The original of this bool< is in the Cornell University Library. There are no known copyright restrictions in the United States on the use of the text. http://www.archive.org/details/cu31924064295326 3 1924 064 295 326 Production Note Cornell University Library pro- duced this volume to replace the irreparably deteriorated original. It was scanned using Xerox soft- ware and equipment at 600 dots per inch resolution and com- pressed prior to storage using CCITT Group 4 compression. The digital data were used to create Cornell's replacement volume on paper that meets the ANSI Stand- ard Z39. 48-1984. The production of this volume was supported in part by the Commission on Pres- ervation and Access and the Xerox Corporation. Digital file copy- right by Cornell University Library 1991. HANDBOOK DOUBLE STARS. <-v6f'. A HANDBOOK OF DOUBLE STARS, WITH A CATALOGUE OF TWELVE HUNDRED DOUBLE STARS AND EXTENSIVE LISTS OF MEASURES. With additional Notes bringing the Measures up to 1879, FOR THE USE OF AMATEURS. EDWD. CROSSLEY, F.R.A.S.; JOSEPH GLEDHILL, F.R.A.S., AND^^iMES Mt^'^I^SON, M.A., F.R.A.S. "The subject has already proved so extensive, and still ptomises so rich a harvest to those who are inclined to be diligent in the pursuit, that I cannot help inviting every lover of astronomy to join with me in observations that must inevitably lead to new discoveries." — Sir Wm. Herschel. *' Stellae fixac, quae in ccelo conspiciuntur, sunt aut soles simplices, qualis sol noster, aut systemata ex binis vel interdum pluribus solibus peculiari nexu physico inter se junccis composita. Stellanim siniplicium numerus est quidem major, at vero non nisi te'r'vel forusse bis tantum major quam systematum compositonim." — 2, MACMILLAN & CO. 1879. (E 0iAChS^ Hazell, Watson, and Viney, Printers, London and Aylesbury, PREFACE. This work has arisen out of our own wants as students of that branch of astronomy which deals with Double Stars, and it is on this account that we think it will be useful to others who are occupied in the same work. There does not exist any book which gives information sufficiently detailed to be of value to any one who seriously takes up this study. He must hunt through scores and hundreds of volumes if he wishes to get an accurate and complete list of the previous measures of any particular double star. These measures are scattered up arid down the astronomical periodicals of all nations. If he wishes to know with what instruments, with what apertures, and what micrometers these measures were taken, a fresh research awaits him. And if he proceeds to attempt an orbit, he will fail, unless he is a tolerably expert mathematician, from want of sufficient guidance and detail in the various mathematical papers and pamphlets that have been devoted to this subject. This branch of astronomy is peculiarly suitable to ama- teurs. It does not require long previous training ; it does not demand unintermittent and severe work, nor the resources of a permanent observatory and staff. All it needs is a good telescope, a good eye, some patience, much conscientiousness, and — more than all — such an amount of guidance and co- VI PREFACE. operation as shall convince the amateur that his work is not useless, but that he is really contributing something, however small, to astronomical knowledge. And the construction of double-star orbits has always had a fascination for amateurs from the days of Admiral Smyth and 7 Virginis to the present time ; and it is perhaps the only branch of mathematical astronomy which is quite within the range of unprofessional mathematicians. We venture to hope that this book will be of use in guiding amateurs in their work, — in pointing out what stars are of especial interest, what stars have had few or conflicting measures taken of them, at what times observations of certain stars are especially needful, and what stars have been so frequently and satisfactorily measured that for the present they need no attention. This sort of information has become a necessity owing to the extension of the subject and the number of observers. The Herschels, the elder Struve, and Madler, might with equal advantage measure every double star they saw ; but later observers must select their objects if they do not wish much of their work to be wasted. And so we find that Otto Struve, and Dawes, and Secchi, and others, have chosen stars that were certainly or probably of interest as subjects for their own work. There has probably been no time in which so much work has been done in measuring double stars as during the last six or seven years. They have witnessed Burnham's lists of new double stars, which testify so highly to his telescope, his eye, his climate, and his industry ; Otto Struve's two im- portant volumes on his father's and his own double stars ; Dembowski's lists in the Astronomische Nachrichten ; Duner's valuable volume of observations made at Lund ; in America, PREFACE. Vll the work of Hall, Stone, etc. ; and in our own country, that of Knott and others. The recalculation of orbits, also, is occupying much attention, both among foreign astronomers and at home ; and every year will enable this to be done with greater accuracy, and to be attempted for a greater number of stars. This work, then, consists of four parts. The first part is historical, and descriptive of instruments and methods ; the second is mathematical ; the third part contains lists of measures of the most interesting double and multiple stars, with historical notes on those which are of special interest ; the fourth part is bibliographical. In Part I., Chapter I. contains a historical introduction by Mr. Gledhill. Chapter II. is on the equatorial and the observatory, by Mr. Crossley ; Chapter III. is an account of the equatorials which have been used by double-star observers, by Mr. Gledhill ; Chapter IV. on micrometers, by Mr. Crossley; and Chapter V. on methods of observing, by Mr. Gledhill. In Part II., Chapters I. and II. give a detailed account, with a fully worked example, of determining an orbit and an ephemeris by a purely graphical construction, founded on Herschel's and Thiele's methods, with some fresh extensions, by Mr. Wilson. Dr. Doberck, who has had very great experi- ence in double-star calculations, has contributed Chapter III., giving an example of the application of analysis to a double-star orbit already approximately known by graphical methods, and shows how greater accuracy may be obtained by it ; and Mr. Wilson gives Chapter IV. on the relative rectilinear motion of double stars ; Chapter V. on the effects of proper motion and parallactic motion ; and Chapter VI. on Vlll PREFACE. the mode of combining observations, and determining their weight. Part III. contains a catalogue of double stars selected as of special interest, with a list of all accessible measures, and notes, etc., by Mr. Gledhill. Finally, Part IV. contains the bibliography of the whole subject, and is due to Mr. Gledhill. We may, perhaps, venture to say a word or two on the importance of this part of astronomy. It can scarcely fail to happen that accurate measures of double stars, especially when combined with a study of proper motion, will give in the future some sounder knowledge of the structure of the heavens. The calculation of double-star orbits, and the comparison of observed and calculated places, will bring out not only errors in the observations or of the computer, but the existence of forces that had been unsuspected. Resisting media and the laws of their condensation, unseen companions, and possibly new laws of force, may be discovered. And these investigations must throw light on the origin of these double and multiple systems, and thus indirectly on our own solar system. Again ; if the difference of the linear velocities of the components of a binary system can be directly ascertained by the spectroscope, this fact, combined with a good know- ledge of the orbit and of the period of revolution, and of the apparent mean angular distance, will lead to a know- ledge of the parallax of the system, and therefore also to a knowledge of their mass. At present we cannot see the significance of all that has been discovered : for example, the fact that the orbits hitherto computed are all elliptical, and very nearly all of PREFACE. IX large eccentricity, is too uniform to be an accident, and yet it is too isolated a fact to build theories on with safety. It does, however, seem to prove that these are genuine systems ab initio, and are not formed by the fortuitous approximation of single stars. Nor, again, have we found the reason why the type of triple stars, such as /t Herculis, 7 Andromedae, f Cancri, fi Bootis — a bright primary and a faint binary companion — should be so common. When, further, we come to examine into the colours of binaries, we cannot yet see to what previous stage in their history is owing the absence of red stars in these systems, and the frequency of other colours which in their turn are rare in solitary stars. Spectroscopic observation will doubtless add some information on the point of fact, but will only remove the difficulty one stage further on. Again, the phenomenon of variable and temporary stars has always suggested the notion of a revolving dark companion. This may need further examination, and light may be thrown on the subject from tracing the gradual development of binary systems. In a word, the further study of binaries will help our successors to know what is the development-order of star systems and planetary systems. The present work, therefore, is intended to facilitate the labours of future students of sidereal astronomy, by sup- plying the materials for the study of double stars in a convenient form, and as complete (so far as it is intended to go) as our utmost pains could make it. The distribution of double stars has not been investigated, and it is perhaps at present premature to attempt it until more is known about them in both hemispheres; but there are already plain indications that it is not entirely fortuitous. X PREFACE. A knowledge of their distribution will scarcely fail to throw light on the great problem of the structure of the sidereal universe. Similarly, it will be observed that we devote no chapters to the variability of colour or intensity in the components of double stars. We have been debarred from this branch of the subject by want of time, by the badness of our climate, and by the unsuitability of our instruments. It is to be hoped that this work will be taken up by some one else. Small telescopes, and especially small reflectors, are well suited to the examination of colour ; but if possible a careful spectroscopic examination of each star should be made. We have, however, provided in the bibliographical part of the book some references to the chief works and papers on this subject. We therefore commend this study to amateurs. They may be encouraged by the thought that, with few exceptions, all the great workers in this branch of astronomy have been amateurs ; and be stimulated to exertion by the thought that observations made now will certainly be of value to their successors. The stars will not stand still. How can we be idle, and let slip the time for observations, which, if not made now, can never be made hereafter .' Bermerside, September, 1879. CONTENTS. PART I. HISTORICAL, AND DESCRIPTIVE OF INSTRUMENTS AND METHODS. CHAPTER I. Historical Introduction — Early Observations — Discovery of Binary Stars— The great Observers and their Work . . . . i CHAPTER II. The Equatorial : its construction and adjustments — The Clock — Observing Chairs — The Observatory 1 1 CHAPTER III. Some account of the Equatorials which have been used by Double- Star Observers 31 CHAPTER IV. The Micrometer — Construction — Methods of testing it and for finding the value of one revolution of the screw . . . -So CHAPTER V. Methods of observing Double Stars — Measurement of Angle and Distance — Special Methods — Dawes's Prism — Occasional Methods — A set of Measures — Specimen Forms of Registry — Weights — Contracted Apertures — Precautions and Hints . . 64 PART II. ON THE CALCULATION OF THE ORBIT OF A BINARY STAR. U/ CHAPTER I. Introduction — Statement of Problem — Method of Solution adopted — Preparing the Observations for Use — Reduction to a Selected Epoch— Drawing of the Interpolating Curve— Smoothing the Curve — Employment of Measures of Distance — Drawing the Apparent Ellipse— Determination of the real Ellipse ... 84 XU CONTENTS. CHAPTER 11. PAGE Example of an Orbit worked by a Graphical Method . . . io6 CHAPTER III. Dr. Doberck's Example of an Orbit worked by Analytical Methods 1 18 CHAPTER IV. On Relative Rectilinear Motion 134 CHAPTER V. On the Effect of Proper Motion and Parallax on the Observed Position Angles and Distance of an Optically Double Star . 139 CHAPTER VI. On the Errors of Observation and the Combination of Observations 144 PART III. THE CATALOGUE AND MEASURES. Introductory Remarks 151 A Catalogue of Binary and other Double Stars deserving of attention 152 Lists of Measures, with Historical Notes, etc 175 Supplementary List of Measures 405 Appendix 4x1 Additional Notes to Measures 417 Binary Stars classified 418 Note on Systematic Errors in the Measures of Angle and Distance of Double Stars ^o PART IV. BIBLIOGRAPHY. LIST A. Some of the most important Works and Papers on Double Stars . 425 LIST B. Some Papers on the Micrometer 440 LIST C. Some Papers on the Colours of Double Stars 457 ADDITIONAL NOTES 459 LIST OF ILLUSTRATIONS. Bennerside, Halifax. (Frontispiece.') Temple Observatory, Rugby The Bermerside Equatorial Observing Chairs . Bermerside Observatory Parallel-wire Micrometer . PACE I ID 28,29 30 5« LIST OF PLATES. Map of the Pleiades Interpolating Curves of Castor Graphical Construction of Orbit of Castor Interpolating Curve of 61 Cygni A 4- B Looped Curve of fCancri — — — and C Facing page 56 112 116 138 24S DIAGRAMS. Inverted field of telescope, showing how position aisles are reeistered ....... Curve on Millimetre paper Apparent Orbit of S. bo 2-73 2. 1 196 2. 1356 Z. 1424 Z. 1516 2. 1523 2. 1670 2. 1687 2. 1728 s. 1757 2. 1888 2. 1937 2. 1938 2. 1998 2. 2032 2. 2055 2. 2120 2. 2173 2. 2272 2. 2382 2. 2383 2. 2579 2. 3062 66 95 180 183 247 2S9 262 269 270 281 286 287 290 303 308 312 320 324 328 335 343 349 359 360 371 403 ERRATA. Page 154. No 100. The Dec. should be 28° 55'; see also No. i(X> in the "Measures," p. 202. 154. No. 116. For the magnitudes, read 6, "]. 163. No. 524. The Dec. is 2° 15'. 163. Line I, read, £ Scorpii. 165. The Ref. No. 623 is given twice ; the second should be 624. 275. The formula given are Doberck's modified by Duner. Doberck's formulce are P = 8i°'25 - o°-567 (t - 1850) + o°-oo57 (/ - 1850)'. A = 2"-47 + o"-oi3 (t - 1850). 373. W. and S.'s positions of J Cygni should be 339'i, 335"8. And in the diagram, 1875 should be at the other end of the curve. 406. Line 34. The date of De.'s measure (38°-9, o"'85) is i867*9. 407. Line 22. The measure of h. 4649 in l837"5 wis also by Hj. The plate facing p. 248, illustrating the looped path of f Cancri f and C V is taken from the Observatioru de foulkooa, vol. ix. DOUBLE STARS. PART I. CHAPTER I. HISTORICAL INTRODUCTION. The history of double-star astronomy begins with the year 1779, a year for ever memorable as that in which the greatest of observers began the investigations which created a new department of observational astronomy. The results of the occasional attention 01 astronomers to this class of observation prior to the time of Herschel were small indeed. Riccioli, about the middle of the seventeenth century, saw that ifUrsse Majoris was double, and Kirsch also noted the same fact in 1700. Huyghens saw 6 Orionis as a quadruple star in 1656; in 1664 Hooke first saw 7 Arietis as a double star and a Centauri appears to have been the fourth double star which yielded to the power of the telescope, as Feuill^e is said to have discovered it in 1709 at Lima. Bradley separated 7 Virginis in 17 18, and both Messier and Cassini watched the occultation of the components by the moon.* Castor was found to be a double star in 1719, 61 Cygni in 1753, ^ Cygni in 1755 ; then followed 7 Andro- medse, e Lyrae, 70 Ophiuchi, X Cancri, /3 Scorpii, f Ursae Majoris, etc. Pigott discovered three in I779.t Nor must ♦ See the Histoire de PAcademie Royale des Sciences, for the years 1678 1720, 1774. + Phil. Trans., vol. Ixxi. I 2 DOUBLE STARS. the numerous wide pairs detected by Christian Mayer pass unnoticed. This industrious observer, working at Mannheim with an eight-feet mural quadrant by Bird and a power of about 60 to 80, observed and catalogued a considerable number of stars with Comites.* A short extract from his book f will give a good idea of the character of the objects and his mode of observation : — 1777- Stella cum comite. Comes Aldebaran Comes Electra Comes Algol Gradus lucis. Differentia Ascensionis rectae. Differentia Declinationis. Jan. I .. 13 8-9 Teles. 8 0° 2' 14" -2 008 2 49-5 0° 12' 29" 32 -5 9 9-5 At the end of the volume a table of the new pairs discovered by him (72 in number) is given ; among them are the follow- ing:— Mag. Differentia in R.A. Differentia Declinationis. Dist. 7 Andromedte Castor j" Cancri 2, 6 1, 6 7> 8 5. 5 3. 7 6, 8 3. 7 sec. 0-9S 07 00 o-s 0-S3 0-2 206 3-8 77 6-3 40 3-0 19-9 15-2 ii-o 77 9-9 8-9 y Virginis a Herculis e Ly rse fi CvPTii 36-6 In 1777, Maskelyne, in a letter to Mayer, says that he saw a Herculis double in August 1777, magnitudes 3 and 6, the preceding star being the fainter, and that the distance of the centres was 7". Mayer also wrote two other papers on this subject. J To return. It was in 1779 that Sir William Herschel began to direct his wonderful energy to the observation of double * Mayer says that Flamsteed first used the word comes for the smaller star of a pair. t See his work, De 7iovis in caelo sidereo Phanomenis, etc., 1779. X " Dc centum stellarum fixarum comitibus, eorumque insigni usu ad determinandum moium proprium fixarum; " and " De tniris fixarum comitumque mutaiionibus a me observatis a tempore eel. Flamsteedii." HISTORICAL INTRODUCTION. 3 stars ; and his famous paper is so interesting, and so fully exhibits the state of this department at the time he wrote, that a short account of it may here with propriety be given. The great historical problem of finding stellar parallax had presented itself to him, and with his usual ardour he set himself the task of grappling with all its difficulties. After noticing Galileo's method, and the previous attempts to carry it out by Hooke, Flamsteed, Molineux, and Bradley, and pointing out the cause of their failure, he proceeds to describe his own method, viz., to measure the position angle of two stars of unequal magnitudes at two opposite points of the earth's orbit. He states the essential conditions to be, (i) that the stars be near each other; (2) that their magnitudes be very unequal. He then criticises the attempt made by Dr. Long, and points out the causes of his want of success, viz., unsuitable double stars, and want of adequate optical power. (Dr. Long had chosen 7 Arietis, Castor, 7 Virginis, etc., and his magnifying power did not exceea 70.) His own method is then shown to be independent of refraction, nutation, precession, change of obliquity of the ecliptic, and aberration. The highest possible power is to be used ; and a figure showing a Lyrse under powers from 460 to 6450 is given. Having fully satisfied himself that the method was sound and practicable, the next step was the selection of suitable pairs of stars. And here his own noble words may fitly be quoted : — " I resolved to examine every star in the heavens with the utmost attention, and a very high power, that I might collect such materials for this research as would enable me to fix my observations on those that would best answer my end. The subject has already proved so extensive, and still promises so rich a harvest to those who are inclined to be diligent in the pursuit, that I cannot help inviting every lover of astronomy to join with me in observations that must inevitably lead to new discoveries." — Phil. Trans., vol. Ixxii. 4 DOUBLE STARS. It was in this spirit, and with this glowing enthusiasm, that Herschel began those sweeps and measures which have added so much to our knowledge of the sidereal universe. A full description of his method of finding the position angle and distance apart of the components of a double star, statements respecting the accuracy of his estimations and micrometric measures, etc., are then given. Then comes the catalogue of his discoveries. The pairs given number 269, and they are arranged in six classes, according to dis- tance : Class I., close pairs requiring " indeed a very superior telescope, the utmost clearness of air," etc. II., those suitable for "very delicate measures of the micrometer." III., from S" to IS". IV., from 15" to 30". V., from 30" to i'. VI., from I' to 2'.* Of these 269 objects, 227 were new, 9 were known before Mayer's time, and 33 were known to Mayer and other observers. A single extract will show the form and character of the information given respecting these stars : — "16. 71 Coronas borealis, Fl. 2. " Sept. 9. — Double. A little unequal. They are whitish stars. They seem in contact with 227, and though I can see them with this power, I should certainly not have discovered them with it ; with 400, less than \ diameter ; with 932, fairly separated, and the interval a little larger than with 460. I saw them also with 2010, but they are so close that this power is too much for them, at least when the altitude of the stars is not very considerable ; with 460 they are as fine a miniature of e Bootis as that is of a Geminorum. Position 59° 19' n following."t In 1803 appeared Herschel's celebrated paper announcing the discovery of binary stars, and this was followed in 1822 by a list of 145 new double stars. * Herschel's first measure of a double star is said to have been that of the trapezium in Orion. t Phil. Trans., 1782. HISTORICAL INTRODUCTION. 5 During the first twenty years of this century, notwith- standing the splendour of the discoveries above described, double stars were but little observed. No doubt the prin- cipal cause was the want of instruments of suitable power and construction. In 1816 Sir John Herschel began to review the double stars discovered by his father, and was soon joined by Sir James South. For a list of his papers containing measures, etc., see List A, Part IV. For this distinguished observer, double-star measurement ever pos- sessed a charm ; and from time to time, all through his long life, catalogues, measures, etc., were contributed by him to the Memoirs of the Royal Astronomical Society. Valuable results were also obtained during Sir John's stay at the Cape of Good Hope; and just before his lamented death he was busy at work on a general catalogue of double stars. Two years before the reviews began at Slough, Friedrich Georg Wilhelm Struve, in the distant and ill-furnished ob- servatory of Dorpat, was turning his attention in the same direction. Although an 8 feet transit by Dollond, and a 5 feet telescope by Troughton (power 126), were the only instru- ments at his command, he began to observe the positions, and occasionally to measure the position-angles and distances, of double stars. These results are to be found in the early volumes of the Dorpat observations. And in order to facilitate the study of this subject, he published in 1820 the places of double stars. In 1821 the fine Ertel Circle was received, and in 1824 the famous Fraunhofer refractor was added. Then began the great survey of the heavens between the pole and 15° of south declination, for the purpose of dis- covering new double stars, and the formation of a general catalogue of them. From 1824 to 1835 Struve and his assistants devoted themselves almost entirely to the execution of this noble scheme, and in 1837 appeared the results in the magnificent work entitled MensurcB Micrometrica Stellarum duplicium et muUiplicium. Nor did double stars '/ O DOUBLE STARS. lose their attractiveness at the observatory of Dorpat after the conclusion of this vast undertaking. In 1839 the splendid observatory at Poulkova was established, and in 1861, on the resignation of his father, the directorship was placed in the hands of Otto Struve. From year to year careful and syste- matic measures have been made up to the present time, and the latest publication of the distinguished son of the great Struve is a noble series in two volumes of measures of the most important double stars. Here, too, must be mentioned the labours of Admiral Smyth. With an 8 feet equatorial, this excellent observer measured 680 stars between 1830 and 1843, and the results were published in 1844, under the title Cycle of Celestial Objects. In i860, the Speculum Hartwellianum, containing later measures, etc., was published. Madler, observing with the Dorpat refractor, measured a large number of double stars between the years 1834 and 1845, and published the results in 1847, in an elaborate work entitled Untersuchungen iiber die Fixstern-systeme. In this fine work are given extensive lists of double stars having probable direct motion, probable retrograde motion, and certain motion ; chapters dealing with the orbits of the most important binaries ; very complete lists of measures ; a chapter on the combinations of double stars to form " higher systems," etc., etc. Between 1830 and 1868 Dawes communicated many important lists of measures and papers on double stars to the Royal Astronomical Society. His great catalogue was, however, not published till 1867. This work is enriched by the addition of valuable introductions, notes, and lists of measures made by previous observers. Valuable measures were made at Lord Wrottesley's obser- vatory between the years 1843 and i860. Powell and Jacob, at Madras, made many useful measures, the former from 1853 to 1862, and the latter from 1853 to 1857. HISTORICAL INTRODUCTION'. 7 The Baron Dembowski began his fine series of measures in the year 1852 at Naples. He proposed to measure all the Dorpat " lucidcz" within the reach of his instrument. This important undertaking he successfully accomplished between the years 1852 and 1858 ; and a more valuable contribution to this department has rarely been made. In 1862 he resumed the examination of those Dorpat stars which exhibited changes in angle or distance ; and the careful measurement of the great binaries has been con- tinued up to the present time. The last review also included the measurement of a large number of the double stars discovered at Poulkova. Secchi, in the years 1856 to 1859, paid considerable at- tention to double stars, and in i860 appeared his Catalogo di 1 32 1* stelle Doppie misiirate col grande equator iale di Merz air osservatorio del Collegia Romano. Some years later he also published Serie seconda delle niisiire microm^triclte, fatte all' equator iale di Merz del Collegio Romano, dal 1863 al 1866 inclusive, stelle doppie e Nebulose dal P. A. Secchi. In 1861, the late Rev. R. Main, Radcliffe Observer, began to observe a selected list of double stars. These observations have been published from year to year in the volumes issued by the observatory up to the present time. They have all been made with the Heliometer. At Mr. Barclay's observatory the measurement of double stars has always held a prominent place in the work of the observers Mr. Romberg and Mr. Talmage. Dun^r, at the Lund Observatory, issued a volume of double star measures in 1876. It contains his results from 1867 to 187s, and is a valuable addition to the works on double-star astronomy. Mr. O. Stone and his assistants at the Cincinnati Observatory have for some time paid special attention to double stars, and several lists of measures have already been published. * The number is really 1 22 1. 8 DOUBLE STARS. Mr. Burnham, of Chicago, has published no less than nine catalogues of double stars, his own discoveries, since 1871 : all these objects have also had their positions and distances either measured or estimated by this most industrious observer. Dr. William Doberck, at Markree Observatory, has taken up this branch of astronomy with great spirit and success. For some of the results of his labours see List A. Professor Pritchard, of the new Oxford University Obser- vatory, assisted by Messrs. Plummer and Jenkins, is making careful measures of the principal binaries, and is also engaged in a re-investigation of their orbits, by a method possessing some new features, and which seems to yield good results. M. Camille Flammarion has devoted himself with great ardour to double-star investigations : his catalogue of im- portant objects, with lists of measures, will shortly be published. This subject has always attracted the attention of patrons and wealthy amateurs, and the names of Lord Wrottesley, George Bishop, Esq., J. G. Barclay, Esq., Colonel Cooper, Edward Crossley, Esq., Isaac Fletcher, Esq., M.P., and G. Knott, Esq., must here be mentioned as deserving of special praise for the spirited manner in which they have established and supported observatories for the prosecution of this class of observation. Lastly, compilers of useful catalogues of binary stars and the writers of handbooks must not be forgotten : among the former, Mr. A. Brothers, F.R.A.S., and among the latter the Rev. W. A. Darby, M.A., and, above all, the Rev. T. W. Webb, M.A., deserve especial mention. Measures by the following observers and others have also been published: Auwers, Bessel, Bond, Brunnow, Challis, Dunlop, EUery, Encke, Engelmann, Ferrari, Fletcher, Galle, Gledhill, Hall, Hind, Hold en, Jacob, Kaiser, Knott, Lassell, Maclear, Miller, Mitchell, Morton, Newcomb, Nobile, Powell, Schiaparelli, Seabroke, Sporer, Waldo, Wilson. THE BERMERSIDE EQUATORIAL. CHAPTER II. THE EQUATORIAL: ITS CONSTRUCTION AND ADJUSTMENTS. In making a few remarks upon the instruments required by double-star observers, it is not our intention to give an ex- haustive description, but rather to confine ourselves to a few points which may serve as some guide to the amateur who wishes to provide himself with these instruments, or who, being already equipped, desires to set to work with confidence. It is first of all necessary to be furnished with a good refractor or reflector, equatorially mounted, of sufficient aper- ture, and driven by clockwork. And we do not hesitate to say that we much prefer a refractor, as being more stable in its adjustments, less disturbed by atmospheric conditions, and more durable in its optical surfaces, — conditions which seem to us to do more than counterbalance any advantages arising from the smallness of the star discs, and the absence of colour obtained from good reflecting telescopes. We will assume that an equatorially mounted refractor is chosen. This should be of not less than six inches aperture, in order to be generally useful. An aperture of eight or nine inches would be a liberal and handsome provision. Good work may be done on some stars with smaller apertures, but we are afraid they would cause disappointment by their limited power. To obtain a good instrument, it is best to secure the ser- vices of a first-class maker, who has made large equatorials his speciality. Among English makers it is hardly necessary to mention such names as those of Messrs. Troughton and 12 DOUBLE STARS. Simms of London, T. Cooke and Sons of York, and Mr. Howard Grubb of Dublin, whose well-known achievements speak for themselves. We will now take up the different parts of the equatorial, beginning with the object glass. This requires the greatest possible amount of skill and patience in its construction, and great care should be exercised in its selection by the employ- ment of suitable tests. After examining the lenses in their cell by transmitted light, to discover any flaws of serious magnitude (for minute sand- holes and bubbles are not serious), and then looking at its two outer surfaces by reflected light to see if the polish is uniform and good, replace the object glass in the tube and turn it upon some elevated object, as a church spire or chimney with a bright sky background. Focus carefully with a low power, and if the outlines are sharply defined and free from colour, the probability is that the glass is fairly achromatic. To render this test more severe, Stokes recommended that half the object glass should be covered by a semicircular piece of cardboard. For the next test the instrument must be directed to the sky at night, and some patience and judgment will be needed in selecting a night suitable for the work. Examine the moon or any of the larger planets at an elevation of not less than 30° above the horizon, the higher the better; and if there be sharp- ness of outline, distinctness of detail, and absence of vibration, the night is one suitable for the purpose. Now turn to stars of different magnitudes, as near the zenith as may be, using a high power; and if clean round discs are obtained, free from wings and stray light, the result is so far satisfactory. Next examine the rings which surround the central small disc, when the eyepiece is moved a little within and without the focus. If the rings are circular, and each of uniform brightness all round, and sharply distinct from one another, the lens may be con- sidered well centered and corrected. If the glass should fail THE EQUATORIAL. 1 3 under this test, it must be carefully adjusted by the centering screws. It is, of course, best to have this done by the maker before the instrument leaves his workshop. The central portion of the glass may now be covered with a disc of paper whose diameter is two-thirds of that of the aperture. Focus sharply on a star; remove the disc, and cover up the outer portion of the object glass with a diaphragm whose aperture is also two-thirds of that of the glass. If the focus remains unaltered, the figure is good. The tests for separating and illuminating power may next be applied. Close double stars and minute points of light will supply the means. This can only be effectually done on the finest nights. For lists of test objects and valuable information on these and other cognate matters, the excellent little book by the Rev. T. W. Webb, Celestial Objects for Common Telescopes, should be consulted. It is scarcely necessary to discuss at length the merits of the different forms of mounting of the equatorial. The German form of mounting is now almost universally adopted, and with modern excellence of manufacture it may be considered quite equal in steadiness to the old English form. The essential points are rigidity, strength, durability, and accuracy, facility, and permanence of adjustment. The tube is often made of sheet brass ; sheet iron is lighter, cheaper, and more durable. The declination axis and polar axis should have plenty of bearing surface, and be of ample strength. The weight upon the polar axis should be relieved by friction rollers. The declination and hour circles should read by opposite verniers to 10" or 20" of arc, and i or 2 seconds of time respectively. The declination circle may be placed next to the telescope tube, so as to be read off conveniently by a reader from the eye-end, suitable illumination being provided. The hour circle should be moveable, and the telescope should have a clamp and slow 14 DOUBLE STARS. motion in declination. The clockwork should be strong and powerful, a weak clock being one of the commonest defects of equatorials. Slow motion is also required in right ascension, and it is usually obtained by means of differential wheels in connection with the driving clock, an endless cord being brought to the eye-end. The tangent screw of the driving arc should be capable of perfect adjustment, and should not have to be removed from the arc for the purpose of releasing the telescope from the clockwork. This should be done by a clamp on the polar axis. The lamp for illuminating the micrometer is best placed at the end of the declination axis, away from the telescope, the axis being perforated for the light to pass through into the tube, whence it is reflected at right angles to the eye-end, either by a re- flector just outside the cone of rays, or by a tiny reflector say one-eighth of an inch in diameter, in the centre of the cone, and carried by an arm in such a manner that it can be moved to one side at pleasure. The first plan is perhaps the least objectionable ; the latter is, however, adopted by Mr. Grubb. In Messrs. Cooke's form of mounting, the whole instrument is carried upon a heavy central iron pillar, which takes up less space in the observatory than any other form, and does not interfere with the observing chair in any position of the instrument. The base of the pillar being turned true in the lathe, is also easily bedded in the foundation-stone. The following principal adjustments should be provided for, viz., (i) the polar axis in altitude ; (2) the whole instru- ment in azimuth ; (3) the eye-end for coUimation ; (4) the verniers of both circles for index errors. The declination axis is commonly set by the maker at right angles to the polar axis. When the bearing surfaces of this axis are not equidistant from the polar axis, or bear unequal weights, there may be a tendency to unequal wear, and therefore to change of inclination, unless the bearing surfaces are proportional to the weights they carry. THE EQUATORIAL. 1 5 Before erecting the equatorial it will be well to see that the stand is carefully marked with a north and south point by the maker, and that a meridian line be drawn through the centre of the foundation-stone to the walls of the obser- vatory. After preparing and levelling the stone, it is now easy to set the instrument to the meridian line approxi- mately, or at least within the limits of the adjusting screws in azimuth. We must now determine the following errors of the instru- ment, and make the necessary corrections : — 1. Error of altitude of the polar axis. 2. Index error of the declination circle. 3. Error of collimation, or deviation of perpendicularity of telescope to the declination axis. 4. Error of azimuth, or deviation of the polar axis from the plane of the meridian. 5. Index error of the hour circle. 6. Error of the declination axis from true perpendicularity to the polar axis. No. I and No. 2 are determined by the same set of obser- vations. Bring the telescope approximately into the plane of the meridian, say on the west side of the polar axis : put in the wire micrometer with a low power, and bring one of the moveable webs into the centre of the field of view approxi- mately. Make a star run along the web by means of the slow motion in declination: move the micrometer through 180°, and if the star will not now run along the web from side to side of the field, bring the web half-way towards the star by turning the micrometer screw, and then set the star on the web by the slow motion in declination. Again, turn the micrometer through 1 80°, and if the star now travels along the web, the latter passes through the centre of the field of view, or the centre of rotation of the position circle of the micrometer. Now set the centered web on a bright star south of the zenith near the meridian whose position is given in the 1 6 DOUBLE STARS. Nautical Almanac. Clamp in declination and read off the declination circle. Unclamp, swing the telescope over to the east side (being careful not to disturb the micrometer), set on the star again, clamp, and read off as before. It the star has north declination, the correction for refraction is subtracted from the readings ; if the star be south of the equator, add the refraction correction. If the star has north declination, and half the sum of the two readings corrected for refraction be greater than the true declination as given in the Almanac, the north pole of the instrument is too high ; if less, the pole is too low. If the star is south of the equator, and the result be too great, the pole is too low ; if too small, the pole is too high. Half the difference between the two readings in either case is the index error of the declination circle. The following example will illustrate this : — Jan. 28, 1878. Aldebaran was placed on the centered web. Dec. Circle. Telescope West, 16° 17' o") ,0 , „ ^t 16° 17' o"/ ™^^° "^ '7 o N. Telescope East, 16° 16' 40") ,<, ,, „ .. 16° 16' o") ™^^" '° '" ^° N- Sum Half sum Correction for refraction . . . Observed declination True declination Error of altitude of polar axis, too high 3" The correction for refraction is obtained thus : — Colat. of place 36° 18' North declination of star 16° 16' 32° 33' 20" 16° 16' 40" 44" 16° 15' 16° 15' 56" 53" Approximate altitude 52° 34' Mean refraction, 44". THE EQUATORIAL. I 7 The mean refraction is sufficiently correct for our purpose. A mean refraction table is to be found in all collections of mathematical tables, and in many astronomical handbooks. 3. If the polar axis is not far from the plane of the meri- dian, the error of collimation, — that is, the deviation of the telescope from perpendicularity to the declination axis, — can easily be determined as accurately as the hour circle will admit of. Thus : place the telescope on the west side, and near both the meridian and the equator. The micrometer having been undisturbed, turn it throug hgo" : the centered web now points to the pole. Set the telescope a little in advance of the nearest bright star, and note by the sidereal clock the time of transit across the web. Read off the hour circle : throw the telescope over to the east side, transit the same star, and read off as before. If the difference between the transit times be greater than that of the hour circle readings, the angle formed by the telescope and the declination axis is too great towards the eye-end, and the eye-end must be moved towards the declination axis. If the difference of the transits is less, the angle is too small, and the eyepiece must be moved away from the declination axis. Half the difference between the interval by the clock and that by the circle is the error. The following example will exhibit the method of proceed- ing in this case : — Jan. 28, 1878. 8 Ononis. Dec, 0° 23' 28". Clock. Circle. M. 5. M, s. Telescope West ... 20 26 25 32 „ East ... 23 45 28 40 3 19 38 Half the difference, 5*5 s. x cos. 23' 28" = error required. As the clock interval is the greater, the eye-end must be moved towards the declination axis so as to diminish the angle between the telescope and the declination axis. 4. The error of azimuth is not so easily determined as the 2 1 8 DOUBLE STARS. previous errors, on account of the difficulty in correcting for the effect of refraction. This can be done by calculation, as is fully explained in Loomis's Astronomy, Arts. 32, 145 ; but it can also be done quite effectively, and much more readily, by the following method. Centre the web of the micrometer, set the telescope to the true declination of a Greenwich star about six hours east or west of the meridian, and from 30° to 60° in altitude. Sweep to the star in right ascension with the finder, and if the star is some distance from the centre of the field, move the telescope in azimuth until it passes a little below the centre of the field. Now take a small clinometer, (which can be readily constructed with a piece of hard wood, a semicircular protractor, and a small plumb-line,) and place it on the telescope ; read off the altitude to the nearest degree. Rotate the micrometer until the fixed wires are approximately in the vertical plane. Find the mean refraction for the ob- served altitude from the Table of Refractions. Now bring the web that is not centered below the centered one by a distance equal to the angle of refraction. Set in azimuth so that the star will pass through the intersection of the lower web and the fixed wires of the micrometer. Repeat the operation on a star in the opposite quarter of the heavens ; and if this star also comes to the corresponding intersection the polar axis is in the plane of the meridian. If the micrometer screw have 100 threads to the inch, and the focal length of the object-glass be measured from its centre, the angular value of one revolution of the screw will be known well enough for the above purpose. (See the chapter on the Micrometer.) 5- The index error of the hour circle can only be determined by an independent observation for time, unless the declination axis is provided with a striding level for the purpose of render- ing it horizontal, or truly east and west. In this latter case, all that is necessary after levelling is to set any division of the hour circle at the index point of the vernier which moves THE EQUATORIAL. 1 9 with the telescope, then adjust the index point of the fixed vernier to the same division, and this will be the south reading. It is, however, still .more convenient, when it can be done, to set the fixed vernier east or west according as the Observatory is west or east, by the difference in time between the longitude of the Observatory and Green- wich : this will save the trouble of always having to add or subtract this quantity from the right ascension of a star when setting the telescope by the circles. If the declination axis is not provided with a level, which is seldom the case, as it is not indeed necessary, then sidereal time must be obtained from occultations of stars by the moon, from Greenwich time when telegraphed to the nearest post-office or railway station, by Dent's Dipleidoscope ; or, best of all, from a small transit instrument of about two inches' aper- ture; for such an instrument will give the time to the tenth of a second, and help to make the Observatory com- plete and independent. The telescope can now be brought into the meridian by a star at the time of transit, and the fixed vernier set as before. 6. The error of the declination axis from true perpendicu- larity to the polar axis should be so small as to fall within the error of the setting of the instrument. It is not usual to provide an adjustment for this error, as such would tend to weaken the construction of the instrument. It should, however, be determined by the following method : — Set the telescope on a star of not less than 40° north de- clination, and near the meridian ; transit, read ofiT the hour circle, and reverse the position of the telescope, as in the third adjustment. If there be no difference between the intervals, there is no error in the inclination of the declination axis to the polar axis : i.e., it is at right angles to it. If, however, the interval by the clock be greater than that on the hour circle, the declination axis towards the telescope is at too great an angle with the polar axis, — and vice versd. Half the 20 DOUBLE STARS. difference of the intervals (expressed in arc) divided by the tangent of the star's declination gives the error of inclination required. The whole of these six adjustments should be repeated several times, and also from time to time, as they are liable to change. As the errors mutually affect each other, the second set of observations will be more accurate than the first, and should be made with greater care. Having completed the adjustments of our equatorial, we are now ready to set the telescope upon any object in the heavens which we may wish to observe, whose right ascension and declination are given in our catalogues. First, set the telescope in declination, and then set the moveable hour circle to the right ascension of the object by the fixed vernier (with no correction for longitude if the fixed vernier is put to the Greenwich meridian, as above recommended). Now sweep the telescope in right ascension until the upper vernier comes to sidereal time by the clock, and the object will be in the field of view. It will now be desirable to determine, approximately, the focal length of the object-glass, the angular value of the field of view with each eyepiece, and the magnifying powers of the eyepieces. The makers usually furnish the first and last of these, but it is well for the observer to ascertain these values for himself with some care. Firstly : to find the focal length of the object-glass. This is not a very easy matter, owing to the difficulty of finding the optical centre of the glass. According to Troughton, " the measure.should commence from the interior part of the convex lens, at a distance from its exterior surface equal to one-fifth of the thickness of the double compound object- glass." (See Pearson, p. 19.) This point can of course be readily found by first ascertaining the thickness of the lens. A long, stout straight-edge, placed on the tube of the tele- THE EQUATORIAL. 21 scope and made level, will enable the observer to find the distance between the object end of the tube and the webs of the micrometer adjusted to stellar focus. A plumb-line gives the two points very quickly and accurately. If the telescope be not a large one, the following method will give good results : focus on a terrestrial object at a well-measured distance, and mark the draw-tube ; then focus on the sun, and again mark the tube ; then the formula P _ P. (r - F) F where F = the length of the solar focus required, F' the length of the conjugate focus obtained from the terrestrial object, and D the distance of the object. Of course, the distance between the two marks on the draw-tube should be measured very carefully by means of a finely divided rule and a pair of compasses. The distance between the telescope and the terrestrial mark must be measured from the object- glass. Again ; the focal length may be accurately determined as follows : find the value in arc of say 50 revolutions of the micrometer screw. This will of course be readily done by separating the webs 50 revolutions, transiting a star near the equator (or, better, a star not far from the pole), and reducing the observed interval by multiplying it by the cosine of the star's declination, and by 15. Next, measure with great accuracy the linear value of the space between the webs,* then the proportion 2 tan ^ the arc : radius :: linear value : focal length will give the required quantity. Secondly: to find the angular value of the field of view of the several eyepieces when in the telescope. This is easily done. Allow a star very near the equator to transit the field centrally, and convert the observed sidereal time into arc. If a chronometer or mean-time clock be used, the mean- * The practical optician can do this with very great accuracy. 2 2 DOUBLE STARS. time interval must, of course, be converted into its equivalent sidereal interval, and then the arcual value found from the table. (See Loomis's Astronomy, p. 363.) Do this with each eyepiece. The angular value of negative eyepieces may also be found thus : as the field of view of a telescope depends partly on the focal length of the object-glass, and partly on the diameter of the diaphragm placed at its focus, the fol- lowing formula will give it : F is the focal length of the object-glass, and d the diameter of the diaphragm of the eyepiece, both in inches : — d F sin. l" This is Delambre's formula.* Thirdly : the magnifying powers of the eyepieces have to be found. One of the following methods may be chosen. 1. Measure the small illuminated circle seen in front of the eyepiece (which is the image of the object-glass), by means of the Dynameter. Then, the aperture of the object-glass is . to the diameter of its image at the focus seen through the eyepiece in the ratio of the focal length of the object-glass to that of the eyepiece. That is, the diameter of the object- glass divided by that of the small image gives the magni- fying power. The small image may, of course, be measured without the aid of the Dynameter, by means of a finely divided scale. Or the " Berthon Power-gauge " t may be used. 2. In the case of small telescopes the powers may be con- veniently found by means of a piece of white paper, say one inch long, on a black ground, fixed at a known distance from * To take Pearson's example : let the focal length of the object-glass be 3'5 ft., and the diameter of the diaphragm of a negative eyepiece o'3 in. : then 4.2 x '000004848 = '000203616, and -r^~-i^^ = Hiz" = 24' 33"- t The Rev. T. W. Webb {Celestial Objects, p. 7) speaks highly of this little instrument, which he says may be purchased for Ts. td. of Mr. Tuck, watch-maker, Romsey. THE EQUATORIAL. 23 the object-glass, a staff divided to inches being also placed near the paper. On looking through the telescope at the paper with one eye, and at the staff with the other at the same time, the number of inches on the latter covered by the paper will be seen, and the power at once found for that distance. From this terrestrial power, P', the stellar power P is obtained from the following formula, F being the stellar focal length and F' the terrestrial : — p_ F X F F' ■ 3. The following method is convenient. Place a staff divided into feet and inches against a wall in a vertical posi- tion ; at a distance of three or four feet from the staff, hold the eyepiece to the eye, and, looking through it with one eye, and at the staff with the other eye, note how many feet and inches are contained in the diameter of the field of the eyepiece. For example, let the distance from the staff be 48 inches, and the observed diameter of the field 40 inches ; then the tangent of half the angle = ^ = o"4i6, and the angle is 45° 14', or 162840 seconds of arc. Now if the angular aperture of the telescope with this eyepiece be 33 sidereal seconds (found by transiting, centrally, a star very near the equator), or 495 seconds of arc, we have n, ., . angular subtense 162840 Magiufying power = — 1— — = • -3i- = 329. ' ^ "^ angular diameter 495 4. Valz's method is useful for small telescopes. Turn the telescope towards any celestial object of known angular mag- nitude, say the sun, whose angular diameter is given in the Nautical Almanac, page II, of each month. Let the image be received on a screen kept at right angles to the tube, and having a line nicely divided into inches and tenths marked on it. Observe the horizontal diameter in inches and tenths of the image on the screen. Then if a be the sun's true diameter, A the angular diameter of the image on the screen' 24 DOUBLE STARS. and D the distance between the middle of the eye-piece and the screen, then we have tan i A = i-^, and the magnifyine power = '15_iJ^ = _^^ _ . ° -^ » ^ tan 4 3 2 D tan i a The measure of the image should be made when the sun is in the centre of the field of view. The thickness of the webs of the micrometer may be found by bringing one up to a fixed web until the bright space between the two is estimated to be equal to the thickness of the web which is moved : read off" the divided head, and then carry the web into contact with the fixed web. Read off again. Repeat five or ten times. Take the mean value, and convert it into arc. The following information, drawn up in a tabular form, may, for convenient reference, be pasted inside the box containing the eyepieces : focal lengths of telescope and finder ; angular value, in arc, of the field of view of each eyepiece of telescope and finder ; magnifying powers of the eyepieces ; value in arc of one revolution of the micrometer screen, and a table for taking out at sight the arcual value of revolutions and parts ; the thickness, in arc, of the webs of the micrometer. For fuller information on these and other matters, the following works may be consulted : Loomis's Practical Astronomy, published by Harper and Brothers, New York. (This work is essential.) Webb's Celestial Objects for Common Telescopes. Pearson's Practical Astronomy. Chauvenet's Practical and Spherical Astronomy (London, Triibner and Co.); and Briinnow's Spherical Astronomy (Asher and Co., London). The Nautical Almanac for the current year, a collection of mathematical tables (such as Hutton's or Chambers's), and a good Star Atlas, are of course necessary. 25 The Clock. A common well-made clock, if the pendulum be properly constructed and suspended, is all that is necessary for double- star observers. The piece supporting the pendulum should, of course, be very firm, and securely fastened to a good wall. The pendulum rod, 46 in. long, may be made of well- seasoned white deal soaked in melted paraffin, and % in. in diameter; the bob should be of lead, and cylindrical, its length (for a seconds pendulum) being, say, I4'3 in., diameter if in. with a hole a little more than f in. in diameter for the rod to pass through. The bob should be supported on the rod by means of a stout nut and screw, the latter having not more than thirty threads to the inch. A leaden bob of these dimensions would weigh about 13^ lb., which is found in practice to be a suitable weight. Such a clock, beating seconds audibly, would keep its rate unchanged for a few hours, and would meet all the requirements of double-star work. The rate would be obtained with the aid of a small transit instrument, or the equatorial itself, if well adjusted ; or the finder of the latter instrument might be used for this purpose. The rate should be small, and a losing rate, in order that the correction which becomes necessary from time to time may be made by putting the minute hand of the clock forward. If the clock be losing, say, ten or twenty seconds per day, the bob may be readily put near its true place by means of the nut under it, with the aid of the following formula : — Change in one day = 43200 y seconds, where L is the breadth of one thread of the adjusting screw, and / is the length of the seconds pendulum ; from this the effect of one turn of the nut on the clock's rate is obtained. Or, to put it in a still simpler way : if n be the number of turns of the screw in i inch, then L = ^, /= 39-138; and the change in seconds for one turn of the screw = ;;^^fp = ^^- 26 DOUBLE STARS. Assuming that the losing rate has been reduced to, say, two seconds per day, and that it is desired to make it about half a second, either of the following methods may be adopted : — (a) Place a small sliding metal collar on the rod, its weight being about xrrW^^ °^ *^^*- ^^ *^^ pendulum (bob and rod). At first this collar should be placed about 9 inches from the spring, and then gradually pushed downwards until the rate is what is desired. (3) Let the sliding collar take the form of a cup into which small shot may be put, and let it be _/£r«// to the rod at 19I inches from the spring. By trial the effect of one shot or of any number may be found, and the necessary change in the rate effected very readily. The following extract from Baily's paper, in the Memoirs of the Royal Astronomical Society, vol. i., will be interesting in this relation. Difference. Sec. + I '02 0-97 o'gi 0-85 079 074 0-68 0-63 0-56 0-51 0*46 0*40 o'34 0-28 0-23 O'll + o-o6 o'oo — o-o6 O'll 0T7 0-23 Distance from axis in inches. Variation in the rate per day. I + I -08 2 2'IO 3 4 S 6 7 3-07 3-98 4-83 562 636 8 9 7-04 767 10 823 TI 874 12 9"20 13 9 60 14 9-94 15 I0'22 16 10-45 17 10*62 18 1073 19 1079 20 1079 21 1073 22 10-62 23 IO-45 24 + 10-22 OBSERVING CHAIRS. 2^ If the pendulum is found to go slower in warm weather zxiA faster in cold, it is ww^^r-compensated, and more mercury should be put into the cylinder ; if faster in warm and slower in cold weather, mercury must be taken away, the quantity in each, case being found by trial. Valuable information may be found in Baily's paper above referred to, in those by Bloxam (" Monthly Notices," vols. xiii. and xviii.), and in Denison's excellent " Clocks and Locks " (Adam and Charles Black, Edinburgh). Observing Chairs. As the work of the double-star observer is laborious, and often protracted, it is essential that he should be in a com- fortable position for his work. Ordinary chairs and steps are quite insufficient for this purpose, though they often constitute the sole furniture of an observatory. A special chair is required which will support the observer from head to foot, in any position of the telescope ; such is Dawes's chair (see Figs, i and 2). We have used it for several years, and should not like to be without it. It con- sists of a horizontal wooden frame on castors, 6 feet by 2 feet 4 inches, well braced to an upper frame, and inclined at an angle of 35° from top to bottom ; upon this upper frame is a sliding piece, carrying the seat which is nearly horizon- tal. The sliding piece is held at any point by a stout catch in a perforated iron plate on one side. The seat is 2 feet by I foot, and is padded ; the back is also padded, and it is so hinged to the seat that it can be raised to any position by means of a handle on the left-hand side, and then clamped to an arc on the right-hand side of the observer : this padded back is 2 feet by 2 feet 9 inches. It may thus Fig. 2. THE OBSERVATORY. 29 be raised and clamped at any angle without leaving the chair. Dawes used a rack for supporting the back, but the clamp is more convenient. An arm is also attached to the chair on the right-hand side ; this can be set at any angle by means of a notched arc, catch rod, and handle ; and it makes an excellent rest for the right arm. An iron hook on the left-hand side of the chair carries a reading lamp. Fig. 3. (A Chair for occasional use.) The Observatory. The best form of Observatory is a square room with cylin- drical dome. The corners of the room are always useful, if not necessary, for tables, shelves, chairs, etc. ; and the cylindrical dome is manifestly more easily constructed than the spherical form. The shutters work horizontally, and are less liable to stick than curved shutters. Sufficient slope should be given to the roof to throw off a heavy fall of rain, and the top at least may be covered with thin sheet 30 DOUBLE STARS. copper well painted. The conical form of roof is very effective, and also very cheap. The Transit Instrument will require a small room, say 12 feet square, or rather less. A Computing Room, on the north side of the Observatory, may be added, and this may be provided with a stove and chimney for heating the hot-water apparatus by means of which the observing rooms are kept dry in wet and cold A'\f- MR. EDWARD CROSSLLY S OlSLRVATORY, DERMLRSIDE weather. The hot water must of course be turned oft some time before the work of observation begins. Four windows, north, east, south, and west, are of great use in ventilating the Observatory, and in rapidly reducing the temperature inside as nearly as possible to that outside, so as to avoid currents of heated air, which are so detri- mental to optical definition. 31 CHAPTER III. SOME ACCOUNT OF THE EQUATORIALS WHICH HAVE BEEN USED BY DOUBLE-STAR OBSERVERS. AUWERS. (See KONIGSBERG.) Barclay. (See Leyton.) Bedford. The mounting of the 8^ ft. equatorial was by Dollond, the Sisson form being used. The object-glass had a diameter of 5 '9 in., and was purchased in Paris by Sir James South. Tulley worked it. " It is considered by Captain Smyth to be the finest specimen of that eminent optician's skill, and will bear, with distinctness, a magni- fying power of 1200." The declination and hour circles had a diameter of 3 ft. : the former read to 10". The negative powers were 22 to 1200, six of the highest being single convex lenses fitted in a polycratic wheel. The powers of the parallel-wire micrometer ranged from 62 to 850. The finder had an aperture of i'6 in. The driving clock was invented by Mr. Sheepshanks, and had a steam-engine governor and absorbing wheel. It worked very well. — Monthly Notices, R. A. S., vol. i., and the Celestial Cycle. Observer: Admiral Smyth. Berlin. The refractor at this Observatory is similar to the famous Dorpat telescope in all essential respects. Observers : Encke, Galle, Winnecke. 32 DOUBLE STARS. BermerSIDE (Halifax). Mr. Edward Crossley mounted his 9^ in. Cooke equatorial refractor in 1867. Its focal length is I48'5 in. The style of mounting is German. The diameter of the declination and hour circles are respectively 23J in. and I2| in., and they read to 10" and 2 sec. The lamp, which gives a bright field to the micro- meter, swings at the end of the perforated declination axis. The aperture, and amount and colour of the light for the bright field, are regulated from the eye-end by means of rods, and a rod and cords at the same end give the observer full control over the motion of the instru- ment in right ascension and declination. The finder has an aperture of 2 J in., and a focal length of 2 ft. 4 in. The negative eyepieces are ten in number: powers, 60 to 1000. There are three micrometers, two filar and a double- image. The double-image and one of the filar micro- meters are by Simms, and the other filar by Cooke. The eyepieces for these instruments are, in all, seventeen in number, and the powers range from 100 to 1200. The new filar micrometer by Simms is divided on the face : diameter of circle 4§ in. The driving clock is by Grubb of Dublin. Observers : Crossley and Gledhill. BESSEL. (See KONIGSBERG.) Bond. (See Cambridge, U.S.) Bonn. The heliometer of this observatory has an aperture of 6 in. The driving clock works "remarkably well," and its EQUATORIALS. 33 construction is similar to that of the Poulkova refractor — Memoirs of R. A. S., vol. xx. BrunnOW. (See DLTNSINK.) BuRNHAM. (See Chicago.) Cambridge (Northumberland equatorial). English mounting : the tube is square, and of deal. Object-glass by Cauchoix, ii| in. aperture, and 19^ ft. focal length; it was received in 1834. Hour circle S^ ft. in diameter, and reads to i sec. The circles were gradu- ated by Simms. — Main's An Account of tlie Observatories in and about London. Declination axis, 5 ft. 8J in. long. Finder, 2f in. aperture, and 28J in. focal length. The declination is obtained by means of divided rods. For a full account, with elaborate drawings, see Airy's account of the instru- ment. — Account of the Northumberland Equatorial and Dome. Observer: Challis. Cambridge (U. S.) This instrument is of the same style of mounting, size, and by the same maker, as the Poulkova refractor. Focal length 22 ft. 8 in., aperture i S in. " No colour except a purple tinge round very bright objects, such as the Moon and Venus." — Monthly Notices of R. A. S., vol. viii. Observers : Bond and Waldo. Cape of Good Hope. Prior to 1847 the equatorial was a 46 in. by DoUond, aperture 3I in. There were four micrometers, viz., a spider-line position, an annular, and two rock-crystal. A flat-wire position micrometer was added subsequently. In 1849 the equatorial by Merz was mounted ; aperture nearly 7 in., focal length 8| ft. The tube is of wood, veneered with mahogany. 3 34 DOUBLE STARS. The declination circle is 12^ in. in diameter, and reads to 10", and the hour circle has a diameter of 96 in., and reads to 4 sec. Tlie Huyghenian eyepieces have powers 86, 128, 200, 302. and 458. Those of the micrometer, 123, 161, 273, 347, and 464. The power of the double annular micrometer is 64. The divided circle of the position micrometer is 4 in. in diameter, is divided to 15', and reads to i' : the total range of the screw is 60 revo- lutions. One head only is divided. Observer: Maclean Challis. (See Cambridge.) Chicago. Mr. Burnham has made most of his discoveries with his 6 in. refractor by Alvan Clark. He has also used the fine 18^ in. Clark refractor of the Dearborn Obser- vatory, the 26 in. of the Washington Observatory, and the 94 inch of the Dartmouth College Observatory. Cincinnati. (U. S.) The object-glass was purchased in 1842 ; it was begun by Fraunhofer, and finished by Merz and Mahler. Dr. Lamont pronounced it " one of the best ever manufac- tured." Aperture 1 1 in., focal length 17 ft. Diameter of hour circle 16 in., of the declination circle 26 in. The powers range from 100 to 1400. The stand is of iron, and is filled with sand. The driving clock is by Clark and Sons, and is good. — Loomis's Recent Progress of Astronomy, and the Cincinnati Observations. Observers : Mitchell, Stone, Howe, and Upton. CROSSLEV. (See Bermerside.) CUCKFIELD. Mr. Knott's equatorial was mounted at Woodcroft, Cuckfield, and the measures lately published were made there between i860 and 1873. The object-glass has EQUATORIALS. 35 a clear aperture of 7J in., a focal length of iiojin., and it was made by Messrs. Alvan Clark and Sons. The filar micrometer was made by Dollond ; diameter of position circle 3J in. ; it reads to tenths of a degree. The powers of the seven eyepieces range from 115 to SIS- Dawes (Rev. W. R.) In 1 83 1 this distinguished observer erected a S ft. achromatic at Ormskirk in Lancashire. It was by Dollond, and the mounting was like that of Smyth's refractor. The aperture was 3I in.; the circles 2 ft. in diameter; the powers used, 225, 285, and 625. — Memoirs of tJte R. A. S., vols. iv. and v. The Newtonian reflector, the mirrors of which were presented to Dawes by Sir John Herschel, was mounted by Dollond, and applied to the polar axis of the 5 ft. telescope. Focal length about 7 ft., aperture 6j in. This instrument was used between 1834 and 1839, but not much. — Memoirs of the R. A . S., vol. xix. In 1845 the Merz and Mahler equatorial was mounted at Cranbrook in Kent. The style of mounting was that of the great Dorpat refractor. The focal length was 8^ ft., and the clear aperture 6^ in. The object-glass was of first-rate quality. The hour circle read to 4 sec, and the declination circle to 10". Driving clock extremely steady and uniform. — Memoirs of the R. A. S., vol. xvi. In 1859 the equatorial by Alvan Clark and Sons (now at the Temple Observatory, Rugby), was mounted at Haddenham (Hopefield Observatory), in Bucks. The glass was cast by Chance and Co. Aperture 8J in., focal length 1 10 in. The figure is excellent to the circum- ference, and the dispersion " but a little over-corrected." The finder has an aperture of 2 in. The micrometer was a parallel-wire by Dollond. Driving clock : this is 36 DOUBLE STARS. very good. Bond's spring governor renders the action very smooth. — Memoirs of the R. A. S., vol. xx. Dawes's micrometer by Merz and Son was made in 1846. It was a parallel-wire, and was used with the 8 J ft. telescope. Powers 120,155,260,322,435, 572, and 690. His Amici micrometer was presented to him by Sir John Herschel : it was a double-image, and had but one power (1000 on the 20 ft. reflector). Dawes added three new eyepieces, which, on the 8 J ft. refractor, were 212, 360, and 508. Dembowski (Baron). This eminent double-star observer used an excellent dialyte by Plossl 5 ft. focal length and 5 in. aperture equatorially mounted, from 1852 to 1862. The power generally used was about 300. It was not provided with a driving clock. In 1862 the refractor by Merz was erected. Its aperture is 'j\ in. The object-glass is a fine one, and the powers range from 100 to 720. The driving clock is moderately good. — Ast. Nachr., vols. xlii. and Ixii. Doberck. (See Markree.) DORPAT. This noble instrument was erected in 1825. It was the work of Fraunhofer. The tube was of deal overlaid with mahogany, and the framework of the stand was of oak inlaid with mahogany and polished. The polar axis was 39 in. long. Aperture of the object-glass 9-6 in. ; focal length 14 ft. The hour circle, with a diameter of 13 in., was divided to minutes, and read to 2 sec; and the decli- nation circle, with a diam. of 19 in., was divided to 10 min and read to 10 sec. Powers 86, 133, 198, 254, 420, 532, 682, 848, 1 1 50, and 1500. The finder had an aperture of 2'4 in., and focal length of 30 in. The driving clock kept a star in the centre of the field when a power of EQUATORIALS. 37 700 was used. — Memoirs of R. A. S., vols, ii. and xxxvi. Pearsons Astronomy. Observers: X., O.S., and Ma. DUNER. (See Lund.) DUNLOP. Equatorial refractor, focal length 46 in. Micrometers, a parallel-wire and an Amici's double-image. DUNSINK. The object-glass is the work of Cauchoix : aperture 12 in. ; focal length 19 ft. The mounting was by Thomas Grubb. Elchies. The Elchies equatorial was mounted about 1850, by- Mr. J. W. Grant, at Elchies, in Scotland. The German form was adopted. One portion of the stand weighed 1 1 tons. Messrs. Ransome and May made the stand, and the object-glass was by Ross. The aperture was 1 1 in., and the focal length 16 ft. The axes were 5 ft. long, and 6 in. in diameter. The circles had a diameter of 30 in., and were i in. thick. The eyepieces were twenty-three in number. The parallel-wire micrometer had two eye- pieces, and one of the three finders had a focal length of 5 ft. Encke. (See Berlin.) Engelmann. (See Leipsic.) Ferrari. (See Rome.) Flammarion. (See Paris.) Fletcher. (See Tarn Bank.) Galle. (See Berlin.) Gledhill. (See Bermerside.) Greenwich. In 1838 the Sheepshanks equatorial was mounted. Grubb of Dublin supplied the stand, which was of the 38 DOUBLE STARS. German form. The object-glass was by Cauchoix : aper- ture 67 in. ; focal length, 8 ft. 2 in. Its definition was' found to be good, the principal defects being outstanding colour, and a diffusion of light from brilliant objects. Negative eyepieces, a wire micrometer, a comet eye- piece, and a double-image micrometer were provided. The driving clock was regulated by governor balls at the ends of a horizontal arm on a vertical spindle. When a certain velocity had been acquired, projections on the balls rubbed against a fixed horizontal ring. The mounting of the great equatorial is in the English style, and was executed by Simms. Messrs. Ransome and Sims made the engineers' work. The object-glass, by Merz and Son, has an aperture of 12J in.,* and a focal length of 16 ft. 6 in., and it is a very fine one. The hour circle is 6 ft. in diameter, and the declination circle 5 ft. The driving clock is in the ground floor story, and the power is given by a flow of water acting through a turbine, the spindle of which passes up to the instrument. A Siemens' chronometric governor regulates the supply of water to the turbine. A Barker's mill drives the hour circle, and the regulation is obtained by a conical pendulum, Siemens' chronometric governor, and a spade dipping into a trough of water. — Greenwich Observations, 1864. Hall. (See Washington.) Hartnup. (See Liverpool.) Herschel (Sir William). The gigantic reflector was erected in 1787, at Slough. Two concentric circles of brickwork, 42 ft. and 21 ft. in diameter, battened from a breadth of 2 ft. 3 in. at the bottom, to i ft. 2 in. at the top, and capped with * In the " Monthly Notices" the aperture is always given 12 j in. See vol. xxxvi. EQUATORIALS. 39 paving-stones 12J in. wide and 3 in. thick, formed the foundation. A vertical beam 12^ in. wide was fastened in the centre, and around this the whole framework had its circular motion in azimuth. The tube was of iron, 39 ft. 4 in. long, and 4 ft. 10 in. in diameter. The speculum was of tin and copper ; its weight 1050 lb., and diameter 4 ft. The power used seldom exceeded 200. — Pearsons Astronomy. See also Phil. Trans., vol. Ixxxv., for a full description. Herschel (Sir John). The 20 ft. reflector was constructed in 1820, by Sir William and his son. The mirrors were fine, diameter 18 in., and focal length 20 ft. With the whole aperture, powers 150 to 160 were ordinarily used, the eyepiece being a single lens of i^ in. focus. — Memoirs R. A. S., vol. ii. The reflector used at the Cape by Sir John was the 20 ft. The three mirrors were all fine ; aperture i8j in. The 7 ft. refractor, aperture 5 in., was also used. — Cape Observations. Hind. (See Regent's Park.) Howe. (See Cincinnati.) Jacob. (See Madras.) Jenkins. (See Oxford University.) Kaiser. (See Leyden.) KONIGSBERG. The famous heliometer of this Observatory is mounted like the great refractor of Poulkova. The focal length is 8 ft. 6 in., and the aperture 6| in., and a distance of 1° 52' can be measured. It was begun in 1824, by Fraun- hofer, and mounted in 1829. The position circle at the object-glass has four verniers, and reads to minutes. For ordinary use there are five eyepieces : powers, 45 40 DOUBLE STARS. 91, IIS, 179. 290. A circle micrometer of the Fraunhofer kind has a power of 65. The ring micrometer and net micrometer have powers of 66, 92, and 165. — As(. Nachr^ vol. viii. ObseiTcrs : Bessel, Anwers, Peters, Luther, and Schliiter. I.ASSELL. In 1 841 the Newtonian reflector, 9 in. aperture and 112 in. focal length, was erected at Starfield, near Liverpool. The declination circle was divided to 15', and read to 30". The hour circle was of the same size, and read to 2 sec. The diameter of the circles was about 2 ft. In 1848, the 20 ft. equatorial was mounted. The tube was of sheet iron, y in. thick, and was 20 ft. long, and 25 in. diameter; its weight was 594 lb. The diameter of the speculum was 2 ft., and its weight 370 lb. The finder was a Newtonian reflector, aperture 4"2 in., focal length 42 in., power 27. — Memoirs of the R.A. 5"., vols, xii., xviii., and xxxvi. The two 4 ft. specula were constructed and mounted in 1859 ^"'^ i860; their focal lengths were 441*8 and 448" I in. ; length of tube n ft. The mounting was equatorial, and the motion in right ascension was given by an assistant. Leipsic. The mounting was by Pistor and Martins, and the optical part by Steinheil. Aperture, 8 Paris inches ; focal length 12 ft. ; powers, 72, 96, 144, 192, 288, 432, 576, and 720. Observer: Engelmann. Leyden. The Leyden refractor is of Munich make. Aperture, 6 in. ; focal length, 8 ft. Observer: Kaiser. equatorials. 4 1 Leyton. The 10 in. equatorial refractor, focal length 12 ft., by Cooke, was erected at Leyton in i860, by J. Gurney Barclay, Esq. The mounting is in the German style. The polar axis is 4 ft. 2 in. long, and the declination axis 3 ft. 2 in. The declination circle is 2 ft. in diameter, and reads to 10" ; and the hour circle is 13 in. in diameter, and reads to 2 sec. The finder has an aperture of 3 in., and a focal length of 3 ft. The driving clock is regulated by a double conical pendulum. Observers : Romberg and Talmage. Liverpool. This fine refractor was mounted in 1848. The mount- ing is a modified English form ; the optical parts were by Simms, and the engineer's work by Messrs. Maudslay and Field. The object-glass, which is a very fine one, was by Merz ; its aperture is 8^ in., and focal length 12 ft. The hour circle has a diameter of 4 ft., reads to 0"I sec, and has two microscopes. The declination circle has the same diameter, and reads to i"-o. There are six negative eyepieces (powers, 90 to I lOO), and the two micrometers (filar and double-image) have powers 150 to 600. The driving clock was made by Simms, and drives fairly. Observer: Hartnup. Lund. The instrument used by Dr. Dundr was mounted at the observatory of Lund in 1867. The tube and object- glass are by G. and S. Merz, of Munich. The rest of the mounting and the micrometer are by M. Emile Jiinger of Copenhagen. The style of mounting is modified German. The object-glass is a very fine one ; its aperture 42 DOUBLE STARS. is 9-6 in., and the focal length 14 ft. The diameter of the declination circle is 21 '2 in., and reads to 2" ; and the hour circle, with a diameter of I9'6 in., reads to 0"2 sec, and, by- microscopes, to 002 sec. The micrometer is a filar. The driving clock is a good one, the regulator being the invention of Professor Holten of Copenhagen. Maclear. (See Cape of Good Hope.) Madler. (See Dorpat.) Madras. The 4 in. equatorial was made by Simms, in the German style ; focal length 6y2 in. The circles were for finding only, and read to minutes of space and seconds of time. The micrometer was a parallel wire ; powers used 170 and 280. The spurious discs of stars were " sharp and round, but rather large." — Memoirs of the R. A. S., vols. XXV. and xxxii. The Lerebours and S^cretan equatorial had an aper- ture of 63 in., and a focal length of 89 in. A second object-glass was furnished by them in 1852, which proved good, but not perfect. — Memoirs of the R. A. 5., vol. xvii. Observers : Jacob and Powell. Main. (See Oxford.) Markree Observatory. This equatorial was mounted in 1834, at Collooney, County Sligo, by the late Mr. E. J. Cooper. The German style was adopted, and the cast-iron stand was placed on limestone blocks. The object-glass was the work of Cauchoix. It is not a very good one. Aperture 13^ in. ; focal length 25 J ft. The diameter of the declination circle is i ft. 9 in. ; it is divided to J°. The diameter of the hour circle is 30 in. ; it is divided to minutes. The micrometer is of Munich make, and very good : EQUATORIALS. 43 powers, lOO, 200, 300, 400, 500, 600, and 800. The position circle is 4 J in. in diameter, and reads to i'. The driving clock is a rough machine. — See Astr. Nachr., No. 2187. Observer : Doberck. Milan. The mounting is in the German style : both mounting and object-glass are the work of Merz and Mahler. The object-glass is a good one ; its aperture is 9*5 in., and focal length 10 ft. 7'9 in. The diameter of the hour circle is II in., that of the declination circle 157 in. The negative eyepieces furnish the following powers: 6"], 95, 155, 223, 322, 468. The filar micrometer was made by Merz: the powers are 87, 144, 210, 322, 417, 500, and 690 ; those generally used for double-star measurements are 322 to 690. The driving clock, by Merz, is not a good one ; it has a conical pendulum. — Ast. Nachr., vol. Ixxxix. Observer : Schiaparelli. Miller. (See Whitehaven.) Mitchell. (See Nantucket.) Mitchell. (See Cincinnati.) Morton. (See Wrottesley.) Nantucket (U. S.) Miss Mitchell's telescope was a 5 in. refractor by Alvan Clark. Naples. Aperture 5 J in. : focal length J% ft. : powers used 268 and 362. Observer : Nobile. Newcomb. (See Washington.) Nobile. (See Naples.) 44 DOUBLE STARS. Oxford (Radclifife Observatory). The mounting of the Oxford heliometer was designed and executed by Messrs. Repsold, and differs from the ordinary German equatorial. Aperture 7'S in. ; focal length 10*5 ft. The polar axis is 42^ in. long; diameter at upper pivot 4f in., and 3'85 in. at the lower. It is of steel, and the pivots turn in collars of bell-metal. It is perforated 2'i in. throughout. The declination axis is 43 '4 in. long, 5 in. diameter in centre, 4-3 in. at the pivots. It is of steel, and perforated throughout, the bore being ig in. The tube is of ham- mered brass; diameter at object-end 13 in., at the eye-end 9"2 in. The position circle is 227 in. in diameter. The hour circle is at the north end of the polar axis, has a diameter of 33"8 in., is graduated to i min., and reads to 0'2 sec. The declination circle has a diameter of 34'3 in., is graduated to 4', and reads to i". The driving clock is governed by centrifugal balls, and the instrument is moved by a weight of about 30 lb. — Radcliffe Obs., vol. xi. Observer: Main. Oxford (University). The equatorial refractor is by Grubb ; aperture 12J in.; focal length 176 in. The declination circle has a diameter of 30 in. There are two filar micrometers, and a double- image. The driving clock is not faultless. — Monthly Notices, vol. xxxvi. Observers : Plummer and Jenkins. Paris. The instrument used by Flammarion is one of the equatorials of the Paris Observatory. The object-glass is by Lerebours, and has a diameter of about 15 in., and a focal length of 29 ft. It is not a very good one, and a diaphragm is therefore generally used. The hour circle has a diameter of 25 in., and reads to i'. The EQUATORIALS. 45 declination circle is divided to 5', and has a diameter of about S ft. The parallel-line micrometer is by Brunner, and the powers generally used are 300 and 400. The driving clock is also by Brunner, and has a Foucault regulator. Plummer. (See Oxford University.) POULKOVA. A very fine instrument was mounted at this Obser- vatory by Merz and Mahler. The weight of the instru- ment is 7000 lb. ; the clear aperture 15 in., and the focal length 225 ft. The driving clock is regulated by the friction of centrifugal balls against the interior of a conical box. There are 6 negative eyepieces, powers 152 to 1218; 21 positive eyepieces, powers up to 2000. Observer : O.S. Powell. (See Madras.) Regent's Park. In 1836 G. Bishop, Esq., erected an observatory in Regent's Park, London. The equatorial was by Dollond, and the mounting English in form. The tube was of brass, and painted. The aperture of the object-glass was 7 in., and its focal length io| ft. The hour and declination circles were of brass, and 3 ft. in diameter, the former being divided to minutes and read off to seconds, and the latter divided to 10' and read off to 10". The eyepieces gave the following powers : 45, 70, 108, 200, 320, 460, 700, and 800, and a polycratic wheel carried six of them. The prismatic crystal micrometer was by Dollond, powers 185, 350, and 520; the parallel- wire was also by Dollond, powers 63, 105, 185, 320, 420, 600; also 190 and 300. The driving clock was by Dollond : it was driven by a powerful spring, and regulated by two fans, and was 46 DOUBLE STARS. found to work "extremely well." — Bishop's Astr. Obs., 1852. Observers : Dawes and Hind, Romberg. (See Leyton.) Rome. This fine instrument is mounted like the great Dorpat refractor. Aperture 96 in. ; focal length 14-2 ft. Driving clock, very good. " The rate of the regulating part of this instrument is controlled by the friction of two small brass balls against the sides of a conical box." — Monthly Notices of the R. A. S., vol. xvi. Observers : Secchi and Ferrari. Rugby. (See Dawes.) Observers : Wilson, Seabroke, and A. Percy Smith. ScHiAPARELLi. (See Milan.) Seabroke. (See Rugby.) Secchi. (See Rome.) Smith. (See Rugby.) Smyth. (See Bedford.) South. The 5 ft. equatorial was erected in 1797 in London. " The whole scheme of its fabric was cast by the late Captain Huddart, many years a worthy Fellow of this Society. All the tinned iron-work was made under the direction and inspection of the same able engineer." The brass-work was made by J. and E. Troughton, and the whole instrument was completed in 1797. The excellent object-glass of 3I in. aperture was by P. and J. Dollond. The powers used were 68, 116, 133, 240, 303, 381. That most used was 133, the others being double eyepieces. In some few cases a single lens, power 578, EQUATORIALS. 47 was used. The diameter of the declination circle was 4 ft. — Phil. Trans., 1824, Part iii. The 7 ft. equatorial had an aperture of 5 inches, and was, at the time it was made, the chef-d'ceuvre of Tulley. " In distinctness under high magnifying powers, it is probably excelled by no refractor existing." The ordi- nary observing power was 179 ; occasionally, 105 and 273 were used. — Phil. Trans., 1824, Part iii. The 20 ft. refractor was mounted in 1829, at Ken- sington. The glass was by Cauchoix, and had a clear aperture of iif in. — Monthly Notices, vol. i. Stone. (See Cincinnati.) Struve and Otto Struve. (See PouLKOVA.) Talmage. (See Leyton.) Tarn Bank. Mr. Fletcher's equatorial was erected at Tarn Bank in i860. The optical part was by Cooke, and the stand w£is made under the direction of Mr. Fletcher. The Sisson polar axis was used in the mounting. The object- glass has a diameter of 9^ in., and a focal length of 12 J ft. The declination circle has a diameter of 42 in., and reads to i" ; the hour circle is of the same size. The driving clock had 22^ lb. as a driving weight, and worked very well. Mr. Fletcher's small equatorial, by Cooke, was mounted in the German style ; aperture, 4' 14 in.; focal length, 6 ft. This mounting was that used by Dollond, with a long polar axis. This axis was of mahogany, 9 ft. long, 9 in. square in the middle, and 7 in. square at the ends. The hour circle was 20 in. in diameter, read to 2 sfec, and was loose on the polar axis. The declination circle had a diameter of 20 in. also, and read to 10". Powers, 50, 100, 160, 230, 300, 420, and 600, with the parallel-wire micro- meter. The power generally used for double-star work 48 DOUBLE STARS. was 300. The driving clock was a very elegant instrument and worked very well. The governor was like that used in steam engines. — Monthly Notices of R. A. S., vols, x., XX., XXV. ; Memoirs of the R. A. S., vol. xxii. Upton. (See Cincinnati.) Waldo. (See Cambridge. U.S.) Washington. (The Great Refractor.) This magnificent instrument has an aperture of 26 in. and a focal length of 390 in. The glass was by Chance, and Messrs. Alvan Clark and Sons were the makers of this noble lens. It was finished in 1872. The mounting is in the German style. The negative eyepieces are four in number, powers 155 to 1360. The positive eyepieces are sixteen in number, powers 173 to 1802. The tube is of steel, Jj- in. in thickness near the ends and \ in the middle. Length 32 ft. ; diameter of the middle one- third about 31 in. The object-glass is com- posed of an equi-convex front lens of crown-glass and a nearly plano-concave flint lens : thickness of the objective at the centre about 2-87 in. The glasses are free from all hurtful rings and striae, and are of nearly perfect figure. There are three micrometers, two filar and one double-image. There are two finders, apertures 2 in. and 5 in. The driving clock was invented by Professor Newcomb : with careful attention to the oiling, etc., it works satisfactorily. — Instruments and Publications of the United States Naval Observatory, Washington, 1845-76. The smaller instrument was made by Merz and Mahler. Aperture 9*6 in., focal length 14 ft. 3 in. The object- glass was under-corrected for colour, and in 1862 it was refigured by Messrs. Clark and Sons : the focal length was increased about one inch, and the glass corrected for defective achromatism ; the definition also was im- proved. The flint disc is not perfect. Hour circle 15 in.. EQUATORIALS. 49 and declination circle 2i in. diameter. Finder 2-6 in. aperture, and 32 in. focal length. Micrometer, a re- peating filar, by Fraunhofer. The driving clock is regulated by a Fraunhofer centrifugal pendulum, but it is scarcely powerful enough. There are eight eyepieces, powers 90 to 899. — Washington Observations, 1865. Observers : Newcomb, Hall, and Holden. Whitehaven. In 1850 Mr. J. F. Miller, of Whitehaven, began his double-star measurements. The instrument was a very good equatorial refractor by Cooke, the mounting in the German style, and of the same size as Mr. Fletcher's instrument. The micrometer was by Simms, and proved to be a very good one. Diameter of position circle 5 in. ; power generally used 300. The clock-work, too, was good. — Memoirs of the R. A. S., vol. xxii. ; Astr. Nachr., vol. xxxiii. Wrottesley. English mounting : polar axis of four mahogany planks 14 ft. 3 in. long and 10 in. square in the middle ; pivots of bell-metal. Focal length 10 ft. 9 in.; aperture 7f in. ; flint glass by Guinand ; crown by DoUond. Mounted at Wrottesley, Staffordshire, in 1843. Decli- nation and hour circles each 3 ft. in diameter : verniers read to 10" and i sec. Parallel-wire micrometer : position circle 4 in. diameter, reads to 6' ; powers used 450 and 320, and 600 and 820, occasionally. Driving clock not satisfactory. — Memoirs R. A. S., vols, xxiii. and xxix. Observer : Morton. 50 DOUBLE STARS. CHAPTER IV. THE MICROMETER. The parallel-wire micrometer is par excellence the instrument of the double-star observer. Though used for many other purposes, it is specially adapted to his work, and has not been superseded by any other form of micrometer.* It consists of the following parts : first, a stout brass tube or adapter fitting into the eyepiece end of the telescope, and carrying at its outer end a position circle divided from 0° to 360° in the direction contrary to the figures on a watch dial, and read off by two opposite verniers to tenths or twentieths of a degree ; it is also provided with clamp and slow motion. The moveable vernier plate has attached to it the micrometer box, which is generally 5 to 6 inches long, \\ to 2 inches wide, and \ inch deep. The micrometer screws enter the box at each end, their divided and milled heads being outside. The screws, of a hundred threads to the inch, enter their respective frames, which fit nicely within the box, and move parallel to one another like two tuning- forks, one just small enough to work within the other. Across these frames, in the centre of the field, are stretched the fine webs at right angles to the direction of the screws. To prevent slack, the two frames are pushed towards one * There are many other forms of micrometer, the most important being Airy's and Amici's, both double-image micrometers. The former consists of a positive eyepiece containing four lenses, the third from the eye being concave and divided into two halves, and each half carried by its own screw. Amici's double-image micrometer consists of two prisms, and has been used by Dawes and Doberck. It is considered the best of the kind. THE MICROMETER. 51 another by spiral springs, thus bringing the inner heads of the screws against the ends of the box. These heads are often made square with the shaft of the screw; but they are much better made spherical, so as to fit into conical bearings at the ends of the box. A flat comb plate is placed over the moveable frames across the open centre, with a fine-toothed comb cut so as to form a chord to the circle of the field of view at right angles to the moveable webs. This comb plate carries two stout parallel wires (called position wires), about 12" apart, across the centre of the field, and at right angles to the moveable webs and parallel to the comb. The eyepieces are attached Fig. 3. (Parallel-wire Micrometer.)* outside the box to a sliding-piece, moved by a screw for centering over the webs in the direction of their motion. The webs, position wires, and comb should be clearly defined with a high power at the same time. The eyepieces should as much as possible slide into the same adapter, to save screwing and unscrewing. * One reading lens is removed to show the slow-motion clamp. 52 DOUBLE STARS. It is usual to insert in the stout brass tube or adapter, close to the position circle, a thin ivory ring with openings all round through the adapter, to admit light for the pur- pose of giving dark ground illumination to the webs. English makers usually furnish both screws with heads divided into a hundred parts, and figured o, lo, 20, etc., so as to give an increasing reading when the webs are moved towards the heads or against the spiral springs. Obser- vations are always taken by setting the screw in this direction, as it is found in practice to give the best results. German makers divide only one of the heads, and simply use the other screw for setting in different parts of the field. It is desirable that both screws should have easy play through not less than fifty revolutions. A divided head to one of the screws is quite suflScient, and for distinction we will call this the micrometer screw, and the other the setting screw.* We have now to determine the value of the revolutions of the micrometer-screw in seconds of arc, and for this purpose we can make the setting screw and its moveable frame an eflScient auxiliary. Let the comb be divided in such a manner that every fifth notch is a longer one, and each tenth notch numbered by small holes — one, two, three, etc., counting from the notch nearest to the setting screw as Zero. Let the following webs be placed on the moveable frame of the setting-screw: No. I, at Zero; No. 2, at 1775 revolutions ; No. 3, at i8'2S ; No. 4, at ig'o; No. 5, at 20'o; No. 6, at 25-0 (in the centre) ; and No. 7, at so'o. On the micrometer screw but one fine web is needed, and it is placed in the centre of its moveable frame : let us call this web No. 8. We are now in a position to step the micrometer screw throughout its whole length with great ease and accuracy, * These are marked A and B, respectively, in Figure 3, and are held simply by friction, so as to admit of being set to any reading. THE MICROMETER. 53 viz., at every five revolutions by webs No. 5 and No. 6 ; at every single revolution by webs No. 4 and No. 5 ; at every half revolution by webs No. 2 and No. 3 ; and also at every quarter revolution by webs No. 3 and No. 4. It will probably suffice to test only the ten central revolu- tions for parts of a revolution. Use a high power and good illumination. The operation may be thus described. Bring No. 5 to Zero and No. 8 beyond Zero : the latter must now be brought carefully just into contact with No. 5, first on one side and then on the other, the head being read off to tenths of a division each time. No. 8 must now be brought up to No. 6 in precisely the same way, and this will complete the first step of five divisions. No. 5 must now be brought to five revolutions, and No. 8 set as before, first on No. S and then on No. 6 ; and this will be the second step : carry on this process throughout the fifty revolutions. Repeat this several times, and the mean readings of each step will give the comparative value of each five revolutions with great accuracy. Each group of five revolutions must now be tested in precisely the same way for each single revolution, by means of webs No. 4 and No. 5 ; and each of the ten central revo- lutions for parts of a revolution with webs Nos. 2, 3, and Nos. 3, 4. It is, of course, impossible for webs Nos. i to 7 to be placed absolutely at the distances named ; but the exact distance will be determined by the observations and the proper allowances made in the computations. Having thus obtained by the most accurate as well as the most convenient method the comparative value of the different parts of the screw, it now only remains to convert these values into seconds of arc. This is done by transits of a slow moving star from web No. i to web No. 7, the distance being fifty revolutions of the screw. The best stars for this purpose are a, j8, and h Ursae Minoris, whose places are given in the Nautical Almanac. If the telescope used has, say, 6 in. aperture and 9 ft. focal 54 DOUBLE STARS. length, the value of the fifty revolutions will be 954'93 ± seconds of arc. This, at the equator, is equal to 63662 seconds of time, or i'' = o"o66 seconds of time: but if we multiply 0066 by the secants of the declinations of P, S, and o Ursae Minoris respectively, we get 0'25i8, vi2J, and 2-859 seconds of time. Now as it is difficult to take a single transit with greater accuracy than 0*25 sec, the advantage of a slow star is at once apparent. If, for in- stance, the transit of S Ursse Minoris be taken to 0'5 sec. by a single observation, the value of the screw will be obtained with an accuracy of i in 2000; but as one obser- vation cannot be relied on, a large number of transits of different stars should be taken, and in this way an accuracy of I in 5000, or even of i in 10,000, can be secured. It is usual to express the value of the screw in seconds of arc for one revolution ; and if an auxiliary table be constructed giving the value of parts of a revolution, any measured dis- tance can be readily converted into arc. The effect of change of temperature on the screw is so small that it may be entirely neglected. The effect of refraction, however, cannot be so disregarded when the above transits are observed out of the meridian; and the following is a simple and convenient mode of dealing with this, since it enables the observer to transit, when away from the meri- dian, and to correct his results at once if the altitude be not less than about 20°. Find the altitude of the object to the nearest degree or half-degree by the clinometer. Observe the transit as above and read off the position circle ; then bring the micrometer box into a vertical position by means of the plumb-line of the clinometer. Read off the position circle, and the difference between the readings will give the angle with the vertical, or the parallactic angle. The full effect of mean refraction on the position of the star, sup- posing the transit to be in a vertical plane, must now be multiplied by the cosine of the angle with the vertical, and THE MICROMETER. 55 this will give the correction for refraction in seconds of arc. It is always subtractive in the case of transits. The interval of transit must now be multiplied by the cosine of the declination to reduce it to the equatorial value, and then converted into seconds of arc. The correction for refraction must now be added. This method is also apphcable to correct the measures of low wide double stars : in this case the correction is always additive. The correction for curvature of path must be applied in observations of a and S Ursae Minoris, but for /3 it is in- sensible. Convert the observed interval into arc. Then twice the sine of half the arc thus obtained, divided by the arc expressed in terms of the radius, will give the factor by which the observed interval must be multiplied to reduce it to the true value. Dembowski preferred /3 to S as requiring no correction for curvature, and taking less time to observe, and so lessening the chance of instrumental disturbance during transit. The micrometer screw may also be tested by two terrestrial marks, and the angular value determined if the distance of the marks from the object-glass be ascertained ; but the definition so near the surface of the earth will rarely be found good enough for this kind of observation. A powerful theodolite may also be used for this purpose, the two telescopes being turned towards each other, and the angular distance of the webs read off on the horizontal circle. If the micrometer will include the sun's disc, its value may be obtained from the sun's diameter. In this case the horizontal diameter should be measured. If the vertical diameter be taken, the sun should have a considerable altitude, and the correction for refraction must, of course, be applied. The sun's semi-diameter for noon of each day will be found in the Nautical Almanac on page II of each month. 56 DOUBLE STARS. Some observers make use of the pairs of stars in the Pleiades whose places were determined by Bessel with the greatest care. The following pairs, consisting as they do of small stars of nearly the same magnitude, will be found very useful for this purpose ; and to aid in their ready identifica- tion a rough map is also given. k (Asterope) 1 8 . 9 • f (Atlas) h (Pleione' 31 • 32 . 35 • 36 • Mag. 7-8 7-8 8-9 8-9 4-5 5-6 8 8 9 9 R. A. {1880). 54 54 55 55 55 2I'I9 28-33 24 '66 58-88 22-16 40-46 53-56 8-23 19-06 3040 Dec. (1880). 24 10 9 23 49 48 23 41 46 24 I o 23 52 51 46-84 1201 15-83 57-27 11-53 11-68 45-54 52-12 41-55 5-57 From the formula r = y (J 8)^ + {A af cos^ mean 8 we find the following distances for the four pairs k 1 ; 8, 9 ; 31. 32; 35.36:— kl 8,9 3'. 32 35. 36 Diff. of R. A. (A a). 127-14 34-22 74-67 131-48 Diff. of Dec. (A {). 94-83 18-56 53-42 95-98 149-92 36-39 86-64 153-86 In order that the observer may be able to check the pre- ceding results and also to select other pairs for special pur- poses, the following extract from Bessel's work {Astronomische Untersiichungen, Erster Band) is given : — '+^ ^ I S fN .^ .^ % .r ^ »«^ THE MICROMETER. 57 K 5 p p b 1 I nn r^ \n U O . r«« i>.'^o 'OvO'Ovo loij^i-nu^^rt* O LTiOr^^^'-oo wvo -^i-i 11 o O N Lor^ ^ rosp T}-p^fOO^p^►-| O •-< On '^vO r-. u^ i— in (N >0 "O >-< vb r^'O o->(S 0"O O b V"" wO^ o ro -^ ro 't^h r^ N N M N N p p b b ++ o 11 r^ t^ N « O pop bob +++ O O ^^"-1 O O^ONfO u^oo ^O t^ ON ON r->. r>. r^ r^ r-^ t^ t^ r-^vo ^ r^vo o vo vo vo vo ^o o "bbbbbbbbbbbbbbbbb H- + + + + + + + -h- a^ONlOO N "-00 '- t^vO ■- N »M I- 00 O *n 1- mo O a^ONO^a^^^TJ-0^'-« ThrOM OnOO 00 00 ON pNoo 00 ON pN ^ y^Np oo oo on on 00 On i~>. ^^oo 00 t^cJo 00 rn '(J- in u "aT '-^ ■ 1^1 • . ■ • PO cj ri u i-« N »-0^^> • 4> * • d ^^ 00 OVOO " N^wg- mmmm 1 -^^ 2 0.0 1 crv^^ 1 1 1 < ;^^< ?< N N N <* The following table from S-'s Mensiira Micrometrica will give a good idea of the accuracy of the work done with the parallel wire micrometer \e is the probable error of a single distance, and /of a single measured angle]. 58 DOUBLE STARS. A. Table of the probable Errors of single measures of 2.'s lucida:, i.e., those whose companions are not below the 8th magnitude. Class. Mean Distance. No. of Stats, No. of Measures. e / I. 070 44 176 0-074 2 309 11. 1-48 III 447 ■086 I 52-4 III. 308 128 563 •099 I 8-2 IV. 5-62 119 469 •116 489 V. 979 SI 222 •127 302 VI. '3-94 46 199 ■127 239 VII. 1938 48 184 ■145 183 VIII. 2819 48 178 •156 149 B. Table of the probable Errors of single measures of S.'s reliqua, i.e., those whose companions are between the 8th and nth magnitudes. Mean No. of No. of / Distance. Stars. Measures. I. 0-75 28 94 0-087 / 2 270 II. 1-54 186 642 •109 2 1-9 III. 293 383 1299 •122 I 29-S IV. 582 426 1428 ■156 I 7-1 V. 10-00 278 783 •184 47-1 VI. 1388 161 455 •201 38-7 VII. & VIII. 22-6o 383 1064 •207 270 C. Table of the probable Errors of single measures of Stars, the companions of which are below the i ith magnitude. Class. Mean Distance. No. of Stars. No. of Measures. e / II. & III. 2''s9 14 49 0176 / 2 27-8 IV. 592 17 55 •221 2 2-1 V. 10-46 22 59 •362 1 20-7 VI. 14-19 II 37 •376 59-6 VII. & VIII. 21-93 12 35 ■371 55-6 Dr. Dundr, of Lund, gives the following results for the value of his micrometer : they were obtained from transits of Polaris : — 1867. Sept. II ... II ... • • i7'3i3 •303 19 ... 20 ... •313 •308 21 ... 24 ... 26 ... •309 •326 .. -336 1868. Oct. 3 ••■ .. 17-322 12 ... •301 21 ... ■309 22 ... •300 25 ... •311 26 ... •315 Mean, r = i7"'3i3 ± o"-oo2. THE MICROMETER. 59 The Baron Dembowski made a very elaborate investigation of his micrometer in 1873. He used star transits, terrestrial marks, and auxiliary webs or types, as he calls them, in the micrometer. The following extracts exhibit some of his results : — Litres means that all the transits taken on any given day are observed with the telescope in the same position with respect to the meridian, E. or W., the time of observation being any whatever within three hours of the meridian passage of the star. Conditionnh means transits observed with the instrument alternately E. and W. of the meridian, at the same culmination, the same number of observations being made on each side. The values of the entire scale, and the probable errors are as follows : — Sets. 10 Inter- vals. Probable error. /S Ursae Minoris libres 84 50 rev. = 1054-484 11 rio-iyo T centig.+28-4 7 »» 60 •874 •198 + 04 lO conditionnes 80 •384 ■150 +30-4 7 *i 84 ■836 •292 - 08 10 »» 80 •486 •209 + 176 S Ursse Minoris 14 28 •942 •311 +21-2 By Gauss' method 18 double sets ... •375 780 +127 And by the method of least squares he deduces the following results : — Value of the 50 rev. = io54"-578 — (T — i9°-72). 0-01420. Probable error of the coefficient of (T — i9°72) = 0-00295. Hence it is inferred that the absolute value of the entire scale is known within the limits ± o"-o6. The next table enables us to see the result of his examina- tion of each S rev. of the scale, four different methods being used : — 6o DOUBLE STARS. Methods used. Polaris : 13 transits (iibres) .. 5 U. Minoris : 14 „ (condit.) .. Terrestrial marks, 14 measures Types, 15 measures Mean Value of I rev The results from Polaris which are underlined in the tables are excluded from the means. Rev. o to 5. 105 247 r. = ■382 r. = ■397 r- = '16 •10 •06 105 -342 2 1 "-068 Rev. 5 to 10. io5"-662 r. = o"2i 105-453 r. = -zi •444 r. = '08 ■372 r. = -07 lo5"-423 2l"-o8s Rev. ID to 15. Rev. 15 to 20. Rev. 20 to 25. Rev. 25 to 30. io5"-573 !■• = o"-29 '°5"'475 >■• = o"'28 •468 r. = -18 ■404 r. = -lo ■423 r. = -07 i05"-358 r. = o"-29 •297 r. = -26 ■381 r. = -09 •388 r. = -07 ios"-498 r. = o"-35 i05"-382 r. = -15 •401 r. -= -12 ■390 r. = -03 •536 r. = -18 •380 r. = -08 •457 r- = '04 ios"-39i 2i"o78 105' '442 2i"-o88 105 -356 2i"-o7i i05"-468 2i"-094 Rev. 30 to 35. Rev. 35 to 40. Rev. 40 to 45. Rev. 45 to 50. io5"-459 r. = o"-34 io.;"'6o7 r. = o"-34 io5"-826 r. = o"-22 •348 r. = -29 •436 r. .= -11 •438 r. = -06 ■53b r. = o"-27 ■484 r. = '09 •499 r. = -05 i05"-690 r. = -32 •670 r. = '08 ■655 r. = -06 io5"-655 r. = o"-2o •632 r. = -07 ■590 r = -05 I05"'420 2 1 "084 io5"-5o6 2l''-I0I i05"-672 2i'-i34 i05"-626 2l"-I25 These results present, on the whole, an increasing value from o to 50 revolutions ; a minimum value appears at 20 to 25, and the maximum is reached at 40 to 45. The probable error of one measure does not exceed o"'07. Then the value of each of the ten central revolutions (20 to 30) is given, by two different methods : — Method. Rev. 20 to 21. Rev. 21 to 22. Terrestrial mark : 50 measures Types: 13 measures Mean 2 1 ".078 r. = o"-o5 •063 r. = 'Oi 21" '070 21 070 r. = 0-05 ■079 r. = 'OI 2l"-074 THE MICROMETER. 6l Rev. 22 to 23, Rev. 23 to 24. Rev. 24 to 25. Rev. 25 to 26. 2 1 "-079 r. = o"o5 ■076 r. = 'OI 2 1 "066 r. = o"'05 ■082 r. = -Ol 2i"-o85 r. = o"-o5 •c8i r. = -oi 2i"'o83 r. = o"'05 •088 r. = -OI 2i"-o77 2l"-o74 2i"o83 2i"-o85 - Rev. 26 to 27. Rev. 27 to 28. Rev. 28 to 29. Rev. 29 to 30. 2l"-o8o r. =-05 ■090 r. = '02 2i"o86r. = o"-04 •095 r.'= .02 2i"o99 r. = o"-o5 •100 r. = -02 2i"-ii7 r. = 0" 05 ■092 r. = -02 2i"-o85 2 1 "090 2 1 "-099 2l"-I04 Here, as in the preceding results, the mean values increase on the whole from 20 to 30; and De. finds that the pro- bable error of one measure does not exceed o"'05. R^sum^ of the mean values of each quarter of the ten central revolutions in the seven different series, and the pro- bable error of one measure : — Series. 1st Quarter. 2ndQ jarter. 3rd Quarter. 4th Quarter. I. 5"-oos 0"l20 5"-i75 o"-o93 5"-5i3 o"-o88 5" -390 o"-o89 II. •301 •107 ■^0* •059 ■733 •099 •336 -088 III. •III •110 ■185 •085 •356 •036 •432 -070 IV. ■143 •079 ■195 •049 •277 •047 ■469 -045 V. •195 •064 •164 •090 ■298 •076 •426 ^108 VI. •281 •097 •139 •043 •270 •063 •394 '062 VII. ■325 ■008 •194 ■024 •199 ■004 ■366 -026 Series. 4th Quarter. 3rd Quarter. 2nd Quarter. 1st Quarter. I. 4"^907 o"^i44 S"-i49 o"-i58 5"-263 o"-i4i 5"-764 o"^i8o II. 5 -lis ^126 •197 •116 ■644 ^104 •127 •OSS III. 4 -920 -076 ■351 •089 ■266 •oSi ■547 -165 IV. •876 ^049 •308 •030 ■332 '069 •567 -069 V. S ^086 -114 •144 •059 •544 ^060 •299 -174 VI. •309 -121 •268 •093 •315 -048 •192 '146 VII. ■276 -022 •241 •026 •562 -029 •004 -024 The objects used in obtaining the series I. to VII. were as follows: — For I., II., double distances of 5 Lyrae; for III., IV., v., double distances of two terrestrial discs ; for VI. double distances of /i Draconis ; and for VII. the distance between two auxiliary webs in the micrometer. 62 DOUBLE STARS. Taking the mean of the values for each quarter of a revo- lution obtained by the positive and negative movements of the screw, the following results for each series are found : — Mean of the values for each Quarter. I. S"-384 S -219 S"-33i 5"- 148 II. •214 •429 •215 •225 III. ■329 •225 ■353 •176 IV. ■355 ■263 •292 •172 V. •247 ■359 •221 •256 VI. •236 •227 •269 •351 VII. •164 ■378 •220 •321 The means of these series for each quarter are S"'276, S"-300, 5"-272, s"-233. Difference between the mean measured value of a Quarter of a Revolution and the mean value ^"'zji. I. II. III. IV. V. VI. VII. + o'-ii3 - '057 + -058 + -084 — -024 - '035 — '017 o '052 •158 •046 •008 ■088 •044 ■107 + o"'o6o — -056 •082 ■021 •050 •002 •051 + + 0"I23 •046 •095 ■099 •015 •080 •050 In making the seven series of measures, the micrometer was removed from the telescope after each series. Remarking on the whole investigation, De. is led to the following conclusions : — 1. The values of the four quarters of a revolution are not equal inter se. 2. Greater inequalities still are found between the + and — readings. 