvement of astronomical measure- 
 ments, and it was not till the years 1622-1633 that 
 Generini suggested that the old alidades might with 
 advantage be replaced by telescopes. This idea was 
 not at first favourably received, and Morin, in 
 ignorance of his predecessor's suggestion, made a 
 similar proposal in 1634. But the only advantage 
 derived from its adoption was an improvement in 
 the definition of the objects observed, and the idea 
 was not of much value until Gascoigne, in 1640, 
 thought of placing parallel wires in the focus of the 
 eyepiece, which could be used in making micro- 
 metrical measures. In 1667 Auzout and Picard 
 suggested the use of wires in the form of a cross, 
 the centre of which could be made to mark the 
 optical axis of the instrument. This happy thought 
 added greatly to the precision of astronomical 
 instruments, and, combined with graduated circles, 
 at once enabled astronomers to fix the exact positions 
 of the stars with great accuracy. 
 
96 ASTRONOMICAL ESSAYS 
 
 The great progress which has been made in 
 accuracy of observation since ancient times may be 
 understood by the following facts. The longitudes 
 of the stars as given by Hipparchus cannot be 
 relied upon as certain within 2. The Arabian 
 astronomers reduced this error to about four or five 
 minutes of arc. Tycho Brahe's observations were 
 probably accurate to within one minute, and Hevelius 
 attained even greater precision by using simple pin- 
 nules. But when telescopes fitted with cross- wires 
 were used in combination with graduated circles, 
 the accuracy was further increased. Bradley's 
 observations are probably correct to within eight 
 seconds of arc, and, at present, observations at 
 Greenwich, Paris, and elsewhere do not probably 
 differ from the truth by even two seconds. 
 
 The same may be said of measures of time. 
 Ptolemy could not find the time of the equinoxes to 
 less than a quarter of an hour. In the Middle Ages 
 they reduced this uncertainty to about five minutes, 
 and, with the aid of astrolabes, to about one minute. 
 But after the invention of clocks a closer approxi- 
 mation became possible. Professor Newcomb finds 
 that eclipses observed by Hevelius were correct to 
 within 24 seconds. From the beginning of the 
 eighteenth century observations were possible to 
 within two seconds, and at the present day the 
 exact time of a star crossing the meridian can be 
 observed to within the tenth of a second. These 
 facts show the great progress which has been made 
 since the time of the ancient observers. 
 
 When the telescope was first invented, the single 
 lenses used in its construction produced what is 
 known as "chromatic aberration," which gives rise 
 
ASTRONOMICAL INSTRUMENTS 97 
 
 to a fringe of colour round the objects viewed. This 
 colouring interferes with clear vision. To get rid of 
 this imperfection at least to some extent the old 
 telescope makers had recourse to instruments of 
 enormous length. Hevelius constructed one of 150 
 feet in length. Bradley measured Venus in 1722 
 with a telescope 212 feet long, and Auzot is said to 
 have constructed one of 600 feet, which, however, 
 he could not use, owing to its enormous length. 
 
 Sir Isaac Newton made several experiments with 
 a view to the improvement of refracting telescopes 
 as telescopes with lenses are called but came to 
 the conclusion that it was impossible to get rid of 
 the chromatic aberration produced by lenses. He 
 then turned his attention to the construction of 
 telescopes with metallic mirrors, and succeeded in 
 making several which gave satisfactory results. In 
 this form of telescope the image, formed by reflection, 
 is free from colour. Newton's telescopes were, how- 
 ever, very small, and only a few of any size were 
 made for about a hundred years, when Sir William 
 Herschel took up the subject and succeeded in con- 
 structing several reflecting telescopes of considerable 
 size, his largest being no less than four feet in 
 diameter. This great instrument was finished in 
 the year 1789, and with it the famous astronomer 
 discovered the two small satellites of Saturn, Mimas 
 and Enceladus, and made other remarkable obser- 
 vations. In after years a reflecting telescope of four 
 feet in diameter and 40 feet long was constructed 
 by Mr. Lassell, who took it to Malta, and, with it, 
 discovered numerous nebulae. These telescopes were, 
 however, soon exceeded in size by Lord Rosse's 
 famous instrument of six feet in diameter, completed 
 
 H 
 
98 ASTRONOMICAL ESSAYS 
 
 in 1845. This great telescope, which is still the 
 largest in the world, is 52 feet in length, and its 
 large mirror weighs about four tons. 
 
 Metallic mirrors have in recent years been super- 
 seded by mirrors made of glass, ground to the proper 
 curvature and silvered over by a chemical process, 
 the silver film being then polished. These mirrors 
 reflect much more light and give better definition 
 than the old metallic mirrors. There is one of these 
 " silver on glass " mirrors of four feet in diameter in 
 the Paris Observatory, one of five feet diameter was 
 made by the late Dr. Common, and another of five 
 feet has lately been constructed by Mr. Ritchey at 
 the Yerkes Observatory (U.S.A.). Mirrors of even 
 eight or ten feet are now spoken of as possible in the 
 future. 
 
 Although Newton despaired of any improvement 
 in refracting telescopes, the problem was not aban- 
 doned as hopeless, and in the year 1729, two years 
 after Newton's death, Mr. Chester More Hall suc- 
 ceeded in obtaining a combination of lenses of 
 different kinds of glass which gave an image free 
 from colour. This was the origin of the "achro- 
 matic telescope," as it is called, which has made 
 such rapid progress in recent years. The combina- 
 tion of lenses now employed was devised by Peter 
 Dollond in 1758, but the credit of the invention is 
 really due to More Hall. 
 
 Further details of the large telescopes of modern 
 times will be found in my book, "Studies in 
 Astronomy " (chap. iii.). 
 
CHAPTER VIII 
 
 MODERN THEORIES 
 
 " Discipulus est prioris posterior dies." 
 
 IN the fourth century A.D., Julianus is said to have 
 thought that the sun, with all the planets, revolved 
 round the earth, that is, that all the planets except 
 the earth revolve round the sun, and the system 
 thus formed revolved round the earth as a centre. 
 This was an anticipation of Tycho Brahe's system 
 by more than twelve centuries. But whatever may 
 have been the ideas of the old astronomers, the true 
 theory of the planetary system was not arrived at 
 until Copernicus appeared. At first methods of con- 
 firmation were wanting. Even when the " De Revo- 
 lutionibus " of Copernicus was published in 1543, 
 the truth of the theory rested only on probabilities, 
 and, to confirm its accuracy, it was, of course, neces- 
 sary to submit it to the crucial test of observation. 
 The retrograde motions of the planets when near 
 opposition were more simply explained by the new 
 theory; but they were also explained with nearly 
 as great accuracy by Ptolemy's system. The idea 
 of motion in simple elliptical orbits had not yet 
 been conceived. Although Copernicus made all the 
 planets revolve round a central ruling body, the 
 sun, he imagined them still to move in the epicycles 
 
 99 
 
100 ASTRONOMICAL ESSAYS 
 
 of the ancients. The old scaffolding had not yet 
 been removed from the temple of Truth, and these 
 antique ideas prevented the heliocentric system from 
 being seen in all its beauty. 
 
 After long intervals, however, facts were observed 
 which seemed to afford some partial confirmation 
 of the new theory. At the opposition of Mars in 
 the year 1582, Tycho Brahe made an important 
 observation. He found that the retrograde move- 
 ment of the planet near opposition agreed with 
 the Copernican theory, while Ptolemy's hypothesis 
 gave an erroneous value of the angular velocity. 
 This notable observation remained for a long time 
 unpublished, and it seems to have been first an- 
 nounced by Mostlin in 1596. 
 
 But after the invention of the telescope, evidence 
 in favour of the new theory was rapidly accumulated. 
 The first piece of confirmatory evidence was the dis- 
 covery of the phases of Venus by Galileo in 1610. 
 These had been predicted by Copernicus in 1543 as 
 a necessary consequence of the revolution of Venus 
 round the sun in an orbit inside that of the earth. 
 Further confirmation was found in the phases of 
 Mercury, which seem to have been seen by Simon 
 Mayer about the year 1615. These observations 
 established the fact that the two inferior planets 
 that is, those inside the earth's orbit revolved round 
 the sun. 
 
 But still a doubt remained with reference to the 
 superior planets, or those outside the earth's orbit. 
 Here, again, confirmation was afforded by the tele- 
 scope. The discovery of Jupiter's satellites, which 
 quite evidently revolved round the planet, showed, 
 as it were, a miniature of the solar system itself, and 
 
MODERN THEORIES 101 
 
 exhibited a sort of " object lesson " as to the con- 
 struction of the larger system, of which Jupiter 
 itself formed a member. With reference to the 
 motions of these satellites round Jupiter, it was 
 pointed out by Simon Mayer, in 1614, that the 
 motion of any satellite with reference to Jupiter 
 and the sun is uniform, but this is not the case 
 with reference to Jupiter and the earth. This fact 
 suggested that it was the sun, and not the earth, 
 which formed the centre of Jupiter's orbital motion. 
 The satellites of Saturn gave similar evidence in 
 favour of the new theory. The discovery of the 
 progressive motion of light from observations of 
 Jupiter's satellites, announced by Roemer in 1676, 
 was further proof that the sun and earth revolved 
 round each other. But this agreed with the theory 
 of Tycho Brahe as well as that of Copernicus, and 
 further evidence was necessary to decide between 
 the two rival theories. This evidence was at last 
 found in the discovery of the aberration of light 
 by Bradley in 1728, nearly 200 years after the publi- 
 cation of the " De Revolutionibus " of Copernicus. As 
 the aberration of light is due to the earth's motion 
 in its orbit round the sun, this remarkable discovery 
 finally decided the question beyond all doubt, that 
 it was the earth, and not the sun, which moved in 
 an annual orbit. If the earth were at rest, there 
 would be no aberration of light. The Copernican 
 theory was finally adopted as the correct one, and 
 all subsequent observations have tended to confirm 
 it. With reference to the earth's rotation on its 
 axis, this was proved practically by the pendulum 
 experiments of Foucault and Fizeau, recently re- 
 peated at Paris ; and theoretically by the precession 
 
102 ASTRONOMICAL ESSAYS 
 
 of the equinoxes, which is only consistent with the 
 hypothesis of a rotating globe. 
 
 Henceforth the solid spheres and the material 
 epicycles and deferents were consigned to the limbo 
 of ancient myths, and the planets were seen to 
 revolve round the sun in regular curves and in 
 free space, unfettered by any bonds except those 
 of gravitation towards the central body. The con- 
 ception of the solar system thus freed from the old 
 material shackles gained in simplicity and grandeur. 
 It is to Kepler that this great reform is really due, 
 although, like Copernicus, his views were to some 
 extent anticipated by previous writers. The Arabian 
 astronomer Arzachel, in the year 1080, noticed that 
 of all the planets the motion of Mercury deviated 
 most from a circle, and he supposed that its real 
 orbit was some sort of oval. From similar con- 
 siderations, Reiiiholdus, in 1542, even suggested an 
 ellipse as possibly the true form of the orbit. 
 Copernicus also seems to have suspected that the 
 planetary orbits are really elliptical. But these 
 writers had not sufficient observations at their 
 command to confirm the truth of their hypothesis. 
 Kepler, however, having found a series of observa- 
 tions of the positions of the planets made by Tycho 
 Brahe, and extending over a period of twenty years, 
 undertook an examination of the subject. For this 
 purpose he selected the planet Mars, the orbit of 
 which, among the superior planets, differs most from 
 the circular form. By an ingenious and accurate 
 process he traced out the shape of the orbit, and 
 found it to be an ellipse. 
 
 The heliocentric revolution of Mars round the 
 sun is nearly 687 days, that is, the period, as seen 
 
MODERN THEORIES 103 
 
 from the sun, occupied by the planet in revolving 
 round the heavens from any given star back to the 
 same star again. But seen from the earth which is 
 also in motion this period will not be the same. 
 However, if at the end of 687 days we observe the 
 geocentric longitude of the planet that is, its position 
 as seen from the earth this second observation, 
 combined with the first, will give the length of the 
 line joining the sun and Mars in terms of the distance 
 of the sun from the earth. From the fine series of 
 observations made by Tycho Brahe, Kepler found 
 the positions for each 687th day after an opposition. 
 In fifteen years the points so found fall in all parts 
 of the orbit, and he obtained eight positions, which 
 gave him a good general idea of the shape of the 
 orbit. This he found was an ellipse with the sun in 
 one of the foci. This was a very remarkable dis- 
 covery, and constitutes Kepler's first law of planetary 
 motion. 
 
 A further effort was, however, necessary to finally 
 upset the old ideas of uniform motion in circles. 
 And this was accomplished in the following way. 
 Kepler found that the sun's apparent diameter 
 was about ^ less in summer than in winter. This 
 could only be due to its being farther from the 
 earth at apogee than at perigee. He also found that 
 the apparent angular motion was about ~ slower 
 when its apparent diameter was least. Following 
 out the motion step by step, he found that the line 
 drawn from the sun to the planet, known as the 
 radius vector, swept over equal areas in equal times. 
 All subsequent observations have been found to obey 
 this law, which is known as Kepler's second law of 
 planetary motion. 
 
104 ASTRONOMICAL ESSAYS 
 
 Following up his investigations, Kepler discovered 
 another and an equally important law. 
 
 of the periods of revolution of the planets round the 
 sun increase with their distances from the central 
 luminary\ Kepler tried to find whether there was 
 any constanf^relation between these periods and 
 distances.\ At first he was much puzzled. He. had 
 no analogy to guide him in the search for such a 
 relation, and was obliged to rely on his imagination 
 and inventive genius to find some connection between 
 the two quantities. For a long time Kepler was 
 baffled in his efforts to find tl^e required relation. 
 After many attempts, he at last arrived at the 
 following result i/tfce squajyg- of the periods of 
 revolution are proportional to the cubes of the mean 
 distances from the suji./ This is the famous third law 
 of Kepler, and its truth has been abundantly verified 
 by all subsequent observations and researches. 
 
 Kepler's laws, combined with the Copernican 
 system, created quite a revolution in astronomical 
 ideas. fAs it was proved that the distance of a 
 planet from the sun was not constant but variable 
 to some extent, the idea of solid crystalline spheres 
 was no longer tenable, unless the material composing 
 them was supposed to be flexible like indiarubber.l 
 Descartes, in his hypothesis of vortices, attempted to 
 make the imaginary spheres fluid. He supposed that 
 the planets are suspended in spherical liquid layers 
 of nearly the same density, which revolve round the 
 sun and carry the planets with it. The spheres 
 being liquid, there would be nothing to prevent small 
 changes in the distance of the planets from the sun. 
 Smaller spheres would, he thought, carry the satellites 
 round their primaries. But he does not explain why 
 
MODERN THEORIES 105 
 
 the supposed liquid is carried round the sun, and he 
 seems to have overlooked the fact that with the 
 same fluid there would be no variation in the planets' 
 velocity, and that the orbits of all the planets would 
 lie in the same plane. This shows how difficult it 
 is for even men of great genius as Descartes un- 
 doubtedly was to free themselves from old ideas. 
 
 The final blow to the system of the spheres was 
 given by the comets, which were found to cut the 
 orbits of the planets in all directions. It was shown 
 by Tycho Brahe that the comet of 1577, among 
 others, described a large curved orbit round the sun, 
 and that this curve intersected the orbit of the earth 
 and enclosed those of Venus and Mercury. This was 
 confirmed by Borelli, who found that the comet of 
 1664 was moving in a parabola. 
 
 For a long time previous to the advent of Sir 
 Isaac Newton, some of the clearest minds saw that 
 in the great system of the sun and planets a mutual 
 action of some sort probably existed between its 
 members. So far back as the ninth century the 
 Arabian writer, Musa-beii-Shakir, thought that at- 
 traction was one of the great forces of nature. 
 Camillus Agrippa, in 1553, thought that all the 
 celestial bodies had an attraction towards each 
 other, and that this action applied to the earth was 
 the cause of the precession of the equinoxes a 
 remarkable and accurate conclusion. Horrox, well 
 known for his observations of the transit of Venus, 
 writing in 1635, considered the moon as a projectile 
 moved by what he called an emanation from the 
 earth, or, in other words, gravity. Bullialdus, in 
 1645, went so far as to say that the attraction 
 existed in the sun, and if so, this action should 
 
106 ASTRONOMICAL ESSAYS 
 
 decrease in proportion to the square of the distance. 
 Borelli, in 1666, also said that on the same principle 
 the satellites should revolve in elliptical orbits round 
 their primaries. These views anticipated to some 
 extent the great discovery of Newton ; but the 
 authors did not prove their views mathematically, 
 and a rigorous demonstration of the law of gravita- 
 tion was reserved for Newton. 
 
 In 1674 Robert Hooke made some experiments 
 with a conical pendulum in the hope of discovering 
 the cause of planetary motion, and in a letter to 
 Newton he pointed out that the curve described by 
 projectiles under the action of terrestrial gravity is 
 an ellipse of great eccentricity. That attraction 
 decreases as the square of the distance was also the 
 opinion of Wren and Halley. The latter did not 
 succeed in determining the nature of the curve 
 described. He sent his views to Newton, but found 
 that this mighty mind had already solved the pro- 
 blem. Newton's results were soon after published in 
 the famous work known as the " Principia." 
 
 Newton's discovery fully explains all the planetary 
 motions, and confirmed the laws of Kepler. If the 
 attraction were inversely proportional to the distance 
 simply, the sun would occupy the centre of the 
 ellipse instead of one of the foci. Newton's dis- 
 covery not only explains the motions of the planets 
 round the sun, but also the flattening of the earth 
 at the poles, the inequalities jn the moon's motion, 
 the libration, the motion of the line of apsides, the 
 motion of the nodes, the moon's nutation, the pre- 
 cession of the equinoxes, and the tides. In mathe- 
 matical ability Sir Isaac Newton has never been 
 surpassed in the history of the world, and Dr. Johnson 
 
MODERN THEORIES 107 
 
 said of him, " If Newton had flourished in ancient 
 Greece, he would have been worshipped as a divinity." 
 
 As the system of Copernicus was not at first 
 generally accepted, so Newton's discoveries were 
 for some years looked upon with suspicion by his 
 contemporaries. Even the famous Huygens was for 
 a long time opposed to them. It must be admitted 
 that these objections were not altogether unreason- 
 able ; for even at the present day the cause of gravi- 
 tation that is, the method of communication by 
 which a body acts on another at a distance is as 
 great a mystery as it was in the days of Newton. 
 But the number of applications of gravity shows 
 clearly that the law is correct, although the cause of 
 its action remains unknown. All the irregularities 
 of motion observed in the large and small planets, 
 the satellites, and comets, have been found amenable 
 to the law, which seems to be a universal one in 
 nature. Each difficulty which has arisen has only 
 added to it another triumph. 
 
 Among the many interesting verifications of 
 Newton's law of gravitation may be mentioned the 
 tides. About 1000 B.C. the Chinese remarked the 
 apparent influence of the moon on the waters of 
 the sea. Indeed, this influence was easily recognized 
 by the coincidence of high tides with new and full 
 moon. It was also known to the Greeks, as accord- 
 ing to Plutarch Pythias mentioned it in the fourth 
 century B.C., and Seleucus about one hundred years 
 later. Cleomedes, writing in the second century A.D., 
 stated positively that the tides are caused by the 
 moon. The Romans held the same view. Cicero 
 states so distinctly, and Julius Caesar, speaking in 
 his commentaries of his invasion of Britain, says 
 
108 ASTRONOMICAL ESSAYS 
 
 that when his troops embarked at Boulogne, the 
 tide was high because the moon was full. 1 Pliny 
 seems to have recognized that the sun, as well as the 
 moon, has an influence 011 the tides. He says, " verum 
 causa in sola lundque" The connection of the tides 
 with the moon seems also to have been known to 
 the Arabian astronomers. But none of these ancient 
 writers offers any explanation of the cause of the 
 moon's action. Roger Bacon, however, in the thir- 
 teenth century, and Kepler in the seventeenth 
 century, state distinctly that the tides are due to 
 the moon's attraction. But they could make no 
 calculation as to the height of the tides, for the law 
 of gravitation had not then been discovered. 
 
 Galileo seems to have differed from the general 
 opinion on the subject. He thought that the tides 
 were in some way caused by the earth's motion of 
 rotation and revolution. But his theory did not 
 agree with the observed facts. Descartes, in 1644, 
 returned to the lunar theory, but as he did not 
 know the law of gravitation, he could not make 
 much progress in the matter. He tried to connect 
 the tides with his imaginary fluid which carried the 
 planets round the sun, but his theory failed to 
 represent the observation, and had to be abandoned. 
 Newton's discovery when applied to the tides by 
 Laplace, was found to be quite satisfactory, and this 
 formed another proof of the law of gravitation. 
 
 Let us now consider some further proofs of this 
 remarkable law. Newton himself seems to have 
 gone no further than to show the cause of the 
 phenomena, and did not enter into any numerical 
 
 1 He says, " Eadem nocte accidit, ut esset luna plena, gui dies 
 maritimas cestus maximos in Oceano efficere consuevit." 
 
MODERN THEORIES 109 
 
 details. These calculations were soon taken up by his 
 successors in the field of mathematical astronomy, 
 /tflairaut found for the motion of the moon's perigee 
 only half the value given by observation, and went 
 so far as to suggest that some change was necessary 
 in the law of the inverse square^ Buff on, however, 
 believing in the truth of Newton's discovery, sug- 
 gested that the difference found by Clairaut was 
 due to an error in the calculations. He therefore 
 tried to induce Clairaut to re-examine his work. 
 This, after some hesitation, Clairaut did, and found 
 that when his calculations were carried to a greater 
 degree of accuracy, the difference disappeared, and 
 his results agreed with observation. This was the 
 first great triumph for the law of gravitation^ 
 
 A second difficulty was soon found in the varia- 
 tion of the velocities of Jupiter and Saturn in their 
 orbits, a variation which had long been a subject 
 of mystery. The deviation is rather considerable, 
 amounting in the course of 2000 years to a difference 
 of 3 49' in the longitude of Jupiter, and 9 15' in 
 that of Saturn. The question having been carefully 
 investigated by the famous Laplace, he found that 
 the observed deviation was due to the fact that five 
 revolutions of Jupiter were almost exactly equal to 
 two revolutions of Saturn. This fact gives rise to 
 a great reciprocal perturbation between the two 
 planets with a period of about 930 years. This was 
 another great triumph for the law of gravitation. 
 
 Another difficulty arose in what is called the 
 secular acceleration of the moon's mean motion, an 
 acceleration which did not seem consistent with 
 the law of gravitation. The acceleration was dis- 
 covered by Halley. The question was considered 
 
110 ASTRONOMICAL ESSAYS 
 
 by Lagrange in 1774, but he only succeeded in show- 
 ing that the variation is not due to the influence of 
 the earth's figure on the moon's motion. In fact, he 
 found no explanation for the observed acceleration. 
 Laplace was, however, more successful, and showed, 
 in 1786, that the acceleration was caused by the 
 secular diminution in the eccentricity of the earth's 
 orbit. Although this theory undoubtedly explains 
 the cause of the observed acceleration, it does not seem 
 to indicate the amount of the acceleration with suffi- 
 cient accuracy, the theoretical amount being about 
 6 seconds per century, while the observed quantity 
 is about 8 seconds. It has been suggested that the 
 difference between calculation and observation may 
 possibly be due to a slow change in the length of the 
 terrestrial day, caused by a retardation of the 
 earth's rotation on its axis produced by tidal 
 friction. This slight lengthening of the day would 
 diminish the number of seconds in a month, and 
 thus make the month apparently shorter. But the 
 amount of this supposed action of the tides on the 
 earth's rotation is at present very uncertain. * 
 
 There are some ojher irregularities in the solar 
 system which the law of gravitation does not 
 explain exactly. Among these may be mentioned 
 the secular movement of the perihelion of Mercury's 
 orbit, which exceeds in amount that indicated by 
 theory. This difference cannot be explained by the 
 action of unknown planets between Mercury and 
 the sun, for if this were the cause, it may be shown 
 that the node of the orbit would also be affected, 
 and observations show that this is not the case. 
 
 There are also some small irregularities in the 
 moon's motion which are not well represented by 
 
MODERN THEORIES 111 
 
 calculation. Professor Newcomb has found one 
 which may perhaps be due to perturbations caused 
 by the planet Jupiter. There are others, however, 
 which have not yet been thoroughly explained, or of 
 which the coefficients in the mathematical formulae 
 have not yet been accurately determined. In fact, the 
 observation of the moon's place at any time cannot 
 be represented to within less than 5 or 6 seconds. 
 But these are minor points, and, notwithstanding 
 slight differences between theory and observation, 
 we may say that Newton's law of gravitation gives 
 a true explanation of very numerous phenomena. 
 It is one of the greatest examples in the whole 
 range of science of the principle of inductive reason- 
 ing confirmed by an appeal to the crucial test of 
 observation. 
 
 After Newton's death, his work was continued by 
 several famous mathematicians. In the words of 
 the unfortunate Bailly, 1 " As the empire of Alexan- 
 der was divided among his successors, so the sceptre 
 of Newton passed into the hands of Clairaut, Euler, 
 and D'Alembert." To these illustrious names may 
 be added those of Lagrange and Laplace. 
 
 1 Jean Sylvain Bailly lost his life during the French Revolution. 
 He was guillotined at Paris on November 10, 1793, on the same 
 day that the " Feast of Reason " was held in the Cathedral of Notre 
 Dame. 
 
CHAPTER IX 
 
 MICHELL'S ASTRONOMICAL VIEWS 
 
 ONE of the boldest and most original thinkers on 
 astronomical subjects was the Rev. John Michell, 
 B.D., F.R.S., who lived in the eighteenth century. 
 He immediately preceded Sir William Herschel, 
 whose fame seems to have eclipsed that of his great 
 predecessor. Michell was born in 1725, and took his 
 degree at Cambridge as fourth wrangler in 1748, 
 when Sir William Herschel was only ten years old. 
 Michell' s name is not even mentioned in many 
 biographical works which give a lengthy account of 
 much smaller men, and his name is hardly known to 
 the general reader. This may be partly due to the 
 fact that his speculations were far in advance of his 
 time; but he certainly anticipated many facts and 
 theories which are now known to be true, and some 
 of his theories have been unfairly credited to other 
 astronomers. The discovery of binary* or revolving- 
 double stars is really due to Michell, although 
 usually ascribed to Sir William Herschel. It was 
 clearly shown by Michell that very close pairs of 
 stars are probably physically connected and revolve 
 round each other, and the fact was afterwards proved 
 by Sir William Herschel from actual measurements. 
 Michell was a Fellow of Queen's College, Cambridge, 
 where he held several professorships between the 
 
 112 
 
MICHELL'S ASTRONOMICAL VIEWS 113 
 
 years 1751 and 1762. He was elected Fellow of the 
 Royal Society in 1760. Later on he became Rector 
 of Thornhill in Yorkshire, and died there on April 
 21, 1793. His views are very original and suggestive, 
 and he is certainly entitled to rank among the 
 greatest of English philosophers. 
 
 In the year 1767 Michell published a very interest- 
 ing and remarkable paper in the Philosophical Trans- 
 actions of the Royal Society for that year. The 
 title of the paper is, " An Inquiry into the probable 
 Parallax and Magnitude of the fixed Stars from the 
 Quantity of Light which they afford us, and the par- 
 ticular Circumstance of their Situation." In this 
 important paper Michell arrives at some conclusions 
 which were very much in advance of his time. Some 
 of these views are now known to be correct, and a 
 short account of his speculations may prove of 
 interest. 
 
 He first states that the distance of the stars is so 
 great that a good determination of their parallax 
 had not been made in his time. In order to arrive 
 at some estimate of their probable distance from the 
 earth, he assumes and his assumption was a very 
 reasonable one that, on the average, the stars are 
 equal in size and " natural brightness " to our own 
 sun. By " natural brightness " he evidently means 
 the intrinsic brightness, or luminosity, of their 
 surface per unit of area. He then attempts to 
 compare the brightest fixed stars with the planet 
 Saturn. He assumes that when the earth and Saturn 
 are at their mean distances from the sun, and the 
 rings invisible, the planet is " nearly equal in light 
 to the most luminous fixed stars." If by this ex- 
 pression he means an average star of the first 
 
 I 
 
114 ASTRONOMICAL ESSAYS 
 
 magnitude, the estimate is about correct, for, accord- 
 ing to the Harvard photometric measures, Saturn, 
 without his rings, is very slightly brighter than an 
 average star of the first magnitude. It would not, 
 of course, be true for Sirius and the very brightest 
 stars, which are brighter than the first magnitude. 
 Taking into account Saturn's distance from the sun, 
 and his apparent diameter, and assuming that the 
 planet reflects all the light which falls upon it, he 
 finds that the light of the sun is 48,400,000,000 times 
 that of Saturn. Hence the sun should be removed 
 to a distance equal to the square root of this, or 
 about 220,000 times its present distance, in order to 
 reduce its light to that of a star of the first magni- 
 tude. This would give a parallax of about one 
 second of arc for stars of this magnitude. This is 
 not far from the truth in the case of a Centauri, the 
 nearest of the stars, but would not be correct for 
 all stars of the first magnitude, most of which are 
 certainly at a much greater distance. Making allow- 
 ance for the want of reflecting power in Saturn, he 
 assumes that it reflects " only a fourth or a sixth " 
 .of the light which falls upon it. But this estimate 
 is too small, and assuming an " albedo " of 0*52, as 
 found by Zollner, the above distance should be in- 
 creased by the square root of - -^-. This would make 
 the distance about 303,000 times, and the parallax 
 about 0*68 second. This is a remarkably close approxi- 
 mation to the parallax of a Centauri (0*75 second). 
 
 Michell suggests, however, that both the magni- 
 tude and brightness of the stars may differ greatly 
 from those of the sun, but that, on an average, the 
 assumption of equal size and brightness may not " be 
 wide of the truth," " some exceeding and some falling 
 
MICHELL'S ASTRONOMICAL VIEWS 115 
 
 short of it." He adds, "we may perhaps judge in 
 some degree of the native brightness of different 
 stars with respect to one another by their colour, 
 those which afford the whitest light being probably 
 the most luminous." This is another remarkable 
 prediction, which we now know to be true, Sirius 
 and other white stars being much more luminous 
 than the sun in proportion to their mass. In con- 
 nection with this portion of his researches he 
 anticipates a method of calculation of the brightness 
 of binary stars which is now used to determine their 
 relative brightness from their computed orbits. He 
 says (p. 238, footnote) 
 
 " If, however, it should hereafter be found that 
 any of the stars have others revolving round them 
 (for no satellite shining by borrowed light could 
 possibly be visible *), we should then have the means 
 of discovering the proportion between the light of the 
 sun and the light of the stars, relatively to their 
 respective quantities of matter [that is, their mass] ; 
 for in this case the times of the revolutions, and the 
 greatest apparent elongation of those stars that re- 
 volved about the others as satellites, being known, 
 the relation between the apparent diameter and the 
 densities of the central stars would be given, what- 
 ever their distance from us ; and the actual quantity 
 of matter which they contained would be known 
 whenever their distance was known, being greater or 
 less in the proportion of the cube of that distance. 
 Hence supposing them to be of the same density as 
 the sun, the proportion of the brightness of their 
 surfaces, compared with that of the sun, would be 
 known from the comparison of the whole of the light 
 which we receive from them, with that which we 
 
 * This is quite correct, as I have shown elsewhere. See my 
 " Studies in Astronomy," p. 113. 
 
116 ASTRONOMICAL ESSAYS 
 
 receive from the sun ; but if they should happen to 
 be either of greater or less density than the sun, the 
 whole of their light not being as affected by these 
 suppositions, their surface would indeed be more or 
 less luminous, accordingly as they were, upon this 
 account, less or greater ; but the quantity of light, 
 corresponding to the same quantity of matter, would 
 still remain the same. 
 
 " The apparent distances at which satellites would 
 revolve about any star would be equal to the semi- 
 annual parallaxes of these stars, seen from planets 
 revolving about the sun, in the same periodical times 
 with themselves, supposing the parallaxes to be such, 
 as they would be, if the stars were of the same size 
 and density with the sun." 
 
 Here we have a clear account of the method now 
 used for comparing the relative brightness of binary 
 stars, and the credit of the suggestion seems certainly 
 due to Michell. The above extract also shows that 
 he saw the probability of the existence of binary 
 stars afterwards proved by Sir William Herschel. 
 He again considers the hypothesis further on in the 
 same paper. 
 
 He states his opinion that the apparent diameter 
 of the stars must be exceedingly small, and that 
 even in the case of Sirius it must be less than " the 
 hundredth, probably the two-hundredth part of a 
 second," and could not be seen with a telescope 
 magnifying 6000 times. This we now know to be 
 quite correct ; the apparent diameter of a Centauri 
 the nearest of the stars certainly does not exceed 
 the hundredth of a second. The impossibility of 
 determining the apparent diameters of the stars 
 compels us therefore to estimate their size by their 
 parallax and the quantity of light which they emit 
 
MICHELL'S ASTRONOMICAL VIEWS 117 
 
 compared with that of the sun. This would, how- 
 ever, give only an approximate result, as some of 
 the stars may be more expanded than the sun that 
 is, of less density, as is probably ^the case with Sirius ; 
 or more condensed, as its satellite may be. 
 
 Assuming the parallax of Sirius to be about one 
 second, he proceeds to determine the probable parallax 
 of the fainter stars. He says that the light of Sirius 
 does not exceed that of stars of the sixth magnitude 
 in a greater proportion than 1000 to 1, nor a less 
 proportion than 400 to I, 1 and he thought that the 
 smaller stars of the second magnitude are about a 
 mean between the two. From this he concludes that 
 stars of the sixth magnitude are at a distance of 
 from 8,000,000 to 12,000,000 times that of the sun, 
 and the distance of small second-magnitude stars 
 would be about 2,000,000 times the same distance. 
 On the hypothesis of equal size and brightness, 
 modern measures would make the parallax of sixth - 
 magnitude stars (compared with Sirius) about the 
 hundredth of a second, or about 20,000,000 times the 
 sun's distance. Compared, however, with a Centauri, 
 their parallax would be about 0*05 second, or only 
 about 4,000,000 times the same distance. 
 
 Michell thought that the collection of the stars 
 into groups or constellations is due to " some general 
 law (such, perhaps, as gravity)," and he considers 
 " what it is probable would have been the least 
 apparent distance of any two or more stars, any- 
 where in the whole heavens, upon the supposition 
 that they had been scattered by mere chance." He 
 shows that for two stars the probability against one 
 
 1 Modern photometric measures make Sirius about 1000 times 
 brighter than an average star of the sixth magnitude. 
 
118 ASTRONOMICAL ESSAYS 
 
 star being by chance within 1 of another star is 
 about 13,131 to 1. We must, however, consider the 
 number of stars in the sky of not less brightness 
 than those in question. For the two stars of fi Capri- 
 corni he finds that the odds are about 80 to 1 
 against the combination being a chance one. For the 
 Pleiades he finds the odds to be 500,000 to 1 " that 
 no six stars out of the number (1500) scattered at 
 random, in the whole heavens, would be within so 
 small a distance from each other as the Pleiades are." 
 He says that the Pleiades, examined with a telescope, 
 show a large number of smaller stars, and that this 
 increases the odds against their collection by chance 
 to " many millions to one." But we now know that 
 this reasoning is not valid ; for although photography 
 has shown over 2000 stars in the group, it has also 
 shown that the surrounding sky is on all sides equally 
 rich in small stars. It therefore seems that most of 
 the fainter stars in the Pleiades do not belong to 
 the cluster, but are probably far behind it in 
 space. 
 
 With reference to the " proper motions " of stars, 
 he says, " This apparent change of situation may be 
 owing either to the real motion of the stars them- 
 selves, or to that of the sun, or partly to the one and 
 partly to the other" (footnote, p. 252). This is a 
 remarkable prediction, and one we now know to be 
 perfectly correct. He supposes that there may be 
 some faint stars which have a " less real magnitude," 
 and may " belong to the same system with the sun," 
 and for these a parallax might be found. This is 
 another remarkable forecast. Several faint stars are 
 now known which have a larger parallax than many 
 of the brighter stars, and these are probably much 
 
MICHELL'S ASTRONOMICAL VIEWS 119 
 
 smaller than our sun. He seems to think that vari- 
 able stars and red stars may perhaps be nearer to us 
 than others. But this surmise has not been verified. 
 Variable stars seem to lie at a great distance from 
 our system, and very few red stars have any 
 measurable parallax. 
 
 Assuming the number of stars belonging to our 
 system at about 1000, and supposing the sun to be 
 an average-sized member of the group, Michell finds 
 that at the mean distance of the other stars he would 
 " probably rank only with stars of the fourth magni- 
 tude," and taking the parallax of Sirius at one second, 
 the parallax of one-half the stars of the group would 
 be about ^j of a second, or about 0*07 second, and the 
 parallax of none of these would much exceed f of a 
 second. Supposing the number of stars in the solar 
 group to be only 350, the sun would then rank with 
 stars of the third magnitude, and in this case the 
 parallax of one-half of the stars would be about 
 0*14 second, and the parallax of none of them would 
 be more than one second. In the case of 1000 stars 
 in the group, he thought that the largest stars would 
 not be more than 1000 times the size of the sun, and 
 if the group contains only 350 stars, the largest stars 
 would perhaps exceed the sun " in the proportion of 
 about 120 to 1." 
 
 He then returns to the Pleiades, and attempts to 
 find the probable distance of the cluster. Assuming 
 that the cluster has no great extension in the line 
 of sight, or, in other words, that it is roughly globular 
 in form, and further assuming that the average dis- 
 tance between the six stars visible to the naked eye 
 is equal to the average distance between the stars of 
 the supposed solar cluster, he finds that the probable 
 
120 ASTRONOMICAL ESSAYS 
 
 distance of the Pleiades (assuming their diameter to 
 be about 2) is " about 57 times as great as the mean 
 distance of the stars of our system from the earth." 
 From this he concludes that rj Tauri (Alcyone) the 
 brightest of the Pleiades is about 185 times larger 
 than Sirius, and possibly this estimate of its size 
 may not be far from the truth. 
 
 With reference to the nebulae, Michell suggests 
 that many of them may consist of stars not distin- 
 guishable by the telescopes in use in his time 
 another remarkable prediction which has been fully 
 verified by modern observations. 
 
 In the Philosophical Transactions for the year 
 1784 there is another paper by Michell with the title, 
 " On the Means of discovering the Distance, Magni- 
 tude, etc., of the fixed Stars, in consequence of the 
 Diminution of the Velocity of their Light, in case such 
 a Diminution should be found to take place in any of 
 them, and such other Data should be procured from 
 Observation as would be farther necessary for that 
 Purpose.'" (In a letter to Henry Cavendish, Esq., 
 F.R.S. and A.S.) In this paper he considers the 
 possibility of finding the distance of the stars from 
 "the diminution of the velocity of light" due to the 
 attraction of the stars themselves. This idea was 
 of course based on the " corpuscular theory " of light, 
 which supposed that light was due to small corpuscles 
 shot out by the sun and stars, a theory which was 
 then in vogue. On this theory the velocity of the 
 particles emitted would be gradually reduced by 
 the attraction of the sun or star, in the same way 
 that a body projected upwards from the earth 
 gradually loses its velocity, and after a time is 
 drawn back to the earth again. If, however, the 
 
MICHELL'S ASTRONOMICAL VIEWS 121 
 
 velocity of projection were sufficiently great, the 
 body would not return. On this theory, if a star had 
 a sufficiently enormous mass it might be able eventu- 
 ally to destroy the velocity of the emitted light cor- 
 puscles and draw them back to its surface. In this 
 case the star would be invisible, as none of its light 
 could reach us. This was a very ingenious specula- 
 tion, but the corpuscular theory having been aban- 
 doned in favour of the wave theory, Michell's views 
 on this matter are now untenable. He gives some 
 calculations with reference to the size of a body which 
 would be sufficient to draw back the emitted light 
 corpuscles, and finds that its diameter should be at 
 least 497 times the sun's diameter, the densities of 
 the star bodies being the same. This would give an 
 enormous mass, but even with such a mass, we now 
 know that there would be no diminution in the 
 velocity of light. 
 
 Michell clearly shows in this paper that he was 
 aware of the probable existence of binary stars, 
 thus anticipating Sir William Herschel. He says, 
 " The very great number of stars that have been dis- 
 covered to be double, triple, etc., particularly by Mr. 
 HERSCHEL, if we apply the doctrine of chance, as I 
 have heretofore done in my 'Enquiry into the Probable 
 Parallax, etc., of the Fixed Stars,' published in the 
 Philosophical Transactions for the year 1767, cannot 
 leave a doubt with any one, who is properly aware 
 of the force of those arguments, that by far the 
 greatest part, if not all of them, are systems of stars 
 so near to each other, as probably to be liable to be 
 affected sensibly by their mutual gravitation ; and it 
 is therefore not unlikely that the periods of revolu- 
 tion of some of these about their principals (the 
 
122 ASTRONOMICAL ESSAYS 
 
 smaller ones being, upon this hypothesis, to be con- 
 sidered as satellites to the others) may some time or 
 other be discovered." This remarkable prediction 
 has been abundantly fulfilled. The orbits of over 
 fifty binary stars have now (1906) been accurately 
 computed, and many others are known to be certainly 
 binary. 
 
 With reference to the real brightness of the stars, 
 Michell says, " It is not unreasonable to suspect that 
 very possibly some of the fixed stars may have so 
 little natural brightness in proportion to their mag- 
 nitude, as to admit of their diameters having some 
 sensible apparent size, when they shall come to be 
 more carefully examined, and with larger and better 
 telescopes than have been hitherto in common use." 
 None of the stars have been found to show any real 
 disc, but some small planetary nebulae are now 
 known which look like faint stars in the telescope at 
 first sight, but show a perceptible disc when examined 
 with high magnifying powers. Michell also suggests 
 that some variable stars, like Mira Ceti, might 
 possibly show a disc with high powers, but this idea 
 has not been verified. 
 
 He makes another remarkable prediction with 
 reference to supposed dark bodies in space. He says, 
 " If there should exist in nature any bodies whose 
 density is not less than that of the sun, since their 
 light could not arrive at us ; or if there should exist 
 any other bodies of a somewhat smaller size, which 
 are not naturally luminous, of the existence of bodies 
 under either of these circumstances we could have 
 no information from sight ; yet if any luminous 
 bodies should happen to revolve about them, we 
 might still perhaps, from the motions of these 
 
MICHELL'S ASTRONOMICAL VIEWS 123 
 
 revolving bodies, infer the existence of the central 
 ones with some degree of probability, as this might 
 afford a clue to some of the apparent irregularities 
 of the revolving bodies, which would not be easily 
 explicable on any other hypothesis." This idea, 
 although based on an erroneous hypothesis, has 
 been fully realized by the discovery of spectroscopic 
 binaries, and the satellites of Sirius and Procyon. 
 
 Michell did other scientific work. He invented 
 the well-known torsion balance for weighing the 
 earth. The invention of this instrument is often 
 ascribed to Cavendish, who used it in his famous 
 experiment. But the invention was really due to 
 Michell, and this was admitted by Cavendish himself 
 in a communication to the Royal Society. In a paper 
 read on June 21, 1798, Cavendish says, "Many years 
 ago, the late Rev. JOHN MICHELL, of this Society, 
 contrived a method of determining the density of 
 the earth by rendering sensible the attraction of 
 small quantities of matter ; but, as he was engaged 
 in other pursuits, he did not complete the apparatus 
 till a short time before his death, and did not live 
 to make any experiments with it. After his death, 
 the apparatus came to the Rev. FRANCIS JOHN HYDE 
 WOLLASTON, Jacksonian Professor at Cambridge, who, 
 not having conveniences for making experiments 
 with it, was so good as to give it to me." l 
 
 1 Phil. Trans., 1798, p. 469. 
 
CHAPTER X 
 
 SIR WILLIAM HEBSCHEL'S ASTRONOMICAL THEORIES 
 AND OBSERVATIONS 
 
 " Ccelorum perrupit claustra." x 
 
 THE famous astronomer, Sir William Herschel, was 
 an excellent observer, and his astronomical theories 
 were bold and suggestive, although always controlled 
 by philosophic caution. In the following pages I 
 propose to consider especially his nebular and 
 sidereal theories. His papers on " the construction 
 of the heavens " and the constitution of the Milky 
 Way, star clusters, and nebulae, are scattered through 
 the volumes of the Philosophical Transactions of the 
 Royal Society for the years 1784 to 1818, and as these 
 volumes are not to be found in every library, an 
 account of Herschel' s theories and observations may 
 prove of interest to the general reader. 
 
 Before considering these theories, let us first 
 glance at some papers of Herschel' s on the distance 
 of the fixed stars, and on the sun's motion in space. 
 In the Philosophical Transactions for 1782 (p. 82) 
 there is a paper by Herschel, " On the Parallax of 
 the Fixed Stars." He says that up to his time the 
 best observations made with a view to determine 
 the distance of the stars had only succeeded in 
 
 1 From his epitaph in the church of St. Lawrence at Upton. 
 124 
 
SIR WILLIAM HERSCHEL'S THEORIES 125 
 
 giving " a distant approximation " to the truth, but 
 showed that the distance of the nearest star " cannot 
 be less than forty thousand diameters of the whole 
 annual orbit of the earth." The want of a base line 
 sufficiently long for the purpose is the great difficulty 
 in this investigation, for, as Herschel says, "the 
 whole diameter of the annual orbit of the earth is a 
 mere point when compared to the immense distance 
 of the stars." After describing the difficulties con- 
 nected with the measurement of the star's parallax 
 by the direct method, owing to refraction, nutation, 
 precession, aberration, etc., he describes the method 
 of measuring the parallax by observations of two stars 
 apparently close together, but in which one of them 
 is far behind the other in space. This method, he 
 says, was first suggested by Galileo, who did not, 
 however, suppose the two stars to be very close 
 together (that is, apparently close). The method 
 was also mentioned by other astronomers. To fulfil 
 the necessary conditions for success, he says that the 
 stars forming the optical double as such doubles are 
 now termed must be close together, and must 
 " differ as much in magnitude as we can find them.'* 
 He thought that by this method it would be possible 
 to find a parallax as small as the tenth of a second 
 of arc, and shows that the errors due to refraction, 
 aberration of light, etc., will be imperceptible in 
 such observations. He advocates the use of high 
 powers for the measurement of the companions of 
 double stars, but says that e Bootis will not bear the 
 same power as Castor; stars which are equal, or nearly 
 so, bearing a higher power than those with unequal 
 components. He found that an eyepiece with a single 
 lens was much preferable to one with two lenses. 
 
126 ASTRONOMICAL ESSAYS 
 
 Modern practice, however, does not seem to favour 
 this conclusion. High powers, he thinks, " absolutely 
 necessary" in the search for parallax among the 
 stars. 
 
 He then gives an account of his search for suit- 
 able double stars for the purpose of parallax de- 
 termination. In this search he depended more on 
 his own actual observations than on the results 
 found by previous observers, and says, "Nature, 
 that great volume, appeared to me to contain the 
 best catalogue upon this occasion." Among the 
 stars he first selected for the purpose were the double 
 star " in the breast of the Virgin," " the first star in 
 Aries," and some near the great nebula in Orion. 
 During this survey of the heavens he collected the 
 materials for his catalogues of double stars which 
 were published in the same volume of the Philo- 
 sophical Transactions (1782). With reference to a 
 few of these objects which had been previously dis- 
 covered by other observers, he makes the rather 
 quaint remark, "It is a little hard upon young 
 astronomers to be obliged to discover over again 1 
 what has already been discovered." 
 
 When the distance between the components of a 
 double star is very small, Herschel estimated the 
 distance in " measures of their own apparent 
 diameters." This method was used when the dis- 
 tance did "not much exceed two diameters of the 
 largest." He gives examples of double stars of 
 various degrees of difficulty. For telescopes of 
 small power, magnifying from 40 to 100 times, he 
 recommends the following as tests for the quality 
 of the instrument: Ursse Majoris, y Delphmi, y 
 1 The italics are Hersohel's. 
 
SIR WILLIAM HERSCHEL'S THEORIES 127 
 
 Arietis, IT Bootis, y Virginis, t Cassiopeiae, and /x, 
 Cygni. He then gives a mathematical investigation 
 of the method of finding the parallax from observa- 
 tions of double stars, but this is too technical to 
 reproduce here. 
 
 In the Philosophical Transactions for 1783, there 
 isja paper by Herschel, " On the Proper Motion of the 
 Sun and Solar System ; with an Account of several 
 Changes that have happened among the Fixed Stars 
 since the time of Mr. Flamstead." 1 He refers to the 
 proper motion of the stars Arcturus, Sirius, Alde- 
 baran, Procyon, Castor, Rigel, and Altair ; and says 
 that on account of the great distance of some stars 
 from the earth, we cannot expect that their proper 
 motions would become perceptible for ages, and he 
 makes the interesting remark, " This consideration 
 alone would lead us strongly to suspect that there 
 is not, in strictness of speaking, one fixed star in 
 the heavens." Modern observations tend to confirm 
 the accuracy of Herschel's prediction. 
 
 He then considers some apparent changes of 
 brightness which have occurred in certain stars since 
 Flamsteed's time. Among these he mentions 80 and 
 81 Herculis, 56 Cancri, 19 Persei, 108 Pisciuin, 73 and 
 74 Cancri, 8 Hydrse, 26 Cancri, 62 Orionis, 71 Hercules, 
 19 and 34 Comae Berenices, which he seems to think 
 had disappeared. But errors of observation by 
 Flamsteed may possibly account for Herschel's failure 
 to find these stars. 
 
 Among stars which have apparently changed in 
 brightness, he mentions a Draconis, /3 Ceti, Serpentis, 
 T] Cygni, 7) Bootis, t Delphini, y3 Trianguli, y Aquilae, 
 
 1 This is Herschel's spelling of the first Astronomer Royal's 
 name ; but it is now generally spelled Flamsteed. 
 
128 ASTRONOMICAL ESSAYS 
 
 rr Sagittarii, 8 Canis Majoris, yj Serpentis, K Serpen- 
 tarii, /? Equulei, 8 Delphini, e Bootis, 8 Sagittae, a and 
 8 Ursse Majoris, y and /3 Lyrse, and Leonis. Of these, 
 the only star which has since been proved to be really 
 variable is /? Lyrse. 
 
