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Un des symboles suivants apparaitra sur la derniire image de cheque microfiche, selon le cas: le symbols — »- signifie "A SUIVRE", le symbols V signifie "FIN". Maps, plates, charts, etc., may be filmed at different reduction ratios. Those too large to be entirely included in one exposure are filmed beginning in the upper left hand corner, left to right and top to bottom, as many frames as required. The following diagrams illustrate the met'iod: Les cartes, planches, tableaux, etc., peuvent dtre filmAs i des taux de reduction diff6rents. Lorsque le document est trop grand pour 6tre reproduit en un seul clich6, il est film6 A partir de Tangle suptrieur gauche, de gauche d droits, et de haut en bas, en prenant le nombre d'images n6cessaire. Les diagrammes suivants illustrent la mithoda. 1 2 3 1 2 3 4 5 6 I WASHINGTON OBSERVATIONS FOR 1875.— APPENDIX II. RESEARCHES MOTION OF THE MOON MAni; Al THE UxiTKi) Statks Naval Oi5servat()RY, WASHiNdiox. SIMON NSAYCOMB, PROFESSOR, V. S, NAVY. PART I. REDUCTION AND DISCUSSION OF 0BSF:RVATI0NS OF THK MOON BFFORE 1750. WASHINGTON: GOVERNMENT PRINTING OFFICE. 1878. PREFACE. For several years after the publication of Hansen's Tables of the Moon, it was very generally believed that the theory of the motion of tliat bod}^, after liaving been the subject of astronomical and mathematical research for two thousand years, \>as at last complete, and that, in consequence, the motion of the moon could now be pre- dicted with the same accuracy as that of the other heavenly bodies. In 1870, the writer showed that this belief was entirely unfounded, and that the correctness of the tables since 1 750 had been secured only by sacrificing the agreement with observations previous to that epoch, so that, about 1 700, Hansen's Tables deviated more widely from observations than did those which they superseded. It was also shown that at the time of writing, the moon was falling behind the tabular position at a rate wliich woidd speedily cause a very serious error in the representation of the Tables. Alto- gether, it appeared that notwithstanding the immense improvement whicli Hansen had made in the accuracy of the inequalities of short period, the theory of those of long period was no nearer such a solution as would agree with ol)servation than when it was left by Laplace. The work oT reinvestigating the subject, and, if possible^ of ascertaining the cause of these deviations, was soon after, with the concurrence of Rear- Admiral Sands, made a part of the anther's official duty at the Naval Observatory. It may be proper to i-emark that this arrangement was largely due to the interest taken in the subject by Captain (now Rear-Admiral) Daniel Ammen, IT. S. Navy, the Chief of the Bureau of Navigation The work as plaimed was divisible into two distinct parts:— 1. The mathematical theory of the inequalities of long period in the moon's mean motion. As the only cause to which such inequalities could be attributed was the action of the planets, this part of the investigation resolved itself into a compu- tation of that action. 2. The study of the inequalities in question from observations, especially from observations before 1750. In the ancient and modern observations of eclipses and occultations, there was believed to be an immense mass of valuable material for the purpose in question, some of which had been almost forgotten, and very little of which had been discussed with modern data. An amount sufficient for the employment of two computers having been appro- priated by Congress, these two investigations were carried on siuuiltaneously, with the intention of completing them in the order in which tiiey have been named. But as the mathematical investigation was sujjposed to be nearly brought to a close, it was found that certain terms, which were at first supposed to be of no importance, woidd have to be investigated, and that this investigation might prove the most tedious part of the whole work, unless some method of shortening it could be devised. Not having PREFACF,. yet been able to decide which is the best method of treatiiiff the sulyect, the invosti- jration is still iiicoinpleto, and the present I'esearch, orij^inally intended as Part IT, is issued as Part I. In 1 87 1, advantage was taken of a journey in Europe to ascertain whether the older observatories and libraries of that continent might not contain unpul)Hshed observations of eclipses or occultations which would be of value for the subject in hand. In this, an unexpected measure of success was attained. At I'aris, M. De- LAUNAY, then the Director of the Ob.servatory, placed all the archives of that estab- lishment uiu'eservedly at my disposal. Among this material were most of the original note-books of the French astronomers from 1675 onward, and here a great number of occultations were found to have been observed, though the observations had been totalh' forgotten. ^Phe observations published in the Memoirs of the Academy were but a small fraction of those actually observed, and that fraction was compo.sed of the least valuable of them. ()ne circutnstance connected with these observations, while greatly increasing 'he labor of the reduction, has also increased the value of the results by insuring the entire genuineness of tiie records. The records made use of consisted, in large part, of the original rough notes of the observations, without any explanation whatever, and without any reductions excejjt the occasional application of a supj)osed clock-correc- tion. In perhaps half the cases, the star occulted was neither named nor described, wliile the methods of determining clock-error had to be ascei'tained by conij^arison and induction. Many of the books were entirely anonymous. As the coj)ies of the records of which use has been made are given in full in the present paper, a minute description is not here necessary. At the observatory of Pulkowa, 1 was fortunate enough, through the kind offices of Director Struve, to find what might be con.sidered as the complement of the Paris observations in the records of Dei.isi.k.'s observations at St. Petersburg between 1727 and 1747. From about 17^0, there was a great falling-oft" in the number of the Paris observations, so that those of .St. Petersburg come in very o])portunely. At Pulkowa I also availed myself of the opjjortunity of making use of the umivalled astronomical library of the establishment to conn)lete the list of pul)lislied data. In these researches at Pulkowa I was actively assisted by Dr. Linde.njann, then acting lil)rarian, who devoted several days to this work. Another series of observations which, though i)ublished, seem to have been nearly forgotten, was found in the Livre de la Grande Table Jlakemitc, translated from an Arabian manuscript by Caussin. These comprise the most valuable of the Arabian observations, but, so far as 1 am aware, they have not before been fully compared with modern tables. The want of accurate data in the beginning has 'added greatly to the labor of completing the present work, and caused nuich imavoidable delay. In the case of many of the Paris observations, the stars coidd not be identified until the times of observation had l)een computed, and the apparent place of the mOon at those times found from the tables. Then the star had to be observed, in order to improve the means of determining its proper motion. The existing data for deteraiining the places of stars PREFACE. two centuries back wore so inHiiffi(;ient that a I'oinplote i-oiiivewtiyatidn of the ri^lit asconHioiis of the Htars became a necessary j)art of tlie work. '^I'liis invostij^iition was rendered successful by Auwers's re-reduction of Braoi.i'.y's observations ; and its results have in part been published. It will be seen that the material most used in the present investigation has iiithcrlo been least known. Possil)ly, the most valuable portion of it is found in the un|)uli- lished Paris observations, wlierel)y tlie moon's mean lon<>itude is determined with astronomical acciu'acy from 1680 onward. Tiie observations of Gassendus, Hevelius, and Flamstked (whereby the mean lon<;itude is carried back with gradually dimin- ishinjf accin-acy a half century farther), thon<>ii published, have never been used for determining the moon's place. Nearly .he same remark will apply to the Arabian observations, though it was by them that the secular acceleration of the moon's mean motion was first determined. On the other hand, the ancient total eclipses of the sun, which have been so nnich discussed during the present century, are b(U"e thrown aside. The reason for this course l)eing given in the ju'oper place need not be rei)eated now ; nor will the writer make any attempt to forestall the differences of ojnnion which may arise respecting its validity. He will only remark that he approached the subject without any bias whatever, unless a general distrust of the scientific pre- cision of ancient authors may be regarded as a bias, and that the various considera- tions which presented themselves to his mind on examining these records are iiere reproduced as exactly as po.ssible. While the result of the examination of ancient solar eclipses has seemed to him to jnstifj' his general distrust, that of the lunar eclipses in the Almaf/esf lias not. Moreover, no part of the discussion has l)een altered in the light of the result finally reached; but, verbal revision aside, each consideration is given as it was originally written. The only a|)proach to an excei)tion occurs in § 2, from which he has expunged a derogatory estimate of Ptolemy's eclij>ses, formed before he had compared them with the fables. The lack of unity and consistency which may thus have arisen in a discussion which has been growing by piecemeal for six years may be excused under these circumstances. The date i 750 is fixed ujion as the terminal point of the investigation, partly because it is that when accurate meridian observations commence, and also because it is the epoch which separates the period within which we have readily accessible obser- vations and copious tables of reduction founded on modern data, from that during which both these recpxirements are wanting. In conclusion, the author wishes to place on record his appreciation of the labors of the skilled assistants, without whose help the completion of the work would not have been possible. He owes much to the conscientious accuracy of his young friend, Mr. Parker Phillips, who, with Mr. Jonx T. Hedrick, assisted him from 1871 until 1873. In the closing parts of the work, most of the necessary computations were prepared by Mr. John Meier and Mr. W. F. McK. Ritter. His engagements rendering it diffi- cult to read the proof-sheets properly, Mr. D. P. Todd has taken an active part in pass- ing the work through the press. Nautical Almanac Office, Washington, April, 1878, ERRATA. Page 13, line 5, for Bii. 60 read Bd. 52. Page 42, Eel. No. 10, for s"" 56'" read 6'' 56'". Page 44, line 19, for + 18' read — 18'. Page 59, line 21, for Lo — m" read Lo + 111°. Page 60, lines 4 and 5, add (7). Page 74, lines 13 and 15, for ir read 11. Page 84, line 8 from bottom, for cpi read 99*. Page 205, line i, add § t2. Page 231, line 8 from bottom, for 3,8" read 38". TABLE OF CONTENTS. § I.— HISTORICAL INTRODUCTION ,j Values of secular acceleration dediicfd Ijy DuNTHOKNE, Tobias Maykr, Lai. ANDK, iind Lapiack . . . (j, lo Researches of Zech, Adams, Hansen, a'ul Dei.aunay id Researches of Mavxk and r>f Fi;Rnri. on tid.il retaidalion ii AiRY's discussion of ihc ancient solar eclipses I2 Hartwio's comparison of Zkch's discussion with Hansen's Tables 13 Inc(|ualitics of long period in the moon's mean motion 13 S 2.— SUMMARY OK DATA FOR DKTERMIMNG THE APPARENT SECULAR ACCELERATION . 17 I. Statements of ancient historians respecting Qcrtain total eclipses of the sun .• 18 H. The series of lunar eclipses recorded by Ptolemy in the Almagfst irj HI. The Arabian observations liy Ebn JouNis 20 IV. Observations by Europeans before the invention of the telescope 21 V. Observations made with the telescope, but without a dock 22 VI. Observations of IIevei.ius 23 VII. Observations approaching the modern requirements in respect to precision 23 VIH. Observations since the time of Bradley 2.) Conclusions respecting the determination of the secular acceleration 25 § 3.— DISCUSSION OF NARRATIVES OF ANCIENT TOTAL ECLIPSES OF THE SUN .... 27 1. The eclipse of Thales 2S 2. The eclipse at Larissa 30 3. The eclipse of Xerxes 31 4. The eclipse at Athens • 32 5. The eclipse of Ennius 33 6. The eclipse of Aoathoci.es 33 7,8. Other ancient and mediajval eclipses 34 §4.— THE PTOLEMAIC ECLIPSES OF THE MOON RECORDED IN THE ALMAGEST 35 Accounts by Ptoi-emv. accompanied by translations 35 Tabular data for eclipses of \he Almagisl 41 Equations deduced from the Ptolemaic eclipses 43 Resulting corrections to Hansen's tabular mean longitude 44 § 5.— ARABIAN OBSERVATIONS OF ECLIPSES, FROM CAUSSIN'S TRANSLATION OF EBN JOUNIS 44 Observations at Bagdad and Cairo 45 Tabular positions of the moon and the sun for the Arabian observations 51 Comparison of tabular and observed times for the Arabian observations 52 Results of the comparison with Hansen's Tables 54 g 6.— MODE OF DEDUCING THE ERRORS OF THE LUNAR ELEMENTS FROM OBSERVATIONS OF ECLIPSES AND OCCULTATIONS 55 §7.— EFFECT OF CHANGES IN THE LUNAR ELEMENTS UPON THE PATH OF THE CENTRAL LINE OF AN ECLIPSE 68 §8.— OBSERVATIONS OF BULLIALDUS AND GASSENDUS 75 Approximate positions of stars for clock-error 76 Observations of Bullialdus 77 Eclipses and occultations observed by Gassendus 79 § 9.— OBSERVATIONS OF HEVELIUS] 88 Position of Hevelius's observatory 88 Observations/romjhe Machtna Coelesiis 88 Observations from the /4»nKr C/tm«'/y IJKl.lsl.i' al ni iiiai ilic LiiMMiilinr^ . . Series IV.— Ohservatlons by llic Cassinis and the Makai Ills . . . Invesligalion of corrections tii the I'aris i|iiadraiit, 1706-1758 Series v.— Observations In 1)11. isiK at St. J'etersliiirg -I'OSITIONS ol' llli: MOON I'ROM IIANSKNS TAHLES. USED IN COMPARING THE PRE. CEDINC OUSERVATIONS WITH THEOUV (I) Omission ol terms unimportant on account of tlu^ir minuteness (21 Modilii.alions when many places of the moon are to lie coniimted 131 Terms of loiij^ period produced by Venus Table of correctioiis of the arguments of Hanskn's Tables for terms of lo Tabular positions of the moon Observations by Fl.AMsri;i-,i) Clock-corrections — Fi.amstki.d Longitudes and latitudes of stars for tSfo "K per: i.-DETAILS OF REDUCTION OF THE OCCl'LTATIONS . . . Tabular exhibit of reduilion of the occultations Occullations obscived bv Hui.I.lALDUS Casskndus IIkvkmus at Uant/.iK the Cassims and others at the Paris Observatory LaHirk Cassini, Ki'c.^Scries II Dki.isi.k at Luxembourg Dklisie i.t St. Petersburg Fi AMSTKia. at Greenwich od 13.— EOUATIONS OF CONDITION CiVEN BY THE PRECEDING OCCULTATIONS OF STARS l>rors to which the equations are liable Provisional solution of the iipiations 14.— OBSERVATIONS OF KCLIPSKS FROM 1620 TO t Longitudes of the sun from II ANSI n's Tables . . . Details of reduction of the eclipses Total eclipse of 1715, May 2-3. as observed in England ■24 SI5' -DISCUSSION OF DEVIATIONS IN THE MOON'S MEAN MOTION Individual corrections to the mean longitude of the moon .... The same, graphically interpolated Equations of condition from all the observations Changes in the earth's rotation which will represent deviations . Representation of observations by a periodic term Table of corrections to Hansks's mean longitude from 1620 to 1900 (Comparison of this table with observations ; lb.— MOTION OF THE MOONS NODE Path of moon's shadow over England during the total eclipse of 1715 Correction to motion of moon's node Vtge. 116 I If) IlS 130 131 148 156 156 I7f. 180 i8g 189 I go 192 196 303 303 203 205 206 206 206 207 210 2tl 313 316 317 221 223 223 231 236 236 237 257 261 261 263 264 265 266 268 269 270 270 274 S 17.— CONCLUDING REMARKS ON THE VALUE OF THE SECULAR ACCELERATION DEDUCED IN THIS PAPER 274 RESEARCHES ON THE MOTION OF THE MOON. Paut I. DISCUSSION OF OliSERVATIONS MADE PRKVIOIIS TO 'IMFK YEAR 1750. IIISTOUICAL INTRODUCTION. In all tlioorlcs of the moon before the beffiniiing of the last century, tlio moan motion of that body was su])[)osc(l to be uniform. The fir.st inequality discovered was the secular acceleration. While the general proposition that a comparison of ancient and modern eclipses shows the mean motion of the moon to have increased since the time of I'TOLKMy is no doubt duo to IIallky, I believe the first careful determination of its amount is that by Dijntiiokne.* Going backward, in the order of time, ho com- pares his tables of the moonf with the following eclipses: — Those of TycHo Braiie in his Progymnusmata ; Those of Waltheb and REaiOMONTANCS (A. D. 1478-90) ; . Two of the Cairo eclipses (A. D. 977 and 978) ; Tlio eclipse of Theon (A. D. 364) ; The eclipses of Ptolemy. The first of these series of eclipses was too near his epoch, and the second too unreliable, to predicate anything certain upon. From an examination of the others, he concludes that the observed times will be best satisfied by supposing a secular acceleration of 10" in a century. Soon afterward. Tonus Mayer deduced an acceleration of 7" from the eclipses of the Almagest, which value ho is said to have used in his earlier tables of the moon. The subject is next discussed by Laland in the Memoirs of the French Academy " /'////. Tmns., No. 492, p. 162. t These tibles were probably those published in 1759 ( f-ALANDR, Biblhgmphie A$tn»tom\que, p. 410). I know of no copy of them in this country, 2 '75Ap. 2 lO RESEARCHES ON THE MOTION OF THE MOON. of Sciences f'n" the yoiir 1 757. Like liar.LiVLDus ami others of his conntiynion, lie has grave douLts of the honesty Avith which i'i'OLEMY lias given the times of his eclipses, ami therefore uses only the fiist of the series, that of — 720. He adds the two ecl'pses observed at Cairo by Ebn JouNis, A. 1). 977 and 978, and reported in the introduction to the Historia Coelestis of Tycho Brake, and thence concludes that the secular accel- eration is about 9".886 per century. Tlio next event in the history of the problem is the discovery by Laplace of the physical cause of the acceleration, and his calculation of its amount, which he fixed at very nearly 10". The exact agreement of this I'esult, and also that of Plana, with those derived by Dunthorne and Lalande from observations, seems to have satisfied the next two generations of astronomers that no more exhaustive discussion of the ancient eclipses was necessary. We find an acceleration scarcely differing from 10" adopted in all the L;inar Tables between those of Lalande and Hansen. I am not aware of any investigation having in view a definitive determination of the secular acceleration from observations alone during the century following Lalande's paper. We have, it is true, two important papers by Zecii in a series of memoirs published at Leipsic under the general title Preisschrijlcn gelront und hcrausfjcffehcn von der FiirstHch JahJonowskischcn Gc- sdlschaflzu Leii)zig. The two papers are: — III. J. Zecii, Aatrommischc Untcrsuclnnigcn iihcr die MomJ/imteinisse des Almagest. Leipzig, 185 1. IV. J. Zech, Astronomisclic UtitersHchmigen iihcr die wicldigeren Finstcrnisse, tvelche von den Schrijistellcrn des classischcu Altcrthmns crirdhid werdcn. I^eipzig, 1853. The first of these papers has formed the basis of all the late discussions of Ptolemy's eclipses; but the author finds these eclipses inadequate to give any deter- mination of the moon's secular acceleration, a result which arises from his including the correction of the moon's mean motion, as Avell as of its secular acceleration, in his equations of condition. If we determine the mean motion, not from the modern observations alone, but from a comiiarison of the latter with those of Piolemy, it is evident that we shall have no accui'ate data rem.aining with which to determine the secular accelei'ation. In 1853 appeared the celebrated paper of Adams, whit'h showed that the theoret- ical value of the secular acceleration found by his predecessors needed a large diminu- tion. This was followed by several accurate calculations of its amount by Adams himself and by Delaunay, the latter finally fixing it at 6". 176.* I conceive that no rational doubt can remain that this result represents the true effect of the gravitation of the planets within a small fraction of a second. In con.structing his Lunar Tables, Hansen introduced the coefiicient 1 2". 1 8, founded on a theoretical computation. A revision of his calculation, leading to a slightly greater result, namely, I2".557, is given in his Darlegung der theoretischen Bcrechnung der in den Mondtafeln angewandten Storiingcn (ii, p. 374). About the time of publica- tion of this work, Hansen wrote that he had never disputed the con-ectness of the result of Adams and Delaunay, and defended his result rather on the ground of its • • diHflts Ktndiis, 1871, i, tome 72, p. 495. RESEARCHES ON THE MOTION OF THE MOON. II representing uncieitl observations than on its theoretical correctness.* It can therefore scai-cely be cited as tending to invalidate the resnlts readied by these investigators. It has long been recognized that there was no necessity for an agreement between the values of the acceleration derived from theory and from observation, becatise a retardation in the earth's motion of rotation would produce an apparent acceleration in tlio motion of the moon, and the friction of the tides must produce such a retardation. The original discovery of this principle is attributed to Mayek; but it would seem to have been lost sight offer nearly a century, when it was taken up again by Fkrrel, with- out any knowledge of Mayer's work. Ferrel's first paper was i)ublished in 1 853 in vol. iii of Gould's Astronomical Journal. It contains the first known attempt to calculate from theory the rettirdation produced by the action of the moon on the tidnl wave. Assum- ing that the tide caused by the moon in the open sea is two feet in heigi lul that it is highest two hours after the moon passes the meridian, he finds that, if the ocean covered the earth, the equatorial retardation of the latter would amount to 50 miles in a century. Deducting one fourth for the hand surface, he finds the retarding effect of the moon alone to bo 37.44 miles in a century, and the combined effects of the sun and moon to be 44.45 miles. If the earth were really retarded by this amount, an apparent secular acceleration of the moon amounting to 84" in a century Avould be produced. As no such acceleration is observed e.