3. These inequalities do not depend on any defect in the division of the head. The micrometer used at Bermerside Observatory (see the illustration, p. 51), was made by Mr. Simms last spring. It is a beautiful instrument, and a very careful examination of the screw by Dembowski's method (see p. 59) has shown that it may be regarded as perfect, at least for the purpose of double-star measurement. THE MICROMETER. 63 From upwards of 200 transits of stars the value of i rev. was found to be I3"'8372, with a probable error ±o"*oo4. The screw (marked A in the illustration) which is the one used in measuring double stars, was tested with the following satisfactory results : — 1. From ten careful settings of the micrometer web close to one of the fixed webs, it was found that the probable error of the mean was ±o""CX33, and the probable error of one setting ±o"-oi4. 2. Careful stepping of the screw by 5 revolutions at a time showed the following differences from the mean value of eight sets of determinations : +o"'Oi4, +o"'003, — o"'006, O'O, — o"-oo8, +o"-oo4, +o"-oo4, -o"-ooi, +o"-oo5, — o"-oo5. 3. The ten central revolutions were then stepped singly, and the differences from the mean result were : — o""Oi4, +o"'00i, +o"'ooi, — o"*oo5, — o"'oo4, —d'-ooj, — o"-oos, +o"-o2i, — o"-oi2, +o"-oo7. 4. Each half revolution of the ten central ones was then measured five times, and the greatest difference from the mean result was +o""04. 5. Lastly, each quarter of the six central revolutions was stepped four times ; the greatest difference between the mean of the whole and the means of the several quarters did not exceed o"'02. These results therefore show that there is no appreciable change of value in the different parts of the screw, and that there is no sensible eccentricity in its mounting. The webs used for double-star work. No. 6 and No. 8, were measured, and the thicknesses found to be o"-4i5 and o"-372. 64 DOUBLE STARS. CHAPTER V. METHODS OF OBSERVING, ETC. It is here proposed to give a somewhat full account of the methods of observing the positions and distances of double stars. The subject will be treated under the following heads : — 1. Methods of observing angles and distances. (a) The methods adopted by Sir Wm. and Sir John Herschel. (d) The methods used by Dawes and Dembowski in the measurement of angles : Dawes' prism. (c) Special methods for very close stars. (d) Methods which may be occasionally used. 2. The number of measures of angle and distance required to form a se(, or complete observation, with an example. 3. Specimens of Forms of Registry. 4. Weights. 5. On contracted apertures. 6. Best time for observing : weather, etc. 7. Precautions to be used while observing. (i) Methods of Observing. {a) The method Sir William Herschel adopted will be best given in his own words : " The distances of the stars are given several different ways. Those that are estimated by the diameter can hardly be liable to an error of so much as METHODS OF OBSERVING. 65 one quarter of a second ; but here must be remembered what I have before remarked on the comparative appearance of the diameters of stars in different instruments. Those that are measured by the micrometer, I fear, may be liable to an error of almost a whole second ; and if not measured with the utmost care, to near 2". This is, however, to be understood only of single measures ; for the distance of many of them that have been measured very often in the course of two years' observations can hardly differ so much as half a second from truth, when a proper mean of all the measures is taken. As I always make the wires of my micrometer outward tan- gents to the apparent diameter of the stars, all the measures must be understood to include both their diameters ; so that we are to deduct the two semi-diameters of the stars if we would have the distance of their centres. What I have said concerns only the wire micrometers, for my last new micro- meter is of such a construction that it immediately gives the distance of the centres ; and its measures, as far as in a few months I have been able to find out, may be relied on to about one-tenth of a second, when a mean of three observa- tions is taken. When I have added inaccurate, we may expect an error of 3" or 4". Exactly estimated may be taken to be true to about one-eighth part of the whole distance : but only estimated, or about, etc., is in some respect quite un- determined ; for it is hardly to be conceived how little we are able to judge of distances when, by constantly changing the powers of the instrument, we are, as it were, left without any guide at all. I should not forget to add that the measure of stars, when one is extremely small, must claim a greater indulgence than the rest, on account of the difficulty of seeing the wires when the field of view cannot be sufficiently en- lightened. " The angle of position of the stars I have only given with regard to the parallel of declination, to be reduced to that with the ecliptic as occasion may require. The measures 5 66 DOUBLE STARS. always suppose the large star to be the standard, and the situation of the small one is described accordingly. Thus, in Fig. 4, A B represents the apparent diurnal motion of a star in the direction of the parallel of declination A B ; and the small star is said to be south preceding at m n, north pre- SoutR. mth -East IToith. Fig. 4. ceding at op, south following at qr, and north following at St. The measure of these angles, I believe, may be relied on W a?o° 0- to 2°, or at most 3° except when mentioned inaccurate, where an error amounting to 5° may possibly take place. In mere METHODS OF OBSERVING. 67 estimations of the angle without any wires at all, an error may amount to at least 10°, when the stars are near each other."* The foregoing diagram will make this method of registering the position angles quite clear. The innermost circle repre- sents the inverted field of view ; the four quadrants are indi- cated by nf, sf, sp, np, and the angle is given by the position circle: e.g., in the case supposed in the figure the position would be entered as 45° nf. The outer circles exhibit the method first suggested by Sir John Herschel, and now in universal use. In this the quadrants are dispensed with, the zero of the position circle is at the north point, and the circle is read all round to 360° in the direction N.E.S.W. ; hence, according to this method, the above angle would be registered as 45° simply. For distances, the methods used by Sir John Herschel and the later observers are identical. {b) To measure accurately the position angle of a double star would seem at first sight to be a sufficiently simple process. Experience, however, has shown that in many cases it is most difficult. A glance at the measures of some double stars by different practised and eminent observers at the same epoch is quite enough to exhibit this fact in a striking way ; and a comparison of the individual measures of the same star on the same night by one and the same observer and instrument, abundantly confirms it. Some of the disturbing causes are obvious enough ; but even when the stars do not differ greatly in magnitude or brightness, and when the sky is clear and the air still, these discrepant measures still present themselves. And in the case of close and unequal pairs, " the eye, often at the very first glimpse, acquires a prejudiced bias." (Hj.) " When such stars are between the wires, the eye may un- consciously be directed to the edge of one wire rather than of * Subsequent and more accurate measures show that Sir William's measures were liable to much greater errors than he here anticipates. 68 DOUBLE STARS. the other ; " there is a tendency to place one of the double wires nearly in the direction of a tangent to the discs of moderately unequal stars." (Hj,.) Further, we are told that there is a tendency in the eye to " accommodate its judgment to the position of the wires " before they are brought up to correct parallelism with the line joining the centres of the star discs. Nor is this all. Not only have we to get rid of widely discrepant results, we must also be on our guard against accordant measures. This latter difficulty is often a very considerable one. However, as we are here rather concerned with the methods by which these tendencies are to be de- stroyed or counteracted, we proceed to describe those used by the most successful observers of double stars : — 1. By repeated small movements of the wires in the same direction till the eye is quite satisfied. 2. By bringing up the wires alternately from opposite sides of the true direction. If three or more measures be made both ways, the mean result will probably be near the truth. 3. By a succession of small movements of the wires, tlie eye being removed from tJie telescope for a moment after each ' alteration. Whichever method be adopted, it will always be well to rest the eye a little, and to carry the webs some degrees away from the last position obtained, after each reading* When the stars are so faint that only very little arti- * " It will occasionally happen that, after taking two or three very co- incident angles, on recommencing after some slight interruption, a sudden difference of two or three degrees will occur, and a new set of angles, agree- ing well inter se, but differing from the former, will be obtained. In such a case it is most probable that the one or other result has been affected by some bias of the kind above alluded to ; and, as it is highly necessary to ascer- tain which it is, the following method of trying such rival measures against each other will often be found ser\'iceable. Suppose the two measures at issue were 63° and 65 ", each being a mean of three or four pretty coincident METHODS OF OBSERVING. 69 ficial light can be used, it is still possible to obtain useful angles by employing the method of oblique vision. The illumination is gradually increased until the webs are just well seen ; and the eye is then directed, not to the star, but to another part of the field. " In this way, a faint star in the neighbourhood of a large one will often become very conspicuous." (H,.) Before concluding these remarks on the measurement of position angles, some account of Dawes's prism should be given. This distinguished observer, soon after he began to measure double stars in 1830, discovered a tendency in his own eye to " obtain a different result in position when the line joining the centres of the stars was nearly parallel to the line joining the centres of the eyes, from that which was obtained when these lines were nearly perpendicular to each other ; and a still more decided difference was found to prevail when those lines formed a very oblique angle." He entirely overcame the difficulty by simply fixing a small prism to the eyepiece between it and the eye. By this means any double star can be placed in any desired position with respect to the horizon ; and it was the uniform practice of this great observer to confine himself entirely to the vertical and horizontal positions. Dembowski and Struve always observed with the head vertical. 0.5"., also, after accumulating a vast mass of measures, became aware of an error resulting from obliquity of position, and under- took a laborious series of measures of artificial double stars, measures. As it is probable that one is decidedly right, and the other decidedly wrong, and as their difference is 2°, let the micrometer be set to 61" and 67°, one or the other of these being necessarily 4° in error, will be violently offensive, while the other will be affected only by an error which experience has already shown may be borne without detection in the particular star in question. Thus the false results will be made evi- dent ; and, in assigning weights to the measures, this must be taken into consideration as materially diminishing the influence due to it." — Sir John Herschel, in Memoirs of the Royal Astronomical Society, vol. v. ^0 DOUBLE STARS. partly for the purpose of ascertaining the amount and law of this error ; and in his measures lately published both the observed and corrected angles and distances are given. The objections to the prism on the score of loss of light and impaired definition were regarded by Dawes, after nearly forty years' use of it, as quite unfounded. It is obvious, too, that the comfort of the observer, and therefore, to some extent, the accuracy of the measures, will be considerably increased by this simple apparatus. Of the extreme difficulty which attends attempts made to obtain accurate measures of distance of close and unequal double stars, nothing need here be said. So keenly was this felt by the late Sir John Herschel, that he devised a method of obtaining the elements of the orbit of certain double stars from the measured angles alone, the measured distances being used collectively for finding the value in seconds of space of the scale used in the construction. Extreme care, much practice, a good sky, patient repetition on different nights, the destruction of bias by removing the eye from the instrument for a few moments, and carrying the web far away from the last setting after each measure, — these and such like precautions naturally suggest themselves to the observer. {c) In the case of close pairs, the following suggestions, if carefully carried out, will often be found of use : — 1. Place one star centrally over a web, and note the change of form which the disc undergoes, e.g., if it becomes elliptical in shape, place the other web so as to produce the same effect on the other star. 2. When the distance is less than one second, the two following methods will frequently give valuable re- sults. Place the inner edges of the webs at a distance apart as nearly as possible equal to that which separates the two stars, using a high power; bring the stars close up METHODS OF OBSERVING. 7 1 to the webs, and compare the two spaces ; correct, if neces- sary, and then read off the divided head of the micro- meter. Repeat this from six to ten times ; then, the reading when the webs are just in contact, together with the read- ings given by the above settings, will furnish the means for deducing the distance of the stars with considerable accuracy. A better method, however, is that of first placing the threads a certain known distance apart, say i", bringing the discs between them, and trying to estimate and express in numbers the ratio between the distance of the discs apart and the distance of i". Make several or many esti- mations ; then, the distance between the threads being known, the true distance of the discs is readily deduced from the ratios. These two methods were used by Struve. Baron Dembowski takes one measure by estimation, then one with the webs, and places great confidence in the mean of the two. This will be a suitable place for a few words on the Barlow lens. It was frequently used by Dawes, and he thus sums up its advantages : — 1. The diameter of the micrometer threads subtends only about half the angle. 2. The moveable parallel threads are both as nearly in focus, with double the magnifying power. 3. The value of the micrometer divisions with the lens is only about half of its amount without it : hence a proportionably fine motion in the measurement of distance. 4. With any given power the threads are distinct to a much greater distance from the centre of the field. {d) The method of oblique transits described by Sir John Herschel may be noticed (see the " Cape Observations," p. 247). " If / be the polar distance of a double star; 6 its 72 DOUBLE STARS. measured angle of position ; a the angle of position of an oblique wire across which both stars are allowed to transit by their diurnal motion ; A the interval of their transits across it in seconds of time, — then will the distance of the stars from each other be given by the formula 15 A sin/ cos a sin (a — 6) Convenient values of a are 100°, or 110°, or (on the other side of the vertical) 260° or 250°. The inclination of the oblique wire ought to be towards the opposite side of the meridian to that of the line joining the two stars. In situa- tions not remote from the pole, a high degree of precision is attainable by this method." Lastly, it is sometimes convenient, especially when the distance is very great, to measure differences of declination, and then to compute the distances of the components from them and the angles of position. 2. Number of Measures. As regards the number of measures of position and dis- tance which should be taken of a star on the same night, the practice of eminent observers differs. However, it is quite certain that at least three of the angle, and three double measures of the distance, should be taken. Six of angle and twelve of distance (six double measures) would be much better. On the other hand, it is better to measure the same object on two different nights, than to make a large number of measures on one night only. Of course the importance of the star and the quality of the night will also affect the number of measures taken. Sir John Herschel usually made ten of angle and ten of distance : Dembowski, four of angle METHODS OF OBSERVING, 73 and four double measures of distance : Wrottesley, ten of position and ten of distance. Dr. Doberck four of angle and one double distance. The making of a complete observation of the position and distance of a double star may be thus described. After lighting the lamp which illuminates the field, and turning on the red or blue glass,* the micrometer is pushed into the tube, adjusted to distinct vision of webs and star, and the position circle set to zero. With eye on the star, the micro- meter is then turned bodily until the star runs along one of the distance webs (which has been placed near the middle of the comb), from side to side of the field. The thick position webs, now coinciding with the meridian, are then moved until the stars lie between them. Then, if Dawes's practice be followed, let the webs be brought up to true parallelism with the imaginary line joining the centre of the stars by a succession of small changes, the eye being removed from the telescope for a moment after each change. Read off the circle, and repeat from four to ten times. If the method of Dem- bowski be preferred, the webs will be brought up alter- nately from opposite sides of the true direction, the same number of measures being made in each direction. The webs should be moved away some distance each time, so that the eye may be freed from any bias. If the circle be not set to zero at the outset, the necessary correction must of course be applied to each reading when the set is complete. It is well to examine the zero reading of the circle after the measurement of each star, to avoid errors from accidental derangement. To take an example, let the star run along * "The colour I employ is that afforded by a brown-red glass of the Claude-Lorraine kind, which throws a strong sunshine glow over a landscape, almost verging to orange. A fuller red is even yet superior for distinct definition of wires." — Herschel, in Memoirs of R. A. S., vol. V. Dembowski and Doberck prefer Cinnabar red glass. 74 DOUBLE STARS. the equatorial wire at 91° 30' by the position circle: then will — i°"S be zero correction. If five readings be now taken, the operation of reduction will be as follows : — 1127 \ 110-5 II4'2 112-3 111-8 / The sum = 561-5 Mean = 112-3 Correction — 1-5 II0-8 For the distance : — Let us suppose that the companion is to the right of the principal star and the micrometer set to measure position. Fix one web, and place it on the centre of the principal star : now move the free web to the right until it bisects the companion star and read off the head. Carry the free web to the left of the fixed one, and bring the companion to the left until it is bisected by the latter; place the free web on the principal star ; and again read oflT. Repeat this double measure, bringing the web up in t/te same direction as before, i.e., from left to right, from four to ten times, reading off the divided head each time. To take an example as before : As the divided head is held on the axis of the screw by friction only, it may be set approximately to zero, when the moveable and fixed webs are superposed. Suppose this to be done, then the following observation will illustrate the method : — i2i7S'700g: — e' Lyrae. d d d d 18-5 100— Si'o = 19-0 18-5 -81-5 = 18-5 iS'o — 8r'o = 19-0 18-7 -82-0 = i8-o d The sum of these eight readings is 148-2, and the mean is d 18-52. It still remains to convert these parts into seconds of arc. This is most readily done by means of a short table from which the values can be taken out at once. METHODS OF OBSERVING. 75 Such a table may be thus constructed, supposing 13 "227 = I'. The first column gives the divisions and the others the tenths. Div. "o '1 '2 ■3 ■4 ■s ■6 ■7 •8 ■9 •0 •007 •015 •022 •030 II II •04s II •052 1' •060 •067 I •07s •083 •090 ■097 ■los •112 ■120 •128 ■13s •144 2 i -'SI •158 •166 •173 •181 •189 •196 ■204 •211 •219 etc. etc. etc. etc. Here 2-3 = o"-i73 at once from the table. 3. Forms of Registry. The importance of having ready a supply of forms for the entry of measures need not be here insisted on. Annexe are copies of those used by Sir John Herschel, Smyth, and Wilson. Sir John HerscheVs Form. Registry of the Micrometric Measures of Double Stars. Number for Reference. N.P.D. Declination. Right Ascension. No. Instrument used. Date. Star's Name. 18 = 18 (Dec. of year.) Diagram. Quadrant. Magnitudes. Colours. Face to Micrometer reads 76 DOUBLE STARS. Form of Registry of the Micrometric Measures of Double Stars — continued. Position. Power. W Mean Z = from » in direction nfsp Distance. I Remarks. Power. >, Rev. Pts. Dec. Mean + Div. by 2 Parts = Seconds = N.B. — When only positive readings are taken, a zero must be used, and the division by 2 omitted. Sky Wind Steadiness Definition of Star Dist. from Merid. General ] Pos. Judgment > ofObs. ) Dist. Observer. Zeros of Position and Distance. Star runs along the thread at .'. Zero for position Z = Threads close at Mean .', Zero for distance Z To be used only in case opposite readings are not taken. + Determination of Place. Clock (or clock + 24h). — Hour Circle : + if East, - if West ; 1 if read on to 24 h. always \ Instrumental correction True R. A. Declination Circle, ) + North, — South I Instrumental correction True Declination METHODS OF OBSERVING. 77 Admiral Smyth's Form. MiCROMETRic Measures of Double Stars, at Bedford, with the SJ Feet Refractor. Star's Name. Right Ascension, 1830. Declination, 1830. Diagram. Quadrant. Magnitudes. Colours. A = B = C = D = Position. Distance. Remarks. Power. w Power. n "(3 c 1 2 a c E 1 1 + H m + + + + + Rev. Pti. Dec. w • - Mean Z = Mean] Sky Wind Steadiness Div. b] Parts Second f 2 Definition of Star Face to from « in direction nfsp = Dist. from Merid. General ( Pos. Judgment < of Obs. 1 Dist. Zero of Position. Date. Star runs along the equa- ) torial wire at \ .'. Zero for position Z = O I 18 78 DOUBLE STARS. The Rugby Form. TEMPLE OBSERVATORY. No. 187 DOUBLE STARS. R. A. Decl. Magnitudes. Position. /^ \ Distance Zero. Readings. Direct. Indirect. J Diff. Position = Distance = 4. Weights. Several practised observers have accustomed themselves to assign weights to every position and distance. Sir John Herschel, for example, gives the following account of his mode of doing this. " Although it is impracticable to estimate correctly in numbers the goodness of a measure, yet such is the powerful influence of atmospheric circumstances on this very delicate class of observations, as to render it imperatively necessary either to observe only on those rare nights when that cause of error does not exist, or to jnultiply observations on inferior nights, and reject, freely, all which exhibit great deviations, or which do not give satisfaction at the time. If this be not done, the greatest confusion will arise. The assignment of a weight to each measure, accord- ing to the best judgment the observer can form, offers a middle course, free from the objectionable point of arbitrary METHODS OF OBSERVING. 79 rejection, and admitting a multiplication of observations on different nights, which is, indeed, quite indispensable for coming at the truth in all the more difficult cases. The scale I have adopted is from i to 10; i applying to the worst possible measurement in the most unfavourable cir- cumstances, and 10 to the most perfect which can be had in the most favourable." In casting up the mean of a set of measures, if the weights were pretty equal the arithmetical mean was adopted : if the weights differed much, the mean was found by the rule for finding the centre of gravity of a number of weights. — Sir John Herschel, in Memoirs of tJie R. A. S., vol. V. It will be understood that the assignment of the weight must precede the reading of the circle or divided head. Dembowski began to use Sir John Herschel's method in 1854. Dawes followed Sir John Herschel's plan after 1831. He observes : " Scarcely any liberty has been taken in the rejection of observations considered tolerably satisfactory at the time. Occasionally the micrometer has been set to a suspected read- ing, and a re-examination instituted. If not found decidedly bad, it has been suffered to remain ; if otherwise, another completely detached observation has been taken. If this last differed widely from the suspected one, and nearly coincided with the rest, it has been taken in its stead ; if not, both the suspected measure and that taken to prove it have formed part of the set." Wrottesley computed the probable errors and weights by the usual formula prior to 1857. After that year a more elaborate method was adopted : see Proceedings of R. S., vol. X. Secchi assigned weights (i to 5) according to the agreement among the individual measures of the set ; 5 was the highest and I denoted an approximate result. For a fuller treatment of this subject, see page 144. So DOUBLE STARS. 5. Contracted Apertures. Sir John Herschel was probably the first obser\-er who made constant use of these contrivances. In 183 1 he has the follow- ing remark in the notes to his measures : " The action of a telescope is often surprisingly improved by stopping out the central rays, by a round disc from a fifth to a sixth of the diameter of the object-glass, which should be well sheltered." * In 1834 Dawes wrote: "The use of a central disc on the object-glass having been suggested to me by Sir John Her- schel, for the purpose of diminishing the images of the stars, I have frequently employed one from an inch to an inch and eight-tenths in diameter. The effect is decidedly good on the stars themselves, if not too faint to bear the loss of light. The separating-^ower of the telescope is increased ; but the concentric rings accompanying bright stars are multiplied, and rendered more luminous, and are also thrown further from the disc. Hence small stars may often be obscured or distorted by the ring passing through them." In the introduction to his last great catalogue, this eminent observer again takes up the use of apertures. His long experience enabled him to speak with much confidence, and the following is a summary of the contents of the chapter. He seldom used the central round disc before the object-glass, because it increased the number and brightness of the rings, and caused the rings to hide faint companions of bright stars and elongate the discs of nearly equal stars ; — a perforated whole aperture was used with great advan- tage, and the " perforated cardboard used for making the Berlin-wool work is very suitable for bright stars." For fainter stars, a piece of cardboard covering the whole object-glass and pierced with holes in concentric circles may be used. These contrivances reduce the size of the discs and the bright- ness of the rings. The concentric prismatic rings produced are so distant as not usually to interfere with companion * " Sheltered : '' i.e., provided with a dew-cap of ample length, blackened inside. METHODS OF OBSERVING. stars. Angular apertures were used by Sir John Herschel, especially the inscribed triangle for destroying the rings round bright stars ; but the rays often obliterate or distort the small companion star. Dawes recommends the inscribed hexagon. In order to destroy the tendency of discs to become triangular, " especially when the wind is in the east or south-east," he recommends " cutting off three equidistant segments from the whole aperture of the object-glass, the base of each of which is the chord of 60°. Then, the chords being placed so as to coincide in position with the angles of the telescopic inverted image, those angles will be reduced by the larger circular aperture between the segments, and a fairly round image will be substituted for the triangular one." , " A smaller aperture may sometimes show a very delicate and close companion to a bright star, when a larger aperture fails to do it." The following table, from Dawes, may be of use in enabling the observer to form a correct estimate of the separating power of his object-glass : — Aperture Least Aperture Least Aperture Least in separable in separable in separable inches. distance. inches. distance. inches. distance. I'O /se 40 i'-'h 8-5 0-536 1-6 2-85 4-5 i-oi 90 0-507 2-0 2-28 50 0-91 9-5 0-480 225 2-03 SS 083 100 0-456 2'S 1-82 60 076 I2-0 0-380 275 1-66 6-5 070 150 0-304 30 1-52 70 0-65 200 0-228 3-5 1-30 7-5 o-6i 25-0 0-182 3-8 1-20 80 0-57 300 0-152 6. Best Time for Observing, etc. The state of the atmosphere during double-star observation should always be described in the note-book. Secchi indi- cates the state of the sky by means of the initial letter of the words signifying very fine, good, middling, and bad. He considers the night very fine when distances under i can be 6 82 DOUBLE STARS. readily measured, the discs being sharp and dear ; good, when distances from i" to 2" can be dealt with, the discs being less sharp than in the preceding; middling, when the discs are badly defined and unsteady ; bad, when discs 3" apart cannot be clearly separated. Some observers express these condi- tions by numbers. From the experience of Dawes and Struve it would seem also to be worth while noting the direction of the wind. Both these practised observers frequently found that easterly winds were associated with triangular discs. As regards the best time for observing, perhaps not much can be said, so much depends on local circumstances. Sir John Herschel, in the south of England, found that " the best time for astronomical observation, and especially for these measurements, is between midnight and sunrise. In the long nights of winter, it is true, distinct vision often comes on an hour or two before midnight, and in all seasons occasionally, of course, much earlier." He then notes the unsteadiness of the discs as morning twilight comes on, and uses the following descriptive terms in his notes : " twirling,'' " moulding," " con- vulsed," " twitchings," "wrinkled," "burred," "glimmering." " The rarest of all states of the atmosphere is that in which the rings are destroyed and the stars are seen perfectly round and tranquil." In conclusion. Sir John's experience with respect to the action of dew and the use of the dew-cap is worthy of note. " The least dew on the object-glass must be most carefully avoided, as it produces a singular contortion in the stars, which I have usually termed wrinkling ; the discs are much diminished, the rings multiplied and rendered narrower, and are kept in constant motion ; and a material change of the apparent angle of position is often produced by the displace- ment of their centres." The remedy he found to be a tube of tinned iron about 20 in. long, bright without and blackened within, and fixed on the object end of the telescope. (This was for his 7 ft. refractor.) methods of observing. 83 7. Precautions. The following precautions and hints may be of use to amateur observers. They are drawn from the experience of such observers as S., H., Da., De., and Se. : — 1. At the outset it must be remarked that the observatory (doors, windows, slit, and ventilators) should be thrown open at least an hour before observation begins, in order to reduce the temperature of the room to that of the external air. 2. If the definition be bad and the motion great, it is useless to attempt the measurement of double stars. In short, if a power of at least 300 cannot be used, the results cannot generally be of any value. 3. Very bright stars should be measured in daylight or twilight. 4. The observations should be made near the meridian if possible. 5. The observer should be in an easy position, — the prism effectually secures this ; and the driving clock ought to go smoothly. 6. The bright-field should be used almost exclusively — red and blue colours are most in use. 7. Use the highest powers possible, and always the same powers. 8. A moderate number of measures of an object on each of two nights is better than a large number on one night. 9. Use printed forms. 10. Enter date, hour, weather, and distance from meridian, before observation begins. 11. Notes on definition, general impression as to the value of each measure or each set, etc., cannot well be too copious. 12. In all doubtful cases make a sketch, and add full de- scription. PART II. CHAPTER I. ON THE CALCULATION OF THE ORBIT OF A BINARY STAR. INTRODUCTION. In his Lettres Cosinologiqiies, first published in 1761, the astronomer Lambert has the following remarkable words : " By observing the groups in which the stars are very much condensed, we may, perhaps, be enabled to ascertain whether there are not fixed stars which revolve in sufficiently short periods of time around their common centre of gravity." At the time these words were written, not more than from forty to fifty double stars were known to astronomers. In 1784 (see Phil. Trans., vol. Ixxiv., p. 477), about four years after Sir William Herschel began his famous discoveries of double stars, Michell wrote : " It is not improbable that a few years will inform us that amid the great number of double stars, triple stars, etc., observed by Herschel, there are some which form veritable systems of bodies revolving about one another." And again, in an earlier paper, {Phil. Trans., 176"/, vol. lii.,) Michell writes : "If, however, it should hereafter be found that any of the stars have others revolving about them, for no satellites shining by a 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 those stars, relatively to their respective quantities of matter." Maupertuis, Cassini, and no doubt other thoughtful astronomers in the early part of the eighteenth century, speculated on the existence of siderial systems, but ox THE ORBIT OF A BINARY STAR. 85 none with such clearness as did Christian Mayer of Mannheim. This diligent observer studied the proper motions of many- bright stars by means of the small Comites he discovered near them, and speculated on binary systems, elliptical orbits, the origin of new stars, variables, a central sun (?), etc.* The actual discovery, however, of pairs of stars physically connected and in orbital motion was reserved for Sir William Herschel. In the year 1779 he began to sweep the northern heavens in search of double stars, and in his first catalogue, presented to the Royal Society in 1782, gave descriptions and measures of 269 of these objects. About twenty-five years after the conclusion of these sweeps for double stars, he carefully remeasured the angles and dis- tances. The observed changes in angle and distance formed the subject of his great paper, "Accounts of the changes that have happened during the last twenty-five years, in the relative position of double stars ; with an investigation oj tJu cause to which they are owing!' {Phil. Trans., 1803, Part ii.) In this paper he showed that "many of them are not merely double in appearance, but must be allowed to be real binary combinations of two stars, intimately held together by the bond of mutual attraction." And Castor is the star whose changes he first submits to examination. Indeed this splendid object seems to have commanded much of his attention for years before the publication of his famous discovery of binary stars ; for Sir John Herschel says of this star that its " unequivocal angular motion seems to have first impressed on my father's mind a full conviction of the reality of his long-cherished views on the subject of binary stars." — Memoirs of R. A. S., vol. v., p. 196. Here too it is worth while noting that in 1798 Dr. Hornsby, reflecting on the well-marked proper motion of Castor, and the fact that the distance of the components had not changed for twenty years, drew the inference that both stars were moving with * See his Gruendliche Vertheidigung, etc., 1777. 86 DOUBLE STARS. the same velocity and in the same direction, but quite failed to see that these facts supplied unequivocal evidence of physical connexion.* In this way Sir William Herschel detected about fifty binaries. Since his time the list has been largely extended, and the researches of Struve, Madler, and others brought the number up to about six hundred. In the paper above referred to, rough guesses at the periods of revolution of some of the binaries were made by Herschel ; e.g., he assigned a period of about 342 years to Castor. It was reserved, however, for his distinguished son, Sir John, to grapple successfully with the interesting problem of finding by a graphical method the orbit which one star describes relatively to the other. If S represent the principal star, to which the motion of the companion is > referred, and if at successive . epochs the positions of the latter have been observed to be as in 4 . ^* the figure, Si, Sj, S3, S4, Sj */ ' it is plain that, assuming that the Fig. 6. observations are sufficiently nume- rous and accurate, a curve can be drawn through them which will represent the orbit. The positions thus marked down will not always form part of an ellipse ; they may lie in a straight line. For instance, the charted positions of the com- panions of Vega, 5 1263, and 5" 1516, appear to be well represented by straight lines ; while 7 Virginis, Castor, ^ Ursae Majoris, certainly move in elliptic orbits. It is possible, too, that the path may be some other curve, the knowledge of which will in its turn throw light on the forces and con- ditions which obtain in these sidereal systems. To describe a method by which the elements of the orbit of a binary star may be obtained without the aid of the higher de- partments of mathematics, is the object of the present section. * See Grant's History of Physical Astronomy, p. 559. on the orbit of a binary star. 87 Statement of the Problem. From the observations of angle and distance at given epochs, to draw tJte apparent orbit which one star describes relatively to the other, and thence to determine the elements of the true orbit, and to construct an ephemeris. The first part of the problem consists, then, in a careful study of the observations to determine their relative value, and in so arranging them as to obtain the apparent orbit. A little explanation will here be necessary. The orbit, or portion of it seen by us, is the apparent orbit : it is the projection on the background of the heavens of the true orbit, i.e., the pro- jection of the true orbit on a plane at right angles to the line of sight. Suppose, for example, the plane of the true orbit to be at right angles to the line of sight, then will the revolving star be seen to describe an elliptic path round the primary star in the focus, and the true and apparent orbits will co- incide. If the plane of the orbit pass through the earth, and present its edge to the observer, the revolving star will appear to recede from, approach, occult, or be occulted by, and again recede from, the star in the focus of the ellipse. The plane of the orbit, again, may be but a little inclined to the line of sight, and then the companion will appear to pass a little below and above the principal star. In one word, the plane may have any inclination to the visual ray, and the projection will present corresponding phenomena. Hence, a circular or elliptic orbit, if its plane were oblique to the line of sight, would be projected into an ellipse ; if the plane passed through the earth, the projection would be a straight line ; and an elliptic orbit might be so situated as to have a circle for its projection. The history of binary stars already furnishes us with illus- trations on this point. Take the star ? Herculis, discovered to be double by Herschel in July 1782. On looking at this object in October 1795, it was still seen double. Soon after the companion disappeared. During 1821, 1822, 1823, and 88 DOUBLE STARS. 1825, the utmost endeavours of Herschel and Struve failed to elongate it. Encke caught it double in 1826. Of this phe- nomenon Herschel says: " My observations of this star furnish us with a phenomenon which is new in astronomy ; it is the occultation of one star by another." Here then is an example of the orbital plane being in the line of sight. The period of this binary is about thirty-five years. Once more : 7 Virginis is already a famous binary. It was Known as a double star in the seventeenth century. Herschel found the distance 5"7 in 1780; in 183 1 it was 2"o. In 1836 Herschel wrote: "7 Virginis, at this time, is to all appear- ance a single star." About 1837 it again separated, and the distance is now nearly 5". 42 Comae is a fine example of a binary, the plane of whose orbit coincides with the visual ray.* Perhaps the accompanying figure will help to render this quite clear. Let C C be the di- rection of the line of sight, A B G the real ellipse whose focus is S and centre C. Then will its pro- jection on a plane at right angles to the line of sight be the ellipse A' B' G'. And it will be observed that S', the projection of S, does not coincide with the focus F. The principal star, therefore, will not in general occupy the focus of the apparent ellipse, but will be displaced into some other position. In many binary stars the observations do not yet extend over a sufficiently long period to enable us to compute any • Examples.— In 2 186, 1967, 2737 (AB) the plane of the apparent orbit coincides very nearly with the visual ray. The apparent orbit is nearly circular in S 1037, 1126, and X Ophiuchi ; the orbit is extremely elongated in 2 1516 (AC), 1909, and 2822. In 2 1348, either the position of A in the apparent orbit is very eccentric, or the plane of the orbit is ffreatly inclined to the visual ray. Fig. 7. ON THE ORBIT OF A BINARY STAR. 89 satisfactory orbit. In some, the portion of the orbit traversed since observations virere commenced does not include any of the critical points ; while in yet other cases complete revolu- tions have been made since the date of the discovery of the stars. Of this last class, f Ursas Majoris, period about sixty- one years, 17 Coronas Borealis, period about forty-two years, and f Herculis, period about thirty-four years, may be given as examples.* The next part of the problem consists in determining the real from the apparent orbit, and the position occupied in the apparent orbit by the principal star. And when all this has been done satisfactorily we are in a position to put our orbit to the test by the construction of an ephemeris, i.e., a series of computed positions and distances for the epochs of past and future observations. And if the computed quantities fairly agree with the measures made in past years, we must then proceed to compute positions and distances for future years at intervals of from a quarter of a year in the case of stars having rapid motion, to five or ten years in cases where the period extends over centuries. That it is quite possible, however, for an ephemeris to represent all past observations in a satisfactory way, and yet to fail completely when it comes to be compared with future measures, will be evident on a little reflection. The subjoined table, however, will bring out the fact very clearly : — Position. Epoch. LiWlJ. Observer. No. of Nights. Computed. Observed. 1848-0 239-0 249-16 Dawes. 7 1850-0 234-4 >j 1852-0 227-3 246-39 I 1854-0 212-6 24621 *f 7 1855-0 195 s 1856-0 164-4 245-44 Dembowski. 7 The computed places are from an ephemeris for Castor con- * In 02 208 and 298 it is probable that we shall soon be in a position to attempt the computation of the elements of the orbits. go DOUBLE STARS. structed by Sir John Herschel from an orbit which he published in 1832. The observations used by him extended from 1719 to 1831. The observed places are put by the side for comparison. The small number of observations at the disposal of the computer, and the very small portion of the orbit dealt with, must, of course, be here remembered. Yet this orbit repre- sented the previous measures very fairly indeed. Even when a star has been measured by skilful observers during more than an entire revolution, it is not always an easy matter to obtain elements which will furnish materials for a good ephemeris. Take ^ Ursae Majoris as an example. Its duplicity was discovered by Sir William Herschel in 1780; the companion was then not far from its apastron ; the peri- astron was reached in 18 16, and again in 1876, and hence its period is about sixty years. Now in 1872 Dr. Ball gave a set of elements, and an ephemeris furnishing positions up to 187875. The subjoined table will show how far the pre- dicted positions agree with recent measures. Epoch. 1872-50 187275 187300 1873-25 1873-50 18737s 1874-00 1874-25 1874-50 187475 1875-00 1875-25 i875'5o 187575 1876-25 1877-25 1878-00 1878-25 1878-50 Position. Computed. Measured. 22-4 17-5 12-5 7-3 2-2 357-2 352-I 347-0 342-2 337-6 333-2 329-0 325-1 321-4 3147 303-2 2961 293-9 291-8 19-39 358-91 333-63 317-56 304-8 294-9 85-5 in 1872-32, by Dembowski. in 1873-33, >. in 1874-35, ,. in 1875-27, „ in 1876-30, in 1877-26, , »» " in 1878-45, by Wilson. The agreement here is of course not satisfactory. ON THE ORBIT OF A BINARY STAR. gi Methods of Solution adopted. The first part of the problem— that is, the determination of the most probable apparent orbit — may be best solved by the methods given by Sir John Herschel (' Memoirs of the Royal Astronomical Society,' vols. v. and xviii.), with some slight additions. We shall give a brief explanation of it, but the method will be best understood by working through an example. To pass from the apparent to the real orbit is a geometrical problem of considerable difficulty. Fine analytical solutions of it have been given by Savary (' Connaissance des Temps pour I'an 1830 at 1832'), Sir John Herschel ('Memoirs of the Royal Astronomical Society,' vol. v.), Encke (' Ueber die Berechnung der Bahnen der Doppelsterne, Berliner Astr. Jahrbuch fiir 1832'), Villarceau ('Methode pour calculer les orbites relatives des 6toiles doubles.' 'Connaissance des Temps pour I'an 1852 et 1877'), and Klinkerfues ('Ueber eine neue Methode die Bahnen der Doppelsterne zu berechnen.' Gottingen, 1855). Purely geometrical solutions have been given by Thiele ('Ast. Nachrichten/ No. 1227, vol. lii.), and by the writer ('Monthly Notices,' vol. xxxiii., p. 375). Of these, Thiele's is by far the most elegant, and it is the one we shall here adopt. The construction of an ephemeris, and the comparison of the observed with the calculated places, is essential for the completion of the problem. This will be effected in the present paper by a graphical method. It must, however, be understood that the graphical method is only introductory, and that subsequent analytical methods are necessary in order to correct the elements, and attain the highest degree of accuracy that the observations permit of. To Prepare the Observations for Use. Some of the earlier measures of position and distance have 92 DOUBLE STARS. to be deduced from the differences of right ascension and declination observed by Bradley, Piazzi, Lalande, and others. The process is as follows : — Let S, S' be the two stars, whose right ascension and declination are a, S, and a + Aa, h -\- Ah respectively, S being the principal star. Let Aa, J8 be expressed in seconds of arc : then if P is the pole, P S Q, P S' Q' Fig- 8. declination circles meeting the equator in Q, Q', and S H is an arc of a small circle parallel to Q Q', QQ' = Ja, S'H = JS. Let P S S' = ^, S S' = p, the position and distance required to be calculated from Aa, JS observed. Then tan e = tan S S' H = |g = ^^^-^ (i.), and p = J8 sec. 0, (ii.), from which Q and p may be obtained. It must be observed that since 6 is always measured in the direction n,f, s,p, if Aa is positive, that value of 6 between o° and i8o°, which satisfies (i.) must be chosen ; and if Aa is negative, the value between i8o° and 360°. p is always positive. Further, if Aa, AB are observed with assigned limits of error, it is advisable to ascertain what are the corresponding limits of error in 6 and p, by substituting in succession those values of Aa, AB which give the greatest and least values to 6 and p. Throughout the whole of the working of this problem it is advisable to have angles expressed in degrees and decimals of a degree. Reduction to a Selected Epoch. In all cases before observations made at different times can be combined, the effect of precession on the angle of position ON THE ORBIT OF A BINARY STAR. 93 must be eliminated. For it must be remembered that angles of position are measured from the great circle which passes through the star and the pole, and that in consequence of precession the pole is constantly shifting its place, having a slow retrograde motion round the pole of the ecliptic. Hence the position that this circle occupies a^ some selected epoch must be taken as the zero of position, and all observations must be referred to it. The subjoined figure will show how the effect of this motion of the pole on the angle of position of any star can be com- puted. Let E be the pole of the ecliptic ; P, P' positions of the pole at an interval of a year; T the intersection of equator and ecliptic, from which the right ascension is reckoned ; S S' a double star in right ascension a° and declination 8°. Draw the circles P S, P' S ; then P S F is the A 9 required. Since T E, T P are quadrants, T P E is a right angle, and therefore P' lies on T P. Draw Y'p perpendicular to S P. Fig. 9. riG. 9. Then P P is known from the constant of precession to be for the year 1850, and very approximately for any other year, 2o"-os64= o°-ooSS7i2; 94 DOUBLE STARS. and P'/ = P P sin P' P/> = P F sin a; also F'p = Ad cos h, as in the last section. .-. J cos S = P' P sin a ; and A6 = o°-oo5S7i2 sin a sec S. The exact formula is {20"os64 — o"-000097(/ — 1850)} sin a sec 8. It appears further that the effect of precession is to increase the angle of position in the case chosen. Hence, in order to bring up to a certain date old observations of position taken t years before that date, we must add to those angles of posi- tion the quantity o°'oo5S7i2 sin a sec S x /. It is plain that this will be + for values of a from 0° to 180°, or from o"* to 12'' and — for values from 180° to 360°, or from I2'» to 24^ Example. — Dawes in the year 183 r34 observed the angle of position of 77 Coronas Borealis in right ascension IS*' 18" 14^ and declination 30° 43' 31", to be SO°-46. Reduce this to the epoch 1880. Converting the right ascension into degrees, it becomes 229° 35' 30". Hence AO = o°-oosS7i2 sin 229° 35' 30" sec 30° 43' 31" X 48-66 = — o°2292 ; and the corrected angle is therefore So°-23. Drawing of the Interpolating Curve. When a table has been thus constructed, giving, for some selected epoch, the angles of position and distances at a number of dates, the next problem is how to use this mass of materials. It will be at once obvious that the observations are not very harmonious, but that there are serious discre- pancies not only between different observers, but between the same observer and himself. And if the points were simply charted out according to the observed positions and distances, they would not lie on a curve, but on a broad irregular band. Sir John Herschel was the first to suggest {Mem. R. A. S., vol. V.) a graphical method of obtaining the positions at any ON THE ORBIT OF A BINARY STAR. 95 selected epochs with a high degree of accuracy; a method which necessarily gives no weight to exceptionally bad obser- vations, and makes use of all the good observations, both before and after any epoch, to determine the angle at that epoch. Take a sheet of paper ruled in fine squares, — that called millimetre paper * is the best, — and let the divisions running horizontally, suppose, represent angles, each division standing for a tenth of a degree, and the divisions running vertically represent years, each division standing for a tenth of a year. On this convention a dot on the chart represents a single observation. The subjoined chart therefore represents the following table of observations, t. 6. 1870-23 210-05 1870-38 209-95 1870-40 210-30 1870-25 212-38 1871-08 211-10 1871-34 212-08 i87i-4i 212-08 1872-10 214-62 1872-19 214-44 1872-20 213-21 mm. zio' in sis' sjf 2u' Fig. 10. and the curve drawn among them cannot be very far from the truth, and is influenced by all the observations except the two outlying ones, which are obviously bad. By this means we can obtain more accurate estimates of what the angle would be at any assigned date, or what is more used, of the date at which the angle would have an assigned value, than we can from the observations directly. For example, from the diagram we see that in 1870-00 the ♦ Millimetre paper may be got at Messrs. Williams and Norgate's. 96 DOUBLE STARS. angle would have been 2095, and that the angle was 213 at the time 187 171. All the measures, therefore, of position of the star must be charted, and the 'interpolating curve,' as Herschel calls it, must be drawn among them. This is a matter of the highest importance. The curve must be smooth and flowing. It may have points of contrary flexure, but it can have no abrupt changes of curvature.* When the curve has been drawn, note the time indi- cated by it at which the angle had in succession a series of values, proceeding by some common difierence, say of 2°, or of 5°, and construct a first table of interpolated angles and dates. Let the subjoined table be a specimen : e°. /. 70 : 1837-34 75 183990 80 1842-12 8s ! i844"25 90 1846-08 95 1847-74 Smoothing the Curve. The next process is to ' smooth ' the curve by an arith- metical examination of this table. Let A( represent the result of subtracting any one number in column 2 from the number below it, and let the series of numbers so obtained be arranged in a column to the right of the column of t. Similarly, let A't be the differences between the numbers in the column of A-i, and be placed in a column to the right ; and A^( be the diff'erences of A-t. * A point of contrary flexure indicates a point where the line drawn to the principal star is normal to the apparent orbit of the star. ON THE ORBIT OF A BINARY STAR. 97 The table will then be as follows : 6°. /. 70 1837-34 75 1839-90 80 1842-12 85 1844-25 90 1846-08 95 1847-74 A/. AV. A^/. 2-56 2-22 - '34 + ■25 2-13 - -09 — •21 1-83 - -30 + ■1% 1-66 - -17 It is plain from this that the numbers are not quite right, that is, that the curve has not been drawn quite smoothly, or that some of the values of t have not been quite correctly estimated. For if they were, then the differences in each column ought to proceed regularly, and not show irregular and abrupt changes, as this series does, in the second and third differences. It is necessary, therefore, to make slight changes in the second column such as will bring the difference columns into more perfect adjustment. To do this is not very easy, and requires patience. The following considerations may help in the process. The column of A^t is on the whole +, and therefore the column of A^t ought to have its terms, which are negative, continually decreasing in absolute magnitude. The -09 is therefore, too small, and the -30 too large. These can be changed in the right direction by increasing the 2-22 or diminishing the 2-13, and these in their turn make changes in the first column. After successive attempts, we obtain the following result : 70 75 80 85 90 95 /. 1837-35 1839-87 1842-16 1844-23 1846-09 1847-74 M. A''/. 2-52 2-29 2-07 1-86 f6s - -23 — -22 — -21 AV. -01 •01 ■00 gS DOUBLE STARS. By comparing this with the previous table, it will be seen that none of the dates have been altered more than '04 of a year, which would be represented on the chart by an almost imperceptible space. The values of t so obtained may therefore be regarded as a still closer approximation to the truth than those obtained directly from the graphical process, and d fortiori than those obtained by direct observation. All small errors arising from imperfect drawing of the curve, or wrong estimation of the decimals, have been got rid of. But it must not be forgotten that these values are still hable to be affected by serious errors of judgment in drawing the curve, or by errors of single observations when the curve depends on single observations. The curve may be smooth, and yet not the right curve. Errors of this kind cannot be detected at the present stage of the problem, but will be revealed later on. Employment of Measures of Distance. In a precisely similar manner all the measures of distance should be charted on millimetre paper, and interpolated distances obtained, at equal intervals of time, and the distance curve ' smoothed.' The errors in observation of distance often bear a large ratio to the distance itself, and the inter- polated distances are far more trustworthy than any individual measures. If now a series of corresponding values of r, 6 is found, and charted, these points will give a general indication of the nature of the curve. They will, for example, indicate whether the orbit is likely to be rectilinear or elliptical, and whether a sufficient portion of it has been described to make it worth while to attempt the computation. But in many cases it will be found that the points so obtained do not lie tolerably well on a curve, and that there will be liability to large error in attempting to draw a curve among them. This arises from the almost unavoidable error in the measurement of ON THE ORBIT OF A BINARY STAR. 99 distances. Sir John Herschel, therefore, devised a method by which the relative distances could be obtained from the measurements of position alone, and this we now proceed to describe. Determination of distance from the interpolating curve for angles of position. If A C E is an ellipse, S C p the focus, it follows from Kepler's second law that equal areas are described in equal times, that the rate of change of angular position is much more rapid in some part of the orbit than in others. I'^i^- n. Let A S B, C S D, E S F, be equal areas ; then they would be described in the same time, and hence the change of posi- tion angle in that time would be A S B in one part of the orbit, C S D in another, and E S F in a third. And con- versely, if the change of angle is greater at one part of the orbit than at another, it follows that the distance must be less, and less to such an amount as to make the areas described in equal times equal. If ;- be the distance at any time, A 6 the small angle described in the time A t, it follows that \ r'^ A6 \s the area described in that time; and therefore that the limit of r^ — must be constant at all parts of the orbit ; and therefore that r' varies as limit of ^. • But from the table given above (p. 96) A 6 \s constant, and A t can be got by subtraction, and the limit of -^ may be got either from the formula A^ _ j_ fiu_ _ _Af , A^^ \ or, very approximately, by taking half the sum of the differ- ences of the times that precede and follow the date selected. lOO DOUBLE STARS. For example, referring to the previous table, A = 5°, and when d — 80°, by the first formula ^2 0C I /2-07 , -21 , -ooN _ yl-T + 1- + TJ - 435, ■436; and by the second formula ^2 ^ if2-29 + 2-07) _ when the angle is 70°, ^^ = L{^^ + '^ + 'f) = -527, and therefore the values of r at 80° and 70° are as v/436 : v/527, or as 2088 : 2295. In this manner relative values of r are obtained for all the values of 6 in the previous table, at intervals of 5" or iO°, and these will be in general more accurate than those obtained from direct measurement, as they depend on measures of position alone. In order to compare with seconds of arc the unknown unit in terms of which these values of r are expressed, it will be necessary to take the whole series of values of r obtained in seconds at suitable points from its own interpolating curve, and the whole series obtained in the unknown scale from the formula above given, and compare the sums of the two series. Thus will be obtained the relative value of the two units to a high degree of approximation. Take the following values as an illustration : — t, r. r^ on scale. 1830 4'5o 12500 1835 462 127-60 1840 475 I3i'40 Sums ... 1387 384-00 Here I3"87 are equal to 384-0 scale divisions, and therefore I scale division corresponds to o'' 036 12. It will further be worth while to reduce to seconds each of the values of r, and chart them along with the interpolating curve which furnished the direct values of r, in order to see how far the calculated and observed values agree. A dis- AN ORBIT WORKED BY A GRAPHICAL METHOD. Id crepancy, systematically recurring between them, may lead, as in Otto Struve's recent investigation of the orbit of the dis- tant companion of f Cancri, to some novel and remarkable conclusions. (See Observations de Poulkova, vol. ix., and the Comptes Rendiis de I'Acad^mie de Paris, vol. Ixxix., p. 1463.) To Draw the Apparent Ellipse. It may now be assumed that we have the values of r for a series of values of Q differing by 5°. Let these be converted into X and y by the formulae x=r cos B, y= r sin 6, and the points charted on the millimetre paper. They will be found to lie on a curve ; and if a sufficient portion of the orbit has been described, the curve will be sensibly an ellipse. And here it may be observed that these points furnish the best possible test of the skill with which our final interpolating curve has been drawn; for if any poitit or points lie out of the curve we must at once redraw that part of tlie interpolating curve. Assuming that the correction has been made, the ellipse passing through the points may now be found either by the graphical or analytical methods. If the former be adopted, an ellipsograph, or a piece of string and two drawing pins, with a little patience, will suffice for this purpose. The line once drawn in pencil should be carefully inked in with a fine pen. This is the apparent ellipse. No care must here be spared in drawing the best possible ellipse, and drawing a fine line. With a pair of compasses we may now at once measure off the maximum and minimum apparent distances, and obtain directly the angles at which they occur. The larger star A occupies the projected focus of the real ellipse. Determination of the Real Ellipse : Thiele's Method. We must next proceed to the method of determining the real ellipse from the apparent one, and in doing this we shall follow Thiele's method, and give a geometrical proof of the elegant theorem he employs. 102 DOUBLE STARS. The problem is this : — Given an ellipse and a point in it which is not the focus, it is required to firld the position and magnitude of the ellipse whose projection is the given ellipse, and the projection of its focus the given point. The determination of the position and magnitude of the ellipse requires the determination of five elements, viz., (i) The angle a that the line of intersection of the two planes, or line of nodes, makes with a fixed line. (2) i the angle of inclination of the planes. (3) ^ the eccentricity of the ellipse. (4) a the semi-axis major of the ellipse. (5) \ the angle between the line of nodes and the line of apsides, or the line to periastre. The solution depends on the following geometrical property of the ellipse : — Let P S Q be any focal chord of an ellipse ; M X N the corresponding directrix ; P M, Q N perpendiculars to the directrix ; P K, Q H perpendiculars to the axis major ; S L the semi latus Fig. 12. rectum, and L R perpendicular to the directrix. Then, by similar triangles, HS:SK::SQ:SP, and by the property of the ellipse S Q : S P : : Q N : P M ; therefore QN:PM::HS:SK ::LR-QN:PM-LR; that is, Q N, L R, P M are in harmonic progression ; but Q N, L R, P M are respectively proportional to S Q, S L, S P j therefore the harmonic mean of S Q and S P is constant. And if along the chord P S Q a point Y be taken, so that S Y is the harmonic mean between S P, S Q, the locus of Y would be a circle of which S would be the centre, and S L the radius. If now the ellipse and this harmonic circle (as it may be called) be projected on a plane inclined to their own, the circle will be projected into an ellipse, the direction of whose AN ORBIT WORKED BY A GRAPIHCAL METHOD. i03 major axis gives the line of intersection of the two planes, and the ratio of whose semi-axes is the cosine of the inclina- tion of the planes. Conversely, if the harmonic ellipse be drawn, by taking, arithmetically or graphically, the harmonic means between the segments of a number of chords through the projected focus in the apparent ellipse, it follows that its major axis is equal to the latus rectum of the true ellipse; that its major axis is in the direction of the line of nodes; and that the ratio of its minor to its major axis is the cosine of the angle of inclination of the plane of the real ellipse to the plane of the apparent ellipse. Further, if C is the centre (Fig. 13), S C A' is the projection of the major axis ; and §| = .?, the eccentricity of the real ellipse, this ratio being unaltered by projection. Hence we find in succession a, i.e. the angle which the line of nodes makes with the axis of ;r, the meridian through the star ; i, the inclination, from the condition cos i = ||, Sa and Si being the major and minor axes of the harmonic ellipse : e = ^- J L S r- ) AC ' and ^ = — -^ = _^, L being the semi latus rectum. Finally, X, i.e. the angle the line to the periastron makes with the line of nodes, is found as follows : — Let X' be the angle X S C, V - /2 the angle A' S a in the annexed figure where A' is the projected periastron, and therefore known. \ is the angle A S a which is required. Draw A' N, A N perpen- dicular to S a. Then tan X = 1^ = M, X "11 = sec i tan (\ - a), ^^^ ^^ and therefore X is known. To construct the ephemeris graphically, it is necessary to divide the ellipse into equal sectorial areas by radii drawn from the focus. This may be accomplished as follows : — 104 DOUBLE STARS. Let A PA' be an ellipse (Fig. 14), P any point in it, S the focus, C the centre ; A Q A' the auxiliary circle, Q P N an ordinate through P. Let e be the eccentricity, a, b the semi-axes of the ellipse, T the periodic time for the whole orbit. Then if t be the time taken in describing the area ASP from perihelion to the point P, ' ~ ' SCQ. t_ T ASP _ ASQ IT ab TT a^ ACQ- and therefore if u is the circular measure of A C Q, t \ua* — ^aeasinu u — ^ sin u In order, therefore, to divide the area by focal radii into equal intervals, values must be given to « — ^ sin u in arithmetical progression. Let A B A' be the semicircle described on the major axis of the ellipse as diameter, S the focus of the ellipse. Divide the arc B A' into any number of equal parts, say of 10° each. Draw the tangent at B, and mark off along it from B parts equal to the arcs of 10°, 20° . . . 90°. Through the points of division of the arc draw lines parallel AN ORBIT "WORKED BY A GRAPHICAL METHOD. IO5 to C X, and through the points of division of the tangent at B draw lines parallel to C B, thus determining a number of points Vi Va . ., and through these points draw a curve B V X. We will call this the ephemeris curve. If now P is any point on the ellipse, Q the corresponding point on the auxiliary circle, V the corresponding point on the ephemeris curve, Q V being parallel to C X, C X' equal to CX,ACQ = u. Then if V N is parallel to C B, X' N = « u. Join S B, draw V H parallel to S B, and join C Q. Since y-N ~ c5 ~ ^> ^""^ CQ ~ ^^" ^' therefore H N = ae sin u, and therefore X' H = a(u — e sin u). Hence 2-^7$ = f-. and therefore the position P in the orbit can be at once found corresponding to any time /, and con- versely the time / can be found corresponding to any position P in the orbitj by simply drawing parallel lines.* Lastly, this method can be adapted to the further problem of dividing an ellipse into equal areas by lines from any point which is not the focus. To do this, instead of the auxiliary circle, an auxiliary ellipse must be taken, which will be similar and similarly situated to Thiele's harmonic ellipse. The working of this will be readily understood from the example annexed. * This problem can also be approximately solved with equal accuracy by mechanical means. The latest and best method is that given by Professor Bruhns in the Vierteljahrschrift der Astronomischen Gesellschaft 1875, Heft. 4. For an improved form of this apparatus, also by Pro- fessor Bruhns, see Heft. 4, 1877. Dr. Doberck, however, prefers to use the tables he has published in the Ast- Nachrichten. I06 DOUBLE STARS. CHAPTER II. EXAMPLE OF AN ORBIT WORKED BY A GRAPHICAL METHOD. For this method we shall select Castor, as a double star of great historical interest, and sufficiently brilliant and widely • separated to be within the reach of all telescopes that are likely to be used by amateurs. The orbit has been frequently computed before, both by graphical and analytical methods, and a comparison of the results arrived at is very instructive as showing the difficulty and uncertainty in problems of this nature, when the portion of the orbit described bears a small ratio to the whole. Table I. gives in chronological order the observations arranged as follows. In column i, headed t, is the date of the observation ; in column 2, the observed angle, headed & ; in column 3, the angle corrected for precession up to the year 1880, headed 6\ in column 4, the number of nights of observation, an important element in estimating the weight to be assigned to an observation ; in column 5, headed r, the observed distance ; in column 6, the number of nights ; and, lastly, in column 7 the initials of the observer.* ♦ For explanation of the initials see Part III. AN ORBIT WORKED BY A GRAPHICAL METHOD. IO7 Table I.— Castor. Angles and Distances : Angles reduced to 1880. R. A. 1880. 7" 26"" 57" = 111° 44' 15". Dec. 32° 9' lo"- Correction = o°-oo55 sin a sec S per annum = o°-oo6. 1719-84 1759-80 1779-85 1780-43 1783-46 1791-15 1792-16 1795-95 1800-27 1802-08 1803-19 1814-83 1816-97 1819-10 1820-34 1821-21 1822 01 1822-10 1823-11 1823-32 1825-24 1826-22 1827-28 1828-69 182889 1829-88 1830-52 1831 06 1831-11 1831-22 1831-31 1831-91 1832-12 1832-86 1833-10 1835-33 1836-88 1838-34 1839-35 184006 184018 1841-11 1842-25 1843-15 1845 '93 1846-34 1846-73 1847-25 1848-18 1848-28 1849-32 e' e No. of Nights. r Obs erver 355°88 356°85 Br. and P. 32378 324-50 Br. and M 30278 303-40 5 •29 H,. it 29305 293-64 )» 292-95 293-50 »» 29727 29781 it 28388 28440 it 284-32 284-81 )t 28277 28325 tt 28055 28103 tt 272-87 273-27 2. 27000 270-39 Hj. 269-60 26997 5-48 S. 26899 269-35 )» 26712 267-47 Hgand So. 26681 267-16 5-36 S. HgandSo. 264-98 265-32 471 tt s. 263-30 263-63 4-77 So. 262-54 26287 s 4-40 s. 26232 26264 4 4-42 II 261-87 262-18 4-64 Hj. 26110 261-41 4-36 ^' 26097 26128 ^'1? Hj. 25902 259-32 4-68 11 259-38 259-68 4-73 Be. 25962 25992 516 H3. 258-15 25845 4-57 Da. 259-58 25988 446 Z. 25935 25964 "s 4"74 H^ 25842 25871 14 4-71 Da. 257-72 25801 4-525 S. 256-73 255-48 25701 255-75 4-89 4-73 Hj. En. and Ga. 256- 1 2 25638 5-28 S. 254-40 254-65 4-81 Ga. 253-73 253-98 5-20 Ka. Da. Ma. 25397 254-21 4-71 25410 254-34 4-94 25282 25306 489 Da. 252-38 25261 491 11 251-71 25194 4-87 Hi. 1?- 24980 25001 250-38 25058 S-89 Hi. Da. 249-46 24966 4 24985 24920 25005 250-39 5 9 5-014 5-008 ■W. C. B. Da. Ft. 249-54 249-73 2 5-20 248-97 24916 4 5-027 io8 DOUBLE STARS. Table I. — continued. t V « No. of Nights. r Observer. 1 85 1 -04 248°67 248°85 6 5'°74 Da. 1851-21 248- 1 1 248-29 10 5-068 2. 1851-88 247-65 24782 5-044 Mi. 1852-04 247-97 24814 "e 5-075 Ft. 1852-20 24639 246-56 I 5-070 Da. 1852-50 246-12 24629 14 4821 Ma. 1853-05 24732 247-49 3 5-083 Ja. 1853-13 245-87 24603 3 5-157 Da. 1853-34 24626 246-42 9 4-931 Ma. 1854-23 246-21 246-37 7 5-098 Da. 1854-38 24472 244-87 18 4-945 Ma. 1854-87 24549 24564 23 5 '442 De. 1855-31 243-61 243-76 3 4-848 Ma. 1855-82 24513 24528 7 5-368 Se. 1 856 20 24544 24558 7 5-145 De. 1856-35 24378 24392 6 4-875 Ma. 1856-73 245-51 24565 4 5-172 Ja. 1857-34 244-25 24439 4 5'l!? Da. 1857-36 24290 243-04 7 4-888 Ma. 1857-77 245-19 245-32 3 5-336 Ja. 1858-26 244-42 244-55 2 5-208 Mo. 1858-37 244-13 244-26 7 4-963 Ma. 1859-26 243-88 244-01 2 5-156 Mo. 1859-36 242-70 24282 11 5-081 Ma. 1859-98 24362 24374 2 5-378 Mo. 1860-22 24277 24289 3 5-395 Da. 1863-02 242-75 242-87 11 5-537 Ro. 1863-03 241-66 241-78 14 5-381 De. 1864-60 241 53 241-88 10 5-59 Da. 1866-02 241-07 24115 14 5-384 De. 1870-32 239-7 23976 1 5-57 Gl. 1870-68 23934 239-40 5 5-488 De. 1871-59 2379 23795 2 5-64 GI. 1872-00 2364 23645 I 5 -73 ,, 1872-39 237-8 237-85 2 5 9 -ft', and S. 1873-24 237-9 237-94 1 5-6 J» 1873-29 2363 23634 I 5-62 Gl. 1873-78 23692 236-96 8 5-557 De. 1874-10 236-6 23663 7 5-7 Gl. 1874-13 236-9 23693 2 5-6 ■W. and S. 1875-66 236-2 23622 15 5-5 GI. These angles and distances are all charted on the millimetre paper as before described, and the result is shown in Plate I., in -which each dot corresponds to an observation. A curve is then drawn as smoothly as may be among the points of obser- vation. The first curve that was so drawn had to be abandoned, but the points at which it crossed the principal lines are shown by fine lines, which are in fact portions of the curve. AN ORBIT WORKED BY A GRAPHICAL METHOD. lOQ The first table of interpolated angles and epochs was as follows : — Table II. — First Table of Interpolated Angles and Epochs. 355 35° 345 340 335 33° 325 320 315 310 305 300 295 290 285 280 27s 270 265 260 25s 250 245 240 235 1723-8 17297 1 735 '4 1740-9 1746-2 i75i'4 1756-5 1 761 -7 1766 '9 1772-1 1 777 '4 1782-7 1788-1 1 793 "6 1799-2 1804-9 1810-7 1816-9 1823-5 1830-6 1838-4 1847-1 18567 1867-3 1879-0 H-t 1 ■7) "} 5 -3 J ::} } 5 3 J ::} } 7 -83 '■'} 9 -6 J 10-6I 1 1 -7-* 5-9 5 5 5 "3 5-2 5 5-2 5-2 5-2 5 5-3 5 5-5 5-6 57 5 6-2 6-6 i-i6 1-08 1-03 1-04 1-05 1-07 1-15 1-28 1-49 1-83 2-23 r = 100 X ^AJ 107-7 1037 IOI-5 102-5 103 '4 105-4 107-2 I131 I22-I i35'3 149-4 106-00 21-76 46-27 74-67 18-70 97-65 35-54 87-90 50-74 78-11 65-54 65-86 78-49 51-72 89-58 36-04 9900 18-63 105-60 II3-I0 123-40 127-10 130-90 1 lO DOUBLE STARS. From these values of r are obtained values of r cos 6 and r sin Q, and the corresponding points charted on millimetre paper, where they are indicated by the small crosses near the curve in Plate II., the values of x being taken horizontally, and those of _y vertically. It is at once seen that these points do not lie truly on any smooth curve, and hence it is inferred that the interpolating curve is wrong. It is necessary, therefore, to redraw the interpolating curve, and it is advisable, in order to save time and trouble, not to do this at random, but to ascertain from the errors of the points found on the erroneous curve, both the nature and as far as possible the amount of the modifi- cation required in the various parts of the interpolating curve. This may be done as follows. If a curve be conceived as drawn through the extreme points and fairly among the others, it will leave the points corre- sponding to the angles 300°, 310°, 320° outside the curve ; but those corresponding to 260° and 270° and 280° inside the curve. Hence the distance ought to be diminished in the neighbourhood of 310° and increased in the neighbourhood of 270°. Also a simple measurement with compasses will show in what ratio the distances at these points ought to be respectively diminished and increased. But the distance varies as ^At, and therefore the ratio in which At ought to be diminished or increased becomes known. Hence the differences {At) in the neighbourhood of 300°, 310°, 320° were changed from 5-3, 5-3, 5-2, 5-2, to 5-2, 5-1, 5-1, 5-1; and those in the neighbourhood of 260, 270, 280 were changed from 7-1, 6-6, 6-2, 5-8, to 77, 6-8, 64, 6-o, and the whole table reconstructed as follows. AN ORBIT WORKED BY A GRAPHICAL METHOD. Ill Table III. — Second Interpolating Curve. e t A/ A/ A« r - y 360 1717-1 6-2 355 1723-3 350 1729-2 5-7-' I -16 106-00 18-70 345 1 734 '9 340 1740-4 5-3-' I -08 97-65 35-54 335 17457 330 1750-9 5 -2 J 1-04 88-32 50-98 32s 1756-1 320 1761-2 5-1J 1-02 77-36 64-92 315 1766-3 310 1771-4 S-iJ 1-02 64-92 77-36 305 1776-5 300 1781-7 5-3-' 1-05 51-23 88-74 395 1787-0 290 1792-4 5-4| I-IO 35-87 98-55 28s 1798-0 280 1803-8 60/ i-i8 18-86 107-00 275 1809-8 270 1816-2 6-4| 6-8/ 1-32 114-90 26s 1823-0 260 1830-7 8-0 J 1-57 21-76 123-40 25s 1838-7 g-y-j 250 1847-4 9 -6 J 1-83 46-38 127-40 245 1857-0 240 1867-6 io-6| 1 1 -6 J 2-22 74-50 129-00 235 1879-2 I I 2 DOUBLE STARS. When these points are charted, they are found to lie satisfactorily on a curve. If they again failed to do so, a third interpolating curve would have had to be drawn. By proceeding to two decimals, and using the second column of differences, slightly more exact results could be obtained. The next operation is to complete the ellipse of which the curve so found forms a part. This part of the problem re- quires much patience and some sagacity. Either an ellipso- graph or a piece of string and two drawing pins may be used, and at last by methods of trial and error an ellipse is found which approximately passes through all the points. No pains should be spared here to make the ellipse pass as exactly as possible through the points. It must be remembered that a very slight alteration in the position of the foci and the length of the major axis will seriously affect the area of the curve, and hence the periodic time in the orbit we shall obtain. In cases like the orbit of Castor, when only a small portion of the orbit has been described, it is impossible to ascertain the apparent ellipse exactly, and hence the periods hitherto obtained by different computers differ seriously. In the figure, Plate II., C is the centre of the apparent ellipse, and the part of it hitherto described is that part where the dots are seen and the dates are marked. By inspection of this curve several facts are at once obtained. If A is the principal star, from axes through which the co- ordinates have been laid out, A must be the projection of the focus of the real ellipse ; and C being the centre of the apparent ellipse, must also be the projection of the centre of the real ellipse. Hence A C produced both ways must be the projection of the major axis of the real ellipse. If this cut the apparent ellipse in N, N must be the pro- jection of the periastron, at an angle of about 338° 30', which from the interpolating curve corresponds to a date of 1742T. Further, the ratio C A : C N being unaltered by the pro- jection will give the eccentricity of the real ellipse. Measuring A.D. ■7<,Cf Pla TE I neo fTBo fsoo r/i>>o «/./) /,, 3i,d X N(: Ij^WBI \POLATIN :gSuF^ sopGasto^ ^^ yxn° x ~H^ ^s 1 1 500 "^^ Si ieo "■*■[« Z60 ''^-* "'4^' '"'•-.•,. H^O 6'o s'.o • i\ .•■ .-i . S '.0 x'.o - • - • - -■ I'.O - ■ - ■■ -■ AJ). taso /gjc 1S',C/ id 70 AN ORBIT WORKED BY A GRAPHICAL METHOD. I13 these distances with the compasses and computing the ratio it is found that ^ = 38 . . . Again, it appears that the nearest approach of B to A was at the angle 314, or at the time 1767-3 at the point U: this distance on the millimetre scale is about 100. Similarly, the greatest apparent distance on the same scale will be about 233-6. In order to ascertain what these distances are in seconds of arc, it will be necessary to make a table of the observed dis- tances, obtained by interpolation at selected epochs from the distance curve (Plate I.), and compare them with the distances on the millimetre scale obtained from the apparent ellipse at corresponding angles. TABLE IV. /. r. r' on scale. 1830 ... 4'so ... 125-6 183s ... 462 ... 127-6 1840 ... 475 ... 131-4 184s ... 4-89 ■- 134-5 1850 ... 5-02 ••■ 137-S 1855 - 514 ... 140-5 i860 ... 5-25 ... 144-5 1865 ... 538 ... 147-2 1870 ... 5-52 ... 150-0 Sums ... 4S"'07 1238-2 divisions. Hence the least distance was 3"'64, and the greatest distance will be 8"-50, at an angle of 174°, at the point V. The next part of the problem consists in the construction of Thiele's ellipse. The axis of ;r is cut by the ellipse at distances 11 1-8 and 233-0 from A. The harmonic mean between these is 151-1. Lay out this distance along this axis in both directions from A, so obtaining the points i, 2. Similarly, from the intercepts on the axis of y obtain their harmonic mean, and the points 3, 4. Two more points can easily be obtained by drawing a '^4 DOUBLE STARS. chord through A which is bisected in A. The extremities of this chord will plainly be points on Thiele's ellipse. Construct an ellipse to pass accurately through these six points, A being of course the centre of this ellipse. Draw the axes Ka, A^ of this ellipse, and find its foci /,/'. Then by Thiele's theorem the ratio A b : b f is cos 7, where y is the inclination of the plane of the real orbit to the plane on which we see it projected — that is, to the plane perpendicular to the line of sight. Hence 7 is found to be 32° 15'. The direction of the major axis of this ellipse is that of the line of nodes. This is found by a protractor or scale of chords. Hence a = 28° 15'. The elements of the orbit so far obtained are e = 38 7 = 32° IS' a = 28° 15' T = 1742-1. To obtain the period some further construction is required. Draw through C lines DC, EC parallel to the axes of Thiele's ellipse : these will be the directions of the axes of the ellipse which is the projection of the auxiliary circle. The ratio of the axes of this ellipse will be of course the same as that of the axes of Thiele's ellipse, and the magni- tudes of the axes can be found from the consideration that C N and A M are radii drawn, one in each, in the same direction relative to the axes, and therefore have the same ratio as the axes. Hence if the proportions AM : CN :: Aa : CD andAM:CN::A<5:CE are worked out, C D and C E will be the semi-axes required. Let this ellipse be drawn ; we will call it the auxiliary ellipse. Draw CT, CT parallel to the projection of the latus rectum of the real ellipse to meet the auxiliary ellipse in T, T', and draw through T, T' lines parallel to C M. AN ORBIT WORKED BY A GRAPHICAL METHOD. II5 Measure off T Y, T'Y' along these lines, the length being found by the proportion i : ^ tt : : C N : T Y. Divide TY, T'Y' into nine equal parts, the points of division being numbered i, 2 ... 8 in the figure ; and draw lines through them parallel to T C T'. From a table of sines, and the known length of C T, compute CT sin 10°, and mark off this length along the line I, I, measuring from the central line C X on both sides of it, thus obtaining Gi Kj, Gj K/ = C T sin 10°. Similarly, lay off G2 K2 = C T sin 20°; G3 K3 = C T sin 30°, etc. And through the points so determined draw the curve X Kj Kg . . . T. We will call this the ephemeris curve. This is \he projection of the curve of sines.* Join A T, A T'. Then, as was before shown, if through any point P on the apparent ellipse P Q be drawn parallel to C T to meet the auxiliary ellipse in Q, and Q O be drawn parallel to C M to meet the ephemeris curve in O ; O H be drawn parallel to A T to meet C M in H ; as P moves with its orbital motion in the apparent ellipse, H will move uniformly along the line X' C X. Select two positions of P whose epoch is known, as at the first and last of the points interpolated, for which the times were i867"6 and i729'2 respectively, giving an interval of I38'4 years. Measure H X = 132, H' X = 15, X X' = 52::. Then by the proportion HX + H'X : 2XX' :: 138-4 years : period, we find the period to be 982*9 years. To construct an ephemeris, divide C X into any number of equal portions, and determine as before the points on the apparent ellipse corresponding to each point of division. To find the angle at any required date, say 1880, proceed as follows. Since 1880 — 1867-6 =12-4 years ; and since 1044 divisions correspond to 982-9 years, 12-4 years correspond to * The curve of sines was first suggested, we believe, by Professor Adams. II 6 DOUBLE STARS. I3'i divisions. Take H. A = 13-1, and determine by the same construction the point marked 1880. The angle is found by the protractor to be 254°'$. In the same manner the angle in the year 1890 is found to be 231-5. In the same manner the date of maximum distance will be found to be A.D. 2147-2. We have still to determine the major axis (a) of the real ellipse, and the position of the periastron (\) on the orbit. Since the major axis of Thiele's ellipse is the latus rectum of the real ellipse, as before shown, and the eccentricity e of the real ellipse has been found, a = 7.. = ^^TT^. = 183-4 divisions. I - e" I - (-38)^ and this reduced to seconds by the equivalence in p. 113, gives us a = 6"-67. Lastly, tan \ = tan (V — a) sec i, where \' = the angle that the projection of the axis major makes with the initial line. This gives \ = 305° 10'. Hence our elements are as follows : — Semi-axis major a = 6" '67. Eccentricity e = -38. Position of node O = 28° 15'. Inclination i = 32° 15'. Position of periastron X = 305° 10'. Period in years P = 982-9 years. Periastral passage A.D. T = 1742-1. It will be interesting to compare these with the elements obtained by a rigorous analytical investigation by Thiele, in Ast. Nach., vol. lii., No. 1227. Thiele's Elements. « = 7-5375- ^ = 0-34382. a = 3'°58'-o. i = 42° 5-4- X = 294° 0-8. P = 996-85. T = 1750-326. Pla te h Graphical Gonstrugtion op Orbit op 6a Tfw Sec fijm I/tt AN ORBIT WORKED BY A GRAPHICAL METHOD. II 7 Since our graphical solution was finished in 1875, Dr. Doberck has also computed the orbit, and gives DoBERCK's Elements. a ■= 7'43- e = 0-329. a = 27° 46'. X = 29713. P = 1001 -2. T - 1 749 75- ii8 DOUBLE STARS. CHAPTER III. AN ORBIT WORKED BY ANALYTICAL METHODS. The following example, in which the orbit of cr Coronas is worked out, will illustrate the application of analysis to the subject of double-star orbits. It possesses some independent interest on account of the discrepancy among the orbits hitherto published, which will be seen from the subjoined table. The method presupposes an orbit obtained approximately by graphical methods, and shows how greater exactness can be obtained in the elements. No further acquaintance with analysis is necessary than that of the elements of the differential calculus. On A Determination of Elements of a Corona (1877). Herschel discovered in 1781 that a Coronae was double, and in 1802 he recognized its binary character. The motion is direct. The distance was small when first ob- served, but afterwards it increased rapidly, thus rendering the measures surer and easier. A re-determination of the elements, in which these later observations were taken into account, seemed to me likely to decide upon the question of the period, about which astronomers hitherto did not agree, as can be seen from the following table : — T Node. K V P a e Authority. / / / yrs. 1835-60 1380 718 41 15 286-60 3-68 0-61 12 J. Herschel. 1826-60 257 6438 2929 608-45 3-92 0-6998 Madler. 1826-48 21 3 6924 2539 736-88 5-19 0-7256 Hind. 1829-70 3« 9653 45 6 240-00 2-94 0-3887 E. B. Powell. 1831-17 157 loi 57 4647 195-12 2-72 0-3088 Jacob. AN ORBIT WORKED BY ANALYTICAL METHODS. I I9 I tried first to determine the elements by Sir J. Herschel's method {Memoirs of the Royal Astronomical Society, vol. v.) A first attempt with an ellipse corresponding to a moderate period failed to represent the observations ; and I subse- quently obtained the following orbit by the aid of ninety- eight annual means of angles and distances : — First Elements of a CoRONiE. T 1828-91. Node 6° 43'. X 89° 17'. r 29° 40. 843'2o years. u 6"*ooi. e 07502. The comparison of the angles of position, and the distances calculated from these elements with those given by the mea- sures, has been published in the Astronomische Nachrichten, No. 2037. I collected afterwards eighteen more annual means, partly in the library of the Royal Irish Academy in Dublin, partly they were communicated to me by Messrs. Wilson and Gledhill, and Dr. Dun^r, of the Lund Observatory, Sweden. The comparison with all these measures proved the calculated angles to be a couple of degrees too small at the first epochs, about as much too large in 1830, and again too small at the present time. The corrections were graphically determined, and, when applied to the calculated angles, furnished new angles of position, from which the distances according to Herschel's method were deduced, and from these the second system of elements was calculated. Second Elements of a Corona. T 1 Node .. 26° 10'. \ .. 62° 14'. 7 .. 35° 8'- .. 82940 years e .. 07463. ^20 DOUBLE STARS. The apparent ellipse was very like the former one, but this time it was possible to lay it nearly through all the points. I thought, therefore, that I had hit the right orbit this time; but the subsequent comparison with observation showed that the angles from 1825 to 1870 came several degrees short of the measures, though the agreement else- where was close. All the angles but for a short interval being represented, I thought that I had better correct the elements by Klinkerfuess method. This method requires six angles of position to be given, from which the six elements are deduced, the axis major being afterwards cal- culated from the observed distances. Sir W. Herschel's two epochs furnished the first two normal places ; the angles measured between i8i9and 1828 the third ; the unrepresented measures 1830 — 1839 the fourth. The fifth place was obtained from the measures 1839 — 1868 inclusive, as it was in this instance allowable to consider the deviation proportional to the time during this long interval, the difference between the observed and calculated angle being nearly constant through- out. The sixth normal place had been previously used to deduce epoch and period of the systems given above. It was determined on Gledhill's, Wilson's, Dun^r's, Dembowski's, and Schiaparelli's measures only. Madler's epochs of i836"47 and 184273 were excluded, as also some of Talmage's measures and Copeland's for i873'40. Six Normal Places for a Coronae. 1 178179 e° = 347"'S3 II 180274 III 182500 IV 1835-00 V 1855-00 VI 1872-11 I r-4o 77°-67 I28°-20 i79°73 i97°'37 There is a well-known proposition which says that when a triangle is orthogonally projected on a plane, the area of the triangle in the projection is equal to the area of the real triangle multiplied by the cosine of the angle between the AN ORBIT WORKED BY ANALYTICAL METHODS. 121 planes (cos 7). Now as the apparent orbit of a double star is the orthogonal projection of the real orbit, areas between the principal star and two places of the companion in the one orbit are in a constant ratio to the corresponding ones in the other, as, r r* sin (u — u') pp' sin (9 — g' ) , 1^ f sin (u' - 1/') pi p" sin (»' - «")' ^ n-^' sin (u — 1/ ") _ pp" sin {0 — 9") r" 7-' sinlu"^^'u') ~ "p" P" ^'n («" — 6") ' where r, r^, etc., are the radii vectores corresponding to p, p, etc., the distances, and the angles of position 6, 0', etc., to the true anomalies v, v, etc. Dividing the first equation by the second, we obtain sin (v' — v) sin (u" — u") _ sin (9' — 0) sin (9" 9") ^ sin (u" — u) sin (u' — v") ~ sin (9" — ») sin (9' — 9")" If we write successively u"', ^™ and v'', ^" in the place of v'', 0" in this equation, we obtain the two equations sin (i>' - v) sin (1;'" - v^) _ sin (9' - 9) sin (9"' - 9") , sin (i^" — v) sin (1/ - u') ~ sin (9" — 9) sin (9' - 9")' ^ si n (u* — I/) sin C^" — u^ ) _ sin (9' — 9) sin (9'^ - 9") sin (u'^ — u) sin (u* — u^) sin (&" — 9) sin (9' — 9')- The right side of the three equations contains nothing but the angles of the normal places ; substituting their values, we obtain the equations as follows : — sin (u' — xi) sin (u'l — u^) sin (u" — v) sin (u' — v^ ~ °'' sin (u' — u) sin (u'" — v") _ sin (u™ — u) sliTCu'^^u') ~ /'" sin (i/* — t/) sin (1;''^ — v") sin (u" — V) sin (u' — v^ ' ' The true anomalies being functions of the eccentricity, epoch, and period, it is theoretically possible to obtain these three elements from the three equations. The peculiarity of the method we shall follow is that it furnishes equations from which the elements fixing the plane of the orbit (node and •inclination), and the position of the ellipse in the plane (X), have been eliminated. It would, however, be very difficult directly to obtain the three elements—^, P, T, — from the 122 DOUBLE STARS, above equations ; but these equations are useful, when we, as in the present case, have already arrived at a very near approxi- mation to the elements, which we want to advance further by representing by the orbit strictly the six angles of position. Instead of the elements e, P, and T, it is a slight improve- ment to substitute the annual mean motion for the period : /* = ^-, and the mean anomaly Mo corresponding to the epoch of periastron-passage in the provisional orbit, e is obtained in degrees, from which its value in the usual form is computed by dividing by the number of degrees in the unit of circular measure — 57°'296. We calculate, firstly, the true anomalies, and hence a, /?, and 7, with the provisional elements, — that is, with M^ = o. Secondly, we calculate the same quantities with the same e and yt,, but M^ = + i°. Thirdly, with the same e, M^ = O, but adding to the mean motion a fifth of its value : ;*' = i'2 /*. Fourthly, with M^ = o, the original mean annual motion /a, but with another eccentricity, e ^ e ^r O'OI. By a com- parison of the results obtained by the three last calculations with that from the first hypothesis, we get to know what influence any variation of the elements has on the three qualities a, /3, and 7, that we are trying to represent, — that is, we learn their partial differential coefficients. The differ- ence between M^ in the two first hypotheses divided into the corresponding variations of a, ^, and 7, give ~, jj^, and -T-TT- The difference ft.' — fi, divided into the corresponding variations of a, /8, and 7, give ^. J^, and -^- Finally, the difference e' — e divided into the corresponding variations of a, /3, and 7, give f^. ^^. and J^- If we now denote by a', /8', and y the values correspond- ing to the first hypothesis, and by a, /3, and 7 the values calculated from the position angles, we obtain by Taylor's formula, — AN ORBIT WORKED BY ANALYTICAL METHODS. 1 23 From which are easily obtained the corrections A M^, Afi, and Ae, to be applied to the values in the provisional elements in order to be able to represent the six position angles of the normal places. Professor Klinkerfues indicates further several processes, which must reduce the amount of work required in the com- putation of the single hypotheses. The true anomalies are calculated from the three elements by the following well- known formulae, — u — e sm. u ■= M^ + jxi, tan\v= -^L+J tan \ u. 1 — e where u are the eccentric anomalies, t the time since the epoch, and e is expressed in the first equation in degrees in the second in absolute measure. From these are obtained the differential coefficients of the eccentric anomaly with respect to the mean anomaly, — —rrrrr:^^ etc. 1 — e cos ti' I — e cos »" I — e cc The eccentric anomalies of the second hypothesis are obtained from those of the first by multiplying the alteration of the mean anomaly, here + 1°, by these differential coefficients. The eccentric anomalies of the third hypothesis are obtained by multiplication of the same coefficients by the correspond- ing alterations of the mean anomalies. Those of the fourth hypothesis are obtained by multiplying the variation of the eccentricity expressed in degrees by the differential coefficients of the eccentric anomaly with respect to the eccentricity : — sin a' sin «" sin «'" sin ti" . ., :,! iJT» j^» etc. I — e cos a' I — < cos u' I — i cos «'" 1 — e cos " 124 DOUBLE STARS. The products are in all cases to be added to the eccentric anomalies of the first hypothesis. The true anomalies are then obtained from the eccentric, by the formula given above. The results of these calculations in case of a Coronze were as follows : — 1 Hypothesis I. HjTJOthesis II. Hypothesis III. Hypothesis IV. Wo. o°. + l". 0°. 0°. M 04340 o°4340 0-5208 o°-4340 e 07463 07463 07463 0-7563 / <^ ' ^ / / u 305 52 307 38 298 56 305 3 u" 325 12 327 47 319 49 324 22 j<" 357 9 I 5 356 34 357 2 w'" "3 5' 17 29 16 28 14 21 u" 39 25 41 47 45 12 40 16 u" 54 33 56 19 61 31 55 22 ', / / / V 253 26 25s 34 245 45 251 14 r' 281 8 285 42 272 20 278 254 j,ii 352 32 2 504 351 352 3 j,iU 35 21 43 56 41 35 37 2oi V-'- 86 27 90 i,\ 95 3 89 54 ?■' 107 3 109 6 "4 43 109 155 a - 4'i55 - 8486 — I -015 — 2-201 /S - 6-941 — 14-600 - 2750 - 4-145 7 + 7 "044 + 10 990 + 0-809 + 2733 The constants calculated from the observed position angles are — a = - 3-382, ^ = - 5-739, and y = + 5-580. Thus we obtain the equations - 4-331 iiM„ + 3-140 A/1 + 1-954 A« = + 0-773 — 7-660 AM;, + 4-191 A/1 + 2-796 Af = + 1-202 + 3-950 AM„ - 6-235 A/1 - 4-31 1 A? = - 1-464 ; from which AMo = — o°-o5i, A/i = —0-0683 X o°-o868, Ac = 0-39 X o-oi ; or T= 1826-81, /I = o°-428i , ^-. 07502; with which we get «305°53, 325° 8, 356°53', i3°38', 39°i8', 54°i6'. V 252° 59', 280° 33', 356° 27', 35° 6', 86° 46', 107° 12'. a = - 3720, /3 6193, r = + 5'*6s. AN ORBIT WORKED BY ANALYTICAL METHODS. 1 25 It has already been remarked that there hitherto existed some uncertainty as to the period of revolution of this system, and that I was by my first investigation led to consider the large period pretty well established. The possibility of fixing separately the eccentricity and period appears by an inspec- tion of the three equations above, as the coefficients of J/i and Ae, are not proportional ; but they are not far from it, and if the measures employed embraced a shorter time than ninety- five years, they would be more nearly so, and it is therefore no wonder that we hitherto were in doubt about the orbit. In reality, a great number of different orbits, corresponding to every value of the eccentricity varying within wide limits, would have been obtained, if the elements had been repre- sented as linear functions of the eccentricity. The values of a, /3, and 7, finally obtained, are far from those deduced from the observations. The differential co- efficients, employed in the calculation of the hypotheses may not be without influence hereupon, notwithstanding that the variations of the elements were small enough. But the dis- agreement arises principally from the circumstance that the higher orders of the differential coefficients of a, j8, and y with respect to the elements are not to be neglected, which has been supposed by confining ourselves to the first term of Taylor's series. To represent a, /S, and 7 better, I extrapolated between the last values of the three elements and those of the first hypothesis. Thus I obtained T = 1826-85, (J = o°-4264, e = 07513. «305°SS'. 325° 5'. 3° 10', 13° 32'. 39° 12'. 54' U'. z/ 252=52', 28o°i8', 351° 37', 34° 57'. 86=45, 107° 18'. a = - 3-425, /3 = - 5-861, r = + 5-530. I substituted now these a, /3, 7, for a!, /?, 7', in the equations, which then turn out as follows : — - 4-33 AMo + 3-14 ^/i + 1-95 Ai? = + °-°43- -7-66 „ +4-«9., +2-80,, =+0-122. + 3-95 >. - 6-24 „ - 4-31 „ = + 0-050. 126 DOUBLE STARS. From which we obtain AM = - o°-032, Aft = —0-049 "* o°-o868, Ae = +o'02 x o-oi. T - 1826-93, h = o°-4227 , e - 0-7515. u 306° 10', 325° 43', 3° If, 13= 24', 38= 54', 53° 52'. J- 253° 9', 28o°3i', 35i°i8', 34° 38'. 86=18', 106° 53'. a 3-778, j8 - - 6-340, y = + 6-405. This very erroneous result shows that the coefficients, deduced for correction of the original elements, cannot be used strictly speaking for rectifying the new elements. The corrections . which resulted from T and e are however so small, that no new approximation appears necessary. I therefore retained them, and calculated a, /3, and 7 with the former value of /i, — that is, u = o°-4264. — The numbers obtained were the following : — T = 1826-93, /i = o°-4264, e = 0-7515. « 305° SI'. 324° 59', 356° 43'. 13° 2/ , 39° 9'. 54° II'- V 252=46, 280- s', 351° 18', 34°45i'. 86° 42', 107° 15^ ■ a 3-34i> P = - 5-69i> r -= + 5-357. This result was then compared with the result from the same values of T and e, but fi = o°-4227. Denoting the constants calculated with fj, = o°-4264 by a^, jSi, and 71, those calculated with fj, 0° 4227 by oj. ^i, and 72, and those calculated from the observed position angles a, fS, and 7, we obtain the following three equations for the determination of the correction to be applied to « = o°-4264 in terms of the difference between the two mean motions : — (aj — a,) A/i - a - a„ {(i.^ - ^1) A/l = /3 - ^, (73 - y^) A/l = y - y,. These equations in the present case are— 437 A;i - 41 = o, 649 A/* - 48 = o, 1048 V - 223 = o; from these it follows, according to the method of least squares, that J/4 = -I- 0°-22 X — o°-o037 = — o°-ooo82. This cor- rection is applied to ^ = o°-4267, and gives the following result. The errors still left behind correspond to errors of the normal places, which are far within their probable errors : — T = 1826-93, /I = o°-4256, e = 0-7515. « 305° 56', 325° I'- 356° 425', 13° 275', 39° 4', 54° 7. V 252=52', 280=10', 351=17', 34=47', 86=34', 107=12'. a 3-406, ^ = - 579°, r = + 5-S74- AN ORBIT WORKED BY ANALYTICAL METHODS. 1 27 These, the so-called phoronomical elements, thus fixed, it remains to settle the position of the ellipse. Professor Klin- kerfues uses three of the true anomalies and the corresponding observed position angles, applying at last a small correction to the node to represent better all the six normal places. He calculates the longitude of the node by eliminating X and 7 from three equations (which are obtained from a rectangular spherical triangle) of the form tan (9 — SJ) — cos y tan (v + X) ; \ and 7 are subsequently obtained from the equations, first 7, and then 7. The formulae are however complicated, and diflferential equations to correct assumed values of the three elements now in question may be preferred to the direct solu- tion of the above equations, whereby besides, by application of the method of least squares, more than three places may be used. The equations obtained from differentiation of the last equation are of the form — £^9 = K9, + cos y '^°^., , ~ ■ , A\ — J tan y sin 2 (6 — O) Ay. ' cos' (u + a) ' ^ ' ' It is, however, still better to calculate the dififerential co- efficients by variation of the elements in the equation. We assume values of 0,7, and \, which are as exact as possible, and calculate with those from the true anomalies v, given by the previous investigations, the respective angles of posi- tion 6. Altering then 7 with a suitable quantity, we again calculate the angles of position. The diflferences between the two values of these divided with the difference between the inclinations are the differential coefficients of the angles with respect to the inclination ^-. Similarly, the differential co- efficients of the angles with respect to \ : ^ are calculated, varying X a certain quantity. We have, of course, ^^ = i, and the equations of condition are as follows : — ^28 DOUBLE STARS. where 6, 6j, etc., are given by the normal places. 6', 6\, etc. are obtained with the assumed a, \, and 7. The equations in the present instance are as follows : — AS + 0-98 AX + 031 Ay — I°-l8 = o ,, + 0-86 „ + 015 ,, — o°-20 = o .. + I 05 ., - o'32 .. - 2°7S = o „ + i-i8 „ + 012 „ - 3°-3S = o ,, + 0-90 „ + 0-25 „ - o°-so = o „ + 0-85 „ + o-o8 „ — o°i8 = o On further consideration, I however preferred to take the mean of the third and fourth equation, and combining this with the two last equations to deduce the three corrections. It must be remembered that Herschel's two epochs are not thereby excluded, for they helped to determine a, yS, and 7, and in consequence the true anomalies used for calculating the position of the ellipse. Applying the resulting corrections to the assumed values of the three elements, we have the third system. Third Elements of o- Corona. T 1826-93. a 16° 27'. X 73° 51'- r 31° 56'. P 845^^ -86. a 5" -885. e 07515. The formulae for calculating an ephemeris from these elements are: — » - 43°'OS sin u = o°-425S (t - 1826-93). tan\v= V i_±_? tan\u= "•^——^ (an i u = 2-655 ^'^" i »• I — C 0'24-o3 tan {9c - l6°2/) = cos y tan {v + 73°Sl') = 0-8486 tan (y + 73°Sl') cos (« + X) , , cos (u + X) „ „„ , p = r 7—-^ ; = u (i — ^ cos a) ' ^ „; = s"-885 (i — 0-7515 •^ cos (8 — a) ' cos (9 — a) ^ ^ ^ '■> -^ ,c os(v + 73° 51') cos «) 72 ./:o„-/\. cos [O — 10 27 )• AN ORBIT WORKED BY ANALYTICAL METHODS. 12g The half axis major was determined from the measured dis- tances by dividing them by (i - ^ cos z() ^^^^~M- The six normal angles of position were represented as follows, — always observation minus calculation : — + 12', +2', -8', + S,+5', + 2'. Had a correction been applied to the node, the square sum of these errors could have been diminished, but as then the errors in the last places, which are the most certain, would have been increased, nothing would be gained. At any rate, the errors above are far below the errors of the normal places. The above elements were now compared with all the obser- vations which I had at my disposal. This comparison has been published in the Astronomische Nachrichten, vol. Ixxxviii., No. 2103. We have as yet seen but a small part of the ellipse described, but this part of the orbit has of course been so much the more observed, and so much the nearer are the measures lying to each other. Much more uncertainty must, however, always prevail about these slow-moving systems than about those of quicker revolution, apart from other considerations, at least because the angle changes so little in one observer's lifetime, that systematic corrections cannot so easily be expressed in laws. Engelmann has made extensive investigations on that part of the correction, which is constant for all the position angles measured by the same observer, in analogy with cor- rections to be applied to right ascensions and declinations in star catalogues. These corrections must, however, vary more or less with the time, as is the case with meridian observa- tions. Exactly determined orbits of many double stars are wanted for the satisfactory solution of these different ques- tions. Even before we may hope to lay the orbits down definitely, they will be of use in this respect. The last-mentioned comparison showed large systematical errors in the angles and distances of a Coronse. Madler's 9 130 DOUBLE STARS. angles are decidedly too large. His first angles, when the position was very oblique, are much too large ; his later angles, when the position went through 180°, are about right, and then the correction changes in sign. His distances are also too large, but the correction is likewise diminishing, and dis- appears at the end of the series. Duner's and Kaiser's distances, on the other hand, are too small, which is a much more remarkable feature. All these distances were excluded in the above determination of the axis major. When I had come so far in the calculation, I got for the first time the series of measures at my disposal which has been made by M. O. Struve with the large refractor in Pulkowa : the comparison of these measures with the last elements showed deviations similar to Madler's. This shows that the corrections O. Struve has applied to his observations, after measures made on artificial objects, do not render his measures faultless. It will be remembered that Madler's evidently faulty angles were introduced with as much weight in the derivation of the normal places as all the others. This is a cause of the small systematical deviations of the measures from the ephemeris calculated after the last elements. I therefore now excluded Madler's, O. Struve's, Galle's, Main's, and Talmage's angles, and Kaiser's first angles. The rest of the observations indi- cated that the normal place for 1835 should be diminished about a degree ; the place for 1855 diminished a few minutes. Such corrections were applied, and then, a , \ and 7 anew calculated from the six normal places. Supposing node = 16° 27' X — 73° 51', and 7 = 31° 56', and var>'ing X and 7 a degree respectively, the equations of condition are as follows : — A9, + 0-92, AX + 0-27, Ay — 0°'20 = „ +0-85 „ -1- 0-05 ,, - o'-os = „ 4- 112 „ - 0-27 „ + o°-i3 = >> + 113 ,, -|- 0-22 .1 + o°'92 = „ -1- 090 >. +0-IS „ -1- o°-o7 = „ -I-0-85 „ + o-oo „ — o°'04 = 0. AN ORBIT WORKED BY ANALYTICAL METHODS. I3I Allowing double weight to the two last equations, I obtained by the method of least squares the following normal equa- tions : — + 8-00 AS, + 7-52 A\ + 0-57 Ay + 0-88 - o + 752 „ + 7'i6 „ +051 „ + 1-02 = o + 0-57 „ +0-51 „ +0-25 „ +0-13-0. After elimination of A a from these equations, we obtain A\ = — 2°-25, and Ay = — o°-57. Substituting these values in the four last equations of con- dition, we obtain AS = + 2°' 14, by taking the mean of the resulting four values of this quantity. — The final comparison of the elements, with all the measures (except those excluded), showed that the representation of the angles could be still further improved by diminishing the longitude of the node by o°-24. These changes in the position of the ellipse were of no appreciable influence on the calculated distances, which came out about a hundredth of a second of arc larger in 1830: in 183s there was no difiference from those previously deduced. From 1840 to i860 they were a hundredth of a second smaller than by the last orbit ; afterwards there was no dil- ference. Definitive Elements OF a CORONiE BOREALIS. T i826'93. Node i8-2i. X 71 36. 7 31^22'. P 845^^-86. a 5" '885. e 07515 132 DOUBLE STARS. Comparison of the Last Elements of a CoroN/E, with Observations. Observer. No Epoch. »0 6= Bo-tc Po P' po-pe W. Herschel t 1781-79 347 '5 347-0 + 0-5 W Herschel .. 2 1802-74 11-6 11-3 + 0-3 W. Struve 3 1819-62 48-0 53*8 -5-8 Herschel & South 4 1821-30 653 60-5 + 4-8 I, ,/ ,t Herschel & South 5 1823-47 72-9 701 ;2-8 1-45 '3^ + o-il South 6 1825-44 77 '5 79-5 — 2-0 1-48 1-28 + 0-20 W. Struve 7 1827-02 89-3 87-5 + 1-8 i"3i 1-27 + 0-04 W. Struve 8 1828-20 96- 5 93'7 + 2-8 J. Herschel 9 1828-50 921 95-2 - 31 W. Struve JO 1830-11 104-9 103-5 + 1-4 1-22 1-27 — 0-05 J. Herschel XI 1830-28 105-1 104-4 + 0-7 1-22 1-27 - 0-05 Dawes 12 1830-52 107-3 105-6 + 1-7 Smyth 13 1830-76 107-6 106-9 + 0-7 1-30 128 + 0-02 Dawes 14 1831-34 111-5 109-9 + 1-6 1-57 1-29 + 0-28 J. Herschel 15 1831-36 108-8 iio'i - 1-3 1-38 1-29 + 009 Smyth i6 1832-37 114-9 1151 — 0-2 1-40 1-30 + o-io J. Herschel 17 1832-52 113-6 115-9 - 2-3 1-07 1-31 — 0-24 Dawes i8 183255 115-4 iie'o - 0-6 W. Struve 19 1832-99 118-8 118 -2 + 0-6 1-30 1-31 — o-oi j. Herschel Dawes 20 1833-26 1199 119-5 -f 0-4 1-33 1-32 + 0-01 21 1833-26 120-6 I20-0 + 0-6 1-30 1-32 — 0-02 Smyth 22 1833-58 120-7 I2I-0 - 0-3 1-20 1-34 - 0-14 Dawes 23 183455 125-6 125-5 + o-i Smyth 24 1835-50 130-9 129-7 + 1-2 1-40 1-39 + 0-01 W. Struve 25 1835-50 130-5 129-7 + 0-8 I -31 1-39 - 0-08 Madler . . 