 Among stars which he thinks have " newly come 
 to be visible," he mentions several stars between 
 the fourth and sixth magnitudes, not seen or over- 
 looked by Flamsteed. He thinks, however, that it is 
 not easy to prove that a star has recently become 
 visible, and he lays " no particular stress on the new 
 appearance of the above stars," but recommends 
 further observation of these objects. 
 
 Herschel then proceeds to consider the question 
 of the sun's motion in space. He says, (1) " The 
 greatest or total systematic parallax " as he terms 
 the apparent change of place in the stars due to the 
 sun's motion " will take place along a line at right 
 angles to the direction of the solar motion." This is 
 evident. (2) The "systematical parallax" of other 
 stars, not in this line, will be the maximum parallax 
 multiplied by the sine of the angle between the place 
 of the star and the direction of the solar motion. 
 This will also be obvious to any reader who under- 
 stands the first principles of trigonometry. (3) " The 
 parallax of the stars at different distances will be 
 inversely as those distances." That is, the nearer 
 the star, the greater its apparent displacement or 
 parallax ; and the farther the star is from the earth, 
 the smaller its parallax will be. This is also suffi- 
 ciently clear. (4) " Every star at rest, to a system in 
 motion, will appear to move in a direction contrary 
 to that in which the system is moving." This is also 
 evident. The apparent motion of distant objects 
 
SIR WILLIAM HERSCHEL'S THEORIES 129 
 
 seen from a railway train in motion will show the 
 truth of this assumption. Assuming these principles, 
 Herschel selected a number of stars, and from their 
 " proper motions," or apparent motion on the face 
 of the sky, he deduced the direction of the sun's 
 motion in space. He first chose seven stars, namely, 
 Sirius, Castor, Procyon, Pollux, Regulus, Arcturus, 
 and Altair, and he found that the proper motions of 
 these stars indicated a solar motion towards the con- 
 stellation Hercules. To test the accuracy of this 
 result, he took twelve stars, namely, Arcturus, Sirius, 
 j3 Cygni, Procyon, e Cygni, y Arietis, y Geminorum, 
 Aldebaran, fi Geminorum, y Piscium, a Aquilse, and 
 a Geminorum. Adding Regulus, and Castor being 
 double, made fourteen stars. From the proper 
 motions of these he obtained 27 motions in right 
 ascension and declination. Assuming a point near 
 X Herculis for the solar " apex " as Herschel termed 
 the point towards which the sun is moving he 
 found that this point satisfied 22 of these motions 
 and he thought that the five exceptions were due to 
 the real motions of the stars themselves. He found 
 that the apparent motion of Pollux " agrees wonder- 
 fully with observations," but Castor not so well, and 
 he thought it probable that " its distance may be 
 double that of Pollux." But modern measures have 
 not confirmed this supposition. 
 
 With reference to the annual amount of the solar 
 motion, Herschel thought that " the diameter of the 
 earth's orbit, at the distance of Sirius or Arcturus, 
 would not nearly subtend an angle of one second ; 
 but the apparent motion of Arcturus, if owing to 
 the translation of the solar system, amounts to no less 
 than " 2*7 seconds a year," and he concludes " that 
 
 K 
 
130 ASTRONOMICAL ESSAYS 
 
 the solar motion can certainly not be less than that 
 which the earth has in her annual orbit." Modern 
 measures, however, make the motion about eleven or 
 twelve miles a second. From an examination of the 
 proper motion of a number of stars observed by 
 Mayer in 1756, compared with Roemer's observations 
 in 1706, Herschel found a confirmation of his previous 
 result. He mentions that Mayer had previously (in 
 1760) suggested a solar motion as possible, and that 
 Lalande had made a similar suggestion in 1776. 1 
 
 The first paper in which Herschel definitely 
 considers the subject of " the construction of the 
 heavens " appeared in the volume of the Philosophical 
 Transactions for the year 1784 (p. 437). He begins 
 by stating that the instrument he used in his 
 observations was a reflecting telescope of the New- 
 tonian form, the mirror having a clear aperture of 
 18'7 inches, with a focal length of twenty feet, which 
 was ia those times a very large telescope indeed. 
 He used this instrument in an investigation of what 
 he terms " the interior construction of the heavens, 
 and its various nebulous and sidereal strata (to 
 borrow a term from the natural historian)." On 
 turning this large telescope on the Milky Way, he 
 found that the nebulous light visible to the naked 
 eye was wholly resolved into small stars. This his 
 earlier telescope failed to do completely, although 
 the Galaxy had been partially resolved into stars by 
 earlier observers. The portion of the Milky "Way 
 first examined by Herschel was that near the hand 
 and " club" of Orion, that is, near the stars v and 
 Orionis, and north of the bright star Betelgeuse. 
 
 1 This was also suggested by Michell in 1767. See chapter on 
 MichelTs views. 
 
SIR WILLIAM HERSCHEL'S THEORIES 131 
 
 He found the small stars in this region very numerous 
 and of various degrees of brightness. To avoid 
 being misled by the " dazzling brightness " of such a 
 multitude of stars, he attempted to ascertain their 
 real number by actually counting those visible in 
 numerous " fields " of his telescope, and taking an 
 average of these various counts. In six fields taken 
 at random he counted 110, 60, 70, 90, 70, and 74 stars, 
 which gives an average of 79. Selecting " the most 
 vacant place " he could find in this region, he counted 
 63 stars in the field of view. 
 
 Now, allowing fifteen minutes of arc for the 
 diameter of the field of view, he concluded that a 
 belt or zone of 15 long and 2 wide " could not well 
 contain less than fifty thousand stars," bright enough 
 to be distinctly counted. In addition to this large 
 number, he " suspected at least twice as many more," 
 which, for want of light in the telescope, he " could 
 only see by faint glittering and interrupted glimpses." 
 The larger estimate would give 5000 stars to the 
 square degree, and, if the whole heavens were equally 
 rich in stars which, of course, it is not would give, 
 I find, a total of 206 millions of stars. 
 
 With the large telescope Herschel found that 
 many of Messier's nebulae described by him as 
 nebulas containing no stars, " appeared to be nothing 
 but stars, or at least to contain stars, and to show 
 every other indication of consisting of them entirely." 
 Even those described by Messier as clusters of stars 
 containing nebulosity were found to be completely 
 resolved. Messier's failure to resolve these " nebulae ' 
 was, of course, due to want of power in the telescope 
 he used. Herschel describes No. 53 of Messier's 
 catalogue as " one of the most beautiful objects 
 
132 ASTRONOMICAL ESSAYS 
 
 I remember to have seen in the heavens. The cluster 
 appears under the form of a solid ball, consisting of 
 small stars, quite compressed into a blaze of light, 
 with a great number of loose ones surrounding it, 
 and distinctly visible in the general mass." This 
 fine cluster lies a little north- west of the star a Comae 
 Berenices. 
 
 At this period of his investigations, Herschel 
 thought that the nebulas and clusters of stars might 
 " surround the whole apparent sphere of the heavens, 
 not unlike the Milky ,Way, which undoubtedly is 
 nothing but a stratum of fixed stars." He found 
 one of the nebulous regions, or " strata," as he calls 
 them, so rich in nebulae that in a period of 36 minutes 
 he detected 31 nebulae, "all distinctly visible on a 
 fine bue sky." He also noticed double and treble 
 nebulae, but probably some of these were various 
 forms of those now known as spiral nebulae. 
 
 Herschel thought it very probable that our sun is 
 placed in the " great stratum " forming the Milky 
 Way, " though perhaps not in the very centre of its 
 thickness." Recent researches seem to confirm this 
 opinion, namely, that the sun is nearly, but not 
 exactly, in the centre of the Galactic plane. Start- 
 ing from this assumption, Herschel then proceeds to 
 explain his famous theory of the Milky Way com- 
 monly known as the " disc theory." This theory, 
 usually ascribed to Sir William Herschel, was 
 originally advanced in 1750 by Thomas Wright, 
 of Durham, that is, 34 years before the publication 
 of Herschel' s paper in the Philosophical Trans- 
 actions. The theory is usually spoken of as the 
 "disc" theory, but in Herschel's original drawing 
 the sidereal system is represented as a rectangular 
 
SIR WILLIAM HERSCHEL'S THEORIES 133 
 
 slab of considerable length and width in proportion 
 to its thickness. This seems to have been his first 
 conception, but it was probably afterwards modified, 
 as in a subsequent drawing he represents the Milky 
 Way in the form of a section of an irregular circular 
 disc. He supposed that the edge of this hypothetical 
 layer was split at one end, in order to account for 
 the division, or apparent division, in the Milky Way 
 between Cygnus and Scorpio. He then considers 
 the hypothesis of a ring shape for the Galaxy, but 
 thinks that it would be " not a little extraordinary 
 that the sun, being a fixed star like those which 
 compose this imagined ring, should just be in the 
 centre of such a multitude of celestial bodies, with- 
 out any apparent reason for this singular distinction ; 
 whereas, on our supposition, every star in this 
 stratum, not very near the termination of its length 
 or height, will be so placed as also to have its own 
 Galaxy, with only such variations in the form and 
 lustre of it as may arise from the particular situation 
 of each star." 
 
 He then proceeds to consider the question, how 
 we are to determine the sun's plane in this supposed 
 stratum of stars, and describes his method of 
 " Gaging the Heavens, or the Star Gage." This 
 method consisted in counting the number of stars 
 visible in the field of his telescope, taking the mean 
 of ten fields " very near each other." He says these 
 " gages," of course, vary with the size of the telescope 
 used in the inquiry, and on this point he quotes a 
 remark of the famous French astronomer, De la 
 Lande, of which the following is a translation : 
 
 " We see with telescopes stars in all parts of the 
 sky, a little closer in the Milky Way or the nebulae. 
 
134 ASTRONOMICAL ESSAYS 
 
 We cannot doubt that a part of the light and 
 whiteness of the Milky Way proceeds from the 
 light of small stars, which are found there by 
 millions ; however, with the largest telescopes we 
 do not sufficiently distinguish them, and they are 
 not sufficiently near enough to attribute to this the 
 whiteness of the Milky Way, so evident to the 
 naked eye. We cannot then affirm that the stars 
 are the sole cause of the whiteness, although we 
 know no other satisfactory way of explaining it." 
 
 Possibly the nebulosity visible in the Milky Way 
 in modern photographs may help to explain this 
 " whiteness." 
 
 Herschel then explains how the sun's position in 
 the supposed stratum of stars may be ascertained by 
 the number of stars in each "gage," which should 
 indicate the length of the " ray," or thickness of the 
 stratum, in the given direction. He finds that the 
 direction of the solar motion in space is nearly in 
 the direction of one of the " nodes " of the Milky 
 Way. By the term " node " he means the " union of 
 two strata," like those in Cepheus and Cassiopeia, 
 and in Scorpio and Sagittarius. He here refers to 
 his observations of the nebulae, and remarks that 
 " the spaces preceding them were generally quite 
 deprived of their stars, so as often to afford many 
 fields without a single star in it ; that the nebulae 
 generally appeared some time after among stars of a 
 certain considerable size, and but seldom among small 
 stars ; that when I came to one nebula, I generally 
 found several more in the neighbourhood ; that after- 
 wards a considerable time passed before I came to 
 another parcel ; and these events being thus repeated 
 in different altitudes of my instrument, and some of 
 
SIR WILLIAM HERSCHEL'S THEORIES 185 
 
 them at a considerable distance from each other, it 
 occurred to me that the intermediate spaces between 
 the sweeps might also contain nebulae ; and finding 
 this to hold good more than once, I ventured to give 
 notice to my assistant at the clock to prepare, since 
 I expected in a few minutes to come at a stratum of 
 the nebulae, finding myself already (as I then figura- 
 tively expressed it) on nebulous ground. In this 
 I succeeded immediately." l This is an interesting 
 observation, and is confirmed by modern observa- 
 tions. 
 
 With reference to the direction of some of the 
 " capital strata," as he calls them, " or their 
 branches," he mentions the well-known nebula of 
 Cancer, which runs from e Cancri 2 towards the south 
 over the 67 nebula of the Connoissance des Temps 
 [Messier 67]. He thought that it probably belonged 
 to " a certain stratum in which I suppose it to be so 
 placed as to be nearest to us." He describes it as " a 
 very beautiful and pretty much compressed cluster 
 of stars, easily to be seen by any good telescope, and 
 in which I have observed above 200 stars at once 
 in the field of view of my great reflector with a 
 power of 157." This description seems to refer to 
 Messier 67. 
 
 Another stratum which he thought is probably 
 " nearer to the solar system than any of the rest," is 
 that containing Coma Berenices, this open cluster 
 perhaps forming one of the clusters in the stratum 
 which he thought " runs on a very considerable 
 way," perhaps even round the heavens, " through 
 
 1 These are Herschel's words. They are often quoted incorrectly 
 in books on astronomy. 
 
 2 This is Messier 44, the so-called Praesepe. 
 
136 ASTRONOMICAL ESSAYS 
 
 the Great Bear onwards to Cassiopeia ; then through 
 the girdle of Andromeda and the Northern Fish, 
 proceeding towards Cetus ; while towards the south 
 it passes through the Virgin, probably on to the tail 
 of Hydra and the head of Ceiitaurus." He thought 
 this stratum lies nearly at right angles " to the great 
 sidereal stratum in which the sun is placed." 
 
 Having " gaged " the Milky Way in various 
 directions, he found that the number of stars com- 
 posing it " constantly increase and decrease in 
 proportion to its apparent brightness to the naked 
 eye." This important observation shows that the 
 varying brightness of the Milky Way is really due 
 to its varying richness in stars, and not to varying 
 distance from the earth as some writers have in- 
 correctly supposed. Modern photographs confirm 
 Herschel's conclusion. 
 
 Supposing that the stars are of various sizes and 
 almost equally distributed in space, he found the 
 following results with reference to the nebulae. 
 
 1. When a star is considerably larger than its 
 neighbours, it will attract them round it, and thus 
 form a cluster of almost a globular form. This idea 
 was evidently suggested by the appearance of the 
 globular clusters, but modern researches seem to 
 suggest that the globular clusters were more pro- 
 bably formed by the condensation of nebulous 
 matter. 
 
 2. In the case where a number of stars, although 
 not much larger than the others, happen to be 
 nearer each other, are drawn together by the force 
 of attraction, thus forming an irregular cluster. 
 Here, again, it now seems more probable that 
 irregular clusters were originally formed by the 
 
SIR WILLIAM HERSCHEL'S THEORIES 137 
 
 condensation of gaseous masses. The Pleiades, with 
 their surrounding nebulosity, is an example. 
 
 3. A combination of the preceding causes may 
 produce another form of cluster, in which large and 
 small stars " are situated in long extended, regular, 
 or crooked rows, hooks, or branches." 
 
 4. More extensive combinations may produce 
 clusters not very far separated from each other. 
 This hypothesis would account for the observed 
 occurrence of clusters in the same region of the 
 heavens. 
 
 5. As the result of these supposed clusterings of 
 stars, " cavities or vacancies " would be formed. 
 This would explain the occurrence of dark spaces or 
 " holes " w^hich are found in various parts of the 
 Milky Way and elsewhere. 
 
 Herschel then considers how the stars in clusters 
 are " preserved from rushing on their centres of 
 attraction." He suggests "projectile forces," meaning, 
 of course, motions of the component stars round their 
 common centre of gravity. He says " these clusters 
 may be the Laboratories of the universe, if I may so 
 express myself, wherein the vast salutary remedies 
 for the decay of the whole are prepared." 
 
 He then proceeds to consider the optical appear- 
 ance of the heavens as viewed from our standpoint 
 on the earth, and considers that "the stars of the 
 first magnitude, as being in all probability the nearest, 
 will furnish us with a step to begin our scale." This 
 was a very natural supposition, but modern measures 
 of distance do not support the view that the brightest 
 stars are, as a rule, the nearest. They suggest rather 
 that the difference in relative brightness among the 
 stars is due more to difference in absolute size, and 
 
138 ASTRONOMICAL ESSAYS 
 
 also to difference in luminosity of their surface. 
 Following, however, Herschel's hypothesis, he sup- 
 poses that, taking the distance of Sirius or Arcturus 
 as unity, stars of the second magnitude are at double 
 the distance, those of the third at treble, and so on. 
 He assumes that a star of the seventh magnitude is 
 seven times as far as one of the first. 1 On this 
 supposition an eye placed at the centre of a globular 
 cluster would not see the whole of it, as the distance 
 of the outer stars of the cluster would probably 
 exceed six times the distance of Sirius from the 
 earth. Outside clusters might possibly be seen as 
 small faint nebulae. He then proceeds to show that 
 his views are consistent with his " gages." He gives 
 a table of these gages taken in various parts of the 
 heavens. This list proceeds regularly in right 
 ascension all round the sky, but varies in declina- 
 tion. The number of stars observed in these " gages " 
 varies enormously, the averages for ten fields ranging 
 from 2'2 to 3*4 stars near the pole of the Milky Way 
 up to 384 near ft Cygni, and 588 in Sagitta. The 
 high results were, of course, in the Milky Way. 
 
 To determine the length of the visual ray in the 
 method of star-gazing on the hypothesis of stars 
 *' equally scattered," Herschel imagined a cone cut 
 into frustra by equidistant planes perpendicular to 
 its axis. Then if we suppose one star placed at the 
 vertex of the cone and another on the axis at the 
 first intersection, " six other stars may be set around 
 it so as to be equally distant from one another and 
 from the central star." The sums of the numbers of 
 
 1 Herschel's values of distances do not agree with modern 
 measures. With a light ratio of 2-512, a star of the seventh magnitude 
 would be nearly sixteen times the distance of one of the first. 
 
SIR WILLIAM HERSCHEL'S THEORIES 139 
 
 stars in the several sections will then be, 1, 7, 19, 37, 
 61, 91, etc. The sum of any number n of this series 
 will be n*. From this he finds that the length of 
 the visual ray may be represented by n 1. 
 
 According to Herschel's first view of the con- 
 struction of the visible universe, " ^ue inhabit a 
 planet of a star belonging to a compound nebula of 
 the third form." This is the heading of a section of 
 his paper in the Philosophical Transactions for 1785 
 (p. 244). He says " the stupendous sidereal system 
 we inhabit, this extensive stratum and its secondary 
 branches, consisting of many millions of stars, is, in 
 all probability, a detached nebula.' 1 He then pro- 
 ceeds to find the length of his " sounding line." The 
 " gages " showed' a maximum of 588 stars in the 
 " most crowded " parts of the Milky Way. This 
 richness continued, he says, for " many minutes," so 
 that in a quarter of an hour's time there passed no 
 less than 116,000 stars through the field of view of 
 his telescope. From this he finds that the length of 
 the sounding line was not less than 497 times the 
 distance of Sirius from the earth. As modern 
 measures make the distance of Sirius about 8'8 
 years' journey for light, this result would give for 
 his farthest stars about 4374 " light years," a high 
 but perhaps not improbable value. 
 
 To assume an equal distribution of stars in space 
 is, he admits, inaccurate, as most probably no such 
 arrangement exists in reality ; but taking all the 
 stars as a whole, " there will be a mean distance 
 which may be assumed as the general one." No 
 unusual collections or clusters of stars were included 
 in the " gages," and he found that the difference 
 between a crowded region and a cluster could be 
 
140 ASTRONOMICAL ESSAYS 
 
 easily perceived by the arrangement of the stars. 
 In a cluster they are generally nearly of the same 
 size, with a certain uniformity of distance between 
 them, and they are also condensed towards a centre. 
 On the other hand, in the rich regions of the Milky 
 Way we find a mixture of stars of all degrees of 
 brightness, and scattered without any special order. 
 Where the " gages " run below 5, Herschel thought 
 that the stratum cannot exceed 100 times the 
 distance of Sirius, and he says " the same telescope 
 which could show 588 stars in a field of view of 15 
 minutes must certainly have presented me also with 
 the stars in these situations as well as the former, 
 had they been there." This is an interesting and 
 valuable remark of Herschel's, and shows that he 
 fully realized the fact that the number of existing 
 stars is really small in the directions where the 
 gages showed a small number. This fact shows 
 " that there must be at least a vacancy amounting 
 to the length of a visual ray not short of 400 times 
 the distance of Sirius ; and this is amply sufficient 
 to make our nebula a detached one," and he adds, 
 "it is true that it would not be consistent con- 
 fidently to affirm that we are on an island unless we 
 had actually found ourselves everywhere bounded 
 by the ocean, and therefore I shall go no further 
 than the gages will authorize." Photographs now 
 show strong evidence that our sidereal universe is 
 practically " an island " in space. Herschel thought 
 that a larger telescope than the one he used in these 
 researches would probably reveal a much larger 
 number of stars. Thus " a telescope with a three- 
 fold power," he thought, would show over 16,000 stars 
 instead of the 588 counted by him. Although 
 
SIR WILLIAM HERSCHEL'S THEORIES 141 
 
 modern photographs taken with telescopes larger 
 than Herschel's show an enormous number of stars 
 in the Milky Way, still Herschel's expectations have 
 not been realized. Even photographs in rich regions 
 of the Galaxy show nothing like 16,000 stars in a 
 circle of fifteen minutes of arc in diameter, and 
 many of the stars visible on these photographs are 
 not visible to the eye with the telescope with which 
 they were photographed. 
 
 With reference to the probable extent of the 
 Milky Way, Herschel says that his telescope had 
 " the power of showing the united lustre of the 
 accumulated stars that compose a milky nebulosity 
 at a distance far exceeding the former limits ; so 
 that from these considerations it appears again 
 highly probable that my present telescope, not 
 showing such a nebulosity in the Milky Way, goes 
 already far beyond its extent : and consequently, 
 much more would an instrument such as I have 
 mentioned, remove all doubt on the subject, both by 
 showing the stars in the continuation of the stratum, 
 and by exposing a very strong milky nebulosity 
 beyond them, that could no longer be mistaken for 
 the dark ground of the heavens." 
 
 He then gives a table showing the length of the 
 supposed " visual ray," corresponding to the number 
 of stars visible in the field of view. Thus for 1 
 star, the length of the ray would be 58 times the 
 distance of Sirius ; for 10 stars, 127 ; for 20, 160 ; for 
 30, 184 ; for 40, 202 ; for 50, 218 ; for 100, 275 ; for 
 200, 347 ; for 300, 530 ; for 500, 471 ; for 1000, 593 ; 
 and for 100,000 stars, 2758. Taking the visual ray 
 corresponding to the different " gages " obtained 
 by observation, and plotting these according to 
 
142 ASTRONOMICAL ESSAYS 
 
 right ascensions and north polar distance, he 
 formed a section of our sidereal system (according 
 to his disc theory) of which he gives a drawing. 1 
 He assumes the north pole of the Milky Way to 
 lie in RA 186, and north polar distance 58 
 (Decl. + 32). This is a little north of the position 
 now usually adopted for the northern Galactic 
 pole. From the figure thus obtained he concludes 
 that " our nebula, as we observed before, is of the 
 third form that is, a very extensive branching com- 
 pound congeries of many millions of stars; which 
 most probably owes its origin to many remarkably 
 large as well as pretty closely scattered small stars, 
 that may have drawn together the rest." 
 
 With reference to the origin of the " nebulous 
 strata " as he calls them he says, " the nebula we 
 inhabit might be said to be one that has fewer 
 marks of profound antiquity upon it than the 
 rest." This idea was based on the hypothesis that 
 the " strata " were formed by a gradual approach of 
 the stars, and as our stratum is apparently not so 
 condensed as the clusters are, it is probably younger ; 
 but such a conclusion is hardly tenable now, as 
 there is reason to believe that our sidereal system 
 includes within its boundaries all known stars, 
 clusters, and nebulae. 
 
 Herschel "surmised" that a nebulous stratum, 
 consisting chiefly of nebulae of the first and second 
 f orm/probably^owes its origin to the decay of a great 
 nebula of the third form. In the same way he con- 
 sidered it possible that our sidereal system might, 
 in the lapse of ages, become divided up into a 
 stratum of two or three hundred nebulae, and he 
 1 Phil Trans, for 1785, facing p. 266, 
 
SIR WILLIAM HERSCHEL'S THEORIES 143 
 
 thought that he could detect the beginning of the 
 gathering of these clusters, such as the nebulous 
 stratum in Coma Berenices and elsewhere. 
 
 According to Herschel's views of the construction 
 of the heavens, some portions seem to have suffered 
 more from the " ravages of time " than others. To 
 illustrate this idea he refers to a spot " in the body 
 of the Scorpion," where he found " an opening or 
 " hole," probably due to this cause. This hole lies a 
 little north of the star 19 Scorpii. Approaching the 
 Milky Way the gages ran up from 9*7 to 171 stars, 
 "when all of a sudden they fell down to nothing, 
 a very few pretty large stars excepted, which made 
 these show 0'5, O7, 1-1, 1-4, 1'8 ; after which they 
 again rose to 4'7, 13*5, 20*3, and soon after to 41*1." 
 This "hole" is about 4 broad. Herschel remarks 
 that the rich globular cluster Messier 80 lies just 011 
 the western border of this hole, and he suggests that 
 the stars composing the cluster might have been 
 " collected from that place," thus leaving a vacancy. 
 He found the same result in the case of Messier 4, 
 which is also on the western border of another 
 "hole," with a smaller cluster north-east of it. 
 Messier 4 lies closely west of the bright star 
 Antares (a Scorpii), and not far from the " hole " 
 near Messier 80, referred to above. 
 
 Herschel then gives observations of what he calls 
 " compound nebulae or milky ways." He thought 
 that some of these "cannot well be less, but are 
 probably much larger than our own system." But 
 this hypothesis is not now considered tenable by 
 astronomers. Herschel's views are, however, very 
 interesting, as all his speculations were. His reasons 
 for thinking some of the nebulae to be external 
 
144 ASTRONOMICAL ESSAYS 
 
 galaxies were as follows. Some of the " round 
 nebulae" consist of stars which, although very 
 small, he could see distinctly with his telescope, 
 and he estimated these to lie at a distance of 
 600 times the distance of Sirius. This estimate 
 was based on the supposition that the component 
 stars of these clusters are closer together than the 
 other stars in our system. On the supposition of an 
 equal distribution of stars, he finds that the distance 
 would be 6000 of the same units. Other smaller 
 nebulae in the neighbourhood of these he estimated 
 to lie much farther from the earth, and he concluded 
 in the case of a nebula "whose light is perfectly 
 milky," that it "cannot be well supposed to be at 
 less than six or eight thousand times the distance of 
 Sirius." Among these supposed external galaxies he 
 mentions " a milky ray " of more than a degree in 
 length, which lies near the star Flamsteed 52 Cygni. 
 A second " faint milky ray," about 15 minutes long by 
 8 or 10 minutes broad, is found a little south-east of the 
 star c Cygni. A third is " a branching nebulosity about 
 a degree and a half long by 48 minutes wide," a little 
 north-west of Cygni. A fourth is another " faint, 
 extended milky ray of about 17 minutes in length and 
 12 minutes in breadth," with another small nebula near 
 it. This object is a little north- west of a Trianguli. A 
 fifth is " a streak of light about 27 minutes long, and 
 in the brightest part 3 or 4 minutes broad." It lies a 
 little south of /3 Ceti. A sixth is " an extensive milky 
 nebulosity" divided into two parts. Near this is 
 " a cluster," which Herschel thought identical with 
 Messier 8 ; but Messier 8 is shown by the spectro- 
 scope to be gaseous according to Secchi. A seventh 
 is Messier 17, now known as the "Omega nebula/ 
 
SIR WILLIAM HERSCHEL'S THEORIES 145 
 
 Herschel describes it as "a wonderful extensive 
 nebulosity of the milky kind." Sir William Huggins 
 finds a gaseous spectrum, so the idea of an external 
 universe must in this case at least be abandoned. To 
 this list Herschel adds the great nebula in Orion and 
 the great nebula in Andromeda. The Orion nebula 
 is now known to consist of glowing gas, and it is 
 certainly not an external galaxy. Herschel thought 
 that the great nebula in Andromeda " is undoubtedly 
 the nearest of all the great nebulae." He found that 
 " the brightest part of it approaches to the resolvable 
 nebulosity, and begins to show a faint red colour ; 
 which, from many observations on the colour and 
 magnitude of nebulae, I believe to be an indication 
 that its distance in this coloured part does not 
 exceed 2000 times the distance of Sirius." This 
 estimate does not, however, denote a comparatively 
 near object. It would represent a journey for light 
 of over 17,000 years. He refers to the nebula near 
 it discovered by his sister, Miss Caroline Herschel, 
 and says " it is not Messier 32, which lies about two- 
 thirds of a degree north, preceding it in a line parallel 
 to (3 and v Andromedae." All modern telescopes have 
 failed to resolve the great nebula into stars, but the 
 spectroscope shows a continuous spectrum with some 
 dark lines, which indicates that it is not gaseous. 
 It is probably partially condensed from the gaseous 
 state, and it may consist of small bodies too small 
 to be visible in our largest telescopes. Photographs 
 show it to be spiral. In all probability it belongs 
 to our sidereal system, and is not an external 
 galaxy. 
 
 Herschel refers to Messier 57, the so-called ring 
 nebula in Lyra, and he seemed to think that it was 
 
 L 
 
146 ASTRONOMICAL ESSAYS 
 
 resolvable into stars, but Huggins finds a gaseous 
 spectrum. 1 
 
 He then refers to the so-called " planetary nebulae," 
 which he thought were possibly external galaxies. 
 One of these lies a little west of the star v Aquarii. 
 He found its diameter to be 10 or 15 seconds ; but 
 Secchi made it 25 seconds by 17 seconds. Herschel 
 found its light of a uniform brightness, and " probably 
 of a starry nature," but Huggins finds it to be a mass 
 of glowing gas. This is one of the finest objects of 
 its class. Another planetary nebula observed by 
 Herschel lies a little south-west of Flamsteed 13 Andro- 
 medae, and he describes it as " a well-defined planetary 
 disc of about 12 seconds diameter, a little elliptical. 
 A third object of this class lies a little north, follow- 
 ing 44 Ophiuchi ; " round, tolerably well defined and 
 pretty bright; its diameter about 30 seconds." A 
 fourth is a little north, following y Sagittae ; " per- 
 fectly round ; pretty bright, and pretty well defined ; 
 about | minute in diameter." A fifth lies a little 
 north, following 21 Vulpeculae ; " exactly round ; of 
 an equal light throughout, but pretty faint, and about 
 1 minute in diameter." A sixth is south preceding 
 39 Cygni ; " perfectly round, and of an equal light, 
 but pretty faint ; its diameter is near 1 minute ; and 
 the edges are pretty well defined." Considering the 
 telescopic appearance of these planetary nebulae, 
 Herschel thought that they could hardly be true 
 nebulae, owing to their uniform and vivid light, and 
 their discs, so small and well defined. On the other 
 hand, he thought they could not be " of a planetary 
 nature." It would also be difficult, he thought, to 
 
 1 For further details of this nebula, see chapter on the ring 
 nebula in Lyra in my " Studies in Astronomy." 
 
SIR WILLIAM HERSCHEL'S THEORIES 147 
 
 consider them as " single stars with large diameter," 
 as we could not then account for their comparative 
 faintness. He also rejects the idea that they might 
 be comets near their aphelion, as their size and 
 brightness is against such an hypothesis. From 
 these considerations he is forced to conclude that 
 they must be nebulae, with the stars "compressed 
 and accumulated in the highest degree " ; but as the 
 spectroscope shows them to be gaseous, Herschel's 
 hypothesis is now untenable. Herschel seems to have 
 been much impressed with the appearance of these 
 planetary nebulae. He says, " If it were not perhaps 
 too hazardous to pursue a former surmise of a renewal 
 in what I figuratively called the laboratories of 
 the universe, the stars forming these extraordinary 
 nebulae, by some decay or waste of nature, being no 
 longer fit for their former purposes, and having their 
 projectile forces, if any such they had, retarded in 
 each other's atmospheres, may rush at last together, 
 and either in succession, or by one general tremendous 
 shock, unite into a new body. Perhaps the extra- 
 ordinary and sudden blaze of a new star in Cas- 
 siopeia's chair of 1572 might possibly be of such a 
 nature." This is an interesting speculation of Sir 
 William Herschel's, and a remarkable forecast of the 
 probable cause of temporary or new stars, most of 
 those which have appeared in modern years having 
 changed into planetary nebulas. 
 
 In the introduction to " A Catalogue of a Second 
 Thousand of New Nebulae and Clusters of Stars " 
 (Phil. Trans. 1788) Herschel speaks of the nebulae 
 " as being no less than whole sidereal systems ; " but 
 such an hypothesis is no longer tenable. He says 
 that " bodies shining only with borrowed light can 
 
148 ASTRONOMICAL ESSAYS 
 
 never be seen at any great distance," and that con- 
 sequently " every star must likewise be a sun shining 
 by its own native brightness." This is an example 
 of the soundness of Herschel's views in matters of 
 fact like this. Some astronomers have since his time 
 suggested that the faint companions to bright stars, 
 like the satellite of Sirius, might shine by reflected 
 light from the brighter star, but I have shown else- 
 where that this is utterly impossible. 1 Herschel 
 thought that all stars had probably "a system of 
 planets, satellites, and comets " revolving round 
 them ; and this hypothesis seems a rational one, at 
 least in the case of single stars. Binary stars and 
 spectroscopic doubles may possibly form an exception. 
 With reference to clusters of stars, Herschel shows 
 the great probability there is of the component stars 
 being contained in a comparatively limited space. 
 He quotes Michell's conclusion that the odds are 
 500,000 to 1 against the six brightest stars of the 
 Pleiades being apparently so close together by merely 
 a chance coincidence, and he argues that the fact of 
 the stars being crowded together in a globular cluster 
 shows that they are " nearly of an equal magnitude," 
 with, however, a certain small variety in size, "in 
 some such proportion as one full-grown plant of a 
 certain species may exceed another full-grown plant 
 of the same species." He also shows that those 
 which are apparently globular in form are really so, 
 the odds against any other form being enormous. 
 These views are undoubtedly sound. He then proves 
 that the globular clusters are in reality more con- 
 densed towards the centre, as they seem to be. For 
 if the component stars were equally scattered through 
 1 See my " Studies in Astronomy," pp. 113-116. 
 
SIR WILLIAM HERSCHEL'S THEORIES 149 
 
 the sphere, it would not have a bright nucleus in the 
 centre. He concludes that this spherical figure has 
 been "formed by the action of central powers." 
 The figure of the earth and planets he considers as 
 examples of this " central power," or central force, as 
 it is now termed ; and that the form of. the globular 
 clusters cannot be due to " any random scattering of 
 stars." The condensation towards the centre proves 
 the action of this " central power " probably " the 
 known central force of gravity." Even in those 
 clusters which are not exactly globular in form, he 
 thought we have evidence of " a tendence towards 
 sphericity by the swell of the dimensions the nearer 
 we draw towards the most luminous place, denoting 
 as it were a course, or tide of stars setting towards 
 a centre." As Tennyson says (in " The Princess ") 
 
 " This world was once a fluid haze of light 
 Till towards the centre set the starry tides, 
 And eddied into suns, that, wheeling, cast 
 The planets." 
 
 In all the nebulae and clusters observed by 
 Herschel about 2300 in number he found this 
 tendency to condensation and increased brightness 
 near the centre, which, he thought, fully established 
 the truth of the hypothesis. There is, however, 
 considerable variety in this appearance of condensa- 
 tion in the middle. This, he thought, might be due 
 partly to the difficulty of seeing distinctly those 
 which lie at great distances from the earth. He 
 thought that the action of this central force " must 
 produce effects proportional to the time of its action," 
 and that consequently the globular clusters are 
 probably older than those of an irregular form. 
 We might thus judge of the relative ages of clusters 
 
150 ASTRONOMICAL ESSAYS 
 
 and nebulae. On this hypothesis he thought we 
 might conclude that a cluster or nebulae " which is 
 very gradually more compressed or bright towards 
 the middle may be in the perfection of its growth," 
 while the planetary nebulae " may be looked upon as 
 very aged." But this view does not now seem so 
 probable as it did to Herschel. A planetary nebulae 
 formed by a temporary star, far from being aged, is 
 comparatively a thing of yesterday. At the end of 
 this paper Herschel makes his famous remark about 
 the nebulae and clusters, " For, to continue the simile 
 I have borrowed from the vegetable kingdom, is it 
 not almost the same thing, whether we live suc- 
 cessively to witness the germination, blooming, 
 foliage, fecundity, fading, withering, and corruption 
 of a plant, or whether a vast number of specimens, 
 selected from every stage through which the plant 
 passes in the course of its existence, be brought at 
 once to our view?" This is doubtless true, but to 
 decide the question as to which are the oldest and 
 which the youngest nebulae seems to require more 
 evidence than we possess at present. 
 
 In the Philosophical Transactions for 1791 there 
 is a paper by Herschel on " Nebulous Stars, properly 
 so called." This is a very interesting paper, as it 
 contains the first evidence of Herschel's change of 
 opinion with reference to the nebula. His first 
 observation of " nebulous stars " was that of " a 
 star of about the eighth magnitude surrounded with 
 a faintly luminous atmosphere of a considerable 
 extent." (The italics are Herschel's.) This greatly 
 surprised him, and seems to have led to his change 
 of views with reference to the real nature of those 
 nebulae which could not be resolved into stars with 
 
SIR WILLIAM HERSCHEL'S THEORIES 151 
 
 his large telescope. He says, " A glance like that of 
 the naturalist, who casts his eye from the perfect 
 animal to the perfect vegetable, is wanting to remove 
 the veil from the mind of the astronomer. The 
 object I have mentioned above, is the phenomenon 
 that was wanting for this purpose. View, for 
 instance, the 19th cluster of my 6th class, and 
 afterwards cast your eye on this cloudy star, and 
 the result will be no less decisive than that of the 
 naturalist we have alluded to. Our judgment, I 
 may venture to say, will be, that the nebulosity about 
 the star is not of a starry nature." (The italics are 
 Herschel's.) Here is the first anticipation we have 
 of the revelations of the spectroscope, which shows 
 that many of the nebula consist of nothing but 
 glowing gas. He then refers to " a telescopic milky 
 way " in Orion, apparently connected with the great 
 nebula in the " sword." This is probably identical 
 with the vast nebula recently disclosed by photo- 
 graphy in that region. Herschel thought that the 
 four stars known as " the trapezium " (Herschel uses 
 this term), and others, are "intirely unconnected 
 with the nebulosity which involves them in appear- 
 ance ; " but it now appears much more probable that 
 the stars of the trapezium are really connected with 
 the nebulous matter surrounding them. 
 
 Herschel speaks of this nebulosity as " luminous 
 matter in a state of modification very different from 
 the construction of a sun or star." He had evidently 
 in his " mind's eye " the probable existence of gaseous 
 masses in space, but says " about things that appear 
 now we ought not to form opinions too hastily." 
 He then gives descriptions of a number of remarkable 
 nebulous stars observed by him. Among these may 
 
152 ASTRONOMICAL ESSAYS 
 
 be mentioned the following: "November 13, 1790. 
 A most singular phenomenon. A star of about the 
 8th magnitude, with a faint luminous atmosphere, of 
 a circular form, and about 3 minutes in diameter. The 
 star is perfectly in the centre, and the atmosphere is 
 so delicate, faint, and equal throughout, that there 
 can be no surmise of its consisting of stars, nor can 
 there be a doubt of the evident connection between 
 the atmosphere and the star. Another star, not 
 much less in brightness and in the same field with 
 the above, was perfectly free from any such appear- 
 ance," and he adds, " This last object is so decisive 
 in every particular, that we need not hesitate to 
 admit it as a pattern." This curious object lies 
 about 2 north of \j/ Tauri, and nearly in a line with 
 o and Persei (north of the Pleiades). Herschel 
 argues that if this nebulosity consisted of stars, the 
 central point must be of enormous size. On the 
 other hand, if the central star be of an ordinary 
 size, the stars composing the nebulosity must be 
 excessively small and compressed. He therefore con- 
 cludes that we " either have a central body which is 
 not a star, or have a star which is involved in a 
 shining fluid, of a nature totally unknown to us." 
 This happy idea has long since been fully confirmed 
 by the spectroscope. Nebulous stars are certainly 
 ordinary stars surrounded by glowing gaseous 
 envelopes, and probably in an early stage of their 
 life history. Herschel says, " But what a field of 
 novelty is here opened to our conceptions ! A shining 
 fluid of a brightness sufficient to reach from the re- 
 mote regions of a star of the 8th, 9th, 10th, llth, and 
 12th magnitude, and of an extent so considerable as 
 to take up 3, 4, 5, or 6 minutes in diameter. Can we 
 
SIR WILLIAM HERSCHEL'S THEORIES 153 
 
 compare it to the coruscations of the electrical fluid 
 in the aurora borealis ? Or to the more magnificent 
 cone of the zodiacal light as we see it in the spring 
 and autumn? The latter, notwithstanding I have 
 observed it to reach at least 90 from the sun, is yet 
 of so little extent and brightness as probably not to 
 be perceived even by the inhabitants of Saturn or 
 the Georgian planet, 1 and must be utterly invisible 
 at the remoteness of the nearest fixed star." Herschel 
 thought that this nebulosity might possibly exist 
 without any apparent connection with stars, and he 
 again refers to the nebulous region in Orion, which 
 he speaks of as " a luminous matter accounting much 
 better for it than clustering stars at a distance." 
 That this opinion was sound is shown by the fact 
 that the great nebula in Orion has resisted all the 
 efforts of the largest telescopes to resolve it into 
 stars, and the spectroscope shows that it is nothing 
 but glowing gas. With reference to the distance of 
 the nebulosity in Orion, Herschel thought it probable 
 that it lay between the distance of stars of the 7th 
 magnitude, and extends perhaps to those of the 9th, 
 10th, and llth magnitude. But even now, after 
 more than a hundred years' further observations, we 
 know little or nothing about the distance of gaseous 
 nebulae. Judging, however, from photographs of the 
 Milky Way, it seems probable that some of these 
 nebulosities are not farther from the earth than 
 some of the stars visible to the naked eye. 
 
 Herschel mentions a number of other nebulous 
 
 areas one preceding $ Cygni, covering about four 
 
 square degrees ; one near 125 Tauri ; another 
 
 preceding a Trianguli ; one preceding 45 Eridani ; 
 
 1 Now called Uranus. 
 
154 ASTRONOMICAL ESSAYS 
 
 and one, in parts pretty bright, following 57 
 Cygni. 
 
 Herschel thought that a consideration of these 
 nebulous stars and diffused nebulosities helps to 
 explain the real nature of "planetary" nebulae, 
 which, he suggests, consists of " a much condensed 
 luminous fluid." He considered the origin of this 
 luminous matter as doubtful, but says, " Let it 
 suffice that its existence is rendered evident by 
 means of nebulous stars." This interesting paper 
 shows clearly that Herschel's views of the nature 
 of irresolvable nebulae had completely changed in 
 the year 1791. 
 
 In a paper on " The Nature and Construction of 
 the Sun and Fixed Stars " in the Philosophical 
 Transactions for 1795, Herschel says, " That stars 
 are suns can hardly admit of a doubt. Their immense 
 distance would perfectly exclude them from our 
 view, if the light they send us was not of the solar 
 kind." The same opinion was expressed by Thomas 
 Wright, of Durham, in 1750, and it was evidently 
 known to Shakspere, who lived over 100 years before 
 Wright's time, for he makes Hamlet say in a letter 
 to Ophelia 
 
 " Doubt thou the stars are fire ; 
 Doubt that the sun doth move ; 
 Doubt truth to be a liar ; 
 But never doubt I love." 
 
 Herschel thought that the fluctuations of light in 
 the variable stars Algol, ft Lyras, 8 Cephei, ?? Antinoi 
 (>7 Aquilse), and o Ceti are due to rotation on their 
 axes ; but this view is not now held by astronomers, 
 the variations of light in the stars mentioned with 
 the exception of o Ceti being probably caused by 
 
SIR WILLIAM HERSCHEL'S THEORIES 155 
 
 the revolution of dark or bright bodies round them. 
 Herschel thought that all the stars had spots like 
 the sun, and this seems very probable. Some of the 
 red stars show a spectrum very similar to that of 
 a sun spot. Herschel' s opinion that the sun might 
 possibly be inhabited is very surprising. He says, 
 " We need not hesitate to admit that the sun is 
 richly stored with inhabitants." But such an hypo- 
 thesis would now be considered absurd. The sun is 
 more probably gaseous to its centre, and its internal 
 heat is probably greater than that of its surface. 
 Herschel thought it probable that many of the stars 
 form the centre of systems of planets and satellites, 
 like our solar system, but from this hypothesis he 
 excluded the compressed clusters of stars, which he 
 looked upon as rather " lucid, primary planets, con- 
 nected together in one great system of mutual 
 support." He thought that in such cases the " stars 
 are united in such close systems as not to leave 
 much room for the orbits of planets or comets ; " and 
 this seems a rational and very probable hypothesis. 
 
 In a paper on " The Method of observing the 
 Changes that happen to the Fixed Stars ; with some 
 Remarks on the Stability of the Light of our Sun. 
 To which is added a Catalogue of comparative 
 Brightness for ascertaining the Permanency of the 
 Lustre of Stars," Herschel gives observations of the 
 relative brightness of stars visible to the naked 
 eye. This catalogue was succeeded by others in 
 subsequent volumes of the Philosophical Transac- 
 tions, and these catalogues are useful for com- 
 parison with modern estimates and photometric 
 measures of star magnitudes. In the introduction 
 to the first of these catalogues, Herschel says, " The 
 
156 ASTRONOMICAL ESSAYS 
 
 hypothesis of an equality and an equal distribution 
 of stars, to which we have referred, is too far 
 from being strictly true to be laid down as an un- 
 erring guide in this research. The stars of the 
 first and second class, when scrupulously examined, 
 evidently prove that, if we would be accurate, we 
 must admit them, in some degree at least, to be 
 either of different sizes, or placed at different dis- 
 tances. Both varieties undoubtedly take place. This 
 consideration alone is fully sufficient to show that, 
 how much truth soever there may be in the hypo- 
 thesis of an equal distribution and equality of stars, 
 when considered in a general view, it can be of no 
 service in a case where great accuracy is required." 
 These views are now known to be undoubtedly 
 correct. The apparent brightness of the stars is 
 no criterion of their distance, and depends as much 
 on their absolute size and relative luminosity of 
 their surface as on their distance from the earth. 
 Herschel's remarks above quoted also show his 
 gradual change of views with reference to the 
 distribution of the stars in space. 
 
 In this paper he gives examples of Flams teed' s 
 estimates of star magnitudes, showing that some 
 stars which he marked as brighter than others are 
 in reality fainter, and conversely. These errors 
 were, he thought, due to the fact that Flamsteed 
 " did not compare the stars to each other, but 
 referred each of them to its own imaginary standard 
 of magnitude." This is evidently the correct ex- 
 planation of the various estimates we find in some 
 catalogues. Although estimates made in this way 
 have some value, considerable allowance must be 
 made for these discrepancies. Herschel says, "We 
 
SIR WILLIAM HERSCHEL'S THEORIES 157 
 
 can hardly allow less than half a magnitude in 
 the higher orders [that is in the brightest stars], 
 and a whole one in the inferior classes, for this 
 uncertainty." 
 
 Herschel's own method was to compare the stars 
 directly with others of a similar brightness in their 
 vicinity, and this is the method now adopted by 
 modern observers of variable stars. The rotation 
 CDE would denote that C was brighter than D 
 and D brighter than E. The relative brightness of 
 C may be found by BCD, and that of B by ABC. 
 We thus obtain a series ABCDE, etc., in which A 
 is the brightest star, B a little fainter, and so on. 
 This is now known as the method of " sequences." 
 
 Herschel points out that the Greek letters 
 given to the brighter stars by Bayer in 1603 do 
 not represent the relative brightness of the stars 
 in each constellation. Even a, /?, and y are not 
 always in the order of brightness. If Bayer had 
 affixed these letters correctly in order of relative 
 brightness, he would have done a really useful 
 work, and would have gained for himself an im- 
 mortality to which he is not now entitled. 
 
 The method of sequences mentioned above not 
 being considered by Herschel sufficiently delicate 
 to give the relative brilliancy of the stars with 
 sufficient accuracy, he adopted the following method. 
 If two stars were estimated to be equal, or nearly 
 so, he placed a point between them ; thus 
 
 30 , 24 Leonis 
 
 30 being placed first as being possibly very slightly 
 brighter than 24. When two stars are equal, but 
 one of them just perceptibly brighter than the 
 
158 ASTRONOMICAL ESSAYS 
 
 other, their relative brightness is expressed by a 
 comma, and the observation is written thus 
 
 41 , 94 Leoiiis 
 
 which means that 41 Leonis is just perceptibly 
 brighter than 94 Leonis. A greater difference in 
 brightness between two stars is shown by a short 
 line; thus 
 
 17-70 Leonis, or 68-17-70 Leonis 
 
 Professor Pritchard finds that the sign repre- 
 sented about 0*09 of a magnitude; , about 0*19 
 mag. ; and - about 0'40 mag. 
 
 A much greater difference is expressed by two 
 short lines ; thus 
 
 32 41 Leonis 
 
 A still larger difference in brightness is repre- 
 sented by three short lines ; thus 
 
 16 29 Bootis 
 
 But this difference must be considered too large 
 to be of any " use in estimations that are intended 
 for the purpose of detecting change." 
 
 With reference to the known variation in the 
 light of certain stars, Herschel says, "If it be 
 allowed to admit the similarity of stars with our 
 sun as a point established, how necessary will it 
 be to take notice of the fate of our neighbouring 
 suns, in order to guess at that of our own ! That 
 star, which among the multitude we have dignified 
 by the name sun, to-morrow may slowly begin to 
 undergo a gradual decay of brightness, like fi Leonis, 
 a Ceti, a Draconis, S Ursse Majoris, and many other 
 
SIR WILLIAM HERSCHEL'S THEORIES 159 
 
 diminishing stars that will be mentioned in my 
 catalogues. It may suddenly increase, like the 
 wonderful star in the back of Cassiopeia's chair, 
 and the no less remarkable one in the foot of Ser- 
 pentarius ; or gradually come on like (3 Geminorum, 
 ft Ceti, Sagittarii, and many other increasing 
 stars." Herschel suggests that the changes in the 
 earth's climate which are clearly indicated by the 
 geological records may possibly have been due to 
 changes in the sun. This seems highly probable. 
 The sun, like other stars, is undergoing a slow 
 processs of evolution, and far back in geological 
 times say ten millions of years ago the sun's 
 physical condition was almost certainly different 
 from its present state. A study of the Carboni- 
 ferous, or coal period, shows that the sun was 
 probably hotter or of larger volume then than it 
 is now ; and going still farther back, we should 
 reach a stage in which the earth's surface was so 
 hot that life would have been impossible on its 
 surface. 
 