\cept what is otherwise accounted for, he con- cludes that this effect of the sun and moon must bo nearly balanced through the gradual contraction of the earth by loss of temperature. After the researches of Adams and Delaunay, and the general concession of the correctness of their results, Ferrel returned to the subject in a paper on The Influence of the. Tides in causinfi an Apparent Secular Acceleration of the Moon^s Mean Motion, read before the American Academy, December 13,1 864.! Reversing the process of his former paper, ho finds that the unaccounted-for a2)parent secular acceleration of 6" cor- responds to a mean retardation of the tidal wave of 8 minutes, or to a retardation of 10 minutes if we suppose the earth to be cooling according to FouRuui's theory. Two or three years after these papers by Ferrel were published, but before they became known in Europe, Delaunay read a 2)aper before the French Academy of Sciences on the same subject, — Sur Fexistence cVune cause nouvelle aijant ime influence sensible sur la valcur dc Vcquation seculaire de la lune.X Here the distinguished author demonstrates the retarding influence produced by the attraction of the moon on the tidal wave, following a course of reasoning similar to that of Mayer and of Ferrel. It was through this paper that the subject was first brought prominently into notice arid discus&ion. Since in the action of the moon and the cooling of the earth we have two known causes which produce a secular variation in the mean day, the accurate effect of which cannoi; be computed deductively, it will probably not be disputed tliat the real result to be derived from observation is, not the acceleration of the moon's mean motion, but tlie retardation of the earth's rotation on its axis. Although tlie j)henomenal effects * Monthly A'olices, A'. A. S., vol. xxvi, p. 187. Tliere is a sliort discussion of this subject by Hansen in vol. xv of licrhhte lii'r Kimii^Uch Siiilniuhut Gi'sclisc/ia/l dir IVis' •schafloi zii Lcifzig, Leipzig, l86j, in which he discusses tiilal retarda- tion, and defends his coelUcicnt on the grounds above indicated, t J'nvmiiiigs of tht American Academy i>/ Arts anil Sciences, vol. vi, p. 379. t C'o/«//i'j' AV»(/«J, tome Ixi, p, I02J, December II, 1865. la RESEARCHES ON THE MOTION OF THE MOON. of these two causes are nearly identical, they are not absolutely so. The longitudes of the sun and of the lunar perigee and nodes will, in fact, be affected by a secular inequality when expressed in terms of a variable unit of time. The effects of these apparent inequalities are, however, too minute to admit of detection by observation for a long time to come. From what has been said, it will bo seen that the value of the secular acceleration adopted in Hansen's Lunar Tables can hardly be considered as having any sufficient H priori foundation. It was not determined from observation at all, but from theory; and the theory was so incomplete as to give a result double that which would have been given by a complete one. If, then, the result agrees with observation, it can only bo because tho effect of the omitted terms chances to bo the same as that of the earth's tidal retardation. Whether they are the same is a question to bo settled by observfitions, especially by those of ancient eclipses. The first of the recent discus- sions of ancient eclipses having this object in view was made by Airy. In the riiilosopMcal Transactions for the year 1853, he has a paper On ihz Eclipses of Afjathocles, Tliales, and Xerxes. Tho feature of this paper of most interest at tho present time is the historical discussion of tho circumstances of each eclipse, more especially of tho localities in which it was observed to be total. Tlie computations are made from I)e Damoiseau's Lunar Tables, with the iipplication of the corrections result- ing from the Greenwich observations, and are, for the purpose in question, supereeded by a subsequent paper. Shortly after the publication of Hansen's Lunar Tables, Airy returned to tho subject in a paper On the Eclipse of Atjafhocles, the Eclipse at Larissa, and the Eclipse of Thales. With an Appcmlijc on the Eclipse at Stiklastad, in the Memoirs of the Itoi/al Astronomical Society, vol. xxvi. Hero he niakes use of the places of the moon calculated by Hansen from his tables, and of places of the sun from Han- sen's Solar Tables. He considers the following conclusions fairly deduciblo from his investigation: — 1. Tlie eclipse at Larissa, — 556, May 19, is established as a real eclipse at a well- defined point, and may bo adopted for critical reference in deciding on the value of lunar tables, as applicable to distant places of the moon. 2. Professor Hansen's Tables very well represent the phenomena of the three eclipses of Agatuocles, Larissa, and Tiiales, as far as we can interpret the historical accounts of these eclipses. 3. If any change is permitted in tho two elements of secular ace jloration of lon- gitude, and change of tho argument of latitude, it must be in the nature of increasing the acceleration, and increasing tho argument of latitude in the distant ages. The eclipse at Stiklastad is discussed in the addendum to this memoir. Han- sen's Tables throw the limit of totality in tho case of this eclipse about a hundred mil'^s south of Stiklastad. To make the eclipses of Stiklastad and Larissa central, it is necessary to increase Hansen's secular acceleration by o".8o9, and his argument of latitude by 49" X uumber of centuries preceding 1800. Hansen's sidereal accelera- tion being 12". 18, this correction increases it to I2".99. The effect of these coitoc- tions is said to be to throw the shadow-tracks of the eclipses of Aoathocles andof Tiiales to the north, and nearer the points over which the historical evidence seems to RESEARCHES ON THE MOTION OF THE MOON, 13 indicate tliat they passed. In the opinion of tho author, a strong prosuniption is thus produced in favor of their reality. A comparison of Ptolemy's series of hmar ecHpses, as discussed by Zecii, with Hansen's Tables, has been made by Hautwig, and published in tho Astronom'ische Nachrichten, Bd. 60. A clear tabular summary of his results is i)rinted in tho Month! if Notices of the Royal Astronomical Society, vol. xxvi, p. 185. The nineteen eclipses indicate a sensible negative corx'ection to the secular acceleration, the mean being — I ".9. Only three out of the nineteen give the correction positive ; find, if we regard the series as consisting of observations really independent, the i)robablo error of. this result cannot be more than o".4, and its reality would therefore bo beyond doubt. The result of these eclipses may therefore be regarded, from this point of view, as incompatible with that derived by Airy from eclipses of the sun; but the stops of tho investigation are not given with sufficient fullness to enable us to judge of the reliableness of any conclusions which might be drawn from it. It will be seen from tho foregoing that the only approach to a definitive answer to the question the question what value, &c., what value of tho secular acceleration is deducible from observations, is to be found in the papers of Professor Airy. If we accept the three most ancient eclipses which he has discussed as all undoubtedly total, then scarcely any deviation from Hansen's value of the secular acceleration seems admissible. But I cannot conceive that the historic evidence bearing on tho subject places the phenomena of totality so far beyond doubt that a discussion of other data is unnecessary. Such a discussion is the more necessary because it has been known, since the time of liAPLACK, that, in addition to the uniform acceleration of which we have spoken, the mean motion of the moon is apparently affected by inequalities of long period, in the satisfactory explanation of which geometers and astronomers have alw.ays found diffi- culty. The first discussion of such .an inequality is, I believe, that of Laplace, in Mecanique Celeste, 2* partie, livre vii, chap, v, under the title Sur une inegdite a longue periode, qui paroit exister dans le motivcmcnt de la lime. Tho discussion is mainly emi)irical, the existence and magnitude of the inequality being inferred from observa- tions which showed that the mean motion of the moon during the second half of the eighteenth century was greater than during the first half. It was then assumed that tho inequality Avas a periodic one, due to the fact that twice the motion of tho moon's node, plus that of its perigfee, is a very small quantity. Tho value of the coefficient concluded from the observations was 47".5i, and the expression for tho resulting inequality was 47".5i (=i5".39) 8in(2a5 + ;r])-3TO). . Using Hansen's notation for the lunar elements, namely, 00 for the distance of the moon's perigee from its node, and oa' for the distance of the sun's perigee from tho same node, tho inequality would be I5".39 sin ( <»-3 a>') = i5".39 sin {173° 26' + (i'^ 57'.4) (t- i8oo)l. RESEARCHES ON THE MOTION OF THE MOON. The following' table shows how the observations on which the inequality was predicated were found by Laplace to be represented by it: — Date. Cor. to Lalande's Corrections hy the Error out- Tables per Obs. Formula. standing. i6gi • - 13.58 — 11.48 + 2.10 • 756 0.00 + 2.10 + 2.10 1766 — 9.26 . - 9.54 — 0.28 1770 - 28.09 - 32.93 - 4.84 1789 - 54*3* - 55.5a — 1.20 1 801 - 87.96 - 85. 86 + 2.10 The tables compared with observation were those in the third edition of Lalanue's Tra'tte iV Astionoiuk. The complete formula for the correction of their mean longi- tude, as deduced from the comparisons in the second of the above columns, was — 39".44 — 98".654 i + 47".5 1 sin (<» — 3 t»') ; * being the number of centuries after 1750. It would seem that Laplace was by no means satisfied with this explanation of the cause of the inequality, as he afterward favored the hypothesis that it was due to an unequal compression of the southern and northern hemispheres of the earth. He found from theory that such an irregularity in the confonnation of the earth would produce an inequality in the moon^s mean motion depending on the same argument* except that the equinox would' have to be substituted for the sun's perigee, and the function cos would have to be substituted for sin. But a careful analysis afterward showed him that this cause was inadequate, the inequality in question being insen- sible on any reasonably admissible supposition of the constitution of the terrestrial spheroid.* The question was next taken up, from a theoretical standpoint, by Poisson, in his Memoire sur le mouvement de la lune autour de la terre, in the Memoires de V Academic des Sciences, tome xiii, pp. 209-325. It occurred to this geometer that Airy's inequal- ity of long period in the motion of the earth due to the action of Venus must involve a corresponding inequality of long period in the eccentricity of the earth's orbit, and must thus produce a corresponding inequality in the secular acceleration, and thence in the mean longitude of the moon ; but the computation of the inequality showed it to amount to only two hundredths of a second. In his account of this memoir, pub- lished in the Connaissance des Temps for 1836, p. 61, Poisson remarks, " II est facile de s'assurer que Taction directe des plan^tes sur la lune, ne kaurait non plus donner lieu, dans le mouvement du satellite, fi aucune indgalitt? de longjie pdriode." He shows that the coefficient of Laplace's first inequality is absolutely zero, at least so far as the terms of the lowest order are concerned. The hypothe .is of an inequality in the length of the sidereal day he also considers entirely inadmissible. He hence concludes that no inequality of long period should be admitted in tables of the moon founded on * CoHHaissamt des Ttmps, 1823, p. 239. RESEARCHES ON THE MOTION OF THE MOON. 15 theory. As to the existence of such an inequality, lio thinks the ohsorvations are too uncertain to ostablisli it. It was reserved for Hansen to show that an inequality of long period did really result from the theory of gravitation, and that it was due to the direct action of a planet.* He first computed Laplace's inequality, and, like Poisson, found that its coefficient was entirely insensible ; but on developing certain terms in the action of Venus on the moon, which Laplace and Poisson had too hastily supposed to be insen- sible, he found the following inequality in the moon's mean longitude : — 61 = i6".o sin i-g - 16 1)hoi'V(mI. Tlio iiltitutlos aro ^'ivou somotinios in wluilo (li>(,n-eo8 only, BOinetiiiieH in coarso fractictus <»f' a (U'<,'reo. If tlioy wcro always f^ivt-n to tiio really uoarcst outiro degree, so as to l)o aH't'cteil with a probaMo (;rror of only liftccn min- utes, the corrosponding error in the moon's mean longitude would average aliout forty or fifty 8ec(uuls of arc, arul would therefore he very suuiU in the mean of all tho observations. Tho most serious .source of error is that already alluded to, — tho uncer- tainty how long after tho first contact the eclipse was first perceived and tho altitude taken, and lutw long before the actual end it was lost night of. It is not of much uso to guess these quantities until wo discuss tho observations; but 1 hope that tho prob- abla error of tho mean of all tho observed times can be rediu-ed to 1(^>^H than two minutes, so that the probable error of the moon's mean longitude will be not more than a minute of arc. IV. Observations hy Enroiwans before the invention of the teleseope. liefjiomnntanus and Walther. — So far as I can learn, we have nothing that can l)roperly bo termed astronomical observations of eclipses between those of tho Arabi- ans and those of Keoiomontams and WAi/ruEu in tho latter i)art of tho fifteenth century, ily authority for them is a volume containing two works, piiged sei)arately, under the respective titles: — (i) Cocli et Siderum in eo crrantiitm observntioncs Jfassiacac illustrisaimi prinriina WUhehni Ilassiae, landf/ravii aiispiciis quondam institidae et spicileyinm biennale, ... qitibiis accesserunt Joannis Begiomontani et Bvrnardi Waltheri observationcs Nuribergicae. Litgduni Batavorum, 1 6 1 8. (2) Johannes de Monte-Bcgio, Gcorgii PHerbarhii, Bernardi Widtheri ac alionini, eclipsium, comctarmn, planetarum ac fixarum observationes. . . . These observations belong to the same class with those of the Arabians, namely, altitudes of the sun or moon at the times of the beginning or ending of tho eclipses, and do not seem in any way more trustworthy. The telescope not being known, tho same uncertainty must rest over the question of the exact phase at which the eclipse became visible or disappeared from view. Tho altitudes are given only in coarse fractions of a degree. The epoch being less than half as remote as that of the Arabian observations, the coefficient of secular acceleration will not be ono fifth as groat. For this reason I do not consider those observations worth using at all. Tycho Brahe. — The observations of Tvcuo follow those of REdiOMONTANis by about a century. The confused manner in which most of the works of this astron- omer have been edited and published makes exact researches into their subjects rather difficult, and it is the less necessary to present any such researches that I have de- cided to make no use of the observations. I have been led to this course by the fol- lowing considersitions. The telescope was unknown to Tycho. Granting that the most careful observations were made by him, the probable constant error of contacts observed without a telescope, and, without any means of determining the smallest amount of impingomont of the moon on the sun or of the earth's shadow on the moon which he could see, can hardly be estimated at much less than 20". A number of accurately determined times of contact would be necessary even to reduce the error to this amount. After devoting considerable time and labor to an examination of what i)ur- 22 RliSKARCHES ON Tllli MOTION OK THE MOON. port to bo tlio obsorvationH of Tvciro, both tbo«e printed, aiul thoso in nmnuHcript at tlio Paris ( )bs»'rvatory, I waH scarcely ablo to find what (•(»uld bo ro>;ardod an nc(Uirato and roliablc oltscrvationH of edipHCH. In tbo I'mfffniuasmatu, tlioro is .. hoHch of Honio Hiirty «(dar and hmar c«dipHo.s obseived by liini bctwoon 1572 and .600. Only a sinjflo tinio iH {fiven for eadi otlipHO, and from a comparison w;*! tho Uistoriu Corkfitis it may 1)o conjt'citurcd that tlioso aro tho timos of greatest phaso. Comparing tlio datoa in tliis Horit'rt with tho ol)sorvntions, winch aro arranged in chronological order, only some of tho later eclipses were to be fonnd at all. Among these few I fonnd scarcely an muMinivocal poraries on tho continent. A partial drawback to these advantages is that his clock- error was not determined often enough, nor near enough to tho times of observations* Another weak ])oInt, which is also a mark of IIeveliu.s'8 observations, is that ho never seems to havo had tlie idea of eliminating any possible index-error of his quadrant by altitudes on opposite sides of the meridian, but would, month after month, if not year after year, determii.j nearly all his clock-errors by observations in the cast alone, or tho west alone. An estimate of tlieir probable error would therefore bo such mere guesswork that I shall not attempt it. The Paris astronomers. — With the foundation of the Pains 01)sorvatory, a yet far- ther improvement was made in the art of determining the time, and one so great thijt the observations of occultations made there between 1680 and 1720 arc frequently comparable in accuracy wit'i those of the present time. The mode of determining tho clock-correction was substantiaii} as follows : — A quadrant, gnomon, or meridian-mark was set as nearly as practicable in the plane of tho meridian, and was left undistiu'bed in position during long intervals. With this instrument, the clock-time of meridian 24 RESEARCHES ON THE MOTION OF THE MOON. transit of eai-li limb of the sun was assiduously observed on every day that the weather permitted. The clock-time of meridian passage was also determined from time to time by equal altitudes of the sun on the two sides of the meridian, observed with a quad- rant. The time deduced from the equal altitudes being compared with that deduced from the meridian passage gives a correction to the meridian-instrument applicable to the particular altitude of the sun on that day. The correction being founcl for various altitudes of the sun, its v.alue for any particular altitude may be found by a curve or by interpolation, and thus the correction for each day may be deduced. From the general accord ^nce of the different results for clock-error and for the correction of the meridian, as well as from the discordance of independent observations of the same occultation, it may be inferred that the probable error of a time well deter- mined in this way was not more than two seconds, corresponding to an error of i" in the moon's longitude. This is so small that it does not exceed the probable error aris- ing from the irregularities of the moon's limb, wliicli, from a comparison of occulta- tions observed at various places, would seem to be nearlj'- i". The probable error of the position of the moon's centre will therefore vary from i" to i".4, according to the point of the limb on which the occultation was observed. The probable error of the star places and of the tabular jjerturbations is larger than this, and may bo expected to increase the probable error to 3". After gleaning out all the uncertain observa- tions, we shall have the equivalent of more than sixty good occxdtations observed at the Paris Observatory between the years 1680 and 1720. These ought to give the mean longitude of the moon for the epoch i 700 wltliout a probable error of more than o".6. Of the same class of observations here described are those made by Delisle at St. Petersburg between the years 1724 and 1748. In fact, during the interval 1720 to 1 753, we have an average of nearly one good occultation per y ar at St. Petersburg and Paris, so that the mean longitude of the moon can bs fixed during this interval within one or two seconds of arc. * VIII. Observations since the time of Bradley. From the year 1750 to the present time, we have a nearly continuous series of occultatlons and eclipses, observed with a high degree of accuracy at observatories whose positions are well known, notably those of Greenwich and Paris. Of course, these observations become more and more numerous as we approach the present time. Let us next Inquire how accurately the mean motion of the moon can be determined from these observations. I conceive that between the epochs 1780 and 1820 we shall find at least 1 50 well-observed occultatlons. If we omit a third of these as being cases where the star was too far from the line of motion of the moon's center to give a good determination of the moon's longitude, we shall have 100 left suitable for this determination. If we take the probable error of each longlfudc derived from a single occultation as 2".o, which I think is not far from the truth, the piobable error of the moan of all will be o".20, and the epoch will be about 1800. Allowing for systematic differences between observers, it may be increased to o".30. Again, from the more numerous observations on l^oth sides of the epoch 1875, wo may hope to obtain the moon's mean longitude for that epoch with the same precision. By a comparison of RESEARCHES ON THE MOTION OF THE MOON: 35 the two, the moon's mean motion during' the first seventy years of the present centmy will bo obtained, with u probable error of o".4, the corresponding epoch being 1837. The two epochs compared, conjoined with the observations between 1820 and 1850, will give the mean longitude for '837 with a probable error which, for our present pur- poses, may be regarded as insignificant. Now, suppose that, with the moan longitude and mean motion thus determined, we carry back the position of the moon to the epochs of the observations previous to 1 720, and, considering the difference as due solely to the secular acceleration, determine the latter from the comparison of the observed and computed longitudes, what will be the probable errors of the several results ? The probable error of the computed mean longi- tude will be, witli sufficient approximation, o".6 T; T being the number of centuries from 1837. If we represent by c the probable error of the mean longitude derived from observation, the probable error of the comparison will be Vo".36r' + e', and the prol)able error of the value of the secular acceleration deduced from the com- parison will be Vo^.36":PTe« _ The values of the several (|uantities which we have estimated for each series of observations or other data are given in the following table, the last sorie^ of num- bers being the probable error of the secuLar acceleration which would result from a comparison of tlie observations with a lunar theory derived from observations between 1780 and 1875. D."ta or observers. T. 1 £. Ptolemy's eclipses Arabi.in eclipses Bi'Li-iAi-Dus and Gasskndus . . . Hevei.ius Paris and Greenwich astronomers . 21.4 200. 8,3 60. 1.95 I 5- 1.6 3. 1.35 i 0.6 0.4 0.8 1.3 1.0 0.6 From this reasoning, we may draw the following conclusion:— (?/•««, the Medes. And, in this time, tliey also bad a night engage- ment; for as they were protracting the war with equal success on each side, in a battle that oc- curred in the sixth year, it happened, as tbe armies engaged, that tbe day wa^ suddenly turned into night. Now tiiis change of day [into night] Tualks, tbe Milesian, bad predicted to the louians, placing as tbe limit of the period [within which it would take place] this very year in which it did actually occur. Now, both tbe Lydians and the Medes, when they saw night coming on, instead of day, ceased from battle, and both parties were more eager to make peace with each other." 1.