26 1836-47 138-5 133-7 + 4-8 W. Struve 27 1836-59 134-7 134-2 + 0-5 1-43 1-42 + 0-01 Dawes 28 1837-47 136-8 I37-S - 0-8 W. Struve 29 183755 140-0 1380 + 2-0 1-42 1-45 — 0-03 W, Struve 30 1838-45 1434 141-3 + 2-1 1-48 1-49 — 0-01 Galle 31 1839-52 1478 145-1 + 2-7 1-55 1-55 0-00 Dawes 32 1839-53 144'3 145-1 - 0-8 1-60 1-55 + 005 Smyth 33 1839-67 1451 145-6 - 0-5 1-60 1-56 + 004 Dawes 34 1840-57 I47'9 148-5 -0-6 1-66 i-6i + 0-05 0. Struve . . 35 1840-82 150-2 149-3 + 0-9 1-54 1-61 — 0-07 Dawes 36 1S41 -48 150-3 151-3 — i-o 1-66 1-66 0-00 Madler 37 1841-56 152-3 151-5 + 0-8 I -60 1-66 — 0-06 Kaiser 38 1841-66 148-8 151-8 - 3-0 1-57 1-67 — 0-10 Madler .. 39 1842-31 156-4 153-7 + 2-7 1-81 1-70 + O'll Dawes 40 1842-37 153'3 153-9 -0-6 Madler .. 41 1842-73 157-6 154-9 + 2-7 1-87 1-72 + 0-15 Smyth 42 1843 '35 155-9 156-6 - 0-7 i-8o 1-75 + 0-05 Dawes 43 184347 156-5 156-9 - 0-4 1-77 1-76 + 0-01 Madler .. 44 1843-51 157-3 157-0 + 0-3 1-89 1-77 + 0-12 Kaiser 45 1843-68 156-3 157 5 — I "2 1-66 1-77 — o-ii Madler . . 46 1844-40 160-6 159-4 + 1-2 205 i-8i + 0-24 Main 47 1644-45 157-1 159-5 - 24 Madler . . 48 1845-51 1630 162-0 + 10 2 03 1-87 + 0-16 facob 49 1846-21 162-0 163 7 - 1-7 2-25 1-91 + 0-34 "Hind 50 1846-32 162-8 163-9 — I"I Madler .. 51 1846-46 165-1 164-2 + 09 2-07 1-92 + 0-15 Smyth 52 1846-60 162*4 164-3 — 2'I 2 '00 1-93 + 0-07 0. Struve . . 53 1847-02 1687 165-3 + 3-4 1-74 1-95 — 0-21 Dawes 54 1847-44 1660 166-4 - 0-4 1-88 1-97 — 0-09 Madler . . 55 184744 166-6 166-4 + 0-2 2-16 1-97 + 0-19 Madler . . 56 1848-41 168-4 168-3 + o-i 2 40 203 + 0-37 Dawes 57 1848-53 168-6 168-6 0-0 1-99 2 04 — 0-05 Dawes 58 184945 170-1 170-4 - 0-3 2 09 209 0-00 0. Struve . . 59 1849-49 172-0 170-4 + 1-6 1-95 2-IO - 0-15 O. Struve.. 60 1850-52 168-9 172-3 - 3-4 1-99 2-16 - 0-17 Madler .. 61 1850-70 173-0 172-7 + 0-3 2-23 2-17 + o-o6 Fletcher . . 62 1851-22 174-4 1736 + 0-8 2-32 221 + O-II Madler . . fi3 1851-25 175-5 173-7 + 1-8 2 34 2-21 + 0-13 Dawes 64 1851-42 173-8 l74'o — 0-2 226 2-22 + 0-04 0. Struve . . 65 1851-63 173-4 174-3 - 09 2-o6 2-23 - 0-17 Madler .. 66 1851-76 176-2 174-5 + 1-7 2-44 2-24 + 0-20 Smyth 67 1852-25 176-8 175-4 + 1-4 2 20 2-25 - 0-05 Miller 68 1852-31 176-5 175-5 + 1-0 2-38 2 26 + 0-12 Madler .. 69 1852-60 177-5 175-9 + 1-6 2-39 2 28 + o-ii O. Struve . . 70 1852-63 173-3 1759 - 2-6 207 2 28 — 0-21 Jacob . . 71 1853-14 177-9 176-8 + i-i 218 2-30 — 0*12 Powell 72 1853-35 175-2 177-1 - 1-9 Madler . . 73 l853'38 177-7 177-2 -t-0-5 2;46 2-32 + 0-14 AN ORBIT "WORKED BY ANALYTICAL METHODS. 1 33 Comparison of the Last Elements, etc. — continued. Observer. No. Epoch. flo 8c e.-fl Po pc po-Pc O. Struve . . 75 i8s3'66 175-6 177-6 — 2-0 2-17 2 '34 - 0-17 Madler .. 76 1853-77 178-8 177-9 + 09 2-65 234 + 0-31 Jacob Dawes 77 1854-05 177-9 178-3 - 0-4 2-22 2-35 - 0-13 78 I8S4'56 178-5 1790 - 0-5 2-26 2-38 — 0-I2 O. Stnive . . 79 1854-66 1790 1791 — 0-1 2-24 2-38 - 0-I4 Morton . . 8a 1854-67 178-5 179-1 - 0-6 2-22 2-38 — 0-16 Madler . . 81 1854-70 179-4 179-2 + 0-2 2-51 238 + 0-13 Dembowski 82 1854-86 179-8 1794 + 0-4 2-37 2-40 — 0-03 Dawes 83 1855-48 180-1 180-3 — 0-2 = ■43 2-43 0-00 Winnecke . . 84 1855-54 181 -6 180-4 + 1-2 2-49 2-43 + 0-06 Secchi 85 >8S5'S9 180-1 1805 - 0-4 2-32 2-44 — 0-12 0. Struve . . 86 1855-61 179-1 180S - 1-4 2-29 2-44 - 0-15 Madler .. 87 1855-78 181-8 180-7 + l-i 2-64 2-45 + 0-19 Winnecke.. 88 1856-39 182-8 181-6 + 1-2 2-52 2-48 + 0-04 Dembowski 89 1856-42 181-8 181-6 + 0-2 2-69 2-48 + 0-21 Secchi 90 1856-43 182-4 181-6 + 0-8 2-46 2-48 — 0-02 0. Struve . . 91 1856-57 1799 181-8 - 1-9 2-46 2-49 — 0-03 Jacob 92 1856-73 181-3 182-0 - 0-7 = •53 2-50 + 0-03 Midler .. 93 1857-39 183-3 182-9 + 0-4 2-46 2-54 - 0-08 Secchi 94 1857-62 183-6 183-1 + 0-5 2-43 2-55 — 0-12 Jacob 95 1857-66 183-1 183-2 — 0-1 2-53 2-55 — 0-02 O. Strove.. 96 185801 181-9 183-6 - 1-7 2-51 ^■5! — 0-07 Jacob 97 1858-20 1840 183-9 + 0-1 257 =■5! — o-oi Dembowski 98 1858-29 183-2 184-0 -0-8 2-66 2-58 + 0-08 Madler . . 99 1858-54 183-6 184-3 - 0-7 2-64 2-59 + 0-05 Morton . . 100 1859-34 184-9 185-2 - 0-3 2-70 2-64 + 0-06 0. Struve . . loi 1859-94 i86-i 185-9 + 0-2 2-62 2-67 — 0-05 Dawes .. 102 1860-36 185-5 186-4 - 09 2-71 2-70 + 0-01 O. Struve . . 103 1861-58 1874 187-7 - 0-3 2-69 2-76 — 0-07 0. Struve . . 104 1862-76 1891 189-0 + 0-1 2-77 2-82 — 0-05 Dembowski 105 J86309 190-1 i89'3 + 0-8 2-76 2-84 — 0-08 0. Struve . . 106 1863-60 1882 189-9 - 1-7 2-77 2-86 — 0-09 Engelmann 107 1864-45 190-5 190-7 - 0-2 3-11 2-91 + 0-20 Dembowski loS 1864-95 191 -2 191-2 00 2-79 293 - 0-14 0. Struve.. log 1865-36 191-9 191-5 + 0-4 2-94 2-95 — O-OI Dawes no 1865-38 191-5 191 -6 — o-i 308 2-95 + 0-13 £n?elmann III 1865-39 192-7 191 -6 + I -I 2-96 295 + O-OI Talmage .. 112 1865-73 1891 191-9 - 2-8 Secchi "3 1865-81 192-5 192-0 + 0-5 2-98 2-98 O-QO Talmage .. T14 1866-43 i8g-2 192-6 - 3-4 3-73 3-02 + 0-71 O. Struve . . >i5 186663 1930 192-7 + 0-3 3-00 303 — 0-03 Kaiser 116 1866-68 193-9 192-8 + 11 2-86 3-03 - 0-17 Dembowski i"7 1866-92 193-2 193° + 0-2 2-89 304 - 015 Main 118 1867-37 192-1 193 '4 - 1-3 3-00 307 — 0-07 Dun& iig 1868-42 194-9 194-3 + 0-6 3-07 311 — 0-04 Brunnow . . 120 1868-55 194 1 194-4 - 0-3 3-11 3-12 — O-QI 0. Struve . . 121 1868-58 194-7 194-4 + 0-3 2-98 3-12 - 0-14 Dembowski 122 1868-8B 195-7 194-7 + 1-0 2-99 314 - 0-15 Talmage .. Dunc'r 123 124 1B68-93 1869-63 194-5 194-8 195-3 -0-3 - 0-3 3-61 3-00 3'i4 3'i7 -t- 0-47 -0-17 •f 0-15 GledhiU . . 125 1870-35 196-8 195-9 + 0-9 3 '35 3-20 Dembowski J 26 1870-95 197-1 196-4 + 0-7 3-09 323 — 0-14 Dun^r 127 1871-35 196-6 196-7 - o-i 3-IS 3-25 — O'lO + 0'02 + 0-25 + 0-04 GledhiU .. 128 1871-45 1965 196-8 - 03 3-28 3;26 Wilson .. 129 1871-51 194-3 196-8 - 2-5 3'5l 3^ Talmage . . 130 1871-86 197-3 197-1 J- 0-2 332 3 28 Copeland . . Wilson .. '31 1872-28 196-5 197-5 - 1-0 . , J 32 1872-53 1977 197-6 + 0-1 3-25 3 '31 — o'o5 — 0-21 0. Struve.. J33 1872-57 1953 197-7 - 2-4 3-26 3-31 Dembowski 134 1872-96 198 -1 197-9 + 0-2 312 3-33 Copeland . . 135 1873-40 196-7 198-3 - 1-6 — p-ei Wilson .. .36 1873-42 198-4 198-3 + O-I 3'i4 3-35 3-36 O. Struve . . '37 1873-56 I97'6 198-4 - 0-8 315 + 0-03 GledhiU .. 138 1873-68 198-9 198-5 + 0-4 3-40 3'37 Copeland .. 139 1874 '33 198-8 198-9 - 01 - 0-8 — 0-05 GledhUl .. 140 1874-41 198-2 199-0 3'35 3-40 O. Struve.. 141 1874-61 199-8 199-1 + 0-7 3'*J 3-41 - o|l4 Dembowski 142 1874-90 '9?'! I99'3 — o'l 328 3 42 Schiaparelli 143 1875-46 198-6 199-7 -0-9 3'34 3-44 — 0-16 Dun& 144 1875-54 199 '7 199-8 — O-I 3-29 3 '45 - 0-17 + 0-29 GledhUl .. 145 1875-56 200-0 199-8 + 0-2 3-28 3 45 NobUe 146 i875'6S 200-6 199-9 -t-o-7 374 3'45 Doberck .. 147 1876-29 I99'3 200-3 - I — 0-22 GledhiU .. X48 1876-48 200-0 200-4 + 0-2 3-28 3 'SO 134 DOUBLE STARS. CHAPTER IV. ON RELATIVE RECTILINEAR MOTION. When two stars happen to lie nearly in the same visual line, but one far behind the other, they are said to be opti- cally double, and not to form a binary system. In this case, if one or both are affected with any proper motion, they will appear to change their relative position both in angle and distance, and the list of changing measures will resemble that of a binary system. But since it may be assumed that their proper motions are approximately uniform and rec- tilinear, it will follow that their relative motion will also be uniform and rectilinear ; and hence that when a series of points is charted as before, they will lie approximately on a straight line. No difficulty will be found in the graphical construction for this straight line, and it is not necessary to give an example. The processes will be as follows. Correct all the observed angles for precession, and chart them as before, thus obtaining interpolated angles for every five or ten degrees. Chart all the distances, and obtain interpolated distances corresponding to the same angles. It will be convenient to convert these coordinates r, 6 into rectangular coordinates X, y by the usual formula x— r zos6,y := r sin 6, referring to the adopted meridian as one of the axes, and then to draw a straight line passing among the points. By observing the times at which the star occupied certain points on this line, it is easy to ascertain what position it would occupy at any ON RELATIVE RECTILINEAR MOTION. I35 intermediate or any later time, and to ascertain by the pro- tractor and compasses what its angle of position and distance would be at that time, and thus either to compare former observed positions with those which would have resulted from uniform movement in the straight line so found, or to con- struct an ephemeris for future years. But the analysis of this problem is not at all beyond the reach of non-mathematical amateurs, and we shall therefore give a specimen of the more exact analytical handling of this problem in the case of 61 Cygni.* In this case the problem is one of great interest. The two stars have very large proper motions nearly identical both in direction and in amount. That of one is given by W. Struve as 517" 4^10" psr century in the direction 51° 16' +^ i", and that of the other as 509" +_ 10" in the direction 53° 38' + 1°. The probability of a physical connection between these two stars is almost incalculably great. Struve has expressed it arithmetically, and illustrates it by saying that the physical connection between the components of 61 Cygni is more than a hundred thousand times more probable than that, after an experience of more than five thousand years, the sun will rise on the morrow. But if they were physically connected, the relative motion would not be rectilinear, but orbital, from their mutual attrac- tion ; and it becomes, therefore, a matter of some importance to examine accurately into their relative motion. What is certain is that hitherto the motion has deviated extremely little from a straight line. The observations are charted on millimetre paper (see Plate III.), and curves drawn among the dots as before ex- plained, and the interpolated angles and distances read off as in Table I. and converted into x and f. * See Monthly Notices, vol. xxxv. p. 323 (1875). This chapter was written in 1876. 136 DOUBLE STARS. Table II. t. e. 1820 827 1825 864 1830 89-9 1835 93-3 1840 965 1845 996 1850 I02-6 1855 J05-5 i860 io8-2 1865 1 1 08 1870 "3-3 1875 1157 ' COS B. 1515 ■35 •60 ■90 1623 •60 17-00 •43 ■89 i8'38 •91 19-49 1-9250 + 0-9638 + 0-0272 - 0-9157 - 1-8373 - 2-7683 - 37084 - 4-6579 - 5-5776 - 65268 - 7-4797 - 8-4520 •9612 •9366 •9429 •9216 •9310 -9401 ■9495 ■9197 -9492 •9529 -9723 15-027 15-320 15599 15-874 16-125 16-367 16-590 16-796 16-995 17-182 17-368 17-562 ^j •293 ■279 •27s •251 -242 •223 -206 •199 -187 ■186 ■194 In this case, however, it is plain from the columns of differences that these points do not lie on a straight line ; for then the differences of the two columns would vary- together. In fact, the differences in the column Ax are nearly- uniform, while those in Ay steadily decrease ; and thus indi- cate a curve slightly concave to the origin. A little consideration, however, will show that this orbit cannot be elliptical. Taking the early observations into account, the companion has described about 80°, and yet has scarcely deviated from a rectilinear path. It is almost certain that the relative path is of a hyperbolic nature. It is given approximately, so far as at present described, in Fig. 16. But if we wish to proceed with the problem in the case of any star, let us assume/ = r cos {6 — a) as the equation to the required line, J> and a being the elements to be determined. No values of a and p can be found which will exactly satisfy the twelve derived equations, and the equations must therefore be combined by the method of least squares, so as to give the most probable straight line. Let the equation be written 7SS0. (*j<■. 139 CHAPTER V. ON THE EFFECT OF PROPER MOTION AND RARALLAX ON THE OBSERVED POSITION ANGLES AND DIS- TANCE OF AN OPTICALLY DOUBLE STAR. If a pair of stars is only optically double, and one is moving relatively to the other, it is plain that there will be a change in position angle and distance due to this cause. If the near one is sufficiently near our system to have an appreciable parallax, it has long been seen that the circum- stances were favourable for the determination of the parallax. The proper motion of either of the stars will of course com- plicate the result, and we proceed to show how in the first place by a preliminary examination the measures may be studied in order to see whether they show any trace of such parallax ; and then how they may be submitted to rigorous calculation for the purpose of ascertaining its amount. It is well known that the annual motion of the earth would cause the nearer star to revolve, apparently, a_^^ in an ellipse round its position as seen from t( j,. the sun, the form of the ellipse being that * which the earth's orbit would assume if seen from the star ; that the ratio of the axes would S be the sine of the latitude of the star, and that the major axis would be the annual parallax. Further, the proper motion of either or both stars would cause one to move relatively to the other in a straight line. If both causes are in operation, the motions of the stars will be combined. Accidental errors being as far as possible got rid of by the graphical methods already described and illustrated, and the I40 DOUBLE STARS. position angles and distances for intervals of, say, twenty- days, having been obtained from the interpolating curve •S (supposed to embody the observations of some years, and taken at all times of the year), the charted positions will •S lie approximately in a straight line; and if the deviations from it show no law, then it is not worth while proceeding further. But if it is found that the points lie alternately on one side and on the other of that straight line, and that the total period is one year, then we have clear indications of a measurable parallax. The graphical proceeding will be as follows : by com- paring the positions at intervals of as large an integral number of years as may be, and using all the measures available, first determine what the proper motion is. Then chart over again the positions that would have been occu- pied by the star if proper motion had not affected it : the resulting points ought to lie in an ellipse whose axis major is in a position six hours distant from the longitude of the star, and the ratio of whose axes is the sine of the latitude of the star. The major axis itself is the parallax sought. The preceding diagrams may help to make this clear: No. I exhibits the effect of annual parallax only ; No. 2 of proper motion only ; and No. 3 the effect of both com- EFFECT OF PROPER MOTION AND PARALLAX. I4I bined. When this has been done graphically, it may be thought worth while to proceed further with the rigorous calculation as follows : Let S be the principal star, o- the companion, at distance D", and let S' be the position of the principal star after the lapse of a year, in consequence of its proper motion, MS' = dS in declination, and S M = d a cos B in R. A, expressed in seconds of arc, S being the declination. Then the change in position angle is — S ff S'. Fig. 17. Let the position angle N S o- be ^, and let E S S' = ^. Here tan . (< 180°), , „ „, 180 X SS'sin S'S cos (9 + ^) j^ (Je^rees :. dQ = — mda. (i) and dTi, the change in distance, = — S N, .-.dT) = -SS'sin {d + ). (2) These equations completely determine the change in angle and distance due to proper motion. There will also be a change of position due to parallax, or rather to the difference of parallaxes of the two stars, and the investigation of this is of some importance, as it may lead to the determination of the parallaxes of some stars. It will be remembered that it was with this view that the examination of double stars was first entered upon by Sir William Herschel. If S be the sun, S a star, E the earth moving in the ecliptic, then the apparent path of the star on the background of the heavens will be a small ellipse, whose major axis is parallel to the ecliptic, and whose minor axis is perpendicular to it, and parallel to the circle of latitude. 142 DOUBLE STARS. Now let C be the place of the star as viewed from the sun, P Q R T the ellipse described in conse- quenceof parallax, L L the circle of latitude, Q the position of the star when the longi- tudes of the earth and the star are the same, T where they differ by 1 80°, a the smaller Fig. 18. star supposed to have no parallax, C the position of the star when the time is t, and the longitude of the earth is L ; then C o- C is the change in the angle of position due to parallax. Then we have, R being the radius factor of the earth at the time t, X the constant of parallax for the star at the earth's mean distance taken as unity, \ the latitude, CR = R.;ir, CT = R.arsinX; therefore if Z' is the apparent position in degrees at the time t, Z the mean position, as viewed from C, D the distance of C o- in seconds, X the angle a C C, ^— — p ^'" , C C being expressed in seconds of 57-3 p. X. sin X arc, or z, = A - ^-^-^-^ (3) where p is the elliptic radius at the time t ; and p and X are calculated as follows : — If L, / are the longitudes of the earth and the star at the time /, I the angle L C C, A the angle L C N, Then from the figure it is plain that T Cm E M sin X , ,-r a • a COS I = cr^ = S;„ = cot (L - /) sm A ; (4) and then p = R sin (L — /) cosec I, (5) and X = Z + I - A = Z' + I — A, very nearly, (6) or 360 - (Z' + I + A), Z' = Z - or Z' = Z - EFFECT OF PROPER MOTION AND PARALLAX. 1 43 and A is computed from the triangle E P C, E being the pole of the ecliptic, P the pole, C the star, by the formula cos E P — cos E C cos P C cos A = sin E C sin P C cos (1) — sin X sin S cos \ cos d (7) , A A/sin S sin (S — (o) ,„, or by cos — = ^ r-^ — j— ^ 8 ■' 2 cos \ cos fl FiG_ ig. where S = HE C + C P+EP). We compute therefore A by formula (8) or (7), which give no ambiguity, since A is < 180° ; I by (4), I being in the same quadrant as L, — i; p by (5), and X by (6) ; and substituting in (3) we get an equation of 'the form Z' = Z + nx. If a series of such observations is taken, they can be com- bined so as to give values of Z and x. But in practice the proper motion will be involved with the parallactic motion, and the constants may be determined together as follows : — Let Z' = Z + nx — m (i — T) da {g) where i is the time, T a fixed epoch, m the constant determined above by (i), X the unknown constant of parallax, Z the position angle at the time T, Z' the position angle at the time t. It will be convenient to subtract from Z' the integral number of degrees z in it, and the same from Z, and put Z - z = ^, and if the weight of an observation or group of observations be w, we obtain a series of equations of the type w^ + wnx — wi'.da ■=■ w a, which must be solved by the method of least squares for J, X, and d a. This was done by Jacob for the star a Herculis, and he arrived at a parallax o"-o6, the proper motion being so small as to be neglected. 144 DOUBLE STARS. CHAPTER VI. ON THE ERRORS OF OBSERVATION AND THE COMBINATION OF OBSERVATIONS. For the general treatment of this subject we must refer the reader to Airy's Theory of Errors of Observation ; but an example or two may be given here of the application of the theory to the Observations of Double Stars. Suppose the following series of measures of position was taken by one observer on one night: 2ii"8, 2i3'2, 209'9, 2I2-0, 212-5, 211-9, 210-8, 212-1. We require to know what is the most probable result of these measures, and within what limits it may be relied upon. The most probable result is shown to be the arithmetical mean, which is easily found to be in this case 21 1-7 7. Make a list of the separate errors of each of the observa- tions from this mean, distinguishing between those in which the observation is in excess of the mean, from those in which it is less than the mean. In this case the errors are + "03, + 1-43, - 1-87, + -23, + -73, + -13, - -97, + -33. Take the mean of the + errors -48, and the mean of the — errors, r42 ; and, finally, take the mean of these -95. This is a numerical quantity, without sign, and is a measure of the goodness of the measures. It is called the " mean error," and furnishes a ready means of comparing the value of the observations taken on one night, or with one instrument, from those taken on another night, or with a different instrument. It further gives a means of comparing the measures of one observer with those of another. Thus if another observer, on the same evening, with the same telescope, took the following ERRORS AND COMBINATION OF OBSERVATIONS. 1 45 six readings, 2x2-3, 2127, 211-5, 2ir2, 211-9, 212-1, it will be found that the mean of the errors is -42, and the most probable result is 2x1-95. This, however, does not show ^& probable error. This expression must not be taken to mean the error which is more probable than any other error, but the limit within which, on either side of the arithmetical mean, it is probable that the truth lies. This is got by the formula, (Airy, § 60) probable error of the arithmetical mean = 0-6745 / ^"°" °^ "'"T °^ 'f '^''°' '"°'^ , « being the number of the observations. To take the first set of readings, the apparent errors of which were given above, the sum of their squares is 7-1952 ; and n is 8, whence the probable error of the mean = -24. In the second case the probable error will be found to be -15. The next question is how to combine the observations made by these two observers so as to get the most probable result. Let , — , . , — 7 rs be called the "theoretical weight," (probable error of mean)'' ° ' or W. Then in the first case w^ = -nr^'' ~ ^7' ^^^ '" *^^ second case Wi = TT^j = 44 ; and the most probable result is shown to be 17 X 211-77 + 44 X 211 -95 _ 2irQO and the theoretical weight of the result is 17 + 44 = 61, and probable error of result = y^ = -13. Generally, if a, b, c, . . . are successive results, whose theo- retical weights are Wi, w^, W3 . . . the most probable result is y, a + w,6 + w,c..^ ^j^j^ theoretical weight Wi + w^ + w^ + . . ., and probable error y ^ .), ^/+ ^^^ + . . ; It must be observed that this method assumes that the observations are really independent of one another and very numerous; and these conditions are not easily observed in double-star measures. No one who has long observed double 10 146 DOUBLE STARS. stars will have failed to notice that the readings taken on a single night tend to confirm one another, and yet may differ appreciably from those taken on another night. They may be taken with all honesty of purpose, yet the later readings are not strictly independent, but tend to confirm the early readings. Hence it is much more valuable work to take a moderate number of readings on several nights than to take very many readings on a single night. And it is not worth while to apply these methods of calculating the most probable result and the probable error to the observations of one night, but to the separate results of many nights, with the view of determining as accurately as may be one place for the year, and the weight to be attached to it. The most useful form in which observations could be published would be to give the number of nights of obser- vation, the resulting position, and the theoretical weight, the last number being thus not an arbitrary number assigned by guess,* but one which arises directly from the observations, and is referred to the same unit by all observers ; a weight I assigned to an observation of position meaning a probable error of i", and generally a weight w indicating a probable error of -7^ degrees. So in determinations of distance the same elements should be given, and a theoretical weight w would indicate a probable error of —7^ seconds. v w It may be observed that the theoretical weight of a re- sult varies inversely as the square of the probable error of that result : now it is also true t that the probable error of the arithmetical mean of a number of equally good obser- vations varies inversely as the square root of the number of observations. Hence the theoretical weight of a number of independent equally good observations varies directly, in the * See p. 64. t Airy, 55. ERRORS AND COMBINATION OF OBSERVATIONS. I47 case of any particular observer, as the number of observa- tions. This confirms what was said above of the importance of observing the same star on many nights. Hence, finally, it is possible to determine exactly the weight to be assigned to a given series of measures of a star by an observer A. It will consist of the product of two numbers, one of which is the number of nights of observation of that star, and the other is his " theoretical weight," or the mean of as large a number as may be of the theoretical weights obtained, as above explained, from his observations on stars of similar magnitudes and distances. It is necessary to say similar magnitudes and distances, as the probable errors of an observer in measuring such stars as 7^ Andromedae, S Cygni, and Castor will be very different, and therefore the theoretical weights of such observations will be very diff"erent. PART III. THE CATALOGUE AND MEASURES. THE CATALOGUE. INTRODUCTION. This Catalogue gives the places, etc., of the selected list of stars. Great care has been taken in the selection ; and, for the most part, the stars will be found to be those which are either binary, probably binary, those in which certain change has taken place, or those deserving of at least occasional careful measure- ment on other grounds. The R. A., Dec, and Magnitudes, are approximate. Column 6 gives Struve's and Otto Struve's numbers, the latter being placed in brackets. Column 7 gives the number in Herschel's great Catalogue {Mem. R. A . S., vol. xl.) Column 8 gives, roughly, the apparent arc described by the star since its discovery. Column 9 the probable character of the object. In this column the following initial letters are used : B (binary) ; PB (probable binary) ; PM (proper motion) ; RM (rectilinear motion) ; CC (certain change) ; PC (probable change). The stars are taken chiefly from the great works of 5., 0.5*., Hj, and Hj. It was our original intention to include a large number of Mr. Burnham's discoveries ; owing, however, to the difficulty in selection, the extreme faintness of many of these objects, and the consideration that, as a rule, well-known stars only are suitable for the amateur, we have omitted them. For the convenience, however, of those observers who, having sufficient skill, patience, and instrumental power, may desire to assist Mr. Burnham in obtaining thoroughly reliable measures of his recently discovered pairs, we have appended to our Catalogue a selection from his published lists. In conclusion, we have to acknowledge much kind help in the form of suggestions, measures, and lists of stars in certain or probable motion; and our best thanks are offered to Mr. Burnham, Dr. Doberck, M. Flammarion, and Mr. Ormond Stone. 152 DOUBLE STARS. Ref. No. Name of Star. I 2 3 4 5 6 7 8 9 lo II 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 45 a Andromedae Cephei 316 B h. 1007 Cephei 318 B Andr. 6g B H. V. 85 42 Piscium Cass. 49 B 49 Piscium XCass. 51 Piscium h. 1041 P. O. 181 7; Cass. \ Toucanse 66 Piscium Andr. 36 B So. 390 P. O. 251 ^' Piscium Ceti 160 B

4,8 [179] 21 7 CC 279 Pollux 37-2 28 19 I, II, 12, 10 29 7 P.M 280 42 65 13 7, II 1 136 40 4 CC 281 41-6 13 43 8, 10 42 54 19 RM 282 46 3 42 7. 7 [182] 3404 7 PC 283 48-5 —2 28 8, 8 "57 20 10 PB 284 51 I 27 7, 7 [185] 41 B 28s 56 26 37 7,8 [186] 82 2 CC 286 56-1 4 30 8,9 1175 88 13 PB 287 56-5 33 24 7, 7 [187J 85 21 B 288 58-1 12 25 8,8 1179 3S°i RM 289 II Cancri 8 i-S 27 5° 7, 10 86 28 PB 290 Lyncis 85 B 2 32 36 7,8 87 33 18 PB 291 f Cancri 5-3 18 I 5,6,5 96 57 B 292 y Argus 5-8 -46 58 2, 5,8 74 6 CC 293 P. VIII. 13 7 II '3 8, 10 : 1202 72 10 PB 294 15-2 — I 13 7,8 ■ 16 3646 42 B 295 " [420] 25 4 PC 701 5' 44 42 7,9 [422] 31 3 PC 702 e Equulei 53-1 3 50 6,6,7 2737 39 10 B 703 54 "5 6 7.9 [424] 44 PB 704 P. XX. 429 54-6 50 6,7 2741 50 10 B 70s P. XX. 440 56 48 13 7. 10. " [425] 61 PC 706 57 I 4 6.7 2744 60 20 PB 707 57 38 47 8.9 46 68 10 B 708 587 3 8,9 49 76 V' B 709 710 61 Cygni 211-4 19 3i 33 7 39 5.6 7,8 1^ 60 8902 81 B PM 7" P. XXI. I 4 29 43 6,8 62 17 2 CC 712 713 714 S Equulei 8-6 93 9 28 28 35 4, 5.„io 8, 8 77 79 1^ 65 54 4 B CC 9 '5 — I 44 8,11 7f 63 2 CC? 71S P. XXI. 50 97 40 39 7, 7 [432] 76 8 B 716 T Cygni lo-o 37 32 6, 8 24 B B 717 A. C. 19 11-4 63 57 7. 7 8998 12 7.8 719 IS'4 2 23 7.8 [435] 9016 7 PC 15-9 31 56 6, 7 [437] 21 13 PB PC 720 20 '9 13 10 7. 8 2797 59 3 721 22-1 79 50 7,8 2801 87 10 B B PC B B 722 723 Pegasi 20 B 23 27 10 33 34 >7 7. 7 8,8 99 02 72 9104 20 2 724 72s Pegasi 29 B iu Cygni 27-1 38-9 20 28 II 12 7.8 4, 5 04 2822 07 9210 15 726 729 730 K Pegasi Cephei 147 B 39-2 40-9 42-9 43-5 48 25 82 2 55 6 18 23 50 14 4. " 8,8 8.9 8,9.9 6,7 24 25 i 40 '3 26 73 40 94 7 II 19 3 3 CC B B PB PC 731 732 733 5" 52-1 21 52-6 51 19 59 59 40 14 8,8 8, II 7.9 [456] 2849 [458] 9328 33 42 5 10 PB PB PB 1 68 DOUBLE STARS. Rcf. No. Name of Star. R. A. 1880. Dec. 1880. Mag. 2's No. No. Arc. Char- acter. 734 h. m. 59-4 to 16 8,9 2860 9391 4 CC 73S i Cephei 2203 64 2 5> 7 63 94°3 6 B 736 l-i 69 38 8,9 65 16 8 RM 737 4 13 9 7, II [463] 29 6 PC 738 P. XXII. II, 12 4-5 58 42 8,8,8 2872 42 10 B 739 7 49 37 7, II [465] 61 PC 740 Pegasi 148 B 8-5 7 23 6, 8 2878 66 5 PC 741 P. XXII. 33 8-5 16 36 6, 10 77 69 40 RM 742 151 24 21 8. 10 95 9516 22 PB 743 15 34 3» 7. 9 [469] 18 2 CC 744 33 Pegasi 17-9 20 14 6,9,8 2900 39 3 B 745 f Aquarii 22-6 —0 38 4, 4 09 80 45 B 746 22-5 22 55 8,9 10 81 3 PC 747 37 Pegasi 23-9 3 49 6.7 12 93 4 B 748 26-5 6 48 8,9 2915 9614 10 CC 749 27-4 20 33 9, 10 19 20 6 CC 750 29-5 69 17 7,7 24 46 10 B 751 33-1 -13 14 8, 8 28 70 8 CC 752 36-1 20 48 8,9 34 9703 20 B 753 38 45 22 7. II [477J 20 26 RM 754 40' I 18 37 7, 10 2941 31 3 CC 755 41 38 51 7> 9 42 36 3 CC 756 t' Aquarii 41-3 -14 41 6,9 43 40 5 CC 757 P. XXII. 219 41-6 -4 5" 7,7,8 44 41 10 B 758 42 77 53 7, 9 [481] 57 2 PC 759 44 '9 67 56 7, 7 2947 71 17 B 760 48 82 31 5, 10 [482] 9815 PC 761 H, N. IS 50-9 -3 53 6, 10 2959 18 5 CC 762 52-5 8 43 7, 7 [536] 32 180 B 763 2. 2966 rej. 52 72 12 7, 8, II [484] 43 28 B 764 52 Pegasi „ 53-2 II 5 6,8 [483] 40 18 B 765 23 16 5 57 8, 10, 9 2976 9901 9 CC 766 T Cephei 4-1 74 44 5, 7 [489] 29 S3 B 767 5„ 56 47 7, 9 [490] 33 7 PB 768 94 Aquarii 12-8 -14 7 5, 7 2998 82 6 B 769 Cephei 137 67 27 5,8 3001 93 22 B 770 ■5'4 34 47 8, 9 06 lOOO,] 10 PB 771 17 19 54 6.9 07 15 PC 772 P. XXIII. 69 17-5 -9 7 7, 8 08 20 18 RM 773 '9 56 52 7, 7 [495] 26 PC 774 P. XXIII. 100,101 24 57 53 5,7.9.10 496] 69 CC 775 31-8 43 46 6,7 500] 117 22 B 776 H, n. 24 : So. 356 39-8 -19 21 6,7 16 CC 777 40 59 48 7,8,9 3037 170 PC 778 40-4 61 59 9, 9 38 4 CC 779 1 2341 37 45 7, 10 1 39 175 3 CC THE CATALOGUE. 169 Eef. No. Name of Star. R. A. 18S0. Dec. 188a. Mag. No. No. Arc. Char- acter. h. m. / 780 23 43 64 13 7,7,8 [507J IO185 i6 B 781 h. 1911 45 41 25 7,8,9 [510] 200 13 B 782 50-2 — 10 10 8,8 3046 235 ID B 783 Andromedae 37 B 53-4 33 4 6, 6 50 258 20 PB 784 B. A. C. 8350 55-9 26 27 6,9 28 PM 78s L. 47206 58-5 33 36 7, 7,9 56 291 7 B 786 59 '9 57 46 7,8 62 304 340 B SUPPLEMENTARY LISTS. A. Ref. No. Name of Star. R. A. 1880. Dec. 1B80. Mag. S's No. Hj's No. Arc. Char- acter. h. m. 787 025-5 -2 43 9,9 35 167 I CC 789 790 37 "3 16 42 8, 9i 51 f^S 4 PB 1 37 '4 39 21 8, 10 149 618 10 PB 42*6 -2 2 8i, 8i 171 666 2 CC 791 792 55 "2 80 56 7,9 [37] 734 9 PB 2 14-8 23 5 8i, 10 254 883 10 CC 793 794 48-2 33 59 8, 10 325 1078 27 CC 3 45 36 46 8,8 360 "55 7 PB 795 10-3 46 35 8, 10 371 92 7 CC 796 44 "2 -38 i-s 1408 3 RM 799 800 4 I 39 51 8, 10 3114 94 II PB 8-5 29 42 7, 9 [78] 1540 6 PB 141 i6-2 55 22 -4 58 7,8 8,9 536 92 97 4 II PB PB 801 34'5 22 30 9, I' 579 1720 5 CC 802 40'2 -12 10 8, 10 596 J"' 7 c c 803 804 5i'5 5 20-8 13 46 69 34 8,9 7, 9i 620 704 1845 2066 7 2 PB CC B 80s Bu. 320 23-1 -20 51 3, II 23 806 36-5 388 -0 1 8,8 782 2249 I RM 809 810 21 16 8,8 r^^^ 64 20 PB 477 52-8 6 8-6 36 55 -I 20 30 10 7, 8 8,9 9, 10 [122] 826 879 ''11 13 4 B PB CC 811 i8-3 22 31 7, 9 [139] 2600 10 PB 812 813 814 81S P. VI. 105 20 '6 44-8 49-6 32 28 22 39 ' 25 7 8,9 6,8 7 10 8,9 910 [152] 974 991 27 2734 2832 84 I 8 6 P B PB CC PB 816 817 7 75 7-8 15 59 14 46 7, 10 9, 12 1047 46 3033 36 3 3 CC CC lyo DOUBLE STARS. Ref. No. Name of Star. R. A. 1800. Dec. 1800. Mag. 2's No. No. Arc. Char- acter. 8i8 h. m. 7 121 73 19 eh^ 105 1 3043 10 PB 819 53-8 23 55 6, loi II7I 3464 8 PB 820 8 IIS 6 50 9. "4 I213 3625 3 CC 821 21-6 17 IS 8, 10 30 3704 2 CC 822 23-8 55 46 7,8 34 18 2 CC 824 277 2 10 8, 10 43 59 4 PB 44"S 21 20 9. 9i 8S 3899 2 CC 82s 9 137 5 31 9,9 1343 4109 2 CC 826 S6-8 56 4 ^'l 1402 4370 2 CC 827 10 432 -3 23 7,8 76 4693 8 PB 828 So. 621 113-9 66 40 74, 7i 13 RM 829 263 25 84, 9i 1 549 4953 CC 830 57-3 42 3 9, i°4 94 5148 4 CC 831 12 9-9 6 18 9, 10 1621 5237 16 PB 832 7 Crucis 24-5 -56 27 2, 5 5317 2 CC 833 834 P. XII. 196 45-1 1323-1 -9 76 41 36 7, 9 8,8 82 [267] 5416 5624 2 RM PB 835 h. 4649 14 06 -59 9 84, 8i 5845 5 PC 836 H,N. IIS 2-6 21 46 oh^ 1804 65 8 PB 837 31 37 19 8, 8, II [276] 68 8 PB 838 H,V. 9 11-9 51 55 5,74 3P1 5932 B? 839 22 — I 41 5,94 1846 93 4 PB 840 So. 184 39-1 -24 56 54,9 CC 841 P. XIV. 212 50-5 -20 52 Si, 64 6172 20 B 842 tr Lupi 56-9 -46 35 5,5 6210 6 PB 843 15 oi" 34 56 I' 9 1908 35 6 PB 844 36-2 -14 48 8, 10 3095 6468 12 CC 84s ir' UrsEe min. 36-5 80 SI 6, 7 1972 90 4 CC 846 Sii 12 5° 74,8 88 6544 PB 847 58 59 15 ^o*'o^ 2006 96 6 PB 848 16 6-6 14 52 8,8 17 6627 3 PC 849 19-3 I 31 7, 10 41 97 3 CC 850 2S-S -6 47 8,8 3105 6729 6 CC 851 34"4 38 34 8, 12 2080 92 I CC 852 38-4 25 22 8, II 89 68ii 6 PB 8S3 41 i 2 17 6,9 96 22 3 PC 854 1717-8 -0 43 8,9 2156 7005 4 PB 8SS P. XVII. 94 19-1 IS 43 5, 10 bo 14 5 CC 856 I9S 42 16 9,9 63 19 6 PC 8S7 A. C. 9 499 29 50 8,9 7203 6 PC 858 h. 5014 59 -43 24 6, 6 57 66 B 859 18 2-2 19 38 7,8 [524] 18 B 860 4 3 31 7, 10 2286 731 5 7 PB 861 ■q Serpentis 15-1 -2 55 3, 12 81 32 RM 862 iS-6 22 45 7, 10 2310 87 4 CC 863 A C. II 18-7 - I 39 J'7 96 6 PB? 864 Bu. 134 22 46 49 8, 10 7 PB THE CATALOGUE. 171 Ref. No. Name of Star. R.A. 1880. Dec. 18S0. Mag. 2's No. No. Arc. Char- acter. 86s 7 Cor. Aust. h. m. 18 58-3 -37 14 5i. 5i 7714 144 B 866 l7LyrK 19 2-9 32 18 6, 10 2461 62 10 PB 867 IO-2 19 49 ^, 10 88 7835 10 PB 868 Il-I 27 14 7. 7 [371] 51 5 PB 869 h. 5113 17-5 -29 32 6,9 7900 48 CC 870 h. 5114 i8-i -54 34 6, II, 7 7897 129? cc 871 29-3 17 51 7.9 [375] 8019 24 PB 872 31-8 61 47 8,9 2553 806s 13 PB 873 35-8 63 33 8, 10 64 8105 9 cc 874 Da. 10 42-8 23 57 8,9 69 6 PB 87S f Sagitta 43 '6 18 51 6,9 85 75 8? B 876 h. 2904 47-1 -24 14 6, 10 94 32 RM 877 A. C. 16 52-9 26 56 7.8 8257 7 PB 878 53-9 41 56 7.9.9 [392] 74. 20 B 879 SS'S 6 36 8,9 2612 82 cc 880 59 35 41 7.8 24 8325 3 PB 881 59-5 30 12 8,8 2626 28 10 PB 882 2012-8 10 37 8, u 62 8472 3 PB 883 Cygni 172 B 13-9 40 21 6J,9 66 B^l 7 PB 884 15-9 44 59 7.8 [406] 8516 24 B 88s Cygni 176 B 15-9 39 I 7. 9 2668 12 5 PB 886 171 12 57 8,9 73 19 6 PB 887 17-2 12 57 9. 'o 74 20 cc 888 Delphini 43 B 39-2 II 53 6, 8 2723 8742 7 PB 889 P. XX. 324 43T 25 57 8, 10 28 75 CC 890 Bu. 269 58-6 7 19 8, II 18 CC 891 Cephei 83 B 58-8 5f 12 6.7 51 8884 4 PB 892 Bu. 368 21 1 -8 43 7'! 6 PB 893 2 '4 4 40 7.8 [527] 207 B 894 Hi I. 47 57 -15 31 8,8 8932 33 PB 8^5 «Indi II-3 -S3 57 5.9 74 14 CC 896 337 20 10 8,8J [445] 9158 6 PB 897 898 899 900 B. A. C. 7578 %' -47 51 31 6, 10 7, 10 2833 9217 60 6 4 CC cc 47 '9 63 28 8,11 42 ^o II PB 50-1 45 13 8, 10 46 9308 7 CC 901 902 903 904 905 P. XXII. 93, 94 SI -9 22 9'i 20 -4 28 -17 4 57 21 8,8 7.8 6J, 6i 47 81 25 9474 9560 12 8 PB PB CC 37 '9 46 30 7. 7 [476] Ki 7 B PB Cephei 241 B 46-7 61 4 6,7 2950 88 7 906 909 910 231-5 7-2 417 Si-8 59-5 60 >9 16 56 17 47 20 25 43 25 7. II 8*. 10 7.8.8 9. 9. 12 8i.8{ 77 89 3041 47 60 9905 44 10180 247 297 II 6 I 5 PB PB PB PB PB 172 DOUBLE STARS. MR. S. W. BURNHAM'S STARS. Ref. No. Bu.'s No. R. A. 1880. Dec 1880. Mag. P. D. Date. Remarks. h. m. / 1800 + 911 394 24 -2 46 52 8,8 3TO I 76 912 233 491 -18 6 8,9 90 1-2 74 913 302 51-9 20 45 7. 8 94 07 74 914 396 56-2 60 26 6, 11 85 I 76 Extremely difiScult. 915 397 1 0-9 46 12 8, 16J 160 10 76 916 303 3-1 23 9 7i. 8 286 06 74 917 398 4-9 47 JO 8,8 60 2 76 918 83 2 39-9 -5 28 7i, 10 123 I '3 72 919 400 3 51 —4 16 7. iJ* 45 15 76 920 308 32-1 -8 3 8i,9J 320 I '2 74 921 401 44-2 -I 52 7, II 260 4 76 922 87 415-3 20 32 5h, 9i 171 2-1 73 Very beautitul. 923 402 17 -I 33 8i, 104 75 5 76 924 403 19-3 —2 20 7.H 1003 2-0 76 Be.'s measures. 925 184 22-5 —21 46 7,8 270 I '2 73 926 186 40-2 -7 12 8, 10 180 17 73 927 312 42-6 — 21 1 »,9i 330 2 75 928 316 468 -5 29 8, 8 180 1-2 75 929 404 49-8 8 58 9. 9j II3"4 15 76 De.'s measures. 930 319 5 21-2 -20 49 7i> loj 225 4 74 931 405 42-3 -13 34 H, II 150 10 76 932 406 43 — 13 28 9, 12 260 8 76 933 16 557 -10 36 54. 10 356 1-8 71 Kn.'s measures. 934 323 6 '87 -1 41 8,9 90 17 75 935 97 i8-5 -I 21 7i, 9 257 II 73 Exquisite. 936 194 28-1 38 6 8, 8i 283 I 74 937 326 49-9 2 28 8, 8J 60 1-2 75 938 329 7 41 -16 2 6, ic^ 95 15 75 939 J97 7 -6 57 8, 10 150 2 74 940 330 13-5 —0 41 8i,9 220 12 75 941 199 19-9 —20 56 7, 9 19 1-2 74 942 198 206 -20 43 8, II 212 3-5 74 943 333 57-4 —22 I 74,9 40 2 75 AB. 84 60 30 75 AC. 944 203 ""6 -27 14 7, 10 246 5 74 945 206 8 30-3 -24 42 8,9 278 1-5 74 946 207 337 -19 19 64, II 99 5 74 A splendid pair. 947 407 45-8 —6 20 8, 10 160 5 76 948 408 48-9 63 54 7, 10 350 2 76 949 409 54-9 -8 43 8, 10 180 10 76 950 410 9 4-5 -25 19 7,9 160 1-5 76 95J 212 10-2 -7 51 7,9 218 15 74 952 214 ,„ 35-9 -17 56 74, 11 264 2-5 74 953 217 10 12 -24 8 74, 74 273 I -5 74 954 218 1-6 -19 7 8,8 109 I 74 955 219 15-9 -21 56 7,9 193 2 74 THE CATALOGUE, 173 Ref. No. Bu.'s No. R. A. 188a. Dec. 1880. Mag. P. D. Date. Remarks. h. m. 1800 + 956 411 10 3° 4 -2°6 3 7.9 310 i"-3 76 957 220 11 6-5 -17 51 6, 6 148 o'S 74 958 412 12 2-2 -17 55 8,9-5 160 15 76 959 343 13 45' -3' I 6,84 120 1-2 75 960 348 14 55-6 20 6, 6 130 0-5 75 Very fine. 961 350 15 8-s -27 9 64,8 170 I '3 75 Very fine. 962 227 121 -23 50 7, loi 184 17 74 [difficult. 963 32 14-4 I II 54. 13 3° 3 72 Splendid, but very 964 36 45-8 -24 56 5i. 10 270 3 ^^ Very beautiful. 96s 417 17 522 39 27 8, 9i 270 15 76 966 418 18 1-5 64 26 84, 114 240 10 76 967 419 257 -7 55 8, 9i 40 15 76 968 56 19 58-2 -4 41 74, 10 180 2 71 Fine pair. [cult. 969 57 59 '4 IS 8 7, 15 140 2 72 Fine, but very diffi- 970 63 20 241 10 28 6, II 340 07 72 Very difficult in- [deed. 971 65 41-4 5 32 6, 10 195 I'2 71 972 66 42-5 26 58 8,8 160 2 72 [cult. 973 67 45 '2 30 26 7. "4 290 1-2 71 Beautiful, but diffi- 974 68 55 3 49 43 84,9 170 15 72 975 69 56-7 21 7 8,9 350 2 72 976 472 57'2 61 23 8i, 84 6 06 77 977 70 58-4 II 31 8 235 70 71 A and B C. 10, 10 no 2-0 71 B and C. 978 473 21 1-4 — 10 42 9, 10 115 17 77 979 71 4 9 37 5,16 10 25 71 AC. 72 23 -5 S8 9, J2 50 2 72 981 73 247 -6 8 3, 16 180 35 77 982 74 29-2 20 49 64, 10 315 1-5 71 983 372 35-8 51 I 8, 104 360 I '4 75 984 75 49'2 10 16 8,9 30 I '2 72 98S 474 22 I 60 25 8i, 12 360 10 76 986 375 4-5 5° II 8,9 330 I 75 987 475 6-2 -8 36 74. II 240 1-5 76 988 376 8-1 59 30 74, "4 ISO 3 75 989 476 87 30 48 94, 10 93 2-6 76 990 477 10-5 30 49 9, 11 46 6-4 76 991 377 11-4 54 4 8, 10 104 65 30 60 3 75 75 AB. BC. 992 378 12-8 60 16 84,9 90 4 75 993 379 16 S3 13 84,9 330 I 75 994 995 76 77 22-9 27-3 -0 -2 52 27 84. 12 8, 10 12 335 210 225 I'S 2 20 72 72 AB. AC. 996 381 27-4 32 47 8,104 210 1-2 75 997 80 81 23 12-2 28-5 4 -12 4? 18 84,9 8, 12 300 20 I 1-5 72 72 Very difficult. 999 1000 279 482 36-5 557 -15 62 12 39 5, 12 84, 10 II 90 360 150 3 4 10 74 77 AB. AC. ABBREVIATIONS USED IN THE MEASURES, ETC. Auwers Au. Bessel Briinnow Bumham Be. Br. Bu. Challis . Cincinnati Observations Ch. CO. Dawes . Dembowski Doberck Duner . Durham Observations . Da. De. Dob. Du. D.O. Ellery . Engelmann El. Eng. Ferrari . Flammarion Fletcher Far. Fl. Fit. GledhiU Greenwich Observations Gl. G.O. Herschel, Sir Wm. Herschel, Sir John Hind . H,. Hi. Jacob . Ja. Kaiser . Knott . Ka. Kn. Luther . Madler . Main Miller . Mitchell (Prof.) Morton . Nobile . Otto Struve Plummer Powell . Romberg Schiaparelli Seabroke Secchi . Smyth . South . Spbrer . Struve . Talmage Vogel . Wilson . Winnecke Lu. Ma. M. Mi. Mit. Mo. No. O.S. PI. Po. Ro. Schi. S. Se. Sm. So. Sp. S. Ta. Vo. W. Wi. Washington Observations W.O. M.M. = Mensurse Micrometricse. M. = Magnitude, h. = Hj. A. C. = Alvan Clark. Mem. R. A. S. = Memoirs of the Royal Astronomical Society. L. = Lalande. P.M. = Positiones Mediae. C. = Colour, B. A. C. = British Association Cataloeue. P - Piazzi. ^ MEASURES. The following measures have been compiled with great care, and the originals have been consulted where possible. Some, however, have been given on the authority of H», Ma., Da., and Fl. The first column gives the position angle (P.) ; the second the number of observations or nights {e.g. 14 or 2n.) ; the third gives the distance, and the fourth the date. Where the angles and distances are the result of two or more nights' work, they are the arithmetical means. In the case of O.S.'s measures the arithmetical means of the " corrected " angles and distances have been given. The whole of the measures by any observer are given at oncp; under the proper initials, and both these groups and the individual results are placed in chronological order. This arrangement has been found convenient in compilation, and it exhibits at a glance the whole of the work of each contributor. The diagrams are not all drawn to one scale ; but a scale of equal parts will at once show the value of i". 2. 3063. R. A. (jli j.jm Dec. 5° 12' M. 8'3, io'2 C. A, yellowish. Slow retrograde motion. Probably a binary. 2. 232-9 3"- 1.78 1831-50 Ma 227-3 in. 45-86 Se. 223-7 3n- 1-85 64-84 224-4 •84 S-5S CO. 221-4 31- -80 77-86 2 a ANDBOUED^. R A. Dec. M. 0^ 2-2" 28° 36' 2, 1 1 -2 C A, wh ite. Rectilinear motion. The proper motion of a in R. A. is + o'-oi3, and in Dec + o"-i3. 1781-96 1830-68 4-64 774 6-38 S>'93 66-68 76-07 7-08 3 t. 2. R. A. Dec. M. o^ 2-7" 79° 3' 6-3, 6-6 C. A, yellow ; B, deeper yellow. This difficult double star was discovered by 2. in 1828, and the steady change in H, 280-6 Da. 264-2 Sm. 267-1 266-9 S. •8 0.2. 269-4 De. 270-7 m. 269-8 Fl. 271-0 in. 557 66-57 65-9 64-8 •94 66-92 69-2 in. ... in. 71-1 176 DOUBLE STARS. angle and distance has secured for it the careful attention of observers. 2., Hj, Da. , Se., Demb., and others have measured it. Hj says, "Charmingly divided with 320. The discs like two grains of mustard-seed separated by one-third of the diameter of either." In 1839 Dawes could not separate the pair, and in 1866 Secchi describes it as "ovale." Between 1828 and 1866 the change in angle amounted to about 20°, but owing to the extreme closeness of the stars it is difficult to detect in the measures the acceleration of angular velocity due to the decrease of distance. " If the measures in 1858 and 1869 are correct, the two stars have already passed their apparent peri- astre." (O.S. in 1877.) Sa. O.S. Ua. Se. Ta. Dn. W. Fl. Dob. 342-5 343 '4 339 3 337-5 344-8 339-7 336-1 338-4 334-9 329-3 3^4-3 .>'36-6 337-9 332-7 336-4 338-8 343 -5 33' -7 335-5 324-9 136-8 295-5 295-6 325-0 3310 334-0 3>5-8 In. 072 -84 -94 •70 -85 1 3 0-7 3n. -743 6n. •522 ion. -443 simple in. 080 -55 ,, -64 ,, •65 ») •62 J* -55 »» -65 »» ■60 )) ■60 2n. •38 ,, •25 in. smgle »» 0-38 single 8 0-30 in. »> elong"". 3 ) 1 1828-22 ■27 32 '20 -24 3-34 0-31 967 4056 8-22 58-50 69-17 41-42 -45 •64 2-45 ■81 3-28 •31 512 -•4 57-52 66-95 3-6 5-7 7-0 5-76 9 '02 ■75 75'7i 2-92 6-85 7-82 OS. 2. R. A. Dec. M. oi" 7-4" 26° 20' A 6'9, B 8-3, c 9-6 This is h. 1007. A slow retrograde movement in A B. Probably a binary. 0.2. 51-5 65-3 57 -o 53-8 AB. m. 0-79 ») -83 •82 tt •78 1844-83 5092 -99 2-67 O.S. 51-9 >f 0-79 1857-71 43-8 •88 74-71 Se. 51-4 2n. -67 58-43 Se. 47-4 3^- •5 66-64 Su. 44-8 •72 9-78 \^ and C. O.S. 226-2 5n- 17-77 14-52 Eo. 224-2 in. -58 62-86 Se. 225-3 3n- •51 6-64 Su. -3 2n. -77 9-72 R. A. t. 13. 318 (B) CEPHEI. Dec. M. 0° 9-4"' 76° 17' 6-6, 7-1 C. S. yellowish white. Se. and De. white. A very difficult object. In 1830, Hj says, " With 320 and full aperture, both discs seen with a momentary hair-breadth separation." Struve calls it " oblonga, ex sequalibus." In 1828 S. could not divide it, but he did so in 1832. "The diminution of the angle is evident. The positions of S. are probably subject to considerable systematic errors. A small increase in the distance appears probable. " —(O.S. in 1877.) O.S. Ua. Se. Se. W. &S. 01. Fer. Sob. 126-7 129-5 125-7 114-2 124-8 116-9 117-6 31 1 -8 125-5 1 16-6 105-9 101-9 1199 101-9 105-9 103-3 -9 -o 104-0 lOO'O 96-2 97-2 102-2 103-5 -1 0-7 101 -o 93-1 181-7 in. 0-54 »> -5 i> -54 ») -55 in. -4 »> -5 )i -4 ,, i 3n- 0-64 6n. •57 ion. •70 3n- ■73 12n. •54 4n. 3"- )> 2n. in. ») 05 tj -6 •47 „ •58 2n. -69 »» -38 9 -5 7 6 0-5 -47 3 1828-22 32-20 2-24 3-34 6-68 -69 -70 0-31 40-58 8-22 58-50 71-22 43-20 55-59 8-56 62-76 3-35 4-69 5-93 9-51 74-82 5-71 57-52 66-95 72-5 3^3 •91 4-82 7-82 MEASURES. 177 6 OX 4. R. A. o"" 10-4"' Dec. 35° 48' Certain retrograde motion, binary. o " O.S. Ua. De. 2067 2n. 0-59 i«7-') 4n. •55 1727 2n. ■5^. 178-0 in. elong^. 29-5 *» 0-25 1847 3"- elongJ. 3S8-« >I M. 7-4, 8-1 Probably a 1845-26 54-01 61-66 5175 -76 66-88 9-61 t. 23. R. A. C. yellowish, have decreased. Dec. -0° 21' M. 7'6, 9'9 Both angle and distance The formulae given in the M. M. by 2. no longer satisfy the observations. From the observations by S., Da., O.S., and De., the following are deduced : — AA=- o"-48- AD= + ll"-40 -o"-o3o(T- 1850-0), -o"-i 10 (T- 1850-0), and the comparison of the observed and computed quantities is very satisfactory.— (O.S. in 1877.) 2. Da. Ka. Ma. 0.2. Ho. De. Ta. W. &S. 61. Bob. PI. CO. 1-2 3597 358-8 356'9 359'« 1-2 359 "9 355 '4 357-9 -4 353-2 355-5 356-7 355-0 354-S 355'° 353-9 351-6 352-8 353-9 ■2 352-8 353-4 348-7 3516 35°-3 3n- 6n. 3"- in. 8n. gn. 4n. }i 2n. in. 6'n. 4 6 6 6 4 2 5 9 4 2n. 4n. 3n. 13-67 12-87 12-25 10-98 1 2 04 11-86 1213 10-72 12-01 11-00 9-44 10-68 -87 9-85 8-84 -72 8-9 6-96 8-2 7-92 1828-52 36-24 42-18 54-00 42-48 3-98 -91 58-00 46-24 54-35 67-88 54'94 6-96 63-33 5-70 -76 9-72 71-78 3-86 -86 4-91 6-95 3'9i 689 7-46 -83 8 t. 24. 69 (B) ANDBOHES^:. R. A. Dee. Qh 12-2" 25° 28' C. white. M. 7, 8 The angle is unchanged, but the distance slowly diminishes. 2. Da. De. Se. Mo. Ta. Dn. Fer. Gl. 248-4 4n. 5-20 246-2 3 247-1 8n. 5-22 -5 4n. -05 -5 2n. -06 2502 4 248-5 ■7 247-3 6 5-21 5 5-98 250-8 4n. 4-84 249-1 5-22 247-9 4 183111 4676 53-05 6-85 8-41 65-70 -76 9-58 -72 70-39 2-95 3-91 9 Hi v. 85. R. A. Dec. oh ij-jm yf 28' C. white. Rapid increase of distance, motion. H,. 10-6 So. O.S. Fl. 13-2 15-4 -I I 30-45 45-31 53-35 in. 62- 5 M. 7-4, 9-5 Rectilinear 1783-04 -63 1824-91 51-99 77-13 10 0.2. 6. R. A. Dec. M. 0*15" 66° 20' A 7-2, B 8-2, c 9-5 2. 26 rej. In A B the angle has probably diminished, A + B, 2 AB. and the distance between " and C. O.S. Ha. De. 0.2. Ma. Bo. De. 143-9 ,135-3 1339 140-4 ■6 4n. 0-77 in. -55 >» •5 ,, •7 31- -6 1849-64 51-76 -77 2-21 67-67 A±B a„d c. 114-8 115-6 -8 -o 114-1 4n. in. 3"- 13-49 ■46 -56 ■26 -28 12 49-64 51-76 -77 62-87 7-67 178 DOUBLE STARS. 11 0.2. 7. R. A. o"" 15° Dec. M. 65° 49' A 7-2, B 8, c 9-8 B C. 0.2. 97-6 in. 0-46 II6-8 ,, -46 Ma. 1067 „ -3 IOO-4 ., -55 De. Too close for measurement 1846-74 7-91 5177 2-21 in 1865. AB. O.S. 76-3 1 2n. 1 52-44 1 47-23 12 R. A. o' 16-2"' t. 27. Dec. 12° 49' M. 6-8, 10-7 C. very yellow. Rectilinear motion. The changes are probably due to the proper motion of the principal star. (See P. M., p. ccxxiv.) 1829-50 51-80 Sm. 341-5 'S 33'9S Ma. -8 4n. 31-84 44-26 De. 33S0 29-73 63-85 O.S. -Q In. 30-14 5-87 - 9-93 Gl. -I 3 29- 73-89 Fl. 337-9 in. 28-q 7-08 344 -o 3"- 31-67 3407 in. 30-20 -I „ OI 341-5 •s -8 4n. 31-84 33«-o 29-73 -0 in. 30-J4 9 ,, -02 -I 3 29- 337-9 in. 28-5 13 R. A o"" 21" 2. 30. Dec. M. 49° 20' 6-8, 8-7 C. A, white ; B, ash. Change in angle and distance. 2. 295-8 Ma. 296-6 TV. & S. 299-3 3"- 21-23 in. 2042 4 18-72 1831-21 45-08 -93 14 2. 32. 49 FISCIUM. Dec. IS° 23' R. A. Dec. M. o"- 24-6"' 15° 23' 6-8, 10-6 The evident change is explained by the proper motion of the principal star. — (0.2. in 1877.) Z. Sin. Ma. Be. O.S. w. &s. Gl. 108-3 107 -6 106-8 2n. 3". 2n. 13-43 •84 15-48 109-5 107-2 106-5 in. 2n. -0 14-87 16-15 105-8 106-6 31- 3 ■I' •8 4 •4 1829-24 32-90 5 1 -84 35-87 44-01 63-92 9-91 73-93 •94 15 0.2. 12. R. A. o"" 25-1" Dec. 53° 52' M. S-6> 5-9 Certain direct motion. Proper motion of X, +o'oo3 in R. A. and +0" -02 in P. D. Du.-s formulae are — 185527 4 =o"-48. p = i3o='-7 + o°-55 (/— 1860-0). 0.2 299-2 m. 1843-14 303-7 ,, 0-48 4-84 295-5 ,, -54 516 127-2 ,, -56 611 305-2 ») -49 7-«3 »3i-3 j» -53 5i-'3 1291 jj ■44 •19 3100 )» •52 4-67 3'5-o „ •65 70-18 Ma. 122-3 2n. •33 45-73 -9 4n. •29 5 1 99 140-3 in. 3-24 Da. 115-9 2n. 0-57 4-36 8e. 124-8 in. -25 9-01 De. 133-1 6n. 66-37 134-3 0-38 9-39 1387 2n. elong. 7069 133-9 2n. 0-5 1-28 136-8 in. obi. 2-61 324-1 in. elong. 3-69 134-3 in. 0-58 5-63 3187 in. -57 7-03 Dn. 142-1 4n. •49 5-80 W. tc S. 140-7 7 •5 -92 16 .2. 13. R. A. Dec. M. 0^ 25" 36° 16' 7-8, 10-9 Probably a slight change in both angle and distance. There is a star of the 10- 1 1 mag. at a distance of 41" (De.) 0.2. De. De. 133-2 131-1 180-9 AB. 4n. I 3"- I 6-19 -39 AC. 2n. I 41-22 1850-06 66-63 66-19 MEASURES. 179 17 R. A. o*" 26-2"' 2. 36. Dec. 6° 17' M. 5. 9 C. A, white ; B, ash, A difficult star to observe. The angle has probably decreased. Madler gives the proper motion as + i"7 and + i"-2, but S. has — o'' -2 and + 3" •4. 1783-63 1820-96 2-22 33 "20 22-87 52-86 3'04 3-85 8-04 8-04 64-94 73-86 H. 89-4 S. 82-9 H,&So. •3 -8 m. 81 -o 80-4 81-9 •9 Se. 82-4 £11?. 81 -8 w. &s. 82-7 22-48 in. ... m. 2T44 3n. ■42 25-87 2n. 2825 in. ■21 in. 27-04 in. •51 in. •29 in. •47 5"- 28-4 18 R. A. o"" 31-9° 2. 44. Dec. 40° 20' C. yellowish. M. 8,9 Direct angular motion and increase of distance. Du.'s formulae are — A = 8" -34 + o"-o237 {i- 1850-0). P-26i°-6 + o°-i39 (^-1850-0). 2. Ua. Se. De. 0.2. Da. W. *S. Gl. 258-8 31- 7-86 260-4 2n. 10-35 259-0 2n. 7-34 262-2 2n. 874 263-2 6n. •66 262-3 in. •76 265-0 7n. •80 264-2 4n. 9-1 263-0 -6 265-4 8 8-8 264-6 4 •9 1829-82 30-16 45-69 57-93 65-09 6-92 70-09 2-64 4-86 6-95 3-9" 19 R. A. o* 33" 0.2. 13. Dec. 48° 42' M. 6-3, IO-8 0.2. Ua. Se. C. yellow. The distance has probably diminished 14-76 25-6 •6 26-7 24-9 3"- in. it 3n. 5-39 14-24 1845-92 49-28 52-84 67-09 20 R. A. o'' 34-7" t. 49. Dec. -7° S3' C. yellowish white. 2. Ha. De. Ta. CO. 321-4 3n- 4 49 320-4 in. -93 319-6 3n. 5-24 304-4 5 •82 320-5 4n. •92 M. 6-5, 10 1830-92 44-05 6518 71-78 7-80 21 R. A. o' 36"" 0.2. Se. De. O.S. 18. Dec. _ 3° 32' Probable direct motion. M. 7-4. 9-5 93-6 2n. 1-40 94-7 ,t -34 99-8 ,» -13 106-2 3°- •55 1845-70 55-18 8-51 66-60 22 R. A. oh 37m 0.2. 19. Dec. 36° 55' M. 7-8, 10-7 Probable change in angle. 0.2. Ma. De. II7-3 3"- 9-56 293-0 1 14-4 3"- 9-74 1847-22 5-85 66-60 23 R. A. Qh 37-5« X. 62. Dec. 45° 35' C. yellowish. S. Ma. De. 25-8 24-8 19-0 18-4 19-3 14-6 17-9 3n. 1-42 1 I -70 in. 1-36 •06 >» -28 ft •33 M. 8. 9 1831-44 45-08 63-97 -87 8-88 70-06 7-87 24 R. A. o* 41-2™ S. 59. Dec. 50° 47' C. very white. M. 7, 8 Probably very slow orbital motion, Du, gives — 1855-42 A = 2"-2I, P = l46°-8 + o"'-o86o (/ + 1855-42). i8o DOUBLE STARS. H,. So. Sa. 2. I40-5 I47"6 148-2 144-9 147-2 146-8 -o •5 ■9 •5 ■4 147-8 ■4 146-2 1477 148 -I W. & S. 149-0 Gl. 148-5 Ha. Hit. Se. Ho. Du. in. 2± 3n. 2-57 •32 411. -19 •3 ■4 3n- -20 J) ■24 »» •05 2n. •49 6 ■25 in. 2-03 3n- •12 2n. ■17 8n. •21 4 •14 4 1783-34 1825-14 30-78 2-33 -87 6-94 45-34 5«-S2 6 70 61-80 47-63 56-76 67-98 58-58 -66 7«-94 3-83 -89 25 R. A. o'' 41 -8" S. 60. )) CASSIOFEIJE. Dec. 57° II' M. 4. 7-6 C. S. A, yellow ; B, purple. Hj. " 3. ij Cassiopeisc, Fl. 24. In cingulo. "Aug. 17, [1779]. — Double. Very un- equal. L. fine W. ; S. fine garnet ; both beautiful colours. Distance 1 1"-275 niean measure. Position 27° 56' n. following." Again, he says {PAt/. Trans., 1804), " The situation of the two stars of this beautiful double star, June 14, 1 782, was 27° 56' north following; and, Feb. 11, 1803. it was 19° 14' ; which gives a change of 8° 42' in 20 years and 242 days. This arises probably from a real motion of ij in space ; for parallax would have had a con- trary effect.' And Hj (nt/. Trans., 1824, part ii.,) re- marks that "The changes, both in position and distance, of this remarkable star, have been regularly progressive." He gives measures from 1779 to 1821, points out that r.'s position for 1814 is not reliable, and finds the angular motion to be 0-5133° per annum in the direction n f s p, and the period probably about 700 years. He ob- serves, ** A connection between these stars cannot be doubted, as they have a common proper motion of nearly 2" per annum. The distance having diminished almost 3", the apparent orbit is evidently elliptic." Hj having predicted that the small star would probably be on the parallel in 1835, Sm. " carefully watched, both before and after, and saw the prediction verified." Sm. further remarks that " The lapse of 40 years after H.'s measure gives a mean velocity of + 0-45° per annum, and the 23 years since elapsed -f 0-70', while the distance may be regarded as but little altered." Da. gives measures from 1831 to 1854 {Mem.K.A.S., vol. xxxv.), and observes that the proper motions in R. A. and N. P. D. applied to the larger star would have dimi- nished the angle and distance, supposing the smaller star to be at rest. The diminution in the distance, and the consequent increase in the angular velocity of this star, are well exhibited by the long list of measures. It may be observed, too. that the proper motion of ij is unusually great, Argelander giving it as -|- 1-97" in R. A. and —0-495" '" ^- (For some inte- resting remarks and results, see Madler's Die Fixstem-Systeme.) Madler was of opinion that the bright- ness of the principal star is a constant source of error in the measures of distance, and was but little satisfied with his own results. He thought that the companion probably passed its aphelion between 1780 and 1803, and that the distance would sink to 2" or 3" about i860. Orbit. — The following are the more re- cent elements : — Doberck, 1876, gives : 7 = 1909-24 R=39°57' jr-R=223-20 »■= 53-50 ? =0-5763 a =9-83" P = 222 -435 yrs. Griiber in 1876 : T= 1901-25 ffi=33°2o' 7r = 229-27 8=48-18 e. 214-8 13-93 64-10 218-6 14-65 72-69 W. &S. 221-5 6 13-0 4-93 27 2. 64. R. A. Dec. M. o" 44-5" 40° 33' 9-2, 9-7 The distance has probably diminished. Duner's formulae are — A = 3""39-o"'" {/-1848-os). 1848-05 P = 272°-8. Ua. Be. Du. 270-7 272-5 274-2 272-0 273-2 -5 272-5 in. 2n. 3-64 -54 •31 •45 •58 •22 -14 1828-85 31-73 45-16 8-07 58-89 70-73 -09 28 R. A. o" 45-9" Ma. Se. S. 67. Dec. 9° 57' Change in angle. Fer. 13-0 12-7 7-2 -5 •9 5-3 1-6 3n- 4 in. 1-58 -82 -9 2-II 1-76 •69 •80 M. 8-3. 9 1830-91 43-35 63-88 6-67 7-63 70-71 3-94 29 X TOUCAN/E. R. A. o" 47 •8" Dec. - 70° 9' Probably binary. Dnnlop. H3. 71-6 76-8 78-5 80-8 •6 20 •46 22-25 20-94 M. 7. 8 1826-80 34-84 5-92 6-73 7-74 30 R. A. o" 47-9"° t. 69. Dec. 83° 2' C. yellow. M. 8-5. 9-7 Certain change in angle and distance, but the nature of it is uncertain. MEASURES. 183 2... 359-8 2n. 2144 1832-23 Ma. 23 22 -06 47 '30 De. 6-6 »» •42 64-02 61. 80 I ■4 74-90 W. ft S. 100 3 •4 4'93 31 o.t. 20. R. A. Dec. M. o' 48- 18° 32' 5 ■9. 7 C. A, yellowish white ; B, bluish white. Direct motion. O.S. 727 4n. o-6i8 1847-33 59-8 3n. •667 6034 Se. 78-8 in. elong''. 57-84 560 It °'35 800 S8-o 11 con- tact. 9-01 De. 841 4n. obi. 5-88 487 3"- 66-85 266 in. obi". 70-71 50-0 1-65 36-9 2-67 45 -I 4-68 311 5-65 iS-2 0-3? 7-87 32 t. 73. R. A. Dec. M. 0" 48"' 22° 58' 62, 6-9 C. S. golden. 30 laJB Discovered by H, in 1830, this star has been assiduously watched by observers, Dawes alone having measured it on no less than forty nights. Hj {^Mem. R. A. S., vol. v.) writes : " A miniature of r/ Coronje. In glimpses, the two discs may be discerned in contact." "Very close; in contact; twirls much. Difficult measures." Smyth {Cycle, p. 21,) says: "This beautiful golden pair is very difficult." He used 600 with a central disc on the object-glass with advantage. From his own and H.'s measures he in- ferred that "there is a decided direct orbital motion." The increase in the distance accords per- fectly with the manifest diminution in the angular movement. The distance appears already to have attained its maximum. (O.S. in 1877.) Doberck gives the following elements: — T = 1798-80 Node = 57° 54' A = 142 19 r = 4' 39 e = 0-6537 P = 349-1 yrs. a = I "-54. Dr. Duner has deduced the following formulae : — Asin. P = — o"-48 + o"'Oi3o(/— 1854-42) + o" -000235 (^-1854-42)^ A cos. P = + i"-ii -I- o"-oi8o(^— 1854-42) — o"-ooo36i (^—1854-42 J''. And on comparing these with the observa- tions from 1830 to 1875, he finds very satisfactory agreement. =2- s. Sm. Da. Ma. 305-0 308-6 307-8 320-4 3157 318-5 332-9 335-8 317-8 319-3 321-2 322-9 324-5 321-4 328-9 329-3 -9 332-0 334-5 336-5 334-4 335-8 340-2 324-7 325-8 329-0 -6 334-0 336-5 -5 340-3 -I 0.2. 324-2 328-6 335-9 344-4 Ka. 323-4 350-9 Mit. 330-2 Fit. 336-4 Ja. .-538-0 2n. 0-849 4n. -775 3"- •847 ,, •937 i-i -I -0 -3 3n- -092 Sn. -080 3"- -102 2n. -007 4n. -117 2n. 5n. 1-120 In. -124 2n. in. 1-227 ,, -173 2n. -078 j» ■218 »» ■170 in. •227 2n. -189 6n. •192 2n. -047 in. -264 3n. •219 •402 •280 ,, -367 5n. -392 •336 a'n- •303 in. -210 3"- •333 In. •360 3"- 0-99 1-25 6 1-05 34 1-12 15 1-26 1830-73 1-79 2-14 6-90 5-92 9-77 43-12 52-83 39-79 40-98 1-87 2-94 3-88 •99 6-93 -96 7-92 -93 50-91 3-87 -89 •90 4-75 9-83 41-59 z-77 6-99 7-90 51-00 3-87 5-29 7-75 8-04 41-64 6-78 54-70 61-74 42-34 67-03 47-70 51-93 3-96 1 84 DOUBLE STARS. Ho. De. Wi. Se. M. Kn. Ta. Br. Gl. W. &S. Du. "W.O. Dob. Sp. Schi. PI. 3401 24 1-25 335 "3 41- ■2 336-3 511. •16 344'o ,, ■12 •3 411. ■14 345'° ,, •22 ■7 511. ■21 350-4 In. •31 349-5 ,, •31 350-1 2n. ■22 352-4 ,, -40 •5 j» •34 •5 ,, ■35 354-4 3n- -26 355-7 2n. -25 356-2 5n. •34 3+4-2 in. ■30 339-2 31- •202 349-5 in. -314 329-0 •10 348-4 2n. •62 344-8 5 -323 •9 7 -393 ■6 6 •322 347 -o 31- ■07 .'?44-2 in. -38 349-5 ,, 347-4 ,, 1-24 351-6 ,, ■29 •8 ,, -03 350-7 8 ■57 349-9 5 •2 350-2 5 •3 352-7 5 ■2 3540 5 -4 356-3 3n- -37 354-8 in. 355-4 6n. 357-2 2n. 352-3 4 1-36 355-0 7 ■14 354-1 4 ■20 353-1 7 ■34 355-9 5 •43 356-0 6 -38 358-6 4 ■28 ■8 12 •33 356-1 5n. •36 3-1 In. -39 0-4 „ -27 356-4 ,, -24 355-7 ,, -46 3S7-0 ,, •12 359-1 5n. 354-9 4n. '-'5 355-9 ■28 •8 In. -275 358-2 4n. -49 1854-91 5-59 62-78 3-82 4-74 5-64 8^65 9-65 70-35 1^62 2^65 3-68 480 5^62 7-27 5609 7-27 66 •OS r8o 511 •67 ■69 ■70 •73 6-83 9-72 7286 3-86 6^86 68-76 70-14 •60 r6o 391 5-54 6^07 7-62 8-45 2-03 3-Si 4-93 -94 6-95 7-94 5-70 ■97 -98 6-00 -00 -01 -08 •75 7-02 ■01 -19 33 R. A. o'' 49"" S. 74. Dec. 8° 44' C. white. M. 8, 9 2. 301-2 2n. 2 96 1829-83 303-3 in. 3-19 32-86 Ha. 302-4 Sn- •15 43-59 Se. 304-9 2n. •13 56-89 34 So. 390. R. A. Dec. M. 0*' 52-2 m -16 ' 20' 7. 7-2 This pair was discovered by South in 1824. The angle has increased consider- ably, and the distance has diminished. So. H,. Se. CO. 32;3 -7 86-8 214-9 16 3"- 7-78 6-67 -65 ■43 •33 1824-90 35-74 7-80 55-95 77-79 35 S. 80. p. O. 251 PISCIUH. R. A. Dec.^ Qh 53-2'° 0° 8' M. 7. 8-2 C. 2. and De., yellow, blue. South, " small, blue." A ^\•ide pair, first measured, probably, by South. Piazzi noted the duplicity of this star : " Duplex, comes 9=" raagnitudinis prsecedit 1" temporisparumperadboream." South measured it at Passy. " Double ; 9th and 1 0th magnitudes ; small, blue ; 24° 43' n.p. i9"-2o6 ; 5 obs. Oct. 25, 1824, extremely difficult." Smith {Cjc/c, p. 23), " A neat double star bearing both illumination and high magnifying power." He observes that Piazzi assigns it to Pisces, but that it should be placed in the Whale ; and, from a com- parison of his own measures with those of South, he infers a direct orbital motion of o°-4 per annum. O.S. finds that the observations from 1 83 1 to 1 868 are exactly represented by the formulas f = i8"-924-fo"-o40(T— 1850-0). P = 305°-o8 + o°-3i (T-1850-0). Engelmann's formulas are P = 299°-82 + o°-3o66 (^-1833-34). A = i8"-264-fo"-04i43('/— 1833-34). And Dr. Duner gives A= l9"-33 + o"-0332 (^—1866-0). P= 3io°-o + o°-3o8 (/-18660). 2. 296-7 -9 299-5 300-6 in. ... 3n. 18-38 1822-29 4-99 31-53 5-83 MEASURES. 185 So. 296-5 Sm. 299-8 301-8 305-1 Ma. 303-8 304-1 305-5 306-3 0.2. 302-4 305-5 311-0 Ka. 303-8 De. 307-3 -I 306-5 308-9 309-1 Ja. 307-4 £ng. 308-8 310-5 Dn. ■9 311-3 -5 310-1 M. 31 1 -4 ■w. &S. 312-9 311-6 -7 3"- 2n. in. 2n. in. 2n. 9n. in. 61. •9 312-9 •9 313-7 31 1 -o 313-3 2n. in. 3"- in. 4 4 7 3 6 6 3 5 in. 18-87 ■4 "5 -8 17-87 18-61 -52 19-05 1869 19-01 •60 17-85 18-80 -63 ■93 19-41 -39 -07 •78 -54 ■62 -69 -73 -51 20-10 -I 19-7 -9 18-4 20-3 -o •31 20-9 36 0.2. 21. R. A. o'' 56°" Dec. [46° 44' 1825-17 32-98 8-03 52-81 42-78 4-94 53-09 8-01 42-84 51-22 68-42 43-10 55-99 6-03 •62 62-84 3-80 57-95 62-97 5-03 8-84 9-71 70-73 69-78 70-77 '-«S •90 2 -co •88 3-81 4-93 -73 6-95 3-9> 7-06 Ua. 0.2. He. 45-1 177-1 0-97 -58 4n. Oblong ? M. 7, 8 1845-68 47-84 64-7 5-7 37 R. A. o^ 58-7" 2. 86. Dec. -6° 7' C. white. M. . 8-7 S. early recognized the angular change, and the measures since made confirm it. The distance may have increased slightly. 1783-08 2. 173-8 in. 12-01 182203 9-90 30-92 5-85 6-58 180-6 I 14-83 i7r8 in. 12-01 171-8 »* -0 -3 If •12 0-0 )» -25 169-4 3"- •11 So. 172-7 4n. 12-89 1824-89 Da. 167-6 -51 41-61 Se. -6 4n. -51 3-59 162-9 3n. •64 63-47 Ka. 169-9 7n. •22 43-59 Ua. 167-3 3n- -36 -55 164-0 2n. -76 53-09 162-2 In. 8-01 0.2. 167-8 2n. 12-34 43-85 163-0 In. •65 66-92 Ta. -5 4 5-70 , -5 6 11-67 -78 161-7 4 ■82 6-84 -8 5 8-84 -6 9-72 160-9 5 11-56 72-77 161 -8 In. 12-38 3-86 -5 in. 11-71 6-89 •W. &8. 163-4 4 12-6 3-93 1-6 IS -5 6-53 Gl. 161 -9 4 -6 3-93 CO. , -4 in. -74 5-87 160-3 Sn. 1 -84 7-81 Dob. 158-9 2n. 1 -50 6-95 PI. 160-1 3n. 1 -65 -94 38 R. A. 2. Ho. Ua. %. 87. Dec. 14° 74' C. yellowish. Se. 61. 193-0 3n- 6-56 1 I95-I 9-14 ■2 3"- 6-55 I96-I -88 -9 m. 7-10 198 -I 2n. -9 2n. ... 195-1 2n. 6-79 198-7 in. -65 195-8 3 M. 8-5, 8-s 1829-85 30-33 43-89 7-95 51-00 2-87 3-08 7-46 66-05 7403 39 t. 88. ;f-' PISCIDM. R. A. Dec. M. o'' 59" 20° 50' 4-9, 5 C. white. A probable increase in distance. Midler gives the proper motion as + 5"-7 in R. A., and — 2"-3 in Dec; Z. gives +7"-6and — 3"-5. This physical pair is easy of observation, and yet the measures are very discordant. 2. Ua. 160-3 159-8 160 -2 159-7 27-50 4n. 29-89 m. -61 tt 30-26 n 29-81 1779-82 1832 1 1 51-80 36-20 44-01 I86 DOUBLE STARS. Ha. Se. Bo. Sq. Ta. 160-3 1 30-53 IS9-S 29-83 161 -8 160 -o f 29-50 •4 , 30-29 159-0 , 29-7S ■4 30-34 160-4 » 29-69 •8 1 30-12 isg-s , -02 l6l-2 4 29-43 159-9 in. -95 ■5 »» 30-01 161 -2 S 29-6 1597 6 •8 i6o-2 3 31-0 40 R. A. X. 91. Dec. - 2° 24' C. yellowish white. Probably binary. 2. Ua. Se. Wi. Se, Fer. W. &S. Gl. CO. 41 0.2. 515. R. 1" Dec. 46° 36' 1845-08 6-74 50-96 -97 •99 4-98 6-98 7-90 ■95 8-04 65-70 9-08 -09 7491 •91 ■94 .328-5 3-63 30. -86 325-5 -77 324-0 2n -35 3223 ») -86 •8 411. •05 ■9 in. 323-2 3n- 4-03 3220 m. 3-69 •3 It 4-06 321-5 ti 3-72 3242 »» 4-02 ■9 6 ... 323-6 4n. 5-57 321-3 2n. 3-94 323-2 in. •66 320-5 )» 4-62 322-8 3-98 321-4 4 40 322-2 5 3-8 •1 4 4-0 320-7 in. 3-9 324-0 3n. ... 321-3 4n. 3-92 M. 6-7. 7-5 1830-67 189 7-49 42-85 5-03 53-08 8-00 4-77 63-88 6-68 7-66 72-67 56-09 ■72 66-51 580 73-96 -01 •8 1 4-93 ■93 3-93 5-97 7-81 M. 4-9. 65 C. A, yellow ; B, green. A binary. O.S. De. 309-9 3039 302-6 267-2 4n. 0-535 3n- ■510 2n. -560 in. obi. single single 1851-51 6-87 64-70 75-14 65-97 7-52 42 R. A. S. 100. Z FI8CITTH. Dec. 6° 56' C. white. M. 4-2. 5 3 Probably a very slow orbital motion manifests itself. The proper motion, ac- cording to Madler, is +i2"-o, — 7"-2 ; S. gives + 14"-!. — S"-l ; and Argelander 4- 17''-! and — 8" -6. Madler found the changes represented by p = 64° 27'-3-4'-o78 (/-I825-I9), A = 23"-45o. See the Dorpat Observations, ix. 63. H,. H2&S0. S. Ma. Fit. On. -v. & S. 67-4 63-5 65-6 63-7 64-0 63-0 64-1 63-0 •9 •7 •7 in. 2217 2n. 24-65 in. 23-33 5n. ■45 in. -60 2n. •31 In. 22-99 3n- 2322 29 •32 3n. •33 3 24-7 1781-88 1821-92 3-87 2-83 51-89 41-65 2-94 5-04 51-66 71-67 3-89 43 R. A. ,h gm 0.2. 28. Dec. 80° 16' M. 7. 8-5 O.S. 324-3 31- 0-527 1847-5 Oe. 313-4 in. -7 65-93 -2 »» -92 7-61 317-5 1* wedge 8-65 2. 101. Dec. -8° 18' 44 R. A. C. yellow. Probably an optical pair. 333-6 337-9 345-0 339-3 340-8 •3 332-2 3402 &S. 341-5 340-8 Gl. .342-3 So. H,. 2. Ma. Se. W. 19-50 •60 2n. •89 3n- 21-33 in. 2n. 21-24 48-32 20-52 2n. 22-30 in. •52 2n. •3 M. 7-5. 9-8 1782-87 3-65 1825-30 9-67 32-22 45-89 53-09 65-80 8-20 74-90 -93 ■88 MEASURES. 187 45 R. A. 2. 102. Dec. M. i"" II" 48° 24' A 7, B 8-2, c 8-4, D 10-8 C. white. A B and A C unchanged. Slight change in A D, both in angle and distance, appears certain ; probably due to the proper motion of the triple system, D being fixed. AB. Ua. OS. Se. 309-1 4n. 0-S7 303-9 in. •5 310-9 4n. •65 3057 4n. wedged 1834-25 53-08 3-14 64-89 ■MandC. ■V 255-7 8n. IO-22 33-89 o.s. 224-6 4n. -32 53-14 Da. •2 4n. -09 64-89 ■4+B and D. S. 0.2. De. 66-3 31- 29-76 64-9 28-99 ■4 -26 65-0 4n. •6 32-45 54-62 69-17 4-89 S. 93. a VB,SJE MIKOBIS (FOLABIS). R. A. i" 13-7"" Dec. 88° 40' M. 2, 9 C. A, yellow ; B, while. 0. 2., after applying the precession cor- rection to the measures of S. in 1834-14, finds the angle 2l2°-24 for the mean epoch of his own observation. The differences — o"-220 and — I°l6 leaves it still un- certain whether any change has taken place in this system. =1- H2&S0. 19 17 203-3 ... 202-6 ... Z08-3 ... ■8 6n. i8-7 1779-8 81-6 -9 2-4 I802-I 23-06 8m. S. Ha. Se. O.S. Se. Sn. Gl. Fl. 209-9 210-0 209-3 210-5 208-9 212-4 -7 213-3 214-6 213-7 21 1 -6 212-4 -9 213-3 18-4 183078 in. -27 34-14 tt 19-1 41-46 2n. 18-67 2-33 in. •39 6-23 ft •44 59-95 2n. •56 61 ^33 in. •44 8-2S >» •55 72-19 •36 S-18 •26 62-90 7n. •54 70-90 in. ■7 3-94 »> •62 7-31 48 X. 113. R. A. Dec. M. C. S., De., and Se., white. This star was measured by S. in 1829. It is a difficult object, and great discrepan- cies are found in the recorded observations. The positions given by Da. in 1841 and 1842 are 33o°-77, 332°-32, 33i°-43. 337°-23. 334° -32, 338° 30, 339" -06, 338° -02, each being the mean of five or six observations on different nights. Sm. {Cycle, p. 34,) says: "A beautiful object, but very dithcult to measure in dis- tance. It seems to have a direct angular movement, to the amount of about 0° -7 per annum ; but this requires verification." Da. thought that the discrepancies were probably due to the closeness and oblique position of the stars, and remarks that it is "still uncertain whether any real change has occurred. " Sm. {Spec. Hart., p. 220) ; " I think the angular motion in orbit is now clearly proved." Se. : " The motion in angle appears cer- tain, though slow." "A feeble angular movement" (0.2., 1877). Sm. Sa. 0.2. Ua. Se. Ta. 333-6 4n. 1-245 3343 3". -177 325-6 332-6 1-2 344 -6 ■3 331-4 3"- -014 335-6 2n. -i8s 33«-4 3"- -164 I 2n. -355 343-9 2n. -39 345-7 m. "=l 340-0 2n. -36 338-9 ,, -16 3397 4n. -169 346-9 in. -48 338-4 2n. •14 339-0 in. -•5 342-3 » ... 1831-61 6-91 I -81 4-84 57-97 42-64 3-86 54-51 44-72 5309 8-01 42-75 5-04 56-48 66-07 5-73 6-84 76-86 i88 DOUBLE STARS. Se. Ja. Ter. M. W. i Gl. W.O. CO. Schi. 8p. Sob. PI. 343-3 2n. l"l ■4 ,, •IS ■4 4n. 342-3 2n. •27 340-5 18 •45 346-5 in. ■406 357-6 ») 0-90 346-2 4 1-35 9-5 4 -24 350-7 3 •63 348-0 8 •45 350-7 4 •5 351-9 in. •24 ■0 ,, •06 349-7 in. •19 347-5 4n. -46 34«-7 >> -38 •8 >» -38 346-3 3n. •29 349-3 »> -38 1855-89 56-13 62-80 63-43 56-78 72-95 61-90 72-07 3-01 •81 4-93 4-94 606 -08 6-79 7-79 -01 -02 6-87 7-37 49 R. A. i"" 14" h. 2036. Dec. - 16° 25' Rapid change in angle since 1870. bably a binary. M. 7. 7 Pro- H,. Ja. Oe. CO. Sp. 53-0 in. 2± 45-0 ,, 1-25 .38 -I t) -82 .36-1 »» -57 26-5 •45 -6 -63 24-0 4n. 26-4 in. 1-64 298 -62 26 4n. -39 -6 in. •51 1830-79 5-72 696 57-97 74-67 5 62 5-94 6-78 •79 7-76 50 R. A. S. 117. Dec. 67° 30' M. A 4, 8 9 5, c 10 C. A, very yellow. A B probably an optical pair. B C pro- bably binary. The magnitude of A is variously given : e,^., Se. 4 ; 2. 4-4, 4-5 ; Heis 5-0; Fl. 4-7. So. Ma. AB IOO-2 33-4 IOI-3 In. ■3 103-3 307 104-4 2n. -24 -5 -36 106-9 in. 29-9 105-7 2n. 30-29 1782-63 1823-20 30-87 44-33 5-53 50-72 2-84 2. Sm. Sa, Mit. Se. M. Se. -w. &S. Per. Sob. Fl. IOI-8 Sn. 32-2 102 -I 31-9 •7 in. 104-9 ,, 30-55 102 -8 in. ■32 104-9 2n. 29-6 103-2 in. 27-73 105-1 3°- 29-74 -5 2 -8 106 m. 28-49 105-4 2n. 106-5 5n. 28-12 105-7 In. 29-5 BC. Sm. Sa. Ma. Mit. Se. Be. ■W. &S. Fer. Sob, Fl. Se. 253-3 252-0 -6 253-1 255-4 251-8 253-3 -o 2564 255-3 -8 257-2 .0 256-1 108-0 4n. 3-01 293 -0 in. ... )j 3-25 in. •16 m. -28 J' -25 2n. 2-25 3n- •82 6 3-06 in. -II 3"- in. 2-9 AC. 2n. I 2696 51 R. A. ,h 20-6" t. 118. Dec. 82° 44' 1831-04 6-28 9-74 54-07 47-67 58-82 62-71 5 50 73-83 483 5-92 6-23 7-12 31-04 2-28 6-28 9-74 54-07 44-33 7-63 •67 58-82 65-50 73-83 4-83 6-12 7-34 65-88 M. 8-5. 9-4 Probable change in angle and distance. H,. 2. Ma. Be. 61.5 62 o 608 69-9 12 4n. 10-75 2n. -52 11-18 1830-00 2-49. 45-10 63-71 52 R. A. jh 20-7" t. 122. Dec. 2° 55' M. 8. 9 C. A, very white ; B, blue. Probable change in angle and distance. 2. Se. Ma. W. &B. 334-2 332-8 326-6 3285 3336 331 -5 329-2 3n. 5-79 2n. -95 In. •60 2n. -97 m. ■44 2n. 6-2 1831-81 3-56 57-97 66-05 43-49 58-00 73-87 MEASURES. 189 53 R. A. i" 20-8"' t. 125. Dec. — 0° 46' M. , 10-3 C. white. On reducing his observations for the effect of precession, converting the results into rectangular coordinates, and treating them by the method of least squares, O.S. obtains the following formulae : — AA = +4"-323±o"o40— (o"-29iod= o"-oo37) (T- 18500). A D = + I9'994±o-04o4-{o-35oi ± 0-0037) (T- 18500). The motion is thus rectilinear. The small star is at rest. (See the P. M., p. ccxxiv.) S. 0.2. Ua. Se. n. CO. 37-3 36-3 35 '9 30-2 •9 29'2 27 '3 21 '2 187 •7 19-3 8-6 9-8 1-6 07 356-3 354-8 -8 3527 353'3 3529 in. 15-82 >» 16-96 a 17-52 it 16-91 )) 17-09 •16 4n. 3n- ■20 18-28 in. •92 -89 2n. 19-05 .» 21-35 in. •30 3"- 24-45 4n. -81 2 3 3 303 -8 4 in. ■34 28-8 2n. 3074 1829-90 30-92 2-79 3-95 5-85 -96 6-62 42-78 4-05 5-04 3 '90 52-91 3'o9 62-94 381 73-87 4-93 •95 6-95 7-08 •84 55 t. 133. 54 R. A. Z 132. Dec. 16° 21' M. ' 25-6'° 16° 21' 7, 10 C. A, yellow. The proper motion of the principal star explains the observed changes. (See the P. M., p. ccxxv.) S. Ua. O.S. Se. W. 4S, Fl. 27-7 5 '4 359-2 0-2 359-7 o-i 358-2 359-0 355-8 356-2 -o 353-6 in. in. 2n. in. in. 16 24-25 28-87 •26 -52 -43 30-89 28-88 32-43 30-99 I 34-0 1783-63 1829-87 51-80 47-10 51-01 2-IO 8-II 1-82 68-91 3-84 73-89 7-08 R. A. M. Dec. 35° 14' jh 25 •9"' A 7, B 10-5, c n-2, D u-6 C. A, yellow. In A B a small increase in an^le. In A C and A D a decrease in distance. AB. Ma. De. W, &S. 179-1 31- 2-99 185-6 in. 2-6 189-2 2n. -7 187-7 in. 189-4 190-0 2n. 2-86 189-8 in. 185-3 5n. 2-87 -0 in. 3-04 182-0 »» 2. Ua. W. &S. 346-2 351-7 347-6 348-1 35 1 -5 -7 Ua. De. W. &S. 199-5 196-7 197-9 >93-9 S. De. 193-3 •8 CD, 3n. 4-76 in. 5-25 . -20 j» -58 4 4-75 2 AC 31- 29-08 in. ... 4n. 27-30 2 ... W. & S. i-o 03 W. & S. 300-0 -7 AD. 4n. AE. I I I I 2 I EP. I ' I 2 33-8 32-3 1833-04 43-97 5-65 7-07 51-18 2-84 3-78 63-59 73-89 4-93 33-04 45-18 -64 7-07 73-89 4-94 33-04 47-07 63-76 74-93 33-04 63-76 73-89 4-93 73-89 4-93 56 R. A. jh 2^ 0.2. 31. p. 1. 107. Dec. 7° 36' M. 7, II The change in angle and distance is very small. O.S. De. 84-9 81-4 83-8 •o 4n. 4-04 1850-02 in. •05 65-88 ,, ■13 6-64 }} •12 7-63 I90 DOUBLE STARS. 57 S. 136. R. A. ,h 28-5" M. 6-9, 8 100 PISCITTM. Dec. 11° 57' C. white. The proper motion, according to M'adler, is — 4 '2, — o"'l ; and 2. has — 4" '4, + i"'9. The former observer gives the following formulse : — * = 78° 4i'-3-7'-o59 (^-1826-54). A = is"-830. H,. H2& So. Ha. 85-0 80-4 79-9 I787 ■9 ■9 79-1 78-6 "4 ■6 •8 77-6 0.2. 79-1 Ta. 78-09 79-60 •06 •20 Dn. 78-8 W. &S. 79-2 m. IS -87 j» i6-o2 '579 in. i6-i6 »» 15-61 „ 16-31 >i ■02 ,, •04 31- 15-15 ,, ■33 In. •36 ,, ■60 5n. 16-17 in. ■31 11 »» 15-48 41- 15-96 5 16-4 1783 I82I 3 8 9 30 I 5 41 2 3 5 4 65 7 72 6 69 73 59 -91 •00 82 -81 92 •93 ■85 -70 -82 ■81 02 ■58 78 ■04 77 86 07 89 58 0.1. 33. R. A. Dec. M. i" 30'" 58° 3' 7-2, 8-3 A probable increase in the distance. 0.2. 74-4 3n- 24-26 1846-80 Ma. "9 2n. -28 51-76 Oe. ■9 in. ■49 65-57 75 ■« ,, -69 6-54 -I ,, -78 7-62 59 %. 138. p. 1. 123 PI8CITIM. R. A. Dec. M. i" 29-7"' 7° 2' 7-3, 7-5 C. A, white ; B, yellowish." H,. (Mem. R. A. S., vol. i., p. 166):— "Oct. 21, 1792. Double, a pretty ob- ject, a little unequal, less than a diameter asunder." "Oct. 5, 1801. A beautiful minute object with 400." Da. (Mem. R. A. S., vol. xxxv.. p. 309): "Though the results of my observations of this star do not run very smoothly, there can be no doubt of its binary character." Sm. {Spec. Hart., p. 221) : " Though the above measures do not confirm the motion in this beautiful star, 1 have no doubt of its binarity." Se. {Catalogo di stelle doppie, p. 22). The measures made by Secchi in 1857 and 1858 seem to him to indicate increase of angle. The angle has increased (O.S., 1877). AB. H,. 10° ± ... 1801-94 2. 20-0 3"- 1-46 30-23 Sm. 19-8 •5 2-86 26-9 ■4 43'i° •3 •5 53'9i Da. 24-1 I3n. •40 41 54 29-3 3n. 53-81 2n. -26 4-09 0.2. 212-9 in. •67 41-70 3i'5 >» •63 S'73 28-s M ■66 56-73 Ma. 24-6 2n. ■53 42-75 23-1 »» •50 3-50 26-5 ,, ■44 5-03 25-7 in. •S3 50-99 166-6 ,, ... 8-04 Se. 209-7 4n. •3 5-89 207-2 2n. -2 6-74 28-2 5n. •66 62-87 29-4 3n- •51 3-96 32-2 m. •58 6-62 212-7 »» •55 7071 •2 >» •53 2-69 317 •38 6-07 Se. 29-1 3n- 'f 57-89 32-2 in. ■85 66-07 M. 3o'4 »> •24 2-02 Ta. 28-5 2n. •53 5-74 26-4 in. •74 6-84 •9 »» 7-04 32-6 j> •30 72-77 W. &S. 31-0 4 •42 2 07 32 '9 4 ■14 3-01 33 '2 7 •36 -81 29-9 7 •59 4-95 30-2 4 •60 -95 61. 33-1 4 •3 3-94 W.O. 341 in. •51 5-98 32-1 »> •38 6-00 34-2 »» •27 •09 Dob. 29-2 5n. ■39 30-8 in. •34 7-91 Schi. 212-0 j» •46 -05 Sp. 32-1 ■46 •05 PI. 30-1 A 3n- B and ■46 C. •32 W.O. 62-3 in. 22-5 75 93 63-4 AC -0 6-00 W. &S. 70-7 2 74^95 7 4 77-3> •95 MEASURES. 191 60 P. I. 127. R. A. Dec. M. I" 30-6°> -30° 31' 6,7 Perhaps the angle has increased a few Hj. 75 ;8 Ja. 82-8 2n. 3-65 2:8^ 1836-64 7-80 46-35 61 S. 142. R. A. i" 33-5'" De( 14° 58' M. 8-2, 8-4 C. white. The relative movement has been in a straight line hitherto. 2. gives the follow- ing formulae : — AA=— (i7"-77o±o"-02i)+(o"-2i9± o"-oo3) (T— 1840-13). AD = +(i7"-o55±o"-o2i)-(o"-o39± 0-003) (T-1840-13). To the proper motion of the smaller star the changes are probably due. (See the P. M., p. ccxxv.) O.S. Ea. Ma. Se. De. &S. Fl. 310-9 311-1 310-8 313"° 3«2-3 3131 3i7'4 3i3'4 3140 3J57 324-6 325 '2 3i4'i 323 'o 3I4'4 ■9 318-2 3'97 321-8 327-2 -6 326-8 in. 26-86 ,j -88 -20 25-23 ,, -48 3"- -29 in. 22-54 ,, 24-84 ,, •3S )* 23-54 It 19-52 ti •46 »» 2375 19-44 in. 23-57 2n. •54 in. 22-53 in. 21-46 20-33 3 19-0 6 17-7 in. i8-5 1828-82 29-81 -93 35-85 •96 6-90 51-88 39-95 41-70 5-74 68-77 -94 41-99 67-05 42-78 5-02 51-01 8-04 63-34 73-87 6-95 7-08 62 R. A. t. 147. Dec. -11° 55' M. 5-3. 6-9 Probably a small change in the distance. The two stars iiave a common proper motion. S. Gives +o'-03o in R. A., and +o".390 in P. D. 2. 86-0 3-53 1822-30 87-2 Sn. 4-01 31-90 88-1 in. •30 51-88 So. 89-6 2n. •19 23-97 Hr 86-1 •30 9-67 89-0 6-0 30-80 86-5 4-27 i-8i -9 •65 7-8o Da. 87-5 3-95 6-97 Ha. -2 in. 44-91 8e. 88-5 3n. 3-62 55-89 Mo. 89-6 10 -78 6-97 De. 88-2 in. 4-04 7-81 CO. 86-5 31- •00 77-87 63 6 ERIDANI. R. A. Dec. M. i" 35-2"' -56" 49' 6,6 Change in angle and distance. Dr. Doberck has lately published the following elements : — a = 81° 42' \=327 15 7= 44 40 '=0-378 Dunlop 343-1 P =117-51 years T = i8i75i a = 3" -82 Ja. Po. £1. 302-3 276-0 -5 270-0 268-7 266-4 264-8 261-1 258-1 263-2 253-4 237-3 18 18 9n. 6n. 2*5 3-65 416 •32 4-30 -14 -70 -49 4-86 5-0 1825-96 35-03 45-88 6-35 9-82 50-80 T-79 2-76 6-09 7-96 3-96 61-03 77-03 64 O.t. 35. R. A. ,b 36,„ Dec. 55° 16' M. 7. 10 Retrograde motion in angle, and increase in distance, are pretty certain. Ho. Sm. O.S. Ma. De. II4-I 9 120-0 lo-o -I in. 9-8 112-0 -81 114-2 „ -91 118-9 4 -54 I II -4 2n. -51 109-2 3n. 10-24 108-6 -29 1831-50 5-74 44-91 7-59 50-13 48-50 51-76 66-58 932 192 DOUBLE STARS. 65 OS. 34. R. A. 36" Dec. 80° 18' C. white. M. 7-3, 7-5 Prob ably a small increase in the angle. O.S. "37 De. ii5'4 •7 1257 3n- in. 0-603 obi. 1847-57 65 '93 6-6i 8-65 66 %. 158. R. A. ,h 39-8'" Certain change Probably a binary. H,. Ua Se. Be. 0.2. w. &s. Gl. 239"? 2467 •2 2512 2507 255-2 ■5 253-6 252-7 '254-5 256-5 255-8 260-8 25 7 -5 256-7 Dec. M. 32= 34' 8-3, 8-8 in angle and distance. 1828-64 31-79 3-II 45 " 50-71 1-17 •79 5-86 7-90 65-87 6-57 7-68 9-95 73-89 -89 10 -5 31- 2-13 2n. -19 In. -18 2n. -II in. In. 2-93 2n. •78 in. -99 »» •15 >i -01 »» •19 4 -05 4 1-9 67 R. A. i" 44-4"' 2. 175. Dec. 20° 31' C. white. M. 8,9 An instance of rapid rectilinear motion. H,. Ua. Se. 61. W. & S. 293-2 327-9 334-0 332-8 336-3 -7 339-3 341-8 343-2 4-8 4n. 10-43 2n. 1 1 -81 J, -93 „ 12-44 ,, 13-27 -26 14 ± 6 ■62 1783-58 1830-22 44-06 5-03 50-97 3-08 63-89 74-01 6-94 68 R. A. !>' 47"> %. 180. y ABIETIS. Dec. 18° 42' M. 4-2, 4-4 Small change in angle and distance pro- bable. Dr. Duner gives A = 8" -68 -o"-oi (/— 1850-0). 1848-91 P=359°-i- H,. i7S°-o 2n. " 1780-3 179-2 in. 1 802 -2 Hj. 177-4 „ 16-81 178-7 3n- 9'ii 22-88 S. 359-9 7n. 8-63 30-84 358-5 in. ■45 51-52 Be. 178-9 4n. •96 30-93 Ma. •3 ,, •82 41-78 •5 I3n. 9-11 3-4 179-9 2n. -53 50-97 180-5 in. 211 358-7 3n- -70 8-05 Ba. •8 6 8-98 46-95 -2 8 -62 7-93 Hit. 357-0 3n. -84 7-65 0.2. 356-4 in. •60 51-82 179-4 „ •45 70-18 Be. 359-3 4n. -71 53-47 Wi. 179-3 4 •34 7-87 -3 4 -48 62-54 •2 9 -49 4-80 Bo. 358-8 in. -79 2-94 359-6 4n. -62 3-49 Ta. -0 2n. -54 5-75 358-9 ,, 9-17 6-94 Bn. ■9 6n. 8-41 71-47 Bob. 359-1 2n. 5-92 358-6 3n- 8-32 7-89 69 t. 183. R. A Dec M i" 48- 3" 28° 3' A 7-5, B 8-2, c 8-8 In A B there has been a diminution in the angle. A C seems unchanged. A B is probably binary. A B. 2. O.S. Ma. Be. Gl. as. Ma. Be. Gl. 25-6 3"- 0-55 31-0 24-8 in. -70 -66 127 8-6 26-5 9-1 2n. -73 -70 •6 oval 2=k I 0-55 AB 2 and C. 163-4 -7 ■5 164-9 -5 162-2 165-4 -7 •7 5-07 5n. -68 in. •86 „ -63 J, -68 ,, -58 2n. -78 M -67 2 -70 1833-12 41-70 5-73 56-73 7-67 44-91 64-04 74-02 28-75 32-31 41-70 5-73 56-73 7-67 44-48 64-04 74-01 MEASURES. 193 70 Z 186. p. I. 209 PISCIUM. M. 7'2 7'2 R. A. Dec. I- 497"' i°iS' C. white. Hj {Mem. R. A. S., vol. v., p. 56) : "In contact. A division seen by glimpses. Like 1) Coronse." And in vol. viii., p. 39, he says: "Very clear and difficult, but less than 1; Coronae. Well separated, and black divisions well seen.'' Da. {Mdm. R. A. S., vol. xxxv., p. 473): " There can be no doubt that this double star, discovered by S., is a binary system. " He remarks that although it was probably not single in 1851, it was probably so in 1863. The distance has clearly diminished. The apparent orbit probably coincides very nearly with the visual ray. (O.S., 1877.) The common proper motion is + o"'09 in R. A., and +0" -22 in P. D. (2.) 1831-12 4170 51-81 30-66 1-80 3-83 41-70 6-11 55-89 7 '03 7-92 9-84 63-85 6-05 59-81 63-85 73-93 6-99 V 64-7 61-3 H,. 56-9 ■4 Sm. 62-9 O.S. 242-8 68-2 De. 252-8 258-8 Se. 87-0 83-0 85-0 96-0 Da. 81-0 85-. w. & s. Schi. 4n. r-23 in. 0-97 single 1-23 2n. 096 1-5 in. III ,, 0-82 3"- oblong in. ,, 0-4 In contact 0-3 o-S 0-3 Less than 0-5 single 71 Z 185. R. A. Dec. M. 1" SI" 74° 55' 7. 8-5 Probable diminution of the angle and in- crease in the distance. Probably a binary. 1831-95 671 39-24 44-33 52-50 7-94 72-31 4-00 Ma. Se. O.S. GI. 40-3 3n- 1-39 .34-9 It -38 36-2 I -31 35-8 in. -25 Si-o 3"- -26 .30-7 2n. 1-48 .33-8 in. 1-79 20-0 I i-S 72 t. 196. R. A. Dec. M. jb ^2-9" 20° 26' A 9, B II, C 10, D 6-5 A B is probably unchanged : the distance between A C has diminished, while that be- tween A D has considerably increased. A B. Sm. Ma. Da. De. En. Sm. Da. Kn. De. Sm. Da. Kn. 55-5 3"- 2-37 53-0 -5 54-b in. -4 53-7 -25 60-7 In. 54-5 ,, 2-24 56-8 „ -II 50-0 ,. -5 167-4 165-0 -6 166-3 -5 359-2 361-6 0-8 A C 31. 39-46 40-0 36-2 37-36 3623 35-01 3606 AD. 165-0 182-5 183-6 1832-42 4-99 45-04 6293 4-73 7-70 867 2-95 3242 4-99 6293 2-95 3-99 7-70 8-67 34-99 62-93 2-95 73 X. 197. R. A. Dec. M. i" 54'" 34° 42' C. white. 7-3. 8-3 The changes are due to the proper motion of the larger star 2. 233-6 3"- : 18-33 1833-48 Sm. '6 -3 -70 Ma. 242-9 20-07 47-12 232-2 2n. -48 51-17 -4 in. -95 2-84 -8 ,, -98 3-09 236-6 » -40 •83 234-1 )» -53 5-83 De. 2332 5". 21-67 64-79 Gl. -0 2 22-1 73-96 74 2. 202. a FISCIITM. R. A. Dec. ih ss'S™ 2° II' M. 2-8, 3-9(2.); 4, 6 (Da.); De. 4, 5-3 C. -. A, greenish white ; B blue; Da. very white, white. 13 194 DOUBLE STARS. Both stars probably vary both in colour and brightness. H, {Phil. Trans., vol. Ixxii., p. 217) : "o Piscium, Fl. ultima. In nodo duonim linoram. Oct. 19. — Double, cousiderably unequal. Both W. With 222, not quite 2 diameters of L ; with 460, about 3 dia- meters of L. Distance 5"'I23 mean mea- sure. Position 67° 23' n.p." This was in 1779- Hi {Phil. Trans., 1804, part i., p. 384) : "The position of the stars Oct. 19th. 1781, was 67 23' n.p. ; and by a mean of 3 mea- sures, taken Jan. 28 and Feb. 4, 1802, it was 63° o'. This gives a change of 4° 23' in 20 years and 105 days. The parallactic motion of a will account for the alteration, unless a proper motion should hereafter lead to a different conclusion, which, from the insulated situation of this double star, is not improbable." Hj and So. (Phil. Trans., 1824, part iii., p. 47) : " A beautiful double star ; nearly equal. This star has undergone no appreci- able change." Hj thinks that 2.'s measure, 70° 48' n.p., l8i9'9 (.see Additamenta, p. 182,) is too large, and in quoting Hj's first measure gives the date 1781-99. Sm. {Cycle, p. 49). He observes that Hj was led to suppose a retrograde motion, and adds, "All the subsequent observations, however, of H^, So., Da., S., and myself prove the fixity of these stars. " Da. {Mem. R. A. S., vol. xxxv., p. 310). He says that his later observations compared with his Ormskirk results indicate a slow diminution of angle and that a slight dimi- nution of distance is possible. He also remarks that the obliquity of position re- quires special care. Se. {Caialogo di stelle doppie, p. 47) thinks the motion in angle is certain, but that in distance doubtful. The colours of the stars he suspects of change. The movements proceed very slowly. It is, however, certain that both the angle and distance have changed. (O.2., 1877.) The proper motion in R. A. is -)- o"oo9, and — o"'oi in N. P. D. Dun^r {Mesures I^Iicromkriqnes, p. 171) : On making a graphical construction of the angles and distances, he found that both diminish, but the latter more rapidly and the former more slowly than according to the time ; that this is contrary to nature, and most probably due to accidental errors of observation ; and that the following formula represents the observations fairly well. P = 330°-3 — o°-29o (/-i85o-o)- (/— i85o-o)-. H. 337 '4 3330 o 001 13 1 1781-8 1 802 -8 Hj&So. 335-8 5 // 5-401 1821-89 ■4 7 -448 ■95 S. 336-9 3 3-94 ■96 3357 5n. •63 31-16 Be. 333 'o 77 0-93 3357 -64 1-16 3320 •76 4-85 333 -o .64 40-03 Sa. 332'i 5n. -756 32-88 330'i In. •479 42-95 •0 ,, 6 '92 328-1 2n. 3-420 53-99 8m. 3347 -6 34-92 Ma. 33 1 -9 3n. •80 41-64 332 'o 5n. ■4 2-8 331-2 4"- •5 4-5 -I 2n. ■4 5-0 329-7 >i -14 52-12 328-4 4n. -38 8-12 Ja. 333'° 3 4-04 42-94 330-2 15 -20 5-84 329-3 3-58 51-26 333-2 -49 1-94 328-4 15 -48 2-6o 327-8 3n- •22 3-96 •I 2n. ■20 6-45 326-8 24 -29 7-94 -9 19 -13 8-15 Mo. 33J-I 30 -63 44-07 326-8 12 -51 58-70 D.O. 329-5 in. ■73 47-10 Mit. ■4 2n. -08 -68 Fit. -4 6n. -40 51-75 -5 ■22 3-94 0.2. 330-4 3n. •557 187 325-0 in. 2-9!50 70-18 De. 327-5 6n. 3-59 54-28 329-4 2n. -79 5 -06 328-4 in. ■40 6-62 327-1 ,, 71 7-61 326-8 2n. ■51 8-63 3257 »> -2 63-76 326-6 311. •04 4-08 325-7 2n. -17 5-52 -7 3n. -II 6-56 -I in. 2-96 7-61 ■5 ,, 3-12 8-07 -7 )> ■34 ■65 -7 ,, -12 9-66 •2 >> -12 70-76 •Q >» -21 1-64 -7 ,, -23 2-67 •7 ,, -15 4-68 -Q ,, -04 5 -08 Wi. 331-5 2n. -41 56-09 Se. 327-8 31- •352 -16 Au. -9 -56 61-18 M. 329-6 in. ■15 -90 3232 ,, -06 8-84 324-3 ,, -13 72-78 323-2 ,, -09 479 322-6 ,, •09 -85 •7 4n. -27 5-76 So. 324-9 2n. •30 62-92 325-3 >> -17 3-54 MEASURES. 195 Kn. 327-1 in. 3-077 1864-01 3257 3n- -237 S-47 Eng. 3285 »J •35 •08 Ta. •9 2n. -48 •76 ■8 in. •41 6-84 325-6 jj •38 70-86 3248 >i •lo 1-78 3257 »» •06 2-77 Dn. •4 in. -CX3 68-84 326-1 2n. -I 71-32 325-6 »i 2-79 2-18 W. &S. 324'4 4 ■3, ■07 -2 3 -16 3-93 325-0 4 -11 4-01 Gl. 3230 6 3-5 3-74 324-5 3 -2 -93 325-3 2 4-03 Dob. 327-2 in. ... 5-99 3252 6n. 377 6-09 324-3 3n- -23 7-83 W.O. 322-1 in. -15 6-02 -I »j -10 ■03 Schi. 324-0 j> -084 7-04 Sp. -0 -08 -05 PI. 325-9 5n. •00 •i8 75 2.2c >5 and O.t. 38. R. A Dec. M. i" 56-. m > 41° 46' 3, 5, 6* c. , jolden, blue.t The duplicity of B was discovered by 0. S. in 1842, and the following is the account given by Sm. in the Cyc/e, p. 50. After ex- pressing his conviction that 7i Andromedas (2. 205 ; H„ iii. 5) is not a binary system, he says : " Since the above was written, Mr. Baily put into my hand a letter which he had received from M. Struve in Oct., 1842, announcing the unlooked-for tidings that he had detected y Andromedse to be * Magnitudes.— O.2., in the Pulkowa obser- vations always make the n.p. star the smaller. Da. had never the slightest doubt about the sf. star being the smaller, by at least half a magnitude. On the other hand, the discoverer says the_ more he looks at the star the more astonished he is that any one could place the smaller star in the n.p. quadtant. ..• . t CoLCUHS.— H, gives Yi (H,, ni. 5), ' reddish white, and fine light sky-blue, inclining to green. H2 and So. call the large star orange, and the smaller emerald green, while, in the Mem. R.A. S., vol. vi., p. 8, the larger is called yellow, and the smaller pale blue, by Hj. De., golden and blue. Se., yellow and green. Sm., orange and emerald green. The components of the smaller star (yj) are registered pale yellow and small blue by Sm., clear blue by De., while Da. uses the following ex- pressions : " both blue ; " " both pale green, precisely the same tint." "A, green; B, deeper green.' Very pale yellow, blue;'" "greenish yellow, bluish green." triple, and that the companion is composed of two stars of equal size, separated by an interval of less than o"-5." Sm. at once sent the news to Da., who readily elongated the star in the direction s.f and n.f., "making it look like a dumpish egg." Sm. also re- ceived a letter from Challis, who could "easily recognise the small star as being double, " and also thought the components unequal. In 1843, Sm., at Hartwell, "fairly saw that the comes was not round, but elon- gated, in a direction n.p. and s.f. It was, however, so slightly oval, that, but for M. Struve's unexpected announcement, I must assuredly have overlooked it." Da. (Mem. R. A. S.. vol. xxxv., p. 311) found that his measures indicated " on the whole a decrease in the angle." O.S. {Catalogue Revu et Corrige, 1850,) says that the Pulkowa observations from 1842 to 1850 indicate no perceptible change in the position of the close stars. Se. gives no measures in his catalogue (l86o\ but in the second series he says that the companion was elongated, but not separated. The progressive diminution of the angle is manifest, and an augmentation in the distance is probable. (O.2., 1877.) A B. — No change in the relative position of this pair since its discovery in 1 777 by C. Mayer. The proper motion of A is -ftf-oo4in R. A., and -|-0"-04inN.P. D. It is worthy of passing notice that neither Messier in 1764 nor Mayer in 1776 ob- served the duplicity of A. B C. — Dun^r gives the following for- mulae : — A=o"-56+o"-07 (/- 1855-0. P = 1 12°-5 -o°-32 (t- 18600) -f o°-oo38 (^-i86o-o)2. The distance formula rests entirely on O. S.'s measures; and Duner thinks the following is better than the one given above. - =o"-50 + o"-o7(^-i855). He observes that the errors in the measured angles of position are enormous. A ^nd B+C s. 62 4 Da. 64-0 -2 Ch. 63-9 ■s 62-9 Ma. 63-0 62-4 61-9 62-6 6n. 3n- 10-33 -62 in. ■47 -61 »» •35 4A. :^I m. -02 8n. 3n- 9-83 •80 1830-02 2-94 6386 41-95 2 92 3-12 •2 Si-«5 3-22 196 Ha. O.S. DOUBLE STARS. Hit. D.O. Ja. Se. U. Bo. Kn, la. W. &I 61. W.O. Schi. 2. Da. 62-1 in. 9 '94 •8 ■60 •4 jj •88 ■4 2n. •63 61-4 ,, 70 63-0 in. 10-57 62-3 ,, •40 64-1 ,, •58 63-2 ») •21 •0 „ •30 62-8 ,, ■42 ■9 ,, ■43 •7 ,, •62 64-6 ,, •52 •3 „ •57 637 ,, ■41 65-5 ,, •50 63-8 ,, ■53 ■3 ,, ■u 64-4 )> ■46 63-8 •41 622 ,j 647 ,^ I0'20 61 4 5 •38 63-2 3n- ■47 •2 2n. •50 •5 31- ■21 64-4 in. •45 63-2 31- ■43 627 ,, •40 63-4 2n. •34 62-4 m. 9-58 631 ,, I02I 6o-6 J, •02 636 2n. ■05 •s ,, 9-86 66-4 ,, 1038 64-9 5n. ■57 626 in. ■33 638 2n. •18 •4 4n. •36 627 in. •47 611 »> •56 62-6 •12 64-5 4 ■45 ■4 2 •50 639 4 ■5 64 7 ■3 •8 4 •0 62-8 I2n. •09 ■4 y> ■56 •6 »i ■10 B C. 126-6 in. 0-51 125-8 in. •47 III-3 4n. -62 108-5 ,, ■§5 1 12-0 in. -60 108-7 5n. •53 107-7 In. -58 106-9 »» -60 1854-25 Ch. 100-2 5-01 112-5 6-19 115-1 7-23 Sm, 1200 8-22 O.S. 125-5 42-72 4-84 117-9 114-9 8-13 113-0 9-22 109-9 50-19 106-9 4-20 105-4 7-23 Ma. 116-9 910 •5 64-21 115-3 6-21 116-5 8-20 114-9 9"'7 115-7 70-18 116-9 2-18 115-2 3>3 Mit. 111-3 5'H Ja. -3 46-65 106-8 •92 116-7 53-92 113-9 4-84 De. 92-7 5-09 280-0 -89 270-8 6-56 274-0 62-80 278-4 3-12 281-5 56 22 107-4 61-85 108-8 2-71 109-1 9-77 104-8 72-77 106-6 -78 107-2 3-78 Wi. 121-7 5-76 Se. 109-7 63-13 108-5 4-14 5-67 Eo. 107-3 •3 •0 -82 Kn. 6-53 101-3 71-78 Ta. 106-3 2-03 104-2 3-81 Du. 103-0 -94 1 12-0 4-93 106-0 7-94 111-3 1-33 "3-7 5-96 iio-i 7-11 109-2 108-9 Br. 101-9 ■Wr. &S. 87-7 95-9 1842-72 105-7 •83 Gl. 93-9 7-82 98-7 53-79 102-4 4-75 •W.O. 109-3 9-81 101-8 63-86 Scbi. 104-1 5-68 Bob. 103-9 m. „ 0-15 „ -31 ■5 3n. -47 Sn. -52 4n. -47 31- -67 „ -70 ,, -63 51- -63 4n. -39 ,, •40 sn. -47 -45 -47 ■45 ■5 7n. -43 6 ■5 18 ■4 m. -5 2n. oblong wedg^. 2n. 4n. m. 3n. 4n. in. 6n. 0-5 in. wedg**. »» 0-5? 2n. •41 6n. -47 In. -45 5n. ■6 In. ■64 4n. ■59 In. •6 2n. •58 m. •64 m. -68 4n. -58 2n. •63 >» -63 »» -69 )) •65 in. -61 ,, -62 6n. -69 4 10 •5 6 3 ■46 5 -56 4 -84 m. -53 5n. •4 m. -48 1842-84 -84 3'3i •33 •55 7-13 9-69 56-84 66-21 9-84 73-17 45-15 5119 2-82 6-20 7-05 -24 8-23 62-55 46-66 52-78 3-94 6-12 8-06 4-81 •83 •88 5 -09 -8s 6-56 62-77 3-31 4-57 S-81 6-71 7-60 56-21 •90 8-99 63-49 4-02 5-67 72-67 65-76 6-84 8-68 9-39 70-12 119 2-13 ■35 3-12 4-17 68-82 72-03 3-81 6-79 3-94 4-93 7-94 4-00 7-10 •05 •71 MEASURES. 197 76 t. 208. R. A. Dec. M. 1^ 56-8"» 25° 22' 6-2, 8-4 C. A, yellow ; B, ash. The common proper motion is +o'"oi3 in R. A., and +o"o3 in N. P. D. Duner's formute are A = i"'68— o"'Oi5 (^— iSso'o). P =30°-5+°°'37 (/-iSso'o) +o°-oo32S (/-i85o-o;-. Da. Sm. Ua. Ch. 0.2. Se. Se. Eng. Da. vr.&i 61. Sob. 25-6 26 'O 25-2 4n. 27-8 301 3n- in. 307 2n. 26-8 30-2 3n- 28-8 in. 30'4 >» 32-6 347 in. 316 361 32-1 in. 29-6 »> 34-1 3". 33 9 6n. 36-3 in. 41 -2 )> •6 ») 441 )> 41 -8 ») 46-1 »» 34 '4 3n- 38-1 in. 40-6 ,, 39-0 5n. 42-0 2n. 40-1 in. 39-0 4 41-1 4n. 430 in. 77 R. A. 2h j-jm t. 216. Dec. 61° 44' C. yellow. 213 183079 •00 2 -80 1-98 3 "05 2 •36 47-90 173 9-00 •84 53 "92 2-2 38-66 I 60 42-77 75 4-12 78 5-09 ■54 5099 •42 2-IO •60 6-21 •28 62-85 •65 44-91 •60 51-76 •3 6-72 ■43 63-07 6-68 I '36 7-65 ■32 9-67 •45 7 '•59 •21 4^7i •29 6-54 ■64 56-98 "51 66-06 •90 5-01 •41 71 ^45 ■44 2-46 •32 3 '93 •4 4-93 •27 7-86 •16 8-08 M. 7-7,8-2 2. 270-s 3"- 0-59 1831-23 Ua. 265-0 in. •75 41-50 O.S. 268-8 3n. •7 5 1 •OS Se. 262-4 •43 7^63 De. 266-5 •6 67-36 78 R. A. 2" 3"' S. 221. Dec. 19° 46' C. yellowish. AB. H.. H2 & So. Da. Ua. Mo. Wi. Se. Ta. 145-7 8-08 150-2 •64 I45-7 4n. •44 -2 3n- •S8 150-1 in. ■64 148-8 ,, •95 >43'5 7n. •43 •I 2n. •15 144-1 4n. -46 147-5 7-91 144-6 SO 8-34 148-1 in. ■95 143-1 2n. •34 144-4 ») •51 •4 in. •79 M. 7-7. 8-9, 12 1783^I3 1822-06 3 1 '36 6-91 22-06 4-87 42-33 3^41 54^50 44^49 55^45 6-09 7^41 65-76 71-78 A C. ■Wi. 226-2 I in. I 6i-o I 56-09 79 2. 227. 1 TBIANGVLI. R. A. Dec. 2" 5-4° 29° 44' C. A, yellow ; B, blue. Duner gives 1847-21 A = 3"-58. P = 77°-4 - o''-o775 (/ - i" M. 5. ^'4 Hi- 85-6 2. 79-1 77-9 80-5 H, & So. 78-0 H,. 74-0 77-9 Sm, 78-1 77-9 78-8 -s Ma. 79-0 77-5 78-1 77-' 76-0 75-4 Da. 79-0 Ea. 77-1 Mo. 78-8 De. 76-9 Se. -9 Bo. 77-6 78-0 m. I 3-02 5n- ■60 3n- -68 in. •88 •60 ■6 -3 ■5 •5 •60 in. -57 2n. •44 In. -51 •55 •41 •68 -48 40 -82 6n. -91 3n. •56 3 4-38 II -OS 847-12). [781-77 1821 03 30-97 6-73 21-94 211 30-95 091 4-17 8-99 57-95 32-84 41-77 7-55 52-25 683 61-87 32-94 40-05 53-52 4-81 S-89 62-90 3-38 igS DOUBLE STARS. Bng. Dn. Fer. Dob. 80 -2 in. 4-04 76 -q 2n. 325 •2 •87 75-6 5n. •86 1865-12 70-55 293 7-85 80 2. 228. \- R. A. 2'' 6-4"' \^ 259 ANDEOMEDa:. Dec. 46° 55' C. 2., De., and Se., white. M. 67, 7'6 The angular motion is decided. The distance does not appear to have changed, unless we suppose that a maximum was reached about 1842, and that it has dimi- nished since. (O.2., 1877.) Duner gives Asin.P= - i"-059 +o"-oi2l5 (/- 1852-0) + o" -000641 (/-i852-o)\ Acos. P= +0' •i73 + 4"-oi243(^- 1852-0) - o" 000169 (/- 1852-0)-. The comparison with the measures is fairly satisfactory. From these formulas it appears that the maximum distance was reached about 1847, that the star is rapidly hastening to its minimum distance, and that it will soon become excessively diffi- cult. (Du.) 1829-16 3>7S 2-02 -20 -21 41-94 70-18 52-19 7-21 6-76 6-76 62-79 3-11 6-07 73-81 6-89 7-62 69-48 75-20 2-04 3-93 4-94 ■s- 264-0 262-2 2588 263-3 262-4 o.s. 274-7 Ka. 2996 280 -2 Oe. 284-1 281-0 286-4 •5 291-6 3044 Se. 314-9 286-1 Du. 299-5 W. &S. 3" '4 308-7 Gl. 309-0 307-2 m. 1-08 ,, -22 ,, •14 ,, 0-93 ,, 1-03 2n. •32 in. 0-86 6 111 m. 0-9 2n. 10 >> •Q )> 0-75 ,, Tl 3"- 0-95 4n. -64 ,, •52 3". •99 4" ■71 31. -52 4"- 3n- 77 2n. -6 81 2. 281. R. A. 2° 7' Dec. - 2° 57' C. yellowish blue. Rapid common proper motion, M. 6, 7-8 2. 0.2. Ma. De. -Wi. Ta. W. &S. CO. Dob. 229 -2 •9 230-2 229 O -2 228-4 -8 230-4 -6 229-8 8n. 15-47 6n. •55 2n. •09 ,, 14-73 5n. 15-36 ■35 2n. •43 3 60 4n. 5-86 2n. 1834-19 52-20 3-09 811 4-83 7-87 6577 73-94 7-79 6-07 82 1. 282. M. 7-5. 7-5 R. A. Dec. C. very white. Duner has the following formulae : — 1848 69. A = 6-49. P = 246° 8 + o°-075 (/ - 1848-69). 2. 244-1 245 -5 Ma. 246-4 0.2. ; 654 Se. 246-8 De 247-2 Mo. 245-5 Ta. 246-4 Du. 248-4 671 3". -56 •45 in. -6 3n- •56 in. •49 2n. •30 m. ■27 2n. •41 1821-00 2-86 32-03 43-67 51-82 5-98 6-83 7-96 65-84 9-86 83 R. A. 2. Ma. 0.2. Se. De. S. 234. Dec. 60° 48' C. white. 239-2 31- 0-84 2327 -82 •3 3". •87 235-6 2n. •83 231-4 3n. ■62 ■4 ii •70 220-4 5n. -6 M. 7-8, 8-7 1831-55 45-65 52-50 46-98 57-91 63-45 71-22 84 R. A. Ma. 0.2. Se. t. 236. Dec. 51° 55' 259-0 31- 0-81 2608 in. •76 258-2 2n. 1-07 257-9 in. -21 258-8 )) 0-5 M. 5. 9'3 1831-87 45"23 7-32 70-18 57-92 MEASURES. 199 85 t. 240. R. A. Dec. M. 2" io°" 23° 19' 7-7, 8-2 C. white. Duner's formulae are — 1854-50. A =4" -73. P =49°7+o°-053(/- 1853-50). 2. 48-0 Ma, 50-7 Ta. 49-2 Dn. 51-1 3n. in. »» 511. U 471 5 "03 473 -46 1832-19 44-04 65-84 72-21 86 o CETI. R. Dec. M. 2" 13-3" 3° 32' 2'S to 9'S. 9-S The period of A is about 331 days : maximum, Dec. 19, 1876 ; minimum, July 23. 1877- The proper motion of A is — o'-0O3 in R. A., and + o"-23 in N. P. D. Rectilinear motion. Cassini. 130-7 H,. So. Sm. 0.2. Po. Fl. 92-5 88-6 88-6 ■9 85-2 84-9 -6 82-2 119 no no 114 "S "5 ii6-o 115-6 24 117-9 so -I in. Il8-2 1683 1779 80 82* 1819-96 24'63 1-90 31 03 51-99 6-07 9-96 77-12 87 R. A. 2'' 12-7' t. 249. Ua. Se. 0.2. Dq. Dec. M. 44° 2' 7.- 9 C. A, very white ; B, ash. 1547 J 92 -3 188-8 192-2 189-4 191-4 187-9 192-2 191-9 3n. 2-28 . •39 2n. •ss »j ■44 in. 2n. 2-38 ■13 >» ■47 7n. -29 I83III 574 45'"7 5 1 69 S-87 62-54 57-89 69-08 73-13 * Oct. 19, 1779. Distance, i' 5o"'468. Dec. 5, 1779. Distance, i'52"*8i2, and i'5o""625, Jan. 4, 1780. Distance, i' 44"'687. Sept. 8, 178c. Distance, i' 5o"'3i3, "with the utmost accuracy." Also i' 5o"'62S. Sept. 20, 1780. Distance, i' 50". Aug. 17, 1781. Distance, i' 47" 54'". Oct. 28, 1781. Distance, i' 52" 37'". Au5. 25, 1782. Distance, i' 54" 36'". 88 R. A. 2'' 14" 0.2. Ua. Oe. OX. 40. Dec. 37° 5/ 56-0 6n. 0-59 54-7 2 •25 53 4 3". M. 7-8, 8-6 1850-64 48-75 67-57 89 R. A. 2h 1 6 -6" t. 257. Dec. 60° 59' M. 7-2> 77 C. 2. yellowish white. Considerable direct movement. The distance has perhaps diminished a little, and this seems confirmed by the recent more rapid change in angle. (O.2., 1877.) Duner observes that there are enormous discordances in the angles. He gives A = o"-47 - o"-oo8 (/ - 1850-0). Ua. 1708 162-1 161-9 169-5 171-6 1 86 -6 183-9 i8o-o 0.2. 172-3 190-8 Se. 183-3 Ue. -5 Du. 186-3 in. 0-60 2n. -5" -69 -65 In. 6 ■55 •5 4 •55 In. 2n. •5 •61 In. -52 2n. •40 obi. ,, 0-28 1829-16 30-22 2-20 6-29 41-50 51-76 2-21 6-21 46-98 70-18 57-48 63-13 9-37 90 S 262. 1 CASSIOFEiE. Dec. 66° 51' M. 4-2, 71, 8-1 R. A. jti ig-2n> C. 2. A, yellow ; B, blue ; C. blue. Dawes says, " This star is P. II. 72, and B. A. C. 744 ; but it is not Fl. 55 Cass., as H] supposed it to be." H„ Phil. Trans., vol. Ixxii., p. 219. — "Aug. 17, 1779. Double, extremely un- equal, L.W. ; S, bluish r. Distance 7" "5 single measure. Position 10° 37' s.f." And he adds, in a note, "In a future collection this will be found as a treble star of the 1st class ; the larger star having a small one preceding, easily seen with 460 and 932." Hj, Phil. Trans., vol. Ixxv., p. 645. — "Treble. 20° 30' n.p. 1782 and 1783." Hi, Mem. K. A. S., vol. i., p. 173.— "No. 65, Nov. 4, 1788, double of the 2nd class. Very unequal." 200 DOUBLE STARS. So., Phil. Trans., 1826, part i., p. 25.— "Dec. 9, 1823. Extremely difficult. Small star is decidedly blue, and bears only an indifferent illumination ; the large star may be suspected close double with 137 ; with 303 is seen such." H; writes, ' ' The position of the distant star "C was stated in 1782 at 10° 37' s.f., and in 1804 at 18° 57' s.f. It is to be pre- sumed that some mistake had been com- mitted in the earlier measure." Da. {Mem. R. A. S., vol. xxxv., p. 313). — " His observations, compared with each other and S.'s, indicate a slow diminution of the angle in the close pair, while the dis- tance may possibly have slightly increased." The position and distance of the more distant star are unchanged. Ma. (Die Fixstern-Systeine, p. 89). — He thinks both the close and the distant pair are in motion, and observes that in the projec'ion the directions of the motions are opposite. Se. (p. 22). — In A B the motion in angle is certain ; in A C there is no certain motion. The common proper motion of the three stars is — o''oo9 in R. A., and + o"'02 in N. P. D. o A B. Da. Ua. O.Z. Oe. Eo. Ta. Br. W. &S. Gl. Dn. PI. Dob. 277-2 280-9 274'4 273'5 277'4 •o 274'3 271-7 265-5 274-6 265-6 269-5 267-6 266-0 263-6 262-5 267-4 266-8 267-4 268-9 265-7 •3 266-4 ■8 268-8 265-5 267-7 265 o 6-0 4-4 265-3 6-7 57 2657 7 264-0 I 5"- In. 2n. In. 4 3n- In. 7"- 31- In. 2n. 5n. 2n. j» 41. 2 2n. 5n. 7 2 4 3 2 6 7n. f > in. '73 -85 -91 -88 ■94 2-19 ■23 "23 249 1-86 I -78 2-oS 1-95 1-45 -90 •97 -88 '■83 1-72 2-04 2-15 2- 2-25 -04 1-8 2-0 1-9 1-94 2 06 1827-27 28-27 30-22 1-26 ■27 •13 7-04 40-91 8-09 1-50 52-51 6-21 45'3S 61-59 5475 •81 •84 -91 5 '09 -90 6-49 6287 3-11 57 49 63 "95 577 8-92 72-04 ■92 3-06 3 '94 •98 4-93 0-91 6-72 ■22 AC. H,. 100-6 108-9 7-5 I779'6 1804-43 80. 106-8 7-91 25 '3° 2. 107 -I in. •57 8-22 108 -I ti •49 •27 lo6-2 It -70 30 -22 107-3 »j 74 1-26 -8 »> ■63 -27 0.2. iiri i> •55 41-21 io8-2 tj •69 2-21 II I -2 ») •87 6-20 7 ,, 75 8-21 110-7 »» •51 9-22 io8-i »» •98 55'25 109-3 »» ■92 7-22 •3 ,, -68 72-31 Ua. 108-5 4 8-45 41-50 IIQ-6 3". 7-5 52-51 I 4 -52 6-21 De. 108-1 in. 8-05 475 107-1 „ ■49 •81 109-2 )r •81 •84 ■9 ,, 73 -91 ■8 ,, ■91 5-09 •5 2n. •91 •90 108-4 5". ■79 6-49 I07S 2n. ■79 62-87 •5 ,j •86 3-11 Se. 108-9 4Q- .84 57-49 Bo. 105-6 2 •76 63-95 Ta. IIOI 2n. •31 577 H. 104-6 in. •21 8-84 108 -I ,, -00 7578 Dn. 1091 4n. 7-47 0-29 W. &S. •0 4 -81 2-92 ei. •0 5 ■9 3 94 7-5 2 •9 •98 Dob. 108-5 in. ... 1 6-22 91 t 26 9. R. A. Dec. M. ■2^ 21 I in 29° 22 7-5. 9-8 C. A, yellow ; B, ash. H,. "Oct. 8. 1781. A cluster of small stars in the Finder ; the middlemost and most north of them is. I believe, a very fine double star." Although Hj examined this object a second time on the same night, and also on the 15th and 20th, he failed to satisfy himself of its duplicity. On the 22nd, however, he readily saw it double. 2. Sm. Da. O.S. Ua. 325 3404 342-1 340-3 341-3 344-1 -I 342-5 2 3n. 1-90 2-3 1-93 •92 4n. •65 2n. -72 If -72 I78I-8 1832-36 4-II 40-96 8-63 6-39 53-90 ■09 MEASURES. 20I Mo, 345-2 2-04 8e. 3447 2n. 1-78 Ta, 334-8 ,, 2-71 W. & S. 346-1 7 1-4.8 345 -6 4 •29 PI. 342-2 2n. •6 1 1856-06 9-94 65-77 73-95 4-00 6-94 92 t. 278. R. A. Dec. M. 2" 28-3'° 68° 47' 8^4, 8^7 C. 2. and Se., white. 2., in 1827, found this object "oblong; two discs in contract." He measured it in It 27, 1831, and 1833, and then Madler took it up, giving measures in 1844, 1845- Se.. in 1857, found the components "well separated." and thought there was "motion in angle." Tliere has been no change in angle during the last quarter of a century. (O.2., 1877.) S. H, Ua. Se. 0.2. Sa. 82-0 4n. 0-43 75 ± 90-1 in. -4 single elong". 102-5 io6-6 0-3 -45 67-7 71-4 76-3 2n. 4n. -4 •62 elong^. i830^77 I -80 44-34 5-35 -65 -74 57-94 9-28 68-74 93 R. A. 2** 32" %. 288. Dec. -11° 54' C. A, yellow. M. 8, II H, 224-8 10-8 1782-7 H, 216-6 -0 1830-20 2. 213-6 3n- 11-92 1-20 Se. -7 -67 67-24 CO. 215-1 2n. 12-48 77-95 94 OX 43. R. A. Dec. 26° 6' M. 7-2, 8^8 Certain increase in distance. Probably binary. O.S. Se. 85 in. obi. 95-9 »» 0-39 90^1 )* ■5; 68 •s 3"- •98 1844-85 5-73 51-72 67-30 95 R. A. 2" 35"° 0.2. De. Da. OX 44. Dec. 42° 10' S8-6 4n. 1-47 54-2 3"- -36 53-4 »» •32 M. 7-8. 8-5 1850-24 66-98 9-51 96 t. 293. R. A. 2" 35-5"' Dec. 56° 31' C. A, yellow. B is probably variable. M. 3-4, 1 1 -7 "V 57-5 4n. 6-61 1830-87 Ua. 68-6 2 52-65 Oe. 71-2 5n. 7-67 66-06 B not seen 7-62 97 t. 295. 84 CETI. R. A. Dec. M. 2" 35-1" — I" 2' 6, 10 C. A, white ; B, lilac. Commor proper motion in R. A. — o"-oo_ and + '-050 in N. P. E . Duner 's formulae are 1850-39. A = = 4"-59- P =329°-3 -0 30 (/- 1850-0). 2 335-1 2n. 4-6 1829-82 334-2 ,, 5'' 33-99 331-6 in. 4-84 51-91 Sm. 334-5 5-0 33-97 Ma. 329-2 ,, 4-27 53-09 330-1 in. K" 8-11 O.S. 326-5 3n. 4-81 6-53 Se. 330-6 2n. -57 8-03 De. 324-7 3". -63 63-97 Du. 323-3 2n. -34 8-84 ■w. &S. 324-1 4 -7 72-08 Gl. 325-0 5 -7 3-94 CO. 323-7 31- -49 7-84 Dob. 325-0 •75 -84 98 t. 296. e FEBSEI. R. A. Dec. M. 2" 35-9" 48° 43' A4, B 10, C9 C. A, yellow ; B, violet ; c, grey. Common proper motion of A B +o"033 in R. A., and + o"-i4 in N. P. D. 202 DOUBLE STARS. The distant star is independent of the system of Persei. Hj. 29o°o in. i3'-'52 1782-64 Hj. 292-4 16-0 1830-20 Z. 294-6 3n. 15-40 2-20 Ma. 296-2 4 15-79 52'26 O.S. 296-8 3n. 16-05 3'09 297-9 2n. -32 72-06 De. 296-4 2n. 16-37 62-97 Da. -9 16-34 4'36 W. &S. -o 3 16-5 7393 215-3 3 ^^ '93 i6-6 I AD -93 The distant star. Hj, in 1782, observed a small star about I ' south of 9 Persei. Sm. 2190 27-0? 1833-65 O.S. 210-5 66-14 51-88 ■6 -08 2-71 211-3 -II 467 215-6 68-17 69-95 99 R. A. 2'' 37-1" 2. 299. Dec 2° 44' M. 3-5. 7 C. A, yellow ; B, blue. Common proper motion R. A., and +o"-i9 in N. P. D. Sm. — o'-oii in Da. Ma. Fit. Ja. O.S. Be. 8e. M. Ta. 283-2 2-83 287-4 5n. •59 289-2 2n. •67 286-1 m. •61 280-7 2-58 ■7 374 289-0 2-6 286-8 ■72 288-8 -8 285-7 •6 289-1 •9 2S6-1 -69 287-6 ■7 •9 288-9 im. 2-72 285-5 5"- •65 289-2 I in. ■77 288-7 -61 201-6 15 -84 289-5 6 ■77 289-8 12 3-17 292-0 3n. ■7 289-2 35 •75 291-0 In. •7 287-3 8n. -92 287-5 6n. 2-9 288-3 5n. •71 2S9-1 -78 290-6 6 295-5 7 2'33 297-9 5 1825-43 32-48 6-74 41-70 28-69 3179 -85 5-89 8-92 43'i6 55 '09 33'90 6-98 7-88 41-65 2-99 9-08 38-90 4i'37 7-12 52-11 807 1-90 3-06 -09 5-06 6-14 62-94 5-84 8-82 72-86 Br. Sob. Sp. PI. 291-9 2-91 292-5 2n. ... 291-4 6n. 3 '40 290-9 2-82 291-1 3n- 73 68-80 75-98 6-08 7-08 7-3I 100 t. 300. R. A. Dec. 2" 37-5°' 38° 55' M. 8,8-4 C. white. Probable binary. s. 299-5 Ma. -8 Ta. 304-3 PI. 299-9 2n. 3"- 4 3n. 2-91 311 2-71 79 1832-80 43-62 65-89 77-02 101 R. A. 2'' 40-6" S. 305. 114 ABIETIS. Dec. 18° 52' M. 7-3- 8-2 C. S., " certainly yellow "' ; Da., "both white;" Se., "white." Hj, in 1830, says : " Beautifully separated with the whole aperture [20 ft. reflector]. Measure excellent ; taken ^vith 320 and 12 inches. 329° -4, i^"." Da. {A/em. R. A. S., vol. xxxv., p. 314) : ' ' The angle of position of these stars is slowly varying in a retrograde direction." A very decided increase of distance has also occurred. Se. (p. 23) says, "the motion appears secure and noteworthy." An increase in the distance and a diminu- tion in the angle are shown by the measures. (O.S., 1877.) S. 331 '8 in. 1-42 1829-81 -90 ... 33'i4 Da. 324-7 6n. -96 41-94 2-91 301 4 02 7-48 8-94 51-99 3-90 4-84 0.2. 325-1 „ 1-96 41-70 573 De. 322-1 3n. 19 56-77 62-83 3H9 Se. 322-2 2n. 2-56 57-89 Ta. g2i-3 4 2-46 65-89 7286 331-8 in. 1-42 333 '5 •67 327-3 ,, •67 324-7 6n. •96 326-5 in. ■93 325-7 )) -91 324-6 2n. -6 ,, 2-19 -8 m. -27 322-5 ,, -32 -4 4n. -33 321-8 in. -26 325-1 ,, 1-96 324-3 r> 211 322-1 3". 1-9 321 -8 ,, 2-53 •8 2n. •51 322-2 2n. 2-56 g2i-3 4 2-45 316-6 6 1-98 MEASURES. 203 Br. W. 4S. Fer. Dob. ScU. Sp. PI. 321-3 2-73 319-4 4 •7 320-1 4 •83 •6 3 ■6 317-5 •77 319-3 6n. 317-8 111. 3-59 3i«-7 in. 2-75 •8 •72 320-9 3n. •77 102 R. A. 2'' 42-2'° S. 311. Dec. 16° 58' Certain direct motion AB H'. log -I 2. 119-6 118-3 119-7 118-5 120-4 Da. -J Ua. -6 122-2 119-3 117-5 Se. 121 -2 128-6 O.S. 126-6 Gl. 121 -2 2-5 M. 4-9, 8-4, 10-2 in A B. 8n. in. 3-o6 »» -40 » ■25 y -40 t -31 6 6 3-24 2-84 18 3-26 4 3-36 3n. 2-94 •66 in. 3-19 5 •2 3 •0 =1- 2. O.S. AC. 109-3 -9 1 10-8 109-8 110-3 109-5 1 105 •o •6 in. 24-43 25-11 -69 •73 •44 24-94 25-12 -57 103 R. A. 2'' 44-1° S. 312. Dec. 72° 24' C. white. Certain change in A B. Duner gives, for A B, A = 3"'39 - o"-oi4 {t - 1850-0), P = i6°-3 + 0°-i3 {t - 18500); and for A C, 1851-75 A = 42" -37, P = l27°-52 + 0°-O26 {t ■ 1851-75). AB. 10-3 4 13-9 5n. 3-59 15-b •71 16-1 in. •54 'Z's -26 18-1 2n. •32 8-9 -37 22-4 2n. -3 19-5 7n. ■10 A C. 127-0 128-0 128 2n. 42-32 3"- -4 it -32 104 2" 44-3" t. 314. FEBSEI 85. Dec. 52° 30' C. white. Probably a binary. H,. 278-4 290-5 So. 291-1 Hj. 2920 S. -I 294-5 ,298 o 297-2 O.S.] -o 296-5 300-2 MS. 297 -9 De. 295-8 Se. 300-7 105 t. 326. R. A. 2" 48"" S. 216-1 Ma. 2152 217-4 Dec. 26° 24' 1830-10 2-08 44-33 57-67 66-42 57-95 62-23 72-31 4-58 31-75 71-75 3-48 in. n 1-32 "r ,, •35 ,, •51 If •55 t* -42 2n. -71 in. •63 »» •45 4 ■5.^ 3". Sep''. ft 1-46 0.2. 106 R. A. 2'' 49" X. 328. Dec. 44° 2' C. white. M. . 7-5 1782-63 1804-18 25-40 30 -20 27-21 30-22 2-20 •22 41-44 54-67 72-18 52-26 5-13 7-62 2n. 9-03 »> •35 »» 8-61 M. 7^5, 9-7 1831-46 44'44 60-32 S. Ma. 299 '3 298-6 2n. in. I 27-06 I 25-71 M. 8-5. 9 11832-18 ! 45-63 204 DOUBLE STARS. 107 2. 333. c ASIETIS, R. A. Dec. M. 2" 52-3™ 20° 51' 57, 6 C. S. and De., white. S. first measured this object in 1827. He was led to tliink that the components are variable, but was struck by the fact that the difference of the magnitudes of the two stars always remained the same, viz., from O to 0*5 of the scale. H J measured it in 1830. He says, "seen double with 320. Measured with 480 ; but measure not good, the illuminating lamp having gone out. 195°!"." Ma. measured it from 1841 to 1845, and thought that the distance had probably in- creased. Sm. (Cycle, p. 74). An increase of angle had, however, become so apparent to him in 1839, that he watched it at Hartwell, and was soon pretty sure that the companion had ** a direct orbital motion" ; and taking this at 0°'85 per annum, he thought "its revo- lution may be made in four centuries, at most.". He adds, "If we may place de- pendence on the observations as to the slight increase of distance, it will probably still widen for a few years longer, until the satellite shall have doubled the southern point of its course, which now seems to be on an ellipse shooting out from 2 in the miscrometric direction of 210°, with a major axis about thrice the length of its minor." Da. on examining his own observations, extending over 14 years, found " a decided increase of distance, with no perceptible variation of angle." Duner's formulas are — A = o"-85 + o"-o:36 (t - 1850-0). r = I96°70 -f o°-2io (/ - 1850-0) - o°-0O43 (/ - 1850-0)- + o°-oooo7 (/ - 1850-0)^ These were obtained by the gi-aphical method, aided by calculation. The co- efficients are still very uncertain. V 186-4 191-1 189-1 188-9 H,. 195-0 Sm. 193-5 1957 199-6 200-1 Ua. 194-3 196-2 •3 in. 0-51 ■57 ■51 •60 •7 ■9 i-o 3"- 071 •76 •78 [827 29 32 I 5 9 43 53 40 I 3 •61 •21 ■13 ■14 ■10 ■08 ■25 ■18 08 02 ■75 ■61 Ma. Sa. Mit. Ja. De. Mo. Se. la. En. Br. Da. Gl. -W. &I W.O. 197-9 198-1 •7 20O-1 198-2 201 -2 198-3 200-5 196-22 195-69 194-47 200-43 198-30 195-97 -61 196-32 195-55 203-9 196-1 -9 192-3 195-0 201 "O 196-3 -15 201 -I Z05-3 203-3 202-9 203-2 206-1 197-3 194-5 -8 196-2 197-4 199-3 198-3 -3 196-73 201 -I 199-0 192-4 198-8 198-3 196-7 199-0 198-4 199-9 198-7 199-8 200-0 198-0 9-7 196-3 200-5 1987 7-5 200-5 1-2 07 200-7 •6 m. 2n. 3n- in. 5n. m. j» In. 2n. 2n. in. 6 5n. 4n. in. 2n. 3"- 2n. 3"- in. 3"- in. 6 5 7 4n. in. 2n. in. 2n. m. 2 4 5 12 9 4 7 6 2n. o-8i ■84 -90 •95 •99 1-02 -06 0-84 •69 0-95 -84 -99 I 01 0-88 -86 ■75 -77 71 •86 0-69 1-08 -08 wedge 10 10 07 0-8 III -04 -08 -13 0-98 0-87 1-09 1-38 •05 1-052 1-34 I 02 -03 -17 -12 •09 ■14 i-o -07 1-26 -5 -69 10 -44 •23 •36 1-52 ■18 I847-I2 9-96 52-72 3-09 6-08 ■21 8 -08 62-39 40-09 I -45 2-10 3-01 4-00 6-91 7-62 9 00 53-99 41-70 2-21 6'I7 7-19 8-21 9-14 6-77 53-49 •68 4-81 •83 •92 -97 5-13 •85 6-26 62-81 3-12 5-93 7-14 8-66 70-76 56-03 ■57 66-07 S-71 6-86 72-86 66-69 8-78 •68 9-18 71-17 2-18 4-17 5-18 0-65 3-94 1-95 2-17 •86 •92 3-14 5-09 7-09 6-06 •06 MEASURES. 205 w.o. Sob. Schi. Sp. 201-8 2n. I -14 204 '6 »» ■20 1981 8n. -52 197-6 In. •169 7 •17 [876-06 ■12 ■09 7-06 •07 108 R. A. 2'' 53= 2. Ma. O.S. Se. S. 334. Dec. 6° 10' 322-8 3"- 1-59 32s '2 in. ■58 3147 2n. •ss 322-5 3". •ss M. 77, 8-2 1830-94 42-97 9-84 57-02 109 R. A. 2'' 54"" O.S. Ua. Se. O.S. 49. Dec. 17° 32' 71-1 65-2 4n. 1-71 I -2 3". 76 M. 7, 10 1846-80 52-1 66-24 110 t. 336 R. A. Dec. M. 2" 54-1'° 31° 56 6-5, 8 Angle unchanged ; distance augmented. 2. 1-5 3n. 8-19 1831-17 Ma. 7-2 In. -61 44'95 Se. -2 2n. -35 58-03 De. -8 „ -34 -09 0.2. -3 in. -83 68-77 111 R. A. 2'- 58"" S. 346. Dec. 24° 47' 2. Ma. 0.2. Kn. Dn. 2. 0.2. Du. 265 -S 266-6 84-2 270-2 269-5 A+B AB. 6n. 073 2n. ■45 3n. 79 2n. 79 6n. •64 M. 6, 6, 10-8 1834-48 41-87 3-36 66-21 72-26 and C. 2 356-5 4n. 5-22 355 'o in. •53 3S7-I 4n. •14 1 3370 41-70 72-68 112 O.S. 50. R. A. 3" 07' Dec. 71° 6' C. white. Probably binary. M. 7-5. 7-5 0.2. Ma. Se. 232-5 2n. 0-88 228 -2 ,, -8, 2161 in. -II 56-4 0-85 302-3 in. 1-56 217-3 3n. I -10 113 R. 3" Ma. Se. S. 355. Dec. 7° 56' C. white. 114 R. A. S. 343. Dec. S^ 4-6™ 83° 34' C. yellowish. Rectilinear motion. Hj. 326-2 2... 325-4 Ma. 326 I Be. 325-2 115 R. A. 3'' 6-9" H,. Ja. Bn. CO. L 3555. 12 EBIBANI. Dec. - 29° 27' 306-1 309-6 3100 316-9 116 R. A. 3" 7"" O.S. 52. p. III. I. Dec. 65° 13' C. white. Retrograde angular motion, unchanged. Probably binary. Ma. 0.2. Se. 1847-22 50-22 75-33 42-30 51-77 67-40 148-8 5n- 27s 149-6 2n. -71 142-8 >, •65 M. 8-7, 9-5 1832-52 43-47 57-11 20 3n- 22-66 in. 238 24-95 M. 8,9 1830-50 2-60 44-34 65-00 m. 3 4-09 21 3-31 2-3 3"- -56 M. 4, 7 1835-86 47-00 56-16 74-80 7-8i 157-4 0-38 150-6 -48 154-2 -54 155-7 -43 153-3 ■57 145-6 ■56 •I -62 137-5 -51 135-6 .3n. -5 I38-S M. 6-4, 7 Distance 1843-31 5-23 6-74 7-22 8-22 57-22 62-23 75-33 66-29 72-42 2o6 DOUBLE STARS. 117 1 . 367. S. 93-7 91-0 4n. 0-75 -82 1827-16 30-16 R. A. Dec. M. 8m. 87-6 ;8 4-19 3" 7-8™ o° i8°' 8, 8 Ma. 88-0 in. 41-79 Certain indirect motion ; probably binary. 