 Herschel then gives the results of his comparison 
 of the relative brightness of the stars in a number of 
 constellations, to which is appended a series of notes 
 on stars possibly variable, and others. These observa- 
 tions were very carefully made, and are still valuable 
 for comparison with modern estimates and photo- 
 metric measures. Speaking generally, I find that 
 they agree well with modern observations. There 
 are, of course, some discrepancies, and these give 
 rise to a suspicion of variation in certain stars. A 
 second catalogue is given in the Philosophical Trans- 
 actions for 1796 (p. 452), a third in the volume for 
 1797 (p. 293), and a fourth in that for 1799 (p. 121). 
 
160 ASTRONOMICAL ESSAYS 
 
 In some introductory remarks to the second catalogue 
 he gives his observations of the variable star a 
 Herculis. He found a period of " somewhat more 
 than two months' duration ; " but modern observa- 
 tions do not quite confirm this result. The variation 
 seems to be irregular. He refers to the probable 
 rotation of stars on their axes as a possible cause of 
 light variation, large portions of the surface being 
 supposed to be covered with dark spots like the 
 well known sun-spots. But this hypothesis of rota- 
 tion is not now considered as probable. The varia- 
 tions of long period are more probably due to internal 
 changes in the body of the star. These changes may 
 possibly give rise to large sun-spots, but these spots 
 would probably be developed at a maximum, and not 
 a minimum, of light. Some of the red stars show a 
 spectrum very similar to that of a sun-spot. The 
 variation of short period has been shown by the 
 spectroscope to be due to the revolution of two 
 bodies round their centre of gravity, which either 
 produce eclipses as in the Algol variables or give 
 rise to periodical disturbances by tidal action. 
 
 In the preface to the third catalogue of " The 
 Comparative Brightness of the Stars," he gives an 
 account of a careful examination of Flamsteed's 
 catalogue and observations, made by his sister, 
 Miss Caroline Herschel, and finds the following 
 results. 
 
 1. There are 111 stars in Flamsteed's catalogue 
 (the British catalogue, at it is called) which were 
 never observed by Flarnsteed, and he says, " This 
 will explain why so many stars in the heavens seem 
 to have been lost." 
 
 2. There are 39 stars in Flamsteed's catalogue 
 
SIR WILLIAM HERSCHEL'S THEORIES 161 
 
 whose positions are incorrectly given. In some cases 
 the error amounts to several degrees. 
 
 3. There are 54 stars in Flarnsteed's Atlas Coelestis 
 which are erroneously placed ; some to the extent of 
 many degrees. 
 
 4. There are 42 stars which must be reduced to 
 21, owing to some of them having "two names in 
 different constellations." 
 
 5. There are 371 stars which, although observed 
 by Flamsteed and their positions recorded, have 
 been overlooked by Flamsteed in forming his 
 catalogue. 
 
 6. There are 35 more stars of which the positions 
 were doubtful, and have been omitted. 
 
 7. There are 86 stars with only the polar distance, 
 and 13 with only the right ascension recorded, and 
 these have been omitted. 
 
 8. Fifty more stars have been neglected, so that 
 " upon the whole between five and six hundred stars 
 observed by FLAMSTEED have been overlooked when 
 the British catalogue was formed." 
 
 " A Fourth Catalogue of the Comparative Bright- 
 ness of the Stars" appeared in the Philosophical 
 Transactions for 1779. Two other similar catalogues 
 were formed, but were not published by Herschel. 
 These, however, were found among his papers at 
 Collingwood in 1883, by Professor E. C. Pickering, of 
 Harvard Observatory (U.S.A.), who has discussed 
 and reduced all these catalogues in volumes xiv. 
 and xxiii. Part II. of the Harvard Annals. A com- 
 plete catalogue of all the stars observed by Herschel 
 is given in the latter volume. The comparison 
 between Herschel's estimates and the Harvard 
 photometric measures is in most cases satisfactory, 
 
 M 
 
162 ASTRONOMICAL ESSAYS 
 
 the average difference for all the stars being only 
 0*16 of a magnitude. Pickering says, " The error 
 of a single comparison but little exceeds a tenth of 
 a magnitude," and "the general accordance of the 
 results renders the deviation of individual stars im- 
 portant as indicating secular variations." These 
 results show the valuable results which may be 
 obtained by careful estimations made with the eye 
 without the assistance of any photometer. 
 
 In the Philosophical Transactions for 1800 there 
 is a paper by Herschel, " On the Power of penetrat- 
 ing into Space by Telescopes : with a Comparative 
 Determination of the Extent of that Power in Natural 
 Vision, and in Telescopes of Various Sizes and Con- 
 struction; illustrated by Select Observations." In 
 this interesting paper he discusses "the method of 
 vision at a distance." He shows that " light, flame, 
 and luminous gases are penetrable to the rays of 
 light." This he proved by an experiment, in which he 
 placed four candles exactly in a line behind a screen, 
 and opposite a narrow slit in the screen, f of an inch 
 long and | inch wide. Lighting first one candle, the 
 nearest to the screen, then the second, the third, and 
 the fourth, he found that all four candles gave con- 
 siderably more light than a single candle. From 
 this he concludes that the sun's disc cannot be 
 uniformly bright " on account of the unequal depth 
 of its luminous atmosphere in different places." This 
 is now known to be the case, the centre of the sun's 
 disc being considerably brighter than the portions 
 near the limb. 
 
 He speaks of " the copiousness of the emission of 
 light from every physical point of the luminous 
 surface " of a body emitting light. This corresponds 
 
SIR WILLIAM HERSCHEL'S THEORIES 163 
 
 with what I have elsewhere termed the luminosity of 
 the surface that is, the light emitted by a luminous 
 body per unit of area. Calling C " the mean copious- 
 ness of light," N the number of points or area of the 
 luminous surface, and L the total light emitted, Her- 
 schel says CN = L. This is obvious. But he adds, 
 " If, however, there should at any time be occasion 
 for distinction, the brightness arising from the great 
 value of C may be called the intrinsic brightness ; 
 and that arising from the great value of N the 
 aggregate brightness ; but the absolute brightness, 
 in all cases, will still be denned by CN." I lay 
 particular stress on this point, as some writers have 
 created a confusion between the total or " absolute 
 brightness " (Herschel's L) and the " intrinsic bright- 
 ness " (Herschel's C), or luminosity of surface, as I 
 have called it. 1 Herschel then proceeds to consider 
 the portion of the total light " which is used in vision 
 either by the eye or by the telescope," and this he 
 calls I. In this case "the equation of light in this 
 present sense" will be CN = I. And since the 
 " density of light " diminishes as the square of the 
 
 distance, we have its quantity for a distance D = =-^ 
 
 Speaking of the increased sensibility of the eye 
 by keeping it for some time in the dark, he says, " I 
 remember that, after a considerable sweep with 
 the 40-feet instrument, the appearance of Sirius 
 announced itself, at a great distance, like the dawn 
 of the morning, and came on by degrees increasing 
 in brightness, till the brilliant star at last entered the 
 
 1 One writer has accused me of inaccuracy in using the term 
 " intrinsic brightness," the very term used by Herschel himself to 
 express the same meaning. 
 
164 ASTRONOMICAL ESSAYS 
 
 field of view of the telescope, with all the splendour 
 of the rising sun, and forced me to take the eye 
 from that beautiful sight." 
 
 Herschel says, "It may be remembered that I 
 have distinguished brightness into three different 
 sorts. Two of these, which have been discriminated 
 by intrinsic and absolute brightness, are, in common 
 language, left without distinction." The brightness 
 referred to by mathematicians is the intrinsic bright- 
 ness, and " this is the only meaning it can bear in 
 the mathematician's theorem." With reference to 
 the sun as seen from Saturn, he says, " The sun on 
 Saturn appears to be a hundred times less than on 
 the earth ; and that consequently, though it may 
 there be intrinsically as bright, it must here be 
 absolutely an hundred times brighter." Herschel 
 also uses the term intensely illuminated for intrinsic 
 brightness. The same view, he says, applies to the 
 stars, and " their absolute brightness must vary in 
 the inverse ratio of the squares of their distances." 
 The visibility of the stars depends on the " penetra- 
 ting power " of telescopes. 
 
 With reference to the power of naked-eye vision, 
 he says that " the Georgian planet " (Uranus) is the 
 farthest object that has ever been seen by reflected 
 light. Assuming that stars of the second magnitude 
 (a Cygni, j3 Tauri) are at double the distance of those 
 of the first magnitude, if I be the brightness of a 
 first-magnitude star, %l will be the brightness of a 
 second-magnitude. He thought that the sun is 
 170,000 million times brighter than Sirius. But this 
 estimate is much too high. It would make the 
 sun's stellar magnitude about 29*6. Taking its 
 value at 26*5, which cannot be far from the truth, 
 
SIR WILLIAM HERSCHEL'S THEORIES 165 
 
 I find that the sun is about 9290 million times 
 brighter than Sirius, so that Herschel's estimate was 
 over eighteen times too large. A third-magnitude 
 star (" pole star, y Cygni, e Bootis ") he assumes to 
 be at three times the distance of a first-magnitude. 
 This would give a ratio of brightness between a 
 second and third magnitude star of 9 to 4, or 2J to 1, 
 instead of 4 to 1, the ratio between a first and 
 second magnitude. Between a sixth and seventh 
 magnitude star he finds a ratio of only a " little 
 more than 1| to 1." But in modern photometry the 
 ratio between all successive magnitudes is supposed 
 to be the same, and is now generally assumed to be 
 2'512. Herschel's estimates of relative distance were 
 mere assumptions, and we now know have no foun- 
 dation in fact. Sirius is at about double the distance 
 of a Centauri, although Sirius is a much brighter 
 star. 
 
 From the faintness of stars of the seventh mag- 
 nitude, Herschel concludes that " no star eight, nine, 
 or at most ten times the distance of Sirius," can 
 possibly be perceived by the naked eye. But this 
 would not now be admitted by astronomers. For if 
 Sirius were removed to ten times its present distance, 
 its light would be reduced 100 times, or five magni- 
 tudes, and as the photometric magnitude of Sirius 
 is 1*6, it would then be reduced to 5 1'6, or 3*4 
 magnitude. Taking three magnitudes below this 
 as the limit of naked-eye vision, it follows that 
 Sirius might be removed to nearly forty times its 
 present distance before it became invisible without a 
 telescope. Arcturus is probably fifteen times farther 
 from the earth than Sirius, and yet it is one of the 
 brightest stars in the heavens. 
 
166 ASTRONOMICAL ESSAYS 
 
 Herschel refers to the visibility of some star 
 clusters which are visible to the naked eye, although 
 their components are only visible in a good telescope. 
 Among these he mentions the double cluster in 
 Perseus, Messier 35 in Gemini, and Messier 13 be- 
 tween 77 and Herculis. He also refers to the great 
 nebula in Andromeda (Messier 31). 
 
 Proceeding from " the power of penetrating into 
 space by natural vision " to that by telescopes, he 
 says the natural proportion would be as A to a, A 
 being the aperture of the telescope and a that of the 
 pupil of the eye. But an allowance must be made 
 for the loss of light by reflection from mirrors and 
 the absorption of light in the lenses of refracting 
 telescopes. He made some experiments with plain 
 mirrors to test this point, and found that out of 
 100,000 incident rays that is, light rays falling on 
 the mirror 67,262 were reflected, and therefore, with 
 a double reflection, " only 45,242 would be returned." 
 With reference to absorption in the eye-glass of a 
 telescope, he found that out of 100,000 incident 
 rays, 94,825 were transmitted through a single lens, 
 and hence 89,918 through two lenses, and 85,265 
 through three lenses. Compounding this with the 
 result found for reflection, he found that for a 
 telescope of his construction (the "front view") 
 63,796 rays out of 100,000 were, with one reflection, 
 received by the eye, and with the Newtonian form 
 with a single-eye lens 42,901, and with a double eye- 
 glass, only 40,681 rays reached the eye. These 
 experiments were made, of course, with metallic 
 mirrors. With modern " silver on glass reflectors," 
 and improved eye-pieces, much better results would 
 probably be obtained. 
 
SIR WILLIAM HERSCHEL'S THEORIES 167 
 
 Herschel then proceeds to " find a proper expres- 
 sion for the power of penetrating into space, that we 
 may be enabled to compare its effects in different 
 telescopes with that of the natural eye." The 
 penetrating power, he says, must be as the square 
 roots of the lights received by the eye. For the 
 naked eye this is expressed by */^a*l. In the New- 
 tonian form of telescope there is some loss of light 
 in the second reflection from the small mirror. If b 
 be the diameter of the small mirror, we have for the 
 incident light A 2 6 2 , and correcting for the value 
 x found above, we have the general expression 
 
 for the same power in telescopes. For refracting 
 telescopes and in reflecting telescopes with only 
 one reflection (as in Herschel's " front view ") b = 0. 
 Then, putting the natural light, 1 = 1, we have the 
 general form 
 
 Va<A 2 - b*j 
 
 a 
 
 " for the penetrating power of all sorts of telescopes, 
 compared to that of the natural eye as a standard." 
 In his subsequent investigations, Herschel assumed 
 a, the aperture of the pupil, to be two-tenths of an 
 inch (that is, one-fifth of an inch), when the eye is 
 in darkness. He then discusses the powers of his 
 own instruments. He tried a 12-inch~r effecting tele- 
 scope of the Newtonian form on a distant church 
 steeple, and found he could read the clock on the 
 steeple, although the steeple itself was invisible to 
 the naked eye in the dusk of the evening. He shows 
 that this is a good example of increase of absolute 
 
168 ASTRONOMICAL ESSAYS 
 
 brightness, the intrinsic brightness of the clock face 
 being actually reduced in the ratio of 7 to 3. 
 
 Herschel used some very high powers for the 
 observation of double stars. He states that these 
 powers ranged from 460 to 6652. l 
 
 He gives some observations of nebulae showing 
 the space penetrating powers of his telescopes. 
 With a 10-feet reflector (that is, of 10 feet focal 
 length), and a space penetrating power of 28'67, he 
 found the cluster Messier 5 (near 5 Serpentis) 
 beautifully resolved into stars. A 7-feet telescope, 
 with a space penetrating power of about 20, failed 
 to resolve it. 2 Other telescopes and clusters gave 
 similar results. With the 40-feet telescope used as 
 a "front view," he saw the 4th satellite of Saturn 
 [Dione] and the ring " without an eye-glass." With 
 this telescope he discovered "the 6th satellite of 
 Saturn " [Enceladus, now called the 2nd] on August 
 28, 1789, and the " 7th satellite " [Mimas, now known 
 as the 1st] on September 11 of the same year. The 
 20-feet reflector showed both these satellites after 
 their discovery, but the 7-feet and 10-feet reflectors 
 failed to show them. 
 
 The 40-feet telescope had a space penetrating 
 power of 191'69. To obtain a space penetrating 
 power of 500, Herschel computed, would require a 
 telescope of 10 feet 5'2 inches in diameter for a re- 
 flector on his construction. But he points out that 
 the light of the heavens on a clear night would set 
 
 Phil. Trans., 1800, p. 70, footnote. 
 
 2 With the 40-feet telescope, giving a space penetrating power of 
 191-69, he counted 200 stars in this cluster, " but the middle is so 
 compressed that it is impossible to distinguish the stars." A photo- 
 graph by Dr. Roberts confirms Herschel's result. 
 
SIR WILLIAM HERSCHEL'S THEORIES 169 
 
 a limit to the faintness of the smallest stars visible. 
 For, he says, the sky light " must in the end be so 
 increased by enlarging the penetrating power, as to 
 become a balance to the light of all objects that are 
 so remote as not to exceed in brightness the general 
 light of the heavens." This is an interesting and 
 important remark of Herschel's. Dr. Roberts found 
 that stars of the 18th magnitude are probably the 
 faintest which could be photographed, for the reason 
 assigned by Herschel. 
 
 Combining the above results for the space pene- 
 trating power of his smaller telescope with the 
 length of the "sounding line" deduced from the 
 " star gages," Herschel concluded that this telescope 
 would show stars 571 times as far from the earth 
 as Sirius, " and only those 653, 734, and 816 times the 
 same distance would have been beyond its reach." 
 Let us see how these distances compare with the 
 results of modern observations and telescopes. The 
 40-inch telescope of the Yerkes Observatory shows 
 stars to about the 17th magnitude of the modern 
 photometric scale. Now, as the magnitude of Sirius 
 is -1-58, it is 18-58 magnitudes, or about 27,000,000 
 times brighter than a star of the 17th magnitude. 
 Hence it follows that if Sirius were removed to 5200 
 times its present distance (V 27,000,000), it would still 
 be visible as a faint star in the great Yerkes telescope. 
 Herschel says that, taking the space penetrating 
 power of his 40-feet telescope as 192, and a 7th 
 magnitude star as the limit of unaided vision, " this 
 telescope would show stars of the one thousand 
 three hundred and forty second magnitude." But 
 there is some mistake here ; for no telescope that 
 could possibly be constructed would show stars of 
 
170 ASTRONOMICAL ESSAYS 
 
 even the 100th magnitude (if any such exist). Pro- 
 bably Herschel intended to say that his 40-feet 
 telescope would show stars 1342 times the distance 
 of Sirius. But according to modern estimates, it 
 Avould probably have shown stars much farther off 
 than this, as the above results for the Yerkes tele- 
 scope will show. Herschel shows that a cluster of 
 50,000 stars l would be visible in his large telescopes 
 if its distance were llf millions of millions of millions 
 of miles." 2 But this result seems very doubtful, as 
 it would imply a journey for light of two millions of 
 years. 
 
 Herschel computes how long it would take to 
 " gage " the whole heavens with the 40-feet telescope 
 and power of 1000, allowing that a year will yield 
 100 hours suitable for the purpose, when the sky is 
 very clear, the moon absent, no twilight, no haze, 
 no violent wind, and no sudden change of tempera- 
 ture, and he finds that the heavens might be 
 "swept" with his 20-feet reflector in about 14f 
 years ; but with the higher power used on the 40- 
 feet telescope it would take no less than 498 years, 
 and a further 213 years for the portion of the 
 southern hemisphere invisible in these latitudes. 
 But the application of photography to the heavens 
 has overcome this difficulty, and the work can now 
 be done much more accurately and quickly. The 
 photographic chart of the heavens commenced some 
 years ago is now approaching completion. 
 
 In the year 1802, Herschel published in the Philo- 
 sophical Transactions for that year a " Catalogue of 
 
 1 First stated as 5000, but afterwards corrected by Herschel to 
 50,000 (Phil. Trans., 1802, p. 498, footnote). 
 
 2 Herschel's number is equivalent to 11^ trillions of miles. 
 
SIR WILLIAM HERSCHEL'S THEORIES 171 
 
 500 New Nebulae [in addition to others previously 
 published], Nebulous Stars, Planetary Nebulas, and 
 Clusters of Stars." In the introduction to this 
 catalogue he makes some remarks on " the con- 
 struction of the heavens." He says that the sun and 
 solar system " can only rank as a single individual 
 belonging to the species we are going to consider." 
 Among what he calls " insulated stars," that is, 
 "stars at immense distances from each other," he 
 includes the Sun, Arcturus, Capella, Lyra [Vega], 
 Sirius, Canobus, Markab [a Pegasi], Bellatrix, Menkar 
 [a Ceti], Shedir, Algorab [a Corvi], Propus, 1 etc. 
 
 Taking the diameter of the earth's orbit round 
 the sun as probably subtending not more than an 
 angle of one second, as seen from Sirius, 2 he finds 
 that, supposing the masses equal, the two bodies 
 would not fall together in less than 33 [millions of 
 years. He thinks that such stars may be considered 
 as "insulated," that is, not immediately connected 
 with any neighbouring stars. He also thought that 
 the opposite attractions of the surrounding Milky 
 Way would tend to keep these insulated stars almost 
 at rest. And here he makes an interesting remark 
 011 the Milky Way, which clearly shows his change 
 of views on the construction of the Galaxy. He says, 
 " For, though our sun, and all the stars we see, may 
 truly be said to be in the plane of the Milky Way, 
 yet I am now convinced by a long inspection and 
 continued examination of it, that the Milky Way 
 itself consists of stars very differently scattered from 
 
 1 Probably a misprint for Procyon. 
 
 2 In other words, that the parallax of Sirius is less than half a 
 second of arc. This we now know to be correct, the best measures 
 of its parallax being 0-37 second. 
 
172 ASTRONOMICAL ESSAYS 
 
 those which are immediately about us. But of this 
 more will be said on another occasion." Here he 
 practically abandons the " disc theory." 
 
 He thought " that probably we can only look for 
 solar systems among insulated stars," other sidereal 
 constructions being perhaps differently constituted. 
 The satellites of Sirius and Procyon were of course 
 unknown to Herschel ; but we can hardly call these 
 solar systems. Planets they may possibly have, but 
 the visible attendants are undoubtedly faint suns, 
 and these bright stars are really binary systems, and 
 not " insulated stars." 
 
 Herschel then considers the binary, or revolving 
 double stars, and says, " there is an essential differ- 
 ence between the construction of solar and sidereal 
 systems." He shows that " insulated stars," like 
 Arcturus and Vega, could never appear double to 
 us, for in order that they should seem close enough 
 to rank as a double star, they should be removed to 
 a distance of 41,253 times the distance of Sirius, and 
 that at this great distance even the 40-feet telescope 
 would fail to show them. This is evidently correct, 
 for the distance given is about eight times the 
 distance at which Sirius would be reduced to a star 
 of the 17th magnitude. He considers the case of 
 the double star Aquarii which has components 
 of nearly equal brightness, and shows that the odds 
 are over 75| millions to one against the hypothesis 
 that Aquarii is merely an optical double star. 
 Hence he concludes that the components of close 
 double stars are really close together, and that 
 "their existence must be owing to the influence of 
 some general law of nature." This, he says, is con- 
 firmed by his own observations, which show that 
 
SIR WILLIAM HERSCHEL'S THEORIES 178 
 
 " many of them have actually changed their situation 
 with regard to each other, in a progressive course, 
 denoting a periodical revolution round each other ; 
 and that the motion of some of them is direct, while 
 that of others is retrograde" 1 He then considers 
 treble, quadruple, and multiple stars, and shows that 
 a number of bodies may revolve round an " empty 
 centre " by the laws of gravitation, " and remain 
 permanently connected without a central body." 
 He considers various cases of three and four bodies 
 of equal mass revolving round a common centre in 
 equal times. But we do not find such simple cases 
 in nature. 
 
 With reference to the Milky Way, he says, " On 
 a very slight examination it will appear that this 
 immense starry aggregation is by no means uniform. 
 The stars of which it is composed are very unequally 
 scattered, and show evident marks of clustering 
 together into many separate allotments." 2 Here 
 we have further evidence of Herschel's change of 
 views. 
 
 He thought that " the construction of groups of 
 stars is perhaps, of all objects in the heavens, the 
 most difficult to explain." In the globular clusters 
 he speaks of " a centre of attraction," round which the 
 components revolve. This was also the opinion of 
 his famous son, Sir John Herschel. With reference 
 to the nebulae, he thought that clusters at a great 
 distance might present the appearance of nebulas, 
 but with instruments of high space penetrating 
 power the latter " are the objects which may be 
 perceived at the greatest distance." He considers 
 
 1 The italics are Herschel's. 
 
 2 Phil. Trans., 1802, p. 495. 
 
174 ASTRONOMICAL ESSAYS 
 
 that milky nebulosity may be either due to " widely 
 extended regions of closely connected stars," or else 
 real nebulosity at " possibly no very great distance 
 from us." He thought that he had observed some 
 changes in the great nebula in Orion, but modern 
 observations do not tend to confirm this idea. 
 Changes are doubtless in progress, but they probably 
 take place very slowly. 
 
 With reference to " nebulous stars," he seems to 
 think that the surrounding luminous haze is due to 
 a "self-luminous milky nebulosity," although the 
 central point of light is really a star. We now 
 know that this is probably the correct conclusion. 
 " Planetary nebulae," he thought, " allied to nebulous 
 stars," and the spectroscope has fully confirmed this 
 hypothesis. He noticed that some of the planetary 
 nebulae showed a bright central point, and these he 
 considered to be "an intermediate step between 
 planetary nebulae and nebulous stars." In this idea 
 he was probably correct, the nebulous stars possibly 
 indicating a more advanced stage in stellar evolution. 
 
 In the Philosophical Transactions for 1803 (p. 339) 
 there is a paper by Herschel entitled, " Account of 
 the Changes that have happened during the last 
 Twenty-five Years in the Relative Situation of 
 Double Stars ; with an Investigation of the Cause 
 to which they are owing." In this interesting paper 
 we have the first recorded observations of motion 
 in binary star systems. The probable existence of 
 revolving double stars was previously predicted by 
 the Rev. John Michell, but he made no observations 
 in support of his theory, and to Herschel is due the 
 proof by actual measurements. The first star con- 
 sidered by Herschel is a Geminorum or Castor, the 
 
SIR WILLIAM HERSCHEL'S THEORIES 175 
 
 northern of the two bright stars in the heads of 
 the Twins. He estimated the distance between the 
 components in the year 1778 to be about two 
 diameters of the larger star, and 23J years after- 
 wards (in 1802) he found the distance about the 
 same that is, about five seconds of arc. The dis- 
 tance had therefore remained nearly constant. But 
 not so the angle of position. This he found in 1779 
 to be 32 47' north preceding, measuring from the 
 north point of the field of view. But in the year 
 1802 he found this angle to be only 10 53', so that 
 in a period of about 23 years the angle of position 
 had changed about 21 54', indicating an orbital 
 revolution of one component round the other, or 
 rather both round their common centre of gravity. 
 This he shows must be the case, and that any other 
 hypothesis, such as the proper motions of the stars, 
 or the sun's motion in space, fails to explain the 
 observed motion with any degree of probability. 
 The famous Bradley had previously observed the 
 position of the components of Castor about the year 
 1759, and found that the line joining them was 
 " parallel to the line joining Castor and Pollux in 
 the heavens, seen by the naked eye." This observa- 
 tion Herschel found represented a position angle of 
 56 32'. This would indicate a total change of 45 39' 
 in a period of about 43 J years. From this motion 
 Herschel computes that the period of revolution of 
 one component round the other would be about 342 
 years. This result agrees closely with the most 
 recent orbit computed by Dr. Doberck, who finds a 
 period of 346*82 years. The total change of angle 
 now amounts to over 100 since Bradley 's time. 
 
 Herschel then considers the motion of the double 
 
176 ASTRONOMICAL ESSAYS 
 
 star y Leonis. For this pair he found a motion of 
 13 58' in 21 years, with a small increase in the dis- 
 tance. From the observed measures he concluded 
 that the period of revolution was about 1200 years. 
 Three orbits have been computed for this star one 
 by Hind, and two by Doberck ; but Burnham has 
 shown that all the measures may be fairly well 
 represented by rectilinear motion, and hence that 
 the binary character of the pair is doubtful. 
 
 Another star mentioned by Herschel is the beau- 
 tiful double star e Bootis. Here he found an angular 
 motion of 12 33' in about 22^ years, with a slight 
 increase in the distance, and he concludes that the 
 period of revolution would be about 1681 years. 
 But modern measures do not quite confirm this 
 result, the motion, if any, being very slow. 
 
 With reference to Herculis, now a well-known 
 and interesting binary, Herschel says that his 
 observations " furnish us with a phenomenon which 
 is new in astronomy ; it is the occultation of one 
 star by another." In 1802 he found it apparently 
 single, with a high power, and concluded that one 
 star was eclipsing the other. But recent investiga- 
 tions of the orbit of this star, which has a period of 
 about 35 years, show that no real occultation ever 
 takes place, the minimum distance between the 
 components being, according to Dr. See, about 0'45 
 second. 
 
 For 8 Serpentis, Herschel found an angular change 
 of 18 39' in about 19 years, and estimates the period 
 of revolution at about 375 years. But measures in 
 recent years show that the motion is now very slow, 
 and its binary character seems to be doubtful. 
 
 For the famous binary star y Virginis, Herschel 
 
SIR WILLIAM HERSCHEL'S THEORIES 177 
 
 found an angular change of 10 24' in about 21J 
 years, with little or no change in the distance. Ail 
 observation by Mayer in 1756 gives a position angle 
 of 54 21' 37", showing a total change of 24 2' in 
 about 47 years. From these observations Herschel 
 estimated the period of revolution at about 708 
 years ; but the best modern orbit gives a period of 
 194 years (See). 
 
 In a second paper on the subject of binary stars 
 in the Philosophical Transactions for 1804, Herschel 
 considers a number of other double stars in which 
 he thought he had detected angular motion. Some 
 of these have proved to be binary, but in others the 
 motion has not been confirmed. 
 
 In the volume for 1805 (p. 233) Herschel describes 
 further investigations made with a view to deter- 
 mine the direction and velocity of the sun's motion 
 in space. He points out that if a solar motion exists, 
 all the apparent parallactic motions will be in a 
 direction opposite to that of the sun's motion, but 
 the real motions of the stars themselves will take 
 place " indiscriminately " in all directions. He then 
 considers the motions of some of the brighter stars 
 as probably the nearest to the earth. He finds 
 that when the lines representing the proper motions 
 of these stars are produced backwards, they meet in 
 various points in Hercules, and near " the head of 
 the Dragon" (Draco). Taking stars of the second 
 magnitude, and combining these with the first, he 
 finds a very similar result. He thought that the 
 changes in the position of the components of some 
 double stars was probably due to the sun's motion 
 in space. 
 
 In a third paper on the same subject in the 
 
 N 
 
178 ASTRONOMICAL ESSAYS 
 
 Philosophical Transactions for 1806 (p. 205), Herschel 
 continues his examination of the subject, and assumes 
 that, roughly, the distances of the stars are indicated 
 by their brightness, the brightest being the nearest. 
 He gives the relative brightness of the brightest stars 
 thus (in his notation described above) 
 
 Sirius Arcturus Capella , Lyra Alde- 
 
 baran . Procyon. 
 
 Here he estimates Aldebaran as equal to, or even 
 slightly brighter than, Procyon, but modern photo- 
 metric measures make Procyon the brighter by about 
 half a magnitude. He gives the following "Pro- 
 portional Distances " : 
 
 Sirius . . I'OO Lyra (Vega) . T30 
 
 Arcturus . 1'20 Aldebaran . 1*40 
 
 Capella . T25 Procyon . . 1'40 
 
 But modern measures of parallax give the actual 
 distances of these stars in the following proportion :- 
 
 Sirius . . I'OO Vega . . . 4'51 
 
 Arcturus . 15'41 Aldebaran . 3*46 
 
 Capella . 4'56 Procyon . . T14 
 
 This shows how unsafe it is to estimate distances 
 of stars by their apparent relative brightness. 
 
 Herschel shows that the proper motions of the 
 stars cannot be accounted for by orbital motion 
 round each other. He then discusses the hypothesis 
 of a central body of great size, which he thinks 
 might possibly exist, but must be considered as 
 "intirely hypothetical." A very massive body at 
 a centre of force might, however, be replaced by a 
 group of stars, whose combined attractions might 
 
SIR WILLIAM HERSCHEL'S THEORIES 179 
 
 produce the same effect, and he refers to a cluster 
 discovered by Halley, which seems to be the great 
 globular cluster in Hercules (Messier 13). He does 
 not, however, limit this hypothesis to one cluster, 
 but thought that the combined attractions of a 
 number of clusters might have the observed result. 
 A further source of attraction might, he suggested, 
 be found in the clustering regions of the Milky Way. 
 He did not arrive at any very definite conclusion as 
 to the position of the supposed centre of attraction, 
 but seemed convinced that the proper motions of 
 the stars and the sun's motion in space must be due 
 to some form of gravitation. 
 
 In a paper in the Philosophical Transactions for 
 1811 (p. 269) Herscfrel returns to the subject of the 
 construction of the heavens. He says, " A knowledge 
 of the construction of the heavens has always been 
 the ultimate object of my observations," and he pro- 
 poses to arrange the objects he observed " in a certain 
 successive regular order." He uses the following 
 memorable words, which show his change of views 
 since the publication of his earlier papers on the 
 subject : " If it should be remarked that in this new 
 arrangement I am not entirely consistent with what 
 I have already in former papers said on the nature 
 of some objects that have come under my observa- 
 tion, I must freely confess that by continuing my 
 sweeps of the heavens, my opinion of the arrange- 
 ment of the stars and their magnitude, and of some 
 other particulars, has undergone a gradual change ; 
 and indeed when the novelty of the subject is con- 
 sidered, we cannot be surprised that many things 
 formerly taken for granted should on examination 
 prove to be different from what they were generally, 
 
180 ASTRONOMICAL ESSAYS 
 
 but incautiously, supposed to be. For instance, an 
 equal scattering of the stars may be admitted in 
 certain calculations, but when we examine the Milky 
 Way, or the closely compressed clusters of stars, of 
 which my catalogues have recorded so many instances, 
 this supposed equality of scattering must be given 
 up. We may also have surmised nebulae to be no 
 other than clusters of stars disguised by their great 
 distance, but a larger experience and better acquaint- 
 ance with the nature of nebulae will not allow a 
 general admission of such a principle, although un- 
 doubtedly a cluster of stars may assume a nebulous 
 appearance when it is too remote for us to discern 
 the stars of which it is composed." 
 
 He then proceeds to divide the celestial objects 
 he observed into " classes," as follows : 
 
 1. " Extensive diffused nebulosity." This can 
 only be seen with telescopes of great light gather- 
 ing power. Modern photographs show this diffused 
 nebulosity in many parts of the Milky Way and 
 elsewhere. Herschel gives a list of 52 places where 
 he observed such faint nebulosity. Photographs 
 taken by the late Dr. Roberts of Herschel' s nebulous 
 regions failed to reveal this nebulosity, except in 
 four cases ; but photographs by other astronomers 
 have shown nebulosity in several of the places in- 
 dicated by Herschel. Herschel was such an excellent 
 and cautious observer, it is difficult to imagine that 
 he could have been deceived in this matter. His 52 
 nebulous regions covered an area of nearly 152 square 
 degrees. He says, "By nebulous matter I mean to de- 
 note that substance, or rather those substances which 
 give out light, whatsoever may be their nature, or of 
 whatever different powers they may be possessed." 
 
SIR WILLIAM HERSCHEL'S THEORIES 181 
 
 2. "Nebulosities joined to nebulae." He found 
 that the diffused nebulosity just mentioned is some- 
 times connected with "real nebulae." Among ex- 
 amples of this class he mentions the great nebula in 
 Orion, and he says " we can hardly have a doubt of 
 its being the nearest of all the nebulae in the heavens." 
 But this now seems doubtful. The stars in its vicinity, 
 and which are probably connected with it, show no 
 signs of any measurable parallax. He says that this 
 nebula contains very bright and also very faint 
 nebulous matter, and argues that the fainter portions 
 cannot be " exceedingly farther from us " than the 
 brighter parts. 
 
 3. " Detached nebulosities." These are small 
 detached portions of nebulous light visible in some 
 parts of the sky. 
 
 4. "Milky nebulae." This term he applies to 
 small detached nebulosities which have a "milky 
 light." 
 
 5. " Milky nebulae with condensations." These 
 objects have a slightly brighter centre, and Herschel 
 thought this might be due either to condensation or 
 to increased depth of the nebulous matter in the line 
 of sight. 
 
 6. " Nebulae which are brighter in more than one 
 place." There are nebulae which have more than one 
 nucleus or condensation of light. Herschel thought 
 that these objects tend to show that the nuclei are 
 due to condensation, and not to increased thickness 
 of nebulous matter. For the latter hypothesis would 
 necessitate the assumption of " very slender and deep 
 projections, all situated exactly in the line of sight," 
 and such an arrangement would, of course, be highly 
 improbable. Assuming that the nuclei are due to 
 
182 ASTRONOMICAL ESSAYS 
 
 condensation of nebulous matter in the brighter 
 portions of these nebulae, he shows that they are 
 most probably due to " the universal gravitation of 
 matter," and this view is clearly the correct one. 
 
 7. " Double nebulae with joined nebulosity." These 
 are small nebulae, each with a nucleus, and connected 
 by a nebulous band. Herschel thought that they 
 were on the verge of splitting into two, and that 
 some had actually separated. Of the objects observed 
 by him some were less than two minutes of arc from 
 each other. The majority, however, were further 
 apart up to 10 minutes. Most of these differ but 
 little in brightness, showing that probably they are 
 at about the same distance from the earth. 
 
 8. " Treble, quadruple, and sextuple nebulae." In 
 addition to the double nebulae mentioned above, 
 Herschel observed twenty treble, five quadruple, and 
 one sextuple nebulae. Among these he mentions a 
 quadruple nebula, in which four nebulae lie within 
 three minutes of arc. The nebulae in the sextuple 
 one " are all very faint and very small." He thought 
 that these compound nebulae probably owe their 
 origin to " the breaking up of some former extensive 
 nebulosities of the same nature." He notes that 
 there are regions where the nebulae of his catalogues 
 "are uncommonly crowded." One of these regions 
 begins " over the tail of Hydra and proceeding to the 
 southern wing, the body, and the northern wing of 
 Virgo. Then to Coma Berenices, Canes Venatici, 
 and the preceding arm of Bootes. A different branch 
 goes from Coma Berenices to the hind leg of Ursa 
 Major. Another branch passes from "the wing of 
 Virgo to the tail and body of Leo." The existence 
 of this nebulous region has been fully confirmed 
 
SIR WILLIAM HERSCHEL'S THEORIES 183 
 
 by modern observations. An " absence of nebulae," 
 Herschel says, is remarkable in a region extending 
 from the head of Capricornus, through Antinous, to 
 the tail of Aquila, and through the body of Hercules 
 to the head of Draco. There is also a barren region 
 in Auriga, Lynx, and Camelopardalus. 
 
 9. " Very narrow long nebulas." These, Herschel 
 thought, were nebulae of small thickness seen edge- 
 ways. Modern observations suggest that most of 
 these elongated objects are spiral nebulae with their 
 edges turned towards the earth. 
 
 10. " Extended nebulae." These are similar to the 
 last, but of greater apparent width. Most of them 
 probably represent spiral nebulae seen at various high 
 angles of inclination. But Herschel was not aware 
 of the existence of spiral nebulae. They were dis- 
 covered by Lord Rosse with his great 6-f eet reflector, 
 and photographs have fully confirmed their exist- 
 ence. 
 
 11. " Nebulae of an irregular figure." This is a 
 term applied by Herschel to small nebulae with no 
 well-marked boundaries. The term might also be 
 applied to the great nebula in Orion and others of 
 the same character. 
 
 12. " Nebulae of an irregular round figure." These 
 he considered as probably spherical in form, and not 
 cylindrical or conical. As in the latter case the axis 
 of the cylinder or cone must point exactly towards 
 the earth, the probability is, of course, in favour of 
 the globular form. 
 
 13. " Round nebulae." These are of a more definite 
 circular form, and Herschel considered them globular, 
 and says, " we may now more confidently assign the 
 attraction of gravitation as the principle which has 
 
184 ASTRONOMICAL ESSAYS 
 
 drawn the nebulous matter towards a center, and 
 collected it into a spherical compass." 
 
 14. " Nebulae that are remarkable for some particu- 
 larity in figure or brightness." Among these he men- 
 tions " a considerably bright nebula about 15 minutes 
 long and 3 minutes broad ; its length is divided in the 
 middle by a black division at least three or four 
 minutes long," and he suggests that it is " a ring in 
 a very oblique position with respect to the line of 
 sight." Here, again, we have probably a spiral 
 nebula with its plane at a high angle to the back- 
 ground of the sky. 
 
 15. " Nebulae that are gradually a little brighter 
 in the middle." This increase of brightness is " always 
 very gradual from the outside towards the middle of 
 the nebulas." This he thought probably due either 
 " to the small quantity of the preponderating central 
 attractive power, or even to the shortness of its 
 time of acting ; for in this case " millions of years 
 perhaps are but moments." 
 
 16. " Nebulas which are gradually brighter in the 
 middle." This class includes those nebulae in which 
 the increase of light in the centre is decidedly greater 
 than in the preceding class. Herschel thought that 
 the gravitating action was here " in a more advanced 
 state," or, in modern language, that these objects are 
 in a more advanced stage in the evolution of stars 
 from nebulas. 
 
 17. " Nebulas that are gradually made brighter in 
 the middle." These seem to show a further step in 
 the condensation process that is, a more advanced 
 stage of evolution. 
 
 18. " Nebulas that have a cometic appearance." 
 In this class Herschel included nebulas with a strong 
 
SIR WILLIAM HERSCHEL'S THEORIES 185 
 
 condensation in the centre, thus resembling a tele- 
 scopic comet, and he suggests that small comets 
 " may be composed of nebulous matter, or may, in 
 fact, be such very highly condensed nebulae." But 
 even the smallest of these nebulae must be vastly 
 greater in size than the largest comet ever observed. 
 
 19. " Nebulae that are suddenly much brighter in 
 the middle." In this class the nucleus is more sharply 
 marked from the surrounding nebulosity than in the 
 preceding class. In fact, they are more like " nebulous 
 stars," except that the nucleus is a nebula, not a 
 star. Herschel thought that this nucleus was an 
 indication of approaching consolidation. 
 
 20. " Round nebulas increasing gradually in bright- 
 ness up to a nucleus in the middle." Here we have 
 clear evidence of " the existence of a central attrac- 
 tion." They seem to closely resemble what Herschel 
 called " cometic nebula." 
 
 Of "nebulae with a nucleus" Herschel mentions 
 Messier 63. A photograph by Dr. Roberts in 1896 
 shows this to be a spiral nebula " with a bright 
 stellar nucleus in the centre of dense nebulosity." 
 Huggins finds a continuous spectrum, indicating, as 
 Herschel supposed, an advanced stage of condensation. 
 
 Among "extended nebulae that show the pro- 
 gress of condensation " Herschel mentions Messier 65, 
 which he describes as "a very brilliant nebula ex- 
 tended in the meridian, about 12 minutes long. It 
 has a bright nucleus, the light of which suddenly 
 diminishes on its border, and two opposite very 
 faint branches." A photograph by Dr. Roberts shows 
 that this is also a spiral nebula. 
 
 Herschel observed some small nebulae of "an 
 almost uniform light." These seem to differ but 
 
186 ASTRONOMICAL ESSAYS 
 
 little from the "planetary nebulae." Some of these 
 objects, he thought, were approaching "a period of 
 final condensation." This, he considered, was shown 
 by the fact that they seem to have " a superficial 
 lustre such as opaque bodies exhibit, and which could 
 not happen if the nebulous matter had no other 
 quality than that of shining, or had so little solidity 
 as to be perfectly transparent." 
 
 With reference to "planetary nebulae," he con- 
 sidered that these objects are considerably compressed 
 from their original condition. Their usually small 
 apparent diameter of 10 seconds to 60 seconds suggests 
 that they have condensed considerably, and that 
 a still further condensation would terminate in the 
 production of a star. He shows that the density of 
 nebulous matter must be very small, and that " a 
 cubical space, the side of which at the distance of a 
 star of the 8th magnitude is seen under an angle of 
 10 minutes, exceeds the bulk of the sun over two trillion 
 times." But as the distance he assumed for an 8th 
 magnitude star is much less than the distance now 
 supposed, his figures enormous as they are should 
 be largely increased. Herschel thought that these 
 planetary nebulae probably rotated on an axis. This, 
 he says, is indicated by their form, seven out of ten, 
 he observed, being "not perfectly round, but very 
 little elliptical." Other nebulae also show a tendency 
 to a similar form. 
 
 He then discusses the probable distance of the 
 great nebula in Orion. Supposing it to be at the 
 same distance as small stars near it, he comes to 
 the conclusion that the distance of the faintest parts 
 of this vast nebula " cannot well exceed the region of 
 stars of the 7th or 8th magnitude, but may be much 
 
SIR WILLIAM HERSCHEL'S THEORIES 187 
 
 nearer ; perhaps it may not amount to the distance 
 of stars of the 3rd or 2nd order." But even now 
 the distance of this wonderful nebula is quite un- 
 certain. Herschel thought he found changes in the 
 nebulosity in the course of 37 years' observation. 
 But such changes have not since been confirmed 
 with any certainty. Probably changes are in pro- 
 gress, but these may take place very slowly. Even 
 a hundred years would hardly count in the life of 
 a nebula. 
 
 He gives a" number of examples of what he 
 terms "stellar nebulae." These are usually very 
 small, and might be easily mistaken for stars with 
 telescopes of moderate power. He thought that 
 these objects might possibly be planetary nebulae 
 " in a higher state of condensation." In some doubt- 
 ful objects about 34 in number he could not 
 satisfy himself whether the object was really a star 
 or a small nebulae. Finally, he concluded that he 
 had found in the heavens examples of Jp stages of 
 evolution, from the purely nebulous one uown to the 
 strictly stellar type. 
 
 In the Philosophical Transactions for 1814 Her- 
 schel again returns to the same subject. But in this 
 paper he considers what he calls "the sidereal 
 part of the heavens," and the apparent connection 
 between stars and star clusters and nebulous matter. 
 He divides these objects into classes as before. 
 
 1. " Stars in remarkable situations with regard 
 to nebulae." These are stars connected, apparently 
 at least, with faint nebulosity. He suggests that 
 some nebulae " may have considerable proper motions 
 by which they are carried towards neighbouring 
 stars." But it now seems more probable that the 
 
188 ASTRONOMICAL ESSAYS 
 
 proper motion, if any, would be in the stars, not the 
 nebulae. 
 
 2. " Stars with nebulosity between them." These 
 are stars (usually two) apparently connected by 
 faint nebulosity. That this should happen by mere 
 chance is, he argues, quite incredible. 
 
 3. " Stars with nebulosity of various shapes 
 attached to them." In these objects the nebulosity 
 is only on one side, apparently attached to the star, 
 and making it look like a small comet. Here, again, a 
 real connection between the stars and the nebulosity 
 seems to be certain. 
 
 4. "Stars with nebulous branches." These are 
 somewhat similar to those in class 1, above. 
 
 5. " Nebulous stars." These have been already 
 described and discussed. 
 
 6. " Stars connected with extensive windings of 
 nebulosity." These are stars apparently connected 
 with irregular shaped nebulosity. With reference to 
 these objects, Herschel makes the following interest- 
 ing remarks, which show clearly his views on the 
 subject in 1814, and prove that his ideas of the con- 
 stitution of nebulae had completely changed since 
 his earlier papers were written : 
 
 " The formation of these objects is extremely 
 instructive, as it manifests the affinity between the 
 matter of which stars are composed and that of the 
 most unshapen chaotic mass of nebulosity. For 
 the vanishing chevelure of a star being equally con- 
 nected, on the one hand, with the generally diffused 
 nebulous matter, and on the other with the star 
 itself, round which it is in a state of gradual con- 
 densation; this double union denotes the mutual 
 gravitation of the whole mass of nebulosity and the 
 stars towards each other ; and unless this proof can 
 
SIR WILLIAM HERSCHEL'S THEORIES 189 
 
 be invalidated, we must admit the fact of the grow- 
 ing condition of stars, that are in the situation 
 which has been pointed out. 
 
 " This argument adds greatly to the probability 
 of stars being originally formed by the condensation 
 of the nebulous matter ; for as it now appears that 
 stars must receive an addition to their solid con- 
 tents, when they are in contact with nebulosity, 
 there is an evident possibility of their being origin- 
 ally formed of it. Moreover, the affinity between 
 the nebulous and sidereal condition being established 
 by these observations, we may be permitted to con- 
 ceive both the generation and the growth of stars, 
 a,s the legitimate effects of the law of gravitation, 
 to which the nebulous matter, as proved by obser- 
 vation, is subject." 
 
 7. " Small patches consisting of stars mixed with 
 nebulosity." These, he thought, might possibly be 
 due to stars and nebulae being " accidentally in the 
 same line of sight," but that " the probability is in 
 favour of a real union." He suggests that in some 
 cases nebulosity might possibly drift by proper 
 motion into a region of small stars, and then be 
 " gradually arrested and absorbed by them," and 
 that thus " the growth of stars may be continued." 
 
 He found some objects of " an ambiguous con- 
 struction," the real character of which he could not 
 well determine. 
 
 Herschel then proceeds to consider the stars 
 themselves as distinguished from the nebulae. He 
 found that star clusters might be divided into 
 different classes. But most of these classes seem to 
 be included in two, namely, irregular clusters and 
 globular clusters. Some of his irregular clusters 
 contained stars of various sizes ; some mostly large 
 
190 ASTRONOMICAL ESSAYS 
 
 stars that is, comparatively large ; others contained 
 extremely small stars only ; some are coarsely 
 scattered ; others apparently much compressed. 
 Among "clusters of a peculiar description" he 
 mentions Messier 4 and 30. Among those " ap- 
 proaching the globular form " he refers to Messier 
 68. This was " clearly resolved into stars of 12th 
 magnitude" by his famous son, Sir John Herschel. 
 Among those he considered as certainly globular 
 clusters, and which he calls " undoubtedly the most 
 interesting objects in the heavens," he mentions 
 Messier 72, containing, he estimated, hundreds of 
 stars ; Messier 2, in which he could see the stars 
 " even in the central mass ; " from its apparent 
 magnitude, 7*7, as measured at Harvard, I find that 
 it probably contains about 800 stars. Messier 5, 
 56, 80, 13, 3, 15, 79, 19, and 53, are all well-known 
 globular clusters. 
 
 He then refers to " more distant globular clusters 
 of stars." These he called " miniatures " of the 
 larger globular clusters. Among these he mentions 
 Messiers 9, 14, 62, and 75. He supposed these smaller 
 objects to be at a greater distance from the earth, 
 as their component stars are faint and closer to- 
 gether. 
 
 Among still smaller objects of the globular class 
 he mentions Messier 69. This is a small globular 
 cluster, about 2J north, following c Sagittarii. 
 