— THE ECLIPSE OF THALE8. (-584,M.iy28.) The account by Hekodotits is as follows. Professor Huntinoton's translation is annexed: — Hd., i(KA.), 74. J/iT« Ss TUUTa {lit) yap Sij i 'i^Aodrrijf iisSiSiiu Ttih^ ^xiiOa^ i;aiTiiii>Ti Kua^d/Jti) i:iiXsixoj Toiat Auihitirt xai TiiiiTi .Vijdi)iiri iysyi'ivss ii: e'rsa TthTV iv TnXm noXXiUt^ iiiv III M/jHiii Tiiui AuSiih; IvixT/aav, itnkhUi-. lik iil Auii,i\ Tiih; )fij3iiui' Iv St, xtt\ vyzn(//a;fi'ijv Tmii iKiiirjaanTii, SiaifipuoiTi Si iripi 'si j'lrijT tov KiiXs'iiiv, tui Sxtio srsi (Tuii^idrji j-si'd/i^vjjj, iTU'^rjvstxs were r^? /J"'/'iT Toyiirrs- lomjt TifV iiiiiprfV i^anhrji -^uxTa ysviaOat, Tijv Se /j.;ro.X- X.ayr/V Ta'JDjy T^f rjni/ir/^ Sa/.f/i 6 .ViAij'tfii)? riiTiTi "luxii ~piirjdf)iuac liteaOai, imnvv TrpiiOiiisyii^ IvtauTuv tuDtwi/, iv u> St/ xal iyl/sro ij iisTa,3iiXij. iil Ss AuSni re xat iil J//J<5f)! imi re stSov vuxra dvTi ^/lipr/i ytvii/iinrji/, rfj^ l^''X1^ T£ ItsauaavTii, xa\ ixakXi'iv rt earrsuirav xat riiKipi'iTS- put elpijvr^v iwuTinirt yivlirOat, Among the ancient solar eclipses, this is the one which has been the most cele- brated, and has given rise to most discussion in recent times. Yet the proof of its reality seems to me by no means convincing. It is true that we may consider the three following propositions to be individually sufficiently well estabH.shed: — (1) That a battle between the Lydians and the Medes was ended by an apparently sudden advent of darkness, substantially as described by Hekodoti:h; (2) That on May 28, 584 B. C, the shadow of the moon pa.ssed over Asia MinoF, as computed from the tables; (3) That Thales predicted eclipses. But that these propositions all refer to one and the same event I see no sufficient reason for holding. Their connection may well be real ; but its reality is not so well established that I should be willing to predicate anything respecting the changes of the lunar elements upon it. It seems to me that commentators on this eclipse have not sufficiently distinguished between the jjlienomenon as seen by the contending armies, and the conclusions drawn by the lonians that that phenomenon "as what their favorite philosopher had predicted. The simple event, as described by Heuouotus, and as wo may suppose it to have been described by the eye-witnesses, would hardly even suggest an eclipse of the sun, or anything else more extraordinary than the regular advent of night, except for the single word i^aTn'ytj? (suddenly). But, in the ardor of battle, the combatants are apt to be nearly oblivious of the lapse of time, and the gradually increasing darkness of evening might well bo unnoticed for some time, so that, when it at last interfered RESEARCHES ON THE MOTION OF THE MOON. n wltli tho progress of the battle, it would seem to have come on moro rapidly thsin usual. Tiie formation of a very dark heavy cloud about sunset, or shortly after, such a one as is seen fifty times to one occurrence of a total eclipse of the sun in any given place, might render the description literally true. If it be urged that the making of peace indicated something extraordinary or impressive, wo may rejoin that there is nothing in the account to indicate it; that if the phenomenon was really that of a total eclipse, the night must have turned back to day again almost before the fight- ing could stop, a fact which the historian does not mention; and, finally, that the term vvHTOfiaxt'tfy would hardly apply to the case of a battle stopped by a total eclipsa in which tho darkuess lasted only a few minutes and tho battle ('eased as soon as darkness commenced. This view of the naked narrative will not, I conceive, be disputed. TJie evidence in favor of an eclipse rests entirely on the construction put upon the account by the lonians, or some other parties to whose ears the narrative came. It cannot be sup- posed that the combatants knew anything about Tuales or his eclipse, so they cannot be the authority for supposing that the darkness was that predicted by Thales. Our belief in the eclipse therefore rests on our faith that the lonians heard a different story of the battle from that given by Herodotus, and that they put a correct interpretation on the circumstances. In trying to form a judgment whether they did so, we must take into account what we know must have been the nature of the prediction, as well as the narrative of the phenomenon; because it is on the agreement of the two that all the evidence in favor of the re.ality of the eclipse rests. Now, keeping within the limits of historic probability, TuAf.ES could not have had any other data for prediction than a knowledge of the Saros, which gave the order in wliicli eclipses would occur, and, at the most, such knowledge of the motions of the sun and moon as would enable him to judge whether a given conjunction was nearly central, and at what time of day it would occur. lie could not possibly have predicted that tho eclipse would bo total and that day would be turned into night, and could scarcely have decided whether it would or would not have been visible in Ionia even as a partial one. If he coidd predict one, he could predict two or three every year, witliout being able to say with any certainty in what places any of them would be visible. But any such prediction necessarily involves a knowledge of the exact day of occurrence of the eclipse, and thus the only means by which the lonians could identify the phenomenon would be the coincidence of the day of its occurrence with that of the prediction. Now, it is remarkable that the narrative says emphatically that the year was correctly predicted, but makes no reference to the yet more striking prediction of tlie day. Astronomically, we are not directly concerned with the jirediction of Thales, but only with the question whether the circumstance described by Herodotus was really the total eclipse which we know octurred in Asia Minor or its neighborhood, H. C. 584. The prediction is important only for the reason that its mention by the historian fur- nishes the only evidence in favor of the phenomenon being really an eclipse. Another very weak point in the evidence is that we have no historic data for deciding who first drew the conclusion that the darkness which stopped the battle was that of the predicted eclipse. It may have been the lonians, it may have been some writer to 30 RESEARCHES ON THE MOTION OF THE MOON. whose knowledge the occurrences came, and it is quite consistent with the character of Hkrodotus to suppose that it may have been liimself. Since, as we liave seen, th.; identification could only have properly rested on the coincidence of the day of the prediction with that of the battle, and since the historian mentions only a coincidence of year, if we accept the eclipse we must suppose that the most striking and important circumstance was dropped from the narrative during the interval between the identi- fif.ation and the narration by the historian. If the historian himself drew the conclu- sion, without any other data than those he gives and those with which we may suppose him to have been acquainted, then the entire evidence falls to the ground. Let us now consider what we may suppose to have been more or less probable states of the case. Thales is supposed to have been born B. C. 640, and to have traveled into Egypt at an early age, where he learned astronomy from the priests. 'Returning home, he probably applied this, and whatever other knowledge he may have gained from research and observation, to the prediction of eclipses. He may have predicted many eclipses from B. C. 610 to B. C. 584, and longer, as he is said to have lived to a great age. His success in the case of the solar eclipse B. C. 584 gave him a wide celebrity, as we know from the tables that this eclipse was total at no great distance from his birthplace. That he predicted only a single eclipse is highly improbable; that, in addition, this one should prove to be total within a hundred miles of his birthplace transcends all reasonable probability. Some time between the dates we have mentioned, a battle was fought somewhere in Asia Minor, probably very tai ii.'^m the home of Thales, in recounting which some of the participants expressed surprise at the suddenness with which it was stopped by darkness. The story may have passed through several mouths before it reached any one who knew about Thales, and may have been somewhat exaggerated in the narra- tion. At length, it reached the ears of the admirers of the philosopher, who, recol- lecting what he was doing, and knowing that he had predicted an eclipse for that very year, seized upon the story as a confirmation of the prediction. Who these persons were, and in what part of the century which elapsed before Herodotus they lived, we can only conjecture. We can make many hypotheses, on which the probability of the correctness of the conclusion becomes smaller and smaller, xmtil we approach the time of the historian, when it vanishes entirely. Under these circumstances, it seems to me that while the hypothesis of correctness is not an entirely inadmissible one, it rests on too slight a foundation to be employed as a basis for cor- recting the lunar tables. The rejection is farther justified by the uncertainty where tlio battle was fought, and the considerable breadth of the shadow, which leaves us a wide range for central line of eclipse. I shall therefore not make any use of the eclipse of Thales. 2.— THE eclipse at LAIIISSA. The account of this eclipse, as translated by Professor AntY, is as follows : — "When the Persians obtained the empire [of the east] from the Medes, the king of the Persians besieged tliis city, but could not in any way take it. But a cloud covered the sun and caused it to disappear completely, till [i. e. to such a degree that] the inhabitants withdrew, and thus the city was taken. Close to this city was a pyra- RESEARCHES ON THE MOTION OF THE MOON. 4,| mid of stone, i plethrum in breadth, 2 plethra in height Thence the Greeks proceeded 6 parasangs, to a great deserted castle by a city called Mespila, formerly inhabited by the Medes. The substructure of its wall was of squared stone, abounding in shells. The king of the Persians besieged it, but could not take it. Zeus, however, terrified tlie inhabitants with thunderbolts, and so the city was taken." Professor Aihy adds, "It cannot be doubted, I think, that the disappearance of the sun at Larissa was caused by a total eclipse." I confess myself unable to share the confidence of the Astronomer Royal and of Hansen that we have here a total eclipse of the sun. The narratives of these times con- tain many accounts of wonderful occurrences^in which we know that a liberal allowance is to be made for the flight of the imagination; and it is not entirely logical. to accept unhesitatingly all tho?'> statements which we can reconcile with our knowledge, while we reject all others. No doubt, if we knew the day, or even the year, of the event * described by the historian, and found it to be identical with that of a total eclipse, we should be justified in accepting the coincidence without question; but as the uncer- tainty of date increases, the probability of coincidence becomes less and less. If, at an epoch so remote, we have a century to find our eclipse in, we can select any place at random, with a decided preponderance of chances in ftivor of our finding one or more eclipses which, making allowance for the uncertainty of the tables, may have been total at the point selected. It appears that the Astronomer Royal had a period of forty yeai"s to find the eclipse in, and the fact that one was found in this interval may be considered as rendering the hypothesis of an eclipse somewhat probable. Notwith- standing my want of confidence, I conceive the pi'obability of a real eclipse to be greater than in the eclipse of Thales, while we have the great advantages that the point of occurrence is well defined, the shadow nariow, and, if it was an eclipse at all, the circumstance of totality placed beyond serious doubt. 3.-THE ECLIPSE OF XERXES (Zkcii, No. 1). ( — 477 to — 480, spring of year.) ,. . ■ This eclipse occurred during the march of Xerxes against Greece, in the same year in which the battlo of Salamis was foiiglit. The descriptions are found in Herodotus and Aristides. ' ' •" From Herodotus, vii, 37: — "When the army, having come out of their Avinterquarters, in the opening of the spring, fully equipped, set out from Sardis, for the purpose of marching to Abydos; and when they had begun their march, the sun, leaving his seat in the li«avens, was con- cealed from view, and night instead of day came on, though the weather was not cloudy, but was exceedingly clear." From Aristides, Scholiast, ed. Fkommel, p. 222 (cpioted from Zech, p. 39): — "As the king was going against Greece, and had come into the region of the Hellespont, there happened an eclipse of the sun in the east; for it portended to him his defeat, that the sun was eclipsed in the region of its rising, since Xerxes also was marching from the east." If any justification for entire want of confidence in the eclipse of Thales, and in 32 RESEARCHES ON Tl^E MOTION OF THE NfOON. ancient total solar eclipses j^enerally, were required, it is found in the fact that this description cannot be identified with any total eclipse of the sun. Of all descriptions of such eclipses by the Greek historians, this is the one which is, all thin{js considered, most clear and oxidicit. No known natural occurrence but a total eclipse of the sun could give rise to the circumstances described by IIerodotis. The place and the sea- son are clearly specified, and the year is one about which I am not aware that chro- nologists have entertained any serious doubt. The time of day (morning) is obscurely indicated by the account of Herodotus, and clearly stated in that of Aristides; yet the astronomical tables seem to show in the most conclusive manner that no total eclipse of the sun could have been visible at Sardis at that time. I am not aware that any one has given any explanation of the occurrence which will reconcile the statement with the tables. Professor Airy considers the most probable explanation to be that the eclipse was not one of the sun at all, but that of the moon which occurred B. C. 479, on the morning of March 14.* On this theory, the circumstance first to be remarked is that it is clearly incompatible with the narrative. The incompatibility is explained by Sir George by supposing that IlERonoTas was mistaken in the single circumstance of the eclipse being one of the sun, that historian repeatedly expressing himself "doubt- fid on matters of detail which occurred during the movements of Xerxes on the eastern side of the Aegean sea". While, however, such, a mistake as the substitution of the niioon for the sun is quite possible, it must be admitted that the words "instead of day it became night" cannot be thus explained. Tlie explanation, therefore, how jn'obable soever it may be, presupposes so nuich play of the imagination on the part of the his- torian as to render him unworthy of that amount of confidence in matters of detail which would justify our changing the lunar tables to accord with his statements. ZECHt proposes yet another explanation, namely, that the eclipse in question was that of — 477, February 1 6, which, according to the tables of De Damoiseau, was annular at Sardis. If this were correct, it would be necessary to change the usually received date of the battle of Salamis by two years. The question is, however, one of purely chronological interest, because, if the eclipse was not total, no conclusion can be drawn from it astronomically. Tiie accounts of the historians do not enable us to decide whether the annulus was formed at Sardis; hence no conclusion respecting the posi- tion of the central line can be drawn. 4.— THE ECLirSE AT ATHENS. (-430, AugUbt3.) The following is the translation of the description by Thucyuioes, ii, 28: — "But in the same manner, at the new moon of tlie month, — as even in that time alone it seems to be possible for the phenomenon to occur, — the sun was eclipsed after midday, and having assumed a crescent form, some of the stars having also appeared, it again became full-orbed." From the circumstance that stars were visible, there would seem to be a consider- able probability that this eclipse was total. This probability is lessened by the fact that Thucydides describes the sun as having assumed only a crescent form, and by the con- * Philosophical Transactions, 1853, p. 199. "" t Loc. cit., pp. 4c -43. RESEARCHES ON THE MOTION OF THE MOON. 33 sideration that it might have been elsewhere than at Atiiens that the Htars were seen. Still, as the sun must have been a crescent before and after totality, I think thu proba- bility in favor of the totality of this eclij)8e is as great as in the case of any other of those under consideration, though not sufficient to justify the introduction of an equa- tion founded on it. 5.— THE ECLIPSE OP ENNUIS. (-399. June 21.) This eclipse is introduced because some stress is laid upon it by Hansen. The description rests upon the following extract from Cicero, T)e Itcjjiiblica, i, 1 6: — " Ennius scribit anno CCCL fere post Romam conditam Nonis Junis soli luna obstitit et nox." The probability that this ecli})8e was total at Rome does not seem sufficiently great to render it worthy of farther consideration. The tables show that there was a total eclipse about the time of sunset; but I see no reason in the statement (juoted for assum- ing that totality occurred before sunset, or that there was any total eclipse at all. 0.-THE ECLIPSE OF AOATHOOLES. (-309, August 14.) Of all the ancient solar eclipses, this is the one of which the totality may be con- sidered as best established, and to which, therefore, we should have least hesitation in making the lunar tables conform. Unfortunately, there is a doubt whether Aoatiio- CLE8, in his passage from Syracuse to Carthage, went on tlie north or tiie south side of Sicily. The arguments on the two sides are so evenly balanced that the question can be decided by the lunar tables alone. This renders the point where the eclip.se was total so uncertain that the eclipse itself is of little use. By a singular fatalit}", the admissible limits of the position of Aoatiioclks correspond almost exactly to those of the limits of the moon's secular acceleration. The shadow was unusually broad; and between the two extreme hypotheses, ( i ) that Aoatiiocles was south of Sicily and the centre of the shadow south of his position by its semidiameter, and (2) that he was north of the island and the centre of the shadow yet farther north, all intermediate ones are equally possible. While, therefore, we may be justified in making it a test of the cori'ectness of the lunar elements that the computed shadow should fall between these limits, we cannot determine those elements from it. 7.— ECLIPSE OF -217, FEBRUARY ii. I was led to consider this eclipse from a statement respecting it by Ricciolus, wiio says {Alnmgestum Novum, p. 365), "Addit Silius Italicus densas fuisse & immensas tenebras in Calabria & subductam esse diei lueem." But, on referring to the original authority, we find the eclipse 'to become indefinite. The lines alluded to occur in describing the wonders which preceded the battle of Cannae (viii, 634), and are: — "Quaesivit Calaber, subducta luce repenle Immcnsis tenebris, & terrain & litora Sipus : Obseditqui" frequens castrorum limina bubo." I find that in this eclipse the central line was far down in Africa, so that it may be dismissed with but a single reflection. If so great a misapplication of the words of a narrator can be made by an astronomer of the seventeenth century, what are we to expect of the aacient historians, and especially of Herodotus I 5 75 Ap. 2 34 RESEARCHES ON THE MOTION OF THE MOON. 8.— A. D. 360, AUGUST 2^. This iw No. 16 in Zkcii's Imt, and, from tlie (leHcription given by Am,mianus Mak- (JELLiNua, would iippeiir to have been total in Eoos. But the tal)le8 show the ecHpso to have boon annular, so that we can deduce nothing' from it. MEDLKVAL ECLIPSES. Boloiigiug to the same class with those we have cited, but too modern to be deci- sive of the (piostion of the moon's secular acceleration, are the eclipse of Stiklastad, A. D. 103c, and the total eclipses in which the shadow of the moon passed over Central Europe in the years 1140 and 1143. The last two have been very (larefully discussed, and many j)oints at which the eclipse was total determined from the chron- icles of the times, by Cei.oria of Milan in his two papers* published in Memoric del It. Istituto Lombardo di Scienze e Lettere, vol. xiii. The preceding list includes, so far as the writer is aware, all the ancient solar ecli[)se8 which have been considered total at any definite point of i]io earth's surt'ace- The general conclusion to which, we are led is that there is no one of these eclipses which we can feel reasonably confident was total at a definite point. The p:'oi)ortion of the eclipses which wo know from the tables must have been annular, or, at least, which were not total at the points to which they are referred, is so great as to destroy any confidence which might have been felt in tiie others. Still, if one value of the secular acceleration should represent them much better than another, it cannot be denied that this fact might militate a little in favor of that value which 1)est repre- sented them. While this ct»nsideration cannot aid us in determining the value of the secular acceleration, it may help us in deciding which of several competing values is the mo.st probable. To enable the reader to judge of the application of this teat, I arrange the eclipses in what seems to me the order of probability of totality, judging from the narrative atone, adding the place where each was supposed to be total (i) Eclipse of Agathocles, —309. Total in or near Sicily. (2) Eclipse of Xerxes, —479 1 (3) Eclipse, —430. (4) Eclipse, -f 360. (5) Eclipse of Xenophon, —556. (6) Eclipse of Thales, — 585. (7) Eclipse, Total at Sardis. Total at Athens. Total at Eoos I Total at Larissa. Total in Asia Minor. Total in Sicily. + 334- Of these seven eclipses, the second cannot be identified, while the fourth and seventh must have been annular. We have therefore only four left to test the tables. Of these, the eclipse of Agathoules, the only one in ^hich I can regard the fact of totality as well made out, allows a range of several seconds in the secular acceleration The uncertainty of the remaining three, that at Athens in the year — 430, and those of Larissa, and of Thales, has already been discussed. Altogether, it does not seem, to me that much light will be thrown by these eclipses on the question of the moon's secular acceleration. It seems to me that the most logical course is to obtain the secular acceleration of the moon from other data, and then to undertake the discussion of the historical evidence anew. • (I) SuWEclissi Solate Totale del 3 Gingno 1239. (2) SugliEclissi Solari Tetalidtl 3 Oiugno 1239 e del 6 Otloire 1241. RESEARCHES ON THE MOTION OF THE MOON. 15 TflK PTOLEMAIC BOFilPSBS OP TRR MOON REOORDBD IN TFIR ALMAOEST. Tlio most comploto diacusHioii of theHO eclipses is that of Zkcii, alroaily quotod, in whidi, however, tlie treatment is such as not to lead to any definitive lesnlt. Zf.cii's (-(mi- parisons were made witli the tables of De Damoiskau, IIanskn's tables Ijcinj^ still nn- iinished when his paper was pre])ared. My general plan of i)roceodin;f is this: — From the data ^\ve>n by PTor.KMV, and from his interpretation of the data, 1 form what seems to mo the best judgment of the time at which any given phase was actually seen by the observers, and of the probable error of this time, taking care to do this without any knowledge of the way in which the tabiUar results will come out. For an epo(;h near this time, the positions of the sun and moon are computed from Hansen's tables, and thence the times of the geometrical phases of the eclipse. This time is then compared with that observed, and an equation of condition thence deduced. In the ecjuations, the only indeterminate quantities which it is worth while to include are the moon's longitude and the error of the estimate of the phases of beginning and ending, arising from the tact that the eclipse nmst have advanced past the phase of beginning before being sean, and must have disappeared before the actual ending In computing the places of the moon, I have not deemed it necessary to take into account the small terms which are included in the tables of double entry, as their probable sum is far below the probable error of the individual observations. The sum of iLo constants added to these tables, or 0.0022240 in units of the fundamental argument, has, however, been included with the terms, to avoid any constant error arising from this source. The positions of the places of observation — Babylon, Rhodes, and Alexandria — have been taken from Zech, as follows: — Babylon, 2'' 56™ east from Greenwich; latitude, +32'' 15'. Rhodes, i*" 53" east from Greenwich; latitude, +36° 27'. Alexandria, 2'' oo"" east from Greenwich; latitude, +31° 12'. Ptolemy's descriptions of the several eclipses are as follows : — (0 Qv Toivuv tlX-^ifaiav ::akaiutv rpiwv ixXsiiliswv h iSiv iv lla,iuli(ovi TSTiipij'iijiov, ij niv KpiOTrj ihayij'pai:- "Of the three Jincienteolipses which we have taken frotii those observoil in B ibvloii, tlie first is recorded as* hiivin;; ouciirred in the tlrst .year Tfli ytpivula TO) iipiiTi/i cTsi Map3itxs,uKditiiu, xar Alyun- of Mardogbupadus, according lo |thH reckon- rioo,(,i>i^x0.l,rii.r. ///,?ani«,y,^ ir; .?? r^. itf. E-atTt Iti, ,fy,nw,n^o et'lipsetl from the soiUh throe (liKits in the middle vdrim ItaxTuliiuf rptli ivjthu roO ftiirnvuxTdiu, of the nij;ht." The indefiniteness of tlie time renders this eclipse of very little value for our present purposes. The estimate of magnitude formerly served to determine the motion of the moon's node, but this can iii»w bo learned witJi far more accuracy from modern data So far as any indication ire given, the middle of the eclipse was at midnight, a statement of which the probable error may be 40 minutes. We have, therefore : — Greenwich apparent time of middle q"* 4™ ± 40'" Equation of time + '4'" Greenwich mean time . . g** 1 8", (3) H di Tpkrj Toiv lxXt( firessed, that the eclipse had not become perceptible at this time; but, on the other hand, had the interval been consid- erable, say one hour or more, it would probably have been described. Pror.BMV sup- poses the interval half an hour I shall assume it to be 25 minutes, with a probable error of 20 minutes, which will make the • Greenwich mean time s"" 58" rfc 20™. (4) —620, April 21. ^a yAp niftKTw irt: Sa^uitoUaadpm, 8 iauv pit" " In the fifth year of NABOPOLA8SAB, wbich <4|P . , - is the 127th year from Xabomassab according to fr,;?