93-1 0.2. 91-1 ,1 2n. •94 2-65 3-71: 2. 28i°2 99-7 103-3 I 06 0-87 -92 1829-90 32-11 3-14 In. ft 122 t. 388. 0.2. 273-9 Ma. 95-8 " •91 ■5 41-70 1-79 R. A. Dec. M. 983 2n. -52 2-89 3" 20" 50° i' 8-2, 9-2 8e. 2665 in. -89 57-12 C. white. De. 2571 6n. 64-01 W. & S. 246-7 6 0-73 72-51 Probably a binary. 2. 108-0 in. 2-93 1828-20 118 OS. 53. 1 10 -8 I II -2 ,, -78 3-05 32-17 5-18 R. A. Dec. S" 10" 38° II' M. 7-2,8 Ma. 2089 ,> 2-82 45-64 0.2. 271-3 in. 072 1844-89 123 2. 389. 274-9 >> •64 6-09 265 ,, 64-21 R. A. Dec. M. Ma. 95-0 in. 07 51-77 3" 20-5" 58° 57' 7, 8 De. 261-6 4n. 0-88 68-18 257-9 -82 74-02 C. A, white; B, purplish. Duner's formulae are — 1852-52. A = 2"-7l P = 64°! + 0°-l25 {i - 18 119 %. 377. 50-0). R. A. Dec. M. 3" 14" 18° 45' 8-3, 8-7 2. 61-8 4n. 2-81 1831-00 2. 115-4 0.2. 121 -5 Ma. 120-6 117-S De. 120-7 3n. in. 0-823 I 013 0-95 •7 1-03 1831-66 46-13 310 7-91 68-99 Da. -7 62-7 Ma. 63-5 65-3 74-4 De. 642 3n. In. -72 •71 •82 -78 ■81 -6 3-90 7-04 54-75 43-77 52-22 61-23 57-96 In. 120 S. 380. Mo. -2 Se. 67-3 2n. •77 -85 986 -95 R. A. Dec. M. Du. 66-9 4n. -4 72-66 31 i5-3'» 8° 20' 8-3, 9-3 61. 63-3 in. -7 3-94 Probably binary. 2. 90-1 Ma. 87-6 3"- in. 1-20 0-8 1831-62 43-97 124 O.S. 54. „ "5 ,, -6 4-13 R. A. Dec. M. 84-2 87-2 " 105 -12 5-04 -08 3" 21" 67° 11' 7-2. 8-5 78-2 ,, -II 58-11 H,. 352-7 ... 1829 Se. 86-8 >) -«5 <; '°^ 0.2. 354-5 4n. 25-82 50-08 De. 75-9 -2 64-00 Ma. 174-6 in. ■71 52-26 W. & 8. 73-5 In. -26 73-93 De. 355-2 3". ■413 66-74 75-4 " 1-3 4'oo ■00 -3 70-1 " 7-09 125 Z 403. R. A. Dec. 121 S. 381. M. R. A. Dec. M. 3" 24-3" 19° 22' 8-5, 8-5 3*' 16-4" 20° 33' 7,8-7 C. white. Probably binar y. Probably a bin ary. MEASURES. 207 H,. 2. H.,. Ka. Se. Se. Gl. 172-8 ... I8I7 178-5 180-9 3n. 2n. 2-91 2 ± 3-26 176-7 178-0 tt 293 -89 -0 in. ■9 1783-05 1829-76 30-50 43'i4 57-11 65-48 74-2 126 S. 408. R. A. Dec . 3" 24-7" - 4° 41' S. 346-1 in. 1-47 348-5 „ •38 -0 „ -26 o.s. 342-5 -62 Ma. 346-7 ,, -15 Se. 338-2 2n. •24 De. -4 ,, •25 ■W. & S. 159-8 5 ■44 1 60 -8 5 -43 Gl. 3392 4 ■4 CO. 3364 2n. •34 Dob. 198-7 in. 0-95 156-5 »> M. 8, 8-2 1829-90 32-86 3-14 41-70 4-13 57-10 64-00 73-93 4-00 3-93 7-86 6-13 7-91 127 2. 400. R. A. M. Certain change Probably a binary, H,. Ma. O.S. Se. De. Gl. 283-0 281-7 2830 276-9 284-5 288-5 291-3 285-3 286-3 293-4 286-2 293-6 295-0 Dec. 59° 38' 7, 8 in angle and distance. 1827-27 31-25 -30 0-79 6-14 45-45 I -21 8-21 54-67 62-23 57-96 67-41 73-96 in. 1-64 »» -50 ») -44 2-24 2n. 1-35 -08 in. •65 jt -35 -36 jj ■00 2n. •OS 3n. ■II in. •2 128 t. 412. 7 TAUEI. R. A. Dec. M. ,h 27-3"° 24° 4' 6-6, 6-7, 10 C. S., A and B yellowish; Se., white; -Sm., A white, B pale yellow, c bluish. This is a triple star, but H, did not see that A was double. H, and So. measured A C in 1821, without detecting the du- plicity of A, their attention being no doubt drawn away by the extreme faintness of C. S. in 1827 found that A was double. Madler measured it from 1841 to 1845 ; he remarked on its difficulty, and thought that after ten or fifteen years it would cease to be separable. Smyth calls it a " fine and very difficult object," and says, "Now the first two epochs exhibited so great an orbital change, in less than forty years, as to excite much attention ; but the accordance of those of 2. and my- self indicate some error of observation or entry. In this conclusion, however, S.'s angle for 1821-95, '" 'he Dorpat observa- tions, is rejected ; since it must be deemed rather an essay than a conclusive measure- ment." Dawes {Mem, R. A. S., vol. xxxv., p. 316,) thinks that the decrease of angle con- tinues in the close pair, and that the distance remains nearly the same. Secchi in 1857 regarded the motion both in angle and distance as certain. In A B there is decided change both in angle and distance. S. [P. A/., p. ccx.tvi.) thought that the relative movement of C was explained by the proper motion of A B. This is probably not the fact. (0.2. , 1877.) AB. H,. 8m. Ma. Da. 0.2. De. En. Ta. ■W. &S. Gl. 271-0 in. ol 2728 ,, -64 274-7 »i -67 266-2 ,, -84 264-9 It -68 263-4 ,, •62 266-4 It •57 257-7 265-0 -7 ■5 -55 264-6 in. -55 254-6 tt -4 258-2 ,, ■4 257-6 ,, -4 256-7 ion. -4 -I in. 252-9 3n. -4 255-5 m. -4 253-3 tt -4 252-7 ,, -4 259-1 tt -3 263-1 31- -4 ■6 259-9 -65 262-3 in. •76 267-4 2n. -74 263-7 in. -61 241 -I »» oblong 256-8 3". 0-420 72-0 In. 71-9 2n. 6o-8 in. -55 261-9 ») 227-0 7 239-7 15 •4 254-1 4 232-0 3 -4 1827-16 9-21 31-22 2-14 -19 6-74 7-05 I -81 321 9-70 41-79 684 7-12 50-96 1-16 2-10 3-88 4-85 5- 6-19 7-06 8-11 41-96 691 I 70 2-21 50-18 73->3 56-35 62-72 3-40 4-93 5-71 72-14 3-14 4-01 3 94 208 DOUBLE STARS, and C. H,. So. Sm. Ma. 0.2. Se. Be. En. Ta. W. &S. 66-8 zo'o 63-5 in. 22-25 "2 .. ■38 62-8 JS -76 •6 ■24 56-1 21-05 61 -9 -8 60-3 in. 2250 61-5 ,, •16 607 )» •07 61 9 »> •05 59-5 ,, •12 6o-i 2n. 61-13 3n. 22 -oi ■45 in. -87 64-8 ,, 6ri 2 60-5 4 3'2 •5 I ■9 3 •3 5 2-3 •6 2 •9 129 R. A. 3" 27-6"" S. 414. Dec. 19° 25' C. white. Da. Se. Ma. Mo. Se. Ta. M. Fer. 185-6 •5 184-6 •5 1S5-2 ■3 184-2 •4 180-9 1S5-1 3n- 7'i in. 7'i5 " •55 -8 ■33 3n- in. ■37 -18 ■25 -i7 130 X. 422. p. III., EBIDANI. i783'i3 1827-16 32-16 -18 -19 21-97 33"2i 4179 51-81 69-10 72-95 3'i3 55-99 63-18 4-93 571 72-17 -86 ■92 3'i4 ■93 4-00 M. 8, 8 [829-76 46-71 57-89 43-14 58-04 8-81 6-68 65-92 6-13 73-06 M. 6, 8-2 R. A. Dec. 3'' 30-6" 0° 12' C. S., deep yellow, blue; Se., yellow, blue ; Sm., yellow, pale blue. H], III. 45, /%;-/. Trans., vol. Ixxii., p. 220 : "In constellation Tauri. nearFl. 10. Oct. 22. 1781. Double. It is near thestar siii pede et scapula dextra. Extremely unequal. L. pale r. ; S. d. Position, 35° 33' s.p." Smyth says, "This is 45°, H„ III., who by measures in 1781-83 made the position anMe 234° 27' ; but H. informs us, that by a MS. note he finds it declared that the H,. 227-5 2. 226-2 232-8 -6 231-3 So. 225-3 H,. 231-2 Sm. -8 observation is too small by 6° or 8°. Hence the first measures for future reference must be those of So., No. 431. 225° 12' 5"-8i2 1824-02. Madler {Die. Fixst. Sys. p. 95) asks whether the companion passed its aphelion about 1833. Secchi (p. 78) says, "Motion certain." Direct motion certain. — (O.2., 1877.) Duner gives — 1860-00 A = 6"-23. P = 239°-5 + o°-27 {t- 1860-0). 1781-8 22-08 32-14 •98 3-14 24-38 30-20 4-93 45-81 2-94 5-09 54-16 46-72 51-88 65-92 57-06 65-92 57-87 64-86 1-93 6-10 8-84 9-12 73-15 4-09 5-95 609 1-95 ■86 3-93 7-09 3-94 7-00 -86 Ma. Da. 0.2. Se. Ta. De. M. Du. -w. &S. Gl. PI. Dob. 255-9 235-3 236-7 239-5 233-7 238-8 239-8 237-3 240-6 238-6 240 o 234-0 237-2 239-5 242-3 243-9 246-6 -I 243-1 241-3 -2 -3 242-0 240-0 242-9 244-5 5-4 in. 6-18 J, -12 J, •09 5-58 7 ± 5-9 6-0 in. 5-64 it 5-69 in. 6-24 »» -26 3". •37 in. ■45 2n. -02 5n. -26 5-89 in. -71 2n. 6-28 in. -22 »t -63 ,, -60 ,, -40 ,, -43 4 5-9 5 6-2 5 •3 7 ■41 3 -4 3n. 5-91 2n. 131 2. 425. R. A. Dec. M. 3" 32-5'° 33° 44' 7-3. 7-3 C. very white. Duner's formulx are — A = 2" -83 — o" -0125 (/— 1850). P = io2°-5-o°-o7(/-i85o). So. H,. 98-2 1037 100 ± 103-4 102 -2 3-43 2 -89 3-23 1783-00 1823-98 6-90 3097 1-87 MEASURES. 209 S. Da. Ma. De. Se. Uo. U. Ta. 01. Dn. W. &8. 104-6 102-9 -8 101-7 102-7 102-0 103-7 •9 102-6 101-9 102-7 S 101-8 -o 102-5 100-8 IOI-9 •3 103-9 IOI-9 98-7 IOI-8 989 99'S •3 3n. 2-87 •99 3-02 2 -81 2'86 -72 310 in. ■39 •14 2n. •0 3n. 2-93 in. •94 It •70 •89 2n. •27 -61 3"- -8 •71 -62 in. -78 »> 4n. 2-33 in. •52 •44 -61 1830-16 -82 40-80 813 -66 9-98 54-03 37-09 41-79 401 511 SI -37 2-18 7-21 62-23 54-86 68-79 57-64 8-12 64-23 5 93 73-94 458 7-09 •15 •16 132 t. 436. R. A. Dec. M. 3'' 35-2 —13° 0' 7, 8-2 Rectilinear motion. Probably an optical pair. Duner has A = 3i"-70+o"-096 {/— 1850-0). P = 233°-H-o°-043 (/- 18500). 2. 232-4 Ua. -6 Be. 233-4 Bu. 234-1 CO. -5 Fl. -3 4n. in. 3"- in. in. 3022 3298 33-53 349 34-1 1832-51 43-14 64-04 8-94 77-87 -08 133 t. 434. R. A. 11^. fm Dec. M. 3" 36-1°' 38° o' 7, 7-8 Rectilinear motion. Probably an optical pair. Duner has A = 29" -00 + 0" -0335 (/- 1848 o). P = 87° -70-0° -029 (/-18480). So. 2. Be. Bn. W. &S. 88-4 -2 87-2 •I -o -4 3"- 5n. in. 28-43 34 2955 ■7 J 30-23 •22 1824-00 30-59 65-13 869 77-15 ■16 134 o.t. 61. , A. 36°' Dec. 7° 31' M. 7) 10 In 1844, 0.2. once suspected duplicity, magnitudes 7, 10 ; distance l"-2 j but on the whole was inclined to regard the star as single, and therefore rejected it from his list. De. in 1867 gave the distance i"'93, and magnitudes 7-2, 10 ; and in 1875 Romberg readily saw the companion with the meridian circle at Poulkova. 0.2. Be. 125-8 obi.? 1842-93 1-2? 4-91 3n. 1-93 67-03 135 S. 447. R. A. Dec. M. 3" 40-1° 37° 58' 7-8. 9 Change in angle and distance (0.2. 1877). Rectilinear motion. 2. 179-2 26-5 1828-15 178-3 3 n. •46 30-59 176-7 2 n. -62 611 Ma. 173-7 I n. 27-56 45-85 174-8 51-17 175-8 27-48 2-18 177-0 28-95 7-21 0.2. 175-0 26-91 060 Be. 173-2 -91 62-97 -I ■97 311 172-6 27-35 7-83 171-6 -14 73-72 136 2. 453. R. A. Dec. M. This star has not been seen double since 1830. Ma. looked for it more than twenty times in the years 1840 to 1857, but saw no trace of the companion. On the 11 th of Jan., 1876, while observing an occuUation of the Pleiades by the Moon, M. Hartwig, of the Strasbourg Observatory, noted that the disappearance of Atlas was not instan- taneous. 1827-16 30-25 1-23 41-79 •99 Ma. J07-5 29-2 in. 0-79 .-35 Single M it 137 R. A. 3° 43-1" 0.2. 65. Dec. 25° 13' M. 6-5, 6-8 14 2IO DOUBLE STARS. A system probably in rapid change. An occultation in 1865 ? Special attention should be directed to this object. O.S. Sa. Ha. Se. De. Ba. 209-2 202-9 4n. 0-74 -66 204-3 2n. -66 201 4 195- 2n. 1-04 elongd. single 29- elongd. 1846-16 47-88 52-14 9-05 65-93 6-67 71-18 4-17 139 R. A. y- 48-2-" H,. s. Ua. So. la. Sn. W. &S. CO. 2. 470. Dec. M. -3° '9' 4, 6 C. A yellow, B blue. 343-4 4-32 1781-81 346 5 in. 672 1833-14 347-6 2n. -68 -15 348-1 in. -75 4415 -I 2n. -62 5-06 3468 4 7-14 63-11 345-5 in. 5-99 5-92 342-6 „ -80 71-78 346-2 „ 69 2-97 -7 2n. -66 0-64 347'2 4 -8 3'93 ■3 2n. -77 7-90 140 R. A. 3'' 47°' 0.2. 67. Dec. 60° 45' C. A, golden ; B, green. O.S. Se. 393 43-8 3n- 1-72 •94 M. 5, 8-2 11847-18 I 66-24 141 R. A. 3" 50" S. 460. 49 CEPHEI. Dec. 80' 22' M. 5-2, 6 C. 2. A. yellow, B. bluish ; Se. both white. Secchi (p. 7) says that the motion in angle is certain. Dembowski, " Cephei 49. Couple toujours difficile." Certain change in angle. (O.S., 1877.) 1828-27 •29 32-28 •29 3-34 6-45 6-76 42-22 4-33 5 35 0-26 6-30 9-23 50-26 7-29 6443 6-49 57-90 5-19 6-71 62-85 3-08 5 '97 7-68 8-65 974 72-68 390 4-18 •83 571 2-92 324 -25 •29 2-10 3 '94 4-12 6-12 Ha. 0.2. Se. De. 348- 35° 354 355 354 355 356-: o I 4 359- 3'' I' 5' 18 22 22 10 7 8 15; 19-: 21- 23-; 25 ■■ 26-( 27 30 w. &s. 29 24 25 'I 28 61. 25 27 Sob. 29 27 5 in. 0-88 6 -80 I •94 2 •96 4 »» -86 8 3n- •86 7 -87 I in. •8 6 ,, -8s 7 2n. •90 22 4n. 74 9 in. 73 -2 •70 •3 72 -8 •97 ■4 •76 7 79 79 2n. -72 79 >> -6 31- i-o -6 4n. 0-8 •s 31- -8 -2 in. I -00 •3 0-85 7 -86 ■4 ■6 1-12 •7 0-93 -6 -87 -8 •89 ■9 •68 ■4 6 7 7 7 -6 ■4 4 •66 •9 4 75 •I 5 •86 ■3 3 -6 •3 3 -8 ■5 4n. 142 R. A. t. 483. Dec. 56-2" H,. Ua. Be. 39° 8' 1-6 31- 2-8 0-0 3-43 5-6 2n. •47 40 in. 2-5 0-4 5n. 1-67 143 R. A. 3" 59" O.S. Ua. Be. O.t. 71. Dec. 206-4 202-8 M. 8, 9-S 183052 1-86 45'i7 5323 64-64 33° 7' 2n. 098 "t could not find It. 3n- 1-08 M. 7. 9 1846-44 j 5218 67-05 MEASURES. 211 144 R. A. o.t. 531. Dec. M. 3" 59°" 37° 46' 6-s, 8-2 The small star partakes in the rapid proper motion of the principal star, the direction and amount of motion being almost identical with that of 50 Persei, which is about 12' distant. These stars deserve special attention. (O.S.) O.S. 148-5 1467 1517 142-4 2n. 3-47 in. •09 >i •45 »i 2-88 1851-16 3-18 9-iS 70-25 145 O.S. 72. R. A. Dec. M. 4" I m 17" I' 6, 9-2 Ha. 228-1 in. 4'49 1845-96 O.S. 322-8 5n. 54'5' Se. 325-3 3n. 4-37 67-44 PI. 329-6 2n. ■97 76-81 146 R. A. 4" 1-7" t. 494. Dnner has, 1852-5 P = 187° -6 - Dec. 22° 47' very white. M. A = 5"-ii. '•100 (^ - 1852-51). ?'• 80. S. Sa. Ha. Hi. Ho. De. Se. Ta. Sn. 185-9 191 -o 190-2 188-4 186-4 •7 187-0 188-2 187-9 186-8 187-4 186-9 187-5 185-8 184-6 187-9 •6 186-0 m. 4" to 8" 6-30 5-09 -06 •09 •11 5-00 -20 •37 -10 5-09 •IS •19 •65 •52 ■51 4-89 •83 1784-88 1825-79 8-19 3118 3'«9 41-98 3-13 8-13 60-08 44-08 5-78 6-74 56-05 6-78 7-39 65-95 8-98 9-I3 72-97 0-64 147 R. A. 4I' 6" O.S. Se. De. o.t. 74. 270-1 Dec. 9° 20' m 0-53 single M. 8, 8-5 1849-16 57-05 65 S. 611. Dec. 58° 29' 148 R. A. Dec. M. 4'' 7-8" 58° 29' 7-5, 8 C. 2. both white. Se. A, white, yellow; B, white, bluish. De. both white. Se. thought that the motion was certain. In 1863 De. found it "extremely difficult." Rapid angular motion. The distance seems unchanged ; but the acceleration of the angular motion since 1845 ls3» -87 -4 31- -93 -3 In. 4-13 152-9 ,, -51 153-0 ,, -40 147-6 2n. -45 143-8 ,, -26 140-4 in. •46 -6 2n. -62 133-9 in. ■27 135-7 ,, •99 1381 It 3-80 i6o-o 3 ± 147-6 2n. 4-45 127-5 3"- -36 1200 2 ± AD. 185-0 I 1 75-85 148-0 I I 37-2 AE. 312-5 I I 89-45 339-2 I I 109-9 1783-13 1824-90 5-05 36-04 27-09 50-94 1-49 3-64 4-79 6-80 7-82 6484 5-89 9-10 72-18 410 56-38 63-47 4-85 71-99 712 ■94 1783-13 1825-12 50-94 1-49 3-64 4-79 6 -80 7-82 6484 5-89 9-10 72-56 3-99 4-10 5-14 51-06 64-80 77-84 64-84 77-12 64-84 77-12 150 S. 520. R. A. Dec. M. 4" 1 1 -I" 22° 29' C. white. 8, 8 2. 0^ I0I-8 5n. 0-88 1834-16 Da. 99-0 -87 41-52 102-9 ■97 54-13 Ua. 97-6 m. ■45 41-79 102-7 3"- 1-18 4-08 0.2. 99-4 2n. 0-96 1-96 Wi. 110-5 ,, •89 56-20 Se. 102-9 in. ■63 7-11 De. 106-3 •9 68-08 151 o.t. 79. R. A. Dec. M. 4" 13"° 16° 14' 7-9. 7. 8-8 C. A, white ; B, ashy. Rapid change in angle. 0.2. 24-3 2n. 0-76 1846-06 Ua 25-2 ,, •32 8-56 27-4 m. -35 52-09 Se. 32-5 ,, •98 9 -OS De. 47-1 4n. •64 67-25 152 0.2. 80. R. A. Dec. M. 4" 15"' 42° 9' 6-5,7 0.2. 188-6 5n. 0-52 1848-44 De. 184-6 411. -5 67-97 153 R. A. 4" i6-8'° t. 535. 230 TATJEI. Dec. 11=5' M. 6-7, 8-3 C. 2. A, yellowish ; B, bluish. Se. both white. Davres {Mem. I?. A . S., vol. xxxv., p. 319) sure that the angle has decreased, and that the distance is unchanged. Se. (p. 24). The motion in angle is certain. The distance has diminished. A retrograde motion is certain. (0.2., 1877.) 1829-19 32-58 -. . . 3-14 Hy 354-1 „ 1-86 Da. ... 5n. 1-95 41-41 •83 355-0 2n. 1-96 353-4 ti ■92 352-5 in. -98 354-1 ,, 5n. 1-95 345 -S 9n. MEASURES. 213 Da. 344-6 343 '6 2n. in. // 1-92 •85 1847-04 813 157 %. 554. 3427 3"- 2n. 2 -06 54-29 •82 80 TATTBI. O.S. 3480 in. •08 170 R. A. Dec. M. 346-8 3407 11 1-97 2 -02 2-21 72-18 4b 23.3m 150 23' e-j^ 9 Ua. 351-3 It 1-76 44-12 C. yellow. Se, Ta. 345-0 341-8 343-6 2n. in. -54 2-15 56-52 65*95 9-08 The dUtance has probably decreased. The common proper motion is + o"-o6l in R. A., and — o"-o03 in N. P. D. The Be. 344-8 343-0 342-2 2n 3n.-- 1-4 •74 72-14 . 56-82 62-90 measures are very discordant, but this may be explained by the faintness and closeness of the stars, and the nebulous character of 341-8 2n -73 3-" the smaller. Ho. 346-0 ** •6 0-02 W. &S. 340-0 6 •95 72-08 S. 12-9 4n. 1-73 1831-18 339-2 4 2-09 3-«4 8m. 13-9 -6 216 340-1 4 '11 -93 ii-o -4 7-22 339-7 9 •66 ■13 13-9 -6 9-16 341-9 5 5-i8 15-2 •8 43-" 339-3 5 75 -19 Da. 9-8 -5 36-96 338-4 4 2-OI 7-09 -66 40-10 Gl. 339-7 5 1-8 3-94 10-6 3-09 59-15 W.O. 338-4 in. 71 6-11 I -41 -4 »» ■68 •II Ma. 1 8 -4 in. -45 44-17 340-8 »» •78 -12 -6 2n. -66 5-09 Sp. Schi. Dob. 335 ;6 336-7 2n. 72 ■11 7-16 -16 21-2 24-3 22-2 In. •33 •29 51-09 2-15 3-92 -9 in. •65 8-08 20-6 1-24 4-15 21-3 18-9 -37 5 -20 7-95 154 .X. 81. 21-4 O.S. 8-4 in. I -31 •61 8-21 I -8s in contact. 72-18 R. A. Dec. M. Ja. 10-2 1-50 53-14 4- IT- 33° 40' 6, 8-8 6-9 10 ■44 6-28 O.S. 53-0 4n. 4-49 1847-86 52-18 66-77 77 Dp. 10-5 "W. & 8. 14-7 II •56 -23 8-09 63-10 Ua. Se. 235-1 50-4 in. 30- -13 -37 6 -29 7007 158 o.t. 85. 155 .t. 82. R. A. Dec. M. R. A Dec. M. 4'' 28"' 48° 10' 7-5, 10 4'' i6- 20" -1° 41' 8-5, 11-5 by various names, e.g., " 754^ Hindmost," " Stella dominatrix," " TAe Bull's-eye," etc. S. 344-3 3n. 4-2? 1831-39 Tycho considered it to be 125 times the size Ma. 344-7 in. 45-04 of our earth, wh lie Rice lolus WOI ked it up 214 DOUBLE STARS. to 2810 times that magnitude.'' (Sm.) " Its ruddy aspect has long been noted, and old Leonard Digges, in his Prognosti- cation Everlasting, 1555, pronounces that it is "ever a meate rodde." (Sm.) "I have repeatedly seen it apparently projected on the disc of the moon, even to an amount of nearly three seconds of time, at the instant of immersion, Vfhen occulted by that body. The phenomenon seems to be owing to the greater proportionate refrangibility of the white lunar light, than that of the red light of the star, elevating her apparent disc at the time and point of contact. " (Sm. ) The proper motion of this fine star has been variously estimated : — Piazzi, + o"'04, — o"'2i ; Argelander, + o"-o8, — a"^l^ ; Bessel, + o"-i2, - o"-i5, in R. A. and Dec. respectively. The B. A. C. gives + o"-oo8 in R. A. and + o"-i5 in N. P. D. The position angle is about 36°, and the distance has changed from 95" to 1 14" since 1781. Mr. Bumham has lately discovered with the i8J-inch refractor of the Dearborn Observatory an exceedingly faint com- panion to this bright star : distance about 30"-S. So. S. Sm. 0.2. Se. Gl. Fl. Bn. 37-0 95 ,vs-i 36-2 90 •0 109 35 -9 107-9 •s III -6 34-1 II27 35-6 In. iio-9± •s 1) 114-5 •2 }f 113-9 1781-96 1802-10 25-04 3606 -98 5 1 '40 6337 7607 7-06 •9 Mr. Bumham gives the follovring mea- sures of his new companion to this star : — 111-6 I in. I 30-16 I03'3 „ -61 H2-I I „ I -27 1877-83 •86 ■99 160 R. A. 4'' 29-5" S. 567. Dec. 19° 14' C. yellow. S. Ma. Se. 302-9 3n. 1-43 •9 It •43 313-7 •68 M. :-S. 9 1831-18 43-80 63-95 161 R. A. 4'' 30-4° 2 CAUELOFASOI. Dec. 53° IS' M. 5,7-4 C. 2. A, yellow ; B, bluish ; Se. A, yellow, B, blue; Sm. A, yellow; B, pale blue. De. A, blue ; B, ashy. Dawes (^Mem. R. A. S., vol. viii , p. 78). "This star should be watched as it may be opening." Smyth (p. 105). "2. recorded it 'Vicinse'; but it is certainly wider and easier of measurement than those usually so classed by him." Certain retrograde motion. Distance probably unchanged. (O.2., 1877.) The common proper motion is -f- o"-oo2 in R. A., and + o"-ll N. P. D. 2. Ma. Sm. 0.2. Ja. Se. Se. ■HT. &S. 31 1 -4 308-3 309-2 305-3 306-9 302-7 303-5 307-9 308-7 307-2 304-6 302-4 295-3 296-7 303-7 301-9 302-7 3063 304-2 298-8 300-9 ■s 294-3 4n. .58 1829^79 2-0 30-80 in. 1-56 4-96 2n. -47 45-29 2n. •41 51-84 ,, -50 2-26 ,7 -39 5 -25 -9 34 49 -7 6-28 •5 47-21 3"- -61 6-44 in. -63 5' 29 ,, •70 66-24 •70 71-26 ID •94 53-19 3n. ... 4-95 5-09 2n. -75 •89 in. 1-6 56 ^26 2n. •87 62-83 in. ■50 4-07 2n. -73 5892 5 •54 1 75-09 162 2. 672. R. A. 4" 31 -I"" Dec. 26° 42' C. yellowish. Duner's formulae are 1852-17 A = 3" P = 207°-8 - o°-i46 {t M. 6-5. 6-5 ■42. - 1850-0). H2&S0. ^- Da. Ma. Se. Se. Mo. Bn. ■w. &S. Gl. 213-5 210-3 209-1 208 -8 210-6 •I 206-5 207-2 204-9 206-0 -4 204-7 •7 •2 205^2 31. 3n. 2n. 2^69 3-17 •92 ■4 •6 •79 -62 •60 -35 •47 •43 -40 -56 -4 •6 1822-27 30-56 23-97 32-30 6-97 43-14 58-23 6-75 68-29 57-01 •08 71-63 3-96 4-04 5-01 MEASURES. 215 163 t. 577. R. A. Dec. 4>> 34-im 37° 17' C. 2. white. Se. white. M. 77. 77 De. white. Secchi (p. 24) says there is "a very- small motion in angle. " Certain change in angle, retrograde ; dis- tance unchanged. (O.S., 1877.) S. O.S. Se. Ma. Be. W. &S. 01. Dob. 2787 272-5 91 5 90'i 79-3 8o-2 87-99 274-2 267-7 ■3 •I 265-1 266-5 264-6 85-1 •3 84-6 -8 260-9 258-6 ■9 84-7 2-1 2-5 260-9 259-7 83-17 76-55 3"- 1-58 •5 in. ■68 »» •79 If •S3 it -70 3n- ■63 •64 m. -«3 2n. •61 in. •67 ,, •90 »» ■66 »» -92 »» ■5 2n. -4 3n. •59 in. 4 1-43 4 -50 4 ■62 10 •47 3 •24 6 •36 in. •35 >» -4 2n. -42 in. •65 164 R. A. 4" 38-5" t. 589. Dec. 5° 4' C. yellowish white. 2. Ma. Da. De. U. Ta. ai. 165 R. A. 4" 48'° O.S. Ua. De. OX 90. 343 '9 352^9 355^3 345-6 Dec. 8° 24' 2n. In. 411. 2-06 1-8 -8 •85 1829-57 32-60 41-70 6-II 70-25 1-26 57-66 35-81 45-17 52-18 1-04 4-85 5-20 7-21 693 8-42 62-88 3-89 73-93 -95 •99 2-i6 5-09 -18 3-94 5-90 7-88 8-08 310-9 3"- 4-47 •7 2n. •41 31 1 3 302-8 •39 2952 •65 306-6 in. -82 303-5 )} •44 M. 8, 8 1831-39 43-09 6-73 63-04 5-05 6-04 7398 M. 7, 9 1845-50 9-14 52-09 66-98 166 OX 89. R. A. Dec. M. 4"' 49"° 73° S3' 6-2, 7-5 From the measures of 0.2. and De. it appears probable that the periastron passage occurred about 1870. 0.2. De. 305^9 104-23I 5n. I 0-45 oblong 11848-28 I 69-02 167 R. A. 4'' SO" OX 91. Dec. 3°o' M. 7, 7-5 Perhaps one of the stars is a variable. 0.2. 62-8 I 3n. I 0-77 11851-85 De. 240-9 I ,, I -7 I 66-61 168 t. 622. 'i- R. 4" H 2, H,. 8m. Da. Ua. 0.2. Se. De. Gl. A. 51-9 Dec. 1° 28' 185-1 179-9 182-0 180-4 175-9 181-1 179-8 183-6 174-9 176-83 -4 -o 173-2 3"- 2-64 2-4 •36 ,, "94 in. •93 »» 2-77 3"- -78 2n. •41 •45 ■7 M. 8-2, 8-2 1783-06 1832-09 29-88 33-92 40-12 2-50 3-14 5-11 58-10 46-02 58-08 66-90 76-07 169 R. A. 4" 52-1° t. 619. Dec. 50° 5' C. white. 2. Ua. De. 106 3°- 5-41 I09-I »» •63 1 10-7 in. -25 II5-I -OS M. 8-7, 87 1830-23 45-67 52-26 66-90 170 X. 615. R. A. Dec- , 4" S3-I- 73° 25' Probable increase in the angle. (0.2., 1877.) M. 8,9-8 2. 337-1 3"- Ua -8 in. De. 345-9 3"- O.S. 346-9 in. 1-26 1831-9 0-8 44-34 1-40 66-81 •41 73-35 2l6 DOUBLE STARS. Dunfei gives 171 0.2. 92. P = 1859-08 A = l"-I4. = 237°-i - i°-2o6 (/- i86o-o). R. A. Dec. M. ,, 4'' 52" 39° 13' 6, 97 O.S. 25083 3". 1-14 1844-53 249 60 2n. 0.98 9-22 // 237-80 ,, 1-24 59-22 Da. 233-3 2 92 1847-08 224-13 3". -09 70-87 0.2. 230-1 3"- -78 49-09 Ma. 258-8 in. 44-05 Ma. 226-3 in. •55 52-18 245-4 »» 52^i5 237 "4 It •66 -26 Da. »» i-'i's 48^ii De. 241 -27 3"- -82 67 '39 240-9 »> -29 54-82 De. 234-0 232-1 228-5 •25 •28 •OS 65-98 172 O.S. 93. 7-1S 814 Du. 224-6 2n. -00 919 R. A. Dec. M. 21 1 -9 )) •22 76-18 4" 54-1"' 4° 55' 7-5. 9 1846-12 Sp. 209-9 0-98 7-i8 Ma. 72-9 in. 0-82 0.2. 65-6 De. 61-9 2n. 3"- 1-37 -07 47-18 66-29 176 2 . 644. R. A 5'' 2-1 m Dec. 37° 9' M. 173 0.2. 95. 6-7,7 Probable change in angle R. A. Dec. M. s. 219-2 3n- I -61 1828-60 4" 58-4° 19° 38' 6-6, 7-2 Ma 2237 2n. •52 45-18 C. white. •2 224-1 in. 73 •64 51-04 2-i8 Probable increase of distai ice. 240-7 •50 7-24 0.2. 344-2 Ma. 347-6 3407 De. 338-2 4n. in. 3n- 3"- 0-S5 ■5 77 •5 1845-96 52-09 63-54 6-97 0.2. Du. 219-6 223-8 2277 224-1 219-1 6n. 1-79 •92 -58 -46 •66 41^22 •70 2.21 69.24 71-98 W. & S . 41-6 4 4-09 174 OX 97. 220-5 221-9 4 4 •60 79 5-09 6-12 R. A. 4" 59-3" De 22° c. 56' M. 6,7-8 Dob 222-1 -I 2n. in. •68 71 7-90 8-08 C A, yellow. Between 1848 and 1861 0.2.'s obser- vations show no trace of angular change. Yet, in 1846, the two stars were so close, that no separation could be effected by him. Probably one star occulted the other about 1844. 177 t. 634. 0.2. De. 248 159-4 round oblong in. I 0-53 elongated 1844-91 6-19 61-20 6 9 175 0.2. 98. R. A. 14 i OBIOKIS. Dec. 8° 20' M 6, 6-) Rapid retrograde orbital motion. R. A. Dec. M. S^ 2-8° 79° 4' 4-5. 7-9 0.2. finds that the following formulae represent the observations : — A A=4"-I2o±o"o38 + (o"-i523± o"-0O24) (T- 1850-0). A D = +28-583±o-o40- {o-3039± 0-0026) (T- 1850-0). Argelander (.^OKW Observations, vol. vii.) gives the annual proper motion of the principal star, — o'-036s in R. A. and + o"-l4l in Dec. The above formulae assign the following values as the apparent proper motion of the smaller star, + o'-oi70 in E.A. and — o".l63 in Dec. These are nearly equal in amount, but in opposite directions. See also the Bulletin de I'Acadhnie de St. Petersbourg, vol. v. In MEASURES. 217 vol. xix. oi this work 0. S. has the following remarks : — "The distance will be 9"*2 in 1932 if there is no physical connection : if there is true orbital motion, it will be discovered in ten or twenty years if good observations are made." 1825-10 31 '30 2'l8 •81 618 •21 •22 3-i6 6-25 45-35 58-33 63-15 6-12 8-25 70-35 3-35 5-09 •37 So. s. 346-4 348-3 •3 •0 349-2 348-9 Sm. -7 •8 Ha. Se. 349-1 350-I 3S3-I 0.2. 355-0 3562 357-7 358-0 vr. &B. 359-4 o-i Fl. 1-4 37-01 in. 34-50 -64 •46 33-47 -46 •72 33-8 2n. 3"- 30-24 26-24 Sn. in. 24-63 23-65 -06 22-51 21-67 3 •30 in. 20-29 178 R. A. S" 3" t. 629. Dec. 83° 18' M. 3-2, 1 1 -2 Certain change in angle and distance. [832-29 -30 3-23 ... -25 Ma. 3484 „ -73 45-35 De. 355-5 3"- -04 67-48 O.S. 357-6 in. 4-53 73-35 -W. & S. 359-5 3 380 75-09 342-5 in. 13-05 340-3 ,, •71 343-0 „ -08 342-7 ,, 12-80 3484 ,, -73 .355-5 3"- -04 357-6 in. 4-53 359-5 3 3-80 179 OX 100. R. A. Dec. 8° I' 0.2. Se. 247-0 244-2 250-5 253-3 249-8 in. 4-57 t* -20 ft ft 3"- •20 -26 •08 M. 7. 9-S 1845-17 813 52-22 71-18 67-45 180 R. A. t. 651. Dec. -7° 14' Rectilinear motion. M. 8, 10 Ha Be. W. & S. CO. IOI-7 2n. 10-81 •0 lO'S 83-5 2n. 1 1 08 82-6 in. -49 88-4 2n. 12-40 64-7 14-1 56-8 6 16-92 55-2 in. -54 1829-67 30-30 44-52 5-19 58-10 65-28 77-94 -95 181 R. A. 5" 6-7" 2. Sm. VLa.. Uo. Gl. 2. 655. Dec. -12° I' c. A, greenish. 359-3 12-33 360-0 .3.^8-1 13-1 337-6 6n. 12-81 -6 -81 336-9 15-0 337-7 2n. 12-60 335-4 10 13-46 337-7 6 12-76 •2 in. 14 ± M. 4-2, 10-5 1783-06 85-08 1829-05 32-25 52-25 36-93 3-56 56-08 708 76-07 182 X. 653. R. A. Dec. M. 5" 7" 32° 33' 5. 7-2 C. A, greenish ; B, bluish while. For A C, Duner gives A = i2"-i6 - o"-020 (^ — 1850-0). P = 345°-ii + o°-i4 {i - 1850-0). A B. Hi. H2 & So. 2. Sm. Ma. Da. Bo. Ta. Du. -W. &S. PI. 232-6 225-6 226-0 224-7 225-7 224-5 225-0 -I 224-6 -I •I -3 225-1 -8 226-3 223-6 226-9 -2 •7 228-0 226-3 225-8 -I 16-13 14-61 in. -62 »» •67 if -67 13-5 2n. •91 in. -87 )) •55 3n. ■45 In. -85 2n. -56 in. •65 2n. 14-91 2n. -S3 in. •86 5 •70 31- -65 2n. 15-08 5 ... 4 14-94 4 -99 31- •8 1781-83 1 822 09 9-23 30-25 218 -81 42-26 426 5-21 51-10 5-20 7-58 8-27 47-78 63-09 8-91 72-21 1-85 5-13 6-12 7-'5 -18 6-69 2l8 DOUBLE STARS. AC. 2. Ta. So. W. 4 1 342-4 ■4 3481 349'4 348-4 3"- In. 2n. m. 2n. 12-58 13-31 1 1 79 13 12 1830-55 66-04 72-17 5-i8 7-16 183 X AURIG/E. R- A. Dec. M. 5" 10-6° 40° 0' 5-2, 8-7 The motion is rectilinear : proper motion, + 0-047 in K. A., and +o"-66 in N. P. D. So. 34-6 102 I 1825-10 Sm. 302 -8 35-88 2. 290 103-5 6-21 0.2. 22-7 109-7 52-14 Fl. 139 in. 121 -8 77-13 184 X. 676. R. A. Dec. M. 5'' I2-9"' 64° 38' 7-5. 8-5 C. white. Certain change in angle and d stance. S. 283-1 in. 0-77 1831-30 S-6 ,, -85 •31 „.. 278-4 ,, •85 229 Ma. -9 41- •81 42-84 O.S. 271-6 in. •88 5-32 2808 ft -88 6-30 278-6 i» •87 7-34 271-8 »» •90 9-27 274-0 >» -91 51-27 269-7 I -10 71-30 273-1 fl •02 2-31 De. 2760 •0 63-20 185 R. A. 5" 13"° t. 677. Dec. 63° 16' C. very white. Ma. O.S. De. 279-8 281-0 282-1 274-7 278-3 273-3 278-8 268 -2 269-5 262-7 •I 265-7 I n. 1-83 ■48 -81 ■83 -67 •81 •85 :^7 4 n. •77 M. 77. 8 1831-30 •31 •32 3-14 44-34 5-32 6-30 9-27 51-27 71-30 2-31 63-«3 186 0.2. 104. R. A. S"" 14°' Dec. 46° 54' O.S. Ha. Oe. 191 -6 in. 15-73 189-8 ») -83 191 -0 )» 16-29 190-5 ;, 191-7 3n. 16-64 187 R. A. 5'' 16-6°' 2. 694. Dec. 24° 51' C. white. s. 6-9 32 2-4 Sa. 357-7 3S«-5 O.S. 359-9 3-9 Ha. 356-2 358-2 3'i7-5 60 -6 5"3 •7 VTi. i8s-8 Be. 159-8 Ta. 359-6 -6 Gl. 3S8-0 W. AS. 4-2 PI. 0-7 M. 7, " 1846-85 7-20 5127 2-26 66-81 in. 1-34 ,, •32 ,, -37 3n- ■20 2n. ■33 In. •44 >t ■41 »» -3 >» -4 »» •3 2n. ■39 ,, •52 In. -37 ,, -20 2n. •27 in. •30 •59 6 in. 1-4 8 -24 2n. •24 M. 8-2, 8-2 1827-16 8-19 33-19 41-80 3-20 6-09 7-16 3-14 4-91 5 -21 52-16 3-1S 5-21 8-10 6-20 7-12 66-04 72-14 3-98 4-10 7-08 188 h. 3752. R. A. Dec. M. S^ i6-8° —24° 54' 6, 10, 10 AB. H,. 100 ± I I 4 11835-05 C. 0. 105-0 I in. I 3-55 I 77-03 A C. Hj- I I 30 i 35-05 189 III TAURI. Dec. R. A. Dec. M. 5" 17-4°' 17° 16' 6, 9 The proper motion of A is + o'-02o in R. A., and -o"-04 in N. P. D. 80. Bm. 273-8 50-4 271-3 61-33 •2 63-0 1783-16 1825-06 32-95 MEASURES. 219 0.2. U. n. •I 65-70 •4 68-58 272-9 72-91 271-5 75-2 1839-95 52-12 62-n 77-13 190 R. A. 5'" 18-4"° ORIONIS. Dec. -2° 31' M. 4, 5 C. white, purplish .white. H„ in Phil. Trans., vol. Ixxv., p. 225, has "vi. 67, Fl. 28, 17 Orionis, double 35° 12' n.f. " H„ therefore, did not observe the duplicity of the larger star. Dawes, on the iSth Jan., 1848, discovered that it was double, using 4I in. of his 6| in. refractor. He thinks the distance may have slightly increased since 1848. (^Mem. S. A. S., vol. XXXV., p. 323.) The proper motion of the principal star is + o»-oo2 in R. A., and + o"-02 in N. P. D. 2. Sa. Ja. En. Dn. W. 4 8. Se. GI. W.O. 88-7 •6 86-2 87-0 837 87-6 89-6 884 89-8 •2 88-0 •3 87-1 83-8 877 8s-i 83-1 87-6 86-9 85-5 •3 847 85-1 86-s 87-3 88-5 84-0 85-8 88-0 86-3 ■3 857 82-4 838 single single 857 ScM. 81-8 CO. 82-6 Dob. 873 in. 0-94 gn. 093 4n. 1-08 14 1-07 10 0-75 5 0-98 10 -90 5 I -08 8 -02 4 •03 in. 0-84 2n. -89 in. •84 »» •85 2n. •97 in. •94 8 1-23 8 •30 2 •3 4 •37 4 •30 ■02 4 •34 5 -0 3 3 i-o 7 ... 6n. 3 1-25 3 ... 5 1-2 2n. ... in. I -20 »» •II tt -II >» -02 »» 0-96 3n. ■97 in. 1-12 848-11 -20 51-69 3-12 •99 6312 ■«3 606 •94 71-99 69-19 71-23 2-18 322 4-17 5-17 2-OI -04 -92 3 '07 •93 -69 •94 •99 4-09 -10 -II •12 ■13 •16 •17 8-05 9-16 6-13 •13 •18 7'i9 •94 808 191 O.S. 107. R. A. 5I' 20" 0.2. found fainter than B. 0.1 M. 6, 10-8 Dec. 17° SI' a. third star C closer and Angle B A C = 30°. Se. 04-1 in. 9-93 1847-25 3t'-4 fl 10-59 9-16 .34-2 It 9-92 52-22 3-6 31- •89 67-93 192 R. A. H,. 80. 2. Ua. De. W. &S. PI. Sob. %. 712. Dec. '.° 50' C. very white. 40-3 2 to 4 46-6 »» 45 '9 ,, 49-8 3-39 45 '4 3n. -08 •I in. 2-85 55 -4 „ •83 54-2 2n. •93 7 -89 53-0 5 m 5b-i 2n. •17 54-6 in. -04 55-2 2n. 2-90 M. 7. 9 1782-77 3-05 1 802 -06 25-10 31 16 44-12 5118 2-18 64-14 74-10 7-08 -91 8-06 193 R. A. jh 21-8" t. 715. Dec. 41° 10' C. very white. 2. Ua. 0.2. Se. ei. 206-0 4n. 0-95 202-3 -86 201-5 in. -85 2085 ,, I -03 200-6 091 202-7 »> i-i M. 8-2, 8-9 1831-47 45 '49 8-22 70-25 67-78 76-07 194 R. A. t. 716. M. 5-8, 6-6 Dec. S" 21-9" 25° 3' C. A, white ; B, bluish white. The common proper motion is + 0'-005 in R. A. , and + o" -07 in N. P. D. (B. A. C. ) Dunir gives — 1856-22. A = 4"-92. P = 198° -o + o°-079 (J 1850-0). 220 DOUBLE STARS. =,- 1928 ^■ 195-0 So. 194-0 2. 196-8 Be. 195 '4 Da. 196-3 Sm. Ha. 0.2. Se. Be. Ho. H. Bo. Ta. Bn. 01. W. 4 8. 195-5 •9 1974 ■5 199-3 198-3 197-8 •5 •I •8 •2 200-5 197-5 198-7 197-7 -6 196-3 -4 198-8 1960 199-8 201-4 200-1 4-51 5n. 4-89 4n. s-i •15 5-3 •0 -5 in. 4-98 j> 5-16 -07 411. •19 2n. •16 tt •10 4-89 in. -84 -95 -78 •71 2n. 5-10 10 4-98 •74 2n. 5-1 3"- -06 in. 4-72 6n. •91 in. •8 4 S-o 1783-74 1817-20 21-97 9-63 30-81 2-87 45-87 33-78 891 5810 43 -«4 5-21 4-17 51-52 2-17 5-22 8-98 1-85 2-16 4-85 6898 56-60 7-07 62 90 -91 3-II 617 71-32 3-98 4-10 195 %. 719. C8-9 R. A. Dec. M. S"" 22-4'° 29° 30' A 7, B 9-5, C. A, very yellow. In A B the distance has increased ; in A C it has diminished ; while the angle has probably increased in both pairs. AB. 2. 326-5 4n. 0-68 1833-47 Da. 328-0 in. •91 42-13 0.2. -5 j» •79 7-20 331-4 •1 1-20 70-25 Oe. 329-6 0-99 68-88 AC. H,. 344-9 345 ± 16-02 1782-98 90-86 So. 351-9 2n. 15-45 1825-17 2. •5 6n. 14-83 33-34 Da. •8 in. 15-20 42-13 0.2. •9 ») 14-96 7 -20 352-7 »» 15-21 70-25 De. 351-0 ■07 67-12 Ta. 344-8 in. •19 6 04 352-1 " 14-40 74-18 196 OX. 108. R. A Dec. M. S" 22" 18° I 6' 7. lo-S 0.2. Oe. 1 39 -5 1381 •5 133-0 in. 3-64 »» -61 »I •52 3". ■43 1847-25 9-16 52-22 68-01 197 R. A. 5" 24-4° t. 728. Dec. 5° 51' C. yellowish. M. 5-2, 6-7 The observations are very discordant. In spite of this, however, a diminution in angle and distance is beyond a doubt. Duner has A=o"-7S-o"oi84 (/- 1850-0). P =20i''-5— o°-255 (^—1850-0) — o°-oo439 (/- 1850-0)'. So. H,. 2. Sm. Ha. 0.2. Sa. Ja. Se. Se. Du. ■W. ftS, Gl. Sob. Sp. 217-8 216-5 203-5 214-5 200-0 204-0 205-2 -8 207-7 205-4 206-2 205-0 203-6 206-0 202-7 203-1 202-3 218-1 212-8 219-2 215-9 205-8 210-9 207-4 -4 185-3 195-2 189-6 202-4 196-2 190-1 188-3 205-1 202-4 203-6 192-2 193-6 1985 190-0 204-2 188-9 2n. In. 2n. in. 2n. in. 3n- 2n. 5n. 2 3 m. 1 to 2 ,, 1-30 -92 ■04 0-99 1-22 0-91 1-04 i-o -o 1-24 0-98 0-76 -73 0-96 -88 •74 -74 •75 •77 -68 -84 0-79 -77 •56 -76 ■57 -62 0-89 1-71 -44 0-3 0-6 -44 1782-05 1802-06 22-10 30-18 0-2I I -21 •21 •23 3-96 1-13 9-20 41-20 3-96 4-II 51-80 2-16 7-21 41-22 2-22 5-23 6-23 8-21 9-23 61-20 3-21 4-21 6-21 8-21 9-21 70-21 3-24 5-19 44-94 53 43 7-67 63-33 73-41 4-10 -14 6-24 7-19 MEASURES. 221 198 Z 727. R. A. Dec. M. 5" 25"' 44° 42' 8, 9-5 C A, yellow. Duner has 1855-25- A = 2" -20. P = 59°-S + o°io {t- 1850-0). S. 567 3n. 2-.8 1830-89 617 in. •30 44-26 62-2 It -08 5-20 Ma. 6o-7 2n. •55 52-26 Du. -I 5n. -12 71-49 199 t . 735. R. A. Dec. M. 5" 27°' -6° 35' C. white. 8-2, 9 Rectilinear mo tion. 2- 355-2 2n. 30-92 1831-15 Ma. 354-2 34-01 47-23 -2 in. •5" 51-20 De. 353-6 36-56 6672 ri. 354-3 in. 38-05 77-13 200 2 ;. 742. R. A. Dec. M. S" 29-2"' 21° 56' 7-2, 7-8 C. y< :Ilowisli white. Certain direct motion. Hi. 233-6 in. 1782-86 S. 246-3 1822-25 247-1 in. 3-i8 2819 244-2 ,, -54 31-22 247-4 ,, -22 -25 251-1 2n. -32 7-10 Bo. 248-3 2-97 26-10 Hj. 246-9 3-40 9-91 O.S. 251-0 in. •56 46-09 250-8 t> ■5t 7-i6 253-7 ,, ■28 9-24 2527 »» •41 50-19 256-1 tf -34 70-25 Da. 249-7 4n. -27 42-01 251-3 »» -26 52-64 Se. 252-5 2n. -21 6-50 Ma. 249-7 in. •47 41-22 -7 „ -27 4-91 252-9 ;, 80 S-21 -4 4n. •40 52-16 -I in. ■33 5-21 250-9 j> -03 7-21 Mo. -4 10 •51 8-45 M. 2517 •46 63-23 Ta. De. W. Gl. PI. Dob. &S. 256-3 257-2 258-r 255-8 256-6 257-1 251-7 255-9 -6 -I 256-6 254-4 256-1 in. 3-62 »» -73 t -93 , •66 1 -62 -35 4n. -67 4 •36 4 ■31 4 -4 4 •2 4n. -16 7 n. [866-09 7-19 8-96 72-14 •18 4-18 55-16 73-93 -99 -94 -98 7-II 6-06 201 t. 748. 9' OBIONIS. R. A. M. Dec. -5° 30' A 7, B 8, C 4-7, D6-3, E 11-3, F 11-3. O.S. thinks that one of the two stars E, F is variable ; and that E and F should be No. 10 of S.'s scale of magnitude. (See his Memoir on the Great Orion Nebula. ) After a very careful discussion of the measures of these stars, 0.2. comes to the conclusion that probably no considerable changes have taken place since the earliest observations. He thinks that the changes in angle indicated by the measures of A E and AF are not real, but owe their existence to the difficulty of the objects. It is possible, however, that the angle and distance in A F have both increased. " From the foregoing observations it may be gathered that in all probability not only the stars of the trapezium, but also many in the neighbourhood, are physically connected with the nebula. This is es- pecially true of the groups, which, to the naked eye, form t, &, c. Ononis. For we see that each of these groups is accompanied by a nebula." (Bond.) A B. H,. 8-78 1776-87 S. 30-8 908 182056 316 8-49 31-18 -6 -74 6-15 Ma. 323 -53 42-14 31-7 -79 5-16 35-6 in. 53-21 33-4 2n. 8-62 4-17 31-0 in. -23 8-II O.S. 32-9 in. •74 72-19 30-8 it -48 S-19 CO. 59-4 it 7-95 222 DOUBLE STARS. =1- 2. 8o. Ma. O.S. CO. Ma. O.S. CO. 8o. Ma. O.S. CO. H,. Ma, O.S. CO. o A C la'Si 1340 •62 13' 1308 •5 ■00 130-8 •45 1 32 -5 12-99 131 4 •88 133 in. ... 131-3 2n. 12-70 1307 m. -75 132-5 13-30 133-2 •3« ■2 •44 131 -3 -22 -9 1299 309-9 ... 95-5 •7 ■4 96-5 95-3 -o •I 96-9 95-1 -2 ■2 94 -S 165-0 i6i-i 162-1 165-0 162-5 -5 163-2 -3 162-3 164-3 163-4 164-4 162-8 163-0 342-2 301-0 299-1 •3 300-5 299-8 298-6 299-6 -3 300-0 -4 299-6 AD 21-15 -37 -41 2099 21-23 in. 2n. 21-38 in. -16 in. 21-41 ti -43 ,, •35 in. BC 17-1 16-74 -85 •68 •75 -78 in. 2n. 16-65 In. -30 in. 17-10 -07 16-71 •79 -80 1776-87 1820-56 31-18 6-15 24-58 42-14 5-16 53-21 4-17 -II 8-23 66-19 9-21 72-19 5-19 7-95 1820-56 3«-i8 6-15 42-14 5-16 53-21 4-17 -II 69-21 72-19 5-19. 7-95 1820-56 31-18 6-15 24-58 42-14 S-i6 53-21 417 ■II 8-23 66-19 9-21 72-19 5-19 7-95t D B 20-39 19-08 -26 -23 18-90 19-04 2n, in. 19-04 -18 -?A 776-87 820-56 3118 6-15 42-14 5-16 53-21 4-17 8-11 72-19 5-19 7-95 H,. S. So. Ma. O.S. s. Da. Ma. Ja. O.S. Ta. s. Da. 0.2. Ja. H,. Da. 0.2. * This is B C in the CO. observations, t This is A D in the CO. observations. D C // 15-21 240-s 13-70 -5 •09 -3 •34 •I 13-58 •4 12-95 •3 13-21 •3 in. ... -7 2n. 13-41 -9 in. -37 -3 13-62 243-2 -40 241-2 -33 ■5 •48 242-6 ■20 7n. 3-86 2n. 3-82 in. »> 3-68 2n. 3-98 m. 4-81 »» ■10 2n. -13 in. -29 »» -17 in. 3-32 » •47 AE. 353-6 352-5 355-0 354-8 352-0 353-1 351-0 349-5 352-2 3476 352-2 BE. 233-4 I 3"- I c p. 127-3 124-5 127-0 124-8 132-3 128-0 129-8 125-8 128-2 I3I-0 132-0 123-4 31- 2-79 in. 4-11 3-38 ■19 •73 -93 4-43 3-95 -31 -71 -94 2n. 3-26 A F. 1I7I 126-6 2n. [3] 3-12 125-9 128-8 131-5 »» 5n. 2n. 3-28 -92 •82 1776-87 1820-56 31-18 6-15 24-58 42-14 5-16 53-21 417 8-11 8-23 66-19 9-21 72-19 5-19 1832-53 41-92 218 4-91 53-02 782 8-23 6i-2i 9-21 72-19 66-09 -16 1 1832-53 1842-33 7-04 314 50-18 6-80 7-21 -82 61-20 •23 9-21 72-19 53-02 1836-50* 43-51 4666 58-85 70-70 ' The C.O- observations also give Aa ii6°'7 i877'95. Cc 35i°'o 'gs- 202 t. 749. R. A. 5" 29-9" Dec. 26° 53' C. very white. Direct motion. M. 7-1. 7-2 MEASURES. Ha. 0.2. Se. Se. Ko. 23-4 in. 0-70 •9 »» ■72 2I-S •60 25-0 »» •66 18-9 •77 230 in. •84 I6-.S ,, •61 198 »> -70 170 »« •80 191-8 3n. •6 186-4 S"- •6 190-4 in. •63 186-9 •8 1827-26 8-19 31-23 -26 44-04 6-09 -22 7-20 9-24 5676 62-98 57-11 64-20 203 R. A. sosi-e" 0.2. 0.2. 112. Dec. 37° S3' Ha. Se. 8o-8 89-0 85-8 90-6 79-8 In. 0-57 »» -69 if -67 >» ■45 3"- elong^. M. 7-3.8 1846-19 7-22 52-26 2-27 67-43 204 0.2. 113. R. A. 5' 33" 0.2. Se. Dec. 12° 57' 28-4 in. 10-13 27-7 >t -16 -3 »» V 29-0 31- 9-84 M. 7. 10-7 1843-19 9-22 S019 67-91 205 0.2. 114. R. A. 5" 34° 0.2. Se. Dec. 16° 10' 273-9 in. 2-70 275-9 »» •99 276-4 »» 3-12 279 -5 3n- 2-79 M. 7-3. 9-S 1844-90 7-16 9-22 67-95 206 R. A. 5" 34-7"" 2. 774. Dec. — 2° o' M. 2, 5-7. 10 C. A, yellow ; B, reddish olive. H„ in 1792, did not see the faint star. The proper motion of f is + o''0O2 in R. A., and + o"-03 in N. P. D. The angles increase slowly both in A B and AC. AC form an optical pair. Hi- 2. H,. Sa. 8m. Ha. Fit. Ja. 0.2. Hi. Ho. Be. ■Wi. Se. Ta. Sn. W. &S. Sp. Sob. Hi. 80. 8in. W. i m. Bob. B 147-8 «Si-3 150-5 »Si-3 149-8 -8 148-3 148-2 -4 -5 146-6 148-4 -7 •7 149-2 148-8 149-4 •6 -8 152-1 148-3 ;5 147-8 149-6 -2 150-0 146-5 151-7 149-6 152-1 149-9 151-6 148-9 154-6 149-0 151 -o -9 152-9 150-0 152-4 154-4 152-2 -8 153-8 -I 151-7 •5 157-2 154-4 AB. not seen. 6n. Sn. in. 4n. 2n. in. 11 3"- in. 3"- 2n. in. 2n. 2n. I* 4n. 16 30 31- in. 9n. 2n. in. 3". A C. 2-35 -47 -55 •73 -62 -76 -68 -70 3-00 2-67 •57 ■63 -64 -48 •5 -5 -39 -47 ■65 •57 -43 -46 -46 -38 ■65 -24 ■19 -60 -64 -64 -29 -32 ■32 -66 -63 3-06 2-45 2-45 -86 3-35 2 28 -51 -56 -38 2-37 7-0 60 -2 •8 56-0 0-7 6 59-7 9-3 60-3 •2 2n. 223 1782 1821-24 31-22 4-93 6-22 22-12 321I 0-93 1-29 2-30 2-56 5-27 41-02 2-99 7-84 53-13 4-17 39-19 46-16 1-24 3-42 4-22 5-20 51-25 -96 2-19 6-81 7-21 8-22 9-17 62-21 51-II -18 3-18 •77 4-06 I -85 2-06 4-lS 4-56 6-21 7-10 66-13 8-98 9-00 77-07 2-12 4-15 5-24 7-19 ■91 8-07 1781-77 1822-61 39-19 74 14 7-17 8-07 224 DOUBLE STARS. 207 t. 3115. Dec. 62° 45' M. 6-7, 7-8 R. A. 5" 37" C. A, white ; B, ashy white. The distance and angle have diminished S. Ua. O.S. Be. 35-6 3n. 1-68 34-5 2n. ■52 307 in. ■50 2q-q „ ■37 V6 ,, •48 28-3 ») •37 ■4 3n. ■48 1831-63 4592 ■32 6-30 9-27 72'3i 66-83 208 R. A. S" 37 '6" O.X. 115. Dec. 15° 2' M. 7, 8 C. A, yellow; B, olive. Probably a binary. O.S. De. 119-6 In. 0-79 123-6 „ ■70 127-7 »> ■72 121-6 ■82 1230 3"- •87 1844-90 6-22 9-23 50-92 67-90 209 O.S. 117. R. A. S" 40"° Dec. 30° 31' C. A, golden. M. 7. 97 O.S. 28-9 in. ll -98 1845-22 30 12-00 6-85 29 ,, 11-79 50-19 Mi. 30-2 ,, 2-27 De. 29-9 Si- 11-51 67-25 210 R. A. 5I' 41" 0.2. De. O.S. 119. Dec. 7° 57' 309 '3 in. 074 304-3 )) -60 298-1 M ■57 3'67 3"- M. 7-5. 8-3 1845-22 8-23 5222 67 '56 211 So. 503. R. Dec. M. 5° 49-1" 13° 56' A 7, B 9, c : Rapid rectilinear motion in A B. AB So. De. 134-1 120-3 119-7 118-8 Fl. 115-3 So. De. Fl. 337-3 335-8 -7 39-95 8-23 7-76 -07 5-72 A C 201-76 230-04 231-6 1825-07 73-79 4-21 5-21 7-80 1825-07 75-21 7-80 212 6 AURIGiE. R. A. Dec. M. 5" 51-5" 37° 12' 3, II, II B and C are fixed. The proper motion of A is A B. H,. Sm. O.S. H,. So. O.S. 286-0 289-0 290-9 150 ± 352-2 350-7 -3 35 ± 30-0 43-29 A C. 124-46 123-42 125-10 1782-68 1832-64 52-12 1780-74 1823-17 40-16 52-16 213 OX 124. R. A. Dec. M. 5>' 52" 12° 49' 6, 7-8 If the observation of 1873-25 (O.S.) be correct, no less than 66° of the apparent orbit have been described in 28 years. O.S. De. 308-7 in. 0-53 311-0 ty -36 242-2 ,, -66 324-0 we Iged 1845-22 6-22 73-25 65 214 O.S. 125. R. A. 5" 52» O.S. Ma. De. Dec. 22° 29' C. red 357-5 in. 1-68 360-7 ») ■56 353-5 ), ■39 253-6 ,, 03 I-I3 3n- 1-41 M. 7, 8-5 [844-90 6-19 52-22 44-21 67-59 215 Z 830. R- A. Dec. M. 5" 55-9 27° 39' 8-5, 9, lo-S C. A, yellow. MEASURES. 225 In A B there has been a slight increase in the angle, and the distance has probably diminished. Duner has 185177. A = i2"-6s. P = 25i°-4 + o°-io (/- 1850-0). AB. 1830-54 45-00 68-48 72-og 7-i8 s. 249-6 3". 1282 Ma. 250-1 in. ■37 Dn. 253-2 3"- -60 254-2 in. ■«3 W. &S. •8 4 AC -I ^ 187-7 3n- 25-21 Dn. -8 2n. ■42 •s „ •03 W. &S. 189-5 3 1 83 1 '56 68-29 72-13 7-18 216 h. 3823. R. A. CO. 1317 122-7 Dec. -31° 4' 6 in. 3 3-85 M. 9. 9 I 1835-47 I 77-13 217 ot. 131. R. A. 5" 59" O.S. Se. 277-3 272-5 282-5 Dec. 36° 16' A, blue, in. 3"- -56 M. 10-2 1846-19 : 8-21 i 66-85 218 S. 840. R. A. Dec. 5" 59-8" 10° 48 C. A, yellow. Probable angular change in B C M. A 6, B 8, c 9 AB. Ua. 0.2. Se. Be. 2. Ua. 0.2. Se. De. 246-2 2n. 20-55 1843-10 247-5 21-53 7-72 -I in. 57-11 -4 3"- B C 21-28 66-68 183-5 3"- 0-91 1830-89 181 -0 in. 44-20 179-4 2n. 0-92 7-72 I8I-5 ,, -55 57-12 172-6 3". -97 66-73 219 0.2. 132. R. A. 6'' o™ Dec. 37° 59' C. A, white. 0.2. Se. 313-95 318-63 2n. 3". 1-58 -64 M. 6-8, 10 [ 1847-20 67-61 220 OX 133. R. A. 0.2. Oe. Dec. 21° 19' 35 -o 36-7 28-9 in. 2-97 3-06 31 ■! „ 3-20 30-5 3n. 2-99 M. 6'9, lo-i 1844-90 6-22 52-26 70-25 67-95 221 LACAILLE 2145. R. A. Dec. M. 61. I •7m —48= 27' 8, 8 The angle has increased, and the dis- tance diminished. Dp. 329-0 3-0 1826-00 Hj. 342-5 -86 35-02 343-5 - 6-88 Ja. 348-5 3-22 46-94 353-1 249 51-09 3507 -82 2-73 351-5 -57 4-00 354-1 2n. -30 6-48 355-1 ,, -19 7-54 354-7 in. -18 8-17 222 R. A. 6" 2-5" Z 853. Dec. 11° 41' M. 7-8. 8-3 Rectilinear motion. Ma. Eng. De. 339-7 340-8 343 '3 345-0 346-2 347-8 346-9 24-09 1829-19 ■01 33-19 25-90 47-12 -83 54-17 26 01 8-n 27-13 63-84 26-15 4-51 223 t. 859. A. 3-2" S. Ma. Dec. 1 5° 40' 249-5 in. 31-18 248-5 »» -66 •6 »» 32-05 •4 34-01 M. 8, 8-5 1828-20 31-20 45-19 63-17 15 226 DOUBLE STARS. 224 2. 861. 229 X. 919. R. A. Dec. M. R. A Dec. M. 6" 4" 30° 46' A 7-8, I 8-2, c8-2 e"- 23- -6° 57' A 5 B5-5,c6 Probably no change in B C. In A and C. white. B4- C the distance has diminished. 2 BC. AB. i/ // 2. 130-0 3"- 7-25 1831-23 2. 318-2 41. 1-58 1830-95 Ha. 131-3 2n. •31 42-21 Ua. 322-4 2n. ■S9 44-28 •8 3"- -18 3-12 0.2. 3245 in. -92 1-23 132-0 2n. •44 4-41 322-6 tt •74 2-21 131-3 7n. •51 S-16 •4 -68 7-20 321-8 2n. -66 70-26 A C. AandB + C. 2 2. Ha. 122-9 124-6 3"- 2n. 9-49 -67 1831-23 42-21 123-8 31- ■97 3-12 2. 14 '6 3n. 67-14 1831-18 125-3 2n. ■43 4-41 O.S. 154 2n. 66-97 44-22 •0 7n. •85 516 ■8 -22 70-26 2. Ha. B C. 225 Z 878. 101-7 103-7 3n- 2n. 2-46 •56 1831-23 42-21 R. A. 6^ 10-2 Dec. 62° 28' M. 7-5, II ■5 105-2 102-4 3"- 2n. 7n. •73 •47 •49 3-12 4-41 S-i6 C. A, yellow, near motion. Rectil 2. 31 1 7 2n. 16-19 1831-30 230 O.X. 142 Ua. Se. 317-2 321-8 3n- 17-07 1916 45-30 65-35 R. A. 6'' 23" 2. De. Dec. 7° II' 352-2 2n. 8-56 353-5 3n. -21 M. 7, lo-S 226 2. 881. 184871 67-74 R. A. Dec. 59° 26' C. white. M. 6-4, 7-6 e" II" 231 O.S. 143. 2. 88-9 4n. 0-81 1830-28 R. A. Dec. M. Ha. 899 3n. -85 42-26 6'' 24°' 17° I' 6-8, 9-9 0.2. 95-6 I4n. -87 7-52 0.2. C. A, yellow. 227 Z 3116. 105-7 104-3 in. 7-30 -29 1844-90 7-23 102-5 tt •74 9-19 R. A. Dec. M. 105-2 »t ■86 68-21 6^ 15-9° —11° 42' 6-2, 10 Se. 103-1 3n. •88 7-29 Certain change in angle and dis 19-2 5n- 4-48 24-0 3-86 tance. 1831 16 64-73 2. De. 232 X. 918. AUBIG.S 229 (B). 228 O.S. 140. R. A. Dec. M. R. A. Dec. M. 6" 243 ^2° 33' 6-7. 77 e"" 20" 15° 36' 7,9-S C. white. C. A, blue. Duner gives 0.2. 123-4 3n. 1 2-79 1 1847-22 1850-80. A = 4" -48. Se. 119-6 411. 1 3-04 1 67-52 P = 324° -3 H r 0°1I (/ - 18 50-0). MEASURES. 327 S. So. H,. Ma. Da. He. 8e. Ho. Eng. Dn. ei. 3i8-8 4n. 4-18 319-9 2n. 5 -09 322-4 3". 4-45 319-4 ,, 5'22 324-7 2n. 4-45 325-1 »» 70 324-6 ■61 323-3 i» •54 325-4 -56 323-9 31- -42 •8 J, •20 -5 2n. ■60 325-6 »» -56 -5 in. •71 324-5 2n. -50 3253 4n. ■84 327-1 7n. •31 328-5 in. •s 1821-03 2'27 9 '26 S-i6 9-99 43-26 4-88 5-29 6 -08 52-28 5-27 2-39 615 9-34 -93 65-46 71-59 411 233 OX 148. R. A. 5h 27™ O.S. De. Dec. 37° 9' C. A, golden. 77-15 72-87 I 4n. 3°- 2-54 •63 M. 7-1, lo-i 1 1849-24 1 67-95 234 R. A. 6' 27-5"" %. 932. Dec. 14° 50' C. 2. and Se., white. M. 8-2, 8-3 Dawes Cyt/^OT. R.A.S., vol. xxxv., p. 329) thinks it is probably a binary. The mea- sures from 1 859 to 1863 confirm his opinion. Se. (p. 64) agrees with Dawes. 0.2. Change very small, if any (1877). 1828-24 30-22 3-14 0-18 2-20 44-13 5-21 SI-15 2-21 48-19 59-15 63-41 57-16 65-27 3-i8 4-10 8-21 72-13 3-93 4-13 3-94 •94 Ua. Da. Se. Se. O.S. -W. ftS. 61. 342-4 in. 2-52 .•Wi-8 ,, -44 340-9 j» •32 346-1 337 -« 2 ± -3 2n. -62 •4 in. •71 336-8 -56 335-9 •71 334 -5 -43 332-1 •56 •3 •26 -4 •04 333-2 •32 -6 3n. -28 332 I in. ■20 334-5 ), •36 33' -0 5 •29 •8 : •14 •0 8 ■30 •0 4 •25 ■6 4 •20 GI. W.O. PI. Sob. .331-6 6 2-26 ' 332-6 in. -II 331-5 ,, •28 334-3 ,, -,p 330-8 2n. •07 331-5 ,) •II 1874-13 6-09 ■OS -06 7-15 8-09 235 R. A. 6'> 29™ t. 935. Dec. 52° 24' C. white. Ma. 322-2 323-4 31. 2n. 3-41 -55 M. 8-2, 9 1829-58 44-24 236 0.2. 149. R. A. Dec. M. 6'' 29"» 27° 23' 6-5, 9 A difficult object. Rapid angular motion. 0.2. 350-73 3n. I 0-53 1848-23 De. 31657 „ I ... , 68-33 237 R. A. gh 30-2" %. 941. Dec. 41° 41' M. 7, 8 C. A, bluish white ; B, purplish white. H,. 76-0 1783-21 So. 85-1 1-66 1824-58 H,. 77-5 ... 9-88 2. -6 4n. 1-95 30-29 Ma. 79-7 in. -67 44-29 0. 2. 82-3 5n. 2-12 9-66 Se. 80-7 2n. 1-93 57-25 •9 In. 2-07 65-27 Gl. -2 ,, -2 7609 238 R. A. 6" 30-3" % 943. Dec. 23° 19' C. white. 2. Ma. De. 165-9 152-7 153-8 148-5 2n. 15-46 ,, 1640 in. 18-00 M. 8-5. 9 1829-74 44-27 5-22 64-67 239 R. A. 6" 32" t. 945. Dec. 4«° S' e. white. M. 7-1, 8 2 28 DOUBLE STARS. The direction in 1841 '23 appears to be 10° in error. It is probable that S.'s measures are also similarly erroneous. — (0.2.) Duner's formulae are 1849-45. A = o"'96. P = 256=-3 + o°-376(^- 1856-0). Ha. 0.2. De. Se. Du. 249-0 6n. 1-05 251-2 -0 2560 3n. 0-88 254-2 in. -86 260-8 2n. 1-09 257-4 i» 0-95 258-6 6n. i-ii 256-7 2n. 085 257-4 in. -82 2S8-9 2n. •85 265-2 3n. -84 1830-77 5-38 44-62 5-29 51-75 5-76 49-59 56-88 65-38 57-27 72-87 240 R. A. 6" 34-4" S. Sm. Da. Ma. 0.2. De. Ta. ■W-. &S. 61. S. 950. Dec. 10° o' C. A, green ; B, blue. M. 6, 8-8, A B. 2oS-6 6n. 2-77 -3 in. -81 206 -2 -5 209-3 3-07 212-3 in. •13 210-2 ,, 2-63 209-3 ,, -86 212-6 -98 3-21 21 1 -6 in. -06 -0 ■02 203-1 2-68 205-1 -62 210-8 -8 -9 3-0 1832-52 6-15 5-13 42-19 3->4 4-22 5-22 51-13 2-18 66-21 8-74 -99 72-14 3-52 ■53 ■^ 12-9 3n- 16-58 31-53 Sm. 150 15-0 5-13 Ma. '2-3 in. -89 43 ->4 0.2. 13-2 »» 16-67 60-21 De. -9 -21 8-74 241 Z 3117. R. A. 6" 34"" Dec. 9° 49 s. 93-7 Ma. 88-3 O.S. 87-5 4n. in. 5n. 1-2 0-65 •70 I-QI M. 8-9. 9-4 183270 45-96 63-22 242 R. A. 6'' 35-4" 2. 955. Dec. -7° 52' C. white- AB. Se. De. 272-6 266-5 276-3 267-4 4n. 0-88 in. ■89 ,, I 09 -0 M. A 8-7, B 9, C8-S 1830-65 6-19 57-12 69-50 A C. ii-5± I fixed. 243 2. 948. 12 LYNCIS. M. 5-2, 61, R. A. Dec. 6" 35-6" 59° 34' 5-2, 6-1, 7-4 C. 2., A B, yellowish white ; c, bluish. " This curious object, of which A and C are Piazzi's 185 and 184 of Hora VI., was discovered to be triple in 1 780, and re- gistered 6 H, I. and 22 H, III." (Smyth.) H, writes: "Oct. 3, 1780. A curious treble star. Two nearest pretty unequal. L. w ; S. w, inclining to rose-colour. With 227, about i diameter ; with 460, full J diameter of s. Position 88° 37' s.p. The 1st and 3rd considerably unequal ; 2nd and 3rd pretty unequal. The 3rd pale red. Distance from ist, 9" 23'" ; too difficult to be extremely exact. Position with regard to the ist, 32° 33' n.p." {Phil. Trans., vol. Ixxii., p. 215.) The 1st and 3rd are A C ; the close pair A B. H, and So. {PAii. Trans., 1824. pt. 2, p. 95.) "Triple; A of 7th mag., B of 7J. C of 9th mag. The distant star C is decidedly blue." "The position of the nearer star has sustained a remarkable change, while that of the more distant has scarcely altered. This star, therefore, deserves particular at- tention." He then remarks that if the observed angular motion should continue uniform, "the lapse of 57 year.^ will bring the three stars into one straight line, and in 646 years a complete revolution will have been per- formed." This was written in 1823. Hj {Phil. Trans., pt. i.. 1826, p. 318,) writes: "There is a considerable change in the position of the close star since the year 1823. At that time the angle was 68^ 39' s.f. Hence it appears that the small star has continued its motion in the MEASURES. 229 direction there assigned to it ; and, if we may confide sufficiently in both data, with an accelerated velocity, for the computed motion corresponding to an interval of 2 'o years, would be — I°'I48, whereas the observations make it — 4° '18 or — 4° "3. Meanwhile, the direction of the motion is as predicted, and we may therefore regard the reality of this star's rotation as fully confirmed." Sm. (Cycle, p. 156) remarks the fixity of C, and says that a rough geometrical cast of the close pair gives "an annus magnus of nearly seven of our centuries. " Dawes {Mem. JR.A.S.. vol. xxxv., p. 330) says, "evidently binary." Hj&So. 80. Da. S. 8m. 0.0. o.s. Ch. Ka. Ko. 181-3 158-6 154 '3 157-2 153-0 -8 •3 149-5 148-4 i43'3 1537 154-3 149-5 143-7 151-9 152-7 153-6 148-4 149-2 146-3 •2 •3 147-8 146-7 143-9 ■4 14Z-3 143-9 •6 138-8 137-2 136-9 132-6 135-2 148-6 -5 149-4 147-5 145-4 146-7 •o 144-8 142-6 147-0 141-5 142-0 140-3 AB. in. 4n. 3n. 2n. 3n- 2n. in. 2n. in. Sn. 12 3"- 2n. 3"- 3n. 11 2n. 4n. 2n. ion. 2n. »» 3n. 30 12 2-59 •52 1-76 •67 1-64 -75 •72 -68 •53 •6 •6 •5 -42 •76 •58 •63 •66 •57 •62 •57 •56 •72 •52 •59 •52 •74 ■72 -84 •75 -66 •84 •77 •51 •47 •31 •59 •90 •60 •54 •56 •65 •63 -60 -87 •55 1780-76 1823-28 S-25 30-24 1-19 1-62 3->3 6-97 41-20 8-22 31-10 2-96 9-27 52-96 40-28 0-31 1-20 5-52 630 7-34 8-32 9-31 50-29 1-28 2-33 3-32 5-32 9-35 60-30 7-31 8-31 9-32 70-35 2-30 42-25 2-26 3-29 4-40 5-12 6-18 7-25 8-35 51-12 43-10 66-31 54-21 8-25 Be. Be. Ta. H. "V. ft 8. 01. Dob. 141 -4 140-7 142-S 143-0 140-0 1381 «42-3 140-1 134-3 136-3 131-4 135-7 134-6 135-8 133-3 -4 134-0 130-1 in. ... 3n- ... 2n. 1-8 ,, •55 in. -70 31. •72 •68 in. 2-04 »» 1-34 ,, ■S3 4 •84 4 •27 5 •56 2 3 3 1-7 5 •41 7n. H,. 302^5 S. 304-2 0.2. 305-1 303 1 305-8 •7 304-9 305-3 -5 304-8 -8 0.0. Ch. De. Ta. VT. ft I 01. Dob. 305-5 306-4 307-1 306-1 305-9 304-4 3060 128-2 304-0 306-8 •6 •6 305-2 •2 •9 303*9 305-2 307-0 306-3 307-9 305-8 307-7 306-5 307-2 306-9 •4 305-4 A C in. 5n. 3"- in. 2n. 3n- >i 2n. 27 3n. in. 311. 2n. f » in. 3"- 8 4 5 2 3 3 3 3 7n. [9-38] 8-67 •83 •71 •46 •55 •63 •68 •62 •59 •75 •70 •76 •90 •55 •61 •73 •50 9-42 8-74 •34 •38 •55 •80 ■80 •63 •97 911 8-58 7-2 8-76 8-6 •5 •7 1854-91 5-18 -90 6-44 62-74 3-'5 57-20 66 09 74-18 68-31 72 08 3-19 -24 •25 -25 -29 4-13 6-10 1782-34 1831-10 40-31 532 7 34 832 9-31 50-29 1-28 2-33 5-32 9-35 60-30 7-31 8-31 9-33 7035 2-30 40-42 2-25 54-9' S-18 -90 56-44 62-74 3-15 2-31 70-25 66-09 70-08 3-19 •24 •25 •25 •29 4-10 -13 6-10 244 OX 154. R. A. Dec. M. 6" 36° 40° 46' 6-7, 84 C. A, golden ; B, purple. 230 DOUBLE STARS. After reducing the angles to the equinox of 1850, and deducing the rectangular coordinates, 0.2. finds the following for- mulae for rectilinear motion : — A A = + 20" -046 ± o" '01 5 + (o" '0324 ±o"-ooio) (<— 1850) ; AD = — 2i704±o'Oi5 + (o"i42i ±o-ooio) {t - 1850); and these when compared with the obser- vations are satisfactory. 0.2. 136-65 2n. 30-41 1846-76 •35 ,, -28 8-76 133-50 in. 20-28 61-26 '3145 2n. 28-77 9-28 Se. 73 3n- 1 77 7-91 245 O.S. 155. R. A. Dec. M. 6" 38" 24° 48' C. golden. 7. 9-9 0.2. 262 '2 m. 15-20 1847-23 '3 •I " 14-82 -86 8-21 9-24 2617 ,, •76 73-24 Se. 260-4 3n. 15-36 67-86 246 a CANIS MAJORIS. (SiRIUS.) Dec. - 16° 32' R. A. Dec. M. C. A, brilliant white ; B, deep yellow. This magnificent star, the brightest in the heavens, has for thousands of years attracted the attention of mankind. Of all the stellar host Sirius stood first in the in- fluences for good and for evil which these bodies were supposed to exercise over the earth and its inhabitants. A lively and interesting account of these and other such matters will be found in Smyth's Celestial Cycle. Such being the brightness of this star, it is not surprising that it suggested to astro- nomers many speculations respecting the magnitude, distance, and relative brightness of the stars. Long before the days of accu- rate telescopic measures, attempts were made to estimate the apparent diameter of Sirius. Maginus made it 10', Kepler 4', Tycho 2',* Ricciolus 18". I'assing by the curious re- sults obtained from such estimates as these, and also from other erroneous assumptions, * Tycho estimated the apparent diameters of •tars of the second magnitude at 1' 30" : Chose of the third at 1-^^' ; those of the fourth at J'. we reach the times of Hevelius, who made the diameter of Sirius to be 6" 21'", of J. Cassini in 1717, who regarded S " *s the most correct value, and of Michell near the end of the 1 8th century, who considered that o"-o2 was too large for Sirius. Natu- rally the subject had a special attraction for our great observer Sir Wm. Herschel, and he did not fail to use the vsist optical powers his genius had created in an attempt to solve this great question. But his success was not complete : in fact, the causes which determine the size of the telescopic disc of a star were far from being understood in Herschel's day. He found that o Lyrae had a diameter of o"-35S3, a value which, as he himself suspected, probably differs widely from the truth.* The dazzling splendour of Sirius, too, early led speculative astronomers to attempt estimates of its distance, on the ground that the brightest star is most pro- bably the nearest to the earth. Gregory, Huyghens, Chesaux, Lambert, Michell, Olbers, and others made attempts in this direction, the general result being that the parallax of Sirius was less than o"-5. Wollaston by means of photometric methods deduced a parallax of l"-8. Hooke was, however, the first who em- ployed the telescope in observations for the purpose of detecting the annual parallax of the fixed stars. -Then followed Bradley, Herschel, Fiazzi (who found 4" as the value of the parallax of Sirius), Brinkley, Pond, Struve, Bessel, etc., etc. Again, when exact meridional observa- tions were made possible by the rapid pro- gress of practical astronomy, the proper motion of the stars demanded the careful consideration of astronomers. Halley was the first to note the fact of stellar proper motion, and was led to it by a comparison of the places of Sirius and other stars iu ancient and modem catalogues. J. Cassini, Bradley, Mayer, Herschel, Maskelyne, Bessel, Argelander, 0.2. , Henderson, Ma clear. Main, Peters, and others have contributed to our knowledge of this subject. The following are some of the values of the proper motion assigned to Sirius : — Piazzi — 0-51 in R.A.and - I •44inDec. Bessel -0-48 „ -1-23 „ Argelander -0-53 ,, -I '23 ,, A careful study of the path followed by Sirius led to the discovery of the fact that it was far from being a straight line ; that the apparent path was, in fact, an irregular sinuous line. Bessel found that the irregu- larity of the proper motion in R. A. was * Chacomac in 1864, operating on the disc of Sirius by means of a prismatic telescope, found no perceptible diameter whatever. MEASURES. 231 very sensible between 1755 and 1844. The earliest suspicion of want of constancy was obtained in 1834. Recent observations have confirmed this, and the periodicity of the changes both in R. A. and N. P. D. has been established. — See Monthly Notices, vol. vi., p. 156, and vol. xx., p. 20. To account for this, Bessel in 1844 suggested the existence of an invisible perturbing body belonging to the system of Sirius, and in 185 1 Peters, adopting this hypothesis, cal- culated the theoretical orbit which would satisfy the observations : he found Passage through lower apsis ... I79i"43i Mean annual motion 7°'i875 Period 5o-""oi Eccentricity 07994.* In Sept. 1861 Safford sent to Briinnow an investigation of the perturbations of Sirius : in this paper he announced the angle of position of the centre of gravity with respect to the invisible mass : he gave for 1862-1, 83°-8; yearly diminution, i°-4. Scarcely four months after this determina- tion was arrived at, Mr. Alvan Clark, using his 18J in. refractor, discovered a close companion to the bright star. The question now arose as to the identity of the new companion and Bessel's invisible disturbing body. Numerous and careful measures were made. Auwers computed the orbit, and gave the following table containing the values obtained from the elements for the quantities. D = distance of Sirius from the centre of gravity, d = distance of the hypothetical companion, assuming its mass to be in the ratio of I : 2 "05 to that of Sirius, and P — the position angle of Sirius in its orbit + 180°. D. d. P. l86l-o 3-159 2'o '255 30 "339 4'0 '412 5'0 '475 6-0 -525 7"o '567 9-64 87-86 ■93 85-81 I0-I8 8386 •41 82-01 •60 80-23 •75 78-50 •88 76-86 The last elements by this distinguished astronomer are as follows : — T = I843-27S- fl = 61° 57'-8. a = 18 54 -5. «■ = 47 8 -7. e = 0-6148. a = 2"-33i. P = 49 399 years. From these the minimum distance (2" -31, • In 1864 Auwers recomputed this orbit, and found the following results : — Passage through lower apsis .. 179.^-890 Annual motion 7^^-28475 Period 49-418 yis. Eccentricity . . 0-60x0 angle 302° -5 in 1841-84), the maximum dis- tance (ii"-23, angle 7i°-7, in 1870-13), and the following ephemeris are obtained : — 862-0 85-4 10-10 5'o 79-9 -78 8-0 75-0 11-15 71-0 70-3 •20 40 65 s 10-95 6-0 62-1 •59 8-0 58-4 •05 80-0 54-2 9'33 On comparing these with the measures observed since 1862, it will be seen that they do not agree at all well. O.S., in 1864, communicated a paper to the Monthly Notices. He says, "Accord- ing to Mr. Safford's computations, the hypothesis that the small star is in no physical connection with Sirius, and has for itself no sensible proper motion, de- mands for the same time An annual change of distance -)- o"-89 ,, ,, ,, position — 5°-8 while the hypothesis that the small star was identical with Bessel's obscure body, would imply a feeble diminution of distance, and also a diminution (but only of i°-4) in the angle of position for the same interval." The writer remarks that he does not regard the hypothesis of accidental juxtaposition as well established ; that the fact of Sir Wm. Herschel not having seen the com- panion strengthens his view ; that its light is probably variable, for in 1863 it was estimated as of the eighth magnitude, and in 1864 (March 28) it was easily seen a few minutes after sunset, when other stars of the ninth magnitude could only be seen with difficulty at greater altitudes. On the whole, he is disposed to attribute much of the uncertainty attending the measures to the existence of systematic errors in the observations. Duner gives the following formula for obtaining the corrections required by Auwers' ephemeris to bring the computed and observed angles into harmony : — dY=- S°-o - o°-48(/ - 1869-0) + o°-03 (t - 1869-0)^ He observes also that some of the mea- sures are certainly faulty, and appear to have been made with bright wires in a dark field, a practice which he condemns in double-star measures of distance ; and he recommends that the observations of the star be made either just before or soon after sunset. STARS NEAR SIRIUS. PlAzzi at the end of the last century ob- served a small star near Sirius ; he wrote. 232 DOUBLE STARS. "alia 8* magnit. prsecedit, 3" temporis, 3' ad Boream." Smyth (Cycle, p. 158) records a distant star of the tenth magnitude and of a deep yellow colour, distance 1 50", angle 45°. GOLDSCHMIDT (see Monthly Notices, vol. xxiii., 1863) in 1863 announced his dis- covery of five new stars near Sirius ; the telescope used had an aperture of 4 inches, and all the stars lay between 15" and 1' from the bright star. Dawes readily saw the star d, but failed to detect the others. Alvan Clark's comes. Marth, at Malta, observing with Lassell's fine reflector, remarked, 1865, Jan. 13, a star considerably nearer to Sirius than d. Secchi in 1865 records having seen a faint star at a distance of about 44". In 1872 Messrs. EUery, Le Sueur, and MacGeorge, observing with the Mel- bourne reflector, saw eight small stars near Sirius. Clark's Companion. A B. A.C. 8s ± Bond 846 82-8 760 Ch. 85-0 Lassell 83-9 8o-3 •I O.S. 82-5 76s 772 ■2 75-2 72-1 CliaeoTBae84'6 Eiitherfrd.8so 81 -2 Kit. 78-s 796 •2 Da. 84-9 Wi. 797 Harth •3 8e. 88-4 Tietjen Bmhns 7S"S 71-3 65-9 768 73-8 69-S Br. 747 Kriter 77-9 72'3 Vo. 7,V6 Eng 76-9 716 3n. in. 9n. 3n. 5n. 4n. 2n. 3n- in. Sn. 10 ± 10-07 9-0 10-42 9S3 -67 10-14 •92 -60 •60 ■93 •98 IO-5 ■9 ■4 -00 10-60 7-62 9 59 10-10 75 10-97 74 "■35 -26 10-78 11-23 9-0 10-95 1862-08 •19 3 '27 5-26 2-23 •28 4-15 -21 3-21 4-22 5-20 -21 6-20 7-22 2-2 -2 31 •08 •15 ■20 •23 •24 •14 •"5 5-22 6-28 7i'i6 65-25 6-20 -20 8-24 9-10 5-22 7-24 9-15 5-26 826 2. 737 m. 10-79 1865-24 •3 ,, 12-91 ■^2 Kn. 77-1 2n. 1043 6-08 W.O.* 74-3 3"- 10 -2 1 ■23 •3 2n. ■65 •25 62-7 I in. "•55 7224 58-0 If •39 4-17 56-2 »» •47 5-23 52-8 5 •35 7-«7 53 '4 5 10-95 -25 Tnttle 78-5 in. •34 66-26 Du. 68-7 ,, 11-17 9-20 64-1 2n. 10-92 71-22 S9-8 ,, II -0 218 60-8 4n. 10-57 3-22 57 -I 73 S-I9 Fechnle 60-1 31- I2-IO I -25 W. ft 8. 65-0 3 11-29 3 '93 Bu. 532 5n. 10-71 7-93 511 3°- -06 803 Smyth's Companion. 45 -o 150 1835-80 Goldschmidt's Companion, d. A D Karth 164-6 I 120 ± 1865-03 '63'9 3 ... 23 Bo. 158-9 104-24 77-87 ■5 102 '99 •99 Pritchetl •4 sn. 103-1 8-21 GL •0 in. 4-iS Secchi's Companion. 169-8 I in. I 44-26 1 1865-06 Marth's Companion. Harth 126-6 127-0 1 14-9 "3-S 115-1 112-3 FTitchettii4-3 Hall Bd. AC I 2 in. 72-09 » 4n. 71-05 •12 69-25 1865-03 •03 77-16 •87 •99 8 30 •21 247 0.2. 156. R. A. 6' 40 •4'° Dec. 18° 20' O.S. Be. 347 'o 339-3 345-6 3382 327-2 324-2 in. 0-38 »» •33 »i •49 J) •49 »» •51 M. 6-5. 7. 1843-26 4-26 523 7-22 73-25 67-35 • By Messrs. Holden, Hall, Newcomb, Sldmin, Eastman. MEASURES. 233 248 OX 157. O.S. 331-17 340-45 3n. 2n. 0-47 -45 1852-66 5-32 R. A. Dec. M. 341-57 3n. •49 ^y^ 6^ 41 -. i"' 0° 29' 7-S. 8 344-40 348-67 2n. 3n- -57 -50 61-84 7-98 C. white. 354-97 »» -58 9-67 0.2. 12-7 in. 0-76 1847-22 35637 »» -51 72-66 Se. W.O. 2-4 357-2 354-8 55 -0 n tt 3n. 2n. •66 •73 11-50 48-25 70-22 68-14 76-1 8-1 Ua. De. 357-03 336-6 354-9 2n. -55 •32 in contact single 5-68 51-42 66-87 8-26 51-1 )t 10-91 CO. Bu. 53-1 50-7 ion. 11-20 10-44 7-1 9-1 251 S. 982. 38 OEMINOBUH. Dec. 249 2. 963. R. A. M. T^riar TO 6" 47-3 m 13 20' 5-4. 7" 14 LTNCIS R. A. Dec. M. 6" 42-5°- 59° 35' 5-9, 7-1 C. A, golden ; B, purple. Probably a slight change both in angle and distance. S. Sm. Ma. O.S. Se. Se. -W. AS. ei. 48-0 51-5 50-0 53-2 •3 54-6 55-6 •6 •2 56-6 59-5 62-3 63-2 64-1 7n. 0-89 i-o 0-86 3n- •95 2n. •79 3". ■77 2n. •75 I4n. •79 3n. •76 -70 in. •63 »i •5 »> •7 1830-18 •88 3-31 8-41 42-26 3-34 4-31 5-19 8-24 57-20 63-44 73-24 4-13 5-10 250 R. A. e' 46-9" O.S. 159. 15 LYKCIS. Dec. 58° 35' M. 5-1, 6-2 C. A, yellow; B, golden; De., A, golden; B, blue. So far the angular change has been very uniform. It may have slackened a little of late, and the distance appears to have increased since 1850. (0.2.) In 1868 De. observed the partial super- position of the discs, the golden image of the larger star covering a portion of the arure blue disc of the smaller. The common proper motion is +0'-004 in R. A., and +o"-i8 in N. P. D. O.Z. 323-45 4n. 0^53 1844^04 323-45 325-67 327-88 332-02 4n. 0-53 3n. -46 Sn. -43 411. •45 6-32 8-72 50-79 C. 2., A, yellowish ; B, bluish. " The colours so marked, that they can- not be entirely imputed to the illusory effect of contrast. " (Smyth. ) This beautiful object was discovered by H,. He says {Phil. Trans., 1804, p. 384) : "The position, Oct. 2, 1782, was 89° 54' s.f. ; and April 6, 1802, it was 86° 6' s.p., m-hich gives a change of 4° in 19 years and 186 days. This cannot be ascribed to parallactic motion." Hjand So. (Phil. Trans., 1824, part ii., p. 98): " Extremely unequal, large, white; small, bluish. The measures of this star would be attended with excessive difficulty, except in such a night as the present ; it is one of rare occurrence. Moon nearly full. Small star appears a beautiful point ; large one quite free from bur or flare." Again, he writes : " This star to-night admirably defined ; the measures were gotten with a power of 133, with the greatest facility. With regard to the angle, a slight change may still be suspected, but the diminution of distance is not to be doubted, even should the rejected observations of March 19 [March 19, 1821, 86° 47' s.f., 6"-698J be the true ones." Dawes {Mem. R. A. S., vol. viii., p. 70) writes : " The measures of this beautiful object point to a continued change in angle, though that in distance is not so strongly confirmed." Smyth (Cycle, p. 165): "From a com- parison of all the measures, a slight but constant diminution in the angle may be inferred. " He also adds that the measures of H„ Hj and S., 2., and Dawes, "suggest a retrograde slow motion of — o°-i6 per annum ; and the distance appearing stationary, hints a period of upwards of 2000 years." Dawes (Mem. R.A.S., vol. xxxv., p. 331) thinks that a slow diminution of angle is 234 DOUBLE STARS. well established ; but that the diminution of distance is doubtful. Secchi says : " The diminution in angle continues; the distance increases." O.S. Hj's distance is probably much too great (1782, 7" -95). Retrograde motion. The distance appears to have increased since 1850. The common proper motion is + o" "04 in R. A., and + o"-o6 in N. P. D. Duner gives A = 6"o3 + o"-oi (/— 1850-0). P= i69°-5 — o°-225 (/— 1850-0). 1781-99 1802-26 22-67 3220 29-24 3292 6-17 41-29 315 5 J -45 36-10 9-17 43 -20 8-22 1-27 2'2I 3-06 4-09 5-21 •23 54-46 46-27 51-10 2-77 1-85 64-30 8-21 923 ■24 70-22 3-26 54-65 61-12 54-46 5 97 6-51 62-92 3-15 56-11 63'i4 70-25 I -21 2-14 5-23 66-09 •16 70-35 2-17 ■98 417 H,. 179- 176- E,ftSo 174-, ^ A>|. Da. 172- 171- 169; 168- 8m. 171- 170- 171- 169- Ma. 171- 170- 169- 171- 169- Ko. 171- 168- Ja. 169- 168- 169- 0.2. 166- 168- 167- 164- 165- 164- 167- Po. 169- 165- Se. 168- 167; i66- Be. 169- U. 167- 166- 163- Schi. 164- Ta. 165- 164- 165- 166 ■9 7-80 -I ... "4 3n- 5-52 -2 7 ± -8 5n. 573 •4 in. ■94 •9 »» •79 ■5 3n. 6 07 ■3 In. -09 -0 2n. •00 ■8 -0 ■7 5-8 -8 60 -6 -0 -8 2n. ■5? -3 in. -16 -6 „ -20 -2 2n. -21 -2 »» •38 -6 -16 •4 -0 ■8 »» •22 -0 10 -00 •5 10 5-98 -2 in. ■74 -0 >» -78 -0 „ 617 -8 ^j "9 J, 6-26 -2 J, -08 •5 ,, ■14 -0 2n. 5-84 •3 5n. -07 •3 7n. 6 07 ■5 in. 573 ■4 2n. •83 •3 3n- 612 "3 2n. •14 ■3 2n. •14 -8 i» 5 95 -I „ 619 •4 »i -16 •7 tf -00 -2 >i -28 -0 >» 5-70 ■2 ft -82 •0 6-8i ■7 »» •67 "3 »» •47 -I 2n. ... Dn. W. &8. Ta. 8p. Dob. Gl. W.O. PI. 165-0 3n. 6-16 •3 5 •42 7 6 -29 166-2 6 ■3 2 57 165-1 5 6-5 7 4 -31 159-4 In. -10 164-3 ■28 •I 8n. ... 165-5 5 6-2 162-8 in. -42 164-3 „ -34 165-3 ,, -42 162-8 ,, -32 ■8 4n. -37 1870-12 2-13 -08 -12 3-16 4-13 •17 •07 5-24 6-09 ■10 •10 -II -12 -13 •74 252 S. 997. H CANI8 MAJ0BI8. R. A. Dec. M. 6" 50-6-° - 13° 53' 4-7, 8 C. A, yellow ; B, blue. The proper motion of this star is o"-O0O in R. A., and + o"-oi in N. P. D. 2. Sm. Ka. Ja. Fit. 8e. De. H. Gl. W. &8. CO. Dob. 343-5 3n- 3-22 342-9 -5 3388 -0 340-8 2n. -13 3382 2-97 335-9 -84 338-1 II -66 25 -95 337-5 ■86 338-9 3n. -98 336-6 -96 337-2 •76 329-4 -90 342-7 in. -28 343-5 •4 341-2 •33 343 9 75 339-9 3-14 342-2 253 1831-20 415 50-79 44-17 6-15 7-10 58-08 2-60 6-24 -47 7-94 64-09 3-i6 4-13 2-14 4-13 5-19 77-19 8-08 253 R. A. 6" 53-4" S. 1001. Dec. 54° 21' C. golden. AB. H,. 58-2 in. 10-04 2. 63-9 5n. 8-9 Ha. -2 in. -89 0.2. 64-6 2n. 9-20 Sn. 65-3 If 8-92 M. 7-1.87,9 1830-00 1-48 4322 58-29 73-52 MEASURES. '■35 AC. s. Ma. O.S. Sn. 3.S4-8 Sn. 1-65 3S8-8 in. 2-05 0-3 2n. 1-87 359-4 ,, •66 1831-48 45 '29 5829 73-45 254 0.2. 163. R. A. 6" 54™ O.S. 3207 323-4 De. Dec. 11° 58' 3"- I 0-57 M. 7-2, 8-s 1 1848-57 I 67-40 255 2. 1009. R. A. 6'" 56-I"" ( Duner gives 1853-' P = IS7°-S H,. 80. H,. 2. Ba. Sm. Ua. He. Se. Ho. H. i:ng. Ea. Dn. 61. Dec. 52° 56' Tery white. 03. A = 3" -2 1 - o°-oss (< - M. 67, 6-8 167-0 m. ... 156-9 2n. 3-89 157-1 tt -94 159-9 »> 4-26 -5 5n. 2-94 160-6 3". 332 158-9 -2 159-4 -0 158-2 411. -02 -5 •II 156-1 3n. •42 -I -08 154-9 in. -28 157-8 3n- •32 -0 2n. -41 156-2 ,, -13 153-3 •21 '56-5 4n. -59 -0 •27 157-4 4n. •18 •0 »> •0 1850 •o). 1782-86 1824-59 988 30-11 -34 1-15 3-21 43-30 2-27 3-13 51-86 696 60-35 54-97 8-27 9-21 62-31 5-21 6-31 70-70 4-11 256 LACAILLE 2640. R. A. Hj. 73-5 74-0 Ja. 78-1 -4 Dec. -59° o' 2-8 2-06 -67 M. 6, 7 1835-03 6-08 38-11 47-24 257 o.t. 165. R. ■7b A. Dec. M. 7° i-5"> 16° 8' 5, '°-7 C. A, golden. Rapid change in angle and distance. 0.2. 130-70 2n. 3-87 "9-35 „ -33 89-70 »» 2-89 1847-22 56-74 70-24 258 X. 1037. R. A. 7" 5-4" Dec. 27° 26' M. 7-1, 7-1 The North Star is perhaps the smaller. C. 2. yellowish ; Se. white ; De. white. Dawes {Mem. R. A.S.. vol. xxxv.. p. 332) thinks there is evidence of slow diminution of angle, and that the distance is unchanged. Madler {Die Fixst. Sys., p. 256,) after remarking the favourable position, bright- ness, etc. , of this pair, and that they can be seen in bright twilight and even before sun- set, proceeds to say that the observations indicate a double motion of the star, if the other be assumed to be at rest, and the existence of a third invisible star. From eight normal sets of observations he de- duced a period of 16 years. As the point round which the star travels is invisible, he thinks that one of the stars may be found double, and that the year 185S will probably be favourable for the discovery of the du- plicity. 0.2. Retrograde motion : distance un- changed. The orbit is perhaps nearly circular. Duner gives 1855-76. ii = l"-29. P = 324°7-o°-3i6 (/-1850-0). 2. 337 332 0.2. 327 148 150 327 323 324 140 Ma. 319 331 324 323 324 Da. 322 326 Ka. 324 325 Se. 317 320 Mo. M. -W. &8. 318 325 312 305 316 2n. 1-24 6n. •32 3n. -II ») -21 in. •41 }» -27 n -23 II -14 »» -II 3". -32 -33 -37 -29 -29 •37 •45 in. ■22 »» •32 8n. •35 -07 6n. 2n. -1 4n. -22 20 •35 m. -52 *» •35 7 •40 1827-28 30-42 6-26 40-27 5-22 50 -26 67-24 8-21 9-24 70-24 41-80 52-36 S-5I -66 9-22 60-55 43-'7 8-17 3-20 67-21 55-20 6-15 63-20 o-ii -25 1-25 72-16 236 DOUBLE STARS. W. *S. Gl. Bn. W.O. PI. 3«S"5 3 317-6 6 1-31 •6 S •3 319-4 3n- •35 V6-6 •28 308-8 m. •34 314-9 ,, •18 312-3 3°- ■36 1872-92 5-19 4-13 1-92 5-II 6-iS ->3 7-13 259 Z 1049. R. A. Dec. -8° 43' C. yellowish white. S. Se. 61. 34-9 3n. 3-63 42-8 -50 46-0 in. 4-0 M. 8,9-8 1830-53 67-71 74-18 260 0.2. 170. R. A. 0.2. p. VII. 52. Dec. 9° 31' C. yellow. Ha. Se. Do. 133-0 2n. 0-96 132-0 ,, I -06 120-6 in. •21 I34-I „ 0-99 127-8 2n. I -08 121-6 3". -29 .4 2n. •OS M. 7-S. 7-5 1844-79 49-25 73-24 46-24 52-72 67-13 72-70 261 Z 1066. £ GEMIB0B1TU. R. A. Dec. M. 7'' 13" 22° 12' 3-2, 8-2 Certain change in angle. Dun^r has 1854-53. A = 7"- 1 5. P=l99°-8+o°-i55 (^-1850-0). 80. 2. Sa. Ha. 193-7 4". ... 195-4 in. 7-25 196-9 4n. •14 •9 •13 198-8 -s 7-1 196-8 •2 199-8 -5 -7 5n. •46 200-4 I» •30 -9 2n. •31 203-5 •08 199-5 •21 1797-53 182214 9-72 31-02 45-89 33-15 8-92 47-33 4-42 51-16 2-74 4-03 s-24 Ma. 199-4 I2n. 7-07 1856-07 200-6 -00 7-21 199-7 •27 8-21 -4 3n. ■16 60-90 Ja. 200 -6 •22 46-50 201 -2 18 •17 57-65 De. 203-5 9n. 7-08 403 199-1 4n. 6-89 6 30 Se. 200-0 3". 716 611 Eng. 201-7 )» •21 65-13 Ta. -3 in. 6-65 609 Sa. 203-0 5n. 7-04 71.46 ■W. &8. 204-0 7 6-74 2-17 •0 2 ■18 203-7 7 7-2 3-14 204-3 4 •I 4-14 202-9 4 •12 6-22 0.2. 204-7 in. 7-14 3-26 203-8 »j -01 4-29 01. 204-0 2 6-9 •09 8p. 202-9 -92 5-25 Sob. 205-4 in. ... -99 201-8 5n. ... 6-os 203-7 2n. -22 204-2 in. 6-41 7-91 •3 2n. 7-37 8-09 262 X 1074. R. A Dec. M. 7" 14-3 m 0° 38' 7-8, 8-2 2. II5-3 3n. 0-57 1831-54 0.2. 129-4 in. -61 52-25 139-2 „ •64 69-24 138-6 )> •62 70-22 140-5 „ •60 •24 Se. 135-8 4n. ... 63-15 W. 4 8. 134-2 7 0-85 74-14 Gl. •5 5 -87 •17 263 R. A. 2. 1071. Dec. M. 7>' 14-4"' 45° 14' 8-2, 10-2 Change in angle and distance. 2. 357-3 ; 2n. 15-52 1829-73 Se. 5-0 ] 3n. -87 I 67-30 0.2. 7-7 I in. I 16-18 I 74-29 264 2. 1076. R. 7" Dec. 4° 17' C. white. 2. Ma. 105-8 in. 2-74 106-3 )i •83 1080 »» •56 1 10-6 2n. •67 109-2 in. •76 M. 8-7, 8-7 1825-21 8-17 33-18 44-20 5-12 MEASURES. 237 265 Z 1081. R. A. Dec. M. yh j^ra 21° 41' C. white. 7-S. 8-S S. Ma. 8e. He. ,0 216-1 220-I 222-9 224-6 3n. in. 1-33 •34 -58 •40 1828-93 36-76 56-11 67-83 266 O.S. 171. R. A. Dec. M. 7" 19° 31° 52' 7. 9-9 C. yellow. O.S. Be. 129-9 1 Sn. 1 0-97 126-4 ' 4n. ' I -13 1851-25 70-03 267 2. 1091. R. A. Dec. M. 7* 21" 50° 13' 8-2, 8-7 The distance has probably increased, and perhaps the angle has diminished. O.S. 336-1 335-6 334-8 •I 332-7 in. 28-69 ») -49 2n. •74 »» -57 ft •78 1828-32 30-25 43-31 9-76 68-80 268 S 1093. R. A. Dec. M. 7'' 2I-I"° 50° 14' 8-2, 8-2 Indirect motion. Hj. 94-1 i-o 1830-40 2. 96-4 31. 0-57 1-94 O.S. 106-5 in. 40-32 107-8 tt 0-88 2-32 103-3 „ -70 5-32 105-1 )» •67 6-33 108-9 »» •75 8-25 107-9 •65 51-28 121 -8 •79 69-31 De. iio-o -6 3-43 269 R. A. 7'' 24"° S. Se. ■W. ft 8. 61. 1. 1104. Dec. -14° 44' C. white. ... 2± 292-4 3". 2-35 312-3 •21 3"4-o in. •55 •2 »» -5 M. 6-7. 8-3 1795-22 1834-88 64-50 74'i7 •17 270 t. 1110. CASTOB. R. A. Dec. M. 7" 27"" 32° I' 3, 3.5, II- C. Hj, both white; S., both greenish; Sm., A, bright white ; B, pale white ; c, dusky. Of this beautiful object H, says, "The largest and finest of all the double stars in our hemisphere, and that whose unequivocal angular motion first impressed on my father's mind a full conviction of the reality of his long-cherished views on the subject of binary stars." It is marked with a t in H,'s catalogue, indicating that it had been observed by "different astronomers before Mr. Mayer." Early History, bradley and pound's observations. " 1718. March 25. — The direction of the double star {Caspar, or) a of Gemini was parallel to a line through Pollux (or /3), which left k to the westward, as also ff tending to near the middle between g and / of Gemini. " 1719. March 30. — The direction of the double star o of Gemini was so nearly parallel to a line through k and a of Gemini. that, after many trials, we could scarce determine on which side of a- the line from K parallel to the line of their direction tended ; if on either, it was towards j3. This observation was made when the air was still, and with the 4j-inch eyeglass, which made the stars appear a good dis- tance from each other. " 1722. October i. — A line through the double star o of Gemini was parallel to another dravm through /3 and k. The southernmost star is brightest." (Rigaud's Miscellaneous Works of Bradley, Oxford, 1836.) These observations and the method adopted by Bradley are fully discussed by Hj in the Mem. Ji. A. S., vol. v.. p. 23, et seq., and he shows that a correction amounting to 2° 43' should be applied to the angles subtractively. The corrected angles then become 352'''28 in 1718-23, 355°-68 in 1719-24, 359''-88 in 1722-75. Then comes the observation by Bradley and Maskelyne in 175980, giving as the angle 326°- 50. (H,, in /'Ai/. Trans. 1802 ) H, ; "Feb. 28, 1781. — I saw with one eye the projection of the stars upon a wall at a distance of about six or seven feet, where they seemed to take up a space not less than four or five inches. I shall en- deavour to construct a micrometer, from this * Dawes observes that Se. has placed the smaller star in the n.f. quadrant five times, and that he suspects a variability of relative brilliancy. 238 DOUBLE STARS. hint, which may serve to measure such very small intervals exactly." H, (Phil. Trans., vol. Ixxii., p 2l6). "April 8, 1778.— Double. A little un- equal. Both W. The vacancy between the two stars, with a power of 146, is one diameter of S ; with 222, a little more than one diameter of S ; with 227, i^ diameter of S ; with 460, near two diameters of L ; with 754, two diameters of L ; with 932, full two diameters of L ; with 1536, very fine and distinct, three diameters of L ; with 3168, the interval extremely large, and still pretty distinct. Distance by the micrometer 5""I56. Position 32° 47' n.p. These are all a mean of the last two years' observa- tions, except the first with 146." In the P/iil. Trans, for 18^3, p. 339, H, announces his famous discovery of binary systems, and Castor is the one he first sub- jects to examination. He says, ' ' I shall therefore now proceed to give an account of a series of observations on double stars, comprehending a period of about 25 years, which, if I am not mistaken, will go to prove that many of them are not merely double in appearance, but must be allowed to be real binary combinations of two stars, intimately held together by the bond of mutual attraction." The Orbit. — As early as 1803 H, gave his speculations on this subject to the world. His results were, of course, merely intended as rough approximations. He found that between the years 1778 and 1803 the dis- tance had not changed, but that the angle had diminished from 32° 47' n.p. to 10° 53' n.p. At great length he shows that orbital motion alone could account for this change. Taking the annual angular motion as 56'' 18, he computes the position for the epochs of the observations, and an extract showing the results is here given : — Times of Observed Calculate observations- angles. 32^ 47' angles. Nov. 5, 1779 32° 47 Mar. 26, 1800 18 8 13 4' ■fan. 10, 1802 >o S3 12 I Mar. 27, 1803 10 53 10 S3 Using an observation of position by Dr. Bradley in 1759, a mean motion of 1° 3'"! was obtained, and this was found to give a still closer agreement between the observed and computed positions. From the arc described in 43 years and 142 days, viz., 45° 39 > ^^ inferred a. period of about 342 years and 2 months. Hj and So. took up the subject in 1821, and H;, after a careful study of all the observations up to 1822, found that the mean angular velocity was o°'965. He used the observations of Bradley and Mas- kelyne in I759'8, taking the angle as 56°'5 n.p., and gave equal weights to all. The results he arrived at may be thus stated : — the orbit is elliptical, and nearly at right angles to the line of sight : there has been a sensible retardation of the angular velocity since 1780. {PAH. Trans. 1824, part ii., p. 103.) Returning to the subject in 1825, Hj found that the observations made since 1823 confirmed his previous speculations. (Phil. Trans. 1826, p. 320.) But it was not till 1832 that this dis- tinguished astronomer fairly grappled with the orbit of this star. In that year his famous paper " On the Investigations of the Orbits of Revolving Double Stars " ap- peared. (^Mem. R. A. S., vol. v., p. 171.) His first example was 7 Virginis, and Castor was the second. The sections on the latter may be thus summarized. The positions from the observations in 1759 and 1802 are perplexing : taking them as 320° 20' and 383° 15' respectively, the in- terpolating curve becomes a straight line, and the orbit a circle, with a uniform angular velocity of — 0° '8745 P^"" annum. He decides at last on the following : — 1718-20, 160° 52'; 1756-00, 144° 22'; 1781-09, 130° 44'; 1803-20, 120° 19': taking up S. 's angles in 1819, 1820, 1822, and 1825, and also those by himself. South, and Dawes, down to 1831, he submits them to the graphical process. The final results are as follows : — Apparent Ellipse. Major semi-axis ... ... 5" '34 Position of major axis 53° 53' Minor semi-axis... ... ... 2"-72 Farthest maximum of distance. . . 6" -67 Position thereof ... 29° 5' Nearest maximum of distance ... 5" '03 Position thereof 270° 30' Farthest minimum of distance... 4" -66 Position thereof ... ... ... 313° 5' Nearest minimum of distance ... o"-66 Position thereof 147° 20' Real Ellipse. Major semi-axis a = 8" -0861 Excentricity e = 0-75820 Position of perihelion ... v = 169° 10 Inclination ... ... 7 = 70° 3' Position of node ... a^ 58° 6' Distance of perihelion from node on orbit ... X = 262° 31' Period in years P = 2525^-66 Mean motion « = — i°-4248 Perihelion passage ... T= 1855-83 On comparing the angles observed, up to 1833, with the computed angles a fair agree- ment was found. The following is the ephemeris from 1833 to 18 J6. For com- parison, the observed angles and distances are given. MEASURES. 239 t 1833-0 36-0 39 'o 42-0 45 "o 48-0 50 'O 52-0 540 56-0 Observed Angle. Distance. 257° 10' 254 22 251 21 248 I 244 7 239 3 234 25 227 19 212 36 164 24 256=73 •12 253 73 252 -38 249 -So ■20 •II ■39 •21 ■44 248 246 245 •89 •28 •20 •91 •008 •068 •070 •098 ■145 Date. 1833-10 36-88 9-35 42-25 5 93 818 51-21 2-20 4-23 6-20 p '•82 •65 ■37 •19 -85 •37 -91 •18 •36 -68 Observer. H. E.&G. G. Da. S'- Da. De. In 1842 {Ast. Nock., No. 452, vol. xix.) appeared the following elements by Madler : a 7"-oo8. X 87° 37'. e o 79725. P 232i'"-i24. 7 70° 58'. T I9i3'90. a 23 5'. n -93'-o54. In 1845 Mr. Hind computed a set of elements. All known observations between 1718 and 1845 were used, and the method adopted was the graphical. In 1846 Cap- tain Jacob obtained a set, and the two are here exhibited together : — Hind in 1845. Jacob in 1846. T 1699-26 1703-30 IT 8° 15' 10° 0' S, II 24 10 >■ 355 41 7 43 14 4317 e 0-2405 0-300 « - 34''i63 -o°-55i2 a 6" -300 6" -30 P 632>-"-27 653J".-i On these Mr. Hind remarks, "The period of revolution of this star appears, therefore, to be very much longer than was formerly supposed, and the eticentricity, instead of beinglarge, ispossibly notgreaterthan 0-25." The next attempt to deal with this hitherto intractable star was by Madler (see Unter- suchungen iiber die Fixstem-Systeme, 1847, p. 233). The observations made use of The extended from 1719-84 to i847"i9. elements are, — T 1688-28. - 4«'-55654- 0-21938. 10° 45' -6 (i€q. 1845-0). 16 r-7. 41 46' -7. 5i9^'"-77. Madler also gives an ephemeris, of which the following is an extract. Appended are the measured angles and distances for com- parison : — Angle. 250° o-i' n e a, \ 7 P 1845 50 55 60 65 70 246 243 240 238 54 49 55-4 9-2 235 29-6 Distance. 4" -849 •955 -064 -177 •291 -406 5 Measured Angles and Distances. Angle, 249-8 248-97 243-61 242-77 241-45 Distance •027 ■848 •395 •678 Date. Observer. 1845-95 H,. 49-32 55-31 60-22 65-31 Da. M. Da. 5 5 5 that ■650 -57 deduced by There is very satisfactory agreement between the computed and observed angles and dis- tances all the way down from 17 19 till the year 1845 is reached, when a divergence is manifest. In 1855-82 Secchi gives 245°-i3, and in 1856-20 Dembowski has 245^-44. In 1870 the following measures may be given for comparison : — De. 239° -34 Ta. 240 -51 Gl. 239 -7 The next orbit was „^ ^„ ., Thiele, and given in the Ast. Nach., vol. lii. No. 1227. His elements are, — T 1750-326. P 996y"-85. « - 21' -6685. e 0-34382. a 7" -5375- X 294° o'-8. 7 42 5'-4- a 31 58'-o (for 1850). Thiele also gives, for comparison, the re- sults for every two years from 1848 to 1880, as deduced from his own and other elements. Subjoined is an extract from this table : — Observed Angles and Distances. 1850 1856 i860 1866 1870 1876 1880 Thiele's OrbiL 248°47 5-215 245-45 -388 243-54 -503 24083 -674 239-12 786 23667 -953 235-106-063 Midler's. o n 246-81 5-106 243-17 -237 240-84 237-50 235-36 232-26 230-27 •336 •477 •567 •700 •789 Hind's. 246°i9 5-193 242-74 347 240-55 237-41 235-41 232-55 230-73 ■45 ■607 711 867 970 248° -29 245 -58 242 '89 241 -15 239 -76 236 -22 234 -2 •9 23s 5" -068 1851-21 •145 56-20 •395 60 -22 •384 66-02 •57 70-32 •5 75-66 •58 76-70 ... 77-31 •35 78-11 Da. De. Da. De. Gl. PI. Dob. 240 DOUBLE STARS. For further comparison, the observed angles, corrected for precession to 1880, from 1850 to 1875, are given in the last columns, together with the observed distances. The agreement between Thiele's angles and those observed is remarkably good, but the dis- tances are not so accordant, and the differ- ence is becoming greater. A careful comparison of Thiele's elements with the observed angles and distances up to 1875 has led Du. to regard 7"-ll9asthe most probable value of a. In 1877 Wilson obtained the following elements by the graphical method : — a = 6" 67 e =0-38 a = 28° 15' 7 = 32 IS X = 305 10 p = 982 '9 years T = 1742-1. Lastly, Doberck (see Ast. Nach., vol. cxi.. No. 8) gives these as provisional elements : a = 27° 46' X = 297 13 7 = 44 33 e = 0-3292 P = IOOI>"'-2I T = 174975 a = 7" '43 (^q- '850). A B. The measures of the last six years appear to indicate that about 1872 the distance reached its maximum ; if so, we may expect it to diminish sensibly ere long. A C. After reducing the angles for A C A _i_ B to those for — — and C, a change m 2 distance to the amount of about o" '2 and 1° in angle appears between 1835 and 1869. The measure by Z. in 1829 was probably over-weighted by him when discussing the changes in this pair (see P. M., p. ccxii) ; and it is probable too that an accumulation of accidental errors of considerable magni- tude exists in the Pulkowa measures from 1851 to 1853. At present the real character of the changes cannot be ascertained. (0.2.) The proper motion of Castor is - o^ois in R. A., and + o"-o8 in N. P. D. AB. Hj. 30278 293-05 292-95 297-27 283-88 288-13 280-51 277 '97 280-88 •47 * The dates of the distances are 1779-84, 1779-92, 178006, 1780-26, 1781-14, 1781-16. H.- H, & So. 5"3i -78 4-69 5-00 •43 •53* H,. Be. Da. 1779-84 83-63 91-14 Sm. 2-15 5-95 1800-23 •30 Encke & 1-99 Galle. 2-02 Oalle. •06 Ea. 291 -62 I 1802-15 283-00 I •16 275-49 2 3" 277-88 I •II 284-59 3 •22 280-88 2 -23 Q-O ... 16-97 267-12 24 ... 21-21 264-98 26 3-11 •65 37 ... 210 263-3 42 4-76 5 -23 262-54 5n. ■40 6-22 -32 4n. -41 7-28 261-10 5n. -35 8-89 259-58 »> •46 31-31 257-72 4n. -52 2-86 255-48 Sn- -73 5-33 254-33 3"- -78 8-34 261-86 -64 28-69 260-96 •52 9-88 259-01 30-52 4-68 -60 259-61 i-ii 5"i6 -19 258-15 4-57 -22 259-7 4n. -7 0-41 260-0 in. -73 -76 259-6 2n. -54 1-30 -5 in. -72 -40 258-42 I4n. ... 2-12 ion. 4-70 -17 6n. -78 3-14 258-1 12n. ... -15 257-23 3"- ... 4-08 ... 2n. 4-85 -13 255-73 3n- -83 6-36 254-95 4n. -87 8-21 -•3 5n. -93 40-20 252-38 6n. •91 2-01 251-72 4n. -87 3-16 249-85 5n. 5-01 7-25 -24 2n. -14 8-13 -16 7". 4-97 -24 248-97 4n. 5-02 9-32 -II ion. -06 51-21 246-39 in. •07 2-20 245-87 3"- •IS 3-13 246-2 7n. -09 4-23 244-25 4n. -38 7-34 242-77 3n. •39 60-22 -08 »» -45 3-51 -II ») -49 4-30 241-49 2n. ■76 5-30 -45 ,, •67 -31 256-3 ■7 34-24 255-2 -8 6-31 254-9 -8 8-33 252-3 ■9 43-13 256-1 in. •28 36-88 253-7 ,, •20 9-35 -9 7n. 4-71 40-06 255-0 6n. ■86 1-35 253-8 8n. ■69 2-37 MEASURES. 241 0.2. 254-9 2S3-8 250-1 7n. 5 -07 1840-30 Se. 245-2 244-5 246-4 Schmidt. ... 4 5 4-99 5-02 2-78 4-28 249-4 4 6 4 -07 5-79 ■7 248-9 -06 -18 7-93 9-28 Mo. 244-4 243-9 '2 3 ■00 50-27 -6 247-0 4 •24 1-28 Po. -2 246-2 245-3 246-0 3 3 3 -27 -44 -33 2-30 3-29 4-94 „ 241-7 M. 240-8 236-4 244-7 3 -41 7-27 248-1 242-9 3 -44 8-96 241-8 243-6 3 •49 60-26 242-2 241-9 4 -41 1-87 241-7 242-4 3 •45 4-28 -5 239-0 -2 241-0 238-9 4 3 •44 •54 6-78 8-27 -I -2 4 3 -li 9-76 71-27 240-7 -0 236-3 238-0 5 3 ■62 -49 2-88 4-28 239-5 238-4 Ch. 250-5 3"- -13 41-13 237-4 Ua. 249-0 252-8 in. 5"- 4-92 -88 4-27 i-ii Bo. 245-1 244-3 -I 245-8 6n. 911. -79 -82 2-30 52-34 243-4 •8 246-3 5n. -8i -66 242-1 -2 9n. -93 3-34 243-0 244-7 1811. ■§4 4-38 241-8 243-6 3n. -84 5-31 -8 •7 6n. 1? 6-35 242-2 242-9 7n. -88 7-36 239-9 244-1 »» •96 8-37 242-3 242-7 I In. 5-08 936 Kit. 241-0 Hi. 249-8 iin. ... 45-95 242-7 •5 4n. ... 6-73 Eng. -8 D.O. 248-0 6-40 Kn. 240-6 5-46 •91 239-7 251-3 -38 7-07 •6 Bond. 249-7 -I 8-30 238-8 „"3 •3 •26 240-4 248-7 -2 -30 237-0 Johnson. 245-7 { 7 5-07 50-21 236-5 Ja. 248-3 20 ■66 Ta. 243-2 247-9 30 5'i 1-74 -3 IS -08 3-04 240-6 -3 II -24 4-03 Hi. •6 32 -04 1-88 Se. 244-6 5°- ■72 3-31 242-9 245-4 )» -60 4-21 -9 246-2 6n. •36 5-14 240-5 245-5 7n. -16 6-19 -9 241-6 6n. -37 62-74 -7 -s 8n. -40 3-24 235-9 ■0 Hn. •38 6-02 Br. 238-9 239-7 3n- •45 70-30 Dn. 239-2 238-7 2n. •54 I -25 238-7 237-8 »» •40 2-27 -4 •2 3n. •67 3-29 237-0 Be. 63-8 in. •19 SS-14 61. 239-7 -8 »j -26 -14 •0 66-2 „ 1 •50 •28 236-9 65-6 „ 1 •S3 6-24 •4 12 20 24 20 35 in. 2n. 4 6n. 5 10 7 7 7 4 4 6 5 S 8 6 6 2n. 8n. 9n. 6n. ion. 4 5 5 4 5 -39 -36 •31 •85 ■21 ■16 -38 •15 -29 -51 -31 -53 •06 -46 -18 -28 -39 -58 -66 -56 "40 6-30 5-85 -27 -47 ■30 -67 ■66 •54 -60 -55 -70 -65 -46 5-6 ■52 -48 -41 ■43 •60 •72 •70 •75 -57 -32 -22 ■44 •29 5-65 -16 -51 •71 ■38 -49 -55 -60 ■57 -6 -69 •73 16 1856-27 -31 -34 5 8 9 9 9 61 1-13 -18 -29 -92 2.31 ■94 3-13 •14 64-23 70-26 I -25 •26 4-19 5-16 62-80 -81 -86 -86 -92 3-08 -10 ••3 -17 -25 -25 •21 -21 4-16 -78 -90 5-05 -87 6-03 71-99 2-02 66-09 •14 -16 -20 -35 708 -27 70-35 1-33 2-17 4-16 69-16 -38 70-79 3-67 5-33 032 I -21 -98 2-00 242 DOUBLE STARS. 01. 236-3 12 S-62 1873-29 -0 3 6-0 4-03 •8 3 5-8 -04 237-2 2 -6 '°A 235 '9 4 6-1 5 5 •5 •06 -14 -11 237-0 2 •6 ■29 W. ftS. •2 7 ■8 2-20 2382 S ... -26 ■9 4 ... -27 2377 4 6-1 ■38 •0 7 -86 •9 5 5'6 3-24 236-9 4 •5 4-12 237-0 6 •7 -14 239-0 4 ... 3-28 2359 4 ... 6-22 23f2 4 ... •35 Fer. 237-5 S-86 3-14 Se. 236-0 3n- -54 5-25 Sohi. 2352 m. -58 -26 234-6 fl •53 7-17 Dob. 236-4 II 5 99 2347 un. 578 613 ■4 2n. -59 U° 235-1 •55 8-11 Do. 2348 12 6-12 •9 2 7-31 PI. •2 7n. 5-58 6-70 8p. •6 AC. •53 7 So. 161 -6 70-2 1823 2. 162-4 72-8 29 -5 7n. •5 35 8m. •0 •9 •8 73-1 7 •2 72-4 8 •6 73 -o *^. O.S. •5 5n. 72-59 1-87 •6 II •52 8-86 163-0 II ■43 52-27 -I •1 -81 60-07 •s It •93 9-06 Fit. ■I -1 52 8e. 161-3 73-0 8 Be. 163-5 72-8 62 Fl. •3 73-2 77 271 OX 175. R. 7' A. 27° C. Dec. 31° 12' yellow. M. 6, 6-6 The distance has probably increased. O.S. De. 333-83 332-13 I2n. 3n. -46 -81 1847-60 67-92 272 t. 1107. R. A. 2. Ma. Dec. 76° I' 200-5 201-8 3"- in. 1-27 -78 M. 8, 10 1832-64 45-25 273 0.2. 176. R. A. 0.2. Dec. 0° 47' C. white. De. 207-5 m. 1-64 2137 II •44 210-0 II -53 214-3 3°- •66 M. 7-3i 93 1848-24 50-28 67-24 8-07 274 PROCYON. R. A. 7" 33° Dec. 5° 33° C. A, yellowish to white ; B, orange. Magnitudes. — Procyon is variously esti- mated : it was rated of the 1st by Hevelius, of the 2nd by Tycho, and at ij by Sin. Smyth estimated the companion seen by him as an 8th magnitude star : Barclay's is of the nth, Secchi's of the 7th, Flamsteed's of the 7th ; those first measured by Powell about the 8th ; and the three discovered at Washington are of the loth magnitude. Companions. — Flamsteed in 1692, and Christian Mayer in 1777, observed a star of the 7th magnitude. The distance was about 600" at the latter date. Powell and Flammarion have made measures of it. It is G in list of measures ; it is H^ I. 23 and 2. 1 126. Sm. in 1833 found a star of the 8th magnitude at a distance of 145" and angle of 85°. "In 1848, Mr. Bond, of the Cam- bridge U.S. Observatory, announced that the small star was 'missing.' In 1850, I saw and measured the position of the com- panion with ease, and estimated it as of the 9th magnitude. My measures gave this result: 1850-17, position 84° -3. During the spring of this year I have looked most carefully for this small star with my 6-foot achromatic, but I have never obtained a trace of its existence." (Fletcher, in 1853.) Smyth himself and Dawes also failed to recover the missing star in 1858 ; but Dawes detected a minute star 48" ± distant MEASURES. 243 from Procyon, and having a position angle of 285° ±. This appears to have been the small star discovered by Mr. J. Gumey Barclay in 1856, of which he communicated an account to the R. A. Society in 1863. Mr. Barclay's star was measured by Mr. Romberg on the 17th of March, 1863 : position 295°'3, distance 45" '8. Secchi in 1856 found a 7th magnitude star in the following place : position angle 83°'6, distance 33"'i6. No other measures of this object are known to us. In 1873 O.S. thought he had detected a close companion to this bright star. Familiar with the star (having observed it yearly for more than twenty years), second to no living astronomer as an observer of double stars, ever on the watch in such cases for false images, the utmost confidence was felt in the reality of this discovery. Special interest too attached to this new companion ; for it might prove to be the disturbing body Auwers and others sup- posed to be the cause of the irregularities in the proper motion of Procyon. Hence the extreme care used in testing the reality of the phenomena by changing eyepieces, reversing the telescope, placing the image in different parts of the field, and calling in the aid of assistants. Careful measures were made on every favourable opportunity, and transmitted to Dr. Auwers, who re-examined his computations, and predicted that the star, if really the disturbing body his theory required, would in March 1874 (when the star would again be visible), have a position angle of 97°. In this case Procyon would have to be regarded as having a mass eighty times that of the sun, and the companion itself would have a mass equal to seven times that of the sun. March 1874 proved very unsuitable for delicate astronomical measurements : however, one glimpse was obtained on the 21st : both O.Z. and his as.sistant saw the companion, and the position angle was 95° 1 Several confir- matory observations were made in April ; other Russian astronomers could see the companion ; Mr. Talmage saw it and measured it. But, strange to say, the American astronomers at Washington, using the magnificent 26-inch refractor, although they examined the vicinity of the bright star on many fine nights during the years 1873, 1874, and 1876, could never obtain a glimpse of the new companion. In conclusion, the distinguished Poulkova astronomer himself announced that the point of light which he had taken for a star was an optical illusion or "ghost." The American observers (Messrs. Holden, Clark, Watson, Peters, Newcomb, Hall, and Todd) did more than this; during their scrutiny of the vicinity of Procyon they discovered at least three close com- panions, A, B, C, and suspected the existence of one or two more (see the Measures). One was strongly suspected at a distance of 10", and an angle of 320° to 330°, Like Sirius, Procyon presents remarkable irregularities in its proper motion. Auwers investigated this case in 1861 : he found that a body moving round Procyon in a circular orbit situated at right angles to the line of sight, and having a distance of l"'2 from the centre of gravity, would explain the observed phenomena ; and he gave the following elements of this orbit : — Epoch of least distance in R. A. 1 79S'S68 Annual motion - - 9 00634 Period .... 39)^-972 Radius of orbit • . - i"-o525. This eminent astronomer on receiving O.S.'s measures of the supposed new star in 1873 proceeded to re-determine the proper motion of Procyon, but did not find that his results and the observations agreed well : these last elements were — Epoch of minimum R. A. - 1 795 '629 Annual motion ... 9 02993 Period 39^^-866 Radius of orbit ... o""98o5. The proper motion of Procyon is thus given : — Piazzi : — o"7i in R. A., and — o"'98 in Dec. Bessel: — o"'63 in R. A., and — i"'05 in Dec. Argelander : — o"'69 in R. A., and — l"'05 in Dec. In conclusion, it appears that none of the small stars hitherto seen near this fine star partake in its proper motion, those discovered at Washington excepted. Procyon and A. W.O. w.o. W.O. 187603 10 I [6 Procyon and B. 36 I I 8-8 I 1876-03 Procyon and C. SO I I 10 I 1876-03 Secchi's Companion. 83-6 I in. I 33-16 I 1856-16 Procyon and D, 1858-11 63-22 64-17 77'7 Ba. 28s 48 So. 294-9 30 45 -8 LaueU. 296 44-6 Fl. 31 1 -8 40 Smyth's Companion 8S l'«45 244 DOUBLE STARS. Procyon and E. Po. 838 •I 80-5 326-6 35 332-2 in. 346-5 1855-91 60-81 77-17 (E is a close double star, 195° and o"-6.) Procyon and F. Po. Fl. 282-1 3843 -9 35 380-4 286-4 in. 37 1 3 1855-94 6083 77.17 Procyon and Flamsteed's Companion. n. 116 5S8 1692 G. l[ayeT.io6 610 1777 Po. 99-7 25 643 i860 Fl. 968 in. 652 1S77 275 t. 1126. p. VII. 170. R. A. 7" 32-7° Dec. 5° 30' M. 7-2, 7-5 The apparent orbit is probably nearly circular. H, : "Nov. 21, 1781. — The nearest of all double stars I have yet seen : in perfect contact with 460 ; nor can I get a glimpse of any separation. The morning not so fine as I could wish, therefore I still doubt the reality of this appearance till more confirmed. — Double. I saw it had changed the direction of position to the horizon in about an hour's time, as it should : this looks not like a deception of the telescope. "Nov. 28, 1781. — Not open with 460. 12', the air very fine ; with 278, J of a diameter." H,. So. H,. S. Sa. Sm. 0.2. II7-3 m. ... 127-8 130-7 1-40 1230 ■41 132-0 iin. -46 •3 •47 133-9 •23 •4 31- •35 J32-9 -4 140-3 in. •50 137-1 -37 139-0 •37 136-6 -27 •5 -03 138-2 •13 137-8 •41 •2 -27 135-9 •49 143-9 ■5' 142-4 •28 1781-91 1823-13 26-18 30-04 29-43 30-09 50-26 32-10 3-22 42-21 629 7-25 8-24 927 50-26 1-26 2-25 7-27 60-25 I -25 0.2. 136-8 139-9 144-2 142-6 145-8 Ma. 138-2 140-8 138-8 141 I Mo. 136-9 140-0 Se. 137-3 Po. 138-4 Ta. 144-1 -5 n8-7 Ea. -4 W. &S. 140-2 139-9 Gl. 143-6 Sp. 139-8 in. 1-23 ,, -32 ,, •25 ,, -23 ,, -24 •50 -64 -53 •46 12 •31 18 -27 4n. -27 •5 in. 0-99 ," 0-92 1-15 4 •45 4 -59 6 -41 •21 1864-26 7-27 70-24 3-24 ■24 5II9 2-23 4-19 5-24 6-24 9-91 6-64 61-03 6-09 7-09 74-23 67-21 74-17 6-22 4-17 5-31 276 O.X. 177. R. A. 7" 34"° 0.2. Se. Dec. 37° 44' Rapid change in angle. 149-9 3"- 0-57 138-9 2n. •64 127-4 3n- ... M. 75, 8-5 1845-60 73'79 68-65 277 %. 1132. R. A. yh 36-2" So. 2. Ma. De W. 4 8. Gl. Dec. -3° 14' C. white. 246-0 18-32 238 I 19-88 •5 2n. ■32 237-4 ,, •19 ■2 •41 236-4 -10 •5 •52 235-7 In. 20 -6 •9 i> -88 M. 81, 8-7 1783-03 1825-03 -08 33-72 6-19 47-23 67-46 74-18 -18 278 0.2. 179. c GEMINOSUM. R. A. Dec. 24° 41' M. 4, 8-5 De. suspects that the light of the com- panion is variable ; but it is probable that 2.'s estimate in 1828 was influenced by the bright field which he used. MEASURES. 245 S. Sa. Sm. O.S. Ua. Ta. De. Bu. Gl. 230 ± .S± 229-62 in. 0.19 228-9 2n. -21 231-9 •0 2323 S-8 231-3 in. b-2S •2 It ■38 232-8 )j ■II •0 j» •07 233-3 »» -36 237-3 in. •30 234-8 j» •21 231-1 7-24 233-1 in. 6-22 •10 3n- -36 235-7 7n. -39 232 ± in. 1826-20 28-27 36-68 8-98 51-21 43-30 4-26 5-25 8-24 57-28 64-24 73-26 46-24 66-59 •73 74-06 6-11 279 POLLUX. R. A. Dec. M. yh 37-2"i 28° 19' A2, B II, C 12, D lO. C. A, yellow. A perspective group. Hj and So. do not appear to have seen C. Is it a variable? So. Sm. n. Fl. A B 65-.? 116-7 66-4 132-3 ■9 130-0 72-1 1750 1781-90 1825-10 32-31 77-08 A C. 90-4 I 205-5 I 77-08 A D. H,- 74-1 So. 72-7 Sm. 73-6 ■V -6 0.2. 74-4 Be. -9 n. 75-2 160-7 198-0 202-7 203-8 213-5 222-2 228-9 1781-gO 1825-10 3231 6-26 50-71 65-31 77-08 280 2. 1136. R. A. Dec. 7'' 42"' 65° 13' Rapid change in distance. M. 7-3. " 2. 0.2. 248-53 3"- I I -61 247-5 In. 10-81 246-4 3) -55 243-8 ,, 9-58 244-9 H -5' 1830-65 46-22 7-34 68-30 9-32 281 X. 1142. R. A. Dec. M. 7" 41 -e-" 13= 43' 8, 10-4 C. A, yellowish. Rectilinear motion. 2. 275-8 4n. 24-36 1829-47 Hj. 272-0 40- 32-30 Ma. 267-6 22-93 47-22 De. 262-0 •83 63-41 Gl. 259-1 in. 23-4 74-17 W. & S. 258-1 ») 22-8 -17 282 o.t. 182. R. A. 7" 46" 0.2. De. 47 -S 51-7 46-6 44-6 -o 39-83 Dec. 3° 42' 2n. in. 31- I -08 -09 0-99 1-22 -10 •23 M. 7, 7'5 1844-28 7-25 50-28 61-25 7324 67-00 283 R. A. 7" 48-5" X. 1157. Dec. - 2° 28' C. white. M. 2. 8,8 Secchi (p. 26) says " certain retrograde motion." 2. Se. Be. ■W. &S. Gl. 267-2 .Sn. 1-59 256-4 )) •30 254-s in. -41 -4 3n. ■2 76-4 in. 256-7 3n- 1-29 257-7 4 •00 256-5 2 257-2 in. 0-88 1831-20 56-47 65-87 57'9' 6293 3-16 72-17 -14 4->3 284 o.X. 185. R. A. Dec. A mutual eclipse has probably place since 1855. O.S. Se. De. 15-3 23-6 -4 198 in. oblong 0-33 -46 oblK-? 240 265 single single M. 6-8,7 taken 844-26 •30 50-28 61-25 9-24 70-24 3-24 55-28 246 DOUBLE STARS. 285 O.S. 186. 290 %. 1187. p. A. Dec. M. 85 L-7HCIS. 7" 56" 26° 37' 7-5, 8-2 R. A Dec. M. C. white. 8" 2° 32° 36' 7-'. 8 O.S. 75°2 3"- 0-83 1844-28 C. white. 74-0 70-9 Ka. 810 in. -72 •73 "55 9-26 57-27 '•33 Certain retrograde motion. Duner gives De. 724 3"- •81 67 '93 1855-00. A = i"-79. Du. 787 2n. •65 71-07 P = S. = 62°-6 - o°-432 {t - 1850-0). 71 5n. I -61 1829-50 286 2. 1175. H,. 70-9 81 in. •45 2-09 3018 ■97 R. A. Dec. M. Ua. 687 1-62 7-60 7"' 561° 4° 30' 7-8, 97 66 6 5n. 'P 43-55 61 9 •81 51-17 C. yellowish, bluish. 62-6 in. 2-23 2-27 2. 204-6 511. 2-37 1831-24 697 2n. 1-74 5-32 H,. 2067 '•5 ' -80 74-7 In. -81 8-29 De. 2178 2-07 6683 591 »> -20 9-14 Ho. 56-2 •7 3n. 2n. -96 -82 60-32 59-14 287 OX 187. ll'S ,, -83 60-28 O.S. 68-1 m. •87 42-30 R. A. Dec. M. 67-3 ,, -92 6-29 7" Sfi-S" 33° 24' 6-7, 7-5 56-7 55 -6 »t 2-II -00 61-19 4-30 Secchi's measure in 1855 probably refers 52-9 •07 9-31 to some other star. 55-6 ,, 1-97 71-30 O.S. 3069 4n. 0-46 1844-02 So""* fi -98 3-31 2992 »i •35 48-82 De. 58-9 In. -8 55-99 2937 2n. •43 58-28 -8 3n- •6 6-14 285-6 »» "52 71-31 59 4 in. •5 7-09 8e. 2504 in. -8s 55-28 57-1 ,, 62-85 De. 2862 3n. 68-32 56-1 5n. -82 3-21 Se. Eng. 61-6 58 -5 2n. 4n. -75 2-03 58-21 65-49 288 2. 1179. Dn. 53-6 30- 1-75 71-25 W. ft 8. 54-3 5 2-14 2-27 R. A. Dec. M. 3-5 4 1-95 -30 yh jg-im ij" 25' 8-5, 8-s 01. 52-7 5 -92 4-13 Rectilinear motion. Schi. 8p. 50-8 50-9 in. 2-22 -22 5-30 5-30 S. 205-5 in. 17-86 1829-24 Dob. 53-1 in. ... 811 204-8 i> -96 30-22 H,. -8 180 2-20 Eng. 205-0 20-71 63-13 291 S. 1196. K CANCBI. 289 S. 1186. R. A. Dec. M. II CANCBI. 8" 5-3" 18° I' A 5, B 5-7, c 5-5 R. A. Dec. 8" 1-5° 27° 50' M. C. H„ A, red ; pale red or red ; B, pale red or c, pale red. S., a, yellower 7-1, 10-4 than c ; B, yellower than A and c. 2. 218-8 5n. 3-i8 1828-26 De. always saw all white till 1864. Sm. 213-5 -2 39-70 He remarked a change in the colour Da. 211 -5 •27 40-12 of c more than eight times in 1864 Ta. 206-4 in. 66-10 and 1865 ; he noted it as more or 219-1 11 30s 74-23 less' jaunatr e et oli) ^atre." MEASURES. 247 'Mf- mr H„ "Nov. 21, 1781.— If I do not see extremely ill this morning (4 a.m.), the large star consists of two." " Feb. 7, 1802. — After long looking, I cannot see the small star sufficiently well to measure its position." H, (Phil. Trans., vol. Ixxii., p. 219), " f Cancri, Fl. 16, Nov. 21, 1781.— A most minute treble star. It will at first sight appear as only a double star, but with proper attention, and under favourable circumstances, the preceding of them will be found to consist of two stars, which are considerably unequal. The largest of these is larger than the single star ; and the least of the two is less than the single star. The 1st and 2nd (in order of mag.) pretty unequal. The 2nd and 3rd pretty unequal. The two nearest both pale r. or r. With 278, but just separated ; with 460, J diameter of S. Position 86° 32' n.f." Writing in the Phil. Trans, for 1804, H, observes, " The change is 9° 57' in 20 years and 78 days ; and may be ascribed to a parallactic motion of the large star, which is in favour of the observed alteration." H,'s measure of A C, on the 5th of April, 1780, was "Distance, 8"'046 mean measure. Position, 88° 16' sp." And the star is marked as one of those doubles known ti astronomers before Mayer. H, on the 2ist of Feb. 1822, wrote, "Double; pretty unequal; is not to be seen triple, although beautifully defined and round." Ten measures of distance gave a mean value 6" '241. "In 40-25 years, then, the change of angle amounts to 23° 42', which is at the mean rate of — o°'58l3 per annum, in the direction n.p.s.f. or retrograde. The change of position has also been accompanied with a consider- able diminution of distance ; and further observations must decide whether this is the result of rectilinear or orbital motion. If the former, the minimum distance will be attained in about 40 years from the present time, and the change during that period much less rapid than heretofore. On the other hand, an orbital motion will be indicated by the distance continuing to diminish beyond that limit, and probably too by an acceleration in the angular motion." So. {Phil. Trans. 1826, part i., p. 332) gives measures of the close pair. " April 3, 1825, 31° 21' n.f. 7 observations : o"'887 5 observations. Difficult." "I see the large star unquestionably elongated. At the time of perceiving the star elongated I was unaware that it had been observed by Sir W. Herschel as a close double star, as also that Mr. Herschel and myself, when we observed it in England as double of the 3rd class, had noted that ' it is not to be seen triple, although beauti- fully defined and round.'" Hj adds, " This star presents the hitherto unique combination of three individuals, forming, if not a system connected by the agency of attractive forces, at least one in which all the parts are in a state of relative motion." He then examines the measures in confirmation of these remarks ; and con- cludes, " If this be really a Ternary system connected by the mutual attraction of its parts, its perturbations will present one of the most intricate problems in physical astro- nomy. The difficulty will not be diminished by the circumstance of the rotations of the two small stars about the large one being (apparently at least) performed in opposite directions, being the reverse of what obtains in our planetary system, or by that of the deviations of the relative angular velocities from Kepler's law, being such as to indicate either great masses in all the three bodies, great excentricities in their orbits, or a different law of gravity from what obtains in our system." In the Mem. R. A. S., vol. v., p. 30, H, returned to this subject. Finding that his latest measures indicated a retrograde movement of — 6°"5o5 per annum, (that given in 1826 being + i 254 per annum, and direct,) he collects the measures by 2. and Dawes, which also show that the motion was retrograde. Hence he is led " to assign the end of March 1873 as the time when it will have completed an entire revolution since the epoch of my father's first observations, in a periodic time of S5'34 years." He adds, " f Ursae has hitherto afforded the only example of a double star of which 248 DOUBLE STARS. the bimestral motion can be distinctly per- ceived and measured. It is now no longer a solitary instance." Hg also points out "the remarkable difficulties in the way of any fair statement of the history of the position of this star [i.e. A C]. Most of the measures have been taken from the point of bisection of the close double star, seen as one or elongated ; some few directly from the larger." On the whole, H, is greatly puzzled, and fears that " mistakes have been committed which it is now impossible to rectify or allow for." Dawes (Afem. R. A. S., vol. v., p. 136) gives his measures in 1831. He says, after examining the previous observations, that it " would appear as if the motion has been performed in a direct sense, or n.f.s.p., for perhaps 30 or 40 years ; and that the star B had then come to a stand, or appeared to do so, faced about, and is now proceeding in the opposite direction." The only ex- planation which offers itself to his mind is that B has performed almost an entire revolution in a retrograde sense, in the 49 years elapsed since H,'s measures. The stars, too, differing but little in size, might lead to an error in placing the f. one as the p. As to C, his observations corroborate the presumed motion of this star in direction, and indicate a considerable acceleration since 1825. H, {Mem. R. A. S., vol. vi., p. 27). " The motion of this star is steadily con- tinued, and its binary nature and rapid retrograde motion must henceforth be con- sidered as established beyond all possibility of doubt." [AB.] Dawes in 1831-2-3, speaking of his measures, says, "just separated," "neatly separated." "AC somewhat difficult from the position of B with respect to A. " And in the Mem. H. A. S., vol. xxxv., p. 337, after giving measures from 1831 to 1S54, he writes that more than a complete revolution has been made by B since 1781, that the motion has been accelerated within the last ten years, and that the distance has diminished. He also says that the motion of C is orbital, but incomparably slower than that of B, and that its period is from 600 to 700 years. Madler in 1848 computed an orbit : — P= 58-2708 years P. passage = 1816-687 P. from node = 133° o'"j a = 33 34 '3 2 = 24 O -4 e = o" -44385. In 1855 Winnecke published the follow- ing elements of A B : — P. passage = i8i5-53 P = 58-94 years a = 18° 23' (1855-0) ir - a = 141 54 i= 48 36 44-S 139-6 128-9 309'4 268-1 240-8 2340 228-2 166-7 267-3 23 1 '5 203-6 188-2 178-2 163-3 142-8 129-4 185-1 1770 "76-3 173-9 160-7 •3 154-7 144-0 141-1 139-2 177-7 175-0 159-5 168-6 169-3 165-5 150-9 141-2 142-2 140-6 1337 o 130-4 108-2 122-1 108-4 104-1 110-3 130-3 108-1 T. Mayer 205-4 C. Mayer 180-0 181-7 1 71 -8 158-3 159-7 157-9 154-6 151-4 148-6 -6 147-6 H, & So. S. 6n. 7n. ion. 2n. 6n. 7n. 12 m. 31- 4n. m. 2n. in. ») 4n. 3t>- 5n. 6 4 3 6 25 5 4 3 4 9 8n. 3"- m. 3n- in. 0-5 -74 •75 •72 1-12 0-69 -63 •79 •65 -6 •95 •72 -46 -41 -53 -66 -59 -57 0-2 -2 •s -5 -5 -6 -4 elong^' 0-71 -78 -63 0-5 -5 -67 -80 •75 -69 •82 0-99 -73 -81 -69 -81 A C. 3-3 7-7 8-0 12 6-24 15 -19 27 S-43 31- -30 „ -31 6n. -40 4n. -52 3"- •47 1801-19 2. 145 I 2-23 150-1 3-19 148-9 •86 Sa. 150-3 4-29 148-8 5-18 147-1 56-24 145-6 63-13 146-7 5-36 •3 626 140-4 •94 8m. 149-4 72-11 147-1 63-25 148-3 638 146-9 9-37 O.S. 147-0 70-30 -I 1-29 149-4 2-33 -1 4-29 150-3 5-33 149-2 0-32 148-4 -80 147-1 1-21 145-9 •32 146-6 200 143-6 •10 •I 3-32 140-6 -94 141-2 410 -I •16 142-6 1-20 144-6 2-16 -I 3-14 145-0 2-18 144-2 •19 143-9 -25 141-4 3-22 138-4 4-17 137-1 -17 Ch. 2-1 •20 i-i 5-26 354-0 -32 Ka. 144-8 •26 146-0 7-i8 137-9 6-21 Ja. 148-0 7-24 147-5 8-08 142-1 7-23 140-0 •25 141 -2 -18 -9 Bond. 149-3 Fit. 143-7 1756 Mo. -2 1778 Po. 141-9 1781 Se. 139-9 1802-11 140-8 22-14 -0 4-22 •3 5-27 141 -0 26-22 139-2 8-99 140-2 31-28 •8 2-28 •I 3-27 139-6 2n. Sn. 3"- in. 4n. in. 6n. 2n. 7n. 4n. 3n. 4n. 3"- sn- 4n. 3n- 3n- in. 2n. ti 3n- in. 2n. 4n. 2n. in. S-35 -66 •62 ■59 -59 -44 4-96 -94 •88 5-04 •4 4-8 5-2 -4 4-92 •6S •77 •87 •81 -92 -98 -97 •93 -92 5-07 4-95 -99 -99 5-04 -02 -06 ■06 -14 4-95 5-11 1-07 -08 tf 0-97 4-72 -81 5-41 4-85 •85 15 -89 8 •94 -95 •94 •6 20 -8 18 5-23 68 m. •26 4n. , •56 m. -63 sn. -36 in. •21 4n. •20 »» •59 sn. ■38 in. •35 4n. •49 1855-27 •3« 36-27 31-30 218 •87 41-07 3-22 8-14 54-07 32-23 4-36 5-28 711 40-29 2-29 3-29 4-27 S-30 6-29 7-54 8-29 9-31 50-29 1-27 2-32 3-30 5-31 7-27 8-28 9-19 60-27 1-37 2-33 4-30 6-27 8-28 70-32 41-22 2-lS 4-09 2-35 3-33 66-28 45-83 6-00 S3-«9 -95 6-20 7-88 48-25 52-49 3-22 4-27 -88 •87 6-43 7 -81 8-23 62-88 3-i8 4-99 5-20 I>«. Be. Ko. W.O. Kn. Ta. W. &1 61. Belli. K. 0.2. 138-3 137 'o >34-6 ■1 1332 1328 •7 •6 131-6 •2 •7 142-8 ■9 140-7 141-8 •4 ■6 137-4 '43-9 •o 138-9 '35-8 137-7 132-1 •33-8 •3 131-2 '32-3 -o •2 «3i-S ■7 "32-7 133-0 130-4 ■6 •7 »S3-S 152-9 149-0 148-1 147-2 144 "3 142-2 139-8 ■4 1381 ■5 139-8 -9 •7 137-8 138-1 134-9 133-8 132-4 7". 4n. 31. m. 2n. 4n. 3". 2n. 51- 2n. 2n. 5 )> »» in. 2n. in. I I 2 14 2 2 4 4 6 S in. 2n. B C. 3n- 2n. Sn. 4n. 3n- t> 2n. 3n. in. 2n. 3"- in. 2n. 4n. A + B and I Bo. 161 -2 160-1 163-2 MEASURES. S-S8 1866-84 Hj. 158% •"1? 8-22 1S9-4 70-21 •2 •61 1-17 '54-5 •46 2-23 s. 159-0 ■40 3'" 156-3 •70 •88 1532 •51 4-19 -4 •40 5-«7 152-2 4-93 SS-'9 1501 ■85 6-25 148-9 •99 7-29 150-5 S'47 65-23 •7 -62 6-28 152-0 5-41 1-30 151 -3 -39 72-11 -7 150-6 -62 3-18 4-59 63 O.S. -5 ■23 •13 •7 ■S3 7-08 152-0 ■43 72-17 151-3 ... 4-23 ■7 ■52 6937 150-6 -78 75-33 149-6 -87 2-18 148-0 'P ■19 147-0 •8s •25 141-9 ■43 3-22 1439 ... 4->7 142-7 ■17 140-4 •72 5-26 -3 ■S3 •27 139-6 s-i 4-10 140-5 ■7„ -16 142-2 •38 5^25 -0 .26 7-18 -3 49S -20 141-0 -6 ,., 1844-28 138-1 136-1 5^30 -8 6-is 8-29 134-7 •19 931 ■3 I33^S •16 50-29 ■39 1-27 i35'o •17 2-32 133'8 -'3 3-30 Sm. 148-2 •09 S-31 147-2 5 97 7-27 Ja. -8 8-28 •82 -78 9-19 60-27 X)e. 140-7 •3 •74 J -37 139-6 •66 2-33 140-6 •31 4-30 139-7 6-27 137-8 ... 8-28 134-2 70-32 -I 133-2 c 132-8 •7 -8 .. 11820-29 1-07 ] H. 141 -8 • ■ 1 S-27 1 J Eng. -3 25^ 7n. 4n. 31- 4n. 3"- tr sn. 4". 