 With reference to the Milky Way, he says that 
 in the constellations Sagittarius and Perseus there 
 are " eighteen different shades of glimmering light." 
 From this he infers that the Galaxy is gradually 
 " breaking up," and he says, " we may also draw a very 
 important conclusion from the gradual dissolution 
 
SIR WILLIAM HERSCHEL'S THEORIES 191 
 
 of the Milky Way ; for the state into which the in- 
 cessant action of the clustering power has brought 
 it at present, is a kind of chronometer that may be 
 used to measure the time of its past and future 
 existence ; and although we do not know the rate 
 of going of this mysterious chronometer, it is never- 
 theless certain that, since the breaking up of the 
 parts of the Milky Way affords a proof that it 
 cannot last for ever, it equally bears witness that 
 its past duration cannot be admitted as infinite." 
 
 In the Philosophical Transactions for 1817 there 
 is a paper by Herschel * on " Astronomical observa- 
 tions and experiments tending to investigate the 
 local arrangements of the celestial bodies in space, 
 and to determine the extent and condition of the 
 Milky Way." In this interesting pa.per he says 
 that the position of a celestial body in space can be 
 determined by three dimensions, which he calls 
 " length, breadth, and depth ; or longitude, latitude, 
 and profundity," the last-named meaning, of course, 
 the distance of the body from the earth. Of these 
 the longitude and latitude can be easily found on a 
 celestial globe or star atlas, but the distance from 
 the earth cannot always be determined with any 
 approach to accuracy. In some cases, of course, such 
 as the sun, moon, and planets, their distance can be 
 found and their exact position in space can be 
 accurately ascertained. But the distances of the 
 stars are so great that satisfactory results had not 
 been obtained in Herschel' s time. He supposed that 
 the diameter of the earth's orbit would not subtend 
 an angle of more than a second of arc at the distance 
 
 1 Here for the first time he calls himself Sir William Herschel, 
 Knt Gu6lp t LLD., F.B.S, 
 
192 ASTRONOMICAL ESSAYS 
 
 of the nearest star, and this estimate is nearly correct, 
 the largest parallax known being that of a Centauri, 
 namely, 0'75 second (or 1*50 second for the diameter of 
 the earth's orbit). He then refers to star magnitudes 
 as some indication of the relative distance ; l but he 
 thought it safer to assume an equal scattering of the 
 stars in space, and thus deduce their distance approxi- 
 mately. He supposes a series of concentric spheres 
 with radii of 1, 3, 5, 7, 9, etc., and finds the number of 
 stars which should be contained in each sphere on 
 the assumption of equal distribution. The volumes of 
 these spheres, and hence the number of stars in each, 
 will be proportional to the cubes of the radii, or as 
 1, 27, 125, 343, etc., the differences being the number 
 of stars in each shell included between two adjacent 
 spheres. He then compares the numbers thus found 
 with the number of stars of each magnitude as 
 given in Bode's catalogue. This catalogue contains 
 17 stars of the 1st magnitude ; but the number, 
 according to Herschel's hypothesis, should be 26. 
 Of 2nd magnitude stars, there are 57 stars in the 
 catalogue, instead of 98 as in Herschel's arrange- 
 ment. Of the 3rd magnitude there are 206 instead 
 of 218 ; and of the 4th magnitude the catalogue 
 shows 454, instead of only 386 on Herschel's plan. 
 For the total number of stars in the 4th magnitude 
 we have 735 in the catalogue, and 729 in Herschel's 
 arrangement a close agreement. The result is, how- 
 ever, not so satisfactory for the fainter stars. Thus 
 the catalogue contains 1161 stars of the 5th magni- 
 tude, whereas " the 5th order of distances has only 
 
 1 We now know that relative brightness is not a safe criterion of 
 distance, some faint stars being nearer to us than many of the 
 brighter stars. 
 
SIR WILLIAM HERSCHEL'S THEORIES 193 
 
 room for 602;" and "of the 6th magnitude the 
 catalogue contains not less than 6103 stars, 1 but the 
 6th order of distances will admit of only 866 stars." 
 For the 7th magnitude the catalogue "points out 
 6146 stars of the 7th magnitude, while the number 
 of stars that can be taken into the 7th order of 
 distances is only 1178." 
 
 Although admitting that brightness is not a cer- 
 tain test of distance, Herschel says, " The statement, 
 however, that, one with another, the faintest stars 
 are at the greatest distance from us, seems to me 
 so forcible, that I believe it may serve for the 
 foundation of an experimental investigation." He 
 then explains a method of "equalizing the light" 
 of two stars by means of two telescopes of equal 
 diameter and focal length. These were placed side 
 by side, and for a bright star the aperture of one 
 was reduced by circular apertures until its apparent 
 brightness became equal to that of a fainter star 
 viewed with the other and full aperture. 
 
 " In the calculation of a set of apertures for the 
 intended purpose," he admitted none that gave less 
 than one-fourth of the light, as the " spurious " discs 
 of the stars rendered an accurate estimate impos- 
 sible. This method of limiting apertures has been 
 sometimes used in modern times, but has now been 
 superseded by photometers, which give more accu- 
 rate results. 
 
 Herschel gives the results of some experiments 
 he made by this method. Comparing Arcturus 
 
 1 We now know that this number of stars of the 6th magni- 
 tude is too large. The total number of stars down to the 6th 
 magnitude is, according to the Harvard photometric measures, 
 about 4340. 
 
194 ASTRONOMICAL ESSAYS 
 
 with a Andromeda?, he found that Arc turns was 
 about four times the brightness of the other, so that 
 "if Arcturus was put at twice its distance from ue. 
 it would then appear, like a Androinedae, as a star 
 of the 2nd magnitude, and it would also at the 
 same time be really a star of the 2nd order of di.-- 
 tances." According to the Harvard photometric 
 measures, Arcturus is 0'24 and a Andromeda? 2'lo 
 magnitude. This makes Arcturus 5'S times brighter 
 than a Andromeda?. Among other stars which he 
 found had about one-fourth of the light of Arcturus. 
 he gives the Pole Star, y Ursa?, and 8 Cassiopeia?. 
 The Harvard measures of these are 2*12, 2*51, and 
 2-80 respectively. 
 
 Taking a Andromeda? as a standard, he found 
 that ft (Fl. 48) Pegasi is a star of the 4th magni- 
 tude. The Harvard measure of /x Pegasi is 3'67, 
 or a little brighter than Herschel made it. Pro- 
 ceeding, then, from /x Pegasi as a standard, he 
 found that q (70) Pegasi had one-fourth of the 
 light of /t Pegasi, "and that consequently Arc-turns. 
 removed to 8 times its present distance from us, 
 would put on the appearance of a star which in 
 our catalogues is called the 5th or 6th magnitude, but 
 which would, in fact, be of the 8th order of distances " 
 (that is, on Herschel's scale of distances). As the 
 Harvard measure of 70 Pegasi is 4'67, it follows that 
 Arcturus is 4*43 magnitudes, or 59 times brighter 
 than 70 Pegasi, and as Herschel makes it 64 times 
 (S 2 ) brighter, his result agrees well with modern 
 photometric measures. 
 
 Starting from Capella, he found that one-fourth of 
 its light would represent the brightness of /? Auriga? 
 and ft Tauri. The Harvard measures make Capella 
 
 
SIR WILLIAM HERSCHEL'S THEORIES 103 
 
 4'25 times brighter than yS Tauri and 5'55 times 
 brighter that ft AurigaB. He found that ft Tauri was 
 4 times brighter than Tauri and t Aurigae, but 
 the Harvard measures make ft Tauri about 3 times 
 brighter than Tauri, and slightly less in the case 
 of i Aurigae. 
 
 He found that a Lyras (Vega) was about 4 
 times brighter than fi Tauri. The Harvard measures 
 make it 4*53 times brighter ; and considering the 
 roughness of Herschel's method, the above com- 
 parisons are not very discordant. 
 
 Herschel's scales of brightness and distances do 
 not agree with modern standards. He speaks of 
 Sirius as if it were comparable with stars like 
 Arc-turns, Capella, and Vega. He says that the light 
 of Procyon is if of the light of Sirius, but the 
 Harvard photometric measures make Sirius 2*06 
 magnitudes, or 6'67 tunes brighter than Procyon. 
 
 For the naked eye he conies to the conclusion 
 that " all the visible stars are probably contained 
 within a sphere of the 12th order of distance," 
 that is, all stars visible to the naked eye are within 
 12 times the distance of an average 1st magni- 
 tude star. This would give 15,625 stars to the 7th 
 magnitude. The catalogue, he found, contained 
 14,144: stars to this magnitude, and this he considered 
 a sufficiently close agreement, but concludes that the 
 farthest stars " are more compressed than they are 
 in the neighbourhood of the sun." 
 
 He then returns to " the construction and extent 
 of the Milky "Way." He mentions several bright 
 spots or "patches" of light in the Galaxy. Among 
 these the "patch under the arrow of Sagittarius, 
 the ^one in Sobieski's shield, those near /?, a, and y 
 
196 ASTRONOMICAL ESSAYS 
 
 Cygni, and some in Cassiopeia and Perseus. He 
 says that the breadth of the Milky Way is " very 
 unequal. In some places it does not exceed 5 ; but 
 in several constellations it is extended from ten to 
 fifteen." For 120, he says, it extends " in a divided 
 clustering stream, of which the two branches between 
 Serpentarius and Antinous are expanded over more 
 than 20." He says the sun evidently lies in the 
 plane of the Milky Way. To examine its construc- 
 tion by means of telescopes, he prepared a set of 
 apertures for his different instruments which would 
 give " space penetrating powers " from 2 to 28. 
 He first tried these various powers on the double 
 cluster in the " sword-handle " of Perseus, " as being 
 probably a protuberant part of the Milky Way, in 
 which it is situated." He found that each increase 
 of "gaging" power increased the number of stars 
 visible in these remarkable clusters. With the full 
 " gaging power " of the 10-feet reflector about 
 28*67 he estimated that the faintest stars extended 
 to the 344th order of distances, while those seen 
 with the lowest power of 2 extended from the 12th 
 to the 24th order. This would evidently involve 
 the hypothesis of a very elongated cone filled with 
 stars, and with its axis pointing directly towards 
 the earth a very improbable arrangement. Herschel 
 seems, however, to have been conscious of the un- 
 certainty of this conclusion, for he says, "With regard 
 to these gages, which, on a supposition of an equality 
 of scattering, were looked upon as gages of distance, 
 I have now to remark that, although a greater number 
 of stars in the field of view is generally an indication 
 of their greater distance from us, these gages, in fact, 
 relate more immediately to the scattering of the 
 
SIR WILLIAM HERSCHEL'S THEORIES 197 
 
 stars, of which they give us a valuable information, 
 such as will prove the different richness of the 
 various regions of the heavens." He found that even 
 his " 20-feet telescope could not fathom the pro- 
 fundity of the Milky Way, and that the stars 
 which were beyond its reach must have been farther 
 from us than the 900th order of distances." 
 
 With the great 40-feet telescope, which, he com- 
 puted, had a space penetrating power of 2300, he 
 found that "the telescopic breadth of the Milky 
 Way considerably exceeds the extent which in our 
 maps is assigned to it." In a spot in the constellation 
 Moiioceros between Procyon and Orion's " belt " 
 the appearance of the Galaxy led him " to suppose 
 that there is a break or vacancy among the stars 
 between our situation and the more remote parts 
 of the Milky Way." He gives a number of other 
 observations, in some of which he found the stars 
 very numerous over 600 stars in some fields ! He 
 concludes this paper by adding "one remarkable 
 conclusion that may be drawn from the experiments 
 which have been made with the gaging powers." 
 This conclusion is, " that not only our sun, but all the 
 stars we can see with the eye, are deeply immersed in 
 the Milky Way, and form a component part of it." 
 But even now this conclusion can hardly be con- 
 sidered as proved. 
 
 In a paper in the volume for 1818 his last paper 
 on the subject he gives the results of his observa- 
 tions and experiments " for the purpose of ascertain- 
 ing the relative distances of clusters of stars, and of 
 investigating how far the power of our telescopes 
 may be expected to reach into space, when directed 
 to ambiguous celestial objects." In this paper he 
 
198 ASTRONOMICAL ESSAYS 
 
 applies the " gaging " principle to star clusters, and 
 concluded that some of these, when examined with 
 the 20-f eet telescope, indicated distances ranging from 
 the 144th to the 980th order of distances. Thus he 
 estimated that Messier 11, 34, and 35 were at the 
 144th order, or 12 times the distance of the faintest 
 stars visible to the naked eye ; Messier 2, 3, 5, 10, 13, 
 15, 53, 71, 72, 74, and 92 at the 243rd order ; Messier 
 4, 9, 19, 22, 30, 33, 56, 68, and 79 at the 344th order ; 
 Messier 62, 69, 75, and 80 at the 734th order ; Messier 
 14 at the 900th order ; Messier 77 at the 910th order ; 
 Messier 57 at the 950th order ; and Messier 1 and 97 
 at the 980th order of distances. But the accuracy 
 of these supposed distances is now more than 
 doubtful. 
 
 He then speaks of " ambiguous objects," that is, 
 nebulae which his telescopes could not resolve into 
 stars. Although he could completely resolve the 
 Milky Way in some places, yet he did not consider 
 it an ambiguous object, and he says, " We may con- 
 clude that when our gages will no longer resolve 
 the Milky Way into stars, it is not because its nature 
 is ambiguous, but because it is fathomless." But the 
 idea that the Milky Way is really " fathomless " is 
 probably incorrect. Proctor says, " Where Herschel 
 thought he ivas penetrating to the extreme limits of 
 the sidereal system, he was in reality only analyzing 
 more and more searchingly an aggregation in which 
 many orders of stars were mixed up. What he failed 
 to do was not (as he supposed) to sound the Galaxy, 
 but to recognize as separate stars the minutest orders 
 of orbs included within such aggregation." * 
 
 1 "The Universe and the Coming Transits," p. 217. The italics 
 are Proctor's. 
 
SIR WILLIAM HERSCHEL'S THEORIES 199 
 
 With reference to the question of the resolva- 
 bility of star groups as a test of distance, Proctor 
 points out that if a star group the components of 
 which are equal in magnitude, and individually 
 visible to the naked eye be supposed to pass away 
 into space, each separate star would become fainter 
 and fainter, and the distances between them smaller 
 and smaller as the group receded from the eye. 
 Now, if the " distances between them became too 
 small to be distinguished while the stars themselves 
 remained visible, clearly there would result a nebu- 
 losity of appearance." " But suppose that, on the 
 contrary, the stars of the group became invisible 
 when the group was at such a distance that the 
 intervals separating star from star would not be 
 indistinguishable (if only the stars were brighter). 
 Then clearly the group would vanish with increasing 
 distance without ever becoming nebulous. Clearly 
 also, if a telescope were employed to bring the 
 retreating group into view, the same conclusion 
 would hold good. A group which would become 
 nebulous to the naked eye before vanishing would 
 become so when examined under a telescope, let the 
 telescope's power be what it might ; while a group 
 which would vanish without becoming nebulous to 
 the naked eye would not become nebulous before 
 vanishing under telescopic vision, whatever the 
 telescopic power employed." ] From this reasoning 
 which seems to be sound it is obvious that the 
 resolvability of a star group, in which the com- 
 ponents are of equal brightness and equally dis- 
 tributed, depends more on the constitution of the 
 cluster than on its distance from the earth. 
 
 1 " Essays on Astronomy," pp. 340, 341. 
 
200 ASTRONOMICAL ESSAYS 
 
 A similar consideration is applicable to clusters 
 containing stars of different classes of brightness. 
 Proctor says, " Supposing a group of this kind to be 
 passing away into space as in the former case the 
 question whether it would become nebulous at any 
 stage or stages of its progress would depend on the 
 question whether or not the orders of stars about 
 to disappear individually were congregated so closely 
 that the eye could not distinguish the distances 
 separating them." 
 
CHAPTER XI 
 
 THE BRIGHTNESS OF THE SUN 
 
 THE sun's brightness has been variously estimated 
 from 340,000 to 800,000 times the brightness of full 
 moonlight, but Zollner's estimate of 618,000 times 
 moonlight is the one now usually accepted. The 
 sun's brightness is so great compared with that of 
 the brightest stars that a comparison can only be 
 made through the medium of the moon, and even 
 then with considerable difficulty. Various estimates 
 have been made of the sun's brightness in terms of 
 stellar magnitudes. Wollaston found it 25*75 magni- 
 tudes brighter than Sirius, and taking the Harvard 
 measure of Sirius as 1*58, this would make the 
 sun's stellar magnitude 27*33, a higher value than 
 now generally adopted. Steinheil found 25*54, 
 Bond -26*02, and Clark -25*47, values probably 
 too small. Professor Young gives 26*3, Professor 
 Newcomb 26*4, and some recent experiments by 
 M. Fabry give the value -26*7. x 
 
 Instead of comparing the brightness of the sun 
 directly with that of the brightest stars, I have 
 recently made some calculations of the probable 
 value of the sun's stellar magnitude by comparing 
 its light with that of some binary stars which have 
 the same, or a similar spectrum, and for which fairly 
 
 1 The Observatory, February, 1904. 
 201 
 
202 ASTRONOMICAL ESSAYS 
 
 reliable orbits have been computed. 1 The method 
 of computation is as follows: knowing the period 
 of revolution of the binary star in years, the semi- 
 axis major of the orbit in seconds of arc, and the 
 star's parallax, we can calculate the mass of the 
 binary system in terms of the sun's mass by an 
 extension of Kepler's third law of motion. Now, 
 assuming the binary pair to have the same density 
 and surface luminosity as the sun, we can find the 
 surface of a single body equivalent in mass to the 
 binary pair. We can thus compare the brightness 
 of the sun with that of the binary star, the parallax 
 and the photometric magnitude of the binary star 
 being known. Again, calling the sun's stellar magni- 
 tude S, we can find what the sun's magnitude would 
 be if it were removed to the distance of the binary 
 star. Equating the two expressions thus found, we 
 eliminate the parallax and obtain a formula for the 
 sun's stellar magnitude in terms of the star's photo- 
 metric magnitude, its period in years, and the semi- 
 axis major of the orbit. This expression will be 
 independent of the star's distance from the earth, 
 and may be applied to any binary star which has 
 a spectrum similar to that of the sun. Applying 
 this method to the binary star a Centauri, the 
 brighter component of which has a solar spectrum, 
 and of which the orbit is accurately known, I find 
 the sun's stellar magnitude 26*33. The binary 
 star Ursse Majoris, which has a spectrum of the 
 solar type (G. Pickering), gave the value 26*34, and 
 77 Cassiopeia (F 8 G) -26*65. The mean of these 
 values is 26*44, which agrees closely with Professor 
 Newcomb's value. 
 
 1 Monthly Notices, B.A.S., June, 1903. 
 
THE BRIGHTNESS OF THE SUN 203 
 
 Some recent 'observations by Ceraski, using Venus 
 as an intermediary, and taking the stars Polaris, 
 Procyon, and Sirius, give a mean value of 26*59. 
 In this volume I have adopted the value 26'5, 
 which is probably near the truth. Possibly, how- 
 ever, the true value may be slightly higher, perhaps 
 -26-7 or -26-8. 
 
 The magnitude 26*5 implies that the sun is 
 40,000 million times brighter than a star of zero 
 magnitude, like a Centauri. To reduce its light to 
 a star of this magnitude it should therefore be 
 removed to a distance of 200,000 times (the square 
 root of 40,000,000,000) its present distance. The 
 parallax would then be about one second of arc, 
 representing a light journey of about 3J years. To 
 reduce the sun's light to that of a star of the 1st 
 magnitude, like Aldebaran, it should be removed to 
 a distance represented by a light journey of about 
 5 years. To reduce it to the 5th magnitude, a light 
 journey of about 32 J years would be necessary, for 
 the 10th magnitude about 326 years, and for the 
 15th magnitude 3260 years. It follows, therefore, 
 that if any of the 15th magnitude stars, visible in 
 large telescopes, are equal to our sun in size and 
 brightness, they must lie at a distance of over 3000 
 years of light travel. There is no escape from this 
 conclusion unless we assume an absorption of light 
 in space, and of this there seems to be no satisfac- 
 tory evidence 
 
CHAPTER XII 
 
 THE SECULAR VARIATION OF STARS 
 
 IN my book " Studies in Astronomy " (chap, xvii.) I 
 gave some examples of stars which seem to have 
 either increased or diminished in brightness since 
 the earliest reliable observations of stellar magni- 
 tude were made. The following are some further 
 interesting cases of probable change in brightness 
 among the naked-eye stars during the last two 
 thousand years. 
 
 Let us first consider as before some stars which 
 seem to have diminished in brightness since the days 
 of Ptolemy and Al-Sufi. 
 
 s (4) Tauri. This star lies a little north of the 
 conspicuous pair of 4th magnitude stars o and 
 Tauri (south-west of the Hyades). It was rated 4th 
 magnitude by Ptolemy (or Hipparchus) and Al-Sufi, 
 5th magnitude by Argelander and Heis, 5-6 by 
 Houzeau, and it was measured 5'11 with the photo- 
 meter at Harvard ( being 3*75). Ptolemy rated it 
 the same as o and , but Al-Sufi made it a little less 
 than those stars. It forms one of a curve of four 
 stars referred to by Al-Sufi. These are / (5), s (4), 
 and o ; / (5) being the most northern, and o the 
 most southern of the four. Al-Sufi rated both / and 
 s as 4th magnitude, but at present s is about one 
 magnitude fainter than /, and it has probably faded 
 
 204 
 
THE SECULAR VARIATION OF STARS 205 
 
 since Al-Sufi's time (tenth century). Its spectrum is 
 of the Sirian type (A). The four stars referred to 
 above were called by Ptolemy aTroro/Arj, " a cutting off, 
 a piece, segment," probably because they are ap- 
 parently isolated or cut off from the rest of the 
 constellation. Al-Sufi says that they form " a slightly 
 curved line with the convexity turned towards the 
 east," and that " between these stars and the Pleiades 
 there is no star of even the sixth magnitude except a 
 faint one [13 Tauri ?], which could only be seen with 
 difficulty." This is quite correct, and there can be 
 no doubt as to the four stars referred to by Al-Sufi. 
 
 TT Leonis. This star, which lies about 4 south- 
 west of Regulus, was rated 4th magnitude by 
 Ptolemy, Al-Sufi, Tycho Brahe, Bayer, Hevelius, and 
 Flamsteed, but it was measured 4*89 at Harvard, 
 thus confirming modern estimates with the naked 
 eye by Argelander, Heis, and Houzeau, who all 
 estimated it 5th magnitude. Both Ptolemy and Al- 
 Sufi rated it equal to p Leonis, but it is now nearly 
 one magnitude fainter. The spectrum of TT Leonis 
 is of the 3rd type, a spectrum shown by many 
 variable stars. 
 
 i Leonis. This was rated 3rd magnitude by 
 Ptolemy, 3-4 by Al-Sufi, 3 by Tycho Brahe and 
 Bayer; but it was estimated 4th magnitude by 
 Argelander, Heis, and Houzeau, and it was measured 
 4*03 with the Harvard photometer. Al-Sufi made 
 it distinctly brighter than p (4 m.), but at present i 
 is slightly the fainter of the two. Its spectrum is 
 F 5 G according to Pickering, or similar to that of 
 Procyon. 
 
 With reference to the " extern stars " of Gemini 
 (those outside the ancient figure), there is some 
 
206 ASTRONOMICAL ESSAYS 
 
 difficulty in identifying Al-Sufi's 7th star. He says, 
 " The 7th follows the three stars (85, 81, and 74 of 
 Flamsteed), and is of small fourth magnitude ; 
 Ptolemy says fourth. Between it and the fourth, 
 which is the northern of the three, there is less than 
 two cubits (4 40') towards the south-east [this would 
 indicate Cancri]. These four stars are found be- 
 tween al-guma/isa [Procyon] and the 2nd bright star, 
 which is in the head of the Posterior Twin [Pollux], 
 nearer the bright 2nd star. The latitude of this star 
 is also erroneous, because it follows them in their 
 direction [that is, In a line with them] towards the 
 north [this indicates ^ Cancri], while as marked oil 
 the globe it forms a triangle with the 4th and 5th 
 [85 and 81]. Ptolemy says that it is bright, but in 
 reality it is of small third magnitude. There is not 
 in this place a star of either fourth or fifth magni- 
 tude, if it is not a faint one of about the sixth 
 magnitude." With reference to these remarks of 
 Al-Sufi, which are very puzzling and difficult to 
 explain, Schjellerup says, " Ce passage relatif a la 7 
 etoile est tout-a-fait inintelligible ; en effect, la de- 
 scription que nous en donne Sufi au commencement 
 s'applique tres bien tant pour la grandeur, que pour 
 la position, a Caucri, tandis que, & la fin il parle de 
 \L Cancri, en changeant meme la grandeur." I find 
 that Ptolemy's positions, as given by Al-Sufi, when 
 plotted, show the 7th star in the position described 
 by Al-Sufi, namely, forming a triangle with the 4th 
 and 5th. This position applies fairly well to Cancri, 
 which was probably Ptolemy's star. But it does 
 not agree at all with Al-Sufi's 7th star, which is 
 evidently ft Cancri, as he says it follows the 4th, 5th, 
 and 6th " in their direction," that is, nearly in a 
 
THE SECULAR VARIATION OP STARS 207 
 
 straight line with them. If Al-Sufi's estimate of 
 "smail third magnitude" was meant for /x- Cancri, 
 it must certainly have diminished in brightness, as it 
 is now about 5|. If, however, intended for Cancri, 
 we must come to the same conclusion, as is now 
 only slightly brighter than the 5th magnitude. Both 
 stars have spectra of the 2nd type (F). From Al- 
 Sufi's description of the 8th star of Cancer, it seems 
 to be ft, and this is confirmed by Ptolemy's positions. 
 We must therefore conclude, I think, that Ptolemy's 
 No. 7 of the " extern stars " of Gemini was really 
 Cancri, and that Al-Sufi was mistaken in thinking 
 that Ptolemy's position was altogether erroneous. 
 Ptolemy's place for Cancri is not quite correct, 
 according to modern measures, but it is not so much 
 in error as Al-Sufi thought. Near the position of 
 Al-Sufi's " faint star of about sixth magnitude " there 
 is one at present which was measured 6'06 at Harvard 
 Observatory. This is DM + 19, 1911. 
 
 With reference to Ptolemy's 21st star of the 
 constellation Leo, Al-Sufi remarks, " Ptolemy says 
 it is placed with the 22nd [0], or al-harkafa, ( the 
 buttocks,' to the south'of the bright 20th star [8], and 
 is of the fifth magnitude ; however, between the 20th 
 and 22nd [8 and 6] no star is visible. It is found 
 removed by a cubit towards the north above the 
 bright 20th star. This indicates 72 Leonis. But Al- 
 Sufi's identification of Ptolemy's star does not seem 
 justified, as M. Flammarion points out in his interest- 
 ing and valuable work, ' Les Etoiles,' p. 351. Flam- 
 marion identifies Ptolemy's star with Flams teed, 71. 
 But I cannot agree with this identification either. 
 71, as shown by Flammarion, lies to the east of a 
 line joining 8 and 0, but on plotting Ptolemy's 
 
208 ASTRONOMICAL ESSAYS 
 
 positions, as given by Al-Sufi, I find that Ptolemy's 
 21st star lies to the west of the line joining 8 and 6. 
 I find that the nearest star in the Harvard Durch- 
 musterung to the position of Ptolemy's star is 
 DM + 17, 2318 (6-8 m.), measured 6'86 at Harvard. 
 This may possibly be identical with the missing star 
 of Ptolemy (or Hipparchus). If so, it must have 
 diminished considerably in brightness, as Ptolemy 
 rated his star as 5th magnitude. The spectrum of 
 this small star is of the second type (H)." 
 
 With reference to the " extern stars "of Hydra, 
 Al-Sufi says, " The 2nd is to the north of the 15th 
 [A. Hydrse] ... it is situated almost in the middle 
 between the 15th and that in the heart of the 
 lion [Regulus]. It is of the fourth magnitude. 
 Ptolemy says third." This description applies ex- 
 actly to the star 15 Sextantis, but does not agree 
 with Ptolemy's position. If Ptolemy's star was 
 really 15 Sextantis, it must have diminished in 
 brightness, as it was measured only 4*50 at Harvard. 
 If Ptolemy's star was not identical with 15 Sextantis, 
 it must have disappeared, or diminished greatly in 
 brightness, as there is no star at present of even 
 5th magnitude in Ptolemy's position, the nearest 
 being 22 Sextantis, which is a little south of 
 Ptolemy's place, and was measured 5'36 at Harvard. 
 The spectrum of 15 Sextantis is A. 
 
 y8 Virginis. This star was rated 3rd magnitude 
 by Ptolemy and Al-Sufi, 3-4 by Argelander, Heis, 
 and Houzeau ; but it was measured 3*80, or only 
 slightly above the 4th magnitude, at Harvard. The 
 spectrum is F 8 G, or intermediate between Procyon 
 and the sun. 
 
 rj Virginis. Rated 3rd magnitude by Ptolemy 
 
THE SECULAR VARIATION OF STARS 209 
 
 and Al-Sufi, 3-4 by Argelander and Heis, and 
 4 by Houzeau. It was measured 4*00 at Harvard, 
 thus confirming Houzeau' s estimate. Ptolemy and 
 Al-Sufi rated it equal to y Virginis, but rj is now 
 one magnitude fainter than y. rj has been suspected 
 of variable light, and has recently been found to 
 be a spectroscopic binary. Its spectrum is of the 
 Sirian type. 
 
 With reference to the 30th star of Centauri, 
 which was rated 3rd magnitude by Ptolemy, Al-Sufi 
 says he could not find any star in the place indicated 
 by Ptolemy about 2 following e Centauri. Al- 
 Sufi says, "Quant a la 30 e , Ptolemy rapporte 
 qu'elle est aussi situ^e au dessous du ventre ; con- 
 formement a son lien rapporte dans I'al-madjisti, 
 il faut qu'il y ait entre elles moins d'une coudee 
 de distance. Mais il n'y a ni en cet endroit ni dans 
 ses alentours d'etoile qui puisse occuper sa place, 
 hormis les etoiles sus-dites et connues." Here we 
 have a star which probably disappeared, or faded 
 considerably, between Ptolemy's time and that of 
 Al-Sufi. Near the place indicated by Ptolemy there 
 are some small stars. Ptolemy and Al-Sufi agree 
 in rating and t Centauri as equal (3rd magnitude), 
 but at present 9 is considerably brighter that t. 
 
 o- Aquarii. Rated 4th magnitude by Ptolemy, 
 4-5 by Al-Sufi, 5-4 by Argelander, 5 by Heis and 
 Houzeau, and measured 4-89 at Harvard. Al-Sufi 
 estimated it as one magnitude brighter than 66 
 Aquarii, and so did Ptolemy, but the two stars 
 are now almost exactly equal (5th magnitude). The 
 spectrum is of the Sirian type (A). 
 
 83 (h) Aquarii. Rated 4th magnitude by Ptolemy, 
 4-5 by Al-Sufi, 6-5 by Argelander and Heis, 5 by 
 
 p 
 
210 ASTRONOMICAL ESSAYS 
 
 Houzeau, and measured 5*62 at Harvard. Ptolemy 
 and Al-Sufi made it equal to <f> Aquarii (a little north 
 of it), but at present h is about a magnitude fainter 
 than <j>. The spectrum is of the Sirian type (A). 
 
 X Aquarii. 4m. Ptolemy, 4-5 Al-Sufi, 5 Tycho 
 Brahe and Bayer, 5-6 Argelander and Heis, 5 
 Houzeau, and measured 5*22 at Harvard. Here, 
 again, Ptolemy and Al-Sufi rated x equal to <, but 
 at present x * s considerably fainter than <. The 
 spectrum is of the 2nd type (H, Pickering). 
 
 K Piscium. This star was rated 4th magnitude 
 by Ptolemy and Al-Sufi, 5-4 by Argelander, 5-6 
 by Heis, and was measured 4'94 at Harvard. Both 
 Ptolemy and Al-Sufi made it equal to <o Piscium, 
 but it is now about one magnitude fainter than <o. 
 The spectrum is of the Sirian type (A). 
 
 g (6) Orionis. Rated 4th magnitude by Ptolemy 
 and Al-Sufi, 6 by Argelander, Heis, and Houzeau, 
 and measured 5' 18 at Harvard. Ptolemy and Al-Sufi 
 estimated it equal to o 2 Orionis, but at present g 
 is about a magnitude fainter that o 2 . The spectrum 
 is of the Sirian type (A). 
 
 Eridani. Rated 3 by Ptolemy, 4 by Al-Sufi, 
 4 by Piazzi, 4-5 by Argelander, Heis, and Houzeau, 
 and measured 4*90 at Harvard. Here we seem to 
 have a certain diminution of light in the last 2000 
 years. The spectrum is of the Sirian type. 
 
 r 2 Eridani. 4 Ptolemy, 4-5 Al-Sufi, 4 Bayer, 
 Hevelius, and Flamsteed, 4| Piazzi, 5-4 Argelander 
 and Heis, 5-6 Houzeau, and measured 4'81 at 
 Harvard, The spectrum is K, or similar to that 
 of Arcturus. 
 
 Columbse. 4 Ptolemy and Al-Sufi, 5 Houzeau, 
 and measured 5*36 at Harvard. 
 
THE SECULAR VARIATION OF STARS 211 
 
 < Hydrse. Rated 4th magnitude by Ptolemy, 
 4-5 by Al-Sufi, 5 by Bayer, Hevelius, and Flamsteed, 
 by Houzeau, and measured 5*20 at Harvard. It 
 was estimated 5'3 at Cordoba. Al-Sufi rated it the 
 same as i Hydrse (4*10 Harvard), but at present it 
 is a magnitude fainter than that star. The spectrum 
 is K (Pickering). 
 
 30 Hydrse. Rated 3rd magnitude by Ptolemy and 
 Al-Sufi, 4-3 by Argelander and Heis, 4-5 by Houzeau, 
 and measured 3*95 at Harvard. Both Ptolemy and 
 Al-Sufi estimated it as one magnitude brighter than 
 e HydrsB, but it is now about half a magnitude fainter 
 than that star. The spectrum is of the Siriaii 
 type. 
 
 The star 8 Ursse Majoris the faintest star in " the 
 Plough " has been suspected of having diminished 
 in brightness, as it was rated 2nd magnitude by 
 Tycho Brahe and Bayer, or equal to the other stars 
 in the Plough. But as it was rated 3rd magnitude 
 by Ptolemy (or Hipparchus) and 3-4 by Al-Sufi, and 
 its photometric magnitude is now 3 '44 (Harvard), we 
 may conclude that it has not diminished much in 
 brightness since Ptolemy's time. Flamsteed, how- 
 ever, in 1700, rated it brighter than the star in " the 
 tail," so that it may possibly vary somewhat in 
 brightness. Flamsteed' s observations of star magni- 
 tudes are, however, rather rough, and not always 
 reliable. 
 
 Among those stars which have possibly increased 
 in brightness, the following may be mentioned : 
 
 a Ophiuchi. This star was rated 3rd magnitude 
 by Ptolemy, Al-Sufi, and Tycho Brahe, 2nd by 
 Argelander and Heis, and it was measured 2*14 
 with the photometer at Harvard. Al-Sufi compares 
 
212 ASTRONOMICAL ESSAYS 
 
 it with a Herculis which lies a little to the west of 
 it and says, " they are both of the third magnitude, 
 only the star of the head of Hercules is less brilliant." 
 (He rates a Herculis as 3-4 magnitude.) This shows 
 that he directly compared the two stars, and found 
 a Ophiuchi only a little brighter than a Herculis. 
 The photometer shows that a Ophiuchi is now a 
 full magnitude brighter than a Herculis, and indeed 
 the great difference between the two stars is obvious 
 at a glance. It should be stated, however, that a 
 Herculis is irregularly variable ; but as it is never 
 brighter than the 3rd magnitude, it seems probable 
 that a Ophiuchi has increased in brightness since 
 Al-Sufl's time. Al-Sufi rated it the same as 8 Herculis, 
 but it is now a magnitude brighter. Its spectrum is 
 A 5 F (Pickering). 
 
 Pollux. This star and Castor were both rated 
 2nd magnitude by Ptolemy and Al-Sufi, Tycho Brahe, 
 Hevelius, and Flamsteed. Pollux was rated 1-2 by 
 Argelander, Heis, and Houzeau, and this agrees well 
 with its photometric mag. 1'21 (Harvard). Castor 
 was rated 2-1 by Argelander and Heis, and 2 by 
 Houzeau, and it was measured T58 at Harvard. 
 Pigott says that Pollux was " undoubtedly brighter 
 than Castor" in the years 1783-1785. The photo- 
 metric measures at Harvard and Potsdam make 
 Pollux about 0*4 brighter than Castor. Pollux is 
 at present nearer to the first than the second magni- 
 tude, and it may possibly have increased in brightness 
 since Al-Sufi's time. Its spectrum is K, or the same 
 as that of Arcturus. 
 
 Sagittse. Rated 6th magnitude by Ptolemy, Al- 
 Sufi, Tycho Brahe, Hevelius, and Flamsteed ; but 
 estimated as 5 by Argelander, 5-6 by Heis and 
 
THE SECULAR VARIATION OF STARS 213 
 
 Houzeau, and measured 4*95 at Harvard. Its 
 spectrum is of the Sirian type. 
 
 8 Sagittae. 5m. Ptolemy, Al-Sufi, Tycho Brahe, 
 and Bayer, 4J Flamsteed, 4 Piazzi, Argelander, Heis, 
 and Houzeau, and measured 3*78 at Harvard. These 
 estimates seem to show a progressive increase of 
 light. Al-Sufi made 8 equal to ft Sagittse, but at 
 present 8 is considerably the brighter of the two. 
 
 Delphini. Rated 6th magnitude by Ptolemy and 
 Al-Sufi, 5 by Tycho Brahe, Hevelius, Flamsteed, and 
 Piazzi, 5-4 by Argelander and Heis, 4-5 by Houzeau, 
 and measured 4*69 at Harvard. Al-Sufi rated it equal 
 to i and Delphini, but it is now considerably brighter 
 than either of those stars. The spectrum is of the 
 Sirian type (A). 
 
 co 2 Tauri. 6m. Ptolemy and Al-Sufi, 6-5 Arge- 
 lander and Heis, 5 Houzeau, and measured 4'80 at 
 Harvard. Al-Sufi rated it one magnitude less than 
 p (44) Tauri, but o> 2 is now considerably brighter 
 than p, and seems to have certainly increased in 
 brightness. The estimates seem to show a progressive 
 increase during the last 2000 years. The spectrum is 
 of the Sirian type (A). 
 
 e Canis Maj oris. Rated 3rd magnitude by Ptolemy, 
 Al-Sufi, Tycho Brahe, and Bayer, 3-2 by Flamsteed, 
 2-1 by Argelander and Heis, 2 by Houzeau, and 
 measured T63 at Harvard. Both Ptolemy and Al- 
 Sufi rated it equal to Canis Maj oris (3*10 Harvard), 
 but according to the photometric measures, it is now 
 about 1^ magnitude, or nearly four times brighter 
 than . The spectrum is of the Orion type (B 1 A, 
 Pickering). 
 
 /8 Canis Minoris. 4m. Ptolemy, Al-Sufi, and Ulugli 
 Beigh, 3 Bayer, Hevelius,'] Flamsteed, Argelander, 
 
214 ASTRONOMICAL ESSAYS 
 
 Heis, and Houzeau, and measured 3*09 at Harvard. 
 The spectrum is B 8 A (Pickering). 
 
 The Pole Star (a TJrsae Minoris) has probably 
 increased in brightness since Al-Sufi's time (tenth 
 century). Al-Sufi says that in his day, y Ursse 
 Minoris was inferior to the Pole Star, or "at the 
 most equal to it." He could not have seen much 
 difference between them, as he rates them both 
 3rd magnitude. As y is now just one magnitude 
 fainter than the Pole Star (according to Argelander, 
 Heis, and the photometric measures), Al-Sufi's remark 
 would seem to show that the Pole Star was really 
 about the 3rd magnitude in his time. Its photo- 
 metric magnitude is 2*12 (Harvard). Al-Sufi rated 
 /3 Ursse Minoris 2nd magnitude, and at present it is 
 only a little fainter than this estimate. He rated 
 y 3rd magnitude, and here again he is correct, for 
 the Harvard measures make it 3'14. The spectrum 
 of the Pole Star is F 8 G (Pickering), or very similar 
 to that of the sun. 
 
CHAPTER XIII 
 
 THE BRIGHTNESS OP STARLIGHT 
 
 IT is probably a matter of common observation that 
 on a clear moonlight night it is never absolutely 
 dark, a eeriain amount of light being given by the 
 stars. Evidently, however, this starlight is only a 
 small fraction of moonlight. Miss Clarke, in her 
 "System of the Stars," gives the light of all the 
 stars down to the 9J magnitude about ^ of moon- 
 light. M. G. 1'Hermite found starlight equal to ^ of 
 moonlight. But this latter estimate is evidently too 
 high ; the difference between a bright moonlight 
 night and one illuminated by starlight only being 
 very considerable. 
 
 Let us make an attempt to estimate the total 
 amount of starlight by computing the light emitted 
 by all the visible stars down to the faintest point of 
 light perceptible in the largest telescopes, like those 
 of the Yerkes and Lick observatories. The data 
 available for this calculation are rather uncertain, 
 but a fair approximation to the truth is perhaps 
 possible. 
 
 To express the total amount of starlight in terms 
 of the light of a star of, say, " zero magnitude " like 
 a Centauri and thence in terms of moonlight, let us 
 assume, as is now admitted by most authorities on 
 the subject, that the total number of the visible 
 
 215 
 
216 
 
 ASTRONOMICAL ESSAYS 
 
 stars is about 100 millions. Let us also assume that 
 the "light ratio" is 2*512 now accepted by all 
 astronomers that is, that a star of zero magnitude 
 gives 2*512 times the light of a standard star of 
 the 1st magnitude like Aldebaran a star of 1st 
 magnitude 2' 5 12 times the light of a star of 2nd 
 magnitude, and so on. To enable us to make this 
 calculation, it will be necessary to estimate the 
 number of stars in each magnitude down to the 
 17th magnitude, which is about the faintest 
 visible in the great Yerkes telescope. From an 
 examination of recent results, Professor Newcomb 
 finds the following numbers for the stars visible to 
 the naked eye : 
 
 
 Total. 
 
 1st Magnitude 
 
 
 
 
 21 
 
 21 
 
 2nd 
 
 
 
 
 
 52 
 
 73 
 
 3rd 
 
 
 
 
 
 157 
 
 230 
 
 4th 
 
 
 
 
 
 506 
 
 736 
 
 5th 
 
 
 
 
 
 1740 
 
 2476 
 
 6th 
 
 
 
 
 
 5171 
 
 7647 
 
 The total shows all stars down to 6'4 magnitude, 
 about the faintest visible to the naked eye. 
 
 Taking the total number to magnitude 6*0 at 
 7000, and allowing a factor of 3 for the total 
 number to each magnitude below this, I find that 
 the total number to the 15th magnitude should 
 be about 137f millions, to the 16th magnitude 
 about 413 millions, and to the 17th magnitude 
 about 1240 millions. Now, as the total number 
 visible down to the 17th magnitude does not 
 probably exceed 100 millions, it is evident that 
 
THE BRIGHTNESS OF STARLIGHT 217 
 
 there must be a diminution in the increase, or 
 " thinning out," of the fainter stars as we descend in 
 the scale of magnitude. This diminution probably 
 begins with stars of the 10th or llth magnitude. 
 
 Assuming Professor Newcomb's figures for stars 
 down to the 6th magnitude, and adjusting the 
 numbers in the remaining magnitudes to suit a total 
 of 100 millions down to the 17th magnitude, we 
 obtain the following table : 
 
 1. 
 
 2. 
 
 3. 
 
 4. 
 
 Magnitude. 
 
 No. of stars. 
 
 Equivalent No. of 
 stars of zero mag. 
 
 Remarks. 
 
 Above zero 
 Zero mag. 
 
 2 
 1 
 
 7 
 1 
 
 Sirius and Canopus 
 a Centauri 
 
 0-0-5 
 
 5 
 
 4 
 
 Vega, Capella, Arcturus, 
 
 
 
 
 Bigel, and Procyon 
 
 i-li 
 
 13 
 
 5 
 
 
 2 
 
 52 
 
 8 
 
 
 3 
 
 157 
 
 10 
 
 
 4 
 
 506 
 
 13 
 
 
 5 
 
 1740 
 
 17 
 
 
 6 
 
 5171 
 
 20 
 
 
 7 
 
 15,000 
 
 24 
 
 
 8 
 
 60,000 
 
 38 
 
 
 9 
 
 240,000 
 
 60 
 
 
 10 
 
 800,000 
 
 80 
 
 
 11 
 
 2,000,000 
 
 79 
 
 
 12 
 
 5,000,000 
 
 79 
 
 
 13 
 
 9,000,000 
 
 56 
 
 
 14 
 
 12,000,000 
 
 30 
 
 
 15 
 
 17,000,000 
 
 17 
 
 
 16 
 
 23,000,000 
 
 9 
 
 
 17 
 
 X 
 
 31,000,000 
 
 5 
 
 
 Total ... 562 
 
 
 It will be noticed that the numbers in column 
 3 of the above table rapidly diminish for the 
 
218 ASTRONOMICAL ESSAYS 
 
 fainter magnitudes. The fainter stars shown on 
 photographic plates are supposed to be about the 
 18th magnitude, and judging from the total 
 light of those of the 16th and 17th magni- 
 tude, we may safely assume that the combined 
 light of all the stars of the 18th magnitude, or 
 fainter, would be very small. If there were 100 
 millions of stars of the 20th magnitude if such 
 faint stars exist their combined light would be 
 only equal to that of a single star like Vega. 
 From this it is clear that the light of all stars below 
 the 17th magnitude may be safely neglected in 
 making an estimate of the total amount of star- 
 light. 
 
 In addition to the stars, there are a large 
 number of nebulae scattered over the surface of the 
 heavens, but the majority of these are such faint 
 objects that their combined light must be incon- 
 siderable. Perrine has recently estimated that the 
 probable number within reach of the Crossley re- 
 flector is about 500,000. Assuming for these an 
 average magnitude of 11, we have their com- 
 bined light equal to that of 20 stars of zero 
 magnitude. Hence the total light of all the stars 
 and nebulae in both hemispheres would be equivalent 
 to 582 stars of zero magnitude, like a Centauri 
 or Vega. 
 
 Now, to find what fraction this is of moonlight, 
 we must consider the relation between sunlight and 
 moonlight, and the light of a star of zero magnitude. 
 Taking the sun's stellar magnitude as 26'5, we 
 have sunlight equal to 39,810,000,000 stars of zero 
 magnitude. Comparing sunlight with moonlight, 
 Bouguer found sunlight 300,000 times the brightness 
 
THE BRIGHTNESS OF STARLIGHT 219 
 
 of full moonlight, Euler found 374,000, Wollaston 
 801,072, G. P. Bond 470,980, and Zollner 618,000. 
 The mean of all these is 512,810 ; but Zollner' s 
 estimate of 618,000 is the one now usually accepted. 
 Assuming this value, we have 
 
 39,810,000,000 
 Moonlight- 618j0 00 
 
 = 64,417 stars of zero magnitude. 
 Hence 
 
 PJQO t 
 
 Starlight = -? = of moonlight. 
 
 As this result is for the whol&sky, we have for 
 one hemisphere (which is all that is visible from any 
 one place at one time) 
 
 Starlight = SO of moonlight. 
 
 In addition to the stars and nebulae, there is a lot 
 of scattered nebulous light visible on photographs in 
 various parts of the sky ; but it would be very 
 difficult to estimate what amount of light this 
 would give. 
 
 An examination of the table given above shows 
 that the combined light of the stars below the 6th 
 magnitude is considerably greater than the light of 
 those above that magnitude ; so that if all the stars 
 visible to the naked eye were extinguished, we 
 should still have nearly the same amount of star- 
 light. 
 
 In a recent investigation by Professor Newcomb, 1 
 
 1 Published in 1902. My first estimate was published in Know- 
 ledge, August, 1901. 
 
220 ASTRONOMICAL ESSAYS 
 
 lie finds as the results of experiments that the total 
 light of all the stars is about equal to 600 stars of zero 
 magnitude, " with a probable error of one-fourth of 
 the whole amount." He thinks that a positive error 
 is more probable than a negative one, and that the 
 number may possibly be greater than 800. He " is 
 inclined to regard this quantity as among the most 
 important constants of astrophysics." 
 
 From some actual experiments, Mr. Gavin J. Burns 
 finds that on an average the light of the sky is equal 
 to that of a star of the 5th magnitude diffused over 
 an area of half a square degree. As the whole star 
 sphere includes an area of 41,253 square degrees, Mr. 
 Burns' estimate would make the total amount of 
 starlight equal to 82,506 stars of the 5th magnitude, 
 that is, 825 stars of zero magnitude. He finds that 
 the average luminosity of the Milky Way is only 
 from two to three times greater than that of the 
 rest of the sky. 1 
 
 Probably, however, the light of the sky at night 
 is not wholly due to starlight. Mr. Burns points out 
 that if this were so, the luminosity of the sky should 
 " diminish near the horizon, just in the same manner 
 as the brightness of the stars diminishes, and for the 
 same reason, viz. the greater absorption of light by 
 the earth's atmosphere. As a matter of fact, the 
 exact opposite is the case. The brightness of the 
 sky increases perceptibly near the horizon." 2 I can 
 fully confirm the observations of Mr. Burns. I have 
 often noticed during my observations of variable 
 stars that on some nights the background of the sky 
 is comparatively dark, while on others, equally free 
 
 1 Astrophysical Journal, October, 1902. 
 
 2 Journal of the British Astronomical Association, June, 1906. 
 
THE BRIGHTNESS OP STARLIGHT 221 
 
 from clouds, the whole sky seems lit up with a 
 sort of phosphorescent glow, evidently not due 
 to starlight. This glow seems to be variable, as 
 on some nights it is much more conspicuous than 
 on others. 
 