^;rd Na^».aa«Ap,m, xar Alyonrioo, Aoo xC ti, ^^^ Egyptian reckoning, on the 27th of Athyr.to- T^v xTj &pa<; ta Xr/youarit, iv Ba^uXtovi ^p^ato 7 (TsXyji^ii ward the 28th, at the closing of the eleventh hour . , , . ■ „ , , , , , - . in Babylon, the moon began to be eclipsed, and ' ' was eclipsed mostly on the south a fourth of the itiTpou. . diameter." RESEARCHES ON THE MOTION OF THE MOON. 37 • The timejiere indicated in 55 minutes before sunrise, which occurred nt 17'' 36"' local apparent time, or tlie h»cul niuiin time of boginnin^f is 16'' ^j"', the efiuatioii of time being —4'"; and the (iroenwidi mean time 13'' 41"". Tlie probaldo error may be estimated at 15 minutes. * (5) -522, July i6. lldXtv Hi, T# c» 't«i Ka/ifioauu, 8 iffT( a,i" ft,,,- " I" the seventh .yfiir o» (Jamhyskh, which U the a25th yeiir I'loiii Naiionassak, nccording ini IVaflovaaadpou, tar Al/urTT{.ui tatit\>d>» i: tli Tijv t„ t|,„ K(,'.V|>tiails, Oil the 17th of I'hHineiloth, - , , „ . / 1 I, o ,- iSYi towuid the 18th, one hour before inidiiiKht in ' ' '^ ' liiihyloii, the inooii wiw eclipsed from the north ij atXrjvri dit" SpxTiuv ri (j/itiro riff HutnlTpim. one hiilf of h«^r diameter." We have then : — Estimated local apparent time of middle of eclipse . 1 1"" 10™ Equation of time — i"' Greenwich mean time S** 13" ± 24™. A large uncertainty of phase is to be added to the probable error. (6) — 501, November 19. Jturipa'/tk, >••""• "The second eclipse happened in the 20th Hivj) Tipx irtt Japtluu Tim /itrd Katt^oarjv, xar Aiyor.- year of DARIUS, successor of CaMBYBBS, Oil the T("u? E^iip\ %i) ik Tijv xfl, rryf mxTix npotXOouarji t(ii":iHXnftv^atX'^^yi ani advanced 64 equinoctial hours, the moon was v6roo Ti sr T^z Sianhpou, ..... n lipsed on the south J of her dia;ineter.'' The sun set at 5*" 11"' apparent time; the equation of time being — 13°. The mean time here indicated is 11'' iS™, and the result is : — Greenwich mean time of middle of eclipse . . . . 8** 22"° ± 25"'. (7) -490, April 25. FMiSo/itv tij itpd>Ti,i/ /ih ixketifiiv Tijf M Japtlnu Tim npi&Tim Ttrij/Jij/i^Kryw iv Ba/3uXu)v: rip itpdrip xa\ Tptaxiiirrip iiliTim tret, xar AlyuKTiim^ To^i y ik t^v d, iupiif 1; nimji, xaff7)v StanaiftUai in i^iXtiittv ij atXijvri iXnti vnxHO itaxTuXou^ /S. " We have taken an eclii)8e observed in the time of Darius the first in Babylon, in his 3i8t year, on the 3d, toward the 4th of Tybi, in which it is shown thxX.tv TTjv iz^j txXtnl'iv iprjai ytymivai apj^mTiii; "Phanostkatks buing aroliou at Arbens, /)vi;(r! 0a/i)(jTpaTiii), H^xt/KKfii/nwxi; /i7jvA(;, xar A'.yun- Oil tlu* 24th of PliailieilOtll, tOWttnl the 2Sth, it was Ti'iioj i?s «Pa/i£v(«tf X'! £!? T>/i z£. E'ihnt ili ^Tjittv a^iu said to be eclipsed Oil HUininer rising [at Baby- ftspivti^ ayaritXiii rfi^ T:iio'Trii wjia- zfiiishikuOuia^. . , , loll |, the Brst liouF being passed. The whole AW i!cs\ V j:!:; -^pirj }; Ti}i ixksi "iiu; topS)/ rpiiov duu- duFcttioii of the uulipsu is recorded as three YpdfSTai, hours." The date is —381, June 18. The sun set at 7'' 3™ apparent time, or 6'' 57™ mean time. The interval mentioned may be roughly estimated as somethino- more than one equinoctial hour, say i hour and 7 minutes, with a probable error of 10 minutes. We have, therefoi e : — Local mean time [of beginning (?)] S*" 4"" Greenwich mean time [of beginning (I)] i . . 5'' 8™ Greenwich mean time of -ind 8'' 8"'. (10) — 381, December 12, Babylon. I'.^ikits W, tpTftnvy SXt) dp^apivri dftu Ssptwuiv fli/«- ''It was said to be totally eclipsed, having T,Mv d wpwv napeHijXu»uiiov. begun On the summer rising, four hoiirs hiiving gone by." The sun's semi-diurnj'l a'-c at Babylon was 5'' 5", the length of the temporary hour was nearly i'' 10'" , the four temporary hours would have been nearly 4 hours 40 n'.inutes; and as they had already passed, we may estimate the probable time at 4'' 50'"' after sunset, with a probable eiTor of 24 minutes. The equation of tine being — 3"', we have : — Local mean time of beginning 9" 52" Greenwich mean time of beginning 6'' 56™. (11) —200, September 22. xfiO' Tjv iip^aro !iiv hhtKstv "The uionn began to be eclipsed, on the one ij (T£/i)jvij irpd ■qiittopiiiii T^? dmriikii^, erTjiuTiiv Ss dvsKkrj- hand, half all lioup befo"<'- the rising, but was ptuft,, rpirr/; aipai iiiirr/^. tilled Up again ill the middle of the third hour." If IIu'i'ARCniTs is here fully and correctly quoted, which is very doubtful, he must have had a very indefinite idea of the difference between a calculated and an observed phenomenon, speaking as he does of an eclipse commencing half an iiour before it was [lost ible for the moon to be seen. Still, as the half hour is probably the result of an estimate from the magnitude of the eclipse at the time the moon first became visible, it is not without value. The moon rose at 6'' o'" apparent time, which was 5'' 53"" mean time. Tlie middle of the third hour was about S"" 32'" apparent time, or 8'' 25"" mean time, making the Greanwich mean time of ending 6'' 25'" ± (2™. RESEARCHES ON THE MOTION OF THE MOON. 39 (12) — 199, March 19, Alexandria. Ilfiiaro 'U Tfi<; mxri)^ irpnsXeouawv w/iBv e xa't "It began .vlieii 5J houra of the night were Tpnij/w/iiou, xa\ i^iXiKtv o/ij. pa88e«l, and it wa.s total." This is 11'' 19'" apparent time, 11'' 29"' local mean time, and 9'' 29"° Greenwich mean time. • (13) — 199, September 11, Alexandria. ///(JUT" <5c T/;? wjxroc T/v.Ufl-yffwviu/Kui-T;-;,, z«! "It began 6§ hours of the night having iU^-iJ^sv okij. h'ai rdv ;i.lti>v 'U r/)? huivstu^ -^imvuv passed, and it was total, and tlie middle of the V,^! r'T">''"" '^/-^ ^r"-^ !"''■''■"''" ^ "'^ rinrrnLopu,:, eclipse arrived, he saya about 8^ hours of the night." Here we have again, in the "middle of the eclipse", a time given which it was impossible to observe, withont any indication of the data from which the time was derived. As the eclipse was total, the most natm-al data would have been the ob- served times of beginning and end of totality, which would be far more accurate than tlie observed times of beginning and ending of the partial phase. The times indi- cated are: — Local apparent times . ......... 12" 41'" «"tl 14" 25'" Local mean times 12" 38'" and 14" 22™ Greenwich mean times 10'' 38" and 12 ' 22'". (14) — 1 73, April 30, Alexandria. •/•,5 r,n.u. C. ?r., 1>0..,nrop..,, o .Vr, y,»5o^ a.i " I" the ^l\^ year of PniLOMETER, which iS tlie S74tli from Nabonassau, on the 27111 of I'ha- Sa{ ovaaadpuu, xar AlyoKTliit,:;

i;ii'Mo/t zC £lj rr^v xji, meuoth, towar(i the 28th, tlie inoon was eclipsed , in Alexandria from the beginning of the eighth i;i)^t'rs>' ij (rsX^vTj TO TsXtiaziiv a-" llpxrim Saxrui.oui :;. north, SCVen digits." , ' ^ These times are : — Local apparent tines 12" 54" and is"" 37"" Local mean times 12" 48" and 15^ 31" Greenwich mean times 10'' 48'" and 13' 31'". (15) —140, January 27, Rhodes. Ildh. <1r, r^i Xy k'r^' rr]; rphr,- xazA hnU::-.^ "... the 607th year from NABONASSAU ^tpM.o, 5 i.TTiv xl «Td Na,io,aaadp„u. xar Alru-riat - [Eg-VPtin" reekoiiiiigl, the second of Ty ..i toward 7«,3) J d; T^v r, ^ «/'Z"/'^"i--, ^•-' /'"'V i"'"'" tli« third, at tlie beginning of the stli hour in {xLiK.r. ii .rUi^v xa-i l,:,ax„r^^ rd 7rAc-rouj xaT AlyOTTTiou; llaymv tX ei> tt/v oj, jT/oi) Tpimv wpiuv ltn)ntpi)imv xa\ rpimv rl/iJtrwv /ndj &paj Tii'j usaiivuxTiDUf xaO' t)v 6/tinioi i^iXenrsv ij aeXijvi^ rd IxTiiv fxipo^ T^f tia/jLiTpou ii:i nearj/iPplaj, (i6) 125, Ain'il 5, Alexandria. " • "On the lytb of Paclion, toward the i8th, 3I equinoctial hours before midnight, the moon was eclipsed the sixth part of her diameter on the south." This is 8'' 24™ apparent time, 8" 26™ meaa time, and 6'' 26'" Greenwich mar time. (17) ^33, May 6, Alexandria. lldXtv wv eiX7lyi tO £l<; Tj/V x, Tiv iti iii- aov jfpovdv ineXoyiad/xeiia yeyovimt /itrd i5 mpa^ lirr/iis- pi.vd^ Tou iisaiivuxTiDU' xal i^iXint rd Tjiitno T^f itia/ti- Tptio dr apxTiov, "The third eclipse happened in the 20th year of Hadrian, on the tgth of.Pharmouthi, toward the 20th : the mid-time we noted to have been four equinoctial hours after midnight, and it was eclipsed the half of it« diameter on the north." le"* apparent time was then iG*" 14"' meantime, and 14" 14" Greenwich mean time. RESEARCHES ON TIIK MOTION OF THE MOON. 41 Tills completes tlio scries iis given by Ttolemv. The tiihul.-u- positidiis of the sun jindnioon derived from Hansen's tables for epochs of Greenwich mean time near the observed phases are shown in the following table. These places have all been com- pnted in duplicate, the two computations being made by two separate computers. The motions in longitude are for 0.0 1 of a day, as the tiibles most conveniently give them. The motion in latitude is supposed to be ,\ that in longitude, positive at the ascending and negative at the descending node. The node can be identified by the value of f-\- a), which is the *ngular distance of the moon past the ascending node. It may be remarked that the probable error of the longitude arising from the omission of the terms in the tables of double entry is about 24". Tabular Data for Eclipses of the Almagest. No. of Hcli|>sc. I Dale. — 720, Mar. 11) Cr. M. T. of Com- putation. Moon's Longitude. 14.4/' Motion in cy'.oi. IT J'arallui. Uuituile. /.- (D's I.onp. (•>'s Seinitliam. ■4.4 A' Motion in 0.60 h m 5 ■7" 59.3 7-37 /■ ■ 55-7 / + 3.6 0.5 351 1 3'-5 15 57 " — 719, Mar. 8 8 160 30.4 7.10 53-9 + 46.7 8.3 340 41.8 16 0.60 .1 — 719, Sept. 1 3 yst 55.4 9.08 61.2 - 37.8 187.6 ISO 54'4 16 o.j8 4 — 6ao, Apr. 21 13 Q 204 id. 2 7.11 54.0 + 52.8 169.8 34 23.S IS 49 0.59 5 - 52a, July iC 8 o 286 37:2 7. .8 S4» - 40.9 352.3 106 33. a 15 48 0.57 6 — 501, Nov. 19 8 a 51 41.8 7.08 53.8 + 50.7 170.3 231 54-2 16 16 0.60 7 - 490, Apr. 25 7 207 55-8 8.13 57-8 + I 1.6 168. 1 28 3'-4 '5 49 0.59 8 - 382, Dec. 22 16 B6 46.9 8.72 59-9 - 57.8 348.7 367 2.0 16 •7 0.61 5 — 381, June 18 4 259 47.0 7-'7 54-3 + 46.5 171. 3 80 27.8 15 45 0.57 ID — 381, Dec, 12 6 75 "-8 9-'4 61.3 — 21.2 356.0 356 9-9 16 17 0.61 II - 200, Sept. 22 5 336 20.4 7.48 5S.4 + 33-4 >73.8 176 0.7 16 4 0.59 13 — 199, Mar. 19 8 173 56-4 8.28 58.3 + 4.9 0.9 355 32. 4 15 58 0.59 >} - 199, Sept. ti 10 343 55. ' 8.33 58.5 + 0.1 180.3 X65 ■ ■7 16 I 0.58 M '5 - «73. Apr. 30 — 140, Jan. 27 10 b a 214 45-9 123 26.4 9.07 9.14 61. J 61.3 - 35.7 + 46.6 186.8 8.9 35 304 40.1 3'.9 '5 16 49 13 0.57 0.60 16 + 125, Apr. 5 6 194 2.6 8.3. 58.4 + 57.4 168.8 '4^ 16.2 "5 54 0.59 >7 18 + 133. May 6 4- 134, Oct. 20 .3 8 223 56.1 25 64. 9 7-33 7.56 54-8 55.7 - ■'SI - 36.8 355 •• 18s. 3 44' 306 11.5 15.1 ■5 16 48 tl 0.58 0.60 >9 + 136, Mar. 5 12 163 5>-8 8.89 60.5 - 53.3 349-7 344 36.9 16 3 0.60 Owing to the somewhat indefinite character of the data given by Ptolemy, it will '.!!•: t the judgment to present both his statements and the tabular results in a form in .v.iicV they can be best compared. This is done in the following table, from which the reader can obtain a clear view of the comparison. The deduction of the numbers in the third and fourth columns has been given with the separate descriptions of the eclipses. They therefore need only these two remarks: (i) that the probable errors are the result of judgment from the terms of the description rather than of calcula- tion; (2) that they were estimated without any knowledge of the way the comparison with theory would come out, and are printed without subsequent alteration. In the column of "Phase described", A means magnitude of the ecUpse. The tabuhir time of geometrical phase gives the time of beginning, middle, or end, as the 'uiso may be. The quantities A, and As in the last column represent respectively the number of minutes a central eclipse may be supposed to have advanced before the observers would see it, and the immbor of minutes before the end that the observers From eclipses (9), (13), and (14), the only ones of which both beginning 75 Ap. 2 ■ . lost sight of it. 4= RKSKARCIIKS ON IIIK MOTION OK Tllli MOON. 1111(1 011(1 were oliservcid, A, -f- A.j ooiiios out — lo"'. But, tliny niust both be positive, and tliis result only iiuliciitu.s that they are very small. I shall put coiijecturally A, = 3"' Aazr a™. (Jrccnwicli No. of Eclipse. Dale. Mean Tunc, iiulicated hy Proi.KMY. Prob. Error. HI Phase ilescribcd by Plol.KMY. Tabular Duration. Tabular Time of Gcomct. Phase. Coir, to Tabular Time. // ni ■ A /( III m I — 720, M.-ir. 19 4 19 12 Beginning . 3.8 4 II + 8 — I . OA 2 — 7lg, Mar. S 9 .3 Middle (?) . 1.9 8 15 + 63 3 - 7'9. Scpl. I 3 58 ■2 • ing • a-4 3 15 + 43 - i-i^i 4 — 620, .\pr. 21 13 41 15 ' ling . I.O 12 57 + 44 - 3-8.il 5 — 522, July If) 8 >3 24 *... .le (?)» 2.6 8 + >3 6 — 501, Nov. i(j 8 22 24 ( Middle (?■■ ) ■ I.I 8 27 - 5 7 - 4<)0, Apr. 25 3 27 *4 ( y .ie (?) ) 0.6 8 17 H- 10 a — 3R2, Dec. 22 15 35 10 Small eclipse (connnciic'g). 1.6 i5 52 - 17 - 2.2A, 1 9 - 3Si,Jmic 18 5 S 12 Hoginning . 2.4 4 25 + 43 - I.5.ii 1 s s 20 End . . . 2.4 b 51 + 77 + J -5^2 10 - 3S1, Dec. 12 5 56 24 Beginning . 3-4 5 57 4- 59 - i.ia, II — 2ix), Sept. 22 3 23 30 Begin, (est.). 3.0 2 57 4- 26 6 25 12 End . . . . . 5 55 + 30 + I . saj 13 — ig(), Mar. 19 9 29 15 Beginning . 3.6 8 51 + 38 — I.Oi, "3 — 199, Sept. 11 10 33 18 Beginning . 3.6 10 13 + 25 - I. Oil, 12 22 20 Middle . . 12 3 + '9 ! U - 173, Apr. 30 10 4S 20 Beginning , 2.7 10 4 + 44 - 1.4^1 13 31 20 End . , . . . 12 45 + 46 + i.4;ij 15* — 140, Jan. 27 8 7 20 Beginning . 1.9 6 44 + 83 — 2. Oil i l6 + 125, Apr. 5 6 26 iS (Middle (?)| 1 ^=.'i f 1.2 6 36 — 10 >7 + 133, May 9 8 13 Middle . . 3-5 8 38 + 30 ^ .3 + 134, Oct. 20 8 46 »5 Middle . . 3-3 8 33 + »3 i "> + 136, Mar. 5 14 14 15 Middle . . 3.2 13 26 + 48 We shall now consider, seriatim, the conclusions that we may draw from the comparison. 1. The discordances of the times in the last column are, on the whole, not mate- rially greater than would result from the probable errors in the fourth column. We therefore conclude that the probable errors have not been vinderestimated to any great extent. 2. There are five eclipses, namely, Nos. (2), (5), (6), (7), and (16), in which the ])haso is not expressly stated by Ptolemy, but in which the middle of the eclipse has hitherto been supposed to be referred to. Hut, in the case of at least the last three, the tabular comparisons give color to the suspicion that it was really the time of beginning which was noted; and this suspicion is strengthened by the consideration that it was the time of beginning which was generally noted by the predecessora of * Zkch supposes an error of an hour in the time of this eclipse.. The alter.-ition does not seem to me justified by t'rj Jiscordincc of two and a half times the probable error. RESEARCHES ON THE MOTION OF THE MOON. 43 Ptolemy. I therefore deem it advisable to reject these five ecHpses, owing to the uncertainty of the phase noted. Quite accordant results might be obtained by sup- posing that the beginning was observed in some cases and the end in others ; but the uncertainty is too great to justify this course. 3. Tlie question whether eclipse No. (8) was really seen is a very serious giie. When we take out the five doubtful eclipses and this one, seventeen observations of phase are left, every one of which indicates a positive correction to the tabular time ; and the results throughout the nine centuries over which the records extend are so accftrd- ant that I do not see how the reality of this correction can be doubted. The serious ])oint is not simply that No. (8) gives a negative result, for this might arise from acci- dental errors of observation, but that a positive correction to the time will render the eclipse absolutely invisible at Babylon. In fact, the account says that there was a small eclipse (not simply that the eclipse was beginning) half an hoitr before sunrise. At this time, however, the twilight would liave been .so bright and the altitude of the moon so low that the eclipse could not be seen for a number of minutes after its com- mencement. On the other hand, the tabular time indicates that tlie ecli})se did not commence geometrically until about nineteen minutes before sunrise; and, in this case, the eclipse could scarcely have been seen at all, because the constantly increasing light and the constantly diminishing altitude of the moon would have drowned out the slowly increasing eclip.se. In fact, when the sun rose, the moon would have been eclipsed only about 3', or one tenth of her diameter. If, again, we take the tabular coiTcction indicated by the other eclipses, we find that the eclipse did not begin until some time after the moon had set. We have therefore this dilennna: either there is a mistake aljout the eclipse of —382, December 22, having been really observed at Babylon, or the seventeen good observations of phases cited b)' I'toi.emy are systematicall}' in error by nearly half an hour. I cannot hesitate in accepting the former as the most probable alterna- tive. The occurrence of the eclipse being expected, it is quite possible that the observers may have thought they saw the moon eclipsed in the increasing daylight, when there was really no eclipse; or, uiuler tiiC unfavorable circumstances, they might have been deceived by a dark region of the lunar disk being near the moon's lind). Nor can a mistake of date be regai-ded as out of the question. On the whole, I think that this eclipse shoidd be rejected, since, if we regard it as a real observation, the results from the other eclipses nmst be regarded as all wrong. We have left thirteen eclipses, of four of which two phases, beginning and end, were observed or estimated. Wo next divide these into groujjs, and take the mean by weights, derived approximately from the probable errors in the fourth cohnun. From eclipses (i), (3), and (4), giving them the respective weights 3, i, and 2, we find : — Epoch - 68;, ^r= + 26'" - 2.0 ^i = + 20"' ± 8'". From (9) and (10), Avith the weights 8, 3, and 2, we find: — Epoch - 38I, ^T= + 53"' - 1 . 1 -/. + 0.3 -'.J = 50'" ± Q" From (11) to (15) inclusive, giving the phases weights i, 6, 4, 3, 2, 2, 2, 2: — Epoch - 1 89, JT = + 3 7'" - 0.6 -/, + 0.6 X = -}- 36"' ± O'". 44 RESEARCHES ON THE MOTtON OF TIIE.MOON. From (17) to 19), giving the weights 3, 2, 2: — Epocli + 134, ^Tir + 30'" ± S"". If we reduce these results to minutes of arc, we find tlie following corrot^tions to the moon's moan lottgitudo, as derived from Hansen's Tables : — Epoch. — 687 -381 — 189 + 134 ft. Wt. 3 2 -ii'±4' -27' ±5' - 20' ±3' 4 -i6'±4' 3 In the light of these comparisons with theory, wo could no doubt amend some of our interpretations of the times given by Ptolemy. I'tolemy's interpretation of the description of the first ecV.pse would seem to be more correct than the one adopted, while, in the case of eclipse (9), it was an error to suppose that much more than an hour had passed. But, although, by thus amending the interin-etations, a better agreement would be attained among the observations, I do not think the final result wouhl be improved, and it certaiidy would not be materially altered. I think we may conclude, with a high degree of probability, that during the eight centuries jn-eceding the Christian era the moan longitude of the moon in Hansen's Tables reipiires a correction of about + 18'.* ^ 5- ARABIAN OBSERVATIONS OP ECLIPSES, EXTRACTED FROM CAUSSIN'S TRANS- LATION OF EBN JOUNIS. Tlie complete French title of this work is, "Le Livrc lU la grnmh Table Ilah'mitc ohsrrire jmr le Sheikh, VImam, le docte, le savant Ahoulha.smn AH ehn Ahderrahman, elm Ahmed, ehn Jounis, ebn Ahdalnala, ehn Mousa, ehn Mn'isara, ehn. Ilafes, ehn JIhjan. Traduif par le C'" Oaussin, professeiir de la lam/ue. Arahe an College de France. A I'aris, de I'imprimerie do la Republiqiie. An xii. [1804, v. s.]." Most of the observations wliich will be quoted were also published, before the appearance of the book, in tho IVIemoirs of the I'aris Academy of Sciences, vol. 2; and tliere are a few discrepancies between the results there given and those in the extended work. I shall, however, use tho latter as my authority. The ideas of the author respecting the errors of instruments seem to have been far ahead of his age, if we may judge from the following description of the precautions which must be taken to obtain good observations. Unfortunately, only a fraction of the observations could have been made by this most tiritical observer, who died in 1008. "/>e VErreiir des Instrumcns qui servent a mesurer. "Jj'art ne pouvant atteindre, dans la fabrication des instrumens, la justesse qui con<,M>it I'esprit do I'artiste, soit pour egaliser leur surfaces, soit pour les divisor et •Since reai'tiing this conclusion, I have been strongly inclined to think that the phases recordcil should be con- sidered KS(iiil)ris. llautuur d'ArcturuH au coiniiu'iicuiiient, 52° orient; liauteiir do IVtoilo a du coclier, 14" Occident; Inuiteiir d'Arcturus i\ la fin, 35°." On tlicHe inconHJHtt'nt altitndes of ArctnruH, Cath.sin remarks that the altitude at coniniciicenicnt may l>o either 12° or 52°, but Houvakd advised him that the latter readinjf nuist he taken. The last altitude of Arcturus, 35°, admits of no doubt in read- ing. The star which had the altitude 14° is also doubtful, the name given in the niaMuscript not l»eing found in the Arabian Htar Catalogues; but he found a similar name in ScAi.KiK.K as j)ertaining to a Aurig.'c. The results for begiiming are : — Fnmi altitude of Arcturus 11'' 41" 23*^ Krom altitu(hM)f a AurigiP 11'' 45"' 40' Adoj)ted rf'sult ii''43'" 2'. (25) l*ago 178 — " £V7/y),w (h soldi ohservre an Cairs h 24 [23] Janvier 1004. (Jrandeur d(( I'cclipse, 11 doigts ; hauteur du soleil, lorso^ue I'dclipse commen(,'a a pa- roitre sur son dis(pu', 16° 30' Occident; connnencement e.stim<5 h 18° 30'; hauteur lorsque le (puirt du diam^tre f^toit t'clipsd, 15°; hauteur lorsque la nioitid du dian:&tre fut edipsi'o, 10° ; hauteur au moment de la plus grande phase, 5°." The diti'erence of the first two altitudes is surprising, corresponding as it does to 1 1 minutes of time. The results are : — The eclipse sensible 4'' 6" 13* Estimated time of beginning ... 3'' 55"° 17*. The local mean times have been reduced to Greenwich 'mean time by applying the longitudes already given, and the results are shown in tabular form in the follow- ing pages. The tabular geocentric positions of tie moon are fii-st given, the times of computjition being generally nearly the same with those of observation. In comput- ing the longitudes, the double-entry tables have been omitted and tlie constant 22240 added, a proceeding which involves a mean error of ± 14" in the longitudes. The moon's motion in latitude is omitted ; it will be sufficient to suppose it equal to i the motion in longitude. Its algebraic sign is, however, given immediately after the lati- tude itself. Respecting the places of the sun, it is only necessary to say that they are from Hansen's Tables, kr:sEAR(MjEs on the motion of the moon, Tabular Pcsitions of the Moon and the Sun /or the Aralnan Obsenuilions, 5' No. of C5r. M. T. Moon's Mot. in .'