3n. 3n. It in. 2n. tj 31- in. 2n. in. 2n. 41. Si- gn, sn. 31. 5-40 »» •54 6n. •67 41. -84 31. -82 2n. ■67 31. •63 ■31 •48 ■31 •42 •30 ■39 •30 •48 •31 ■42 •29 -38 ■42 •56 •56 ■54 ■73 -56 •56 ■54 ■50 -50 ■43 ■42 ■44 •30 ■30 •56 •69 •61 •69 ■61 ■63 •39 ■43 •I •o -o 5-39 •35 ■15 •48 -47 •58 •61 -60 ■46 -40 -57 -4 -41 ■49 1822-14 4^49 30-21 2-20 ;6-26 8-99 31-28 2-28 3-27 5-31 6-29 40-29 2-29 3-30 4-28 5-31 6-27 0-29 2-29 3-30 4-28 S-31 6-29 7-33 830 9 '32 50-29 1-28 2-32 3-30 S-31 7-27 8-28 9-30 60 27 1-27 231 4-30 6-2Z 8-28 9-32 70-28 1-31 231 3-28 4-28 39-32 47-11 7-28 6-29 SS-18 6-42 8-is 63-05 5-17 7-26 70-21 1-53 2-23 3-23 4-09 61-30 4-31 ^52 DOUBLE STARS. Su. Br. W. &8. 01. Sp. Dob. I35I 8n. 5-47 133-2 7n. -46 '327 •54 133-3 •46 132'0 ■64 131-6 -63 -4 in. •39 127-7 i> •2 I30-4 •38 •6 -27 «3i-5 in. ... •0 6n. ... 127-2 4n. S-62 132-0 in. ■48 [87070 502 119 2'l6 3-70 5-27 5-17 6'22 5-25 7-i8 5-99 6 20 7-26 8 -08 292 y ARGtJS. R. A. 8" 5-8" Dec. -46° 58' M. A A B 5, c 8 Certain change in the angle of A B. AB. El. £1. 2207 41-19 219-6 ■12 214-8 42-5 AC 151-6 •I 62-4 ■6 1835-03 -)8 77-03 35-10 77-03 293 1. 1202. R. A. p. VIII. 13. Dec. 11° 13' C. white. M. 7-7, 9-i S. discovered this double star, and was led to think it a binary from the results of his own measures. A subsequent set, however, seemed not to confirm this opinion. Dawes {Mem. R. A. S., vol. xxxv., p. ^39) thinks that the obliquity of direction jnay partly account for the discrepancies in the measures. 0.2). thinks that a retrograde movement is very probable. Duner gives 1854-83. A = 2"-32. p = 331° -9 — 0°-22O {t — 1850-0). 1829-55 36-19 2-27 44-21 8-31 51-22 2-27 48-24 56-17 65-28 s. 335-9 337-4 Sm. 338-0 Ma. 333-6 332-2 329-2 I)a. 328-5 Se. 325 -5 331-9 ^n. 2-35 in. •28 -5 2n. ■57 3"- -36 2n. ■27 »t -52 in. •21 ,, -07 m. -10 Se. O.S. Sn. ■w. &S. 61. 327-4 2n. 2-5 328-4 in. •64 324-6 11 •35 328-1 4n. -34 326-5 3 ■I -6 2 -09 324-2 6 -09 328-9 9 1-9 324-9 S 2-15 325-5 5 -I 1863-11 9-24 75-27 3->9 -22 •24 4-14 2-28 5 -28 4-10 294 S. 1216. R. A. gh i^.jni Dec. -1° 13' Rapid change in angle. 109-5 0.2. Se. Se. -W^. &8. 01. 115-2 142-0 136-9 149-9 151-1 1700 1687 166-2 164-8 167-0 m. 0-53 411. -48 m. -54 »» -44 7n. est. 2 0-4 3 4 6 0-5 M. 7-5, 8-2 1825-20 31-24 51-27 •28 7-34 6335 73-19 •24 5-27 -28 4-18 295 2. 1223. R. A. 8'' 20° Duner' P = 0' CANCBI. Dec. 27° 19' s formulae are 1851-02. A = 2i3°-7-o°-07 M. 6, 6-5 2. H2 & So. Sm. Sa. Ma. Mo. Se. Se. Ka. Bu. O.S. 33-3 in. 4n. 4-58 207-8 in. 3-89 2I2-0 7n. 4-56 214-3 2n. -82 211-2 4n. 5-51 212-5 4-8 -6 m. -95 214-4 3n- -99 213-3 >» •88 215-4 7n. •90 214-3 31- -73 •1 5n. ■71 215-1 »» -75 35-0 in. 5-OI 4-75- (t — 1850-0). 1783-06 1820-17 2-23 9-45 38-34 22-48 33-25 40-15 53-59 4-24 -46 6-20 66-24 7310 4-27 296 t. 1224. R. A. 8" 19-5" CANCSI. Dec. 24° 56' M. 6, 7- MEASURES. 253 Duner gives 1849-52. A = 5" -89. P = 39°'6 + o°-lo (i - 1850-0). 2. So. 8m. Ba. O.S. Ma. Uo. De. 8e. H. Bo. Eag. Ta. Ka. Ba. Gl. W. ftS. S7'2 34-5 37'4 •3 •s -8 38-4 -6 37'9 38-6 40-1 38-3 39-8 •9 40-9 368 37-2 38-0 •7 ■3 39 -o 41-0 39-5 •I ■4 40-2 -2 39 '5 407 38-3 39 '2 •5 40-6 -2 •o 41-2 40-2 38-6 41-0 39 '4 40-5 ■Q 42-1 43"2 41-2 -6 7n. 411. 9n. in. 5n. 3"- 2n. 4n. 211. 4n. 3n- in. 5n. 3°- 31- 5n. 4n. In. s'n- in. »j 5n. 3n- 2n. in. 6-28 578 •84 -91 6-05 74 •47 -04 -o 57 ■8 6-24 5-87 603 -27 •II 5-98 -91 ■99 6-05 -02 ■02 5-93 •83 •60 73 •95 •63 •59 -76 •58 6-20 5 "99 6-06 S-8i 6-0 5-89 •95 6 -04 •13 5^65 •74 •79 R. A. 8" 19-5" Dec. -40° 36' 1783-07 1820-60 2-i8 30-76 40-24 22-12 5-26 30-18 1-07 •17 7-26 43-18 0-88 3'i7 9-54 0-24 4-28 6-30 9'32 51-28 3 '30 7-26 62-29 42-32 403 5-98 51-15 2-95 5-24 6-27 7-29 8-10 61-33 52-25 4-16 4-89 6-20 62-11 3^14 5-41 6-10 9^38 6-24 9'S4 74^ 1 7 •18 •18 297 h. 4087. Probably a binary. Ja. 146-6 I 147-5 0-83 I34"9 12 ••45 M. 7-8,8 >837^iS 8-o§ 58-20 298 OX 193. R. A. S"" 21°' O.S. Dec. 33° 57' C. yellowish. M. 7. II Be. 297-1 in. 14-14 1844-30 293 '9 ,, -36 8-25 294-6 »» -17 50-26 •9 „ -12 61-26 295-6 3n. 13-64 8-11 299 Z 1263. R. A. Dec. M. 8" 37-1°' 42° 8' 7-6, 8-2 On reducing the angles of position to the equinox of 1850, O.S. finds twelve relations, and on converting them into rectangular coordinates and treating them by the method of least squares, he obtains A A = (+ 5"-S03 ± o"-o32) + (o"-2646 ± o"oo24) (/ — 1850-0). A D = (+ 19-054 ± 0-016) -f (0-6554 ± 0-00I2) {i — 1850). Uniform rectilinear motion perfectly satis- fies the A D. In the A A the differences are less satisfactory. He thinks it probable that 2.'s measures contain systematic errors. 2. O.S. Ba. Ea. Fit. Mo. Be. H. la. Bq. 359-0 41 •9 7^3 8-0 •4 9^3 10-3 •3 11-8 12-4 •3 14-8 15^7 -6 16-7 17-8 18-9 13-2 17-1 15-5 l6-6 17-1 16-4 18-3 i7"o 18-2 i6-8 19-0 21-6 19-6 i8-7 in. 4-86 1828-36 7i 5-43 9-46 tt 7-08 31-31 ft •46 2-33 »» •97 3-29 »i 8-93 4-36 ft 9-59 5-35 t. 10-34 6-42 „ •47 7-o6 it 11-63 8-34 tt 12-88 40-27 4n. 13-05 -28 »» 16-50 5-08 »l 18-89 8 -80 »» 20-56 51-05 »» 22-64 4-07 2n. 27-06 60-27 3"- 34-35 70-63 14-28 41-33 22-47 54-13 14-59 4269 22 20-84 52-15 22 21-22 319 30 22-50 4-22 20 26-74 60-08 23-04 55-37 29-12 63-38 in. •72 4-30 tt It 31-24 6-10 70-03 tt 36-01 6-26 31- 35-12 I -91 254 DOUBLE STARS. W. *8. GI. Bp. Dob. K. R. lb-4 4 ... •2 4 3S-6 •I 3 •8 S 37-iS l9'o I i8-6 37-44 •6 2n. •9 f» 38-57 •8 -9 1872-25 -30 3-J9 5-27 472 5-27 6-13 -36 7-25 300 S. 1273. R. A. 8" 40-4°' ( EYSRS. Dec. 6° 52' M. 3-8. 7-8 C. A, yellow ; B, blue. It is extraordinary that this beautifiil star should have escaped the scrutinizing eye of Sir Wm. Herschel. S. (M. M., p. 4) had no doubt about the motion. Sm., at the request of Dawes, examined this object and thought that the angular motion was about + o°'8 per annum, "or a circuit of 4^ centuries." The later observations only partially sup- port his former impression of a diminution of distance. (Dawes.) Secchi says the motion is orbital. 0.2. in i860 and 1864 suspected that A was oblong in the vertical direction. The common proper motion is — 0"0I3 in R. A., and + o"-04 in N. P. D. Duner gives 1853-39 A = 3"-34 for the distance ; and for the angle, P = 206° '5 + o°-543 (' - 1850-0). 2. Da. Sm, Ch. Xa. 192-4 195-9 198-3 •6 200-8 195-2 197-6 199-1 197-9 201-6 203-5 205-7 206-7 208-5 198-4 199-1 203-2 197-8 202-7 200 -o 203-0 209-1 208-3 212-4 210-7 3n. 3-31 f) ■14 ft •16 *i •20 2n. •39 in. 4-34 2n. -26 in. 3-6S »» i6n. 3-50 3n. •42 in. •42 31- -50 in. •43 -4 •5 •6 m. •44 tt •82 i» 2-83 7n. 3-32 4n. -37 »» -28 2n. •04 I in. -39 1825-23 31-29 5-28 6-27 40-30 3«-i3 2-20 4-00 7-23 40-95 3-21 8-14 -83 5>-32 37-11 9-22 43-14 I -20 3-17 4-16 2-64 S2-30 6-25 7-29 60-28 Ea. O.S. Ja. Ho. De. Po. W.O. Ta. W. *8. Dn. Schi. 8p. Dob. PI. 203-0 7n. 3-13 203-5 2n. -50 208-5 3n. -27 21 1 -0 »» •43 217-5 tt -44 203-6 -74 209-1 9 •33 -6 10 -26 212-7 3n- -21 208-0 m. •69 -9 3n- •04 210-6 2n. -42 211-3 m. -74 -9 5n. ■44 210-9 2n. •24 211-3 in. -65 213-0 ,, -S3 212-8 3"- -45 216-3 91- ■44 2170 in. •36 218-4 2n. -26 217-5 in. •32 -8 It -45 218-5 i» -40 2I0-0 4n. •33 215-6 in. •48 213-2 IS -06 199-3 2 •32 200-9 in. •40 2IO-1 *> 216-5 »» 359 215-6 »i •37 216-8 3"- •41 204-7 3n- •87 207-2 m. •68 216-8 » 2-94 217-6 ,, 216-2 5 3-28 219-3 S -18 -3 I 216-7 6 3-33 221-5 7 -47 216-2 3 •4 219-3 5n. •20 217-9 in. •31 •9 •31 219-2 In. •7 gn. ... 216-7 2n. 3-67 1842-36 3-3« 8-97 61-62 8-88 46-20 5324 ■99 7-39 2-27 4-28 8-30 4-92 5-21 6-15 7-08 62-92 3-20 6-01 8-25 70-27 117 3-23 5 -28 56-19 65-27 1-27 63 •17 70-26 1-22 -23 65-18 6-10 7-20 74-23 6-34 2-19 3-19 -19 4-18 532 4-09 5-28 -29 •29 •99 6-20 ■73 301 2. 1281. R. A. Dec. M. 8" 41-4°" 0° 28' 7-3, 8-3 The motion appears to be rectilinesir hitherto. S. De. Fl. 329-6 5n- 25-02 328-6 25 ± 326-7 27-15 323-!* 29-47 321-9 in. 31-10 1833-48 2-30 4723 64-50 77-31 MEASURES. 255 302 S. 1280. R. A. Dec. M. 8" 44-4"' 71° 16' 7-5, 7-6 C. yellowish. The angle has increased and the distance has diminished. H, ft So. 2. Ko. Be. Da. 31-2 2n. 8-75 34-0 4n. 7-43 3X9 in. •42 360 3n.. 6-6i .37-S S' 36-2 3"- •67 37 -S t* SI 40- 1 6n. •14 1823-33 31 90 43 'OS 5213 6471 56-27 64-71 73-83 303 Z 1287. R. A. Dec. 8" 44-9°' 12° 3S' Probably a binary, Z. 109-4 I S"- I I '41 Be. 95 'o I I -86 M. 8, 10-3 1 1830-60 I 63-20 304 2. 1291. (r< CASCSI. R. A. 8' 47" Hi- H, * So. 2. ■a. O.S. Be. Be. Ko. Bn. Dec. M. 31° 2' S-9. 6-4 s formulae are 1850-50. A = . I" -42. 334°-i-o°-o6(/-i85o-o). 338-2 in. ... 1782-28 340-2 ft 1-89 1822-14 333-3 5n. -5' 9-71 335-4 1* -47 42-90 ^^2-8 2n. -41 S-28 •2 in. •28 7-36 •I i> -'3 830 •0 tt -24 9-32 •5 It •S3 S3-30 33S-2 n •42 9-30 334-0 tt -SO 60-28 -0 f •47 •29 33«-o 2n. •2 5619 333-« 3n- ■34 •27 336-0 2n. •40 7-29 334-9 3n. -29 60-15 332 -s 4n. •43 71-02 305 o.t. 196. I VBLSSi HAJOSIS. R. A. Dec. M. 8" SI" 48° 31' 3-«. «o-3 Orbital motion has distinctly shown itself. The conunon proper motion of this system is no less than — o'-047 in R. A., and + o"-28 in N. P. D. 8m. Ch. 0.2. Ha. Be. 348-8 -o 3S0-0 351 -8 -8 355 -o 356-9 350-7 357-1 12-0 in. 10-68 4n. -69 Sn. -54 in. •18 2n. 9-78 10-14 9-72 I83I-7I 9-12 41-19 s-27 51-68 61-24 71-80 52-27 69-38 306 2. 1296. R. A. gh J,. go Dec. 35° 25' M. 8-S. 9 Probably a binary. Duner has A = 2"-59 — o"-oi28 (/— 1850-0). P = 73°-7-fo°-i36(<- 1850-0). 2. 71-2 31. 2-83 1831-59 Ha. 72-6 2n. -67 44-27 Bn. 76-6 If •3" 71-26 307 Z 1300. R. A. 8" 54-6" 2. H, Be. 0.2. W. AB. 01. Dec. •5° 45' C. yellow. 2I0-0 3n. 4-11 21 1 -0 2 204-2 24:1 3". In. 4-67 -98 •68 203-3 ff -86 202-4 ff ■79 203-4 -4 4 6 •83 •s 204-0 4 •6 M. 8-7, 8-8 1830-19 2-20 56-58 65-27 6-28 8-29 70-28 4-18 -18 -18 308 2. 1306. R. A. 8" 59-8" Dec. 67° 37' M. 5. 8-2 The dimination in distance and increase in angular movement have been marked since 1850. The apparent orbit is probably consider- ably elongated. The proper motion of A is — 0^-005 in R. A.f and +o"-ll in N. P. D. H,. 283-0 in. [7-93] 1783-68 hJ. 267-3 50 1832-10 2. 263-2 sn. 4-59 -99 8m. 2624 50 5-27 256 DOUBLE STARS. O.S. Da. Ka. Ho. Se. Se. Ta. W. 4S. 01. 260-3 •6 257-5 ■5 249-5 246-8 262-8 258-2 261-6 258-3 257-2 253-5 252-6 247-5 245-2 261-8 258-1 249-5 246-7 249-8 246-8 247-2 2n. 4-50 in. -24 „ 3-89 ,1 -71 >» •17 •16 2n. 4-46 »» 3-92 4-36 30 3-61 3"- -41 8n, -25 »> -22 3n. 2-88 2n. -68 3-51 2-76 4 -85 4 3-07 4 ■20 4 -20 5 2-9 1840-34 6-37 51-39 4-37 66-42 72-41 41-20 51-28 4249 54-26 6-34 63-19 5-8i 71-52 5-21 66-IO 71-39 2-28 -30 324 -29 418 309 t. 1316. R. A. 9' i-9"» Dec. -6° 39' M. a8-2, b II -5, c 10-5 C. white. Certain change, but of uncertain nature. 2. 146-3 3n. 6-78 1832-88 Se. 139-6 in. 5-79 57-26 138-9 ., 6-94 65-19 De. -4 -74 4-84 W. & S. 139-7 in. -18 74-17 CO. -8 7-38 7-18 2. Se. Oe. W. &S. 61. CO. CO. A C 153-1 31- 13-05 156-2 in. 11-28 153-9 »» 1005 158-7 -08 157-8 in. 9-5 155-0 „ 163-5 .. 9-06 BC. 28-7 4-20 32-88 57-26 65-19 4-84 74-17 4-18 7-i8 77-18 310 R. A. g"" 2-5"° 2. 1313. Dec. 70° 28' M. 8-5. 87 The angle has probably increased. 2. O.S. Se. 240-8 3n- 0-84 242-2 4n. -87 50-5 i-o 1832-39 45-84 66-74 311 X . 1321. R. A. Dec. M. gh g.jm 53° '3' 7-4. 7-4 The distance is probably unchanged. The proper motion of A is probably large. Duner has A = i9"-87 — o"-oi (<— 1850-0). P = 52°-4 + o°-24 (^-1850-0). 2. 43-8 in. 1820-92 ... I in. 21-12 2-07 48-1 3"- 20-14 31-35 ■9 ,, 19-93 5-73 So. 45-8 5n. 20-80 24-46 H,. 51-5 -0 31-40 0.2. 50-5 3"- -17 40-32 52-2 4n. •00 8-57 Da. 50-8 5n. -22 2-89 51-8 19-87 8-29 Ma. -4 2n. 20-10 6-29 53-0 m. 19-47 51-09 -0 2n. •23 2-42 54-9 in. -91 8-38 52-3 fi •38 61-67 De. 55-7 Sn. ■74 3-12 H. 53-4 •3f -25 la. in. 20-23 6-35 56-2 „ 19-63 7-23 58-0 2n. 20-17 71-39 55-0 in. 19-92 2-18 S7-0 »» 20-29 4-23 Bl. •0 •0 •22 Dob. 58-4 n 6-07 312 s. 1329. R. A. Dec. M. 9" 9-6» -0" 44' 8-3, 8-5 C. white. S. 65 -5 4n. 27-68 1831-21 -7 •19 4-26 Eng. 67-4 24-56 63-25 De. ■3 23-73 4-76 313 2 3121. R. A Dec. M. g"" lo-;" 29°' j' 7-5. 7-8 The orbit of this system was computed in 1866 by Fritsche from the observations between 1831 and 1864. The predicted places for 1874 are, however, far from repre- senting the observations. 0.2. explains MEASURES. 257 this by saying that the distances were not corrected for systematic errors, and he pre- dicts that the star will be single in 1877. The period is about 39 years. Fritsche's latest elements are — (I) Q = 19° s6'-4 u> = 143 17 -2 e = 0-347 « H = +9-188 TT = 52° 23' 'O a — o"-696 p = 39^"- 18 Epoch 1850-0 (2) 23°-S 141 -6 0-3725 + 8-862 S4-II o"-7iS 40-62 1850-0. The elements in (2) are based on the same observations with O.S.'s corrections applied. According to this system of ele- ments Duner finds that the distance in 1878 would be o"-49 ; but the star was oblong in 1874. 2. O.S. De. Gl. 20-0 m. 0-85 I 239-1 3n. elong^- 190-2 m. »» so »» 1-25 18-8 0-48 210-7 -45 29-6 ■44 34-4 ■4« 250 in. oblong ? 246 ob.&sep. 243 "S 0-40 198-4 oblong 8-5 0-33 27-6 •55 214-2 -54 330 ■s§ 43 3 •48 228-6 ■42 59-7 ■33 Certainly double 8-9 „ 0-67 13-0 »» "'I 29-5 »» •78 23-8 i» -85 26-1 •88 35-3 j» •82 215-4 }f 'It 36-4 ft •68 40-4 »» ■64 53-0 J, •43 250-1 11 oblong 14-8 °7o 19-6 •68 21-3 •7 ■8 -7 27-6 32-6 0-6 210-5 elong"- 213-9 it 214-9 f > 251-9 »» 210-4 s 1 0-5 1832-31 40-32 4^28 •30 6*29 7'34 8-25 9-32 028 •32 ■35 4-26 ■30 6-29 7-34 8-25 9-32 50-30 1-26 61-29 •30 4-30 8-29 -30 931 71-28 ■31 2-31 4-28 •28 5-29 63-11 6-22 7-26 8-25 9-85 71-21 2-23 3-38 4-21 53' 0-44 01. Su. Sp. 212-7 4 0-5 ; 214-5 4 •5 206-9 2n. •65 208-2 31- •75 209-3 m. •68 220-0 2n. •3 225-0 in. -2 245-2 •3 279-9 •35 1871-21 3-70 0-33 1-27 2-09 4-24 5-20 -29 718 314 2. 1333. R. A. Dec. 35° 52' M. 6-6, 6-9 Duner gives 1853-82. A = i"-49. P=4i°-7 + o°^io (<-l85o^o). S. Ma. 0.2. Se. De. Ho. Eng. Du. 38-6 39-4 40-5 42-6 •5 •9 •8 43-6 •4 41 5 43^o 39' 2 453 41-4 4n. 1-42 3n- •38 5n. ■46 6n. •57 2n. •38 6n. •633 2n. •43 in. •78 »» •3 •51 3"- •44 4n. •65 tf •45 1782-86 1828-59 31-12 45-5> 53^'3 9-83 0-13 6-32 65-19 57-92 6646 59-27 65-55 72-24 315 2. 1334. R. A. gt il-4"> Dec. M. 37° 19' 4, 6-7 C. A, white ; B, blue. The common proper motion is — o'-oo7 in R. A., and +o"-04 in N. P. D. Duner has A = 2"-8o. P = 240°-4 - o°-o5 (^-1850-0). H,. H2&S0. S. 8m. H,. Ua. De. Se. Ko. 244-2 242-7 240-2 •7 241-6 239-2 240-8 ■9 241-7 240-6 -4 239-5 241-5 239-1 241-5 238-3 in. 1780-90 4n. 2-89 1822-46 6n. •69 9-17 in. -70 52-00 -8 32-35 -5 2-40 5n. •97 43-30 -47 7-19 -62 5430 -46 6-44 7-43 2n. -84 9-83 3"- 3-0 5-19 2-80 66-56 4n. -84 57-36 2n. •91 9-16 17 258 DOUBLE STARS. Sd. 239-0 in. 2-90 1862-13 Ta. "O -89 6-16 Sn. 240-8 2n. •49 71 "25 W. &8. 238-8 in. ■82 3'i9 01. •6 t> •92 418 316 0.2. 199. R. A. Dec. Si° 46' M. 6-1, 10-2 The distance has probably diminished. O.Z. Oe. 116-781 4n. 117-171 3n. 5-74 11847-02 -32 I 68-11 317 X. 1338. 157 LTNCIS. R. A. Dec. M. 9"" I3'4" 38° 42' 7. 7'2 C. white. From the measures between 1827 and 1833, 2. suspected a slow direct motion. Se. (p. 27) says the motion is certain. 0.2. A gradual angular change, the di.«;tance remaining as in 1829 ; the ap- parent orbit is, therefore, probably nearly circular. Duner's formulae are 1854-50. A = i"-67. P = i33°-i +o°-6257 (/-1850-0). 1829-53 30-25 219 8-10 43 '42 5 '04 2-78 478 983 40-33 2-30 7-36 54-25 -26 68-34 73-31 41-23 2-23 3-17 817 50-12 4-20 ■24 5-20 •91 6 04 62-85 3-1S 4-07 Ma. 0.2. Da. Ho. Se. I2I-I 5"- 1-76 119-7 2n. 2-51 Ii6'4 in. 1-42 1271 -70 130-3 6n. -66 132-7 2n. •80 134-8 5n. -70 135-5 }) •71 140-5 2n. -61 128-1 4n. -82 130-2 in. ■89 128-2 »> -58 134-5 )» -66 135-4 II -82 142-4 f 1 •84 149-8 »i -72 125-9 3"- ■75 127-3 ,, •72 -7 in. ■66 131-8 3"- -66 -9 2n. -69 134-6 5n. •65 137-0 4n. -92 135-7 3"- -6 in. 1-2 138-6 11 ■5 -8 X •73 141-3 3n- •51 -0 in. •63 Se. Eng. Kn. la. Dn. W. & 01. Sp. Bchi. Dob. S. 137-1 143-5 142-5 143-4 142-6 141-2 145-2 142-9 150-0 149-0 151-8 145-8 147-7 -6 •8 150-0 •5 •o 147-0 149-3 -3 •6 2n. 1-63 3"- 2-00 2n. I-7I -66 in. •58 ,, 1-24 >) 2n. 1-26 •66 4n. •63 4 •87 8 •46 2 ... 6 1-57 4 ■73 4 ■55 5 ■78 4 •7 -76 in. -76 5n. 2-13 R. A. 9'' 16-6" Dec. 52° 5' Slow direct motion. Ua. 0.2. Da. Se. Da. 334-4 337-2 335-2 338-5 333-7 338-3 •5 R. A. 9" i6-8'° Ma. Dec. 28° 24' 0.2. Se. 236-3 230-3 229-9 233-4 229-2 1856-31 65-31 -47 6-67 71-40 2-18 4-23 S-I8 6-34 1-24 6-29 2-27 3-19 -23 4-17 527 •29 626 4-18 5-33 -33 621 318 OX 200. 4n. 1-39 2n. -52 5n. •41 in. •56 3"- 1-34 2n. •54 M. 6-7, 8-4 1845-64 51-34 47-09 8-28 60-25 7-60 71-36 319 0.2. 201. 1-24 •33 •47 6n. •45 31- •48 M. 7-5. 9 1843-25 6-32 7-41 52-43 67-72 320 2. 1346. 21 T7BS.S: MAJOBIS. R. A. Dec. M. 9" 17°' 54" 32' 7. 8 C. A, white ; B, bluish. Hi. 306-7 317-6 Hj & So. 309-0 S. -o 310-9 in. s'n. 6-47 5-69 1782-87 1802-39 22-12 -12 30-99 MEASURES. 259 Ha. Oe. Se. Ho. Da. GI. 310-2 ■3 •8 3" -9 3IO-3 ■7 3127 •o 7n. 5-65 2n. •95 ,1 •94 in. •4« 3n. •80 •81 2n. •51 in. •3 1842-57 Siii 6 '29 5 '99 698 818 71-69 426 321 2. 1348. 116 (B) HYDEJE. R. A Dec M. 9" 18- 2" 6° 5: 7-5, 7-6 C. white. Slow angular chanee. The distance has probably increased. V 334-3 4n. 1-09 1831 ^02 Ha. 3313 -27 40-38 O.S. ■I in. -07 5-31 325-4 ,, -21 8-25 -8 ,, -64 64-30 1493 ») •67 829 Se. 327-7 2n. •41 56-74 Be. 328-1 -66 63-15 W. &S. 323-8 5 ■78 72-19 325-3 4 •61 -26 326-1 4 -70 322 .1 2 •7 •24 -2 II •69 4-16 324-3 4 •80 6-28 ■9 4 •29 Gl. 3260 in. 16 4-18 Sp. 323-2 ■70 7-19 Dob. 325-3 2n. ■45 •31 322 X. 135 w LEOm 6. s. R. A. Dec. M. 9'' 22" 9" 35' 6-2, 7 e C. A, yellow ; B, yellower. This very difficult double star was discovered by H, in 1781, and he early suspected that these two stars were receding from each other, and subsequent observations confirmed his suspicion. '-On the 2lst of April, 1795, they were ^ diam. of the small star asunder. Feb. 5. 1804, with a power of 527, the vacancy between them was nearly i diam. of the small one." Between Nov. 13, 1782, and Feb. 4, 1802, the angle had changed 19^59', "proliably owing to a real motion of w Leonis, for the etlect of a parallactic motion would have shown itself in a contrary alteration of the angle of position." (P/ir/. Trans. 1804.) So. (Fhil. Trans. 1826, p. 154). A power of 420 with refractor by Lerebours, 8-4 inches aperture and 11 ft. focus, at the Royal Observatory, Paris, separated the small star "J a diam. of the large star ; with 560, } of a diam. ; with each power the stars are admirably defined, and as round as possible." This was on March 15, 1825. Hj adds, "There can be little doubt, therefore, that this very curious double star is entitled to a place among revolving stars or Binary systems." Neither Hj nor So. could get measures of distance ; they could only wedge it. Dawes in 1831 says, "decidedly elon- gated." O.S. It is evident that the distances in 1840 and 1842 were estimated by me much too great. Madler's elements, from observations to 1846, are T = 1843-408 S=-i59''5o'-5 X =120 27 -5 i = 50 38 -2 ^=0-62564 =sin. 38°43'-8 m =i83'-7ii a =o"-8505 Jr'=o -03544 I' = ii7-577 years; while those from observations extending to 1841 are Perihelion passage Mean annual motion Node Perihelion from node Inclination Excentricity Semi-axis major Period Klinkerfues, in elements : — 1858, 1849-76 +261-72 135° II' 185 27 46 34 0-64338 o"-857 82-533 years. gave the following I. II. III. Node. iii°5i' 169 12 162 13 Y k e p T a 1 57° 14' 60 13 54 25 217° 22' 84 10 107 9 0-3605 -7225 •6286 i33'"-35 227 -77 142 -41 1876-44 41-40 43 39 0-703 1 I -307 ; I -092 ! 26o DOUBLE STARS. uoDercK- in is as "definitive 70 puDiistiea tne louowmg until further observations Ja. .^43-3 2n. 0-45 1853-18 -96 6-22 7-98 under the now more favourable circum- 350-0 It ■4 stances have been taken " : — 2'3 S'S 4-6 ■4 S •4 Node 148° 46' 8-10 7 64 s Be. o-o 5n. 529 \ 121 4 2'3 11 0-35 7-86 e 0-5360 32-9 111. •30 66-30 P 1 10-82 years Wi. 6-2 55-34 T 1841-81. Mo. 355 elongated 7-29 On these Duner remarks that they are probably in better agreement with the So. 30-0 257 52-4 round in. wedg*** 1 8-29 65-25 8-12 7C-15 observations than any preceding elements. 11 '* __ Hj. 110-9 " {783-26 51-5 it tt 113 1 30 9 1804-09 53-9 J> " 2 -20 2. 153-9 163-4 172-8 1 73 '9 358-7 Sn. 2n. 3"- 0-97 •51 ■44 25-21 32-25 329 5 '34 6-28 Eng. Du. 60-2 64-6 23 337 37-9 4n. sn. 2n. 2n. in contact 046 :^7 •27 3-42 5-25 65-67 7-34 70-33 1800 8-33 42-7 in. 1 -3 I -31 80. 154-2 8m. 180-0 6 2611 66-7 5n. 1 -42 5'^ J 0-? 32-11 W. &8. ^^■^ 4 ! -57 2-18 round 4-25 67-3 5 4 ■19 355 elongated 9'33 58-7 747 2 3-23 193-0 0.2. 247-5 2n. 0-3 ■49 4314 c-29 2 5 °i ■23 626 30-2-3 4"- ■41 231 72-3 4 ■29 316S 3209 32 10 322 9 2n. ■37 3-30 Gl. 57-0 3 ■4 329 3I1- 2n. •48 •44 ■45 4-29 5-31 6-30 Schi. Sp. Dob. 62-7 7 52-6 m. 3n- •49 ■49 5-25 -26 6-23 32S-S „ ■53 7'33 73 'o 1' 0-51 7-21 332 I 4n. •43 8-32 PI. 71-2 5n. ■54 ■21 331 -s 3n- ■43 -48 9-32 50-63 335 -S 339-0 348-7 2n. •46 ■47 2-66 323 2. 1365. 3SX-I 6-7 in. 2n. z 7-28 9 30 134 ( B) HYDRff;. IO-2 „ •62 60-28 R. A. Dec. M. 11-9 ,, •56 1-28 9" 25"' 2° 0' 7.8 29-2 in. •52 4-30 44-2 31- ■55 8-63 C. A, yellow ish ; B, bluish white. 53-6 2n. •58 70-28 56-7 31- ■57 1-30 So. 164-3 3-76 1825-11 58 -s 2n. •52 231 2. 163-0 in. ■17 •28 63-6 3n- ■59 3-96 164-3 ,, ■03 8-27 Da. 354-5 I 41-18 1620 ,1 ■00 3 1 '29 300-6 3 2-26 -Q ,, •13 526 299-0 2 0-45 317 Ua. 161-5 2n. ■52 42-28 347-' 3 •6 54-17 •7 ,, •33 3-22 345-7 3 "53 •26 163-3 in. •41 5-13 Ua. 280-2 •85 43-14 6-28 33'-' -0 33'^ -4 337-1 7-24 8-33 324 X. 1374. 342-5 350-0 I 4n. 0-47 51-24 2-30 30 (B) LI :ONIS MINOEI 8. 346-5 ■35 3-36 R. A Dec. M. 351-9 359-3 ... 431 5-28 9" 34 m 39° 30' 7. 8-3 i-o 0-36 6-42 C. A, yello wish ; I 3, very bl ue. MEASURES. 261 Duner gives 1855-72. A = 3"-37. P = 277° -8 + o°-25 (/ - 18500). H,. 26r5 in. " 1783-06 S. 2747 3"- 3-31 1828-34 5?: 273-5 >t •79 30-21 Ma. 274-9 in. •77 44-27 Mo. 275-0 2n. •35 52-28 277-7 6n. •54 5 '30 279-0 2n. •43 6-12 Dn. 284-1 7n. •II 72-81 325 Z 1377. p. IX. 161 SEXTAKTIS. R. A. Dec. M. gh 37.3™ 3"! i' 7-9, " C. A, yellowish ; B, blue. The change in angle between 1830 and 1868 amounts to about 4°, that in distance to about o"-3. Secchi's measure in 1856 appears to be so seriously in error that one is led to suppose it refers to another sys- tem. (0.2.) S. Ma. 0.2. W. &S. 142-2 4n. 3-31 140-6 ■37 i37-« -22 129-4 in. -12 145 '9 »» •75 136-8 »> 1830-24 6-41 47 'SO 56-28 68-29 73"24 326 o.X. 521. V 1TBS£ MAJOSIS. R. A. Dec. M. 9" 42°» 59° 36' 4 '2. '"'8 C. yellowish. The two stars have a considerable com- mon proper motion. 0.2. 295-3 I 7n. I 11-32 I 1855-58 327 R. A. 9" 43 '4° 2. 1385. Dec. 17°/ M. 8-5, 10-7 2. 0-2 Ma. 3566 De. 351-0 3"- 2n. 1-23 •10 •10 1829-94 42-18 63-53 328 R. A. 9" 44"" Magnitudes.— 2. 2( &m Mi -O.2., 5 38. LJOBIS. Dec 54° 3 ,5-6;M 7' idler, 5, 5; Dawes, 5 J, 5}. Secchi "estimated the diameters as 4:5." Dawes was sure that the star in the n.f. quadrant was the smaller. One of O.S.'s discoveries. Madler, with the observations from 1845 to 185 1 before him, thought that a direct motion had been maintained, and that the distance had decreased since 1843. Dawes, too, was of opinion that there was a slow increase of angle ; and after he had received all 0. 2.'s measures, he was convinced of the binarity of the star. 0.2. , writing in 1875, suspects a feeble increase in the distance between 1873 and 1875, and observes that if this be so the periastre has been passed, and the elements of the orbit may soon be calculated with success. 0.2. Da. Ma. Se. Kn. Sn. W. &8. 8-0 10-5 14-9 •9 18-3 36-7 47-9 48-3 77-6 96-6 115-0 25 9 193-8 196-8 207-2 209-7 30-6 45-9 46 44 80 83 4n. 3"- 4n. 5"- 3"- 2n. »» 3n. 2n. 5 3". 2n. 4n. 0-48 ■36 •33 •32 ■36 -38 •37 •25 -23 oblong »» 0-4 -4 ■3 -31 •24 •3 •24 oblong oblong ? single 1843-11 7-65 50-39 1-90 3-64 880 61-74 5-42 72-42 3-45 54-28 46-01 7-41 51-39 2-40 7-34 66-40 9-37 -43 70-42 •43 324 329 t. 1389. R. A. 9" 45-5" Dec. 27° 33' C. yellowish. Ma. De. 329-2 327-2 316-7 3"- 1-67 -64 •99 M. 8,9 1830-61 43-19 63-66 330 %■ 1386. R. A. 9'' 45-6" Dec. 69° 28' M. 8-2, 8-2 This star is in the Nebula Messier 81. Very slow retrograde motion. 202 DOUBLE STARS. H,. V Ma. 0.::. Kn. Se. Gl. 302-3 ■-S 296-0 .in. •98 293-1 2n. -84 291-3 in. -22 II5-8 5"- 2-01 295-7 in. I -61 294-2 -89 291-4 in. 1831-10 3211 42-69 S-3« ■93 64-10 9-15 70-12 331 8 SEXTANTIS. R. A. Dec. M. 9" 46-6"' -7° 32' 6, 6-5 A star first seen double by Mr. Alvan Clark when observing with one of his earliest glasses 4f in. aperture in 1854. Dawes had a strong impression that this ';tar would prove a binary. Sa. vr. &s. De. 50-1 51-2 38-2 173-8 169-0 0-6 -5 -5 single ? elongated Se. Sn. 333 X. 1406. R. A. g" 59™ 2. Ma. 0.2. A. 0.2 Se. 1854-17 •26 60-34 72-19 3-26 S-30 332 0.2. 210. R. A. Dec. 9" 55-1™ 46° 57' Very slow retrograde motion. 0.2. Ma. 270-6 3n. 0-93 278-1 -8 269-5 •7 272-0 -8 268-3 -8 267-7 8n. •75 -2 .3". -80 271-9 2n. •84 M. 7-5. 8-3 1845-27 3-31 5-43 6-32 7-41 8-38 68-57 70-80 Dec. 31° 40' 228-2 231-6 236-0 3"- 2n. 3n- 1-14 0-96 I -21 M. 8, 8-7 1830-27 44-28 5-60 334 0.2. 213. Dec. 28° T II7-7 in. 0-87 I2I-6 -96 '15-3 I 02 114-7 -19 107-0 0-93 II5-I -99 113-2 3'n- i-ii M. 7-8. 9-5 1843-30 4-26 8-25 60-29 71-28 4-28 67-83 335 0.2. 215. R. A. Dec. 18° 20' M. 7. 7-2 The distance has increased, and thia has been accompanied by a considerable dimi- nution in the angular movement. 0.2. Ma. Se. Se. Sp. 266-52 4n. 0-47 258- so 2n. -45 254-52 4n. -48 243-70 2n. -60 23360 .3". -74 231-50 2n. -68 229-15 ,, •82 257-8 •30 243-5 in. -47 233-6 31- -74 223-4 -63 [844-54 8-32 51-34 6030 7-20 9-78 75-81 49-04 57-34 67-20 75-32 336 0.2. 523. R. A. lo"" 10-6"" 39 LEONIS. Dec. 23° 42' M. 5-8, 1 1 -4 The companion is probably variable. The two stars have a large common proper motion : it amounts to — o"-44 in R. A., and + o"-o8 in N. P. D. 1851-26 61-24 54-28 66-86 0.2. 295-65 4n. 6-73 298-05 2n. -96 Ba. 295-55 in. Se. 300-33 3"- 6-69 337 2. 1423. R. A. lo*" 12-6" Dec. 21° 10' M. 8-6, 9-3 c yellowish. Probably a binary. 2. 99-3 Se. 768 Be. -8 6n. in. 1-12 0-40 1-27 1830-94 56-28 65-23 338 R. A. lo'' 13-4" 2. 1424. y LEONIS. Dec. 20° 27' M. 2. 3-5 '. 2., A, golden ; B, greenish red ; H,, '- white, white with a little pale red" ; H, and So., "both reddish" ; Sm., "bright orange, greenish yellow." MEASURES. 263 I ms. ■00 '/TOM. This beautiful double star was dis- covered by H, in 1782. In his famous paper {PM. Trans. 1803) he examines the motion at length : he finds that the change in 21 years and 38 days amount to 13° 58', and thence infers a rough period of 1200 years, and that the changes must be ascribed to orbital motion. " The result of a great number of observations on the vacancy between the two stars made with the mag- nifying powers of 278, 460. 651, 840, 932, 1504, 2010, 2589, 3168, 4294, 5489, and 6652, is that with the standard power and aperture of the 7 feet telescope, the interval in 1782 was J of a diameter of the small star, and is now f. With the same tele- scope, and a power of 2010, it was formerly i of a diameter of the small star, and is now full one diameter. In the years 1795, 1796, and 1798 the interval was found to have gradually increased, and all observa- tions conspire to prove that the stars are J a diameter of the small one farther asunder than they were formerly. The proportion of the diameter of 7 to that of x [the com- panion] I have, by many observations, estimated as 5 to 4." Hj wrote, in 1824: "There can be no doubt of the motion of 7 Leonis, though it is probably less rapid than supposed by Sir W. Herschel. That no mistake in the quadrant (n.f. for s.f.) was made in the observations made in the years 1782-3 is proved by the diagrams made at the time." " The mean annual motion from the most distant observations comes out + o°'30, direct, or in the direction n.f.s.p." In 1826 Hj adds, "The present observations, therefore, confirm this motion fully in point of reality and direction, but indicate an acceleration which (considering the number of observations) may have some claim to probability. The distances disagree more than might have been expected." Madler paid much attention to this fine star, and was strongly impressed with the idea that measures of it made after sunset were very likely to be erroneous. He strongly recommended that this star should always be observed in full sunshine. The slow increase in the angle was noted by all the great observers, Z., Sm., Da., Ma., etc. O.Z. The distance has augmented con- siderably, with a corresponding diminution of the angular movement ; for the change in angle per annum between 1782 and 1828 was o°-4i, and but o°-28 between 1828 and 1872. For some account of the distant star see Lists of Measures ; it is of the 7th magni- tude. Whether or not it forms with 7 a Ternary system the measures are insufficient to show. The proper motion is thus given : — Piazzi, R.A. + 35 Dec. — O-20 Bessel + 35 - o-is Argelander + 30 - 0-14 Doberck has published the foUowins elements :- _ 1876. 1879. T 1741-11 174100 Node 111° 50' in- 34' \ 194 22 I9S 22 7 43 49 43 6 e 07390 0-7327 P 402-62 yrs. 407-04 yrs. a 2"-oo. i"-98. Feb. 16, 1782 : 7° 37' n.f. April 18, 1783 : 5 24 n.f. Jan. 24, 1800 : 3 15 -75. Feb. 19, 1800 : 5 33 -45 ; sure is too open ; — 3° 22' _ better, but still open enough. Mch. 26, 1800 : 3° 46'-8. Jan. 22, 1802 : 6 4 s.f. Feb. 10, 1803 : 3 33 s.f. Mch. 22, 1803 : 6 34 s.f ,and6°3l's.f, the mea- 5 ; this is AB. H, & So. Da. Sm. 98-4 3"- 3 "24 1822.24 IOI-3 6n. 2-71 5-30 102-4 »» 3 '03 30-28 104-2 m. 2-65 3-22 102-0 6n. •45 28-14 103-2 5"- •48 3 1 '34 ■4 }j •50 275 104-9 ,, •56 S-16 IOI-8 3n. ■54 0-39 102-8 51- ■52 1-33 ■9 8n. -64 2-31 103-7 3r- ■^ 318 105-8 ,, -84 40-29 lo6-2 2n. •83 1-23 •5 i» •72 2-33 107-4 ,, •85 3-26 -8 »f -80 7-28 108- 1 Sn. -82 8-46 7 2n. •80 SI -87 109-7 3n. -84 437 -2 2n. 312 9-37 110-3 sn. -09 60-37 -I in. •01 4-50 •3 3n- •17 5 "37 103-2 2-6 3' 36 104-9 •s 6-42 264 DOUBLE STARS, 8m. Encke. Ga. Ka. 0.2. Ch. Ma. Ja. Hi. D.O. Bond. Fit. Ho. Be. 106 -o 2-6 107-2 -8 ioo'6 2 3-26 I04°2 4 ■54 105-8 12 2-90 •8 -90 107-6 6n. -89 105-2 ,, •96 107-1 8n. -72 109-7 711. •97 110-3 3-" io7"5 Sn. 283 -2 -81 106-9 m. •51 107-1 2n. •74 109-6 in. •81 108-5 2n. •79 -0 3n- -81 107-5 4". -66 106-8 3"- •79 107-3 m. -88 108-7 it •74 107-7 ,, •85 109-0 „ 3-02 112-1 »» 2-96 110-7 ») 315 109-3 „ -24 1 10-8 3"- -04 III -2 2n. -05 110-2 m. ■35 1130 2n. •15 II I -2 in. •12 114-2 2n. -26 ■3 m. -27 102-9 >» 2-76 105-4 »» -85 io6-i »» -87 105-1 8n. •78 •9 4n. •77 107-1 5n. ■78 7 Ion. •64 108-0 8n. •74 •9 3n- -81 107-9 i6n. -78 108-7 gn. ■88 •7 •67 •7 I2n. •94 •9 9n. •92 105-6 ■90 107-8 10 •91 108-4 10 3-07 109-6 3"- 2-92 ■0 »» 3-09 107-4 lOI-I 3 '40 111-5 2-96 108-3 ■9 •I 25 -84 ■4 38 3-0O 105-6 20 -16 108-8 30 ■05 iio-i 20 -07 108 I 6n. 2-94 109-6 sn. 303 1839-23 De. 43-18 37"9 8-33 9'34 9-36 4015 1-35 2-37 3-33 66-28 Se. 40-35 1-40 2-43 4-31 •Wi. S-3S 6-34 An. 7-35 Po. 8-36 9-35 50-32 U. 2-37 5-32 7-28 8-38 9-35 60-33 1-36 Bo. 2-36 636 Eng. 836 70-35 Kn. 1-34 442 Ta. 41-20 2-28 4-25 126 223 6-27 8-39 Dn. 51-28 3-82 4-48 6-21 7-34 838 Gl. 9-34 4580 53-22 -96 6-79 •W. 4 7-76 45-89 7-22 •26 8-27 50-91 321 8p. 2-29 Schi 5-34 Dob. 60-12 5436 PI. 5-23 Fl. 109-9 5n. 3-14 -3 2n. 2-91 •3 9n. -84 110-3 71. •99 I II '2 2n. 3-00 IIO-6 3". -12 -2 4". -13 -8 3n. -15 III -2 2n. •29 •6 4n. -14 1081 „ -05 110-3 5n. 2-97 108-1 4n. 3-05 1 10-3 .3"- -18 iii-i -07 ■6 2-87 1096 3-35 108-7 30 -22 109-8 43 108-8 60 3-32 107-3 in. -10 iio-o »» •16 111-9 -55 109-6 ij •53 1136 •56 112-3 ,, -69 III -8 3n. •50 109-6 2n. -24 •7 •25 112-9 3n- •39 IU-5 -24 1 10-5 3n- -21 112-7 »» •03 109-1 2n. •38 1 08 4 in. •17 111-6 ,, •16 110-4 2n. •97 108-6 31- 4-53 109-2 in. 2-62 1 12-9 -93 III'2 I in. •98 •9 4n. 3-10 112-3 8n. 2-98 -4 „ 3-14 113-2 3n- -06 -4 6n. •10 110-7 5 •II 113-0 4 ■1 III-O 6 ■0 1109 5 ... II2-6 5 3-7 113-0 4 •78 II2-6 4 •36 •5 5 •50 -6 4 •43 110-2 4 -04 nr8 8 112-9 5 ... 1 10-9 3-38 -8 in. •38 112-7 7n. •84 iii-i 8n. •63 •8 2n. •51 1I2-0 in. -30 1856-19 62-78 3'35 6-90 8-37 70-27 I 28 2-34 3-25 5-27 55-35 6-95 887 65-04 5529 6-29 61 32 54-13 5-10 61-13 2-35 7-34 8-39 71-23 ■44 4-32 5-16 63-21 -21 4-31 5-42 6-21 71-38 66-27 7-23 8-18 70-32 1-38 4-32 6-34 69-39 70-38 1-44 2-44 4-12 5-46 0-30 '■32 -41 3-30 412 1-48 2-19 3-23 4-20 323 6-25 5-29 -28 6-16 7-23 6-45 7-41 MEASURES. 265 AC. Be. 8e. Po. n. 295-2 300-0 294-8 293-6 •o •s 292-8 in. 10 III 196-5 215-0 2178 -I 229-3 1782 83 1825 56 59 61 77* 339 t. 1426. 145 (B) LEONIS. R. A. lo"" 14-2" Dec. 7° 2' M. A7-8,B 8-3, 09-3 C. A and B, yellowish. S. discovered the duplicity of the larger star. Se. says " the motion in angle appears certain"; but Dawes, writing in 1867, observes, "The measures at different epochs scarcely decide the question of relative motion in the close pair ; the discordances being rather unusually large even for so difficult an object." He also says, "There seems to be no doubt of the fixity of the small distant star with respect to the close pair." A B. The distance appears to have in- creased about o"-l, and ihe angle about 4°, between 1833 and 1847. (0.2.) A + B and C. Here also there has been 2 an increase in the distance. 2. 0.2. Ha. Ss. 8e. Be. W. ftS. AB 256-7 3n. 0-62 267-2 in. -8 262-6 3"- •77 263-7 in. •88 262-0 3n. •55 257-7 •73 263-3 •88 271-8 3n. •65 269-7 •78 w.o. Sob. single ? could not divide it 278-3 276-3 277-6 3n 274-0 2 in. 0-72 •60 AC. EjftSo. 2. 5-0 9-8 ■I 8-5 7 6-72 3n. 7-43 in. -29 1832-26 6-28 40-30 68-29 42-25 •30 54-16 6-25 69-15 74-21 6-26 •35 •36 •26 1782-13 1821-10 32 22 6-28 * This star was also observed by Flamsteed in i6qi. T. Mayer in 1755, and C. Mayer in 1777, the differences of R. A. being, respectively, 2, 4, 4 75 seconds. 0.2. 8-3 120 Da. 9-4 8e. 4-8 De. 9-7 Ta. 11-3 8-58 01. ii-o W.O. 9-3 10-5 •w. &s. -9 Dob, ■7 7-8 31- in 7-83 •88 2n. 7-68 •57 in. •79 -88 2 8-0 in. 7-81 t» 8-03 3 2 -25 7-78 4n. 9-17 341 X 1429. R. A. lo"" 18-4" H,. Da. De. W. &S. 01. 272-2 267-4 270-0 265-8 263-2 -3 262-5 342 t. 1428. R. A. 10^ 18-4"' Dec. 53° 14' C. white. 1840-30 68-29 52-33 6-25 67-17 71-36 6-34 4-22 6-35 •36 -26 •29 -24 340 O.S. 216. R. A. Dec. 10^ 16-3° 15° 57' M. 7. lo-S 0.2. 167-9 150-6 De. 151-1 3n. 2 -06 1-66 1845-62 73-29 6689 Dec M. 25° 14' 8-3. 8-3 3n- 1-48 1827-29 -58 33-26 I 230 -37 49-76 •09 6655 in. 0-95 73-24 ngated 4-21 in. ... 3-30 M. 7-5. 7-! Duner's formulse are A = 3"-68 - o"-oi5 (/ - 1850-0). P = 85° 7 + o°-i02 {( - 1850-0) + o°-oo04 (if - 1850-0)'. H,. 83-7 2n. 4-10 1830-60 S. 84-3 3n. 3-84 1-69 Sm. 85-0 -6 249 Ma. 86-7 2n. -99 44-21 De. 85-5 in. -69 58-00 Se. 86-6 2n. -75 -44 Mo. -2 „ -42 9-27 Du. 88-2 4n. -36 71-32 266 DOUBLE STARS. 343 OX. 217. 348 %. 1450. R. A. Dec. M. 49 LEONIS. lo'' 20"' 17° 50' 7-3. 7-8 R. A. Dec. M. 0.2. 150-4 2n. 0-49 1844-27 10" 28-7'» 9° 17' 6, 87 I43'5 149-3 151-8 In. •55 ■60 8-^33 75 '33 2. 161 -0 -I 2n. 2-43 -39 1825-31 30-76 Oe. 148 -I ^n. -82 6724 -I -37 3-50 160-5 Ma. 1595 2n. •49 -54 5-31 7-47 344 OX. 218. 158-9 -4 -59 •73 42-29 51-26 R. A Dec. M. -6 •75 2-26 jQh 21" 4° 10' 7-3. 9-2 Sm. 158-1 159-0 •5 -8 38-37 55-29 0.2. 66-7 2n. 1-24 1844-29 0.2. -0 ■97 2-09 63-1 in. -21 8-31 Ba. 155-3 -60 4-28 60 -6 ,, -26 61-24 Se. 1571 2n. •3 6-74 61-8 »» •23 4-3« M. 1698 -53 63-19 59-1 »» ■oii 8-29 Ta. 1549 in. 6-14 Be. 65-2 »* 0-91 57-34 i6o-2 ,, 1-97 7-23 Be. ■9 3n. •98 67-28 ,, 2 29 76-34 GI. 156-6 •W. & 8. '• -8 4-70 -20 345 O.X. 219. R. A. Dec. M. 349 t. 222. ,0h 22" 5«' 36' 7. io'3 R. A. Dec. M. 0.2. 299-2 in. 13-22 1844-31 lo" 30" 60° 46' 6-7, 10-7 297-6 •9 •3 )» •15 ■25 12-78 8-25 50-39 6793 0.2. 340-3 3n. 4-56 1847-72 De. 3". De. 345-5 4n. -58 68-70 346 t. 1439. 350 %. 1457. R. A. Dec. M. R. A. Dec. M. lo"" 235 21° 25' 8, 8-5 10" 32-5" 6° 21' 7-4. 8-4 2. I3i'4 3n. 2 02 1829-26 C. whitish yellow. H,. 129-2 I 31-30 Se. says " the motion in angle is beyond Os. -0 in. 40-29 doubt ; " and Dawes observes that there is 8e. 123-4 2n. 1-98 56-78 but little doubt of its binarity. Is. 0.2. De. 01. W. &8. 124-3 122-3 I2I-0 1239 122-5 121 -O 122-3 i-o in. >i 4n. in. 2 4 2-33 -89 -81 2-0 1-96 •82 66-37 71-36 4-32 68-29 -72 74-22 5-27 -30 2. 287-8 0.2. 302-0 310-1 3161 315-0 Ma. 3049 305-9 312-4 31 1 -2 41. 3n. m. tt j> 5n. in. 3n. 4n. 0-71 -75 I -01 -11 0-69 -66 -84 -99 1829-55 4029 64-30 8-29 71-31 42-24 630 51-27 2-29 347 X. 1445. 310-1 2n. 4n. •97 3-29 ■34 R. A. Dpr. M. Da. 302-7 2n. 0-92 0-78 10^ 26-6" -0° 15' 8-8, 1 1 -8 Se. 307-5 De. 304-6 5n. 4n. -76 1-0 6-24 8-30 C. A, yellowish. „ « 309-8 31. 0-91 63-20 W. ft 8. 312-3 5 •81 72-2g 2. 167-4 3"- 1 2-42 1827-58 -7 3 ... 3-2° De. IS9"4 1 •95 64-87 316-1 4 1-26 MEASURES. 267 W.&S. 313-6 315-3 5 7 1-20 ■12 187528 -32 355 2. 1472. 314-2 5 ■>7 6-34 Gl. 311-9 4 -0 3-20 R. A. Dec. M ScM. 9 in. -18 5-36 lo' 41°" 13° 36' 7-8, 8 5 Sp. 312-0 Dob. 316-6 2n. •18 -37 6-31 The distance has increased considerably. 314-5 u 1-38 7-21 .1, ° ■ ■ " 2. 39-S 0.2. -5 31- 33-74 34-36 1828-55 2n. 40-33 351 o.t. 224. -I 388 in. ■62 -88 2-32 6-33 39-1 M -II 9-32 R. A. Dec. M. De. 386 6n. 35-81 6457 10" 33-4°' 9° 28' 7-2, 9-2 Retrograde motion. The distance may have increased. 356 OX 228. 0.2. 20 in. wedg°- 1844-31 352-6 ,, 0-48 51-27 R. A. Dec. M. 348-8 »* -59 61 26 lo"" 40-7™ 23° 12' 7-2, 8-1 328-4 336-8 i» -59 -55 71-31 2-31 O.S. 203-3 2n. ! 0-53 1844-30 Ma. 15-6 -22 48-29 179-6 in. -43 8-24 Se. 13-6 in. elong^- 57-34 192-4 -33 50-38 De- 339-3 67-32 201-7 De. 199- 1 in. 3"- ■63 71-31 67-20 Sp. 13-2 -37 75-35 352 O.S. 225. R. A. Dec. M. 357 OX 229. 10" 33" 19° 52' 7-5, 9-8 R. A. Dec. M. 0.2. 3SI-3 2n. 6-57 1844-30 lo" 43-1°' 41° 44' 67. 7-1 350-8 in. ■62 5 -28 349-2 »> •64 8-31 C. white. 350-3 351-2 De. -7 3". •51 ■4' •08 9-32 67-26 O.S. 347-0 344-2 Ma. 350-2 Da. 347-3 De. 338-3 51. 411. 2n. In. 0-68 1846-65 59-84 45-42 9-27 66-95 3". 353 OX 227. Du. -7 4n. -78 72-05 R. A. Dec. M. 10^ 35"' 11° 21' 7-5, 8-5 358 t. 1486. 0.2. 326-4 2n. 0-54 1844-30 -7 in. 5' 8-33 R. A. Dec. M. De. 334-1 3"- 67-38 lo" 48'" 52° 45' 2. 102-8 2n. 28-32 7-5, 8-8 1831-38 354 S. 146 5. Ma. 104-5 '"- -66 40-40 R. A. lo' 36-2"" Duner gives Dec. 45° 'S' M. 8-5, 8-8 1855-76. A = 2" -23. = io*6-o°-i (^-1850-0). 2. Ma. Da. P = io^6 14-4 7-3 1 1 -2 359 0.t. 230 3". 6n. 2-24 -15 •39 1829-32 44'59 71-13 R. A. lo' 48"" O.S. De. Dec. 21° 24' 5-9 3-5 4-7 11-4 in. 890 »> -59 „ •45 31- -30 M. 7-7, 11-2 1844-30 5-28 51-27 67-27 268 DOUBLE STARS. 360 R. A. lo*" 49-1" X. 1487. 54 LEONIS. Dec. 25° 23' M. 5. 7 Slow increase in angle and distance. The proper motion of A is — o''oo2 in R. A., and o"-oo in N. P. D. Duner has i850"02. A=6"*20. P = i03''7 + o°-o64 (/ -1850-0). H,. 99 '2 ioo'6 Ho & 80. 98-3 2.' 1035 6m. Da. 0.2. Ka. Be. Ho. Be. Bo. Ta. Sn. W. Gl. Bp. Dob. &8. I02-8 ■5 7 1038 •8 •5 104-3 •6 ■3 103-9 o 104-4 103-3 -8 102-5 104-3 103-8 103-6 105-4 103-5 106-1 105-4 -o 104-6 ■s •9 in. >) 2n. 4n. I4n. 4n. 2n. 4n. 6n. 5n. »» 2n. ion. 4n. f ) in. 3"- in. 2n. in. 4 6 in. 4n. 7-02 6-20 •17 ■5 -2 -22 -26 ■34 -21 •40 •02 -II •34 •03 ■24 578 6-34 •33 •35 ■43 ■28 -81 7-05 5-90 6-3 -o •5 ■25 -50 1782-13 1802-10 21-68 ■17 •60 30'35 2 26 933 40-30 50-19 40-61 7-68 60-34 4378 51-27 3-85 61-14 52-25 5 '94 4-27 6-59 63-15 6-33 7-23 8-21 70-32 6927 73-24 4-20 -21 5-32 7 32 361 t. 1500. R. A. io'> 53-9" Dec. -2° 51' M. 7-6, 8-2 C. white. The distance has increased, and the angle has diminished. 0.2. 330-9 321-4 320-2 317-3 2n. 1-06 4n. 096 2n. i-ii in. -53 1825-22 32-09 40-30 7i-3« Da. Ka. Be. Ta. •w.ts. Gl. Bp. Dob. 317-1 315-8 322-9 318-3 314-4 319-5 313-8 315-4 314-1 3'7-i 316-9 315-6 316-2 3>4-2 313-2 324-1 091 1-15 •06 31- •05 in. -46 »» 2-09 3 1-37 S •39 I -40 4 •27 7 5 ■34 5 •31 5 -42 -41 2n. •76 1841 -20 60-34 42-24 5628 67-23 76-34 323 -24 4-22 5-28 -29 6-34 -36 4-22 5 37 6-31 362 %. 1504. R. A. Dec. 4° 17' M. 7-5. 7-6 The relative brightness of the two stars is probably variable. Other observers have always noted the following star as either of equal or of greater magnitude than the preceding. Our measures between 1845 and 1848 are decisive as to the superiority of the preceding star. (0.2.) 2. Bm. Ua. 0.2. De. ■W. 4 8. Gl. Bp. 275-6 280-0 279-0 2781 283-4 284-5 •7 286-4 285-5 286-7 283-9 286-3 Sn. 1-07 -3 0-95 3"- 1-07 5n. •II 7 •19 10 •14 4 •08 4 -12 4 4 1-2 •16 1829-13 36-29 42-27 54-99 6667 7423 ■23 5-28 -29 6-34 4-22 5-37 363 R. A. 11" 4-1° 2. 1514. Dec. 66° 46' M. 8-5, 10 2. 334-9 41. I-15 1832-92 Ua. 336-6 2n. -02 45-55 De. 344-0 •15 66-70 364 2. 1516. R. A. 11" 7-4" Dec. 74° 7' M. 7-5. C. 2., yellowish, ashy yellow; Sc. and De., white. MEASURES. 269 2. states that the first observation of this star is found in the Mem. Acad. Parisiensis 1790, p. 389. He thinks that South's dis- tance is probably not very accurate, and that the motion is probably orbital. Se. found that the graphical construction gives a straight line for the apparent orbit with minimum distance about 1853. 0.2. in 1858 discovered a third star near A. Finding that the latest measures of A B depart widely from the rectilinear path deduced by 2. (see P. M., p. ccxxviii.), the investigation was repeated with the follow- ing results : — A A = - l"-3i8 + o"-407o (T - 1850-0). A D = — 2"'9i4 - o"'io77 (T — i85o'o). According to these the minimum distance 2" '48 was reached in l8S4'8, and the angle was 14° 50', and on the whole the observa- tions are well represented. The difference between the formulas of S. and O.S. is pro- bably due to application of the systematic corrections. The star B is therefore fixed, and has no physical relation with A. The star C, on the contrary, participates in the large proper motion of A. 80. Ea. Oe. Uo. Se. Eng. Sa. W. &S. Gl. Fl. O.S. Sa. 298-6 298-7 299 '3 7 300-9 301-6 302-6 304-0 296-2 301-0 300-0 308-3 310-6 322-8 329-6 3417 22-5 48-0 64-4 76-9 81-2 86-0 3J2-6 8-3 16-1 237 26-0 44-2 68-6 70-5 6-8 56-5 29-5 7 J -4 256-9 258-6 80-3 78-5 82-9 86-8 87-3 90-5 269-1 -o 89-6 270-5 91-0 AB. 2n. 4n. 8n. 3n- 3". 2n. in. 3". 2n. 3°- 6n. in. 3"- 5n. in. 3"- 30 26 31. In. 4n. 2n. in. 3". 4 5 4 4 in. AC. 29-26 14-22 993 •56 8-94 ■42 •'3 778 12-48 12 9-85 6-66 ■17 4-17 337 2-97 ■32 -96 370 5-i8 6-30 7 -go 5-23 2-70 -81 2-66 •87 4'03 •18 2-49 3-25 2-61 4-43 578 6-i8 5-29 •58 6-49 7-02 •32 8-81 7-6 9-1 •5 294-1 3n- 8-i8 297-0 2n. -06 ■2 3"- 773 7 •60 299-4 2n. •48 1790-21* 1823-92! 3' '54 2-84 3-46 4 '43 5-56 6-64 7-61 24-28 31-40 3-26 40-45 1-92 6-94 8-94 50-92 5-47 8-87 61-33 5-43 8-58 72-54 43-65 54 55 5-14 •99 6-16 8-29 62-95 3-48 54-26 60-21 56-29 64-44 7-27 8-40 6-29 7-78 9-51 70-46 1-49 5-54 2-30 325 5-28 4-13 7 37 1858-87 61-33 6-49 72-54 5-54 * Lalandius. + S. from six observations with the transit instru- ment. DOUBLE STARS. 385 t. 1517. R. A. Dec. 20° 47' MagnUiides.—ri. 7"3- Se. 7-5, 77 The variability of the relative brightness was suspected by 2., and the observations of his dis- tinguished son confirm the sus- picion. 2. and Se. generally noted the following star as the brighter ; O.2., on the contrary, tias invariably regarded it as the fainter of the two. The common proper motion is — o"-377 in R.A.,and +o"'i6 in N. P. D. Duner has obtained the for- mulae A =o"-89 - o"-oi3 {t - 1850-0). 1849-94. P - 287 "-3. 1821 •s. Sm. Da. O.S. He. Da. Ta. Gl. W. &I Bp. Dob. 108-4 8n. 1-08 286-4 in. •06 288-0 »> •19 289-3 »> 0-81 288-6 »» 1-2 •9 •09 283-6 In. 0-91 108-8 ,, •93 104-8 »» •81 100-3 »» ■88 287-4 3"- •78 285-0 2n. elong^- 2873 5n. 0-59 288-8 in. •64 286-8 •S8 284-3 283- S 4 105 -I 4 0-82 6-0 4 75 284-0 •67 104-5 in. -8 31- 0-61 1832-20 52-22 30-24 1-07 3-3" 40-30 54-17 45-31 ■32 71-25 56-98 7-97 69-39 72-40 5-20 2-40 4-22 5-28 6-34 5-39 6-30 7-26 366 0.2. 232. R. A. 1 1" 8'» Dec. 0.2. Ma. De. Dn. 238-1 237-0 234-0 2355 38^ 14' Sn. 0-72 4n. -55 3n- •6 6n. •56 M. 7,7-8 1849-93 47-05 67-66 74-49 367 0.2. 233. R. 11" 0.2. De. A. II" 334-72 337-671 Dec. 67° 21' 4n. 3". 4-9 -93 M. 6-9, 9-8 1849-87 68-59 368 2. 1523. R. A. Dec. M. 32° 13' 7-3, 8-2 I8S6. This remarkable pair was discovered by H, in 1780. He writes, " 1780, May 2nd. A fine double star, nearly of equal magni- tudes, and S of a diameter asunder ; exactly estimated. May 21. Unequal stirs; very bright ; one diameter of the large star asunder. But the air is rather tremulous. A little wind. Feb. 4, 1802. 7° 31' s.f. ; very accurate. Jan. 29, 1804. 2° 38' s.f." In his review {Phil. Trans. 1804, p. 363) Hj says : " This double star has undergone a very extraordinary change in the angle of position. Dec. 29, 1781, the smallest of the two stars was 53° 47' s.f. ; Feb. 4, 1802, it was 7° 31' ; and, Jan. 29, 1804, the position was only 2° 38'. "This gives a motion of 51° 9' for 22 years 41 days, and amounts to 2° 19' per year." And he pro- ceeds to point out the possible causes of these changes. Hj (Phil. Trans. 1824, p. 146) writes, " The position and dates here given (11° 33' s.p., 1823-29; 2"-8o9, 1823-19, — means of 58 and 20 mea-sures respectively), as well as the distance, are all derived on the sup- position of each measure being independent of all the rest, and all equally good. The angle thus obtained from no less than 58 measures, with its corresponding mean date, will serve for an epoch in which the com- puter, at some future period, may rely with confidence in any investigation relative to the orbit of this star. A double star in which the two stars are nearly equal, con- nected undoubtedly in a binary system by their mutual gravitation, and revolving round their common centre of gravity, with a motion so rapid as to admit of being traced and measured from month to month, must be allowed to be a phenomenon of no com- mon interest, and deserving every attention, MEASURES. 271 both from the practical and theoretical astronomer. " And he further observes that the observations "indicate a remarkable alteration in its velocity, which can only be accounted for by supposing the relative orbit to be one of great ellipticity. " And in the Memoirs of the R. A. S., vol. v., p. 34, he adds, " In the interval from 1839 to 1841 we may now securely predict that this star will have completed a full revolution from the epoch of the first measurement of its position in 1 781, having occupied therein a periodic time of about 59 years." In 1830 Savary's elements appeared in the Connaissance lies Terns; tliey are as follows : — « = 3"-8S7 e =0 '4164 T = 304° 58' O = 95 22 7 = 59 40 X = 131 38 P = s8"2625 years « = - 6^-1786 T = 1817-25. H, published the following in 1832 ; they were obtained by means of his graphical process : — Apparent Ellipse. Major semi-axis' Position thereof Minor semi-axis... Greatest maximum of distance ... Position thereof Least minimum ... Position thereof Greatest minimum Position thereof Least minimum Position thereof 3" -1 69 281° 20' l"7S6 4 •loi 1 10° o' 2"-338 257 35' 2" -1 19 206° o' i"-059 0° 40'. Real Ellipse. Major semi-axis Excentricity ... = 3"-278 = 03777 Position of perihelion ,, node Inclination Angle between major axis and line of nodes Period Mean motion Perihelion passage ... 7 = 307° 29' 97 47 56 6 = 134° 22' = 6072 years = -S°-9289 = "81673. Savary's orbit represented the observa- tions very well; Sir John's not so well, as he himself points out and explains Midler, making use of the observations to 1847, arrived at the following elements : Period = 61 -30 years a = 96^2i'-9 \ = SO 55 -4 X = 132 28 7 = 23 48 7 T = 1817-102.* These also satisfied the observed angles and distances very well on the whole. Villarceau computed an orbit for this star and obtained the following results : a = 2" -439 e = 0-43148 a = 95°-83 7 -= 52 -82 X = 128 -95 P = 61-576 years 6 = 1816-86. And Captain Jacob : — t = 1816-66 a -= 96° 6' X = 129 28 T = 53 52 e = 0-4116 P = 61-175 years a = 2" -82. The following extract from Dr. Ball's paper will show the relative value of some of the above orbits : — Epoch. Observed Savary. | H2. Madler. ViUarceau. CalC- Dififer- CalC- Differ- Calc"- Differ. Calc"- Differ- P°""°"- position. ence. position. ence. position. ence. position. ence. 1781-97 14378 143-89 +0-H 140-08 -370 14-85 -0-93 144-12 +0-34 1840-29 150-85 143-65 -7-20 148-92 -1-93 153-80 +2-95 155-48 +4-63 52-13 122-28 112-84 -9-44 116-22 -6-o6 121-37 —0-91 122-22 -o-o6 63-23 96-66 90-92 -5-74 92-85 -3-81 98-54 + I-8S 98-48 + 1-82 68-30 77-50 72-02 -5-48 75-27 -2-23 83-02 +5-52 84 02 +6-52 72-28 24-19 20-57 -3-62 41-62 + 17-43 57-19 +33-00 62-10 +37-91 * Madler also published the following elements : a = 2"'4i7, e =■ 0*41350, S3 = 98^*87, y = 54°'93, A = i3o°'8o, P = 6i"464 years, e 1816*44: these were obtained from the measures made up to 1843. This eminent astronomer, using; the measures made up to 1836, computed the foTlo-wing; elements : — 6 = 1816 95, J3 = 95°i A = 129° 41', y = 52° 16', e = '40368, P = 60*4596, a = 2 '29a 272 DOUBLE STARS. On this Dr. Ball observes that Savary's elements represent the observations up to 1825 very well, and then begin to fail. Sir John's, although but a first approximation, present no violent differences till 1872, — a point vchere both Midler's and Villarceau's also fail. Dr. Ball's elements are, a = ?"-59l e = 0-3786 a = iof-6 y = S3 -I >' = 135 -3 P = 59 -88 years K = 6°OI2 e = i8i6'405. A short extract from his Table VI. vfill exhibit the results when these elements and the observations are compared : — Epoch. Observed position. Computed position. Difference. Observer. 1781-97 I43°78 147-37 + 3°-59 H,. 1802-09 97-52 98-53 + I -01 ,, 23-29 258-45 259-20 + 0-75 Hj and So. 32-27 196-72 I95'i3 - 1-59 Da. 4029 150-85 152-95 + i-io »» 52-13 122-28 120-87 - I -41 Mi. 6323 96-66 94-87 - 179 De. 72-28 24-19 26-47 + 2-28 Br. Dr. Ball also gives an ephemeris showing the position angle at intervals of three months from 1872-50 to 1878-75, and says, "The greatest velocity of change in the angular position occurs about 1873-25. At this date the rate will be fully 20° per annum. The periastron passage takes place about 1876-28; thus the period included in the ephemeris contains the most critical part of the entire orbit." A portion of the ephemeris is here given, together with the observed positions by De. up to 1877 : — Observed position. 1 Observed position. Epoch. Compnted position. Epoch. Computed position. » Angle. Date. 1 Angle. Dale. Q 1800+ 1 1800+ 1872-50 22-4 19-39 72-32 187575 321-4 75 17-5 7600 317-9 73-00 12-5 •25 3147 304-8 76-30 ■25 7-3 358-9 73-33 -50 31 1 -6 ■50 2 2 -75 308-6 75 357-2 77-00 305-8 74-00 352-1 -25 303-2 294-9 77-26 -25 347-0 333-6 74-35 -50 300-7 ■50 342-2 -75 298-4 75 337-6 78-00 296 1 75-00 333-2 •25 293-9 ■25 329-0 317-5 75-27 -50 291-8 -50 325-1 •75 289-7 Duner, in 1876, computed a set of ele- ments : he gives T - 1875-29 w = 234 3' Si = loi -5 (Equ, 1850-0) .- = 56 -9 e = 0-3952 /. 5-9215 a = 2 '-549 p = 60-79 years, A table is also given comparing the ob- served and computed quantities from 1 78 1-96 to 1876-48. How well the agreement is maintained all through this period the fol- lowing selection will show : — MEASURES. 273 Date. A P dA dP 1 Observer, 1781-96 i43°8 - 1-4 H,. 1820-13 It 276-4 // + 4-6 2. 31 "25 1-90 201 -I + 0-21 -2-6 H,. 40-25 2 -08 152-4 -0-13 - 1-8 Ka. 50-30 338 124-3 + 0-43 - i-o h- 60-08 2-84 105-3 — 0-06 + 0-7 Mo. 70-33 1-35 57-2 + 0-09 0-0 Gl. 72-24 1-06 22-1 + 0-13 - 2-6 W. and S. 73 '33 0-98 358-9 + 0-09 + 0-5 De. 73 "42 0-85 358-4 — 004 + 2-2 Du. 7413 I -00 338-4 + 0-05 - 1-5 Gl. 74-35 1-02 333-6 + 0-04 - 1-7 De. 75-27 109 3«7-6 — 0-04 - 1-4 ,, 75-45 1-08 316-4 - 0-08 + 0-1 Du. 76-48 I-3I 303-8 — 004 + 0-2 " Duner observes that his elements are in- tended merely to represent tolerably well the existing observations, and to give the normal places, and that we must wait till about 1880 before correct elements can be obtained. The most recent elements of this interest- ing star are those published in No. I. of the observations of the C/niversity Obsei-va- tory, Oxford ; they are as follows : — T = 1875-26 P = 60-80 years a = 100° 13' 7 - 56 40 X = 235 o « = 0-41590 a = 2" -580. H,. 143-7 97-5 92-6 H, & So. 258-4 244-5 2245 212-3 201-1 189-8 2. 238-7 228-2 213-5 203-8 195-9 188-4 180-1 171-2 165-3 160-3 Be. 203-1 199-0 Da. 201-9 196-7 189-8 i7'-3 in. ff 58 2-81 55 -44 -0 -0 4n. 1-90 2-06 31- 1-74 4n. ■71 7n. -67 5n. •70 1) ■75 •76 J> -76 4n. •97 3n- -92 gn. 2-26 m. ■29 1-85 -93 I7n. •98 ion. •76 4n. •98 in. -92 1781-97 1802-09 4-08 23-29 5-22 8-39 30-20 1-25 3-14 26-20 7-27 9-35 3' '44 2-41 3-84 5-41 6-44 7-47 8-43 40-44 30-86 1-39 1-34 2-27 3-23 6-2S Da. Sm. Encke. Oalle. Ka. O.S. 150-8 147-9 144-7 142 1 131-6 -4 129-5 -3 1 26 '6 122-9 119-9 115-8 196-9 i8o-2 170-9 165-5 160-7 156-9 143-2 168-5 166-8 157-9 -9 152-2 145 -I 140-2 87-8 29-7 153-6 150-5 147-5 140-4 138-1 137-2 I33-J 130-0 127-6 124-1 122-9 120-6 1 19-0 II5-9 -2 5n. 2-44 4n. -40 »I -44 7n. •48 in. •57 »» •75 »» •70 3"- -94 5n. 3-01 2n. 2-98 m. 3n. 2-95 1-9 -9 -8 -8 2-1 -0 •3 9 -48 17 -56 4 1-89 -89 7n. 2-08 -7 ■55 •08 I -00 6n. 2-28 I» -22 4n. -34 3"- -45 2n. -51 4n. -56 3n- -6i 5n. -66 4n. -78 •67 5n. •80 4n. -75 »i -88 ,, -90 3n. -85 1840-29 1-21 2-27 3-28 7-30 •34 8-13 -19 9-30 51-31 2-38 4-36 32-29 5-37 6-33 7-28 8-48 9-23 43-16 37-31 -49 9-46 -47 40-25 2-50 3-60 66-45 72-09 40 40 1-40 2-40 4-34 546 6-37 7-41 8-41 9-37 50-39 I -4 1 2-40 3-40 4-38 5 44 18 274 DOUBLE STARS. o.s. Ch. Ua. DO. Bond. Ja. rit. Mi. Ho. Se. IIO'2 1049 101 ■ I 99'3 957 94-2 85-4 81 o 72'6 59 '2 457 17-8 358-4 338-1 150-6 148 -2 139-3 I50'2 146-9 122-1 120-8 118-8 II6-3 115-7 112-7 109-7 108-8 1061 99-9 131-1 127-3 128-6 129-7 124-2 120-9 119-4 117-0 1231 119-8 118-9 122-3 118-8 117-7 io8-i 105-3 116-5 115-4 112-3 108-6 •o 981 96-4 93-6 go- 1 86-7 82-2 ITS 57-7 47-7 19-3 358-9 333-6 317-5 3n- 2 96 857-46 Se. 1 14-3 in. 2-96 I ^^n -g6 8-39 113-9 4n. 3-13 6 26 5"- •84 9-57 109-7 2n. •II 7-36 411, •6g 61-40 89-9 in. 2-53 65-51 2n. •62 -55 2-39 3-46 86-5 Au. 100-4 )> •26 3-03 6-31 1-56 3"- -33 4-42 So. 95-5 in. 2-79 3-14 -II 6-40 93-3 j» ■59 ■50 2n. 191 7 '47 M. 87-2 in. •60 -19 411. ■63 8-42 gi-6 >j •62 •21 -32 70-18 77-0 >» 1-77 8-39 2n. -12 1-40 Eng. 95-8 6n. 2-58 416 3"- 096 2-41 91-4 ign. -44 5-12 511. •96 3-43 Ta. g3 5"- -72 6^23 3"- 1-03 4-41 82-2 in. 7-23 2n. 2-45 41-19 79-1 2n. 2^49 8-23 -71 2-30 70-8 m. ... 70-35 in. ■53 4-25 66-2 ») ... 1-39 7n. •44 1-29 68-0 2n. 1^28 2-35 411. -41 2-24 335-6 „ 4-29 gn. 3-02 51-78 334-5 in. 1^64 6^34 6n. 2-75 2-35 Dn. 68-6 im. ■2g 69-40 1311. •93 3-32 53-8 gn. ■16 70-43 1411. -89 4-37 40-0 im. o-g8 1-47 2n. •87 5-44 16-6 I4n. -91 2-46 1311. •97 6-42 358-4 in. •85 3-42 8n. 75 7-43 335-1 4n. •93 4-45 5n. -92 8-42 316-4 14n. ro8 5-45 3"- -97 9-37 61. 593 5 ■4 0-22 411. -go 62-35 55'' 6 •3 -44 3-12 47-11 50-8 5 ■3 1-13 2-78 •12 44-6 5 •I -50 -7 8-45 32-0 5 •I 2 00 3-1 -4S 29-4 5 •0 10 10 ■37 50-30 356-0 5 -0 3-50 5 •01 2-29 342-2 3 08 -93 10 •01 3-19 343-0 3 •7 •93 10 11 ■93 338-0 5 10 4-12 611. 2-83 1-19 339-0 5 0-8 -13 , •g2 2 20 338-3 1-2 '"? jt ■98 3-23 W. & S. 43 -g 4 -I 1-48 56 •8g 2-13 23-1 7 -04 2-13 32 3-01 3-19 22 -g 14 0-97 -17 3"- 2-90 2-34 23-0 6 i-ig ■20 -85 8-20 •3 4 ogi -20 2n. •84 60-08 20-3 3 ■24 7n. 3-16 54-64 19-7 4 i-'i'8 ■33 5n. •2 5-21 22-2 4 -07 -38 711. •19 6-34 23-9 23 o-go 3-22 in. 7-89 359-6 4 -36 5"- 3-14 8-25 338-0 9 o^g2 4-17 3"- 2-81 62-85 334-5 2 -23 l6n. -50 3-29 317-6 4 1-30 5-28 ion. -27 4-37 316-9 5 •22 ■29 gn. -18 5-32 318-0 5 -31 -32 ion. -06 6-30 316-3 10 -43 8n. i-go 7-31 304-9 4 1-59 6-34 jj •73 8-30 306-4 9 -45 -36 gn. •39 70-24 305-2 6 •30 ■37 8n. ■20 1-22 294-1 6 •47 7-39 ion. ■07 2-32 -7 7 -59 -40 jj 0-97 3-33 295-0 7 •50 -41 6n. i-oi 4-35 Fer. 15-4 0-97 2-47 8n. -og 5-27 337-0 I 1-47 420 MEASURES. 275 En. Schi. Sp. Dob. PI. 29-6 i6-8 317-5 •4 3117 306-3 3042 301-2 297-0 3"- I 08 ,, •II in. •31 •3J in. ... I3n. 173 ion. 74 Sn. •52 yn. •57 1872-08 ■44 5-30 ■31 •99 6-27 7-26 6-46 7-20 369 X. 1527. R. A. LEOWIS 339 (B). Dec. 14° 56' C. yellow, blue. M. 7,8 A appears to be variable : its magnitude is thus given: South, 8 ; Dawes, 8, 7-2; 2., 8,6-9; Du-. 6'5, 6. Certain change. Duner has the following formulae : 1851- DI. A = = 3"79- P=ii°-8 + o°-09 (<- 1850-0). 2. 97 in. 373 1822-20 10-2 ,, ■88 9-30 So. ■4 3"- 4-93 4-60 Da. •2 in. -00 40-60 11-5 ,, 3 "90 54'27 Ma. 10-4 ,, 410 44-27 Mo. 11-6 ,, 3-93 557° Se. 12-2 2n. 74 6-70 De. 13-3 3"- •99 8-16 Ta. 12-8 2n. -68 66-28 «53 in. ■24 7-24 14-2 ,, ■05 72-40 10-9 ,, -16 432 14-0 ,, •08 6-36 Du. "4 4n. ■43 5-30 PI. 1 1 -4 1 3"- -48 6-57 370 S. 1534. R. A. 2. Se. De. 0.2. V. &s. Gl. Dec. 18° 51 342-2 2n. 479 3390 " -88 3322 in. -oS 33° 6 4n. 74 •9 m. 5'i3 .335 ■« 5 3 -61 3-6 5 4-5 3 336-2 2 4-2 1 M. 8, I I -2 1828-24 33-28 56-30 64-76 70-30 4-23 ■24 6-35 4-13 371 S. 1536. I LEONIS. R. A. ii" 7-5- Dec. -j"" 17-6™ 11° 12' Magnitudes. — 2. 3-9, 7-1. Sm. 4, Se. 4-2, 8-5. De. 4-8, 7-9. C. 2., A, yellowish ; B, blue. One of S.'s discoveries. He found the angular motion indirect, and by the method of least squares obtained for the angle ai = 92''-38 -o°-834 (/ - 1832-01). Smyth and Dawes assert its binary character. Of late years the angle has not changed, and this accords with the increase in the distance. (0.2.) The common proper motion is +o"-l33 in R. H., and + o"-028 in N. P. D. (2.) Main gives + o"-oo7, + o"-07 in R. A. and N. P. D. respectively. Duner has the following formulae : A=2"-45+o"-oi (^-1855-0). P = 78°-9-o°-526 (/■- 1855-0) +o°-oo2i (/- 1855-0). Da. Sm. 0.2. Ch. 97-0 93-0 904 ■3 ■I 91-8 87 -6 86-8 85-3 -3 83-6 81-6 80-6 79-5 76-0 72 I 90-5 87-7 86-0 81-3 91-0 92-3 87-5 86-3 83-> -6 78-9 80-8 75-3 766 -o 86-0 89-3 87 -4 2n. 4n. 3". ,, in. 3'n. 7n. 4n. 3n- 2n. in. 3n- in. 211. in. 2n. in. 2n. 2 -29 1-99 2-17 -40 ■41 ■44 •44 -52 •45 ■63 ■47 -64 •61 -55 -68 -80 ■4 ■4 •5 ■5 •67 -22 •49 •29 ■23 ■42 -40 •70 -58 -58 -80 •66 ■41 -61 •84 182781 30-62 3-34 5-33 7-39 4 00 40-29 I -29 2-27 3 -'7 772 9-29 51-55 4-3S 60-29 5-40 3640 9-32 43-38 53-29 4059 I 40 2-34 7-36 9-36 5 1 '37 2-37 8-38 61-42 2-39 636 8-36 41-23 2-32 4-28 276 DOUBLE STARS. Xa. Ja. Ko. Fit. Se. Se. Po. U. Eng. Ta. Br. Gl. W. ftS. 8b -6 Sn. 2-29 "I 4n. ■27 82-8 sn. •31 8i-3 8n. •35 8o-o 4n. •47 790 7n. ■42 78-9 8n. 70 •8 6n. "53 76-1 7n. •48 ■0 4n. •38 7S"i 2n. •46 88-2 sn. ■30 71-5 75 81-2 •34 797 10 ■44 787 II •63 76-6 •64 83-2 2n. 71 817 •09 80-4 in. •2 78-6 2n. •48 79 4 in. S 767 3n- •6 7 7n. ■5' 74 9 9n. •56 73-3 2n. ■55 717 »» •53 7 ,, •54 70-6 in. ■54 •I »» •66 71-1 *i •57 70- 1 2n. •54 76 '4 sn. •26 74-5 73-9 in. 72 72-8 »» 75 •8 »» ■84 75-9 • i> •88 67-6 ») 308 76-8 sn. 2^92 75-8 3n. ■91 76-8 in. •91 •8 rt ^•o6 78-9 2-85 •2 2n. 77-0 ,, 2-71 76-6 in. •46 69-2 »» •46 74 'o 2 73 717 4 ■6 720 4 •5 71 -2 2 7 67 S 7 ■5 3 7 710 6 7 68 -o 5 •69 70-3 5 32 71 7 70-1 4 2-57 ■5 4 7 68-8 6 ■81 69-8 5 71 68-5 4 77 70-5 8 •69 •2 6 ■62 I84I 32 2^22 6^31 7 '35 SI -28 2-38 3 '34 4-37 6-37 7-37 8-35 42^59 66^32 48^30 5320 •96 821 3"3S 5 '27 •95 6^25 7-08 8-34 63 '23 6^o8 824 70'26 1^24 2^27 3 '22 4'22 519 56-26 6118 2-25 7 '27 8^40 71-27 536 6570 628 7-24 8-21 9-19 71 '37 2-41 4-32 636 69-24 70-44 1-32 3 29 4-10 ■12 •'3 •17 227 •35 3'9 •23 ■25 4^22 5-28 6-35 •36 Fer. Dn. 8p. Schi. Bob. W.O. PI. 73-2 2-01 70^6 4n. ■58 68^i 73 •I in. 73 69 •& ,, 657 8n. 2-88 64-5 4n. •82 703 ,, 73 69-4 „ •81 677 31- •86 1873-28 5-3' ■32 •32 •99 6^27 723 6^29 •3" 710 372 %. 1543. R. A. ii"" 22-6" S7 uss.a: UAJOBis. Dec. 40° o' M. S'2, 8^2 B is probably variable. Dawes notes it as of the 9th mag., South as of the loth, and H| saw it as a mere point of light. The common secular proper motion is -7"-2_and + 2"-4. (S.) Duner has the following formulae : 1851-77. A = 5" -40. P = io*-o-o''-ii (?-i839-o). H,. 14-4 in. ... So. io'3 2n. 5-86 S. 7 6n. •37 7-2 ■43 Sm. 9 9 •9 8-3 5 Ja. ■3 "5 6-8 2n. •26 Da. 7-2 •52 Ha. •6 in. •61 9-5 J, 4-89 Mo. 6-0 ,, 538 Se. ■5 2n. •16 De. 5-5 »> •42 H. 355-6 in. 472 Sn. 5-8 sn. S-46 Gl. 6-5 in. Sp. 5 '3 S-62 Fl. •2 in. •80 783-10 825-25 31-91 48-24 35-42 46-38 •32 53-24 48-70 5 '-27 8-43 7^28 •89 8-16 6443 73-05 4-29 5 33 7-41 373 T LEONIS. R. A. 11" 21 •8" Dec. 3° 31 M. 5. 7 The proper motion of r is — o"-ooi in R. A., and +o"-02 in N. P. D. So. Be. 2. Se. Eng. Fl. 169-8 1669 169^6 90 95-2 96-9 947 252-2 •42 1717 93-4 172-2 in. 92-2 1782-28 1823 25 34-94 59-21 63-26 77-42 MEASURES. 277 374 OX 234. Dec. 41° 58' R. A. ,,h 24-3"' C. white. Very distinct orbited motion. O.S. Oe. 1 77 -4 188-9 20O'3 243 257 282 3n- 042 )» •37 ,, •3> 2n. oblong SI- >» in. .simple »> oblong elong 'ated M. 7, 7'4 [844 '66 8-66 52-09 8-88 61-35 6-49 70-46 66-20 375 OX 235. R. A. ,jh 23-8" Dec. 61° 45' M. 6. 7 '3 C. A, yellow ; B, red. Since 1856 the distance has increased considerably, and the angular motion has diminished in a corresponding degree. O.S. Se. 293-0 2n. o'6o 3ii'3 318-6 ii •ss •52 327-9 „ •54 331-S 348-7 3.S8-7 3"- 2n. -55 •52 •68 1,-6 3"- •68 293 2n. •81 40-2 38-2 >» ■11 1 844 'go 6-94 9-89 51-42 2-94 6-51 8-92 61-74 5-46 71-53 68-59 376 t. 1652. R. A. 11" 28-5" Dec. 17° 28' A B, probably binary, linear motion. H,. 208-8 So. 210-0 208-9 V 2094 207-3 210-9 2II-0 -3 2 10 -6 Sm. Ho. 209-1 208-9 -0 209-6 AB 4-45 3-01 5n. 3 -13 •18 289 3-22 -5 20 •10 30 •10 20 •18 60 -46 M. 6, 7-3. 8-5 In A C, recti- 1 782^28 1802-18 22-27 9-94 32-40 4-54 5420 6-36 7-37 35-38 46-40 8-32 54-37 5-31 Da. H. Bo. Be. Ta. 01. ■W. 4S. 80. Sm. Se. W. Gl. 210-8 3-03 208-8 m. •28 212-3 )» -31 2I4-I -55 2I3-I in. 4-14 210'8 »» 3-58 2II-7 >» -2 •I -25 &8. AC. 234-9 -2 53-72 233-3 60-75 -9 58-8 234-5 63-33 235-4 in. 234-0 f» 1851-30 61-33 317 5'33 8-21 70-35 4-24 -24 1782-28 3-29 1822 27 35-38 65-33 74-23 5 20 377 OX. 236. R. A. 0.2. Be. Dec. 67° o' 209-2 213-4 3n- In. 2-33 •71 M. 7-5> " 1 847 00 68-13 378 X 1553. R. A. 11" 30" Dec. 56° 48' 7-3. 7-8 Probable change. Duner gives 1851-37. A = 5"-40. P=i7o''-7— o°-044 (^—1850-0). Ua. Da. De. Ho. O.S. Sn. PI. I7I-5 3". 5-34 170-2 2n. ''^k 171-3 in. ■32 170-4 ,, •38 -4 2n. -30 168-3 »» -56 169-5 4n. -51 -I 2n. •66 1832-58 44-38 51-29 8-01 9-25 65-86 75-30 6-94 379 X 1555. R. A. Dec. 28° 27' M 6-4, 6-1 A B, probably binary. Of A C no other measures but Smyth's are known. Duner gives A = o"-98 — o' -115 {t— 1850-0). P = 34i°-7-f o°-i5 (/- 1850-0). A B. s. 339-3 5n. 1-24 1829-12 H,. 338-0 in. 30-26 Da. 340-3 >> •45 2-24 Sm. 1 •4 4-31 278 DOUBLE STARS. 0.2. 341-4 in. ■ 0-93 [1 841 -41 s. i8-2 3n- 1-43 1829-26 338-1 M i I '05 2-34 Ma. 24-1 ■54 37-45 •8 0-86 6-37 28-5 •89 47-30 337-1 JJ -79 9-36 Se. 26-6 in. -08 56-39 343-3 342-0 ■70 ■67 66 42 8-36 Ha. Se. 339-0 •0 5n. 3"- ■94 -80 42-96 55-95 384 S. 1596. De. 338-6 in. i-o 6-09 Mo. 342-8 2n. ■14 9-35 R. A. Dec. M. Eng. 343-7 Sn. 0-92 65-75 11" 58" 22° 8' 6, 75 Du. 345-9 6n. •78 70 06 61. 344-0 2 10 4-29 Motion doubtful. Duner gives these W. AS. 343-8 7 0-7S 5-28 formulae : — 342-8 4 -74 -30 I854-79- A = 3"-65. •8 3 ■75 6-35 P = = 239-7 - -o°-025 (/- 1850-0). 8p. 344-0 ■74 5-37 1782-30 1827-28 Dob. 337-1 In. •71 7-33 H,. 2. 242-3 239-9 in. »» 3-82 AC. 242 '6 >t -60 8-23 Sm. 145-0 1 1 17-0 34-31 240-2 „ '-77 9-30 Mi 2398 239-1 >> ■73 -76 33'37 41-32 380 0.2. 237. -6 238-9 2n. •61 •47 2-23 3-33 R. A. Dec. M. 239-6 i> -89 4-3« ii" 32-5 41° 48' 7-4, 9 Mo. ■5 3n- -92 55-33 238-5 9n. -72 9-27 If Madler's angle is correct, th e angular Se. 239-5 3n. •76 6-96 change has amounted to 164° in 28 years. De. 240-0 in. -84 8-07 0.2. Ma. 287-0 274-8 113-2 4n. 3n- 0-74 •92 •64 1845-82 61 -68 47-40 Du. W. 4 8. Gl. 2395 •2 •8 3n. 2n. in. -54 •77 •6 71-27 4-23 -30 De. 272-0 277-0 3". 1-08 •02 67-94 75-36 Sp. 385 S. 3123. 381 O.S. 243. R. A. Dec. M. R. A. Dec. M. 11" 59-4 n 69° 20' 7, 7 ii"" 53-6 m 54° 5 / 7-8, 8-8 A ver V difficu t object in 183 2. Since If Madler's angle be correct, 18^ of the apparent orbit have been described in 21 years. 0.2. Ma. De. 10-9 31- 0-71 26-6 -42 8-9 3n. -90 1846-04 ■41 67-96 382 2. 1588. R. A. u" 561 Ha. De. Dec. 73° 2' -7 2n. 16-49 •33 •6 1 5 '3° M. 8-5. 8-7 1831-59 45-55 63-56 1 85 1 there has been no trace ot the com- panion. 0.2. De. 289-7 4n. ' 0-3 1832-20 79 in. oblong 40-42 271 ,, ^^ ■45 88-7 ,, 0-44 1-41 23' oblong 51-44 ; single »» »» 8-44 61 26 2-39 8-56 2-95 386 Z 1602. 383 S. 1593. R. A. i" 57-4" Dec. -I°47' M. 8 8-3 R. A. 12'' I -I" 2. Ma. Dec. 69° 45' 179-8 178-7 13-00 ■70 M. 7-5. 9 11831-56 I 45-54 MEASURES. >79 387 t. 1604. TIEGINIS 59 (B). K. A. 12'' 3-2" Dec. -11° n' M. a6'5, B9, c8 In A B the distance may have decreased slightly since 183 1 : the angle appears to diminish veiy slowly. C is in motion, rectilinear and uniform ; and Duner gives the following formulae : A sin P= +52" -05 —o" -3074 (/—1 850-0) ; AcosP= — 5"-2o + 3"-o99S(^- 1850-0) ; whence it appears that the minimum dis- tance, 10", will be reached in a.d. 2008. 2. Ma. Se. De. Sn. n. s. Se. Se. Dn. n. AB. 93'3 3n. 11-98 94-8 in. ■01 92-8 j> 75 92-7 •16 91-6 2n. -46 91-5 in. -6 AC 96-9 an. 58-00 1 95-2 in. 50-38 94-8 47 '85 -0 2n. 46-04 931 in. 41-9 1821-95 44-35 56-40 64-19 9-85 77-40 31-95 56-40 64-19 9-85 77-40 388 X. 1608. R. A. ,2h ^.ym Dec. 40° 34' M. 6-3. 7 The angle diminishes slowly. Probably binary. Duner gives the following formulas : 1853-01. A = i"-29. H,. 2.' Ua. Se. Se. Su. = 346- 3484 ■6 349-3 246 -8 344-7 ; - o^-i (^ - 1850-0). 3"- in. 2n. 5n. 0-89 1830-87 1-39 31-48 -43 43-21 -I 56-46 -23 7 -,36 •21 69-38 389 2. 1607. R. A. 12" 5-5'" Dec. 36° 45' M. 7-8, 8-3 Considerable change both in angle and distance. 1830-99 0.2 350-3 ! 3n- ! 33-07 352-5 In. 32-43 45 35 -3 ,, -42 6-42 356-1 1 )* 31-25 68-36 Ma. Be. Gl. W. &S. 352-7 32-91 355-0 2n. 31-35 -0 2 32-0 357-2 6 30-77 1847-27 63-31 74-30 648 390 O.S. 249. R. A. 12'' 18-1°' 0.2. Se. Dec. 54° 49' AB. M. 7-2, 8, 1 1 -2 315-1 5n. 0-53 1853-19 3II-4 3n- -5 68 04 308-0 -5 7246 0.2. A+B 2 149-7 I and C. 2n. I 13-23 I 55-86 391 R. A. 12'' 18-4" t. 1639. COttE 68 (B). Dec. 26° 15' M. 6-7, 7-9 The distance has diminished considerably. Probably binary. 2. 0.2. Sp. 290-9 6n. 1-18 1 293-2 289-8 288-7 in. 2n. in. 0-98 1 I-I3 -20 -0 ,, 0-93 279-8 285-8 2n. -73 •85 273-1 -4 1831-40 41-39 236 4-34 55-32 70-31 56-90 75-39 392 O.S. 250. R. A. 12" 18"° 0.2. Se. 330-7 321-3 Dec. 43° 45' 3"- in. M. 7-7. 8 0-44 1 1845-98 ... I 6816 393 X. 1641. R. A. 12" 18-6" Dec. 38° 24' Rectilinear motion. Se. 53-4 1 4 50-4 2n. 6-14 42-3 1 7-73 M. 10, 10 1830-40 1-38 67-59 394 a CRUCIS. R. A. 12" 19-9"" Dec. -62'^ 34' M. 1-5. 2, 6 >8o DOUBLE STARS. Proper motion of A, -0'-009 in R. A., and +o"-02 in N. P. D. A B form a binary system, while A C are probably an optical double-star. AB. •834-39 5 20 619 7-i8 8 -08 47-10 58 20 6i-i8 Ja. To. Ja. 121 -6 S-26 ■0 75 120-8 -61 •0 ■55 •0 -96 ■4 74 II7-6 II 477 120 57 118-5 40 4-98 A C. 201-5 •9 202-0 -2 92-4 35-27 899 730 89 47-25 90 58-20 395 2. 1643. R. A. Dec. 12" 21-2"° 27° 42' Probably binary. 71-2 66-2 54-4 2. Be. 5n. 1-95 20 1-79 M. 8,8-3 1830-36 2-35 6475 396 2. 1644. R. A. Dec. M. ,2b 21, 3m go 3, g.^ ^.^ The distance has probably diminished. Be. 248-6 247-0 ■o 3"- 21-82 •08 20-88 1827-55 67-89 70-31 397 0.2. 251. R. A. Dec. M. 12" 23- 32° 2' 74, 9-1 Extraordinary discrepancies are presented by the measures of this difficult star. 0.2. Be. 128-35 132-05 '56-55 149? 2n. 0-42 '1843-77 ■33 I 9-88 -49 I 52-42 single ; 67 obi-? 8 398 2. 1647. 191 (B) VIEGINIS. R. A. Dec. 12' 24-5™ 10° 23' Magnitudes.— -S,., 7-5, 7-8. Se., 7-5, 7-6. De., 7-5. 8-2. " The relative brightness is undoubtedly variable." (2.) C. 2. and Be., "vfhite." S. discovered the duplicity of this star, and also, from five years' observations, sus- pected direct motion. In 1836, however, he saw cause for changing his opinion. Dawes' observations in 1840 "showed that the variation of angle continued in the same direction, accompanied possibly by a slight increase of distance. " Secchi says that "direct motion is un- doubted. " With an increase of distance there has probably been a diminution in the angular motion. Secchi's distance is too small. (0.2.) Ha. 0.2. Ba. Be. 8e. -w. &S. Gl. Fer. 8p. -w.o. Bob. 198-6 202-8 203-5 205-2 204-1 198-6 204-2 214-3 212-3 213-5 •9 217-6 -6 207 o 2I2-I 210-9 214-2 2I2'9 21 1 -6 218-0 216-I 214-2 217-2 216-9 215-7 2091 216-2 2I4-I 215-8 220-3 216-3 214-4 2n. 3n- 1-25 •J3 •19 •21 •24 1-20 -35 -26 2n. -50 in. -46 ,, -57 -65 m. -27 2n. -17 in. ■36 •2 3n- -39 2n. ■19 •58 S •42 6 •15 5 -28 4 •08 3 •2 -44 •30 in. -33 ,, •19 ,, -28 3n- 2n. 1-55 1828-36 9-37 32-34 3-34 6-32 0-34 5-06 51-27 2-31 40-32 6-37 61 24 74-28 40-31 8-43 54-37 5-81 63-24 56-36 64-31 73-36 4-29 5-29 •30 4-34 -23 5-31 6-35 ■39 -39 6-24 7-22 399 2. 1658. R. A. 12'' 29" 8° Probably binary, Dec. !° 6' M. A 8, B 98, c8 AB. 2. Se. Be. 0.2. -V. AS. Gl. Bob. 0.2. 341-5 348-8 349-1 350-6 352-0 ■4 -o 340-2 257-6 3". 2-02 2n. 1-90 2-24 in. -37 8 1-97 5 218 3 i m. •27 A C m. I 10-8 1830-64 56-90 69-08 70-31 4-29 -30 -34 7-26 70-31 MEASURES. 281 400 t . 1661. 403 y CENTAURI R. A. Dec. M. R. A. Dec. M. 12'' 30° 12° 4' 8-5, 8-5 12" 34-9"' -48° 18' 4.4 2. 2260 // 2-56 1828-67 A binary system. Ma. 228-2 •63 43 33 Common proper motion — R. A., and + o"^-03 in N. P. D. o'-022 in 221-1 ■42 4-24 Se. 227-3 De. 234-4 0.2. 232-6 2n. •62 •41 7 S6-85 66-84 70-30 H,. 35 '-6 357-4 1-9 Ja. 20-6 13-7 IS 0-8 •8 i-o 0-7 i-i 1835-38 638 7-14 401 2 1663. 56 -20 7-97 R. A. 12'' 31-2" Dec. 21° 52' M. 7-8, 87 1830-38 Po. 12-8 El. 8-5 27 70 1-3 60-68 76-63 2. 117-S 3n- o-»i Ma. 123-3 ■55 42-33 404 1. 1669. "97 •64 4-32 0.2. 124-1 411. •72 -26 COEVI 58 (B). Da. 112-4 -91 52-22 R. A. Dec. M. Se. 1 18-0 De. 110-7 •40 77 7-34 68-55 ,2h 2jm —12° 21' 6, 6-5 W. & S. 100-3 in. -8 74-31 S. 298-9 3"- 5-44 1828-66 iii-l tt 7 5-83 Hj. 301-4 6-50 30-26 Gl. 100-8 4-36 302-6 9-2 I 30 Dob. 95-2 m. 7-30 o'3 7-38 73' Sm. 298-9 Se. 302-4 M. 301-5 4n. 5-4 •78 •95 5-50 402 X. 1664. 56-53 63-30 R. A. ] 3ec M. 12' 32-1"" — 1 C. A, 3 o°'si' 77, S fellow ; B, blue. -8, II, II 405 2. 1670. Rectilinear mo tion. y VIEGINIS. 2. 271-6 De. 254-7 3"- 17-10 I9'44 1830-23'' 65-25 R. A. Dec. 12" 35-6" -0° 47' M. Gl. 253-2 In. 74-26 3, 3 W. & S. 252-7 ,, -36 C. yellowish. 283 DOUBLE STARS. The variability in the relative brightness of the tw.o stars has long been observed. In 1851 and 1852 0.2. paid special atten- tion to this point, and the following results made when the stars passed the meridian will be read with much interest : — A is the south star, and B that to the north. 1851. April 17. A > B by 07 mag. 28. ,, „ OS „ May 1 5 and 22. Very nearly equal. Perhaps A a little larger than the others. June 3. A > B by o'2 mag. 4. Equal, perfectly. 5. A a little larger than the others. 1852. March 10. Equal, perfectly. April 3. A > B by 0'5 mag. 6. A the larger, perhaps. 8. Very nearly equal. A a little the larger, perhaps. 21. A > B by o"2 mag. 29. Perfectly equal. May 4. A > B by o'2 mag. 19- ,. .. .. 25. Verynearlyequal. A may be a little the larger. June 7. Very nearly equal. 14. Perfectly equal. And he then observes that it is very re- markable that in the seven years 1825 — 1831 B was certainly the predominating star, while his observations almost give the superiority to A. His conclusions are that the amount of variability is about o"'7; that it is impossible to say how far each star participates in the changes ; and that, owing to the hopeless nature of such obser- vations in the climate of Poulkova, he has discontinued the observations. The Story of y Virginis has already been written, and to Admiral Smyth's most interesting "story" but little remains to be added. The following is a summary of the statements in his paper {Spec. Hartwell- ianum, p. 335) :— Although various occultations of this double star by the moon have been re- corded, allusion to the two components has rarely been made. Nine observers watched an occultation in 1780 (March 20), yet at Paris only is mention made of one star being occulted 10' before the other. Four astro- nomers watched the occultation on Jan. 21, 1794, but no mention is made of the du- plicity. Yet Cassini, in 1720, saw the two stars, and noted that "the western dis- appeared 30" before the other behind the moon's dark limb." The Orbit. — H, was the first to compute a set of elements for this system : they are as follows ; — a = ii"-830 TT - 17" 51' e = 0-88717 T = 1834-01 P = 513-28 « = - o''-70i37 7 = 67° 59' a = 87 50. " If they be correct," says Sir John, " the latter end of the year 1833, or the beginning of the year 1834, will witness one of the most striking phenomena which siderial astronomy has yet afforded, viz., the perihelion passage of one star round another, with the immense angular velocity of between 60° and 70° per annum, that is to say, of a degree in five days. As the two stars will then, however, be within little more than half a second of each other, and as they are both large and nearly equal, none but the very finest telescopes will have any chance of showing this magnificent phenomenon." ^Mem. R. A. S., vol. v.) In 1833, however, the measures were found to deviate materially from the ephemeris, and Sir John recalculated the orbit, with the following results : — a e ir X = 12 '-090 = -8335 = 36° 40' = 282 21 7 = 67 2 p = 97 23 = 628-90 n T = - 0°-S7242 = 1834-63. {Mein. Ji.A.S. vol. vi.) " From the extreme delicacy of so novel a case, all the conditions were not yet met, so that this bold prediction was not circum- stantially verified, although it was admirably correct in substance. Whilst rushing to- wards the nearest point of contact, or short- est distance of the revolving star from its primary, and the proximity became extreme, the field was left, so far as I know, to Sir John Herschel at the Cape of Good Hope, Professor Struve at Dorpat, and myself at Bedford." In 1836 Smyth was the first to observe 7 Virginis a single star. " The companion now took such a movement as quite to confute a large predictive diagram which I had constructed." In fact, was now seen to be extremely elongated. Madler's first elements are as follows : (2) are the corrected elements of 1841 {Dorpat Observations) : — (I) (2) Perihelion passage 1836-103 1836-313 Node 58° 23' 60=38' Perihelion from j node 266 o 78 22 MEASURES. 283 Inclination — 35° 48' 24° 39' Excentricity ...0-86805 0-86815 Meanannualmotion i37'o886 - i48'-453 Period I57'562 i454S3yrs. Semi-axis major ... 3"-638 3" '402. (See Ast. Nachr., No. 363 ; Dorpat Observations, 1 84 1.) In 1836 Sir John was convinced that Bradley's observation in 17 18 was wrong, and that it had misled " Miidler and all of us." He rejected it, and considered that the period was about 143 years. In the Cape Observations he gives his final results : — • e = 0-87952 1 = 23° 35' 40" a = 5 33 ^ = 313 45 P = 182-12 years T = 1836-43. Henderson's elements, published in 1843, are — Perihelion passage .. Mean annual motion Excentricity Perihelion on orbit . . . Inclination Node Period 1836-29 ?°3o'-59 0-8590 319° 23' 23 5 70 48 143-44 years. (Spec.Hartw., p. 345.) In his Untersiichungeu iiber die Fixsterne- System, Madler gives elements deduced from observations up to 1847 : they are — Perihelion passage ... 1836-279. Angle between perihelion and node ... ... 79° 4'. Node ... ... ... 62 9 Inclination ... ... 25 25 Excentricity ... ... 0-S8064 Period ... .., ... 169-445 yrs. Mr. Hind, in 1845, computed the orbit of this star : his elements are- Perihelion passage Perihelion on the orbit Node Inclination Excentricity Period 1836-228 3i9°46'-i 78 28 -4 25 14 'I 0-85661 141 -297 years. {Mem. R. A. S., vol. xvi.) Lastly, Thiele published the following set (^Ast. Nachr., vol. xviii.) : — T = 1836-68 w = 283^-7 S = 35'6 (Equ. 1850-0) i = 35'i e = 0896 M = - i°'9459 a = 3" '97 P = 185-0 years. 1864-76 II 4-13 164-4 -0-14 -i-i 66-46 ■01 165-9 -0-38 + i'4 68-28 •31 ■63'S —0-21 0-0 70-72 '63 162-3 -0-06 +0-1 71-05 -72 162-1 +0-01 +0-1 72-12 ■47 161 -2 -0-32 0-0 1 73'9S •97 161 -4 +0-07 + 1-0. 75''4 •55 159-1 -0-42 -0-6 1 Cassini. Tobias Uayer, H,. H, & So. Amici. Be. Da. I30'7 120-3 1030 97 '9 91-5 88-3 80-9 73'S 65-5 51-6 33-6 331 '5 257-9 231-1 103-4 96-8 87-7 82-8 77-4 70-2 61-7 43-1 34-9 21-5 237-4 262-1 78-4 69-9 60-1 47 '3 351 '6 347 '4 233-4 214 6 205-7 200-0 194-9 192-7 191-5 183-7 1 82 -8 -I 180-4 -6 179-0 176-5 175-2 174-1 172-5 And the following comparisons by Duner will show that Thiele's elements satisfy the observed angles, but not the distances : — De. Ka. De. GI. Du. W.&S. Du. 1720-31 56-6 81-89 1803-20 22-00 5-32 8-3S 9-39 31-36 2-52 3-37 4-38 4-84 6-41 7-41 8-43 22-25 5-32 9-19 30-24 '-32 2-26 3-20 4-37 -54 5-11 8-08 23-19 30-59 1-29 2-31 4-29 6-27 -29 8-32 9-32 40-38 ■-34 2-38 3-37 -46 6-90 7-29 -41 8-36 -38 9-37 51-40 2-32 3-36 4-39 9-1 7-49 4-4 6-50 2-86 6n. -37 In. -07 Sn. 1-78 ,, •49 4n. -26 7n. '05 5n. 0-91 in. 3n. 0-25 6n. -58 I In. -80 2n. 3-79 4n. -26 2n. 1-79 5n. 2-21 ion. 1-73 i8n. -21 I2n. ■41 8n. -51 7n. 8n. ... in. 3-30 1-59 6n. -98 9n. -33 8n. -13 in. 2n. 1-26 I in. -24 7n. -57 9n. -73 6n. -82 4n. 2n. 2-45 ,, -32 6n. -48 2n. -63 7"- -60 5n. -85 -99 2n. 3-01 311- •06 7n. -19 r84 DOUBLE STARS. a. 172-8 m. 3-22 854-40 I71'2 4n. -36 5-33 •I •3° •46 170-1 7n. -58 7-35 169-9 6n. ■56 •42 168-8 8n. •68 8-45 -2 511. •77 9-46 166-5 ■94 6203 165-4 4n. 4-10 4"44 164-0 7n. ■37 5-42 )m 74-9 1-6 31-38 71 "4 •2 2-40 62-7 -3 3-44 45-5 0-8 4-39 15-0 ■5 5-40 round 6-06 -15 blotty -25 35° "9 -30 348-6 -39 265-4 2357 0-6 •8 7-21 8-28 192-8 1-9 43-08 191 -6 ■9 •33 185-4 2-1 5-34 181 -8 -6 7-41 1 79 -5 •8 836 I75'S 3-2 52-42 i73'9 -2 3-35 171-6 ■4 5-40 170-6 •5 7-41 169-9 ■8 8-39 Encke. 113-9 m. 36-59 117-5 7-19 83-8 3"- 0-77 •38 74'3 ion. •65 •48 49-0 4n. •70 8-46 30-3 in. •93 9-24 36-1 4n. 1-37 -36 Galle. 35-5 -29 39-35 Xa. 27-9 •30 40-26 I4"5 •76 2-82 345 '9 5n. 4-01 6646 0.2. 21 1 -6 Sn- 1-42 40-45 202-4 4 11 I -41 197-1 4 •86 2-41 184-5 2 2-23 5-46 182-9 2 ■35 6-38 '5 3 ■39 7-42 179-1 3 14 8-43 172-9 2 ■64 9-41 175-2 4 V SO -39 173'° 3 -87 I -41 -0 3 •99 2-43 172-0 4 3->3 3-40 171-6 4 -36 5-18 170-2 2 ■63 7-44 169-2 2 •67 8-44 167-9 3 -76 9-38 166-9 4 •93 61-15 165-9 2 ■97 2-40 167-3 2 -90 3-46 165-0 3 4-05 4-42 164-0 2 -29 6-42 1632 2 •30 1 8-44 o.s. Ua. Ch. G.O. Ja. 163-3 3 4'44 159-9 3 -64 160-9 3 ■54 -4 3 ■86 2CO-I I2n. 1-72 196-6 ion. •58 176-4 4". 3-30 174-6 2n. -16 -2 6n. •25 172-0 8n. •44 174-0 2n. •41 I7I-7 6n. ■59 170-2 9n. •59 169-8 2n. 4-00 ■1 gn. 3-88 200-9 2n. 1-42 192-2 „ -85 180-7 in. 2-05 189-0 M -63 197-8 m. 1-62 199-2 »» -64 197-6 „ •83 195-0 1} ■74 193-6 it 2-08 182-9 tt -20 184-7 »> •30 191-0 ,, •28 183-3 >» •18 190-8 »» -38 195-2 ,, -36 180-2 ,, •65 »» •70 180-7 »> -55 174-4 »» •90 176-6 ») •96 180-0 >» •90 179-9 )> 3-02 182-9 )» 2-82 178-1 >» -98 177-8 }} -96 1 79- 1 it •98 ■75-3 j» 3-09 174-3 n -05 179-1 I ■19 186-I I -16 173-8 1 •24 175-8 1 •32 178-9 1 -29 174 10 -40 173 10 •49 169 12 14 171 10 -81 174 10 •59 174 10 ■56 173 10 -61 168 10 •90 168 10 -79 170 25 4-18 179-9 in. 2-88 175-4 15 312 173-2 10 -12 -0 10 •06 170-5 4n. •44 170-6 5"- •50 178-0 9 2-9 1870-77 2-41 3-43 4-41 41-35 2-21 51-96 2-43 3-39 4-39 S'4S 6-38 7-42 8-37 9-37 41-19 2-35 3-30 4-33 2-33 •34 •34 ■35 3-39 4-34 6-36 -38 -41 7-41 •41 8-42 -42 -52 9-40 -41 -43 50-46 -47 •48 •50 1-34 •36 •37 2-42 •50 •50 3-38 -38 5-37 -39 6^28 •93 •94 •95 •98 8^46 -47 9-39 47-94 52-24 3-24 •91 6-10 57-96 60-30 MEASURES. 2^5 Ja. 1777 Bond. 179*2 i8i-6 179-8 M. 180-5 177-0 179-6 176-3 179-7 177-3 1 66 -2 169-0 167-7 1 68 -2 166-5 ■9 168-4 164-6 167-3 164-1 165-2 •2 161-4 1608 -o 159-3 i6o-i ■2 •5 ■3 161-5 i6o-8 ■9 161 -o 159-9 160-9 •2 158-4 159-7 176-6 175-9 -4 174-5 Hartimp.176-4 178-6 Hi. 175-9 Fit. Be. 174-9 353-6 171-2 170-6 169-5 348-5 345 '9 164-9 344-5 163-6 •4 162-6 161 -7 ■3 i6o-2 159-9 158-9 2n. 3n- 4n. 3"- i» 2n. in. 4n. m. 4n. 211. 6n. 7n. in. 3". 2n. m. 5n. 6n. 5n. 6n. 15 48 56 7"- 4n. 5"- in. 6n. iSn. 8n. 9n. I3n. 6n. 5n. 31- Sn. 3-12 iS6ri9 Se. 172-5 5n. 2-5 48-45 171-6 6n. •7 •45 170-7 7n. 3-0 9 '45 172^0 3"- •0 •45 169-4 2 -60 8-48 BazeiideUi72-9 •92 9-42 Kn. 169-2 2n. •94 50-48 165-3 3 '04 .-36 164-3 3'n- •19 2-48 159-7 «) •30 3-38 161-4 m. 4-11 61-26 Hit. 171-9 in. •06 •27 167-6 3"69 -29 170-1 ,j 4-09 •29 Bo, 165-1 2n. .0 2-38 Bug. 346-3 9n. •12 3-21 166-3 •02 •25 Ta. *•. in. ■05 •30 ■30 4^39 163-4 J, •24 •41 162-8 •28 5^36 160-5 •34 6-44 159-5 jj -42 7-38 158-6 'P 8-42 1631 2n. •8s 9 49 158-6 in. 'i^ •49 159-3 tj •89 •50 •9 •70 70-36 Ou. 341-8 I7n. •79 •40 ■I -44 '•33 339-1 I4n. •56 •34 Br. 164-9 2 ■59 •34 Gl. 163-2 7 -49 •36 162-0 5 ■60 •37 ■3 5 •72 2^39 ■0 5 •91 •45 161 -0 5 •87 3^40 159-7 5 5-33 4-33 •4 5 -09 5-29 160-0 3 2-94 50-36 •0 3 3-04 1-40 •9 10 -14 2-42 158-5 4n. •18 3-32 •5 13n. ^'21 0-30 ■5 2n. •88 •30 •6 In, 3-04 1-47 W.&S. 160-1 6 ■12 2-26 159-2 6 •10 3-27 162-S 5 •26 54-46 161-6 10 •55 5-19 162-6 8 •58 6-25 161-9 8 ■79 7-09 -8 7 •79 8-34 160-4 6 4^o8 63-33 340-5 5 •09 4-28 Undstedt. -5 | 3n- •18 5-26 Schi. 339-5 m. •23 7-05 Sp. •6 •31 8-28 •0 •61 70-25 CO. 159-8 4n. •64 1-26 158-1 8n. •54 2-37 ■w.o. 160-0 in. •64 73-34 159-9 ,, •65 4-35 i6o-8 »» •84 5-28 159-8 » 3-37 •54 •73 •61 -91 •58 4-05 •27 ■33 ■49 •82 •33 -01 -01 -07 •37 5^iS -28 •05 •33 4-76 ■80 5-39 4-43 •58 -66 •77 •7 -6 ■7 •6 5-0 4-4 •7 •6 5-0 -16 4-86 -78 5-00 •30 •40 •59 4^9 5-0 -02 4-97 •96 -91 •91 -84 5 •30 -19 -17 -24 -08 1855 -39 6-38 7-39 8-40 9-44 7-40 60-44 4-44 5-45 71-38 2-40 61-44 -46 2-45 3-27 5'i4 •14 6-21 •31 •48 7-24 8-26 9-25 70-39 1-38 2-37 4-32 6-36 69-98 72-12 5-'4 69-22 70-22 ■44 1-33 -41 •85 2-30 3-32 -50 4-00 •53 5-22 6-27 7-07 935 1-37 -40 2-30 •33 •38 3-23 4^30 •31 5^30 3-69 5-37 •37 6-45 •38 7-30 6-39 -41 -41 •4" 286 DOUBLE STARS. Dob. 336-2 .Sn. 534 1876-26 ,S,SS-8 4n. ■04 7-28 Fl. .S.3«-4 in. 4-96 "43 PI. i6o-o 5n. •6; -24 Goldney I57-I 3n. 5 -06 8-37 406 s. 1678. R. A. Dec. M. 12" 39 ■4' ■a 15° 2' 6-3, 7 Rectilinear motion. The angle has diminished, but the tance has changed very little, if at all. Duner gives 1852-57. A = 32"-34. P = 207°-4 + o°-24 (/-i85o-o). dis- So. Z. H,. 0.2. Ua. Da. Be. H. Su. W. PI. &S. Sob. Fl. 2I3'4 212-5 210-7 •4 209-6 -I ■4 208 o 202-7 20&-2 207-7 206-4 •Q 205-7 204-8 7 207-6 205-5 204 o 201-9 202-7 -o 201-3 -I 200-4 •3 2n. 3n- 3n- in. 5n. 3n. 4n. 2n. 4 2 4n. 3n. 4n. lu. 33-36 273 ■45 3°' 32-83 -87 -70 -54 -31 -01 ■39 31-76 -90 3209 3 ■■99 32-75 -96 -06 -45 -17 35-06 32-41 •2 ■4 32-28 31-9 -I 1825 8 36 2 40 2 45 68 45 5' 2 4 5 6- 8 61 51 8 63 6 9 73 4 6 7 -30 -29 -25 -28 -29 -41 -42 ■35 ■36 -29 -27 -32 -38 -57 -36 -36 ■41 ■29 ■35 23 -43 -94 ■35 ■30 •95 ■16 -29 •35 407 S. 1687. 35 COII.S: BEB£KIC£S. R. A. Dec. M. 12" 47-4"" 21° 54' 5, 7-8, 9 C. 2., A, yellowish ; B, blue. 2. discovered that the larger star was double. H2 and So., " Double : a small star, ex- tremely faint ; so much so, that it has been overlooked in former observations. " A.C. .says there is no good ground for thinking that there is anything but a small relative motion, and that the earlier obser- vations may be faulty owing to the faintness of the smaller star. Dawes writes : " My measures at Mr. Bishop's observatory in 1842 left no doubt of the close pair having an orbital motion." ' ' There is no evidence of change in the more distant star." The distance may have dimiiished of late, but the decrease in the angular change is opposed to this view. A C still un- changed. (0.2.) A B. ^ 25-3 5n. 1-43 28-4 in. -38 Sm. 30-0 -0 42-0 -5 Sa. 36-6 5n. -50 38-9 4n. •41 39-2 3"- 2n. -57 40-q ,, -55 43-8 3"- -61 ■6 ,, -50 44-7 in. ■59 47-7 ,, ■44 0.2. 39-6 >» •58 ■6 ,, •53 41-2 ,, -53 52-8 ,, ■17 51-8 ,, -26 Mit. 40-4 •32 Ua. 43-1 4n. -23 -9 31- ■23 40-5 in. •17 44-5 ,, ■33 42-2 4n. -26 43-3 ,, -23 Se. 41-4 5n- ■31 De. 46 I JJ -2 -6 3"- 2 42-8 4n. -3 54-3 in. 49-6 6n. •26 53-2 7n. -23 54-3 3n. -27 57-4 in. -16 -5 ,, •23 56-5 3n. -40 55-2 ,, -50 57-4 2n. -29 58-2 ,, •33 Vo. 45-4 12 ■44 Kn. 52-8 in. ■31 Vf. &S. 57-0 5 -28 1829-99 33-37 4-28 43-32 2 39 3-34 8-12 -45 9-33 53-38 4-41 7-45 60-34 42-39 5-31 -31 66-42 74-40 47-57 5 1 00 2-32 4-38 5-42 6-39 8-12 6-41 •48 7-66 8-44 62-95 3-31 5-94 832 70-15 1-33 2-43 3-41 4-31 5-31 57-28 65-31 73-24 "MEASURIES. 287 vr.&s. a\. Schi. Sp. Dob. PI. 0.2. Uo. Sn. la. ■W. 4S. Sob. 587 6 1-33 591 56-8 t 1-44 577 58-4 611 ■ 4 7 7 •40 •27 56-2 58-s S I '40 571 3 591 613 4 In. I 32 •07 660 3n. ■07 61 -s 2n. 1-40 ■3 2n. ■34 AC. 1247 •9 •2 •8 125-5 61 -6 125-3 124-9 •I 4n. 28-60 in. ■56 12 •16 »> •32 ,, 27-94 j» 4 869 2n. 4n. 8-68 1873-35 4"26 •30 5-30 •32 ■39 -43 6-36 •36 4-34 5-31 •32 6-34 7-29 •00 30-13 45-31 57-29 65-31 71-39 6-36 5-30 6-33 7-27 408 OX 256. R. A. Dec. M. 12'' 50-3"' -0° 18' 7-2, 7-6 One of the two stars is probably = vari- able. Probably binary. 0.2. He. Sp. 57 -2 242-1 244-1 6n. 0-65 3n- -50 -71 1848-70 67-37 75-36 409 0.2. 257. R. A. 12'' 51™ 0.2. 353-5 De. -8 Dec. M. 46° 16' 7-5. 8-2 3n. I 13-08 [184673 „ I 1278 I 67-22 410 t. 1703. R. A. 12'' 53-1" Ua. Be. C. 283-1 -2 -o Dec. 8° 33'. A, yellowish. 22-65 -78 19-71 2n. in. 411 R. A. 12!. 55-3". 2. Ua. Se. Z 1707. Dec 16° 31' -8 3"- 10-22 -3 in. -76 9-22 M. 8-5, 10-3 1828-94 44-25 65-30 412 t. 1711. R. A. Dec. 12" 56-5" 14° 7' Probably binary. s. 355-9 De. 348-4 W. & S. 352-3 2n. '■tl in. -«3 M. 8-7, 9-5 1829-35 63-24 76-41 413 OX 260. R. A. 13," 1-8"" Dec. 27° 35' M. 7-9, 8-3 Ha. 1200 0-75 1843-30 107-0 ■50 6-28 0.2. 111-3 Sn. •75 S-75 Be. 115-2 31- •78 67-39 414 X 1722. R. A. Dec. 16° 8' M. 7-8, 8-! C. A, yellowish ; B, bluish. Slight retrograde movement. Se. 0.2. W. ft S. 61. Sob. 343-9 339-8 336-8 335-0 339-8 341-5 339-2 340-6 341-9 335-1 2n. 3-54 It -30 in. •36 z ... 5 3-41 -07 4 -09 4 -39 5 -37 6 -4 5 -35 1829-30 56-40 68-36 74-26 -30 •30 -3° -41 5-30 -31 4-34 7-31 415 2. 1728. R. A. 42 COM.£ BEEENICES. Dec. M. 18° 10' 6, 6 lO ^ 66 ■30 V|8«' S*' .19- !88 DOUBLE STARS. C. A, yellow; B, yellower than a; De., both white. ^f"^^ ^'^JJ[^?'^°^""' ^"''es thus in the m. M. : This star is worthy of all attention ; for there IS a suspicion that its period is smaller than that of f Ursse. It seems certain that m five years the angle has changed 1 80°, and that the minimum distance fell between 1829 and 1833, and nearer to 1833." ^^ In the P. M. he adds, " Between 1829 and 1851 the star has twice become single, first in the years 1833 and 1834, and then in the years 1845 and 1846." Sm. found it round in 1832, and in 1839 he ' could not palpably notch them. " Dawes writes, "One of the closest of S.'s discoveries. It requires the finest and largest telescopes." In 1874 O.S. discussed the observations made at Dorpat and Pulkowa, and found a period of 2S7I years. In 1866, under less favourable circumstances, the period deduced was 25-5 years. ^^^"^''^?f'''■ "^"""g the last forty years [the star] has presented three times more the rare phenomenon of an occultation of one star by another. " His elements are T= 1859-92 ±oJ-o8o ^= 99° ii'±o''.45-6 a= o" -657^=0" -0126 £ ^ o '480 ± o '0239 m = 14° o'-2± 2'7S, or revolution = 2S''7i±oJ'-o84. (See Bull de Acad. Imp. de St. Pkersbourg, t- 111. and v). *' The common proper motion is - o"-4?-! in R. A., and - o"-i8 in N. P. D. O.S. 66-8 's-s 127 8-6 11-4 7-0 io'9 ■8 141 91 77 8-5 185 -6 191 6 1893 192-5 188-5 1930 1958 19s oblong? „ 0-20 ■26 -42 •48 -48 •56 •57 •60 -62 ■43 ■38 in. 3n. 40. 3n. in. 2n. ... single In. 3n- In single 0-43 ■54 ■s^ ■51 -40 •36 -21 obi.? Ma. 20 9 9-2 47 15-5 194-5 190-9 194-0 •93-6 1987 1927 188-2 195-2 215-8 3-8 189-1 1971 194-9 190-4 191-6 9-0 18-5 11-5 In. 2n. I In. 4n. 3n- 6n. I4n. 8n. 2n. Sn. 2n. 6n. 3n. 4n. 7n. oblong 0-20 •30 ■32 0-46 ■52 •62 ■68 ■57 •58 ■50 -40 •2 ■42 Sm. Sa. O.S. 1846-40 7-42 842 9-42 so '39 1-42 2 '43 340 4-38 S'44 7 '49 8-44 9-37 61-42 2-40 3 "44 4-42 6-44 8-44 9 '47 70-44 '■43 2-42 346 441 41-40 2-45 5 1 -96 2-42 3-35 4-40 5-38 6-40 740 8-40 9-36 1-42 63-23 8-13 71-19 69-25 9 70 2 MEASURES. 289 Probable change in angle and distance. The increase in distance has been accom- panied by a retardation in the angular movement. (0. S.) Duner gives A=o°-8i+o"-025 (/-i86o-o). O.S. Ha. De. Sa. Sp. Pi. W. &S. 359 -2 3565 352-5 35°"4 366-0 362-7 386-2 350-7 35' '3 349 '6 353-5 3S0'9 348-4 2n. 0-63 4n. •55 3n. -91 2n. 1-08 0-48 •35 •55 ■99 ion. 1-05 •16 3n. ■II 5 ■14 9 -22 843-80 7-17 5776 66-86 45-86 8-00 51-27 66-99 70-04 5-35 7-20 •45 ■46 417 Z 1734. R. A. 13'' 14-6" Dec. 3° 34' C. white. M. 7'2. 79 Very slow change. Probably a binary. 2. I98-I 4n- 073 1830-35 Ma. 200-0 I -I 41-37 202-5 0-85 2-46 203-0 -96 3-30 196-1 -96 51-35 200-4 102 2-39 0.2. 204-0 5n. 0-96 47-16 8e. 198-2 in. -84 56-31 ■8 „ -79 -38 61. 192-6 „ i-i 74-32 Vf.&S. 191 -3 2n. -06 -32 195-0 3n. -06 5-35 Sp. 193-2 -24 -37 418 S. 1742. R. 13" A. Dec 18"" 2° 2 C. yellowish 2. Ha. O.S. 351 -I 4n. •0 2n. 346-1 3n. 1-29 -39 •18 M. 7-4. 7-9 1831-85 43-30 50-99 419 2. 1744. R. A. ,jh ,g.,n; HIZAS. Dec. 55° 33' C. greenish white. M. '■1, 4-2 A very fine object, and probably the first star which was observed to be double. Riccioli discovered it in 1650; it was seen double by Kirch in 1700, and first measured by Bradley in 1755. The common proper motion of the pair is + o'-oi7 in R. A. and + o"-04 in N. P. D. Alcor also seems to have the same proper motion as Mizar. Between these two stars Einmart in 1691 discovered one of the 8th magnitude : its position in 1839 was l02='-6, distance 8' 45". (Sm.) In 1857 Bond tried some experiments in Stellar photography. Mizar and Alcor were the objects chosen : the distance between these two stars was found to be 707" -8, and that between Mizar and its companion 14" -6. The following results were obtained from an examination of eighty-six photographs: "the probable error of the distance of the centres of the photographs of Mizar and its companion is ± o" -072 for a single pair of images : the probable error of a single micrometer measurement of a double star of this class, taken in the ordinary way, is ±o"-i27 ; so that the relative value of the photograph is \^^) ; or the photograph is worth three times as much as a single direct measure.'' Duner gives the formula: 1852-16. A =14-29. P = i47°-7 + o''-025 (/— 1850-0). Bradley. 1431 H,. 146-8 141 -2 2. 145-6 H.. & So. 147-6 Sm. Be. Encke. Ga. Ha. 0.2. Da. Be. •o -4 148 -I 147-7 146-8 147-2 1477 148 -2 •I -4 •3 •6 -2 -6 -8 147-8 1480 -o •47-9 3"- 7n. 2n. in. 2n. 6n. I 2n. i 3n- 4"- 2n. 3n- l6n. 14n. 8n. 9n. In. 9n. 13-88 •2-3 14-0 -3 14-74 -36 •45 -21 -6 -4 •2 ■43 •70 •65 •42 •58 -53 •22 •20 -10 ■'5 -13 -03 -12 ■39 -16 -24 -52 1755-00 79-76 80-40 1-88 1802-75 21-80 2-76 30-63 2? -44 30-44 -85 9-32 54-72 30-79 7-63 8-62 9-59 41-55 2-80 51-18 •86 3-32 456 6-07 7-39 61-99 46-55 8-49 52-14 8-54 19 290 DOUBLE STARS. 8e. Bo. Eng. Ta. Da. W. &S. 61. Fl. 148-1 2n. 14-6 -5 4n. •4 146-8 in. 13-90 148-8 J, •04 •I 2n. 14-48 ■4 )) •51 in. 15-06 I48-I „ 13-90 -6 ion. 14-52 •0 2n. •5 147-9 in. •7 148-7 j» •55 '855-30 7-70 62-44 9-57 3-27 4-33 5-57 71-39 69-50 73-28 4-22 7-50 420 X. 1746. R. A. Dec. M. 13'' 22° 10° 5' 7-7> 10-3 C. A, yellowish. 2. 250-3 m. 29-32 1828-31 251-4 )» 30-08 9-36 250-8 t> 29-47 31-21 Ha. 248-7 II 28-72 47-27 249-4 j» 29-11 •28 421 OS. 266. R. A. Dec. M. 13" 22-6" 16° 21' 7-3. 7-8 C. white. The angle ha.s increased, and th e distance may have increased also. 0.2. 324-2 4n. 1-15 1846-10 Da. 3253 7-34 326-2 1-07 50-80 32.7-2 -08 4-27 Ma. -7 -18 49-27 Be-. 333-5 in. -71 56-44 De: -4 3n. -34 67-30 w.-*^. 336-2 5 •27 77-45 -I 6 -22 •46 422 OX 269. R. A. 13" 27" Direct motion. Dec. 35° 31' 0.2. De. 2180 222-3 240-4 230-5 228-9 223-6 242-8 257-1 45? in. 0-33 M It »> •39 oblong in. 0-33 »» •27 ji -33 )» oblong obi.? simple M. 6-5. 7 1844-31 46-37 -38 ■39 9-47 5' 39 5-47 61-26 72-47 65 68 423 2. 1757. R. A. 13'' 28-2" Dec. 0° 18' M. 7-8, 89 -90 t977. C. Se., A, white ; B, bluish. Sm., A, pale white ; B, yellowish. From his measures made between 1825 and 1835, 2. inferred direct motion. Sm., from his own and Z.'s measures, found that the angular progress was at first 2° per annum, that it then diminished to 1°, and that "it is now on the increase, amounting to lj°." Hence he concludes that the object was then seen "full face," and that its period is about 240 years." Dawes, having the measures up to 1863 before him, considered that the increase in angle was established, and that the distance remained unchanged. 0.2. The distance has increased, and the angular change has diminished. 1825-37 9-82 33-38 6-42 8-48 42-52 52-38 41-38 5-88 53-09 4-37 8-37 936 4239 60-34 -35 43-51 472 50-38 66-01 Sm. Ka. Da. Ka. 0.2. Ja. 10-0 in. 1-60 19-5 2n. -44 23-9 )t •54 25-s 3n- •66 29-4 2n. ■64 31 -o •7 37-9 -7 51-7 20 36-0 4n. 1-74 40-8 2n. 2-02 52-2 3n. •OS 50-1 5n. •16 54-7 2n. 1-91 53-7 »i •82 .^7-4 »> -67 38-8 ,, 54-3 in. 231 53-4 II •08 40-9 43-7 3". 1-89 48-8 »> -85 6o-8 »> 2-34 48-0 15 •14 52-8 1-76 53-73 8-08 MEASURES. 291 Se. Ko. Se. la. Sp. Sob. 51-3 •8 59 -o 60 '4 627 63-5 ■4 51-9 54-2 52-9 637 64 '3 ■I 673 69-8 ■4 ■8 ■o ■o •5 ■9 •2 ■5 2 6 •6 6i-i 64-2 4n. 2n. Sn- 3n. in. 12 10 2n. in. Br. 63-4 2 W. ftS. 648 8 ■0 S 65-0 S •5 7 •9 4 64-2 S 66-5 6 67-2 6 Scbi. 66-6 in. 3n- 2n. 17 •s 2"OI ■09 •04 ■03 •13 •01 •00 1-84 2 -60 2'00 i-o8 2-59 ■30 ■05 •00 •15 2-i6 •21 ■'S •00 •00 2"33 1855 'SI 6-32 63-32 S'97 8-30 7015 I-I9 56-42 7 "29 6-88 67-27 9-24 7o"37 2-37 4'32 69-22 72-33 3 '23 "35 4-32 ■32 •41 6-41 •36 5-31 •31 6-32 7-23 424 t. 1768. 25 CANUB VENATICUM. R. A. Dec. M. 13" 32-I'" 36° 54' 5. 7-6 C. S., A, white ; B, blue. 2., from his measures between 1827 and 1836, suspected orbital motion, and subse- quent observations proved the correctness of his suspicion. 0.2. says, "The feeble angular motion from 1833 '° '841 indicates that the satel- lite was in aphelio in that period. The apparent ellipse is evidently very narrow. We shall probably see the companion emerge from the rays of the principal star under an angle of position between 180° and 90°. If so, the period of revolution does not greatly exceed a century. " Dr. Doberck, in 1877, found thefoUomng elements for this pair : — a X 7 e P T 82''-o 202 -o 51 -5 o -66 = 124-50 years = 1862-98. 2. Ha. 79-5 5n. 1-05 72-4 »» •09 71-7 3"- •07 70-8 4n. 0-99 $(>■$ 6n. •39 1829-89 33'i2 6-50 41 '39 51-28 Ma. 0.2. Da. 8e. Se. Su. 447 36-2 26-7 72-6 69-8 65-6 677 36-2 10° or 15° round 25-7 180' 315 178? 186 47? W. &S. w.o. 01. Schi. 161 -3 Sp. 4 41. In. 2n. 4n. 31- 4n. 3". I 0-31 •35 •2 I -01 71 •65 smgle 0-99 •35 •«5 elong^- I single elongated round single round in. I 0-42 I -42 1852-33 3-32 8-65 4117 6-80 977 5972 42-35 54-43 60-36 5-44 5649 7-59 62-95 3-15 -50 9-40 70-43 •-4S 5 49 2-38 5-36 •40 6-44 -45 425 SM. 488. R. A. Dec. 28° 56' C. white. M. 9-5. '0-5 This close pair was discovered by Smyth in 1835, while looking through H,'s 20 ft. reflector at Slough. It was afterwards elongated by Smyth, Challis, and Dawes. Smyth also noticed "a small blue telescopic companion in the n.f. quadrant." Sm. Challis. Sa. 191 -5 195-0 193-0 196-5 I i-o elongated i-o 1835-48 43 51-37 42-47 842 426 t. 1771. R. A. 13" 33 S" 2. Ma. Dec. 70° 23' M. 7-8, 8-5 69-9 71 74-6 73-5 75-1 in. I -81 1829-81 2n. -67 31-73 -76 45-56 •82 52-67 71 4-21 427 t. 1772. R. A. Dec. M •3' 34-9" 20° 33' 6-2, 9-1 C. A, bluish white ; B, very blue. 292 DOUBLE STARS. H,. 140 60 1477 4-88 146 '8 5 145-0 6 V 150-4 2n. 471 147-6 3"- -92 in. 5-i8 Sm. 147-1 4 9 Ha. 149-2 79 144-8 5-22 0.^. in. •18 145-6 „ 4-81 149-4 2n. -82 7 In. ■95 Ee. 144-1 -60 U. «40-3 •63 Fl. '37-9 in. -68 1826-00 8-33 31-00 2-00 28-30 3374 52-16 3223 44'34 8 -35 52-16 68-36 7o'33 4-28 56-93 62-44 77 '43 428 t. 1776. R. A. Dec. M. 13'- 368 46° 50' 8, 8 C. white. Duner ^ formulas are A = 7" -23 — o"-oo6 [t — 1850-0). 1849-09. P = i99°-3. H,. 199-9 in. 8-58 1830-32 2.' 200-2 3n. 7-32 2-09 Ha. 199-4 2n. •55 4357 Se. 158-5 )» 6-93 57-55 Ho. -2 716 9-22 Du. 199-5 )» -10 70-90 Ta. 201-0 6-90 3-37 429 %. 1777. R. A. 13" 37" Dec. 4°9' M. 5-8, 8-2 C. A, yellow ; B, very blue. The colour of B probably changes. A beautiful pair : binary. Common proper motion — 0^-023 in R. A., and + o"-05 in N. P. D. Duner 's formulae are 1853-01. A = 3"-45. P = ^33°-3 -o°-09(/ -1850-0). H|. 240-9 239-8 2. 234-1 235-3 234-0 Hj & So. 229-8 232-9 235-3 231-8 228-8 in. 5n. 4-23 in. 3-39 ■67 »i -91 4-06 2-5 1782-10 ■V. 1802-31 21-30 877 52-22 21-37 30-20 1-28 2-00 Sp. 3-26 Dob Sm. 2329 3-7 1831-19 231-8 •6 6-35 233-4 •5 9-?7 Ma. 2348 233-1 •42 606 42-40 2345 3'5« 3-31 2339 ■44 4-30 232 5 5n. ■50 51-56 233-3 6n. -18 4-96 232-7 2-89 8-38 235-0 61-41 Sa. 2334 3n. 372 41-24 231-8 in. ■61 3-34 234-1 -61 , '59 233 '6 in. •60 60-38 Hit. 231-9 n -49 47-57 Se. 233-4 )l ■33 56-41 2350 -50 67-80 Se. 231-6 31- •26 57-03 Ho. 230-8 2n. •35 8-28 Eng. 231-9 4n. -79 65-35 Ta. 227-8 2n. •87 6-40 -7 In. -86 9-25 0.2. 2366 »» 4-03 70-35 Gl. 231-7 „ 3-52 1-32 Du. •7 4". ■39 2-53 ■w. &S. -5 2n. ■54 3 35 232-5 in. •22 4-32 230 „ •60 646 Sp. 231-7 •54 5-44. Dob. 232-3 4n. 6-34 Fl. 2294 3-58 7-45 PI. 230-1 3n. -25 •51 430 X. 1781. R. A. Dec. 1 3'- 40-2'" 5° 43' C. yellowish white. A binary. 2. H,. 0.2. Da. Ha. Se. De. Ta. Gl. &I 240-3 3"- 1-35 2357 ■5 244-2 2n. •40 238-6 >t -20 242 -2 -09 246-5 2n. 099 249-8 3"- 1-2 251-7 ,, •15 255-6 in. 256-0 5n. ■I 257-5 4 095 256-4 5 I 20 261-4 5 ■23 260-7 4 ■02 256-0 8 ■23 •5 9 ■3 2617 5 -20 262-5 6 -20 259-S -21 256-3 31- ■03 M. 7-8, 8-2 1830-31 2-00 41-91 2-31 3 34 56-39 8-07 64-75 9-25 71-32 238 323 -34 -35 4-23 -32 6-36 ■45 5-37 736 MEASURES. 293 431 O.S. 270. R. A. i3'> 41-6"' Dec. 18° 3' M. 4-8, 11-4 C. greenish yellow. These stars have a common proper motion. 0.2. 347'8 I 5n. | 10-26 11849-54 -De. 348-9 I 3n. | 9-03 I 6736 432 t. 1785. R. A. if 43-6" Dec. 27° 35' M. 7-2. 75 Change in both angle and distance. The measures by Dembowski differ consider- ably from those by 0.2. It is probable, however, that those by the former observer are the less accurate of the two, seeing that the angular movement has not augmented in so great a degree as the diminution in the distance demanded. (0.2.) The common proper moi ion is — o"-5o in R. A., and + o"-o03 in N. P. D. Duner has the following formulae : A sin. P= -o"-o38 - o"'0437 (/- 1852-50) -o" -000033 ('-1852-50). A cos. P= - 3" -240 + o"-o267 (/ - 1852-50) + 0" -000857 (/- 1852-50). 1823-40 9-41 31 '53 0-20 I "34 40-85 3-48 4-88 51-28 5-66 61-59 46-41 51-41 66-42 8-38 70-31 ■35 56-36 8-38 6327 4 '39 5-34 6-81 8-34 70-32 1-30 2-38 3-39 4-46 5-30 So. 160-4 V 164-0 165 '3 H... 164-6 166-2 Ua. 172-1 174-6 ■9 178-7 1837 191-1 Po. 176-2 O.S. •0 194-1 198-2 200-5 198-3 Se. 185-9 Se. 1S4-7 190-7 191-9 192-7 1945 196-8 199-1 200-1 201-5 202-4 204-4 205-8 5-07 2n. 3 '44 in. ■57 4-62 2n. 3-47 ■39 8n. ■47 2n. •48 3n. ■03 in. •52 4n. •20 2n. •18 in. 2-66 •96 ti •68 »» -91 2n. 3-24 5n. ■12 7n. 2-69 4n. •60 6n. •60 9n. •56 4". ■51 >» •46 »» •40 If •32 if •32 3". •21 4n. •16 Ho. U. Eng. Gl. 185 192 199 198 "93 198 201 206 204 199 En. W. & S. 200 203 201 204 206 207 206 208 208 ■ Lindstedt2oo Schi. 205' Sp. PI. Dob. 206 208 206 4 2n. 2-89 8 In. ■69 •3 ii ■65 •9 j» •32 ■5 ■88 -8 7n. •87 •5 5". •46 ■7 2n. •59 •4 4n. ■39 -I 5 •46 -0 4 •6 4 ■4 •8 II •7 ■2 3". •5' -2 5 •47 -2 4 •47 -0 4 -46 •5 9 •4> -I 5 -46 ■9 7 •58 ■7 5 ■4 6 •28 •8 5 ■14 •2 2n. ■4' ■3 In. ■34 4 •34 9 V 9 2n. •61 8 6n. •21 1859-30 63-31 71-27 •44 64-47 5 '42 70-19 2-43 5-24 1-32 0-32 •55 1-32 •38 2-38 323 ■35 4'32 5-35 •39 •41 6-41 7-47 342 5-32 ■33 6-45 ■42 7-32 433 t. 1788. R. A. Dec. M. 13* 48-6°' - 7° 28' 67, 7 9 C. white. The common proper motion is -0"-i37 in R. A. So. 5'7 2-76 1825-39 Hr 496 •57 30-27 50-6 •68 •■44 S. 54-0 5". •36 138 64-9 2n. , -66 5223 Sm. 55-0 •5 34-29 Ma 60-4 ■49 44-35 61-0 •44 54-38 63-3 ■47 8-37 Se. 62-6 2n. •46 6-39 U. 64-2 in. •38 62-32 De. 677 •46 4-85 Gl. 69-6 in. •58 71-32 W. &S. 75 '4 »> •55 2-38 70-0 3". •64 3-63 Sp. •0 ■45 5-40 CO. •2 2n. •62 7-39 Dob. 67-5 4n. -68 7-31 434 O.S. 272. R. A. 13" 49" Dec. 30° 29' C. A, white. M. 7, 9-9 294 DOUBLE STARS. Ma. 22-2 25"5 II '-1 1 843 '33 9 34 439 OX. 280. 0.2, 23-4 4n. -89 •56 De. 178 ^n. 78 66-71 R. A. Dec. M. • 14" 7" 60° 58' C. A, golden. 7. "-2 435 0.2. 273. */ O.S. 20-5 3n. 7-20 1848-61 R. A. Dec. M. De. 245 „ 695 66-67 13" 50° 5° 50' 7-5. 8 0.2. 106-1 3n. 0-74 De. 111-2 ,, 0-98 1845-99 6773 440 t. 1813. R. A. Dec. 14" 7-4" 5° 58' M. 436 2. 1808. 8, 8-1 C. white. R. A. Dec. M. Probably binary. 14" 47°" 27° 'o' 8,9 Duner gives C. white. 1850-61. A = 4" -95. P = i92°-6 + 0°04 U - 1850-0). Probably binary. Duner has H,. 180-0 1793-36 H,&So. 190-7 in. 6-06 1823-34 A = 2" -70 - o"-oo7 [e - 1850-0). 192-5 ^, 4-5 31-00 P = 72°-i +o°-i87 (/■ - 18500). 2. 191-0 4n. -76 29-81 2. 68-8 3n. 2-82 1832-31 Ma. 193-9 5 -34 4J-37 Ma. 71-0 Dn. 76-1 2n. -76 ■54 44-39 71-32 192-9 191-5 194-7 4n. -21 -24 3-07 4-30 6-25 193-1 •I in. 4-83 51-28 838 »' 437 t. 1812. Da. 192-2 7n. 'V' 42-27 194-0 2n. -84 3-35 R. A. Dec. ly r. De. 192-9 •92 55-30 14" 7" 29° 17' A 7-8, 1 i 8, c 9-3 Se. 193-9 3n. -82 705 M. 199-8 in. -86 63-31 A B probably binary. Eng. 192-5 4n. •98 532 Ta. 1932 2n. -67 6 40 A B. -0 ,, 7-37 o.s 3337 4n. 0-42 1845-85 "94-5 m. 3'83 7348 344'3 31. ■47 65-42 -8 ,, 4-21 433 Se. 3427 In. •4 56-44 Dn. 192-4 3n. -88 9-38 61. -7 in. 5-2 1-32 ■*• -^ and C. 2 32-37 "W.&S. 193-1 PI. 192-7 5'n. -0 -0 3-36 7-27 2. 108-2 3n. 14-18 0.2. -I 7n. •02 54-24 441 OX 279. Pi. 107-4 2n. 13-89 77-51 R. A. Dec. 14" 8°' 12° 34' M. 6-8, 9 438 OX 278. C. A, yellow. R. A. Dec. 14" 7-° 44° 46' M. 7-5. 7-7 0.2. 248-4 3n. 2 27 De. 251-8 „ -11 1845-68 6671 Probably a binary. 442 2. 1861. 0.2. 146-0 3n. 0-40 1846-03 145-1 2n. ■45 54-00 R. A. Dec. M. 124-2 De. 128-2 in. 3"- •53 75-48 67-48 14" 8" 29° 40' 7, 7-1 Dn. -3 tt 0-32 9-48 1 C. yellowi sh. MEASURES, 295 Very slow change. Probably binary. Duner gives A = i"'68 — o"-oi22 (t - iSso'o). P = 8o°'3+ o°-o87(/- 1850-0) + o°-ooo6 (/ — 1850-0/'. 2. H,. Ok. Ma. O.S. De. Se. Du. 01. W. &S. 80-1 5n. 1-86 76-3 In. -92 79-4 3n. -69 78-4 fi -84 79-8 2n. •73 ■s 6n. ■79 80-9 2n. 81-8 3". 1-57 82-5 in. "57 80-4 2n. ■49 84-7 4n. ■32 79-8 in. -6 -6 2n. •55 I83I 3 41 3 2 S3 5 66 74 S6 71 •33 ■26 ■88 ■34 ■88 •43 ■27 58 ■23 ■41 •16 •32 443 2. 1820. R. A. Dec. M. 14" 9-1" 55° S3' 8-2, 8-5 Direct motion. Dembowski's distance in 1866-75 is probably too small ; it is pro- bably explained by the note that the obser- vation was made in haste. Duner has 1850-57. A = 2"-35. P = 54°-o + o°-422 (/ — 1850-0). 2. Ha, Se. On. O.S. 47-3 6n. 2-40 52-0 2n. -50 S0-3 in. ■17 63-1 )» ■35 60-5 3n. -II 63-2 5n. •27 68-0 in. •64 1834-14 45 '47 51-27 4-21 66-75 71-45 470 444 2. 1821. R. A. Dec. 14I' 9-2"» 52'' 21' MagniiuJes. — 2. 5 ' i , 7-2. The estimations of the magnitudes differ considerably. Du. has 35, 6-5 ; 4, 7 ; 5, 75 ; 4, 6. C. 2., A, yellowish ; is, bluish. The colours also are variously given. The proper motion of /c is + o'oog in R. A. and + o"-02 in N. P. D., and in this the companion probably shares. Duner gives 1847-34. ^ = i2"-68. P = 237''-2 — 0°-05 (J - 18500). H,. 240 I in. ; ... 17797s ,, I i2-o8 80-56 242-5 I „ ; ... 2-29 ... j I 11-09 97-75 240-7 I In. I ... iSo2'66 So. Sin. Ma. Mo. Se. Su. •W. &S. 233-6 237-7 -7 2387 -8 237-9 238-1 237-0 236-4 237-0 2361 237-3 ■I 238-6 ■I 236-3 242-8 in. 7n. 1260 in. •50 4n. 13-14 12-79 -5 8n. 5n. •7 -76 •63 -65 4n. 2n. ■49 ■66 >> -66 3"- 2n. ■■11 Sn- •92 in. -99 1821-78 32-50 7-70 22 '62 30-48 -93 8-78 43-42 4-90 52-37 5 '37 61-57 54-46 5-46 73 72-90 646 445 t. 1819. R. A. 14" 9-3" VIEBINIS. Dec. 3° 41' M. 7-9, 8 C. 2. yellowish ; Se. white ; De. white. 2. discovered this double star, and in 1836 pointed out that it was a binary. 0.2. says, "The increase in the distance is certain, but slow ; it is confirmed by the diminution in the angular motion." H... Ma. Sa. Ea. Se. Se. M. Ta. GI. 88-0 2n. 8i-7 ,, 76-1 3n. 83-3 65-2 in. 63-2 3"- 57-1 in. 54-1 5n. 49-6 ,, 44-4 4n. 66-4 2n. 52-9 ,, 36-5 in. 60-5 8n. 61-9 in. 62-8 43-7 2n. 34 -S 44-0 3"- 40-8 7n. 21 1 -4 4n. 32-8 7n. 31-6 6n. 27-9 2n. ■0 ,, 25-5 ,, 38-2 31-9 in. 25-7 4 26-7 4 26-3 6 26-2 S 0-86 1828-35 i-io 32-42 -12 643 -0 2-00 0-95 4'-35 •86 2 40 1-04 5 39 -16 7-38 -26 51-30 •14 4-40 ■07 41 93 •19 9-36 -43 66-42 -oS 42-81 -02 3-34 •24 0-9S 56-39 1-17 64-41 56-45 -0 8-41 -32 62-47 -28 3-31 -23 5-85 -17 841 •25 70-35 "34 1-22 -0 58-38 -9+ 67-28 -2 7032 ■27 •34 -22 -43 •32 1-24 296 DOUBLE STARS. 61. W. &S. Brhi. ■WO. Sob. PI. 27-0 251 247 239 257 27-4 25-0 23-5 •2 222 26-5 23-6 ■2 21.5 •6 2017 199-3 ■4 17-2 i8-9 3 4 6 8 10 3 4 6 6 4 3 7 5 2n. 411. 3"- 1'4 •34 ■4 ■25 •13 •17 •35 •33 ■33 ■40 1-37 ■46 ■47 ■25 ■37 ■'5 187 1 2 3 •32 •36 ■42 •38 39 •23 •36 •36 ■41 ■35 ■39 ■41 ■41 •36 •36 ■39 ■39 •41 ■33 •27 ■47 446 2. 1825. R. 14" Ma. Se. Se. Gl. ■w. A. 107" Dec. 20° 41' &S. Dob. PI. 186-5 i85^5 ■7 3n- 184-5 1 J 183-8 182-2 3"- 1788 I So -J in. 178-0 3n- 177-5 in. 174-7 4n. 179-1 3n- 4-0 2-5 3-45 4-05 3-89 •74 •90 4-2 -I 3-93 4-02 3-67 M. 6-8, 8-5 : 1830-00 I 2-00 0-66 ■ 41-52 2-40 3-31 57-77 64-47 71 -22 3-36 4-93 7-39 -51 447 S. 1830. R. A. Dec. 14'' 1 1 -9" 57° 14' C. -. A, yellowish ; Se. A, -white ; Certain change both in angle and Duner gives A = 5"-3o + o"-oi9 (/- 1850 P = 273' -9 + 0° -4 54(^-1850-0) (/-i85o)^ ^. 263-0 266-0 Ua. 267-6 271-3 275-3 276-2 277-4 276-9 Se. 278-2 Du. 279-9 2n. In. 3n- In. 2n. 2n. 3ii- 4-86 -79 S-12 -40 -30 •48 -67 •71 -31 -65 M. 8-5, 9-8 ; B, blue. distance. -o). o°-ooi67 [82971 33-26 38-19 45-48 51-27 2 -69 6-46 8-72 60-06 71-50 61. 0.2. 2864 282-4 285-3 283-9 285-9 2 5 '7 in. -76 j» •60 4 •5 4 1871-32 2-54 4-70 3-25 ■29 448 2. 1832. R. A. Dec. 14" 13° 4° 27' Probable change in angle. 0-47 0.2. 132-6 in. -66 ■58 Se. W. &S. II8-3 3n. 132-6 in. 122-1 »» 1319 >> I20-6 2n. 120-5 z ■51 •41 ■4 M. 9.9 1830-28 47-40 9^37 53-41 6-41 76-46 449 O.t. 281. R. A. 14'" 14"" 0.2. 161-4 De. 152-5 Dec. 9" 8' 3n. , 1-25 •59 M. 7'3. 1°-^ j 1847-72 I 67-33 450 2. 1834. R. A. Dec. M. 14" 15-9" 49° 3' 7'«. 7-2 Rectilinear motion. Duner has A = i"-04 — o"oi75 (/-1850-0). P = ii3°-8 + o°-o5 (^-1850-0). H,. Da. Ma. De. Se. Ta. Da. 61. W. &S. 104-0 108-3 1 15-0 113-7 111-8 112-7 iii-i 113-9 1140 -8 110-9 115-5 -3 113-7 2n. 1-09 1830-24 -20 1-37 3-26 4n. 1-36 1-20 3n- -•4 40-51 2n. -04 8-50 •10 9-48 2n. ■37 3-23 in. 57-51 2n. 0-92 7-57 in. -87 66-49 4n. •66 71-21 in. -6 1-53 )) -6 4-52 451 R. A. 14" 18-2" S. 1837. Dec. -11° 7' M. 7-1, 8-7 A physical pair. Common proper motion. 4n. Sm. 326-9 325-8 321-5 1.41 -6 -3 1829-83 33-36 7-48 MEASURES. 297 Ua. Mit. Se. M. Se. Gl. W. &S. Sp. CO. 323 '4 I-5S 324'5 m. .50 3«23 2n. •40 348-8 in. •05 3141 ■34 3i3'o in. •41 3" -6 »> ■33 309-8 •26 307-0 2n. ■45 1848-38 •45 56-47 62-37 5-07 71-40 3-36 5-87 7-42 452 R. A. 2. 1842. Dec. 4° 14' C. white. Probably a binary. 2. Ha. Se. Gl. "W. &S. Doll. PI. 10-9 4n. 2-84 9-4 0-96 11-9 3-06 '3-« 2-90 i.s-« 3n. -80 13-7 ■9 14-5 2n. -75 12-7 J) -97 ■9 jj •86 M. 8-7, 8-7 [828-86 30-34 4-18 44-35 56-77 71-40 4-42 7-38 -51 453 2. 1847. R. A. Dec. I4'> 22-2" — 9° 40' M. 8-s, 9-8 2. 248-4 Ma. 251-5 Mit. 253-1 De. 256-0 4n. 18-73 -22 20-17 21-67 1829-81 44-34 8-45 65-36 454 0.2. 283. R. A. Dec. 14" 28™ 49° 44' M. 7-3, "-2 0.2. 134-6 3n. 4-93 De. 1301 „ 511 1848-19 66-79 455 Z 1858. R. A. 14'' 2^°" Dec. 36° 6' C. white. M. 7-2, i Ma. Se. De. Mo. 0.2. 30-7 1 2n. 1-44 1830-78 35-2 ' 3n. 2-20 1-84 33-0 m. ■73 51-80 3-; -6 in. ■34 43-46 -8 2n. •36 56-89 34-7 in. 8 -23 31-5 3n. 2-51 9 33 30-9 in. ■73 70-45 Dn. Dob. PI. 34-2 Sn- 2-45 -4 4n. •59 35-6 2n. •61 1870-99 7-32 -51 456 a CENTAURI. R. A. 14." 31 -8" Dec. • 60° 20' M. i> 2 C. "Both strong reddish yellow" (Dun- lop). " Both yellowish ; " "a, yellow; B, greenish yellow" (Jacob). "Both yellow" (H2). A fine double star discovered by Feuillee in 1709. He wrote : "Je trouvai cette etoile composee de deux, dont I'une est de la troisieme grandeur, et I'autre de la quatrieme. Celle de la quatrieme est la plus occidentale, et leur distance est egale au diametre de cette etoile." * Richer was probably the first to examine this fine star with a telescope : this was in 1673, ^t Cayenne. Halley observed it at St. Helena in 1677, but neither observer records it as a double star. La Condamine observed it while in Peru. See PAi'L Trans, for 1749. In 1709 the distance was probably about 7" ; in 1751, when Lacaille observed il, 22"-5 ; in 1761 Maskelyne found it 15" or 16" (see J'hii. Trans, for 1764) ; and in 1825 Dunlop made it 23" {Mem. k. A. S., vol. iii. ) In 1848 Captain Jacob computed the orbit : his elements are — TT = 26° 24' 7 = 47 46 a = 86 7 X = 291 22 e = 0-950 T= 1851-50 P = 77-0 years «=4°-675 a- iS"-5- Maximum distance, 21-85 at 207^-5. Minimum ,, 0-50 at 5°-o. Greatest daily motion = 2° 40'. Mass = } of solar mass. Mr. Hind in 1851 published the follow- ing elements : — Perihelion passage 1859-42. ffl = 16° 42' X = 26 2 ^ = 0-7752 7 = 62° 53' a = l3"-57 P = 80-94 years. • See FemUie's ymmal lies OiserTa/h«s Piv s/fnes, etc., tome i., p. 425- Paris, 1714- The telescope used was one of 18 ft. focal length. 298 DOUBLE STARS. In 1854, Powell published the following elements : — (I) (2) T = i8s7'oi2 1858-012 IT = 30° 14' 29° 33' R = 2 35 177 so 7 = 77 194 77 50 e = 0-96887 0-966 n =4° -35882 4-78 P = 82-59 yrs. 753 yrs. a = 3i"7574 30". Powell thought that the correct elements lay between the two sets given ; that the next periastral passage would occur between 1857-5 and 1858-5; that the semi-major axis of the orbit is a little greater than 30" ; that the sum of the masses of the two stars is between six and six-and-a-half times the mass of the sun ; and that the orbit is something like a magnified image of the path of Halley's comet. In 1877 Mr. Hind computed an orbit (see Monthly Notices, vol. xxxvii., p. 96). In this the observations made by Lord Lindsay in 1874-85 were used : — Periastron passage, 1874-85. a = 21° 48' -o. 59° 82 32'i- 18 -4. Node to periastron on orbit Inclination e — 0-6673 a = 2i"-797 P = 85-042 years. And the comparison of the elements with the observations from 1752-2 to 1874-85 shows a very satisfactory agreement. Mr. Hind remarks that "Lord Lindsay's measures fall exactly at the computed time of nearest approach of the component stars in the real orbit." " If, for the annual parallax, a mean of Henderson's value, as corrected by Peters, and that of Moesta, be taken, giving o"-928, we find the mass of this system = 1-79 X the sun's mass, and for the semi-axis major of the orbit 2349." Mr. Maxwell Hall has measured this star with great care. His results are — 1878-38 i39°-i 2"-4. See Nature, vol. xviii., p. 225. Lastly, Dr. Doberck in 1879 obtained Ausseii the following elements : — a = 25° 14' X = 45 58 7 = 79 24 e = 0-5332 P = 88-536 yrs. Lindsay T = i875i2 Gill a = i8"-45. '/ Fenillee ... 6 — 9 1709 lacaille 218-7 ; 20-51 52-2 Haskelyne Fallows 209 Brisbane 215 Dunlop 213 Johnson 215 Taylor 216 H, 217 218 219 220 Uaclear 223 262 Ja. Po. 232 234 235 238 250 251 267 276 283 307 320 329 270 277 281 283 2S9 293 294 301 340 345 348 35' 353 354 358 £1. 5 20 o 5-2 30'5 50-6 69-1 22-3 •9 25 '3 28-1 30 o 47-0 76-1 34'2 69-4 80-6 75 '3 80-5 ■7 15—16 28-75 22-45 ■45 19-95 22-56 19-85 18-67 17-4 16-52 •II 1474 5-03 10-96 9-82 •45 8-05 5-97 -90 4-55 ■21 6n. 392 ,, 4-01 2n. -29 22 JS5 25 38 128 140 4-07 26 140 3 '95 125 5-12 no -68 10 •6 130 6-08 60 -2 30 -29 80 79 7-2 -85 10-24 -0 8;s 2n. 9-4 in. 10-2 )j 8-3 ,, -0 31- 3-9 5n. -I 3n- 10-46 2n. 12 ,, 973 In. •5 2n. 7-96 >» 4-35 5n. 2-23 in. ;;: 1 761 1822-00 4-00 601 30-01 I 00 2-16 3-00 479 6-30 7-34 40-00 52-56 46-21 -87 7-09 802 50-96 1-05 3-05 4-00 ■63 6-38 7-29 8-12 3 59 4 06 •38 •63 5-04 ■32 ■50 6-02 9-38 60-11 ■48 1-05 •30 -58 2-20 303 4-11 70-00 62 375 4-72 8-18 70-65 3-i6 4-15 6-72 7-25 074 I '47 2-47 333 4'47 6-41 7-54 74-85 7-55 ■56 "57 ■59 -61 MEASURES. 299 457 S. 1863. R. A. 14" 34" Dec. S2° 6' M. 7-1, 7-4 C. yellowish white. Certain change in both angle and distance. Duner gives 185572. A=o''-6l. P = ioi=-s-o°-25 (/- 18500). 2. Ha. 0.2. Se. Se. Eng, Sn. W. &S. 61. 1097 4n. 0-65 104-1 ■60 1 01 -6 •6 ■4 7". ■55 987 2n. •68 97-6 »» ■77 100 -2 " ■58 91-2 •67 1073 s'n- ■65 105-0 2n. ■67 94-6 in. ■88 97 '3 elong*- 952 3"- >) 101-5 in. 077 108 -I 2n. ■76 101-7 Sn- •50 99-6 in. •58 S 4 •6 89 s 4 •6 94-3 4 •57 •I I •6S 93-4 3 "5 1830-14 8-94 41-56 3'32 51 -27 2-67 4-50 8-69 41-21 5014 72-54 56-03 64-37 59-52 65-80 9-49 75-52 2-41 325 ■30 •36 4-36 458 2. 