CHAPTER XIV 
 
 THE NUMBER OF THE VISIBLE STARS 
 
 THE total number of stars visible in the largest 
 telescopes and on stellar photographs is usually 
 estimated at 100 millions. To test the probable 
 accuracy of this estimate, I have made a number 
 of counts of stars shown on the photographic prints 
 given in the late Dr. Roberts' s volumes of stellar 
 photographs. These counts were made by means of a 
 rtfseau ruled in squares on transparent celluloid. By 
 careful measurement I find that the side of a square 
 on the r^seau used is 7*62 millimetres, and therefore 
 the area of the square is 58 square millimetres. By 
 counting the number of stars in one of these squares 
 in various parts of the print, a good average may be 
 obtained, and as the scale of each photograph is 
 always given by Dr. Roberts, it is easy to compute 
 the probable number of stars per square degree on 
 each plate. The photographic prints show stars 
 down to the 16th or 17th magnitude, but probably 
 some faint stars, visible on the original plates, have 
 been lost in the reproductions. The time of exposure 
 of the plates varies from 1J to 4 hours, but this 
 seems of little consequence, for Dr. Roberts says in 
 the preface to the second volume (1899) 
 
 " The group of the Pleiades has been photographed 
 
 222 
 
THE NUMBER OF THE VISIBLE STARS 223 
 
 with the 20-inch reflector during numerous in- 
 tervals between 1886 and 1898, with exposures of 
 between one minute and twelve hours. The results 
 are that only the same faint stars and nebulosity 
 seen upon plates which have had an exposure of one 
 and a half hours are depicted upon those which have 
 been exposed during ten or twelve hours. 
 
 " Several photographs of the region of the Milky 
 Way in Cygnus (Plate 5) have been taken with the 
 20-inch reflector between the years 1886 and 1898, 
 and, on comparing two of them (one with an exposure 
 of 60 m the other with 2 h 35 m ), no fainter stars could 
 be found on one than on the other; there is no 
 reason for suspecting that this result was due to 
 some abnormal condition in either case, and it has 
 been confirmed by photographs which have been 
 taken in other areas in the sky." 
 
 In making the counts I have carefully avoided 
 the clusters and nebulae shown on each plate. The 
 number of counts made varied from 15 to 50 on 
 each print, depending on the richness of star dis- 
 tribution. On some prints, in which the stars were 
 few in number, counts were made on 600 squares. 
 
 In these counts the number of stars per square 
 degree ranged from 5460 in a rich region of the 
 Milky Way north of 77 and x Cygni down to 245 in 
 a spot in the constellation Leo free from Milky Way 
 light. Some portions of the Milky Way, such as 
 those in Auriga and Monoceros, are much less rich 
 in stars. These parts are fainter than those in 
 Cygnus, which have a larger number of stars per 
 square degree. This shows clearly that the fainter 
 portions of the Milky Way owe their faintness to a 
 smaller number of stars, and not to greater distance 
 from the earth, as some astronomers have errone- 
 ously supposed. 
 
224 ASTRONOMICAL ESSAYS 
 
 The average results I have found are as follows : 
 
 Milky Way .... 4137 stars per square degree 
 Near Milky Way . . 1782 
 No Milky Way ... 408 
 
 Professor E. C. Pickering gives the following esti- 
 mates of the areas covered by the Milky Way and 
 the non-galactic regions : 
 
 Rich Milky Way . . . 10,999 square degrees 
 Painter portions . . . 4,613 ,, 
 No Milky Way .... 25,641 
 
 Hence we have 
 
 10,999 X 4137 = 45,502,863 
 
 4,613 X 1782 = 8,220,366 
 
 25,641 X 408 = 10,461,528 
 
 Total . . 64,184,757 
 
 or, in round numbers, about 64 millions. 
 
 The real total may be somewhat greater, as 
 probably some of the fainter stars, visible on the 
 plates, are lost in the prints given in Dr. Roberts' s 
 volumes. 
 
 By the same method I have also counted the 
 number of stars in some of the irregular clusters 
 shown in Dr. Roberts' s photographs. These clusters, 
 I find, vary in richness from about 12,000 stars per 
 square degree down to 2520, the average of 12 clusters 
 being 5752 stars per square degree, or only a little 
 more than the richest parts of the Milky Way. The 
 globular clusters are, of course, much richer than this. 
 Professor and Mrs. Bailey's counts of stars in the 
 great globular cluster w Centauri give about 25,000 
 stars to the square degree. This would give for the 
 
THE NUMBER OF THE VISIBLE STARS 225 
 
 whole heavens, if equally rich, over 1000 millions 
 of stars. But as Centauri is, of course, unusually 
 rich in stars, we may conclude with confidence that 
 the actual number of the visible stars is far short 
 of 1000 millions. An estimate of 100 millions is 
 probably a maximum. 
 
 Q 
 
CHAPTER XV 
 
 STELLAR BRIGHTNESS AND DENSITY 
 
 SEVERAL attempts have been made to determine the 
 brightness of the sun in terms of the brightest stars. 
 This is a matter of no small difficulty, as the sun is 
 so enormously brighter than any of the stars, and 
 cannot, therefore, be directly compared with them. 
 By indirect methods, however, a close approximation 
 has been made to the truth, and the best recent 
 determinations makes the sun's brightness between 
 26 and 27 magnitudes brighter than the zero of 
 stellar magnitudes. This zero is fairly represented 
 by the brightness of the star a Centauri ; and Vega 
 and Arcturus are only slightly below this zero. The 
 number 26'5 may be taken as the mean of the 
 best estimates of the sun's brightness. This implies 
 that the sun is 40,000 million times brighter than 
 a Centauri. Now, as light varies inversely as the 
 square of the distance, it follows that the square 
 root of this number, or 20,000, will represent the 
 distance to which the sun should be removed in 
 order to reduce its brightness to that of a Centauri. 
 That is, if the sun were removed to 20,000 times its 
 present distance, its light would be reduced to that 
 of a star of zero magnitude, like a Centauri. As the 
 distance of some of the stars has been determined 
 with considerable approach to accuracy, we can 
 
 226 
 
STELLAR BRIGHTNESS AND DENSITY 227 
 
 compare the total light emitted by them with that 
 which the sun emits. Let us consider those stars of 
 which the distance has been most accurately deter- 
 mined, and see how their brightness compares with 
 that of the sun. 
 
 For a Centauri the parallax has been well deter- 
 mined, and is about 0'75 of a second of arc. That 
 is the angle which the distance between the sun and 
 earth would subtend at the distance of the star. 
 Placed at the distance indicated by this parallax 
 the largest yet found for any star the sun would, I 
 find, be reduced in brightness to a star of 0*69 magni- 
 tude, or a little fainter than the bright star Procyon. 
 This implies that a Centauri is about 1*79 times 
 brighter than the sun. It is a well-known double 
 and binary star, the brighter component being 0'36 
 magnitude, according to the Harvard photometric 
 measures, and the fainter 1*61 magnitude. The 
 brighter component is therefore only a little brighter 
 than the sun would be if placed at the same distance 
 from the earth, and as its mass has been shown to be 
 equal to the sun's mass, and its spectrum the same, 
 we may consider it as about a duplicate of our sun. 
 A slight increase in the assumed value of the sun's 
 stellar magnitude would make them exactly equal in 
 light. On the other hand, the fainter component of 
 the pair has only 0'43 of the sun's light, and as its 
 mass is also equal to the sun's mass, it is either of 
 smaller size that is, more condensed or has a 
 smaller luminosity of surface. Its spectrum agrees 
 with this conclusion. 
 
 The bright star Sirius has a parallax of about 
 0'37 second. This, combined with its magnitude of 
 1*58, or 1*58 magnitudes above the zero of stellar 
 
228 ASTRONOMICAL ESSAYS 
 
 magnitudes, makes it about 33 times brighter than 
 the sun that is, the light of Sirius is equal to that of 
 33 suns. 
 
 The bright star Procyon, with a parallax of 0*325 
 second, is about 6 J times brighter than the sun ; and 
 Aldebaran, with a parallax of 0*107 second, has a 
 brightness equal to that of 35 suns. Capella seems 
 to have the light of about 128 suns, although its 
 mass is only about 17 times the sun's mass. As its 
 spectrum is almost identical with the solar spectrum, 
 we have here an anomaly which has not yet been 
 satisfactorily explained. 
 
 If any reliance can be placed on the small parallax 
 found for some of the bright stars, they must be suns 
 of enormous size or great brilliancy of surface. Thus 
 I find that Arcturus is no less than 1486 times 
 brighter than the sun, Antares 787 times, a Gruis 
 648 times, Regulus 642 times, Achernar 331, J3 
 Centauri 227, and a Crucis 166 times. 
 
 Some of the stars are, however, much fainter 
 than our sun. For the small star Lalande 21,185 
 (magnitude 7 '60), Mr. H. N. Russell has recently 
 found a parallax of 0*344 second. This indicates that 
 the sun is about 100 times brighter than the star, and 
 suggests that this star is a comparatively small body. 
 The character of its spectrum has not been deter- 
 mined, but if we assume that it has the same density 
 and surface brilliancy as the sun, the above result 
 would imply that its diameter is only one-tenth of 
 the sun's diameter, or about 86,000 miles or about 
 the diameter of the planet Jupiter. The small star 
 known as Cordova Zone V. 243, which has the large 
 proper motion of 8*7 second per annum (the largest 
 known), has been found to have a parallax of 0*312 
 
STELLAR BRIGHTNESS AND DENSITY 229 
 
 second. This gives a brightness of only O'OOl of the 
 sun's brightness, and would indicate a still smaller 
 body. But in this case also the spectrum is unknown. 
 
 The brightness of a star, or its so-called " magni- 
 tude," depends on three factors (1) its distance 
 from the earth ; (2) its diameter ; and (3) its intrinsic 
 brilliancy, or the actual luminosity of its surface per 
 unit of area. The first of these factors the distance 
 from the earth has in a few cases been determined 
 with considerable accuracy, either by micrometrical 
 measures of comparison stars, or from spectroscopical 
 observations of binary stars. The second factor 
 the diameter of the star is more difficult to deter- 
 mine, and its measurement has not been satisfactorily 
 accomplished, except perhaps in some variables of the 
 Algol type. An approximation to its probable value 
 may, however, be arrived at from other considera- 
 tions. The third factor the luminosity of the star's 
 surface may be inferred, to some extent at least, 
 from the character of the star's spectrum. This 
 luminosity of surface, or intrinsic brightness l as it 
 is sometimes called probably depends on the mass 
 and density of the star. Two stars may have the 
 same mass that is, quantity of matter but one may 
 have a large volume and small density, and the 
 other a small volume and greater density. The 
 difference is probably due to temperature. And 
 then the question arises, which of the two stars will 
 be apparently the brighter? We know that heat 
 causes a mass of gas to expand, and the greater the 
 heat, the greater the expansion. And with a given 
 mass, the greater the expansion, the smaller the 
 density will be. This is evident. Hence a star with 
 
 1 This term was used by Sir William Herschel. See p. 163. 
 
230 ASTRONOMICAL ESSAYS 
 
 a high temperature would have a large volume and 
 small density. And it seems probable that, the 
 higher the temperature the greater will be the 
 luminosity of its surface. From this it would follow 
 that a star with a high temperature would have a 
 large volume and light-giving surface, and also a 
 greater luminosity of surface, and both cases would 
 thus combine to increase its apparent brilliancy. It 
 is probable, however, that this would not apply to 
 the nebulae, but only to bodies, like the stars, which 
 have consolidated to a certain extent. 
 
 It is now admitted by many eminent astronomers 
 that stars with the "Orion type" of spectrum (B, 
 Pickering), such as Bellatrix (y Orionis), 8, e, and 4 
 Orionis, are with the possible exception of the 
 " Wolf -Ray et stars " the most luminous among 
 the brighter stars. Next to these come stars with 
 the Sirian type of spectrum (A, Pickering), followed 
 probably in decreasing order of luminosity by stars 
 of the second or solar type, and then by the third, 
 and perhaps fourth type stars. The " Algol vari- 
 able " U Ophiuchi has a spectrum of the " Orion 
 type," and some of the other " Algols," such as Algol, 
 X Tauri, and V Puppis, show a spectrum intermediate 
 between the B and A type. These will be considered 
 further on. 
 
 The probably great luminosity of stars with the 
 " Orion type " of spectrum is shown by the fact that 
 Sir David Gill finds that the parallax of Rigel is 
 almost certainly not more than the hundredth of a 
 second of arc, and yet it is one of the brightest stars 
 in the sky seventh in order of brightness accord- 
 ing to the Harvard photometric measures. At the 
 vast distance indicated by this minute parallax, our 
 
STELLAR BRIGHTNESS AND DENSITY 231 
 
 sun. would be reduced to a star of about the 10th 
 magnitude, and would therefore be invisible even 
 with a binocular field-glass. Rigel is therefore about 
 7800 times brighter than the sun would be if removed 
 to the same distance from the earth. It has a small 
 companion of the 8th magnitude, but as the pair 
 have not yet been proved to be a binary (although 
 the companion, which is double, probably is), we 
 cannot determine its mass. But it is evident that it 
 must be a sun of enormous size and great luminosity 
 of surface to shine as brightly as it does at such a 
 vast distance from the earth over 300 years' journey 
 for light. Comparing it with Sirius, whose mass and 
 distance have been well determined, I find that the 
 mass of Rigel is probably about 20,000 times the 
 sun's mass. 
 
 The great brilliancy of stars with the Sirian type 
 of spectrum is shown by Sirius itself, the distance of 
 which has now been satisfactorily determined. From 
 its apparent brightness and parallax, I find, as 
 already stated, that Sirius is about 33 times 
 brighter than the sun would be at the same distance. 
 From the orbit of the satellite, Dr. See finds its mass 
 to be 2*36 times the sun's mass, and from this it 
 follows that its real brightness is about 18 times 
 greater than that of the sun in proportion to its 
 mass. Its spectrum shows that it is probably at a 
 higher temperature than our sun. 1 Its volume is 
 therefore probably larger, and, as Dr. See says, there 
 " is some reason to suppose that Sirius is very much 
 expanded, more nearly resembling a nebula than the 
 sun." But here the question arises, is its greater 
 
 1 Hale, Huggins, and Schuster agree in the opinion that Sirian 
 stars are hotter than solar stars. 
 
232 ASTRONOMICAL ESSAYS 
 
 brilliancy due to its larger volume, and smaller 
 density, or to its greater surface luminosity, or to 
 both cases combined? As it is 33 times brighter 
 than the sun, a diameter equal to the square root of 
 33, or 5'74 times the sun's diameter, would give 
 the necessary brightness (if the surface luminosity 
 of Sirius and the sun were the same). Assuming 
 this for a moment, I find that with a diameter of 
 5*74 times the sun's diameter or about 5 millions 
 of miles its volume would be about 189 times greater 
 than the sun's volume, and its density only ^j of 
 the sun's density. Now, as the sun's density is T40 
 (water = 1), we have density of Sirius on the above 
 assumption of equal surface luminosity only 0'017 
 that of water. This seems improbable, judging from 
 the known case of Algol, which has a much higher 
 density than this. We may therefore conclude, I 
 think, that the great brilliancy of Sirius is probably 
 due to both causes combined, namely, a somewhat 
 larger volume and a greater luminosity of surface 
 than the sun. If we assume that its density is the 
 same as that of Algol, say 0*34, we have the diameter 
 of Sirius about 1,860,000 miles, and its surface 
 luminosity about 7 times that of the sun. 
 
 For 8 Equulei, a binary star with the very short 
 period of 5*7 years, Professor Hussey finds from 
 spectroscopic observations a parallax of 0*071 second 
 and a combined mass of 1*89 times the sun's mass. 
 He says, " The components of the pair are slightly 
 unequal in brightness, and perhaps also in mass. 
 One may be as massive as the sun, but it cannot 
 much exceed it." 1 The parallax found by Hussey 
 would, I find, reduce the sun to a star of about 5*81 
 1 Astrophysical Journal, June, 1903. 
 
STELLAR BRIGHTNESS AND DENSITY 233 
 
 magnitude, and as the photometric magnitude of 8 
 Equulei is 4*61, we have the star 1*20 magnitudes, or 
 3 times brighter than the sun. Assuming that the 
 masses of the components are I'OO and 0*89 (as sug- 
 gested by Hussey), I find that if the density and 
 surface luminosity of each were equal to that of 
 the sun, the combined light of the two components 
 would be 1*9247, or nearly twice the sun's light. The 
 star's spectrum is of the type F, indicating probably 
 a somewhat brighter star than ours. This difference 
 in the results found above is not inconsistent with 
 the parallax found by Hussey. Indeed, it seems 
 probable that his result cannot be far from the 
 truth. A comparison with Procyon is also, I find, 
 confirmatory of Hussey 's result. 
 
 For the famous binary star y Virginis, which has 
 also a spectrum of the F type, Lewis finds a period 
 of 182 years. Numerous orbits have been computed 
 for this remarkable pair, but the orbit found by 
 Lewis seems to be the best. From meridian observa- 
 tions Lewis finds that the components are nearly 
 equal in mass, as they are nearly so in light. 
 Assuming a parallax of O'lO second which seems a 
 very probable value Lewis finds that each com- 
 ponent has about nine-tenths of the sun's mass. 
 With this parallax the sun would be reduced to a 
 star of about the 5th magnitude. The photometric 
 magnitude of the star is 2'91. The magnitude of 
 each component would therefore be 3*66. From 
 these data it follows that the light of y Virginis is 
 about 7 times the light of the sun. If of the 
 same surface luminosity and density as the sun, the 
 combined light should, I find, be only T86 times 
 the sun's light, or only a little more than one-fourth 
 
234 ASTRONOMICAL ESSAYS 
 
 of what it actually is. This shows that the surface 
 luminosity of y Virginis is considerably greater than 
 that of the sun. If the components had the same 
 surface luminosity as our sun, let us see what 'their 
 density would be. Each has 3*5 times the sun's light, 
 and the diameter of each would therefore be the 
 square root of 3*5, or 1*87 times the sun's diameter ; 
 and with a mass of 0*9 times the sun's mass, the 
 density would be only P 2 (water = 1). This seems 
 improbable, as it is so much less than the sun's 
 density (1*4). If each had, say, 1/2 times the sun's 
 diameter, we should have a total of (1*2) 2 x 2 = 2*88, 
 as due to the increased surface. This would give a 
 factor of about 2'4 for the surface luminosity, and 
 the density would then be about 0*73, which seems 
 a probable value. 
 
 In these cases of B Equulei and y Virginis, we 
 see that the factor of surface luminosity is probably 
 less than in the case of Sirius, and suggests that 
 Sirius is a brighter body, as its spectrum would seem 
 to indicate. 
 
 Let us now consider the case of the bright star 
 Procyon, which has a spectrum F 5 G, or inter- 
 mediate in character between that of y Virginis and 
 the sun. Its parallax is about 0'325 second, and the 
 mass of the system is therefore, from Dr. See's orbit 
 of the satellite, 3'627 times the sun's mass, that of 
 the bright star being about 3 times the mass of 
 the sun. At the distance indicated by the parallax 
 the sun would, I find, be reduced to a star of 2' 51 
 magnitude, and as the photometric magnitude of 
 Procyon is 0*48, we have the star 2-03 magnitudes, 
 or 6*487 times brighter than the sun. As, however, 
 the mass of Procyon is 3 times the sun's mass, 
 
STELLAR BRIGHTNESS AND DENSITY 235 
 
 the star should be if of the same density and 
 surface luminosity as the sun only 2'08 times 
 brighter than the sun. Hence it follows that 
 
 &*A Q 7 
 
 Procyon is really i^p or 3<1 times bl> ig nter tnan 
 our sun in proportion to its mass. This may be due 
 either to a proportionally larger size, and therefore 
 less density than the sun, or to a greater luminosity 
 of surface. Probably both causes combine to pro- 
 duce the increased brightness, and the result seems 
 to agree well with the star's spectrum, which indi- 
 cates a slightly more luminous sun than ours. 
 
 The binary star 70 Ophiuchi has a spectrum of 
 the second type (K, Pickering), probably indicating 
 a fainter sun than ours. An orbit computed by Dr. 
 See, combined with a parallax of 0'16 second found 
 by Schur, gives a combined mass of 2'94 times the 
 mass of the sun. This parallax would reduce the 
 sun to a star of about 4'05 magnitude, and as 
 the photometric magnitude of 70 Ophiuchi is 4'07> 
 the star is about equal to the sun in brightness. 
 But as the mass is 2*94 times greater, the star should 
 be if exactly comparable with the sun about twice 
 as bright as it actually is. Hence it would follow 
 that the surface luminosity is less than that of the 
 sun, and the spectrum indicates that such is probably 
 the case. 
 
 Let us now consider the case of the "Algol 
 variables." For Algol itself Vogel found from spec- 
 troscopical observations the diameter of the bright 
 star to be 1,074,100 miles, with a mass of four-ninths 
 of the sun's mass, and for the " dark " companion a 
 diameter of 840,600 miles, and a mass of two-ninths 
 of the solar mass. This result was obtained on the 
 
236 ASTRONOMICAL ESSAYS 
 
 assumption that both components are of equal 
 density about one-third that of water. But that 
 a " dark " body of such large size should have the 
 same density as a very bright body like Algol seems 
 highly improbable. The density of the planet 
 Jupiter, which has probably some inherent light of 
 its own, is about T30, and that of Saturn about 0'72. 
 We should therefore expect that a large body like 
 the companion of Algol would have a considerable 
 amount of inherent light or surface luminosity. Let 
 us see what brightness it could have without sensibly 
 affecting the observed light variation of Algol. That 
 is, what is the maximum brightness which the com- 
 panion might have without producing a secondary 
 minimum when hidden behind the disc of the bright 
 star? Chandler finds for Algol a parallax of 0*07 
 second. The sun, if removed to the distance indi- 
 cated by this small parallax, would, I find, be reduced 
 to the light of a star of 5*84 magnitude, and the 
 photometric magnitude of Algol being 2'31, it would 
 be 3'53 magnitudes, or nearly 26 times, brighter than 
 the sun. Let us assume that the companion has 
 this magnitude of 5*84. Then when in the course 
 of its orbital revolution round Algol it is hidden 
 behind the bright star, the normal light of Algol 
 would be reduced by its 27th part. This means that 
 the light of Algol would be diminished by about 
 0*04 magnitude, or from 2*31 to 2*35, a difference 
 which would not be perceptible to the naked eye, 
 and could hardly be detected with certainty by even 
 the most delicate photometer. 
 
 The spectrum of Algol is, according to Pickering, 
 B 8 A, that of Sirius being A. It is therefore nearer 
 to Sirius in character than the stars of the " Orion 
 
STELLAR BRIGHTNESS AND DENSITY 237 
 
 type " (B). Comparing the two stars, and assuming 
 the surface luminosity to be the same, I find a 
 parallax of 0*11 second for Algol. This would reduce 
 the sun to a star of 4*84 magnitude, and if we 
 suppose the companion to Algol to have this bright- 
 ness, then Algol would be over 10 times brighter 
 than the companion, and when the latter was hidden 
 behind the bright star, the light of Algol would be 
 reduced from about 2*31 to 2*41, and even this 
 difference could hardly be determined with certainty. 
 It is therefore quite possible that the companion to 
 Algol may shine as a star of the 5th or 6th magni- 
 tude. It is much too close to Algol to be seen with 
 the largest telescopes, and even the spectroscope 
 would show no trace of its existence. 1 Observations 
 by Plassmann and others seem to show some fluctua- 
 tions in the light of Algol during its so-called 
 " normal " period, but to a greater extent than indi- 
 cated by the above computations. It would seem 
 probable, therefore, that the companion has some 
 inherent light of its own, and is not quite a " dark 
 body." Assuming a parallax of 0*07 second, I find 
 that the surface luminosity of Algol itself would be 
 about 17 times greater than that of the sun. 
 
 In the Algol system the components are separated 
 by a distance of over two millions of miles (between 
 their surfaces}, but in some of the " Algol variables " 
 the components are supposed to revolve in contact, 
 or nearly so. They have also both the components 
 bright. Examples of this type of variation are 
 ft Lyrse, U Pegasi, V Puppis, X Carinse, and RR Cen- 
 tauri. The characteristics of the light fluctuations 
 
 1 Astrophysical Journal, May, 1904. Paper on 8 Orionis, by J. 
 Hartman. 
 
238 ASTRONOMICAL ESSAYS 
 
 in these cases are, according to Dr. A. W. Roberts, 1 
 as follows : (1) " continuous variation, indicating 
 that the component stars are in contact," and (2) 
 two maxima and two minima, showing that the 
 components are both bright bodies. The variation 
 of /? Lyrae is well known. It is not usually con- 
 sidered as an Algol variable, but it now seems pro- 
 bable that it should be included in that type. Myers 
 finds that j3 Lyrse probably consists of tw^o ellipsoidal 
 components revolving nearly in contact, the mass of 
 the larger component being 21 times the mass of the 
 sun, and that of the smaller 9| times the sun's mass. 
 He thinks the mean density of the system " is com- 
 parable with atmospheric density ; " that is, that 
 they are "in a nebulous condition." If this con- 
 clusion is correct, the diameter of the bodies com- 
 posing the system of fi Lyrse must be enormous. 
 Taking the density of atmospheric air as 814 times 
 less than water, I find that the larger component 
 would have a diameter of about 25 millions of miles, 
 and the smaller about 19 millions. The parallax 
 of J3 Lyrse has not been ascertained, but supposing 
 it to be about one-hundredth of a second of arc, the 
 sun would be reduced to a star of about the 10th 
 magnitude. The maximum brightness of /3 Lyrse is 
 about 3*5. It would therefore be with the assumed 
 parallax 6| magnitudes, or about 400 times brighter 
 than the sun. From the diameter found above, the 
 combined surfaces of the two components would be 
 1332 times the sun's surface. Hence the intrinsic 
 luminosity of their surface would be less than one- 
 third of that of the sun. This agrees with Homer 
 Lane's law, by which a gaseous mass gains in heat 
 1 Monthly Notices, K.A.S., June, 1903. 
 
STELLAR BRIGHTNESS AND DENSITY 239 
 
 as it consolidates, and /? Lyrse is probably in a very 
 early stage of stellar evolution. If the parallax is 
 larger than that assumed above, the surface lumi- 
 nosity would be still smaller. 
 
 Another remarkable star is the southern "Algol 
 variable " V Puppis (Lacaille 3105). Both com- 
 ponents are bright bodies. The spectrum of the 
 brighter component is, according to Pickering, of 
 the " Orion type " B 1 A, and that of the fainter 
 B 3 A. The period of light variation is T454 days. 
 The spectroscopic observations show that the relative 
 velocity is about 380 miles a second. The combined 
 mass of the system is therefore about 70 times the 
 sun's mass. As the star is variable, the plane of 
 the orbit must necessarily pass through the earth, 
 and the accuracy of this result for the mass is there- 
 fore certain. This enormous mass and the star's 
 magnitude about 4*50 shows that it is probably 
 at an enormous distance from the earth. As it lies 
 in or near the Milky Way, it may possibly be one of 
 the larger stars of the Galaxy. Dr. A. W. Roberts 
 finds that the components " revolve round one 
 another in actual contact." The star is thus a very 
 remarkable and interesting object. Its mass is very 
 large. Its density is probably small, and the intrinsic 
 luminosity of its surface very high. Its distance 
 from the earth is very great. Its orbital velocity is 
 very rapid, and the variation of light is small and 
 very regular. It is, in fact, one of the most remark 
 able objects in the heavens. 
 
CHAPTER XVI 
 
 THE SIZE OP STELLAR SYSTEMS 
 
 AMONG the numerous binary or revolving double 
 stars now known to exist in the heavens, there are 
 about 50 for which satisfactory orbits have been 
 computed. That is, the apparent dimensions of the 
 real orbit are accurately known. Unless, however, 
 we can find the star's distance from the earth, we 
 cannot calculate the real dimensions of the stellar 
 system. For some of these binary stars, however, a 
 satisfactory " parallax " has been found, and for these 
 we can compute the real size of the system. Let us 
 consider those binary stars which have the most 
 trustworthy parallaxes. 
 
 a Centauri. For this fine binary star the nearest 
 star to the earth a good orbit has been computed 
 by Dr. See. This gives a period of 81*1 years, an 
 apparent semi-axis major of 17 "7 seconds, and an 
 eccentricity of 0*528. A satisfactory parallax of 
 0*75 second has been found by Sir David Gill. We 
 have thus all the necessary data for computing the 
 real dimensions of this interesting system. Calling 
 the apparent semi-axis major a, the parallax p, and 
 s the real length of the semi- axis major in terms of 
 the sun's mean distance from the earth, taken as 
 
 unity, we have s = = 23-6, or a little more than 
 
 240 
 
THE SIZE OF STELLAR SYSTEMS 241 
 
 the distance of Uranus from the sun. To find the 
 greatest and least distances between the components, 
 let the eccentricity = e. Then the maximum dis- 
 tance = s(l 4- e)> and the minimum distance = s(l e). 
 This gives for a Centauri the maximum distance 
 = 36-06, and the minimum distance = 11'14. The 
 components were at their minimum distance in the 
 year 1875, that is, the minimum distance in the real 
 orbit ; the minimum distance in the apparent orbit 
 occurred in 1877. The maximum distance in the real 
 orbit will take place in the year 1918, but in the 
 apparent orbit this occurred in 1897. Calling the 
 brighter component A, and the fainter B, the photo- 
 metric measures at Harvard Observatory make the 
 " magnitude " of A 0-36, and that of B 1*61. Now, 
 knowing the distance between the components, and 
 the star's distance from the earth, we can easily cal- 
 culate the apparent brightness of each component as 
 seen from the other. Making the necessary calcula- 
 tions, I find that the brightness of B, as seen from A, 
 will vary from 17*8 to 20'35 magnitudes, and that 
 of A, as seen from B, from 19 to 21*63. As the 
 sun's stellar magnitude is about 26-5, it follows that 
 the components of a Centauri, as seen from each other, 
 will shine as small suns. It is sometimes stated that 
 each component would only appear as a very bright 
 star, as seen from the other. This is to a certain 
 extent true, as the mean brightness would be about 
 the same as the brightness of the sun as seen from 
 Neptune. But still they would be incomparably 
 brighter than any of the fixed stars. The light of B, 
 as seen from A, would, even at its minimum, be about 
 200 times the light of full moonlight on the earth. 
 The parallax combined with the period and mean 
 
 B 
 
242 ASTRONOMICAL ESSAYS 
 
 distance between the components gives a combined 
 mass of just twice the sun's mass, and as measures 
 have shown that the components are practically 
 equal in mass, each of them has a mass equal to 
 that of our sun. The spectrum of the brighter com- 
 ponent is similar to that of the sun (G), and it is 
 probably almost a duplicate of our sun. The spectrum 
 of the fainter component is K 5 M, or between the 
 second and third types of stellar spectra, and as it 
 is 1*25 magnitude, or over 3 times fainter than the 
 primary star, its light is much less in proportion to 
 its mass. It is therefore probably in a different 
 stage of its evolutionary history, although both 
 components are in all probability of the same 
 chronological age. 
 
 Sirius. The parallax of this brilliant star the 
 brightest star in the heavens has also been satis- 
 factorily determined by Dr. Gill, who finds 0-37 second, 
 or a distance of 8-8 years' journey for light. A new 
 orbit for the satellite has recently been computed by 
 Dr. Doberck, who finds a period of 49'49 years, with 
 a = 7'513 seconds and e = 0'5871. From these data 
 the combined mass of the system is 3*415 times the 
 sun's mass, and the mean distance between the com- 
 ponents 20*3 times the sun's mean distance from the 
 earth. Owing, however, to the large eccentricity of 
 the orbit, this distance will vary from 8*4 to 32'2. 
 Taking the brightness of the satellite as 10th 
 magnitude, I find that its brightness, as seen from 
 Sirius, will vary from 11 to 14 magnitude, its 
 mean brightness being therefore about the same as 
 that of full moonlight on the earth. Sirius seen from 
 the satellite will, I find, vary in brightness from 22 
 to 25*7, or from ^ of sunlight on earth to f 
 
THE SIZE OF STELLAR SYSTEMS 243 
 
 sunlight. Although Sirius is a much brighter sun 
 than ours, its great distance from the satellite will 
 reduce its brightness considerably. 
 
 70 Ophiuchi. Dr. See finds a period of 88*4 years, 
 with a 4'55 seconds and e = 0*500. A parallax 
 of 0*16 second was found by Schur. With these 
 data the mean distance is 28*4, and the greatest and 
 least distances 42*6 and 14'2 respectively. The magni- 
 tudes of the components being about 4 and 6, I 
 find that B, seen from A, would vary in brightness 
 from 16*4 to 18*8 magnitude ; and A, seen from B, 
 from 18*4 to 20*8. The mass of the system, from 
 the above data, would be nearly 3 times the mass of 
 the sun. The spectrum is K, and the intrinsic lumi- 
 nosity seems to be small in proportion to the mass. 
 
 S Equulei. Period 5'7 years, a = 0*28 second, and 
 e = 0*46 (Hussey). From spectroscopic measures 
 Hussey finds a parallax of 0*071 second. From these 
 data the mean distance between the components is 
 4 times the sun's mean distance from the earth, 
 the distance varying from 2*16 to 5*84. Taking the 
 magnitudes as 5 and 5*5, 1 find that the brightness of 
 B, as seen from A, would vary from 23*0 to 25*1, 
 and that of A, seen from B, from -23*5 to -25*6. 
 Each component would therefore appear as a small 
 sun as seen from the other. The sun placed at the 
 distance indicated by the above parallax would shine 
 as a star of about 5*8 magnitude, the combined light 
 of the components of S Equulei being 4*61. Hussey 
 finds the mass of the system to be 1*89 times the 
 sun's mass. The spectrum is F, and the intrinsic 
 luminosity somewhat higher than that of our sun. 
 The star is also a spectroscopic binary, so it is really 
 a triple star. 
 
244 ASTRONOMICAL ESSAYS 
 
 y Virginis. Belopolsky found by the spectro- 
 scopic method a parallax of 0*051 second. Dr. See 
 finds a period of 194 years, with a = 3*99 seconds 
 and e = 0*897. This would make the mean distance 
 between the components 78 times the sun's mean 
 distance from the earth, but owing to the great 
 eccentricity of the orbit, the distance varies from 8 to 
 148. The components are nearly equal in brightness. 
 Taking the magnitude of each at 3*65, I find that the 
 brightness of each component as seen from the other 
 will vary from 18'53 to 24*85, or over 6 magni- 
 tudes. The mass of the system, according to 
 Belopolsky, is 15 times the sun's mass. The spectrum 
 is F, and the intrinsic brightness considerably 
 greater than that of our sun. 
 
 With reference to the " spectroscopic binaries," 
 most of them seem to be constructed on a much 
 smaller scale than the visual binary systems. As 
 the spectroscopic measures give the actual orbital 
 velocities in miles, the real dimensions of the system 
 can be calculated, although their distance from the 
 earth remains unknown. Some of these remarkable 
 systems are comparatively quite small. Thus in 
 j3 Aurigae the distance between the components 
 is about 8 millions of miles. In the variable star 
 Algol the distance between the components from 
 centre to centre is about 3J millions of miles, and 
 in Geminorum the mean distance is only a little 
 over one million of miles. But in other cases the 
 distance is greater, and probably there are stellar 
 systems of all dimensions from a few hundred 
 thousand miles to many millions. 
 
CHAPTER XVII 
 
 THE SATELLITE OP SIRIUS 
 
 THE brilliant star Sirius the brightest in the heavens 
 has a faint companion of about the 10th magni- 
 tude, that is, so faint that it would be quite invisible 
 in a binocular field-glass even if it shone alone on a 
 dark sky. But placed as it is, close to a brilliant star 
 like Sirius, it requires a large telescope to see it at 
 all. Since its discovery by Alvan Clark the famous 
 American optician in 1862, it has been carefully 
 observed and measured, and the numerous measures 
 of position now accumulated show that it is re- 
 volving round the bright star in a period of about 
 50 years. From its orbit, and the distance of 
 Sirius from the earth found by Sir David Gill, it 
 has been computed that, faint as it is, the satellite 
 has a mass equal to that of our sun. I find that if 
 the sun were placed at the distance of Sirius, its 
 light would be reduced to that of a star only a little 
 below the 2nd magnitude. In other words, the 
 sun is about 1\ magnitudes brighter than the small 
 star. This means that the light emitted by the sun 
 is a thousand times that emitted by the faint com- 
 panion of Sirius. This fact is so anomalous that it 
 seems to deserve more consideration than it has 
 hitherto received. 
 
 The faintness of this small star must be due 
 245 
 
246 ASTRONOMICAL ESSAYS 
 
 either to its small size that is, small volume or to its 
 small luminosity of surface. I will proceed to show 
 that a small volume is inadmissible, and that a small 
 luminosity of surface is the only tenable hypothesis. 
 I have shown elsewhere that the satellite of Sirius 
 could not possibly shine merely by light reflected 
 from the bright star. 1 For in that case it would be 
 absolutely invisible in the largest telescopes hitherto 
 Constructed. 
 
 If its faintness were merely due to its small size, 
 its surface luminosity being equal to that of our 
 sun, the sun's diameter should be the square root 
 of 1000, or 31J times the diameter of the faint star, 
 in order to produce the observed difference of light. 
 But on this hypothesis the sun would have a volume 
 31,500 times the volume of the star, and, as the 
 density of a body is inversely proportional to its 
 volume, we should have the density of the Sirian 
 satellite over 44,000 times that of water (the sun's 
 density being 1*4). This is, of course, entirely out of 
 the question, and the result shows at once that the 
 luminosity of the satellite's surface cannot possibly 
 be comparable with that of the sun. Its surface 
 must be enormously less luminous than the sun's 
 surface. 
 
 Let us consider what luminosity of surface the 
 satellite could have consistently with its having a 
 comparatively low density. As it shines by inherent 
 light, it must be very hot, and hence its density 
 cannot be very high. If the earth were intensely 
 heated so as to become self-luminous, it would ex- 
 pand in volume, and therefore diminish in density. 
 Suppose it expanded to twice its present diameter, 
 1 " Studies in Astronomy," p. 113. 
 
THE SATELLITE OF SIRIUS 247 
 
 then its volume would be increased 8 times, and 
 its density would diminish from 5 '53 its present 
 value to 0*69, or about the density of the planet 
 Saturn. If we assume that the satellite of Sirius 
 has a surface luminosity of, say, 0*01 of the sun's 
 luminosity or about the same as that of the binary 
 companion of 40 (o 2 ) Eridani we have surface of sun 
 10 times the surface of the star. In this case the 
 sun would have 31*63 times the volume, and the 
 density of the star would be 44*28 (water = 1), a 
 value which also seems inadmissible, as there is no 
 known substance with nearly so high a density. 
 Further, if it could possibly have so high a density, 
 it would certainly be a dark body, and not self- 
 luminous. Assuming a luminosity of 0*002 of the 
 sun's luminosity, the density would be 3*96, which 
 seems an improbably high value for a self-luminous 
 body. 
 
 If we assume a luminosity of 0*0015, the density 
 of the satellite becomes 2*57, a value which seems to 
 be still too high. A luminosity of 0*001 would of 
 course make the satellite of the same volume and 
 density as the sun, but if it had the same density 
 as the sun, there seems to be no reason why its 
 luminosity should be so small. 
 
 We may therefore conclude, I think, with great 
 probability, and almost certainty, that the lumi- 
 nosity of the Sirian satellite does not exceed 0*0015 
 of that of the sun. But even this small luminosity 
 would give a considerable amount of light. As- 
 suming that sunlight is about 600,000 times moon- 
 light, we have the luminosity of the satellite equal 
 to 900 times that of the moon's surface. This is, 
 however, very small for a body shining by inherent 
 
248 ASTRONOMICAL ESSAYS 
 
 light, and suggests that the satellite has cooled down 
 considerably, and that it is probably far advanced 
 on the road to the total extinction of its light. It 
 is unfortunate that its spectrum cannot be observed, 
 as it should be a most interesting one. But perhaps 
 this may be possible in the future with a gigantic 
 reflecting telescope. It is, of course, possible that the 
 satellite may be a large globe of very low density 
 and small luminosity, like the gaseous nebulae. In 
 that case we should expect to find a spectrum of the 
 nebular type, that is, one with bright lines on a dark 
 ground. But it is said to have a reddish colour, 
 which points rather to its being a cooled-down sun, 
 in which case it would probably show a banded 
 spectrum of the third or fourth type. From these 
 considerations it seems that the satellite must have 
 either a comparatively high density or else a low 
 one, and its spectrum would probably decide the 
 question. 
 
 In the case of the companion to Procyon, which is 
 a fainter star, and has a smaller mass than the Siriaii 
 satellite, Mr. Lewis noted in March and April, 1898, 
 that " the appearance of the companion to Procyon 
 was not so like a star as that of Sirius, and that 
 while the wire of the micrometer totally eclipsed 
 the companion of Sirius, the companion of Procyon 
 was seen on both sides of the wire." J This is very 
 suggestive, and seems to show that the faint satellite 
 of Procyon is probably a small gaseous nebula. Its 
 colour is said to be " purplish," which perhaps points 
 to the same conclusion. 
 
 1 Monthly Notices, R.A.S., April, 1898. 
 
CHAPTER XVIII 
 
 " HOLES IN THE HEAVENS " 
 " Sed patet immiani et vasto respectat hiatu." l 
 
 THE Milky Way is not of uniform brightness. There 
 are many dark spots in it which seem to be openings 
 or holes through that wonderful zone of stars. These 
 dark spots, or " coal sacks," as they are also called, 
 seem to have been first noticed by Pinzon in 1499. 
 These were also described by Lacaille in 1763, and 
 Sir John Herschel mentions several of these curious 
 spots in his " Cape Observations." 
 
 The most remarkable of these spots is the well- 
 known "coal sack" near the Southern Cross. It is 
 of a roughly oval or " pear-shaped " form, about 8 
 in length by 5 in width, and forms a conspicuous 
 object in the sky of the southern hemisphere. It is 
 completely surrounded by the nebulous light of the 
 Milky Way, which is here rather bright. The bright 
 stars a, and fi Crucis the brightest stars of the 
 Southern Cross nearly touch its north-western 
 border, and the star Muscse lies close to its south- 
 eastern edge. It contains only one small star visible 
 to the naked eye within its boundaries. With refer- 
 ence to its northern border, Sir John Herschel says, 
 " The transition from rich Milky Way to almost com- 
 plete darkness is here very sudden." It is, however, 
 
 1 Lucretius, " De Eerum Natura," v. 373. 
 249 
 
250 ASTRONOMICAL ESSAYS 
 
 by no means devoid of faint stars. On a photograph 
 taken by Mr. H. C. Russell at the Sydney Observatory 
 in 1891, numerous small stars are visible, but there 
 are several spots which seem to be completely void 
 of stars and absolutely black. One of these re- 
 markable holes is near fi Crucis, and another near 
 a Crucis. 
 
 There are other remarkable " coal sacks " in the 
 Milky Way. A long, narrow dark spot runs from 
 a Centauri for several degrees towards the north- 
 east. There are several in Scorpio ; one of larger size 
 between /? and e Cygni, and one south of a Cygni. 
 
 Examined with a telescope, the Milky Way shows 
 many examples of small "coal sacks," and some 
 may be seen on very clear nights with even a good 
 binocular field-glass. One night, when Sir William 
 Herschel was examining a part of the Milky Way 
 closely east of the globular cluster 80 Messier, which 
 lies between v and o- Scorpii, he suddenly exclaimed 
 to his sister, the famous Caroline Herschel, "Hier 
 ist wahrhaftig ein Loch im Himmel " (" Here, truly, 
 is a hole in the heavens"). It was an absolutely 
 black spot about 4 in width, perfectly free from 
 any stars, and especially remarkable owing to its 
 proximity to one of the richest globular clusters in 
 the heavens. 
 
 Closely south of Herschel's dark "hole" just 
 mentioned, Professor Barnard has photographed a 
 great nebulous surrounding the stars p Ophiuchi 
 and 22 Scorpii. 1 This photograph shows several 
 dark lanes in what seems to be at least a com- 
 paratively thin sheet of stars, and this distinguished 
 
 1 The rings round the brighter stars in the photograph are due 
 to a photographic effect, and do not exist in the sky. 
 
"HOLES IN THE HEAVENS" 251 
 
 astronomer thinks "it is certain that these stars 
 are at the same distance as the nebula, for they form 
 part of it." With reference to the Milky Way in 
 general, he thinks that the stars composing it are 
 " comparatively very small bodies, and that they 
 consequently differ vastly, in point of size at least, 
 from the ordinary stars of the sky." If this be so 
 and the evidence seems to point in this direction it 
 would follow that their distance from the earth may 
 not be so great as their faintness would lead us to 
 imagine. In his " Cape Observations " Sir John Her- 
 schel gives a list of 49 spots in the southern hemi- 
 sphere " totally devoid of any perceptible star." But 
 probably photography will reveal some faint ones. 
 
 Close to the star 6 Ophiuchi is a " dark chasm 
 which passes south and west of that star," and there 
 are other dark spots or holes in the vicinity clearly 
 visible on a photograph taken by Professor Barnard 
 at the Lick Observatory. Another small black spot 
 was observed by Barnard a little north-west of the 
 star 7 Sagittarii. This seems to have been previously 
 seen by Trouvelot, who says, " C'est comme un sac a 
 charbon en miniature, ou une ouverture de Voie 
 lactee a travers laquelle la vue penetre au dela de 
 ce grand assemblage d'etoiles.' 
 
 A little south-east of a Cephei, a photograph by 
 Barnard shows a ring of nebulous light with a com- 
 paratively dark interior, at least the stratum of 
 stars filling the ring seems pierced by several holes. 
 
 The " key-hole " opening in the great nebula 
 surrounding the variable star rj Argus is a remark- 
 able feature of that wonderful nebula. A little 
 south of this hole there is a " kidney bean " shaped 
 opening shown on Sir John Herschel's drawing in 
 
252 ASTRONO MICAL ESSAYS 
 
 the " Cape Observations." This opening is visible on 
 a photograph taken by Sir David Gill in March, 1892. 
 The photograph confirms the accuracy of the draw- 
 ing, and shows that the opening is in all probability 
 a real hole through the surrounding nebulous matter. 
 
 In the region round the star 12 Monocerotis there 
 is a remarkable nebula of irregular shape, somewhat 
 resembling in its general character the great nebula 
 in the " sword " of Orion. Dr. Roberts, describing a 
 photograph he took of this nebula, says, " Some re- 
 markable tortuous rifts meander through the nebu- 
 losity on the north preceding half of the nebula ; 
 their margins are sharp and well defined in the midst 
 of dense nebulosity. They are as clearly cut as we 
 see the canons of great rivers, but their width may 
 be millions of miles, for we have no reason to assume 
 that the nebula is nearer to the earth than the stars. 
 It is indeed possible that the stars which dot the 
 surface are nearer to us than the nebula." l 
 
 About 3 north-west of the star Canis Majoris 
 is another nebula of irregular form. Dr. Roberts 
 says that the star D.M. 1848 "is on the margin 
 of a dark sinuous vacancy or rift in the nebula, 
 through which we see into the starless vacancy 
 of space beyond it." This opening closely resembles 
 the "key-hole" opening in the great nebula in 
 Argo. Dr. Roberts adds, " These vacancies are most 
 conspicuously seen where the surrounding nebu- 
 losity is dense, though they are also visible in some 
 parts where it is relatively faint. The margins of 
 the vacancies are often sharply defined and sug- 
 gestive of the idea that in consequence of some 
 internal strain, operating from opposite directions, 
 1 Knowledge, June 1, 1899. 
 
"HOLES IN THE HEAVENS 253 
 
 the nebula was rent asunder, and the parts separated 
 from each other." l 
 
 In another nebula in Monoceros, photographed by 
 Dr. Roberts, a little west of the triple star 15 Mono- 
 cerotis, there is a remarkable vacuity or hole. Dr. 
 Roberts calls it " a dark tortuous rift," and says the 
 rifts prove that the nebulae are not globular, but are 
 like clouds with relatively small depths, and that we 
 can see through them into the darkness of space 
 beyond." There are also very noticeable areas 
 devoid of stars in the region surrounding this nebula. 
 
 A cluster of small stars in Cygnus (N.G.C. 6819) 
 was described by Lord Rosse as " full of holes," and 
 another (N.G.C. 2548) as containing " dark lines and 
 openings." 
 
 On July 12, 1891, Dr. Max Wolf, of the Astro- 
 physical Observatory of Heidelberg, discovered three 
 dark markings close together in the Milky Way, 
 about 1J west of the star y Aquilse. He calls them 
 "the triple caves," and on his photographs they 
 certainly present a very remarkable appearance. 
 Closely east of the same star a photograph taken 
 by Professor Barnard shows some curiously shaped 
 dark markings, which seem to be openings through 
 the stratum of stars composing the Milky Way in 
 this region. 
 
 On a photograph by Max Wolf of the region near 
 Cygni there is a remarkable black hole, and some 
 smaller ones. 
 
 The question naturally suggests itself, what is 
 
 the real nature of these curious black spots ? Some 
 
 astronomers have suggested that they are due to 
 
 masses of cooled-down, or partially cooled-down, 
 
 1 Knowledge, November 1, 1899. 
 
254 ASTRONOMICAL ESSAYS 
 
 matter which absorb the light of the stars behind 
 them. The term " hole," which I have used in the 
 present chapter, implies that my own view is 
 that they are really holes or openings through 
 regions of stars or nebulous matter, and in this view 
 of the matter I am supported by the opinion of 
 several astronomers, as some of the extracts quoted 
 above will show. Photographs of the great " coal 
 sack " near the Southern Cross prove conclusively, I 
 think, that the darkness of this remarkable spot is 
 due to a real paucity of stars compared with the 
 richness of the surrounding regions, and probably 
 the same thing is true of all the other dark spots 
 in the Milky Way. We have really no evidence of 
 the existence of dark bodies in space. Professor 
 Newcomb thinks that there is probably little or 110 
 extinction due to dark bodies, and he says, " We 
 may say with certainty that dark bodies are not so 
 numerous as to cut off any important part of the 
 light from the stars of the Milky Way, because if 
 they did, the latter would not be so clearly seen as 
 it is. Since we have reason to believe that the Milky 
 Way comprises the more distant stars of our 
 system, we may feel fairly confident that not much 
 light can be cut off by dark bodies from the most 
 distant regions to which our telescopes can pene- 
 trate. Up to this distance we see the stars just as 
 they are." l The companions of some of the Algol 
 variables are usually spoken of as "dark bodies," 
 but I have shown elsewhere that we have no reason 
 to think that they are really dark. The companion 
 of Algol, for example, may be a star of the 5th 
 magnitude, and yet be quite invisible to us, as neither 
 1 Harper's Magazine, October, 1904. 
 