•'0 Latitude ; Paral- The Sun's T Log. of Radius vector. I 1 Semi- Eclipse. Dato and Phce. of Coin- Longitude 0''.OI. increasing +- lax. ^ongilude. diam. pulalion. diininislilng- 1 i B.lgiitld. h m t\ • t • f • 1 i t 83ij,iNov. 39 16 36 14 251 37.6 7.86 + 22,1 - 56.9 353 37.0 9.99270 16.2 18 36 54 252 38.1 7.87 H- 16.8 - 56.9 353 41-7 9.99269 16.2 J a 85.(, Aug. II 13 I 7 321 403 8.81 + 18.3 + 60,3 143 35.4 15-9 J 3 836, June 31 13 21 58 373 34.5 8.25 - 45-2 + 58.1 94 10. fi . . . I5-7 D 4 933, Juno I fi 56 33 255 '9.8 8.60 - 43-8 - 59.6 74 43-4 . . . 15.8 S 023, Nov. 10 16 21 8 232 37.3 9.07 4- 33.4 - (.1.3 233 26.8 999355 Ifi,3 17 32 32 333 22.4 9.07 + 28.2 - bl.2 233 29.8 9-99354 '' 16. a J) 6 935, April 11 2 38 36 204 16.7 8.43 + 3&-8 - 59 26 8.0 . . . '5-9 7 •17 49 207 18.5 8.46 +20.1 — 59-1 26 20.5 • • 15.9 J 7 937, Sept. 13 12 50 46 354 28.7 9.09 + 5''2 + 61.3 175 '2.0 . . . 1(1.0 8 938, Aug. 17 15 29 29 149 7-5 7.8fi - 13.1 - 56.9 149 37-0 0.00304 15.9 3) 9 929. Jan. 37 8 5 3» 131 48.5 8.51 + 30.6 - 59.3 3'3 '4.1 . . , 16.3 ]> 10 933, Nov. 4 Cairo. •3 «7 15 46 54-7 7.24 - 5.9 - 54-5 227 48.8 1O.3 II 977, Dec. 12 18 19 3 365 49.0 9. II + 35-2 - 61.4 367 1.7 9.99106 J6.3 30 36 10 267 16. I 9.11 + 27.3 - 61.4 367 7-5 9.99105 16.3 13 978, June 8 32 29 i 81 58.5 7.10 - 0.2 f 54.0 81 ■ 48.9 0.00733 '5.7 • 2 42 13 \ 83 7.3 7.10 + 0.3 + 54.0 81 54.4 0,00735 15-7 J 13 979, May 14 ? 52 238 51.2 8.30 + 32-5 - 58.5 57 57.0 • • • 15.8 M 979, May 28 4 12 58 , 71 475 7.61 + 39-0 + 55-9 71 '5.' 0.00713 13.8 3) 15 979, Nov. 6 8 3 40 1 48 42-7 8.31 -- 37-6 + 58.6 229 27.1 • • • 16.3 II 18 i 50 34.8 8.29 — 27.2 + 58.5 229 35-3 • • • 16.2 J) I6 980, May 2 14 26 1 328 24.4 7-47 — 12.0 — 55-4 47 31-3 ■ • ■ 15.8 J "7 981, April 31 13 28 i 216 14.9 7.09 - 45-9 - 53-9 36 46.0 '5.9 I 18, 981, Oct. 15 14 7 27 24.4 9-03 4- 46.6 + 61. 1 208 1.6 • • • i 16. 1 J) 19 983, Mar. I 9 55 , 165 18.7 8.64 + 31.9 - 59.7 346 '3.3 16. 1 13 40 167 33.5 8.61 + 19-4 - 59.6 34O 22.6 . . . i 16. 1 20 985, July 20 2 56 30 122 43 3 8.17 + 150 ~ 58.0 122 17.6 0,00587 ,15.8 4 18 13 123 29.7 8.18 + 10.9 — 58.1 122 20.9 0.00587 1 15.8 1 ]) 21 986, Dec. 18 "4 53 i 92 '^•9 7.10 + 3"-3 - 54.0 272 49-4 '6-3 ]) 33 990, April 12 7 42 1 306 43.9 7.10 - 37-5 + 54.0 27 34-2 • • • 15.9 II 4 ; 208 23.4 7.IO — 28. 3 4- 53-9 27 42.4 . . . 13.9 33 993, Aug. 19 17 36 5 150 28.6 9-04 4- 5-3 + &I.I 151 54-6 00288 15.9 S 24 1002, Mar, I 9 41 18 165 37-4 9-13 — 12. I — 61.4 346 3&.0 • 16. 1 25 1004, Jan. 34 I 51 1 310 9.4 8-39 -t- 15-8 4- 58.8 308 43-3 9-99444 1(1.3 52 RESEARCHES ON THE MOTION OF THE MOON. Comparison of Tabular and Observed Times for the Arabian Observations. o. of Eclipse. Dale and Place 2 3 4 •5 6 9 10 >3 14 15 l6 «7 I8 >0 829, Nov. 29 854, Aug. 1 1 856, )une2i g23,June i 923, Nov, 10 925, Apr. II o/iT. Sept. 13 928, Aug. 17 929, Jan. 27 933, Nov. 4 Cairo. 977, Dec. 12 978, June 8 979, May 14 979, May 28 979, Nov. 6 980, May 2 981, Apr. 21 981, Oct. 15 983, Mar. I .,35, July 20 24 21 986, Dec. 18 22 990, Apr. 12 23 993, Aug. 19 Phenomenon Observed. 1002, Mar. I 25 1004, Jan. 34 Keginnlng Ending J) Beginning 2) Beginning }) Ending Ending J) Beginning ]) Ending }) Beginning Ending ]) Beginning ]) Beginning Beginning (S.) Ending Beginning (S Q Ending ]) Ending Beginning (S, }) Beginning D Ending D Beginning ]) Ending D Beginning J> Ending D Beginning ]) Beginning (S, }) Ending Beginning Ending 3) Beginning (S.) 3> Beginning (at) Beginning Ending ) Beginning D Endiiig Beginning (est. Local M. T. Obs. "9 33 44 21 24 24 "4 58 37 15 iq 28 9 54 3 20 30 2 7 20 6 10 45 19 15 48 16 18 26 59 1132 16 15 15 20 22 2 4 7 6 10 ■3 16 15 '7 16 15 5 6 16 9 >') 22 II 24 4 41 12 27 31 47 15 57 2 18 o .9 50 22 52 38 8 28 42 8 44 18 15 37 58 I 32 23 "5 56 6 45 59 41 23 22 37 43 a 3 55 >7 Gr. M. T. of Obs. h m s l6 36 14 18 26 54 12 ' 7 12 21 58 6 56 33 17 32 32 4 22 36: 7 47 49 12 50 46 «5 29 29 8 5 32 :3 17 45 18 ig 2 20 36 10 22 29 2 42 13 5 52 0. 4 12 58 3 4 48 II 17 50 D too high 14 33 06 »3 23 40 15 3 42 14 13 13 loo high ■3 32 56 2 56 30 4 18 13 14 5« 4 7 40 57 17 36 21 20 "7 35 9 38 unavailable | I 50 15 Tabul a Gr. Time of Geomet. Phase. h m 5 15 50 20 18 8 56 II 53 59 T2 18 13 6 49 49 17 15 50 4 27 8 7 45 35 13 4 I 15 19 26 9 4 20 13 15 54 18 10 30 20 33 23 57 47 2 38 20 5 40 44 4 2 38 8 I 26 II 3 55 10 39 14 28 19 13 20 50 15 5 l3 13 58 25 9 59 39 13 15 14 2 3a 10 4 3 32 14 28 56 3 6 9 17 36 I 19 57 43 9 35 28 12 59 2 I 39 6 A.' H- 45. + 18. + 7. + 3. + 6, + 16. - 4. + », - 13 + 10. - 58.8 + 1.8 + 3.5 + 3-2 + 24.7 + 3.5 + II. 3 + 10.2 + 3-4 + 13.9 + 4- + 2.8 - 1.6 + 14.8 + 17-7 + 24.3 + 14-7 + 22.1 - 25.2 + 0.3 + 19.9 + 2.5 + II. I 0.51 0.42 0.51 0.40 0.51 0.45 0.51 0.37 0.35 0.28 0.48 0.51 0.52 0.51 0.43 0.62 0.51 0.41 0.51 0.44 A/ Cla*s. - 23-2 - 7.6 - 3-6 - I 9 - 3-4 - 6.7 ■f 2-3 - 1. 1 + 6.7 - 4.5 + 29-7 - 0.9 - 3-2 - I.I - 6.9 + 1.9 - 5.8 - 5-3 - 1-7 - 70 - 2.4 - 14 4- U.8 - 7.7 - •B, ^ - 10.6 - 91 - II. a + 12.8 - 0.1 - 10.2 I - 1.3 I - 4.4 I Researches on the motion of the moon. 53 Next is 8hf>wn the comparison of the tabular and observed times. In the cohimn " Phenomenon « bserved ", S. signifies that the time of observation is that at which the echpse was said i'^ be sensible to the sight, whereas, in other cases, only the phrase beginning or ending is used. As these phenomena necessarily occur after the times of geometric fii-st contact, they must be a little too late. The observed times of ending must be supposed too early by a less amount. In the table, however, the comparisons are made with the geometric contacts only. Column Jt shows the difference between the observed time and the computed tabular time of the geometric phase. It is next necessary to multiply this difference by the appropriate factor to reduce it to correction of the moon's mean longitude. For the required factor has been taken dt de' these quantities being computed by the formula; given in the next section, on the reduction of eclipses and occultations. In the case of eclipses of the moon, the factor may be supposed to have the constant value 0.51. Column Jl gives the indi- vidual corrections to the moon's mean longitude thus obtained. In the last column, an attempt is made to classify the results. The letter a gener- ally signifies that the materials for the determination of time are unexceptionable ; b, that there is room for error, owing to the vertical circle drawn through the object of which the altitude w as observed for time being too near the meridian, or to the eclipse being a smnil one ; c, that the data for time are yet more defective, or that the time determined by the observers had to be used. Passing now to the consideration of the results, we remark that these observations are not of the class in which a system of weights determined a priori can be adhered to, owing to the liability of the observations to abnormal errors. With a view of form- ing a judgment how far the observations are thus affected, we begin by finding the narrowest limit? within which a majority of the results can be included, making no distinction of weights, and Including all discordant observations. We readily find these limits of Jl to be — o'.8 and — 6'. 8, between which are included 1 7 out of the 33 results. This, taken alone, would indicate a mean correction of — 3'.8, and a probable error of 3' for each observation. Extending the limits still farther, we find that 27 out of the ^^ are contained on or between the lii.ilts + 2'. 3 and — 10'. 6, or, omitting the two contained on these limits, three fourths of the whole number of results are contained between them, while the outlying results are eq:uil in number on each side. This would indicate an individual probable error of 3'. 8, with nearly the same mean result. Reversing the reasoning, if we suppose a probable error of 3', then three fourths of the whole number of observations, or 25 in all, ought to be contained between limits extending through 10'. 2, while 27 should be contained between limits differing by 1 2', and the remaining 6 should lie but little outside the limits, always supposing the admitted law of error to hold. Most of the six outlying observations are so far from fulfilling this condition as to show conclusively that the law in question does not hold, and, therefore, that the arithmetical mean is not the most probable final result. 54 RESEARCHES ON THE MOTION OF THE MOON. The following results are so far outside the limits of probable error as to be sus- picious, if not certainly abnormal : — 829, November 29. — Beg'mning. — The tables show that the eclipse began at or before sunrise. How a real beginning could have been observed more than half an hour afterward, it is hard to see The observation is, therefore, clearly inadmissible. 927, September 13. — Though the time from the altitude of Sirius is of the second order of accuracy, the observation with the astrolabe confirms it, so that the discrep- ancy is hard to account for. Possibly, the keen eye of the young observer caught the penumbra some time before the actual advent of the shadow. The smallness of the e- '^36 would only admit of giving half weight to the observation, even were the resitJt good. 929, January 27. — Nothing can be done with this eclipse, the observed time appearing exceptionably free from a liability to possible eiTor. 990, April 12. — Here we have nothing to check the record that the moon was ^^i"^ high "au moment de I'attouchement ". I think the result should be rejected, espe- cially as the term translated attouchement seems to be of doubtful meaning. Of the four discordatit eclipses, there will, I conceive, be no question that those of 829, 929, and 990 should be rejected. Respecting that of 927, doubt maybe enter- tained ; I, therefore, retain it. In taking the mean, it may seem advisable to give classes b and c half weight, compared with a. We have, before taking any means, to consider the cases of those eclipses of which the phases of beginning are distinctly stated to be those when the eclipse was apparent to the view, which are marked (S.) in the third column. It might seem that all the observed beginnings should be referred to this phase, but the general run of the comparisons seems to favor the belief that the times were made to refer to the actual contacts by an estimate of the observer in each case. The correction to be applied for the phase in question does not admit of a definite determination, but must rest upon our estimate of the acuteness of the Arab vision. 1 conceive that we may assume 2 J', a probable mean correction to reduce to geometrical contact; but what we really want to do is, not to reduce to real contact, but to the greatest phase of invisi- bility, so that the times of beginnings shall correspond to those of the endings when the eclipse was no longer visible We shall, therefore, apply a correction of plus i'.5 to each value of Jl dependent on a phase of beginning marked (S.). The observa- tions are clearly divisible into three groups, separated by pretty wide intervals. The mean results are: — 850 Jl = — 3'.8 ± 2'.4 3 phases. 927 — i'.6±i'.7 7 jihasea. 986 — 4'.5 ± I '.3 20 phases. The probable errors are obtained on the supposition tliat the probable error of a result of class b is ±4'. 5, and that each grouj) is affected with a probable systematic error of :i= i' in addition to all accidental errors. RESEARCHES ON THE MOTION OF THE MOON. $^ §6. MODE OF DEDUCING THE EBROKS OF THE LUNAK ECLIPSES AND OCCULTATIONS. ELEMENTS FUOM TUE The method of computing eclipses and occultations may generally be divided, though not perhaps with entire sharpness, into two classes: in the one, the position of the observer relatively to the cone, or cylinder, which circumscribes the moon and the occulted object is computed by geometric methods, and the condition of an occulta- tion or of the beginning or end of an eclipse is that the observer shall be on the surface of this cone; in the second class, the apparent position and magnitude of tlie two bodies, as seen by the observer, are computed, and the corresponding condition is, .that the apparent distance of centres shall be equal to the sum of the apparent semi- diameters. The first method is preferable on the score of elegance of treatment and of general certainty and convenience in cases where the phenomenon has been observed from several stations. It requires, however, that the positions of both bodies be known before the computations of the phenomenon are commenced. This require- ment has prevented its use in the present investigation, because it was desirable to postpone the final determination of the positions of the stars to the latest practicable moment, in order that the best available data might be used. The method adopted is, therefore, to determine separately and independently the apparent })08iti6ns of the moon and of the sun or star, and then to deduce equations of condition from the difference between the computed distance of centres and the sum of the semi-diame- ters; or, in the case of solar eclipses, from the differen', the observer's geocentric latitude; T, his sidereal time expressed in arc; aj, the obliquity of the ecliptic, compute u and W from the formula? k' sin M = p sin q>'; 111 cos u=. p cos ip' sin r. Then, p cos ft, p sin yff, and K are given by ' ■ p cos ft cos A =: /o cos p sin ) — cos a? p sin sin m — sin \ (/' — i) V coslTcoa 77; sin \ D cosmzz sin A (b' — B) ; the angle m being counted from the south point of the moon's disk toward the west. Wo have also , ^ .<,,.,, T>^ cos b' COS B =z cos* i {V + /»•) - sm* i (''' - '0- 6o RESEARCHES ON THE MOTION OF THE MOON. Since the last term of this equation can never amount to ;^, wo may substitute eoH ^ (J/ -f J}) for V COS b' cos li in the first of equations (6). Wo may also dotermino ]) and m with all necessary accuracy from the approximate equations, • Ds\nm=:(l'-L) coa^(b'-{-Ii), . Dcosmzzh' — B. ' Tiie error in this determination of m will bo of no importance, because this angle i» never observed with such accuracy as to be used as a datum for con-ecting the moon's place, while tho error in B is so small as to bo entirely unimportant. In fact, if we represent by B' the approximate value of B derived from (7), wo have : — D" = (r - z)" cos« i (^' + -B) + (^' - ■»)'; while developing tho sines of J 2>, i Q' — L), and i (6' — B) in the rigorous equation to quantities of the third order, we have : — sin JD = JD A -j-^'^y m^ ^{l' -L) = ^ (l' - L) (^1 - ^{l' -Lyy sin i (fc' - «) = Hi' - ^) (i - 74 («*' - ^)')- Substituting those values in the rigorous equations, and taking the sum of the squares of tho two equations, we find 2)'=(Z' - Lf cos' i (b'+B)-\-ib' - Bf + ^ (2>* - ^l* cos" i {V -{-B)- Jb* ), where we have put, for brevity, Jl-V -L; Jb = b'-B. Substituting the above value of B", we have (D - B') {B + D') = n ^^* ~ ^'* *'^^' ^ ^^' + -^) - ^^')' showing that the maximum value of D — B' is 43 B^, or less than o".oi. The equa- tions ( 7) are therefore exact enough for all practical purposes. 4. — Equations of Correction. If all the elements of reduction were correct, we should have, in case of an occul- tation, tho value of B from (7) equal to that of s' from (4). Wo have now to find the equation of condition which must subsist among the corrections to tho lunar elements in order that we may have B = s'. Owing to the minuteness of these corrections, their coefficients need not bo accurate to more than two significant figures; wo may therefore suppose cos .J (b'+B) to be equal to unity, since its minimum value exceeds 0.995. If tli6" ^^ P"*> ^'^^ brevity, a; = (i' - i) cos J {V + B), y=zb'-B, J {b' -j- B) differs so little from 6 that we may put Sx = (SI' — 6L) cos 6, Sy = Sb' — SB; from which RESEARCHES ON THE MOlION OF THE MOON. 6D = {,61' — SL) cos h sin m + {SV — SB) cos 6i m. («) (9) Lot US now rofor to the equations (i) and (3). If wo put, for brevity, p = p cos fi sin TT, qzz p sin /3 sin tt, we have from (3) and (i) • i /;/ A P sin (J — ^) tan (I —l) = — ^ — -^ /r — T\' ^ cos b —I) cos (,« — A) J? sin y = siii & — (7. Tlio angle /' — I, or the parallax in longitude, is so small that wo may suppose it equal to its tangent, while the denominator, cos h — p cos {I — A), is always contained between the limits 0.98 and unity. Again, the quantity 11 is always contained between the limits 0.982 and unity. Wo may then put, without an eiTor of more than one hundi'edth in the coefficients. I' — Izzi.oi p sin {I — A), sin ^' = 4 (sin ^ — Q)- (10) From these equations we obtain 81' =\i-\- i.oi p cos il—\)\6l-\- i.oi m\{l—X)Sp— i.oi p cos,{l—\) 6X; and, putting cos h and cos V equal to unity, dV = I.OI Sh — i.oiSq — ^^ (sin b - q) 6It. (II) Owing to the minuteness of p, q, Sb, Sj), and 6q, the factor i.oi may be entirely omitted in the above expressions. We have next, from (9), putting cos ff equal to unity: — 6 p — p coa fi Stt — q Sft. 6 q zz: p sin fi Sff + p 6/3. The longitude and latitude of the observer's geocentric zenith, A and 0, are functions of his lat^Uide and of the local sidereal time. The former must be supposed to be known; but the variation of the latter may be taken into account in order to determine the effect of an error in the time of observation upon the lunar elements. The most simple formulae for expressing errors of longitude and latitude in terms of the errors of right ascension and declination are those of Gauss, in his Theoria Motus Corporum Coelesfmm, § 68, and are these : —Determine the angle E between 0° and 1 80° from the equation cos E zn sin CO cos r sec /? = sin 00 cos A sec gi'. Then SX = CCS ', S/3 zz — cos g>' cos E Sr + sin E Sq>'. ' 52 RESEARCHES ON THE MOTION OF THE MOON. The l(i8t term in each equation is included only for the sake of completeness in writing. The substitution of this value in dp and Sq, neglecting Sq)', gives :— Sj) zz p co» /3 6 TT -{- q cos q)' cos J'j St. 6q =. p sin ft Sir — p cos q}' cos E St. The correction to the tabular ecliptic longltudo is represented by SI. For the sake of completeness, we shall suppose the local mean time of observation to require the correction St, and the west longitude of the piano to require the correction S\'. We shall then have, for the total con-ection to the moon's geocentric longitude and latitude, Sl-\-{St+ SX'Y^^, sb + {st + sr)^, which are to be substituted for SI and <56 in (i i). By taking the square root of the sum of the squares of ecpiations (i), neglecting terms of the second order with respect to the parallax, we find: — Hence E=:i —p cos h cos (l—X) — q sin b. SB=z — cos b cos {I — X) Sp — sin b Sq -{- p cos b sin {1 — \) (SI — SX) + (ps,\nbcos{l—X) — qcosb)Sb; or, by substituting for Sj), Sq, and SX their values, SB = p cos b sin {I ~X)Sl+ (p sin b cos {l — X)~q cos b) Sb +p cos q>' sin tt {cos fi cos E sin 6— sin E cos b sin (l—X) — sin 13 cos E cos b cos {1—X)\St — p (cos ft cos b cos (i — A) + sin /? sin b) Stt In these several equations, t is the sidereal time expressed in arc ; and, by taking for the unit of time that in which the earth rotates through unity of arc, we may suppose St-zST. If wo substitute these several expressions in (u), omitting the factor .oi, which renders the terms in which it occurs unimportant, omitting also the terms which contain sin b sin 7t or sin' b as a factor, we find : — <5/' = { 1 +j> cos {l—X)\ Sl+ \i+p cos {I- x)i'l,r + { [i -\-p cos (/ — A) ] 1: + p cos q>' sin tt [sin /? cos E sin {l — X) -sinJJcosC^-A)] \St + p cos /? sin (Z - A) (J;r. (12) SV = <56 + at ^\ db di ~\- p cos q>' cos E \ St ) + { sin & cos /? cos b cos (i — A) — sin /? | p Stt. RESEARCHES ON THE MOTION OF THE MOON. 63 The coefficients of Stt iii tlioso equations nmy be obtftined with {greater ease, and with ample accuracy, from the expressions : — ill' _l'-l drr ~ 7C ' * dh' _ //- i dn ~ Tt ' Our next step will bo to substitute the corrections of the moon's lon<>itudo in orbit and of the position of the plane of the orbit for those of the ecliptic longitude and latitude. Let us put , 1', the moon's longitude in orbit, counted from a departure point in tiio orbit ; 0, the longitude of the node ; as, the longitude of the perigee ; ?, the inclination of the orbit ; «, the argument of latitude ; and /?', a latitude counted in a direction perpendicular to the plane of the orbit: the ecliptic longitude and latitude will then be given in terms of «, 0, and i, by the equations tan {l—O) = cos i tan », • . , ... sni t» = sm t sm w ; whence wo derive, for the differential variations, cos I 81 — cos h 8d -\- sec h cos i Su — sin \) cos (/— 0) Si, cos b Shz=. sin i cos u Su + cos i sin m di. As we have defined v and /3', their vai-iations are given by the equations 6v = Su + cos i SO, S/S' = sin u Si — sin i cos u SO. (13) The relation of these four equations is such that cos b SI and Sb admit of being expressed as functions of Sv and » -\-a) Su,-\- cos {m + a) sin u 6i 4- [cos i sin (»i + «) — sin i cos (»i + a) cos m] 50 ^ Representing tho moon's mean longitude counted in the usual way by f, wo shall have Q representing tho equation of the centre and the other inequalities, and being a func- tion of f, ai, and 0, and of tho sun's mean longitude, which we represent by e'. Wo then have: — dv ( ^'^Q\,„''^Q,'^^ dm dQ d9 di = ''y'^de)^ de' + d^-'dt-^ded'f Owing to tho minuteness of the terms of E which contain «', as well as of d(3 -, dd . -,- and -,;, we may put dt dt de~ de ~ n' dt' without an error of more than — of tho whole expression. Wo have also, with sufli- 500 (16) cient accuracy. dJl__ doo z= — 2ecoag; g being tho moon's mean anomaly. The coefficient J^ may be omitted entirely. Sub RESEARCHES ON THE MOTION OF THE MOON. 65 Btituting ill ( 1 5) the value of fift' from ( 1 3), luul tliat of <5r from ( 1 6), after makiiifr tlio Hu1)8titiitionH just indicated, we find ^lizzfX sin (m + «) ^' . |^J (54 — 2 nin (/« + a) com // v. '5w + com («i + a) sin if di — COH (/» 4- o") c»»n '« sill « <5(9 >, In the use of this formula, ' nmy be Hiilhstitiited for ' '', owintr to the comparative minutenosH of the difference between the two exjjresHions. Next, to find the value of -. or - , we .substitute the projier terms (if (12) in (^8). From the latter we have —.7- =: sm m cos b dt \ dt dt ) + cos m dh' 7lt' and from the former, omitting the factor /= i -{- p (uis (/ — A), ., z=. + p cos ip' sin TT \m\ /3 cos 1'J sin (/ — A) — sin U cos (/ — A) |, db' dh , , „ ,7 = „ + p cos <» cos i. dt dt For the terms of .-, independent of the moon's parallax, we find, willi sufficient approximation, dv . , , ^ dl . ■ . . J- sm (m + a), or ,^ sm 1 in + a), dt ^ ^ dt ^ For the other terms, wo determine the tpiantities // aiul tj) by the equations cos h =z cos /3 cos E = sin oj cos r ; sin h sin {if> — X) =. sin Jv; sin h cos (^i* — A) zr sin /? cos i:,'. The angle h is to be taken between 0° and 180°, so that sin h, like sin it,', is always positive. With this restriction, ip — A may be obtained from the foi-mula . / / -1 \ tan E tan (0 — A) =:-.- sm /^ The angle ^ — A must therefore be included between the same limits. If we omit the factor cos b, the terms which depend upon the parallax now become : — p cos Ip' sin TT (sin h sin m sin (l — ip) + ) + cos A cos m) — -- sin /«. dt lit dt h, being a function <>f <• simply, aiul independent of the place of observation, may be tabulated with t as the argument. 9 75 AP.2 66 RESEARCHES ON THE MOTION OF THE MOON. For the coeflficients depending on the longitude of the pUice, we have for which we may put For the coefficient in respect to the paralhix, we have dn- TT IT Li those of the precedin.r expressions which depend on tiie adopted unit of time, it will b«> remembered that this unit is tacitly supposed equal to the time in which the earth rotates through the radias imit of arc, or 24 sidereal hours in or. In sidereal time, 13751"= 229'".2 = 3\82; In mean time, 13713' = 228'".6 = 3\8i. Numerical factors will be roipiired when the si cond is taken as the unit of arc. The t".)rnml!