1864. R. A. J13 I 77- BOOTIS. Dec. 16° 56' C. very white. M. 4-9. H,. "Sept. 20, 1879. The Rev. Mr. Homsby told me it was a double star, and I found it so. He observed that this had been found to have changed its place 16"." H,. (/%i/. Trans., vol. Ixxii., p. 219). "ir Bootis, Fl. 29. Sept. 20 [1781] Double. Pretty unequal. L, w ; S, w inclining to r. Distance, 6"-i7. Position, 6''28's.f." Hj and So. {Phil. Tram. 1824, p. 199). " Nearly equal ; large, white ; the smaller perhaps inclines to blue. " Sm. (Cycle, p. 323). From the words used by Piazzi, and the measures of H, and Hj and So., he infers a slight direct orbital motion. "This suspicion," he adds, "would have been confirmed by my observations, but that 2. found the angle 9° 50' s.f. in 1819-61 ; and ten years after- wards he concluded 9° 12' s.f. to be the mean position." Duner gives the following formulae : — 1852-21. A = 5"-87. P = 100^-3 + o°-o65 (/ - 1850-0). So. 5:. Da. Ha. Po. D.O. De. Se. Ho. Bo. Ea. Ta. U. On. W. 4S. 61. Schi. PI. Dob. Fl. 96-5 976 ■9 987 99-3 -2 •5 100-3 -2 loi-o 100-8 ■4 98-8 100-7 97-3 lOI-I 102-3 100-9 -6 101-8 100-6 IOI-6 98-9 100-4 102-5 100-5 •8 101-6 100 -o 102-7 ■2 101-2 1020 -6 101-5 100-8 101-3 102-2 ■5 103-7 -o 102-5 101-2 -o ■9 ■o 103-3 m. 2n. 13 in. 3"- 5n. ion. 4n. I4n. 6n. 31- 5n. in. 3n- 2n. 6n. in. 31- 4n. 5n. 4n. 2n. »» 6 4 6 7 2 4 2 8 2 in. 4n. 6n. 6-17 6'-88 -08 5-93 -71 6-28 5-50 -89 6-01 5-85 -96 6-08 ■90 ■76 5-76 5-97 6-14 -01 5-73 6-35 5 -94 6-14 6-22 5-92 6-i8 5-99 6-39 -40 5-89 •5' •82 5-90 6-11 5-96 •86 •91 6-22 5-95 6-2 -84 6-16 -11 459 S. 1865. I BOOTIS, R. A. Dec. 14" 35-4'" 14° 14' C. white 1781-83 1803-19 22-05 7-28 9-35 31-50 3-19 45-39 3-33 52-36 608 60-73 4643 -40 7-31 54-46 521 6-79 7-34 63-27 6-45 -49 7-34 8-40 70-30 -39 1-37 -44 3-40 437 5-33 69-47 71-47 2-47 -38 3-36 •37 4-41 -42 7-46 -46 -47 4-36 5-47 6-96 7-31 -47 M. 3-5> 3-9 The angle w-is unchanged from 1756 to 300 DOUBLE STARS. 1841 ; a slow retrograde movement then began, accompanied by a diminution in distance. Duner has the formulae A = i"-03 - o"oio {/ — iSso'o) + o"-oooi4 (/- 1850-0)'. P = aog^'s - o°-i244 (/ - 1835-0) - o°-ooi5(^- 1835-0)^ X. Be. Da. Em. Galle. O.S. Ma. Ch. la. Hit. Fit. Hi. Se. Se. Ho. 3120 in. 307-0 2n. 1-68 312-6 in. -58 308-5 ,, •15 309-1 )) •0 -2 I in. •19 312-2 •16 3050 •17 310-7 •29 307-5 -33 308-3 -32 31 1 -2 In. -20 310-I ... 307-0 in. I 04 3065 4n. -08 -6 -03 309-9 -3 308-6 ■3 307-3 -2 308-2 -0 309-8 -20 310-4 6n. -24 307-5 8 -00 303-9 7 ■00 304-5 II 0-99 303-1 6 -88 301-5 4 -83 310-0 1-31 311-0 ■16 309-4 l6n. -14 308-4 •05 309-7 -19 -2 ion. -23 308-7 -23 310-0 In. -21 307-8 6n. -04 306-7 In. -23 305-1 •34 308-1 -02 307-8 ■07 308-0 •26 306-5 -24 -7 2n. -5 307-0 -2 306-2 -24 •6 ■35 307-2 2n. -II 308-4 In. 0-93 305-8 12 11 307-2 32 •19 305-7 4n. 0-99 306-1 9n. i-o 303-2 6n. -02 304-7 2n. -18 306-0 In. 0-87 1796-59 1823-27 30-34 1-39 3-24 047 3-42 44-40 3>-i8 2-34 -47 3-30 4-43 43 32 8-11 8-43 3339 8-45 42-43 52-38 38-66 4116 7-72 61-12 2-95 8-68 73-01 41-39 2-36 ■85 3-40 5-26 6-88 7-65 8-36 52-54 5-94 7-43 8-44 9-38 61-42 2-63 42-50 6-19 53-49 5-44 46-67 7-57 5J-75 3-31 5-70 •83 64-78 59-34 64-50 Ta. Dn. •W. &S. Gl. En. Sp. Sob. 307-2 in. i-io 303-1 I5n. 0-75 I 2in. -75 301-4 9n. •72 298-9 3 301-6 10 0-93 300-2 5 -88 302-2 7 -92 301 6 •98 308-2 5 1-38 303-1 in. 0-97 299-4 •91 2985 •88 302-0 4n. •8 300-6 5n. ■88 461 0.1. 284. R. A. 14'' 36-1"° Dec. 49° 15' 1866-49 9-16 71-37 5-42 2-38 3-36 4-41 -42 -36 0-47 5-40 6-50 6-32 7-33 460 X. 1866. R. A. Dec. M. 14" 35-9 m 10° '.' 8-2, 8-2 c. yellowish. V 19-1 in. , o^86 1827-27 -2 ■99 8-32 •3 -90 33-22 Ha. 270 •65 42-36 25-8 -77 335 29-6 •89 7-27 33-5 •80 52-43 32-8 -79 4-42 27-5 •75 7 43 38-4 •70 8-39 De. 19-9 •89 65-08 ■wr. &s. 23-5 in. •93 7442 22-9 -77 5-41 Gl. ■4 in. i-o 4-53 M. 7-2, 1 1 -2 If De.'s angle be correct, a great change took place between 1852 and 1866. O.S. 106-3 Ma. 143-5 141-6 De. 102-3 3"- 3n- 6-98 6-79 848-19 629 52-69 66-69 462 2. 1871. R. A. 14" 37-5"' Dec. 51° 55' C. white. M. 7, 7 Probably a binary. Duner has 1844-80. A = 6"-8o. P = 286°-i - o°-2o (/ - 18500). MEASURES. 301 2. 2832 •0 Wn 279-0 285-1 286-5 Oe. Se. Da. 287-2 •9 2898 3"- 1-82 •80 5n. 6n. 2n. •55 •93 -82 in. 2n. 1-68 »' ■61 1829-10 36-18 0-47 43'6i 52-67 7-u •57 71-42 463 %. 1876. R. A. 14'' 40°" Dec. -6° 53' M. 8-1, 8-6 C. 2., yellowish ; Se. and De., white. Probably a binary in rapid motion. 2. 517 396 49-2 55-4 Ma. 57-2 Hit. 59-8 Se. [60-8 63-8 Oe. 64-2 61-8 .57-5 bs-S W. &S. 68-6 697 56-0 GI. 69-1 CO. 67-0 in. 0-89 jj 1-19 »> 0-94 4n. 1-31 -24 in. 095 i-o elong^- in. i-l " ■0 3'^- 1-2 7 ■17 7 •27 2 ... 2 13 in. -40 1829-31 3'37 2-34 3"32 44'34 8-45 56-88 65-48 56-49 7 '49 8-42 6339 72-38 3-36 4-42 •54 7 '41 464 2. 1877. e BOOTIS. R. A. Dec. 14" 397"" 27° 35 M. 3.6-3 C. Hi, A, reddish ; B, blue, or rather a faint lilac. Hj and So. A, yellow ; B, blue-green. 2. A, decided yellow ; B, decided green. Sm. A, pale orange ; B, sea-green. Se. A, yellow ; B, blue. H, {PAH. Trans., vol. Ixxii., p. 213) : "1. eBootis. Flamst. 36. Sept. 9, 1779. — Double. Very unequal. L, reddish ; S, blue, or rather a faint lilac. A very beau- tiful object. The vacancy or black division between them, with 227. is J diameter of S ; with 460, li diameter of L ; with 932, near 2 diameters of L ; with 1159, still further ; with 2010, extremely distant, 2i diameters of I/. These quantities are a mean of two years' observations. Position 31° 34' n.p." In his paper read June 9, 1803, H, says : "This beautiful double star, on account of the different colours of the stars of which it is composed, has much the appearance of a planet and its satellite, both shining with innate but differently coloured light. There has been a very gradual change in the dis- tance of the two stars ; and the re.sult of more than 200 observations, with different powers, is, that with the standard magnifier, 460, and the aperture of 6-3 inches, the vacancy between the two stars in the year 1781 was 14 diameter of the large star, and that it now is i}." He found, from many observations, that the proportion of the diameters of the two stars was 3 : 2. Hj and So. {PAH. Trans. 1824, p. 204) : ' ' Large, yellow ; small, blue-green ; a very marked contrast of colours. "Nothing can be more unsatisfactory than the measures of this very difficult star, especially in position, the difference between the greatest and least among the single measures amounting to the enormous quan- tity of 16° 10', and even among the mean results of the whole sets of observations extending to 10° or 1 1°." Hj then remarks on the difficulty of accounting for this, and rejects bias of eye, error of judgment, refrac- tion, imperfection of vision, closeness, and difference of size and colour, as insufficient. " The angular motion is indisputable." In 1826 {Phil. Trans. 1826, p. 337) he writes : " The motion of this star is therefore satisfactorily confirmed." In vol. v., p. 46, of Mem. of R. A. S., he observes, " After a long and obstinate contest with e Bobtis, which is certainly one of the most difficult double stars to measure correctly, Rigel itself excepted, I remain unconvinced of its motion. My father's measure in 1796 differs only 3° from 2.'s in 1826 ; yet this might arise from the conspiring effect of extreme errors. But, again, the mean of my measures for 1830, which I believe to be the truth, tallies within 0° 26' with the joint result of Sir James South and myself in 1822, which rests on upwards of sixty individual measure- ments." 2. (^M. M., p. 49), referring to the dis- crepancies in his own measures, says : — "These probably arose from neglecting the position of the eye and head." He thinks that a slow direct motion is beyond doubt, and that Hj and So.'s angles for 1822-55 and 1825-34 are too large. Sm. {Cycle, p. 325), after referring to the observations and conjectures of H, and H^, submits the following details and epoch which have led him to consider the question to be, as yet, unestablished : — H,. 301° 34' Dist. 4"-oo± I779'67 H., &So. 322 59 3 -93 1822-55 2. 320 58 2 -64 1829-39 D. 321 35 - '83i'35 302 DOUBLE STARS. Dawes (Mem. H. A. S., vol. xxxv., p. 374): " Recent measures seem to confirm Ua. 323-8 2 70 the idea that this is really a binary system. " 325-5 .7n- ■61 Writing in 1865 in Astronomical Aegister, •7 6n. •57 he says, "All my measures of this star 326-0 ,, •63 point to a slow increase of angle. " 320-0 in. -90 The changes are very slowly produced 326-9 7n. •61 in this system. The angle has increased, ■5 ,, ■77 but the distance has not changed probably. 6.0. 319-3 -75 The more rapid change in angle of late years 321-6 -75 leads us to expect that a diminution of dis- o.s. •6 I2n. •67 tance will manifest itself. (0. S. ) 323-4 5"- -56 Duner has the formulae 324-8 23n. •70 1 847 40. A - 2" -67. Ja. 329-1 4n. •68 P = 323°-9 + o°-i65 (/ - 1850-0). 323-3 -I 10 2-63 '57 Hi- 32° 19' Aug. 31, 1780. Uit. 320-8 2n. 30 21 Mch. 13, 81. Bond. 326-7 32 33 I May 10, 81. 3220 -2 38 26 Feb. 17, 82.* -I •I 45 32-4 Aug. 18, 96. Fit. -7 36 2-77 49 18 Jan. 28, l802.t Hi. 321-2 25 •83 43 55 ) Se. -8 5n- •64 42 42 \ Mch. 23, 1803. 324-0 2n. -24 44 33 ) -I 3n. 3-03 40 29 n.p. 1 -3 in. ■02 44 33 \ Mch. 26, 1803. 323-0 »» 2-80 44 52t ) 322-9 5n. •88 305-1 6 1781-73 324-0 2n. -78 314-6 8 1803-01 325-0 4n. •69 Amici. 2-35 1 6 04 Se. 323-6 •61 Hj & So. 322-9 5n. 3-93 22-55 322-9 3n. •59 324-3 6n. 1^ 5-43 324-7 in. 3-29 322-4 5"- -87 30-27 Uo. 327-8 12 2-95 2. 3182 22-39 325-0 22 -72 317-9 2n. 2-69 6-79 M. 324-4 in. •60 323 s in. -55 7-27 1482 )) -88 321-4 9n. -68 8-56 140-4 »» •81 •2 in. -61 9-58 141 -2 •74 320-0 3"- -59 31-56 ... ,, -32 321-8 2n. -55 3-41 ... ,, 3-16 Sa. -5 In. 1-36 J45-7 »» 2-97 320-8 2n. 2-90 41-43 324-0 2n. ■93 322-1 5n- •67 8-19 328-0 ,, -80 -9 3"- -68 54-52 Ro. 323-5 in. -79 323-6 in. 'P 5-53 Eng. 326-5 3n- •92 324-4 3n- -83 60-05 Ta. 323-1 -97 325-5 I* -91 5-48 321-3 in. •87 Sm. 321-6 ^1 31-46 324-9 »> 3-08 323-8 •8 3-53 ... ,, •05 321-2 2-9 8-68 Kn. 323-9 ,, 2-73 322-1 -8 48-54 Du. 326-8 2n. '52 Be. 316-2 ■96 31-56 327-6 4n. -75 Encke. 321-3 3-37 7-44 326-1 8n. -64 Oalle. -9 2-88 8-67 327-6 7n. -67 324-9 -66 9-45 -3 6n. -56 Ka. 320-0 6n. •80 40-05 328-3 »» ■77 319-8 9n. •74 2-37 327-6 7n. •63 325-3 5n- 'P 66-48 Br. 332-4 2 3-04 Ch. 321-4 in. •88 41-38 W. &S. 327-2 4 2-97 316-6 »» -34 2-43 3269 3 3-06 3"-3 It 0-86 3-33 •9 5 -00 " Very exact. 327-6 6 •00 t Very accurately taken. 326-1 8 2-9 } Theb est. 327-1 6 3-19 1843-92 50-74 4-41 7-03 7-42 8-47 9-38 42-35 4-44 -49 55-33 64- 14 73-26 46-28 5320 46-66 8-38 •38 -45 50-95 2-94 448 522 639 -49 8-49 63-50 546 5537 6-50 65-49 57-44 8-46 62-39 7-36 9-55 •55 -56 70-39 340 436 5-31 63-53 5-40 6-40 9-62 70-46 I -41 67-34 -72 856 9-55 70-49 1-56 2-52 68-46 71-56 2-38 3-36 4-42 -44 5 39 MEASURES. 303 61. Schi. Sp. w.o. Sob. PI. 327-0 4 2-9 328-2 in. •8o 327-6 )) -75 32«-3 -80 327-6 -75 328-6 in. •94 3304 »» •90 327-2 ,, 3-09 324-5 I in. -13 -7 2n. 2-95 329-1 6n. -92 1874-54 5-41 6-49 S-4I 6-49 -41 -43 -43 -42 7-23 6-70 465 Z 1879. R. A. 14'' 40-4" Dec. 10° 10' C. yellowish. Probably binary. 2. Ma. Da. Da. 678 66-3 59-2 2n. in. single elongated single perfectly round 466 ot. 285. R. 14" 0.2. De. A. 41" Dec. 42° 53' C. white. 72-1 57-8 53-9 36? 3n. 0-60 4n. -50 3n. -5' obi.? M. 7-1, 7-6 1 845 80 52-74 5-84 65-53 467 t. 1883. R. A. 14'' 42-9'" Dec. 6° 27' yellowish. =2- S. Ua. Se. De. W. &S. Gl. Sp. 266-7 271-2 270-0 272-0 269-8 270-0 267-8 265-0 264-5 262-7 265-6 261-3 262-7 261-7 •9 262-2 259-6 1-20 •25 3"- •24 •07 -10 0-91 I -03 -03 -15 2n. 095 -80 •80 in. -88 „ •95 „ i-i 0-81 M. 7. 7 1830-23 1-37 2 00 027 8-59 42-40 3-37 54-43 7-43 8-41 6-41 813 6328 72-37 3-36 4-54 542 468 S. 1888. e BOOTIS. R. A. Dec. 14" 45-8'" 19° 36' M. 4-7, 6-6 /Mf C. H,, A, pale red ; B, garnet or deeper red. 2., A, yellow; B, reddish purple. Se., A, golden ; B, red. Sm., A, orange ; B, purple. H, (/%//. Trans. 1804, p. 367). He first observed this star on the 15th of April, 1782, when the position angle was 6553' n.f On the 20th of April, 1792, it was again observed, and the angle recorded was 85° ^3''5 n.p. He then discusses the observations, pointing out the changes which would be observed if the companion moved round the larger star, the plane of the orbit being coincident with the line of sight. He thus infers a retrograde orbital motion. Hj {PM. Trans. 1824, p. 208). Dis- cussing the observations between 1 782 and 1823, he is constrained to admit that a physical connection is probable. When, however, he came to examine the measures between 1780 and 1830, he remarked, "That the motion is not rectilinear, but orbitual, there seems little room, from the later observations, to doubt ; but the probable errors in the positions from 1795 to 1804 prevent any certain determination of the orbit." (Mem. R. A. S., vol. v., p. 36.) In 1833, in vol. vi. of the Memoirs, H2 gives the elements of the orbit. He finds, by his graphical method, the follow- ing results : — a = 1 2" -56 e = 0-59374 7r 138° 24' \ = 100 59 7 = 80 5 S, = 359 59 P = 1 1 7- 14 tropical years Perihelion passage, Dec. 17, 1779. 304 DOUBLE STARS. Sra. {Cycle, p. 328). " If the relative path of the small star be really the straight line it appears to be, the angle of position will never reach 50° n.p., and the angular velocity will diminish continually from the present moment (1823). On the other hand, if the stars form a binary system, the present angular velocity of about 1° per annum will continue for some time nearly uniform, and in about fifteen or twenty years the limit of 50° n. p. will be attained or passed." Midler's elements are as follows : — T = 176171 o, = 3i5°-2 S, = 1727 (Equ. 1850-0) i = 527 e = 04540 /x = - 2=2403 '^ = 5"-59i P = 160-695 years. And Duner has compared these with the measures made since 1865. He finds the differences considerable and increasing. Br. Doberck's latest elements are — a = 26° 22' X = 117 46 7 = 36 55 e = 0-7081 P — 127-35 years T = 1770-69 a ^4" -86. Hi- 24-: 3557 354-8 352-8 353-9 Hj & So. 342-3 340-I 337 -o 335-9 333-6 330-7 335-8 334-1 33I-I 328-9 S. Amici. Encke. Be. 8m. Da. 327-1 327-0 331-2 332-1 327-4 224-8 3229 330-3 324-0 338 6-o± in. 9-25 ,, 8-41 4n. 7-77 2n. ■•7 5"- ■62 2n. -53 •54 4n. •21 2n. -14 311- -07 4n. -08 2n. 6-85 -66 -79 7-30 •3 -0 -I 6-9 3"- 7-54 >) ■«5 1780-69 2-28 91-39 2-30 5-22 1802-25 4-25 21-20 3-34 5-37 8-54 30-29 3-23 22-69 946 32-40 5-43 647 8-47 23-30 7-41 31-40 •53 7-49 9-61 42-42 34-44 40-43 Da. Ga. Ka. Ua. 0.2. Hi. Ko. D.O. Fit. Mi. De. Wi. Lti. Se. Po. An. 323-3 322-6 318-8 317-9 3" -9 309-9 326-5 325-8 -I 322-1 -2 299-6 324-6 321-5 320-8 -4 3'9-3 318-0 315-3 314-4 3"2-4 311-6 312-4 31 1 -2 309-8 -3 325-1 319-3 3134 304-9 -I 301-9 295-3 286-7 3223 318-6 319-2 3078 324-1 321-5 317-4 316-6 3" -5 312-6 310-8 308-9 ■2 303-1 -o 302-0 301-1 299-0 297-4 293-8 291-6 290 o 288-3 287-4 285-2 3"-7 -8 310-0 300-8 305-0 303-4 in. 2n. 3"- m. 5n. 4n. 5n. 6n. 5n. I5n. 8n. 5n. 2n-. 4n. 5n. 7n. 31- 5n. 3n- 3 5 4 5 4 3 28 20 12 36 32 5n. 3"- 8n. 2n. 5n. 4n. ion. 2n. 7n. nil. 5»- 4n. I2n. 4n. 35 7-26 -02 6-80 •7i -26 5-90 7-26 -07 670 -72 -64 5-20 7-09 6-90 -8i -69 •67 ■63 •21 -3' -06 •06 5-89 ■76 -65 -56 7-03 653 -22 5-77 -58 -67 -09 4-62 6-12 -76 ■75 5-93 7-22 656 -51 5-84 6-15 5-99 -96 -82 -65 •56 ■50 -38 -31 -05 -04 4-83 ■68 -63 -62 0-00 •71 -02 5-41 -52 -93 1841-42 2-30 7-44 8-50 54-46 7-42 38-54 9-41 40-26 1-65 3-68 66-44 41-43 436 5-36 6-29 7-37 8-28 52-56 3-44 4-48 5-38 6-39 740 8-54 9-38 41-06 7-82 53-54 61-57 2-47 3-56 9 02 73-19 45-37 -40 6-46 58-38 46-42 7-41 Si-ii 2-30 4-46 5-22 6-45 7-57 836 62-55 3-38 4-46 5-42 6-86 8-36 70-39 1-34 2-40 3-42 439 5-38 56-55 -75 -88 65-77 I -29 2-15 MEASURES. 305 K. 305-9 in. 5-68 1862-33 S.O. 228°-0 3". o'-'68 '845 '35 295-4 J> ■50 P^ 222-5 2n. ■53 8-96 294-7 )) •33 8-40 204-4 3". 1-12 63 '44 291-4 it •52 955 De. 200-4 •21 6-72 292-7 »> ■21 ■55 W. &S. 197-8 6 -16 73'37 293-0 »» ■33 '^l 196-5 4 •55 ■44 -I »» •30 70-38 198-2 4 -26 4 '44 292-9 ,, •53 •39 195-8 9 •49 7 '45 -6 71 -02 1-34 -8 6 ■3' -46 ■9 »» 4-83 ■36 PI. -2 6n. ■12 -2i 286-0 283-9 286-5 4n. ■93 -92 •76 3-39 4-36 5-36 471 X. 1893. Bo. 302-4 579 63-28 Eng. 303 '4 in. ■32 4-46 R. A. Dec. M. 301-4 -48 5-54 14'' 50-2"" 29° 58' 8-4, 10 Ta. 298-5 4n. ■59 6-37 •0 in. -42 9-61 2. 261-3 2n. 21-30 1831-49 295-8 >j 4-66 70-46 ■4 in. •82 229 296-4 tt I -41 259-7 )» -42 4'43 286-6 It 471 3-48 Ma. 2579 19-36 44-41 288-6 it -19 4'33 256-7 20-76 5 '49 286-0 "54 255 '9 ■'? 52-51 Ln. 295 '4 6n. 5-05 69-65 256-1 -08 5'33 292-9 7n. 479 71 94 De. 252-3 ■14 64-76 286-6 4n. 5 5 ■44 -I -88 5 '51 2-38 3-36 W. &S. 291-8 2893 472 O.S. 289. -4 s -81 •38 288-4 5 •72 4"44 R. A. Dec. M. 283-0 5 ■46 7-46 14" 51™ 32° 46' 6-3, 9-8 Lindstedt 287-0 GI. 289-2 No. 286-3 in. 5 -84 5-0 3 '43 4-54 5 '38 0.2. 120-3 De. 115-6 3n. 4-56 1846-34 "43 67-54 op- Z043 440 -40 Schi. Sob. ■3 -8 in. 5n. ■40 •5 -40 6-34 473 S . 1901. PI. W.O. 282-9 284-9 3n. 8n. in. •70 •22 •59 7-24 6-99 ■41 R. A. I4'' 56" Dec. M. 3'° 51' 77. 9-5 280-6 ,, -67 ■43 S. 203-9 m. 30-22 1831-46 284-6 ,, ■^^ •43 -5 '47 -52 FI. 282-7 •28 7-44 Ma. 201 -0 'I 29-52 47-20 200-6 „ 2875 •32 469 O.S. 287. R. A. Dec. M. 474 S . 1909. 14" 47 1 45= 25' 7-5. 7-6 4 4 Boons. C. white. R. A. Dec. M. Probably a binary. 14" 59-8"' 48° 7' 5-2, 6-1 O.S. 97-3 105-4 108-4 1190 2n. 4n. 3". in. 0-58 •47 •54 74 1845-51 52-74 5-84 68-56 C. Hj, white. 2 Sni., A, pa Se., A, yelk ;., A, yellowish ; B, bluish, le white; B, lucid grey, w ; B, blue. Se. 30o"3 -64 7-23 - Hi {/'Ail. Tn tm., vol. Ixxii., p. 216) : "Aug. 17 [178 unequal. Both almost to touch, ]. Double, considerably 470 OX 288. W. With 227 they seem or at most i diameter of R. A. , h ._._ Dee. 16= 12' M. 6-4, 7-1 S asunder ; with 460, i or 1 diameter of S. This is a fine obj ect to try a telescope, and 14* 47 / a miniature of a Geminorum. Position Certain change m ang e and di stance. 29° 54' n.f." 20 3o6 DOUBLE STARS. Hj (Phil. Trans. 1824, p. 218) examines Ihe observations between 1781 and 1821, but finds them quite intractable ; indeed he H unable to make quite sure that the obser- vations relate to the same object. He thinks, however, that tlie positions given by :2. in i8i9-43, and that by H, and So. in • S2 1 '33, " go to destroy 2. 's idea of several revolutions having been performed in thirty- eight years." In 1830 he says, "The history of the star 44 Bobtis is singularly beset with difficulties and apparent contradictions ; " and it was not until the observations made in 1831, 1832, and 1833 were before him that he felt sure of the binary character of the system. He says, "Comparing the present results (or 44 Bootis with the whole ^eries of former measures, there can hardly remain a doubt of its constituting a binary ^ystem in which the orbits are very oblique to the visual ray, and the rotation performed in a period of about sixty years in the direction n.f s.p., or direct ; so that in about nine years more it will have com- pleted a whole period in an apparent ellipse of great excentricity. This conclusion is grounded on a presumed mistake of 180° in my father's first position for 1782, and on the presumed corricittess of his correction of a similar error in his second measure for 1S02." Dawes (Mem. R. A. S., vol. viii.) says that the stars are most probably rapidly .^^eparating, and that the " mystery arising from the apparent contradictions in the earlier measures of Sir Wm. Herschel will, ere long, be satisfactorily solved." Madler, writing in 1847 [Die Fixstern- Systevie, p. 157) says, " Probably the con- nexion is physical ; but the plane of the orbit passes nearly through the solar system." In 1855, however, excluding H/s position 62° 57' for 1802-25, he found the following elements : — Node 60° 15' 7 77 36 \ 12 36 e 03837 P 181 years T 17847 3"io. Doberck's latest elements are — Node 65° 29' 7 70 S X I 18 e 071 P 261 12 years T 178301 » I 23' a 3"093. 'ITie proper motion of this system is -3-045 in R. A., and — o"-03 in N. P. D. H, & So. Da. Sm. 0.2. Ch. Ea. Ua. Hi. Mit. Bond. Fit. Ui. Ja. Uo. Se. 6o-i 62-9 228 o 231-0 233 '6 2344 235 2 2348 2360 229-1 2346 231-1 232-9 235 '3 •6 •6 ■9 •7 236 o 235-6 8 2377 -2 236-7 2377 2338 235 I 234'9 2353 •9 236 -2 2386 2363 237-2 238-3 236-5 235 '2 2360 •I 237-0 238-1 2379 ■4 2380 •3 237-0 2400 239-6 237-9 240-1 238 5 -4 239;9 238-8 -4 239-5 240-1 238-9 240-0 239-6 240-5 239-6 in. 2n. 3n. 6n. 4n. 2n. in. 4n. 3n. In. 4n, 2n. 5n. 4n. 2n. In. 3"- in. 5n. 3n. 4n. 711. in. in. 2n. 9n. I5n. 7n. in. 32 39 9 20 I in. 2n. 5n. 41- 6n. 2n. 1781-62 1802^25 1-5 19-43 2-23 2679 ■hS 9^20 -90 32-95 3-17 5-51 ■30 6^66 ■39 7-75 2-27 21-33 -99 3053 -71 -44 -97 1-34 3''2 2-56 •28 3-39 ■44 4 59 -76 658 -86 40-58 4-00 1-48 3-84 2-40 •79 71 4-21 8-49 •36 9-48 ■49 51-52 •58 4-74 29 3082 3 3 455 -6 67' •s 9-62 -7 42-58 4-1 7-45 3-86 0-76 4-23 8-36 •67 56-81 ■79 63-44 3-68 41-36 •58 •65 ■74 375 •88 7-32 •99 51-27 4-18 -87 ■25 2-65 -25 364 •26 47-09 3-74 o'57 45 8-55 -3 -55 -3 -54 •3 51-47 •6 65-60 •35 53-28 '^l •27 •58 4-46 -44 -55 •68 -75 6-48 ■69 8-41 'V> 63-3' -82 6-45 •70 7-42 •72 836 •93 9-61 •78 70-30 -97 '•15 MEASURES. 307 Se. To. Eng. Ta. Sn. Gl. W. &S. ScM. Sp. Dob. PI. Fl. 2388 7n. 4-55 239 '3 m. -93 238-0 40 3-29 2399 9 5-38 238-8 36 •04 •0 in. 4-6l 56-9 J) -68 571 ») •80 240-0 ,, 5-06 -6 ,, •50 239-1 •70 237-3 2n. 4-62 239-5 In. ■4 }) 4-37 236-8 ,, ■7> 237-5 »> -88 239-9 ion. ■73 241-0 I4n. •79 242-3 4n. -67 240-0 4 •69 239-0 5 •86 "9 5 ■5 -8 4 5-3 240-6 4 ■3 239-5 In. -16 ■6 4-90 240-3 4n. -82 23«-5 5»' 5-04 240-7 7n. 480 241-8 In. -61 i836"40 66-58 56 02 -02 61-29 2-42 9-55 ■57 75-28 64-67 5-29 6 40 9-62 71-41 3-48 4-55 69-16 71-28 5-51 0-32 1-13 4-22 '•57 3'2S 5-41 •41 626 7-29 •18 ■56 475 R. A. ,jh j.gm X 1910. Dec. 9° 41' C. yellow. M. 7. 7 Motion probably orbital ; Duner has very slow. 1850-86. A = 4"03. P = 2io°-3 + o°o6o {t - 18500). H, & So. Sm. Ma. Po. Hit. 0.2. Se. 8e. Ko. -W. &8. SI. Fl. 205-5 m. 3-98 2092 80 -2 3n- 4-78 2101 fl •29 209-7 -0 212-2 31 ■ •1 2IIS in. -21 -I 4n. -19 212-4 in. •33 209-1 I2n. 3-91 2U-6 2n. 4-48 210-5 6n. •22 21 1 -3 2n. •22 209-9 in. •II 21 1 '4 2n. •09 -I 4n. ■00 ■4 in. ■3 •3 ■4 212-7 in. -2 •9 »j •27 i823^33 32^08 23-42 909 35 "39 43-98 52-43 5-92 61-41 45-78 7-71 51 00 6-05 -40 8-33 71-38 4-44 5-41 4-44 7-43 476 X. 3091. R. A. Dec. -4° 26' C. yellow. M. 7-7, 7-7 Ma. 47-3 35-9 6n. I 0-50 |i832^-59 2n. I •so I 43-91 477 R. A. O.S. Se. 0.2. 294. 251-2 247-8 Dec. 56° 30' I 3n- I 3-26 •23 6-8, 1 1 -3 1 1848-59 I 67-57 478 R. A. 15" 10-4"' 2. 1926. Dec. 38= 45' M. 6i, 84 C. yellowish, blue. Duner gives A = i''-42 — o"-0O9 (/ — 18500). P = 262°-5 + o°-io (/ - 18500). 2. Ma. Bn. 260-6 4n. 1-59 261-0 2n. -46 264-9 »j •37 •9 ,, ■»7 1830-60 42-69 71-42 2-51 479 0.2. 295. R. A. is"" 10-4" Ma. 0.2. S3. Dec. 37° 16' 114-9 0-77 111-9 -75 115-6 -6 1284 4n. 'I* 122-9 3»- -85 M. 7-4. 9 '843-33 628 7-32 638 66-84 480 R. A. 15" 10-5" 2. 1925. Dec. -7° 50' C. A, yellowish. 2. Mit. Se. Se. CO. 6-7 3n. 4-18 7-3 in. •19 III 3n. •70 10-4 •44 9-3 2n. -9 M. 7-8, 9-3 1831-69 48-49 56-28 68-40 77-40 3o8 DOUBLE STARS. 481 S. 1930. S. S SEBPENTIS. Da. R. A. 15" 13'" Thp star Dec. C. yellowish. =; hnvp a ranid comm M. 5, 10 on DroDer 0.2. Hii. motion. Orbital motion seems to be indi- cated by the slight increase in distance and diminution of the angle. (0.2.) 0.2 Se. 50° to 60° 40-9 ■6 39'2 37-' 3". 10 07 ,, •33 2n. •52 ,, •58 1783-38 1831-69 6 '42 48-38 58-52 482 R. A. 1. 1934. Dec. 44° 14' C. white. M. 8-5, 8-5 45-1 3n. 5-29 447 6-19 42-8 5-94 40-1 6 -co 417 571 39 ■> 6-07 40-3 2n. 5-84 38-1 4n. 6-05 37-2 in. •23 3.S-9 4 •2 .347 S 5-8 35 -5 6 6-2 3b- 3 4 ■30 3.S-3 5 ■33 30-2 5 -27 33-2 4n. •36 Considerable change in both coordinates. [830-88 H... 44-7 ' 6-19 31-41 Ma. 42-8 ';-94 43'59 51-59 3-76 4-71 8e. 40-3 2n. 5-84 8-57 De. 38-1 4n. 6-05 6488 O.r. 37-2 in. -23 8-52 ■W. & S. 35-9 4 -2 73-25 ■33 4-43 7-43 _ _. -44 Gl. 36-2 5 -27 4-49 Dob. 33-2 411. -36 7-56 483 2. 1932. I (6) COBON2: BOB£AIIS. R. A. Dec. 15" 14-5"' 27° 36' M/a^ni/u,/es.—1.,s-6,6-l. Se., 6,6-5. De., 6-9, 7-2. 2., suspected variability. C. white. Certain change in both coordinates. Duner gives the following formula" : A = i"-37 - o"-oi46 {( - 1850-0). P = 282°-2 + o°-57i {( - 1850-2) + o°-oo55 (/ - 1850-0)2. Se. De. En. Eng. Dn. Gl. Schi. 8p. Dob. 273-8 4n. 1-62 268-4 3". 53 267-3 in. •31 271-2 -44 281-0 2n. •46 284-0 in. •36 279-3 2n. •6S 280-6 in. -40 295-6 2n. ■21 278-6 »i •50 283-6 4n. -45 287-5 6n. -32 •32 289-4 5n. •34 285-3 2n. -'4 286-9 3". -2 •3 ,, •2 290-2 4n. •18 288-8 in. •34 293-1 2n. •57 297-0 ion. ■10 299-2 3". 0-99 296-3 7 1-02 •8 5 •21 298-6 6 ■07 299-4 6 •I 300-2 5 •29 301-5 ■07 298-9 4 -2 118-5 in. ■16 298-6 •16 303-5 3n. •26 R. A. 15'' 16-4"' Dec. - 1° 6' Ha. De. C. -\, yellowish. The distance has diminished. 33-28 2-57 •35-5 137-3 138-6 ■15 1830-28 -29 1-37 3-39 48-49 54-40 41-46 51-49 70-55 42-42 51-88 7-27 8-54 60-70 56-40 -60 8-45 63.-28 -78 4-48 70-29 5-51 2-49 3-36 4-44 -49 5-39 7-47 4-49 5-42 ■43 7-37 484 S. 3093. M. 8, 9-2 1829-36 47-32 65-35 485 t. 1937. ■n COBOK£ BOBEALIS. R. A. Dec. M. 15" 18-2™ 30° 43' 5-2, 5-7 C. A, yellow ; B, certainly yellow. MEASURES. 3 eg H,. "Sept. 10, 1781.— They are fairly separated so as to see the dark heaven between, but that isall. Oct. 4, 1781. — In the greatest perfection. Very near in con- tact. Oct. 22, 1781.— With 278 beautifully white and distinct." H, {Phii. Trans., vol. Ixxii., p. 216). 1 78 1. "Sept. 9.— Double. A little un- equal. They are whitish stars. They seem in contact with 227, and though I can see them with this power, I should certainly not have discovered them with it ; with 460, less than J diameter ; with 932, fairly separated, and the interval a little larger than with 460. I saw them also with 2010, but they are so close that this power is too much for them, at least when the altitude of the stars is not very considerable ; with 460 they are as fine a miniature of i Bobtis as that is of a Geminorum. Position 59° 19' n.f." (Phil. Trans. 1804, p. 370.) "This very minute double star has undergone a great alteration in the relative situation of the two stars." " Aug. 30, 1794, they were so close that, with a 10 ft. reflector, and power of 600, a very minute division could but just be perceived." "And, May 15, 1803, I saw the separation between the two stars, with the same 7 ft. reflector, and mag- nifying power of 460, with which I had seen it 22 years before." He also observes that the change in angle was retrograde, and that "a parallactic motion of the largest alone " would not account for the change. Hj and So. (Phil. Trans. 1824, p. 224). Hj thinks that the position of 1802 "is erroneous, and that the surmised motion of the stars, if any, is much less rapid than that assigned to them by H,." Hj (Mem. X. A. S., vol. v., p. 37). After giving the measures from I78i"69 to l830'30, he observes that the star is very difficult, and that he does not fully rely on his recent measures. On the whole, how- ever, he thinks there are good reasons for regarding this object as a binary. He con- cludes that 7; has made more than a revo- lution since 1781, and that the motion has been direct. He remarks the obvious difficulty of readily ascertaining which star precedes or follows, owing to the closeness and small diflerence of magnitude of the two stars. Assuming that Hj misplaced the companion, he finds that the period has been 43 2 years, with a mean annual motion + 8° '34. This is the only star which up to that time had completed a whole revolu- tion. Finally, he states that "as the actual motion is much less, the orbit must be elliptic, and the actual velocity, at one time or other, must have been 20° or 30° per annum, which will account for the enor- mous change of position which (on the above explanation of the MS. memorandum) must have happened between 1781 and 1 794-" In 1833 (Mem. R. A. S., vol. viii., p. 50) he writes, " I am sure rj Coronae is closer than it used to be. The distance is below measuring. Surely not S of a second." Dawes about the same time says " not quite separated," "only elongated." Hj (Mem. R. A. S., vol. vi., p. 154). Having obtained measures from 2. and Ua., he computed the orbit and found the fol- lowing elements ; — « = o"-8325 e = o "26034 X = ssS-' 38' T = 1 761 '96 and i8o6'2o 7 = 37° 24' S, ^ 220 35 P = 44242 years « = -4-8°- 1369; and he finds that these agree well with the observations. With respect to the orbit of this star, he observes — 1. That the excentricity is moderate. 2. That the major axis almost coincides with the line of nodes, and that hence we see it of its natural length, the conjugate axis only being foreshortened by the effect of perspective. 3. The greatest distance in the apparent or projected orbit is i"'049, and was at- tained in 1828 ; the least, about o"'S388, in 1800 and 1812. He is almost sure that ' ' the distance has decreased of late," and learns with regret that Mr. Dawes has given up observing the star on account of this difficulty. He regrets these things the more because ' ' the portion of the orbit to be passed over in the next ten or twelve years will be most important in aiding the improvement of the elements." S. (M. M., p. 5) says the period is about 43 years as deduced from the observations of H] and himself; and he thinks that the stars will soon become so close as to defy the separating power of the largest tele- scopes. Using the measures up to 1856, Dr. Winnecke made a very careful examination of the orbit of this star with the most satis- factory results. His elements are thus given in his De Sielld 17 Corona Borealis, etc. . a = o"'9567 c = o -2865 a = 22° 18' A = 215 29 »' = 60 40 P = 43'iiS years T = 1850-329. Smyth (Cycle, p. 34°)- When this observer besan his measures of 1), he found 310 DOUBLE STARS. the work ' ' difficult enough ; " the observa- tions of position were mostly unsatisfactory, and those of distance were estimations. In 1842 the angular velocity was "under rapid and direct acceleration, while the distance was diminishing, so that the fine black division seen between the stars in 1832 had not only disappeared, but the object was not always elongated. "The general mean [annual motion] drawn from a comparison of my own and other obser- vations was -(- 9°'4i, and the period about 44 years. The excentricity, by the graphic process, is 0-3561. The connexion of the components is therefore ' fully proven. ' ' ' Da. (Mem. R. A. S., vol. xxxv., p. 379). After noting the closeness, rapid motion, and the fact that two complete revolutions have been made since 1 78 1, he says he is "sure now that H,'s position in 1802 should be s.f. instead of n.p." He re- marks, too, that the components have .separated since 1854, and that it is now an easy object. "The question will be decided in between three and four years' time." In 1841 Madler computed the orbit, and found the following elements : — 7. T = 1815-20 X = 263° 10' a = 22 35 i = 71 29 - 20 43 a — I"-I9I2 U = 43-310 years. In 1842 he published the following ; - 11. T = 1S15-230 \ = 26l'^2l' a = 24 19 1 = 71 8 = 19 44 (z = i"-o879 U = 43-246 years And in 1847 his last results were as fol- lows : — m. T = 1807-21 X = 215' n' £3 = 20 6 ! = 59 28 = 16 48 a = o''-9024 U = 42-500 years. These last elements Madler regarded as very accurate. Villnrceau published two solutions about 1852, and .sought to decide between the claims of the two rival orbit,s, viz., those of forty-three and sixty-six years. The former (the orbit of Hj and Ma.) was ob- tained when the position for 1802 was reversed, and the latter when that for 1 781 was so treated. Villarceau, thinking that the two orbits might be separated before 1853, solicited careful observations from O.X., Da., and others; and a glance at these was sufficient to show that the obser- vations since 1847 would not agree with the orbit of forty-three years. Here are given the three sets of elements by this eminent astronomer: in (I.) the observation in 1 781 was taken as 210° 21', and that in 1802 was left intact; in (11.) the angle in 1802 was reversed, and that in 1781 taken as 30° 21'; in (ill.) are exhibited his last results : — I. T = 1780-124 X = 194° 37' 8 = 4 25 (1835-0) 1= 58 3 ■^ = 28 o a — i"-iio8 U = 66-257 years. II. T = 1805-666 X = 227" lo' a = 10 31 (1S35-0) '■ = 65 39 = 28 19 a = l"-OI25 U = 42-501 years. ITK T = 1779338 X = 185" o' Si = 9 52 (1850-0) ' =- 59 19 = 23 51 a = l"-20I5 U = 67-309 years. In conclusion, Villarceau rejects the orbit of forty-three years, and thinks that the longer one is not susceptible of being ' ' sensibly modified by ulterior observa- tions;" that 66-257 years satisfied the observations anterior to 1848 ; and that the true period cannot exceed 67-309 years more than a fraction of a year. Mr. Wilson in 1875 carefully compared the observations from 1863 to 1875 ^''''' Winnecke's orbit, and found a "systematic and increasing divergence, which is too large to be accidental." He finds on the whole that the " hypothesis that would best satisfy the observations is, that there exists in each successive revolution some shortening of the period, accompanied perhaps with a progression of the line of apsides." He thinks that the period is most probably about 41-2 years. See Monthly \olicef, vol. xxxv. MEASURES. 311 M. Wijkander has lately computed the following elements : — T = 1850-26 u = 2II°'4 a = 26 7 (18500) i = 58 -o > 70-2 »» 0-83 36-0 3n- 106 46-8 In. •3 456 5n. •00 29-2 in. •12 36-9 41. •14 40 9n. •02 437 7n. 0-97 47-3 9n. •87 Si-2 7n. •84 550 2n. I 08 687 Iin. 069 1965 446 II ri 45 9 5 0-9 47-0 4 10 55 -o 5 •0 54-0 7 085 52-2 7 55-9 10 i-i'6 53-5 8 58-8 10 IIO ■0 10 ■07 590 2 o-S 76-s 4n. 73-8 2n. o'-8 71-6 ,, 7 75-5 )♦ 45-2 5 1-47 50 4 •38 510 7 01 580 5 ■01 57-6 3 •22 55-6 5 •09 58-4 •I 8 6 0-93 667 6 •94 68 -o 7 1858-52 62-56 3 '42 4"43 5 '49 6-44 7-50 8-39 70-38 145 2 '44 3 '44 4-42 5 '41 63-56 5 '52 4'4S 6-33 7-52 962 70-46 1-41 2 29 3-48 4 44 5-38 6-45 6734 70'47 1-54 67-69 8-65 953 70-51 '•53 2-58 372 S'55 70-44 1-50 •63 3-60 •47 ■50 ■52 •51 4'36 ■32 ■49 7629 ■33 •34 ■35 41-55 ■57 249 336 •38 ■45 4 '44 •49 7 '30 ■32 W. &S. Fer. Br. Schi. Sp. w.o. Sob. 66-6 t 68-7 6 -8 8 82-9 9 S17 0-92 64-2 •90 66-1 in. ■90 72-3 j» •79 66-1 •91 723 79 250-4 In. 76 •3 ,, -86 249-7 »» 71 2517 ,, 75 70-3 8n. •84 82-0 4n. 92-6 2n. o-6i 94-6 In. -61 1847-32 •32 ■43 ■47 2-48 3 '34 5 '41 6-51 5 '42 6-51 ■41 ■43 •43 ■44 6-38 7-30 7840 "55 486 Z 1938. C. greenish white. H, (/'-iz/. TVoBJ., vol. Ixxii.. p. 217). 1781. " Sept. 10. Double. It is a star near fi not marked in Flamsteed's catalogue. Con- siderably unequal. The interval with 460 is I diameter of S. The position of the small star is turned towards jj, a little fol- lowing the line which joins L to ^ Bootis." In the /%!/. Trans, for 1804, p. 372, H, discusses the change in angle, gives his measures in 1781, 1782, and 1802, and shows that a change of 1 1° had taken place in 19 years and 361 days, and that this was most probably orbital. H2 and .So. (Phil. Trans. 1824, p. 227). "A very close double star. In the 5ft. equatorial with a power of 133 it is seen elongated, but 303 shows it decidedly double. A power of 179 applied to the 7 ft. shows the discs of the two stars in contact, but 273 distinctly separates them. This double star is a severe test for a tele- scope, and is easily found by means of AC Bootis." MEASURES. 313 " If this double star be a binary system, of which there can be little doubt, its period IS about 622 years, and the most probable mean annual motion is o°-5783, in the direction n.p.s.f., or retrograde. " Hj {Mem. R.A.S., vol. v., p. 38). Having the measures from 1782 to 1830 before him, he says, "It will probably, erelong, become excessively difficult or close up entirely, as both the diminution of the micrometrical distance and the rapid increase of angular velocity sufficiently indicate. " " None but the finest telescopes are competent to deal with it." Dawes {Mem. R. A. S., vol. viii., p. 87). He gives measures in 1830 and 1832, and says "neatly divided; requires a superb night like this." Smyth {Cycle, p. 343). "From the earliest epoch here registered [1782-68] down to my latest, an annual mean movement appears = - o°-8s ; but from Herschel junior and Sir James South's period it averages - l°-44, so that the period may be within 460 years ; but the annual rates are as yet distressingly irregular." Engelmann {Ast. Nack., 1673 — 1676) writing in i860 observes, "The period niust be about 150 years ; the minimum distance o"'35, which will be reached in 1868; the maximum about l"75. Since 1857 the companion has passed through 50°." " Dawes {Mem. R. A. S., vol. xxxv., pp. 381 and 484). After noting the rapid de- crease in distance and the acceleration in angle, he says that this object now requires " about a 9 inch aperture to completely separate the components. " The angle in 1852 presents an extra- ordinary anomaly which partly disappears when the measure is combined with those of 1851 and 1852. (0.2.) Mr. Wilson in 1873 obtained by graphical processes the following elements : — e = 0-51 a = 172° o' D= 45 o X = 20 5 TT = 186 30 p = 200-4 ys. t = 1865-2. In 1875 Dr. Doberck computed an orbit for this interesting binary star. The proper motion of /i' agreeing with that of fj. Bobtis "suggested the existence of a phy- sical connexion between these two stars. Actual measures have, however, rendered such a supposition more than doubtful." Making use of Sir John Herschel's first method, the following elements were ob- tained (No. 2 in the table subjoined) :— [No. T a A V p «. ! e Computer. 1 / years. I 1860-88 163 n 54 27 41 52 314761 I-761 0-6832 Hind. 2 3-51 182 59 17 41 44 26 290-07 •500 -6174 Doberck. i •51 173 42 20 39 57 280-29 ■47 •5974 )» 4 S-2 172 20 5 45 200-4 "5' Wilson. S l"5 169 23 39 46 22 198-93 ■4957 Klinkerfues. b 6-00 166 8 23 I 47 31 182-6 I -165 -491 Winagradskij. Duner says, "The connexion between u. Bobtis and S. 1938 is indubitable ; other- wise the motion of /i Bobtis which is con- siderable would cause a very great change in the relative positions of the stars. If the mass of /i Bobtis were equal to the sum of the masses of S. 1938, the orbital motion would be only — o°-oo3 per annum, or — o°-l5 in fifty years. In reality, an annual motion of — o°-oo6 is perhaps probable : and if this is confirmed the mass of /u Bobtis would be seven times greater than that of S. 1938." The common proper m.otion of the three stars is — o"-l6 in K. A., and o"-lo in X. P. D. H.. 357-2 3462 3307 327-0 2n. 1-38 324-0 y> -24 1782-68 1 802 -66 2221 6-77 973 Da. 3197 318-6 315-0 -o Hj & So. 333-7 •5 324-1 322-7 3'9-7 314-8 306-0 303-2 300-9 286-5 280-0 276-2 266-5 262-2 254-6 249-3 190-0 232-3 3n- I-19 10 f > -06 in. 0-90 3n- 1-65 5n. -42 2n. 0-85 31- 1-03 In. -IS ,, -0 3n. 083 6n. -85 in. •8S ty -65 i> -65 2n. -68 >> -52 in. -55 ,, ■50 3n- -46 j> -48 in. -45 1833-85 5-55 6-65 7-70 23-41 5-46 30-24 2-56 3-39 7-37 4039 1-66 2-40 7-30 8-52 9-44 51-42 2-52 3-71 4-41 546 7-47 314 DOUBLE STARS. Sm. 0.2. Ua. Ka. Hi. Bond. Ja. Se. Se. Bo. Kn. Eng. 3I9"9 3'4-8 3106 3061 255-0 3>3-i 303 '4 287 I 2727 262-6 268-2 247-2 242-1 237'9 2283 21 1 -2 179-2 167-5 158-2 308-7 305 I 3049 301 S 287-7 282-4 276-7 264-9 263-2 261-2 256-2 9 239-2 236-2 226-4 303 3 295-8 281-2 282-0 283-0 282-8 283-8 265-1 2557 2341 180-3 202-9 196-3 189-5 184-6 178-7 i74"5 i66-i i6i-i 154-9 150-9 147-8 141 -9 195-8 193-6 152-0 187-5 179-3 411. 2n. 31- 411. 2n. 3n- 2n. 4 2n. 3"- 2n. 15"- 2n. 3n- 411. ion. 6n. 2n. )j 4n. 3"- 9 9 2n. 3n- I2n. 5n. ion. 1311- 5n. 7n. 8n. 7n. 6n. Sn. in. 4n. in. 2n. 1-2 -o 0-9 -8 -s -98 •84 -57 •53 -44 -48 •53 •59 -57 ■57 -58 -60 -54 •63 -82 •71 ■78 -76 •47 -82 -40 -31 -33 -41 -35 -42 ■35 •32 -43 0-82 0-5 ■5 -6 ■7 0-45 ■5 -50 0-5? -5 0-5 •5 -5 -62 •6 •6 -71 -81 -69 -75 •5 -5 -57 -70 834-56 7-29 9-32 42-52 53-60 40-46 2-23 6-68 50-46 1-48 2-65 5-11 6-57 7-65 8-56 60-95 6-40 9-54 73-09 41-47 2-40 -66 3-54 7-38 8-38 50-70 1-28 -78 2-61 349 5-53 7-38 8-57 9-38 41-67 2-35 3-67 7-08 8-53 •52 -51 •51 •49 53-23 4-05 6-97 66-54 2-55 3-38 4-48 5-45 6-94 8-38 70-39 1-43 2-43 3-41 4-77 5-41 63-63 4-41 72-46 65-78 7-57 Ta. Du. ■W. &S. Gl. Schi. Sp. -w.o. Dob. 197-9 196-4 170-8 166-6 155-7 ■3 171-1 163-9 160-8 158-0 146-7 167-9 164-5 162-3 151-0 152-0 1 50- 1 1491 143-5 147-6 144-6 150-6 140-4 152-0 -7 150-6 -5 164-0 158-4 143-3 -3 146-5 148-9 143-0 I -6 131-5 137-7 in. 3"- in. 2n. in. 6n. 4n. 5"- 2n. in. 4 I 3 4 3 7 7 8 9 7 7 13 10 5 10 12 5 170-4 171-5 Fiazzi. Hj & So. 170-4 S. 172-6 171-9 -9 O.S. Ua. Se. Kn. M. Du. Fl. -I ■6 •7 -7 ■6 •6 -8 172-0 17 1 -6 -4 -5 -7 -6 2n. 4n. 4n. 0-85 0-53 -59 -66 •55 •80 -76 -4 -3 -45 0-6 •7 0-7 ■84 0-65 -46 •5 -58 -5 ■5 -63 -64 ■78 ■70 •72 -73 0-55 ■63 jj} and /i,'". 1865-72 6-42 70-65 2-22 3-47 4-54 69-49 70-52 1-54 2-52 5-52 1-57 2-33 -38 3-25 •33 ■44 4-44 7-43 -44 -52 -59 •45 3"47 -48 4-22 ■26 0-44 1-65 5-46 ■47 6-41 •43 -43 -44 -35 7-36 8-49 in. 7n. in. 3"- 3"- 3"- in. 128 1781-80 112 1800-00 108-9 21-35 ■7 -78 109-1 2-67 108-4 34-64 -8 40-95 -7 7-69 -7 51-50 -6 6-77 -4 61 -60 6-22 108-9 46-29 ■ 3 53-46 -5 63-25 ■I 4-40 -4 6-53 -I yi-52 -6 7-69 MEASURES. 3IS 487 2. 1944. R. A. Dec M. is"- 21 -S™ 6° 3 r 7-5. 8-1 C. white. Probably a binary. 2. 34I°6 4n. 1-34 1832-40 Ma- 339-3 -35 9-00 •2 ■30 42-42 338-1 -34 3-33 336-9 54-40 331-4 1-33 7-39 335-6 -00 65-52 Se. 7 2n. •18 56-44 W. & S. 334-9 in. .09 75-45 488 o.t. 2 96. R. A. Dec M. jjh 22-2'» 44° 2 6' 7, 8-6 Change in angle. 0.2. 327-9 2n. I -52 1845-53 321-2 ,, .44 52-10 3'7-3 4n. •63 7229 Da. 325-2 in. .60 48-53 De. 319-6 3"- •51 66-70 •W. & S. 316-0 6 •47 73-37 ■9 2 .61 -44 •8 5 •33 4-50 315-9 5 .40 5 49 •5 5 ■34 7-45 489 t. 1954. 8 SEBPENTIS. R. A. Dec. jjh 29-I™ 10° 56' Ma^niiudes. — 2. 3, 4. Se. 4, 4-5. Sm. 3, 5. De. 3 -9, 5 -6. One of the stars is probably variable in its light. C. 2., A, yellowish white ; B, ashy. Sm., A, bright white ; B, bluish white ; " but under the very best vision both have a bluish tinge, which, in such a pair, is rather against the theory of contrast." II, (/>/«-/. Trans. 1803, p. 380). After observing that the position 42" 48' s.p. on September 5, 1782, was "an accurate mea- sure," and that in 19 years and 155 days " the small star has moved, in a retrograde order, over an arch of 18° 39'," he proceeds to show that "the most natural way of accounting for the observed changes is to admit the two stars to form a binary system. In this case we calculate, with considerable probability, that the periodical time of a revolution of thesmall star round S Serpentis must be about 375 years." Hj and So. [f/ii/. Trans. 1824, p. 231). An examination of all the observations up to 1821 show that on the whole the distance had increased. " The angular velocity has undergone a considerable diminution, and as this corresponds with the increased dis- tance, the orbit is probably elliptic, and so situated as to allow its ellipticity being visible without distortion. The mean annual motion is — o°-726, or retrograde." So. {fhil. Trans. 1826, p. 341). Mea- sures for 1825 are given. On these Hj remarks: "Either there is a considerable error in these or the measures of 1821, or the result is unfavourable to the motion assigned to this star, as, instead of advancing 3° in its apparent orbit, it seems actually to have receded nearly 50'. Further obser- vations must elucidate this difficulty." And in the Mem. R. A. S., vol. v., p. 45, he writes of the measures he made in 1830, " My present observations afford no support to tire evidence of motion offered by former measurements." "The present apparent fixity of S Serpentis contrasts strongly with its former rapid motion. A considerably elongated orbit can alone account for this." Dawes, too, with his measures in 1831 and 1833 before him, writes, "This star appears to have come to a standstill." So also 2., Se., Sm.,and others, all note the diminished rate in the angular motion. Smyth adds that " a small movement in space has been detected in A, which, when surer known, will afford fiirther demon- stration of its physical connexion with B." Hind, however, says, "The proper motion in R. A. appears to be nil, but a very small one may exist in declination." The distance by 2. in 1852 is con- siderably in error. The angular change has diminished of late years, and the dis- tance has augmented. From 1782 to 1834 the angle changed considerably ; between 1834 and 1855 but little ; since 1855 it has again been subject to change. The maxi- mum distance, probably, has already been attained. (0.2.) Duner 'nas the following formulae : A = 3"-03 + o"-oi38 (/- 1850-0) -o"-oooi5 (/'-i85o-o)^ P= i99°-o-o°-273(/- 1830-0) + o°-oo25 (/- 1830-0)= — o°-oooo= (/-i830-o)^ The common proper motion is in R. A., and o"-o5 in N. P. D. - o" -06 227-2 1782-99 208-5 1802-10 & So. 199-3 in. 3-05 21-33 198-4 6n. ■29 9-50 -4 2n. -04 32-31 3I& DOUBLE STARS. Ba. Ha. Ch. Ka. Hi. Hit. Se. Se. Ho. U. Ec. Ta. 20I-2 3n. 2-44 197-2 511. -66 196-9 3n. •56 192-4 in. 3-79 196-5 29 197-3 -7 196-2 -8 -5 3-0 I SB -9 3n- 2-91 •957 5n. •97 •8 in. -85 194-9 3"- 300 -8 2n. .09 ■2 ») •03 193-1 in. -08 -7 »> ■17 192-3 ,, •04 191-4 ,, -37 -2 M -23 197-4 5n. -46 196-1 4n. -04 194-3 2n. •28 193-1 3n- -12 -2 4n. ■17 -4 31- -22 195-5 m. 2-66 196-8 -76 197-8 -92 193-9 3-15 194 -2 2n. -03 193-4 in. 2-15 197-0 5n. 3-08 194-5 -23 -I in. -58 193-0 6n. -23 192-4 2n. -16 "I 5n. -32 -2 ,, ■19 195-5 7n. •06 190-4 In. •35 193-1 2n. -37 190-3 in. 2-96 193-5 ,, 3-21 188-4 ») -33 186-7 „ -37 188-5 ,, -33 190-5 ,, -49 189-9 »i -46 190-2 j» -09 193-6 ji -24 I90-I »j -03 189-9 ■33 190-4 2n. •18 9-5 m. •30 IO-5 4n. -64 •9 „ •50 192-2 7n. -28 189-9 3"- •32 190-7 2n. -20 1898 3"- -46 193-5 in. -23 190-7 ,, 2-96 104-6 >> -63 iSS-8 •44 1822-68 33-07 6-30 5222 31-43 8-38 42-35 51-32 32-35 41-06 3-44 8-52 9-44 5258 7-52 •56 -74 65-39 -55 41-32 237 52-34 4-55 6-68 9-38 41-41 -65 3-66 65-62 45-27 7-70 53-66 4-54 5-13 6-52 7-55 8-47 63-43 55-89 65-52 57-40 6233 7-37 8-40 •48 9 49 -61 70-38 -40 1-34 ■36 -48 2-39 3-39 4-41 5-42 65-05 5-41 5-51 6-37 9-36 71-42 2-29 3-48 Ta. Da. Gl. W. ftS. Schi. Sp. Sob. PI. 189-2 -o ■o 187-0 189-7 191-4 189-8 193-0 1921 191-5 192-9 191 o 190-0 189-6 ■6 186-9 188-5 2n. 2-33 ,, ■57 in. 3-11 »» •12 ,, -17 6n. -06 4n. -02 5 5 3-56 5 -51 4 •1 2 -23 8 -41 in. •28 -28 6n. -37 4n. ■79 1874-36 5-39 66-49 9-52 74-62 68-32 75-56 1-22 •56 3-36 4-50 -50 5-51 -61 •61 6-30 •97 490 2. 1956. R. A. Dec. M. 15'' 29" 42° 13' C. A, yellowish white. 8,9-5 Ha. Se. 0.2. Dn. 41-4 40-6 37-3 41-4 37-9 3"- in. 2n. In. 31- 2-71 -82 •52 •61 -27 1831-53 45-48 57-60 68-52 70-44 491 o.X. 297. R. A. Dec. M. 15b ^^m 25° 25' 7-5. ii-s Change in distance. 0.2. De. 147-3 I 146 -I 147-7 in. : 13-56 -06 ,. 12-53 1023 1845-31 6-37 50-40 67 00 492 X. 1957. R. A. 15'' 30-2" Dec. 13° 19' Ha. De. Gl. -W. & 8. 164-6 161 -7 158-4 157-6 156-3 153-6 155-7 152-5 155-1 152-0 161-5 156-6 2n. 1-47 ,, -35 1-37 -25 1-48 -53 in. -4 2n. •24 in. •5 2n. -4 in. •5 M. 7-9. 9-6 1828-85 33 35 42-42 3-40 57-39 61-55 3-51 71 49 3-38 4-50 5-51 6-48 MEASURES. 317 493 2. 1961. R. A. 15" 30 •3"' Dec. 43° 57' ■V 56-0 2n. 21-55 H«. •2 Ka. 52-4 21-63 ■I 1 ■18 49-4 ! Se. 47-8 22-23 M. 87. 9 1830-65 3 1 "43 4730 51-27 376 65-77 494 0.2. 298. R. A. Dec. M. 15" 317"° 40° 13' A 7, B7-3, C7 C. yellow. About a quarter of a revolution has been described by A B, and the minimum distance A 4- B has been attained : -H— and C probably 2 unchanged. (O.S.) Duner has the following formulae : A = o"-93 - o"-oi7 {t — i86o-o) + o"-ooo38 {t - i86o-o)^ p = i99°-5 + i°-352 it - 1860-0) + 0°-02i8(< - i86o-oy. Ha. O.S. De. Sa. W. & S. A B I79'5 I-I2 186-5 3"- -42 i88-6 •51 191 -8 2n. -40 181 -6 3n- •20 195-2 4n. -18 212-5 In. 0-84 23 s -8 ,, -58 264-3 ,, ■53 208-9 3n- •99 2808 214-1 ,, 0-58 i«7-3 2 7 190-9 2 ■5 234-0 s A+B and C. O.S. 328-3 -o -0 327 '9 3282 in. 122-53 •38 121-87 122-23 •38 1843-35 6-28 7 '33 5174 46-49 58-83 68-52 72-58 5-52 66-44 76-46 69-46 74-50 •50 3-40 57-68 61-44 8-52 72-58 5-52 495 OX 299. R. A. O.S. Se. 20-9 23-4 Dec. 64° 15' 3n. M. 7-2, 9 5 3-20 I 1848-34 -24 I 66-81 496 t. 1965. R. A. Dec. M. 15" 34-9™ 37° «' 4-1. 5 C. A, greenish white ; E, greenish. The motion has been rectilinear so far. Duner has computed the following for- mulae : 1849-76. A = 6"-i2. P = 30i°-7+o°-o54(/- 1850-0). So. H,. Be. Sm. Sncke. Ga. Ea. Ma. Po. Hit. Sa. Uo. O.S. Lu. Se. H. Ta. 295-8 ■5 299-9 -6 300-9 -9 -o ■5 ■7 301-2 300-9 301-2 3024 301 I ■5 302 2 301-0 -8 3024 •o 3032 302-1 •6 301-3 302-3 -2 -5 303 300 30 300 301 299 30 302 303 301 299 296 302 301 302 Da De. Gl. Dob. 300 Goldney 301 in. 6-25 3n. 5-88 Sn. 6-0 4n. 7-17 6-0 in. -2 •18 ■4 -5 -I -53 -21 5-92 6-07 6-33 ■24 5-99 601 •27 5-90 608 5-68 6-13 3". ■07 6n. ■07 in. -16 -21 •18 31. -20 in. -29 30 -00 30 -«4 30 •13 I7n. •05 •66 41- -21 in. 5-93 ,, 6-31 2n. -19 6n. -30 in. -62 3". •66 ,, -03 •21 in. -38 3". •60 41. •36 1781-27 1802-25 19-62 22-26 9-70 2-30 6 00 32-57 0-68 i-6i 9-50 42-57 37-44 8-59 40-26 1-47 2-40 3-37 4-37 7-32 51-41 2-47 3-30 4-65 S-77 7-46 8^50 61^32 -97 45-93 7-70 54-55 43-63 7-99 8-45 5-43 6-43 52-53 4-58 6-17 •49 62^23 9-57 4-48 6-32 7-52 9-52 8-60 •70 71-36 6-25 8-51 3i8 DOUBLE STARS. 497 t. 1967. 7 COBON£ BOBEALIS. R. A. Dec. 15'' S??" 26° 41' Magnitudes. — S., 4, 7. Piazzi gives the magnitude as 6. Dawes strongly insists upon its being registered as of the 4th, and he gives the companion of the 7th. C. 2., A, greenish white ; B, purple. Sm., A, flushed white. Se., a, greenish ; B, purple. Da., A, light yellow ; B, "purphsh."' "The star will probably become single, and after a time the companion will emerge on the opposite side." (2.) Ten years after its discovery he could not elongate it. Hj, during 1832, examined it "with 320,480,600. With all, a. round disc seen, but no companion." Madler always measured this star at sunset and sunrise, as the companion was invisible by day, and at night was hidden by the rays of the larger star. Smyth, in 1839, on "a superb night," after much gazing, thought there was an elongation in the direction s.p. and n.f. In 1842 he found it "still a dumpy mis- shapen object, with an axis major perhaps n.p. and s.f." Dawes, in 1843, saw it "with the com- panion coming out again." The plane of the apparent orbit of this star, like that of 42 Comas Ber., approximately coincides with the visual ray. Between 1826 and 1833 the companion was on the follmoing side of the principal star ; it then passed to the north at a mini- mum distance, and reappeared on the pre- ceding side in 1840, where it has been found up to 1873. Lately the angle has diminished considerably, and in 1874 the companion was invisible. Probably it has passed southwards to reappear on the following side under an angle of about 120°. The period may be about eighty years. The angle in 1840 seems erroneous. (0.2.) In 1877 Dr. Doberck published the fol- lowing : — First elements (from 2.'s observations), ffl = 111° 7= 83 X = 239 e = 0-387 P = 95 '5 y"- T = 18437 a = o"75. Second elements. £3 = 110° 24' 7 = 85 12 X = 233 30 e = 0-350 P = 95-50 yrs. T = 1843-70 a = o"-70. The common proper motion is small, -o'-007 in R. A., and — o"-09 in N. P. D. Sm. Encke. 0.2. TH'i. Da. Hit. II I -o 110-7 1 03 9 105-8 225-0 295-0 90-9 95-0 252 293"5 290-4 296 o 287-7 295 '5 288-5 289-1 290-0 287-6 288-8 286-6 279-0 283-6 288-7 284-9 ■3 287-7 298-9 284-2 288-5 286-0 264-5 255-8 3323 271-9 292-2 296-4 284-4 291-0 286-4 284-0 290-4 288-8 285-0 284-3 281-0 282-5 286-8 292-5 293 ■« 2n. 0-72 1826-75 31- ■54 8-98 5n. -40 32-66 2n. -40 3 '34 single -00 round 4-66 0-3 9-69 elong"- 42 -58 0-5 8-37 in. IIO 36-48 2n. 0-87 8-70 In. wedg"- 40-48 suspected •51 " oblong If wedg^- •57 It oblong 1-57 2n. 0-38 2-60 In. •47 471 5n. •44 5-60 2n. ■44 6-69 3"- ■44 7-68 2n. ■49 8-71 In. •59 971 2n. ■42 50-51 4n. -48 1-50 3"- •45 2-65 2n. •48 3"54 yi •52 5-65 ,, •43 6-56 ,, ■45 7-63 3"- •44 8-56 2n. ■48 9"59 3"- -42 61-89 In. ■43 2-74 ,, •34 3-58 ,, •45 4-60 2n. •43 6-62 In. -40 7-47 ,, •33 8-56 ,, wedg^- 9-52 prob. " wedg"- 70-52 ,, single 1-58 ,, wedg''- 2-56 " prob. oblong 3-54 »» single 4-57 ion. 0-18 41-50 2n. ■47 2-80 6n. -40 51-70 7n. •45 2-60 4n. -40 3-32 in. -40 476 2n. •32 7-39 4n. ■33 8-58 3"- 9-38 in. 0-6 43 -45 ,, •57 52-07 2n. -69 4-40 in. ■5 7;52 3"- •45 ■S3 46-66 in. 72 >t 7-70 MEASURES. 319 Hi. Bond. Ja. Wi. De. 300-0 2947 290-5 2930 294-2 295-4 289-0 ■3 294 278 280-5 292-9 Eng. 280-0 Du. companion not seen single W.O. Schi. Sp. Dob. 190 •95 in. o-'e »> ■3 1) ■3 ion. •5 ■67 3n. •45 5n. •36 In. elong*"- It It round 3n. T> elon'g'i- in. 5n. ... in. ... single single ... 1847-08 8-51 ■49 ■46 S3'i9 6-37 ■59 7-52 64-46 5-52 ^■55 58-51 62 56 5-51 779 8 964 70-56 1-45 2-52 5-57 2-45 3-36 -40 5 97 -98 6 7 498 S. 1983. R. A. 15'' 46° 2. Uii. Dec. 35° 51' M. 8-7, lo-i C. A, yellow. 77-0 I 3n. , 17-44 1830-65 76-7 I in. j 16-58 I 45-55 499 S. 1989. R. A. 15'' 46-2°' S. Dec. 80° 22' C. very white. 0.2. Ua. Se. Se. 24-1 3n- 0-71 23 '9 It •S3 281 •70 23-0 •85 21-1 2n. •60 single 1 >> 1 M. 71,8-1 1832-68 676 40-95 1-46 58-59 65-00 70-00 600 t. 1984. R. A. IS* 48I'' Dec. 53° 16' C. white. M. 6-2, 8-5 Duner gives 1846-91. 4 = 6"-42. P = 275° -3 + o°-o85 (/- 1850-0). H,. 270-3 in. 1830-20 2. 273-8 411. 6-53 ■72 Jlla. 274-3 31- •49 43-42 276-1 -38 51-27 •I 3n- ■29 2-42 Se. -6 in. -39 7-6i Du. -2 2n. -42 70-90 501 R. A. IS"" 49-7" % 1985. Dec. - 1° 49' M. 7,8-1 C. A, yellowish white ; B, ash. Duner gives the following formuls : 1854-13. A = 5" -70. r = 328°-3-o''-i37(/- 1850-0). H,. So. H^. 2. Ua. Po. Da. Hit. De. Ho. 0.2. U. Eng. Ta. Dn. W. &I CO. 316-1 325-3 326-5 -5 327-0 326-2 327-5 328-1 327-0 •I 325-S 328-5 •5 327-7 330-1 -o 325-6 330-8 329-0 331-1 334-6 331-7 in. 2n. 6-88 in. 7-19 4n. 5-42 6-20 5-78 ■96 in. -74 j> -57 in. 5-39 4n. -83 2n. -48 ■93 3»- -61 2n. -70 in. ■3; 3n- -98 in. 6-77 6n. 5-66 5 6-IO 2n. 5-66 1783-32 1823-42 30-23 I 95 41-47 3-44 3-35 54-47 46-18 6-42 8-54 55-88 6-96 65-48 58-42 61-44 4-43 5-44 9-36 71-12 6-46 7-48 502 R. A. 15" 54" H,. 2. 0.2. Ua. t. 1993. Dec. 17° 43' C. white. 17-9 37-85 .37-7 3n- 33-96 38-0 t» •93 37-4 2n. 32-93 M. 8-2, 8-2 1783-09 1831-76 40-79 7-29 503 o.t. 303. R. A. Dec. Certain direct motion. M. 7-4. 7-9 320 DOUBLE STARS. 0.2. Ma. Se. Sp. PI. HI 4 31- 0-60 126-6 2n. 75 134-4 in. 77 iio'6 ■51 II6-6 •60 119-9 •72 •2 in. •4 127-8 4n. 77 131-2 •85 1327 2n. •95 1846-78 65-44 75-45 43-46 7-35 51-40 7-57 67-20 76-52 ■6i 504 2. 1998. ^ SCOEFII. R. A. Dec. 15'' 57-8" -11° : M, A 4-9, B5-2, C7-2 Magnitudes.— SoMlh, A 7, B 7, c 9. 2., 4-9, 5-2, 7-2. Sm., 4J, 5, 74. Se., 6, 7, 8. Argelander gives A as 4-3 (decimal). C. H„ A B, fine white. South, c, "deci- dedly blue." S. A, B, yellowish white, c, bluish white. Se., a, yellow ; B, white ; c, blue. Sm., a, bright white ; B, pale yellow ; C, grey. H, {Phil. Trans., vol. Ixxii., p. 218). "May 23, 1780. — Double-double. The first set very unequal. Position 1° 23'. n.f. The other set both small and obscure." In a note he adds, " In a future collection this set will be found as a treble star of the first class, the large white star, with a power of 460 and 932, appearing to be two stars. —Ori^." Here the "first set" are A and C, about 6" apart, and are Hj II. 20; the "other set " are a faint pair not further alluded to. When H] discovered the duplicity of A, he registered the close nair I. 33. Hj and So. (Fhil. Trans. 1824, p. 243). Up to 1822 these observers had not seen A double. Referring to A C, H, says, '-This is perhaps a binary system with a mean annual motion of — o°-256." So. (^Fhil. Trans. 1826, p. 343). "A and B equal. Measure of the close pair A B, June 19, 1825, 84° 43' s.f. orn.p." H, in 1831 saw "the division [of A B] quite well. " Da. (Mtm. R. A. S., vol. viii., p. 69) says, "The whole series of observations distinctly points to a direct motion, and shows that nearly a whole revolution has been completed since 1782." Sm. {.Cycle, p. 352) quotes S., who says of A B " that if Hi made an error in the quadrant of the star, which the nearly equal magnitude will easily admit of, and SO 1782. /aja. if, from similar causes, we add iSo" to South's deductions, it will show a direct motion of 182° in 55 years; giving about a century as its annus magnus. The stars A and C, however, are evidently retro- grading at about — 0° -2 per annum, which is not accountable on proper motion con- ditions." Da. {Meni.R. A. S., vol. xxxv., p. 386). He remarks that probably variability in the relative magnitude of the stars led to Hj placing the companion in the n.f. quadrant. It was really in the 3rd quadrant. South's position in 1825 is similarly in error. Of A B he writes that the orbital motion has been considerably accelerated, and that the distance has diminished, "and it will, no doubt, ere long require the most powerful optical means to fairly separate the com- ponents." And in 1867 he says, " The anticipated approximation of the compo- nents has come to pass, and it is now extremely difficult for any ordinary aperture to separate them, at least in this latitude." Madler, using the observations from 1782 to 1846, obtained the following elements for the close pair : — ,T =1832-611 a =4° 45' -2 Annual motion = -|- 204'-6S8 P = 105-522 years i = la° 1 3'- 3 tt' = o"-o5772 Semi-axis major = i"-287. For the distant pair, 183985 : 6"-8oi ; 74° 29'-o - i4'-704 ^ ; G = o" -02909 ; J = 1469-0. MEASURES. 321 Dr. Doberck in 1876 published tlie fol- lowing circular orbit of A B : — a =■ 10° 51' : i = 72° 27' : P =95 years. Least distance o"'38 in 1859 '62. Greatest distance i"*2S in i883'37. In 1877 the following elements by the same astronomer were published : — ffl = 12° 15' 7 = 68 42 X = 89 16 e = 0-0768 P =95-90 years T = 1859-62 a = i"-26. The common proper motion of the three stars is — o''"lo3 in R. A., and — o"-lo5 in N. P. D. AB. Se. Xn. On. Gl. H,. 187-9 178236 T^ 33S-9 3"- 1-14 1825-47 44 »» -21 3246 ■w. & 5-8 2n. -21 3-91 77 )» •23 5-00 8-0 4n. '16 6-49 12-5 2n. -09 7-51 H2&S0 351-9 8n. ■35 25-49 Fer. IS 4n. •49 30-27 Schi. 92 2n. -32 "-38 lo-o 8n. -41 5-40 CO. Da. 6-2 in. -15 3 39 7-8 8n. -16 4-50 w.o. S-9 2n. -52 16-7 J, 1-27 9-61 18-6 3"- -19 4056 Dob. •9 ■19 I -58 21-5 2n. 2-46 23 5 ») 1-08 3-40 24-5 in. •45 30-5 3n. 119 48-54 46-2 In. 53-53 156-9 2n. '-57 65-54 H,. Sm. 6-6 ■4 34-42 H,& 13-3 •I 8 -60 23-5 , -2 42-56 24-9 •0 6-49 V Ha. 16-7 4n. -28 1-48 20-4 J1 -OS 2-42 Hit. 23-6 3"- 0-96 6-46 •I It ■96 •47 25-5 -q8 ■'^f Sm. 26-0 in. I-71 7-58 272 »» 0-84 8-54 Ja. 46-5 15 -93 52-98 Da. 48-3 10 •9 4 06 Ha. Be. 50-5 3"- oblong 5-31 57'i 5"- tt 6-33 318-7 3n. wedg"- 62-55 Ka. 322-0 9n. ,, 3-44 33 "•9 ion. oblong 4-50 333* I »» »» 5-44 Hit. 156-6 8n. 0-5 6-46 o.s. 160-7 7n. ■82 7-45 165-3 J> •89 8-40 &s. 168-7 I70'2 173-0 -8 176-4 178-7 180-5 53-6 70-0 106 ± 166-5 176-9 172-5 173-3 174-8 177-4 181 9 1682 174-0 1828 176-5 "77-3 180-4 183-1 i8o-o 184-9 355-7 182-0 184-1 185-6 184-3 2-5 5-5 3-8 186-4 179-4 Sn. 7n. 8n. 5n. 411- 1211. 6n. in. 5n. m. 3"- 2n. 088 1S69-52 -88 7045 1-06 1-41 -II 2-46 -19 3-42 -05 4-49 ■10 5-43 0-47 55-55 -36 6-49 single single? 8 0-99 68-48 1-12 72-46 0-8} 69-51 -88 70-54 -88 i-6o -96 2-53 '•25 5-56 0-2I 1-0 1-49 -15 3-49 -I -68 0-95 2-45 1-04 3-36 -19 4-44 ■33 5-51 -27 746 10 2-50 -18 5-50 -20 6-51 -04 •44 ■26 7-46 -23 6-46 •14 -S3 -05 -54 -61 096 A+B and C. 88-6 6-3S 78-3 2n. -76 76-6 4n. 7 -07 78-6 3n. 6-95 ■6 4n. -75 76-1 3"- -70 75-4 2n. 7-02 74-7 3n. ■06 -7 in. 6-99 76-1 7-2 74-2 ■2 68- 1 -0 69-4 in. -43 74-7 6-75 72-8 -I 6-93 73-3 -53 68-8 ■91 70-2 -98 72-9 9n. in. 7-37 71' -8 ,, 7-45 69-8 >. -18 742 178236 1822-46 5-46 8-40 5-48 32-46 5-00 6-49 52-22 34-42 8 -60 46-49 0-56 1-47 2-42 61-42 43-39 65-49 6-51 46-82 52-22 6-58 61-43 21 322 DOUBLE STARS. Ja. Be. 68 69- 71- 70 71 70 69 Se. U. Eng. Sn. 70 69 68 70 69 72 68 69 72 Ta. Vf. ft 8. 69 68 72 I 3 Fer. 243 Lindstedt. 65 Schi. 66 67 66 67 66 68 65 66 CO. w.o. Dob. 5 9 3n- 2n. 3n- 4n. 6n. 2n. 3n- 2n. in. 2n. ion. 6n. in. 4 in. in. 2n. in. )» 2n. in. 7-51 ■73 ■26 6 90 714 •16 'II •II •03 •21 699 7 08 •19 •04 •20 •03 •50 10 693 7 '41 •19 ■08 •15 •5 6-25 •87 •91 •7 ■38 762 "30 •08 •27 •69 ■32 •27 •33 7-51 1853-12 4'o6 5-31 6 39 62-55 3 "49 5-38 6-96 8-53 950 7035 1-36 2-48 3 43 4-47 5 '44 55-54 65-45 1-42 4-48 9-48 70-52 1-52 2-52 I 42 4-37 2-45 336 7 49 2-50 3-45 5-5« 6-51 •44 7-51 646 ■54 -46 7-61 606 2. 2007. R. A. Dec. 1 6'' 0" 13° 39' M. 6-5, 8 HjftSo. 328-7 2. -2 Ma. 5 2n. in. 3 1 '93 •97 33-05 1823-42 30-14 43-45 606 R. A. 16" 2-6° t. 2010. Dec. 17° 22' M. 5, 6 C. both yellow. 2. {P. M., p. ccxvi. ) found the proper motion of the principal star was — 8" -9 and — o"-4, that of the companion — 8"-o and — 4" -6 ; hence both orbital and common proper motion 0. S. by the method of last squares finds the following : — A A = + S"-342 ± o"-o30 + (o"-oii4 ± o"-ooi9) (T —1850-0) ; A D = + 3o"-28o ± o"-oi8 — (o"-o257 ±o"-ooi2) (T - 1850-0); and these show that there is no trace of deviation from rectilinear motion. Duner has these formulae : — A = 30" -79 — o"-020 (t — 1850-0). P = 9''-84 + o°-02o {t — 1850-0). FIam8teedi3'4 H,. H2 ft So. 2. 0.2. Ha. Se. Se. Eng. Da. -V. ftS. Dob. 7-6 9-6 -5 -6 -6 -4 -7 lOI •I -3 9 9 log -5 •7 -6 97 -4 -2 10-2 9-8 10-4 -4 -2 -4 9-9 in. 61-7 »» 39-98 >> 3i-'7 2n. -45 3n- ■23 4n. •01 3". -14 in. -03 30-72 3066 ■44 •39 12 ■21 -20 5n. ,, 31-07 in. 30-74 3n- -41 4n. -59 2n. •59 )» -15 4n. -5 .1 -75 4n. 29-83 R. A. 16" 3-5"' Dec. 83° 58' 2. 115-0 31- I -41 0.2. 1 18-4 2n. -60 Ma. 121-3 in. -64 118-4 2n. -34 De. 1203 »» -2 Dn. 118-5 3°- •44 608 R. A. l5h jm V SCORPII. Dec. - 19° 9' 1703-31 81-82 1821-39 2-69 31-52 6-33 40-88 1-60 7-69 5191 2-55 66-62 8-55 72-57 -59 3-57 41-35 3-02 8-38 57-20 812 63-65 4-36 9-61 76-46 7-35 607 2. 2034. M. 7> 5-8 1831 -86 41-14 2-72 S-61 57-63 71-25 M. 4, 7. 7, 8 The wide pair was discovered by H,. In 1847 Jacob detected the duplicity of B, but it was reserved for the keen eye of Bumham in 1874 to see that the principal star itself was also n. ..close double star. A very striking group. MEASURES. 323 AB. Bu. 3577 6n. 0-45 1874-41 Newcomb. 5-2 in. ■47 Be. 359' I 3"- 0-84 -49 CO. 8-9 2n. -59 7-48 A B and C. 5'- e 334-8 38-33 17S1-4 Hj&So 338-2 336-6 40-82 1821-4 36-5 Sm. 338-S 40-00 1-5 Hit. -9 3n. 43-00 46-54 Ja. 336-5 •57 77 Se. 331-3 •58 55-5 De. 336-9 211. •78 74-49 C D. Hit. 39-0 2n. i-ii 46-58 Ja. 42-2 -8 7-4 45-4 -6 8-0 Bu. -7 6n. 74-41 De. 48-4 2n. rSg -49 CO. 462 in. -86 7-37 509 2 2021. 49 3EBPENIIS. R. A. Dec. M. i6» 77 m 13° 5 i' 6-7, 6- C. 2., white. Sm., A, pale white ; B, yellowish. H, {Phil. Trans. 1804, p. 376) : "In the year 1783, March 7, the position of the two stars of this double star was 21° 33' n.p. May 20, 1802, 32° 52'; and April 2, 1804, 35'^ 10' ; which gives a change of 13° 37' in 21 years and 26 days. The stars are now a little farther asunder than they were formerly. A parallactic motion would ac- count for the change of the angle, but not for the increased distance. " Hj and So. {Phil. Trans. 1824, p. 247) : " The motion of this star, first pointed out by Sir W. Herschel in 1804, is thus clearly established. The disagreement between our observations and M. Struve's is rather more than usual (4° 6'); but the star is close and difficult. The mean annual angular motion is about o°-5lo in the direction n.f.s.p., or direct." Measures in 1822 and 1823 are given. So. {Phil. Trans, for 1826, p. 347). Hj having the observations by So. in 1825 before him, says that the change in this star is confirmed ; that the amount 6° 13' is greater than calculation gives, viz., i°6'; that probably the measures in 1823 were faulty, and S.'s measure in 1820 (46° 33' n.p.) worthy of more confidence. Sm. {Cycle, p. 355) : "A rough investi- gation gives above 600 years for the orbital revolution of the satellite about its primary, — or, rather, of one sun around the other. More observations at longer epochs are, however, necessary, before it can actually be pronounced a binary system." Later, Dawes and Secchi express their conviction that the orbital motion is certain. These stars are transported through space by a considerable common proper motion. The distance appears to have already reached its maximum. (0.2.) Dun^r gives the fomiulEe A cos P = 2"-22 -f o"-024i {t - 1830-0) - o"-oooio{^ — 1830)*. A sin P = — 2" -27 + o"-oo52 {t — 1830-0) + 0" -000066 {t — 1830)^ The common proper motion is +o"-i52 in R. A., and — o"-369 in N. P. D. H,. 291-5 302-9 305-2 in. 1783-18 1802-39 4-25 H2&S0 3" -9 2n. 4-15 23-28 318-2 4n. 3-5 5-41 316-8 2n. 2-95 30-02 S. 315-5 3n. 3-19 29-48 316-6 in. •03 32-53 319-2 ,, -24 4-39 317-0 4n. •25 5-45 316-8 2n. -29 6-71 Da. 314-8 m. ■17 1-40 318-0 ,, •43 41-38 321-3 9-44 Sm. 317-8 3-7 32-43 318-1 ■3 9-29 323-0 -2 54-58 Ma. 3'9-3 in. 40-84 -2 4n. 3-62 1-45 320-5 3"- -40 2-38 319-6 4n. •39 3-34 318-6 2n. •36 4-38 321-2 m. -34 S-11 322-2 -39 51-40 321-9 2-04 322-4 4n. 352 4-62 324-7 2n. ■37 7-39 3237 -58 8-42 -7 •70 9-38 324-7 7n. 71 60-67 Hi. 318-9 in. •23 45-26 Mlt. 319-1 »» 4-34 7-58 Fit. 322-9 16 325 51-66 De. 321-2 6n. -67 4-63 324-6 3"- -53 64-80 Ho. 322-7 JJ •65 55-49 Se. -3 6n. -46 601 325-8 in. -80 65-48 M. 323-7 )» -53 2-37 324-2 >» 4-02 8-43 327-0 j» 3-81 70-39 325-4 »» -59 1-37 324-9 >» -88 2-45 326-5 )» -66 3-39 325-9 )) -70 4-42 329-7 >) -94 5-63 324 DOUBLE STARS. Eng. 3257 411. 376 Ta. in. -91 325-8 ,, ■69 327-2 ,, -9S •6 ,, 4-26 328-4 2n. 3-76 327-9 4-11 Br. 329-1 3 3-60 Du. 327-9 8n. ■S2 EaU. •2 -94 •6 4-27 328-8 3"- 3-81 W. &S. 3277 in. 73 329-4 ,, -44 ■7 >» -94 327-0 „ -Sb Sp. •6 -69 Gl. 328-5 in. ■9 Scbi. 147-6 -69 Sob. 327-4 3"- •90 1865-51 6-32 9-57 71-42 2-29 4-46 5-42 68-46 70-35 1-42 2-29 6-34 2-45 5-51 -63 6-48 5-48 -60 -47 6-25 510 R. A. 16" 7'° 0.1. 303. Dec. 34° 43' M. 7-2, 8-7 Probable change in angle and distance. O.S. De. 61-4 58-3 48-0 55 -8 45 60 In. 0-40 ,, -40 »» -27 *) -33 obi.? 1845-65 -71 638 8-49 65-47 -52 511 X. 2022. R. A. Dec. 16" 7 •8" 26° 59' Angular change is certain. 2. 129-5 .3n. 2-77 Ha. 131-2 -89 Be. 130-5 2n. -40 -0 in. S-26 0.2. 138-7 ,, 278 M. 6-2, 98 1 1830-56 44-36 58-09 ' 65-52 i 8-50 512 S. 2023. R. A. 16" 8-6° Dec. 5° 50' C. both yellowish. M. 8, 9 2. Ka. Be. 236-0 232-7 231-0 229-1 S 2317 229-3 4n. I -55 : ■51 -50 -41 -8s in. •65 2n. -77 18 2-41 9-74 42-42 51-40 2-63 6-42 65-54 513 1. 2026. R. A. 16" 8-9"' Dec. 7° 40' C. yellow. M. 8-6, 91 2. 345-9 4n. 254 1830-94 Ua. 342-0 -4 8-05 337-8 -22 44-35 334-4 -II 52-63 Be. 330-1 2n. 178 6-56 325-7 in. 0-97 65-53 De. 326 I 1-50 -39 ■w. &S. 318-9 -4 72-45 315-7 -5 3-46 321-0 -4 5-51 Gl. 316-0 in. -3 -60 514 2. 2032. a COBON^: BOBEALIS. isoe. I H, {/'Ai/. Trans., vol. Ixxii., p. 215) : " Aug. 7. — Treble. The two nearest pretty unequal ; the third very faint, with powers lower than 460." H, (/%;-/. Tratis. 1804, p. 373) : "This star has undergone a great change." " The great number of small stars in this neighbourhood is not favourable to a sup- posed connexion between any of them and r-a / e a P T Observers. 138 i / 0'6lI2 3''679 years. 286-6 1835-60 Herschel. 20 43-9 65 S4-I 40 52-2 •5899 2-38SI 42024 1825-31 Klinkerfues. 3 « 96 S3 45 6 ■3S«7 2-94 24-0 1829-7 Powell. 25 7 64 28 29 29 •69978 3918 608-45 1826-60 Madler. 21 3 6924 25 39 •7256 5-'94 736-88 -48 Hind. 1 » 57 loi 57 4647 •309 2719 195-12 1831-17 Jacob. 1 In 1875 Doberck made a redetermination of the elements of this star : his results are as follow : — T = 1828-91 a = 6° 43' ^ =89 17 , 7 = 29 40 \Sec also p. 131. P = 843-2 years « = 6" -001 e = 0-7502. H., & So. 8m. AB. s. H., & So. 347-5 11-4 48-0 89-3 104-9 118-8 1 304 1347 1 39 '9 7>-5 77-5 92-1 4n. 1-31 3"- -22 -29 5n. •30 6n. •43 5n. ■4' 2n. •44 On. •48 1781-79 1804-74 19-62 27-02 30-11 2-99 5-50 6-59 7-55 22-83 5 '44 8-50 Ba. loc-o 108-7 Ii3'5 119-9 107-6 1 14-9 120-7 130-9 145-1 155-9 162-4 176-8 115-4 120-6 125-6 136-8 144-3 147-8 150-3 153-2 156-5 166-0 168-6 1 70- 1 173-8 9n. 6n. 1-22 •3S -07 3n. ■33 ■3 ■4 •2 ■4 -6 -8 20 -2 3"- 4n. 1-30 3n- ... in. 1-60 3n- •65 1 in. ! 2n. 1-77 -88 1 S"- •99 1 in. 209 -26 1830-28 31-36 2-52 3-26 0-76 2-37 3-58 5-50 9-67 43-35 6-60 52-25 32-55 3-36 4-55 7-47 9-53 40-57 1-48 2-37 3-47 7-44 8-53 9-45 51-42 126 DOUBLE STARS. Da. 177-8 4n. 178-4 3»- i8o-i m. 185-5 2n. 191-4 m. Ga. 147-8 0.2. 149-3 5n. 153-7 in. 168-2 2n. 169-6 in. 170-8 ») 172-4 31- 168-9 ,, 173-4 6n. 174-3 5n. 175-6 6n. 179-0 2n. •I 4n. ■9 „ 181 -6 3n. 182-3 2n. 185-9 3"- 186-8 m. 187-4 5n. 189-5 m. 188-7 y> •2 4n. 190-2 m. 192-7 2n. in. 192-0 ») 193-5 •2 Sn. 192-8 ig6-6 195-6 ■3 3"- 198-7 in. 196-6 199-8 4n. Ka. 148-8 156-3 193-9 Ua. 152-2 7n. 156-3 4n. 157-5 >> 105-0 I in. 166-5 14n. 168-3 2n. 173-0 ,, 174-S 6n. 176-2 9n. 177-5 im. ■7 6n. 178-7 2n. 179-4 5n. Cb. 148-2 153-5 in. 160-4 ,, G.O. 157-2 Hit. 166-7 in. Bind. 171-2 172-5 Fit. 174-4 43 Mi. 176-4 24 2-38 •25 ■43 •71 3"o7 1-55 ■53 •56 •76 -69 •91 •96 •99 2-05 •06 -17 •24 •29 •46 ■50 -5> •58 •72 •69 •77 •77 ■77 •89 •96 2-92 3-01 2-97 -99 3-26 -17 ■12 -41 •57 •66 2-86 1-59 •81 ■86 2-07 -16 -39 •23 •34 •43 •39 •46 •65 •5« 1-56 •35 •63 •53 •33 2-2 •2 •32 •38 1853-63 Uo. 178-6 4-56 184-9 5-48 60-36 Ja. 177-9 •8 5-38 181 -2 39'52 183-0 40-63 -9 ^,-60 De. 179-7 6-68 -9 7-69 181-7 8-74 i8o-o 9-74 184-7 50-52 '.-63 189-3 190-4 2-63 -9 3-65 191-7 4-66 193-2 5-6' 6-57 195-2 196-4 763 -9 8-57 197-1 9-68 •8 60-74 198-3 1-57 •8 2-74 199-0 -79 Wi. igi-6 •!-6o ^60 5-74 i32-8 Se. 180-8 182-3 -74 183-5 6-49 Eng. 190-5 -49 Bo. 189-1 -65 Ta. •2 8-55 193-7 -61 195-1 •61 196-7 72-57 197-9 354 200-5 -57 199-2 4-61 -8 41-56 -8 3-68 M. 12-0 66-68 200-5 41-56 Dn. 195-5 2-31 194-7 ■73 195-1 6-46 196-5 7 '44 199-5 8-41 En. 194-3 50-70 195-3 1-25 Br. 194-0 -76 ■w. &S •3 2 "60 197-7 3-38 198-4 -77 200 -6 4-70 202-2 41-54 Sehi. 198-6 2-41 Dob. 199-4 3-68 -5 4-44 201-3 7-70 PI. 199-2 8-42 202-3 ■42 vr.o. 201 -I 51-22 200-0 2-31 1 199-0 20 2-22 1854-67 20 -70 9-34 2n. •i8 3-14 3n- -24 4-05 -52 6-73 ^ -52 7-66 5n. ■5! •38 8-20 4-66 3"- -40 5-18 6n. -68 6-42 2n. ■52 7-66 6n. -73 8-49 5n. •84 62-53 9n. •74 3-39 6n. -75 4-48 ,, •83 5-41 I in. •88 6-92 5n. -94 8-36 4n. 304 9-53 6n. -09 70-43 ^j -07 I 46 •16 2-83 " •27 3-48 -30 4-48 s'n. -25 5-39 -49 55-54 -52 6-39 4n. -30 r^' 2n. ■45 6-43 J ■42 7-61 -11 64-45 5-72 2n. 3-73 6-43 in. -62 8-29 ,, •59 9-57 »> •30 71-42 »i -34 2-29 t) -63 3-55 2n. •16 4-46 in. -55 5-42 2n. ■44 6-56 in. •00 67-37 ,, -55 74-44 m. 2-79 67-72 4n. 3-14 8-59 5n. •01 •62 4n. •15 71-35 5"- •28 5-54 3n- 2-97 67-34 4n. 322 71-53 4 •11 68-55 3 •51 71-51 8 ■25 2-53 5 -14 3-42 5 -47 5-50 6 -68 7-46 m. ■34 5-46 411. •89 6-28 5n. -58 7-32 4n. •14 8-53 31- •78 6-52 5n- •62 7-65 in. ■44 6-44 »» -58 -46 -44 -45 MEASURES. 327 H,. O.S. HaU. So. Sm. 2. O.S. Ma. De. W.&S. n. 244-9 231-6 221-7 A C. Sn. 20 20-41 15-92 AD 65 24 90-6 42-2 89-2 44-2 90-0 43-3 88-7 44-1 ii9■^ ■0 88-9 -2 QO-O 46-3 88-8 4375 -6 44-J7 -6 -88 87-9 47-52 7 -98 90-I •83 88-4 51-0 -2 In. 52-6 87-9 >» •9 ») 54-i8 •6 )) ■'5 1832-60 S4'40 76-40 1781-00 '82S-S3 8-40 30-76 2-37 6-50 9-67 52-00 36-69 7-66 40-58 50 26 1-69 3 '32 62-00 72-53 3-42 6-48 7-46 515 ot. 309. R. A. 16'' IS" Dec. 41° 56' M. 7-5. 7-1 The relative brightness of the two stars is probably variable. O.S. He. 234-4 in. 0-50 55-3 „ •66 239-4 „ -54 56-7 „ •40 231 -5 31. 1842-71 5-65 7-55 51-67 67-98 516 Z 2044. R. A. 16'' 20"" Dec. 37° 19' M. 7-8,8 C. white. Duner gives 1854-98. A =8"-46. P = 345''4 -o°-o65 (/- 1850-0). 823-41 30-03 Hgft So. 346-4 2. -9 Ma. -7 Se. 3446 De. -5 Du. -5 2n. 1015 3"- 8-54 in. •68 2n. -54 3n. -09 sn- -49 43-61 5756 8-22 69-89 517 0.2. 310. R. A. 16'' 2I'°- Dec. 38° 13' M. 7-6, IO-2 O.S. De. 221 -5 in. 3-15 -9 »» 2-88 217-5 ,, -97 224-4 ,, •96 225-7 3". 3-1S '845-35 -68 51-67 74-67 67-43 518 OX 312. R. A. ,5h 21™ Dec. 61° 47' M. 21, 81 Probable increase in the distance. O.S. Sa. Ma De. Dn. W. &S. 143-9 .sn. 4-66 142-2 4n. -86 -I 2n. -99 '45-5 ,, 5-20 141-4 in. 4-71 144-8 2n. -01 142-0 4 ■90 -4 3n. -9 -5 in. -9 1843-71 51-21 60-11 73-67 47-41 52-69 66-50 70-52 3-42 519 2. 2054. R. A. igh 22'° 2. O.S. Ma. Se. De. Dec. 61° 58' 35' -S ... 7-4 6n. 0.90 6-1 •96 6-9 sn. 1-08 1-9 3n. •01 0-7 in. -07 3-4 -06 2-0 •16 -8 0-92 -2 2n. -94 •9 I-I2 M. 5-7, 6-9 1830-24 2-22 5-76 41-44 55-63 72-61 43-53 52-33 9-40 7-74 67-85 520 a SCORPII (Antares). R. A. 16'' 22"" Dec. ■26° 10' M. 1-5. 7-7 C. Da., A, red; B, "blue," "purple," "very blue," "green." Discovered to be double by Professor O. M. Mitchell with a refractor of I if in. aperture, in 1846. Dawes could see and measure this object with his 6J-inch refractor. The proper motion of Antares is — o"-oo6 in R. A. and + o"-o34 in N. P. D., and in this the companion most probably partakes. Burg. Mit. 270 270 273-0 ion. 2-52 4n. -8 2n. 3-II 1819-28 46-59 7-50 8-59 3=8 DOUBLE STARS. Ba. Bond. Ha. Ja. Se. Em. Ho. Po. Ka. Be. •W. &I Gl. Belli. 8p. CO. 2739 2 ■6 9 3-47 270-0 5 •64 271-6 5 ■41 275-9 S -24 7 5 •67 ■3 in. -8 277-0 )) -8 272-7 > ■6 2731 , -6 272 » ■4 270-4 , ■4 276-2 80 -69 272-8 15 2-94 273-5 3n- 3-20 275-0 ,, -40 273 -s 6n. -07 ■3 4n. •25 -2 2-69 272-9 -92 270 3-5 275-8 411. ■30 271-9 2757 411. 3-37 270-4 3"- 2-99 268-7 4 3-4I ■4 10 -29 267-6 8 ■32 273 '9 in. -22 274-0 -22 2733 4 n. 2-85 1847-29 -29 8-55 •59 9-40 6443 48-28 -28 •49 ■58 •55 9-52 -68 52-63 622 7-18 5-56 6-55 7-5+ 66-17 57 '40 8-35 61-09 4 '44 5-56 73-42 -62 •63 5-81 -81 7-42 521 0.2. 311. R. A. Dec. M. 16" 22-6' 21° jo' 7-5, 10-3 The distance has diminished about 4". 0.2. I8V5 in. i3'-'57 1845-35 ■5 -55 6-37 ■5 I2-8l 52-46 189-0 10-40 68-67 i88-i „ •15 73'47 Ua. 183-5 ■4 13-94 50-45 2-61 Be. 186-6 3"- 1073 66-60 W. &S. 1S9-0 8-00 77-46 522 S. 2049. R. A. Dec. M. 16" 23" 26° 15' 6-5, 7-5 Duner gives the following formulae : 1854-84. A = l"-I2. P = 2I5°-I -o°-l8o {t- 1850-0). s. 215-6 6n. I 04 1833-08 2I6-I 3n. 03 6-54 o.s. 2200 m. 0-20 223-8 ,, 1-25 40-69 -7 2n. -03 1-52 0.1 Ha. Se. Be. Bu. Bob. 217-6 2137 21 1 -3 217-6 216-7 213-2 214-9 210-2 ^■08 -5 in. I 06 »» -36 ,, -22 3"- -00 in. -09 2n. •10 ,, •I I in. •19 4n. 0-95 1847-47 68-67 74-58 42-63 6-39 56-50 7-05 70-29 7-47 523 t. 2052. R. A. la"" 23-6"" Dec. 18° 40' M. 7-5. 7-5 The common proper motion is — o"-33 in R. A. and - o"-36 in N. P. D. Duner gives 1855-85. A = 2"-85. P = io6°-2 — 0150 (^—18500). So. H,. Ha. Be. Se. Ho. U. Eng. Bu. GL •w. &S. Sp. 109-3 -7 ■2 107-9 109-8 105-4 103-2 1042 103-1 104-8 96-2 1041 103-0 •o -3 101 -o in. 3'i- 5n. 2n. 3n- 3"- 2-66 -98 3-24 2-86 •80 3-14 2-99 -95 75 -62 75 3-16 -46 -65 ■63 •61 1822-69 9-52 3-43 30-27 42-45 54-69 65-55 56-49 68-99 58-44 6475 5-53 70-46 4-50 -60 6-31 524 S. 2055. A. OPHIUCHI. R. A. le"" 24-9" Dec. 2° 15' M. 4, 61 C. A, yellow ; B, bluish. /«7#. H, (/%;■/. Trans. 1804, p. 375) : "The position, March 9, 1783, was 14° 30', n.f. May 20, 1802, it was 20° 41'. "The differ- ence in 19 years and 72 days is 60° II'. March 9, 1 783, the distance, with 460, was MEASURES. 329 } or i diameter of the small star. May I and 2, 1802, I could not perceive the small star, though the last of the two even- ings was very fine. May 20, 1802, with 527, 1 saw it well, but with great difficulty. The object is uncommonly beautiful ; but it requires a most excellent telescope to see it well, and the focus ought to be adjusted upon f of the same constellation, so as to make that perfectly round. The appearance of the two stars is much like that of a planet with a large satellite or small com- panion, and strongly suggests the idea of a connexion between the two bodies, espe- cially as they are much insulated. The change of the angle of position might be explained by a parallactic motion of the large star ; but the obser\ations on the distance of the two stars can hardly agree with an increase of it, which would have been the consequence of that motion." Hj {Mem. H. A. Soc, vol. viii., p. 53). His measures were made in 1831, 1832, and 1833 ; his notes are " a very good and measurable elongation and notched disc," — "a distinct notch in the wedge." Da. also wedged it in these years. 2. (/I/. M., p. 6) "gives his measures from 1825 to 1834. He notes the probable error of 183° in H,'s measure in 1783 and 1802. The measure in 1783 taken as given by Hj, when compared with S's in 1834, shows an angular change of 275°'I in 5 1 "24 years. This indicates a period of revolution of about sixty-six years." Smyth {Cycle, p. 365): "My observa- tions are not indicative of the acceleration which has been spoken of by other astro- nomers." " From the shown course and velocity, it is evidently making an elliptical and rapid orbit, of which the annus magntis may be between eighty and ninety years." Subjoined are the elements obtained by Madler and Hind : — Perihelion passage ... Position at perihelion Ascending node Inclination Angle between ir and a on orbit Excentricity Semi-axis major Period Midler. Hind. 1798 1791-214 177° 50' 184° 30 23 45° -50° 49 40 135 24 0-37 0-4772 l"-l o"-847 88 yrs. 95 -88 yrs. Dr. Doberck gives the following {Ast. Nachr., No. 2126) : — a = 157° 21' \ = 94 16 7 = 44 44 e = 0-4930 P = 233-89 years T = 1803-91. 0.2. (in 1876) writes: "My father has already remarked {M. A!., p. 6) that one of the two observations of H[ appears to be gravely in error, and he has suggested that the direction in 1802 should be changed 180°. It appears to us, however, it would be quite as admissible, and more in accord- ance with the most recent observations, to suppose that in his observation of 1802 Hi was mistaken in the designation of the quadrant in which the companion was seen. In his memoir of 1804 he admits tl'.at in 1802 the companion was found b.s.q., as in 1783. If we write a.s.q. for b.s.q., we shall have for 1802-39 the angle llo°-68, and in the interval between 1802 and 1825 the companion described an arc of 220° in passing its apparent periastre at a very small distance from the principal star. The continued increase of the distance since 1825 indicates that the position of the principal star in the apparent orbit is very excentric. H,. Sm. Sa. 75-5 693 33>-8 342' I 349 "4 350-6 352-4 353-3 3568 3377 347-5 -8 351-2 352-9 356-5 1-4 15-5 349-5 354-8 358-3 359-4 -4 1-6 0-3 8-8 -9 14-0 19-5 2-7 4-4 6-3 8-1 9-3 -9 12-3 n-6 -5 17-2 -I 19-7 18-6 29-5 3"- o'83 ■81 2n. 1-04 ,, 0-98 Sn. •99 »» I 01 in. -03 4n. >) 107 3"- TX) -0 -I -0 -I -2 6n. 0-93 in. 117 3"- ■07 4n. ■13 3"- -10 2n. in. 1-09 2n. •24 7n. -26 4n. ■31 in. 6n. 0-97 2n. I 03 in. 0-98 3"- I 09 2n. ■12 >» 0-97 in. 1-30 »» -29 -21 ^_ ■28 ,, -51 ,, -30 ,, -35 ,, -61 1783-18 1802-39 25-51 8-si 31-90 4-42 5-55 6 50 7-59 1-37 2-57 3-33 4-48 6-51 9-67 42-50 53-25 3455 7-68 40-54 1-54 2-58 3-47 -41 8-47 -85 54-14 60-36 40-57 1-58 2 -60 5-63 6-69 7-67 '52-55 3-55 ■57 6-58 7-59 8-56 61-63 662 350 o.:2. Ch. Ma. Bond. Ja. Se. Se. Ho. Bo. Ta. Du. 01. 301 in. 1-43 298 2n. •48 33-9 ,, "49 52 )) 0-97 357-4 in. I -OS 2-4 ,, ■10 •8 7n. •29 1-6 5n. •II 103 4n. •17 129 „ •OS 148 in. •25 15-9 8n. •06 17-8 4n. •09 ■5 3n- •29 198 5n. •27 9-8 1-4 12-6 15 •21 152 IS •35 ■5 6n. •37 i6-8 3n. ■39 '5'3 „ i'+ •5 4n. r2 14-4 6n. •2 15-9 4n. •2 •9 Sn. ■24 i8-2 7n. •45 21-5 sn. •65 25-2 7n. •51 265 I in. SI 27-4 sn. •45 28-2 4n. •59 •6 „ ■5' •8 sn. ■57 301 4n. •64 ■5 3"- ■68 322 4n. •58 33 '9 „ •62 17-9 3n. •36 i8-2 2n. ■37 19-8 3n. ■33 15-6 2n. ■29 207 In. •16 21 2n. •10 227 ,, ... 267 31- 1-41 •7 in. •56 •3 ,, •86 25-8 3"- ■53 23-6 In. •83 26-8 »» •98 23-9 yt •34 28-3 *> •42 262 >» ■47 »» •41 32-0 ,, •49 26-3 3n. •41 ■7 7n. ■50 ■5 3n. •53 28-9 >> •45 33-0 2n. ■48 28-2 7 •6 27-9 4 •7 29-0 5 •5 30-0 4 ■5 33-5 10 •26 DOUBLE STARS. 186856 72-58 4-57 41-52 243 340 41 59 2-38 7-43 50-58 1^40 2 57 4-63 6-73 862 48-56 52-67 4-06 6-44 8-12 5-30 ■35 6-56 7-58 8-50 62-55 3 '44 5 "49 6-95 8-46 9-55 70-45 1-41 2-44 3 43 4-56 5 '44 55-58 6-59 7^51 7-58 63-57 552 6-41 70-50 1-49 3-55 4-44 5-42 6-61 67-61 846 -41 71-48 •50 68-68 9-62 70-57 1-62 5-55 0-44 1-32 •63 3-68 4-62 w. &s. 28-9 5 1-56 1872-45 30-3 8 -62 3-42 33-6 4 -31 4^62 -4 6 •54 S-52 -w.o. •7 in. ■74 4-74 36-1 ■45 6-44 33-7 -48 -45 -7 -52 •45 3i"7 •46 32-1 •64 ■53 Schi. •8 ■44 5^49 ■8 •43 658 Sob. 30-5 S'n. •44 ■50 32-3 2n. •56 7^42 33-5 ,, •59 8-47 PI. 31-2 4n. •82 653 525 O.S. 313. R. A. Dec. M. 16'' 29" 40° 21' 7^2, 7^8 Probable change. O.S. l62^I in. 0-81 1842-71 i6l-2 ,, •81 5-71 162-7 ,, ■71 7^55 1640 ,, ■89 9-71 160-8 »» •77 51-67 Ka. 155-8 4n. •8 46-30 156-7 sn. ■9 5203 Da. 159-6 in. •94 47 •41 Se. 153-8 4n. •92 66-76 Da. 152-6 ft •93 9^51 526 2. 2084. ^ HEECDLIS, R. A. 16" 36-8" Dec. 31° 49' M. 3>6-S C. A, yellowish ; B, reddish. H, : "July 21, 1782.-20° 42-. "Aug. 30, 1782. — Saw it better than ever I did. I could plainly distinguish that the small star is ash-coloured, and the large fine blue-white. " Sept. 20, 1802. — I cannot see the star double. A conjunction of the two stars may have taken place." Although looked at every evening, it wasnotseen "lengthened" or ' ' wedye-formed " till the 29th of Sep- tember. Hj {Piil. Trans. 1803, p. 378) : " My observations of this star furnish us with a phenomenon which is new in astronomy ; it is the occultation of one star by another. This phenomenon, whatever be the cause of it, will be equally remarkable, whether owing to solar parallax, proper motion, or MEASURES. 331 motion in an orbit whose plane is nearly coincident with the visual ray." H, discovered this object July 18, 1782, and measured the angle and distance. He gives his measures up to 1803, and then examines the several ways in which the phenomena may be explained, observing that ' ' the observations I have made on this star are not sufficient to direct us in the investigation of the nature of the motion by which this change is occasioned." Hj and So. (^Fhil. Trans. 1824, p. 267) : "April 27, 1821. — Decidedly single, with powers 1 33 and 303. The evening exceed- ingly favourable, and the star perfectly round and well-defined." June 19, 1822. — Fine evening. Powers 133 and 381 would not separate it. Oct. 17, 1823. — Gave the same result. South, on July 28, 1825, failed to divide the star with powers 181, 327, 413, 512. and 787 ; nor was there any truce of elon- gation. " With 787 it was exquisitely defined, and as round as possible." 2. (^M. M., p. 6). He gives his measures from 1826 to 1834. In 182871, he found the distance o"'6s and the angle 349°"5 ; but in 182876 he was "uncertain whether the point of light seen " was the companion or a spurious image. In 182877 he writes, "not double : fine air : just after sunset." Up to 1831 his remarks are "not double " — " certainlynot double," "nocomts," and so on. But in 183275 he says, "no doubt the comes is seen," and gives the distance o"-8l and the angle 220 "5. In l833'27, "no comes seen;" i833'4i, "a red point suspected in the direction 105°;" 1834 '45, "air very fine: f Librae ex- amined with altitude 20° bears 1000 : X Ophiuchi was then examined, and finely seen double ; then f Herculis was ex- amined, and the companion detected at once." Distance, o""92, o"'9o: angle, 203°-5, 202°'5. This sudden reappearance of the comes at first led him to suspect that variability was the cause of the difficulty he had so long experienced, and he was much surprised to find the companion in almost the same straight line as that in which he saw it eight years before. Great was his delight, on copying the observation into the book containing mean results, when he found that the comes was in the same line nearly, but in the opposite direction. There had been an occultation, and all the diffi- culty which had so often vexed him for eight years was completely explained. 2. says this star "offers the astounding velocity of an apparent and very elliptical orbit revolving in little more than fourteen years." Sm. (Cycle, p. 369). This observer elongated the star in 1835, but could not ' notch ' it till 1838. He prefers an orbit " with an excentricity of 0*4186 and a period of about thirty-five years." The following are the principal orbits hitherto computed : — Midler. Viilarceau. Dunir. Perihelion passage 1 829 "50 1830-481 1830-01 Node 39° 26' 214= 21' 45° 56' Perihelion from node 262 4 284 55 Inclination . . 50 53 + 136 17 34 52 Excentricity 045454 0-4482 0-4239 Semi-axis major i"-i89 I "-223 Mean annual motion -73o"4S Period 3i>"-4678 36-357 34221 The common proper motion of the sys- tem is — o''034 in R. A., and — o""45 in N. P. D. 2. 69'3 23 '4 220'5 203-5 169-9 186-2 1 75 '4 1686 160-4 159-9 I •■■ I J782-5S 5n. I 0-91 I 1826-63 single from 1828 to 1831 in. 2n. 5n. 4n. 2n. in. 4n. o-8l •91 1-09 •09 •09 •03 •16 -29 183275 4"4S 5-45 6-60 7-47 8-44 967 40 '66 Hj and So. : " Decidedly single, with powers 133 and 303," in 1821-320. "Per- fectly round with 381" in 1822-465. " No elongation with 578 on the 5-feet equa- torial " in 1823-794". " Perfectly round," with powers up to 787", in 1825-57. Sm. Encke. 0.2. 190-0 0-5 1835-68 176-3 •7 673 1690 •2 8-65 1369 •2 42-57 108-5 •0 8-59 83-8 •3 52-53 190-6 2 ■24 36-59 168-4 4 •37 8-70 170-3 2 •97 9-50 iS7"4 1-20 1? •I 5n. •24 40-66 1477 3n. ■23 I -60 146-0 •21 2-64 125-4 2n. -12 4-71 121-3 3n. •24 5-03 1 10-5 2n. ■33 6-69 II 1-3 »» -42 7-68 104-2 >) •53 8-76 98-5 ,, ■49 9-73 93-8 in. -52 50-53 88-4 5n. •47 1-62 84-1 »» '^l 2-63 79'9 4n. •48 3-59 76-8 3n- •56 4-66 70-8 4n. •44 5-62 64-7 3"- ■49 6-62 58-4 411. ■49 7-64 51-0 ,, •63 8-62 42-3 ,> -29 9-63 32-5 in. •38 6074 332 DOUBLE STARS. 0.2. Da. Ha. Ka. Ch. Kit. Fit. Ja. Se. Se. 171 341 '2 2286 204 '6 2027 1796 168-8 171-5 167-2 162-9 161 -9 1506 142-9 138-4 129-8 II2-I 107-9 102-0 99-2 86-9 80-0 69-5 45-7 235 I 229-2 225-0 149-2 141-5 ■4 130-3 104-6 98-7 91-4 848 -6 77-2 74-3 72-3 60 o 48-6 41-2 140-1 138-6 109-2 91-7 89-3 84-0 8i-> 78-0 66-2 57 -o 69-7 64-1 59-5 54-6 43-2 80 86 68-5 708 63-7 59-0 49-9 411. I 05 in. -00 2n. 0-97 in. I-I3 „ •34 ,, ■34 31. ■14 2n. -10 in. •37 4n. -40 ,, ■22 8n. -23 4n. 3"- -23 -06 •29 511. in. -62 6n. •56 3"- ■50 m. ■70 3"- 7n. •59 -66 In. -59 On. 3n- 2n. ■33 0-85 -82 ,, -98 9n. 111 3n- 4"- 0-91 •98 -91 I7n. 3»- 1-30 -08 -26 Sn. -29 -18 ,, ■23 3"- -19 5n. -33 4n. •07 7n. •20 4n. -10 •42 In. -19 ,, -og 10 48 ■4 *3 32 ■24 10 •5^ 14 •52 •60 •46 3n- 6n. •52 •41 2n. -29 -06 „ -06 in. round " " 8n. " 4n. I5n. 12 5n. 8n. •25 •0 1861-57 2-74 6-74 8-56 -61 71-52 2-60 3-50 -52 4-62 39-76 40-66 165 258 3-64 6-S9 7-53 S-6I •61 9-4S 5 1 -bo 3 40 568 9-61 66-70 -81 -99 41-44 2-40 -75 3-58 7-47 841 50-55 1-23 •88 3-39 •82 4-68 7-39 S-OD 9-39 42-55 43-01 7-71 50-54 1-51 2-64 3-15 4-06 6-25 7-86 5-53 6-53 7-59 8-48 9-52 65 54 ■54 •55 4-80 5-23 6-52 7-75 8-55 De. Mo. Du. Br. Knott. W. & S. Gl. Schi. W.O. Dob. 1-7 342-4 244-6 225-6 2106 200-9 190-8 180-7 173-8 102-4 157-0 149-0 73-1 602 221-4 213-2 203-1 193-6 iS«3-7 177-2 166-3 154-9 147-3 212-4 206-5 183-3 165-4 166-8 168-0 153-S •59-3 149-4 15 1 -2 153-S 157-3 147-2 138-1 147-1 138-0 144-0 .142-6 1290 124-9 9n. 4n. 51- 0-5 7n. -8 ,, •94 ,, 1-08 I in. -09 12n. ■27 j> -34 im. ■39 ion. •36 8n. -41 4n. ■45 3n- •60 2n. -03 5n. ■05 I In. ■05 6n. -21 12n. -iS 6n. -22 4n. •40 in. •35 12n. •27 2 •19 4n. 0-99 5n. I 02 3 -2 3 8 0-76 4 1-06 4 -I 5 5 5 0-75 8 -81 1-21 •17 in. -21 ,, ■17 ,, -29 1 " 33 1 3'>- -40 1 -28 1852-53 3-49 6-46 7-52 8-42 9-58 70-49 1-50 2-48 3-52 4-53 5-52 55-66 7-46 67-72 8-67 9-62 70-59 1-60 2-58 3-70 4-65 5-61 68-73 8-48 71-54 3-45 -46 -47 4-55 -62 5-57 -58 4-51 •63 5-55 6-54 5-55 6-54 ■45 •55 8-45 •61 I 527 X. 2094. R. A. Dec. M. ] 161" 39"" 23= 44' 7-3, 7-6, II I In A B a retrograde movement is very ! probable. A C unchanged. [831-41 41-52 61-44 43^45 56-47 7-50 9-49 77-48 ^. 82-8 0.2. 79-6 77-6 Ha. 81-7 Se. 79-9 De. 80-5 Dn. 81 -0 Dob. 80-6 A B 5.1. 1-62 3"- •71 in. -59 5n. -23 31- ;5i in. •3 4n. -26 3n- •39 A C. De. 312-6 I 24-97 61-44 MEASURES. 333 528 R. A. Dec. Id" 40'3"' 43° 42' C. white. Discovered by Baron Dembowski 1869. Rapid change in angle. M. 8, 8 Be. Sp. I3I7 0-93 117-5 •67 1 14-0 ■s i870'44 6-68 7 '44 529 2. 2097. R. A. iS' 40-5"' 2. Ha. Dec. 35° 57' Se. 89-9 86-9 85-6 84-3 3n- 2-14 ■14 1-93 2n. 2-is M. 8-5. 87 1829-63 43'36 4-35 65-54 530 0.2. 315. R. A. 16" 45-3° Dec. r 25' Slow retrograde motion. O.S. Ma. Se. Da. Se. 173-3 164-6 162 -I 2n. 4n. in. 087 ■71 I -01 175-8 168-6 0-63 -6 i6o-o 167-6 162-6 2n. 5n. elong''- 0-86 M. 6-2, 8-1 1844-49 54-46 73-47 45-51 7-35 57-50 65-60 67-38 531 R. A. le"" 45-4° X. 2106. Dec. 9° 37' C. white. M. 6-7, 8-4 Change both in angle and distance. S. Ua. 339-0 337-2 336-5 335-8 -9 331 -• Se. .328-4 Se. 321-3 0.2. 323-3 320-4 324-7 -w. *S. 310-7 316-6 311-9 329-8 GI. 310-s 2n. I -08 in. 0-86 ,, I 00 „ '25 080 -8 3n. 'I 2n. •5 in. 71 »» •70 j> -59 3 •5 I 0-6 4 -4 4 ■5 1825-52 9-53 32-52 3-45 42-42 3-55 4-35 56-45 63-53 8-50 71-50 5-48 3-45 -46 -46 5-57 4-40 532 2. 2107. R. A. Dec. M. 16" 471"' 28° 52' 6-5, 8 C. A, yellowish ; B, bluish. /es9. IB1B. ' ■ so Discovered by 2. and measured by him from 1828 to 1836 : at the latter date he wrote, "There can be no doubt about the increase in the angle." Dembowski says, "Very difficult owing to the sombre colour ofB." O.2., in 1877, says the angular move- ment has increased considerably in the last twenty-five years, and this augmentation has been accompanied by a notable dimi- nution of distance. Duner has published the following for- mulae : A cos P = - l"-04 + 0"-00475 (t- 1825-5) + o"-ooos9{/- 1852-5)^ A sin P = + o"-i2 - o"o2ooo (/ - 1852-5) - o"-oooio {t - 1852-5)^ 2. 0.2. Sa. Ua. 1486 156-4 159-2 1603 164-3 165-7 169-0 -9 170-1 172-4 170-4 175-2 174-7 1757 -3 185-5 194-0 203-4 208-9 218-7 162-0 170-0 175-7 1787 163-2 162-7 166-9 168-3 3n. f 12 1829^91 -25 36-54 >> -05 7-74 2n. •06 40-54 -08 1-54 in. 0-85 8-46 2n. •73 9^74 ,, •85 51-58 2n. -80 2^63 in. -79 357 •97 5-50 •92 6-58 2n. •93 7-63 in. •89 8-56 2n. 1-02 61 53 ,, 0-78 6-67 in. •91 8-67 ,, •75 72-58 •72 4-67 )j •72 5^48 4n. 1-26 40^95 in. •23 843 ,, o^93 54-40 ,, 112 •52 2n. -0 41-55 3n. •03 2-4D 6n. o^88 6-41 3"- •83 7-35 334 DOUBLE STARS. Ma. Ea. De. 8e. 61. W. & S. Sp. Schi. Da. 1747 I76'0 •6 1801 178-2 1 62 "9 176-8 189-7 188-9 185-7 189-5 193-8 195-8 198-2 202-0 203-6 208-0 •9 212-3 175 '4 191-2 190-0 193-8 200-3 203-0 208-4 •I 2100 207-5 208-4 216-3 215-5 207-4 ■3 212-3 3". 6n. ion. 4n. 3"- »» iin. 5n. 4n. 5n. 7n. 8n. 5n. 3n- 6n. 3". 5n- 411. 5n. 5 S 10 8 5 6 3 3 5 911. 0-88 -87 •80 •74 -86 1-27 0-93 -6 -8 1-08 0-93 -85 -78 •80 -90 -8 •77 -72 •97 -42 -6 •94 •s •5 ■78 -84 •77 •7 •7 0-84 ■84 •99 1851-20 ■77 2-6i 348 4-72 41-68 2-81 56-54 62-55 3-36 4 '47 5-50 7-11 8-48 9-55 70-46 1-59 2-44 3 '50 4-35 5-45 56-60 65-59 4-43 5-48 7055 1-70 4-63 •66 2-49 3-48 4-65 5-58 -59 -55 -55 -61 533 O.S. 317. R. A. Dec. M. 16" 49" 44° 36' 7 '2. 11-8 Considerable change in both angle and distance. O.S. in 1874 observed a third siar of the 8th magnitude. {See Measures. ) AB. O.S. 2356 in. 15-86 1845-73 -0 „ •61 7-69 232-9 ,, 52-69 226-4 ,, 16-91 74-74 A C. 0.2. 318-1 I I 13-67 4-74 534 0.1. 318. R. A. 16' 51"" Dec. 14° 18' C. A, yelloH-. Ma. 254-0 253'7 2n. in. 2-48 -49 M. 6-7. 9-3 1845-44 52-61 O.S. Se. Da. 250-9 3". 2-74 253-1 »» ■51 255-8 2n. •68 1847-74 66-22 70-96 535 t. 3107. R. A. iffi 52-5" Ka. Ma. Se. De. O.S. ■w. &s. Gl. Dec. 4" 10' II2-3 3n. 1-6 •27 162-9 92-0 104-0 in. 0-13 -4 1-32 109-0 in. -58 106-4 „ -44 104-7 ■5 102-0 -6 104-0 -4 M. 8-5, 8-5 1831-87 41-68 2-81 2-43 59-51 64-53 8-50 75-48 3-47 5-58 -70 536 0.2. 321. R. A. 16" 54" Ma. O.S. Se. De. Dec. 14° 29' 4-9 8-0 0-37 -3 1-7 4-6 3n. 2n. •51 elong^- 5-2 „ M. 7-7. 8-7 1843-29 52-61 48-82 57-59 66-45 537 X. 2118. R. A. 16" 55-8" Dec. 65° 13' M. 6-4, 6-9 The distance has diminished from o"-85 to o' -27 ; in the angle there has been but little change. H,. H,. S. Sm. Oa. 0.2. Ma. Mit. De. 245 251-5 242-6 246-1 ■4 247-0 245-0 243-7 252-0 242-9 241-6 245-3 235-7 238-0 248-4 244-6 243-3 244-6 241-0 single 5n. 3". 3". 2n. in. Se. •w. &S. Du. 240-1 I 3n. 303-2 ' 2 single 0-63 -70 •84 -70 -8 0-61 -77 -58 -27 -8 -65 0-65 -61 0-4 1781-76 3-26 1830-32 1-37 2 30 6-75 2-41 9-72 4-57 40-77 54-81 41-24 59-67 72-42 43-32 7-97 -71 -97 54-81 62 50 3-49 57-35 74-70 6-68 MEASURES. 335 538 R. A. j51i jg^jm Z 2114. Dec. 8° 37' C. white. M. 6-2, 7-4 H, in 1831 found it "extremely difficult." Da. thought it was not a binary, and noted the fact that S.'s measures differ largely inter se. A small change in angle with sensible change in distance. (0. 2.) Duner has computed the following for- mulae : i8so'9o. A = i"'25. P = i43°-9 + o°-3'25 (t-i&so-o). •37 '9 i34'5 1281 140-0 1390 H,. 1329 1340 Sm. 137-0 0.2. 145-1 ■4 150-7 156-5 «53'9 Ufa. I43'5 142-8 in. 1-51 y) -26 211. •32 in. -28 -91 0-84 I -5 4n. in. •19 •26 ft it •27 •58 )) -29 4n. 2n. ■23 -28 1825-53 9-53 31-61 2-52 3-45 1-37 2-41 ■41 41-81 2-60 61-52 8-52 75-48 42-41 52-22 Ua. Da. Hit. De. Se. Mo. Du. ■W. &I 61. Schi. Sp. Sob. 142-7 "9 148-2 «43'3 1397 147-1 1457 147-5 145-2 147'3 149-6 151-9 152-2 151-7 146-5 152-2 153-2 151-4 -5 153-3 1-25 -18 in. -10 »» •4± »i 0-83 3". 1-2 4n. -07 31. •30 ,, -25 in. •31 5". -28 9 -6 6 -39 4 0-9 4 1-33 10 -6 6 •3 in. -16 ••7 3". -10 539 % 2120. R. A. Dec. '853-35 5 -63 61-56 47-63 -57 55-52 6-49 63-39 56-84 9-30 69-79 73-46 -47 4-62 2-49 4-66 -69 5-57 -58 7-48 M. 6-4, 9-2 Magnitudes. — De. has 6-8, 9-7, and suspects variability in B. C. S., A, yellow or red ; B, fine blue. De. gives A white, B blue. /S77. A beautiful double star discovered by S. In the M. M. he gives his measures irom 1829 to 1835, and from them alone he inferred change both in distance and angle. Treating the distances by the method of least squares, he finds the formula x = 3" -445 — o'-ii2 (/■ — 1833-25). Computing the distances for the epochs of the observations, he finds the agreement between the observed and computed values all but perfect. The motion he found was retrograde. He notes the great discrepancies between the angles made in autumn and those in spring. At p. 293 he gives his measures in 1835 and 1836, and pronounces the change in angle and distance beyond doubt. O.2., in 1877, after having reduced the observations to 1850, found that the results were not well represented by uniform recti- linear motion : a term depending on the 336 DOUBLE STARS. square of the time then being introduced, he was led to the following formulae, which on the whole are satisfactory : — AA= — l"'6l9 ± o"-0203 — (o"'II22 ± o" -00130) {(—iSs^'o) + (0""0OO42 — o"-oooo35) (^— i85o'o)-. A D = + i""647 ± o"'oi95 — (o"'ioi8 ±0" '00125) ('— 1850-0)4- (o"'ooio 4- o" '000033 (' ~ 1850-0)^ Duner has made a special investigation of the movement of this star (see Ofversigt af Svenska Vetenskaps-Akademiens Forhatid- lingar, 1 873). A similar special treatment by 0.2. is found in vol. v. of the Melanges Mathemaiiques et Astronomiques de St. Petersbourg. The former astronomer found the following two systems of equations : A cos P = + :" -7493 - o" -10298 (t - 1 850-0) ; A sin P= — i"-4902—o"- 10662 (/—1 853-0). A cos P = + i"-7827 — o"-i0242 (/ — 1850-0) — o" -000200 {t — 1850-0)-; A sin P i"-5252 — o"-l0724 (t — 1850-0) -f o" -000209 {t — 1850-0)-. In this investigation all observations (except those by O.S.) from 1828 to 1S72 were employed. According to the first formula the motion is rectilinear and uniform ; the second re- presents a curve of which the centres of curvature are on the same side of the principal star. An extract from Du.'s table showing the results of his latest formula compared with the observed angles and distances is sub- joined. 1783-20 1 1" -88 42° -2 4- 1 "-68 4-8°-9 H,. 1837-00 3 -06 359-8 4-0 -01 + 3 -o S. •847-57 2 -19 324 -6 -0 -13 -3 ;• O.S. 1851-97 2 19 306 -9 —0 -oy ,, 1857-60 292 7 4-0-8 De. 186509 2-98 272 -9 —0 12 -0 -2 ,, I87I-IO 3 -73 263 -5 —0 -04 4-0 -8 Gl. •87353 3 -88 261 -0 -0 -18 4-0-2 W. &S. •874'34 4 -03 258 -8 -0 -13 -0-5 Gl. •99 4 -21 258 -1 — -04 -° -5 De. •875-53 4 -37 259 -1 -fo -07 4-1-0 Du. On the whole, Du. is inclined to think that the movement is rectilinear and uni- form, and that therefore the observation of H] is erroneous. A physical relation is, however, possible, but more good measures must be obtained before the question can be decided. 1783-20 1829 60 32-52 3-47 4-67 5-38 6-55 5-65 0.2. 345-8 2n. 2-83 41 12 7-57 50-00 1-97 5-10 7-12 61-63 7-70 73-66 Ma. 3470 3n. 2-8 41-44 2-49 3-57 4-38 5-42 7-15 42-0 in. 11-88 1 1 -4 2n. 3-83 8-2 in. -54 2-5 4n. •45 4-9 2n. -25 358-4 ,, -18 o-i 4n. •10 • ■9 3"- •20 345-8 2n. 2-83 324-6 31- -•9 314-5 ,, -25 306-8 ,, -19 206-5 2 -29 290-7 2 -49 281-5 1 •97 269-2 2 3-48 260-7 2 4-21 347-0 3"- 2-8 345-9 5n. -76 342-2 58n. -62 339-4 6n. -52 336-0 I5n. -y2 328-9 27n. -46 Ua. Ka. De. Ho. Se. Eng. So. Ta. 315-0 6n. 237 32!'3 42n. •35 288-1 im. ■37 283-9 I5n. -88 Sn. -56 342-8 7n. 297-8 31- 2-85 294-0 2n. •6 289-2 5n. -5 278-4 4n. 3-03 275-9 6n. 2-99 274-0 4n. •87 272-1 6n. 3-05 269-2 9n. -26 265-7 4n. •45 •7 3"- -5^ 264-0 4n. -79 262-5 ,, 75 261-2 ,, -96 259-8 ,, 4-08 258-8 ,, •16 257 -5 »t •26 398-1 2n. 2-58 290-4 3". •49 269-8 »» 3-60 272-9 -56 268-7 31- ■4^ 270-6 272-9 2n. 3-56 273-0 ,, -58 270-4 In. 2-97 1851-09 3 00 8-28 60-97 42-55 2-93 55-51 6-34 8-47 62-51 3-39 4-48 5-49 7-16 8-45 9-55 70-45 •-44 2-42 3-50 4-52 5-45 55-62 6-76 65-59 •40 ■36 6-41 841 7151 MEASURES. 337 Ta. Gl. Bu. Ea. Schi. Sp. w.o. Dob. PI. Fl. 255-9 258-3 259-9 257-6 261 '2 258-9 253-4 264-0 263-2 •4 259-2 258-6 •5 265-1 259-1 263-3 262-9 261-7 258-5 257-9 ■9 255-9 257-2 256-7 257-3 258-1 256-5 -5 in. 3-89 2n. ■13 111. •38 6n. 4-05 3-8o 7 5 S 4-25 3-8 ■6 -8 4 4-1 10 -0 10 -0 31- 3-64 711. 3n. 4 6 4-49 3-86 •78 -65 4 in. 4-2 -16 -16 in. •66 »» -55 -58 3n- -19 4n. •30 5n. ■39 in. -32 1873-55 4-48 5-42 6-6i 0-38 -41 4-47 o-6o I -21 •50 3-6S 4-66 -69 1-14 5 -53 '■5' 2-48 3-50 4-62 5-54 -54 6-45 -53 ■54 -51 •S3 •65 7-64 541 t. 2130. R. A. 17" 2-9™ SBACONIS. Dec. 54° 38' C. white. 540 OX 323. R. A. Dec. M. 17" i-6'» 47° 8' 7-4. IO-5 Change in angle and distance. 0.2. 112-3 In. 6-98 1845-73 III-4 „ -73 6-69 112-8 „ 7-o8 9-71 108-6 6-85 51-61 Ma. 284-9 5-50 45-71 281-6 -50 9-40 278-4 ■5 52-69 De. 103-4 i m. 7-52 66-88 M. 5. 5-1 Discovered by H, October 19, 1779. H, (Phil. Trans. 1804, p. 364) : " The change in the relative situation of the two stars of this double star is pretty consider- able." "The two stars being nearly of an equal magnitude, we can have no inducement to suppose them to be at very different dis- tances from us. This makes it not probable that the difference of their parallactic motion should be the cause of the change in the angle of position ; otherwise, the direction of that motion would be sufficiently favour- able." (Hj and So., Fhii. Trans. 1824, p. 271.) Hj finds that their recent measures confirm the motion announced by H„ the average amount per annum being— o°-5792. "There can be little doubt of its being a binary system — a miniature of a Gemi- norum." Having the measures made by So. in 1825 before him, Hj finds the change in 4-55 years has been — o°-44 instead of — 2° 36' ' ' which a computation founded on a mean motion of — 0^-5792 per annum would give." He thinks that the position for 1820 is not very reliable. (Phil. Trans. 1826.) 2. (AJ. M., p. 51.) His own measures from 1826 to 1835 show that " the dis- tance has diminished steadily." But his observations in 1836 " do not favour the opinion before expressed as to decrease of distance." Smyth {Cycle, p. 380): "A geometrical rough-cast of the whole [of the observations] yields a period of about 600 years for the orbital revolution ; since the velocity has appeared to decrease to — q° -3 per annum, and then to accelerate to — 0-7, during this small S.W. portion of its orbit." Certain change in both angle and dis- tance. The diminution in the distance will probably soon be followed by a much more rapid angular change : hitherto the angular change has been very uniform. (0.2.) Dr. Doberck has the following formulae for this star : — A = 3"-44 — o"-oi9 (/ — 1830-0). P = 205°-32 — o°-6274 (/— 1830-0) — o°-ooiS32 (J — 1830-0)^ " The latter formula represents very nearly the five positions on which it is based," and the comparison with the measures is very satisfactory. The proper motion of /i is — o"-i2 in R. A., and — o"-07 in N. P. D. Hj.. 23-2 219-5 221-0 215-9 Hg & 80. 208-4 -9 2. 2io'8 207-2 ■8 209-2 204-4 203 -6 -Q 202-8 in. 4-35 i> 6 3-90 35 4-33 m. 3-61 )» -15 »» -25 2n. -20 in. •24 3"- -23 4n. -35 1781-73 1802-17 4-09 •10 21-38 5-52 I 80 689 8-7-, 9-94 32-43 3-37 5-39 6-78 22 338 DOUBLE STARS. 8m. 2067 2003 191-6 1907 0.2. 199-5 196-1 191-1 182-0 18. -5 177-9 176-2 G.O. 199-2 Sa. 198-4 1993 1797 Ka. 1971 195-9 Hit. 190-9 ri. •I Mi. 188-0 Se. -2 -I 187-3 182-7 •2 181-3 178-3 176-3 175-1 173-8 172-7 171-8 Ho. 188-4 Ee. -4 181 -0 U. 355-S 173-2 177-8 Bo. Ta. 175-1 177-8 176-2 180-6 Da. 179-6 176-8 172-5 W. &S. 177-5 Gl. Sob. 174-0 -4 173-7 172-3 171-8 -9 172-2 -6 •4 171-0 •o 3n- in. ty 2n. in. 26 In. 28 48 5n. 6n. 4n. 2n. 3n- I2n. In. 2n. in. 2n. 30 4n. 31- m. 2n. in. 3"- in. 3n- 8n. 2n. 4 8 4 4 4 4 6 9 7 3 4n. 2n. 3-6 -3 -o •o 3-20 -06 2-82 -75 70 •66 •50 3-13 2-98 -95 ■66 3-17 -06 2-90 309 2-97 2-89 3-13 2-92 -73 •56 -59 -49 -49 -49 -51 -39 -49 ■93 -75 ■72 ■84 •91 -81 -82 3-03 .00 ■26 2 -62 ■-69 -65 -62 2-44 -7 -5 •8 •85 -64 -53 -9 -9 -9 -68 -49 1830-79 9-53 47-51 54-48 40-83 2-73 51-74 61-47 6-73 72-42 4-73 40-59 1-65 3-88 66-75 43-36 5-47 7-63 51-75 2-25 3-71 4-71 6-63 62-80 3-39 4-76 9-60 71-56 2-52 3-67 4-59 5-75 54-68 7-51 65-99 2-41 7-37 9-76 72-49 65-72 6-40 8-51 71-51 5-52 68-36 71-80 5-65 1-56 2-50 ■78 3-50 4 62 5-57 6-58 4-66 -69 -70 6-54 7-64 542 OX 324. R. A. 17" 3"° Dec. 31° 23' . A, yellow. M. 6-3, I0-! O.S. Se. 221-4 m. 3-79 219-8 j» -99 212-8 •» 4-03 217-7 >» 3-73 219-9 3"- -98 1845-47 6-69 53-40 68-61 7-12 543 2. 2135. R. A. Dec. M. 17" 7" 21° 22' 7-1, 8-4 C. A, yellowish ; B, bluish. Duner gives the formulae 1852-51. A = 6"-78. P = i68°-9 + o''-i33 {i - 1850-0). 2. 166-1 4n. 6-70 1829-45 Ha. 167-2 3n. •60 43-12 168-9 I"- -82 50-69 Ho. 171-1 2n. -95 5-61 Se. 170-5 I „ •86 6-98 169-5 ' If- 7-03 6538 Du. 1711 5n. 6-79 71-34 544 36 OPHiucHi. R. A. 17' 8" Dea -26° 25' M. A 4j, B 6}, c 7j C. A, ruddy ; B, pale yellow (Sm.) It is probable that one of the two brighter stars is variable in its light. Ho and So. [P/iil. Trans. 1824, p. 272). Measures in 1822 and 1823 are given. On the loth April, 1823, "the measure of a distant small star of the loth magnitude was 19° 5' n.p., and 3' o""735," and this "will ser\'e to verify the proper motion of A (36). which has been supposed in some way connected with the star 30 Scorpii, though at a great distance (12') from it, by reason of an observation of Bessel, that they have a common proper motion." In 1825, however, more measures were made, and the distance of C from B as given above was found "decidedly wrong." Then follow many measures con- necting A with 30 Scorpii ; a diagram is given, and the proper motions and their effects examined at great length ; and he shows that 36 Ophiuchi and 30 Scorpii are "journeying together through space. Smyth (Cycle, p. 381): "Mayer made the two stars to be exactly on the same meridian [in 1780], with a difference of declination = 13": this accidental statement was the cause of considerable error ; " for this position, combined with those of Hj and So., seemed to indicate direct motion. Smyth's measures, however, " show a motion exactly contrary," and an obser- vation made at his request by the Astro- nomer Royal in 1843 confirms this. Sm. MEASURES. 339 gives the following measures of a small sta in the neighbourhood of B : — AC289°-9, i93"'8. This small star is double having "a most minute comes near the s.f. vertical." (Sm.) The proper motion of A is — o'"029 in R. A., and + i"-20 in N. P. D. Bessel first pointed out the fact that a com- mon proper motion animates 36 Ophiuchi and 30 Scorpii (see his Fundanunta Astro- nomuc). The differences between these stars observed since Flamsteed's time are as follows according to Flammarion : — Diff. in R. A. Diff. in Dec. Observer. 1690+ 13' 32' •4 + 2' 56" -0 Flamsteed. I7SS + 3 2 7 Bradley. 1756 + 13 13 •I T. Mayer. 1800+13 7 •0 + 3 4 "2 Piazti. 1831 + 13 II ■4 + 3 3 -6 Smyth. 1839+ 13 10 •6 + 3 4 '4 J) i860 +137 •8 + 3 6 -05 Greenwich. 1864+13 7 •0 + 3 7 "24 )) The proper motions of A, B and 30 are respectively - o'-029 in R. A., and + i' - o -043 + I - o -042 + I •2oinN. P.D. ■OS •17 Several small stars * are seen in the neighbourhood of this remarkable system : C, of the loth magnitude, distant about 200" from A ; D of the loth magnitude, and E of the 12th. From the investigations of Flammarion it appears probable that C and D are fixed, and that E partakes of the common proper motion of the system. A B. E^&So 227-3 12 5-5° 1822-52 228-5 15 ■2 4-86 Sm. 226-1 •2 31-57 221-4 -0 5-33 219-5 ■3 9-28 216-6 4-9 42-46 213-8 -6 57-30 Da. 219-3 -78 4' -59 Airy. 213-3 in. 5-32 3-52 Ja. 2161 4-66 6-21 214-9 -49 50-62 ■4 10 -23 4-07 Hit. 215-8 in. -27 47-62 Bond. -5 ,, -34 8-55 Ho. 213-0 20 -45 54-69 ■3 24 -40 8-42 Se. 212-9 2n. -59 658 21 1 -3 in. -25 7-56 208-6 -2 66-72 Po. 210-0 -62 I 06 De. 212-4 •22 2-40 * Challis in 1839 detected four small stars, in addition to those seen by Sm. u. 218-8 in. 4-2 1862-43 209-0 ii •41 8-49 208-2 i« •69 9-51 206 j> •21 72-49 209-1 ,, 3-93 3-73 ■w.o. 205-8 7 4-99 63 202-2 in. ■47 76-55 Ta. 210-6 5-00 1-51 W. AS. 204-2 4 4-6 2-51 ■5 4 ■52 -I 2 ■53 Schi. 203-5 In. 4-25 5-58 Sp. -6 •25 •58 CO. 204-3 2n. 5-17 6-54 Dob. 2001 in. 3-98 7-44 FI. 204-1 ,, 4-28 -SO PI. 203-3 3"- A C. -16 6-57 Sm. 289-9 193-8 31-57 la. 298-3 4 180-0 54-07 B C. Ja. 296-8 54-07 545 2. 2140. R. A. 17" g-i" a HEBCUIIS. Dec. 14° 32' M. 3. 6-1 Hi: "Aug. 29, 1779. Double. On May 2, 1 78 1, Dr. Maskelyne very politely offered to show me a double star which he men- tioned having discovered about four years ago." This was o Herculis. ' ' Not the slightest change of relative position since 1779." (0.2.) Duner's formulae are 1851-83. A = 4" -58. P = ii8°-o - o°-o8o (/ - 1850-0). 1782-69 1803-40 21-74 9-63 35-74 092 48-52 32-51 40-73 1-62 2 -60 5-65 51-91 2-67 3-57 8-59 61-63 5-72 H,. 117-2 121-9 H2&S0. 119-5 s. 118-4 119-4 Be. 118-5 Sa. 1 19-7 118-5 Sm. 119-4 O.S. •6 121-2 118-0 117-6 1180 116-9 117-3 1 16-8 1 18-0 ■0 in. 5 -04 yj 3". -26 I2n. 4-64 I3n. -63 6n. •99 4n. -90 3n- •65 •6 3"- ■76 2n. •77 in. -69 -68 •69 •62 •59 -70 •69 •68 340 DOUBLE STARS. Ma. II8-8 un. : 4-42 1842-67 117-5 2n. ■82 6-97 ■9 ,, •51 5265 1 166 I4n. •44 6-67 117-3 I In. ■57 61-71 Hi. 119-8 2n. •69 45-69 Hit. 117-6 in. ■93 7-6i Po. 118-0 2n. -68 6-66 Uo. 116-6 in. -92 52-62 118-1 3"- •57 7-62 Ja. 117-9 36 •51 3-30 7 70 •56 7-00 Se. 118-2 5n. -62 3-63 Se. 117-7 6n. 74 6-32 Eng. •9 in. -86 64-52 Ea. 115-4 7n. -64 5-69 Du. 7 5n. •44 907 W. &S. ■3 3n- •68 72-86 Gl. •6 -60 4-68 Dob. •2 4n. -76 6-54 546 2. 3127. s HEBC1TLIS. R. A Dec. M. I?"" lO jtn 24° 5 9' 3. 8-1 C. 2., A, green; B, ashy white. De., A, dear yellow ; B, blue. Hjand So. [Phil. Trans. 1824, p. 276): "There can be no doubt of a material change both in position and distance having taken place in this star ■ + 9° 42' in the one, and —5" -349 in the other, are quantities too large to leave any room for doubt. The proper motion of S, if correctly stated in Piazzi's catalogue, should have carried it in forty year-s, — 8" in R. A. and — 5" 6 in declination, in the direction s.p., at an angle of 37° with the parallel. Had the small star then remained at rest, the angle of position, instead of 82°, would now have been only 54° s.f., and the distance 32" -3." So. {Phil. Trans. 1826, p. 364). After recording the measures made by So. in 1825, Hj says, "The change stated to have taken place in this star is confirmed by the present observations ; according to which, compared with those of 1821, a motion of + 1° 23' in angle and — 2" -175 in distance has taken place since our former measures. This is a. remarkable verifica- tion of the relative motion both in position and distance ; and as the change is contrary to what the presumed proper motion of the large star would alone produce, this star merits particular attention. " S. (A/. M., p. 195). He gives his own measures from 1829 to 1835, and adds, " A notable decrease of distance, conjoined with a small increase of angle, is shown by these measures." He finds that the distances computed from the formulae 25" -422 — 0-1766 (^—1833-49) agree well with the observations. Sm. {Cycle, p. 387): "My last epoch [1839-62] was under the very best atmo- spheric and instrumental circumstances ; and on the whole I am led to infer that if all the series could be depended on, B had lately passed its apastron in the S.E. portion of its orbit, and that it is slackening its march as it recedes from the extremity of the ellipse, now barely moving a degree in ten years." 0.2. finds that the following formulae represent the observations quite well, and hence that there has been no deviation from uniform rectilinear motion : — AA = + i"-233 ± o"-o27 - (o"-o833 ± o"-oo2o) {t— 1850-0). AD = - 22"-539 ± o"-oi6 -t- (o"-i6i8 ± o"-ooii) {t— 1850-0). Assuming that the relative change is entirely due to difference of proper motion, the minimum distance, 9"-2, will be attained in 1963. If, on the contrary, the stars form a binary system, the distance will continue to diminish for a shorter period. The proper motion of J is — o"-io in R. A., and -|-o"-i2 in N. P. D. Duner gives A cos P = —22" -65 -I- o"-i6o5 {t- A sin P = -I- 1 -29—0 -0808 (/- H,. 162-5 , H, & So. 172-2 8 173-5 28 2. 2n. 1737 In. 174-1 3" ■Q 2n. ■2 5n, ■8 •3 i73'9 3n- Sm. " 174-9 1751 O.S. 177-4 in. 175-2 2n -8 in -7 ,, 176-0 ,, 177-7 ,, -5 ,, -2 ,, 178-3 ,, 179-2 3" 180-7 in 183-0 »> 182-5 2n 34-69 33-75 34-22 2886 26 -69 27-84 2611 25-63 -37 24-98 ■88 -58 26-0 24-7 -5 -06 -27 23-95 -40 -23 22-49 21-98 -73 -12 ■71 1928 18-52 -61 1850-0). ■1850-0). 1779-76 80-53 1-80 1821-36 5 -50 1-85 9-77 31-67 2-78 5-62 6-58 7-74 0-71 7-49 9-62 40-83 i-6i 2-60 5-68 6-71 9-73 53-83 5-64 8-56 61-48 8-67 74-58 5-48 MEASURES. 341 Ma. Ka. Ja. Se. 175-1 177-1 176-9 178-1 180-8 I74-9 175-9 177-0 -6 -2 •I 178-2 •5 1760 178-6 -o 1777 178-6 J 79 4 -2 •6 180 -I •9 •9 181 '4 •5 ■4 •6 Eng. Kn. Sn. W. &S. Gl. Dob. n. in. in. 6n. 7n. 10 18 4n. 2n. in. 3n- in. 3"- 4n. 5n. 8n. 7n. 4n. 'l 31- 5"- I78-I 3n. in. 181 -o 179-9 .6 2n. 180-2 3"- „ 9 181 -2 4n. 6 180-I 7 181-2 4 •5 10 ■7 3 -I in. -0 ,_ •6 2n. -6 in. 24-17 23"Z4 22-03 2' '33 20-98 23-89 -42 22-31 21-99 -86 ■55 -28 ■97 ■79 ■64 •7J -08 -18 20-55 -46 -18 J9-9S -68 -48 •38 ■II •33 18-82 ■67 •59 21-63 20 -02 -07 ■34 ■19 19-33 •17 20 -o 19-3 -2 ■3 18-8 19-0 ■3 18-43 547 Z 2145. R. A. 11-8" 17' 2. Ma. Dec. 26° 43' 1841-53 7'3z 54-69 8-6i 62-74 41-67 3-97 5273 3-15 4-08 6-22 7 '94 479 5-22 -80 6-47 7-54 8-39 62-75 3-43 5-48 6-94 8-49 9'54 70-45 1-49 2-49 3-50 4-54 5-54 57-22 62-38 74 '44 64-42 6-74 71-60 0-80 1-48 2-48 •52 ■53 350 -68 5-60 6-62 7-00 Se. W. Fl. &S. 174-4 in. 1770 3"- -2 176-9 178-0 176-8 178-8 4n. -2 -8 in. I79-I )» 9-72 •87 io-6i •74 11-29 -26 -12 1 1 32 12-93 •64 M. 8,9-5 1829-68 : 32-30 43-65 , 5-'7 i 5' -69 I 2-33 478 I 8-72 I 63-41 ' 76-47 7-45 548 1. 2153. R. A. Dec. M. 17" 14-8™ 49° 26' 8-6, 9-1 C. yellowish. Dun^r's formulae are 1847-98. A = i"-90. P = 276°-7 - o°-2i4 {t - 1850-0). S. 282°3 2n. 1-67 1828-74 280-2 In. 2-22 3293 282-0 ,, 1-98 4-91 Ma. 277-3 2n. 2-06 4370 275-0 in. -18 5-60 •2 2n. 51-74 -2 in. I -91 4-78 Se. 276-5 2n. •59 8-89 270-0 in. •96 6684 De. 271 -I 3". ■92 •48 Du. 274-0 >> -85 71-20 549 X. 2161. R. A. 17'- 19-5" HUBCULIS. Dec. 37° 15' M. 4, 5 I C. both white (H,). A, greenish white ; B, greenish (S.) This was one of the double stars known to Mayer and other astronomers before H, began his survey. Piazzi enters it "Double, the smaller precedes." It was first examined by H„ Aug. 29, '779- Hj and So. (/%//. Trans. 1824, p. 277). Measures from 1871 to 1822 are given. "It seems extremely probable that this elegant double star has undergone a sensible alteration in its position. The distance has increased materially." Sm. {Oyck, p. 390). All the observa- tions subsequent to 1824 " tend to prove its fixity." Da. {Mem. R.A. S., vol. xxxv., p. 399). H,'s distance in 1 781 is probably much too small, and that of H^ and So. considerably too large, "as is frequently the case." He thinks that the binary character of the star is doubtful. Duner gives 1853-02. A = 3"-8o. P = 3O9°-4 + 0°-ii4 (/- 1850-0). H,. 300-3 301-2 Hj & So. 307 o 2-96 4-46 1781-79 180217 21-38 342 DOUBLE STARS. 2. Da. 306-2 '6 308-0 ■4 in. »» 2n. 368 -60 -56 -86 1876-89 8-71 32-89 0-63 ■W. &S. 3ii°3 ■9 •6 -2 4 3 4 6 4-28 -48 3-96 4-04 1871-52 -S3 2-51 -52 ■9 3 -77 40-83 3127 4 -'7 -52 ■3 5 -85 7-48 311-7 10 3-46 3097 S -75 8-51 -9 4 3-8 -63 308-9 5 -78 53-76 312-6 II -85 6-48 Sm. •7 ■5 3"- -86 ■6 9-72 31-60 Gl. -0 PI. 310-8 9 4n. 4-00 371 4-70 6-52 ■9 -7 9-74 Schi. 312-6 in. -65 5-54 309-1 -8 47-61 Sp. -6 •66 -54 310-5 •5 53-79 Bob. 31 1 -2 dn. .87 6-54 O.S. 3099 in. •77 39-88 ' 310-1 2n. -83 40-83 1-62 3117 ■82 310-1 in. -62 2-73 550 2. 2165. -0 ,, -62 S-6S 311-0 ,, ■75 51-67 281 (B) RERUULIS. 3io"4 ,, -66 9-62 309-8 3n- -70 61-52 R. A. Dec. M. Ma. 3io'5 3097 " -87 41-44 238 lyh 21 -e" 29° 34' 7, 8-S 310-4 2n. 3-72 3 '49 A gradual increase in distance ; motion 309-2 in. ■79 4-43 rectilinear hitherto. -6 5n. -65 5-36 Duner has 310-2 -74 6-si A = 6"-9i + o"-oi25 (;■— I 550-0). ■4 -74 7-67 P = 48°-7 + o='-i82 {t - 185 0-0). ■5 4n. -68 8-45 311-1 3"- -62 52-13 2. 