PLATE 2. GREAT NEBULA NEAR p OPHIUCHI. 
 From a Photograph by Professor E. E. Barnard, YerJces Observatory. 
 
"HOLES IN THE HEAVENS" 255 
 
 telescope nor spectroscope would show any trace of 
 its existence. The little evidence we have tends to 
 show that the satellite of Algol is not a dark body. 
 The idea of " dark bodies " seems to have been based 
 on the existence of this eclipsing satellite ; but it 
 has been recently found that a difference of bright- 
 ness of two magnitudes between the components of 
 a spectroscopic binary would be quite sufficient to 
 obliterate the spectrum of the fainter star. Dark 
 bodies may exist in space, and probably do, but as 
 yet we have no positive evidence of their existence. 
 The " holes in the heavens " are, I think, real, and 
 " dark " companions of Algol variables have pro- 
 bably no existence except in the imagination of some 
 astronomical writers. 
 
 It has been stated by several writers that the 
 existence of these " holes " indicates that the Milky 
 Way has, in these parts, a small extension in the 
 line of sight, or, in other words, that it forms a com- 
 paratively thin stratum of stars. Sir John Herschel 
 says, " Where we see, as in the coal sack, a sharply 
 denned oval space free from stars, insulated in the 
 midst of a uniform band of not much more than 
 twice its breadth, it would seem much less probable 
 that a conical or tubular hollow traverses the whole 
 of a starry stratum, continuously extended from the 
 eye outwards, than that a distant mass of compara- 
 tively moderate thickness should be simply perfor- 
 ated from side to side, or that an oval vacuity should 
 be seen foreshortened in a distant foreshortened 
 area, not really exceeding two or three times its 
 own breadth." 1 This conclusion, which seems to 
 me correct, is challenged by Professor Seeliger, who 
 1 " Outlines of Astronomy," 10th edition, p. 574. 
 
256 ASTRONOMICAL ESSAYS 
 
 shows that, according to the Law of Probability, 
 " the occurrence in the Milky Way of dark places in 
 the midst of stellar accumulations is indeed very 
 improbable, but in every case the probability remains 
 just as slight if we compress the same number of 
 stars into a smaller space, if this covers the same 
 portions of the heavens as before." x But, if I 
 understand Sir John Herschel's remark correctly, 
 he intended to imply that " in the thick and thin 
 portions of the Milky Way zone the stars are sup- 
 posed to be uniformly distributed " 2 in both cases ; 
 and it seems evident on this assumption that the 
 occurrence of dark spots in the Galaxy would be 
 more probable where the Milky Way has a small 
 extension in the line of sight than in other places 
 where the thickness may be considerably greater. 
 
 The cause of these " holes " must, I think, be 
 looked for in the influence of some " clustering 
 power" as Sir William Herschel termed it which 
 tends to draw the stars away from certain parts 
 and accumulate them in others. The existence of 
 globular and other clusters close to dark and com- 
 paratively starless spots seems very suggestive in 
 this connection. If these dark spots were due to 
 intervening dark bodies, we should expect to find 
 them scattered indifferently in rich and poor regions 
 of the Milky Way, and there seems to be no reason 
 why they should be so often associated with rich 
 regions of the Galaxy. 
 
 1 Astrophysical Journal, vol. 12 (1900), p. 377. The italics are 
 Seeliger's. 
 
 2 That is, the same number of stars per unit of space volume. 
 
PLATE 3. THE MILKY WAY BOUND OPHIUCHI. 
 From a Photograph by Professor E. E. Barnard, Terkes Observatory. 
 
CHAPTER XIX 
 
 THE MAGELLANIC CLOUDS 
 
 THE Magellanic clouds are two spots of nebulous 
 light of roughly circular form in the southern 
 hemisphere, somewhat resembling in appearance 
 portions of the Milky Way, but quite unconnected 
 with the Galaxy. They seem to have been first 
 described by the famous navigator Magellan, about 
 the year 1520, and hence their name. But the larger 
 of the two was also mentioned by Anghiera in 
 1515, and by Corsali in a work published in Venice 
 in 1563. They are included by Schiller (1627) in 
 a list of stars in the southern hemisphere. Accord- 
 ing to Houzeau, Magellan's attention was directed 
 to these celestial " clouds " by the Indians of South 
 America. The natives of Patagonia thought that 
 these luminous spots were composed of the lightest 
 feathers of the ostriches killed in the chase by their 
 ancestors. 1 Houzeau also states on the authority 
 of Ideler that the larger cloud was seen by the 
 Persian astronomer Al-Sufi in the tenth century 
 from the south of Arabia and the Red Sea. But 
 this seems doubtful, at least I can find no mention 
 of it in Al-Sufi's " Description of the Fixed Stars." 
 It could not possibly have been seen by him from 
 
 1 Prichard, " Physical History of Mankind," third edition, vol. 
 v. p. 490, quoted by Houzeau. 
 
 257 S 
 
258 ASTRONOMICAL ESSAYS 
 
 his station in Persia (Schiraz), as it was below the 
 horizon of the place. These luminous spots were 
 called by the Portuguese the " clouds of Magellan," 
 and by the Dutch the " clouds of the Cape." They 
 were also called "sacks of coal" by the early 
 navigators, but the term " coal sack " is now usually 
 applied to the dark spots or openings visible in 
 various parts of the Milky Way. 
 
 The Magellanic clouds are also called nubeculcv, 
 the larger cloud being known as the nubecula major, 
 and the smaller the nubecula minor. According to 
 Houzeau the smaller cloud is not very noticeable 
 to the naked eye, and its brightness scarcely reaches 
 that of a 6th magnitude star. The larger cloud is 
 much brighter, and about equal in brightness to 
 that of a star of 5-6 magnitude. The larger cloud 
 lies partly in the constellation Dorado and partly 
 in Mensa. It extends from about R.A. 4 h 40 m to R.A. 
 6 h O m , and lies between 66 and 72 south declination. 
 The smaller cloud lies partly in Toucan and partly 
 in Hydrus. It is much smaller in size, and its limits 
 are about R.A. O h 28 m and l h 15 m , and 72 to 75 south 
 declination. 
 
 The nubeculce were carefully examined by Sir 
 John Herschel during his residence at the Cape of 
 Good Hope in the years 1834 to 1838, and he gives 
 an account of his observations in his interesting 
 and valuable volume usually known as the " Cape 
 Observations." He determined the position of 919 
 stars, nebulae, and clusters in the nubecula major, 
 and 244 objects in the nubecula minor. He describes 
 the larger cloud as consisting " partly of large tracts 
 and ill-defined patches of irresolvable nebula and 
 nebulosity in every stage of resolution up to 
 
THE MAGELLANIC CLOUDS 259 
 
 perfectly resolved stars like the Milky Way, as also 
 of regular and irregular nebulae properly so called, 
 of globular clusters in every stage of resolvability, 
 and of clustering groups sufficiently insulated and 
 condensed to come under the designation of * clusters 
 of stars ' in the sense of which that expression is 
 always to be understood in reading my father's or 
 my own catalogues." It covers an area of about 
 42 square degrees, and contains about 278 clusters 
 and nebulae. It is thus very rich in these objects, 
 and Sir John Herschel says, " Even the most crowded 
 parts of the stratum of Virgo, in the wing of that 
 constellation, or in Coma Berenices, offer nothing 
 aproaching to it. It is evident from this, and from 
 the intermixture of stars and unresolved nebulosity, 
 which probably might be resolved with a higher 
 optical power, that the nubeculae are to be regarded 
 as systems sui generis, and which have no analogues 
 in our hemisphere." One of the nebulae contained 
 in this extraordinary collection of objects, Sir John 
 Herschel describes as " very bright ; very large ; 
 oval; very gradually pretty much brighter in the 
 middle ; a beautiful nebula ; it has very much 
 resemblance [to the nubecula major itself as seen 
 with the naked eye, but it is far brighter and more 
 impressive in its general aspect as if the nubecula 
 were at least doubled in intensity," and he adds, 
 " And who can say whether in this object, magnified 
 and analyzed by telescopes infinitely superior to 
 what we now possess, there may not exist all the 
 complexity of detail that the nubecula itself presents 
 to our examination ? " 
 
 Among many other remarkable objects contained 
 in the nubecula major, we may mention the great 
 
260 ASTRONOMICAL ESSAYS 
 
 " looped nebula " 30 (Bode) Doradus, of which Sir 
 John Herschel gives a beautiful drawing. He de- 
 scribes it as " one of the most singular and extra- 
 ordinary objects which the heavens present." Near 
 the centre of this nebula is a star of the 9th magni- 
 tude, forming with some fainter stars a small cluster. 
 Immediately south of this is a pear-shaped opening, 
 somewhat similar to the "key-hole" perforation in 
 the great nebula round rj Argus, but of propor- 
 tionately larger dimensions. North of the central 
 star there is a bright nebulous ray like the tail of 
 a comet. Near this is a round hole, and a little 
 further north three plumes like branches diverge 
 from a common nebulous stem. The fainter portions 
 of the surrounding nebulosity seem to be also 
 pierced by similar "coal sacks," features which 
 appear to be characteristic of these irregular-shaped 
 nebulae. Many faint stars are scattered over this 
 nebula, and Sir John Herschel gives a catalogue of 
 these ranging in brightness from the 10th to the 
 17th magnitude. He found the nebulosity to be 
 quite irresolvable into stars, and it is probably 
 gaseous. It covers an area of about one-fifth of a 
 square degree, or about the area of the full moon. 
 Near it are two large and rich clusters. There 
 are many other remarkable nebulae and groups of 
 nebulae in the nubecula major. Sir John Herschel 
 found the zone south of the nubecula "dark and 
 starless." 
 
 The smaller cloud, or nubecula minor, is only 
 about one -fourth the apparent size of the other, 
 and covers an area of about 10 square degrees. It 
 is not connected in any way with the larger cloud, 
 or the Milky Way. To the naked eye it is of apparent 
 
THE MAGELLANIC CLOUDS 261 
 
 uniform brightness. The surrounding regions are 
 remarkably free from stars. Sir John Herschel says, 
 "The access to the Nubecula Minor on all sides is 
 through a desert." Examined with his large reflect- 
 ing telescope, he found it to be "a fine, rich, large 
 cluster of very small stars, 12 ... 18 magnitude, 
 which fills more than many fields, and is broken 
 into many knots, groups, and straggling branches, 
 but the whole (i.e. the whole of the clustering part) 
 is clearly resolved." In addition to the stars, there 
 are numbers of nebulae and clusters. 
 
 Closely preceding (that is, west of) the smaller 
 cloud is the magnificent globular cluster known as 
 47 Toucani. It was discovered by Lacaille in 1752. 
 He described it as " a nebula without stars ; it re- 
 sembles the nucleus of a small comet, and is visible 
 with a telescope of 2 feet in length." It is visible to 
 the naked eye as a star of about 4J magnitude. 
 Sir John Herschel says "it is completely insulated' 11 
 that is, although so close to the nubecula, it has 
 apparently no connection with it. It has a more 
 condensed central portion, which Sir John Herschel 
 saw, of a " pale pinkish or rose colour . . . which 
 contrasts evidently with the white light of the rest." 
 He estimated its diameter at 15 to 20 minutes of arc, 
 with the stars nearly equal, and of 12th to 14th 
 magnitude. On a photograph of this cluster taken 
 by the Harvard observers at Arequipa, Peru, over 
 2000 stars were counted within 11 minutes of arc 
 of the centre of the cluster. Six variable stars 
 have been detected in this cluster at the Harvard 
 Observatory. 
 
 The Magellanic clouds have been photographed 
 by Mr. H. C. Russell at the Sydney Observatory, and 
 
262 ASTRONOMICAL ESSAYS 
 
 also by the Harvard observers at Arequipa. These 
 photographs show that the larger cloud is probably 
 a vast spiral structure, and Professor Pickering thinks 
 that the nebula 30 Doradus, described above, forms 
 the nucleus of the spiral. Mr. Russell calls it " the 
 grandest spiral structure in the heavens." The nube- 
 cula minor also seems to be spiral in structure, but 
 this is not so clearly marked as in the larger cloud. 
 Photographs of the larger cloud taken at Harvard 
 show about 300,000 stars. 
 
 No less than 152 variable stars have been dis- 
 covered in the larger cloud at Harvard on photo- 
 graphic plates taken with the 24 -inch Bruce telescope 
 at Arequipa. The variation of nearly all these is 
 rapid, and about half of them occur in groups. This 
 grouping of variable stars seems to be a characteristic 
 of these curious objects. I have pointed out this 
 peculiarity elsewhere. The new variables are faint, 
 and the amount of light variation usually small. 
 Some of them, however, show larger fluctuations of 
 brightness. A few have a variation of about two 
 magnitudes, and one of about four magnitudes (11J to 
 15|). The period of this variable is probably long. 
 In one curious case near the centre of the " cloud " 
 there are two stars of about the 15th magnitude 
 which seem to be alternately variable, " one is always 
 bright when the other is faint. Period probably 
 short." 1 In the smaller cloud no less than 910 vari- 
 able stars have been detected at Harvard. Professor 
 Pickering says, "It is estimated that the number of 
 stars photographed in the small Magellanic cloud is 
 about 280,000, of which 910, or one in 308, is variable. 
 ... It is very difficult to count the faint stars which 
 1 Harvard College, Observatory Circular, No. 82. 
 
THE MAGELLANIC CLOUDS 263 
 
 crowd the background, on account of their close- 
 ness to one another, and the number is certainly 
 underestimated." l 
 
 It was pointed out by Sir John Herschel that the 
 real form of the Magellanic clouds is, in all proba- 
 bility, roughly globular. For otherwise we should 
 be obliged to consider them as cylindrical, with their 
 axes pointing directly towards the earth. This might 
 be possible in one case, but that two such objects 
 should exist is utterly improbable. Admitting that 
 they are of a spherical form, we have the curious fact 
 that within a comparatively limited space there exist 
 stars, clusters, and nebulse, apparently mixed up, and 
 not differing much in their distance from the earth. 
 If we take the apparent diameter of the larger cloud 
 as 7, we have its real diameter about one-eighth 
 of its distance from the earth, whatever that may 
 be. This would make the distance of the nearest 
 and farthest parts of the " cloud" in the proportion 
 of 15 to 17. 
 
 As to the real dimensions of these wonderful 
 objects it is not easy to form even an approximate 
 estimate. So far as I know, 110 parallax has yet 
 been found for any object contained in the " clouds." 
 Assuming a parallax of one-thousandth of a second of 
 arc for the larger cloud, its distance would be about 
 200 million times the sun's distance from the earth. 
 This would make its real diameter about 25 million 
 times the sun's distance, or about 45 times the distance 
 of Sirius from the earth. This is, of course, an enor- 
 mous diameter, but not improbably so when we con- 
 sider the large number of different objects contained 
 in the cloud. The sun, if removed to the distance 
 1 Astronomische Nachrichten, No. 4032. 
 
264 ASTRONOMICAL ESSAYS 
 
 found above, would be reduced to a star of about 
 the 15th magnitude. The majority of the stars in 
 the cloud are perhaps brighter than this, and as we 
 can hardly suppose that most of them are larger than 
 the sun, we may perhaps conclude that its distance 
 is not greater than supposed above a sufficiently vast 
 distance, however, considering that it implies a light 
 journey of over 3000 years ! 
 
 Taking the apparent diameter of the large cloud 
 at 7, and the number of stars it contains as 300,000, 
 I find that the average distance between the com- 
 ponent stars would be about 9| " light years," or more 
 than the distance of Sirius from the earth. For the 
 smaller cloud I find an average distance of about five 
 years, or a little more than the distance between a 
 Centauri and the earth. 
 
 The association of such diverse objects as stars, 
 clusters, and gaseous nebulae in the Magellanic clouds 
 shows that all these objects can coexist in a com- 
 paratively limited space, and renders it highly pro- 
 bable that all the visible objects in the heavens 
 belong to one and the same sidereal system, and 
 that none of the nebulae can be considered as 
 "external galaxies." If such "island universes" 
 exist in space, they are probably quite invisible 
 from the earth, and may perhaps lie at such a vast 
 distance that no telescope which could ever be con- 
 structed by man would be sufficiently powerful to 
 reveal their existence. Sir John Herschel suggested 
 in a letter to Proctor l that our stellar system " may 
 contain within itself miniatures of itself," and the 
 Magellanic clouds are probably examples of this 
 relation on a large scale. 
 
 1 Knowledge, November, 1885, p. 21. 
 
THE MAGELLANIC CLOUDS 265 
 
 The star A.G.C. 6886 in the large cloud was found 
 at Harvard to have the large proper motion of T28 
 second per annum. As a large proper motion usually 
 indicates comparative proximity to the earth, this 
 star may possibly lie between us and the cloud. 
 During an examination of photographs of the smaller 
 cloud for variable stars, a star of about the 13th 
 magnitude was found at Harvard to have the com- 
 paratively large motion of 0'73 second per annum. 
 Professor Pickering says, " No such motion has here- 
 tofore been detected in so faint a star." This large 
 motion may indicate that this small star is much 
 nearer to the earth than the cloud. Its position for 
 1900 is R.A. l h 6 m 1 s , Dec. S 72 45'5'. 
 
CHAPTER XX 
 
 THE RINGED PLANET 
 
 " Eedeunt saturnia regna." * 
 
 SATURN, the ringed planet, is the most interesting 
 and wonderful member of the solar system. Next 
 to Jupiter, it is the largest of all the planets, and its 
 rings render it quite an unique object. Its mean 
 distance from the sun is about 886 millions of miles, 
 and it revolves round the central luminary in a 
 period of 10,759 days, or 29 years 167 days. The 
 eccentricity of the orbit is 0'0560713, and its inclina- 
 tion to the ecliptic 2 29' 40". According to micro- 
 metrical measures made by Professor Barnard with 
 the great Lick telescope of 36 inches' aperture, the 
 equatorial diameter of the planet is 76,470 miles, and 
 the polar diameter 69,770 miles. It is therefore con- 
 siderably flattened at the poles, and this polar com- 
 pression is very noticeable in a good telescope. The 
 mass of Saturn is about ~^ of the sun's mass. In 
 volume it is over 700 times that of the earth, but in 
 density it is very light, about 0'7 that of water. Its 
 period of rotation on its axis is, according to Professor 
 Asaph Hall, 10 h 14 m 24 s . This is for the equator, but 
 the " north temperature zone " of the planet seems 
 to have a slower rotation, for Denning finds 10 h 38 m , 
 
 1 Virgil, Eclogues, iv. 6. 
 266 
 
THE RINGED PLANET 267 
 
 and Comas Sola 10 h 38 -4 m . A bright spot in the 
 northern hemisphere of the planet observed by 
 Barnard in 1903 gave a period of 10 h 39 m . A similar 
 difference has been observed on Jupiter, but not to 
 so great an extent. The light reflecting power of its 
 surface, or " albedo," as it is termed, is about 0*50 (a 
 perfect reflection = 1), but Mtiller finds 0'72. Like 
 Jupiter, it is probably in a very heated condition, 
 but possibly its surface temperature is not so high as 
 to produce any inherent light of its own. Its surface 
 does not seem to be so disturbed as that of Jupiter. 
 It does not show such well-marked belts and spots 
 and other markings as make the " giant planet " such 
 an interesting object in the telescope. " Belts " are 
 fairly visible in good telescopes, but, according to 
 Denning, well-defined irregular markings are rare on 
 the disc of Saturn. Professor Asaph Hall saw a 
 marking of this kind in December, 1877 ; but Barnard 
 with the 36-ixich Lick telescope, Young with 23-inch, 
 and Hough with 18|-inch refractor, failed to see any 
 spots. Some round spots were observed by Denning 
 and Stanley Williams, but Barnard finds that spots 
 observed with smaller telescopes are not visible with 
 the great Lick telescope ! 
 
 Saturn is probably in an earlier stage of planetary 
 evolution than Jupiter is. Its small density shows 
 this. It is lighter than water, and would float in it. 
 As it must be much denser nearer the centre, its 
 outer surface is probably in the gaseous state. It has 
 been objected that if Jupiter and Saturn were highly 
 heated they would have a reddish colour. But they 
 may be very hot and have some inherent light with- 
 out being actually red hot. It was shown by H. F. 
 Weber in 1888 that filaments of platinum, gold, and 
 
268 ASTRONOMICAL ESSAYS 
 
 iron, when heated, give a " gray glow," which " is 
 evident at temperatures much below that of dull red, 
 namely, 525. Gold gives the gray effect at 417, iron 
 at 377, and platinum at 390 . 1 M. Rogovsky thinks 
 that Saturn, Uranus, and Neptune have high tem- 
 peratures, but " considerably lower than that of 
 Jupiter." He thinks that the great albedo of Saturn 
 found by Mitller " may be caused by the reflection 
 from its clouds being more perfect than that of 
 Jupiter, which is enveloped probably by vapours 
 of denser substances." 2 But Zollner found the albedo 
 of Saturn less than that of Jupiter. 
 
 Owing to Saturn's great distance from the sun, 
 the light and heat received from the central luminary 
 will only amount to about ^ of that received by 
 the earth. The sun would show an apparent 
 diameter of only 3' 22'', and its disc would therefore 
 be hardly visible to the naked eye. Of the planets 
 nearer to the sun than Saturn, the only one visible 
 would be Jupiter, all the others remaining perma- 
 nently invisible, owing to their small size and 
 proximity to the sun. Jupiter would be seen 
 alternately as a morning and evening star, and 
 would show phases similar to those of Venus, but 
 would never form such a brilliant object in the sky 
 of Saturn as he is to us when in opposition, his 
 greatest apparent elongation from the sun being 
 only 33, or about 12 less than that of Venus, as 
 seen from the earth. Uranus would be visible from 
 Saturn as a star of about the 4th magnitude, but 
 Neptune would not be within range of naked-eye 
 vision such as ours. 
 
 1 Nature, February 2, 1888, p. 331. 
 
 2 Astrophysical Journal, vol. 14, p. 249. 
 
THE RINGED PLANET 269 
 
 Saturn is attended by a retinue of 10 satellites. 
 These have been named Mimas, Enceladus, Tethys, 
 Dione, Rhea, Titan, Themis, Hyperion, lapetus, and 
 Phoebe. This is the order of their distance from the 
 planet, Mimas being the nearest and the recently 
 discovered Phoebe the farthest. Titan, the largest 
 of the satellites, was discovered by Huygens in 1655, 
 lapetus by J. D. Cassini in 1671, Rhea also by Cassini 
 in 1672, and Tethys and Dione by the same famous 
 observer in 1684. Mimas and Enceladus were found 
 by Sir William Herschel in 1789, Hyperion by G. P. 
 Bond in America, and independently by Lassell and 
 Dawes in England in 1848, Phoebe by Professor W. H. 
 Pickering in 1898, and Themis also by W. H. Pickering 
 in 1904. The mean distances of the satellites from 
 the centre of Saturn are approximately as follows : 
 Mimas 117,000 miles, Enceladus 157,000, Tethys 
 186,000, Dione 238,000, Rhea 332,000, Titan 771,000, 
 Themis 906,000, Hyperion 934,000, lapetus 2,225,000, 
 and Phcebe about eight millions of miles. Their 
 periods of revolution round Saturn are : Mimas 22 h 37 m , 
 Enceladus l d 3 h 53 m , Tethys l d 21 h 18 m , Dione 2 d 17 h 41 m , 
 Rhea 4 d 12 h 25 m , Titan 15 d 22 h 41 m , Themis 20 d 20 h 24 m , 
 Hyperion 21 d 6 h 39 m , lapetus 79 d 7 h 54 m , and Phoebe 
 about 546J days. With the exception of the two 
 outer satellites, the periods of revolution are less 
 than that of our moon. Their diameters are some- 
 what doubtful. That of Mimas is perhaps about 
 600 miles, Enceladus 800, Tethys 1200, Dione 1100, 
 Rhea 1500, Titan 2500, Themis 38, Hyperion 500, 
 lapetus 2000, and Phcebe perhaps 42 miles. The 
 orbit of Themis is inclined about 39 to the plane of 
 the ecliptic, but the others have a smaller inclination. 
 The orbits are nearly circular with the exception of 
 
270 ASTRONOMICAL ESSAYS 
 
 Hyperion, which has an eccentricity of about 0'12, 
 that of Phoebe 0'22, and of Themis 0'23. Owing to 
 their great distance from the sun and the diminished 
 intensity of sunlight, the combined light of all these 
 moons, as seen from Saturn, would be small. 
 
 Seen from Mimas, the globe of Saturn would 
 appear as a large disc of about 33 in diameter. 
 From Enceladus it would have an apparent diameter 
 of about 25f, from Tethys about 20f , from Dione 
 16, from Rhea 11J, from Titan 5, from Themis and 
 Hyperion about 4, and from lapetus about 1'7. 
 Even from the distant Phcebe, Saturn would show 
 a disc of about 28 minutes, or nearly as large as 
 our moon. 
 
 The new satellite Phoebe was discovered by 
 means of photography. In the year 1888 a photo- 
 graphic search for a ninth satellite of Saturn was 
 made by Professor W. H. Pickering, of the Harvard 
 Observatory, at the station at Arequipa, Peru, with 
 a 13-inch telescope, but without success. The satel- 
 lite was discovered in August, 1898, on plates taken 
 with the 24-inch' Bruce telescope. It appeared as 
 a small star of about 16th magnitude, and its 
 detection among a crowd of small stars was a 
 matter of no small difficulty. The satellite was 
 again photographed in the years 1900, 1902, and 
 1904. The eccentricity of the orbit is, as has been 
 said above, about 0'22, an unusually large eccentricity 
 for a satellite, and about equal to that of the minor 
 planet Eros. The period of revolution is about 
 546^ days, or " about one day short of a year and a 
 half "an unusually long period for a satellite. Its 
 mean distance from Saturn is about 8 millions of 
 miles, but owing to the eccentricity of the orbit, this 
 
THE RINGED PLANET 271 
 
 distance varies from about 6| to 9J millions of miles. 
 The motion in its orbit is retrograde, or in an 
 opposite direction to that of the other satellites. 
 At first sight this would appear inconsistent with 
 Laplace's nebular hypothesis, but Professor Picker- 
 ing points out that very possibly the rotation of 
 Saturn, when in the gaseous state, was originally in 
 a retrograde direction, but that owing to tidal action 
 this retrograde motion was reversed after the 
 formation of Phoebe. From this point of view the 
 retrograde motion of Phoebe would be merely a 
 survival of the original motion of the primitive 
 nebulous mass from which Saturn and his satellites 
 were evolved. The motion of the lately discovered 
 sixth and seventh satellites of Jupiter is, however, 
 direct, and this fact is unfavourable to Professor 
 Pickering's hypothesis. The diameter of Phoebe is 
 probably about 42 miles. Seen from Saturn, its 
 brightness would vary from about the 5th to the 
 6th magnitude. 
 
 The tenth satellite, Themis (so named after one of 
 the sisters of the god Saturn), was discovered on 
 photographic plates by Professor W. H. Pickering, 
 in 1904. Its apparent magnitude is about 17^. It is 
 therefore the faintest known member of the solar 
 system, and is invisible to the eye with the largest 
 telescope yet constructed. Professor Pickering says 
 that " a ball of rather less than one inch in diameter 
 at a distance of 3000 miles would reflect as much 
 light to us as Phoebe or Themis." 
 
 The satellite Titan, as seen from the earth, shines 
 as a star of about 8| magnitude, and is easily visible 
 in a 3-inch telescope. From observations in 1892, M. 
 L. Radeaux found that its brightness varies about 
 
272 ASTRONOMICAL ESSAYS 
 
 half a magnitude, from 8*0 to 8'5, and this fluctua- 
 tion of light seems to occur regularly. The period of 
 rotation is like our moon probably equal to the 
 time of revolution round Saturn. He finds that all 
 the satellites of Saturn at least the larger ones 
 have periods of rotation equal to their respective 
 periods of revolution. The variation of light is, 
 he thinks, due to dark spots on their surface as 
 their light varies periodically with the satellite's 
 position in its orbit. lapetus varies from about 
 the 9th to the llth magnitude. This was con- 
 firmed by Dr. See, who thinks that " only one side 
 gives sufficient light to enable the observer to recog- 
 nize a disc." The disc is visible when the satellite 
 precedes the planet. Dr. Guthnick finds that Dione 
 and Tethys vary about 0'75 magnitude, and Rhea 
 about 1 magnitude. The small satellite Phoebe 
 varies about 1-| magnitude, according to Professor 
 Pickering, but the light of Themis seems to be 
 constant. 
 
 There is a wide gap between Titan and lapetus, 
 in which there are two small satellites, Themis and 
 Hyperion, and Ledger suggested that there may be 
 others in this interval. But the gap between lapetus 
 and Phosbe is still wider, and other faint satellites 
 may yet be discovered. Hyperion is very faint, 
 about 13th magnitude. Its orbit is much dis- 
 turbed by the attraction of Titan. Hussey finds 
 from his own observations that Mimas is probably 
 larger than Hyperion, and that the supposed 
 diameter of Titan is too large. He estimates it to 
 be about 2500 miles. 
 
 Saturn and its satellites form a most interesting 
 system, but the most remarkable and wonderful 
 
THE RINGED PLANET 273 
 
 feature about Saturn is the marvellous system of 
 luminous rings which surround the planet. This 
 extraordinary appendage is quite unique in the solar 
 system, and consists of three flat circular rings, of 
 very small thickness in proportion to their extent, 
 completely surrounding the planet, but nowhere 
 touching it, in fact, poised in space like Saturn itself, 
 and, like the satellites, revolving round the planet. 
 The outer ring, known as ring A, is somewhat 
 fainter than the middle ring, from which it is 
 separated by a narrow dark division, discovered by 
 Cassini in 1675, and hence called " Cassini's division." 
 This middle ring is brighter on the outside, and 
 fades gradually towards the planet, merging on its 
 inner edge into a dusky or semi-luminous ring, 
 termed the " gauze " or " crape " ring, also known as 
 ring C. The existence of this dusky ring was only 
 discovered in the year 1850, independently by Bond 
 in America and Dawes in England, and seems to 
 have entirely escaped the notice of the Herschels 
 and other careful observers. 
 
 From observations made at Poulkova in 1850-51, 
 compared with former observations, Struve concluded 
 that the outer ring remained constant, but that the 
 inner diameter of the middle ring decreased at the 
 rate of 1-25 second a century. Further measures 
 by Struve to test this supposed change in 1881-82 
 showed a decrease of only 0'04 second in 31 years. 
 Seagrave, in 1904, found by measures made by him- 
 self, compared with those of good observers in the 
 last 75 to 80 years, that there is no constant decrease, 
 and he thinks that Struve's theory should now be 
 abandoned. The earlier observations were made 
 with inferior instruments, and are therefore not 
 
 T 
 
274 ASTRONOMICAL ESSAYS 
 
 reliable. 1 The following dimensions of the ring 
 system are given by Professor Barnard from micro- 
 metrical measures made with the great Lick tele- 
 scope : 
 
 Outer diameter of outer ring . . . 172,310 miles 
 
 Inner diameter of outer ring . . . 150,560 
 
 Outer diameter of inner ring (B) . . 146,020 
 
 Inner diameter of inner ring . . . 110,200 
 Inner diameter of crape ring . . . 88,190 
 Width of Cassini division .... 2,270 
 
 The mass of the ring system is very small. Tis- 
 serand estimated it as ~ of the mass of Saturn ; but 
 it is probably very : much less than this. Hermann 
 Struve has shown that the mass is inappreciable, as 
 it produces no effect on the motions of the satellites, 
 and he calls the rings " immaterial light." They 
 must, however, have some small mass, as they are 
 quite opaque ; at least, the bright rings. The " crape 
 ring" is, however, partly transparent, as the body 
 of the planet is visible through it. M. Antoiiiadi, 
 the well-known French astronomer, thinks that the 
 crape ring is not really a dark ring, but that its 
 apparent darkness is simply due to the smaller 
 number of the individual particles composing the 
 ring, 2 and that the shade thrown by the ring on the 
 ball of the planet is probably due to "penumbral 
 shadows," the particles being too small to cast real 
 shadows. 
 
 The thickness of the ring system is very small. 
 Sir William Herschel found 856 miles, and Schroter 
 539 miles. But these estimates are certainly too 
 
 1 Popular Astronomy, February, 1904. 
 
 2 Monthly Notices, B.A.S., May, 1899, and supplementary 
 number. 
 
THE RINGED PLANET 275 
 
 large. The Bonds found the thickness less than 43 
 miles, but Trouvelot thought this estimate too small. 
 The ring system must, however, be very thin, for in 
 1892, when the plane of rings passed between the 
 earth and sun, the rings were completely invisible in 
 the great Lick telescope. 
 
 The plane of the rings, which probably coincides 
 with that of Saturn's equator, is inclined to the 
 plane of the ecliptic at an angle of about 28. 
 As the plane of the ring system always remains 
 parallel to a fixed plane during the planet's revolu- 
 tion round the sun, this plane will at Saturn's 
 equinoxes pass through the earth at intervals of 14| 
 years (half the period of revolution). The rings 
 then disappear. 
 
 Several divisions, or partial divisions, have been 
 observed from time to time in the bright rings. One 
 in the outer ring (A), known as Encke's division, has 
 been seen by several observers. It was seen by Mr. 
 C. Roberts with a 6i-inch mirror in April, 1896. He 
 found it decidedly outside the centre of the ring. It 
 was also seen by M. Leo Brenner in the same month. 
 It was also seen by Ph. Fauth in June, 1897, with a 
 7-inch refractor/ Keeler, in 1888, detected a very 
 fine division in the outer ring (A) with the Lick 
 telescope. It was about one-sixth of the breadth of 
 the ring from its outer edge. Some dark radial 
 markings were seen by Antoiiiadi on the outer ring 
 in April, 1896, with 9f-mch object glass, and four 
 concentric markings on the middle ring (B). In 1897 
 Professor Schaeberle detected a partial division in 
 the middle ring. It was 0'7 second from the inner 
 edge of the ring, and of about the same width as 
 1 Astronomischc Naclirichtcn, No. 3436. 
 
276 ASTRONOMICAL ESSAYS 
 
 the Cassini division. Barnard considers that the 
 so-called Encke's division in the outer ring is not a 
 real division, but merely a marking. M. Leo Brenner 
 saw a division between the middle ring and the 
 " crape ring," but this Schaeberle failed to see. 
 
 Seen from Saturn, the whole system of rings 
 would disappear below the horizon at a Saturnian 
 latitude of about 66. It is fortunate for us that 
 the earth does not possess such an appendage as 
 Saturn's rings, for although they form a beautiful 
 spectacle as seen from our standpoint, they produce 
 numerous eclipses of the sun as seen from Saturn 
 eclipses lasting in some latitudes for over a year ! 
 An observer on any of the larger satellites would see 
 the rings edgeways as a line of light across the 
 planet's disc; and, viewed from Saturn's equator, 
 they would appear as a line of light across the sky. 
 
 Professor Vogel found some years ago a strong 
 absorption band in the spectrum of Saturn which 
 was very faint or absent in the spectrum of the 
 rings. This observation was confirmed by Mr. Eller- 
 man at the Yerkes Observatory in August, 1898. 
 From this Professor Hale concludes that the rings 
 have no atmosphere, thus confirming the results 
 formerly found from visual observations. Indeed, 
 this result might well have been anticipated from 
 the small mass of the ring system, which would be 
 incapable of retaining an atmosphere owing to its 
 small power of attraction. 
 
 The constitution of these wonderful rings was for 
 a long time a matter of mystery. Proctor has well 
 shown that the thickness is so small in comparison 
 with the vast dimensions of the rings that even if 
 composed of wrought iron they would form very 
 
THE RINGED PLANET 277 
 
 flimsy bodies indeed, utterly unable to resist the 
 enormous strains to which they would be subjected 
 by their rotation round the planet. That they must 
 rotate round Saturn is obvious, for if they were not 
 rotating, the enormous attraction of Saturn's mass 
 would soon shatter them to pieces, and precipitate 
 the fragments on the planet's equatorial regions. 
 Laplace found by mathematical analysis that the 
 stability of the rings could not be maintained unless 
 their mass was distributed unequally, but he did 
 not determine what arrangement of weight would 
 be necessary to ensure stability. Professor Bond, in 
 1851, pointed out that the changes observed in the 
 aspect of the rings, especially the appearance of 
 divisions, was inconsistent with a solid constitution. 
 Bond's views were confirmed mathematically by 
 Professor Peirce, of Harvard University, but the 
 latter thought that they might possibly be liquid. 
 It seems, however, to the present writer that Peirce 
 overlooked the consideration that the cold at Saturn's 
 great distance from the sun would freeze them solid 
 if formed of any ordinary liquid. In 1857 Professor 
 Clerk Maxwell investigated the question in an essay 
 written for the Adams Prize, and he showed clearly 
 that the rings could be neither solid nor liquid, and 
 that they must consequently consist of a multitude 
 of separate solid particles, each revolving in its own 
 orbit round the planet. This theory was originally 
 suggested by Roberval in the seventeenth century, 
 by J. Cassini in 1715, and by Thomas Wright of 
 Durham in 1750. It was Wright who originally 
 suggested the so-called " disc theory " of the Milky 
 Way, usually, but erroneously, attributed to Sir 
 William Herschel. In 1888 Prof essor Seeliger pointed 
 
278 ASTRONOMICAL ESSAYS 
 
 out that the constant brightness of the rings at all 
 angles of solar illumination could only be explained 
 on the satellite theory. The theory was finally con- 
 firmed by Professor Keeler by spectroscopic observa- 
 tions in 1895. The photographed spectrum of Saturn 
 and the ring system showed that the velocity of the 
 planet's limb was about 6'4 miles a second, and the 
 mean velocity of the rings about 11*2 miles a second. 
 It further showed that the velocity of the inner edge 
 of the bright rings is greater than that of the outer 
 edge, and that within the limits of error of the 
 method used the relative velocities of the different 
 parts of the ring system are such as satisfy Kepler's 
 third law of motion. 1 According to Kepler's law, the 
 nearer a satellite is to a planet the greater should be 
 its velocity, and as this is the case in Saturn's rings, 
 we may safely conclude that the rings consist of a 
 multitude of small bodies, each revolving in its own 
 orbit round the planet. Were the rings solid, the 
 velocity at the outer edge would evidently be greater 
 than 011 the inner edge, and this is the reverse of 
 what the spectroscope shows. Keeler' s results were 
 fully confirmed by Belopolsky, Campbell, and Des- 
 landres, and the constitution of the rings is no longer 
 a mystery. These little bodies are so small and 
 numerous that they 'present the appearance of a 
 continuous surface in the telescope. The thinness of 
 the rings is at once explained by this theory, for the 
 attraction of Saturn's protuberant equator would 
 compel each of the little satellites composing the 
 rings to travel in or near the plane of the planet's 
 equator. 
 
 It was shown by Kirkwood in 1867 that the 
 1 Nature, June 13, 1895. 
 
THE RINGED PLANET 279 
 
 Cassini division is due to the disturbances produced 
 by the attractions of the large satellites, and this 
 conclusion was confirmed by Meyer. Trouvelot 
 thought that the observations of Perkins, Offord, 
 Davis, Stanley Williams, Stroobant, and others con- 
 firmed his opinion that, " so far from being stable, 
 the rings of Saturn are, on the contrary, essentially 
 variable, and subject to continual fluctuations." 
 Proctor has shown that the disturbing forces acting 
 on the rings caused chiefly by the attractions of 
 the large satellites would produce a series of waves, 
 the effects of which might occasionally become visible 
 in the form of " a temporary division or dusky stripe," 
 like Encke's division in the outer ring. 
 
CHAPTER XXI 
 
 THE STELLAR UNIVERSE 
 
 THAT our visible universe is limited in extent there 
 is ample evidence to show. The number of stars 
 visible to the naked eye is not only comparatively 
 small, but absolutely so ; and the number which 
 will appear on the photographic charts of the 
 sky, now in progress, will probably not exceed 100 
 millions. And even this large number is compara- 
 tively small. The richest man in the world is said 
 to possess as many sovereigns ; and in a ten-acre field 
 of ripe oats the number of grains of corn probably 
 exceeds the number of the visible stars. Taking the 
 population at 1500 millions, we have the remarkable 
 fact that for every star in the sky there are fifteen 
 human beings living on our little globe. 
 
 The number of stars visible to the naked eye has 
 been variously estimated. The photometric measures 
 made at Harvard Observatory show the following 
 figures : under magnitude 2, 38 stars ; under 3'0, 
 99 ; under 4'0, 317 ; under 5'0, 1020 ; and under 6'0, 
 2805 ; total, 4339 to the 6th magnitude, which is 
 about the faintest distinctly visible to average 
 eyesight. The coefficient of increase for each magni- 
 tude is about 3 ; that is, the total number down 
 to any given magnitude is about three times the 
 number of stars brighter than that magnitude. 
 
 280 
 
 
THE STELLAR UNIVERSE 281 
 
 According to Professor Newcomb, there is no 
 evidence of a decrease in this coefficient to the 
 10th magnitude. But a diminution in the rate of 
 increase must set in somewhere below the 10th 
 magnitude, for otherwise the number of the visible 
 stars would be considerably greater than it actually 
 is. Taking the number of stars down to the 6th 
 magnitude as 4339, and assuming a factor of 3 for 
 the total number to each magnitude below this, I 
 find that the total number down to the 15th magni- 
 tude should be about 85 millions ; to the 16th 
 magnitude about 256 millions; and to the 17th magni- 
 tude about the faintest visible in the great Yerkes 
 telescope about 768 millions. It is evident, there- 
 fore, that there must be a diminution, or " thinning 
 out," of the visible stars at some point in space. 
 This diminution in the increase probably begins 
 with stars of the 10th or llth magnitude. Now, 
 what is the cause of this decrease in number as the 
 stars become fainter? Is it due to an actual de- 
 crease in number as we approach the limits of the 
 visible universe, or is it caused by an extinction of 
 light in the ether of space? The latter seems im- 
 probable, for Professor Seeliger finds that stars of 
 the llth and 11| magnitude are comparatively few 
 in number near the poles of the Milky Way, but are 
 very numerous in the Galaxy itself. This is also true 
 for fainter stars such as those seen by Sir William 
 Herschel in his " gages." Photographs give similar 
 results. Dr. Roberts's photographs of the Milky 
 Way in Cygnus and elsewhere show over 5000 stars 
 to the square degree, while a photograph taken near 
 the North Galactic pole shows only 178 stars to the 
 square degree, the average for the whole sky being 
 
282 ASTRONOMICAL ESSAYS 
 
 about 1500. It seems reasonable, therefore, to con- 
 clude that if faint stars are apparently few in 
 number near the poles of the Milky Way, the real 
 reason is that the stars are not there, and that, in 
 this region at least, there is real " thinning out " of 
 the stars at a certain distance from the earth. It is 
 clear that if absorption of light by the ether had any 
 real or at least appreciable effect, it would have the 
 same effect in the direction of the Milky Way as in 
 that of the Galactic poles. We must therefore con- 
 clude that the paucity of stars near the poles of the 
 Milky Way indicates that the stars are really few 
 in number in that direction, and that here, at least, 
 the visible universe of stars is limited. And it seems 
 highly probable, and indeed we may say certain, 
 that even in the direction of the Milky Way itself 
 the stars thin out beyond a certain distance and do 
 not extend indefinitely into space, for if they did, 
 the Galaxy would be much brighter than it 
 actually is. 
 
 Now let us consider what is the probable extent 
 of the visible universe. The faintest stars visible 
 on photographs are probably about the 18th 
 magnitude; that is, about one magnitude fainter 
 than the faintest visible in the Yerkes telescope. 
 Assuming this magnitude and taking the sun's 
 stellar magnitude as 26'5, I find that to reduce the 
 sun's brightness to that of these faint stars it should 
 be remove* to a distance represented by about 12,500 
 years' journey for light. The sun, if placed at the 
 distance of Sirius (parallax = 0*37 second), would 
 shine as a star of about 2'22 magnitude, or 3*8 magni- 
 tudes fainter than Sirius appears to us. From this 
 it follows that Sirius is about 33 times brighter than 
 
THE STELLAR UNIVERSE 283 
 
 the sun. Sirius might therefore be removed to 5'75 
 times (\/33) its present distance and still shine as 
 a star of 2*22 magnitude ; and to reduce it to a 
 star of the 18th magnitude it should be removed 
 to 8241 times its present distance. This would re- 
 present a light journey of about 72,000 years. If, 
 therefore, any of the 18th magnitude stars in the 
 Milky Way are suns similar to Sirius that is, of the 
 same size and intrinsic brightness they may lie at 
 a distance of 72,000 " light years " from the earth. 
 That is, provided that light suffers no extinction in 
 traversing this vast distance. And if similar to our 
 sun, they may be at a distance of our 12,000 years' 
 journey for light. 
 
 There seems to be evidence, however, that the 
 greater portion of the light of the Milky Way does 
 not come from these faint stars, but from stars con- 
 siderably brighter. Mr. C. Eastoii finds, from an ex- 
 amination of a photographic plate of a very brilliant 
 region of the Milky Way to the south of the bright 
 star y Cygni, that about half the total light of the 
 Milky Way in this region comes from stars of the 
 9th to 12th magnitude. From this he concludes 
 that neither the bright telescopic stars (6th to 9th 
 magnitude) nor the very faint stars (below 12th 
 magnitude) have any great influence in producing 
 the light of the Galaxy. From an investigation of 
 a much fainter portion of the Milky Way he finds 
 the same result. 1 This agrees with my own compu- 
 tations of the total brightness of starlight, which 
 show that the greatest amount of the light comes 
 from stars of the 9th to 12th magnitude. 2 Easton 
 
 1 Knoivledge, July, 1903. 
 
 2 Ibid., August, 1901. 
 
284 ASTRONOMICAL ESSAYS 
 
 also thinks it " extremely probable that the great 
 majority of the faintest stars of the Milky Way 
 so far as their existence is revealed to us by photo- 
 graphy or direct vision are not much more distant 
 from us than stars of the 9th or 10th magnitude, at 
 least in the regions to which our researches have 
 extended." 1 
 
 Professor Newcomb thinks that there is evi- 
 dence to show that the stars of the Milky Way are 
 probably situated at a distance between 100 million 
 and 200 million times the sun's distance from the 
 earth. These distances correspond to 1579 and 3159 
 years of light travel. Placed at the greater of these 
 distances, I find that the sun would be reduced in 
 brightness to a star of the 15th magnitude. 
 
 There seems to be evidence that the faint stars 
 of the Milky Way have spectra of the Sirian type. 
 Supposing with Easton that the fainter stars of the 
 Milky Way are of the 12th magnitude, and further, 
 that they are comparable with Sirius in size and 
 brightness, I find that their distance would be 
 represented by about 4600 years of light travel. 
 But Sirius is perhaps a larger body than an average 
 Galactic star. Its mass is about two and a half 
 times the mass of the sun, and its total brightness 
 about 33 times greater. Possibly the stars of the 
 Milky Way may be much smaller. Professor Kapteyii 
 a great authority on this subject finds, from an 
 investigation of the probable distance and bright- 
 ness of a number of stars of various magnitudes, 
 that in a volume of space containing two millions 
 of stars of the same luminosity as the sun, there 
 would probably be about half a million brighter 
 1 Knowledge, August, 1895. 
 
THE STELLAR UNIVERSE 285 
 
 than the sun, and about 12J millions of smaller 
 luminosity; that is, out of a total of 15 millions 
 of stars, about 12| millions would be smaller than 
 our sun. 
 
 To reduce the sun to the brightness of a star 
 of the 12th magnitude, it should be removed to a 
 distance of about 790 "light years." Considering 
 thirteen stars, for which fairly reliable parallaxes 
 have been found, I find that the average distance 
 of these stars, if removed to a distance which would 
 reduce their light to the 12th magnitude, would be 
 2921 "light years." As these stars are of various 
 sizes and brightness their "relative brightness," 
 compared with the sun, ranging from 0*122 to 128 1 
 we may perhaps assume that they represent nearly 
 all classes of stars, and the average distance of 12th 
 magnitude stars is about 3000 " light years." 
 
 If we assume that the stars of the Milky Way 
 are much smaller than Sirius, say one-half the mass 
 of the sun, or one-fifth of the mass of Sirius, I find 
 that the distance of 12th magnitude stars would be 
 if of the same density and surface luminosity as 
 Sirius about 2700 "light years." Assuming with 
 Newcomb that the outer boundary of the Milky 
 Way is at about 3000 light years, let us see what 
 average distance this will give between each pair 
 of stars, on the supposition of an equal distribution 
 of stars in a globular space. We know, of course, 
 that the visible stars are not equally distributed, 
 but the calculation will give the average distance 
 between any two adjacent stars. Assuming a total 
 of 100 millions, and that each star is placed at 
 
 1 See my paper on; "The Relative Brightness of Stars" in 
 Monthly Notices, Royal Astronomical Society, January, 1905. 
 
286 ASTRONOMICAL ESSAYS 
 
 the angle of a tetrahedron, I find that the average 
 distance between two stars would be about 21'24 
 light years. This corresponds to a parallax of 0-153 
 second. Now, I find that the average parallax of 
 the thirteen stars referred to above is 0*243 second. 
 If we exclude four stars with a parallax of over 
 0'3 second which may perhaps be considered as 
 exceptionally near our system we have nine stars 
 with an average parallax of 0-155 second. 
 
 With a distance of 21*24 light years between two 
 adjacent stars at a distance of 3000 light years from 
 the earth, I find that the apparent distance between 
 such stars in the Milky Way would be about 24 
 minutes of arc, and as the stars in the Galaxy are, 
 on an average, much closer than this, it seems 
 highly probable that the stars composing the Milky 
 Way are much nearer to each other than a distance 
 of 21 light years and this the crowded appearance 
 of the Galaxy would lead us to suppose. 
 