« to be actually employed in the computations nniy now be recapitu- lated as fo.lcws : — (A From the geocentric latitude of the place, sin r. Five-place logarithms are always sufficient for this computation. (2) Tut ]) ■= p cos /3 sin T, * H z=. p sin /? sin w; and compute i^ /', V , and s' from the equations 11 cos h' sin (/' -l)=P sin {I - A), H cos y cos (/' — = t-os h—p cos (/ — A), li sin //=:sin h — q, , __ [4.75002] sin TT RESEARCHES OM THE MOTION OF THE MOON. 67 jf, b, and tt being tlie tabular geocentric longitude, latitude, and parallax of the moon for the moment of observation. Here 5-place logarithms ai'e enough for terms having sin /T as a factor, i^lsewhere, 6 are required. (3) Having found the apparent longitude and latitude, L and B, of the eclipsed sun or occidted star, find D and m from the equations D sin m = (I' — L) cos J (h' + Ii), D cos m zzh' — B, ; .■ v '■_,[' using 5-place logarithms. In the coniputati»ms of the difterential coefficients which follow, 3 places are sufficient. (4) Find the angles E, i(> — A, and /(, all between 0° and 180°, from the equations cos E zz sin co sec /3 cos r, cos A rr sin QJ cos r, / V , . , .V tan E ^ svn /y For any one place, these angles ma}' all be tabulated as a function of t ; and the values of sin h and cos /«, being indejiendeiit of the latitude, will answer for any place whatever. (5) Find cc from the equation a =z 5^.14 sin », which ma}' be tabulated as a function of it. (6) Put (/') for the motion of the moon's geocentric longitude in o^oi, expressed in minutes of arc. Then '//'_.(0. ->:-:•■ ;:,--::^;- , ': de 7.90' (7) Find the moon's mean anomaly,//. Wiien Hansen's tables are employed, the disturbed anomaly may be used, and found by the formula ,7=i3".o65(.'-i5.i8). (8) The several differential coefficients which admit of being determined from the eclipse or occultatiou are then as follows : — de f/e dh f du) dp idd =: ~ 2 cos // sin (/» + '•')> =: — cos H cos {m -f a). dJ) . / , ^ ,. i::sni 11 cos (111 + a), di - - =z sni w + " cos in. dir TT /T 68 dfi' RESEARCHES ON THE MOTION OF THE MOON. ■J rr cos (»i -f- a). dt 14.4 ^ ^ + 15.05 /3 COS ^' sin ;r {sin h sin wi sin (/ — ';&) + cos h cos >»} — > — -* sin »n. ';[!=z-('l)-sinO« + a). f/A 14.4 In case of an occullation, tlie equation of condition will be '^ 5 e + i^ c .565 + etc. = s' - 7>. de cdw ' A similar fornuila will hold for eclipses of the sun computed in this way, except that the distance of centres determined from the observed phase must be substituted for s'. $ 7. EFFECT OF CHANGES IN THE LUNAR ELEMENTS UPON TUE PATH OF TOE CENTKAL LINE OF AN ECLIPSE. Not only in all ancient eclipses, but frequently in modern ones, the data derived from observation are not times, but the lines along which the edge or some point of the shadow passes. To utilize such observations, it is necessary to express the change in the central line due to changes in the moon's co-ordinates or elements. This I have done by Bessel's foraiuloe, in the very simple form in which they are developed by Professor PfiiROE in his TrUjommctrij. The notation is as follows: — A, the moon's geocentric longitude, minus that of the sun ; /?, the moon's latitude, diminished by that of the sun, if necessary; e, the obliquity of the ecliptic; )(, the angle of position of the great circle drawn from the centre of the sun through that of the moon, measured toward the east from the circle drawn to the pole of the ecliptic; Q), the angle which tiie same circle makes with the meridian passing through the sun ; TV, the sun's equatorial horizontal parallax at the time; n, that of the moon ; y, the angular geocentric distance of the centres of the two bodies ; m, the ratio of their linear distances from the earth's centre ; c, the ansrular distance of the centres of the earth and moon as seen from that of the sun ; a', d', the right ascension and declination of the sun ; a, d, those of the line joining the centres of the sun and moon ; L, the sun's longitude. 69 (0 RESEARCHES ON THE MOTION OF THE MOON. We then have : — tan y sin M = tan A. tan y cos u zz tan /3 sec A. sin ;r sin 11 c zz 206265" m tan y cos y. tan (h — o)) z= cos i tan e. • ' rf = 6' — c cos OJ. / a = a' — c sin GJ sec (5'. Gj' = 07 — c sin CO tan 6'. ' j^_sin(y-fc) sin // The co-ordinates of the point in wliich the centre of the shadow intersects the plane perpendicular to it passing through the centre of the earth will bo, when reck- oned in the usual way: — X z= li sin co' . " ,.. y zzlt cos CO . Next, putting 9>', the geocentric latitude of a point on tlie earth's surface ; p, its distance from the earth's centre ; ; /i', the west hour-angle of the axis of the shadow counted from the meridian of the place ; or, fi' zz sid. time — « = apparent time + <-" si" '^ sec <5'; the corresponding co-ordinates of the place are , H z=.p cos (p' sin yu', ff=p (sin 9>''cos d — cos

), So) — Sti =. tan e cos" (» — &») sin L SL. (9) The maximum value of this term is 0.4 6L. The probable error of the sun's tabular mean motion does not exceed i" per century ; the right-hand side of tliis equation can, therefore, scarcely ever amount to 10" during historic times. The greatest error in Sx and 61/ which can arise from omitting it will therefore be of the order of niagni- tutlo M X 10" or -^. 20000 The maximum value of II being about 4000 miles, the corresponding error in the path of the shadow will bo less than 400 yards fitr the most ancient eclipses, and less than 50 yards for tlio lodern ones. It may therefore be entirely omitted, which will make dcoziiSu. Wo have thus made the variations of :c and y to depend on those of 11, y, and /I by the equations (7), (8), and (9). We have next to express the variations of u and y in terms of the variations of the elenients on which they depend. Since we suppose cos y, cos A, and cos /? to be sensibly unity, we find, by differentiating the first two of equations (i), m\ u 6y -\- y co9,nSuzz.S\, com Sy — y mxudn-zzSft; i Avhich give f>y — sin !< <5A -f cos M 6ft, y 6uzz COS ^^6\ — sin m 6ft, T2 RESEARCHES ON THH MOTION OF THE MOON. If WO substitute in (7) for B is apin'oxlmato value -. — -, and foi* SB, and <5ai' the SHI 11 values derived from the equations (8) and (9), the expressions for Sx and Sy reduce to cos (« — <»') _, 8in(M — oj') ,. r sin oj' „„ ^^ Bin, 11 "'^* ai»i« II ' 8y: sin/? sin (m — <»') *i ^os (« — a>') Sin n ' Sin // sin'-' 11 dfi. Y cos CO (10) sin"// rsn. As already shown, if wo put « in place of &>', the error thus introduced will be, at its maximum only about ^ of the total amount of the corrections, which will be quite nnipnportant in all cases. If we suppose the right ascension and declination as well as the longitude of the sun to bo known, we have , . sin a' COB (m — oj) = -: — r > sin (« — oj) = cot L tan ) — F cos (« — «). • AT d^ _ -X' cos {u — aj) -f F sin (« — m) sin// -r,^-= F sin go' — X' cos co' V x'^-j-y-'' dll ~ sin // The most convenient fornuihc for computation will be: ■S) •90°). (12) dJ _ sin (m — (o- dy sin 77 dJ _ cos {u—co — S) d'fi ~ sin 77 ■ dJ _ Y cos {co — S) (/77~ ' '^v^ n ■ In the.se exi)ro.ssions, the unit of J is tiie earth's o(iuatorial radius, and that of A and /? is the unit radius of arc. It will be rouiembeied that J is here the smallest perpendicular distance of the place from tlie centre of the shadow, and uuist not be confounded with the corresponding distance measured on the surface of the earth. If nothing more is known of an eclipse tiian that it was total at a given place, J may have any value less than the radius ' 10- .75 Ap. 2 74 RESEARCUKS ON THE MOTION OF THE MOON. ./'beiiiff the aiiglo in ([lU'Htioii, mid / th« distfineo or radiuH vector of the sun, its mean distance being unity as given in the ephemeris. I'ho formula , . ,. [7.6678] ... log sni / = '■' — /—^ r will answer for all practical purposes. Compute also the distance of the moon's cen- tre from the fundamental plane, , _ cos (x + c). sin // ' z-zi and compute the value of 8, for the place from the third of formula (3). Then we have /ai = (z — 5) tan/ — 0.27227 sec/; (13) Pj being the radius of the shadow. If now ^„ represent the tabular distance at which the axis of the shadow passes, as given by formula (6), the value of J^ + ^d must be contained between the limits + Pi Jind — p,. The expression for this function is The condition sought is therefore We have now to introduce, in place of A and p, the mean longitudes of the sun and moon and the longitude of the moon's node. Introducing the notation of the preceding article, where we have put e, the moon's mean longitude ; I, its true geocentric longitude ; (/'), the motion of its true longitude in minutes of arc in o''.oi ; and Gy the longitude of its node ; we shall then have 6\ = 6l—6L= ^''^ 7.90 St - SL ; 6fJ = sin i sec /? cos (l—O) (61—60) = m\ i sec /3 con (I— 0) ( ^^"' 6e — SO). \7-90 / In the case of a central eclipse of the sun, we may put .sec /? cos (/ — ^) =: posi- tive unity when the ecli|)se occurs near the ascending node, and negative unity when it occurs near the descending node, without an error of mon* than ;,'- of the whole co- efficient, and may take ± .995 as its mean value. We may also suppose sin / = .090. The value of Sfi will then become S/3z=±.oSgs(^y Se — So\ Substituting these expressions for <5A and 6/i in the expression for SJ, we find 6 J = / (^i ± .089s l^f ") Se =F .0895 ' 7-90 \d\ (I ft) (' %"> + %'"- n"- (■*) RESEARCHES ON THE MOTION OF THE MOON. JfJ in which the tUflFerontial coefficients are to bo taken from (12). This equation f^ixcs the condition which must he fulfilled by the corrections to t\w elonicnt.s in order that the path of the shadow may 1)0 thrown to the north by the quantity <'^J. The upper sign is to bo used when the eclipse occurs at the ascending, the lower when it occurs at the descendinff node. In this ff)nnula, wo tacitly suppose the error of tlie moon's true lond from the observed altitudes, using the mean places of the stars given on the next two pages. The geographical positions of tiie ])laces of observation of the two observers have been adopted as follows: — Long, from ' Latin Name, j Modern Name. Latitude. | Qf„„n\vich '°^ '' '"" ^ ' '°^ '' '^°^ ' ' Paris. . Loudon . Juliodunum Lridununi Dinia . . . Digne Aqua: Sexlln: Aix . 48 5» 47 « 44 5 43 3* s 21 E. 20 E. 24 57 E. 21 47 E. 9.8747 9.S622 9.8403 9.8358 q.8192 0-8344 9.8570 9.8610 It will !)«> remembered that in making these observations the observers used no clock, but determined their time by ob.serving the altitude of some well-determined object at the moment of the phenomenon. The star-positions used in reducing the observed altitudes of all the observers whose work is discussed in the following sec- tions are shown in the following table. No refinement has been aimed at in their derivation, nor have the j)laces been corrected for nutation and aberration. All the corrections which should be apitlied are completely nuisked by the probable errors of the observed altitudes. 76 RESEARC'lES ON THE MOTION OF THE MOON. Approximate Posilions of Stan for Clock-error, carried back from the Positions ofh^ Verrikk. (Ammles, ii, p. [63],) n ANt)ROMED.«. Ycir. Right Ascension. Dec i linalion. // m 1 , ■ 1650 23 50 25.48 + =7 y.5 171K) 52 58.11 36,0 1750 55 31.17 48.5 1800 23 53 4.66 ' 27 5'). I 1850 38.58 28 157 iqOO 3 12. 03 +28 32-3 Year. 1650 1700 1750 ' 1800 i 1850 iq/oo 1600 1650 1700 1750 1800 1850 1900 1650 1700 1750 1800 1850 I goo 1600 1650 1700 1750 1800 1850 1900 1600 1650 1700 1750 1800 1S50 igoo 1650 1700 1750 iSoo 1850 1900 11 Akietis. h m .t I 44 4023 47 35->3 50 21.51 53 9.40 55 55.78 1 58 4365 2 I 32.02 II Ceti. h m s 2 44 3-' 46 38-7 49 I4.S 51 50.4 54 26.5 2 57 »'9 + 21 21 + 22 46.7 37-7 22.7 1.7 34.8 1.9 i 23.1 i + 3 40.9 53-3 5.f> 17.8 29.9 4t.3 Aldebaran. 4.17 54.61 45-32 36.31 27-57 19. II 10.92 + >5 15 16 -I- 16 37 44 52 58 5 12 18 37.4 54-0 l.o 55-7 39.0 10.9 31-4 CAPEI.1.A. 18.16 ! 56.94 ! 36.21 { •5-97 I 56.22 j 3'i-97 I 18.20 I + 45 ■45 29.8 34.3 38-6 42.7 46.6 50.3 53.8 /J Orionis. 450 8.5 32.1 55-9 19.8 43-8 SiRIITS. Right Ascension. 1650 1700 1750 1800 1850 1900 1600 1650 1700 1750 1800 1850 1900 1600 1650 1700 1750 1800 1850 1900 1600 1650 1700 1750 1800 1850 igoo 1650 1700 1750 1800 1850 19UO 43-a 555 7.8 act 32.4 44.7 Declination. - 16 - 16 IV.I 20.2 23.5 27.1 30.8 34.7 'I Orionis. /( III s I 36 38 41 44 47 49 I 4 7 10 13 16 19 14.57 56.59 38.69 20.86 3. II 45-43 /( Tauri. J 5. II 13-38 21.88 30.61 39-57 48.77 58.19 t- 7 >7 7 18 44 20 10 21 24 32 27 23 18 26 + 28 I'ROCYON. 19.00 56-75 34-41 I 11-97 49-44 26.81 I 4-09 I Pol.I.UX. J 43.08 48.62 53.86 58.81 3.46 7.8. 11.87 Rii;ui.iis. + 5 + 28 38 10 51 14 50 18 35 22 7 25 25 28 30 31 21 10 50 4 18 57 35 50 41 43 36 36 30 a8 53 54 42 4'* 47 42 39 36 19 29 46 9 10 10 lit s ^ 49 .19.78 + "3 52 20.91 55 1.77 13 57 42.37 13 22.70 3 2.77 ■+- 12 23 16 I 3 39 1-9 24 53.8 1 10 39.6 ■ 56 19-4 41 53-2 27 31.3 RESEARCHES ON THE MOTION OF TflE MOON. Approximatt Ppsitions of Stars for Clock-trror, (Sf*-.— C''> 9.40 43-43 17. as I 50.87 24. 28 57-49 Sl-ICA. h 13 13 I, 13 14 14 4 6 ') 46.4 37.1 24.1 ARCTURI'S. 43-0 59-5 16.0 32.6 49.3 5-9 + 21 20 2U + 19 1-7 45-7 29.7 13.8 57-9 42.2 1650 1700 1750 1800 1850 1900 1650 1700 1750 1800 1850 I9CX) 1650 1700 I 1750 i l3oo 1850 KJOO h 18 5.8 47-a 38.6 10. 1 51.6 33-2 + 38 38 39.5 31.7 34-0 36.3 39.8 41.4 a Aqcti.H. 19 19 h 20 41.91 8.44 34.94 1.4" 27-S3 54.22 n CyGNI. + 7 31.00 13.95 54.96 37-02 19.14 1.3" H- 44 44 59-2 6.4 "3-7 31.11 38.6 36.3 3-4 13.6 23-9 34-3 44.8 554 a COROS.T. BOKEALIS. 1 a Pegasi. h m / . /; m ^ ' - ■ 15 19 53-1 , + 27 55-6 1650 22 47 22. 06 + 13 20.0 31 51.8 t 44.9 1700 41) 50.74 35-9 34 6.6 34.3 1750 53 19-54 13 M.9 2() 13-4 23.7 1800 54 48.47 14 7-9 28 30.3 13-4 1850 57 17.52 24.0 «5 3" 27.2 i 3.. 1900 22 59 46.70 + 14 40.1 Observations of Bulijaldvs. From Anlionomia I'hilolmiu, p. 159. Anno 162.} .lulij ilie 5 cum Liintie centrum iiitum eswr g. lyj I'aiiaiis obaervnvi occiiltationtMii SpicHC VirginiN a 3> . BiJLt.lAi.Di?.s adds that the moon appcnrcd 13' north of tlit> star in latituth^ ; and having thence compnted its position, \u' achls:— "fuit Honi Parisiis ox altitndiiio Spicau p. 17.7'. post nieridiurn ix. 30'." There is then-fore some doubt whether the actual observation of altitude was made on the moon or on Spiea. The corresi)ondeni'e between the dirtereiico of altitmles and diHercncf of latitude is somewhat susi)icions. The apparent places of the two objects are, as a first approximation : — Hpica, A. H. = 13" 5™ 27'; 1^««'- --9° 10'. Moou, A. li. - 13' 4"' 40'; l^ec. = - 8° 46'. f$ RESEARCHES ON THE MOTION OF THE MOON. The jilftco ot'tlio moon is tlint roinpnted tVoni IIanmkn'h 'ruldoH fi»i' 9'' 33™ 37* I'uriH tinu', 1111(1 coiTi'C.tod for piinilliix. TIio local tiiiK'H tlieiici' (Icdiicctl niv: — From alt. of Sjiini, i;'' 7', t5id. '1',= 16" 27'" 15"; M. T. = 9'' 33'" >8". -Moon, 17° ao' 16" 26"' 58'; 9" SS" I". Tlic ivsnlts ajiTco well enough, Imt the fact is that at thin time the tables, which can- not he ,^' in error, show the ii|)]iarent distance of the ceiitn* of tlu^ moon and .Spicii at this time to have been aliout 2S', so that the star must liav«f he<'ii Home 13' distant from the moon's dnik liiid). 'I'he moon was then a few hours past her first (Hiartor. Moreover, the moon was about 20' north of tlm star in latitiule, so that there could not have been an occiiltation at all. Indeed, a careful readinj;" of Hii,!,iaM)Ih's dodnc- tioiis from his observation seems to indicate that he considered the two bodies to have the same loiifiitiide at the moment of the ohservntion. Now, we must adopt 0110 horn of this dilennna: either (i) wo have to deiil with sn»di u blnnderin}i' ol)Mervor thiit ho thonyht ii star at the moon's liinli when it was 23' distant, and in foiijnnction when the dillficnce of htngitiide was some 20', and that when the ditdiotomi/.ed position of the moon was most favorable to the observation; or (2) he made 11 mistake in readinnil I'i(;toiit's cniu.-' Meridiinnis riMMovctiir a I'arisiciisi o('casnin vt-rsas, (|ihi(hMiitn IVrnii' lioiac unius, oljserViVviowinltatioaiMa iin^uli oriiMiliilis qaailrilatcri I'lt'iiiilnni i|n;M- iK: lucida IMciadnin ili(;itiu' interveata Lanae t'^ictain l)cc«-rnl)i'is die 30 ia distaiitin (K-nIi Tanri a vcrticc p. 57. icS'. IIoi-. 5. 42' vi'sperc. The position of Louiloii is ' '''■ A. iit inctlio II. 9. 54.' viili l.iiiiiini linilio (iltsciiio imciiIIiik* Htcl- lain <|uiiita« Mii)({iiitiMliiiiH, <|iiMi' «>st in oii^'iiii* citiiiii llorciilis 'runii. The roHiilt of tin* ultitndr of I'rocyon is; — liociil mean timn 9'' <)'" 42" liuciil Hidcn-iil time 10'' 13"" 13* (iruoiiwic'li iiioaii tinio , 9'' o'" 21*. Tho Htar ti(Tiilt«'il in r'l'iiiiri. I'h|Iu 167. — AiiiKi 1641. A|iiiliH (lie 13 aitu VfrMnn occmihiiiii IlnriitTo Dcxtni OtioiiiM );. 34 o'. Ilor. 8. 8' I'aiiHiiH, l.inia iiiilii (ircultavit ociiluin llonniiii S. (liociis Tyirlidti U t;. j. >'7'') Tho roHuhiiij,'' hu-al tiincH arc: — Sideri'al 9'' 42'" 7' .M(!au 8'' 13'" 4'. The oce'ulted Mnr i'« e Tauri. Tklipsca nnd ncciiltations ohservril bi/ (tAstsENnuH. 1631. MvUHe Maio, Die 20. (Men nt vul[(ii(« laiinurat, die 21. Man*-) Kclipsin HoliH liaiu; obHorva- bam A<|iiiH-8(i>,sitnM|nt< varioH arvoininiHlato impositiiin. AdtM'at il)i (itMiiiatiim iihmim, qui IVIi'Hcopiuiii iiiotitaiido, eiict' min liicis in roncavo, sen infcrioro vitro appariMili'in continno irstitncret, dcstincrt'tcpic in int-dio. KxL'ipicbani vffn Haiiios atViM'tu piano solido, pap.vro Candida ol)du('t(i. Diixci.ini in co ('IicM' lain, in tpicni radii c()(;crenlnr, tit in cilipsin nun cxcnrrcicnt. Diainctinni pcdc I'ariMicn.si ali- (piiinto inajoi'cin diviHcram in partciH acqnali'iM, sen Di^itos 12. i*^ ipicinlilii't Dij^itnni ila Hubi'iis- tinxcrani in dciuiH & qiiinaM partcis, nt liucrct ctiaiii sin(;nla iniinita per Into hI ilia colli^'cic. UtraiiKjiic ctiani Ncnii'Cir<;niii(ercntiain in 180. parties 'lisnibncniin (initio ntrinsijnc divisionis facto al> ipsa Kadicc priini di^^iti.) tnni nt in nni^iia occidlationo liccrct si-inpcr, usnrpata liciiu^ iiidc acqnuli ail iiiterl'cctionct* ('irciilorani Incis, \- nnihrac tlistantia, cop'ic radios in Circninni iV iiiinorcin inaxiinnin iiinbrao in Dianictrnai rcjiccre; tnni nt exindc Dianictrtu'nni ntrinsijac asiri appariMitiiitn liabcri poxsct inntna proportio. Adcralpracdictn.s Galtcrins in proxinia Caaiuni, aHsidne scctatns SSoliHaltitndincni (jnadrantc Kadii pliistpiaiii bipcdalis. Erat vero penes iiie, ipii statini ati|ue apparcrct oliscnraiioniH ves- tijiiain, iciii parieti iinpacto, inoineiilnni ipsi si;;nitiraret. tjinirc iioi; si^nui iit'tavit praecise Solis allitiidiiiHin initio KclipseoM; iie<|ne ratiiuie alisiniili cainlein accnrate accepit in line, sen (pio iiioinento obscnratio ex circnlo prorsiis evannit. OinniliaH ei'p> appiiine instrnetis, oliseivatnri adfaiiiins al> liora circiter 6. ita scilicet vere- bainnr, lie rallentecalcnio initinin praeteriaberctnr. (Jiinnpie© tempore Kelipseossnpponatnr Inisso in o. j{rnd. 15. iniii. [I apparvit nobis praedic'a die 20. Kctiipseos. Initinni bora 19. min. 5. sec. 28. ele\rtto neiiipe 25. ^rad. 30. min. Finis liora 21. min. 31. sec. 12. elevato s<'ilicet © 51. {{'"''• '7- '"'"• Ac; medinin proinde coiitifrit bora 20. min. 18. sec. 20. Et teinpiiM inciileiitia" tuit bora 1. iniu. 12. sec. 52. Et tota diiratio borarnin 2. mill. 25. sec. 14. Di(;iti ecliptic! iiiaxiinae ob^enrationis fnernnt 9. min. 2^, Et qnia tuni deticicbant utriinqne ex circiinifereiitia ((radim 77. min. 30. liiniic aeqnalos visau nrguuiitnr Liiininarinni Diametri. Fuit LuDH Soli SupteiitrioMuliR; quod circuloH tiobiH citra telescopiiiin tenierari caoperit ail Austrum. 8o RF.SF.ARCIirS ON THE MOTION OF THE MOON. FiiitCoi'liiin iiitt'rs|H'iHiim toliim toiiiport^ Kdipsi'os niriorihimnubiliH. .Iiivalmiil illii ntOpoK- Hut Roiispici ociilo It'll' iiK'OMiiivt'iiti, i*t spi'('illo<|iii(UMii inaxi.iiit'. (Jonspci'tus vt'io ♦'8t t'tiiiiii iiiiioxit- tiiiii in spt'ciilo, Iniri in :i'|ua iiinpiilii; cum ntntbiquo tics vl('erentur i-xliitieri Sol^s, i|UH8i trw Lniiii*' coi-nicnlatjii' ex oi'ilinu posiliic, vorMin ooriiiliiiH ail <>i;rasiini. Ik? iiltitudos yiv(! I.ik'mI ini'iin time of huiiiiiiiiiiij- jgi, ,... ^--. ,,f,>,„i^ 21'' 27'" 17" (iri'iMiwicli iin'iin time of Iteffiniiiiii;' . 18'' 39'" 50"; ofiiiiil, 21'' 5'" 30". 1627. MciiMo .liuiio, I)ii' 17. Vespori, luinc (MsoiilliitioMiMn CiirilJH Leoiiis i\ Lunn observabani Dinliie, ciini siMlicct t'invt (.'aiida .vl altu ail Ud'aKiun 25. urtul. 13. uiln. hoc mt, hunt 10. luiii. 30. praor.is)' (iitol)ai' ilicto iaiu antt' (juadrato, cuius umbra ivcta, scu tant;(Mi8 oxliibiiit parteis 4710) Luna, liiin corniciilata lirnbo huo OrliMitali, hi'II parte oliscura Cui'. ^\\, subiit. I'Diiii tiiiii U'ctura trii'iito A cDrnu inti'riori; tandem veri) texit. iioii xiidlo anipliiis i|nndrante. Observatii est autum non niido suh'ini visii, (|Uo Stella videbiUur Luiiain, quasi adreperido, radere; viM'iim etian) pitr Telescopiiitn, quo distnntiola qiiaeiiuu ad iieeultationoin usque diHtini;!!") percepta est. TIio iiltitiidi' of ft Leoiiis <(ive8: — Loral nioMii tiiiu> of oc'cultation 10'' 30'" o' (irt'C'iiwirli iiicau timo 10'' 5'" 3". 1630. Caeterum eopiain s\ Sebiekardo iiostro tibi iaui oxistimo factani niuae illius observationis oirca Kelipsin Solis nuperani diei 10. Juiiii. I'age 545 — Nisi luerit, seito nobis in hac Civitato (cujiis latituilo est 48. t;i'iid. 52. inin.) illiiis initiuu! I'untiKissc Soleadnceasuni altof^rad. 14. min. 40. sen liora pj, Fiueni videre non potuisse, proper Holis oeeubitiim, ciiui dnonim prope diKitorum foret adiiui; obseuritaB. Medium, ipiateiius licuit, observatum pruxime fuisse Sole adliuc eluvato grad. 6. min. 30. seu bora t'irciter 7. nnn. 12. Tlio pluco of observation was Paris Tlie altitude {jfivcs ; I..ocal moan tiiiio of l)i'fiiiiiiiii postea e^ri'ssu, etsi vapores iam I'uerant loi'^e iimplins deiiHiiu'es tacli, varieKataqiie irradiittio ('ileum Luiniiii dittundebatur ; apparvit tamen cmer^'ens In miilta iam niclinalione ultra planum verticalis, cum idem limbus Lunae supreuius esset alius ad ocu.isum gr. 39. min. 57. eodem({UC inoniento ad ortom I'oret Lneida Lyrae nita ^nu\. 31. inin. 54. The oltservtUivMii'i f;ivo: — Immersion, fnmi altitude of .\ntunis, Loral M. T. 15'' 18™ 39"; G. M. T. is" 9"' iS'. Kmorsion, from altitude of « Lwii; Local .M. T. 15" 47'" 31"; G. M. T. 15" 38'" 10". RESEARCHES ON TIM. MUTIUN UK THE MOON, Edipse oj 1633, April 8, o/wnvil tit Dignf. Sr PhBHUH Kcli|>Hir(is. I. 2. 3- 4. 5- 6. 7- 8. lu. II. u. >3. '4- 15- 16. »7- 18. !(}. 20. 21. 22. n- as. 36. »7- V*i>aiilitu8 OvfuctiiN Gndui lilnc inUe (Itticiciitcs dig. m. Rr. Ill 4. 30. 5". 5. 42. f8. 7. 0. 65. 7 30- 68. 8. 6. 70. 8. 12. 7>- 8. 18. 7a. 8. 18. 73- 8. 6. 70. 7 4a- 68. 7. 30- ('!■ 7. 12. 65. 6. 48. Oj. 6. 36. 62. 6. 12, 60. S. 30- 55. 5. 18. 53- 5. 0. sa. 4. 30. 50. 4. 18. 48. 3- 42. 45- 3. 0. 39- 2. 4a. w. 2. 0. 35. 1. 36. 30. 0. 54. 30. Finii. 0. rimtluft incH- nallii. L>la- nicir.iTuiii uil Alt. ., In luirtibiis I.UM. Veiilc. V. R Kf 111. 32. 3S. 50. 62. 72 85. 107. 112. :i7. 122. 125 12a. 132. "34. 136. 138. 140. 141. 142 143 145- 147- 14? 150. S«u rcft|>cctu habllu tinii rclr tiitii paralUxcuH I Kratl. mill. 5150. 4050. 3950. 3800. 3720. 354')- 3150. 33. 3030. 2(>20. 2850. 2800. 2750, 3670. 2560. 2450. 2350. 2260. 2230. 2160. 2060. 2ono. Il/K). .74"- '.(*yt. 1430, 35. 15. 20. 20. "). •')• 18. IC. 16. I5' 15- Ij 14. 14 13. 13 12. 12. 12. II. II. 10 3 33 48 a4 30. 2. I 16, i "•I "7- I 54- i 3<), S3, i "• I 23. ' 46. ' 13. 44- 34 II. 38. I.J. 45, ■2. 5- S' i 37. 13. 23. 21. 20. I 20. I'l 18. 18. 16. if.. IS- IS- 15 14 I» 13 12. 12 12. II. II. o. 2iy. 43- 19. as. 56. <)■ 41 'J- 4'' 3' 15 48. 13 37 4- 35- 35 I. 23. '(■ 31 41 m. 53. Hro|«>rllo Dia- ; liiL-tri C ad ' Diaiiiutr. ^.t Sit v>. Sum. ' 15. m 2«. HCI-. ; A Sviii < I mill. sec. , 3. 56. 3. 0. 26. H. 2.,. 8. .33i. I-J. 36. IS- 41. 