45-6 in. 6-94 1829-68 310-3 7-39 •5 2n. -64 32-78 •3 ion. 3-63 60-88 46-2 in. -62 3-43 Ja. ■6 4-05 41-46 Ha. -4 J, -75 40-61 309-0 20 3-72 52-78 47-4 >f -81 2-72 Hq. •2 36 -87 45-51 48-7 -68 3-41 307-0 30 -78 6-55 46-9 6n. -80 5-42 3097 60 -84 55-65 484 1» ■8c 51-94 Po. D.O. 307-9 7n. -81 46-09 47-3 4n. 7-09 975 •I 4-14 -48 Mo. 49-6 12 -0 7-48 Oe. 309-9 5n. 3-50 53-66 Se. 50-0 4n. •20 -62 •3 in. *" S-13 De. 51-2 6n. -10 64-57 ■I i> 3-91 . '77 Du. 52-9 4n. -19 72-23 Hit. •s -61 62-30 ■w. &S. 51-5 in. •7 3-50 -4 in. 4-91 4771 537 II -6 4-63 Se. Br. H. •7 2n. 3-83 56-60 52-5 »» -42 5-57 ■9 2 V 68-59 »» -54 6-58 ■I in. -61 2-37 Gl. 53-5 3"- -68 4-71 310-4 >> 4-02 8-46 Fl. -8 in. -71 7-77 305-7 306-6 31 1 -2 » 3-23 -97 9-61 -76 70-38 Dob. 50-7 4n. -59 -54 >t -90 308-9 31 1 -2 It -93 •74 -78 1-37 551 X. 2171. 309-9 2n. ■79 2-49 •0 »* •93 3-72 R. A. Dec. M. 312-9 In. ■94 4-70 17" 22-6" -9° 54' 7-5. 7-6 31I-2 2n. 4-05 5-73 Eng. •s 4n. 3-81 65-51 2. 75-6 4n. I 61 1830-53 Ta. ... in. -81 6-32 0.2. 71-9 in. -68 41-55 306-6 ,, •85 -46 Ma. 72-1 •59 37-35 308-2 „ 4-01 8-54 737 m. 4241 Ka. 31 ID 3-67 6-68 70-1 „ '54 342 On. 310-6 2n. -66 7-71 65-0 2n. -55 5 43 3" -9 „ ■69 8-66 Mit. 68-1 in. -41 8-58 313-3 in. -85 71-72 Se. 70-0 2n. -52 56-47 MEASURES. 343 652 t. 2173. 221 (B) OPHIUCHI. R. A. Dec. - o' 58' Magnitudes.— %■&, 6-i. 0.2. suspects a variability in the light of these stars, and De.'s observations confirm it. C. yellow. Discovered by 2., and often measured by him without artificial light. He mea- sured it easily in 1829 and 1832, but in 1836 with the finest sky it was single. ' ' We have therefore a new example of occultation or very close conjunction, such as y Coronae, and u Leonis, and others have presented. This star is worthy of the most careful attention." Da., who regarded this object as a binary, could just discern a slight elongation in 1840. From that time he found that the distance increased. Owing to the equality in magnitude of the two stars, and to a probable variability in one, it is difficult to determine whether the occultations in 1836 and 1864 embrace a revolution or merely represent two peri- astron passages, the smaller star having been alternately on the N. and S. side of the principal star. If the companion has already been on the N. side, the period is about 28 years. The measures of 1874, however, seem to favour the hypothesis that the period is about 46 years. The two passages through the apparent periastre thus divide the elongated orbit into two branches, one of which is passed over in about 28 years, and the other in 18 years. The distance has diminished since 1872, and 1875 "65 gives a relation between the stars, the sign of the direction being changed, identical with that of 1829. (0.2.) ^ Duner has computed the foUowmg elements : — T = 1874-35 u = i°-84 a = 152 "56 i = 80 -01 e = 00839 M = - 7°-630 a = i"-05i. Not satisfied with these, and the small excentricity of the true orbit rendering the graphical method uncertain, Duner, with the aid of the method of least squares, has sought the general equation of the second degree which best represents the rectilinear coordinates deduced from the normal places: he finds the following : — - 29-8609 j;» - 8-7106^ - 29-8333 jt^* + 0-0622 X + o-3363>' + I -0000 = o. This equation gives the elements w, S3, i, e, a of the orbit : ^ and T are found by another method. The results are— T = 1872-91 u = 7° -26 a = 152 -65 (Equ. 1850-0) ' = 80 -53 e =0-1349 M 7° '9248 a = i"-0O9 P =45 '43 years. With these elements the observations are compared, and the following extract will exhibit the resulting errors : — 1829-57 o"-62 327° -2 -o"-23 -,"■0 2. 31-68 -68 318 -6 —0 05 -7 '3 ,, 4064 ■55 35s '7 +0 -13 +0 -8 O.S. 51 60 I -07 33° 7 —0 -07 -I 7 ,, 61-63 -51 315 -2 +0 -09 +4 -7 ,. 67-79 -6s 174 -5 +0 "17 +6 -3 Du. 7°'3S -Ss 336 -5 +0 -12 -2 -5 GI. 74 57 -ss 151 -3 +0 '01 -t-o -3 „ 74 59 -90 33' '7 + -04 +0 -4 w. &s. 76-63 •72 148 -6 —0 -04 + 1 -6 Du. To aid those observers who wish to watch the star through its next minimum, Duner supplies the following short ephemeris: — 1876-43 o"-78 i47°-4 8-43 -62 142 -I 1880-43 ■40 131 -8 2-43 -20 97 -I 4 '43 ■25 21 -8 6-43 •46 353 -I 8-43 ■68 344-8 1890-43 •87 340 -4 Da. 327-2 321-6 318-6 324-4 single 167-0 ■4 163-3 161 -2 159-4 2n. 0-62 in. ■11 ,, -67 3"- in. 0-5 2n. -71 3"- 6n. •75 -9 in. no 1829-56 30-86 1-68 2-52 6-69 40-47 1-64 2-67 3-54 8-45 344 DOUBLE STARS. 0.2. Ha. Ka. Hit. Se. Se. Ho. Su. Gl. 355-S 3n- 352'2 ,, 3447 2n. 339-8 in. 334 2n. 338 -s J, 335-6 »» 331-5 m. 333-0 »» 149-2 II 151-3 II 146-6 II 326-0 11 325-7 2n. -7 m. 323-4 2n. 315-2 in. 190-8 II 3557 2n. 164-5 In. 159-7 2n. 157-0 II 334-9 3"- 3293 2n. 172-4 6n. 3"- 168-2 8n. 165-0 3n- 162-9 9n. 159-4 5n. ■2 2n. '54:| 4n. 150-5 .3n- 148-3 2n. 174-9 5n. 165-2 ion. 2n. 160-4 in. 3300 5n. 0-61 •67 -75 ■72 •83 •93 •73 1-07 -08 0-82 I -21 0-90 ■85 I 00 0-81 -65 •48 •53 -44 •58 ■68 1-02 0-81 •77 ■55 -70 -76 •80 -89 I 07 •16 -26 •37 0-88 i6i-i 2n. 157-2 5n. -0 6n. 155-0 4n. 152-3 5n. 150-8 4n. •0 II 147-5 II 145-9 2n. in. 160-0 174-5 in. 161-3 3n- 169-1 6n. «59-7 4n. 156-5 6n. 152-6 in. 148-7 5"- -6 4n. 336-2 5 •7 4 330-9 10 331-7 7 [840-64 I -61 2-60 4-71 5-63 6-69 7-70 51-60 2-66 3-57 4-63 5-66 6-58 7-67 8-71 9-64 61-63 5-72 6-62 7-47 8-53 71-51 2-58 4-62 41-35 2-50 3-48 4-35 5-47 6-46 7-47 51-32 224 4-66 8-62 42-46 3-65 0-68 71 1-23 8^58 -0 56^51 64 5 0-5 860 ■.58 9-57 -82 70-44 -99 1-44 -89 2-54 •78 3-50 -91 4-46 •74 5-53 ■84 .S8-.S6 -25 ■61 •6 64-45 ■(", 7-79 •65 8-66 ■66 9-63 77 70-67 •84 1-64 1-06 3-67 0-87 5-67 -72 6-63 -9 0-24 -8 •46 •7 4-51 ■99 •63 W. AS. ■w.o. ScU. Sp. Sob. CO. 334-1 -o 331-6 330-9 327-8 -2 330-4 148-3 152-6 146-3 146-5 143-8 146-5 143-8 331-4 333-4 322-5 141-6 7 9 6 4 7 in. 3n- in. 2n. 1-10 0-91 -90 i-o •07 -10 0-66 ■90 -76 -82 •83 -83 -83 0-66 •52 •55 553 OX 331. R. A. Dec. jyh 26"" '.° 55' Probable change in angle. 0.2. Be. 554 X. 2185. R. A. 17'' 29°" 2. Ha. 5-3 •I Dec. 6° 6' 2n. ' in. 555 X. 2190. R. A. 17" 30-9" 2. H,. Ha. Se. Kn. ■w. &S. Dec. 21=4' 33-2 2n. 10-17 18-4 10 33-6 in. ■16 28-0 -18 23-3 4n. 9-63 24-9 in. 10-58 J873-SO •51 4-55 -63 5-57 4-66 •72 6-45 ■53 ■54 5-57 6-59 S-58 660 •67 7^68 8^40 -49 M. 7-5i 9 324-1 in. 0-8S 1845-62 330-3 ,, -88 6-69 324-4 „ -78 52-67 332-6 •89 66-22 M. 7i 10 27-50 1 1830-49 -97 I 47-36 M. 6, 9-5 1829-66 3' -50 43-74 63-39 72-40 6-53 556 X. 2192. R. A. ' 35-4" 17° 2. Ua. Se. Gl. W. Dec. 29° 18' &S. 88-4 88-2 85-7 -5 76-2 73-4 72-4 73-5 3n- 10-34 2n. -52 II -09 3n. -45 -23 in. -42 2n. -4 m. -54 M. 7-5. 99 1832-63 4-67 43-72 5-68 64-72 74-60 -60 5-58 MEASURES. 345 557 X. 2199. R. A. tf 36 •4°' Dec. 55° 49' M. 7-2, 7-8 Distance perhaps unchanged : a gradual diminution in angle. Duner's formulas are 1858-50. A = i"-52. P = io8°-8 - o°-378 (t - 1850-0). 2. Ma. O.S. Be. Be. Sq. W ts. Gl. 116-3 II 1-4 •5 107-2 106-6 1037 102-8 103 9 I II -2 101-2 io6-8 101-4 102-0 99-6 98-4 100-7 ■4 100-8 •7 •9 Sn- 1-66 4n. •s in. •5 3n- •52 ,, ■S3 2n. ■62 •62 ») ■56 3"- ■67 2n. •60 ,, •56 3n. ■65 5n. ■38 10 •51 8 ■54 7 ■44 9 ■73 10 •51 6 •47 5 •5 1830-94 43"SO 5-09 52^37 7'i3 9"39 60-87 1-89 4873 72-52 57-64 63-06 71-38 2-50 3-33 4-70 5-58 4-73 ■79 •80 558 2. 2203. R. A. 17" 37 •5'' Dec. 41° 43' M. 7-5. 7-8 Probable change in angle. Duner gives 1849-66. A = o"-7l. P=332°-2 - 0°-i40 (/— 1850-0). 2. 333-4 Ua. 336-6 334-9 328-3 O.S. 335 9 332-2 327-6 Se. 328-3 Be. 329-3 Sn. 330-3 W.O. 325-8 Sp. 327-8 3"- 3n- 0-72 "'I •78 4n. 2n. 0-79 ■85 in. 77 2n. )» 0-63 3n. -70 •89 75 1830-13 -13 43-31 55-29 41-13 54-51 72-61 55-29 7-18 70-52 4-73 5-59 559 2. 2202. R. A. 17" 39" Dec. 2° 38' Duner's foi-mulse are 1851-60. A = 20" -47. P = 93° -9-0° -020 (^-1850-0). H,. H; & So. z. Ua. De. Eng. Da ■W. &S. 01. 90 in. 93-s 2n. 20-52 94-1 4n. -54 -4 2n. -25 •I 3n. -01 -5 2n. -10 937 3n- -25 in. 21-06 •8 „ 20-48 •6 5n. 21 03 •4 3"- 20-38 -3 2n. -60 -5 ») -84 1781-55 1821-77 7-37 36-61 43-27 52-63 5-68 61-56 57-64 63-63 9-30 74-55 -57 560 t. 2218. R. A. 17" 39-5" Duner gives A = 2"-38- P = 354°-o. H,. S. Sm. Ma. Se. De. Mo. Du. Dec. 63° 44' M. 6-5> 7-7 o"-oo8o (/— 1850-0). -o°-o84(/- 1850-0). 359-9 2-78 336-7 3". -50 355-1 It -47 3567 -5 334-5 3n. -53 353-3 ,, •30 358-5 in. •60 353-0 2n. •5 351-6 -22 ! 353-1 2n. -29 , 352-1 4n. -08 1 1831-36 2-72 6-78 5-70 44-63 57-53 66-85 58-00 68-41 59-35 72-34 561 t. 2213. R. A. 17" 40-3"' Dec. 31° II' M. 7-5. 8 Duner has 1851-48. A=4"-43- P = 332°-5 — o°-o64 (<— 1850-0). So. 335-5 2n. 5-03 1825-47 s. 332-3 31- 4-29 9-43 333-3 .. -45 36-60 Ma. -3 2n. -55 43-60 Se. -I 3n. -61 56-82 De. 331-2 2n. -59 7-83 Mo. 332-2 12 -23 8-52 Du. 331-2 5n. -40 69-49 562 X. 2205. M. R. A. Dec. 5-5, 5-8 17'' 40-4" 17° 46' M. 8-3, 8-7 346 DOUBLE STARS. Duner's formulae are 1849-56. ii = 2"'36. P = 296°-i +o°-270 (/— 1850-0). s. 291-4 290 I Ma. 293 '4 294-1 295-5 Se. 297-3 Oe. 301-6 Du. •6 2n. 2-52 ■53 •49 2n. -28 3"- •62 »» -16 •19 31- -19 1829-58 33-45 9-28 42-71 5-59 57-23 69-31 ■3« 563 t 2215. R. A Dec. M. 17" 40-e m 17° 45 5-9. 7-9 Change in angle uncertain. ^ 310-6 7n. 0-74 1831-53 307-8 3". -81 5-99 O.S. 3II-6 4n. -85 41-56 304-6 2n. •77 70-54 Ma. 31 1 -4 8n. -75 42-22 Se. 304-6 3n- -66 5592 Oe. -6 •67 -92 306-0 m. i'5" Du. 307-0 4n. 0-74 68-45 ■w.o. 296-5 -91 74-66 8p. 300-7 -70 5-54 Dob. 306-6 4n. 7-54 564 2. 2220. /1> HEBCUIIS. R. A. 17" 41-8'° Dec. M. 27° 48' A 3-8, B 9-5, c 10-5 C. 2., A, yellow. Sm., B, cerulean blue. Da., B and c, white. H, IV. 41 forms the double star whose components are designated ^ and yii,, the latter preceding and being the smaller or companion star. This object was measured by H,, S., etc., the distance being about 30". In 1856, however, Mr. Alvan Clark, with an aperture of 7J in., discovered that /ii was itself double. 2. with apertures of 9-6 in. and 15 in. had overlooked it; and Madler did not notice the duplicity of the companion.* A B. 2. measured it from 1829 to 1836, and thought there was no sign of motion. Smyth found it "difficult to measure, especially in distance, from its bearing illumination badly." He also gives as " the assigned values " of its proper motion * Dawes in 1859 writes, " Seen double with A.C. 's 8-in. O.G." "Seen double with powers 312 and 697. Best measured with 697," and "very difficult in dis- tance, as the small star bears but httle illumiuation." P R.A. -o"-29 B -0-36 A —0-39 Dec. - o"-84 — o -72 — o -72. 2., on the ground that the two stars have a common proper motion, thought "it very probable that they are physically con- nected." B C. Dawes says "probably binary," but in the notes to his observations in 1864 he writes, "undoubtedly binary. Annual motion = -f 3°-l2 ±." 0.2. The recent measures of B C indi- cate a very rapid revolution ; this would produce changes in the relative situation of B and C in the period preceding the dis- covery of C by Clark which may perhaps explain why the star was not seen earlier. In i860 the measures of B C presented no difficulty, but in 1873 t'l^'"' separation could not be effected on any but the finest nights. In the case of 2. the fact that his measures were made with a bright field sufficiently explains how it was that he never detected this object. In A B the distance increased from 1830 till i860, and then began to diminish. The angle seems to have in- creased up to 1850, and to have been nearly stationary since. The discrepancies in the distances are in part removed when the measures made before Clark's discovery are referred to — . Since 1859 the optical 2 centre between B and C has remained fixed with reference to A. So. 8m. Ma. 0.2. Se. Da. M. Eng. Kn. De. "W. &S. n. AB 240 18" -8 29-30 241-0 in. -83 -5 2n. -91 ■8 3n. 30-25 •8 -I 242-9 -8 241-6 3n. -2 -7 in. -14 242-7 ,, -69 'I -27 -8 -29 243-8 in. -33 244-6 ,, 3242 •5 »> 31-62 243-9 >» -37 244-6 j» -04 243-4 »> -19 -2 •35 242-6 -5 ... 244-0 in. 3' -78 -4 -50 243-8 2n. -32 •6 -32 244-8 3 -2 245-2 2 -0 •I in. -15 I78I77 1825-50 9-68 32-55 6-51 7-67 57-73 43-74 4-43 6-39 51-89 6-36 1-88 60-30 2-83 6-62 -73 57-85 9-76 60-87 1-42 -46 4-49 5-43 6-86 71-51 3-50 7-75 MEASURES. 347 B C. Da. 59'2 2n. I -81 1857-50 60-3 3n- 2-os 9-70 77 -S in. I -So 64'43 Se. 717 •74 S7-8S O.S. 677 •64 60-30 78-s -50 2-83 91-0 -18 6-62 88-0 •02 73 987 0-88 8-50 156-8 -62 71-52 185-5 •63 350 Eng. 67-5 17 64-49 Kn. 79-6 2n. •84 5 '43 De. 82-0 -2 •44 987 0-88 8-50 single 73-67 2l6-o 0-83 6-68 229-7 -87 7-54 W. & S. loo-o in. •6 1-51 90-0 >> •6 3-50 61. 100-9 •6 1-51 ■0 10 •4 4-63 lOIO 6 •4 -66 W.O. 202-4 •76 •48 A and B+C. VS M. 244-0 in. 3178 61-46 O.S. -2 ») ■23 8-50 •s »» -09 71-52 565 OX 337. R. A. Dec. M. 17'' 44 -S" 7° 1/ 7-5. 8 Probable small change in a ngle and distance. Wa 307-6 0-47 1843-37 O.S. 305-0 in. •68 5-62 304-3 • ) •67 -73 3060 j» •52 51-67 1230 )» •56 5-66 Se. 298-1 2n. -42 7-05 De. 1 14-8 4n. oblong 67-32 Dn. 293-8 Sn. 0-39 70-44 666 OX 338. R. A. Dec. M. 17" 46-5°' 15° 2 [' 6-6, 6-9 C. golden. Considerable retrograde motion increase probably in the distance. a slight Ua. 43-0 0-58 1843-37 0.2. 44-2 4n. •68 5-21 38-9 3n. -6S 52-30 36-1 J> •70 5 -63 27-8 >J -82 72-56 Se. 33-0 De. 2S-9 W.O. ■3 w. as. -4 26-6 2n. 0-60 4n. 0-85 7 -83 7 •86 1857-05 67-33 74-72 7-45 -46 567 %■ 2262. T OPHIUCHI. R. A. Dec. M. 17" se-S" -8° II' 5, 5-7 C. H„ both pale red or white red; Sm.,both pale white ; 3., yellowish. H,. " April 28, 1783.— The closest of all my double stars ; can only be sus- pected with 460 ; but 932 confirms it to be a double star. It is wedge-formed with 460; with 932, one-half of the small star, if not three-quarters, seem to be behind the large star. The morning is so fine that I can hardly doubt the reality ; but according to custom I shall put it down as a phe- nomenon that may be a deception." S. examined this object three times by day in 1825 without being able to see the companion. Nor was he more successful in 1827. In 1835-66 and 1835-67, how- ever, S., his son, and the aminuensis all agreed that it was oblong ; and a few days later "two stars of the 5th and 6th magni- tude " were seen in contact. The powers used were 480 and 600. On trying 1000, " in moments of best definition," S. saw the stars separated. He notes that the motion is direct, and that the period may be from 80 to 90 years. Sm. failed to elongate it in 1832 ; but in 1838 he found it measurable. Da. says that the low altitude and oblique position render it difficult, although its dis- tance has increased. .Sm. also observed a small star of the lOth magnitude : — 1832 114° -5 83" -I 38 115 -o 82 -7. The Orbit. — Hind in 1852 found that the period was about 120 years, and the ex- centricity 0-575. Dr. Doberck in 1875 obtained the follow- ing definitive elements : — T = 1818-50 a = 67° i' \ = 36 26 7 = 46 8 e — 0-6055 P = 217-87 years a = i"-i93 ; and a comparison of the elements with the observations from 1783 to 1871 shows very satisfactory agreement. 348 DOUBLE STARS. 1- 33I-6 elong"- 1 1783-34 Ja. 239-5 II I -10 852-65 360 J, 1802-74 243-6 -41 8-20 360 ,, 4-44 Mit. 229-4 8n. 0-78 46-51 single 25-67 -7 2n. 1-18 810 1 46-0 elong^- 1 7-28 Se. 238-1 31- •26 5-48 2n. single 5-65 240-5 6n. -2 6-58 356' In. wedg'd | -71 241-3 4n. ''I 7-62 326 It „ 7-28 -8 6n. -16 8-52 1967 „ oblong 1 35-65 244-3 7n. •36 62-60 1935 >» J) -66 -8 6n. •43 3-55 i90"3 )» 0-35 -67 245-6 8n. -41 5"1I "2 ,in cont"| -68 246-1 ion. •43 7-06 192-4 J) „ •71 -6 4n. •37 8-53 196-6 0-35 247-4 J) •43 9-57 " 5 eparat"' -71 -8 »» •42 70-50 197-3 »> 0-35 6-42 -3 »» •55 1-50 203-3 »> •46 -64 248-2 ft -56 2-52 200-0 •46 -68 -6 ti -63 3-59 199-2 yt -45 -70 -5 j» •56 4-57 •7 J» ■46 ■71 249-0 5n. -64 5-55 m. round 2-55 Se. 236-9 2n. •27 55-55 214-0 0-5 8-58 240-7 4n. •20 6-24 227-0 -9 42-52 239-6 31- -26 -55 238-8 l-I 55-34 245-8 in. ■30 60-77 ).2. 223-1 in. 0-94 40-51 247-6 3"- -60 6-72 228-1 3n- -86 I -61 Kn. 246-8 4n. •20 3-57 232'4 in. ■87 5-65 Eo. 243-1 in. -17 5'F 230-5 2n. -96 6-69 »» -29 /^5 233"9 in. -97 7-82 Ta. 246-2 -65 6-43 238-2 ft 1-19 51-67 -3 ,, 8-59 237-4 -29 2-64 2484 ,, ... 9-56 241-9 j> ■18 -67 -9 ,, 211 73-55 236-: »» -20 4-70 250-7 >» 1-48 4-57 240-3 2n. •30 5-67 On. 248-1 6n. -40 69-64 239-9 in. -47 7-67 250-9 3"- -29 71-35 240-5 »> •42 -67 Gl. 247-6 •70 0-32 -9 >» •47 8-71 -0 8 -50 1-73 242-7 jt -64 9-63 249-6 4 -60 3-60 ■9 ii •43 61 63 248-5 10 -66 4-80 244-1 ji •51 5-72 H. ■74 0-48 243-3 >) -75 6-62 250-1 in. -56 -49 248-1 »j -69 72-58 -3 ,j -60 -50 251-1 )j -63 4-67 253-5 2n. •45 3-73 Da. 221-5 4n. 0-88 40-68 ■w.&s • 248-9 4 -67 2-49 225-7 5n. -79 1-66 250-3 4 •70 -52 226-9 In. 2-64 -8 10 •71 3-52 228-9 2n. 0-9S 3-6i 249-4 4 •64 4-63 232-7 m. I -01 8-66 -9 5 -71 6-60 2380 »» -22 54-67 Schi. 248-9 in. -61 5-60 Ma. 217-3 0-75 41-53 247-6 )» -73 6-59 225 -6 T 2-57 Sp. 248-9 -61 5-60 228-8 ■80 3-54 247-6 -73 6-60 229-8 -79 4-34 CO. 250-4 In. 2-05 -2 238-6 1-27 52-66 -5 8n. 1-90 7-61 •3 -17 3-79 Dob. 248-9 4n. -70 6-61 -2 -09 4-71 251-3 3n- -47 7-53 240-0 244-0 Ka. 2246 •44 -29 0-80 8-64 6i-6o PI. 249-8 2n. -64 6-55 43-" 568 2. 2271. 228-9 249-4 -95 1-40 -61 65-52 R. A. Dec. M. 17' 57-7" 52° 51' 7-3, 8-3 Ch. 218-7 m. 0-79 44-74 Ja 239-5 i-o 6-20 Dun^r's formulae are 230-7 0-96 6-69 1851-27. A = 2"-07. 234-0 21 •0 1 50-77 P = = 264° -6 + o=-i 27(t-l 850-0). MEASURES. 349 2. Ka. Sa. O.S. 259-5 2n. 1-70 262-2 3n- -87 263-6 in. 2-36 266-1 2n. •S3 271-1 in. •43 266-9 4n. -06 -6 in. •37 265-2 ,, •41 1829-71 31-48 42-72 59-72 66-85 9 "45 70-87 473 569 2. 2267. R. A. 17" 57-8" Dec. 40° II' S. Ua. 0.: Ka. 234'i 236-8 239"5 237-0 238-1 237-2 241-7 243'5 -6 62-5 56-2 59-5 239-5 236-9 8e. 240-0 Sp. 242-6 W. & 8. 241 -I 3"- I 41 -48 -48 •08 •32 -42 ■25 -40 in. -65 3"- -54 2n. -47 in. -33 2n. -48 in. 2n. I -59 ») -46 -00 6 -09 M. 8, 8 1830-68 9-07 42-68 3-35 51-72 2-33 3-38 9-88 40-84 1-55 54-51 70-87 42-67 4-36 5-46 57-64 75-63 6-60 570 t. 2268. R. A. Dec. M. 17" 58" 25° 22' 8, 9 S. 218-2 2a. 18-12 1829-70 Ua. 214-7 »» •87 43-75 215-1 n -76 5-47 571 R. A. 17* 59-4' 2. 2272. 70 OPHItTCHI. Dec. " 33' C. S., A, yellow ; B, purple. H[ {PM. Trans., vol. Ixxii., p. 217) : "Aug. 29, 1779.— Double. Considerably unequal. With 227, 1 1 diameters of L ; with 460, much above 2 diameters of L. " Hi (Pkil. Trans. 1804, p. 374): "The alteration of the angle of position that has taken place in the situation of this double star is very remarkable." The change amounted to 131° 59' in 24 years and 234 days. ' ' This cannot be owing to the effect of systematical parallax, which could never bring the small star to the preceding side of the large one." Hj and So. {PAH. Trans. 1824, p. 288). H J says that the angles of 1779 and 1781 contradict each other; that that of 1779 is preferable ; that the motion seems exceed- ingly capricious, the diminution of angular velocity since 1821 being so great and sudden as almost to throw a doubt on the observations. He is unable to say which observation is in fault. Having numerous observations by So. made in 1825 before him, Hj finds the angular velocity greatly below that indi- cated by the observations up to 1820. An examination of the observations of distance leads him to put the distance in 1780 at 3"-5, in 1804 at 2"-s625, and hence to regard a decrease as established for that period. With the decrease of angular velocity there has also been an increase of distance. An examination of the measures from 1779 to 1830 shows " the extreme uncer- tainty which must attend any determination of the elements of the orbit of a double star on principles which include the measured distances among the data. " — (Mem. R. A . S., vol. V.) 2. (Af. M., p. 98): "A fine series of measures were made by 2. between 1825 and 1835. He often measured the star during the early twilight. Sm. iCycle, p. 404) : "70 Ophiuchi was designated by the letter (f> in the British catalogue ; but as there is no such letter in Bayer s map, Mr. Baily has properly re- jected it in his late edition of Flamsteed. " " It may be stated in round numbers that 70 Ophiuchi describes its ellipse in a period of about eighty years." Hj's investigations led him to think that 2.'s distances in 1818, 1819, 1825, 1826, 1827, and 1828 were "the only irrecon- cilable contradictions to the curve," owing to their being too small. 2., on comparing his measures with the small telescope used in 18 19 with those by the great Fraunfoper equatorial, found that the latter instrument gave smaller results than the other. He at last appealed to Bessel and the Konigsberg heliometer : "A comparison of the dis- tances of 39 stars, taken by both [observers], shows that those of Dorpat are, on an 350 DOUBLE STARS. average, o""l9 smaller than those of Kbnigs- berg? Da. says, "one of the most interestmg and beautifLil of the binary systems." The proper motion of A is thus given : — R. A. Dec. Piazzi +o"'30 — I"'I7 Bessel -(- o '26 — I '09 Argelander + o '22 — i 'lo. The Orbit. — Encke was the first to compute the orbit of this splendid object ; his elements are as follow : — Perihelion passage ... 1806 '87 7 Position of perihelion 283° 3' Node 147 12 Inclination 46 25 Angle of excentricity 25 28 Semi-axis major ... 4" "3284 Mean annual motion — 292''43 Period 73"76 years. In 1832 appeared a set of elements by H;, obtained by means of his graphical method ; they are — a = 4" -392 e — o '4667 ir = 292° 25' 8 = 137 2 7 = 48 5 X = 145 46 K = - 4°-48l2 P = 8o'34 years. T = 180706 A.D. ; and the following selection from his table of comparison of elements and observations will exhibit the nature of the agreement : — Date. Angle. Distance. Observer. Observed. 'Computed. Observed. Computed. 177977 / / QO ' 90 13 H,. 1819-63 168 42 ; 163 8 4" -66 3"-S 2. 21-51 156 50 '57 3 Hj, and So. 22-54 154 30 i 155 »» 22-60 4-40 4'36 2. 25-56 148 12 147 12 Hj and So. 27-40 143 54 ! 144 8 4-51 5-20 2875 j 479 5-42 ,, 30-50 137 28 ; 138 13 5-65 5-61 Be., Hj, Da. Madler in 1835 published the following elements : — Perihelion passage . . . Position of perihelion Node Inclination Angle of excentricity Semi-axis major Mean annual motion Period 1806-746 287° 14' J 33 47 42 52 28 30 4" '3 1 59 - 267'-9S7 8o-6i years. Discussing the measures made up to 1841, this eminent astronomer found that the law of gravity does not hold good in this system ; he found that the elements which were on the whole most satisfactory gave angles widely different from those observed be- tween 1804 and 1823. (See yirf. Nachr., No. 444.) Hind and Jacob have arrived at the following results for this star : — Jacob. 1807-60 293° 17' 128 33 51 30 0-4820 87-52 years 4'675 Hind. 1807-48 294° 6' 122 14 47 20 0-4973 88-48 years In 1868 M. Schur published the elements which follow (see Ast. Nachr., No. 1681). T= 1808-79 w = i55°-7 a = 125-4 (1850-0) '■ = 57-9 e = 0-49149 // = - 3°-8i48 a = 4"-704 P = 94"37 years. From the ephemeris Duner has constructed a table of comparison of elements and observations from which the following is extracted : — 1863-72 70-51 71-49 71-53 73'57 7351 74-12 76-62 "84 97°-6 '45 94 o -60 92 '6 -27 92 -6 01 88 -6 Differences. ■'■53 -o°-6 ■ o '67 -o -38 - o -70 ■o -66 ■a -78 -o -66 - I 'oi — I 7 — I 5 -1-5 — 2-1 — 2-0 — I "2 -30 Du. Gl. W. &S. De. ■w. &S. De. GI. Du. s. 90-0 3-6 4'4 99-2 3361 319-0 168 -5 5n. 160-2 2 1779-76 80-49 173 1802 -25 4-41 19-64 20-77 MEASURES. 351 2. tS7-6 5 182174 O.S. 153-9 3 2-64 148-2 I4n. 3-98 5-57 1451 2 4-37 7-02 140-2 4 •78 871 138-0 6 5-08 9 '59 1357 2 •31 30-84 «347 5 •41 1-68 i33'9 3 •55 2-75 131-1 4 •85 4"47 130-7 6-10 5 -60 129-5 8 •13 6-66 E,& So. 156-2 3-68 21-31 154-8 4-85 2-42 1536 3-35 148-2 3'98 5 '57 142 5 7-51 Ka. 138-1 ■95 30-36 136-1 •97 1-52 i35'5 ■49 2-57 129-3 6-97 6-65 Ma. 120-8 77 45-43 Be. 135-6 6n. 5-45 30-41 7 2n. •51 -69 Da. 137-3 6n. ■53 ■57. 1327 5n. 71 2-55 -8 31- 6-14 3-42 130-6 7n. -12 457 125-8 2n. ■55 965 124-8 411. •62 40-59 123-4 ■63 1-68 2n. -72 253 II8-8 3n- •80 8-12 114-6 7n. ■48 53-60 "37 411. •33 4-73 II2-6 in. ■51 5-66 113-2 2n. ■46 -69 iio-o in. ■38 7-57 ■2 2n. •52 ■58 109-3 5n. •24 9-72 Ch. Sm. 136-4 5-43 30-76 i32'5 6-0 3 59 130-6 5 '97 5-56 Hi. -8 6-II -60 D.O. 128-6 ■19 6-81 127-5 •25 7-64 Hit. 126-5 -25 8-51 Ja. 122-4 -64 42-55 "97 •8 7-48 114-9 ■5 52-44 Encke. 1280 3"- -46 36-50 -2 5"- -72 T'^^ 126-6 7n. •63 8-56 125-2 2n. 78 951 O.S. -7 4n. •34 -87 Bond 127-1 7n. ■59 40-75 125-8 3n- •65 1-65 De. 124-7 5n. ■62 2-70 121-5 In. -62 471 120-9 4n. •55 5-68 121-3 2n. -61 6-73 "97 j> -50 7-76 118-5 >y •78 8-79 117-8 3"- •54 9-78 115-4 Sn. •52 51-67 115-0 1 13-6 II2-8 111-9 -7 iio-i 109-8 108-5 106-4 105-2 102-7 101-2 100-4 99-1 93-6 87-4 127-9 123-4 122-6 100-6 125-4 124-4 •7 123-3 122-5 -o 120-8 II9-8 II8-2 116-7 115-4 -5 II4-7 113-3 *3 "1-5 108-9 106-0 105-2 125-0 123-S I2I-5 I20-I II7-I -2 120-3 -5 II5-I II40 113-6 II I -9 -4 110-6 109-7 I18-I 117-7 116-4 "3-5 -I III-7 109-5 -3 105 -5 1042 103-5 5n. 6-55 3"- •47 J» •54 3"- •49 2n. •37 4n. ■40 2n. •21 3n- •19 m. 5-88 2n. ■85 In. -32 J) •26 4n. •29 2n. 4-69 4n. -08 3n. 3-78 m. 6-00 »» •53 2n. •48 J) 5-31 8n. 6-45 2n. 4n. 6-25 I4n. ■42 3n- •43 5n. •48 I7n. -58 ion. •64 -83 •94 •67 •67 •56 •56 •31 •32 5-94 -85 •70 2n. -86 3"- 6-69 In. 5-96 6-14 7-43 -19 In. 5-53 6-83 10 •86 15 -73 21 -36 -45 •39 -46 -10 m. -9 2n. -8 6n. •45 I in. •26 in. -52 6n. •40 4n. -31 4n. •09 9n. 5-73 It •60 I in. •46 1852-67 3-78 4-69 5-66 6-73 7-69 8-72 9^68 61-63 2-77 5-72 -80 6-66 8-71 72-60 4-69 40-35 1-74 2-59 65-62 41-44 2-39 -66 3-53 -72 4-57 5-54 6-57 8-50 50-64 1-47 -74 2-73 3-76 4-68 6-50 8-63 61-97 2-72 42-62 3-56 4-59 6-46 •56 7-45 ■59 6-OI 50-48 2-74 4-08 6-12 -37 7-13 8-12 48-52 -52 53-54 4-58 5-21 6-63 7-63 8-44 62-62 3-51 4-60 352 DOUBLE STARS. Se. Se. Fit. Ho. An. U. W.O. So. Eng. Kn. Br. On. Gl. 102-3 101 -o 990 96s 94 5 92-6 907 88-8 86-1 837 I II '6 106-3 lOI'I 112-3 iio-i 108-6 1090 107 9 o 278-1 2778 281-8 275-1 274-2 276-4 -6 270-8 268-9 7 88-7 84-8 1062 9n. iSn. 7n. 8n. 9n. 8n. 9n. 1311. 3"- 12 12 2n. In. 2n. 4n. it 5 6 6 W. &S. 105-9 6 -0 6 104-8 6 •5 in. ■5 ,, 103-9 2n. 104-8 101-8 6n. 100-5 in. loi-i 2n. 100-2 In. 94"4 2n. 96-7 in. 84-7 ,, 88-6 ,, 99-8 2n. 98-5 »» 94-5 3n. 98-0 5 97-5 4n. 96-9 3"- 92-6 in. 947 8 932 7 92-9 S 931 5 92-1 5 89-5 6 87 -5 10 92-8 3 ■5 4 5-37 1865-51 •17 7-01 4-85 8-46 71 9-60 ■56 70-51 •27 '■S3 •08 2-49 3-89 3'5« •66 4-56 •48 5-52 6-25 55-45 •07 60-61 5-27 6-61 6-36 57 -42 ■15 -67 6-08 8-39 ■61 9-75 •49 60-74 5-89 1-46 •33 7-41 •27 8-46 4-96 -69 •83 70-45 •80 -47 •84 -50 •65 ■79 •28 2-49 •20 3-41 ■23 •73 ■00 4-47 3-84 5-65 5-19 63 74 63 6-04 63 5-87 63 -72 63 74 63 76 63-55 ■30 553 ■24 ■55 •42 4-48 •26 6-49 ... 7-52 5-49 864 ■31 9-61 4-62 70-60 ■34 1-55 3-95 3-55 ■67 4-58 S-22 67-44 4'97 8-56 •30 71-59 ■92 68-90 •83 -72 •58 969 •20 71-72 4-6 0-30 •3 -72 ■4 1-50 •4 •63 •08 -80 3-90 3-5" -92 4-73 4-6 1-48 ■60 -49 vr. &B. Per. Schi. Dob. PI. CO. 90-7 91-9 .8 88-8 •5 95-1 80-5 -4 91-5 84-1 81-2 78-9 77-6 75-4 80-2 78-5 -5 3n- 4n. 4n. 5n. 4n. 4-61 -32 ■17 -07 -I 3-93 -49 3-37 4-30 3-44 -34 ■46 •46 -03 -55 -39 -12 [872-49 •50 •52 •54 351 -63 5-62 6-61 •61 2-49 5-62 6-59 ■52 7-52 8-54 6-54 7-65 -68 572 Z 2275. R. A. 17" 59-3°' Ma. 127-9 126-8 Dec. 39° 21' 3n- : in. 1-08 o-8o M. 9. 9-2 ' 1832-20 44-37 573 S. 2277. 401 (B) HEEC0LIS. R. A. Dec. 18'' o°> 48° 27' Duner's formulas are 1850-91. A = 27"-29. P = ii9°-09 +o°-o630 (/— 1850-0). M. 6-3, 8-2 2. Ua. 117-9 1 18-6 3n. in. 27-59 26-94 Be. Dn. 119-9 120-3 3n. 27-71 : 03 1830-06 44-90 57-70 71-49 574 2. 2278. R. A. 18" i" Dec. 56° 26' C. white. M. 6-8, 7-3. 7-8 Duner has the following formulse : A = 38"-62 — o"-oi7l (C— 1850-0). P = 22°-99 + o°-o348 (/- 18500). AB. H,. 21-8 .3n. 38-78 1830-34 2. 22-5 -92 1-56 Se. 23-0 2n. -66 57-00 Be. •3 in. -63 8-11 Du. •7 4n. •18 69-61 MEASURES. 353 BC. H,. 147 -I 2n. 6-65 1829-64 146-5 in. 1 5-60 3173 2. 147-8 .Sn- ■97 1-56 Ma. 146-1 in. -87 44-90 8e. 147-1 2n. 6-24 57-00 De. •3 ■12 8-11 Su. •6 5"- 5-99 69-41 Ta. ■0 In. 6 -05 74-59 Sob. 145-8 2n. 1 6-61 575 O.S. 349,. 72 OPHIUCHI. R. A. Dec. M. iS"" 1-6 [U 9° 33' 4.8 A very difficult object, if really double. 0.2. has examined it with very great care on twelve nights since 1841. Sometimes the companion was readily seen, sometimes there was no trace of it, and on other occasions there was some appearance of the principal star being oblong. He sus- pects the companion of rapid variability. 0.2. Ma. Sa. He. ■W. ScS. 156-6 162-4 168-1 169-6 208-7 206-6 345-9 Sp. in. 1-3 1842-72 -61 7-59 .. : -6 -70 ,- i -49 51-67 ' simple ' 2-63 0-35 45-74 1 -27 7-75 single 48 tt 54 >i 6-53 elongated 7-57 single 64 round 73-5" elongated ,-62 single 6 576 2. 2281. 73 OPHIUCHI. Dec. 18" 3-6-" 3° 58' Duner's formulse are R. A. 3.6m M. 5-7. 7-2 A = i"-33— o"-oii2 (/— 1850-0). p = 255°-5-o°-i8i (/-1850-0). H,. So. Sm, 265-7 264-3 257-6 259-7 260-5 259-9 255-0 2n. ... 1 in. 2n. ... 4n. 1-99 7n. -48 -7 -5 •4 1783-35 1802-38 22-46 -93 34-86 -60 8-74 42-39 Ma. O.S. Da. Mit. Fit. Mo. Oe. Se. Eng. Ko. Ta. Du, 61. 8p. Dob. R. 18' 0.2. De. 257-8 1-35 256-1 -43 258-9 -06 254-5 4n. -30 -6 •28 252-0 •32 254-1 -20 253-7 I4n. •25 252-7 -27 248-7 -20 252-8 I in. -17 254-2 5n. -61 251-6 4n. -35 247-5 5n. -13 256-2 4n. -47 255-0 in. -38 253-3 »» -27 256-2 24 ■5 253-9 in. -47 -9 4n. -2 255-1 2n. -35 251-6 in. •24 2534 »> -09 252-4 >» -05 251-7 j> -17 254-6 7n. -33 252-3 3". -47 247-8 2n. -91 250-8 3n- 1° 249-2 2n. •61 245-3 in. -64 253-9 6n. 0-92 252-8 6 1-45 253-7 4 -37 -6 3 255-9 6 1-35 -6 3 -29 254-2 4 -06 -7 5 -12 252-9 4 -19 253-9 5 -14 254-4 8 -06 250-4 0-93 -0 3". '•03 577 0.2. 344. A. 4". Dec. 49° 41' 1840-81 2-70 4-35 51-21 •71 4-68 5-66 6-81 8-65 9-81 61-89 41-26 9-72 70-12 44-58 9-48 7-59 51-37 4-60 5-69 62-69 5-34 6-68 70-66 7-74 56-27 65-92 4-48 5-54 6-46 74-61 1-07 -50 2-54 -54 -55 3-53 4-64 5-62 6-55 ■61 4-73 5-61 6-61 156-2 -I 153-1 147-9 in. 2-22 1 -08 -20 3". -21 M. 6-7, 10-8 1842-67 8-73 51-67 66-55 578 2. 2289. 417 (B) HEECULIS. R. A. 18" 4-8» Very slow angular change. Dec. 16° 27' M. 6, 71 23 354 DOUBLE STARS. Duner's formulse are i8S3'46. A = l"'o6. P = 238°-2-o°-2i2 (/-i8so-o). H,. Ha. 0,2. Se. Se. Du. W. &S. 61. Sob. 243 ■« 241-6 240-1 239-1 -o 235-0 232-4 2342 232-s 239-2 237 '3 236-1 23s '3 2343 235-8 234-9 235 '7 236-3 235-8 238-1 237-2 235-3 234-5 237-6 235-9 411. in. I2n. 2n. 8n. 8n. 5n. 3n- 4n. In. 3n. 9n. 4 5 7 5 4 4 4 7 4n. I -20 •26 ■01 0-95 I-15 •03 -OS -07 -08 ■33 -16 -05 ■24 -24 -67 -OS •97 -25 •03 -14 ■12 •39 •33 ■15 0-I2 0.2. Se. 65-8 64-7 -3 R. A. Dec. 27° 37' 1829-96 30-67 40-11 3-49 52-63 '6-79 9-81 60-86 1-99 41-11 54-69 7-08 65-63 2-95 5-66 70-59 2 50 -50 3-54 4-64 5-65 6-55 -61 469 7-50 579 o.t. 345. R. A. Dec. 5° 47' M. 7-3. 10-3 in. *> 3n- 1-02 1-07 •32 1842-71 5-73 7-59 66-61 580 2. 2292. M. !, 8-1 Duner's formulze are 1859-06. A = i''-23. P = 26i°-3 +o°-i4(^- 1850-0}. 261-2 260 4 ■3 258-4 259-8 2636 260-2 •o 258-9 264-2 265-7 Liiidstedt.264'6 0.2. Ha. Se. Se. Bu. 4n. 1-39 2n. -60 j» •44 in. ■62 >» •38 ,, -71 in. -22 2n. •25 in. ■s 8n. ■II 2n. •22 in. 1830-40 40-78 1-57 56-56 68-50 73-53 42-63 56-55 6-78 71-94 6-71 ■75 581 S. 2294. R. A. Dec. M. 18" 8-4" 0° 9' 7-4, 7-7 Probable change in angle and distance. o // 2. 91-8 4n. l-o6 1831-00 0.2. 87-8 , m. -04 41-55 84-2 „ 0-85 65-80 ■9 .. -66 72-56 Ma. 90-3 'So 43-60 Se. 93-3 -62 56-83 Sp. 89-2 -37 76-11 582 0.2. 349. R. A. 18" 12-2"' 0.2. Be. Dec. 83° 54' 99-3 In. 0-66 94-4 ,, -71 92-3 ,, -48 103-5 4n. M. 7-5. 8 1842-73 5-71 51-73 67-62 583 2. 2303. R. A. 18" 13-6"' So. 2. Ua. Hit. Mo. Se. CO. 213-0 216-4 219-4 220 '6 225-7 223-3 219-9 222-9 227-0 222-1 223-1 225-0 221-3 225-3 222-4 Dec. Sn. 2n. in. 3-22 •31 -52 -50 -22 ■56 2-79 3-23 2-94 3-15 2-70 •79 M. 6-7 9-2 1825-20 31-20 7-1S 43-64 50-75 1-77 48-62 55-64 S-60 7-59 64-59 6-68 7-61 72-52 7-51 584 2. 2311. R. A. 18" 17°" Ma. 170-7 168-9 Dec. M. 11° 23' 8-9, 9-9 4n. I 8-65 I 1830-30 in. I ... I 43-19 585 0.2. 347. R. A. 18" 19"" 0.2. Be. 342-2 337-5 347-6 Dec. 7° 10' in. j 3-12 -. I -59 3n. I -07 M. 7-2, II 1847-59 51-82 66-27 MEASURES. 355 589 OS. 351. 588 t. 2816 E. A. 18" 21" Dec. 0° 7' A, yellow ; B, blue. Duner has these formulas P = i85r69. A = :3i5°-o+o°-os Hi- Da. Sm. Ha. Hit. Ja. Se. Mo. Se. Bo. Ta. Sn. W. ft I Gl. 3I4-S 3«2'4 ■3 318-6 3I9-8 318-1 3"4'2 3i5'o 3I4'2 313-8 3I4'3 •2 3I6-S 317-0 3 '4 "4 3137 3 '4 4 317-6 3" 3 •4 3i0'4 305-6 3i7'6 316-1 31S6 4n. Sn. in. 3"- 6n. 3n- 511. 6n. 3"- 711. 4". 2n. (/- 1850-0). 1781-79 1802-34 22-72 5 '54 9-0 2-95 862 36-22 o-6l 40-69 33'S3 42-53 5-61 7-61 52-76 4-70 5-61 7-89 65-57 6-53 9-55 70-65 •76 3-06 480 4-46 5-10 4-15 3-94 •83 4-34 3-94 4-3 3-9 ■73 ■54 ■66 -96 4-00 3-79 •81 •95 3-92 •80 4-08 3-58 R. A. 18" 22-1°' O.S. Dec. 48° 42' 31-7 in. 0-49 22-3 ,, •5> 20-9 »» -48 44'S •33 42-1 •35 30-6 5n. M. 7-3. 8 1842-67 4-85 51-67 43-65 6-68 67-69 590 t. 2323. 39 DBACONIS. Dec. M. 58° 44' 4-7. 7-7 ■Very slow changes. Distinct retrograde R. A. 18" 22-1"" Ho. 0.2. Se. M. W. &I No. A B. 9-6 2n. 4-0 5-3 359-8 02 5-9 7n. 5-5 4-1 -4 3-2 4-9 7-2 4-6 0-6 0-2 2n. 359-6 12 ■3 in. 20 " ■: 3"- 39 3-4 3 [-2 0-7 ■5 3 4 1 I AC. H,. 26-6 i. 22-2 21-7 So. •9 ■4 Sm. •7 O.S. •4 M. -3 m ■w. &S. 20-7 2 21-6 3 No. •5 3-6 -59 3-14 -3 •13 •3 2-21 3-45 •36 •03 -22 •45 •26 ■86 -70 •35 ■76 3-97 -85 88-96 89-61 88-94 892 •14 -69 90-58 1 79 1 'So 1823-63 5-55 9-99 30-26 3-20 6-39 43-38 7-42 51-85 2-34 3-39 8-80 61-45 45-71 56-58 1-90 66-73 70-87 57-59 65-44 75-74 3-55 -58 6 -So 1780-77 181952 34-27 23-46 5-55 3639 51-90 66-48 73-58 5-74 6 -So BC. No. 22-4 i 86-85 I 76-80 356 DOUBLE STARS. 591 A. 24'" 0.2. Se. O.S. 353. DBACONIS Dec. 71° 17' 63-6 I 6n. 62 '9 I 5n. 0-56 M. 4-8, 6-5 1 1856-13 I 6773 592 Z 2330. R. A. 18" 257° Ma. De. W. Gl. Dec. 13° 6' & S. 177-2 20-94 -0 in. -19 176-9 2n. -38 174-4 •09 175-0 •18 174-5 19-26 173-4 2n. •0 •6 in. ... iS' i. A. 29-6"" Ha. R. A. 18" 30-4" Dec. 20° 59' Ma. Se. 1 82 -6 iS)(j-o -o -6 i8S-o -I 194-1 7-43 7-33 -44 to -51 -45 •70 M. 7-3. 9 1828-65 ■71 9-58 47-57 52 62 64 90 74-68 4-79 593 2. 2342. Dec. 4° so' 2-0 m. 26-60 ■I -80 -I »> 27-17 1-7 ■06 -9 2n. -89 ! 0-6 28-32 1 M. 5-7, 8-5 182871 9-62 31-69 2-8i 43-61 5-46 594 0.2. 357. R. A. Dec. M. 18" 30" 11° 37' 7-5, 76 Certain retrograde motion. 0--- 275-5 2n. I 0-48 1845-15 55-67 72-58 595 Z 2345. 275-5 2n. 0-48 264-4 3n- ■53 256-9 2n. ■53 84, lo-i [82975 1-84 5-59 30-50 43-77 7-48 65-21 596 O.Z 358. R. A. Dec. M. Considerable change in both angle and distance. Duner has A = i"-46 4-o" -022 (/- 1860-0). P = 209°-9-o°-55 (/-1860-0) +o°-oo822 (/-i86o)^ Ma. 223°8 I o'-82 1843-54 0.2. 227-0 3n. 1-23 5-41 207-9 2n. -73 63-16 203-9 „ -83 72-58 Da. 2i8-6 in. -18 4856 8e. 214-2 „ -35 57-71 207-2 215 65-63 De. -5 4n. 1-72 6-68 Du. 205-4 6n. -67 9-58 2033 „ -65 71 -o^ -2 2n. -81 5-69 8p. 202-5 -67 -62 ■I -73 6-59 PI. 200-8 3n. -72 -57 597 Z 2346. R. A. 18" 30-5' 2. Ma. Dec. 7° 26' De. ■w. &S. Gl. n. 282-9 286-6 287-2 288-2 289-4 ■2 ■7 ■5 4n. 15-41 16-41 1704 -14 1806 2n. 190 in. " '9-34 -26 M. 7-5.9 1829-64 43-69 52 -62 9-84 64-83 74-65 7-62 4-79 7-80 598 0.2. 359. R. A. 18" 31"° Da. 0.2. Ma. t>e. De. Du. Dec. 23° 31 356-9 2n. 0-73 358-6 ,, -60 354-1 6n. -66 35S-0 3n- -69 357-6 2n. -58 173-3 4n. 352-6 8n. 0-57 M. 6-6, 6-9 1848-56 54-16 49-54 51-77 7-19 67-91 7080 599 a LYR.ffi. R. A. Dec. iS" 32-8" 38° 40' Afag7iitudes. — 2., i, 10-5; Sm., i, 11. C. 2., «, bluish white. Sm., A, pale sapphire ; B, smalt blue. Hj, A, fine brilliant white. H, {Phil. Trans., vol. Ixxii., p. 223). " Sept. 24, 1 78 1. —Double. Excessively- unequal. By moonlight I could not see the small star with 278, and saw it with great difficulty with 460 ; but in the absence \ of the moon I have seen it very well with 1 MEASURES. 357 227. L fine brilliant white ; S dusky. Distance 37" 13"'. Position 26° 46' s.f." On the 22nd of October Hj applied a power of 6450 to his telescope and examined this fine star for fifteen minutes. He found the image "perfectly round, and occa- sionally separated from rays that were flashing about it." He was led to think that this star has light enough to bear a power of 100,000 with 6 inches of aperture. The diameter of the disc of a, taken with his new micrometer, was o"'3553. Hg and So. measured this double star in 1822. From a consideration of the change indicated by the measures and the proper motion of a given by Piazzi, Hj was led to believe, "First, that the proximity of the large and small stars is merely apparent and accidental, no connexion existing between them ; and, secondly, that the proper motions assigned to a are not very remote from truth. " bo. measured it again in 1825, and Dawes has measures in 1 830. Both Hj and Dawes observe that the small star bears illumina- tion well. Smyth measured this pair in 1830, 1837, and 1843. He says (Cyc/e, p. 423), " a Lyras is one of the insulated bodies, and is worthy of ranking with Sirius, Canopus. and Capella. Yet, by the experi- ments of Dr. Wollaston, it appeared that the light afforded us by this star is about -T th part of the Sun's light, or 180,000,000,000 ^ ^ only about one-ninth part of the light of Sirius, but still it offers a glorious blaze." Brinkley found its parallax between 2" and '"•52, Struve o"-i25, while Airy "has pronounced that its annual parallax is too small to be sensible to our best instruments." Briinnow remarks that the proper motion of this fine star appears to have decreased : the movement as deduced by three eminent astronomers is here given : — R. A. N. P. D. Years. Bradley o"-2839 o"-29o8 1750— 1830 Argelander -2661 '2675 1837— 1852 Briinnow '2414 '2643 1852 — 1869. The following are some of the values of the parallax which have been found : S. o"'26i 0.2. -147 Br. ■212 Pe. -103. H,. So. Sm, n6-8 38 •2 43 1321 41-52 1 37 '9 40 ms 41-13 I.SS-2 43-1 137-9 427 140-3 43-4 1782-36 92-3« 1822-87 30-00 25-56 30-84 7-51 43-34 O.S. Se. He. Br. 150° v. lea. Gl. Fl. 144-5 44-16 147-7 Sn. 45-24 150-2 6n. 46-16 5«'-SS -23 151-8 4 57-64 152-5 6 49-09 -2 6 47-50 154-0 3 48-4 -5 a -0 6 153-8 10 48-5 •8 9 -61 -7 4 ■5 -4 4n. ... 154-7 3"- 155-1 in. 48-14 1851-85 7-47 65-63* 69 t 71-58 2-72 3-45 4-70 -62 3-79 4-79 -So ■85 75-71 8-60 7-00 600 0.2. 360. R. A. Dec. M. 18" 33'» 4° 45' 6-5, 10 0.2. 292-6 I 3n. I i-n 1849-67 De. 291-3 I 4n. | -40 ' 67-16 601 %. 2356. Dec. 28° 36' R. A. igh 23-6"' Duner gives 1858-69. A=o"-96. P = 53'-2-f 0° -205 (/- 1850 M. 8, 9 -o). Ua. Se. Eng. Se. Du. W. &S. 01. 47-1 52-6 53-2 57-9 58-7 66-3 3"- 4n. 2n. 3n. single 3"- 54-3 58-2 54-9 56-8 55 -4 m. 9n. in. 1-03 0-86 ■85 -88 ■80 -55 0-96 -99 1-13 0-98 118 18 •42 43-94 51-88 7-26 9-40 62-73 3-53 5-31 -54 6-63 70-65 4-69 5-62 4-80 602 2. 2367. R. A. Dec. M. 18" 35-9" 30° II' 7. 7-5. 8-4 Probable change in angle (A B). AB. 2. 58-7 72-2 64-5 m. single ' elong^- 9) ft )) 11 [829-75 32-31 -80 -86 4-91 * " Distance corrected for refraction = 46" '171.'' t Position and distance determined from a very large number of observations extending over four- teen months. 358 DOUBLE STARS. 0.2. Ha. De. Sp. 2. 0.2. 0. Bond. 79-3 in. 0-S3 77-3 »» •54 76 7 ,, ■51 62-9 jj ■53 70-4 elong^- 735 ,, 242-3 0-32 1841-65 7-59 51-62 66-68 4377 64-67 75-65 A±B and C. 2S 1 93 '9 194-4 1937 ■3 194-8 '9y3 5n. 1 14-13 32 '53 in. ' -40 41-65 ,, 1 "23 7-59 - -28 51-62 ! -20 66-68 in. 51-62 603 Z 2384. R. A. 8" 38-4"' Dec. 67° o' C. yellow. M. 8, 8-5 A small double star discovered by 2. He says "there is scarcely any doubt that change has here taken place." In Mr. Bishop's volume, p. 141, Hind says, "Notwithstanding the strange coinci- dence of 2.'s individual measures in 1836, t seems very doubtful whether any alter- tion has taken place since the star was first measured." Dawes {Mem. R. A. 5., vol. xxxv., p. 408) writes, "Notwithstanding the strong doubts expressed by Mr. Hind, 1 cannot but regard this star as constituting a highly interesting binary system ; though its orbital move- ment is far less rapid than was indicated by the comparison of 2.'s measures in 1832 and 1836. 0. 2. (1876). The angle has not changed since 1836, but the distance has probably slowly diminished since 1832. 1832-34 6-87 0.2. 315-1 in. ... 40-57 -61 6-69 51-67 307-1 3n- 0-82 318-3 5n. ■65 315-1 in. 319-0 ,, 0-85 313-6 ») -53 321-3 ») -46 604 2. 2375. R. A. 18" 40°' Dec. 5° 23' Duner's formulas are 1851-40. A = 2"-22. M. 6-2, 6-6 P = iii°-2 +o°-i53 (/-1850-0). 2. Da. Ha. Se. Se. Ho. H. Su. 107-8 -8 108-6 103- 1 109-4 108-8 109-8 -5 111-5 -4 •6 -4 1 12-9 II I -9 -5 112-1 113-4 110-1 I II -6 113-S •o 1120 114-6 2n. 2-22 m. ■34 2n. -20 1-88 2-48 ■14 -27 -27 in. ■07 -OS -27 6n. ■33 -37 4n. -27 -24 in. -28 5n. in. in. in. 5n. ■30 -28 -23 -02 •33 •50 1-85 1825-60 8-66 3288 28-65 9-80 31-60 2-56 4-50 48-56 1-62 2-54 3-42 50-86 1-72 2-01 7-26 9-81 4-59 6-92 66-56 58-68 65-67 71-47 605 2. 2382. R. A. 18" 40-4"' e LTE.E. Dec. 39° 33' M. 4-6. 6-3 C. 2., A, greenish white ; B, bluish white. H„ A, very white ; b, a little inclining to red ; Sm., A, yellow ; B, ruddy. ina -an H, {Phil. Trans., vol. Ixxii., p. 217) : "Aug. 29, 1779. A very curious double- double star. At first sight it appears double at some considerable distance, and by attending a little we see that each of the stars is a very delicate double star." {Phil. Trans. 1804, p. 373.) " This re- markable double-double star has undergone a change of situation in each double star separately, which is not very considerable, but deserves our notice on account of a cer- tain similarity in the directions of the alter- ation. The position of n. 5, Nov. 2, 1779 MEASURES. 359 was 56° s' n.f ; and, by a mean of three obser- vations, taken Sept. 20, 1802, May 26 and 29, 1804, it was 59° 14', which gives a change of 3° 9', the motion of the angle being retrograde." He then states that this change could not be due to "the position of the apex of the translation of the solar system;" that the parallax thus arising would explain the change of the preceding, but not of the following star ; and adds, "The situation of both, however, is in a part of the heavens which is so rich in scattered small stars, that a variety of casual and merely apparent combinations may be expected." Hj and So. {Phil. Trans. 1824, p. 311) made measures in 1822. "The measures on the whole are favourable to a slow vari- ation in the angle of position." But as the change is so small, " it must be regarded as still open to further inquiry. " Ha, in the Mem. R. A.S., vol. v., p. 42, says, " The strong suspicion that these two elegant double stars, so very similar to each other in appearance, distance, and velocity of motion, form in reality a twin system, and have a combined rotation about their common centre of gravity, is increased by the fact that their rotations are performed in the same direction, which, from the analogy of the planetary system, and from that of t Cancri, the only ternary star hitherto suspected on any grounds of obser- vation to exist, might be expected." S. {M. M., p. 52) : "A small indirect angular motion appears indubitable." am. {Cycle, p. 429) : " The proper mo- tions in space assigned to this quadruple related system form a link in the chain of evidence which proves the connexion. In- deed, it may be roundly stated that B will revolve round A in about a couple of thou- sand years;" "and possibly both double systems may move about the central ones in something less than a million of years." 0.2. " The indirect motion still con- tinues. The distance appears to have changed very little. Our measures of dis- tance in 1841 and 1856 are no doubt too large." Duner's formulae are i854'o6. A = 3"'I2. P = 2i°-6 - o°-i85 (^-1850-0). The coefficient of/ — 1850 is very sure. AB. Hi- H, & So. S. 33 '9 in. ), (3-44) 3o'8 3n. 259 26 4-01 ■3 in. 3-62 24-2 ,, 2-95 270 2n. 3-I4 I779-S3 ■93 1803-84 22'12 3I18 2872 30'94 S. Da. Be. fSm. Encke. Oa. Ea. 0.2. Ua. Po. Ja. Kit. Bond. Fit. Hi. Se. Se. 25-5 in. 3-09 26 '0 3"- 2-98 20-5 3-12 237 2n. ■57 25-2 In. 24"3 2n. 3-32 21-9 Sn. •25 •7 In. ■16 ■4 3"- ■14 204 2n. ■20 19-6 4n. •12 •5 2n. •03 ■3 in. •06 25'2 •31 ■3 •s 23-9 •2 21-9 •3 20-6 ■2 197 ■0 24-0 ■42 22-3 ■50 23-8 •34 2I-I •06 24-9 ■19 •7 ■n 19-9 6n. ■•4 i8-s 2-95 22-5 4n. 3-52 23-6 in. •33 I9'i ,, ■31 i8-8 ,, •19 2I-I •16 i8-8 »» •37 ■5 3"- •22 19-5 »» ■06 161 •26 17-3 2n. •12 19-2 in. 174 ,» 221 3-19 23-2 I2n. •12 24-0 •23 217 7n. ■20 ■9 ■22 ■9 ■26 •3 •10 20 "6 •20 •9 •02 •5 I in. •13 •2 •16 19-4 131- •05 207 4n. •09 21 '9 •95 20 '4 in. 2 '46 21 'O ») 31 197 43 •15 214 35 •18 sn- •33 207 4n. ■35 194 In. •u 20 -o 3"- •18 193 4n. ■03 4 ■06 224 i9'o 3"- in. ■07 •28 i83r96 2 '50 4271 30'53 2-57 4-52 41-38 695 8-59 5371 471 •84 973 3072 73 645 978 42-59 5371 37-59 872 9-99 41-67 3-03 -94 31 65 65-80 40-74 2-71 51-88 273 7-51 7-76 8-57 61-50 2-83 3-53 6-48 49 4247 3-68 4-67 7-53 50-54 I 84 258 375 4-70 643 8-47 61-35 45-64 6-45 7-60 8-47 51-65 1-82 3-63 4-70 5-21 6-49 62-64 3-53 55-90 66-72 36o DOUBLE STARS. Uo. Eng. Ta, Br. 61. Schi. Sp. Sob. Goldney. 207 187 •8 20 '4 13-8 14-0 136 17-4 151 149 153 190 17-2 190 14-2 ■2 19-8 23-0 :s:^ I7'4 i8-3 •o 197 >4-3 171 l6'o •6 17-4 'o -J, i6-i I ■7 i •2 ' ■9 •9 I 17-4 15-3 163 i8-6 2n. 3n- 2n. 7n. 2n. In. 3n. 2n. 3n- 411. 2 4 4 3 8 II 6 8 5 2n. 6n. 2n. in. 3"- 411. 3 '09 ■20 •16 ■06 •29 •00 ■22 ■37 •18 •28 •29 ■18 ■24 ■25 •19 ■10 •29 •41 •60 •14 ■15 2 96 3 '09 ■33 •18 •13 3-02 ■22 31 3 '07 •08 3 '24 ■04 •18 606 S. 2383. R. A. 1 8*' 40 •4"' Dec. 39° 29' -90 : 1 845 "64 58-43 9'co 61-45 7-41 879 976 70-38 •41 ■43 •79 2-45 •47 3-43 4-59 5 -69 64-45 6-51 7-54 •73 873 973 73-84 68-59 71-57 •52 •53 3-55 6-59 3-48 -81 •50 5->8 ■56 8-63 5-63 ■63 •93 7-43 8-56 71 M. 4-9, 5-2 Magnitudes. — " The difference in bright- ness seems variable." (2.) The mag- nitudes of E, F, G, are 9-5, 12, 12, respectively. C. H„ -white ; S. , very white ; Sm., -white. H, {Phil. Trans., vol. Ixxii., p. 217) : "The stars of the second set are equal, or the preceding of them rather larger than the following. The inten-al between the equal set with a power of 227 is almost 1 4 diameter of either; with 460, full I J diameter ; with 932, two diameters ; with with 2010, 2j diameters. These estimation.s are a mean of two years' observations. Position of the equal set 72° 57' s.f." H, {Phil. Trans. 1804, p. 373) found the position on Sept. 20, 1802, May 26 and 29, 1804, was 83° 28' and 75" 35' s.f. ; this gives a difference of 7° 53', the motion being retrograde. Hj and So. {Phil. Trans. 1824, p. 314) : " The change surmised by Sir \Vm. Herschel in 1804 seems to be well borne out by sub- sequent observations, the total alteration in the angle being no less than 13° 51', averaging o°-325 per annum in the direction n.p.s.f, or retrograde.-' H, {Phil. Trans. 1826, p. 375). After giving his observations in 1825-53, ^^ '■^" marks: "The change of position in 31 1 years amounts to — o°-45. Calculating on the presumed angular motion — o°-325, it should have been — i°o'. The difference is nearly insensible." 2. {M. M., p. 52) : "Indirect motion is beyond doubt." The angular movement in this pair is in the same direction, and very nearly of the same amount, as in the preceding pair- Both the distance and the angular change have been very constant: between 1779 and 1831 it was — o°-355 ; between 1831 and 1862, -o°-335 per annum. (0.2.) Duner gives 1853. A -2" -58. P = i49°-2 — o°-36o (/- 1850-0). C D. H2& So. s. Da. 'nn. 1878. 173-5 m. 1779-83 167-3 5 1804^08 159-9 8 3-8o 22 42 -2 28 -34 5-53 156-4 8-72 157-0 3-26 32-57 159-6 m. 2-50 28-72 I54-I 2n. •68 30"94 156-3 in. •69 1-96 154-0 3n- •48 2-50 157-3 5n. ■92 0-57 156-2 m. •62 2-57 154-2 2n. •86 4-52 152-8 ,, •57 40-72 151-8 ,, •65 1-66 149-9 in. •44 6-95 MEASURES. 361 Sa. Be. Sm. Encke. Ga. Ea. O.S. Ua. Ja. Po. Kit. Bond. Fit. Ui. Oe. Se. Mo. U. 1489 1 47 '4 I46'2 145 '9 ■8 I44'8 I56"i 157-1 i54'3 150-9 148-1 1537 1 55 '4 152-8 151 -o 152-7 -o i5f3 149-0 143 'o 142-6 151-1 150-1 147-6 ■9 144-6 143 '9 144-6 146-2 145-6 •5 142-6 i53'6 -2 151-9 ■5 150-2 149-6 148-5 149-2 147-4 146-8 -6 ■3 144-5 145-2 150-7 -8 149-2 -o 147-0 146-7 147-0 146-7 147-5 143-8 144-2 148-4 150-8 146-7 152-6 318-2 139-4 137-6 4n. 2n. m. 6n. 3n- 2n. m. 2n. 3"- 2n. m. I2n. 7n. 1311. 3"- m. 45 24 5n. 411. 2n. 4n. 4n. m. 30 3n. 2-59 -45 -42 -47 -54 -55 ■82 -8 •5 -6 -5 ■95 3-35 2-5 -71 -49 -61 •69 -52 -34 •37 -73 -50 -78 •51 ■55 •42 -49 -52 ■54 -45 2-50 -85 -72 -79 -74 •83 •81 •48 -93 -66 •70 -65 •21 -62 3-10 2-76 •55 ■5 -42 -49 •60 •70 ■68 -50 •45 •57 ■49 •75 •48 -43 -10 -57 -44 1848-54 53-71 4-72 -84 9-73 65-75 30-72 •73 4-52 42-59 53-71 37-59 8-72 9-78 -99 41-67 3-03 -94 51-65 65-80 6-84 40-83 2-71 51-88 2-73 7-63 8-50 •61 61-50 2-83 3-53 6-48 41-49 2-47 3-68 4-t>7 7-53 50-54 1-84 2-58 3-75 4-70 6-43 84-7 9-40 61-35 46-14 -63 7-60 8-47 5>-57 ■82 3-63 4-69 6-46 62-64 3-53 56-06 65-54 45-64 58-42 61-45 7-41 8-79 9-76 Eng. Bo. Ta. Da. Br. ■W. &S. GI. Schi. Sob. Goldney. 137-2 in. 2-37 1869-76 138-4 »» -48 139-6 ») 2-52 7043 -8 11 ■40 -45 -s „ ■47 -79 137-2 2n. •50 2-45 138-3 in. •38 3-42 -2 2n. •35 4-61 143-4 7n. •55 65-39 m. -49 -54 141 2n. 6-51 142-3 m. 2-53 7-54 139-4 ,, 74-61 143-2 2n. 2-41 67-71 139-9 j» ■29 8-73 141-4 3n. •35 9-73 -5 4n. ■43 73-84 -8 2 -64 68-69 146-3 4 ■48 7>-57 142-0 4 ■7 -52 144-2 I -53 141 -2 4 2-7 •55 1394 12 -62 6-59 141 -2 7 3-48 142-1 6 2-5 -81 138-6 2n. 5-28 136-3 6n. 6-56 138-2 Sn- 2-40 8-63 139-2 m. -39 5-63 ■3 -40 -63 -3 3n- -93 137-3 ») 2^35 7-43 139-1 )» -24 8-56 -3 4n. -43 •71 Small stars between e^ and e'. A C. w. &s. 173-0 -0 -8 4 3 1 AE 207-0 206-2 ... 1871-57 ■52 •53 w. &s. 135-2 134-7 -5 I 2 I A F 144 2-52 ■52 ■53 w. &s. 180-5 -0 I 1 AG 139 -52 ■53 w. &s. 167-5 164-6 I 2 C E. 108 •52 •53 w. &s. 36-6 35-9 37-9 1 1 1 C F. 129 -52 -53 -53 ■w. &s. 338-4 339-3 I 1 71 ■52 -53 362 DOUBLE STARS. W. &S. 1-2 •4 vr. & s. 248 9 250-0 C G. E E 11872-52 I '53 ■52 •53 W. & S. 268-5 I I I 77 I '52 •si I I ... I -53 GF.* So. 220 i I 53 I 23 H,. 221 48 31 W'. ft S. 219-2 in. 44 72 Bu. 38-4 : I 46-7 I 78 E H. Bu. 357-0 I I 25-0 I 78-36 c' and e\ Sm. 172-5 207-3 3073 -9 2u6-8 6-45 S. -2 207-1 5-23 Be. -9 -7 63-15 Eng. -8 206-3 4'4S M. 4 In. 209-7 6-47 W. ft S. 1730 „ 206-6 7205 Fl. 172-8 „ 207-1 7-52 * The values for A E, A F, A G. C E, C F, C G, E F, E G, F G, given by W. and S., were calculated, not measured. 607 S. 2398. R. A. iS*" 40-9°' s. Ha. Dec. 59° 25' C. A yellowish, B bluish. De. n. I34'4 12-42 J 37 -4 ■97 138-6 13-27 142-8 15-56 1447 in. 16-52 M. 8-2, 8-7 1832-17 44-91 7 "32 65-04 77-88 608 2. 2896. R. A. Dec. M. 18" 42-8"" 10° 38' 7-7, 11-2 2. {P. M., p. ccxxx.) shows that the smaller star does not partake in the con- siderable proper motion of the larger star ; and 0.2. finds that the following formulae represent the observations quite well : A A = — ii"-790 ± o"-o5i — (o"-i222 ± o"-oo44) (/— 1850-0). A D = + 2" -204 ± o"-o5i + (o"-4579 ± o"-0O44) (/— 1850-0). S. Ha. 232-6 31. 11-74 285-3 2n. 12-28 267-4 10-31 1829-60 51-90 4371 Ma. 0.2. De. W. &S. n. 2757 276-5 284-7 286-3 287-6 278-2 292-4 3047 •4 3i3'S 31 1 -9 3I4'6 10-32 11-75 12-57 -40 3n- 11-71 2n. 13-96 ,, 16-64 ■39 4 19-9 4 -92 in. 21-02 1846-73 777 5075 173 2-78 49-09 S7'i4 65-76 ■44 74-65 563 775 609 0.2. 363. R. A. Dec. M. 18" 43° 77° 33' 7-5. 77 0.2. 199 5 In. 0-57 1842-73 13-8 »» •63 4-85 20-2 »» •50 6-69 26-5 ,, ■49 75-34 De. 19-7 3". 67-61 610 2. 2400. R. A. 18" 43-5" Dec. 16° 7' M. 8-1, 10-6 At first glance the observations seem to indicate an occultation produced by orbital motion : this view, however, is not con- firmed on a more careful scrutiny. On discussing the observations, it was found that the changes have been caused by the proper motion of the larger star, and that in 1871 the minimum distance would be reached. Some uncertainty still remains for future measures to remove. (0.2.) 2. Ua. 0.2. 305-2 2n. 2-96 303-2 )» -74 300-1 1-99 301-0 2-20 299-9 1-80 275-3 in. -77 1 ± 246-? 0-8? I ? single 238 I ± 236-3 I 02 1829 33 43 6 8 SI 4 5 7 18 16 70 47 45 62 •63 67 •61 67 ■53 59 72 •61 611 R. A. 18" 44-1"° 2. 2402. Dec. 10° 32' M. 8, 8-4 The measures by 0.2. and Secchi seem to indicate a slight angular change. MEASURES. 363 Ua. 0.2. vr. &s Gl. ■w.o. Schi. Sp. 196-3 •2 20I-8 204-3 208 °4 212-0 229-4 218-5 215-6 218-4 208-8 213-4 203 -8 206-9 205-9 202-1 -2 207-1 203-2 205-7 204-2 206 -6 -6 2n. 0-68 m. •85 -70 -68 -68 in. 0-91 -81 ,, •95 2n. in. 7 1-04 0-89 -84 •98 2 I'O 3 -0 4 -0 4 0-8 6 •97 in. 1-09 in. 0-85 •85 1828-68 9-64 3377 8-83 43-65 52-63 61-66 40-51 1-55 •66 72-61 56-64 65-63 72-51 -55 -56 4-65 5-63 4-73 •68 -68 5-66 -67 612 Z 2409. 2. o.s. R. A. 18" 46°> The amount still uncertain. 32-5 48-0 49-7 45-3 42-4 38-5 43-1 371 38-5 31-7 Dec. M. 613 ox 364. R. A. Dec. M. 18" 48°" 25° 12' 7-5, 10-5 O.S. could not see the companion in the years 1845, 1847, and 1852. De. in 1865 found it " not round." O.S. 162-8 I in. I 0-74 I 184267 614 2. 2420, R. A. 18" 49 •4" Dec. 59° 14' M. 4-6, 7-6 Probably a case of rectilinear motion. The proper motion of A is + 0*005 in R. A., and — q"-oi in N. P. D. So. Sm. O.S. Ma. Ea. De. U. Fl. 306-0 350-8 346-5 345-6 349-2 3476 345-5 -I •I 3427 338-9 -9 344-8 -2 •o 345-0 341 '5 3406 341 o 339-4 26-65 3n. 30-26 6n. -38 29-95 304 •3 In. •52 ,, ■64 ,, -82 ,, 31-52 „ -66 32-10 30-59 -48 -27 3n. •93 4n. 31-01 in. 32-10 „ 31-87 178076 I8I4-I3 32-60 639 22-14 30-78 7-89 9-85 40-84 51-67 70-87 4-73 41-48 332 7SI 1-74 58-21 63-14 5-43 77-76 615 OX 525. R. A. Dec. 18" 50" 33° 48' M. A 5-1, B10-3, C7-1 I 3° 23' 8,9-3 f angular change, if any, is 6n. 0-98 1832-76 in. i-oo 40-57 »» 0-82 1-55 I 03 2-72 -18 7-59 873 I -06 ■74 -12 52-67 •01 72-61 2 n. -05 5665 C. A yellow, c blue. O.S. observes that it is very remarkable the stars A C should have been measured three times without B being detected. De. has estimated the magnitude of B as the 8th and 9th. O.S. has twice entered it as the nth. AB. 0.2. De. 1280 132-8 7n. 2n. AC '■5| ■36 1 1849-70 1 69-77 O.S. De. 350-5 •6 ion. 2n. 45-50 -43 46-98 69-77 616 X 3130. 0.2. 365. R. A. 18" 52" Dec. 44° 4' M. A7-4, B8-5, c ii-i A B. — In August 1841 the star A was readily seen to be double, but in the Sep- tember following it was twice examined with- out the companion being detected. It was oblong till 185 1, quite round in 1852 and 1854, and again readily separated in 1857, the relative position being the same as in 1841. Hence the period is probably six- teen years : possibly, however, the pheno- mena may be explained by the variability of the companion. (0.2.) A C, probably unchanged. 364 DOUBLE STARS. AB. 0.2. 168 -I 212 232 235 212 226 242 250 276 273 1661 262 '9 266'2 26o'3 2657 261 6 262 6 264 '2 256-5 264-6 •4 0-50 oblong obi. ? oblong obi. ? '■ 0-20 ' oblong ' single ! 0-50 A C 6n. 2-69 m. ■94 •59 78 •78 •36 •74 •64 ■99 •96 S41 -65 485 •85 5 '65 6-69 7 '59 8-74 9-82 51-60 •75 2-63 4-64 ■69 7-67 33'37 41-65 4-85 7-59 8-74 9-82 52-63 4-64 -69 7-67 617 s. 2422. R. A. Dec. M. 18'' 52-2 m 25° 56' 7-6, 77 Probable change in angle. Duner gives 1849-08. A = = o"-79. P = 104-4 -o°-i /— 1850-0). 2. 106-0 6n. 0-85 1832-10 0.2. •5 2n. -98 4069 loi-i in. •74 52-67 100-3 ■87 1 7-61 96-8 „ ■85 72-61 Ua. 105 -I 7n. •77 43-08 Se. 106-8 3n- •83 56-88 Se. 100-6 in. •7 63-53 99-0 ■79 ' 5-73 100-5 •84 8-66 98-0 „ -8 : 73-49 100-6 ,, ■74 4-49 Du. ■5 6n. -72 ' 69-16 W.O. 97 4 ■97 74-66 Sp. 98-5 •76 5-68 618 X. 2424. R. A. Dec. 13° 28' Considerable changes (.see /'.jl/., p. ccxxi.), probably due to the proper motion of the brighter star. Smyth's magnitude of A is from Piazzi : his own estimate was that "it certainly- appeared bright enough to be rated among the 6th, on careful comparison." He gives B as of the loth magnitude, A as of the 7th. Dun^r's estimates are 5, 10. Duner gives A sin P= — 16"-55. A cos P= — 6"-9i +o"-iii (^-1850-0). So. Sm. Ma. Se. 0.2. Da. W. & S. Gl. Dob. M. 57, 9-2 238-6 236-4 241-6 248-6 240-5 •9 244-9 247-5 ■5 248-1 252-1 254-2 -Q 255-8 258-5 2S5'9 257-4 256-7 3"- 2n. 5n. 31- 2n. in. 4n. in. 2n. 4 5 4 4 2n. 7 20 06 18-66 17-82 19-66 17-07 •45 16-50 •13 17-43 16-87 17-23 16-9 17-7 -29 ■5 16-74 1802-76 20-64 31-31 51-90 25-11 3261 44-22 52-05 6-82 62-72 3-48 8-75 977 74-65 -65 5-63 473 7-52 619 2. 2429. R. A. 18" 54" H,. So. Ma, Ta. Dec. 285-0 290-3 289-5 288-8 287-9 2n. 5-47 3"- •32 in. •67 ,, -96 M. 8-3. 9-8 1783-21 1825-57 9-83 43 "40 66-47 620 S. 2438. R. A. Dec. M. 18" 55-5- 58° 4' 7, 7-6 Certain change in angle and distance. The periastre was probably passed either between 1842 and 1870 or since the latter year. (0.2.) H,. 355 358-4 I 1782-68 3-26 H,. 337-8 0-7 1830-00 2. 340-6 4n. 72 2-53 Sm. 341 •7 4-53 O.S. 348-7 2n. ■69 40-57 341-8 in. •52 6-69 306 ») •53 70-87 single •92 Ua. 338-0 346-6 0-6 41-48 3-32 Da. 335-1 in. 0-65 I -80 Se. 333-2 4n. -4 57-54 De. 330-0 elongated 63-62 W. &S. not elongat :d 73-58 MEASURES. 36: 621 2. 2434. R. A. 18" se-s" Dec. M. - 0° 53' A 7-9, B 8-4, c 10-3 C. Sm., A and B, white ; c, blue. A B is H, IV. 127. B C is S. 2434. Between 1831 and 1864 the distance of AB seems to have diminished about i", and the angle to have decreased about 10°. The change in the angle of B C also amounted to about 10° in the same time, the distance remaining nearly as when first measured. In A B the motion is rectilinear. B C form a physical system in rapid motion. Duner, exclud: Madler, finds the 1854-2 P = 74°-8 - ing the observations following : I. A = o"'92. o°-3i2(/- 1850-0). of Ua. A B. H., & So. So. 2. Ma. Hit. H. W.O. Se. W. &S. 61. CO. Fl. 159-9 •7'7 148-8 10 26-01 -6 25-8 146-8 -6 147-0 4n. •56 145-8 ■45 142-9 -66 141-3 in. ■77 139-8 24-24 138-9 -48 136-8 2n. ■23 137-1 m. 23-28 133-4 6 24-73 136-8 2n. -29 132-7 2 23-5 •2 4 24-1 134-1 7 -0 133-4 6 132-9 4 24-0 133-4 3 -18 -2 6 23-8 -6 2n. 24-31 ■8 in. 23-89 ! BC. 2. Sm. Ua. Hit. Se. De. W. &S. CO. 80 5 85-0 80-6 72-4 68-7 72-0 69-6 70-4 67-5 63 -2 1783-60 1823-48 31-48 8-59 1-57 5-53 4-45 8-65 5>-75 6'93 66-65 47 0.2. Be. Du. vr. &S. Gl. Sp. 80-8 82-9 76-7 74-0 70-5 65-8 53-8 62-3 63-0 74-1 72-5 74-4 71-4 74-7 66-4 71-6 68 5 71-4 65 -s 72-7 62-8 68-5 67-0 68-3 -o 67-9 70-7 Sn. 8n. 2n. 1-08 -o 0-99 -93 •98 i-oi 0-45 •6 I» •7.') 2n. 1-36 in. ■04 fj ■02 tt 0-96 ») '•05 .1 -02 2n. 0-94 in. -s 41. •8 in. 1-06 5n. 0-80 4 -86 6 i-o 3 0-86 4 -8 4 -8 II 1-02 •02 1830-79 I -00 9-60 44-26 52-22 5-26 8-81 9-74 62-70 40-76 2-76 6-69 7-59 9-73 72-61 57-10 66-73 3-06 4-49 70-09 2-50 3-55 •56 4-67 6-52 4-73 5-6i 3n. 1-93 2-0 -20 2n. 1-54 »> ■73 in. •0 2n. -79 2 ■5 4 ■09 2n. ■5' 1 63 4-66 623 t 2441. 72-56 -62 R. A. Dec. M. 3-55 ■55 4-67 18" 58-1"' 31° 13 7-7, 9-3 Indirect motion. 5-66 2, 291-9 3"- 5-22 1830-34 ^V Ma. 290-1 -19 7-33 7-67 •76 288-4 -II 43-77 •5 -20 5'4t 287-4 4-69 51-88 283-8 5-03 2-68 1831-58 2S5-5 •18 7-99 8-59 Se. -3 2n. •64 ■'3 44-45 284-0 in. -77 65-63 8-12 0.2. 281-7 -49 8-6T 57-12 ' 280-4 -05 74-72 66-57 De. 285-1 -36 63-47 4-66 1 284-4 -22 6-54 72-56 1 283-4 -26 9-50 3-55 ! •I ■14 74-70 7-68 j 282-4 ■27 7-78 622 Z 2437. R. A. Dec. 18" 56-6"' 19° o' Certain but slow movement. 624 t. 2442. M. 7-8, 8 I R. 18" 2. Ma, 207-6 •2 Dec. M. 16° 48' 8, 9-5 2n. I 23-05 I 1828-77 in. I 22-55 i 43-70 366 DOUBLE STARS. 625 X. 2454. M. 8, 9-2 R. A. Dec Considerable angular change. While setting for this star in 1840, 0.2. detected another pair, of which he gives the following measures : Angle. Distance. Magnitudes. 160° o"-68 1840-51 8, 9 i55°-8 -43 2-72 In 1866 a careful search failed to reveal the existence of this object. 1831-50 0-84 6-68 66-68 72-61 4376 57-57 65-32 72-45 3-55 -56 663 469 5-89 M. 8-2, 8-2 1829-43 44-90 7-85 50-81 2 02 9-86 64-46 -82 76-63 7-86 V 203-9 o.s. 223-7 214-9 233-9 236-3 Ma. 20S-I Se. 217-0 Se. 225-9 Da. 235-2 W. &S. -I 230-0 232-4 w.o. 231-6 Sp. 235-0 3n. 0-75 in. 100 »» 0-80 It •95 -82 -6 in. -45 1-26 5n. 0-81 in. i-o )) 0-79 -88 -87 626 S 2456. R. A. igh 16" 2. Ha. Eng. Se. Sob. Fl. Dec. 38° 21' 13-6 31- 29-07 : 120 ii-o 27-50 -4 28-00 -2 27-34 10-7 9-0 26-76 •3 •48 7-1 in. -5 »» 25-59 627 2. 2455. R. A. 19" 1-8™ Dec. 21° 59' M. 7-2,8-3 Duner has computed the following for- mulae : AsinP = +3"-Il +o"-OH (/ — 1850-0) — o" -00031 (/ - 1850-0)-. A cos P = — 2"-48 + o"-o58 (/ — 1850-0) + o"-ooo25 (/ — I85o-o)^ The measures appear to indicate a physical relation, but the curvature is so slight that the movement may possibly be rectilinear and uniform. H,. 140 4 2. 144-S 3"- 4-93 m. 136-6 -42 132-6 6n. •16 125-2 in. 3-74 124-9 2n. 4-07 -2 Sn. 3-66 122-2 2n. -65 120-5 in. 4-04 116-1 2n. 373 Mo. 124-3 31- -98 Se. 123-0 )> -70 i'3-4 in. •77 Se. 1 15 -6 411. -52 -3 2n. -55 114-4 4n. ■39 111-8 in. -48 109-9 >j •22 -7 »» -48 106-5 -40 -5 »j -08 105-3 »» •35 Eng. 114-2 3"- -51 Du. 1 10-8 6n. -41 W. &S. 109-7 6 -7 107-2 3 109-2 4 3-42 ■7 8 ■37 Gl. -5 10 ■30 Schi. 104-8 in. -48 Sp. -8 •49 1827-64 8-77 39-29 44-57 50-74 2-64 3-99 873 61-74 2-84 55-66 7-29 65-64 4-60 5-66 7-20 9-63 71-65 2-67 3-71 4-67 5-67 65-58 9-95 72-64 ■55 3-55 4-67 4-73 5-61 -61 628 2. 2464. R. A. Dec. 11° 41' M. 8-2, 10-5 Ma. Se. W. &S. 19-2 16-2 24-1 33-5 21 26-5 3n- 2n. m. 1-36 1-10 1-25 -0 1830-36, 42-36 3-67 51-73 7-12 76-32 629 2 2471. R. A. Dec. 7° 56' M. 7-9. 10-7 Certain change in angle and di stance. 0.2. 121-8 126-6 127-9 4n. in. 7-63 8-24 10 1830-18 72-56 4-72 630 2. 2479. R. A. Dec. M. 19" 5-9" 55° 8' A 7-1, B 8,09-4 Duner has 1847-57. A = 6"-63. r = 36=-4 -o°-io it - 1850-0). MEASURES. 367 AB. Se. 2. Ua. Be. De. Sn. 40-9 36-8 20 '2 elong^' 0-6 A C. 38-0 411. 6-65 37-0 in. ■40 34-0 j» 7-23 •9 )» 672 35-6 2n. •66 1863-87 70-83 4-09 32-61 44-37 59-80 63 "49 7i'i3 631 %. 2481. R. A. Dec. M. 19" 7-1" 38° 35' 8, 8, 9 The common proper motion of A B is — o"-29in R. A., and + o" -097 in N. P. D. C is Secchi No. 3. Duner gives the following formulae ; 1853-72. A = 3"-90. P = 23i'^-6 - o=-23 U - 1850-0). A and B + C Hi- 2. Ua. Po. O.S. Uo. 8e. De. U. Sp. Du. Lindstedt. 261-6 234-3 3"- 3-83 235-3 in. 410 231-5 j> 3-73 49-3 4n. 4-02 230-3 2n. 3-96 -8 3n- -99 ■I In. 4-73 223-7 ,, •3' 226-0 n -32 225-5 3-95 224-5 3n. ... Se. O.S. Sp. 93-4 98-2 88-7 86-5 BC- in. 0-4 -4 -59 -52 1783-33 1830-45 43-74 8-53 55-56 6-59 7-80 8-44 65-44 9-77 75-65 6-75 -75 56-83 9-61 66-74 75-64 632 t. 2484. R. A. jqU gm 2. Ma. Se. Dec. 18° 52' 218-4 220-3 224-3 221-9 223-3 229-9 224-0 ■5 227-7 -8 228-4 5n, 2-50 -47 -43 ■43 -64 31- 2-49 in. •58 ^1 -68 )» •68 )» -29 M. 7-4, 8-9 1831-76 6-46 43-72 51-80 2-63 61-70 57-26 63-48 6-70 7-63 72-75 0.2. w. &s. 01. 224-8 3n. 2-61 232-3 in. -5 224-6 ») ■78 232-5 n -51 1871-34 4-73 6-31 4-84 633 2. 2488. R. A. Dec. 49° 37' M. 6, 6-5 The distance has diminished. The common proper motion is — o"-22 in R. A., and - o"-647 in N. P. D, (2.) Duner's formulae are A = io"-28 - o"-oi2 (/- 1850-0). P = 223° -2 - o'-o8 (/ - 1850-0). 2. Ua. Po. 0.2. Uo. De. U. Dn. Gl. Dob. 224-7 6n. 10-49 2236 -23 222-8 2n. -38 -I •53 -5 31- ■17 -3 2n. •55 -8 4n. -22 221-8 2n. •28 222-3 in. -18 220-9 )» 9-90 222-6 6n. 10-17 -8 Sn. -21 221-9 9-97 223 3n- IO16 221-8 9-99 ■8 4n. 1007 -4 4 9-8 222-1 7 lo-i 221-3 4 -26 ■4 10 -2 2203 4n. 9-81 O.S. Ua. De. W.O. 217-5 2190 2171 214-5 235-6 635 t. 2491. R. A. Direct motion. Dec. 28° 4' 1834-62 43-84 5-85 7-85 51-90 60-65 47-36 51-85 70-92 4-73 56-70 4-76 67-64 57-52 63-31 9-73 74-72 ■78 5-66 4-84 7-45 634 O.S. 368. R. A. igli 10-5" Dec. M. 15° 57' 7-3. 8-5 6n. o-8i 1850-40 -60 43-39 -67 51-73 single 6-67 ; o-8o 7-71 4n- ! -93 67-13 i 1-84 74-72 M. 7-9. 9-2 368 DOUBLE STARS. 2 206 '6 4n. 1-08 1828-77 Da. 2II-5 3"- •23 41-41 Ma. 204.4 0-96 2-56 "4 I -20 8-45 Se. 2II-5 2n. •05 56-68 O.S. 2221 in. •19 72-61 W. &S. 208-8 •03 5-67 Sob. 215-8 in. 6-71 636 t. 2509. p. XIX. 108 DEACONIS. R. A. igi> 15-6°' Dec. 62° 59' M. 7, 8-1 2. says (M. M., p. 296) : •' Angular motion is very probable." Ho (VI/fOT. k. A. S., vol. vi., p. 53) writes in 1830, "perfectly divided with 480 and the whole aperture : 320 gave a sensible elongation, but would not reduce the discs small enough, and separate them from the flare surrounding them." Probable diminution in angle and increase in distance. (0.2.) 2. Sm. 0.2. Ua. Se. De. Gl. 3567 347 'o 353-6 3=47 345-8 349-0 352-4 347-7 345-2 343-8 339-3 346-5 340-3 3397 345-1 341-7 -6 ■4 342-3 341-8 in. 0-42 ,, -45 ,, -66 ,, •55 3"- -57 S in. -76 ,, -6S •• -64 0-55 •67 3n- •69 I ,, 0-8 2n. •9 5 •81 4 -81 7 -66 10 i-o [831-96 2-34 -45 •45 6-93 8-78 40-61 5-69 6-69 1-47 3-40 8-20 57-43 8-53 62-70 3-39 72-64 3-58 4-73 -84 637 t. 2514. R. A. ig'- 16-8" De. 277-0 306-8 Dec. 67° 28' 3"- I 7-39 8-12 M. 9, n-3 1832-67 66-58 638 2. 2515. R. A. Dec. 21° 17' M. 8,9 Ha. 18-3 19-8 20-4 •I De. 21 -I 22-5 18-74 17-07 16-49 •42 •78 14-60 1829-20 47-69 50-74 1-85 2-64 65-04 639 O.S. 372. K. A. Dec. M. ig" ig-gm 46=59' A 7, B 88, C IO-5 B C form a binary system, most probably. AB. 0.2. De. 57-2 •2 2n. , 31- I BC. 79-44 ■53 O.S. 293-6 4n. 3-38 Ma. 298-0 2-95 286-9 3-20 De. 2g6-i 3n- ■74 1849-67 67-93 47-46 3-65 5-68 67-93 640 R. A. 2. 2521. Dec. 19° 39' M. 5-5. '0-3 Certain change in angle and distance. Sm. 0.2. 45 46-4 43-5 40-9 44-8 43-5 40-2 39-6 3n- 2n. in. 15 20 22-64 23-36 25-0 2226 23-96 1827-64 30-00 29-40 51-89 33-58 48-06 66-74 875 641 S 2524. R. A. Dec. ig"" 21-6'" 25^ 15' Duner has 1854-23. A = 6"-8o. P = i02'-8 — o"-09 (t — 1850-0). M. 8-3, 8-5 Ma. Se. Mo. Du. 104-6 103-5 105-6 101-7 -I •3 31- in. 5n. 7-i6 6-31 •67 7-18 6-93 ■57 1829-76 43-63 56-59 7-65 -64 68-51 642 2. 2525. R. A. Dec. 27° 5' M. 7-4. 7-6 The angle and distance have diminished. MEASURES. 369 o.s. Da. Ma. Se. Se. W. &S. Gl. Sp. 255-9 5n. 1-33 1830-43 ■5 2n. •30 6-14 251-8 in. -04 40-56 2531 »» •52 -84 246-8 )» -05 54-63 240-6 »» 0-75 65-72 242-4 »» -73 -80 234-0 1* -66 72-61 255-5 1-25 40-62 251-0 0-82 2-41 254-0 -95 3-69 247-1 -8s 56-61 239-9 in. -40 65-64 240-8 7n. -60 •22 232-6 4 72-64 225-8 2 o-s 3-57 237-8 2 -5 4-75 3f 3 5-66 234-2 TO 0-48 4-84 232-2 -43 6-00 643 %. 2538. R. A. So. H.. 2. Se. Sn. 0.2. W. ft S. Gl. So. H,. 2. Ma. Se. Sn. 0.2. W. &S. 01. Dec. 36° 27' M. 245-2 242-1 245-2 244-7 246 I 248 I 243-2 ■4 56-5 53-9 52-5 52-8 54-5 -6 53-9 AB 2n. 53-23 In. 55-06 2n. 53-04 ,, 51-78 3"- 52-95 in. ■8i J' -85 B C. A 8-2, B 8-3, C 8-7 1825-57 30-60 -85 57-90 69-68 70-92 4-75 -85 25-57 30-08 -87 43-75 57-90 69-58 70-92 4-75 -85 2n. 6-30 31- 7-04 6-07 2n. 5-95 ,, 6-02 5n. 5-92 -96 in. -9 ,, 6 04 644 2. 2541. R. A. ig"* 30-2" Dec. — 10° 42' 8m. Ma. Mit. 0.2. Se. Ba. U. 339-9 338-4 -4 336-9 -2 337-6 -6 340 323-0 3n. 2-84 2n. 3-61 -2 2-86 2n. 3-02 -36 2n. -47 2-5 in. 3-25 M. 8-2, 9-8 1831-01 51-85 35-58 43-63 8-19 51-91 7-17 9-80 61-74 De. W. &S. CO. 329-1 It 3-29 1864-59 332-0 tt •48 667 -3 ,t -49 7-6i -3 »» -42 72-71 370-2 2-76 6-6i 319-8 3n. 3-69 7-56 645 R. A. OX. 376. Dec. 33° 57' M. 7-1, 9-8 O.S. De. 228-6 233-5 6n. I 2-60 I 1848-52 3". I -72 I 66-65 646 2. 2544. R. A. 19" 31-3" A C unchanged. Dec. 8=3' AB. s. «?- Ha. De. 218-4 221 '2 217-8 208-9 W. ft 8. 207-7 Gl. 3"- 1-14 1 -5 -2 -2 in. 0-5 »> -42 205-2 A C. 239-2 I Sn- I 161 M. 7-8, 9-5 1828-99 30-00 42 7 1 64-21 74-17 -84 2899 647 O.S. 377. R. A. Dec. jgh 22"> 35° 22' Direct motion in A B. AB. 0.2. De. Du. M. 51-2 2n. 0-88 45-0 ,, -86 .38-3 3n. -7 45-0 5n. -85 De. Du. 154-7 -7 -A- + B and C. 25-14 -36 3"- 4n. A 8-4, B8-5, C9-2 1842-68 53-20 67-64 71-07 67-64 70-70 648 0.x. 378. R. A. O.S. De. 283-8 287-4 Dec. 40° 44' I 3n- 1-29 -25 I 24 M. 7-2, 9 1 1846-05 I 66-44 37° DOUBLE STARS. 649 2. 2556. R. A. 19" 34-3°' Variable ? 0.2. Ha. Be. Oe. Dti. W. AS. W.O. 8p. Dec. M. 21° 59' 7'3. 7'8 Certain indirect motion. 1829 83 40 '84 5077 6-58 72-64 41-56 2-67 3 '04 4 '44 56-88 64-91 896 73'57 4-68 5-6i 188-4 3n- 0-56 183-4 in. •73 176-1 ,, •59 345-9 ,, •57 1 63 "4 •55 191-I ■5 •7 •45 188-1 7n. •98 189-9 •55 179-1 3n. ■49 1 167-7 175-0 4n. 0-52 round 167-7 m. 0-63 126-2 •45 1 650 0.1. 380. R. A. Dec. M. 19'' 36-9" "° 33' 6, 7-2 Slow retrograde motion in A B. In 1842 0.2. discovered the small star C, but it was invisible in 1844, 1849, 1851, and 1872. Dawes never saw it, but De. sus- pected its existence in 1865 and 1869. A B. Ha. 80 -8 1 67-8 1 H,. 72-4 i 74-6 1 73-0 0.2. 74-9 ' '7 1 8n. Be. •0 1 77 •o 1 in. Se. vr.o. 79'7 j 69-6 77^4 ■' 5"- 0^73 ■33 -20 •59 •49 •47 -62 •54, elong"- 0-51 0.2. Ha. De. AC 160-3 I '"■ I •'21 69-0 I 342 •? I C invisible < in. I 1^33 I C invisible I , I 30 I C invisible 349-3 346-9 in. 355'9 „ "•7 363-3 359 ? C invisible j m. I 1-71 C suspected i843'53 5"^73 2-72 45-53 8-65 53-71 0-72 6-83 7-71 9-61 67-82 74-69 42-72 4 9 51 6-57 72 43-54 5' -73 2-72 9-61 65-46 ■74 8-65 9-74 -74 -78 651 R. A. 19" 38-8" Ha. 0.2. Da. Be. De. -W.O. 0.2. 383. Dec. 40° 26' 25-4 0-62 27-4 31. ■91 23^7 ■85 21-7 2n. •76 2S-I 4n. •81 24-2 •85 M. 7, 8^S i843^39 5-07 53-75 8-22 67-64 74-70 652 2. 2574. R. A. 19" 39-1" Dec. 62° 23' M. The angle has increased and the distance diminished. 0.2. Ha. De. 131-3 5n. 0-90 1 39^4 in. -92 137-0 ,, ■81 134^7 ,, •75 136-9 1-05 131-7 0-75 132-5 •65 208-9 1-20 1834-10 40-61 5-69 6-69 1-47 3-39 4-90 64-21 653 2. 2576. R. A. Dec. 33° 20' M. 7-8, 7-8 Certain change in angle; probable dimi- nution in distance. Duner has i86l-44. A =3" -27. P = 3i3°-6 - o''-295 (^-1850-0). So. Ha. 0.2. Ho. Se. De. H. Da. 326-2 ... 322-8 4-33 318-8 3". 3-59 141-9 •55 316-9 •53 3I5-I 3n- •46 313-0 2n. •35 3"-' 3n. •37 -4 in. -21 131-3 3n- -40 124-4 m. -42 125-3 ,, •24 312-2 2n. -47 132-0 4n. -49 308-6 •31 310-8 2n. •49 308-8 •27 -4 2n. •19 296-8 in. •46 307-3 I2n. 2-97 1823-65 9-65 31-80 51-80 37-89 43-99 51 -So 7-18 9-86 1-82 66-76 70-92 56-56 7-15 6-6o 8-02 63-35 5-64 6-46 71-61 MEASURES. 371 w. &s. Gl. Sp. PI. 304-2 5 3'32 1872-63 306-4 7 2-93 •75 304-2 4 3-23 3-59 7-6 6 •51 4^73 126-7 4 ■52 6-68 125-0 2 ■«4 -61 305-7 9 •48 4-85 ■3 5 •25 •85 3049 •14 5^65 ■5 in. -26 7-64 654 2. 2579. R. A. jg"" 41-2" S CTGNI. Dec. 44° 50' M. 3. 7'9 Afagnitucles.—^., 3, 7-9. Sm., 35, 9. 2. gives the magnitude of B as 6-5 on one occasion ; Da. always 8 or 9. De. thinks that B varies both in colour and magnitude. Dawes, on the other hand, never "suspected its brightness to be variable." O.S. confirms 2.'s sus- picion that B is variable. L, A, greenish ; B, ash. Sm. yellow ; B, sea-green. A, pale H, {Phil. Traits. 1804, p. 377) : "This double star, I believe, has furnished us with a second instance of a conjunction re- sembling that of f Herculis. The position, September 22, 1783, was 18° 21' n.f. January 3, 10, and 11, 1802, I could no longer perceive the small star, which mu.st have been at least so near the large one as to be lost in its brightness. January 29, 1804, I examined this star with powers from 527 to 1 500, and saw it as a lengthened star, but not with sufficient clearness to take a measure of its position. May 22, 1804, in a very clear evening, I tried 527 and 1500, with the lO-ft. reflector, which acted remarkably well on the double stars, but I could not perceive the small star of S Cygni. " He then tried the 20-ft. reflector with powers 157 and 360, with the same result. He then adds: "A parallactic motion of 5 will perfectly account for this occultation, for the situation of the two stars, in 1783, was such, that this motion must have carried the large star, by this time, nearly upon the small one." Hj and So. [Phil. Trans. 1824, p. 339). These observers, using the 5 -ft. refractor, examined S carefully in 1823, but could not see the least appearance of elongation. "The star perfectly round and admirably defined ; the night beautiful." 2. (^. M., p. 25). In 1826 2. turned the Fraunhofer equatorial on this object, and saw it double on the first examination. He says, " It is very probable that between 1783 and 1826 the small star performed a whole revolution + 34° in an orbit very elliptical, so that the period may be less than forty years." At p. 297 he thinks the above remarks need correction, the period certainly not being forty years. H,'s inability to see the companion in 1802 he thinks inexplicable, unless due to variability or periastron passage, the latter being perhaps the more probable. Dawes {.tfem. P. A. S., vol. xxxv., p. 416). Speaking of the difficulty of this star, he observes that this is a case "in which great perfection of telescope is of far more importance than large aperture beyond about six inches." In the Astronomical Register, 1865, p. 225, he expresses his opinion that Behrmann's elements are far from correct if his own measures are not "egregiously in error." "According to my own measures, the distance has scarcely varied for the last twenty-five years." Behrmann's ephemeris gave 32o°± o"-4 for 1865, while Dawes's measures in 1865-58 were 349°-62 and i"-675. The Orbit.— Mr. Hind was probably the first to publish elements of this system. Making use of the observations from 17S3 to 1842, he obtained the following re- sults : — T = 1862, Nov. 14. fl- — a = 243° 24' S3 =» 24 54 '■ = 46 23 e = 0-6067 P = 178 years and 256 davs a = l"-8u. About 50° of the apparent orbit had then been described. Behrmann in 1865, using Klinkerfues' method (see .4str. Nach., No. 1 127), deduced the elements which follow : — T = 1866-3512 TT — S = 280° 20' -6 U = 166 26 -4 i = 64 38 -4 e = 0-8470 /^ = - i°-283 P = 280-56 years a = 3"-i65. 372 DOUBLE STARS. His ephemeris gives the following quan- tities : — 1826 40-9 i-8i6 30 37-3 ■772 40 27-2 •635 50 14-8 ■432 60 355-6 •000 70 H76-8 0702 78 157-0 1518 79 «55'9 •58s 80 1547 •646 Behrniann used the measures made from 1783 to 1856. A comparison of the com- puted with the observed quantities shows that the elements require corrections. In 1866, having received the careful measures by Dawes, Dembowski, etc., Behrmann computed a fresh set of elements ; they are as follows : a = 2"-30974 e = 0-28583 IT = 289° 42' 7 = 37 46 a = 91 8 X = 203 2 V = 415-11486 years « = 0° -86723 T = 1904-1023. Behrmann also compares the observation from 1783 to 1865 with the elements, and a very satisfactory agreement is found. Finally, he gives the ephemeris from 1826 to 1878: the following extract will be of interest : IS26 41-5 1-93 i860 3587 1-49 30 37 -87 65 3507 -47 35 32-3 •79 70 342-5 -454 40 26-6 •72 75 334-1 -452 45 20-3 •b5 7* 332-5 -453 50 13-0 ■59 77 i 330-8 -454 55 b-4 •54 78 329-1 -456 Engelmann gives the following simple formula for the angles of position : P = 20^-4 — i°-4io (/ — 1845-0). A = i"-68. On this Duner remarks that it fairly repre- sents the modern observation.s, but makes that of H, in error to the extent of 36° ; and that if, instead of 18° 21' n.f., we read 18° 21' s.f , perfect agreement is produced. Dr. Doberck's formulas are e = i2°-48 - i°-402 (t - 1850) +o°-ooo6 (t - 1850)^ P = i"-64 — o"-oo67 (t - 1850). H,. 71-6 1 1 2-50 178372 single 1802 >» 4 H2 & So. "perfectly round" | 23 "round" 5 32-5 •5 32-72 S. 40-6 2n. -91 26-55 36-9 in. ■91 8-80 -7 »» ■57 31-73 •2 2n. -70 3-81 34-7 in. •68 5-66 3' -9 4n. -80 6-52 Ma. -3 26-6 -61 7-27 41-50 21-6 1-46 2-77 22-7 -28 3-45 23-9 -47 4-36 21-9 •32 S-6S 20-2 •33 6-35 19-0 7-18 13-8 1-19 52-44 Sm. 30-9 -5 37-78 25-6 -8 42-56 14-7 -5 52-69 Da. 27-4 25-1 2n. •5 39-66 40-67 23-7 4n. 1-66 1-89 16-7 31- 7-39 14-5 176 875 II-5 2n. -65 51-51 10-7 ,, -68 2-74 7-3 3n- -76 3-73 4-3 in. -68 4-56 357-7 3n- -67 9-58 349-6 2n. -67 65-38 Ea. 25-7 •72 41-94 -8 -71 3-12 0.2. 19-6 3"- -68 4-78 8-3 -51 52-70 3-3 ,, -65 871 353-8 ,, -60 63-74 3417 2n. -47 72-81 Fit 10-3 30 75 51-68 Ho. 10 26 •II 4-79 0-4 30 •27 5-74 Se. sin gle 55 3-2 I -41 6-84 350-4 3n. -23 66-08 De. 355-4 Sn. 275 ■5 7n. 1-58 3-61 351-3 4n. -68 472 350-5 I4n. -55 5-64 348-9 I5n. •5' 7-06 3472 sn- •56 8-61 346-4 -58 9-60 343-4 7n. -72 70-56 342-3 5n. •59 1-50 339-3 7n. •51 2-60 336-2 6n. ■55 3-56 -3 7n. ■61 4-62 333-7 sn- -58 5-58 £iig. 354-4 2-30 64-74 En. 349-0 2n. 1-70 5-43 348-3 >t -70 6-68 MEASURES. 373 Kn. 337 9 4n. 1-6, 330-2 in. •69 3407 J* 3447 »» ••50 349-0 •52 3437 I3n. ■53 33C-5 4n. ■52 •8 S 70 91 7 s-« 7 Compar ion not seen 187174 2-67 6573 6-59 8-69 70-85 5-69 278 470 S70 77 655 OX 385. R. A. 19'' 42"" O.S. Se. 55 -o Sii Dec. 40° 16' 3"- 1-31 ■38 M. 7-S. 9-8 1845-07 66-62 656 X. 2583. R. A. 19" 43" Duner has Dec. 11° 31' M. 6, 6-i 1856-19. A = i"-43. P = i23°-i -o°-o88 (^-1850-0). So. 2. Sa. Sm. Ha. O.S. Mo. En. Ka. Du. W. ft I Gl. Sob. 124-4 127-5 1 35 "5 123-5 127-4 120-7 124-5 120-8 122-0 121-3 123-2 120-8 122-3 120-8 121-1 117-6 119-0 ■7 121 -4 119-9 4n. in. 6n. 2n. m. 4n. 2n. 4n. 2n. 4n. 6n. ion. 3n. 2n. 4n. 1-96 ■55 -68 •50 ■83 •63 ■5 7 •39 -40 -50 ■49 •45 ■34 -27 -48 -48 ■27 1783-65 1802-72 23-70 5-61 32-56 29-96 30-56 65-74 31-70 681 42-17 7-96 8-24 55-88 65-67 5-84 72-17 3-37 4-85 7-70 657 O.S. 386, R. A. 19" 44'° Dec. 36° 5'' M. 7-7,8 O.S. 77-5 3n. 0-97 1846-63 Ua. 83-8 in. •75 47-73 Sa. 78-6 ,, -97 8-55 Se. 79-9 31- •84 58-68 Be. 77-8 •92 67-27 Bu. 82-2 7n. -80 70-69 658 O.X. 387. R. A. Dec. 35° o' 19° 44-2" Rapid direct motion, Ua. O.S. Sa. Se. Be. Sp. 118-3 1 19-4 94-7 129-4 103-8 90-7 78-4 897 91-9 198-2 526 ■5 396 26-6 23-0 20-7 22-0 177 23-2 0-52 -60 -52 2n. -50 3n. -47 2n. •57 „ -60 3n. -53 in. -3 ,, -25 3"- in. oval oblone wedg^- 6n. oblong 5n. ,, 3n. 0-34 2n. •46 ... •38 M. 7-2, 8-2 1843-39 7-73 53-78 44-18 5 '-97 61-22 5375 6-83 9-61 68-25 7056 1-57 2-55 3-73 4-57 5-40 7-67 557 660 o.t. 388. R. A. 19" 47" Dec. 25° 33' A 7-6, B AB. M. 7-6, c8-8 Ma. 1569 in. 3-89 O.S. 140-5 5n. T Sa. 1398 in. ■85 140-0 „ 139-4 „ 3-89 Be. -5 3"- -70 Su. •3 4n. -63 1847-73 8-51 -5' 53-73 472 6589 9-59 374 DOUBLE STARS. 664 t. 2606. Dee. 32° 57' Dun^r gives 184977. A = i"'i6. P = i33°-3+o°'o9('-«850'o)- M 7-5. 8-2 R. A. Dec. 19" 48 -e™ 69° 58' Is B variable? The proper motion of R. A., and + o"'oi in N Duner gives 1853-19. A = P = 357°-i+o°-iS2 333'2 354-5 Hr 355-3 348-5 353-2 Da. 354-8 353-2 in. 356-5 354-5 6n. •6 356-3 355-7 358-8 357-8 358-0 360-4 353-1 359-3 349-0 6n. 1-19 -22 in. -'3 4n. -33 : 2n. -•9 , m. -I 2n. -01 1 4n. -17 1834-39 42-42 4-34 5-48 51-24 6-65 -80 68-25 2. Sm. Ua. De. Ee. Ho. M. 0.2. Bo. Ta. Sn Gl. Bob. CO. 355-9 360-5 •9 359-8 360-0 4n. In. 2n. 4n. In. 2n. ft \n. 7n. 2n. in. 4n. 2-5 1781-81 1804-39 2-59 23-58 3-27 8-64 -27 30-67 -09 -67 2-84 43-78 -83 8-87 -79 32-44 3-1 3-68 -0 46-77 2-69 1-54 -81 3-88 ■92 56-53 -74 •75 3-06 9-75 2-6S 61-82 304 3-66 -02 5-65 •01 9 49 •03 74-61 2-99 0-79 3-20 4-72 •15 -84 289 6-61 ■93 7-97 M. B 9, C 9-2 A B. The angle has diminished. No change in A C. AB. o.s. De. 2. O.S. 330-0 In. 0-50 317-9 2n. -41 316-6 in. •38 310-2 „ •40 323-5 j» -41 318-0 „ -53 306-9 41- ... A C. 293-4 31- 322 292 in. -29 290-3 2n. -20 in. -07 •5 )» •29 290-1 It ■33 •9 ,, -41 1842-67 5-65 51-62 4-69 7-67 8-59 67-45 31-52 42-67 565 51-62 4-69 7-67 8-59 663 R. A. 19'' 49"" 0.2:. 0.1. 632. B AQ1TII.S. Dec. 6° 6' I7-I -0 4n. ''■1 2n. 12-36 -60 -63 -67 M. 3-4. 1 1 -3 1852-44 8-12 63-70 74-74 666 O.S. 393. R. A. 19'' 54" Dec. 44° 4' M. 7-5. 8-4 The distance has diminished. O.S. 225-7 3n- 21-75 1847-44 226-7 -12 71-48 De. -I 2n. -21 65-96 Du. ■3 1 >» 20-78 9-78 AIEASURES. 375 667 ox 395. R. A. Dec. igh 56-9° 24° 36' Probable direct motion. Ma. 89-2 67-4 74-2 •5 7«-3 91-0 O.S. 79-3 80 -0 96-3 Da. 8o-6 Se. 931 Eng. 829 De. 8qi W.O. 91-4 Sp. 927 Sn. 917 0-50 in. •45 ti •45 •52 in. ■40 J, ■6 2n. ■64 ,, •57 in. ■68 2n. •57 in. elong*"- 2n. 0*64 4n. 0-67 •69 2n. •63 M. S-8, 6-2 i843'S3 579 773 •86 5172 2-85 44-16 50 22 7476 52-60 9-61 65-60 7 '41 7472 5-63 •69 668 S. 2619. R. A. ig" 57° Dec. M. 47° 56' a8-i, b8-i, C12 Probable change in A C. C was discovered by O.S. in 1851-82. AB. s. Va. Se. V.O. De. 244-9 245-8 246-3 244-5 •0 O.S. Du. 639 245-9 O.S. 296-6 302-7 4n. 4-29 in. 3-99 3n. 4-37 2n. •21 in. -42 3"- •25 8n. 3-9> A C. 17-79 16-88 1831-91 43-80 57-54 71 8-39 9-14 70-37 54-69 7092 669 t. 2627. R. A. 20'' 2"° Dec. 4° 26' M. 9. "5 S. Ua. 23-2 25-3 3n. I 1-96 11829-37 in. I 2-21 I 42-72 670 Z 2640. R. A. 2oh ^.2" Dec. 63° 33' U. 6, 9-9 s. 30-5 in. 4-73 288 >i •95 24-9 2n. 5-01 Da. 23-3 4-99 Bo. in. •72 2S-3 >» 5-07 Br. 22-8 ■13 23-8 •02 Ta. 26-9 in. ■51 W. ftS. 21-0 ^, 4-77 23-6 S-36 Gl. 203 Dob. 227 3n. ';-2i 1831-87 2-02 338 41-80 65-65 ■74 873 969 ■49 7373 570 3-79 7-74 671 2. 2637. 6 SAeiTT.£. R. A. 20'' 4-6"' Dec. 20° 33' M. 6, 8-3 Probable increase of distance in A B : certain increase in A C. The proper motion of A is probably the cause of these changes. The common proper motion of A B is given by S. as +o"-o6l in R. A., and -o"-l47 in N. P. D. 80. H,. 2. 8m. Ma. O.S. Mo. M. H,. 80. Sm. O.S. Mo. M. AB. 11-07 328-0 -78 3200 10 325-9 i8-o 326-7 8n. 11-40 327-1 -4 328-1 •17 3257 ■37 326-3 -21 ■5 -72 ■3 in. 73 328-3 j» -54 -7 »» -74 326-7 60 -40 ■2 in. -62 -8 ,, 12-33 428-5 i> 11-50 AC. 226-8 -8 -6 -6 -o 225-1 -I ■7 -o 224-8 -7 4n. 5"- 26 in. 158 69-66 j 70-22 ! -98 -I ' 72-86 75-83 •65 72-91 73-09 -93 74-73 1781-64 1824-98 7-64 30-00 2-82 4-77 4271 3-62 7-08 51-80 -80 74-72 79 53-68 61-79 6-46 75-63 1781-64 1824-98 8-73 35-28 4'77 51-80 74-72 ■79 53-70 61-79 6-46 75-65 376 DOUBLE STARS. 672 2. 2636. 677 2. 2646. R. A Dec. M. R. A. Dec. M. 20'' S'3 m - 4° 56' 8-2, 9-2 20'' 8" - 6° 25' 7, 8-8 2. 201 -8 2n, ; 12-51 1827-24 So. 50-6 ; 3n. 1 25-11 1825-69 Ha. 204-0 •3 ': J3-27 i ''' 43-75 52-39 2. Ha. 51-6 „ 1 24-70 •2 1 1 -30 9-42 4381 *2 1 ... 3-79 Hit. CO. 202-3 203-7 in. 1 12-23 in- : -73 48-66 77-73 678 R. A. 20'' 10" 0.2. 403. Dec. M. 41- 45' A 7, B 7-2, C 9-5 673 2 2641. Dembowski's distance is probably too R. A. Dec. M. great. 20" 5-9" 3° 27' 7-5, 1 1 -2 A B. 2. Ua. 170-1 1695 2n. ; 20-34 m. 1 -78 1827-76 43-70 0.2. Se. Sn. 173-0 -4 171-6 5". 3n. 2n. 0-59 i-oo 0-79 184810 66-85 75-68 674 0. 2. 400. ■A- + ^ and C. 2 0.2. 33-1 1 5n. 11-83 48-10 R. A. Dec. M. Se. 34-0 1 3n. -70 66-85 20' 62 43" 37' ary system in retrograd ance is sensibly constant. 7-2, 8-2 e motion. A bin The dist 679 2. 2658. 0.2. 334-9 3n. 0-64 1845-73 R. A. Dec. M. 3246 2n. -59 53-23 20" 10-5 " 52° 45' A 7 B9, c 10 319-3 )> -62 60-10 Ha. 326-7 -50 43-39 C A yellowish white, B blue. Da. 3205 3II-2 in. ■65 53-89 65-51 AB. 130-3 separat" -94 H,. 126-6 5-36 1829-70 De. 307-8 3n. 6-67 2. ■9 4n. -49 31-62 121-9 in. oblong 8-55 Ha. 124-8 2n. ■34 43-58 W. & B. not divided 73-62 122-4 4-80 7-85 elongated ? 6-77 127-9 -58 51-87 Belli. 267-9 in. 0-33 5-67 122-2 •29 3-38 Sp. ■9 •33 -67 Se. W.O. 123-0 I25-I 5 '45 4-89 63-51 76-77 675 2. 2652. A C. 220-2 ! j 33-48 30-76 R. A. 20" 7= 281-3 292-5 Dec. 61° 43' M. 7-3> 7-6 1834-18 40-61 2. De. 216-8 3n. 1 32-07 213-2 1 37-80 2-14 63-51 2. 0.2. 5n. m. 0-43 wedged 680 0.2. 405. 289-4 282-2 }} oblong 0-4 1-62 54-69 R. A. 20' I4'' 0.2. De. Dec. 32° 52' 152-6 3n. o-6i 144-7 M. 7-7, 8-7 676 2. 2649. Dec. M. 1846-43 67-72 R. A. 20'' 76 m 31° 43' 7-7, 8-8 681 2. 2690. 2. 152-3 3n. 1 26-08 1832-19 R. A. Dec. M. Ha. 151-1 in. 25-94 47-79 20'' 25-5 I 0=51' A7, B 7-5. c 7-6 MEASURES. 377 In A and B + C the distance has gradually increased. In 1840 Dawes detected the duplicity of B. In this pair there is probably a slow retrograde motion, with decrease of distance. The star was also detected by O.S. inde- pendently in 1842. AB. 2. Ma. Bo. Sa. Sm. 0.2. Bo. Se. W. &S. 256-3 255-2 257-2 21 1 -4 -2 210-5 215-0 210-7 34-5 37-1 207-0 202-2 2200 227-3 4n. 14-19 -20 3"- ■73 BC. Iln. 0-65 4n. -58 •7 •5 in. •63 ,, -60 »» •57 ,, •49 2n. •49 3n- est"- I AC. 125 I Aandl^. Da. O.S. De. W. &8. Gl. PI. 256-0 ■5 •4 ■4 257-0 256-1 257-1 256-1 255'3 256-3 ■5 255-0 254-7 682 t. 2695. R. A. 20" 26-8 2. O.S. 76-5 75-0 Dec. 25° 24' I 5"- I 4". 0-79 1-04 R. A. 20'' 27-5" Dec. 5° 2' 1831-26 53-76 65-68 41-95 50-19 42-58 57-71 42-67 5-75 7-71 51-67 65-64 6-30 7«-53 3-68 fixed 2n. 14-05 »» -33 4n. •56 in. •87 -61 »» -61 „ ■77 4n. -88 3 15-2 4 -39 2 -09 4 -I 4n. ■13 1829 32 41 2 5 7 51 65 71 3 5 3 7 64 88 -37 ■67 -75 •71 -67 IS 53 68 ■74 91 07 M. 6-2, 8 11831-78 I 50-84 683 2. 2696. M. 8, 8-4 O.S.'s measure in 1872 shows that the angle is probably unchanged. The more recent measures seem to indicate a slight increase of angle and decrease of dislance. Ua. Se. 01. Fer. 300-0 298-5 290-1 3028 308-5 302-6 309-7 310-3 303-4 305-2 306-0 304-4 3-7 in. 3"- 1-27 -32 ■o 099 -90 •90 •90 •72 -66 •85 0-.8 I -80 I in contact I in. 5 4 S 1825-71 32-84 i-oo 8-27 42-72 3-69 61-76 56-62 72-64 3-69 5-75 3-91 -91 4-54 684 %. 2703. R. A. 2o>> 31-2" Dec. 14° 19' M. 7-6, 7-6 Increase of distance in B C and A C. Duner's formulae for the motion of C with reference to A + B , 4 sin P=46"-ii-o"-0250 (/'-1853-0). ii cos P = — 39" -80-0" -0582 (^—1853-0). AB. Hi- 288-5 S. 290-5 291 -I So. 290-0 Ua. 291-4 290-6 Se. •9 De. 291-0 290-9 Da. -5 in. 26 4n. 25-28 2n. -08 24-89 in. 25-06 2n. -06 ») -II 4n. ■15 Sn- •23 AC. Se. De. Dtt. 238-6 ... 1 239-4 3n- 66-72 238-s in. ■2 2n. 67-27 •2 4n. 68-66 : •0 3"- -75 1 BC. s. 216-8 217-9 3n So. -I Se. ■7 1 in De. ■3 2n -2 ' 4n Dn. -4 »» 54-38 ■30 56-07 55-92 57-02 -03 1783-65 182214 9-52 4-81 42-13 769 57-26 817 64-60 8-53 21-85 940 5669 817 64-60 8-53 21-88 9-42 4-78 56-69 817 64 60 8-53 378 DOUBLE STARS. 685 1. 2704. /3 DELPHINI. Dec. 14° II' A 3-5, C. A green. R. A. 20'' 31 'g" M. B4'5. A B. — In 1873 Mr. Burnham discovered that A was a close double star, and Dem- bowski's measure in 1875 seems to indicate rapid angular change. According to 2. {P. M., ccxxxi.) the star C does not partake in the proper motion of the system. A B. Buni]iam355 0-7 1873-60 15-5 5n. •65 466 20-1 4n. •54 565 25-8 »» -48 6-63 ^97 Sn. •51 7-71 O.S. 80 in. ■69 473 ■A^ + B and C_ H,. 348-0 27-4 1781-58 -• 343-8 3248 1829-40 339 9 in. 33^77 51-88 Sm. 3418 30-0 34-79 Ma. 342 I 43-63 340-6 51-80 0.2. 338-6 in. 33 -yj -81 De. 336-6 34^64 64-94 W.&S. 338-9 3 ... 75-74 686 OX. 533. R. A. Dec. M. 20" 33-3°' 9°40' 4-7. 1 1 -3 The proper motion of A is + o'-0227 in R. A., and + o"-340 in Dec. This star, owing to the great difference in the brightness of the components, is very difficult to measure. The distance is probably unchanged since 1851. 0.2. has deduced the following formulae : A A = — o"-262 ± o"-036 — (o"-285i ± 0-0040) (/ — i86o"o). A D = + 10-021 ± 0-036 — (0-0155 ± 00040 {t — 1860-0). It is probable that the changes are due to the proper motion of k. There is a third star following k about 3' -5 distant which most probably forms with it a binary system. 0.2. 1-9 2n. 10-26 p-8 in. -25 -8 »> -63 5-4 » •22 [851-71 2-63 3-82 6-57 0.2. 359-4 in. 10-32 348-3 tt -12 338-2 i» •34 335 -J ,, -88 1859-62 65-78 72-64 4-79 687 2. 2708. R. A. 20'' 34-1" Dec. 38° 13' M. 7. 87 C. A yellow, B blue. The formulae for rectlinear motion de- duced by Z. (see P. M., p. ccxxxii.) still fairly represent the observations. 0.2. obtains the following : A A = — 4"-8oo ± o"-o40 — (o"-i786 ± 0"-0O29) (t — 1850-0) ; A D = + 14" -528 ± o"-040 4- (0-1939 ± o"-0O29) (/— 1850-0) ; and the differences show that there has yet been no departure from rectilinear motion. Duner finds the following formulae : AcosP= +i4"-47 +o"-i875(/- 1850-0), AsinP = — 4"-69 — o"-i745 (/— 18500); and A cosP = + i4"-34 + o"-i865 (/- 1850-0), A sin P = — 4"-76 — o"-l693 (/— 1850-0). So. Da. 2-3 355-J 352-3 354-6 35 « -2 349-3 348-1 352-8 -o 351-1 350-S 347-4 346-9 345-9 •6 342-2 340-5 0.2. 346-0 343-2 3402 336-2 Ka. 345-9 337-5 Ha. 343-4 1-lt. 342-0 Uo. 340-4 l)e. 339-1 338-6 337-1 Se. 338-3 Po. 337-7 U. 336-7 411. in. 5n. 2n. m. 2n. 3n- 6n. 37 5n. in. IS in. 9-65 10-45 11-32 10-82 -96 11-97 12-23 11-24 11-46 ■70 12-61 -91 13-16 -46 13-69 16-01 13-06 14-58 16-52 19-52 1304 18-66 14-34 15-76 1610 15-91 16-69 18-31 17-26 18-10 17-93 1823-68 8-76 32-34 29-86 32-36 5-78 6-89 0-71 2-56 3-87 4-55 775 9-79 40-67 «-63 2-65 3-86 53-82 39-86 46-69 54-82 67-74 41-83 65-85 44-76 5 1-79 4-66 5-13 7-38 63-02 57-91 9-85 62-48 Eng. So. Su. Ta. W. &8. Gl. Bob. PI. n. 336-2 in. i8"8o 1865-58 335-3 2n. J7-77 -71 336-2 19-83 9-40 ■9 5 71-54 335-5 4 21 -o 3-69 -0 5 •0 -69 334-7 3 •2 •72 336-6 5 •28 5-74 333-2 3 22-08 6-77 335 -o 8 21-4 3-91 333-6 2n. 6-62 -6 >» 21 -81 7-69 -3 4n. -86 ■20 ■9 in. -67 -78 ess O.S. 410. R. A. 20'' 35-1° Ua. O.S. Da. Se. O.S. Dec. 40° 9' AB 23-1 0-52 28-9 -42 23-3 7n. -63 27-7 -53 24-1 ■5 -I 4n. •40 M. A 6-4, B 6-7, C 7-7 1843-42 693 50-60 3-82 67-35 57-35 MEASURES. 0.2. Da. Ha. Mo. Oe. Bo. Ka. Du. Ta. Fer. Sp. Sob. Fl. A + B 2 69-8 I 4n. and C. I 68 69 I 51-45 6S9 O.S. 411. R. A. 20" 38-3™ Dec. 45° 25' M. 7-4, 10-2 Direct motion : change in distance. 0.2. Ha. He. 273-7 2n. 15-26 ; 278-7 3"- 14-80 291-5 in. 15-02 273-7 14-28 2889 3n- -62 52-11 70-92 46-04 66-91 690 2. 2725. R. A. zo"" 40-6"" Dec. 15° 28' M. 7-3.8 Change in angle and distance. Duner has A = 4"-s6 + o"-oi54 (/- 1850-0). P = 358*-! + o'-lio (/ - 18500). So. 2. 353-9 355-8 3584 359-8 355-7 356-8 -4 357-0 -o 358-3 357-9 358-9 3594 . "9 ■5 -9 -8 358-7 ro 0-4 3586 •6 359-7 0-9 3n. 4-58 2n. -61 »» ■95 m. •94 41. •65 3n- -74 -78 -54 ion. ■78 .3n- 5-00 ,, 4-61 5n. •71 •71 4n. •77 in. -60 -78 Sn. -67 in. 6 5-05 4-73 -85 3n. 5-6 2n. -06 .3"- 4-44 m. •81 691 X. 2726. R. s. Se. 0.2. Sob. Dec. 30° 17' C. A very yellow. R. A. 20'' 41 ■8"' y DELFHIiri. Dec. 15° 42' 379 1839-86 44-62 59-66 72-64 41-16 54-32 41-57 2-74 3-30 9-79 54-'5 -68 67-39 56-85 65-71 6-75 8-55 -69 71-68 2-59 6-11 •78 7-69 8-58 -82 57-2 4n. 6-6i 59-6 3«- •33 61 -2 2n. -44 60-5 »» •28 M. 1830-82 57-35 62-26 77-70 692 2. 2727. M. 4. 5 C. A, golden : B, bluish green. B appears to vary in colour : it is given as yellow, green, and blue, by different observers. The common proper motion is — o' -004 in R. A., and +o"-i9 in N. P. D. Dimer's formulae are A = ii"-9i-o"-oi70 (/- 1850-0). P = 273° 5-0° -035 (^-1850-0). H,. 348-7 in. 1783-29 355-0 sn. 1825-08 4-98 -40 357-6 4n. •28 31-78 274-5 273-3 "V' -6 •8 So. •7 Ba. -4 272-1 I in. I -01 4n. ... in. >» 11-83 5n. ■90 in. 12-32 -07 11-52 1780-17 -6s 1804-44 23-34 30-89 23-68 3' -59 59-05 38o DOUBLE STARS. Bm. 2736 ■4 ■3 H,. •I Ua. 272-8 273-5 •2 ■3 272 -s Po. -3 Ho. ■4 Se. ■5 De. 271-4 272-4 271-5 M. 270-8 Bo. ■9 En. 272-7 Ka. 271-7 Bn. 272-4 ■w. &S. 271-7 Gl. 272-2 Fl. 270-8 Dob. 272-1 Goldney. -4 121 1831-60 ■3 4-52 1 1 -8 971 2n. 12-05 2-57 6n. ■03 5-84 ,, 11-46 42-52 in. •44 572 3"- •39 9-64 2n. ■36 5481 3n. -70 45-70 2n. -28 56-51 7n. -69 703 3n- ■42 8-23 in. •45 63-89 ,, •52 5-88 2n. •29 7-53 In. -40 371 ,, •54 574 ,, 73 578 6n. •18 6-74 ,, •42 828 in. -I 7369 ,, ■36 •91 ,, ■25 7-82 Sn. -16 8-74 ,, •12 75 693 0.2. 413. R. A. X CYGKI. Dec. 36° 3' M. S. 6-3 20° 42-5°" C. Da., pale yellow ; Sm., all bluish. H] VI. 32, is X Cygni, a wide double star, the components being of 5th and I2ih magnitude, according to South, and the distance about ij minutes. The measures indicate fixity. In 1843 the larger star was first seen double by 0. S. Dawes(/I/«K. Jf.A.S., vol. xxxv., p. 427) writes, "A close and beautiful binary, dis- covered by Mr. Otto Struve." " On one night Madler observed an object which he has called 0.2. 413 ; but the angle recorded is so far from the true one, that the star cannot have been seen really elongated, though it might reasonably be expected that the Dorpat telescope of 9 '6 inches aperture would be capable of even sepa- rating such an object." At p. 498 he adds, ' ' The retrograde movement in the position of this close double star continues so as satisfactorily to prove its binary character." He notes the great discrepancies in the measures, the great difficulty of the object, and the absence of change in the distance. A C unchanged. The angular motion has probably slack- ened. (1878.) 0.2. Ha. Sm. Da. Se. De. Da. W. ft S. Schi. Sp. Dob. 122-3 4n. II8-I 3"- 109-5 4n. 106 -8 95-5 3"- 93-4 ,, 86-3 2n. 114-3 36-8 130-0 108-8 in. 103-4 5n. 96-5 in. 92-5 »> 1002 31- 92 '6 6n. 85-. 30. 93-8 4n. 91-2 In. 89-8 ,, 88-7 5n. 83-9 92-5 7'n. 90-5 4n. 87-4 3"- 88-5 4 937 2 82-5 in. -5 86-7 in. 0-65 -60 -56 •55 -67 •66 •70 •55 •3 •7 -7 ■64 ■71 •68 •64 oblong 0-4 ■5 0-6 -51 •62 •71 •68 •45 0-72 -72 -58 184266 5-18 8-80 52 02 6-98 6097 7175 43-53 7-82 3-74 51-99 4-07 60-81 6-99 58-76 66-39 55-88 65-73 6-84 8-55 71-41 6-71 69-68 71-26 5-70 2 65 3-69 5-59 -60 -76 694 OX 414. R. A. 20'' 43" Dec. 41° 59' M. 7-2, 8-3 The distance appears to have increased. Ha. 0.2. De. Dn. 94-2 95-9 -5 •6 in. i 9^25 1847-82 6n. I -88 I 8-30 3n. I -92 j 66-80 6n. I 10-02 I 9-72 695 2. 2729. R. A. 20'' 45-1" 4 AQTTASII. Dec. -6" 4' M. 5-9. 7-2 H, {PM. Trans. 1804, p. 371) : " The position of the two stars, July 23, 1783, was 81° 30' n.p. ; and, by a mean of two observations, August 28 and 29, 1802, it was 61° 5' n.f. Both the last measures are positive with regard to the position being following, and not preceding, as it certainly was in the year 1783. This proves a change of 37° 25' in 19 years and 37 days. The distance is perhaps a little increased. MEASURES. 381 September 5, 1782, it was J diameter of s. August 29, 1802, less than 4 diameter of s." He infers "a real motion, the nature of which cannot remain many years un- known ; its velocity, hitherto, having been at the rate of nearly two degrees, per year, of angular change. " 2. (M. M., p. 8) began his measures of this star in 1825, but was unable to separate the components till 1833. His measures in 182976 led him to think that H,'s measure in I783'56 was erroneous, an entire revolution between 1802 and 1829 being at variance with his observations from 1825 to 1833. He found it a very difficult object even in 1836, but suspected a decrease of distance and a direct angular motion. Sm. [Cycle, p. 488) found this object excessively difficult ; ' ' but after succeed- ing in making it wedge-shaped in a direction towards a 14th magnitude star in the n.f. quadrant, long gazing brought up a bright point of light in the same direction." Da. {Mem. R. A. S., vol. xxxv., p. 427) says that the distance has diminished, and that there has been an acceleration of the direct motion since 2. measured this star. A careful examination of the measures led him to think that it was H,'s result in 1802 that was in error rather than that in 1 782 ; and he further notes that 2.'s positions differ 18° inler se, and that the mean result is too small. The common proper motion is +o"'o6l in R. A., and - o"-043 in N. P. D. (2.) H,. 2. H,. Sm. Da. Ma. Ka. Se. So. Be. Sp. Schi. W. &S. CO. 351-5 0-5 28-9 25-0 in. o-8i 300 ,, ■80 13-4 ,, -69 23-0 >» 31 -2 »» 0-67 46-6 -67 45 '0 -5 621 2n. 65-5 ,, 0-6 727 in. 817 ft 95-9 it 0-5 1017 ,, -3 24-6 -6 27-2 -45 31-8 •52 817 107-9 in. °'3 . 125 ,, elong^- 143-6 ,, n 140 n 157-0 0-42 -0 in. -42 not separated | 158-5 in. 0-5 1 1783-36 1 802 -66 25-59 •61 30-92 2 90 3-77 273 4-69 9-68 40-72 1-80 3-76 53-70 4-75 41 49 2-82 3-70 3-76 56-81 65-71 -74 6-12 75-62 -62 6-86 77-70 696 0.2. 416. R. A. 20'' 47-7" Dec. 43° 19' M. 7-8, 8-1 Duner gives '859-79. A = 6"-98. P = I43°-I - o°-2 (/ - 1860-0). 0.2. I Ma. ! Da. I De. i Du. "W. &S. 1467 3n- 6-97 142-4 2n. 7-17 145-9 in. -3' 143-8 ,, 6-80 -6 in. 7-05 141 -7 3"- -01 -3 »» 6-99 139-8 in. 7-35 1846-13 63-23 43-56 7-82 53-89 6610 9-80 76-78 697 0.2. 417. R. A. Dec. M. 20'' 48™ 28° 41' A7-5, b8-i, C9-4 A B. 0.2. 39-4 I 5n. I 0-57 11847-98 i De. 35-4 I in. I ... I 69-78 ! ^ + ^ and C. 0.2. 109-0 I 5n. I 30-49 I 47-9S De. -3 I 3n. 1 '87 | 66-86 698 2. 2734. R. A. 20" 48-3'" 2. 181-7 De. 187-9 ■W. &S. 191 -7 Dec. 12° 39' 3n- 28-50 26-72 in. 27 M 8-2, 87 1829-79 63-54 7677 699 0.2. 418. R. A. 20" 49-9" Dec. 32° 15' M. 7-3. 7-4 Gradual decrease in angle and increase in distance. 0.2. 8e. De. W.O, 301-8 292-8 287-9 291-2 293-0 112-6 292-4 1 10 -4 2n. 0-56 ,, -67 ,, -74 -88 in. -96 2n. -75 3"- I -01 -04 1842-67 8-81 53-20 60-64 8-77 5857 66 90 74-72 382 DOUBLE STARS. 700 OX 420. R. A. Dec. 2o>> JO"" 40° 15' M. 7. ii'2 O.S. 0-6 3n. 5-79 1 Be- 47 ,. -54 1 1848-30 67 00 701 O.S. 422. R. A. Dec. 20" 51" 44° 42' M. 7-4, 9'i O.S. 331-9 5n. 2-72 De. 334-8 4n. -60 1851-35 6743 702 S. 2737. e £aiTlTL£I. R. A. Dec. 2Qh 53-101 30 JO Magnitudes.- ' De., 6-2, - A + B , „ For '- — and C, 2 1853-19. A = io"-68. P = 76°-8 - o°-o833 {t - 1850-0). A B. A 5-7, D 62, C 7-1. 7-1. 7'5- A C— H, {Pii/. Trans., vol. Ixxii., p. 219): "Aug. 2, 1780. — Double. Consider- ably unequal. L. w ; s. much inclining to R. Distance 9"-375 mean measure. Position 5° 39' n-f-" This is A C. It was measured by Ho and So. in 1823, and they noted the increase in distance. 2. also measured this star as a double from 1825 to 1832. A B. — In 1835, however, S. discovered that A was double. " 1835-62 : power 4S0; elongated ; 800 gave o"'4. 300°-5 ; in contact." He could not separate the pair in 1835. Smyth says {Cycle, p. 490), " It is clear that A and B are binary." Da. {Mem. R. A. S., vol. xxxv,, p. 429) says " an -increase of distance has certainly occurred in this close pair ; and a very small diminution of angle is probable in both sets.'' O.S. (1877). In A B the distance has increased : in and C there has been 2 but very little change. The plane of the apparent orbit of the former coincides very nearly with the visual ray. The common proper motion of the system is — o'-oii in R. A., and +o"-l3 in N. P. D. For A B, Duner gives A = o"-87 + o"-oi65 (C- 1855-0) —o" -00035 (/— 1850-0)^ P = 288-^17 - o°-i86 (/- 1855-0) + o''-o04i5(<- 1850-0)^ s. 300-5 in. 0-4 1835-62 287-3 ,, •35 •64 293-9 »» ... •68 295-4 ,, -69 293" J „ 0-3 •70 Sm. 290 •5 8-83 Da. 286-3 in. •7 9-69 285-7 2n. ■7 40-66 290-9 ,, •59 1-82 287-8 in. •7 2-82 285-2 2n. -66 3 77 287-0 in. •73 7-63 -2 2n. -87 8-67 285-1 3"- ■97 53-85 -5 in. 1-04 9-67 -I ») 0-86 63-85 lla. 297-5 •65 41-53 293-4 9n. -60 ^■57 290-1 -6 3-68 296 -6 4-88 290-4 in. •93 50-75 288-9 3n- •94 1-20 291 ion. •89 5-48 292-4 -91 6-79 -6 •97 8-8i 290-8 6n. 1-02 61-43 O.S. 287-5 2n. 0-68 43-64 281-7 ,, -80 52-26 285-3 31- 1-02 9-63 283-8 2n. •15 70-32 Mit. 288-1 ,, 0-57 47-63 Ja. 286-8 9 53-88 De. 280-2 5n. 4-62 •3 2n. 5-84 285-1 6n. i-o 6-66 •3 3"- -0 8-49 283-8 4n. 0-6 62-64 Se. 287-4 5"- -81 55-88 '5 3n. 1-02 66-72 Kn. 287-1 2n. -01 3-66 290-5 ,, -II 4-74 288-1 in. •07 5-70 Eo. 285-6 ,, 0-79 -68 Ka. 283-0 6n. 1-02 -85 Du. 288-6 4n. 0-99 9-69 289-0 in. I 00 70-73 288-8 2n. •06 5-68 W.O. 296-6 in. -16 W. &S 287-2 5 0-86 72-65 285-2 8 1-09 -85 286-9 6 -15 3-70 289-2 4 -12 5-79 Gl. 287-0 4 -10 3-91 Sp. 286-4 0-97 6-44 Schi. -4 In. ■97 -43 Dob. 288-1 3"- •83 7-74 -4 2n. 8-78 MEASURES. 383 AB 2. Sm. Da. O.S. Ha. Hit. Ja. Se. Se. Po. Bo. H. Su. W. &S. and C- 84-3 80-4 77-5 79 '4 78-0 79-1 780 77-8 79 3 70 77 '6 78-1 77 'o ■2 76-8 ■7 77'3 76-2 78-8 76-5 •8 77'3 780 77-4 78-1 769 ■4 ■5 77-3 76-5 ■4 ■4 75 '3 76-4 ■I 75'9 76'3 ■I 74-6 76-8 75 '6 77 "6 75-8 76'o 77-5 76-5 74-5 75-6 72-8 74-1 ■6 75-0 ■3 ■6 74 '9 •2 75-0 74-3 •3 76-2 75'9 6n. 10 51- 2n. in. 9 5n. 2n. 5n. 2n. 4n. 5n. 15 in. 2n. 3n- 3"- 4n. 3"- 4n. 2n. in. 4 4 •AC. 9'37 10-56 •98 •77 •81 ■92 "75 12-37 II 10-7 1 1 -2 10-76 10-74 11-25 -22 10-33 11-20 -II -19 10-52 -50 ■30 -48 -86 •24 •44 10-43 •47 11-08 lo-o -60 ■51 ■58 •56 •83 •90 •58 ■39 II-IO 10-59 ■25 •74 SI -62 -81 -68 •53 10-89 ■62 ■99 11-36 •38 10-66 •57 9 '3 1781-81 1821-25 5-62 990 31-57 2-88 35-65 23-57 7-79 33-77 883 9 -68 40-80 1-84 3-79 8-66 53-75 41-39 56-68 70-32 41-54 2-76 3-68 4-88 9-26 51-73 3-80 5-79 8-83 61-39 47-63 53-88 4-89 5-84 6-61 846 62-64 55-88 •89 63-66* 4-74 5-67* •68 7-6i -65 8-62 -62 9-54 -67 -61 -67 70-78 2-79 3-76 4-70 5-66 69-66 7°-73 2-65 •85 vr. &s. Ta. Schi. 8p. Fl. Dob. 73-7 5 lOIO 77-5 3 9-65 76-5 in. 75-2 )» 10-68 -3 -69 73-4 in. •82 75-3 »> -77 1873-70 5-79 3-74 5-90 •90 7-76 -81 703 OX 424. R. A. Dec. M. 20'' 54"" 15° 6' 7-5. 8-7 O.S. 325-4 3n. 0-42 1848-34 Se. 330 oblong 65-74 704 Z 2741. R. A. Dec. M. 20'' 54-6 ■n 50° 0' 6, 7-3 The observations are very discordant. H,. 43-6 in. 1-15 1783-73 H,. 36-2 -41 1828-55 34-2 2-89 961 33-7 1-81 3063 -2 in. -76 1-62 Da. 32-8 -I ti 2-42 0-57 4-50 ■3 tt 2-04 41-80 ■2 6-98 -3 1-71 7-91 s. 35-8 3n. •93 31-49 Sm 34-6 2-1 369 Ha. 35-3 -06 4-27 33-6 -19 41-48 •8 7n. -II 2-68 34-9 in. 1-71 51-85 O.S. 33-0 2n. 2-07 41-22 Ho. 3»-3 4n. 1-88 55-75 De. 32-4 2n. 2-0 601 Se. 30-2 3"- 1-94 7-16 M. 29 -6 in. -85 62-49 Engf. 30-9 4n. 2-25 5-49 Bo. 33-9 2n. -15 -69 Du. 31-4 7n. 1-99 72-95 Ta. 27-7 in. -74 3-74 Fer. 31-3 -39 4-55 vr.&s. ■4 in. 2-05 -85 32-2 ,, 1-97 5-79 Gl. 33-7 »» -89 4-91 PI. 30-3 2n. 2-12 6-86 Dob. 28-6 )> i-gl -77 705 OX 425. R. A. 20" 56"" O.S. De. Dec. M. 48° 13' A7, B 10-5, c II AB. 27-6 29-9 3"- 12-32 •71 1847-49 67-60 384 DOUBLE STARS. AC. O tl 0.2. 46 "o I in. I 11-59 B C. 0.2. 135-0 I in. I 4-II 706 2. 2744. R. A. Dec. 2& 57"' 1° 4' Retrograde motion. 2. H.,. Ua. Sa. De. 0.2. Se. W. &s. 61. Sp. 707 t. 2746. R. 20' A. 57" Direct motion. Dec. 38" 47' 0.2. S3. De. Sp. W. &I 276-2 279'3 270-9 279-2 281-2 2837 282-9 290-3 708 t. 2749. R. A. 20" 58-7' Dec. 3° 3' Probably a ternary system. A B. 2. H,. Ma. Se. Sa. i49'5 148-7 150-0 149-4 1510 •o 51-70 51-70 '2S"5 5n. 1-52 188-3 2-0 ■5 "75 187-8 •60 189-2 7> 185-8 •43 I77-.S 6n. •50 184-5 2n. •93 170-6 in. 77 184-3 4n. •57 175-2 4 -27 •7 6 •60 174-5 6 ■31 176-2 4 •5 172-9 •52 M. 6-3. 7 1830-16 I -00 41 '63 273 375 8-68 6324 43'24 74-84 56-46 72-65 372 579 391 6-63 5n. 0-87 2n. -98 >» •98 ,, 1-03 ,j 0-88 -80 -96 1 5 1-09 1 M. 8, 8-6 1830-82 5-63 40-72 58-22 6-86 6333 75-67 6-78 i 3-61 ! 5n. -51 -5 -74 -47 •54 M. 7-7, 8-9 1825-60 30-10 i-oo 43-70 56-70 63 -go B C. Se. 127-0 Be. 141 -7 Bn. 150-0 0-6 56-64 6371 74-82 709 2. 2758. R. A. 2,h ,.^» 61 CYGNI. Dec. 38° 7' M. 5-3. 5-9 C. golden. H, {Phil. Trans., vol. Ixxii., p. 221) : "Sept. 20, 1780. — Double. It is a star preceding t. Pretty unequal. L. pale R ; or L. R ; S. garnet. Distance 16" 7". Position 36° 28' n.f." H2 and So. {Phil. Trans. 1824, p. 365). These observers give a complete list of measures from 1753-8 to 1819-9, and after observing that the proper motion given by Piazzi is + 5"-38 in R. A. and +3 "-30 in Dec. , Hj goes on to say, ' ' This affords indisputable proof of their connection in a binary system, otherwise the lapse of nearly seventy years, during which they have been observed, one of them would doubtless have left the other behind, without supposing a coincidence too extraordinary to^have re- sulted from accident." From the measures he finds a mean an- nual motion in angle amounting to -|-o°-730, and then, computing the positions for the dates of the observations, he finds a very fair agreement. ' ' The mean angular motion of these stars then about their common centre of gravity is not far short of that of the two stars of Castor, while their apparent mutual distance is at least three times as great. This circumstance, taken in con- nection with the rapidity of their apparent proper motion, affords a presumption of their being much nearer to us, and renders 61 Cygni a fit object for the investigation of parallax." 2. {M. M., p. 169) gives his measures from 182 1 to 1835, and from them infers an increase in angle and distance. Trejiting the distances by the method of least squares, he arrives at the formula i5"-727 + o"-o749 (t - 1832-58) ; and the computed and obier\'ed distances then agree very well. In the P. M., 2. states that the motion up to 185 1 had been recti- linear, and gives the following formulae : A sin P = + i6"-i63 + o"-o620 (/ — 1840-02). A cos P = — i"-959 — o"-i850 (i — 1840-02). Smyth {Cycle, p. 494') says : "It affords a positive instance of a double star which. MEASURES. 385 besides the individuals revolving round each other, or about their common centre of gravity, has a progressive uniform motion towards some determinate region. This path is relatively spiral, but still so vast as to appear rectilinear ; but too little is yet known of its amount and direction to refer it to definite laws. " ' ' The difference between the proper motions of the components here shown would produce a change in R. A. of 7"'2 since Bradley's time, and an alteration of declination amounting to 18" "9, corre- sponding to a change in distance of I9"7. Bessel considered the series of positions and distances very inadequate to afford a trustworthy set of elements. He concluded that the annual angular motion is some- where about o°"67, and that the distance at the beginning of the present century reached a minimum of about 15". Hence, he remarks, we are enabled to conclude that the period of revolution must be more than 540 years, and that we see the semi- major axis of the orbit under an angle of more than 15°." (Hind.) In making his observations for the de- termination of the parallax of this star, " Bessel chose two stars cf about the g'lo magnitudes, one being nearly in the direc- tion of the line joining the double star, and the other perpendicular to this direction. The distance of each of these stars from the point which bisects the distance between the two stars of 61 Cygni, was measured sixteen times every night of observation." The resulting parallax was o"'3i36, equiva- lent to a distance from the sun 657, 700 times the length of the semi-axis of the earth's orbit. (See Mr. Bishop's volume of Obser- vations.) After reducing the angles to the equinox f iSso'O, O.S. finds the following formulae : A A = + 1 6" -659 ± o"-036 + (o' -0464 ±o"-oo28)(/ - 18500). A D = - 3"783±o"-oi3 - (o"-i9o6 ±o"-ooio) (/ - i8so'o). An examination of the differences resulting from a comparison of the measures with the calculated quantities shows that the formulae are not satisfactory. Hence it is evident that the traces of orbital motion may soon be very distinctly recognized. Duner has found that S.'s formulas do not represent the observations between 1866 and 1876, and he gives the following : Asin P = + i5"-o9 -f o"-0788 (f - 18250) - o"ooo62 (C — 18250)2. AcosP = -f o"-89 - o"-i8s8(;- 18250). He observes that the deviation from a straight line is already apparent ; that his formulae give very considerable differences in the early observations ; and that probably no formulse would agree well with both the early and recent measures. The proper motion of this object has been carefully determined. Argelander's values are — First Star, Second Star. R. A. -f 5"-ii Dec. R. A. Dec. + 3"'23 +5"'i9 +3"'oo H, {PAz7. Trans. 1824, p. 367) gives the following list of the early observations : No. No. No. Decl. No. Date. Position. (n,f.) of Distance. of A R.A. of of Authority Obs. Obs. iObs. Obs. I I7S3'8 54° 36' 19" -628 14-40 2 i6-o Bradley, cited by Bessel. 1778-0 39 2 15 244 1500 6 9-6 5 C. Mayer, ditto. 1781-9 36 II 2 J5 '333 3 Hi, Catalogue and MS. 1784-4 22-50 I 6-9 I Dagelet, cited by Bessel. 1793-6 37 14 14 '873 15-00 I 9-0 I Lalande, ditto. iSoo-o , 19 43 19 -267 21 -60 17 6-5 13 Piazzi, Catalogue for 1800. 1805-0 ! II 12 14 -502 i8-oo 6 2-9 8 ,, cited by Bes<:el, Fund"* I8I2-3 10 S3 16 -741 19-80 ! 31 Bessel, Fund'" Astronom a. 18138 iy6o ' 37 Lindenau, cited by Bessel. 1814-5 I8I9-9 20-32 2 Struve, Catalogus primus. 6 ^8 5 15 -20 19-10 14 1-85 ,, Additamenta, p. 180. 1822-9 5 '9 35 -425 33 Herschel and South, mean result. Bradle7. 35 -4 C. Uayer. 50-9 H,. 53-8 Lalande. 52-7 Fiazzi. 70-2 78-5 19-63 15-24 16-33 14-87 19-27 14-50 1753-80 78-00 81-90 9360 1800-00 5-00 Bessel. 79-1 Lindenau. 69-1 2. 68-9 83-5 85-8 89-4 16-74 i8i2--?o •56 13-80 17-20 14-50 I5-II 2J-5I «4-93 2-72 I5'3i 8-72 25 386 DOUBLE STARS. 2. 911 4n. 15-63 92 -o in. -79 93-8 6n. •97 94-4 16-08 95-4 15-93 So.. 86-9 63 -44 H,. 89-3 -43 ■9 •43 90-8 •61 7 •45 Sa. •3 2n. •69 92-4 in. •88 93-3 2n. 16-12 94-8 It •20 96-0 »» -57 97-2 »» -40 ■9 in. -55 98-9 ,, •76 99-6 2n. Sm. 90-5 15-6 92-3 -4 93-2 i6-2 •6 15-8 951 ■9 96-3 16-3 99-8 •4 1037 17-0 Ma. 94- 1 15-59 98-5 16-49 990 -86 989 -78 lOO-l -35 I03I 4n. -80 104 I ign. -83 ■4 •90 105-0 17-63 106-9 I2n. -48 107-6 ■56 108-7 22n. -93 Encke. 95-2 16-27 Oalle. ■4 15-91 96-1 16-70 Ka. 97-1 6n. -0 -6 J J •I 111-2 ,j 18-47 0.2. 99-0 31- 16-67 100-9 ,, 17-02 102-4 2n. -18 103-6 3"- -34 104-5 2n. -46 105-2 >) •57 106-5 jj 18-02 108-7 3n- •22 112-5 4n. -81 116-1 2n. 19-42 Ja. 99-3 1602 90-7 17-12 100-8 16-81 102-9 II 17-43 103-3 20 -48 104-3 10 •40 ■7 10 -68 106-4 ■9 107-2 18-0 ■3 17-9 1831-70 D.O. 99-3 17-12 1846-71 2-77 Hit. 101 -I in. •85 7-54 5-65 Fit. 102-9 19 16-96 50-90 6-57 103-9 27 17-20 2-72 7-71 107-5 ■7„ 6-67 25-70 Ho. 104-3 3"- •28 2-76 8-52 105-4 )) ■45 4-83 9-47 108-3 2n. •88 9-91 30-56 Mi. 103-9 ■y 2-93 1-74 De. 105-5 7n. •29 4-73 0-66 106-1 2n. •34 5-84 3-80 •4 4n. •45 6-62 4-62 107-3 3n- ■73 7-61 7-56 •8 4n. •73 8-53 975 109-4 8n. 18-36 62-76 40-73 -6 4n. •37 3-39 1-87 110-4 ion. •53 4-74 3-76 •9 8n. •57 5-65 -98 III -7 i6n. •72 7-16 30-81 112-8 5n- •83 8-68 2-65 113-5 7»- •96 9-70 4-76 •9 19-16 70-58 5-59 114-2 ,, •23 i-SS 7-65 -3 8n. -33 2-60 9-69 •8 7n. -44 3-55 48-07 115-3 6n. ■52 4-53 53-80 -9 71- -58 5-56 35-54 8e. 105-7 2n. 17-56 55-55 41-49 -2 jj -89 6-63 %-62 111-8 in. 1881 60-84 3-76 Po. 106-6 40 17-88 55-92 4-48 108-6 7n. i8-2 9-89 50-95 M. 109-9 in. 17-64 61-79 2-44 108-9 J, 18-13 •84 3-«3 107-7 )> 17-89 •is 4-55 108-4 -66 2-57 7-56 110-4 4n. 18-63 5-56 9-54 111-8 iti. -89 8-60 61 03 112-7 >» -71 -60 37-63 -5 •51 •61 -71 in-8 „ 19-06 9-54 8-73 112-8 18-24 ■62 40-05 -6 ,j 19-48 70-48 1-81 •1 J, -07 •50 65-89 114-1 ,, -77 2-78 43-53 115-1 i8n. ■55 5-51 7-46 Eo. 109-7 in. 65-75 50-30 111-4 )» 18-76 -76 1-81 Kn. -6 2n. -76 6-72 2-67 113-4 3n. 19-16 71-60 4-25 114-4 2n. -60 3-00 7-20 Ta. 112-8 in. 18-84 66-74 60-80 113-6 ,, -93 72-70 8-54 -6 j> -68 3-71 74-74 1 1 7-4 ,, 5-34 45-87 116-1 ,, 19-43 -38 6-70 115-9 ,, 20-03 -59 7-96 -9 ,, -81 50-62 Dn. 1 12-0 4n. 18-49 67-89 1-77 -2 6n. -62 8-82 2-75 113-0 8n. •82 9-89 3-89 -5 2n. •91 70-90 6-81 115-1 31- 19-41 3-87 7 -32 -7 ,, ■39 5-95 8-27 Gl. 113-8 6 -12 0-20 MEASURES. 61. W. &8. PI. Fl. Dob. Goldney. "39 6 114-0 6 ■I 6 6 113-9 6 116-1 4 115-9 3 -0 4 -2 10 -6 8 116-3 4n. •3 I2n. ■7 7n. 1131 5 1 15 -6 6 Jtl4-2 4 ■4 4 -0 7 ■5 5 7 4 7 9 1 17-0 7 115-9 6 1 16-2 10 115-8 8 116-6 4 ■2 5 "4 2n. •3 7n. -2 in. 7 411. •7 » 19-38 -00 -18 ■32 ■20 19-5 •46 •60 19-61 -68 -I -o i8-7 19-40 "59 •68 -96 •66 -72 20-03 19-78 •76 -52 20 -02 1870-65 -80 1-32 73 373 -68 -81 -70 4-91 -91 571 646 8-66 I '59 2-65 •72 73 74 74 75 372 579 6'59 •60 -61 •61 -62 75 777 79 8-60 -72 710 t. 2760. R. 21" A. Dec. M. 1-9" 33° 39' 7-3. 8'i The distance has diminished considerably, but the angle has probably not changed at all since 1830. O.S. finds that the distances are represented by *= ii"-55S±o" -017 -(o"-og9i±o" -00137) (/— 1850-0) ; and the differences between the observed and computed values are very small. Duner gives A = li"-37-o"-io2 (/-i85o-o). P:=224°-i +o°-047 (/- 1850-0) +o°-ooo43 {t - 1850-0)". So. 0.2. 222-8 2n. 14-32 2239 in. 13-49 -2 2n. •66 222-9 •38 223-5 3n. 12-95 224-1 ,, -70 ■0 )> -76 •9 2n. 13-02 223-5 4n. 11-67 2n. •02 224-3 )> 9-70 -2 ft •23 i825^6i 9-84 •87 32-40 5-63 667 7-77 9-86 47-90 55-81 68-76 73-72 Ha. Da. Ea. Ho. Be. Da. Ta. W. &S. Gl. PI. Fl. 222-7 12-42 223^3 3n- 11-75 •8 •70 -7 3n- ■40 ■? ,, 10^90 •6 2n. •79 221-4 »* •78 223-9 m. 12-15 -4 3"- 11-98 •9 6n. •92 225-4 ,, 9-64 224-3 3n. 10-91 -5 m. •57 225-0 •52 224-7 •12 •9 984 225-0 •68 -5 -35 •3 •24 •2 8^99 -2 -79 224-5 4n. 9-58 ■7 6n. ■54 225^2 3"- 8^29 222 -6 6 7-35 223^2 8^58 224-4 S 9-5 225-3 4 •42 224-2 2n. 8^72 225-4 •22 387 \ [841 -50 5-68 7-76 5094 1-93 6^92 9^86 41-67 3-82 I 81 65-91 54-72 5-86 7^o8 6302 5-22 7^12 919 70 96 3-05 5-03 68-55 9-83 74-81 2-70 3-74 ■72 4-70 6-79 7-83 711 X. 2762. R. A. 21" 4" Dec. 29° 43' M. 6, 8 C. A greenish white, E bluish. Duner-s formulje are 1855-0. A = 3"-43. P = 3i4°-3 - o°-047 (/ - 1850-0). 11783-70 1824-70 9-75 47-70 54-U2 6-45 7 06 68-59 73-72 480 H,. 3153 m. So. ■2 2n. 3-57 2. •6 3n- •S4 Ha. 314-7 in. •62 De. 310-7 5n. •42 3151 m. •60 Se. 3137 3"- -53 Du. •I 5n. ■19 ■w. &S. •6 in. •4,^ Gl. ■0 )» -40 712 t. 2777. R. A. 2ih g-e" Dec. 9° 28' M. A 4-1, B 10, C 10 A B. The orbit has a great resemblance to that of 42 Comae Berenicis. The period is still uncertain : it may be six or seven years, or about double that time. 388 DOUBLE STARS. A + B and C. The observations being reduced to 1850, and weights being assigned, M. Doubiago finds the following formulae for uniform rectilinear motion : A A = + i6"'i36± 0-030 — (o"'o6oo ±0-0024) (J— 18500); A D = + 26"'267±0'03i + (o"'2943 ±0-0024) (' — 1850-0) ; and the differences indicate no deviation from such movement. -(O.S.) The proper motion of 5 is + o" -08 in R. A., and - o"-28 in N. P. D. In this C has no share. A -1- B For and C, Schiaparelli gives A sin P = + i6"-90 — o"-o632 (t - 1839-0). A cos P = + 22" -98 + o"-2873 (t - 1839-0). 0.2. Sa. H,. So. H,. 2. 