 From some counts of stars which I have made 011 
 Dr. Roberts's photographs of the Milky Way, I find 
 a total of about 45 millions of stars, or about two or 
 three times the number due to an equal distribution 
 of stars. This agrees with some experiments made 
 by Mr. Gavin J. Burns, who finds that the average 
 brightness of the Milky Way is from two to three 
 times greater than that of the rest of the sky. 1 
 
 Easton thinks that the stellar universe is of " a 
 fairly thick lens shape, filled with stars, which are 
 much more closely congregated near the edges than 
 near the centre of the lens." Professor Newcomb's 
 views are somewhat similar. But this is returning 
 to Sir William Herschel's " disc theory," and it seems 
 1 Astrophysical Journal, October, 1902. 
 
THE STELLAR UNIVERSE 287 
 
 doubtful whether such a conclusion is warranted by 
 the evidence. As is well known, this disc theory 
 was abandoned by Herschel himself in his later 
 writings. I have never seen any answer to the 
 argument against the disc theory advanced by me 
 in " The Visible Universe." The argument is as 
 follows: as the thickness of Herschel's supposed 
 disc extends on both sides of the earth beyond 
 the theoretical distance of stars of the 9th magni- 
 tude, the stars of this magnitude should be as 
 numerous in the direction of the Galactic poles as 
 in the direction of the Milky Way itself. But this 
 is not the case. Argelander's maps show that 9th 
 magnitude stars are more numerous in the Milky 
 Way than at the northern Galactic pole in the ratio 
 of 2| to 1. Even the stars visible to the naked eye 
 show a tendency to aggregation on the Milky Way, 
 and Easton finds that the fainter stars of Arge- 
 lander's catalogue about 9J magnitude "present, 
 in the manner in which they are distributed, a 
 remarkable correspondence with the luminous and 
 obscure spots of the Milky Way." These facts seem 
 to be inconsistent with theMisc theory as originally 
 propounded by Herschel. From the evidence quoted 
 above, it seems evident that if the stellar universe 
 is in any way shaped like a " thick lens," there must 
 be a considerable crowding of stars along the edge 
 of the disc; that is, in the direction of the Milky 
 Way. 
 
 Struve's modification of the " disc theory," namely, 
 a disc of a certain thickness, but of infinite, or at 
 least indeterminate diameter, seems an improbable 
 hypothesis, and one not in agreement with observed 
 facts. Even on this theory our sidereal system is 
 
288 ASTRONOMICAL ESSAYS 
 
 supposed to be limited in the direction of the 
 Galactic poles. If Struve's theory were accepted, 
 we should be obliged to accept his hypothesis of 
 the extinction of light in the ether ; for otherwise 
 the Milky Way would be much brighter than it is. 
 The comparatively feeble gleam of the Galaxy on 
 even the clearest nights should, I think, be sufficient 
 to convince the thoughtful observer that its light is 
 not due to a vastly extended stratum of stars. Even 
 Sir John Herschel's reflecting telescope of 18| inches' 
 aperture (now far surpassed in space-penetrating 
 power by modern telescopes) sufficed in some places 
 to show the component stars of the Milky Way 011 
 a black background devoid of any nebulous light. 
 With reference to one of his "sweeps," he says, 
 " The northern end of the zone, though pretty rich 
 in stars, is yet quite free from brightness of ground. 
 It is as black as a coal," clearly showing that his 
 optical power could here at least fairly penetrate 
 through the stellar stratum into the starless void 
 beyond. Modern photographs show the same thing 
 in many parts of the Milky Way. More powerful 
 telescopes and more sensitive plates will probably 
 disclose the existence of many fainter stars, but all 
 the evidence we have at present seems to point to the 
 conclusion that the utmost limit of telescopic vision 
 will soon be reached, and that the most powerful 
 telescopes which man can construct will ultimately 
 show that the stars, even in the richest portions of 
 the Milky Way, are strictly limited in number. 
 
 With reference to the clusters and nebulae, the 
 distance of these objects has not been ascertained ; 
 but from the fact that stars, clusters, and nebulae 
 are mixed up in the Magellaiiic clouds in a space 
 
THE STELLAR UNIVERSE 289 
 
 which is apparently of a nearly globular form, we 
 may conclude that all these diverse objects may 
 coexist in the same region of space, and that, conse- 
 quently, the nebulae are not, as a rule, farther from 
 the earth than the faint stars seen in the same 
 direction. Photographs of the Magellanic clouds 
 taken by the Harvard observers, show that these 
 objects are very rich in small stars. Photographs 
 of the large " cloud " show about 300,000 stars. This 
 would give about 300 millions for the whole sky if 
 equally rich. The small cloud seems still richer, as 
 the photographs show about 280,000 stars on an area 
 of about 10. This would give the enormous total of 
 1155 millions for the whole sky, and it is perhaps 
 the richest spot in the heavens. Assuming a distance 
 of 3000 light years, I find an average distance between 
 the component stars of the large cloud of about 9J 
 years, or more than the distance between Sirius and 
 the earth ; and for the small cloud an average dis- 
 tance of about five light years. It will be seen that 
 both are considerably less than the average for the 
 whole sky, and show that the stars in the " clouds " 
 are crowded together. 
 
 Seeliger estimates that the limits of the Milky 
 Way lie between 500 and 1100 times the distance 
 of Sirius, that is (the distance of Sirius being 8'8 
 " light years "), between 4400 and 9680 light years. 
 At these distances our sun would be reduced to the 
 magnitudes 15'7 and 17*4 respectively. As most of 
 the stars in the Milky Way are much brighter than 
 this, and as most of them are, according to Kapteyn, 
 smaller than the sun, we may, I think, reasonably 
 reject Seeliger's distances as excessive. Newcomb's 
 estimates are probably much nearer the truth. 
 
 u 
 
CHAPTER XXII 
 
 A POSSIBLE CELESTIAL CATASTROPHE 
 
 " The heavens being on fire shall be dissolved, and the elements 
 shall melt with fervent heat." 
 
 THE above words are from the third chapter of 
 the Second Epistle General of St. Peter (verse 12). 
 It is a matter of some uncertainty whether this 
 epistle was really written by the apostle Peter. 
 There are no certain traces of it earlier than the 
 third century. Its authenticity was questioned by 
 Origen, and St. Jerome says that many in his time 
 rejected it. The difference in style between the 
 First and Second Epistle is so great that modern 
 critics think it improbable that the Second Epistle 
 was written by St. Peter. But there is "no con- 
 sensus of opinion against it," and as it is now 
 universally admitted into the canon of Scripture, we 
 may, perhaps, accept it as genuine. However this 
 may be, it seems remarkable that in the great Sans- 
 crit epic poem, the Mahabharata, there is a distinct 
 prediction of the destruction of the world by fire. In 
 that ancient work the following passage occurs : J 
 " O king, towards the end of those thousands of 
 years constituting the four Yugas, and when the 
 lives of men become so short, a drought occurs 
 
 1 From an English translation of the " Vana Parva," by Pratup 
 Chandra Buy, C.I.E. ; 2nd edition, 1889, p. 561. 
 
 290 
 
A POSSIBLE CELESTIAL CATASTROPHE 291 
 
 extending for many years. And then, O lord of 
 the earth, men and creatures, endued with small 
 strength and vitality, becoming hungry, die by 
 thousands. And then, O lord of men, seven blazing 
 suns, appearing in the firmament, drink up all the 
 waters of the earth that are in rivers and seas. 
 And, O bull of the Bharata race, then also every- 
 thing of the nature of wood or grass that is wet or 
 dry, is consumed and reduced to ashes. And then, O 
 Bharata, the fire called Samvartaka, impelled by the 
 winds, appeareth on the earth that hath already 
 been dried to cinders by the seven suns. And then 
 that fire, penetrating through the earth and making 
 its appearance in the nether regions also, begetteth 
 great terror in the hearts of the gods, the Ddnavas 
 and Yakshas. And, O lord of the earth, consuming 
 the nether regions as also everything upon this 
 earth, that fire destroy eth all things in a moment," 
 etc. This agrees with St. Peter's words, " the ele- 
 ments shall melt with fervent heat, the earth also 
 and the works that are therein shall be burned up." 
 The idea of " seven suns " in the Mahabharata is also 
 in curious agreement with the words of the prophet 
 Isaiah|(chap. xxx. ver. 26) : " Moreover the light of the 
 moon shall be as the light of the sun, and the light of 
 the sun shall be sevenfold, as the light of seven days, 
 in the day that the Lord bindeth up the breach of 
 His people, and healeth the stroke of their wound." 
 Assuming the truth of these remarkable predictions, 
 let us see how the catastrophe of a general confla- 
 gration might be brought about by the operation 
 of natural causes without the intervention of a 
 miracle. 
 
 Some have supposed that such a catastrophe 
 
292 ASTRONOMICAL ESSAYS 
 
 might possibly be produced by an outburst of the 
 internal fires of the earth. But such an hypothesis 
 in itself very improbable in a cooling globe like the 
 earth is directly opposed to St. Peter's words, " the 
 heavens being on fire shall be dissolved," clearly 
 indicating, I think, that the fire is to come from 
 the outside. " The heavens," not the earth, being on 
 fire is to be the cause of the catastrophe. Others 
 have thought that an outburst in the sun would 
 perhaps produce the conflagration, and this certainly 
 seems much more probable. Were the sun to sud- 
 denly blaze out, like the " temporary " stars recorded 
 in the annals of astronomy, and of which we had 
 such a brilliant example in February, 1901, in 
 Perseus, then, of course, the earth would certainly 
 be burnt up, and, at least everything on its surface, 
 would at once be reduced to ashes. But although 
 this is, of course, within the bounds of possibility, 
 such a catastrophe is not, I think, at all probable. 
 There are, to be sure, small outbursts daily taking 
 place in our central luminary, as indicated by the 
 " prominences," or red flames visible round the 
 sun's limb during total eclipses, but these are of 
 comparatively small importance, and not likely at 
 any time to endanger the earth's safety. An out- 
 burst on a much larger scale would be necessary to 
 produce anything in the way of a catastrophe, such 
 as would destroy all life on our terrestrial abode. 
 Now, is there any cause which would produce a 
 great outburst of light and heat in the sun ? I think 
 we have such a cause in the possible collision of the 
 sun with a dark body in space. The distance of the 
 stars is so great that the collision of the sun with 
 a star is a contingency which may be at once 
 
A POSSIBLE CELESTIAL CATASTROPHE 293 
 
 dismissed. Such an event, if it ever took place, could 
 not possibly happen for thousands of years to come. 
 To pass over the distance which separates us from 
 even the nearest fixed star would take, at the rate of, 
 say, ten miles a second, about 80,000 years. 
 
 The existence of dark bodies in space has been 
 suspected by astronomers. I say suspected, for really 
 we have no direct evidence that such bodies exist. 
 The idea seems to have originated in the so-called 
 " dark companion " of the variable star Algol. But 
 we have 110 evidence that Algol's companion is really 
 a " dark body," that is, a body devoid of all inherent 
 light, like the earth. It is true that the spectroscope 
 shows no sign of a second spectrum, as in some 
 variables of the Algol type, in which both com- 
 ponents are of nearly equal brightness. But it has 
 been recently found by, Professor Hartmann that 
 " a difference of only about one magnitude would 
 be sufficient to bring the spectrum of the fainter 
 component to almost complete disappearance, and 
 a difference of two magnitudes would make it im- 
 possible for even a trace of the fainter spectrum to 
 be visible on the plate." l The companion of Algol 
 might therefore be a star of 4J or 5th magnitude, 
 and neither telescope nor spectroscope would show 
 any trace of its existence. But apart from the above 
 considerations, it seems very probable that many 
 dark bodies do exist in space. In the case of large 
 bodies of this kind, they would have their origin in 
 cooled-down suns. Stars cannot go on shining for 
 ever. They commence their career with a limited 
 amount of potential energy, and this energy is being 
 incessantly dissipated in the form of radiant light 
 1 Astrophysical Journal, May, 1904, 
 
294 ASTRONOMICAL ESSAYS 
 
 and heat. This dissipation of energy clearly cannot 
 go on continually, and in the course of ages it must 
 become exhausted. It is like a man living 011 his 
 capital. If he receives no interest on it, and goes 
 on spending the money steadily, the day must come, 
 sooner or later, when the capital will disappear, and 
 the man be reduced to bankruptcy. So it is with a 
 sun. It can receive no energy from without, and it 
 is constantly wasting its capital of energy in the 
 radiation of light and heat. It is true that this 
 waste may be apparently compensated for a time by 
 the contraction of the sun's mass due to gravity. 
 But this is only the conversion of potential energy 
 into heat, and eventually the process must cease, as 
 after a time counted, of course, by ages the sun's 
 density will become so great that the contraction 
 will cease, owing to the overcrowding of the mole- 
 cules, no f urther heat will be produced, and the body 
 will begin to cool down. When this cooling process 
 has sufficiently advanced, the sun will lose its light, 
 and " roll through space, a cold and dark ball." 
 There is evidence to show that in some of the 
 variable stars this permanent waning of light has 
 already commenced, and it seems highly probable 
 that in many cases the cold and dark stage has been 
 actually reached. These dark bodies may indeed be 
 very numerous. We have no means of observing 
 them, as they show no light, and would not be 
 visible, even as faint stars, in the largest telescopes 
 which could ever be constructed. 
 
 It is now well known that the sun is moving 
 through space with a considerable velocity, and, of 
 course, carrying with it the earth and all the planets 
 of the solar system. Various estimates of the point 
 
A POSSIBLE CELESTIAL CATASTROPHE 295 
 
 towards which the sun is moving have been made, 
 but the most recent and accurate calculations seem 
 to point to a spot near the bright star Vega (a Lyrse). 
 In its flight through space it seems quite within the 
 bounds of possibility that the sun may some day 
 come into collision with a dark body. Should such 
 an event occur, the collision would, of course, produce 
 an enormous amount of heat and light, and St. 
 Peter's prediction would at once be fulfilled. " The 
 heavens " would be " on fire," and the whole surface 
 of the earth and everything on it would be reduced 
 to cinders in a few minutes. It would be like the 
 destruction of St. Pierre on a colossal scale. The 
 world would end 
 
 " In unremorseful folds of rolling fire." * 
 
 But such a catastrophe could not occur without 
 our knowing of the coming disaster months, and 
 perhaps years, beforehand. When the approaching 
 dark body came within a certain distance of the sun, 
 it would begin to shine by reflected light, like the 
 planets. If a very large body, comparable with the 
 sun itself in size, it would first become visible far 
 beyond the confines of the solar system. For some 
 months or years its motion would be very slow, 
 owing to its great distance from the sun. It would 
 probably be first discovered as a telescopic star, not 
 differing in appearance from other stars of the same 
 magnitude in its vicinity. It would then perhaps 
 shine as a star of the 9th magnitude, as any much 
 fainter star would probably be overlooked. Doubt- 
 less it would at first be mistaken for a " new " or 
 " temporary " star, or a variable star at its maximum 
 1 Tennyson, " The Holy Grail." 
 
296 ASTRONOMICAL ESSAYS 
 
 light, but the comparative constancy of its light, and 
 its great parallax, or apparent change of -place among 
 the neighbouring stars, would soon show astronomers 
 its true character, and that it was really near the 
 earth compared with the distance of the stars. It 
 might, however, be mistaken for a distant comet, 
 but if coming directly towards the sun, its change 
 of place would be small, and its light examined with, 
 the spectroscope would show a solar spectrum, show- 
 ing that, like the planets, it was shining by reflected 
 sunlight. Further, its distance could be calculated 
 from its parallax, and the result would show thafc 
 no comet could be visible at such a distance from 
 the sun. . >; 
 
 I have made some calculations on the motion of 
 this hypothetical body after it became visible as a 
 star of the 9th magnitude, and therefore easily 
 visible in a telescope of 3 inches aperture. Let us 
 suppose the approaching dark body to have the same 
 mass as the sun and the same density as the earth. 
 Taking the earth's density as four times that of the 
 sun, and the sun's diameter as 866,000 miles, I find 
 that the diameter of the dark body would be about 
 546,000 miles. Now, taking the diameter of Uranus 
 as 33,000 miles, its stellar magnitude as 5*7, and 
 assuming that the dark body has the same " albedo," 
 or light-reflecting power, as Uranus, I find that the 
 dark body would shine as a star of the 9th magni- 
 tude when at a distance from the sun of 8*68 times 
 the distance of Uranus, or about 15,000 millions of 
 miles. Further, assuming that the sun is moving 
 through space at the rate of 11 miles a second 
 (about its probable value), and that the dark body 
 is moving directly towards the sun with the same 
 
A POSSIBLE CELESTIAL CATASTROPHE 297 
 
 velocity, we can calculate by the laws of dynamics 
 the time taken by the two bodies to come together, 
 starting with a distance between them of 15,000 
 millions of miles. The motion for the first few years 
 would be comparatively slow, and, as I have said, the 
 increase in brightness would at first be impercep- 
 tible. To reduce the distance to 12,000 millions of 
 miles would, I find, take about 3'4 years. At the 
 end of 6*7 years the distance would be reduced 
 to 9000 millions and in 9 '8 years to about 6000 
 millions of miles. At this distance the brightness 
 would increase to about the 5th magnitude, and it 
 would then be distinctly visible to the naked eye. 
 In about 11 '8 years the distance would be reduced to 
 4000 millions, and in about 14 years the dark body 
 would reach the orbit of Uranus, or rather it would 
 be then at the same distance from us as Uranus, for 
 its path would not intersect the orbit of the planet, 
 as I will show presently. It would then shine as a 
 star of about 0*4 magnitude, "or a little brighter 
 than Arcturus, and would, of course, attract general 
 attention. After this its distance would rapidly 
 diminish, and its light quickly increase. After 
 about a year from this time it would reach the 
 distance of Jupiter. Its light would then be greatly 
 increased. It would appear as a star of about 6*5 
 magnitude, or about 4 magnitudes brighter than 
 Jupiter at its brightest, and about 2 magnitudes 
 brighter than Venus at her greatest brilliancy. It 
 would then be the brightest object in the heavens 
 with the exception of the moon, and would be " the 
 observed of all observers." After this its motion 
 would become very rapid, and in about 51 days it 
 would be at about the same distance from the sun 
 
298 ASTRONOMICAL ESSAYS 
 
 that the earth is. From this point my calculations 
 show that the velocity would be very rapid, and if 
 a direct collision took place, the sun and dark body 
 would meet in a little less than eight days, the 
 velocity of each body being then over 400 miles a 
 second. The effects of such a collision may be easily 
 imagined. Both bodies would be reduced to the 
 gaseous state within an hour, and a stupendous 
 amount of heat would be produced, heat sufficient 
 not only to destroy the earth, but probably most of 
 the planets of the solar system. 
 
 If the dark body approached the sun in a straight 
 line, it could not strike the earth itself or any of the 
 planets, for the direction of the sun's motion is in- 
 clined to the plane of the earth's orbit at an angle of 
 about 60. The nearest approach of the body to the 
 earth would depend on the time of year at which its 
 collision with the sun took place. If this occurred 
 about the end of December, the dark body would not 
 approach the earth nearer than the sun's distance ; 
 but if the collision took place about June 21, I find 
 that the body would approach the earth within 
 about 80 millions of miles. In this case its attrac- 
 tion on the earth would be greater than that of the 
 sun, and it would probably draw the earth out of its 
 orbit. In either case, when the collision took place 
 the sun's mass would be suddenly doubled, and, 
 according to Professor Young, the earth's orbit 
 " would immediately become an eccentric ellipse, 
 with its aphelion near the point where the earth was 
 when it occurred." l But, of course, this would not 
 concern humanity, after the earth and all its in- 
 habitants had been reduced to ashes. 
 
 1 ' Manual of Astronomy," p. 294. 
 
A POSSIBLE CELESTIAL CATASTROPHE 299 
 
 It is, of course, possible that the dark body would 
 not approach the sun directly in a straight line, but 
 along an elongated ellipse. In this case its path 
 might intersect the earth's orbit, and a direct collision 
 with the earth itself would become possible, although 
 not very probable. But in this case, if it missed 
 striking the earth, it would also miss the sun, and 
 there would be no collision. But the earth's motion 
 in its orbit would be much disturbed by the powerful 
 attraction of the dark body, and it is not easy to 
 determine what the exact result would be. If, how- 
 ever, the body were moving in an ellipse sufficiently 
 elongated to pass inside the earth's orbit, it would 
 probably pass close enough to the sun to produce a 
 great disturbance in that body due to tidal action, 
 and a large amount of extra heat would probably be 
 developed. Should the two bodies merely graze each 
 other, an enormous amount of heat would certainly 
 be produced, quite sufficient to cause the earth's 
 destruction. 
 
 The approach of the dark body to the sun would 
 form a magnificent celestial spectacle. When it 
 arrived within the sun's distance from the earth, it 
 would, I find, shine with about the same brightness 
 as the moon when full, but with a smaller diameter, 
 and it would increase rapidly in brightness of surface 
 as it approached the sun. It would then especially 
 if the approach occurred in the month of June begin 
 to show phases like the moon, and we should then 
 have the curious spectacle of two moons in the sky, 
 one somewhat smaller than the other ! 
 
 Instead of a dark body of the mass of the sun, we 
 may suppose one very much smaller, say of the size 
 of Jupiter. In this case, the masses being so unequal, 
 
300 ASTRONOMICAL ESSAYS 
 
 the sun's motion would be much smaller. On the 
 other hand, the dark body would not become visible 
 until it was much nearer to the earth. In the case 
 of a body like Jupiter, say 87,000 miles in diameter, 
 I find that it would become visible as a star of the 
 9th magnitude at a distance of about 3| times the 
 distance of Uranus from the sun, or about 6000 
 millions of miles from the earth. If the diameter of 
 the dark body was the same as that of the earth, it 
 would shine as a star of the 9th magnitude at about 
 the distance of Uranus from the earth, and in this 
 case it would fall into the sun in about 3 years. 
 The amount of heat produced by the collision would, 
 of course, be much smaller than in the case first con- 
 sidered, but it seems very probable that even a body 
 the size of the earth, moving with such a high velocity 
 when it struck the sun, would produce the most 
 disastrous results to the earth. Such a body may 
 possibly be now approaching us. If only the size of 
 the earth, it might easily escape detection until well 
 within the orbit of Uranus, and we might then have 
 only a few months' warning before the final catas- 
 trophe occurred. But, it may be asked, is there any 
 star visible at the present time which might be 
 identical with an approaching dark body ? Well, all 
 I can say is this, that I have carefully examined the 
 region round Vega with a powerful binocular field- 
 glass, and that at present (April, 1905) there is no 
 star brighter than the 7th magnitude within 5 
 of Vega, which is not perfectly well known to 
 astronomers. A careful examination with a 3 -inch 
 telescope, or, better still, a photograph of the region, 
 would, however, be necessary before a decided 
 opinion could be formd on the subject. 
 
CHAPTER XXIII 
 
 RECENT ADVANCES IN STELLAR ASTRONOMY 
 
 IN my book "Studies in Astronomy" I gave some 
 account of recent advances in stellar astronomy up 
 to the end of the year 1903. The following are the 
 most remarkable discoveries and advances which 
 have been made since that date. 
 
 Mr. W. F. Very has come to the conclusion that a 
 parallax of 0*05 second may be definitely adopted for 
 Nova Persei. This would imply a light journey of 
 about 65 years. This parallax would " infer entially 
 represent the distance of the Milky Way in its 
 vicinity." The only objection which can be urged 
 against this result is that "it gives much smaller 
 values for the dimensions of the Galaxy than appears 
 probable from other considerations." But possibly 
 portions, at least, of the Milky Way may be nearer 
 to us than is generally supposed. The great brilliancy 
 which Nova Persei attained seems to suggest that its 
 distance was probably not greater than some of the 
 stars whose parallax has been determined. Mr. Very 
 points out that if we assume a parallax of only O'Ol 
 second, as given by Aitken and Chase, the velocity of 
 the radiation which lit up the surrounding nebula 
 " would be 1,500,000 kilometres a second, or greater 
 than that of light, but of such velocities we have nc 
 
 301 
 
302 ASTRONOMICAL ESSAYS 
 
 knowledge." * A parallax of 0'05 second would make 
 this velocity 300,000 kilometres a second, or about 
 the same as that of light. 
 
 A new orbit of Sirius has been completed by 
 M. O. Lohse. He finds a period of 50-381 years, with 
 a semi-axis major of 7 '4 27 seconds, and an eccentricity 
 of 0*598. It was measured by Professor Barnard in 
 October, 1903, and he found 115'06" : 6'33". The 
 companion is now within reach of medium- sized 
 telescopes. 
 
 From observations of the colour of 53 variable 
 stars of short and long period, Mr. Paul S. Yendell 
 comes to the following conclusions. From 7 short- 
 period variables he finds "no suggestion of any 
 relation between colour and length of period among 
 these stars." He finds a mean coloration of only 
 0'8 (on a scale of to 10) ; 7 " intermediate " stars, 
 with periods of 46 to 165 days, show a marked pro- 
 gression in the lengths of their periods, corresponding 
 to that in their observed colours; 38 long-period 
 stars show a marked correspondence "between 
 depth of colour and length of period," which con- 
 firms Chandler's conclusion, "The redder the star, 
 the longer the period." "From 6'8 of colour scale 
 upwards, the stars of irregular variation become 
 relatively numerous " ; the reddest star, R S Cygiii, 
 being of this type of variation. 2 
 
 Professor H. C. Wilson finds on photographs taken 
 with a 6 -inch camera large patches of nebulosity in 
 some of Sir William Herschel's nebulous regions 
 where Dr. Roberts found none, and he adds that Dr. 
 Roberts's failure "leads us rather to believe that 
 
 1 Astrophysical Journal, March, 1904. 
 
 2 Astronomical Journal, No. 564, June 20, 1904. 
 
ADVANCES IN STELLAR ASTRONOMY 303 
 
 Dr. Roberts' s work was not done under the most 
 favourable conditions, and that, therefore, there is 
 hope that under better conditions more of these 
 regions given by Herschel may be proved by 
 photographs to be nebulous." With reference to 
 the Pleiades and Orion regions, he says that Herschel' s 
 words are " abundantly justified." l 
 
 From spectroscopic observations of the famous 
 binary star a Centauri (the nearest of the fixed 
 stars), Messrs. Palmer and Wright find a difference 
 in the radial velocities of the components of about 5 
 kilometres a second. On the assumption that this 
 difference is due to relative orbital velocity, they 
 find by the formulae of Lehmann Filhes, and the 
 elements of the orbit found by Roberts, a parallax 
 of 0*76 second. This is in good argument with the 
 parallax of 0*75 second found by Sir David Gill. A 
 parallax of 0*76 second gives for the combined mass 
 of the system 1*9 times the mass of the sun. 
 
 Professor Simon Newcomb finds that the main 
 stream of the Milky Way " is not on the whole a 
 great circle, for the mean latitude obtained is 1*74, 
 showing a small but well-marked displacement of 
 our system from the central plane towards Coma 
 Berenices, where the north Galactic pole is situ- 
 ated." 2 In an article on " The Extent of the Visible 
 Universe," in Harper's Monthly Magazine for October, 
 1904, Professor Newcomb says, " Speaking roughly, 
 we have reason, from the data so far available, to 
 believe that the stars of the Milky Way are situated 
 at a distance between 100,000,000 and 200,000,000 
 times the distance of the sun. At distances less than 
 
 1 Popular Astronomy, June and July, 1904. 
 
 2 Nature, July 28, 1904, 
 
304 ASTRONOMICAL ESSAYS 
 
 this it seems likely that the stars are distributed 
 through space with some approach to uniformity. 
 We may state as a general conclusion, indicated by 
 several methods of making the estimate, that nearly 
 all the stars which we can see with our telescopes are 
 contained within a sphere not likely to be much more 
 than 200,000,000 times the distance of the sun." 
 With reference to the possible extinction of light in 
 the ether, he thinks there is none, and that probably 
 there is little or no extinction due to dark bodies. 
 He says, " We may say with certainty that dark 
 stars are not so numerous as to cut off any im- 
 portant part of the light from the stars of the Milky 
 Way, because if they did the latter would not be so 
 clearly seen as it is. Since we have reason to believe 
 that the Milky Way comprises the more distant stars 
 of our system, we may feel fairly confident that not 
 much light can be cut off by dark bodies from the 
 most distant regions to which our telescope can 
 penetrate. Up to this distance w^e see the stars just 
 as they are." These views support the opinions 
 advocated by the present writer for many years 
 past. 
 
 Dr. See says that, according to Stockwell, the 
 maximum and minimum values of the constant of 
 precession are 52-664080 seconds and 48-212398 seconds. 
 " Stockwell's mean value, 50*438239 seconds, gives 
 25694*8 years as the total period of the precession, 
 and this appears to be comparatively near the 
 truth." l 
 
 The short-period variable W. (y') Sagittarii has 
 been found at the Lick Observatory to be a spectro- 
 scopic binary. The period is nearly the same as 
 1 Astronomische Nachrichten, No. 396G. 
 
ADVANCES IN STELLAR ASTRONOMY 305 
 
 that of the variation, but there seems to be no 
 eclipse as in the case of Algol. The elements of 
 the orbit are similar to those of 77 Aquilae and 
 8 Cephei. 1 The short-period variable S. Sagittae 
 (discovered by the present writer in 1885) has also 
 been found to be a spectroscopic binary with a 
 wide range of radial velocity. The curve is similar 
 to those of 17 AquilaB and W. Sagittarii. 1 Mr. V. M. 
 Slipher finds that the bright star y Geminorum is a 
 spectroscopic binary with a period (about 3| years) 
 comparable in length with that of 8 Equulei (5*7 
 years). The orbit is "quite eccentric," for the 
 change from maximum to minimum velocity takes 
 place in much less time than the change from 
 minimum to maximum. 2 Mr. Adams has computed 
 an orbit for the spectroscopic binary Tauri, and 
 finds a period of 138 days, with an eccentricity of 
 the orbit of 0*180. " No trace of the spectrum of 
 the second component has been found " on any of the 
 photographic plates yet secured. Mr. Heber D. Curtis 
 has computed an orbit for the spectroscopic binary 
 star i Pegasi. He finds a period of 10*21312 days 
 with a nearly circular orbit. The range of velocity 
 is from -{-43*7 kilometres to 52*1 kilometres a second. 
 There is " no evidence of a second spectrum." 3 If we 
 suppose that the plane of the orbit passes through 
 the earth, the distance between the components 
 would be about 4 millions of miles. But as the star 
 does not seem to be an Algol variable, the orbital 
 plane is probably inclined to the line of sight. In 
 
 1 Publications of the Astronomical Society of the Pacific, December 
 10, 1904. 
 
 2 Astrophysical Journal, July, 1905. 
 
 3 Ibid., April, 1904. 
 
306 ASTRONOMICAL ESSAYS 
 
 this case the distance would be greater. For an 
 angle of 60 with the line of sight, the distance 
 between the components would be about 8 millions 
 of miles. The high velocity and short -period 
 indicate that they are comparatively close. Pro- 
 fessor Vogel contests the validity of Tickhoff's 
 conclusion that ft Aurigse is quadruple. Vogel 
 finds a period of 3 d 23 h 2 m 16 s 5 s with a nearly 
 circular orbit. 1 Professor J. Hartmann has com- 
 puted an orbit for the spectroscopic binary star 
 S Orionis. He finds a period of 5 d 17 h 34 m 48 s 17 s . 
 The system is receding from the earth with a 
 velocity of about 14*3 miles a second. The mass 
 is probably greater than the sun's mass, and " pro- 
 bably of the order of from 5 to 10 times the solar 
 mass." 2 The star has long been suspected of 
 variable light, and Auwers found a period of 16*08 
 days. If of the Algol type, Hartmann says that the 
 dates of minimum light may be computed from the 
 formula 1902, February 14-02 + nP. Observations 
 made specially by the present writer to detect this 
 supposed variation have proved without result. The 
 companion is comparatively dark, but the components 
 are probably of nearly equal mass. With reference 
 to the invisibility of the spectrum of the companion, 
 Hartmann says, "A difference of about one magni- 
 tude would be sufficient to bring the spectrum of the 
 fainter component to almost complete disappearance, 
 and a difference of two magnitudes would make it 
 impossible for even a trace of the faintest spectrum 
 to be visible on the plate. The slight difference of 
 
 1 Astronomische Nachrichten, No. 3944. See " Studies in 
 Astronomy," p. 291. 
 
 2 Astrophysical Journal, May, 1904. 
 
ADVANCES IN STELLAR ASTRONOMY 307 
 
 magnitude necessary for the extinction of the fainter 
 spectrum explains the fact that among the numerous 
 spectroscopic binaries so far discovered, there are 
 very few which show the lines of the second com- 
 ponent in the spectrum." This shows that the com- 
 panion of Algol is not necessarily a " dark body," as 
 is usually stated. It may be a star of, say, the 5th 
 magnitude, without the spectroscope showing any 
 sign of its existence. 
 
 For the binary star y Coronse Borealis, Dr. 
 Doberck has computed a period of 79*63 years, with 
 a semi-axis major of 0*598 second. 1 From this it 
 follows that the " relative brilliancy " of the star is 
 about 24 times that of Ursse Majoris (taken as a 
 standard). Its spectrum is of the Sirian type ; that 
 of Ursse being of the solar type. For the star 
 Scorpii, Mr. R. G. Aitken finds a period of 44 J years, 
 with a semi-axis major of 0*701 second, and an 
 eccentricity of 0*767. He finds that Dr. See's orbit 
 is now in error to the extent of +100*9 in position 
 angle, and "instead of being nearly circular, the 
 orbit is highly eccentric." 2 Aitken' s orbit gives a 
 " relative brilliancy " of 6*53. The spectrum is F 8 G 
 (Pickering). 
 
 From a plate taken of the great cluster in Hercules 
 (Messier 13) at the Yerkes Observatory on August 15, 
 1900, Mr. W. E. Plummer finds that the number of 
 stars in the cluster brighter than the 15th magni- 
 tude " does not greatly exceed 2000. 3 According to 
 Perrine, about one-third of the total number of 
 stars in the globular clusters lie between the llth 
 
 1 Nature, August 24, 1905. 
 
 2 Lick Observatory Bulletin, No. 80. 
 
 3 Monthly Notices, B.A.S., June, 1905. 
 
308 ASTRONOMICAL ESSAYS 
 
 and 13th magnitudes, while almost all the remainder 
 are very faint, about 16th magnitude. He says, 
 " The appearance is that of two layers, one of bright 
 stars superposed upon another of very faint stars ; 
 but few of 14 to 15 J magnitude are found in the 
 cluster. This fact may be due either to an actual 
 difference in the size of the stars, or to a difference 
 in constitution or physical condition. The first 
 appears more probable." Perrine says, "In this 
 connection attention may be called to the relation 
 which has been supposed to exist between the 
 nebulae and star clusters. The belief has been 
 gaining way, since photography has shown the real 
 structure of so many of these objects, that they are 
 but different stages in the process of evolution ; that 
 a star cluster has been formed by the condensation 
 of the matter in a nebula. A study of the nebulae 
 observed with the Crossley reflector shows that a 
 large proportion are spiral, and that practically all 
 the spirals are lenticular or disc-shaped. Many of 
 them are relatively very thin. Now, if the globular 
 clusters are really spherical, how could they have 
 originated from a disc-shaped nebula? " 
 
 Perrine now estimates the probable number of 
 nebulae within reach of the Crossley reflector to be 
 about 500,000, instead of 120,000 estimated by the 
 late Professor Keeler. He thinks that with more 
 sensitive plates and longer exposures this number 
 "will ultimately be found to exceed a million." 
 These small nebulae seem to be distributed over the 
 whole heavens with some approach to uniformity. 
 
 A series of photographs of Eros taken with the 
 Crossley reflector gives for the solar parallax 
 8-788" 0-008" (Perrine). 
 
PLATE 4. MILKY WAY AND NEBULA NEAR ir 2 CYGNI. 
 From original Photograph by Dr. Max Wolf, Heidelberg. Exposure 4 hours (16-inch telescope}. 
 
ADVANCES IN STELLAR ASTRONOMY 309 
 
 According to Professor Perriiie, observations at 
 the Lick Observatory show that the spectrum of 
 novce, or new stars, eventually becomes " continuous 
 without bright lines." The spectrum of Nova Cygni 
 has according to Palmer already reached this 
 stage, and that of Nova Persei is evidently approach- 
 ing it. Perrine thinks that the whole cycle of changes, 
 from the spectrum characteristic of new stars when 
 at their greatest brightness, through the nebular 
 spectrum, on to a continuous spectrum, " occupy but 
 a few years, even in the case of so great an outburst 
 as that of Nova Persei." l On July 30, 1903, Nova 
 Persei was estimated 11^ or 12th magnitude at the 
 Lick Observatory, so this famous star seems to be 
 still slowly fading. 2 
 
 Dr. Max Wolf has photographed an interesting 
 nebula in the constellation Cygnus, which is very 
 curiously placed in a dark vacuity in the Milky 
 Way. It lies about 2 south-east of the 4th 
 magnitude star ?r 2 Cygni. Wolf says, " The nebula is 
 somewhat round, and is about 10 minutes in diameter. 
 It is of a very complicated structure, somewhat 
 resembling the trifid nebula in Sagittarius. It is 
 placed centrally in a very fine lacuna, void of faint 
 stars, which surrounds the luminous cloud like a 
 trench. The most striking feature with regard to 
 this object is that the star- void halo encircling the 
 nebula forms the end of a long channel, running 
 eastward from the western nebulous clouds and 
 their lacunae to a length of more than two degrees." 
 Dr. Wolf suggests the question, "Is there a dark 
 mass following the path of the nebula, absorbing the 
 
 1 Astrophysical Journal, January, 1904, p. 83. 
 
 2 Ibid., p. 81. 
 
310 ASTRONOMICAL ESSAYS 
 
 light of the fainter stars ? We are far from knowing 
 enough to settle these questions ; but one thing we 
 learn anew from this interesting nebula, and in 
 a very illustrative manner that the nebula is 
 geometrically encircled by a ring which is void of 
 faint stars, and that this lacuna is the end of a long 
 starless hole" 1 (The italics are Wolf's). He says 
 further, "Similar relations seem to exist for all 
 extended nebulae." Among these he mentions 
 Messier 8 and 20; the nebulae near y Scuti, p 
 Ophiuchi, S Ophiuchi, Antares, v Scorpii, 77 Carinae, 
 S (15) Monocerotis, Persei, /3 Cassiopeiae, and y 
 Cygni. The nebula near 7r 2 Cygni described above was 
 afterwards photographed by Mr. W. S. Franks with 
 the 20-inch reflector of the late Dr. Roberts, and his 
 photograph fully confirms Dr. Wolf's result. Mr. 
 Franks says, "I have often noticed the curious 
 thinning out of stars in the immediate vicinity of 
 nebulae, and undoubtedly there must be some 
 physical cause to account for the fact, of which Sir 
 W. Herschel was well aware. Is it possible that 
 some of these objects are surrounded by dark and 
 relatively cool nebulous matter, which, viewed in its 
 greatest darkness round the edge, is sufficient to 
 absorb and obliterate small stars behind it? We 
 have no grounds for assuming that the nebulae 
 generally are more distant than the stars ; indeed, 
 from their vast apparent size, they may be much 
 nearer. Considering, too, how few of the stars show 
 any sensible parallax, it may be that some of the 
 nebulae, when they are seriously attacked, will yield 
 positive results. The long barren channel preceding 
 
 1 Monthly Notices, B.A.S., vol. Ixiv., No. 9, Supplementary 
 Number. 
 
PLATE 5. NEBULOSITY ROUND THE STAB 15 MONOCEROTIS. 
 From a Photograph by Professor E. E. Barnard, Terkes Observatory. 
 
ADVANCES IN STELLAR ASTRONOMY 311 
 
 this detached nebula is a very curious feature, and 
 offers an inviting field for speculation." 1 
 
 From measures made at the Yerkes Observatory 
 by Messrs. Adams and Frost with the great 40-inch 
 telescope of the velocity in the line of sight of twenty 
 stars of the " Orion type " of spectrum, they find the 
 following results. The stars examined vary in mag- 
 nitude from Rigel (0'3) to 102 Herculis (4'5). The 
 velocities found range from + 32'6 kilometres (20*2 
 miles) in the case of ft Canis Majoris, to 26*3 kilo- 
 metres (16'25 miles) (c Delphini). The results show 
 clearly the direction of the sun's motion in space, but 
 are, of course, too few in number to determine 
 accurately either the position of the "apex" or 
 the velocity of the solar motion. Assuming, how- 
 ever, Professor Newcomb's position of the "apex" 
 (R.A. 277-5 ; Dec. = + 35), and Campbell's solar 
 velocity of 19'9 kilometres per second, they find a 
 mean velocity for the 20 stars of only 7'0 kilometres 
 (4'34 miles). Omitting y Corvi, which has an excep- 
 tional proper motion of 0*162 second, the mean proper 
 motion of the others is only 0'015 second. Considering 
 the brightness of the stars examined, this is very 
 small, " much smaller than for solar stars of corre- 
 sponding brightness, and indicates that the stars of 
 the Orion type are as a class very remote." Messrs. 
 Adam and Frost think that these Orion type stars 
 " seem unquestionably to occupy a position very 
 early in the scale of stellar evolution. Their chemical 
 constitution is simple, the chief elements showing 
 lines being hydrogen, helium, oxygen, silicon, nitro- 
 gen, and magnesium. The presence of helium is the 
 principal characteristic of the type, whence they are 
 1 Monthly Notices, B.A.S., December, 1904. 
 
312 ASTRONOMICAL ESSAYS 
 
 frequently called helium stars." In those stars of 
 the type which are probably the earliest in order of 
 development (such as K Draconis, t and X Orionis), 
 there are no lines visible in the spectrum except 
 those of "hydrogen and the stronger helium lines, 
 and these are faint, and extremely broad and 
 diffuse." In the stars next in order these lines are 
 stronger, narrower, and better denned. In the 
 spectra of those stars further developed (t Herculis 
 and Rigel) the lines are well defined with traces of 
 silicon. Faint metallic lines also begin to appear, 
 showing a connection with subsequent types. Some, 
 however, of the Orion stars show oxygen and nitro- 
 gen lines, and the order in which these should be 
 placed with reference to the others is not clear. The 
 observers, however, think that the relationship be- 
 tween the two groups is " one of parallelism rather 
 than succession." l 
 
 A careful investigation of the spectra of the red 
 stars of Secchi's fourth type has also been made at 
 the Yerkes Observatory by Professor Hale, Ellerman, 
 and Parkhurst, and they arrived at the following 
 conclusions. The spectra contain a large number of 
 bright and dark lines, in addition to the flutings of 
 cyanogen and the flutings of the " swan spectrum." 
 The velocity of 8 of these fourth-type stars range 
 from 4- 5 kilometres to 28 kilometres. Measure- 
 ments of 307 dark lines indicate the presence of the 
 following elements : carbon (as cyanogen and in 
 the elementary or combined state corresponding to 
 the swan spectrum), hydrogen, vanadium, calcium, 
 magnesium, sodium, iron, chromium, titanium, nickel, 
 manganese, and possibly two or three others. " The 
 1 Publications of the Yerkes Observatory, vol. ii. 
 
ADVANCES IN STELLAR ASTRONOMY 313 
 
 carbon and metallic vapours are very dense, and 
 lie immediately above the photosphere. Above these 
 dense vapours of the reversing layer rise other 
 vapours or gases, represented in the spectra by 
 bright lines." About 200 of these bright lines were 
 observed, but could not be identified with certainty 
 with those of any known gases. A few of them may 
 possibly correspond with bright lines in the Wolf- 
 Rayet stars. The appearance of the dark lines sug- 
 gests, but does not prove, that the temperature of the 
 reversing layer in these stars is lower than in the 
 case of the sun. The appearance of some of these 
 also suggests the presence of numerous sun-spots. 
 About 20 per cent, of the fourth-type stars are 
 variable. This is a larger proportion than in the 
 case of the third-type stars. " The condensation of 
 fourth-type stars in and near the Milky Way is very 
 marked. Stars of the third and fourth types re- 
 semble each other in colour, tendency to variability, 
 spectra, possible presence of sun-spots, physical con- 
 dition, and probable relationship to solar stars. They 
 should therefore be classed together, as co-ordinate 
 branches leading back to stars like the sun. Varia- 
 tions in the relative intensities of certain titanium 
 lines indicate that fourth-type stars are probably 
 very widely separated from Wolf-Rayet stars in 
 point of development. Fourth-type stars probably 
 develop from stars like the sun through loss of heat 
 by radiation." 1 The observers consider that these 
 fourth-type stars " represent the last stage of stellar 
 development." 
 
 Dr. Doberck has computed a new set of elements 
 for the orbit of the satellite of Sirius. He finds 
 1 Publications of the Yerkes Observatory, vol. ii. p. 135. 
 
314 ASTRONOMICAL ESSAYS 
 
 a period of 49*49 years, with a semi-axis major of 
 7*513 seconds, and an eccentricity of 0*5871. This 
 does not differ much from previous determinations. 
 With Gill's parallax of 0*37 second, Doberck's orbit 
 gives a combined mass equal to 3*434 times the 
 sun's mass, the mass of the satellite being about 
 equal to the sun's mass. 
 
 In the nebulous region near p Ophiuchi, 72 new 
 variable stars have been discovered at Harvard 
 Observatory. Among these the greatest variation of 
 light amounts to 4*1 magnitudes. All these are faint 
 stars, only 10'5 to 14*2 magnitude at maximum. In 
 the globular cluster Messier 4, 33 variable stars were 
 discovered. Greatest variation 1*6 magnitude. These 
 are also faint, from 10*5 to 13*1 magnitude at maxi- 
 mum. In the "trifid nebula" (Messier 20), 16 
 variables were found, the largest variation being 4 
 magnitudes. The stars are mostly faint, from 9*5 to 
 14 magnitude at maximum. 1 
 
 Professor E. C. Pickering finds that the spectrum 
 of the star X Cephei (5*6 magnitude) is peculiar, and 
 identical with that of Puppis. 2 This is a very rare 
 spectrum, and shows some hydrogen lines which 
 have not yet been seen in laboratory experiments. 
 
 Dr. J. Moller finds the following results for the 
 colours of stars down to magnitude 3*4, estimated on 
 a scale of 1 to 9, 1 being nearly white, and 9 full red : 
 Antares, 7*5 to 7*8 ; Betelgeuse, 7*4 to 7*6 ; Arse, 7'4 
 to 7*6 ; Aldebaran, 7*2 ; Cephei, 7*0 ; e Crucis, 7*0 ; 
 8 Virginis, 7*0. 3 
 
 From an investigation by Messrs. F. W. Dyson, 
 F.R.S., and W. G. Thackeray, of the Greenwich 
 
 1 Astronomische NacHrichten, No. 3994. " Ibid., No. 3995. 
 
 3 Ibid., No. 3980. 
 
ADVANCES IN STELLAR ASTRONOMY 315 
 
 Observatory, based on the proper motions of a large 
 number of stars of different magnitudes, derived 
 from a comparison of Groombridge's Catalogue 
 (1810) with modern Greenwich observations, they 
 find that "the most probable. value of the position 
 of the apex of the sun's motion derived from the 
 discussion is R.A. 275, or 18 h 20 m , declination +37." 
 This point lies between Vega and K Lyrse a little 
 nearer to K. This result is in good agreement with 
 the results found by Boss (1890) and Newcomb (1899). 
 
 In Popular Astronomy for May, 1905, Mr. S. M. 
 Hadley gives formula for finding the relative masses 
 of the components of binary stars from measures of 
 a third star near the binary. From measures of 
 or Coronae Borealis (period 370*0 years, See) and a 
 third star which has varied in distance (owing to 
 the proper motion of the binary system) from about 
 44 seconds to 62 seconds, he finds that the masses of 
 the components are in the ratio of 1 : 1*08, or about 
 equal in mass. The magnitudes of the components 
 are 6 and 7 (yellow and bluish), or the primary is 
 about 2| times brighter than the companion. For 
 j3 Delphini the ratio of the masses has not yet been 
 determined. In this case the components are 4 and 6 
 magnitudes, or the primary star is about 6'31 times 
 brighter than the companion. 
 
 Professor H. C. Wilson (U.S.A.) finds that on a 
 photograph taken by him of the Pleiades region with 
 a 6-inch Brashear star camera, this region (one of 
 those described by the late Dr. Roberts as contain- 
 ing no nebulosity) "is really filled with nebulous 
 matter covering an area equal to that allotted by 
 Herschel to the whole of the nebulosities in his 52 
 regions." 
 
316 ASTRONOMICAL ESSAYS 
 
 From measures of photographic plates, H. N. 
 Russell, Ph.D., finds a parallax of 0'074 second for 
 the star y Virginis, and 0'344 second for the star 
 Lalande 21,18s. 1 The latter star has long been 
 known as one of the nearest stars in the heavens. 
 Its magnitude is about 7J. If our sun were removed 
 to the distance indicated by] the above parallax, it 
 would, I find, shine as a star of about 2'4 magnitude. 
 The sun is therefore about 100 times brighter than 
 the star, and Lalande 21,185 must be either a com- 
 paratively small body, or else the luminosity of its 
 surface must be considerably less than that of the 
 sun. It has a very large proper motion of 4' 7 5 
 seconds (one of the largest known), and this, com- 
 bined with the above parallax, would imply a motion 
 of 40'6 miles per second at right angles to the line of 
 sight. As it may have some motion in the line of 
 sight, its actual velocity is probably greater than 
 this. 
 
 In the Astronomische Nachrichten, No. 3946, M. 
 Adalbert Prey, of Vienna, gives the results of an 
 investigation of the ratio of the masses of the com- 
 ponents of the binary star 70 Ophiuchi, using 33 
 meridian observations of the principal component. 
 He obtains the remarkable result that the mass of 
 the companion is four times as great as that of the 
 bright star 1 Using Schur's parallax of 0'16 second, 
 he finds the masses of the two stars to be 0'32 and 
 T28 times the sun's mass. 
 
 No less than 910 variable stars have been dis- 
 covered in the smaller Magellanic cloud on photo- 
 graphic plates taken at Arequipa by the Harvard 
 observers. "It is estimated that the number of 
 1 Monthly Notices, E.A.S., June, 1905, 
 
ADVANCES IN STELLAR ASTRONOMY 317 
 
 stars photographed in the small Magellanic cloud 
 and adjacent clusters is about 280,000, of which 910, 
 or 1 in 308, is variable. In the surrounding region 
 about 40,000 stars appear 011 the best negatives, of 
 which 12, or only 1 in 33,000, have been found to be 
 variable, although all have been examined with 
 great care." 
 