13. 431- 7- 48. I7». 5"- 15- 5')- M . I. 17. '■ 7- S- 4. 12. 7 10. , 10, 13. 5' 13 '5- 16. 10. -■ "'< 2. , 30. 5 22 6. 25 2. 27- 2. 30. 1 1. 52. *• 35. "*' t^ '>3J- 10. 45- • Tlio rosiilts ;»f flu! (ihstM'Vfitiitii.s will he yivou in (lisciissiii(>' the eclipses. 1635. .\HK. 26. — Occult alio iiriu'ri'dciilis iliianiiii Caiidiii' '} a ([.iinia IvcpK'iiis iiioiiiu'rat loiv lit d Stt'lliis Cttiidat' > tt'fjcri't iiolii.s, idcirci) atttMidoiidiiin dii.\i ipiid liae do re (•()iitiii;;i'ii't. VA iiiiIk'h quident puroxigiiain relJi|iiL>rniit .spcin qiiiuqiiain obHorviuidi, ac ])otisMiiiMim cin-ii pnu'ccdi'ii- ti'iii diianini }- in taiitii ([ viciiiia, ob illiiis oxilit.tttMii ; vi'ii'iiii tainctNi iili.stilciuiit, i|ii(i iiiiiiiis ii'licta i\ d deti'ffi iisi|uaiii potiirrit, |H'riiii.« taiiicii ip.siii.sciinsiu'ctiiiii, ciiio inoint'titi) olilc},'! (-(u'pif. Viiric, iic noil sine laltoro st'ctatii.s illaiii fiu'raiii ctiaiii in iNlinoTclc.si.iipin, oli imivi'isi |iiiipi.|iiiidiiiii iii'iiH inibilo.sitattMii ; soil ravtirc cvimio di.stiiicli.ssiiiio vi.sa est :^ .scn.siliili iiittT.stilio, i|ii(;iotiu siipciitiii.s paili.s Mauiilau );>'i><>ilii>^>'*'l:tt'i '■'^ '^'■'lOi^t^-'i'i-'^ rutiiiidai', qiiiic ost ad laevaiu nnibilici, hoc «'st infra im-diiiin oriciitalis inaiKiiiis parte rtit' dimdf ciiiia totiiiH aiiil>itim LiinarJH. Knit aiitfiii tunc liicida V Jam t-Ii-vata ad Oiliiiii jjv'- f'"'" '**• Kiad. 31. miii. nude proditiir liora I), mill. 47. l''uit & iiiarjji) .superior roxiiii(>, iiiidc prodiliir bora 1;. iiiin. 501... Knit deiiiqiii^ aililndii Capitis Andionie) iiiiii. 50 credideriiii lioraiii u iiiin 19. II 7.". Af. '-' 82 KKSKARCHES ON THE MOTION OF THE MOON. Tluf results tVom tlio tlireo altitudos of stars are : — From '5Aric'tis: Localiucantiino, 9*" 47'"49"; lumr-aiiylo, Kntiu a Aiulroinutla-: Local moiuitime, 9'' 52'" 25"; liour-aii:tt Stullsiu iii-oiiiiii|iiStrllau aiigaliortivc in a.stni liicidac rioiadiim cuiitigit cum alliladuc.vtivar coriiii Uorc'i ii I'oix't 26. grad. 35. aiiii. ac proiudc bor. 9. miii. 45. fait eoiisefpiuiiter altitado Aldubarac 10. Kiail. JO. mill, mule bora . min. . & coiiseipu'iiter ({ 6. grad. 50. iiiiii. Tlie altitudes j,nvo : — ' IimiuTsion of Klectia; Alt. of Aldebaraii: l..ocal lueau time, 8'' 4.S" 58". Immersion of Maja ; Alt. ttf .Mdebaraii: Local mean time, 9'' I iiiuicrsutn o f M M'l ! Alt. of // Taiiri: Local mean time, 9'' 4—« / 18" Imiiii Tsioii of ^^(•r'o|K•: Alt. of Aldeliaran: Lcx-al mean time, 9'' 32"' 3". Immersion of .Mero[)e; Alt. of /y Tatiri: Local mean time, 9'' 33'" 10". Immersion of //Tauri; Alt. oi fi'Www'i: Local mean time, 9'' 49'" 41". immersion of //Tauri; Alt. of .\ldebaiaii: Local mean tiim;, 9'' 48'" 57". 1638. Jaiiuaiiu. Diu 2|.— Vespuii, appuLsu.s, & ocjultatio I'leiuduui a c; Uictaiidam (piidciii tait cam vciito, scsc ob iiimiam violciiliani qii()(|iiovcrsaiii iiisiiiaaiitc, itL'impio ciiiii co tVigor ', ipio iiilcii.sius iiicihiiiil iicinii; scd iioii licait spcctacaltim dimiltciv, iiioli.scivatiim. I'aiicis itii piu ([ liaiisiit |U' tfloliali iliitiH muJori.'<, <|a('m ('artbiisiaiii dici'i'u .soico, rait taiililliiiii iiiforias; idipu' roliaiH^ sillo .(6. giad. 30. min. boc est liora 7. mill. 31. ^ to.vit lacidaiii IMciadiiiii,sca aiiKiiliim ., ortiaam p.irli) diaiactii ipiiisi !,.ii lioivasiii cas|iidt>, sciliet't in medio saperioris maris. lOrat aiitem tunc Liiuida in ore ^'l alta32. grad. 15. min. (l*ollu\ / n (i( iiiiii'Oinii ohsrrrrd til Diijur. i^ij.S. I)p(!oiiil)ri. Die 21. — l'ot(M'iuM cinii (t .jiim prorsiis ('xucrct hmimtmIjIc iiiilliiin olitnioliia- t'oiicin ill situ piioiir licic (lusrrlpto.itii prnmotit iiilfris'i fiiit versus caui Ktclliiui^iiuiiccst iuextrcnio p('(l(> (!iist()iis, iiiitf-coilitvi! tiliaui ill pcdi- proi'oili'iitis 1 1, ut iilaiii mi'diu siildi'i'jt, tcrranipip oripuiMit iii(i\ ante ipsi (>ripii<>i'iit BoU'iii ; scilicet ipsaiii (i(;(Miliiit puiiln iiifia iiiiiei,liin piirv iiiii ipiaiii itiitio ill pnrto ({ orieiitali descripsiuius, ac taiito qiiiileiii iiitorvalli), ipiaiititui iiineiil,. lou;,'a est : aileii ut locus fiicrit (|uasi iiieilius inter priiiiatn liet'ei^lioiieiu, & recnperatimiciii liicis. I'liit auteiii tunc liiiiiieriis dexter Oriniiis ad Occideiiteiu ad'iin: alius _•^5.seu 15. ;;rad. 54. mill, atipie ide.irco exstitit liora I*'), mill. 37. The altitude <;ives : •W Local mean time, 16^ 36'" 34"; Cireenwich mean time, i^** 1 i' . J-lcHpse 0/ tliv ,Uiii ohscrnil at ili.r, idy), •fiiiir I. 1639. Muii.su Jiniio, Die 1. A iiuM'idie, ICulipsis 0. Fuerat Cneluiii vespere toto Diei jo. ob-scu- ruin; a iiieridie vero diei 31. eliaui ))luv. grad. 36. iiiiii. IF (•am decliiintioue IJ.ireas 2:-. f;rad. 7. iiiin. (!()lli;;itur aUitiido I'oli 43. };rad. 36. iiiin. lunjor ncfpio triiuis, vol 4. iiiiiiutis. Apparata iiiterea est sceiia in supremo Solario, iiiide lielipsis oliservaretur, iiidu('ti'ir|ue in cam macliina, ipialiMii l»ni':ie iiiuxpie lialtueram eiica ICdipsiii aiini 1633. lieiiu; par I'uit oliservaiidi modus, .sed iioii aecpia lelicitas piiipter iisur|)atuni Teloseopiuui majus, (pioil H|u>cietn Solis in ciiciilo trciniilaiii niiiiis exhilmit, |)iopten|ue ipsaiii iiuudiiiiam, tpiae iioii satis aeqiialiilis seciiiidiiiii oiiiiieiii motioiiem t'liit I'^tl'i-etuiii neiiipe exiiide Ci-'t, ut tametsi Corlieraiius dirij^erer macliinam, i|)se eiiruliiiii teiiiperarem, adjulaientipie etiaiii viri in civitate priiici|ies, (alias prol'eiMo iinporttini) in adnotandis partiluis tain i|>siiisdianietii, Siili4 altiludiiieiii. itcspiindit ipse monieiito povi earn esse 2S. ;;rati. 30. 111:11. iimie indicat t est bora 4. in in. n' .•■ "luiii veio inter dij;ii(iM'eiiiliiiii innn esHct vei iiuaciiam luarsiiiis inaetpiaiitas, vei iimbrii d siilueiis {iidile & inter rtspoiitleiiiiiim) laiitiim teinporis est clapsum, lit taiitiilns iiiteit;i del'ecliis occiipave potiierit ,,',„. iliametri; idciKci visum est iiiiliuni posse exipiisilc rert'ii.i ad iuu. 4. iiiiii. 44. en nunc sciiciii olisei\atioiiis, ciim ilediiciis per cftlculiiin. »4 RESEARCHES ON THE MOTION OF THE MOON. [ I'nitcs ion. Siiiei n.Mliirll>inc ilinmclri ilc- 1 in iliuili'S cl ticlcniCT. 1 iniiiulu. j 1 frniliiscircilin- ' crciitiftchciiu- ' mil' ilolii icn- [ El ilium. iiilf colli- suitjM'slta 30. L'ltiitdmm. , in. 74. sec. (Ill- ; 1'""""" " liKl.ur .Hum. 1 «• i MUtuiIort su- ra hnri/ontcm.! M»iiicnln Inrtc clirila. 1 .Kg. Ml. urail. mill. Mc. K'- '"• hor. min, 4. 44 Initio. I 1 38. 30. 5- <). 36. .8. ; 06. 29. II. 28. 0. 4- 47- 7. 0. 50. 20. 77»- 23. 31- 27. 40. 4. 49- 10. I. la. 25- ; 89. 27- 3- 27. 20. 4. 5'- It. 1. 26. 28. 95i- 29. 2. 27. 0. 4- 524. 14. I. 41- 30. j 93. 28. 16. 26. 37. 4- 5fi. 18. 2. II. 35- . 104. 3'- 37- 36. Ill, 4- 57- ao. 1 a, 34. 37. 101. 30. 42. 26. 2. 4. 58. aa. a. 38. 38. 1 14l. 28. 44. 35. 30- 5. I. 25. 3. "• 1 40. ; OOj. 27- 31- 25. 24. 5. >i. a7. 3. 14. 43- 1 99- 30 . 6 . 25. 0. 5- 4. 30. 3- 3f'- 1 45. 1 qf.j. 29. 20. 24- 40. 5' 5- 33. 3- 58. "• 95- 28. 52. 24. 25. 5- 7- 36. 4- IQ- 50. t 99- 30. 6. 24. 5. 5- 9' 39- 4. 34- 51. ! 97. 29. 29. 23- 40. 5. M- 39- j 4- 41- 52. .,8. 39. 48. 33. 30. 5. 12. 3gi. '< 4. 45. 52. 9f'i. aq. 20. 23. 30. 5. 13- 41*. ; 5. 0. 54. 99. 30. 6. 23. 0, 5. 15. 4aJ. j 5. 6. 55- too. 30. 24. 22. 55. 3. I5i. 46 J 5- 35. 57. 97i. • 29. 38. 22. 30, 5. 18. 47- 5. 38. 57- ,/,J. 29. 20. 23. 15. 5- 19. 50. 6. 0. (>o. 100. 30. 24. 33. 0. 5. 21. 5S- 6. 36. 65. I04t. 31. 4''>. 31. 2. 5. 26. bo. 7. 12. 67. 101. 30. 42. 30. 30. 5- ag. bli 7. 23- 68. JOI. 30. 42. ao. 30, 5. 30. ! 6a. i 7- *(>■ 67. ()8. 29. 48. 20. 3. 5- 3>i. ' 62 7- 26. 68. looi. 30. 33. 19. 45. 5- 33- f>4. 7. li- 68. 98. 29. 48. 19- 3'>- 5- 34*. ft;. 7. 48. 70. lOOj. 30 33- ! .9. 25. 1 5. 35. W)». 7- SQ- { 7". 99. 30 . 6 . 1 19- 5- - 5. 37. (17. 8. 2. 71- 100. 30. 24. 18. 55. 5. 38. 68. 8. 10. 72. 101. 30. 42. 18. 36. 1 5- 4". 1 67J. 8. 6. 1 '"■ i 98. 39. 48. i 18. 0. 1 5- 43. 68. 8. 1". ! 70. I 98. 29. 48. ! 17. 16. 5- 47. 68. 8. 10. 1 70. , 98. 29. 48. 1 16. 40. 5- SI- 67.- 8. 2. ; 69. 1 97. 29. 29. 1 I 6f.. 7. 55- i 68. 'J6J. 39. 20. 16. 0. S' 54*. 62. , 7- 2fi. 68. looJ. 30. 33- ; 15- 30- 5. 57*. ' 50. 7. 5. 66. i u». 30. 24. , 15. 0. 6. 0, i 58. 6. 58. 65. 90J. 30. 15. j 14. 4". 6. 12. ' a fi. 36. 64. loa. 31. 0. 1 13. 58. 6. 6. i »•• 6. 15. 60. 96. 29. II. j 13- 35- 6, 8*. 1 |0. . 58. j 98. 29. 48. 13. 5. f , . II. 1 . 46. 5. 31. 57- 'W- 30. 6. 12. 48. 6, (3. n- ». 4t- 5t' 1 .07. Ju. 32. S4- 4- S- 4<). 1 86, 36. 9. ' t • RKSEARCilES ON Tlir; .MOTION Ol' Till; MOON l*arleH loti. dUnictri dv- ticicntes. 3'. 28. 27- as- 23. 20. iq. 17. 12. Sen ei tciliirliin in nrlitin) ^ . Iii;itiir diain. min. Hcc. Rr. in. 54- 43- 24- 14. 0. 2. 4''. 2. 24- 2. 17- 2. 2. 1. 26. 48. 47. 44. 43. 4". 38. 37. 35. 33. 28. 102. 103J. 100. W. Sr). lOI. 08. 92. <)ik 3>. 3". 30. 3". 27- 27- 30. 20. 27. 2.). 28. 2|. fi. 3'. 3. 42. 48. 58. II. 10. 10. 10. 10. 8. 37- 27. 45. <)■ 3". ,). o. MoiiiL-nlii itxic cUiita, hor. min. ! f>. 22. f>. 23*. (k 25*. f). 27. (1. 2.S|. <<. 2<)i. 1 31. (>. 3U- 6. 35J. IlttctoiiuH tenuiora solum i\ul)ilu foci-iant ncKotiam; e.\ hoc vei<> toiiipoic .siiliortu, ac. sfiisim u.scouaeiis ab occasii ora.ssi.ssiinivmibos ita Solom snhiit, ti-xitiiinMit laotii.s cxiiidi' liuuit iiit-oii spicmis. Soqnitur Huliiaiai observatio, quao o.st in>nifta I'.irisiis, opiiosito Moh circuli), ciijiis (liaini'tcr fsset \n\ew bos lu'.li.s P,ui.si»'nsi.s. Et ilianu'tnim ilivLst'iat (luitU'iii in partei.s 2 j. ciiciiliim in part.'i.s iSo. atiinod sohjs VU.\m'\>* notari't, altitu.liiu's c.ipm>t, vS: sinRula opi'iaretiir, noii pofiiit HJinul ml .liainctroruin incliiiatioiioH attonilere. (iiiml supcn'st obsorvationcin i-citmn ad miniituin liaU.MHla.n pcrsc.ripsit, & bac Ibrina ad mo traiisuiisit. AlliliuliiiC!! Mumcnla AUitudines parall. it Refract, corrcctae. ex altitiidlnibus Diftiti obscrvatc. corrtctis. rCcliplici. gr. m. grad. min. sec. 33. 35. 59. hor. mill. sue. 3a. 35- 4. 21. 4. Cocpit ({ Miliiucii- marBimm 31. 30. 31. 30. 5". 4. 27 39- H. »8. 57- 28. 57- 25. 4. 43- >2. 4. 0. 47. 56. 27. 5f>. 2»- 4 4'). 24. 5. 0. id. 56. 2f). 56. 7- 4. 55. 31. ft. 0. 35. 13. 25. II. 3''. 5. 0. 8. 7J. 33. 55. 23 54- >')■ 5. 14. 0. 8. 0. 1 21. 51. 21. 4'>. 37 5. 2(1. 47. Si|. !lfo\im(i« 'lrt('(Mn< j 2• 3. •• 14. 2^1. 14. 20. 31 ft. 13. 33. a. OL 13. 3S. ' 13. 3a. "■ 6 18. 43 I. 12. 41. j 13. ». 49- e. 2|. 4g. 0. 1. ("iiiis >•■! \»ttmt^ ■«» scrnpul" cinm*. 1 ._« _ , - -. - - S6 Ri:SKARCIIi:s ON Tin. MOTION OF THE MOON. ICcliiinf <)/ if>5:, Ajifil 7, ohscrrnl a I IHgiic. I'l^:. — Mfiiso .\|ii'ili, i1i(sS.iinU> iiiniilitMii r>i'li(isi!< O Diiiiau iii)v«!iiili>(;iiii iiiitr aiiiii.IIi)(miii1;u> ir.iicliiiiac, iS: Iikmuii pri)xiiiiiiiii (liipliimliM Siilis iillihiilinibii.s in ipsi.miicl I'riiopo.sitiirat' acililms apparavcrarn. i}iun\ pi'ovidis.scin )ii)ii'(> tori-, III liiii.M (>clipsi>i)s .suit ini'i'idii'Mi ciiiitiii^^crct, ac proimli' fcnipiis ex paniiii vaiiati.s Soiis altitmli- iilliii.s.sati.-t; idcirco appararaiii Si:i()tci'i(!iiiii,cpiot Niippi-tia.-* ipsi.s alliliiiliiiibiis fcrri't. 'iuod vcrcrt'i- aiitoiii, nc iiiKiavi'S(!i'iiti', (jiiao al)ali lial»i« l):il. ft'l)rit:iila. adi's.sr^ ohscrvando noii po.s.sou); id*>o (■oiiiiiiiin.sti'Aniii) nnii iinxlo Taxili, Toniatoii, lid(i Aaiaiiiii'iiHiAiitoaio I'i)ti>ria(>, sed itiMiipiM' rtiaiii Javciii pi'acclaro (''njiciscM) ntTiicrio, qiiciii totiM diii)l)ii.s iiKMi.HJIiiiM, ciirn nic iiivisi.ssi>t, j.iai dctincldiii, (|'iiil iiaii;ui(|iii^ pracslaiidiini foivt, iit. iiiivio vi(M's siippliM'ciitiir. l'',iir inilii taniMi pr.)pitia:ii iinai lc.siMpii> una caai tiiaii)r(^ iiiiihrai' liiiiari.>i S;>lis nidio.s, ix; a.lai>t.iri< Hiiniil fi)i'ai ini, i|iiiiiititii- t(Mnipi4> ip.HJii.s doli'ctiis; iidjatahat vcro adnotautn praetor ToriiatortMn cxiiiiiiis .loaiiiics l''raiii;is(Mi.s Aiig^HiiiH Ito^ius cojjiiitor, & riMiiin lioimniiii appriinn stiidiosiis, ipii iiiii^ ciiii opliiin Ij-iiitnrntio (li>n i>arti(M'ps spcctaciili voliiit. .Mudi'r.ilialiir intcrc.i l>>>rMi>riiiH iiiacliinaai inaiitilirio, Taxilis extra s:-t>iiaiti (pi'iilratiiai, Potcria ad loa^iiin aiil'in f'.t(;ia!ii, nvii totain pro ii)()r«* sic iiao pn>.'4i>i>clii ah ocuIom pono. Cam Icinpiira lit'it' lialN-antur ex Knli.s altitiidinilxis dfdiicta, taccii iioii di-liot SciotcricMiin (>\)iilMiiss(> initiiiin diiolais propc iniiiiitis aiit<>, IIihmii dii(>l)ii.><, uiit tiil)us po.^t. Kt i|iir>d ad initiiiin i|iiid<>in attiiict, altiliidiiii iiiauis lido: (piod ad liiifiii aiiloai sju'ctat, inaKi''* liaccrt'o; ac ]>(>tiHsiiniiin, ipiia Mii'iiiiiii, tainct.si |irip<>iidicu!iiMi vi.siiin est coiLstaiitins liacrcrc ad partem uad)ra(> vcrHao 711. ixi'iirriN.s« tarwn iiitctlum vtMsns 740. it ad .Siiotcriciim cum rcspoxi, iiinhra styli Hatl.s jiraocisc ad mciidiaiiaiM liiicnm i|iiadrali:il ; ipiod cxc-fssi.ssc t>iiim pilsim vid*'l>aliir, id spoctarc poliiit ad toinpii.", ipii) ail i|iiadiatiim luc attciiliim pradiiii. I'tcuinipio fiicrit ex dcdneta .■•iTie, (M)iili;.'it ceiiiiseiw. Iniliiiin lior. 9. iniii. 43. iiiediiim lior. 10. niiii. 51. IIiiih lior. n. iniii. 5^. Si('i|iio fait tnta dnratio lior. j. miii. 15. dimidiiiiii lior. 1. miii. 7' .. Here aiiiciii maxiiiiae oiiNciiralioiii.s di};it. 9. miii. <|. Diainetrorum prnportio satis inconstaiiN; veriiiitaiiien, tie eain, ipiae lialietiir cirra initiiiin, ac liiii'iii inoror, videliir omnil)iis expensis, iV oli I'iiaseis alitpiot, ipias coaimemiiii dill;;eiiliiis notatan p isse rem ila deliiiiii. at si diameter snpponalur I'lii.^se min. 31. .see \. diameter ([ tiicrit mill. ■,>'• sei\ 55. sin ampliiis, aiit minus pari )ir()p a lliilllMldd A);!irnili;;iii eeliptiiM 10. mill. 70. I)e ipiantit.ite ei^lip.scoN nihil perseripHit. i''iiiis lior. 1 1. mm. 5,3. « RESKARCIIES ON THE MOTION OF THE M(X)N, «7 liilipsi- oj ifisj, A('iil 7, I'l'sctvi (//•}• CiAssi-Nins at Di^iw. l>h»M8 Alllt 11I0 ■■ Ti-mpiira j Inde clk'lta ' ScmlurcllA (Ifficicll- j llnoruo©! OiiRlluni Unmet. 0, 71^1 titlitl cliiiiiir ftcmi- dittinet. C (Idiic iliaiii. 30 mill. 4c.«it;f. 1 flciltii-ltur Acniitliiiin. C Ac pn.iiiilc ipSli HCIlli- iliutiictcr ti ilo(cctu> Umbra rcctR Uillltl 92500 gruil. iitin. 43 46 )ior. mill. 9 43 Rriid. mill. MC. 1 111)11. «vc. Iniliu . oj 930 43 la 9 46 16 638 26 45 13 22 I. 955 43 40 9 49 34 764 33 33 16 16 It 9f.a 43 54 9 51 29 7^4 30 50 i 15 3S ' 3. 977 44 20 9 54 34 748 3" 5'J >5 55- aj 901 V.V. 44 44 9 57 38 740 31 31 ^ 15 45 3. 999 45 » 10 43 751 32 If, 3i 99' 45 16 10 3 45 719 30 38 15 i'> 4. 977 45 40 lu 5 48 6g8 2') 44 11 52 4i 965 46 1 10 8 5» 743 3> 39 15 5" 5. 948 46 31 10 13 55 74a 31 36 15 4« Si 935 46 54 10 15 58 739 31 2() 15 45 ; 6. 9»4 47 «4 10 l8 fioj 730 31 6 15 33 t-i 9"5 47 3» 10 31 64 746 31 4f' 15 53 7. goo 48 10 2; (.7 740 3. 3. 15 45 74 8()i 48 .7 in 28 70 749 15 44 15 57 8. S78 48 43 JO 32 73 751 32 16 84 865 49 9 10 37 7.6 750 31 5<' 15 57 <»• 84y 49 39 10 42 79 748 31 51 15 55 •iA 938 50 3 10 45 3o 719 31 54 15 57 qA 838 50 13 10 48 81 753 32 5 1(1 3J 9A 834 50 30 10 50 82 753 32 5 Id 2 9i*j S22 50 34 10 ji »2 753 , 33 5 IC 2 9 A 820 50 3S lu 52 S3 763 33 37 If. 14 9/11 8-1 S 5" 43 I" 53 82 753 32 5 Ifl 2 Ql'tt IH4 50 5> 10 55 81 -f'5 32 35 15 >« 9> «^ *l • 10 58 80 762 32 37 III 14 ^ 7W» SI M II 3 75 7U 31 34 >5 47 S. 787 S« 47 II 8 73 751 , .■'2 lO « 7* ii > i II n 6,, 734 31 16 15 38 i^ ' a*- » » u t* (-Si 7S3 30 47 15 24 « ^ w* ' Sft n M 1» ('3 72(1 .3" 55 15 27 •». -^ 1 » » « n 60 7J(J 3" 1" 15 20 # lift m -m •t » S» 739 .u 39 1 " 1 i> i»- s» n ! It m » 742 )» ♦'' 15 48 4k »i> m 9» i< 3B 5^ 775 33 ' iG 311 *. 7i» ss « M ^ ; 41 753 33 5 i(. 2; 3t 7W i S3 *• m ft 4* n» 33 51 Id Qi s. TW ' S3 H ' » «• "' * 7S« 32 ') III >) «t »« S3 *« i M ■^ 3« 740 31 3« 15 45 *. ■$m n w ! W 4? M JlS 31 «,! 1 '5 » I* m , ss m ' »■ « W T43 27 34 i 13 42 ** 1 ^ i S3 as- t» s» »3 (72 23 2i> , 14 30 «» S3 » ii u H> Cj? 30 45 13 23 , :m » a» 1 .1 1 i j ■ • 1 1 1 i . — — - ■ - - 88 RESliARCIIES ().\ Tin; .MOTION OK Till. MOON. Obsenalio lUliqmt So/aris die n. Aii^iisH i6^^. /li/iiis-StJC/iit /iiitit ai J/ononilo Galleno. DlKiii Inliin. I. I. a. t- 3- i- 4. i. <6- i. 6. i- 7. J. 8. Aliltudo © Kf iiiin. 3S. 30. 3f'. 15. 38. 35- 39- 45- 41. lo. 41. 35. 4a. 35. ■43. 6. 4$. 35- 47. 14. 48. 10. icu ratio SolU r.i RccupL ratio luminis 1 V. T CIII|H) Altitude V Tcm|io .J. Kr. niin. liiir III ill sec. OiKili. Hf. mill. gr. iiiin. lior. iiiin, a. 18. SIC 1 S4. S7. 3. 39. .9.1 49- 7. 34. «7. 53- 3'J. 3. 34- ')■ . 50. 30. 51. 10. 53. 2. 33. 35. 30. 58. 21). 15. 3. 1). 3. 4. .'• 57. 10. . sa. 2(i. 37. 37. 1. 49 (.. 50. 3a. 3- 32. 3. 53. 12. 27. 31. 1. 49. 2, 48. 50. 3- 15- 5. 53. 50. 26. 8. I. 44. 46. 46. 3- 7- 54. 21. 54. 55. 25. <). 34. I. 1. 40. I. 3<>. 1. 1 46. 8. 3- 1 s. 55. au. 23. 9. 1. 33. 9. 4I. 40. 2. 58. lu. 55. 33. 33. 43. I. y>. 13. 43. 53. a. 55- t. 55. r8. 56. 18. 31. 50. 21. 14. 1. 37. 1. 35. 5. 40. 6. a. 40. b- 57- • I.). 31. 1. 18. . 37. 30. 2. 30. . Finis. 57. 30. 18. 45- 1. 15. 36. 5. a. 24 . 1. t ' • liiitiiiiii liiir H. mill. 20. nit'diiiiii lior. i). min. ■}(>. Urns h.>r in. nii.i. 4;. tola liiiiatio lior. 2 mill. 3;, OIJSKItVATIONH UP HEVKLIUS. Tlie olwiviifiiiii.s »it' IIkvkmi 8 artj touiid in tlio MuiliiiKi Cdvlr.stii, pars po.storior. Owiii/i' tn tlio furity nl' t\\U work, the o1)sorviitioii.-( I luivo iisod iiro '= 9.90795. Loiifritiiilc. i'' 14'" 36" oast of Givciiwicli ; log p ctm of tlio oliscrvations.* I'iijj,' ■J. — OltHcrvntio H(!li|wc().s Palilicii. .\iiiio 1^141, ilie 15, Novciiib. iiiaiu' iiiHtitiitii |i()i'is iiliHcrvaiKli noii ilaltatai' (ii;ca.sio) Intra 3. iicitiit. 5'- Occaltaliatiir i\ Laaa circa 96. {;i'ail. linilii. iM-in|ii' oriciitalis, ad .Moiitciii .Malia.striimia Mai'i.s I'iol; <|ii() tiMiip.iru gradas liiiiia' 75. liiubi. viTticali.'* cxisti'liat. JCincrKt'liat lior. 4. 5'. 30". circa j;ia(laiii 317. liiiiUi occiilciifaliH, MonteiiKj; Alan- iiatii. iiaiiliilt'iiii KUpra Palixlciii .Macotideiii ; qao tciniiori.sarticalo f,'radii.s liinlti Laiia> 78. Crat verti. cali.s. Ilt>rii4. 10' 1,0" pof^t cmcrNioiioiii, I'aliliciinii taiilo spalio a liinlto rcinnvcbatiir, i]aaiiti> Kcilici-t lai.t <*rat I'ahis MuMitis, partu iiiaiin'iia damli'ciaia circilcr diaiai 'ri riiiMiu'i.s. .\s tlir altniidcij ffom which these times are deri lod are nut ;.iiveti, wi' have to iU^ the uin'»Mt;iinty of tlit; elements of reduction ii.sed hy IIkvki.iih to that of his * I'bis reiuari y IlKVKi.iim . . . 15'' 5'" Moan tiiiU'H tliuuco di'diicod 14'' 50" Oruoiiwicli mean tiiiicH '3'' 35" 0" 16" 5"" 30' 9" 1 5" 50'" 39' 3" 14" 36"' 3*. Lclipsis Siilis. Anno Afrae C/iristinnae tl 45 , h. m. s. - 1 ! _ Inillum n. aj. 4S. . . 7}- Dig. 45- 30- ' - tDig. II. 37. 0, . 7J- 50. 40. ... j . II. 3'- 3"- 47. 15- "• II. 31. (>. 7- 54. 45- [ - • • 'li.Dlg. II. 33- so- . 6i- 1. 50. 1 a. il. 38. 0. . 6. h. (1. 45- 41' "'• 1. 6. 8. St. II. .»3 . 30- . Si- 8. 30. 3t. II. 45- so- . Si - 13. 20. 4t. il. 5fi. 0. • . • 4t. 15- 3f>- 45- 5- 0- 1. 15- J'l 5- 13. 1. 30- . 3(1. 0, ... • Si- 13. 7- 30. . 4. 33. 45. 44. 3'>- O- 1. 24. 25 < 6. 13. II. 30'- . 3- 31. 3«- ; - • • ^. .3. If>. 30. . i- 47- 30- - . • . f-i. 13. 31. 0. . i. 41). 0. ... 7- 13. 33. 0. . Finis. 53. ». . . . 7l. 13. 35. 0. . 5f). 0. 41. 55. "• I. 55- 50 7i- 13. 37. 0. . 36. 0. 38. *(>■ "• 3. 3r>. 40 71. 13. 30. 0. . • 30. 0. 38. 34. 0. 3. 30- 1 7i. 13. 31- 0. . • • • , 13. 3fi. 3<'. 47. 0. 0. 13. 37. 13. 1 . 1 . 71 . 12. 41. 30. 4f>. 50- 0- i 12. 41. 53. • ' [ ' ."_ ■ Tlio ^un's di'dination at 110011 Wn\» -f 11° 59'-0» ♦'»' lioiir-an«rlo« f,Mv<'i» in tin- lant .•olunin sc'Oin very nearly corivct. 'I"iu> jrcMioral a^r,-(.<.incnt of tlic .Hun-dial with tlio times dedneed from the altitudes aiVords a Mroiij-' piesumi.tion in favor of the acenrary of both. The following' arc thecorrcctions to n'diiic the -mi-dial to moan time, as d.-diiccd from the nine individual altitudes: — -f 1"' 50" 5"' iS"(0 3"" 30" 2"' 5" 3" '9" ■ 3"' a'" 3" i2» 2"' 48". 2" 53' - VI 75 Al'. J 90 RKSKAKCIIKS ON THE MOTION OK THE MOON. Ill tlif ciisn of till! sixtli altitude, thorn is fi (lisfrepiiinry of two iniiiutcs Ix'tweon tlio i'lUH'H '/\\{'n liy IIkvki.ii'h and tliat ilcdiirililc tVoin tli(t altitinli*, which woiiKI Htteiii to arise iVoin an error in |)rintin|ijii(|ain-ct a|iri'lu'iiHA est in |)la(;ii OritMit, 36° 15' I'l'inciiiiani oltscarati I'alilivii incidcUat in altitinlint^ ilovis, 38° 48' 43" lOau'rucntc riMsiis I'lililico «'x ainlira Lana;, allitado hunu'i'i lucidi Orioais, in pIhriI Orient invchiflmtar, 38^ 45' . " . 2''. 57'". The position of .lupiter for tlio timo «>f immorsioii hiw been dorivod from Uou- vahi/h tal)los, with the result:— Geocentric rij^ht ascension 6'' 24" 34" Geocentric dei^lination + 23° 4'.o. Hence, from th»! secoml altitude, we have, for the local mean time of tlu» immersion, '3*' jX" '^"" 'he e(piation of time is — 12'" 25", so that tiiere is a ditlenmce of more than two niiiuites hetwcfon this reduction and tliat of IIevi;i,hs. The discrepancy is tho same in the time derived from the first altitude, so that tiie ditrerenco can urlHO only from the difference of the adopted positions of .Iupit,tiiH lUiim k •M. Nihil adh. Iniliiim. 3l. 3- 3i.fri*. 3) . A: )>aul6 . plui. 7- |)|US. .)i.l>i8. 8i. (.■i. J5J. 37')- 507. 6J5. 853. laSr. 1985. 3155- 3330. 2484. 3598. 3681. 3H36. 3308. 330a 3503- 3574- 3657 • 3750. 3«3». 3954. 4130. 4314. 4370 4588. 4f>90. 54f'« 5590- 5735. <8i6. 6313. 6488. 6883. 7103. 740a. THiri p«n>. dcilui lull). late 10. 3. M. i(>. fi . 4() . lu. 9. 44. 10. 13. 41. ID. >7. 47. 10. 37. 41. 10. 43. 55. 10. lu. 47. 51. (t. JO umtbm TemiHira fterft- ICWtC' ilfiin li<>riil trUiiii urn iitilmlaiu rlum. — — tliiluillnH lAriiirtliimTamp. uiuliini. 10. 11. 10. (1. 10. 10. 55. 2i. 10. 57. 30. 10. 58. 8. 11. 14. 30. It. \(>. 36. II. 19. o. II. 3<>. 39. II. 33. 34. M. 33. O. 10. 13. U. I 10. n. o. , ' 10, 3U. » to. JO rt. I lo. 4<>. o. l«. ;o. o. 10. 54. o. 10. ;8. o. It). 57 \.>. II. <>■ o. 10. o o. II. o. 45. II. 3. 30. II- <>• 13. II. 14- 30- "• '7. 30. II. 16. ;.. II. 19. o. II. 31. o. •I. 34. 43. It. a6. 4<;. 1 1 3q. 36. II. 33- 17. II. J? 37. II. S*"' 4J. II. 4t- 6. II. 4'>. 38. 13. 4 19. li. 7. '4. 13. I". 35. 11. 19. 30, II . 21 . 18. II. 23. 58. II- 35- 53- "• as. •>- I,, rt. a6. II. 37. o. I }i>. o. II. 3" 39. II. 33 35. 11. 3J. o. II. 3'>- I" II. J? 30 "• SQ. a" II. V o. 11. 40. o. II- 47- 7. II 49- .19. 11-44- "■ 11. 4'i 3"- 12. 4- 30. 13 13. 58. O. 30. 12 13. 30. PH.ASKS DECRESCENTES. 13. 13. 37. 13. 35. M- 13. 38. o. 13. 37- 8- 13. 40. 18. 13. 49- 13- 13. o. 12. 26- O. 13. 38. 30. 13. i;. •). 13. 39. i>. 13. 31. 31. 13. 37. O. 12. 40- 13. 40. O. 4t. 4^. 7494. 7558. 12- 51 12. sa l.clrc. 8444. I. 13 i 8514- .. u }. 8575. 1. i( Finis. 8694. ,. I. ,. 8. . ft. 12. 49. 5«. 0. 0. 13 la 1. 45 IS. 53. 30. la (. 15- ■a. 30. |. 51. 15- 0. J. 17. 16. 30. }• 2. I. 19. 0. 13. 43' 33. 54- 3>. Sft. II. I. 16. 40. 19. 31. I. 30. 45. 33. 0. '■%' i' fft- ^>. IMAGE EVALUATION TEST TARGET (MT-3) 1.0 !.l us 1^ l^ 1.8 l\\25 mi£ IIIIIJ4 V] ^;; 7 >^ T, Sciences Corporation 23 WEST MAIN STREET WEBSTER, NY. 14580 (716) 872-4503 92 RESEARCHES ON THE MOTION OF THE MOON. Obscn'atio Eclipseos Solaris, Gcdani, Anno aerae Christianae 1652, die 8 Aprilis sf, n. peracia — Continued. O.'ilo I'has. ' I'hasium DlRiti ^"*' CrescSt. Kcliplici. I"-' uli. atio lies lic- \*enim atcj. gen- uinuin tein. ex vibrationihiis perp. deductum. Tempus secundfim exqiiisitd sciate ricuin liorizon- tale. Tempora secu- dftm liorologi- um ainbiilato riura. AUitU(lin6s C6tri Solaris. ,\cciirntum Temp- us ex alt. © erutum. h. m. s. gr. m. 9096. t. 28. ig. I. 29. 0. I. 33- 0. 39- 50. I. 29. 22. i . 9244. I- 3>. 45- I. 32. 0. I. 36. 5- 39. 32. 1. 33- 29. 9454. I. 3^. 36. I. 37. 0. I. 41. 0. 39. 10. I. 38. 19. ! 10664. 2. 4. 35. 2. 5. 0. 2. 8, 47. 2. 19. 30. 2. 23. 20. . i 2. 21. 0. 2. 24. 52. 2. 25. 47. 35- 13- 2. 22 5. 1) 461. 2. 23. 2. 23. 0. 2. 27. 0. 35. 3- 2. 23. 39. 2. 24. C. 2. 28. 0. 2. 29. 0. 34- 44. 2. 25. 14. 2. 29. 0. 2. 32. 30. 34. 37. 34- 27. 2. 28. 10. 2. 29. 16. 2. 33. O- 34. 9- 2. 32. 0. _ 2. 36. 0, 4. 48. 15. 4. 50. 15. 33- 50. 17. 4. 16. 50. 2. 35. 0. 4. 45. 9. 4. 46. 51- 4. 49- 0. 4- 53- 0. 4. 57. 0. 5. I. 0. 5. 3. 0. 5. 6. 45. 14. 30. 5. 3. 4. • 5. 6. 0. 5. lo. 20. • RESEARCHES ON THE MOTION OF THE MOON, Animadveriendtt. 