8m. Ha. 0.2. A B. 22-5 i8-8 191-9 207-6 211-5 16 -8 I3S 216 2033 24-0 221-2 8-0 in. >> sin, ;Ie '" in. 0-21 ,, ■23 >j -40 j» •39 -50 ± oblong wedged oblong in. 0-33 2n. ■25 1 -J? and C. 78-4 41-9 40 39'5 41-4 397 37-8 ■8 ■4 367 38-8 37-6 36-8 345 •9 -8 32-2 30-9 ■9 29-2 7 ■4 19-53 25-81 20- 27-83 3n- 26-64 27-48 2n. -56 4n. -63 28-07 -26 27-1 -9 28-2 29-88 in. 2882 30-48 31-07 -38 ■57 -65 32-36 1852-64 -67 3-91 4-69 6-57 -67 -67 8-59 9-65 61-57 5 -91 74-67 -73 74-75 0-73 1781-80 1825-26 7-63 30-35 28-80 32-10 4-90 5-64 6-65 777 0-67 6-78 8-59 41-49 3-63 1-65 7-82 51-84 2-64 3-91 4-69 6-58 28^7 in. 32-59 1857-67 •4 >» •84 8-59 -2 »j •87 9-65 26-1 34-70 65-91 Ka. 34-0 28-5 42-64 33-9 29-2 4-17 De. 27-0 33-76 63-14 25-0 -70 74-80 En. 27-5 34-46 65-72 Dn. 25-5 2n. 35-80 9-67 ■w. &s. 24-2 in. 37-66 76-81 •El. -0 »» -57 7-82 713 t. 2779. R. A. Dec. M. it g.jm 28° 35' 8-5, 8-5 C. yellowish. Change in both angle and distance. Duner gives A = i8"-6i— o"-029 (('—1850-0}. P = i87°-i-o°-i2S (<■- 1850-0). 2. H,. Ma. 0.: De. Du. Fl. 189-4 2n. 19-22 185-4 In. 23-8 188-0 >, 1830 186-6 -40 187-7 3n- -70 -2 in. 77 1847 », 17-99 185-I „ -90 -I ,, -71 -2 Sn. 18-13 184-2 4n. -07 182-8 in. 17-86 I82S-8I 9-80 4371 802 50-93 39-83 68-76 -77 74-84 64-59 9-81 77-82 714 S. 2778. R. A. 2ih g.jm 2. Ua. Dec. ■1° 44' 267-0 2684 4n. in. I 21-19 I 20-10 M. 8-4, 10-6 1828-24 43-70 715 O.S. 432. R. A. 2ih g.yn Ua. 0.2. Da. De. Du. -w. &S. Sp. PI. 130-4 -4 129-7 126-4 128-3 -3 -4 •7 126-4 124-6 Dec. 40° 39' 4n. 2n. in. 4n. 2n. In. 3"- 1-04 -19 -07 -03 -16 -23 -17 •17 •21 -32 M. 6-8, 7-2 1843-65 7-94 53-86 968 67-01 9-72 73-73 5-80 -63 6-86 MEASURES. 389 716 R. A. 21'' 10™ T CYGNI. Dec. 37° 32' C. yellow, blue. M. 5 "6, 7 '9 Rapid change in angle. Discovered by Alvan Clark in 1874. The position of Holden's third star in 1 876 -9 was 26o°'3; distance is"*68. W.O. De. Bn. i62"6 161-5 i6o'2 174-8 ■5 170-5 161 -5 iS5'3 150-0 i-io 1874-83 ■25 6-79 •04 -90 in. •06 4-90 2n. •24 5-12 31- ■32 -b9 2n. •24 6-79 8n. •26 7-70 •06 8-41 717 R. A. 21'' 11-4"' A. c. 19. Dec. 63° 57' M. 7. 7 This double star was discovered by Alvan Clark in Dawes's observatory, on July 8, 1859. Dawes says, "a neat star, sharply defined and pretty steady ; " and in his notes he ob- serves, " if there is no error of identity, it must have rapidly separated in the interval [since the date when 0.2. frequently exa- mined it and entered it as single], and may now perhaps have arrived nearly at its maximum distance ; the plane of the orbit lying nearly in the line of sight." O.S. Sa. W. ft 8. De. single 246-2 0-88 •4 •93 244-5 -98 247-4 4 •93 251-2 4 ■99 247-6 •95 1842-00 5973 60-70 6-83 72-78 3-8i ■II 718 R. A. 21" 15-4°' Variable ? Ua. O.S. Da. Se. 0.2. 435. Dec. 2° 23' 24-2 0-45 17-0 -52 16-0 •45 23-8 3"- ■59 201-8 4n. •55 196-2 3"- ... M. 7-5. 8 1843-65 5-88 51-71 48-13 52-43 6603 719 ox. 437. R. A. 2il> tyg" Dec. 31° 56' M. 7, 10-5 Indirect motion. 0.2. Ka. Sa. Se. On. W, &S. 67-7 S8-i 63-7 61-8 -2 60-2 54-6 53-2 51-4 4n. 1-37 1845-43 3n. ■51 58-74 in. 45-63 i» 1-29 51-76 4n. -29 -98 •29 3-50 4n. •40 66-57 7n. -35 71-15 5 •32 3-73 •55 630 720 2. 2797. R. A. 21'' 20-9°' H,. 2. Ma. Ko. De. Dn. Dec. 13° 10' 213-3 in.. 4-65 •3 3"- 3-17 215-5 -20 216-4 ■18 215-9 -23 216-5 •23 2I8I •31 222-2 in. •63 214-5 2n. -53 216-0 7n. •0 -3 5n. ■18 M. 6-7. 8-2 1828-64 31-26 42-71 5-52 51-75 2-72 5-81 8-81 682 7-64 6894 721 R. A. t. 2801. Dec. 79° SP' M. 7-3. 8 The common proper motion of this pair is -f o"lo8 in R. A., and— o"-io6 in N. P. D. 2. 273-1 3n. 1-42 1832-38 7-07 O.S. 2699 „ -52 46-74 75-46 59-92 273-1 3n- 1-42 271-6 2n. -45 2699 ft -52 265-7 in. ■73 279-4 )) -16 722 R. A. 21" 23" t. 2799 20 (B) FEOASI. Dec. 10° 34' M. 6-6, 6-6 Dawes first measured it in 1832, anil says {Mem. R. A. S., vol. xxxv., p. 436), "there is sufficient evidence of a retro- grade orbital motion since the first obser- vation. " 390 DOUBLE STARS. 0.2. (1877). Indirect motion : distance not sensibly changed. 1825-68 876 9-64 3291 377 0-64 5-81 276 5075 174 3-80 479 8-8o 9-88 61 81 276 4072 51-96 4"74 4375 53-20 5-52 6-57 62 67 3 '64 56-28 66-89 59-81 65-67 6-74 71-70 371 74 68-70 72-66 373 5-81 3-80 6-44 ■45 7-54 8-62 M. 8, 8 80. 338-1 2. •9 335-8 333 '4 332-2 =.• 334-6 Ua. 3329 330 -I 3289 324-4 -7 322-7 323-7 318-5 321-6 317-8 Da. 327-4 322-6 320-3 0.2. 329-8 320-8 Oe. 142-3 137-8 3'7;9 8e. 320-7 317-8 Ho. 320-8 Bo. 315-2 Ta. 3"7-i 315-4 309-9 312-4 Br. 325-8 W. &S. 314-0 312-5 01. 3>37 Schi. 128-7 8p. 308-8 PI. 310-0 Dob. -8 1-20 in. -26 ,, -44 3n- -37 in. -30 •0 •58 -34 :S ■1 •36 •37 9n. 3"- -47 •38 -26 -26 5n. 2n. -17 -48 ,, ■44 4n. -2 5n. -2 4n. -45 3n- -43 4n. •23 in. l6 •24 -38 2n. -29 in. »i 1-47 ,, -00 »» 8 5 4 2-98 ,-36 -28 -26 4 •4" In. -21 -22 Sn. •33 3n. -33 723 S. 2802. R. A. 2ih 27"° Dec. 33° "7' Duner gives 1852-79. A = 3" -90. P = lo-o -o°-0S9 {(- 1850-0). 80. 2. Ma. 8e. He Bu. 10-6 2n. 4-32 II-3 3n- 3-84 12-3 in. 4-25 100 3n- 3-94 99 2n. -93 -I in. •75 87 4n. ■86 1825-65 30-48 43-78 8-72 56-82 7-64 71-61 724 S. 2804. 29 (B) FEOASI. Dec. 20° II' R. A. Dec. M. 21" 27-1" 20° 11' 7-3. 8 This object was discovered by 2. and South. The former {M. M., p. 55,) says that the angle had increased between the years 1828 and 1834, and that the motion was almost beyond doubt. Dawes {Mem. Ji. A. S., vol. xxxv., p. 436) writes : "There can be no doubt of the binary character of this object." The direct angular movement suspected by my father is perfectly confirmed by the later observations, the distance remaining unchanged. (0.2.) Duner gives 1852-90. A =2" -90. P = 320-9 + o°-2685 (t— 1850-0). So. 2. Da. Ha. Hind. Ho. Se. H. Da. Bo. Ta. 0.2. Do. Kn. W. &8. Gl. 7n. 8n. 8p. PI. 6n. 2-58 1825-70 71 864 3-38 30-66 -22 1-73 2-93 28-75 -79 35-35 3-12 2-87 •i8 5-44 2-93 41-44 •83 6-18 •88 54-00 •86 38-24 -80 42-76 -90 3-85 •89 51*01 •77 -87 •90 4-45 -92 6-67 •68 8-86 3-13 62-26 2-62 45-45 6-54 3-02 54-77 2-87 6-47 3-02 66-81 2-85 4-67 •75 -87 -65 5-67 -60 6-78 3-16 73-74 2-94 68-67 -92 74-67 -76 0-68 -96 1-78 •99 2-91 2-66 •8 3-73 5 -81 3-02 4-79 •80 2-91 5-96 -96 7-60 MEASURES. 391 725 Z 2822. R. A 21 jU, CTGNI. Dec. 28° 12' C. A white, B bluish white. M. 4, 5 This bright object was first seen double by C. Mayer in 1777. Considerable diminution of distance com- bined with a very slow increase in the angle. It is strange that the former change has not been accompanied by a proportionate augmentation of the angular motion. The distance will no doubt be very small when the apparent periastre is reached. The ap- parent orbit is probably very elongated. (O.-S.) The common proper motion of this object is about + o''Oi6 in R. A., and -f- o"'z6 in N.P.D. The small star C does not belong to the system. Duner gives the following formulae : A = 5" •60-0" -0330 (t—iSjo-o) -o" -00021 (/- 1830-0)^. p = ii3<'-s + o°-o6707 U - 1830-0) + 0° -000555 (i— 1830-0)' + 0-0000052 (;- 1830-0)'. Hi. 80. S. 8m. Ha. Da. Hit. Po. o.s. Ho. Be. 109-2 2n. 113-1 ,, S-74 112-7 m. -67 114-5 4n. -55 1 13-8 -6 1 14-3 •4 115-0 -10 114-9 4-63 II7-1 S-32 115-8 -51 •I -41 ii6-i 4-76 11S-3 -37 -3 -25 ■8 -22 •4 ■5? 116-9 8n. -18 114-3 6n. 5-46 1121 in. 4-89 -2 3n. ■94 -4 in. -78 115-7 i> -66 1160 »» -44 ■4 ,, -34 •6 -88 115-2 6n. •50 116-7 2n. -41 •4 -66 -4 6n. -40 117-0 5n. -14 -8 ft 3-94 1780-84 1823-69 30-77 1-63 2-79 9-62 41-60 2-77 3-96 4'88 7-92 50-83 1-87 3-54 7-83 8-06 62-16 42-08 7-61 -69 51-84 4-69 61-63 6-72 54-84 5-84 9-75 5-62 6298 6-18 72-85 8e. H. Sng. Bo. Ta. Ea. Ba. Br. -w. &S. Fer, GI. PI. PI. Dob. Ooldney. 116-7 117-0 114-8 115-8 -7 116-3 "3-4 117-2 115-5 116 "9 118-3 117-3 118-5 117-8 -6 118-2 119-4 -4 116-8 117-7 -5 •6 120- 5 II9-3 118-4 119-2 II6-S 3n- 4-63 -39 in. -46 31- -12 in. .. . »» 4-64 -82 )i 3-56 5n. 4-00 J> 3-89 6n. -51 4-18 •12 5 3-91 3 3 4 -83 3-65 3 4-05 4 3-84 4-08 1 3-89 2n. •76 5n. in. 2n. 4n. 3-79 -76 -65 •76 R. A. 2,h 39-2" Dec. 25° 6' Sm. Uii. De. W. ftS. Gl. R. A. 21'' 40-9™ S. H,. Dec. 0° 18' 1856-94 66-90 253 5-37 ■68 6-78 8-75 73-74 6684 8-17 75 46 68-75 71 68 3-73 ■73 -78 5 -81 678 -83 2-62 3-80 4-91 6-22 8-75 7-42 -57 8-82 -79 726 2. 2824. 308-5 S"- 11-01 3100 12-0 3073 11-49 3065 •20 -60 3028 982 303-9 11-6 301-7 in. -6 -8 ,, -8 303-3 ,, ... 3025 »> 12-1 M. 3-9, 10-8 1831-56 5-66 44-89 8-01 51-00 60-82 4-84 71-51 3'73 589 4-80 727 t. 2825. '2- Ha. Se. De. W. &8 100-2 -1 -3 -o 118-8 107-7 105s 106-5 107-9 1 107 3"- 1-09 -0 0-95 ■95 -97 m. -95 2n. -87 in. •7 1-08 m. -06 i M. 8, 8-2 1827-72 31 42-69 433 51-78 5-78 7-34 6685 -06 7686 392 DOUBLE STARS. 728 2. 2837. R. A. 21'' 42-9° Dec. 82° 23' M. 85.9 2. 3213 3n- 216 1832-30 Ma. 3110 •49 44'44 De. 3063 •3> 66-24 W. & S. 3022 in. •57 76-94 729 S. 2828. R. A. Dec. M. 2,b ^j.jiD 2° 50' 8, 9 A B. — The angle is unchanged, but the distance has increased considerably. Secchi's angle in 1856 is probably 10' in error. In B C the angle may have increased about 3°. Duner gives A = 24" -87 + 0"-0Sl {t- 1850-0). 1855-26. P = i42°-6. A B. 2. Be. Se. Sn. 0.2. w. &s. ri. 2. Ha. De. 0.2. Dn. W. & S. Fl. 142-4 141-9 142-4 J43'4 142-6 •3 I43"4 142-7 36-9 37'3 40-0 •3 •9 385 41-0 3n- 2379 2n. 25-17 3"- •61 2n. -86 in. 26-26 »» •26 2 •15 in. •52 B C. 31- 3 '64 •93 3"- ■91 in. ■77 5n. 4-06 2 3"93 -89 Dn. 133-4 W. &8. 134-5 -2 AC in. 25 '32 25-78 1829-09 56-64 64-68 8-80 75-68 4-84 5-89 7-88 29-09 4273 64-68 74-84 0-45 5-89 7-86 75-68 -81 730 X. 2840. R. A. 21" 48" Dec. 55° «4' M. 6, 7 C. A greenish white, B bluish white. Duner has A-2o"-i4-o"-oi84 (/-1830-0). 1850-63. P = i94°-6. H,. H, ft So. 2. Bichard' Ua. De. Eng. Da. W. &S. Gl. 192-2 193-8 195-3 193-8 194-2 ■195-1 194-8 196-1 195-0 194-8 •4 •5 -5 195-4 194-9 in. 21-22 2n. 20-31 •31 2n. ■08 »> 19-94 ■59 in. 20-15 2n. 19-69 -20 3n- •60 •68 3n- •28 in. •9 20-16 R. A. 0.2. De. Dec. 51° 59' 257 30-6 R. A. 2,h ^2.jn 2. De. Dec. 19° 40' R. A. 2|b 52-6" Dec. 59° 14' 1782-97 3-62 1823-74 30-76 2 46 3-46 40-50 2-81 4-90 5-58 52-20 7-70 64-43 8-49 74-85 •91 731 0.2. 456. M. 7-8, 8 3n. I 1-35 11847-73 4n. I -50 I 66-64 732 2. 2842. 274-7 2n. I -14 267-9 in. •00 264-7 »> •30 -0 ■4 M. 8-2, 10-7 1829-17 32-90 42-72 63-91 733 O.X. 458. M. 71, 8-6 In 1873 M"-- Bumham detected a distant star, position angle 40°, distance 25". 0.2. 3488 Ha. 44-6 De- 353-7 7n. 3n- 0-71 1 1851-75 elong^-l 45-74 0-80 I 6694 734 t. 2860. R. A. 21'' 59-4" Dec. 60° 16' M. 7-7. 9-3 C. A very yellow, B blue. 2. Ha. De. 250-8 3n- 3-32 252-4 4-45 254-0 -50 ■6 5-15 1832-30 44-43 7-95 64-94 MEASURES. 393 735 %. 2863. R. Dec. M. 22° o'S"" 64° 2' 47, 6'S C. A yellowish, B blue. Dun^r gives ^ = S"'96 + o"-0226 (/ — 1850-0). P = 287°'8- o°-i28 (/- 1850-0). H,. So. H,. Sm. 2. Ua. Po. Kit. Se. Uo. Ba. W. &I in. 5-0 290-3 ,, 293-8 ,, •2 „ 5-82 290-8 6-37 289-5 5-6 2888 -8 ■9 3"- -60 287-2 7n. 7 288-5 in. •87 287-6 3n- 71 •3 6-22 •s ti 5-88 •4 in. 6-17 •5 yn. -00 286-0 8n. •30 ■4 2n. S-85 285-5 n 648 284-4 »1 •45 •8 in. •6 1780-37 81-96 1803-22 23-62 30-67 -91 9-65 177 45-57 50-72 2-66 61 -80 45-90 7-69 54-83 64-84 58-66 70-95 1-86 4-91 736 X. 2865. R. A. Dec. 69° 38' 60. H,. 2. Ua. Se. 1737 16-61 172-3 16 I75-I 2n. •36 177-6 17-50 181 -3 i8-o8 M. 8-5.9 1825-27 31-40 3-38 47-90 63-56 737 0.1. 463. R. A. 22'' 4°' O.S. Se. 346-8 352-7 Dec. 13° 9' 4n. I 3n. I 4-53 •51 M. 7-5. "'4 1 1848-08 I 66-55 738 S. 2872. R. A. Dec. M. 22" 4-5°" 58° 42' A 7-2, b8, c8 The relative brightness of B and C is variable. AB. 2. 3'6-5 I 8n. I 21-35 11834-42 0.2. -4 I 4n. I -75 I 51-24 Sm. Ma. 0.2. Se. Be. B C ti 334-s 2n. 0-54 335-6 3"- •45 330-0 •5 332 -I -52 333-2 5"- -62 328-3 2n. •40 325-9 •5 i833^63 6-17 9-77 41-54 9-11 56-95 67-65 739 OS. 465. R. A. 0.2. Be. 324-3 323-5 Dec. 49° 37' 3"- 15-31 14-94 M. 7-2, 10-7 1 1848-10 66-66 740 t. 2878. R. A. 22" 8-5" V Ma. Dec. 7° 23' 0.2. Ma. Mo. Fer. Gl. W. 4 1 Sp. 130-8 132-6 135-2 134-8 137-8 134-7 132-7 130-I 132-2 125-6 1289 132-2 125-6 4n. 1-36 -34 -34 3n. -33 •26 -38 •27 2n. 16 -44 -26 in. 0-98 1-26 }> -45 -20 M. 6-5,8 830-31 9-70 42-72 50-99 46-32 51-82 988 6-82 9-84 73-71 -80 5^92 6-90 741 2. 2877. p. XXII. 33 PEGASI. R. A. 22h g.^m Dec. 16° 36' M. 6-4, 9-6 C. 2., A, yellow ; B, blue. Sm., A, lucid yellow; B, sea-green. H, (PAiL Trans., vol. Ixxv., p. 649) : "Fl. 33 Pegasi. Double. 89° 12' n.f.") Hj and So. (,PM. Trans. 1824, p. 379) : " The proper motions assigned by Piazzi to this star are + o"-40 in R. A., equivalent to o"-38 on the parallel, and — o"-oi in decli- nation. In forty years, therefore, it should have moved 1 5" -2 from its place in a direc- tion almost exactly coincident with the parallel ; and supposing the small star at rest and the position of 1783 correct, the angle at present should be 75° 38', coinciding exactly with the observed. The proper motion of this star appeal's therefore to be well established in fact, and correct in quantity. " 394 DOUBLE STARS. The proper motion of A is - -o"-2o in R. A., and 4-o"-ll7in N. P. D. 744 2. 2900. Duner gives A cos P = + 7"-53 + o"-0925 (t -1850-0). R. A. Dec. M. A sin P = — 3 -71+0 -0730 {i -1850-0). 22' 17-9" 20° 14' a6,b 9-2, 07-9 The movement is rectilinear and uniform. In A B there has been no sensible change. -rr ° ■ " 2. (see P. M., ccxxxii.) shows that C is H,. 310 ... 1827-65 fixed : his formulae are 2. 316-8 315-2 3349 Sm. 315-4 Ha. 322-4 31- in. 7-59 6-5 7-83 8-72 9-64 51-91 33-63 6-57 P= -(i8"-299To"-035)-(o"-3482 hF 0" -0053) (T- 1838-0). / =+ (54"-2So-(-o"-o35) + (o"-02i8 + 0" -0053} (T- 1 838-0). 328-8 8-36 43-64 0.2. finds that the following formulae 335-5 3364 339 '4 3n. 2n. 7n. -49 •71 -57 9-21 50-99 1-85 6-99 represent the observations well : A A = - 22" -307 ± 0" -049 - (0" -3266 341-0 6n. 61-63 ±o'-oo33)(^- 1850-0). Kit- 33' -5 in. 8-04 47-61 A D = + 54" -32 1 ± 0" -049 + (0" -0094 O.S. 332-5 M -5" 51-90 ±o''-oo33 (/— 1850-0). 350-1 Be- 337 4 345-2 »> 10-26 74-73 A B are probably a physical pair, while 3n- in. 8-56 9-53 57-35 66-90 the changes in A C are due to the proper motion of A. De. 342-2 Du. 345-6 3"- 4n. 8-99 9-48 3-67 8-53 AB. /' _ H. -8 in. ■3« -70 Da. 1813 3-12 1830-75 348-6 „ •55 9-77 •7 -04 2-86 347-9 ,, •26 73-78 1791 2-83 40-15 W. & S. 349-0 4 •8 2-66 •2 51-58 348-2 7 -8 3-73 180-8 2-40 4-78 349-1 6 ■7 4-84 Sm. 181 -6 ■7 31-74 61. 347-9 5 3-74 180-2 •5 8-88 348-5 4 lo-o ■79 178-9 •7 9-69 351-0 3 •79 2. 180-4 I in. ■45 5-06 0.2. i8i-8 in. •83 -64 -60 9-88 74?! S. 2895. 45 '74 7-87 R. A. Dec. M. \ll'l " •40 -46 51-71 65-91 22'' IS'I"" 24° 21' 8-5, 10 178-4 »» ■^5 74-66 Dun^r's formulae are 176-3 »» •81 -72 ^ = 5"-43 + o"-0290 (/- 185 0-0). Ha. 179-2 180-2 •57 •07 42-78 5-51 7 97 P = I7 -5 + 0=5125 (;■- 1850-0) -o°-oo288 179-5 •24 (i - 1850-0)^. 182-5 51-01 2. 6-1 3n- 4-85 1830-09 181-3 2-50 2-26 Ha. 15-0 4n. 5-61 44-39 180-9 3-80 60-82 20-3 3"- ■33 52-36 Hit. 178-9 in. 1-74 47-61 18-2 in. ■'5 6-79 Se. 177-7 ,, 56-76 25-8 >» ■73 61-76 De. -6 2-25 63-25 De. 23-1 3"- •86 3-73 Ta. -46 70-59 Dn. 27 5 6n. 6-00 9-93 184-8 6 -40 •60 W. ft S. 28-5 2n. -5 74-85 ■WT. 4S. 175-8 4 1-93 01. -8 in. •62 -91 176-5 2 3-73 177-0 175-5 4 4 1-8 4-87 -85 743 o.X. 469. Gl. -I 7 -83 -91 176-2 ■; -88 •QI R. A. Dec. M. 22" 15" 34° 31' 7-2. 8-8 AC. O.S. 280-5 3n. 31-80 1846-79 H,. 360-8 45-05 1783-62 282-2 in. -05 74-72 So. 345-7 56-04 1823-71 •4 „ i 30-89 6-74 Da. 343-4 -61 30-66 De. 281-4 3"- 1 31-01 66-71 340-7 57-9 40-15 MEASURES. 395 Sm. 0.2. Ho. 8e. Se. So. Ta. W. AS. Gl. Fl. 344'° 569 341-0 ■6 343"2 Sn. 341-8 6n. 3407 2n. 57-79 337-8 3n- 58-60 331-7 „ 61-90 336-7 26 59-16 335 -6 3n- 60-06 334-1 -s ... in. -47 332-2 >» 61-85 331-7 '» 62-28 -7 4 -7 330-0 4 •4 331-2 2 ■4 3 60-0 330-2 I 68-5 •4 5 63-3 332-1 4 331-9 5 63-3 330-2 in. •5 1831-74 8-38 2-25 6-07 9-88 48-44 71-76 54-85 6-85 63-25 5-68 70-60 3-71 I -61 •93 3-73 4-85 6-83 3-80 ■80 4-91 7-84 M. 4.4-1 745 2. 2909. t AQUAEIl. R. A. Dec. 22" 22-6" -0° 38' C. Mayer saw this star double in 1777; distance about 3", angle about 18°. H, {PAi/. Trans., vol. Ixxii., p. 217): "Sept. 12, 1779. — Double.* Equal, or the preceding rather the larger. Both W. With 229, I J diameter; vrith 449, ij diameter ; with 460, 2 diameters ; with 932, 2j diameters ; with 2010, pretty distinct, but too tremulous to estimate. With my 20-ft. reflector, power 600, full 2 diameters, very distinct. Position 71° 39' n.f. Distance 4" -56, mean of two years' observations." H, (Phil. Trans. 1804, p. 367). He finds an angular change of 6° 58' in 22 years and 38 days. The equality of the stars, and the insulated situation they occupy, lead him to think a physical con- nexion highly probable. Hj in 1825 and 1829 discussed the mea- sures, and was led to conclude that the indirect motion was fully confirmed. S. (M. M., p. 55): "There can be no doubt concerning the indirect angular motion. The distance has probably dimi- nished, as it should if the angular velocity has increased.'' Sm. (Cycle, p. 518): "By roundly as- suming a mean of J" yearly, there may be a period of 750 years." Da. (Mem. R. A. S., vol. xxxv., p. 440). He says that some of the earlier measures ^ Known to Mayer, etc were enormously too large, and that 2, early pointed this out. Dr. Doberck's elements are T = 1924-IS J2 = 140° 51' X = 134 40 7 = 44 42 a •= 7"-64 e = 06518 P = 1578-33 years. Duner's formulae are 1854-46. A = 3"-49. P = 346°-4 - o°-4945 [t- 18500). The proper motion of the system is -f o'-oio in R. A., and — o"-04 in N. P. D. H,. 189 Be. Sm. i8'4 17-9 120 H, & So. 3605 3611 356-2 •4 -2 3S2;4 2- 359-8 355-2 3530 3495 3557 354-3 3560 355-3 353-8 352-4 ^ ,. 348-9 £iicKe. 3520 351-8 350-6 -7 ■I 348-4 •o 349-1 348-1 -2 3475 3468 •4 345-2 3436 3403 3363 3504 35«-6 349-3 3502 3392 Da. Oalle. O.S. in. 4-22 1779-73 ,, 5-3' -94 »» -62 80-48 4-38 -60 1-73 ,, 2-38 ,, 1802-00 22 4-98 22-27 70 •01 5-73 in. 5-22 8-56 »» 4-73 9-60 2n. 3-84 31-64 in. -55 5-55 ,, -91 6-43 2n. -6 25-73 5"- ■46 32-81 in. •50 9-83 »» -77 51-89 •52 30-98 -69 4-77 -16 1-83 *o 271 3-8 4-90 -5 8-04 2-7 42-59 4-05 36-52 3-8 -60 -78 7-61 2n. •57 -38 6n. 73 9-77 2n. ■47 41-86 •54 2-67 -43 -89 •53 3-72 4-00 3n- 3-48 695 ■38 7-93 •27 805 9n. -43 53-53 2n. •32 4-91 4n. -44 9-69 in. -33 66-99 •85 3867 in. •67 9-83 ,, -84 -85 ,, 4-05 -85 3-36 65-91 396 Ka. Ua. Hind. Ja. DO. Mit. Fit. Ui. Po. Uo. Se. Se. Ln. An. H. 3537 7n. 3-49 3500 4n. -29 3389 5n. •17 3522 4-12 35°3 3-47 3487 in. •27 345'8 j» ■58 346-5 ■60 3450 77 3433 ■47 344-4 ■89 343-8 •65 342-2 ■5" 3404 9n. ■63 348-2 m. ■53 •6 ,, ■57 •I )» ■I 3-2 347-8 •82 •6 •94 •0 10 •59 346-8 )) •78 3423 3n- •28 347-4 •83 348-1 392 346-7 in. •95 345-5 >) •6 3481 40 "35 347-0 16 •21 346-7 32 ■34 3457 16 ■53 •8 35 342-3 30 3-66 3456 3n. •61 •9 ,, •57 344-8 6n. •74 343-9 5n. -61 342-6 )> •59 341-9 M ■54 •0 4n. ■67 3393 gn. -53 3385 6n. •50 337-0 yn. •34 336-9 2n. •34 3353 in. •38 336-7 ,, -39 •4 »> ■31 334-6 )> ■54 •9 ,, ■4 ,, 3-45 ■4 31- •33 345-1 ,, ■47 343-0 2n. •32 337-8 j» •50 349-4 4-01 342-1 332 341-6 ■5! 340-7 in. -28 3332 „ •56 3357 ») •44 3335 »» ■49 3355 ,, •63 -2 )i •58 332-6 1) •68 DOUBLE STARS. 1840-01 1-82 6689 41-48 2-76 7-86 52-80 3-85 4-86 578 6-79 8-01 •80 61 81 43-79 5-63 6-53 5-87 6-48 •80 5173 2-73 7-87 46-75 •85 •86 7-57 8-72 50-88 2-91 1-72 2-94 377 579 3-94 5-83 4-88 5 '90 6-74 7-82 8-74 62-76 3 '69 7-18 8-72 9-85 70-50 1-59 2-52 372 4-73 571 5577 6-76 66-77 56-19 62-85 1-45 •78 7-65 8-62 •82 9-66 77 70-81 Bo. En. Ta. Dn. Bt. Gl. W. &S. Schi. Sp. CO. PI. Dob. Goldney. 334-5 in. 3-56 3339 ,, ■60 335-1 *> ■47 333-6 6n. •37 332-6 7n. ■41 3394 in. •20 338-8 5n. •27 337-0 3n. ■64 333-6 »> •34 339-8 2n. 4-24 •I t, ■42 333-3 in. ... 334-0 2n. 3-8 337-2 »» •34 3366 *) •22 3374 ») •17 -2 in. •35 336-1 ,, •52 •6 •42 335-9 s •27 3368 5 •40 •2 4 3359 5 3-6 336-8 3 335-2 6 3-44 334-9 9 •6 •9 8 -59 333-2 2n. -3 •2 4n. ■6 334-0 2n. 3-79 335-2 4 •81 336-2 4 ■7 335-7 4 ■9 3366 5 334-3 6 3-52 335-3 3 -I 4 3'-48 -7 2 78 •0 5 336-1 4 3-48 3344 in. •40 154-8 ,, •38 3345 ■40 -9 ■39 335-3 9n. •73 334-5 6n. •38 3380 in. gn. 3-52 333-9 6n. •26 332-9 5n- •35 746 X. 2910. Dec. 22° S5' 1870-83 2-72 •77 3-77 5-74 63-18 5-69 6-71 71-61 66-74 8-76 70-63 3-67 67-69 8-84 9-48 70-99 5-71 68-76 70-63 1-70 3-73 ■74 ■80 -87 4-91 •91 5-69 6-60 8-77 I -61 -75 2-67 71 •74 3-73 •78 •81 •83 5-92 6-85 5-65 6-87 5-65 6-88 ■77 7-67 •32 •54 8-8o •80 R. A. 22'' 22-5"' Duner gives 185612. A = 5"-33. P = 345*1 - o°05 {i - 1850-0). M. 8-3, 8-8 s. Ha. 347-2 345 •5 344-7 31- 5-30 In. -49 •S8 3n. •28 1832-14 45.65 51-01 2-10 MEASURES. 397 Ho. 344°2 an. 5-45 1856-75 So. 169-7 ti 12-90 1825-74 ^■i.« 343-^ 3n- -27 i 68-44 2. -0 3n. •27 7-76 w. & s. ■^ 2n. -30 74-85 5«- '71-9 15 31-00 Gl. -8 in. -38 -91 Ma. 166-5 13-03 4371 De. 158-9 12-20 63^75 747 t. 2912. 37 PEGASI. 749 2. 2919. R. A. Dec. M. R. A. Dec. M. 22" 23-9"' 3° 49' 5-8, 7-2 22" 27-4"" 20° 33' 9, lo-s 2. thought there was no evidence of 2.__ 273-8 1 4n. 14-30 1829-75 orbital motion. Ma. 2708 : 43^79 Hg (Mem. R. A. S., vol. vi., p. 67) writes : De. 267-8 ! 15-54 65-24 "Divided with 320 and 6 inches aperture." Sm. {Cycle, p. 518) writes: "It is clear that the angle is undergoing a rapid change direct, already indicative of a period of 750 S. 2924. about five centuries." R. A. Dec. M. Da. {Mem. R. A. S., vol. xxxv., pp. 442, 22" 29-5" 69° 17' 6^8, 7^3 502) says that the angle is probably in- creasing and the distance possibly dimi- s. 257-3 3n. 0-84 1831-76 nishing, but that the question of binarity is 259-1 ■72 6-69 still unsettled. And Secchi was of opinion H,. 2583 1-0 1-80 that the angular motion was then doubtful, 0.2. 254-8 2n. 0-97 41-12 but that the distance had certainly dimi- Ma. 263-7 -84 51-66 nished. Se. -5 in. -84 9^54 0.2. 's measure in 1852 shows that the W. & S. 265-3 ,, 1-24 73^83 angular change is very slow. 266-5 ,, -23 4-84 The common proper motion is — 0" '063 Gl. -5 ,, -14 -91 in R. A., and + o"-i23 in N. P. D. S. 114-5 in. 116 1825-69 109-3 j> ■24 32-82 751 2. 2928. 114-1 ,, -08 4-84 -I ,, ■31 51-89 R. A. Dec. M. Sm. 116-8 ■3 35-81 22" 33-1'" - 13° 14' 8, 8 1 18-9 Ua. II 7-8 -I 0-91 9-66 -70 The angle has diminished. 106 -2 •65 41-64 So. 326-8 6-OI 1825-29 I2I-I -8s 2-80 2. 327-7 3"- 4-69 30-82 1 20 -2 •83 3-63 Ma. 325-9 5-34 43^71 119-8 -82 6-74 Mit. 324-2 in. 4-09 8-74 126-3 -67 51-85 Se. 322-0 2n. -39 57-40 II8-S -81 De. 319-3 -38 63-11 O.S. 123-5 in. i«3 1-65 Fer. 321-4 •55 7-91 1 16-4 0-83 2-67 ■W. & S. 318-8 3 -42 72-71 Da. -2 i-io 43-87 316-0 S 3-86 •75 ii8-5 0-91 54-44 319-5 4 5^97 119-8 ... 60-70 Gl. 317-5 5 4-07 3^82 Kit. 121 -8 in. 0-98 47-57 CO. 316-8 3"- •43 lis 8e. 117-6 it 74 57-09 66-71 single Ja. 1 16-3 1 1 0-7 W. & S. elongated 57-87 72-71 752 S. 2934. 119-3 4 0-5 3-78 R. A. Dec. M. 122-3 Gl. 119-6 I 6 ■5 ■5 1-92 3-87 22" 36-1"" 20° 48' 8-2, 9-2 Secchi thought that there wa some ground for suspecting varia s perhaps iility. 748 t. 2915. 2. 186-3 in. ; I-31 1828-86 R. A. Dec. M. 191-6 1 ,, -26 9-72 22" 26-5" 6° 4 8' 8-5, 8-7 1856 ii •10 33-77 398 DOUBLE STARS. Ma. 182-2 177-9 176-0 i8i-i 169-0 Se. 172-7 168-2 De. Fer. 164-7 168-S W. 4S. 164-1 163-8 162-0 Gl. 158-0 163-6 1-20 -20 -10 ■25 2n. i-io 31- -21 -00 1 6 1-22 5 ■IS 4 6 I-16 183819 42-77 377 5-64 S3"99 6-80 -87 63-82 7-91 72-71 378 4-84 5 '97 3-87 753 OX 477. R. A. 22'' Dec. M. 2^ 38" 45° 22' 7-2, ii-i Rapid change in angle and distance. O.Z. finds the following formulae : AA = + 5"-687 — o"-i795 (t — 1860-0); D A = — 4"-972 + o"-oi67 (/— 18600) ; and the differences are very small. 0.2. De. 122-7 3n. 9-60 148-2 2n. 5-54 J38-S 3n. 6-48 1846-06 7574 67-06 754 Z 2941. R. A. 22'' 40-1' Ma. De. Dec. " 18° 37' 270-s 3n- 8-73 269-5 9-27 267-1 •67 265-1 267-6 9-40 ■0 71 M. 7-5, 10-2 1830-07 4370 7-83 51-81 303 64-58 755 S. 2942. R. A. Dec. M. 22l> 41m 38° 51' 7, 9-2 The distance has increased a little. 2. 0.2. Se. 282-4 4n. 2-65 278-2 3n- •83 279-3 2n. 3 '04 276-3 3n- 2-96 831-61 46-76 69-86 56-93 756 2. 2943. R. A. 22b 4 J. 311 s. 112-2 2n. Ma. •5 m. CO. 114-9 3"- Dec. -14° 41' 307 28-32 M. 6, 9-2 [831-80 4771 77-80 757 S. 2944. R. A. Dec. M. 22" 41-6" -4°S'' A 7, B 7-5, c 8-2 In A B the angle has increased and the distance diminished. 2. (see P. Af., ccxxxiii.) showed that the changes in A C are produced in a straight line : his formulae are P = + (22" -210) T o"-045) + (o"-2038 to" -0060) (T— 1837-0). / = — (5o"-iio) T o"-045 + (o"-3io2 T o"-oo6o) (T — 1837-0). 0.2. finds that the following formulae represent the observations well : A A = + 24" -862 ± o"-044 + (o"-i997 ± o"-oo34) {i— 1850-0). A D = — 46"-i49 ± o"-044 + (o"-3036 ±o"-oo34) {( — 1850-0). Duner has the following formulae : For A B, A = 4" -25 — o"-oiS9 [e — 1830-0). P = 256°-7 + o°-i257 {f - 1830) + o°-ooo57 {t - 1830-0)'. For A C, A cos P = — 46" -20 + o"-3ooo(/- 18500), A sin P = + 24"-95 +o"-23i8 [t- 18500). AB. 2n. m. 8n. 3"- 3"- in. So. Sm. Ma. Da. O.S. Se. Mo. De. Bo. Ta. Dn. W.&S. GL CO. PI. 243" I 245-6 2469 247 '5 •4 -8 251-1 2486 247-1 251-5 249-5 248-9 250-4 252-2 253-0 254-3 251-5 253-8 254-1 -o ■4 255-1 m. 3n- n 2n. in. in. 3"- 3 in. 2n. 3n- 4-35 -12 -19 -2 -00 3 '99 -98 4-20 -28 3SI -69 ■68 -69 ■92 432 -86 3 '46 ■4 •38 73 •68 1792-72 1822-90 32-98 6-33 5-88 44 '99 5886 46 06 -78 58-16 5-84 7-91 62-68 573 6-74 8-75 70-60 3-64 68-82 7378 -82 5-83 6-94 MEASURES. 399 AC. So. 2. Sm. Da. O.S. Be. Se. Ho. Du. W. &S. Gl. Bo. Ta. W. AS. 162-5 «577 1567 ■3 158-0 154-8 150-9 148-8 150-2 145-1 148-4 146-7 148-7 I44"5 142-5 141-7 •5 •5 325-6 326-0 318-9 3237 317-2 in. 57-38 4n. 56-03 3n. 55-11 4n. 54-93 55-1 2n. 52-12 51-09 M •65 in. 49-89 51-48 50-67 2n. 51-28 3n- 49-96 4 48-2 49-08 BC. 3n. 2n. in. 54-95 I 758 S. 481. R. A. Dec. M. 22'' 42 n 77° S3' 7-5. 9-3 There is a third star (8-9) about l'-5 distant. (O.S.) O.S. 267-7 6n. 2-43 1855-18 De. 269-2 3"- -37 66-61 759 s. 2947. R. A. Dec. M. 22" 449 11 67° 56' 7-2, 7-2 Hi- 86-4 1782-74 H^ 78-6 3-53 1828-64 74-4 -56 30-63 73-9 -37 173 2 76-0 .31- 2-98 2-45 Ma. 74-6 3-72 44-42 Ho. 70-5 12 •24 58-72 U. 72-8 •25 64-69 Se. 69-9 -31 527 760 OS. 482. R. A. 22" 48° 0.2. Se. 30-2 33-0 Dec. 82° 31' 6n. 3"- 3-46 •70 M. S"2. 9-9 11850-59 66-61 1822-90 31-84 761 2. 2959. 6-41 i;-88 R. A. 22" 50-9 Dec. -3° 53' M. 6-5. lo-s 45-63 ,/ 51-90 S. 96-7 4". 15-66 1832-10 8-16 Ka. 97-8 14-88 43-64 6-34 98-4 -05 8-00 66-96 De. 101-7 •21 64-78 57-90 CO. ■5 2n. -14 77-80 62-68 57-91 68-82 72-78 762 O.S. 586. 77 R. A. Dec. M. 't 22" 52-5 8° 43' 7. 7-5 The common proper motion is +o"-4? in R. A. and +o"-24in N. P. D. 65-70 6-74 70-63 368 ■77 O.S. 338-4 2n. 0-36 1852-67 343-7 -46 ' simple ' 3-9' 9-65 261 oblong ? 61-66 763 O.S. 484. R. A. Dec. M. 22'' 52" 72° 12' A7-1, b8, cii In A B there is rapid retrograde motion. AB. 0-36 1846-42 -46 ! 55-56 ... I 67-66 0.2. 117-7 99-3 2n. Se. 89-5 )> A+B and C. O.S. 255-4 I 2n. I 30-72 I 55-56 764 OX. 483. R. A. 22'' 53-2" 52 PEGASI. Dec. 5' II" Change in angle and distance. 0.: Ha. Sa. Se. Se. vr. &S. PI. i8o-8 2n. 0-94 187-9 31- -94 191-8 2n. 1-24 1863 0-73 -91 190-9 1-23 2034 2n. 096 1985 4n. 1-14 202 2 4 -4 204-2 15 -21 203-9 4 -43 -5 2n. M. 6-2, 7-7 1845-28 52-78 9-66 45-70 7-86 53-88 7-85 65-24 73-83 -82 4-84 6-92 400 DOUBLE STARS. 765 X. 2976. R. A. 23'" I '6" Dec. 5° 5/ A 8 -3, M. B IO'2, c8-8 In A B the distance has changed con siderably, the angle very little ; while in A C there is decided change in both angle and distance. AB. s. 262-0 3"- 7-94 1828-43 H,. 263-3 6-5 31-00 Ma. 2628 7-08 4374 Se. 2630 2n. 5-09 57-38 O.S. 265-0 in. 8-06 65-99 264-2 1) 7-22 75-90 W. &8. 265-1 •97 2. H,. Sm. Ua. Se. 0.2. •W. &B. Gl. AC. 177-6 -8 3". 15-88 -0 179-7 180-6 16-0 15-86 182-4 16-81 183-2 2n. •31 185-1 in. ■40 187-4 ,, -72 -2 186-7 4 2n. ■5 ■8 -0 4 ■45 28-43 31-00 7-72 43-74 52-93 7-42 65-99 73-78 5 '97 3-82 766 R. A. 23" 4-1"" O.S. 489. IT CEPHEI. Dec. 74° 44' C. A yellow, B purple. M. 5% 7-5 The wide pair, h. 1852, was measured by Sm., who gives the magnitudes as a 5, the small companion 10, B 12. His measure of the wide pair in 1838 was 24I°'5, and difference of R. A. 1 1"-8. O.2., however, detected the duplicity of the principal star, the close companion being of the 8-9 magnitude, and the distance about ij". On being apprised of this discovery, Sm. examined the object at Hartwell in 1843, and was able to see the companion and estimate its position and distance. Mr. Lassell and Mr. Dawes in the same year saw it with theg-in. Newtonian, power 400. Rapid direct motion: the distance has probably increased. The proper motion of v is +0'-002 in R. A., and +o"-04 in N. P. D, 0.2. 35 1 -4 2n. 1-15 1846-48 358-5 ,, ■21 51-42 23-9 in. ■32 76-25 Sm. 330-0 -8 43-77 De. 142 2n. •24 65-88 17-0 In. ... 6-43 10-8 1-42 7-60 17-6 -16 9-78 W.&B. 21-4 ■38 73-81 19-3 ■26 4-84 Gl. -9 -24 -91 i6-o 2n. S-18 767 0.2. 490. R. A. Dec. M. 23'' 5"° 56° 47' 7-2, 9-2 0.2. 308-5 3n. 1-36 1846-80 De. 301-9 ,, -56 66-95 768 2. 2998. R. A. Dec. M. 23" 12-8" - 14° 7' 5-2, 7-2 C. 2., A yellow, B ash. Hi. in. 13-75 1781-63 342-8 ... 1802-67 So. 346-7 »» 14-99 22-87 2. 345-2 3"- 13-37 30-90 344-7 >» -82 6-65 Sm. -9 -5 1-87 345-4 140 8-91 Ma. 347-0 2n. 13-83 44-69 De. 344-8 »» •71 58-12 Du. 346-1 )j 14-02 68-34 CO. 348-6 3"- 13-30 75-91 346-8 2n. -70 7-71 •W. & S. -6 in. -83 5-97 Fl. 348-8 )» -74 7-92 Goldney. 345-2 31- -82 8-89 769 2. 3001. CEPHEI. R. A. Dec. M. 23" 13-7" 67=2 7' 5-2, 7-8 C. A very yellow, B very blue. Discovered by 2., and measured by him in 1832 and 1833. Sm. says, " Little can be said upon the dates, until a longer lapse of time has inter- vened, when it may very probably prove to be a physical object." Secchi (p. 60) writes, "motion certain." The common proper motion is — o'-oig in R. A., and - o"-02 in N. P. D. Sin „ 173-8 •8 I74;9 MEASURES. 401 2. 3n. 2-5 •5 -35 1831-00 4-95 2-84 771 Z 3007. Da. Ua. 138-2 179-8 -30 -39 -54 4-02 42-80 R- A- Dec. M. 23" 17" 19° 54' 6-5, 9-5 Mit. O.S. i8o-i 184-9 183-0 187-0 196-9 183-9 187-2 m. -28 -20 •81 •65 •88 •57 ■73 4-43 52-65 47-69 51-87 70-18 54-82 S-8i 2. 79°-2 82-9 0.2. 83-3 3n. in. 5-68 6-13 •12 1829-83 51-80 69-79 De. S'n. in. 772 Z 3008. 184-S 185-4 2n. -46 -52 6-49 8-57 p. XXIII. 69 AftUAEII. 187-0 6n. •47 64-68 R. A. Dec. M. Po. 182-6 184-3 ... 55-92 61-01 23" 17-5"' -9° 7' 7, 8 Ja. 186-8 2-53 56-92 The proper motion of A is — o"-ii in Se. 187-1 2n. •47 8-44 R. A., and + o"-09 in N. P. D. V.O. 185-7 186-9 m. -56 •60 66-97 58-62 So. 2741 1 10 7-98 1824-80 M. 182-3 m. -28 62-57 De. 2647 3n. 5-95 57-84 178-7 J -57 •8 in. ■f 8-57 0-6 ^ 2'56 9-67 263-1 1 4n. -60 62-74 W. &S 188-0 4 -57 72-80 262-4 1 2n. •58 3-74 181 4 -69 ^•82 ■0 On. .32 6-42 191-0 4 -56 4-84 2606 in. -18 8-55 189-6 4 -81 -85 259-9 -07 70-52 61. -8 7 3-80 •4 -05 1-59 191-0 -81 2589 •11 2-56 190-7 8 2-7 4-91 ;4 4-88 ^ii 189-9 191-2 8 2n. •6 -91 5-69 256-6 2n. -83 -88 -88 4-86 189-9 m. 671 Eo. 2607 W.&S. 2481 2490 in. 2n. 3 4 -75 5-81 4-8 5-02 5-60 65-72 770 2. 3006. 72-75 -75 R. A Dec. M. ^"^^'l 4 •17 ■f5 23" 15-4 r 34° 47' C. white. 8-5, 9 GI. 259-6 CO. 258-0 2559 5 4n. 3"- -16 4-90 3-82 5-90 7-75 Dunei 's fonnu se are PI. 2570 >» -72 6-91 1858-2 = i76''-9 183-8 .■;. A=a"-q7. P = So. io=-25 211. (/-i8s( 5-12 ro). 1825-70 773 O.S. 495. ^■ 188 182-9 176-2 -5 5-05 7-88 9-67 30-76 R. A. Dec. M. 23" 19"" 56° 52' 7-3. 7-5 Da. 178-3 in. -48 -81 0.2. 310-4 3n. 0-56 1846-57 176-9 J) 4-93 41-30 De. 140-3 4n. 67-89 177-0 176-4 ») 5-22 3-78 S-51 S. 182-8 3"- 4-65 31-55 774 OX. 496. Ha. 177-1 •32 43-80 183-5 m. 5-22 4-90 R. A. Dec. Uo. 174-7 2n. 4-98 56-88 23'' 24°' 57° 53 Se. 173-5 yn. •94 64-92 M. Bo. 172-9 2n. -95 5-71 A 5-4, B 7-4, C 8-9, D 10. Du. 171-6 3"- -98 70-20 Ta. 168-7 m. 5-05 3-64 C. A white, B reddish, c red W. &S. 170-4 173-0 169-9 172-9 2n. m. 4-92 -Q4 -80 4-85 Of the existence of D there can be no ei. J) 5-0 4'9 3-87 4-91 doubt. 0.2. saw detect it in 1853 it in 1 De. 845, but has not failed to seen it. 26 402 DOUBLE STARS. Da. discovered the du plicity of B inde- pendently. The companions given by H, 778 2. 3038. in his quarto catalogue probably do not exist. (O.S.) R. A. Dec. M. AB. 23'' 40-4 61° 59' 9. 95 O.S. 269-2 5n. 76-1 1849-64 C. white. De- -3 3n- 75 '63 68-68 It _ r. 275-0 3n- 4-36 1833-83 BC. Ma. 277-8 •30 4575 O.S. 224-2 5n. 1-38 49-64 278-2 •6 414 7-95 8-13 De. 223-8 4n. -39 67-94 279-4 •47 52-65 AD. O.S. 3368 1 in. 1 1-51 51-76 779 t. 3039. R. A. Dec. M. 775 O.S. 500. 23" 41' 27° 45' 7-3. 97 R. A. Dec. M. C. A very yellow. 23I- 31 -S- 43° 46' 6-1, 7 s^; 39-S 36-5 in. 1782-89 1824-81 6. A white, B blue. 2. -3 2n. 30-1 30-52 Probable direct motion. •6 in. •6 1-73 Ma. -0 »» 31-57 42-77 Ma. 92-9 0-3 1843-90 35-4 2n. •58 5-32 ii3'3 2n. ■35 •45 5175 45-24 O.S. 229-4 308-S De. 313-6 4n. •45 52-82 67-21 780 0.2. 507. W. & S. 140-8 Gl. 141-2 6 0-66 74-86 R. A. Dec. M. in. ■7 -91 23'' 43" 64° 13' A 6-8, B AB. 7-5. c 7-8 776 So. 356. O.S. De. 224-4 2n. 0-56 240-9 3n. 1847-01 67-96 R. A. Dec. 23'' 39-8" - 19° 21' M. 6, 7-S AJ=„»o. 2. I43'4 5-12 1821-91 O.S. 353-8 2n. 48-83 47-01 So. -5 -96 379 De. ■9 31- -89 67-96 Hj. 141 -3 6-12 8-0 30-67 1-70 "•s! Sm. 141-8 Se. 140-7 5-5 -68 2-80 55 '93 781 O.S. 510. De. 139-9 •63 66-40 CO. 140-7 3n. 75-90 R. A. Dec. M. i39'4 >> 6-34 6-75 23" 45°' 41" 25- A 7-5, B 7-8, C 9 C is pi-nhaWv vorijiVilo f\ T 1.0c ocf,-. mated it as 9 and lo-il ; De. as 11 and 12. 777 t. 3037. AB. R. A. Dec. M. O.S. 347-8 3n. 0-40 184843 23" 40- 59° 48' 7,8-5 De. 163-6 67-63 C. A very yellow, B blue A + B ^„d c. S. 214-3 3n. 2-72 1831-73 2130 in. •67 3-47 0.2. 344-0 in. 1 20-78 47-91 Ma. 229-1 3n. •15 45-95 De. 345-1 4n. 21-03 67-21 MEASURES. 403 782 t. 3046. R. A. Dec. M. 23" so-2"" — 10° 10' 8, 8-s Direct motion. The common proper motion is - o'-38o in R. A., and + o"-097 in N. P D. S. 232-2 4n. 2-5 1 1830-15 239-4 in. -81 51-88 Ma. 234-8 -46 43-80 Se. 241-2 2n. •78 57-42 238-0 3-02 67-91 De. 241 -0 2n. 2-90 3-92 W. * S. 240-5 S 72-89 ?^A S 2 3-2 3-87 CO. 243-0 3"- ■03 7-75 783 Z 3050. R. lb Dec. M. 23° 53-4" 33° 4' 6, 6 Probable change in angle and distance. Duner gives A — 3"-6o - o"-oi96 {i - 1850-0). P = i94°-8 + o°-278 {t — i86o-o) + o°-ooi5i (/- 1850-0)2. Da. S. Ha. Se. So. Be. Eng. Bo. Dn. ■W. ft 8. Gl. 180 180 188-4 »95 189-7 •o 191-7 193-0 196-0 •4 191-0 190-8 193-6 196-0 198-2 196-5 199-5 196-6 •4 200-2 -I 199-4 200-7 203-0 202-2 201-0 200-7 201 -o 202-1 203-6 201-0 •2 200-7 202-5 2n. 5-26 -5 3n. 4-37 4n. -07 -14 in. 3-65 -47 •60 3n. •78 •60 •43 2n. •87 8n. •34 .66 ion. •18 3n- -50 ,, •44 •63 2n. -49 »» •40 3"- •09 2-96 5 •94 6 •93 5 3-21 4 •13 9 •01 8 •20 4 •09 6 ... 6 ... 5 7 3-i6 1790-91 94-71 1821-92 7-88 30-04 ■73 7-03 43-81 54-81 5-47 32-65 6-49 45-65 50-85 62-20 54-68 64-84 55-98 7-5' 66-97 5-38 •73 8-56 75-70 1-94 2-89 •80 -80 -80 3-81 6-06 3-79 -81 •82 4-91 784 B.A.c. 8350. R. A. Dec. M. 23" 55-9 26° 27' 6, 9 Probably variable in magnitude. The rapid changes are due to the proper motion of A, which is 4-o'-o64 in R. A., and -)-o"-97in N. P. D. Briihnow has found a parallax of o" -054 for this star. Br. 77-0 I I 16-0 1 1870-00 ri. 49-8 I in. 14-0 I 7-94 785 t. 3056. R. A. Dec. 23' 58-5° 33° 36' A 7-4, Slight change in the angle of A + B and C the distance has M. B 7-4, eg AB. In increased considerably. A B form,a binary system, most probably. AB. s. 0.2. Ua. Se. Se. 2. O.S. S3. 159-6 156-7 •55-0 146-8 156-9 159-0 154-2 152-3 2n. 0.60 17 ■60 »» -57 t1 •57 -44 -40 2n. 5n. 0-6 4+B and c. 352 '5 355-5 2n. 20-25 •3 31- -63 356-1 2n. 21-04 ■4 5n. -45 182884 33-81 4I-II 53-70 41-56 2-76 56-87 64-84 1827-88 8-84 33-51 53-70 64-84 786 t. 3062. R. A. 23" 59 •9"' Dec. 57° 46' M. 6-9, 8 le/a. 404 DOUBLE STARS. H, {Phil. Trans., vol. Ixxv., p. 645) : " Double. 50° 42' n. prec." S. {M. M., p. 9). Measures in 1831 and 1833 are given. 2. notes the great angular change in two years with dimi- nished distance. In 1822 he saw the stars separated in the 5-ft. meridian instrument, and presenting no difficulty. In 1824 he could see them with difficulty. Hence he puts the distance in 1823-81 at from 1" to i"-25, and this places the continued decrease of distance from 1822 to 1834 beyond doubt. Thus, 147° -87 have been passed over in 5 1 '06 years, in a direct sense. The appa- rent orbit must thus be very elliptical. Madler {Die Fixst. Sysi.') discusses the observations made up to 1846. He finds the observations in 1782-65 and 1823 in- tractable ; but by giving a double weight to the later observations he finds the following elements : T = 1834-01 U = 146-83 years •^ = 35° 7'-S X = 42 10 -3 a = 77 21 -2 i = 38 35 -9 a = o"-9982 tt' = o -03456. He is of opinion that another fifty years' observations are needed to enable the orbit to be fairly dealt with. M. Schur's elements are T = 1835-196 w = gfs a = 32 -2 / = 29 -9 ^ = o -5009 ^ =+3°-'9S9 a = i"-3io P = 112-644 years. Duner's comparison of these elements with the observations exhibits considerable differences. M. Schur gives an ephemeris from which the following have been taken : 1870 278°-2 i"-5Si 72 281 -6 -576 74 284 -9 •600 76 288 -I •620 78 291 -1 •639 80 294 -2 •6SS 82 297 -2 •670 84 300 -1 -680 86 302 -9 -690 Dj Doberck's provisional elements are a=38°3S'.'^=92°7',7 = 32°«i'.'^=o-46i2, P = 104-415 years, T = i834-88, a=i"-2y. The proper motion of this system is -f o"-346 in R. A., and - o'-020 in N. P. D. Hi. 3I9-4 1782-65 •I 3-05 2. 367± I-2± 1823-81 87-5 2n. 0-82 31-71 108-5 31- •56 3-71 O.S. 186-5 4n. •65 40-32 220-3 2n. -97 6-42 219-7 »> 1-14 8-22 232-5 3n. -09 9M9 235-8 ,, -16 50-04 235-7 2n. •35 1-16 238-3 3". -23 2-49 243-4 4n. -47 4-II 242-6 3n- -38 5-05 247-8 2n. -40 6-66 250-4 3n. -49 7-37 255-3 j> "45 9-16 261-7 2n. -54 6fl-i8 270-4 ,, •47 6-20 276-5 »» •59 8-98 279-2 >> -48 70-18 Da. 187-0 0-8 40-78 193-4 ■95 1-86 2I0-0 ■94 3-80 2288 I 16 8-87 23s -2 ... 50-93 244-3 1-28 4-32 265-6 -40 63-86 Ma. 193-6 0-89 41-58 2073 •87 2 -80 213-8 •85 4-50 216-8 -96 5 '54 220-7 1-05 6-53 225-1 •12 7-53 232-3 •28 50-71 237-0 •16 i-i8 234-6 -27 •76 241-3 -02 2-21 238-0 •25 ■72 2488 ■43 6-81 De. 249-8 3n. 4-91 ■9 ,, 5-05 -2 6n. 1-2 -69 250-2 5n. -22 6-37 252-2 4n. -2 7-71 -4 2n. -2 8-54 263-6 9n. -48 62-73 265-4 ,, •43 3-57 266 I 2n. ■37 4-10 268-7 6n. -40 ■67 270-7 7n. •35 5-61 274-1 im. •40 7-25 277-8 5n. ■42 8-55 280-0 )» -47 9-68 282-2 7n. -44 70-52 283-9 »» •39 I -55 285-7 6n. -47 2-63 287-5 9n. •44 3-63 289-6 6n. •40 4-63 291-9 5n. •46 5 -60 293-0 in. •54 6-00 Ko. 247-9 ■33 55-91 Se. 253-4 -25 7 -60 2700 •34 66-97 MEASURES. 405 En. Bo. Ta. 01. 2657 269-9 2827 271-9 270-3 268-3 280-6 297-8 299-1 281-0 284-0 289-4 2867 in. 31- 2n. 3n- In. 1-40 1863-32 •43 S7« ■38 7260 •14 6S7I •46 6-64 •66 8-76 •63 70-64 0-91 3 -So 108 4-72 •s 0-44 •6 1-60 •5 3-8i ■6 -87 Gl. W. & 8. Da. PI. Bob. 29I-I 8 1-4 -0 9 •3 293-2 in. •0 3"- 295-6 2n. ... 293-5 in. 286-3 4 1-45 287-8 8 •45 291-2 8 -37 298-8 6 -44 2929 Sn. ■43 294-5 I) -46 302-1 >» •3« 1874-91 -91 5-18 6-41 7-95 8-73 2-80 3-82 4-86 6-93 5-69 6-99 8-89 SUPPLEMENTARY LIST OF MEASURES. Ref. No. 787 Oe. 788 2. 8e. 789 s. Se. 790 s. Se. 791 Ha. Be. 792 2. w. 793 2. 61. 794 2. Be. 35. 268-3 267-5 8-69 7-88 51. 131-5 127-6 4-16 -05 149. 118-2 108-0 1-35 -33 171. 157-6 159-1 27-9 29-14 [37.J 223-1 214-6 1-39 •41 254. 334-2 343-8 13-33 12-9 325. 253-4 228-0 11-70 9-2 360. 146-4 139-1 1-34 •67 1830-1 68-2 30-8 57-9 33-2 67-7 29-9 654 43-3 67-7 31-7 74-0 30-9 74-0 31-2 693 Ref. No. 795 2. Be. 796 H,. Ja. 797 2. Be. 798 Ua. Be. 799 2. 0.2. 800 w. 801 2. w. 802 2. 371. 74-7 8i-7 199-3 202 3-35 ■32 9-06 7 3114. 190- 1 179-4 1-92 2-26 [78.] 241-7 247-7 2-25 -72 531. 291-9 395-2 0-8 1-07 536. 149-S 160-2 1-75 -40 579. 30-1 35-6 16-48 -21 596. 280-8 287-5 11-12 10-33 1831-2 674 35-9 57 32-4 64-6 46-1 66-9 30-5 71-2 31-0 74-1 31-5 7S-I 3>-' 74-1 4o6 DOUBLE STARS. ReCNo. 2. Ref. No. s. 803 620. 816 1047. 2. 225-9 3-70 1828-2 2. n 19-5 20-66 1828-5 W. 232-0 -63 75-1 De. 223 2151 68-4 804 704. 817 1046. 2. 8-5 26-53 3>'3 2. 231-0 12-07 29-4 Be. 10-4 23-77 651 De. 234-2 10-92 67-7 805 Bu. 320. 818 1051. Bu. De. 269-0 2-8 292-3 306 74'9 7yi s. Ha. 268-5 1-23 278-4 -22 31-3 58-1 This is A B. A C is fixed at 81° 31". 806 782. s. 309-2 35-96 30-1 819 1171. De. 308-6 38-66 66-6 2. 338-6 2-8 28-9 De. 330-1 -5 64-8 807 787. 2. 81 -I [ 1-37 30-3 820 1213. Gl. 75-3 1 -3 791 2. 3277 8-43 309 De. 324-0 7-26 67-7 808 Ma. [122.] 117-8 1 0-22 43 "2 821 1230. De. single. 65 2. 194-1 28-0 29-2 PI. 192-8 30-82 77-8 809 826. 822 1234. 2. 115-5 1-84 32"4 W. 128-6 -76 75-2 2. 71-3 20-77 31 -o Fl. 69-0 21-75 77-8 810 879. 823 1243. 2. De. 67-7 8-40 71-6 7-46 27 '3 67-9 2. De. 221-3 1-99 225-3 1-84 33-9 67-2 811 [139.] 824 1285. Wii 132-5 0-77 43 '2 2. 339-2 27-57 28-3 De. 317-2 elong^- 73'S Fl. 337-9 25-45 77 3 812 910. 825 1343. 2. 170-9 0-67 29-5 2. 271 -I 10-22 36-2 De. 165-6 -7 69-1 Fergaaoii 269-4 6-79 633 813 [152.] 826 1402. 0.2. 40-2 0-86 50-0 Er 96-0 1 20-42 30-2 De. 33-9 -85 Fl. 98-7 1 23-12 77-8 814 974. 827 1476. H.. 216-9 23-5 1782-8 H,. 351-9 2-27 31-0 n. 224-1 22-2 1877-8 W. 3S9'i "57 75-3 815 991. 828 So. 621. 2. 173-2 3-72 28-2 80. 25-5 43 '43 25-2 Gl. 167-0 -7 74-2 Fl. 38-8 57-84 77-5 MEASURES. 407 Ref. No. 2. v4 829 1549. // Ref. No. 842 w LUPI. s. iiS'9 I4'03 ■2 12-98 1828-7 77-4 ,^: 112-8 0-8 106.2 1-2 ''iPr 830 1594. 843 1908. s. 165-0 16-95 161 -2 13-31 31-9 7S-8 s. 137-2 1-46 143 "8 -26 32-5 74-5 831 2. 1621. 124-0 3-44 30"3 844 3095. De. 140-0 -13 679 s. 3497 2-85 31 -.1 832 y CRUCIS. Oe. 337 '5 -84 69-3 ?>• 2? 120 35 845 1972. To. 36'5 99 60 ?■• 86-8 28-0 1783-5 833 1682. De. 82-1 30-6 1865-8 2. 308-8 33-65 316 846 1988. Bn. 306-2 31-98 78-3 z. 263-3 2-91 30-0 834 [267.] w. 262-3 3'04 764 0.2. 300-8 1 0-25 49-6 847 2006. Se. single? 72-4 835 h. 4649. 2. De. 203-5 197-4 1-69 •65 287* 68-9* 2. 224-0 43-72 28 •7t H,. 64-4 12-0 35-4 De. 221-0 44-31 68-5t 69-4 -0 37-5 836 1804. 848 2017. ^■: 27-6 19-9 420 1796-6 i874'3 2. De. 249-7 25-03 251-2 -95 31-4 676 837 [276.] 849 2041. 0.2. 202-7 o"S 42-0 2. 4'4 3-06 lo""* Oe. 194-3 elong^- 694 De. 1-5 2-58 68-0 This is 74°-2. 9" A B. AC seems unchanged : 57, 1869 De. 850 3105. 838 3124. 2. De. 59-4 0-41 53-2 -50 30-9 70-0 2. w. 150 elong''- 13s 36-2 74'4 851 2080. 839 1846. 2. De. 39-3 5-61 28-2 4-42 30-4 68-4 2. w. 108-8 3-69 112-6 4-27 26-8 75 4 852 2089. 840 So. 184. 2. Oe. 610 2-30 67-3 -41 306 68-3 Hi- st. 128-2 11-88 129-8 9-68 1783-0 1876-4 853 2096. 841 H.- 93-1 20-45 178^-2 KJ^CA. 01. 905 23-0 1874-S 80. 270-1 10-82 23-3 Ba. 291-3 15-62 78-3 * AB. t AC. 4o8 DOUBLE STARS. Ref. No. 854 2. YT. 855 2. Gl. 856 2. Bn. 857 Da. Sp. 858 H,. Ja. 859 0.2. Se. 860 2. De. 861 H,. n. 862 2. W. 863 Da. Sp. 864 0.2. De. 865 ?»• St. 866 2. vr. t. 2156. O n 31-8 3'54 3S"4 -3' 1829-5 74-6 2160. 61-9 4-15 66-7 3-97 29-6 74-7 2163. 103-5 I'Si 97-2 -58 30-0 78-3 A. c. 9. 231-2 I-I2 237-4 0-91 57-5 75-6 h. 5014. 69-2 0-75 135-1 -ss 36-7 57-3 [524.] 865 0-37 68-8 elong^- 53-3 70-8 2286. 322-0 2-42 315-1 '53 317 65-6 SERPENTIS 1. 99-1 81 67-1 142-8 1781-8 1877-S 2310. 233-7 5-07 237-6 -25 29-7 75-6 A. C. 11. 1 78 -I 0-42 172-0 -33 54-7 75-6 Bu. 134. 141-0 I -I I 134-0 -07 51-8 75-0 y Cor. Aust. 37-1 1-23 253-1 -67 34-5 76-6 2461. 330-6 1 3-72 321-9 1 -86 30-7 76-6 Ref, No. 867 2488. 2. w. 868 // 318-5 1-29 329-5 -28 [371. J 1829-0 76-6 Ua. Newcomb. 149-3 072 154-0 -96 43-4 74-7 869 h. 5113. St. 129-1 25 169-8 16-72 37-5 77-6 870 h. 5114. H,. Ja. Ja. 131-0 260-0 270-7 266-0 1-75 69-43 66-37 37-6* 57-8* 37 -et 57-2t 871 [375.] Ha. Newcomb. 872 119-5 0-55 144-4 -67 2553. 43-5 74-7 De. 873 78-0 0-7 91-6 -98 2564. 30-0 74-1 2. Bti. 184-0 10-78 175-1 -04 32-3 78-4 874 Da. 10. Da. Sp. 314-4 0-53 308-2 -60 59-6 75-8 875 2585 H,. Dob. 304-2 8-83 312-4 -64 1781-9 1877-7 876 h. 2904. St. 1^3-5 20 141-4 18-32 31 -o 77-7 877 A.C. 16. Da. Newcomb 234-3 0-35 241-4 -45 S9-6 74-7 878 [392.J Ha. De. 2. De. 324-3 304-3 293-4 291-8 0-2 elong^- '■11 43-8* 69-5* 31-st 70-it AB. t AC. MEASURES. 409 Ref. No. 879 s. Bn. H,. W. H,. W. 881 s. 882 s. Se. 888 s. s. w. 886 2. w. 887 s. w. 888 s. De. 889 s. Se. 890 H,. Bu. 2. 2612. 52-8 S3 '3 36-6 38-0 880 2. 2624. I79-3 176-8 320 "o 328-8 2 -06 42-3 2626. 1217 1301 I-I7 098 2662. 38-9 41-8 172 •6 2666. 239-9 246*2 2-59 •S3 [406.] 884 0.2. Sp. 885 2668. 136-3 H2'9 0-54 •4S 293-6 288-3 3-30 •OS 2673. 33S-I 329-4 2-S3 1-92 2674. 1-3 3-2 'S'S' 14-8 2723. 85-6 92-2 1-49 •22 2728. 24-7 -s 4-22 S-'7 269. 234-8 252-6 > AB. I I -08 t AC. 18277 78-S 1783-7* 1875-7* i783-it i87S-7t 3I-I 75-7 31-0 67-4 28-8 7S-7 45-8 76-8 3«-i 7S-7 30-7 74-7 29-6 7S-7 3«-7 66-7 31-8 67-4 1783-4 1876-2 Ref. No. 891 H.. Se. 892 Se. 893 0.2. Bn. 894 Hi. St. 895 H,. Bnssell. 896 o.s. Se. 897 H,. Ja. 898 2. Be. 899 2. Se. 900 s. Se. 901 2. w. 902 So. •V. 903 H.. St. 2751. 345-9 349-3 2-42 1-62 Bu. 368. 99-4 93-8 0-5 ■64 [527.] 306-2 99-4 0-4 -64 Hi I. 47. 354-8 I ... 3M-8 I 3-0 e iNDi. 306-7 I 3-68 292-0 I [445.J 113-1 107-7 13-3 7-2 0-78 -So 30-11 33-91 2833. 341-7 337-2 8-73 9-29 2842. 99-4 1 10-7 3-08 ■41 2846. 264-6 268'5 2847. 3-19 •28 293-8 305-1 1-35 -38 2881. 111-3 103-2 300-0 30s -9 1-79 -52 ID-O 8-42 1828-6 69-6 75-8 7-8 46-8 77-7 1783-5 18777 34-5 71-0 47-5 72-2 36-6 56-8 25-7 66-6 31-9 67-3 3' -8 66-3 30-7 76-9 25-7 75-9 36-0 76-7 4IO DOUBLE STARS. Ref. No. 904 Ua. 3a. 905 s. Fer. 906 2. Oe. 907 s. Oe. 2. [476.J 335-6 elong^- o-6s ■3 2950. 3191 3121 2 '04 •48 2977. 335 I 3441 2-19 •38 2989. 1441 138-9 "•47 ■f2 1843-5 74-8 32 '2 74-8 33-2 669 287 679 Ref. No. 908 2. De. 2. Se. 01. 910 2. De. 2. 3041. 183-4 180-5 347-6 349-4 3-27 -21 71-I 69-0 909 3047. 64-7 72-7 I-I2 1-02 3060. 109-7 II4'6 BC. t A and 1832-2* 66-3* 32 -2t 66-2+ 31-7 74-9 3-79 -49 B + C 28-7 76-5 APPENDIX. While the last sheets of the Measures were going through the press, the following list of double and multiple stars was most kindly placed at our service by their discoverer, Mr. Burnham. Most of them are very interesting objects ; many are quite recent dis- coveries, and as yet unpublished ; many, too, are naked-eye stars ; and several are well-known Struvian pairs which Mr. Burnham has found triple ; and, lastly, the measures have been largely supplied by that most excellent observer Dembowski. It is therefore with much pleasure and gratitude that we give this valuable list as an Appendix to our book. As before, Bu. = Burnham ; De. = Dembowski ; HI. = Hall ; CO. = the observers at Cincinnati Observatory. Ref. No. Name or Catalogue. R. A. iSSo. Decl. 1880. p. D. Mags. 1870. s 1 h, m- / ^, + lOOI 483 2-8 40 II 447 2-37 7-5, 1 1 -8 8-7 Bu. I0O2 391 B. A. C. 10 3-2 -28 39 97-2 0-78 6, 6 6-8 CO. 1003 253 41 57 51 49-9 0-39 8-3. 8-5 S"f De. 1004 255 5 '6 27 45 99 'o 0-3S 7-5. 7-9 5-8 De. 1005 492 B. A. C. 201 38-5 54 34 152-6 I -91 6, 12 8-7 Bu. 1006 495 42-4 18 2 230-9 0-58 l'^' l'^ 8-7 Bu. 1007 232 AB 43 "6 49 59 288-4 0-44 8-0, 8-5 6-2 De. AC 292-8 28-70 10-2 6-0 De. ICX38 I AB 45-6 55 58 81 -0 1-42 8-1, lo-i 5-3 De. AC «33 3 3-70 8-9 S-3 De. AD 192-9 8 '82 9-5 5-3 De. AE 360- ± i5-± De. 1009^ 23s AB 1 3-5 50 22 74-0 0-45 TO, 7-4 5-6 De. 1010 258 5 -5 61 4 260-4 0-79 6-2, 8-9 P De. lOll'' no 141 -16 26 24-6 1-50 7-2, 7-3 6-2 De. I0I2 4 i6-6 ■ 10 44 81 0-37 7-0, 7-S 77 Bu. IOI3 399 Cetiaii 21-8 -II 31 302-8 1-39 6-5, 10 8-7 De. IOI4 506 17 Piscium 251 14 44 12-9 I 02 4, II Bu. IOI5 s 103 Piscium 32'8 16 I 289-4 1-34 7-0, 9-0 5-5 De. IOI6 6 387 -7 22 167-1 2-59 6-4, 9'2 5-5 De. 1017° 510 AB 42-1 IS 43 337 '4 I -59 8, 12 8-1 Bu. AC 326-4 53-56 8-1 Bu. IOI8 260 467 14 SI 228-0 °'lf 8-3. 9-0 5-8 De. IOI9 7 S8 Ceti 51-9 -2 39 121 2-86 7-0, 1 1 -8 5-5 De. ■ This is the principal star of the wide triple, 0.2. 24- » Identical with Hj 2036. ' The The distant companions have minute attendants, wide pair is Hi V. 92. 412 DOUBLE STARS. R«f. No, u 1 Name or Catalogue. R. A. 1880. Decl. 18S0. P. D. Mags. 1870. > h. m. / + I030 513 48 Cassiopese 52-1 70 19 264-4 1-04 5.7 8-7 Bu. I02I 8 2 150 8 20 200-4 0-96 8-1, 9-4 5-3 De. 1022" i6-8 3258 233° 1-30 7-5. >3 8-9 Bu. 1023 518 Ceti 389 23-2 9 2 139-0 I -57 7. II 7-9 Bu. 1024 521 Persei 67 35-0 47 45 1537 5-86 6, II 87 Bu. 1025 306 Arietis 107 36 '9 25 8 17-3 2-93 6-4, iro 6-8 De. 1026 9 39'6 35 3 160-6 1-52 6-3, 8-4 5-9 De. I027« 524 20 Persei 461 37 51 158-7 034 5-5. 5-5 87 Bu. 1028 II p' Eridani 56-8 -8 9 87-2 2-72 5-4. 9-6 5-6 De. 1029 526 (3 Persei AB 3 0-3 40 30 I5S"3 58-79 13 8-0 Bu. AC 1447 67-72 13 8-2 Bu. AD 192-6 81-92 10 77 Bu. DE 1151 10-64 I2i 77 Bu. 1030 84 lO'I -6 22 10-3 0-50 7-2, 7-4 5-8 De. I03I 533 B. A. C. iioi 281 31 17 149-3 0-43 7> 7 8-7 Bu. 1032 53S 38 Persei 36-8 31 54 6o-5 0-96 4.8-5 7-8 Bu. 1033' AB 37 -o 31 47 o-5± 8-5. 8-5 AC 37-9 23-87 87 8-9 Bu. 10348 536 AB 39'i 23 49 336-4 0-44 8.9-5 8-7 Bu. AC 302-4 36-72 80 87 Bu. 103s 537 39-9 23 28 185-9 0-60 8-5, II 7-9 Bu. 1036 263 48-8 32 5° 71-6 0-67 8-2, 8-5 5-9 De. "037 545 59-4 37 42 310-0 1-02 8, II 8-2 Bu. 1038 547 47 Tauri 4 7-4 8 58 3597 0-89 5. 7 7-8 Bu. 1039 3" Eridani 315 21-9 —24 21 147-5 0-89 6-5. 7-0 7-1 CO. 1040 550 Alilebaran 29 16 16 109-0 30-45 I. 14 7-9 Bu. 1041 46 Eridani 29-1 -7 57-1 1-28 6, 105 9-0 Bu. 1042 AB 44-6 lo 52 17-S 0-35 7. 7 9-0 Bu. AC 148-5 18-35 14 9-0 Bu. 1043 3'4 Leporis 3 53-6 -16 34 149-9 0-43 ,6-6, 6-9 67 De. 1044 188 T Ononis AB 5 II-8 -6 58 250-1 35-98 ' 4, 14 6-2 HI. AC 59-8 35-97 12 6-2 HI. BB 49-3 3-77 16 6-2 HI. 1045 189 Ononis 81 14-5 -S 29 283-6 4-27 6-8, 11-5 5-9 De. 1046'' 190 Orionis 82 14 -6 -8 9 355-3 0-61 7-9. 8-7 61 De. 1047 5S6 187 -236 238-2 0-79 6-5, 11-8 8-2 Bu. 1048' AB 20-2 34 19 223-5 i-ii 8-5, 10 8-9 Bu. AC 131 -4 18-04 10 8-9 Bu. AD 200-7 20-77 "5 8-9 Bu. 1049 320 j3 Leporis 23-1 —20 51 288-3 2-68 .4, II 7-9 Bu. 1050-1 557 AB 23-3 3 3 149-8 24-32 7 8-1 Bu. BC 142-4 0-46 9-5. 9-5 81 Bu. 1051 558 S Orionis 25-9 - 23 227-0 33-79 2, 14 8-9 Bu. 1052 321 Leponis 45 A B 34-0 -17 55 1445 0-65 6-8, 8-3 7-3 De. CD 357-7 1-26 9-3. 97 7-3 De. AC 136-0 89-46 6-6 De. loss" 89 31-5 -I 30 344-2 0-55 7-9. 8-5 57 De. 1054 16 3 Monocerotis 562 - 10 36 354-8 1-62 6-0, 9-7 5-6 De. loss' 17 4 Monocerotis A B 6 2-8 — II 8 178-0 3-16 6-8, 10-5. 5-9 De. AC 244-5 8-95 11-5 6-8 De. 1056" AB 12-4 28 29 133-3 0-27 7-5. 7-5 9-2 B. AC 250-3 2-83 9-5 9-2 B. " The principal star of 2. 258. A C i4S°-4 : 68"-7o (1878-9) ; C D 28°-8 : 6"-i6 (1878-9). • As a wide pair this is 2. 318, 236°^ ■ i4"-o8 (1829-1). f A and C = 2. 439. K A and C = So. 437. This and No. 38 in the Pleiades. I" The wide pair, A C, is 2. 692. 2. gives, 4°-2 : 34"-86 (1831-5). No change since. ' The wide pair, A C, is 2. 707. J Struve's companion (2. 721) found to be a close pair. k Moving? Eu. 36i°-7 : o"-7i (1879-1). A mean of three measures in each case. ' C discovered by Mr. George Knott. » A and C make 2. 888. APPENDIX. 413 Ref. 'h Name or R. A. Decl. 1 No. 9 Catalogue. i8Jo. 1880. P. D. Mags. 1870. h. m. / ^^ + 1057 Monocerotis 97 6 447 - 23 30-9 5-60 6-5. 12 9-1 Bu. 1058 327 AB S2'5 - 2 52 loo-i 0-96 75, 8-0 6-8 De. AC 102 -6 13-22 11-5 6-8 De. 1059° 328 CanisMaj.i39AB AC 7 10 -II 7 1284 360- ± 0-3 20- =b 6-3. 7-5 10 5-9 De. 1060° 575 AB 9"3 -15 16 199-0 0-68 8, 8 8-2 Bu. AC 21 15-87 9-8 8-1 Bu. 1061 65 Aurigs A B 14-0 36 59 8-3 10-36 6, 12-5 8-9 Bu. AC 26-8 36-10 13 8-* Bu. 1062P 577 i4'5 38 1368 0-90 7-5. 7-7 8-2 Bu. 21 9-9 14-54 13 8-2 Bu. 1063 11 Canis Mai. 21-6 7 II 27-4 4-09 5-5, 11-3 5-6 De. 10641 332 AB 22-2 — II 19 166-3 o-8o 6-3, 8-2 5-5 De. AC 312-1 20-20 87 (32-1) S. AD 157-2 23-41 9-8 8-1 Bu. AE 41-4 31-06 13 8-1 Bu. 1065' 579 AB 267 33 23 219-1 0-84 8-0, 1 1 5 8-2 Bu. AC 232-2 i6-6o 12 8-z Bu. 1066 S8o Pollux A B 38-0 28 19 274-9 43 2, 13-14 7-9 Bu. AC 70-8 174-52 8-2 Bu. CD 132-6 1-40 9. 12 8-2 Bu. 1067 lOI • Argus 46-2 -13 35 289-4 0-46 51- i"' 57 De. 1068 581 AB 577 12 38 176-9 0-40 8,8 8-1 Bu. AC 185-3 4-76 ii-o 8-1 Bu. 1069" 582 AB 58-1 12 25 204-5 19-75 8i, 8^ 8-1 Bu. BC 59-8 3-76 12 81 Bu. 1070 204 8 7-0 10 45 302-1 1-06 7-1. loi 5-9 De. 1071' 584 P. VIII. 124 33 '0 19 58 291-1 I -61 8,12 8-0 Bu. 1072 585 Cancri 109 34-3 20 54 106-4 0-40 7-5. 9-0 8-1 Bu. 1073° 587 15 Hydrae 457 -6 44 159-9 0-46 6.9 8-2 Bu. 1074 211 Hydrae 68 557 3 9 257-8 III 7-5, lo-o 5-2 De. 1075 105 K Leonis 9 177 26 42 203-8 3-05 4-9. 10-7 6-2 De. 1076 590 29 Hydrae 21-3 -8 42 176-8 10-80 7, 12 8-2 Bu. 1077 591 23 '5 -2 36 35-8 0-78 7-7, 8-5 8-2 Bu. 1078 215 487 —27 26 337-8 1-78 7-5. 10-5 7-1 CO. 1079 592 49'3 -15 38 192-8 980 6-5,12-13 8-2 Bu. 1080 594 Leonis 150 10 163 IS 58 143-4 1-58 6-5, ii-o 8-2 Bu. 1081 596 Leonis 222 43 '0 17 47 277-3 2-39 6-5. 13 p Bu. 1082 597 49"3 24 14 469 0-88 8-5, II 8-2 Bu. 1083 599 65 Leonis 11 1-8 2 30 82-4 1-78 5-5. II 5 8-2 Bu. 1084" 600 AB 10-9 —6 29 226-4 1.25 6-5, 12 8-1 Bu. AC 97-3 61-53 8 8-1 Bu. 1085" 601 AB 22-9 — 16 40 331-5 28-16 Z'5 i'3 Bn. BC 226 9 o-8i 8,9 8-3 Bu. 1086 456 307 — II 41 68-2 0-65 9,9 7-3 HI. 1087 Corri 17 12 9-6 — 22 41 232-4 077 6-5, 7-0 9-4 Bu. 1088 605 B. A. C. 4149 14*0 — 21 30 144-2 1-25 6, 8 8-2 Bu. 1089 28 B. A. C. 4213 23 '9 -12 44 3537 1-95 6-4, IO-2 5-3 De. 1090 31 Virginis 35'9 7 28 28-7 3-56 6, 12 9-3 Bu. 1091 341 Hydrae 348 57-3 -19 56 136-4 0-78 ^1' r 6-3 De. 1092 48 Virginis 577 -« 55 229-4 0-48 6, 6 9-4 Bu. 1093 B. A. C. 4389 13 05 45 54 109-2 2-68 6, 12 9-3 Bu. 1094 608 15 Canes Ven. 4-2 39 10 284-9 1-22 5-5. lo-si P Bu. I09S 609 4-5 -4 18 356-1 0-89 7. II 1 8-3 Bu. " A and C make 1. ioj6 nj. "^ ^"j ^ """^^ J '°"- P A and C make 2. .074- I ^ ^"i £ '^t^ I "^^■ ' A and C make 0.2. 173. ^ , ■ A and B make 2. 1.79. ' The principal st.ir of a very wide pair (So. 571). " The large star and two distant companions make Hi V. "o. • • xi iv • The wide pair is H, N. 26. " The wide pair is H, IV. 414 DOUBLE STARS. Ref. No. IS n Name or Catalogue. R.A. 1880. Decl. 188a. p. D Mags. 1870. 1096 Virginis 454 h. m. 13 4-9 / >3 57 205-1 5-06 6-7, 12 + 9-3 Bu. 1097 610 Virginis 504 17-6 —20 19 183 4-02 6-8, 10-5 8-2 Bu. 1098 113 23-1 12 6 188-8 1-57 8-4, 1 1 -I 5-3 De. 1099 114 28-0 -8 1371 1-49 7-6, 8-6 5-3 De. IIOO» Virginis 550 28-5 -12 36 81 -2 0-47 6,6-5 9-4 Bu. IIOI^ AB 29-1 33 45 30-4 1-98 8-5, 9-0 9-3 Bu. AC 21-6 34-43 12 9-3 Bu. 1 102 612 B. A. C. 4S5S 33-7 II 21 56-1 0-23 6,6 8-3 Bu. 1103' 86 Virginis AB 39-5 -II 49 298-4 I -61 5-5. 10-5 9-3 Bu. CD 274-2 1-72 1 1 -5. 13 9-3 Bu. AC 164-7 26-94 9-3 Bu. 1 104 614 48-0 10 44 268-4 0-60 8, 12 8-4 Bu. 1105 224 14 7-6 13 8 71 -o 0-67 8-9. 9-3 57 De. 1 106 7-8 -7 58 160-5 0-69 8, 8 9-4 Bu. 1 107' 225 AB i8-8 — 19 26 295 "5 35-03 6 57 De. BC 101-9 1-40 7-3. 8-2 57 De. 1 108 52 Hydras 2I-I -28 57 276-8 4-00 5. II -3 9-4 Bu. 1 109 616 y Bobtis 27-3 38 50 986 2618 3. 13 8-2 Bu. IIIO 346 Librs 23 41-8 — 16 50 2357 1-18 7-2, 8-0 ^■3 De. nil'' 617 42-4 -23 45 219-6 336'6 59-44 2-71 6^, 8 9 ?'3 8-3 Bu. Bu. III2 106 Ij. Librae 427 -13 39 335-0 1-38 5-4, 6-3 5-6 De. III3 239 59 Hydrse SI -6 -27 10 129-S 0-93 6, 6 8-4 Bu. 1114° 618 4' Librae AB 15 5-4 -19 20 110-5 57-46 6 8-3 Bu. BC 24-3 1-86 10, 10 8-3 Bu. III5 25-6 48 8 128-5 10-74 6-5, 12-5 9-3 Bu. III6 122 33 'o -19 23 204-0 1-76 7-0, 7-3 5-4 De. III7 619 Serpeirfis 55 37-6 14 3 3597 0-57 6-5, 7-0 8-3 Bu. 1118" 620 AB 38-9 -27 41 166-8 0-86 7-5. 7-5 8-4 Bu. AC 214-1 50-25 9-0 8-4 Bu. III9 B. A. C. 524? 447 55 45 152-0 1-31 5-2, ii-o 9-3 Bu. 1 1 20' P Scorpii 58-5 -19 58 87-0 0-73 2, 10 94 Bu. II21'' Librae 213 AB 59-3 -558 150-3 I -51 6-5. 9-5 9-4 Bu. AC 233-7 28-54 10-4 9 4 Bu. AD 192-7 52-28 10-7 9-4 Bu. 1 122 39 II Scorpii 16 09 — 12 25 256-5 3-35 6-1, 10-4 57 De. 1 123 355 4"2 45 42 279-3 0-34 7-3. 8-0 6-3 De. 1 124 I20 V Scorpii AB 5-0 -19 9 359-9 0-73 4'3. 6-7 5-9 De. CD 47-9 1-89 7-0, 8-0 5-4 De. AC 336-5 40-77 5-4 De. II25 625 w Herculis AB 19-9 14 19 175-3 1-90 5. 12 8-6 Bu. AC 103-2 33-80 IIS 8-6 Bu. 1 126 627 52 Herculis 457 46 12 309-4 1-83 5. 10 8-4 Bu. 1127 54 Herculis 510 18 38 175-4 2-56 5. 12 9-4 Bu. 1128 282 17 8-5 -14 27 J541 4-23 6-7, 1 1 -8 5-4 De. 1 129 126 P. xvn. 43 AB AC 129 -17 38 261-3 iSo-± 1-74 20-± 6-4. 7-5 5-1 Da. II30 242 AB 17-3 -II 35 68-9 0-96 8-2, »-9 5-9 De. AC 63-4 8-90 10-4 60 De. AD 63-8 47-46 6-0 De. II3I 129 B. A. C. 5896 21-2 -25 25 100-3 0-89 7-5. 8-0 7-4 CO. » A variable star, discovered in 1866 by Schmidt. There is a distant faint companies, i56°'5 : J3"-88 (l879'4). y A and C make H2 3261 . ■ As a wide pair this is 2. 1780 rej. Both components are double, and the smaller very difficult. ■ The wide pair is H] N. 80. ' The wide pair is So. 663. = The wide pair is H, IV. 44 (= Str. 376). ' The wide pair is Hj 4803. " Just as this page is sent to press a letter from Mr. Bumham announces that he has succeeded in dividing the principal star of ^ Scorpii. The old companion is thus given by Struve : AC, 3i2°'4; i3"io: 1823-3. Mag. a, 4. ' The large star and two distant companions is S. 2005 rej. APPENDIX. 415 Ref. h Name or R. A. Decl. ^■MM No. 1^ 3 CO Catalogue. 1880. 1880. P. D. Mags. 1870. 1 h. m. / + 1 132 26 Draconis 17 33-7 61 58 I49°i 1-36 5-5. "0-5 9-3 Bu. "33 631 Ophiuchi 255 33-8 -0 35 70-2 0-36 7-7 8-6 Bu. "34 130 90 Herculis 49-4 40 3 123-0 1-82 5-8, 9-1 5-5 De. "35 633 7 Draconis 53-8 SI 30 152-1 20-88 2-13 8-4 Bu. 1 136 '3? B.A.C. 6158 18 4-1 -19 52 240-1 0-78 6-8, 7-2 5-0 De. "37* 638 AB 4-3 2 34 152-0 22-33 8-9, 8-9 8-1 Bu. BC 10-5 I -71 11-8 8-6 Bu. 1 138 286 16 Sagittarii 8-1 -20 25 218-S 5-67 6,13 8-5 Bu. "39" 639 AB "•7 — 18 40 •55-3 0-57 7-5. 7-5 8-6 Bu. CD 330- ± 4-± 8,1-4 8-6 Bu. AC S1-7 17-30 8-6 Bu. 1 140 133 B. A. C. 6261 20-3 -26 42 265-3 1-80 7-5. 7-5 5-7 Schi. 1 141 «35 Scuti Sob. 45 3«-3 - 14 6 184-0 2-40 6-7, 1 1 -5 5-1 De. 1 142 Draconis 205 44 4 49 18 353-6 0-59 6-5. 8-5 9-3 Bu. "43 26s 44-6 II 23 235-9 1-46 71, 9-1 5-3 De. "44 137 AB 49-8 37 14 123-8 '-15 8-2, 8-7 5-6 De. "45 648 B. A. C. 6480 52-5 32 45 312-5 0-60 6, 9-5 8-5 Bu. 1 146 287 1 Aquilae ,„ 59-9 13 41 59-6 4-92 ,3> '2 8-5 Bu. "47 J 39 Aquilae 59 19 7-2 16 39 "39-5 0-72 6-7, 8-0 5-9 De. 1 148 248 2 Vulpeculae 12-6 22 49 125-0 1-83 5-7, 9-5 5-6 De. 1149! 141 AB i6'8 22 17 go-6 071 7-5. 9-1 60 De. AC 155-2 26-53 "•5 5-3 De. AD 90-5 50-75 ii-o 7-8 1150' 652 AB 27-3 28 I 331-4 4-78 7-9. 13 8-5 Bu. AC 3-7 5 -60 9-7 8-5 Bu. "5» 654 52 Sagittarii 29-4 -25 10 160-8 2-93 5-11 8-6 Bu. 1 152 658 B. A. C. 6762 39-0 26 50 295-2 0-57 6-5, lo-o 8-5 Bu. "53 148 45-4 — 10 40 333-2 0-93 7-9. 8-3 5-3 De. "54" TjCygni „„ S''* 34 46 21 1 -7 7-54 5. 12-5 9-4 Bu. "55 428 20 I -I 12 36 343-7 0-52 7-2, 8-5 6-5 De. 1156' 430 AB 6-8 3528 17-7 I-I2 9-5. «o-o 6-6 De. AC 5«-3 16-91 9-7 6-6 De. "57 661 Cj^i 1 66 12-6 40 67-0 12-60 o^'5'J3 8-4 Bu. 1 158 431 15-4 3| 53 221-4 0-55 8-5, 8-8 7-1 De. "59 60 T Capricomi 20-4 -1836 145-2 3-27 5-1, 8-7 5-0 De. 1 160 62 23-1 29 44 135-5 1-20 8-5, 9-4 5-5 De. 1161 668 B. A. C. 7080 25-8 — 10 16 29-0 4-64 6, 12 8-6 Bu. 1 162 670 27-3 13 32 58-3 0-75 8-5, 8-8 7-7 De. "63" 151 j3 Delphini 3' -9 14 II 15-6 0-61 4-3. 5-7 i"' De. 1 164 675 SI Cygni 38-5 49 54 101-5 2-78 o5' " 8-2 Bu. "65° 64 39-3 12 17 172-4 0-64 8-7, 9-0 6-2 De. 1166 152 Cephei 55 39-3 56 57 11 1 -0 044 7-2, 8-0 6-0 De. 1 167 268 432 41 38 221-4 0-38 7-4, 8-2 5-9 De. 1168 367 AB 49-9 27 38 115-7 0-55 7-5. 7-9 6-4 De. AC 28-2 30-88 12 5-6 De. 1 169 156 57-6 46 6 241-6 1-05 7-1. 9-4 ^'i De. 1 170 368 Aquarii 45 21 i-o -8 43 97-1 0-55 7-2, 7-6 6-8 De. 1171° 159 AB 6-3 47 >2 318-7 1-32 6-1, 9-2 6-4 De. AC 189-5 134-10 6-8 4-1 De. 1172I' 270 AB AC AD 7-5 643 354-6 30- ± 173-0 0-62 20- ± 183-2 7-4, 9-7 „ 7-8 5-8 De. >'73 289 AB «3'4 34 35 137-8 0-90 8-2, 12 §■5 Bu. AC 262-1 5-39 13 8-5 Bu. B The wide pair is 2. 2287 nj. ' The wide pair, A C, is Sh. 364. ' A and C make Ha- 2867. J A and C make 2. 2539- •■ H. noted two very distant and larger stare (= Hj i455). ^ A and C make Ha 1489. , _ „ ,x t • .u • 1 / o ^ » Binary in rapid motion. Bu. 53°-7 : o"24 (■878-6). Itjs apparentljr single now (1879). » The wide pair is 0.2. (App.) 209. P The wide pair, A D, is So. 781. I" The wide pair is 0.2. (App.) 215. 4i6 DOUBLE STARS. Ref. 1 d No. |z a Name or Catalogue. R. A. 1880. Decl. 1880. P. D. Ma£s. 1B70. 5 > 1 h. m. §52 + 1 1 741 164 AB 21 192 241-6 o'-'s? 8-0, 8-5 5-5 De. AC 242-2 26-51 87 1 175' 167 Cygni 363 31-0 39 31 89-2 2-08 7-0, 1 1 -4 6-5 De. 1 176 686 AB 337 55 14 127-9 0-38 7-7, 8-0 7-7 De. AC 11 -0 41-67 8-0 8-1 "77" 449 AB 347 41 u 19- 1 6-78 7, 12 6-8 Bu. AC 170-S 1371 10-8 De. AD 248-2 17-94 77 6-8 De. 1 178 688 377 40 30 209-2 0-38 7-5. 7-5 8-1 Bu. 1 179 690 M Cephei 39-8 58 14 259-8 19-28 5. "2 8-5 Bu. 1 180 276 77 Piscis Austr. S3'9 —29 2 1174 1-71 5.6 6-6 CO. 1181 694 Lacertae 4 59-1 43 54 352-2 0-50 6-0, 8-5 87 Bu. 1 182 696 587 15 19 353-8 0-65 8-5, 9-0 8-2 Bu. 1183 172 SI Aquarii 22 17-9 -5 27 21-9 0-44 67, 6-7 57 De. 1184 290 34 Pegasi 20-5 3 47 223-3 2-61 6, 12 5-7 HI. 1185 291 21-6 3 55 157-8 0-32 8-4, 8-4 5-8 De. 1 186 76 23 '4 -0 49 335-3 1-47 8-2, lo-i 6-2 De. 1187 277 34-2 40 45 199-4 050 8 -a, 8-4 5-3 De. 1 188 480 35-3 4 6 65-8 0-86 9-0, 9-8 7-5 De. 1 189' 382 B. A. C. 7983 A B 48-3 44 7 205-7 1-07 6,8 6-4 De. AC 353-6 26-43 10-7 6-2 De. 1190 'l^ Aquarii 252 49-0 -5 38 324-6 o-s± 6-2, 8-0 5-0 De. 1191 384 Aquarii 265 S6-2 — 19 11 72-2 1-27 7-2, 9-2 7-1 De. 1 192 180 23 2-2 60 II 176-8 0-57 7-5. 8-0 5-1 De. 106-3 ,34-50 105 5-5 De. 1193° 38s AB 4-5 31 50 1358 0-42 7-1. 7-9 6-4 De. 1 AC 77-1 58-05 8-7 6-7 De. I 194 1181 Aquarii 286 A B 7-5 -'4 3 309-2 1-5' 7-1, 10-4 6-3 De. AC 234-9 18-78 12 77 Bu. "95 1714 B. A. C. 8084 7"9 -3 17 145-5 0-57 7, 10 8-6 Bu. 1196 1717 8 Andromedae 12-2 48 22 161-4 7 -61 5. 13 8-2 Bu. 1 197 :7i8 64 Pegasi i6-o 31 9 86-9 0-46 6, 8 8-7 Bu. 1 198 1720 72 Pegasi 28-0 30 40 127-7 0-40 6,6 87 Bu. 1 199 1730 27 Piscium 52-5 -4 13 265-8 1-42 6, II 8-4 Bu. 1200' 1733 85 Pegasi SS-9 26 27 274-0 0-67 6, 12-5 8-7 Bu. 1 Measures of A C from Struve (= 2. 2793). ■■ A and C make 0.2. (App.) 220. • A and C make 0.2. 447 (= Hi III. no). ' AandC=Hji828. ^ A and C = H2 5532. ' The principal star has a large proper motion and sensible parallax. There is a om. companion 330-6 : 14" 40 (1878-5). This does not partake of the proper motion of A. There is also a foutth faint star, 227°"i : 6i"'73 (1879 'o). Mr. Bumham's latest measures are as follows :~ ' AB, 276-0 4n. 0-75 1878-75 287 2 in. ■73 9-46 AC, 330 711. 14-55 8-70 29-0 in. iS'oo 9-32 AD, 2771 in. 61-73 896 C is of gth and D of the 13th mag. A B evidently for.-n a physical system. 417 ADDITIONAL NOTES TO MEASURES. No. 86 (o Ceti). H, on Oct. 20, 1777, wrote, " Double. Very unequal. Large, garnet ; small, dusky. Distance, mean of some very accurate measures i' 44"'2l8 ; mean of other very accurate measures i' 53"'032." The earliest measure of this star was probably made by Cassini, about 1863, with a telescope 34 feet in length. No. 169 (a Tauri). H, in 1781, Dec. 19, wrote: "Double. Extremely unequal. Large, red ; small, dusky. Distance, 1' 27" 45'" ; position, 52° 58' nf. With 460, the apparent diameter of this star, when on the meridian, measured l" 46'", a mean of two very complete observations ; they agreed to 6"' ; with 932, it measured i" 12'", also a mean of two excellent observations ; they agreed to 8'". The apparent disc was per- fectly well defined with both powers." No. 274, p. 244, line 4. The duplicity was detected by Bird in 1864. No. 800 (2. 1273). Hall discovered a faint companion in 1875 '■ Position, 190°+; distance, 12" ± ; and Mr. Bumham gives a measure in 1878, i92°-2, I4"74. No. 456 (a Centauri). Mr. EUery's latest measures of this star are, 1879-252 ; I74°'4 : 3"-4l : 13 observations. (See Observatory, No. 27.) No. 520 (Antares). Burg, of Vienna, was the first to see the companion of this star : he was watching an occultation of Antares by the Moon in April 1819. Mr. Grant detected it in 1844 in India. No. 1120 (;3 Scorpii). "Aug. 19, 1761. — Found the little star, which is 14" north of /3 Scorpii, to precede it one second of time, by my parallactic wires, with my watch, which makes four beats to a second of time. If anything, the difference was something more than a second of time ; the little star may therefore be supposed to precede j3 Scorpii 17" in R.A." The difference of Dec. was 13" '97. — Maskelyne {Phil. Trans., vol. liv.) Powell, in 1859, found the difference of R. A. + 6"'3. Smyth's magnitudes are A 2, B 5i, C 5 Powell's, A 25, B 5, C 7. No. 708 (2. 2749). The magnitude of C is 9. No. 725 (,11 Cygni, A C, 7'S). 1800 62°'3 2i6"'S Piazzi. 77 57 ■' ao9 -9 Fl. 27 4)8 CLASSIFICATION. For a very exhaustive and interesting classification of double stars we must refer our readers to M. Flammarion's Catalogue of these objects. A few general remarks and a much more simple classification are all that we can here present. Sir John Herschel's great Catalogue gives the places of 10,320 double stars. Adding 700 of Mr. Burnham's and a few hundreds for the discoveries of other astronomers we may take 12,000 as a rough total of the number of known double stars. Unfortunately, observers of these objects have confined their attention till lately too much to the Herschelian and Struvian pairs, and hence at present in our attempts to ascertain the number of physical double stars we deal almost exclusively with the discoveries of those great observers.* A very extensive examination of nearly all known measures of these and many of Sir John Herschel's stars leads us to believe that the number in which orbital motion has already shown itself since discovery may be put at about 600. If to these be added the relatively fixed pairs which are known to possess a common proper motion, we get at least 700. But this is not all : Mr. Burnham's discoveries will in all probability yield a large number of binary systems. Hence it does not appear too much to say that if this branch of astronomy continue to command the attention which has been given to it during the last ten years, the number of known physical systems will soon rise to at least 1000. The careful examination of Herschel and South's and Burnham's stars by Dembowski, Mr. Burnham, and the Cincinnati observers, is almost weekly adding to this important and interesting class. * It is with much pleasure that we find Mr. Burnham and Mr. O. Stone ener- getically protesting by word and deed against this nan'ow circle of observation. The extremely clear, compact, and complete form in which 2. published his double- star work no doubt led to this custom. CLASSIFICATION. 4 1 9 SYSTEMS FOR WHICH ORBITS HAVE BEEN COMPUTED. Name. 42 Comae Ber. f Herculis S. 3121 ij Cor. Bor. S. 2173 7 Cor. Anstr. t Cancri ( Ursae Maj. a Centauri 70 Ophiuchi 7 Cor. Bor. ^ Scorpii S. 3062 u Leonis p Eridani 2. 1768 I Bootis 7 Virginis T Ophiuchi T) Cass. X Ophiuchi 44 Bootis 11' Bootis 36 Andromedae 7 Leonis « Cygni* ff Cor. Bor. Castor f Aquarii a e P Computer. II years. 0-65 0-48 25 0.2. I '22 •42 34 Du. 071 •26 37 Dob. 0-82 •26 4' WijV- I'OI ■'3 45 Du. 2-40 •69 55 Schi. o"90 ■33 58 Dob. 2-55 •39 60 Du. 18-45 •53 88 Dob. 470 •49 94 Schur. 070 ■35 95 Dob. 1-26 •07 95 )» 1-27 •46 104 »> 0-85 •55 114 J» 3-82 •37 117 >> 075 •66 124 >» 4-86 •71 127 »» 3'97 •89 185 Thiele. 1-40 ■60 217 Dob. 9-83 •56 222 ,, 119 •49 233 >) 3 '09 •71 261 j» 1-47 •59 280 )j 1-54 •65 349 j> 2 "00 •74 402 »j 2-31 ■28 415 Behrmann. 5-88 •75 845 Dob. 7 "43 •33 lOOI »» 7-64 •65 1578 M The period of O.X 365 (No. 616) may be about sixteen years, while that of O.Z. 535 (No. 712) is either seven or four- teen years. TERNARY SYSTEMS. Under this head may probably be placed all the following systems: 7 Andromedae, Z. 183, 719, 948, lOOi, mo, 1196, 1938, 1998, 1426, 2006, 2220, 2479, 2481, 2607, 2737, 2749, 2607 ; and 0.5. 276, 380, 392. QUATERNARY SYSTEMS, el and ^ Lyrae, v Scorpii, 5. 2576 and 17, x Cygni (see Flammarion's Catalogue), d Ononis Q). * These elements are quoted rather to give completeness to the table than because of their intrinsic value. They depend mainly on H,'s angle; it should have been taken as sf., and not nf. Dr. Doberck's formula give better results in every way (see p. 372). 4 20 DOUBLE STARS. Lastly, if we tabulate the most important binaries accord- ing to the arc described since discovery, we find the following approximate numbers: — One or more revolutions 14 Between 270° and 360° 5 180 ,, 270 10 90 „ 180 IS 45 .. 90 20 20 ,, 45 100 o „ 20 200 NOTE Oil systematic Errors in the Measures of Angle and Distance of Double Stars. From our remarks on p. 418, it might be inferred that we wished to discourage the study of the Struvian stars. This is far from being the case. There are scores of X's and O.S.'s stars which need careful remeasurement in order to determine the amount of change, if any ; and where change has taken place, to find out its nature. More than this : no one with even a slight acquaintance with the distressing discrepancies and difficulties which are met with in attempts to deal in a satisfactory way with the orbits of Hi's and S.'s binaries would desire that attention to them should be re- laxed. And it is quite certain that there are some difficulties which numerous and careful series of measures (especially at the critical times) would considerably diminish or alto- gether remove. We have said careful series of measures. By this expression we mean series of measures by practised observers on a uniform plan, and supplemented by a rigorous determination of systematic error. Mistakes and accidental errors are not serious matters, but constant personal errors (if the observations are so made that the constant error cannot be ascertained and the correction applied) may render worthless the honest work of long years under the most favourable circumstances. To ascertain his systematic errors in the measurement of the position angles and distances of 'double stars, Struve made extensive series of NOTE. 421 measures of artificial double stars. His distinguished son O. Struve employed the same method ; and to ascertain any change in the errors he repeated the observations about every ten years. Dawes as we have seen got rid of the error, or some portion of it, as regards the angles, by the use of his prism ; and the Cincinnati observers keep the line joining the two eyes parallel to or normal to that joining the two stars measured, and then from the results deduce the necessary corrections. Dembowski, in order to ascertain the corrections to be applied to his angles and distances, has undertaken a most laborious series of measures of twenty-four double stars in which the changes are so small that they may be disregarded ; and other eminent observers have promised to measure the same objects. For the con- venience of those who may wish to join in such an investi- gation, the names, places for 1875, and magnitudes of these selected pairs are subjoined.* o.s. s. 170 191 1 169 1321 1350 1603 1685 2034 2326 353 363 2452 2571 2603 267s 2796 2801 2806 2893 2924 2923 O.S. 481 489 305 « Dec. h. m. 1 I 43-9 -H75 3« 52 '4 73 16 7 S7-5 79 52 9 5-« 53 14 22 -o 67 19 12 19 56 10 4S7 19 51 16 37 «3 5« 18 ly-s 81 27 22-6 71 16 43-5 77 34 57-4 75 37 19 .347 77 59 48-6 69 ■''Z 20 131 77 18 21 i6'9 7» 4 22 -2 79 49 270 70 22 io'6 72 43 29-4 69 «5 297 69 44 41-8 77 52 23 3-9 74 43 55-6 79 3t> Mag. 67, 7-8 6 , 8-9 7-8,8 7-8, 7-8 7 .7-8 7 . 7-8 7 .7-8 7-8.8 7-8, 8-9 5 . 7 7 . 7 67, 7-8 7-8,8 4 ,7-8 4 ,8 7-8,9 7-8, 8 3 '^o S-6, 7-8 7 ,7-8 7 .9 7 . 9 5 .7-8 7-8, 9'io * See Obsirvatory, vol. ii., p. 214, for some valuable remarks by Dr. Doberck on this subject. 422 DOUBLE STARS. Just as this sheet was ready for the printer an excellent paper on systematic errors was received from the author, M. Thiele. The subjoined results are taken from it : — Mean error of one night's work. Distance. Angle. Briinnow o"-l49 2°-44 Dawes •095 -41 Dembowski •ii6 •69 Doberck •'53 I 00 Duner ■099 -94 GledhiU •062 •89 HerscheUSirJ.) •460 •91 Herschel (Sir W.) •39 4-4 Knott ■109 -ei Madler ■141 71 Main ■171 2 -97 Plummer fW. E.) •123 1 -30 0.2. •082 -95 2. •09S ■86 Talmage •«73 I -OS Wilson, Seabroke, 1 and others ) ■'45 The numbers given above for Dawes, Dembowski, Main, and O.J. are the arithmetical means of the values at different periods. And as an example of the way in which these systematic errors change in the course of series of measures extending over many years, the case of one of the most experienced and skilful observers, Dembowski, is here given more fully : — Mean error of one day, 1853 to 1856 o"'079 o°^59 ,, „ 1862 „ 1871 o 'log o -46 „ ,, Since 1871 o ■id i ^04 The above results were obtained by comparing the several observers' measures of Castor with the computed position angles and distances. For a full explanation of the process, see Thiele's " CASTOR. Calcul du mouvement relatif et critique des observations de cette etoile double. Copenhagen, 1879." PART IV. BIBLIOGRAPHY. LIST A. PAPERS ON DOUBLE STARS, ETC. Adolph. Measures of 70 Ophiuchi.— /4j^. Nachr., vol. Ixxi., p. 155. Airy. On the Parallax of a 'Lyr^.— Memoirs of R. A. S., vol. X., p. 265. Amici. A few of his Double Star Measures (1815 to 1823). — Ast. Nachr., vol. xc, p. 304. Argelander. On some Double Stars. — Ast. Nachr., vol. Ixii., p. 253. AUWERS (Dr. A.) "Nachtrag zu den Untersuchungen iiber die Veran- derliche Eigenbewegung des Procyon." — Berlin, 1873. " Untersuchungen iiber veranderliche eigenbewegungen Von G. F. T. Arthur Auwers."— Erster Theil. " Inaugural-Dissertation zur Erlangung der Philoso- phischen Doctorwurde." — Konigsberg, 1862. It con- tains investigations of the proper motion of a Virginis, ^ Orionis, a Hydrae, the elements of the orbit of Pro- cyon, etc. On the Companion of Sirius. — Ast. Nachr., No. 1371. On variable Proper Motions. The Proper Motion of 426 DOUBLE STARS. Procyon. The Parallax of Procyon. — Ast. Nachr., vol. Iviii., pp. 33, 35, etc. Measures of Double Stars with the Heliometer. — Ast. Nachr., vol. lix., p. i. 1859 to 1862. On 61 Cygni, Procyon, f Ursae Majoris, 7 Lalande. — No. 21258, Ast. Nachr., vol. lix. On the general Method of Observation ; On the Errors in Measures of Distance ; On the Micrometer Screw, etc. — See same paper. On the Orbit of Sirius. — Ast. Nachr., vol. Ixiii., p. 273. Barclay. " Leyton Astronomical Observations," 4 vols. Behrman. On the Orbit of 8 Cygni. — Ast. Nachr., vol. Ixvi., pp. I, 141. Bessel. Ast. Nachr., No. 514, 515, 516: on the Companion of Sirius. " Astron. Untersuchungen" (Konigsberg, 1841), On the Double Star 70 Ophiuchi. " Fundamenta Astronomize, pro MDCCLV." Measures of some Double Stars ; On the common Proper Motion of Groups and distant Pairs. " Abhandlungen von F. W. Bessel," edited by Engel- man. 3 vols. Leipsig, 1876. Papers on the Parallax of 61 Cygni. " Verzeichniss Von 257 Doppelsternen," etc. — Ast. Nachr., vol. iv., p. 301. "Von Doppelsternen und Vergleichung mit Struves," vol. X., p. 389 ; see also p. 317. " On 70 Ophiuchi," vol. xiii., p. 11 ; vol. xv., p. 105. "On 61 Cygni," vol. xvi., p. 65 ; vol. xvii., p. 257. " Ueber Veranderlichkeit der eigenen Bewegungen der Fixsterne," vol. xxii., pp. 145, 169, 185. PAPERS ON DOUBLE STARS. 427 " On the Change in the Proper Motion of Sirius," vol. xxii., p. 172. See also his " Fundamenta Bradleianis." Bishop. "Astronomical Observations," 1852. Bode. See Bode's Jahrbuch for 1784 for a list of Double Stars known before Sir William Herschel's time. Bond. On the Companion of Sirius. — Asi. Nachr., No. 1353, and No. 1374 ; see also the American Journal of Science for March 1862. Measures of Mizar. — Ast. Nachr., vol. xlviii. Stellar Photography. — Ast. Nachr., vol. xlix., p. 84. " On the relative Precision of Measures of Double Stars taken photographically and by direct vision." — Monthly Notices, vol. xviii. Brinkley. Parallax of a Lyrse. — Phil. Trans., vol. c. ; Mem. ef R. A. S., vol. i., p. 329 ; Phil. Trans., 1824, pt. ii., p. 471. Brothers (A.) Catalogue of Binary Stars. — Mem. of the Lit. and Phil. Soc. of Manchester, vol. iii., 3rd series. See also Astron. Register, 1868. BrunnoW (Dr.) " Astronomical Notices," No. 28. On the Companion of Sirius. See also Dunsink Observations. BURNHAM (S. W.) Catalogues of New Double Stars. — Monthly Notices of R. A. S., vols, xxxiii., xxxiv., xxxv., xxxvi., xxxvii., xxxviii. On X 2344. — Ast. Nachr., vol. Ixxxviii., p. 285. See also Ast. Nachr., vols. lxxx\'., Ixxxvi., Ixxxviii. 428 DOUBLE STARS. Calandrelli (J.) "Atti deir Accademia Pontificia de Nuovi Lincei, S Aprile, 1853." " On the Companion of Sirius." " On the Proper Motion of Sirius." See Ast. Nachr., vol. li., p. 224. Cassini. "A New Double Shar." — Histoire de I'Acad^mie Royale des Sciences, tome i. 1678. " Occultation of 7 Virginis Star seen Double." — His- toire de I'Acad^mie Royale des Sciences, 1720. Chacornac. " On the Companion of Sirius." — Ast. Nachr., No. 1355. Also No. 1368 (vol. Ivii.) Cincinnati Observatory Volumes : — Mitchell's Measures ; New Double Stars ; Measures in 1875-76-77. Clark (A. C.) " New Double Stars discovered by Mr. Alvan Clark." — Monthly Notices of R. A. S., vol. xvii., p. 257 ; vol. xx., P-SS- " Discovery of Companion of Sirius." — Ast. Nachr., vol. Ivii., p. 131. Cooper. "Double Star Measures in 1832 and 1833." — Ast. Nachr., vol. xc, p. 303. Darby (Rev. W. A.) The Astronomical Observer. D'Arrest. "On the Influence of Aberration on the Position Angle and Distance." — Ast. Nachr., vol. lix., p. 231. Darquier. " Memoire sur les ^toiles doubles et le mouvement des fixes. Par M. Darquier." — "Histoire et M^moires de VAcad. Royale des Sciences de Toulouse, tome ii., 1784. papers on double stars. 429 Dawes. " Double Stars discovered by Dawes." — Monthly Notices of R. A. S., vol. xxiv., p. 1 17. Measures, in vols, ii., iii., x., xv., xxvii. On Measuring Angles of Position, vols, xviii., xxvi., xxvii. On Star Magnitudes, vols, xi., xiii. On fi Herculis, 70 Ophiuchi, a- Orionis, Sirius, vols, xv., XX., xxiii., xxiv. On Eyepieces, vols, xxiii., xxv. On H. I. 13, vol. xxiii. On 6 Cygni. — Ast. Nadir., vol. Ixv., p. 251. The following papers are in the Memohs of the Royal Astronomical Society : — "Observations of the Triple Star f Cancri," vol. v., P- 135- " Observations of Double Stars," vol. v., p. 1 39. " Micrometrical Measurements of the Positions and Distances of 121 Double Stars, taken at Ormskirk during the years 1830, 1831, 1832, and 1833," vol. viii., p. 61. " Micrometrical Measures of Double Stars, made at Ormskirk between 1834 and 1839-40," vol. xix., p. 191. " Catalogue of Micrometrical Measurements of Double Stars," vol. xxxv., p. 137. DembowSKI (Baron). The following papers are in the Astronomiscke Nach- richten : — His method of observing Double Stars, Instruments, etc., vol. xiii., p. 231. Naples, 1855. Measures of the Dorpat Double Stars (lucidse), vol. xiii., pp. 47, 77, 109, 285, 359, 375. Measures of Double Stars, vol. xliv., p. 57. Introductory Remarks on his Second Series of Measures, vol. xlvi., p. 267. Measures, vol. xlvi., p. 317. 430 DOUBLE STARS. Measures, vol. xlvii., pp. 79 to 333 ; vol. 1., pp. 129 to 317; vol. li., pp. 55 to 139. Mean Places of Fifty-two Double Stars, vol. liii., p. 113. Measures, vols. Ixxii., Ixxv., Ixxvi., Ixxvii., Ixxix., Ixxxvii., xcii. New Double Stars, vol. Ixxiii. ; also Ho. 1475, vol. Ixii. New Double Stars, vol. Ixxxiii., p. 170. Measures in 1872-3, vol. Ixxxiii., p. 161. On the Value of his Micrometer, vol. Ixxxi. DOBERCK (Dr. William). The following papers are in the Astronomische Nach- richten : — Elements of fi Bootis, a- Cor. Bor., t Ophiuchi, — vol. Ixxxv. Elements of t Ophiuchi, 7 Leonis, etc., — vol. Ixxxvi. Elements of t) Cass., - Cancri, p. 363 ; Castor, pp. 79, 364 ; 42 Comae Ber., p. 364; ij Coronae, p. 364; 7 Coronae, p. 266 ; a Coronae, p. 363," etc., etc. " On 70 Ophiuchi," — vol. xix., pp. 201, 349. " The Orbit of ^ Ursae,"— vol. xxi., p. 93. " List of 504 Dorpat Double Stars which show no change of place since the earliest Measures," — vol. xxi., p. 147. *" Observations of t) Coronae, {f Herculis, 70 Ophiuchi, and X 1938, at Dorpat, in 1843," — vol. xxi., pp. 151, 152. " Second List of Dorpat Double Stars which appear unchanged since the earliest Measures," — vol. xxii., p. 27. " On the Proper Motion of Procyon," — vol. xxxii., p. 8 1 . See also Untersuchungen uber die Fixstem-Systeme, 1 847 ; Coviptes Rettdus, vol. vi.. On the Direction of the Orbits of the Multiple Systems of Stars ; Popular Astro- nomy ; Schiiviacher s Jahrbnch, 1839; and the Dorpat volumes. Main (Rev. R.) See the Radcliffe Observations for Measures. PAPERS ON DOUBLE STARS. 44 1 Marth (A.) On a Centauri. — Monthly Notices, vol. xxxvii. Maskelyne (Dr.) "Annual Parallax of S'lnMS."— Phil. Trans., vol. li., 1760. Mayer (C.) "De novis in Coelo sidereo Phaenomenis." — Acta Aca- demics Theodoro Palatines, vol. iv. " Griindliche Vertheidlgung neuer beobachtungen von Fixsterntrabanten." — Christian Mayer, Mannheim, 1778. Messier. "A New Double Star." — Connoissance des Temps, 1783. " Occultation of 7 Virginis by the Moon in 1775." — Histoire de VAcaddrme Roy ale des Sciences, 1774. MiCHELL (Rev. John). " On the Means of Discovering the Distance, Magni- tude, etc., of the Fixed Stars/' etc. — Phil. Trans., vol. Ixxiv., 1784. " Parallax of the Fixed Stars." — Phil. Trans., vol. Ivii.. 1767. Miller (J. F.), Whitehaven. The following are in the Astronomische Nachrichten : — " Measures of Binary Stars (X 2708, 17 Cass., Castor)," — vol. xxxiii., p. 367. " Measures of e Lyrae, ^ Ursas, 5. 1263, /a Draconis," — vol. xxxiv., p. 213. " Measures of 7 Virginis, f Bootis, Aquarii," — vol. xxxvi., pp. 129, 361. See also Monthly Notices, vols, xii., xiii., and Mem. R.A.S., vol. xxii. Mitchell (Prof. O. M.) Measures of 176 Double and Triple Stars, 1846 to 1848. — Cincinnati Observatory publications. Mitchell (Miss). American Journal of Science and Astronomy, vol. xxxvi. Measures, 1859 to 1863. 442 DOUBLE STARS. NOBILE (A.) "SuUe due stelle multiple, S. 1263 e o- Cor. Bor. nota per A. Nobile." — Accad. delle Scienza, Naples. " Saggio di un nuovo metodo per I'osservazione delle distanze seambievoli delle stelle multiple." — Naples. "Misuri di Angoli di Posizione di Stelle Multiple." — Firenze, 1875. Oeltzen. "New Double Star." — Ast. Nachr., vol. xxxvii., p. 395. Pearson (Dr.) "On a doubly-refracting property of Rock Crystal, considered as a principle of Micrometrical Measurements, when applied to a Telescope," — vol. i., p. 6t. On the Construction and Use of a Micrometrical Eyepiece of a Telescope," — vol. i., p. 82. " On the Construction of a new Position Micrometer, depending on the doubly-refractive power of Rock Crystal," — vol. i., p. 103. Peters (Dr. C. H. F.) The following papers are in the Astronomische Nach- richten : — " On the Parallax of Polaris," — vol. xxi., pp. 84, 87. " On the Proper Motion of Sirius," — vol. xxxii., pp. i, 17, 33, 49 ; and vol. xxxi., p. 219. "The Elements of the Orbit of Sirius," — vol. xxxi., P- 239- " Measures of Binaries," — vol xliv., p. 158. "On the Companion of Sirius," — vol. Ivii., p. 176. "On the Proper Motion of 5". 1300,"— (Dr. C. H. F. Peters), vol. Ixxi., p. 240. Pierce. On 7 Virginis. — Gould's Astron. yournal, vol. xviii. PiGOTT. "Double Stars discovered in 1779." — Phil. Trans., vol. Ixxi., 1 78 1. PAPERS ON DOUBLE STARS. 443 POGSON. Measures.— 5nV, Assoc. Report, 1858. Pond. " On the Changes which have taken place in the Declination of some of the principal Fixed Stars." By J. Pond, Esq., Astronomer Royal. — Phil. Trans., 1823, pt. i. ; see also 1823, p. 529. " On the Parallax of a Lyrae." By J. Pond, Esq.— Phil. Trans., vol. cxiii. " On the Parallax of o Aquilae." — Phil. Trans., vol. cviii. Powell (E. B.) " Observations of Double Stars taken at Madras in 1853, 1854, 1855, and the beginning of 1856." — Mem. R. A. S., vol. XXV., p. 55. "On the Orbit of a Centauri."— i>/m. R. A. S., vol. xxiv., p. 91. " Second Series of Observations of Double Stars," etc. Madras, 1859 to 1862. — Mem. R. A. S., vol. xxxii., p. 75. The following are in the Monthly Notices : — On Orbits, vols, xv., xxi., xxiv. Measures, vol. xvi. RiJMKER (Ch.) " Positionen von Doppelsternen." — Ast. Nachr., vol. xvi., P-3I- Safford (T. H.) "The observed Motions of the Companion of Sirius, considered with reference to the disturbing body indi- cated by theory." By. T. H. Safford. — Proceedings of the American Academy of Arts and Sciences, vol. v., 1863. See also Monthly Notices, vols, xxii., xxiii. Savary. " On the Orbit of f Ursae Majoris," — See Connoissance des Terns, 1822 and 1830. Schiaparelll "Measures of Double Stars." — Ast. Nachr., vol. Ixxxix., p. 317. "Orbit of 7 Cor. Anst," — vol. Ixxxvii. 444 DOUBLE STARS. SCHJELLERUP (Dr.) "Einfacher Beweis des A. N., No. 1227 angefflhrten geometrischen Satzes zur Berechnung von Doppelstern- Bahnen." — Ast. Nachr., vol. Iv., p. 230. " On some New Double Stars."— .(4j/. Nachr., vol. Ixxii., P- 331- SCHLUTER. " Measures of Double Stars with the KSnigsberg Helio- meter." — Ast. Beobachtutigen, edited by Busch. 1838. Schmidt (J. F. J.) "On the Colour of Arcturus." — Ast. Nachr., vol. xlii., p. 226. " Measures of Double Stars." — Ast. Nachr., vol. Ixv., p. 104. Schubert. " On the Companion of Sirius." — Astronomical Journal, vol. i. ; see also Gould's Astronomical Journal, 16. SCHUJLTZ. "On H. VIII. 20. Measures of 104 St&rs."— Ast- Nachr., vol. Ixxx. SCHUR (W.) " Orbit of S. 3062." — Ast. Nachr., vol. Ixix., p. 49. " Orbit of 70 Ophiuchi," — vol. Ixxi., p. i ; also vol. Ixxiii., p. 301. SCHWAUS. "On 61 Cygni." — Ast. Nachr., vol. xvi. Secchi (A.) The following papers are in the Astronomisclie Nach- richten : — " On some Double Stars, Colours," etc., — vol. xli., p. 109. "Measures of Binaries," etc., — vol. xli., p. 238. " On the Companion of Antares," — vol. xli., p. 238. "Measures of 2.'s Double Stars," — vol. xliii., pp. 139, 141 ; vol. xlv., p. 251. " On h Cygni," — vol. Ixvi., p. 62. PAPERS ON DOUBLE STARS. 445 " Measures of Double Stars," — vol. Ixviii., p. 87 ; also vol Ixiv., p. 84. "Descrizione del Nuovo Osservatorio del Collegio Romano, D.C.D.G." Roma, 1856. " Catalogo di 1321 stelle Doppie." i860, Seeliger (H.) " Zur Theorie des Doppelsternbewegungen." — Leipsig, 1 872. Inaugural Dissertation. He gives historical sketch and new formulae for computing an orbit. SiRlUS. Papers in the Astronomisclie Nachrichten, vols. Ixi. to bcxx. : — vols. Ixii., Ixiii., Ixiv., Ixvi., Ixvti., Ixx., Ixxi., Ixxiv., Ixxvi., Ixxvii., Ixxviii., Ixxix. ; by Auwers, Bruhns, Dun6r, Engelmann, Eastman, Foerster, Gylden, Hall, Newcomb, Pechiile, Tempel, Tietjen, Vogel, Gddschmidt. See also vols. Ixxxiv., Ixxxviii., xc. In the Monthly Noticee, see vols, xviii., xx., xxii., xxiii., xxiv., XXV., xxvi., xxvii., xxviii., xxix. Smyth (Admiral). •■ A Cycle of Celestial Objects," etc. 2 vols. London, 1844. " Sidereal Chromatics." 1864. " Speculum Hartwellianum." i860. " Observations of 7 Virginis," etc. — Mem. R. A. S., vol. xvi., p. 19. South (Sir James). " Observations on the best mode of Examining the Double or Compound Stars ; together with a Catalogue of those whose Places have been identified." — Mem. R. A. S., vol. i., p. 109. "Measures of 458 Double and Triple Stars," etc. Also, " Re-examtnation of 36 Double and Triple Stars," etc., 1823, 1824, 1825. — Phil. Trans. 1826, pt. i. See also Phil. Trans. 1824, pt. in.— Edinburgh Journal of Scienct, vols, vii., viii. 446 double stars. Steinheil. "On the Separation of bright Double Stars."— ^jA Nachr., vol. xiv., p. 205. Struve (F. W.) The following paper is in the Memoirs of the Royal Astronomical Society: — "A Comparison of Observations made on Double Stars," vol. ii., p. 443. The following papers are in the Astronomische Nach- richten : — Papers on his Review of the Heavens, New Double Stars, etc., — vol. iv., pp. 50, 62, 65, 474. "On 7 Virginis," — vol. xii., p. 271. " Double Star Measures at Dorpat," — vol. xiii., p. 249. "On 40 Eridani," — vol. xiv., p. 315. "On the Parallax of a Lyrae," — vol. xvii., p. 177. " On 70 Ophiuchi," — vol. xix., p. 203. "Rapport fait a la classe physico-mathematique, sur un nouvel ouvrage relatif aux ^toiles doubles et multi- ples," — vol. xxii., p. 49. "An Account of the Instruments at Pulkowa," — vol. xviii., p. 33. "Description de I'observatoire Astronomique Central de Poulkova." Par F. G. W. Struve, St. Petersbourg, 1845. " Catalogus 795 stellarum duplicium." 1822 : — " Ueber die Doppelsteme nach einer mit dem grossen Refractor von Fraunhofer," etc. 1832: — " Memoire sur let etoiles doubles." 1832: — "Ueber doppelsterne." 1837: — "Catalogus novus stellarum duplicium," etc. 1827: — "Stellarum fixarum positiones mediae." 1852: — "Mensurse micrometricae." 1837: — " Additamentum in mensuras," etc. 1840: — Report on Double Stars {Edin- burgh Journal of Science, vol. ix.) 1828: — "Stellar Astronomy." PAPERS ON DOUBLE STARS. 447 " Catalogue de 5 14 6toiles doubles et multiples." St. Petersbourg, 1843. " On Waldbeck's Computation of the Angle and Dis- tance of 7 Virginis in 1720." — See Brewster's Edinburgh Journal, vol. i. Struve (O.) " Catalogue de 256 6toiles doubles principles," etc. St. Petersbourg, 1843. " Catalogue revu et corrig^" etc. — See the Recueil de M ^moires des Astronomes de l' Observatoire central de Russie, vol. i. St. Petersbourg, 1853.! " Mem. Acad." St. Petersbourg, vii., 1853. "M^m. dePoulk,"i., 1853. The following papers are in the Bulletin de VAlad^mie Impiriale des Sciences de St. Petersbourg: — " Bullet. Scient. Acad., St. Petersbourg, — x., 1 842 ; xiii., 1855 ; xvii., 1859. " On the Companion of Procyon," — tome xxii., 1 876. " On the Orbit of 42 Comae Ben," — tome xxi., 1875, and tome X., 1866. " On X 2120," — tome xxi., 1876. " On 1,. 634," — tome xix. "Observation du Procyon, com me etoile double," — tome xviii. " Results of some Supplementary Observations made on Artificial Double Stars," — tome xii., and tome iv., 1866. " On the Companion of Sirius," — tome x., also vii. " Observations of some Double Stars recently dis- covered," — totne i. "Nouvelle determination de la parallaxe des dtoiles a Lyrae et 61 Cygni." — M^moires de I'Acad^mie, vii. serie, tome i. St. Petersbourg, 1859. On the Orbit of 5. 1728 and Z 2120. — Bulletin de VAcad^mie de St. Petersbourg, tome xxi. 448 DOUBLE STARS. " On 5" Cancri, ^ Ursae, 7 Virg., rj Cor. Bor., w Leonis, and 5'. 2173." — Ast. Nachr., vol.xviii., p. 43. " Notice sur une revision de I'hemisphere celeste bordal/' etc. — Ast. Nachr., vol. xix., p. 283. On New Double Stars. — Monthly Notices, vol. xx. On Sirius, — vols, xxiii., xxvi. " Observations de Poulkova," — vol. ix., 1 878. Tempel (W.) "On the Companion of Sirius." — Ast. Nachr., vol. Ixii., p. 119. " On the Stars in the Trapezium of Orion." — Ast. Nachr., vol. Ixxx. Thiele (Th. N.) "On the Orbit of f Lihrx."— Ast. Nachr., vol. 1., P- 353- " On the Orbit of Castor." — Ast. Nachr., vol. lii., p. 39. TISSERAND. " On 70 Ophiuchi." — Comptes Rendus, vol. Ixxxii. ; and Acad, of Sciences of Toulouse, iSjd. ViLLARCEAU. "Elements of ? Herculis." — Ast. Nachr., vol. xxvi., p. 305- " On 77 Cor. Bor." — Ast. Nachr., voL xxxvii., p. 57. * Mdthode pour Calculer les orbites relatives des 6toiles doubles." — Conn, des Temps, 1852 and 1877. See also Comptes Rendus: vols, ixviii., xxxvi., on t\ Cor. Bor. ; vols, xxviii., xxxviii, on f Hercules ; vol. xxix., formulae for the case of an orbit whose plane coincides with the line of sight ; vol. xxxiv., method of com- puting an orbit in general terms, and on the effect of the velocity of light on the form of the orbit of a double star. Waldo (L.) Double Star Measures made at Harvard Observatory in 1876. — Ast. Nachr., vol. xcii. PAPERS ON DOUBLE STARS. 449 WiCHMANN (Dr.) " On the Konigsberg Heliometer Observations." — Ast. Nachr., vol. xliii., p. 17. "On the Influence of Temperature on the Observa- tions," p. 20 ; also on other cognate matters. Comparison between the Oxford and Konigsberg heliometers. See also Enganziings-Heft zu den Ast. Nachr. Altona, 1849. Wilson (J. M.) On Castor, f Ursas, f Cancri. — Monthly Notices, xxxii. On Castor, f Ursae, % Cancri, ii^, Bootis, — vol. xxxiii. On e Lyrae and Sirius, — vol. xxxiv. ; On 61 Cygni and 1) Cor. Bor., — vol. xxxv. Wilson (J. M.) and Seabroke. Catalogue of Micrometrical Measurements of Double Stars, made at the Temple Observatory. — Mem. R.A. S., vol. xlii., p. 61. Second Catalogue of Measures. — Mem.R.A.S.,VQ\.yX\\\. WiNNECKE (A.) " The Orbit of ? Cancri and i) Cor. Bor."— ^ j/. Nachr., vol. xli., pp. 102, 107. " Measures of Double Stars." — Ast. Nachr., vol. Ixxiii., p. 145. Wrottesley (Lord). "A Catalogue of the Positions and Distances of 398, Double Stars." — Mem. R. A. S., vol. xxix., p. 85. LIST B. PAPERS ON THE MICROMETER. Airy. "On a New Construction of the Divided Eye-glass Double-Image Micrometer. By G. B. Airy, Esq., Astronomer Royal." — Monthly Notices of R. A. S., vol. vi., p. 229; also vol. X., p. 160. Mem. R. A. S., vol. xv., 29 450 DOUBLE STARS. p. 199. Cambridge Trans., vol. iii.; and "Account of Northumberland Equatorial," p. 34. Arago. " Popular Astronomy," vol. i., p. 382, AUZOUT. Phil. Trans., Ho. 21. 1666. He used two silk threads, one fixed and the other moveable by means of a fine screw. Babbage. "On a new Zenith Micrometer. By Chas. Babbage, Esq., F.R.S., etc"— Mem. R. A. S., vol. ii., p. lOi. 1825. Barlow (P.) " On the Principle of Construction and general Appli- cation of the Negative Achromatic Lens to Telescopes and Eyepieces of every description." — P/d/. Trans. 1834, pt.i. Bidder. "On a new Form of Position Micrometer. By G. P. Bidder, Esq., Q.C."—Moutk/y Notices of R.A.S., vol. xxxiv., p. 394. BOGUSLAWSKI. "On the Use of a New Micrometer," etc. — Monthly Notices of R.A.S., vol. vi., p. 219. A single web is placed in the focus of the object-glass as a diameter across the field of view. It is so arranged that it can be turned round the centre in every direction, and make with the declination circle any given angle. It was specially designed for the "observations of Mars and neighbouring stars for the purpose of determining his parallax." Also Mem. R. A. S., vol. xv., p. 193. BOSCOVICH. " Of a new Micrometer and Megameter. By the Abb6 Boscovich, etc." 1777. — Phil. Trans., vol. Ixvii. Bradley. " Directions for using the common Micrometer." — Phil. Trans., vol. Ixii. 1772. PAPERS ON THE MICROMETER. 45 1 Brewster (Sir David). "Treatise on New Instruments." 181 3, Brunnow (Dr. F.) "Spherical Astronomy." A valuable chapter on the Heliometer and Micrometer. London, 1865. Casella. " On a Micrometric Diaphragm." By L. P. Casella. — Monthly Notices of R. A. S., vol. xxi., p. 178. Cavallo (Mr. T.), F.R.S. " Description of a simple Micrometer for Measuring Small Angles with the Telescope." — P/dl. Trans., vol. Ixxxi. 1 79 1. This was a thin and narrow slip of mother- of-pearl finely divided, and placed in the focus of the telescope. Chauvenet. "A Manual of Spherical and Practical Astronomy," etc. By Prof. Chauvenet. Triibner and Co. : 1 868. A chapter on the Micrometer. Clark. "Mr. Alvan Clark's New Micrometer for Measuring Large Distances." — Monthly Notices of R.A. S., vol. xix., p. 324. 1859. Clausen (Th.) " Beschreibung eines neuen Micrometer." — Ast. Nachr., vol. xviii., p. 96. Dawes (Rev. W. R.) " On an Improvement in Mr. Dollond's Micrometer." — Monthly Notices of R.A. S., vol. ii., p. 180. " New Arrangement of two Solar Prisms for use with the Micrometer." — Monthly Notices of R.A. S., vol. xxv., p. 218. Valuable hints and information may be obtained from the following papers by this eminent observer : — Mem. R. A. S., vol. viii., p. 62 ; vol. xix., p. 191 ; vol. XXXV. Also Monthly Notices, vol. xviii., p. 58. 452 double stars. Dembowski. " D etermination de la valeur en arc des Revolutions du Micrometre." — Ast. Nachr., vol. Ixxxi., p. 247. DOBERCK. "On Amici's Double-Image Micrometer and Graham's Square-Bar Micrometer." — Ast. Nachr., vol. cxii. Examination of the Merz Micrometer. — Ast. Nachr., vol. cxii. DOLLOND (John). Contrivance for Measuring Small Angles. — Phil. Trans., vol. X., pp. 364, 462 ; also vol. x., p. 409. " Account of a Micrometer made of Rock Crystal." By G. Dollond, F.R.S.— /'M. Trans., 1821, pt. i. " An Account of a Concave Achromatic Glass Lens, as adapted to the wired Micrometer when applied to a Telescope, which has the power of increasing the magnifying power of the Telescope without increasing the diameter of the Micrometer Wires.'' By George Dollond, F.R.S., etc. — Phil. Trans., 1834, pt. i. Encyclopaedia Britannica. Article " Micrometer," — vol. xiv., p. 742. Epps. " Formulae for reducing Micrometric Observations." — Monthly Notices of R. A. S., vol. iii., p. 198. FRAUNHOFER. " Mikrometer, iiber eine neue Art." — Ast. Nachr., vol. ii., p. 51 ; vol. ii., p. 36L Gascoigne. " On Mr. Gascoigne's Micrometer. By Mr. Richard Townley." 1667. — PhiL Trans., vol. ii., p. 161. " Description of Mr. Gascoigne's Micrometer. By Mr. Hook." 1667. — Pliil. Trans., vol. ii., p. 195. " An Account of Mr. Gascoigne's Micrometer by Bevis." — Phil. Trans., vol. x., p. 369. See also Costard's History of Astronomy, and Baily's Account of the Rev. John Flams teed. 1835. PAPERS OIT THE MICROMETER. 453 Halley (Dr.) " On Cassini's Micrometer." — Phil. Trans., No. 363. HersCHEL (Sir William). "Description of a Micrometer for taking the Angle of Position. By Mr. Wm. Herschel, of Bath." 1781. Phil. 7>a«j., vol. Ixxi. 1781. " Description of a Lamp Micrometer, and the Method of using it. By Mr. Wm. Herschel, F.R.S." 1782.— Phil. Trans., vol. Ixxii. "A Description of the Dark and Lucid Disc and Periphery Micrometers. By Wm. Herschel, Esq., F.R.S." 1782. — Phil. Trans., vol. Ixxiii. " On Fixing Spider Lines." Capt John Herschel. — Monthly Notices, vol. xxxiv., p. 396. Hire (De la). "On Huyghens's Micrometer." — Royal Academy of Sciences, 17 17. Hooke. See Sprat's " History of the Royal Society," Hooke's " Micrographia," and Hooke's " Posthumous Works." HUSSEY. "Description of a Lamp Micrometer." — Ast. Nachr., vol. X., p. 385. HUYGHENS. See his Sy sterna Saturnium, published in 1659. By placing a strip of metal at the focus of the telescope, and making its breadth equal to that of the object observed, the apparent diameter could be deduced. Kaiser (Dr. F.) " On Airy's Micrometer." — Ast. Nachr., vol. xlv., p. 209. " Erste Onderzoekingen med den Micrometer van Airy." — Ast. Nachr., vol. xlviii., p. 109. " Measures of Double Stars with Airy's Double-Image Micrometer and the Parallel-Wire Micrometer." "Annalen der Sternvvarte in Leiden." Dritterband, Haag, 1872. 454 DOUBLE STARS. See also Monthly Notices of R. A. S., vol. xxvi., p. 305, and vol. xxvii., p. 1 1 ; Ast. Nachr., vol. xlv., p. 209 ; vol. xviii'., p. I ; and vol. Ix. Klinkerfues. " Mikrometer von Repsold, fiir den Gottinger Meridian Kreis ueber dasselbe von Klinkerfues." — Ast. Nachr., vol. xlii., p. 107, and vol. Ix. Lamp (Dr.) On Bessel's Formula for the Correction of Micrometer Screws. — Ast. Nachr., vol. Ixxxviii. MalvasIA (Marquis). See his " Ephemerides," published at Bologna in 1662. This micrometer was a network of fine silver wires, forming small squares in the focus of the telescope. See M^m. Acad, des Sciences, 17 17. Maskelyne. " Description of a Method of Measuring Differences of R.A. and Dec, with Dollond's Micrometer; with other New Applications of the same. By the Rev. N. Maskelyne, B.D., F.R.S." 1771.— Phil. Trans., vol. Ixi. " Of a New Instrument for Measuring Small Angles, called the Prismatic Micrometer. By the Rev. Nevil Maskelyne, D.D., F.R.S., etc." 1777.— Phil. Trans., vol. Ixvii. Mosta. "Mikrometer, Untersuchungen iiber periodische Un- gleichheiten derselben, von Mosta." — Ast. Nachr.,vo\.\\-x.., p. 257. Pape. " Untersuchung der Microscop Mikrometer des Altoner Meridiankreises, von Dr. C. F. Pape." i?,S9.—Ast. Nachr., vol. 1., p. 337. Pearson (Rev. W., LL.D., F.R.S. , etc.) " An Introduction to Practical Astronomy," etc., 2 vols. London, 1829. In this work will be found "An Historical Account of the different Methods of Measuring small PAPERS ON THE MICROMETER. 455 Celestial Arcs," and also full descriptions of reticles, parallel wire, angular, circular, and double-image Micro- meters, etc., etc.* POGSON. " On the Ocular Crystal Micrometer." — Brit. Assoc. Report, 1858. PORRO. "Nuovo micrometre per mezzo di linee luminose ad uso deir astronomia." J. Parro. — Ast. Nachr., vol. xlviii., p. 65. 1858. Powell (Rev. B.) " On a New Double-Image Micrometer." — Monthly Notices of R. A. S., vol. vii., p. 24. Ramsden. " The Description of Two New Micrometers. By Mr. Ramsden, Optician." 1779. — Phil. Trans., vol. Ixix. Rees's Cyclopedia. Dr. Smith on Micrometers. Reslhuber. " Mikrometer mit Lichtpunkten im Refractor zu Kremsmiinster, iiber dasselbe von Reslhuber." 1858. — Ast. Nachr., vol. xlviii., p. 149. Rogers. "Modification of the Micrometer Head, devised by Mr. Joseph A. Rogers, Aid U. S. Naval Observatory."— Ast. Nachr., vol. Ixiii., p. 78. 1864. Savery. " On a Double-Image Micrometer." — Phil. Trans., vol. xlviii. 1783. Secchl " Doppel-bild Mikrometer, iiber dasselbe von Secchi." — Ast. Nachr., vol. xlviii., p. 309. 1858. Seeliger (H.) Theory of the Heliometer. Leipsig, 1877. ♦ See also Mem. R. A. S., vol. i. 456 DOUBLE STARS. SIMMS. "Notice of an Improvement in the Double-Image Position Micrometer. By William Simms, Jun., Esq." — Monthly Notices of R.A. S., vol. xviii., p. 64; also vol. xxvii., p. I r. Smeaton. " An Equatorial Micrometer," invented by Mr. John Smeaton, F.R.S., with Observations. 1786.— PM. Trans., vol. Ixxvii. Steinheil. "Mikrometer-Ocular mit leuchtenden Faden." Remarks on, by Steinheil. 1859. — Ast. Nachr., vol. li., p. 353. Valz. " On the Divided Eyepiece Micrometer."— See Monthly Notices of R.A. S., vol. x., p. 160 ; also ZacJis Corre- spondance Astronomique, tome i., p. 353- Wilson (Dr.) "An Improvement proposed in the Cross Wires of Telescopes." — PhiL Trans., vol. Ixiv. 1774. WiNNECKE (A.) Ueber ein neues Hiilfsmittel, die periodischen Fehler von Mikrometer-Schrauben zu bestimmen. — Ast. Nachr., vol. cxi. (See Tlie Observatory, No. 12.) Wollaston. " Of a Single-lens Micrometer," by Dr. Wollaston. — Phil. Trans., vol. ciii. " On a Method of Cutting Rock Crystals for Micro- meters," by Dr. Wollaston. — Phil. Trans., vol. ex. "A Description of a New System of Wires in the Focus of a Telescope," etc. — Phil. Trans., vol. Ixxv. 1785. Wren (Sir Christopher). See Sprat's " History of the Royal Society." Zenger. " The Stereo-Micrometer. By Professor Chas. V. PAPERS ON THE MICROMETER. 457 Z¬x!'— Monthly Notices of R. A. S., vol. xxxvi., p. 252. See also J.'s Mensura Micrometricce, O.S.'s last vol. of the Poulkova Observations (vol. ix.) ; 5'.'s Description de F Ohservatoire Astronomique Central de Poulkova. 1845. LIST C. SOME PAPERS ON THE COLOURS OF STARS. Andre and Borrosch. Ueber das farbige Licht der Doppelsterne. Prag., 1842. Arago. See his Astronomic Populaire. Ballot (Dr.) Papers in Poggendorff's Annalen 1845, and vol. Ixviii. Bolzano (Dr.) See Pogg. Annalen 1843, DOPPLER (Dr.) His papers are to be found as follows : — In vol. viii. of Sitzimgsberichte der Mathematisch-Naturwissenschaftichen Classe der Kaiserlichen Akademie der Wissenschaften. Wien, 1852. Weitere Mittheihmgen meine Theorie des farbigen Licktes der Doppelsterne betreffend, in Pogg. Annalen 1850 and 1851. Ueber das farbige Licht der Doppelsterne und einiger anderer Gestirne des Himmels, in Abhandlungen der Koniglichen Bohmischen Gesellschaft der Wissenschaften. Prag., 1843. Klein. " On the Changes of Colour of the Fixed Stars." — Ast. Nachr., vol. Ixx. Kreil. " On Doppler's Theory," in Ein Astrojtomisch-Meteoro- logischen Jahrbuche fiir Prag. 1844. 458 DOUBLE STARS. NiESTEN. " On the Colours of Double St3iVs."— Bulletin de I'Aca- detnie royale de Belgiqiie. 1879. SCHMIDL (Dr.) In den osterreichischen Bldttern fur Literatur nnd Kunst. Schmidt (Dr.) " On the Colours of the Stars." — Ast. Nachr., vol. Ixxx. " On the Colour of Arcturus." — Ast. Nachr., vol. xlii. Sestini. Memoria sopra i colori delle stelle del Catalogo di Baily. Roma, 1845 ^'^^ 1847. See Gould's Astron. Jotirnal, 1850. Smyth (Admiral). "Sidereal Chromatics." London, 1864. Smyth (Prof. Piazzi). See his " Teneriffe." Zenker (Dr.) " On Doppler's Theory." — Ast. Nachr., vol. Ixxxv. Zollner (Dr.) Ueber Farbenbestimmung der Gestime, vol. Ixxi. See also Monthly Notices, vols, x., xi., xx., xxvi., xxvii. 459 PAGE 176. S. 13. I02°-5 in. ... 1879-66 177- 0.2. 4. 'S5°-3 o"-s6 78-6 186. 0.2. 515. 273° -0 0"'2 777 272°-3 o"-2S 8-8 O.S. 28. 3i4°-o o"-8s 787 ADDITIONAL NOTES. Bu. 187. S. 93 (Polaris). " Some three years ago the discovery by M. De Bbe, of Belgium, of two small companions about 4" distant was announced, and several observers subsequently claimed to have seen them in the described places I have no hesitation in saying these supposed stars do not exist." — (Mr. Burnham's Double Star Observations, p. 87.) 193. 2. 196. 52° -o '."-49 18777 Bu. 199. oCeti. 82°-8 ii5"-62 77-8 Mr. Bumham thus describes his new companion : 9i°-5 74"-ii Mag. 13 1877-8. 201. 2. 293. 7S°-5 8"-3o 1878-6 Bu. 209. 2. 453. Mr. Bumham, with 6 in. and 18J in. apertures, finds no trace of duplicity. (1874 to 1879.) 211. O.S. 531. i38°-5 2"-6o 1878-6 Bu. 2.518. ABi25°-4 3"-66 79-0 „ ADi45°-6 37""io 77-8 i37°'3 3S"'99 79'o 212. S. 547. Companion not seen. 1865 De. 18737 Bu. 9°-8 2"-46 77-9 i4°-o -25 79-0 ,, 213. 2. 554. 7°-o o"-6o 78-0 „ 216. 0.2. 92. 247°-4 2"-78 78-0 220. 2. 728. i96°-2 o"-45 78-0 221. 2. 748. A E (5th star) 354° -3 4"'02 77-9 CF(6thstar) U9°-8 3"74 77'9 Bu. has never suspected the existence of any other star either within the trapezium or near the principal stars. Nor does he thinli the 5th and 6th stars variable. 224. So. 503. Bu. has discovered a faint star nearer than C. i57°-3 28"-o9 Mag. 13. 1878. 227. S. 943. I47°'4 «9"'6S '878'2 Bu. 233. 0.2. 159. 36i°-o o"-48 78-1 Bu.'s third star C is thus given : 3i"-4 23"-64 Mag. 12-13. 1878-1. Bu. 46o DOUBLE STARS. 235- 0.2. 165. 78°-i 2"-4S 1878-1 Bu. 236. 2. 1074. 140° -o o"7i 78-0 ») 237. 2. io8r. 226°-i i"-36 78-1 »» 243- Procyon and D. 262°-3 S6"-59 367* 3ii°-8 44"-S9 74 Newcomb. 3i7°-3 ■62 77 Bu. 245. 2. 1 142. 254° -s 22" -84 78-2 Bu. 246. 2. 1 1 75. 222° -5 i"-8i 78-1 J, 252. 2. 1216. isS^-S o"'6i 78-2 ^, 256. 2. 1329. 248° -4 22" -84 78-1 ft 256. 2. 3121. Dr. Doberck's provisional elements are : a 16° 0', ) 149° 30', 7 74° »S'. '0-2600, P 37'03 yrs.. T 184278, a [o-"7i]. 260. 2. 1356. Dr. Doberck's latest elements are : a 149° IS' X 122° 19', 764° 5', ; 0-5510, P 114-55 yrs.. T 1841-57, a o"-Ss. 262. 8 Sextantis. 11 7° -4 o"-2 -t- 78-2 Stone. i6i°-o o"-2± 78-2 Bu. 0.2. 523. 298°7 6" -67 78-1 it 2. 1423. 69° 7 I" -28 78-2 267. 0.2. 230. i3°-4 8" -36 78-2 ,, 277- 0.2. 234. 282° obi. 70-5 0.2. i87°-i o"-35 + 78-2 Bu. «5i°7 o"-27 78-3 tt 0.2. 23s. Dr. Doberck's elements are : a 96° 17', ^ «29"5S'. 7 60° 13'. f 0-5870, P 94-406 yrs.. T 183910, a i"-o66. 278. O.S. 243. 14° -5 o'-94 783 it 279. 2. 1607 = Hj 202 = H, 516. A B 358°-i 30--85 Mag. 7 8, 8-3 1878-2 Bu. B C 309° -8 2l"-04 78-2 „ 0.2. 249. A B307°-i o"-46 1878-3 Bu. A C i48°-3 i2"-68 78-3 2. 1641. 39°-2 8" -96 78-3 ,, 280. 2. 1643. 46°-6 i"-76 78-3 ,, 287. 2. 1703. 28i°-5 I8--79 78-3 ») 2. 1707. 3S°-S 9"-84 78-3 290. 2. 1757. Doberck's formulae are : P = 46°-6i + i°-o94 (^- - 1850) — o°-oi53(/- 1850)^ A = i"-83 + o"-oi6 {/- - 1850). 293- 0.2. 270. 35i°-9 8-71 1878-3 Bu. 295. 2. 1820. 67° -4 2" -32 78-3 tt 2. 1819. Doberck finds : P = 5i°-i6 - i°-49i {t- 1850) +o*'-oi38(/- 1850)^ A = i"*09 + o"*oio (/ - 1850). * Annalen K»nig. Stern. Munchen., xvii. t " Too large." ADDITIONAL NOTES, 46 I PAGE T 1812-96, ao"'886. 322. V Scorpii, Bu. 120. 360° -6 o"79 363° 7 l"'04 333- 2. 2106. 323"7 o"'64 346. A. C. 7. 234° -9 i'-05 355- S. 2315. 251° 7 o"-3i 357- a Lyrae. AB iS4°-9 48" -01 ■9 •II 297. 0.2. 283. l4i°-3 5"-27 1875-5 0.2. I3i°'i 5"'oo 78-3 Bu. 303. 2. 1879. 39°'i o"-37 77-4 Sclii. 42° '9 "34 77 "5 De. 2i7°'i '42 78-4 Bu. 305. 2. 1888. 279°-4 4"-22 79-40 Dob. 307. 2.3091. 225°-o o"-2S± 78-4 Bu. 0.2.294. 248°7 2"7S 78-3 „ 0.2. 295. i28°-7 o"-7S 784 „ 2. 1909. 24l°-4 4"-93 79-34 Dob. 308. 2. 3093. i39'=-9 3o"-79 78-3 Bu. 313. Doberck's second elements were obtained from equations of condition. 317. 2. 1961. 44°-6 22"-45 1878-3 Bu. 0.2. 298. 295° -2 o"-3 77-4 De. 3lo°-7 o"-27 78-3 Bu. 0.2. 298. Dr. Doberck gives the following : a 14° 38', \ 342° 31', 7 56° 10', 4-0-4872, P 68-802 yrs. 77-5 De. 783 B"- 78-4 78-S .. 78-4 ,. 78'4 78-5 .. A faint companion of the 12-13 ™*g- ^^s discovered by Winnecke in 1864. A C 298°-8 46"-87 1864-8 \Vi. 289°-9 .5i"-66 78-3 Bu. 292°-9 -97 78-4 293°-i -93 784 Mr. Bumham has never seen the slightest trace of the faint stars supposed to have been seen by Mr. Buckingham and others. 363. 0.2. 364. Mr. Burnham has hitherto failed to see the companion. 365. 2. 2434. 64°-! i"-S3 1878-6 Bu. 367. 0.2. 368. Bu. gives the following measure of a new small star : AC 98°-2 i7"-37 1878-6 Bu. AB2i6°-2 i"-03 78-7 368. 2. 2514. 3i6°-3 8"-5i 78-4 2.2515. 23°-8 12 '-98 78-6 ,, 370. 0.2. 380. Neither Burnham nor Newcomb can see the star C. 370. 2. 2574. 145 °-o o"-63 1878-5 Bu. 374. 0.2. 532. i6°-5 i2"-oo 78-6 ,, 2. 2607 AB = 0.2. 392. 3i7°-o o"-3i 78-5 375. 2. 2619. C was first observed by Hj. 294°-2 i8"-40 78-4 4^2 DOUBLE STARS. PACE 376. 0.2. 400, Single in 1878 (Bu 2. 2658. AB ii9°-9 5" -2 1 78-6 Bu. AC2i2°-4 40" -50 78-6 »» 378. O.S. 533. 329° -2 io"-S9 78-2 ,j 381. 2- 2734- I9I°-2 2S"-82 78-6 jj 0.2. 418. 294° -8 l"-2± 777 ,, 383. 0.2. 424. 327°7 o"-45 78-6 If 384. 2. 2749. Secchi discovered C in 1856. 148° -9 i"-i3 77-8 It 389. T Cygni. i50°-o I "-06 78-4 J, 392- 2. 2860. 255°-6 5" -96 78-5 ,, 397- 2. 2912. i3o°-o o"-32 78-6 2. 2915. i5S°-i 12" -29 77-8 ,, 398. 0.2. 477. iS4°-i 4" '62 786 5) 399- 2. 2959. I02°-2 i3"77 77-8 J» Mr. Bumham's new star C is thus given : 9S°-9 8-31 1877-9 Mag. I: 399- 0.2. 536. Round ... 74-8 Bu. i6i°-s o"-47 77-8 »l 406. No. 804. i2°-3 22" -63 1879-21 Dob. No. 818. 27S°-8 o"-99 79-15 if 2. 1058. : Mag. 8-2, 117. 282° 7 23"78 32 s. 283° 22" -47 44 Ma. Companion not seen 65 De. " " 74 75 Bu. 28i°'o 22" -84 79 M •0 •32 79 )» Is one of the components variable? (Bu.) The place for 1 880 is R. A. ; ^h ,Q.2m_ Dec. 9' ' 37'- INDEX. Adjustments, 15. Airy, 50, I44. Amici, 50. Apertures, 80. Auwers, 31, 40. o Centauri, i, 417. a Herculis, 2, 143. o Lyra, 3. Ball (Dr.), 90. Barclay, 7, 8. Bedford, 31. Berlin, 31. Bermerside, 32. Bessel, 8, 40, 56. Binary stars, 4. Bishop, 8, 45. Bond, 8, 33. Bonn, 32. Bradley, I, 3. Brothers, 8. Bruhns (Dr.), 105. Briinnow, 8. Bumham, 8, 34, 151, 411. /3 Cygni, 1, 2. /3 Scorpii, i, 417. Cambridge, 33. Cape of Good Hope, 33. Cassini, i, 84. Castor, I, 2, 3, 106. Catalogue, The, 152. Chairs, 27. Challis, 8, 33. Chicago, 34. Cincinnati, 34. Classification, 418. Clock, The, 25. Coloured glass, 73. Combination of observations, 144. Cooper, 8, 42. Crossley, 8, 32. Cranbrook, 35. Cuckfield, 34. Cygni, (61), I, 135. Darby, 8. Dawes, 6, 35, 81. Dembowski (Baron), 7, 36, 59, Distances, 70, Doberck (Dr.), 8, 43, 117, 452. Dorpat, 6, 36. Duner, 7, 41. Dunlop, 37. Dunsink, 37. Elchies, 37. Ellery, 8. Encke, 8, 31, 91. Engelmann, 8, 40. Equatorial, 1 1 . Errors of observation, 144. Errors, Systematic, 420. f Lyrse, I, 2. Ferrari, 8, 46. Feuillee, i. Field of view, 2 1 . Flammarion, 8. Flamsteed, 3. Fletcher, 8, 47. Focal length, 20. Forms, 75. GaJle, 8. 31. Gledhill, 8, 32. Grant, 37. Greenwich, 37. 7 Andromedse, I, 2. 7 Arietis, i, 3. y Virginis, I, 2, 3. Hall, 8, 49. Herschel (Sir Wm.), 2, 38, 64. Herschel (Sir John), 4, 39, 64, 94. Hind, 8, 45. Holden, 8, 49. Hooke, I, 3. Homsby (Dr.), 85. Howe, 34. Huyghens, I. d Orionis, I. Jacob, 6, 8, 42. Jenkins, 8. Kaiser, 8, 40. 464 INDEX. Kiisch, I. Klinkerfues, 91, 120. Knott, 8. Konigsberg, 39. Lambert, 84. Lassell, 8, 40, Leipsic, 40. Leydeii, 40. Ley ton, 41. Liveqjool, 41. Long (Dr.), 3- Lund, 41. Luther, 40. Maclear, 8. Madler, 6, 37. Madras, 42. Main, 7, 44. Markree, 42. Maskelyne, 2. Maupertuis, 84. Mayer, 2, 4, 85. Means, 144, 422. Measures, The, 175. Messier, i. Methods of observing, 64. Michell, 84. Micrometer, 50. Milan, 43. Miller, 8, 49. Mitchell, 8, 34. Molineux, 3. Morton, 8, 49. Nantucket, 43. Naples, 43. Newcomb, (Prof.), 8, 49. Niesten, 458. Nobile, 8, 43. Number of measures, 72. I Ursae, I. Observers, 174. Observatory, The, 29. Ophiuchi, (70), I. Otto Struve, 6, 37, 45. Oxford, 44. Parallax, 3, 139. Paris, 44. Peters, 40. Pigott, I. Pleiades, 56. Plummer, 44. Position angles, 7. Poulkova, 45. Powell, 6, 42. Power-gauge, 22. Powers, 22. Precautions, 83. Prism, 69. Pritchard (Rev. C), 8. Probable error, 145. Proper motion, 139. Quaternary systems, 419. Regent's Park Observatory, 45. Riccioli, I. Romberg, 46. Rome, 46. Rugby, 46. Savary, 91. Schiaparelli, 8, 43. Schliiter, 40. Seabroke, 8. Secchi, 7, 46. Smyth (Admiral), 6, 31. Smyth (Prof. P.), 459. South (Sir James), 5, 46. Sporer, 8. Stone (O.), 7. Struve (W.), 5. Systematic errors, 420. 0- Cor. Bor., 118. Talmage, 41. Tarn Bank, 47. Ternary systems, 419. Tests, II. Thiele, 10 1, 422. Upton, 34. Villarceau, 91. Waldo, 8. Washington, 48. Webb (Rev. T. W.), 8. Weights, 78, 147. Whitehaven, 49. Wilson (J. M.), 8. Winnecke, 31. Wrottesley (Lord), 6, 49. f Cancri, I, 2, 101. f Ursae Majoris, I. Hazell, Watson, and Viney, Printers, London and Aylesbury.