 Mr. Lampland, of Mr. Percival Lowell's Observa- 
 tory, finds that the faintest stars shown on charts 
 made at the Lick Observatory with the 36-inch tele- 
 scope are perfectly visible with the 24-inch telescope 
 of the Lowell Observatory. 1 
 
 Professor C. L. Doolittle finds from 15,000 obser- 
 vations, extending over a period of 7 years 1896 to 
 1903 at the Flower Observatory, and from similar 
 work at the Sayre Observatory, a value for the 
 constant of aberration of 20*540 seconds. 2 The 
 corresponding value of the sun's parallax would be 
 8*76 seconds. From measures of lines in the spectrum 
 of Arcturus, Herr K. Kiistner finds a value of the 
 solar parallax of 8*844 seconds. All the values of 
 the sun's parallax found in recent years seem to 
 cluster round a mean value of 8*80 seconds, which is 
 the value now usually adopted by astronomers. 
 
 A new star in Aquila was discovered in August, 
 1905, on plates taken at Harvard. Its magnitude 
 was about 7. Professor Max Wolf found it 9*3 on 
 September 4 ; Dr. Guthnick estimated it 10*2 on 
 September 4, and of a yellowish colour ; and Pro- 
 fessor Hartwig 10m. on September 5. Its position 
 for 1905-0 is R.A. 18 h 57 m 5 s , S. 4 34*8', or a little 
 north-west of the star A Aquilse. This will be known 
 
 1 Popular Astronomy, August and September, 1905. 
 
 2 Astronomical Journal, July, 1905. 
 
318 ASTRONOMICAL ESSAYS 
 
 as Nova Aquilse, No. 2, the first nova in this con- 
 stellation having been discovered in July, 1900 ; but it 
 was visible as 7m. on a plate taken on April 21, 1899. 1 
 In a paper by J. Halm in the Proceedings of the 
 Royal Society of Edinburgh, he advances further 
 arguments in favour of Seeliger's theory that the 
 phenomenon of a temporary star is due to "the 
 collision of a dark solid body with matter of 
 nebulous consistency." He says that after the 
 collision occurs a central photospheric radiation 
 would be formed, and this would be surrounded by 
 an atmosphere showing bright lines in its spectrum. 
 All the particles of this atmosphere will be moving 
 radially outwards from the star's centre. All the 
 rays leaving the photosphere from the hemisphere 
 turned towards the earth will thus have to pass 
 through the absorbing atmosphere, and will show a 
 spectrum with dark lines. Bright lines will also be 
 visible formed by the atmosphere itself. As all the 
 particles of the absorbing atmosphere are moving 
 with high velocities towards the observer, the dark 
 lines will be displaced towards the violet end of 
 the spectrum. This displacement of the dark lines 
 towards the violet has been the characteristic feature 
 of all the temporary stars hitherto observed with 
 the spectroscope. Other facts in the history of 
 new stars are also satisfactorily explained by this 
 hypothesis. 
 
 A remarkable variable star of the Algol type has 
 been discovered on photographic plates taken at the 
 Harvard Observatory. It varies from 7*14 magnitude 
 to about the llth magnitude (photographic), with a 
 period of 2*77 days. The variation is " much greater 
 1 Nature, September 14 and 21, 1905. 
 
ADVANCES IN STELLAR ASTRONOMY 319 
 
 than that of any other Algol star as yet discovered," 
 the light at maximum being about 35 times the light 
 at minimum. Its position for 1900 is R.A. 3 h 57 ra 45 s , 
 N. 37 51'. It lies about 50' north-west of 41 Tauri, 
 and about 1 10' south-west of \l/ Tauri. At maximum 
 it may be seen with a good binocular, but at minimum 
 it would be quite invisible with such an instrument. 
 It may be followed, however, through all its phases 
 with a 4-inch telescope. Its spectrum, like that of 
 all the Algol variables, is of the first type. 
 
 Mr. J. Miller Barr, of Ontario, Canada, finds that 
 the star 32 Cassiopeise is variable to the extent of 
 0*4 magnitude with the remarkably short period of 
 7 h 59 m . The variation (about 5-2 to 5'6 magnitude) 
 has been confirmed by Mr. Paul S. Yendell, of Boston 
 (U.S.A.), the well-known variable star observer. 1 The 
 colour is yellowish, and the spectrum of the Sirian 
 type (A). Another still more remarkable variable 
 has also been detected by Mr. Barr. This is 
 D.M. -f 30,42, and lies about 3| north-east of the 
 bright star a Andromedse. Mr. Barr finds that it 
 is variable to the extent of 0*4 magnitude, with the 
 phenomenally short period of 2 h 41 'l m , which would 
 be the shortest period known. He thinks, however, 
 that it may be necessary to double this period, 
 making it 5 h 22 m . This would still be the shortest 
 period known with one exception, W. Ursae Majoris, 
 which has a period of only 4 h O m 13 s . The new 
 variable is of a yellowish colour, and its spectrum 
 of the Sirian type. The variation is about from 5*5 
 to 5*9 magnitude. 
 
 1 The variation is, however, disputed by J. A. Parkhurst and 
 F. C. Jordan, from photographic measures [(Astrophysical Journal, 
 January, 1906). 
 
320 ASTRONOMICAL ESSAYS 
 
 With reference to the distribution of stars with 
 different types of spectra, Professor Pickering finds 
 that the stars of the first or Sirian type, " although 
 frequent in all parts of the sky, predominate along a 
 certain plane, thus forming the Milky Way." The 
 stars of Class B. (the " Orion " or " helium " stars) 
 "are nearly all in the Milky Way. Only four per 
 cent, are in the half of the sky north and south of 
 it." The stars of the second and third type " show no 
 concentration in the Milky Way, but are, in general, 
 uniformly distributed in all parts of the sky." ] 
 
 Professor Ceraski has recently made some observa- 
 tions with a view to determine the value of the sun's 
 stellar magnitude. He compared the light of Venus 
 with a reflected image of the sun during the day- 
 time, and at night compared Venus with the stars 
 Polaris, Procyon, and Sirius. Taking the photo- 
 metric magnitude of Polaris as 2*15, that of Procyon 
 0*56, and Sirius 1*09, his results give for the sun's 
 stellar magnitude -26*51, -26*66, and -26*67, and a 
 weighted mean value of 26*59. Instead of using 
 the minus sign, he calls the sun's stellar magnitude 
 26*59 super magnitude. 2 The magnitude of Sirius 
 found at Harvard, viz. 1*58, would, however, 
 give a somewhat higher value than that found by 
 Ceraski. 
 
 M. H. E. Lau, of Copenhagen, found the star 
 ft Herculis below its normal brightness in August 
 and September, 1905, and as it is a spectroscopic 
 binary with a period of about 41 Of days, he suggests 
 that it may be a variable of the Algol type. Variation 
 was suspected by Sir William Herschel. 
 
 1 Annals of Harvard College, vol. Ivi., No. 1. 
 
 2 Astronomische Nachrichten, No. 4065. 
 
ADVANCES IN STELLAR ASTRONOMY 321 
 
 From a comparison of the spectrum of sun-spots, 
 observed at Princeton (U.S.A.), with that of fourth- 
 type stars recorded at the Lick Observatory, Mr. 
 Walter M. Mitchell finds that carbon is apparently 
 absent from sun-spots, while its presence in fourth-type 
 stars is strongly indicated by the absorption bands in 
 their spectrum. The magnesium lines are prominent 
 in the fourth-type spectrum, but are of small import- 
 ance in the spot spectrum, no observation of these 
 lines being recorded at Princeton. " In contrast 
 to this is the behaviour of the manganese lines, 
 which are of relatively great importance in the spot 
 spectrum, and are apparently of minor importance in 
 the spectra of the fourth-type stars." He concludes 
 that " it seems improbable that spots, such as exist 
 on the sun, constitute a characteristic feature of 
 fourth-type stars." l With reference to third-type 
 stars, a comparison made by Adams and Hale between 
 the spectrum of a Orionis (Betelgeuse) taken with 
 the Snow telescope and the sun-spot spectrum 
 " affords strong evidence of the general agreement 
 between the spectrum of a Orionis and that of sun- 
 spots." 2 
 
 The fainter component of the well-known binary 
 star Castor was found some years ago to be a spectro- 
 scopic binary with a period of 2'93 days. Professor 
 Heber D. Curtis, of the Lick Observatory, confirms 
 this, and finds that the brighter component is also 
 a spectroscopic binary with a period of about 9*2 
 days, the whole forming a remarkable quaternary 
 system. The spectroscopic measures indicate the 
 remarkable result that the mass of the fainter 
 
 1 Astrophysical Journal, April, 1906. 
 
 2 Ibid., June, 1906. 
 
322 ASTRONOMICAL ESSAYS 
 
 component is six times the mass of the brighter 
 component. 
 
 In a paper read before the British Astronomical 
 Association in June, 1906, Mr. Gavin J. Burns says 
 that the luminosity of the sky on a moonless night 
 is not wholly due to starlight, for if this were 
 so, the light should diminish near the horizon, as 
 the lucid stars do. " As a matter of fact, the exact 
 opposite is the case." The light also varies in bright- 
 ness. This I can fully confirm from my own obser- 
 vations. Sometimes the night sky is comparatively 
 dark, while at others there is a sort of phosphorescent 
 glow over the whole sky. 
 
 From meridian observations of the binary star 85 
 Pegasi, and measures made from a third star of the 
 9th magnitude, "which seems to be fixed," Messrs. 
 W. Bowyer and H. H. Purner, of Greenwich Observa- 
 tory, find that the mass of the bright star is to the 
 mass of the companion as 3 to 8, that is, the 
 companion has nearly three tunes the mass of 
 the primary. 1 As the magnitude of the primary 
 star is 6, and that of the companion 10, this is a 
 very remarkable result, the apparent brightness 
 being in the ratio of 100 to 1. 
 
 From photographs taken at the Cambridge Ob- 
 servatory, Messrs. Arthur E. Hinks and Henry Norris 
 Russell find a parallax for Mira Ceti of 0*136 second. 
 With reference to this result, which is of great 
 interest, Mr. Russell says, " If the other long-period 
 variables resemble it, and their maximum rather 
 than their minimum light is comparable with the 
 sun's, the brighter ones must have easily measurable 
 parallaxes, and it would pay to observe them. 
 1 Monthly Notices, R.A.S., May, 1906. 
 
ADVANCES IN STELLAR ASTRONOMY 323 
 
 Campbell and Stebbins find that the radial velocity 
 of Mira is constant and equal to + 63 km. per 
 second. As its cross velocity is only 8 km., it 
 is moving almost directly away from us in a 
 direction making an angle of only 7 with the 
 line of sight. If the present value of the parallax 
 is correct, it follows that Mira was nearest to the 
 sun about 110,000 years ago. It was then in Ursa 
 Major, and had a parallax of 1*1 second, and a 
 proper motion of 15 seconds per annum. If its 
 intrinsic brightness varied between the same limits 
 as at present, it was of the 5th magnitude at 
 minimum, and at maximum was as bright as 
 Sirius." 1 The star passed through an unusually 
 bright maximum in December, 1906, when it was 
 fully 2nd magnitude, or perhaps slightly brighter. 
 It has not been so bright at maximum for over 
 sixty years. 
 
 Aitken finds that the binary star 13 Ceti has 
 the short period of 7*42 years. This is shorter " than 
 any other known visual binary except B Equulei " 2 
 (5* 7 years). 
 
 1 Monthly Notices, R.A.S.; December, 1906. 
 
 2 Publications of the Astronomical Society of the Pacific, February 
 10, 1907. 
 
CHAPTER XXIV 
 
 THE NEW COSMOGONY 
 
 IN Laplace's nebular hypothesis, the original mass 
 from which the solar system is supposed to have 
 been evolved was considered to consist of gaseous 
 material filling a space of spheroidal form and ex- 
 tending to the orbit of Neptune, or somewhat beyond 
 it. The whole gaseous mass was supposed to be in 
 hydrodynamical equilibrium, and rotating in a period 
 equal to the period of revolution of the present 
 farthest planet. We might also assume that the 
 original mass consisted of a swarm of meteorites, 
 for Professor G. H. Darwin has shown that such 
 a swarm would have nearly the properties of a gas. 
 On either assumption the mass would contract by 
 its own gravitation, and the angular velocity gradu- 
 ally increasing, the centrifugal force would in time 
 flatten the spheroidal mass at the poles. From this 
 flattened spheroid Laplace thought that rings would 
 be detached at certain intervals, and that these rings 
 consolidating, would eventually form the planets and 
 satellites as we now see them. 
 
 It has been shown, however, by Professor P. R. 
 Moulton, that the matter detached from the rotating 
 gaseous spheroid would be " shed continually," and 
 that no separate rings could be formed. This would 
 occur whether we consider the original mass to have 
 
 324 
 
THE NEW COSMOGONY 325 
 
 been gaseous or composed of meteorites. But sup- 
 posing the rings to have been, by some miracle, 
 detached from the parent mass, we should expect 
 to find that the plane of Mercury's orbit would 
 deviate less than the other planets from the average 
 plane of the planetary system ; also that the orbits 
 of the "terrestrial planets," Mercury, Venus, the Earth, 
 and Mars, would be less eccentric, that is, more 
 circular, than those of the outer planets. But the 
 known facts concerning Mercury's orbit are quite 
 opposed to these conclusions. The inclination of its 
 orbit to the plane of the ecliptic (7) is greater than 
 any of the large planets, and the eccentricity of its 
 orbit (0-20) is only exceeded by that of some of the 
 minor planets revolving between Mars and Jupiter. 
 Further, Moulton shows that the distribution of 
 masses among the planets of the solar system 
 indicates that the original nebulous mass must have 
 been very heterogeneous, and not homogeneous, as 
 Laplace's theory postulates. 1 
 
 There are numerous other difficulties connected 
 with Laplace's hypothesis, and many attempts have 
 been made to overcome them. But these efforts have 
 proved only partially successful, and for some years 
 it has become increasingly evident that the hypothesis 
 must be abandoned for something in better agree- 
 ment with modern telescopic discoveries. The idea 
 that the planets were formed by the condensation 
 of Brings detached from a nebulous mass is an hypo- 
 thesis for which we find no warrant in the heavens. 
 Laplace's idea of a nebular hypothesis was probably 
 suggested by a consideration of Saturn's rings. But 
 modern researches on tidal action tend to show that 
 1 Astrophysical Journal, March, 1900. 
 
326 ASTRONOMICAL ESSAYS 
 
 this wonderful system was not originally formed as 
 a ring left behind by Saturn during the process of 
 condensation from the nebulous stage. More pro- 
 bably the matter composing the rings was originally 
 separated from the planet in one mass. This mass, 
 being too close to Saturn to consolidate into a 
 satellite being within what is known as "Roche's 
 limit" was torn into fragments by the force of 
 tidal action, and its particles were scattered round 
 the planet in the form of a ring (or rings) as we 
 now see it. On this view of the matter the course 
 of events was exactly the reverse of what was sup- 
 posed to have happened in Laplace's hypothesis. 
 Instead of a ring being first formed, and then a 
 number of small satellites from this ring, we must 
 conclude that a mass of matter was first detached 
 from the partially consolidated planet, and that then 
 this mass was broken up into small fragments by the 
 enormous tidal action of the central mass. 
 
 We see in the heavens numerous forms of nebulae 
 spiral nebulae, planetary nebulae, etc. but there is 
 no really good example of a ring nebula. Those which 
 have been termed " annular nebulae " are most pro- 
 bably spiral nebulae seen foreshortened. Of the 
 numerous nebulae recently discovered with the 
 Crossley reflector at the Lick Observatory, it has 
 been found that "a large proportion are spiral, 
 and that practically all the spirals are lenticular 
 or disc-shaped. Many of them are relatively very 
 thin." l At one time the photographs of the great 
 nebula in Andromeda were thought to show signs 
 of ring formation, but Dr. Roberts, describing his 
 
 1 Publications of the Astronomical Society of the Pacific, December 
 10, 1904, 
 
THE NEW COSMOGONY 327 
 
 photograph of this wonderful nebula, says, "That 
 this nebula is a left-handed spiral, and not annular, as 
 I at first suspected, cannot now be questioned ; for 
 the convolutions can be traced up to the nucleus, 
 which resembles a small bright star at the centre 
 of the dense surrounding nebulosity." Even the so- 
 called " ring nebula " in Lyra, which is sometimes 
 adduced as an example of ring formation, was found 
 by Professor Schaeberle, of the Lick Observatory, to 
 be " a two-branched spiral which commences at the 
 central star, and in a clockwise direction emerges 
 on opposite sides near the minor axis." l Even the 
 apparent ring form of this nebula seems to be ficti- 
 tious. Instead of being annular in shape, it appears 
 to be a hollow spheroid, the ring representing the 
 thickness of the shell. To any one who still persists 
 in maintaining the hypothesis of ring formation in 
 nebulae, it may be said that the whole heavens are 
 against him. 
 
 It has always been difficult to imagine how rings 
 could possibly have been formed from the parent 
 mass, considering the extreme tenuity of the original 
 nebula. Computing from the total mass of the bodies 
 composing the solar system, the density of the 
 primitive nebulous mass supposing it extended to 
 the orbit of Neptune would have been almost in- 
 conceivably small. The density of atmospheric air 
 would be millions of times greater, and how rings 
 could be formed in such a tenuous gas has always 
 been a serious difficulty in the discussion of Laplace's 
 hypothesis. But there is a still more fatal objection. 
 The original idea was that the detached " rings " 
 would at first break up into separate masses, and 
 1 Natwe, August 6, 1903. 
 
328 ASTRONOMICAL ESSAYS 
 
 that these fragments would afterwards by their 
 mutual attraction consolidate into planets. But 
 Moulton has shown by a mathematical investigation 
 " that the tidal forces coming from the interior mass 
 would more strongly tend to scatter the material 
 than its gravitation would to gather it together into 
 a planet. Consequently, a ring could not even start 
 to condense into a planet." 
 
 Compelled therefore, as we apparently are, to 
 abandon Laplace's nebular hypothesis in its original 
 form, are we therefore obliged to relinquish all 
 attempts to explain the formation of suns and solar 
 systems from the consolidation of gaseous matter? 
 By no means. The heavens, which are clearly 
 against Laplace's hypothesis, are strongly in favour 
 of a new theory, a new cosmogony, which will pro- 
 bably stand the test of mathematical analysis. This 
 is the evolution of suns and systems from spiral 
 nebulae. Of the half-million nebulae discovered by 
 the Crossley reflector, a large proportion are spiral, 
 and the study of these remarkable and interesting 
 objects will probably form an important part of the 
 work of future astronomers. 
 
 Laplace's original nebula was gaseous, and a 
 gaseous spectrum shows bright lines. But the 
 spectrum of the spiral nebulae is continuous, indi- 
 cating that they are partially consolidated from the 
 gaseous condition. We can therefore easily imagine 
 that masses might be thrown off or detached from 
 the parent mass by the centrifugal force of the 
 rotation. This seems much more probable than the 
 formation of rings from a highly tenuous nebula. 
 Photographs of spiral nebulae show us masses in the 
 act of being detached from the spiral branches. This 
 
PLATE 6. THE SPIRAL NEBULA M. 74 PISCIUM. 
 From a Photograph l>y Dr Isaac Roberts. 
 
THE NEW COSMOGONY 329 
 
 is particularly noticeable in the accompanying photo- 
 graph, in which we see the process going on before 
 our eyes. 
 
 The theory of the evolution of suns and solar 
 systems from spiral nebulae has recently been investi- 
 gated mathematically by Professors T. C. Chamberlin 
 and F. B. Moulton. This investigation consists in 
 an attempt ." to test, by an appeal to the laws of 
 dynamics, the consistency of the ring theory with 
 known phenomena. Contradictions were uniformly 
 found, and in some cases the results were so con- 
 clusive as to compel us frankly to abandon it as an 
 untenable hypothesis." * An outline of this new 
 cosmogony, called by Chamberlin the " planetesimal 
 hypothesis," and which certainly seems a great 
 improvement on that of Laplace, may prove of 
 interest to the general reader. 
 
 The origin of the nebulous mass from which the 
 solar system is supposed to have been evolved was 
 not considered by Laplace. He assumed its existence, 
 and then proceeded to show, as he thought, how the 
 sun and planets might have been formed from it by 
 the consolidation of the nebulous matter in the 
 course of ages. As we have seen, his hypothesis 
 has broken down badly, and something else must 
 be substituted for it if we are to retain a nebular 
 hypothesis in any form. The origin of spiral nebulas 
 is, of course, unknown, but of their existence there 
 can be no doubt. Photography has fully confirmed 
 the discovery originally made by Lord Rosse with 
 his giant 6-feel; telescope. They are very numerous 
 in the heavens. Professor Keeler thought that pro- 
 bably one-half of the nebulae found with the Crossley 
 1 Astrophysical Journal, October, 1905. 
 
330 ASTRONOMICAL ESSAYS 
 
 reflector are spiral, and that "any small compact 
 nebula not showing evidence of spiral structure 
 appears exceptional." Spiral nebulae were, of 
 course, unknown to Laplace, and, had he known 
 of their existence, we should probably never have 
 heard of " ring formation." 
 
 A spiral nebula may possibly have been formed 
 by the " grazing collision " of two solid masses, or by 
 the near approach of two bright stars. Supposing 
 the near approach of a large body to another of 
 larger size, the effect on the latter body would be 
 the production of a gigantic tide on the side turned 
 towards the approaching body, and another tide of 
 almost equal size on the opposite side. These tides 
 would produce explosions and eruptions of nebulous 
 matter from the interior of the star, and Moulton 
 shows that the ejected material would assume the 
 spiral form. This has also been shown by Herr 
 E. 1 J. Wilczynski, of Berlin. 1 Now, it is a remarkable 
 feature of spiral nebulae that the spiral branches 
 (usually two) almost invariably issue from the central 
 nucleus at diametrically opposite points, thus agree- 
 ing with the new hypothesis. The spiral nebulae 
 which we see in the heavens are, of course, con- 
 structed on a colossal scale, and probably represent 
 a stage in the evolution of star systems rather than 
 solar systems like ours. But the principle would be 
 the same in both cases. 
 
 In Chamberlin's " planetesimal hypothesis " the 
 original nebulous mass " must have spread out in the 
 form of a relatively thin disc," and instead of being 
 homogeneous, as in Laplace's hypothesis, "it may 
 have had almost any degree of heterogeneity." In 
 1 Astrophysical Journal, vol. 4 (1896), p. 98. 
 
THE NEW COSMOGONY 331 
 
 this theory fluid pressure, which was of fundamental 
 importance in Laplace's hypothesis, is of minor 
 consideration, and "110 general shrinkage with loss 
 of heat " plays any part in the evolution of planets 
 from the parent mass. 
 
 Moulton shows that on the new theory the result- 
 ing planets will all probably revolve round the 
 nucleus in the same direction as the original rota- 
 tion, and that the planes of their orbits " will nearly, 
 though not exactly, coincide ; " also that the orbits 
 of the larger planets will show smaller deviations 
 from the general plane than those of the smaller 
 planets, like Mercury and the asteroids. This we 
 know to be the case in the solar system. He shows 
 that the present rotation of the sun is due to the 
 original rotation of the mass from which it was 
 formed, combined with the disturbance caused by 
 the body which approached it, and that the more 
 rapid rotation of the sun's equator is due to the same 
 cause. He also shows that the larger the planet, 
 " the more nearly circular in general " its orbit would 
 be ; and this also agrees with the known facts of the 
 solar system. The orbits of the so-called " terrestrial 
 planets " Mercury, Venus, the Earth, and Mars are, 
 on the average, more eccentric than those of the 
 large planets Jupiter, Saturn, Uranus, and Neptune ; 
 and those of the small minor planets between Mars 
 and Jupiter are still more so. 
 
 With reference to the rotations of the planets on 
 their axes, Moulton shows that these would probably 
 be direct, that is, in the same direction as the orbital 
 revolutions, and that the inclinations of the axes of 
 rotation to the planes of the orbits might be different 
 for different planets. Any well-marked deviation 
 
332 ASTRONOMICAL ESSAYS 
 
 from the general rule might be expected in the outer 
 planets of the system. This we see in the case of 
 Uranus and Neptune, which have always been stumb- 
 ling-blocks in Laplace's hypothesis. We should also 
 expect, he thinks, " to find the larger planets rotating 
 more rapidly than the smaller," as we know to be 
 the case. 
 
 With reference to the satellites, the direction of 
 their motion round the primary may, on the new 
 hypothesis, be either direct or retrograde, according 
 to circumstances. Retrograde motion might be ex- 
 pected in satellites very remote from their primary, 
 and revolving in orbits of high eccentricity. This is 
 the case with Phoebe, the recently discovered ninth 
 satellite of Saturn. The position of the satellites of 
 Uranus could not have been predicted by the new 
 theory, but Moulton thinks that "they do not 
 definitely contradict it as they do the ring theory." 
 A satellite might also, on the new theory, revolve 
 more rapidly round its primary than the planet 
 rotates on its axis. This is the case with Phobos, 
 the inner satellite of Mars, which revolves round the 
 planet in 7 hours 39 minutes 15 seconds, while Mars' 
 period of rotation on its axis is 24 hours 37 minutes 
 22| seconds, or over three times as long. This un- 
 usually rapid rotation of a satellite formed another 
 objection to Laplace's hypothesis, but it seems to be 
 consistent with the new cosmogony. 
 
 With reference to the so-called "moment of 
 momentum " of the solar system, Professor Cham- 
 berlin has shown that the greater portion belongs 
 to the planets, and that Jupiter alone contains about 
 95 per cent, of the moment of momentum of the total 
 mass within the orbit of Saturn. This is, according to 
 
THE NEW COSMOGONY 333 
 
 Moulton, "an inevitable consequence of the spiral 
 theory, but, on the contrary, the whole question of 
 the moment of momentum is a rock on which the 
 ring theory breaks." 
 
 According to the new cosmogony, the outer 
 portions of the matter ejected from the original 
 body would evidently be formed from the surface 
 portions of the star, while the matter which followed 
 would " come mainly from the lower depths," and 
 would probably consist of materials of greater density. 
 The smaller planets should therefore be cool and of 
 high density, and the larger planets hot and of small 
 density. This also agrees with the known facts of 
 the solar system. The average density of Mercury, 
 Venus, the Earth, and Mars is about 4| (water = 1), 
 while the mean density of Jupiter, Saturn, Uranus, 
 and Neptune is only 1*03, or about that of water. 
 We know that the earth is cool, and that probably 
 Mercury, Venus, and Mars are so also, while there is 
 good reason to suppose that the large planets are in 
 a highly heated condition. 
 
 On the whole, Moulton concludes that " the spiral 
 theory is even now a good working hypothesis." It 
 seems to explain satisfactorily all the observed 
 phenomena upon which the ring theory was based, 
 and many others which are in contradiction to La- 
 place's original hypothesis. " Nothing has yet been 
 found which seems seriously to question its validity." 
 
 The new cosmogony will, of course, raise many very 
 difficult questions in celestial mechanics, and will 
 give a considerable amount of work to mathematical 
 astronomers before it can be placed upon a satis- 
 factory basis ; but the work which has been already 
 done by Chamberlin and Moulton shows clearly that 
 
334 ASTRONOMICAL ESSAYS 
 
 the spiral theory is far superior to Laplace's nebular 
 hypothesis, which should now be definitely abandoned 
 and consigned to the limbo of unproved theories. The 
 heavens show us thousands of spiral nebulae which 
 are evidently in a state of rotation round a central 
 nucleus, but which will probably take ages before 
 they have finally consolidated into suns and solar 
 systems. But ages are but moments in the evolution 
 of the stars, and we need not expect to find much 
 evidence of rotation and consolidation during the 
 brief span of human history. Empires rise and fall, 
 dynasties are founded and dissolved, but the heavens 
 move on in their silent course, and the human race 
 will probably have perished before the universe has 
 reached its final destiny. 
 
INDEX 
 
 Absolute brightness of stars, 1G3, 
 
 164 
 
 Abul Wefa, 47, 88 
 Accadians, 10, 23 
 Aohernar, 81 
 Adams, 311, 321 
 Adar, 12 
 Adonis, 17 
 Agathocles, 29 
 Aitken, 307, 323 
 Al-abur, 22 
 Albategnius, 88 
 Albireo, 87 
 Alcor, 83 
 Aldebaran, 20, 82 
 Alderamin, 87 
 Alexandrian library, 35 
 Algenib, 87 
 Algol, 86, 235-237 
 Almach, 85 
 Almagest, 67, 68 
 Almanacs, 31 
 Alnilam, 83 
 Alnitak, 83 
 Alpetragus, 49 
 Alphard, 85 
 Alphecca, 86 
 Alpheratz, 85 
 Alphonsine tables, 88 
 Al-Sufi, 22, 79, chap, xii., 257 
 Altair, 25, 81 
 Alwaid, 87 
 
 Anaxagoras, 10, 17, 53, 59 
 Anaximander, 38, 58 
 Anaximenes, 17, 59 
 
 Andromeda nebula, 145 
 
 Anghiera, 257 
 
 Antares, 82 
 
 Antoniadi, 274, 275 
 
 " Apex," Sun's, 129, 315 
 
 Apollonius, 46, 64 
 
 Aquarius, 23 
 
 Aquila, 24 
 
 AquilsB, Nova, 318 
 
 Arabian astronomers, 24, 47, 49, 
 
 55, 89, 108 
 Aratus, 8, 10, 63, 65 
 Archimedes, 34, 45, 53, 60, 63 
 Argelander, 287 
 Aristarchus, 37, 51, 53, 62 
 Aristophanes, 31 
 
 Aristotle, 16, 19, 37,43, 54, 60, 92 
 Aristyllus, 62 
 Arzachel, 102 
 
 Assyrians, 28, 38, 39, 54, 56 
 Astar, 12, 18 
 Atlas, 24 
 Autolycus, 61 
 Auwers, 306 
 Auzot, 95, 97 
 
 13 
 
 Babylonian astronomers, 36, 39 
 Badovere, 94 
 Bailly, 111 
 
 Barnard, 250, 251, 266, 267 
 Barr, 319 
 Belalcacar, 27 
 Bellatrix, 83, 230 
 Belopolsky, 244, 278 
 335 
 
336 
 
 INDEX 
 
 Benetnasch, 83 
 
 Berenice, 21 
 
 Betelgeuse, 81 
 
 Binary stars, 121, 172, 174-177 
 
 Bode, 192 
 
 Bond, 201, 273 
 
 Book of the Dead, 20 
 
 Borelli, 105, 106 
 
 Bowyer, 322 
 
 Bradley, 97, 175 
 
 Brenner, 275, 276 
 
 Brightest stars, 66 
 
 Brightness of stars, 155-162, 194, 
 195, 229 
 
 Brightness, intrinsic and abso- 
 lute, 163, 164 
 
 Brugsch, 31 
 
 Bullialdus, 105 
 
 Burns, 286, 322 
 
 Caesar, Julius, 3, 14, 43, 107, 108 
 
 Calendars, 13 
 
 Callimachus, 21 
 
 Callippus, 15, 42, 61 
 
 Campbell, 278, 311, 323 
 
 Canis Major, 24 
 
 Canopus, 8, 22, 79 
 
 Capella, 20, 80 
 
 Capricornus, 23 
 
 Cassini, 277 
 
 Cassiopeia, 6 
 
 Castor, 174, 175, 321 
 
 Catalogue of Nebulae, 147 
 
 Cavendish, 123 
 
 Centauri, a, 227, 240, 241, 303 
 
 Centaurus, 24 
 
 Cepheus, 6 
 
 Ceraski, 203, 320 
 
 Chaldean astronomers, 10, 17, 29, 
 
 31, 32, 44, 49 
 
 Chamberlin, 329, 330, 332, 333 
 Chandler, 236, 302 
 Chaph, 87 
 Chi-King, 7 
 Chinese annals, 6, 27, 28 
 
 Chinese astronomers, 4, 6, 15, 16, 
 17, 20, 24, 29, 30, 31-35, 38, 39, 
 44, 45, 49, 107 
 
 Chun-tsiou, 27 
 
 Cicero, 3, 16, 29, 107 
 
 Clairaut, 109, 111 
 
 Clark, 201, 245 
 
 Claudianus, 45 
 
 Clearchus, 38 
 
 Cleomedes, 41, 55, 65, 107 
 
 Clepsydras, 11, 33 
 
 Clocks, 90, 91 
 
 Clusters, globular, 148, 189, 190 
 irregular, 147-150, 189 
 
 Colours of stars, 314 
 
 Coma Berenices, 21, 145, 303 
 
 Comets, 54 
 
 Confucius, 7, 27 
 
 Conon, 21, 63 
 
 Constantinople, Council of, 3 
 
 Construction of the heavens, 130- 
 155, 171, 179 
 
 Copernicus, 48, 55, 99-102 
 
 Corsali, 257 
 
 Cosmogony, New, chap. xxiv. 
 
 Cursa, 87 
 
 Curtis, 305, 321 
 
 D'Alembert, 111 
 
 Dante, 56 
 
 Dark bodies, 122, 123, 254, 255, 
 
 292-300 
 
 Darwin, Prof., 324 
 Davis, 279 
 Dawes, 273 
 Dee, John, 93 
 Deferent, 46 
 Delambre, 55 
 Democritus, 10, 44, 54, 59 
 De Morgan, 65 
 Deneb, 82 
 
 Denebola ( Leonis), 85 
 Denning, 267 
 Descartes, 104, 108 
 Deslandres, 278 
 Digges, 93 
 
INDEX 
 
 337 
 
 Dilgan, 20 
 
 Diogenes Laertes, 58 
 
 Diphda, 86 
 
 " Disc theory," 132, 287 
 
 Distances of the stars, 285 
 
 Doberck, 175, 176, 307, 313 
 
 Dollond, 98 
 
 Doolittle, 317 
 
 Draco, 6, 24 
 
 Draconis, o, 7, 16, 19, 54 
 
 10(0,7,54 
 Duns Scotus, 16 
 
 E 
 
 " Earth-shine," 38 
 
 Easton, 283, 286, 287 
 
 Eccentricity of earth's orbit, 46 
 
 Eccentrics, 46 
 
 Eclipses, 38-41 
 
 Ellerman, 276, 312 
 
 Empedocles, 10, 59 
 
 Enceladus, 97 
 
 Encke, 31 
 
 Enif,86 
 
 Ennius, 29 
 
 Epicurus, 54 
 
 Epicycles, 46-49 
 
 Equant, 48 
 
 Equation of the centre, 46 
 
 Equulei, 5, 232, 233, 243 
 
 Equuleus, 66 
 
 Eratosthenes 10,63,64 
 
 Eros, 308 
 
 Etanin, 86 
 
 Euclid, 9, 62 
 
 Euctemon, 44 
 
 Eudemus, 40, 61 
 
 Eudoxus, 19, 42, 44, 60, 63 
 
 Euler, 111 
 
 Euripides, 59 
 
 External galaxies, 144 
 
 Extinction of light, 288 
 
 Fabry, 201 
 Fauth, 275 
 
 Festus Avienus, 63 
 Flamsteed, 160, 161 
 Fomalhaut, 82 
 Fracastor, 92 
 Franks, 310 
 Frost, 311 
 Furner, 322 
 
 G 
 
 " Gages," star, 133, 134, 136, 138- 
 
 141, 143 
 
 Galaxy. See Milky Way 
 Galileo, 94, 100, 108 
 Gascoigne, 95 
 Gaseous nebulaa, 151 
 Geber, 88 
 Geminus, 44, 66 
 Generini, 95 
 Genesis, 3 
 Germinus, 55 
 Gill, Sir David, 252, 303 
 Globular clusters, 148, 189, 190 
 Glorioso, 93 
 Gnomon, 26, 61 
 Great Bear, 6, 7, 20 
 Gregorian calendar, 14 
 Guthnick, 272, 317 
 
 II 
 
 Hadley, 315 
 Hale, 276, 312, 321 
 Hall, Asaph, 266, 267 
 
 Chester More, 98 
 Halley, 106, 109 
 Halm, 318 
 Hamal, 85 
 Hanumana, 20 
 Hartmann, 293, 306 
 Hartwig, 317 
 
 Harvard Observatory, 277, 280 
 Heliacal risings and settings, 10 
 Helicon, 40 
 Heraclides, 48, 54, 61 
 Heraclitus, 16 
 Herculis cluster, 307 
 
338 
 
 INDEX 
 
 Herodotus, 17, 32, 57 
 Herschel, Caroline, 145, 160, 250 
 Sir John, 173, 190, 249, 
 
 251, 255, 256, 258, 259, 260, 261, 
 
 263, 264, 288 
 Herschel, Sir William, 97, chap. 
 
 x., 274, 281, 287, 302, 303 
 Hesiod, 3, 9, 10 
 Hesperus, 9, 58 
 Hevelius, 91, 96, 97 
 Hi and Ho, 39 
 Hia, 11 
 
 Hieroglyphics, 9, 35 
 Hindoos, 4, 7, 12, 20, 24, 25, 31, 
 
 33, 38, 39, 49, 56 
 Hinks, 322 
 Hipparchus, 10, 11, 24, 30, 34, 39, 
 
 44, 46. 51, 53-56, 64, 96 
 "Holes" in Milky Way, 143, 
 
 chap, xviii. 
 Homer, 3, 6, 8, 9 
 Hooke, 106 
 Horapolla, 37 
 Horrox, 105 
 Horus, 18 
 
 Hours, origin of the, 2, 3, 11 
 Houzeau, chap, xii., 257 
 Hussan-Ali, 47 
 Hussey, 232, 233 
 Huygens, 91, 107 
 Hyades, 6 
 Hydra, 24 
 Hyginus, 10, 21 
 Hypothesis, nebular, chap. xxiv. 
 
 Ibn Yunis, 88 
 
 Ilskhan-Olagon, 88 
 
 Incas, 27 
 
 Indians, 4, 7, 49 
 
 Insulated stars, 171 
 
 Intrinsic brightness of stars, 163, 
 
 164, 229 
 
 Irregular clusters, 147-150, 189 
 Istar, 12 
 
 Jews, 15, 18 
 Joshua, 17 
 Julianus, 99 
 Julian year, 14 
 Jupiter, 9, 16, 31 
 
 K 
 
 Kapteyn, 284, 289 
 
 Keeler, 275, 278, 329 
 
 Kepler, 37, 48, 102-104, 107, 278 
 
 Kien-siang, 45 
 
 Kirkwood, 278 
 
 Koran, 19 
 
 Koue-yu, 44 
 
 Kustner, 317 
 
 Lacaille, 261 
 
 Lagrange, 110 
 
 Lalande, 133, 134 
 
 Lampland, 317 
 
 Laplace, 27, 28, 108, 109, 277, 
 
 324-333 
 Laprey, 94 
 Larissa, 29 
 Lassell, 97 
 Lau, 320 
 Layard, 35 
 Lens, 91, 92 
 Leo, 7 
 
 Leonis, 7, 176 
 Le Verrier, 30 
 Libra, 23 
 
 Lick Observatory, 304 
 Limited number of visible stars, 
 
 280, 281, 282 
 Limiting apertures, 193 
 Lippershay, 94 
 Livy, 3 
 Lohse, 302 
 Lucifer, 9 
 Lunar calendar, 13 
 
INDEX 
 
 339 
 
 Lupus, 24 
 Lyra, 7, 21, 22 
 Lyra, 0, 228 
 
 M 
 
 Magellanic clouds, chap, xix., 
 288, 289 
 
 Magnitudes, star, 164, 165 
 
 Mahabharata, 18, 28, 290, 291 
 
 Maha-yuga, 56 
 
 Manilius, 6, 10, 67 
 
 Markings on moon's surface, 4 
 
 Mars, 9, 12, 13, 16, 30, 102, 103 
 
 Martianus Capella, 45 
 
 Masses of stars, 316 
 
 Ma-touan-lin, 30 
 
 Maxwell, Clerk, 277 
 
 Mayer, 101, 130, 177 
 
 Megalosaurus, 39 
 
 Menander, 3 
 
 Menelaus, 67 
 
 Menkalinan, 84 ' 
 
 Mercury, 12, 16, 30 
 
 Merodach, 12 
 
 Meteoric stones, 19 
 
 Metius, 94 
 
 Meton, 15, 27, 60 
 
 Michell, chap. ix. 
 
 Milky Way, 7, 59, chap, v., 95, 
 130, 132, 133, 171, 173, 190, 
 191, 195-197, 223, 224, 249, 256, 
 281, 282, 284, 285, 288,301,303 
 
 Mimas, 97 
 
 Mira Ceti, 322, 323 
 
 Mirac, 86 
 
 Mirfak, 84 
 
 Mitchell, 321 
 
 Mitra, 18 < 
 
 Mizar, 86 
 
 Moller, 314 
 
 Moon, 16; distance of, 51, 52 
 
 Moore, 19 
 
 Motions, proper, 127 
 
 Moulton, 324, 329, 331, 333 
 
 Miiller, 267 , 
 
 Musical notes, 43, 44 
 
 N 
 
 Nath, 84 
 Nebo, 12 
 
 Nebulse, 147-150, 180-186 
 spiral, 308, chap. xxiv. 
 
 stellar, 187 
 Nebular hypothesis, chap. xxiv. 
 
 regions, 182 
 Nebulous areas, 153 
 
 stars, 150-153, 173 
 Nebus, 35 
 Nergal, 12 
 
 New cosmogony, chap. xxiv. 
 " New " stars, 318 
 Newcomb, 96, 201, 202, 281, 284, 
 
 286, 303, 311 
 Newton, Sir Isaac, 97, 98, 106- 
 
 111 
 
 Nile, rising of, 13 
 Ninip, 12 
 
 Nova Persei, 292, 301, 309 
 Number of stars, chap. xiv. 
 
 Obliquity of ecliptic, 10, 61 
 Odin, 18 
 Offord, 279 
 
 Ophiuchi, 70, 235, 243 
 Oppolzer, 28 
 Orion, 20 
 
 nebula, 145, 174, 186, 252 
 " Orion type " stars, 230, 311, 312 
 Orion's " belt," 6, 197 
 Osiris, 18 
 Ovid, 8 
 
 Palmer, 303 
 
 " Paradise and the Peri," 19 
 
 Parallax of stars, 124-127, 316 
 
 Parkhurst, 312 
 
 Peirce, 277 
 
 Perkins, 279 
 
 Perrine, 308, 309 
 
340 
 
 INDEX 
 
 Persei, Nova, 292, 301, 309 
 
 Phases of moon, 4 
 
 Philolaus, 59 
 
 Philostratus, 41 
 
 Phobos, 332 
 
 Phoebe, 220, 271, 272, 332 
 
 Phosphorus, 58 
 
 Picard, 95 
 
 Pickering, Prof. E. C., 161, 236, 
 
 265, 314 
 
 Pickering, Prof. W. H., 269 
 Pingre, 54 
 Planetarium, 45 
 Planetary nebulas, 146, 147 
 Plato, 3, 19, 35, 60 
 Pleiades, 6, 17, 20, 118, 119, 148 
 Pliny, 4, 41, 59, 108 
 Plough, 20 
 Plummer, 307 
 Plutarch, 27, 29, 30, 38, 41, 54, 
 
 58, 59, 107 
 Pole star, 8, 84, 214 
 Pollux, 82, 214 
 Porta, 93 
 
 Posidonius, 38, 45, 53, 65 
 Precession of equinoxes, 55 
 Proclus, 55 
 Proctor, 276, 279 
 Procyon, 20, 22, 81, 195, 228, 234 
 Proper motions, 127 
 Prosneusis, 47 
 Ptolemy, 19, 21, 24, 28, 34, 44, 
 
 46-50, 52, 53, 66, 67, chap, v., 
 
 96, 100, chap. xii. 
 Pulkowa Observatory, 273 
 Puppis, V, 239 
 Pyramids, 15, 32, 57 
 Pythagoras, 9, 43, 58 
 Pytheas, 61, 107 
 
 R 
 
 Ra, 18 
 
 Radeaux, 271 
 Ramses, 7 
 Ras al-ague, 85 
 " Red bird," 7 
 Red stars, 312, 313 
 
 Reflected light, 166 
 
 Reflecting telescopes, 166-170 
 
 Regulus, 83 
 
 Reinholdus, 102 
 
 Rigel, 22, 80, 230, 231 
 
 Rig- Veda, 24 
 
 Ring nebula, 145, 326 
 
 theory of Milky Way, 133 
 Rings of Saturn, 273-279 
 Ritchey, 98 
 Roberts, C., 275 
 
 Dr. Isaac, 168, 169, 185, 
 
 222, 223, 224, 252, 281, 310, 
 
 326, 327 
 Roberval, 277 
 Roche, 326 
 Roemer, 101, 130 
 Roger Bacon, 93, 108 
 Rogovsky, 268 
 Roman astronomers, 40 
 Rosse, Earl of, 329 
 Russell, H. C., 250, 261, 262 
 H. N., 322 
 
 S 
 
 Sacred fires, 18 
 
 Sagittarius, 23 
 
 Saros, 39 
 
 Satellites of Saturn, 269 
 
 Saturn, 12, 16, 31, 43, 114, chap. 
 
 xx. 
 
 Scandinavian mythology, 2 
 Schaeberle, 276, 327 
 Scheat, 87 
 Schedir, 86 
 Schiller, 257 
 Schmalkalde, 17 
 Schmidt, 37 
 Scorpio, 7, 23 
 Scotus, 16 
 Seasons, 5 
 Secular acceleration of moon, 109, 
 
 110 
 Secular variation of stars, chap. 
 
 xii. 
 
 See, Dr., 231, 304 
 Seeliger, 255, 281, 289, 
 
INDEX 
 
 341 
 
 Seleucus, 107 
 
 Seneca, 16, 19, 33, 48 
 
 Seti L, 7 
 
 Shakspearc, 4, 154 
 
 Sidereal system, chap. xxi. 
 
 Signs of the zodiac, 23, 24 
 
 Simplicius, 61 
 
 Sirius, 5, 10, 13, 14, 20, 22, 78, 79, 
 
 117, 164, 165, 169, 170, 172, 
 
 227, 231, 232, 242, chap, xvii., 
 
 282, 283, 302 
 Slipher, 305 
 Smyth, Admiral, 84 
 Socrates, 16, 59 
 Sola, Comas, 267 
 Solar " apex," 315 
 Solstices, 5 
 Sosigenes, 43 
 Southern Cross, 6, 249 
 Spectacles, 92 
 Spectra of red stars, 312, 313, 
 
 321 
 
 Spectroscopic binaries, 244 
 Spheres, celestial, 24, 34 
 
 crystal, 41-44 
 Spica, 82 
 
 Spiral nebulse, 308, chap. xxiv. 
 Stadium, 66 
 Star clusters, 147-150, 189, 190 
 
 groups, 199, 200 
 
 magnitudes, 164, 165 
 Stars and nebulse, 187, 188, 189 
 Stebbins, 323 
 Steinheil, 201 
 
 Stellar brightness, chap. xv. 
 evolution, chap. xxiv. 
 nebulae, 187 
 universe, chap. xxi. 
 Stockwell, 304 
 Strabo, 27, 92 
 Stroobant, 279 
 Struye, 273, 287 
 Sulpicius Gallus, 40 
 Sun, 16 ; distance of, 51 ; sun's 
 
 apex, 129, 315 
 Sundials, 32 
 Sun's motion in space, 127-130, 
 
 Sun's parallax, 308, 317 
 
 Sun-spots, 30, 160 
 
 Sun's stellar magnitude, chap, xi., 
 
 226 
 
 Suriya-siddhanta, 45, 50 
 Syene, 27 
 
 Tacitus, 3 
 Tai-pi, 12 
 Talmud, 45, 93 
 Tamerlane, 89 
 Tammuz, 17 
 Tatius, 10 
 Taurus, 7 
 Tchang-tse-sin, 45 
 Tcheou-kong, 6, 27 
 Tcheou-li, 29, 33 
 Tcheou-pey, 34 
 Tchong-kang, 28 
 Telescopes, 93-98, 166-170 
 Temporary stars, 318 
 " Terminator " of moon, 51 
 Thales, 16, 28, 57 
 Themis, 270, 271, 272 
 Theon, 10, 55, 59 
 Thor, 18 
 
 Timocharis, 55, 62 
 Torsion balance, 123 
 "Trifid" nebula, 314 
 Trouvelot, 251, 279 
 Tubes, 92, 93 
 
 Tycho Brahe', 47, 48, 56, 89, 91, 
 96, 100, 101, 103, 105 
 
 Ulugh Beigh, 89 
 Ursa Major, 24 
 Minor, 24 
 
 Variable stars, 127, 154, 31.6 
 
 " Variation," 47 
 
 Variation, secular, chap. xii. 
 
 z 2 
 
342 
 
 INDEX 
 
 Varuna, 18 
 
 Vedas, 7 
 
 Vega, 25, 80 
 
 Velocity of stars, 311 
 
 Venus, 8, 9, 12, 16 
 
 Very, 301 
 
 Vesta, 18 
 
 Vindemiatrix, 87 
 
 Virgil, 19, 56 
 
 Virginis, 7 , 176, 177, 233, 244 
 
 Virgo, 23 
 
 Vishnu, 18 
 
 Visible stars, chap. xxi. 
 
 universe, chap. xxi. 
 Vogel, 276, 306 
 
 W 
 
 Walther, 21 
 Waning moon, 4 
 Waxing moon, 4 
 Weber, 267 
 Wezen, 84 
 Wilczynski, 330 
 
 Williams, Stanley, 267, 279 
 
 Wilson, H. C., 302, 315 
 
 Wolf, Max, 253, 309, 317 
 
 Wollaston, 123, 201 
 
 Wren, 106 
 
 Wright, 303 
 
 Wright of Durham, 132, 154, 277 
 
 Yao, 6, 20, 26, 54 
 
 Year, 5 
 
 " Year books," 31 
 
 Yendell, 302 
 
 Young, Prof., 201, 267 
 
 Zenophon, 3 
 
 Zoan, 3 
 
 Zodiac, signs of, 23, 24 
 
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