93 Cum coeliim.al) ipso (liliiculo iiiatutino, imbibus iindiqut' ifa csset olMluctniii, ut liiiroloffiiini aitificiiile, tain .siiijrnla inimita se .iiiiila, (iiiam dona ti'itia acciiralc (•oiiiiiioiisIimiis, lU'fiiie ad alti- tiuliiK'H Solait's, iicqtie ad SciattMicuin diiigi aKj; coiiigi posse, ul la spcs siipeiessi't ; coiiMiltnm esse diixiiniiti, hora statini lo, turn majoiis fvideiitiiu' H'litia, t it fo fcitiiis coiistaivi, (piot eaium horain adiiiipU'reiit intOKiani, peipeiidiciili aimotaip viltrntioiics. AniiiiiMhcisuiii auti'in sii; I'uit, tain t'x Sciaterico iiostro singula niiiiiita inilicaiitc, afrpiead liiicani iiuTidiaiiaiii lidi-litiT appli" cato, quaiii ex altitudiiiiliUs Solarilius, 2595 osnillationcs coiilict'ii' horaiii intt'siaai, & 4314" iniimtuai priiiium ; tot plaue scilicet, qiiot ante bienninm, ciica Eclipsin Solaiem,in sirnili tenipoiis intervallo ejusdeni perpendiculi ope depieliendiinns. Jnstante igitnr initio Eclipseos, praeter I'eie ornneni speni, Sol adspectu mio nos exliilaiavit adniodnm; sic ut Iioni 11 secnndiiin llorolof-iuni anibuiatoriuin, & Sciateiicuni, & Vibiationes per- pendiculi, exquisite siniul conjuKeie octalq; coiifei re liicultas daretur. Sole interim tuni teuiporis prorsus existente puro, & A Luna illaeso. Post initiuin vero quod accnratissitne anuotatUMi, Sol iternm sub nubibus aliqiiantuliim lelituit ; quamquam postmoduni i)er iiitervalla satis teniporis nobis consessuni fuerit multas diver sissimasq; (attestante observationis fncoTiisnio) & (piideiii bene- ticio limitatioris Telescopii, in camera obscurata, per iMacliinain, in Se!enograi)liia nostia p. 98 descriptam, ritfe & fldeliter anuotare. Quod autem in ipso Eclipseos principio altifudines Solares iion fuerint a nobis eapta, causa hoc est: quod in tali Solis circa meridiem situ, parum iis admodum sit fidenduni. Quocirca alti- tudines circa exordium rejecinuis, usque dum Sol h meridiano moveretur longius; atque tuin denuim aliquot luerunt notatae, ad majoreni scilicet observationis fldem. Quae oninei, ut cum sciaterico & perpendiculi reciprocationibus quAm optiine conveiiiunt; sic simul cum sciaterico & oscillationibus. indicant, in quantum horologiuin nostril meclianiium, tam circa initium, quam tineni. a vero aber- raverit temimre; ob quam tanien deviationem l.orologium islnd rion est plane conteninendum Inde nauique verum atque exactuin teinpus, aeque ut ex sciaterico & altitudinilius, excessu tantum, vel defectu probe atteuto, elicitur: imo denegatis interdnm, ob coelu subnubiluni, altitudinibus, & interrupta adulterataq; Solis in sciaterico umbra, ejusmodi automata in observationibuscoelestibus summoper^ sunt necesaaria. Caeterum nolui omnino circa phases delinendas, (ut ut [)Ierumque istud fieri solet) non tantum iutegroa elit;ere digitos. semidigitosqne; sed quascunq: designavi,quHe se se commode ott'erebant & quas uit6, & exquisite acquirere me posse jiraevidebam, spretis reliquis omnibus. Qui|)ite ob leve etiam impedimeutum, & ob motum Solis velocissimum, haec vel ilia phasis, licet maxiaie eam attendamus, t'acil6 nonnunquam praeterlal)itur. Adhaec phases ipsas, in adjecta flgura I. aliter plau(>, quam in Observatione Anno 1649 habita, nimirum cum ipais indinationibus, nti in Tabellft cameraque obscurata sunt observatae, onines tanieu sub uno eodemque per|»endicul<), depinximus. Proinde constat, Solem circa initium in 77 gradu it puncto Nadir, ACricain veraiis, bora scilicet II. 3'. 21" fuisse obscuratum; atque circa 25 circiter gradum iY puncto Zenith, Aquilonem versus, hora videlicet i.ig'.o" desiisso obscurari. Medium vero, sive maxima obscuratio liujus deliquii, incidit circa phasin nostrum 16, hora scilicet 12.10' 35", id quod pariter ex diversissimus faciebus in- ter se collatis satis certe patet. Vera itaque ejus magnitudog^a digitorum, sive 9 digit. & 23' hie Dantisci esstitit. liatio autem semidiametrorum Solis & Lumie inventa fuit hac vice, ut 1000 ad 1033 circit. Quomodo praetereil in Eclipseos progrcssu phasium cornua se se praebuerint conspicienda, & quern limbi gradum in omni positu tetigerint, ipsum Schema deliquii cuique baud cnrrente oculo id perlustraturo, sufflcieuter o8teu. 47™. 3". 4- 9. 49- 0. 4289. The times in the second column are deduced from the "vibrationes perpendiculi" in the last by assuming 39 vib. = i min., and correcting the count by the altitude. But in the last there is an en-or either of one minute f)r of forty vibrations: it h hard to tell which. I deduce the apparent time, g*" 46" 55', from the altitude, 13' less than that of Hevelius. . . RESEARCHES ON THE MOTION OF THE MOON. nlj Page 45. — Observatio Edipseog Solaris. Gedani. Anno 1656, die 26 Januar. hubita. ! Quantitas Phasiuin observat. Oscilla- > tioncs pcrpen- diculi. 1 Tempus ex ^Ititudines Oscillationibus C^'"'" ^"'""^ erutur . P"'"^' A'"""' : captae. Azimulha © Occident. 'I'cnipus ex Altitudinibus © supi)utatuin 0— Tempus ex Aziniuthis de- ductum. Tempus ' secundfi horo- logium anibulatorium. h. m. s. h. m. s. h. m. s. i • . • . 16. 57. 15. 0. 0. 12. 0. 0. 12. 0. 0. 12. 0. 0. • • • 15. 27. 15. 16. 56. 1 I. 10. 12. I. 9. 0. I. 9. 10. • 0. I 30. 0. . . . I. 30. 0. • 587. I 44. 55- . . . . I. 45. 0. ' Inilium. 827. I 51- 2. . . . • I. 51. 12. ^i- dig. 1000. I. 55- 25. . . . I. 55. 35- H. 1096. I. 57- 22. . . . . I. 57. 32- I. 1170. I. 59- 50. • 2. 0. 0. li. fe'fe. 1282. 2. 2. 33- . 2. 2. 49. ij. fer6. 1495- '■ 8. 0. . 2. 7. 45. • 1639. 2. II. 40. II. 46. 0. 3r. 34- 2. 12. 0. 2. II. 22. 2. II. 29. 2i. 1745. 2. 14. 22. II. 33. 0. 32. 17. 2. 14. 42. 2. 14. 0. 2. 14. 18. Paul6 plus. 1811. 2. 16. 3- . . 2. 15. 54. 3. dig. i860. 2. 17. 17. . 2. 16. 56. . 1961. 2. 19. 51. II. 8. 0. 33. 33- 2. 19. 48. 2. 19. 45. 2. 19. 46. 3i. 2029. 2. 21. 35. . . 2. 21, 29. 3?. 2110. 2. 23. 49. . 2. 23. 32. 4. 2213. 2. 26. 16. 10. 37. 30. 35. 0. 2. 26. 21. 2. 26. 10. 2. 26. 15. 4i. 2302. 2. 28. 31. 2. 28. 34. • 2400. 2. 3'. I. 10. 13. 0. 36. 7. 2. 31. 7. 2. 31. 8. 2. 31. 5- 4i.&pau.( 16 ampl.) 2478. 2. 33- 0. 10. 4. 0. 36. 28. 2. 32. 50- 2. 32. 42. 2. 32. 58. 5- 2589. 2. 35- 49. . . 2. 35. 59- _ 2595- 2. 36 0. 9. 48. 0. 3". 12. 2. 35- 54. 2. 35. 58. 2. 3fi- 3- 5*. 2676. 2. 38. 2. 9. 36. 0. 37- 3f>. 2. 33. 10. 2. 37. 47- 2. 38. 5. • 53. 2766. 2. 40. 20. • i . . 2. 40. 24. 2814. 2. 41. 33- 9. 20. 0. 38. 24. 2. 41. 15. 2. 41. 21. 2. 41. 38. 5«. 2820. 2. 41- 42. • • • 1 2. 41. 49. . 2898. 2. 43- 40. 9- 7. 30. 38. 54. 2. 43- 32. 2. 43. 37- 2. 43. 50. 6. 3004. 2. 46. 22. 8. 52. 30. 39- 31. 2. 46. 14. 2. 46. 24. 2. 46. 35. bi. 3325. 2. 54- 33. 8. 8. 0. 41. l8. 2. 54. 19. 2. 54- 32. 2. 54. 58. 6». 3469. 2. 58. 7- 7- 47. 30. 42. 6. 2. 57- 53- 2. 5S. II. 2. 58. 38. 6J. 3598. 3. I. 28. 7. 28. 0. 42. 39- 3- 0. 25. 3. 0. 45. 3. I. 53- 7. frert. 37". 3- 4. 21. ;. 12. 0. 43- 23. 3. 4. (>■ 3. 4- 6. 3- 4. 41. • 39'3- 3. 9- 29. 6. 42. 0. 44. 30. 3- 9- 5. 3- 9- if>. 3. 9- 51. 7.& pau-i 16 minus.) 4055. 3- 13. 6. 6. IS. 0. 45- '8. 3- 13. t. 3- 13. I. 3- 13. 4°. 6H. 4077. 3. 13. 30. J . 3. 14- 12. 6J. 4578. 3- 16. 23. 5- 59- o. 46. 0. 3 16. 6. 3. i6- 17- ' 3. 16. 46. 6J. 4734- 3- 20. 21. 5- 33- 0. ^ 46. 49. 3. 20. 16. 3. 20. 8. 3. 20. 43. 5136. 3. 30- 35- • i i 1 3. 3t. 0. HEVELurs states that tion of time is + ' 3'" 20', times in the third column. his pendiihim made 2360 vibrations in an hour. The eqna- and tliis lias been taken as the correction ajiplicable to the liut, as scarcely more than half the eclipse was observed, 96 RESEARCHES ON THE MOTION OF THE MOON. there is no way of eliminating tlie systematic errors of observation. Tlie observations are therefore of no great valne. Page 49 —Occultutio Stellulae in Ariete. Anno 1656, (lie, 9 , i Martii vcspcri, diias Stt'llnlas, scd glolm liactiMins iiondnm adscriptavS i\ Lima pIus()Mani linnata ti'i',ta.s olt.si'ivavi ; prior a supra ednctioncin (iaiidac Aiictis .sita est, ad 17' vcl 18' Hon-ani vtTSii.s; n in longitudint' vero ad n' |)i'oinotioi' est, (piaui dicta Stflla cognita. Tt^gebatiir autein a Luna, alto Palilicio 38° 13' 30". The mean time dedncible from this aUitude is 8'' 34™ 45' Greenwich time 7'' 20'" 9". Page 89. — Obnervatio Occultationis Binarum Stellularum in 8 1658 Oct. 14. venperi. Stella una fuit aequens duarum Australior in Collo 8 , euJuN longitntlo 1° 18' n. Latitudo B. 0° 46'. Stella altera non hahetur in Catalogo aut globis: Krat auteni pauloOrientalior priorc & Borealior, quain rursivs sequebantur duae aliae Slellae, tanto intervallo, ut omnes HJmul Tubo (•aperentur. Teni Horo pus iuxta. m.ajus. Alt. C.a- pella. Tem JUS ex tud. Alli- 9- 23 .(6. 34. 45. 9- 25. 43. g- 37 10. 36. = 5. ')■ 3Q- 4- Hinc propter inlcrvenicntes nuhes & pluvias Luna & Ingressus Stellae sub Lunani videri non potiiit. 10. S 5 0. .5. ■4I)- • 2S. II. If). 23. Stella incognita paulii minus disiahat a Luna diametro Lunari : & pauli) plus ((ua du;u; Stellulae eandeni sequentes il so invlce. II . 20 0. • 11. 21. 15- Ingressa videbatur Stella discum Lunarem supra Monti"! Alabastr. • • • • Stella Incognita non amplius conspicua, videbatur subiissc discum Lunarem. Tlie following are the mean times actually resnlting from the three altitudes of Capella, together with the corrections to the apparent times of Hevelius, and the computed clock-corrections : — Mean Times. Dlff. from Hkvelius. Clock-cor- rection. A m s m s m s 9 II 34 - 14 14 ~ 12 12 9 24 50 - 14 i-l — 12 20 ti I 39 - 14 58 - 13 36 The equation of time is actually 14™ 3". The first two altitudes agree well enough with this. But, in the case of the last, there is clearly an error of about ten minutes in printing the clock-time: it may be assumed that th'e minutes should be 15 instead of 5. But there is still a discrepancy of more than a minute between the correction from this and from the firsi two altitudes. A change of 5' in the altitude will reduce the difference from IlEVELurs to 14'" 23", and the clock-correction to 13™ i". The mean of this, and of that computed from the altitude as given, is 13"" 18", winch I shall accept as the most probable result of tlie altitude. The first two altitudes give a result i" less. RliSEARCUKS ON Tlir-: MOTION OF lUK MOON. y7 Notwitlistivnding the lapse of two hours, I cciiisidor tlioiu entitled to some little wei<^ht in the result, .and shall, therefore, adopt the dock-correction 13'" 5", which gives ior the time of occultation 1 1'' 6'" 55". The probable error of clock-correction may be estimated at 30", and that ot the observed clock-time at 15". We then have, for the fJreenwich mean time of the occultation, c/ 52'" 1 9" ±3 5". To this probable ei-ror (jf time is to be .added the uncertainty whether the actual occultation was re.ally seen, as it must have taken place at the bright limb. Page 2i'j.—Occul(atio Clarae Boreal infronte Scorpii, 1660, 27 Apr. mnm': li in ITorolog. I. 32. 57. Alt. Spiea I. 49. 35. " Arctnri 47. 58. o. 16. 43. o. Toinp. ex altitii. i. 38. 15. I. 50. 10. 47. 52. o. I- 54- 3- I- 54- S^"- 2. 39. o. 3- 35- 34- 3- 42. 7- 3. 44. 6. 2. 34. 30. Exitiis Sk'Ua. Optiine coiisiK-xiinus. 3' 30- 30' Alt. Ar(;t. 34.42.0. 3. 36. 15. 33- 46. o. 3. 38. 3S. 33- 29- °- The clock-corrections resulting- from these altitmles are: — (i)-f4"-42» • , . (2)-f 3'"3i" (3) + 3'"4«" (4) + 3" 50' (5) + 4™ 36" ■ •■ (6)-^ri5". The resulting mean (dock-correction is + j['" 7^ and the probable error of both clocks and observ.ations al)out 8". T\w Cireenwich mean time of the occultation is therefore 13'' 24'" i» ± i2». Page 23S.—Occultatio Spieae Vir7- 10. 23- 0. 10. 24. 27. 3h 10. 34- 24. 10. 34- 10. 10. 35. 3'- 4h 10. 43- ... .0. 43- 5- 10. 44- 20. ■ 5». 10. 5'- 53- 10. 51- 43- .0. 52- 53- 5;. 10. 52- 49- 10. 52- 45. .0. 53- 54- 6 d. & amp. 10. 54- 36. .0. 54. 31- 10. 55- 40- l*ortio circlili I.unarib per centrum Solis 61. 7.circiter. 10. 10. II. 55- 57- 1 . 31- 26. 56- 10. 10. II. 55. 57- I . 26. 23- 55- 10. 10. 11 : Sfi- 34- 53. 29. 3. 0. transiens, vel obscurata pars Sdlis, hora 10. 55' contineliat in Limbo i Solari wa". 1 7.paul6 plus. II. 5- 6. II. 5- 0. ... (,. 4- Ratio Diametri © ail Dianict. C • obser- ' 7i.circi. II . 6. 19- II. 6. 15 ... 7- 17- vat, est ut 1000 ail 1105. Data if^itiir 75. 7i. ... ... .2. .4- 10. 15- ... ... .2. 14- It. 14- ... II. >3- 8 I;. 9. scmid. ex meis observatis 15' 54" provenit scmid. D in hac Kclipsis 16'J4". 1 7i. .1. 33- 44- ... 33- 4.. ... 34- 34- Max. obsc. II. JO. e^.feri. .1. 46. 54- ... 56- 50. 4j.fer6. ... 57. 47- ... 57. 45- 45. I.. 59- 36. ... 59 31- ■ 3i. .2. .. 20. .2. .. 19- . al. 12. 8. 25- .2, 8. 20. . 28. .2. 9- 32- .2. 9- 28. . ai.fer . .2. ... 0. .2. ... 0. • »i. .2. 12. 15- 12. .2. 15- , « »t. 12. 13- 0. 2.paul6 plus. 12. 13- 45- 12. 13- 45- . li.feri. .2. 15- 15- 12. 15- 15- »i- 12. If). .0. 12. .f). 10. . l«. 12. 17- 0. 12. .7. 0. , , it.feri. 12. IS. 20. 12. 18. 17- * . ih .2. "9- 20. .2. 19. 19- . iS. .2, 19. 57- 12. iq. 57- I. fere. .2. 2.. 9- .2. 21. 9- i. 12. 22. 8. 12. 22. 8. . 1. .2. 23- 34- 12. ■•3- 34- . 1 ■ . 39- 21. 40. .2 26. 17. Finis. 12. 26. 39- 12. 26. 40. . .2. 27- 3- Finis circa 81° 4 puncto Zenith, occidit. . .2. 51- 55- dub. 3S. 33- 20. .2 51. 46. + 2' 2" + 6 .8 . .2. 57. 49- . 38. .6. 35. 12 58. 6. .57 6 39 . .2. 58. 49. 38. 13- 25- .2 59- 14- .52 6 42 . I. 0. 35- • • • 38. 7- 30. I I. 17. • 47 6 54- 100 Ur.SEAUCllF.S ()\ THK MOTION Ol' TIIK MOON'. AnimaHferteHtln. Inatunte liao Eclii)si 8olis, oimu'in ad liibuiinus operain, ut cum loiigJ) ex optatissimo nostro liospito J)ri Ismacli BuUialdo, oinniii ilia, iiiiao ad oclipsiri oliscrvaiidam spectaie arbitrabar, esseiit ill promtii; itiipriimia, diias oamcviis obsciirataM adornavi, altoraiii pro Miijoribiis, alteram pro Miiioribiis, qui iu magna aderant frequcutia, et (juidem en ralione, qua videbautur commclloref. Multo mane, die 30 Martii, orieiite Hole, qiianiqaam CoeUini undiquo erat sercuum, sub lioram tameu oetavani nubibus satia obscuris obduei coepit, adeo ut Solem Qiiadrante, nee JIajori, nee Minori iiostro aenco rimari potuerlinus. llora verb 9, ai-r pabuliuu attenuabatur, ut satis accurate alti- tudiues Solares caperentur ; quo tempore Ilorologium tam perpendiculare, quam asitatum ambu- latorium, una cum Seiaterieo iu ininutis distributo, i)raeei.si! admodum conveniebat. llora 9. 30', Camerani iiigressi siimns oculos delixos oniniuo iu Tabula observatoria, praesenti" bus praecipuis Nostrac Urbis Luuiinibus, tenentes, nc nobis initium, quod iustare judicabam, ela- beretur. lluic nostro proposito Coelum tum claia etiam facie aunuit, sic ut ipsum Lunae sub Solem ingressum, punctuinquo attaetns dilmiide admodum eonspiceretur, in 117° a puncto verticali, occasum vert-iis; & quidem primiini a Praeelarissimo BuUialdo minimeotiosum se praebente specta- torem. • • • • Semidiamelrum Lunae notabiliter uiinorem esse, in boc deliquio, qutYm quidem Calculus proraiserat; quae iu peculiari cbarta, ex tribus in periplieria Lunae, i\ tribus diversis obser- vrttionibus, simul notatis panctis, multoties explorata est. • • * pbasiu tamen istam maximam aeeurato obtinuiraus: 73^ digit, iiempi- Imud fidase uiajorem. • • *. Hora 12 26' 17" alto Sole 39° 21' 40". (Juadrante Azimulliali uostro. in altera satiy longe dissita specula nostra coustituto, alias Obscrvator, liarum rerum alias bene gnarus, (iuem Eclipsis in pinnacidio Quudrantis, per nudum foramen depreliendit. Quod etsi cum uostro, ojte Teleseopii, in Gameril obscarata, annotato fine, in upsis secundis non conveniat (nee sane adeo occurale ista rations unquam fieri potest.) tameu lubens etiam banc Observatiouem api)oner« volui; 39 58 49 6 42 • 60 35 54 Taking the means, we have : — At 9''.25, corr. Uor. amb. + z" 27"; corr. Hor. p. + 7'" 38". At I2^93, corr. Hor. amb. + 6'° 38"; corr. Hor. p. + 6™ 38'. (?) These corrections being interpolated to the times of observation, the mean result from the two clocks i,s taken as the local mean time. RESEARCnr.S ON TllF, MOTION Ol' Tin: MOON. 101 ^ I'ngo 330. — Ovcultalio tSaiitrni, iCCi. ;i Avguad Vesj). si. n. 'Jliero is only ii single colnnin of times, wliieli is lieadcd "IVnipus ex liorolog; rtostimat siniul coiTOctuni". [ am tlierofoio in doubt how tlio observations ■wore inado, Hie following extracts are all tliat ean lie of any nso: — Teinpiis ex Sec: — 7. 58. o. h Liiiil). J striiigcbat. 7. 58. 20. Vcrum iuitiam occult. Hubivitdiiiiidio copore qimiitmii conjicoic liciiit. 7. 59. 50. Tertiii pars ndhiic vidcri potiiit. 8. o. 25, Sutiu'inis totus occiiltat. 8. 6.30. Alt. D limb. Slip. 16^ 2j' ciic. 9- 3- 35- Iiiitltnn eiDcrsloiii^. 9. 4. o. Jam luiijor particula de '? appaniit. 9. 4. 10. Finis occultatioiiis. Jlediri 'p corp. visfi. 9. 4. 35. Nondfi totus cOspcct. 9. 4.45. Finis totalis cmcrsioiiis. 9. 50. S3. Altit. Arcturi 27. 31. o. 9. 54. 36. " Sclieat Pcgasi 38. 33. o. • 9- 57- 44- " " " 39- 2°- °- 11. 1.36. " Scbedir. Cassiop S3" i3' o. ir. 7. 7. " Capella 17. 56. o. II. 8. 4^- 18, 4. o. II. II. 3°- 18. 17. o. Uesidea having to take the times entirely on credit, these observations are subject to other sources of doubt. That Saturn should have ajjpeared half-covered, "quantum conjicere licuit", twenty seconds after it touched the moon, wjiile one third was still visible a minute and a half longer, is something ditlicult to accept, even making all allowance for uncertainty of oliservation, and leads to 11 susj)icion of an error of a minute in the second time. Page 419. — OccuUatio Irium SMIidarum in Capite Taitri 1663, 14 AJar. tcspcri. Stellula interior A quartao magnitudiiiis, cnjiis longitiido est i'' 54' II & Lat. 5° 33' Aiist. • * St. IJ. Austral, sequentium. Tempiis sec. boi-. nmb. 11. M. S. 8- 53- 3°' Initium occultationis, * A. 8. 55. o. Altitudo Arcturi 27°. 3'. 9- 42. o- " " 34. 12. 9. 44. o. I'riucipium occultationis, * IS. 9. 47. o. luitiuin occultationis, * C, 9. 52. 30. Altitudo Arcturi 35°. 42'. The clock-corrections given by the three altitudes are : — (0 +45" 45" (2) +48" 5' (3) +48'" io\ The clock-corrections I .shall adopt are, for the first occultation, -j- 45™ 55'; and, for the two others, -f48"' 7'. Hie Greenwich mean times of the occultations will then be: — Star A (71 Tauri) . . 8'' 24™ 49" ±40" Star B ((9i or ©a Taiu'i) . 9" 17" 3i'rt2 5'' Star C (©a or 0, Tauri) . 9'' 20™ 3i'±25». 102 RKSEARCIIKS 0.\ THE MOTION or Till- MOON. I'lige 423.— iMi, Any. 18. Occiilldtion of a star during lunar ccliiinc. Ilorol. aiiili. ' ' «. SI. 2«- Alt. Alotllli . . . 27. .s« **• 53- S3- " " ■ . ■ 2 7- .V) 9. II. 36, Stella. jiun occiiltntii. '). 42. 43. Alt. liiicidiieCoronnc. 37 9. 44. 4«- " '* " 37 9. 46. 36. J Ljtiibi HiiiJorioriH. i:1 10. I. 30. Stella nu'siis prodiit 11. 14. 37. Alt. Lvrae, . . . 58. 37 1 1. 18. 4 sS- 1' 1 1. 19. 40 12. 8. 46 12, 10. 25 3'- I 2. 54- 57- 45- SO- 39- o. 26. .1 Temp. iMiir «. S-'. 5-^ X- 55- 3 <). 13. o, 43- 3.S 4S- 45 47- 3<' 2, 'S 19 ') ') 9' 10. 1 1, 1 1. 12. II. 3°- 1 1. 11. 21. 12. 10, n- 3' 39' 'lie ressiilts of the altitudes of stars are : — Moan Tinits. Diir. from llKVEI.IliS. m s Clock-cor- rcclion. 1 A m t m J ' 8 55 40 + 2 48 4- 4 12 i 8 57 50 + 2 47 + 3 57 9 46 3'5 + 2 55 + 3 47 9 48 40 + 2 55 + 3 52 11 17 54 •4' 2 43 + 3 17 II 21 3 -t- 2 I ( + 2 59) 11 24 12 + 2 55 4- 4 32 12 13 8 + 3 5 + 4 22 12 "4 37 + 2 53 4- 4 12 The eqiintion of time was -|-3'" 15", so that the ajiparent times of Hkveuus seoii ahout 20" too small. 'i'he sixth correction may bo rejected on account of the discrepancy between the altitude and the time computed by IIi:vi:lius. The mean of all tlie other clock-cor- rections is +4" r, and there does not seem to be any sensilde. dock-rate. Applying- this correction, we have : — Greenwich mean time of immersion of f'^ Aquarii . 8'' 1'" i''-j-.r2'' Greenwich mean time of emersion of e'^ Aquarii . 8'' 50'" 55' ± 12" I'age 4^)5.— Occ«i<«<('o PaUlicii, 1664, die i vcup. 31 Marlii, quarfa die post. 6 . Toinp. sec, hor. aiiib. ir. M. S. 9. 14. II. luitium occult; Palilicli A J. 9. 17. 30. Altitudo Procyonis . . 9. I 35- 10. 4. 20. Finis occult. 10. 7. 50. Altitudo Procyouis . . 10. 9. 57. " ". . . 3I.O 22.' 0." Quad. p. Or 31. 10. 0. 25, 7, 0. 24. 47. 0. rksi:ar(Iii:s on tiii; motion oi- tiik moon, 103 Tlio (•lock-coiTcctioiiH I'l'siiltin;,'' t'nini the four ii]titii" '••'■ I'liicr.Hioii, 'I'lio results ftre: — (ireouwlc'Ii nu'im tiiiu' of iiiniicrsioii (rrcc'iuvicli monn timo of ciiicrsioii I'iigo 474. — ikUpHis SulariH 1666. 2 Julii maiir. S'' c/' 44" ± iS- 9'' 1'" ,iO" ± ^S^ ■ . - 1 ~- -" --^ — -• — - Temp. 1 Quantilas Phasium. avstlmatuin secundum IIi>riilo}j. Tt-'hipus CornTiuni. '» A nib. -1 n. M. S. Inilinin. 6. 55. 3"- (>. 57. y>- &^ 7. 55- 45. '.'.(life'. f). 57. 30. 5'>. 3". v„* . piitito iniiMi^ 7- 59- 5- 3- 7. 0. 23. 2. 23. 8i. 8. (>. 3». 8. 8. 30. li. 7. 2. 30. 4. 30. 7.'. 8. II. 25. 8. '3. 25. Mil-, si'inid. S ail R" ij. 7. 4. 5<'- (1. 50. 7\.k;i: •■ 8. 17. 30. 8. 19. 30. VL'l i}" major ;i|)|)aniii. li'.feri'. 7. >"• S7. '2. 5?. ■J.inri:. 8. "9. 41. 8. 21 . 41. 33- 7. M. 5. 7. 3'. 50. 33. 50. 3- 8. 47- 32. S. 49. 32. 63. 7. 36. 55. 38. 5.i. 23. 8. 50. 57. 8. 52. 57- 6|.paulu plus. 7. 38. 5. 40. 5. 2i.ffic. 3. 54. 15. 8. 56. 15. 7i. 7- 39- 45. 41. 45. . ■! 8. SS. 24. 9. 0. 24. 7}.pauli) plus. 7. 42. 30. 44. 30. ] 1 8. 59. 35. 9. I. 35. 7i. 7. 44. 6. 46. f>. o\\. 9- I. 33. 9- 3. 38. 73 • 7. 46. 0. 43. 0. «;. 9. 3 . 20 . 9. 5. 20. 8.fer6. 7. 48. 25. 50. 25. Finis. 9. ('■ 53. 9. 8. 53. 8^. 8i.paul6 plus. 7. 5'. 15. 7. 53. 37. 53. 15- 55- 37- 0alt. . ©alt. 47- 33. 0. 9. 23. 6. 9. 25- 28. 17. 45. 0. 5. 51. II. ^. 53. 12. 47. 42. 0. 9- 24. 16. 9- 26. 45- 18. 37. 0. 5. 57. 5- 5. 59. 23. 4S. 10. 0. 9. 28. 29. 9. 30. 40. 18. 55. 0. 6. 0. 0. • 6. r. 23. 48. 23. 0. 9. 30.- 36. 9. 33- 12. *Semid. J aequalis cxiitit Solari. 104 RESEARCHES ON THE MOTION OF THE MOON. Til ' "notauda" whii.li follow contain nothing worthy of remark. Tho corrections to reduce the clock to mean time, as given by the individual alti- tudes, are as follows : — Hor, amb. Corr. h m S m s 17 51 II + 5 4S 17 57 5 6 4 ,S 5 16 21 23 6 + 5 53 21 2-t 16 5 58 21 28 29 5 36 21 30 36 5 56 The mean correction derived from the iirst group is +5™ 43", and from the last + 5'" 51". The uncertainty of the corrections is as great as their ditference; we there- fore adopt the constant correction +5" 47' ^'* reduce tlie clock to mean time. Pago 550. — 1671, A/«>y;/( 14. 0(ct(U(ttion 0/ lu-o itarn. Hor. amb. 7. 16.40. Alt. ralilidi, 40-3^. J- Quad p. Or. 7. 35, 30. Alt. iner. Pollucis, .... 64. 23. 40 (^iiad Ax. M. 8. 10. 20. Alt. Palllicii, 33. 40, o. 8. 12. 15. '• " 33. 29. o. 8. 51. o. Stellala incognita supra medium caudam T a D corniculalA tcota. 8.54. o. Media candib T il Luna tt'cta. Alt. Palilicii, 27. 29. o. 9. 42. o. Iiiitium eniersionis Mediae caudae f. 9. 57. 40. Alt. Humeri dextri Orionis, . 22. 29. o. 10. O. O, " " " " . 22. 12. O, The following are the results for clock-corrections : — Clock Times. , Mean Times jfrom Altitudes. Clock-cor- rection. C. /t m s // m s m s ;« s 1 16 40 7 27 47 + II 7 + II 8 10 20 8 21 58 + II 33 + II 53 8 12 15 ' 8 23 18 •h II 3 + II 55 8 54 9 f' 9 + 12 9 + 12 37 9 57 40 1 :o 12 14 + M 34 + 13 41 10 , 10 14 17 + 14 17 + 13 43 The clock-corrections are quite uncertain, owing to uncertainty whether the differ- ence of throe mituxtes between the clock-correction given by Aldebaran and that given by « Orionis is the result of clock-rate, or of systematic error in the observations of one of the stars. If we suppose a rate of one minute per hour, the mean correction RESEARCHES ON THE MOTION OF THE MOON. los will be as in the last column. I shall adopt this correction as on the whole the most [)robable. The results arc: — Greenwich mean time of immersion of star Greeiiwich mean time of immersion of star Greenwich mean time of emersion of star 7" 48" 5^^ ± 2 5" I" it 25' 7" 52" 8" 40™ 49" ± 40'. I have not succeeded in identifying these stars. The descriptions would seem to refer to S and 5 Arietis, but neither of them were near ihe computed position of the moon's limb at this time. Ooeultatio Spica Virf/iim, 1671, 22 Aprilis. H. M. S. Ilorol. Ami) 9- S-'- 45- Altitiulo PoUucis . . . • 35- 27- 0. 9. 55. 20. " " .... 35- 8. 0. JO- 45- 35- Initiiim Oectiltatiouis. . . . •■• '5- 5- Alt. B limb, infer 25' 50- 0. 1 1. 54. 0. Spica iieediim conspecta. II. 55. 0. Aillinc (It bitescebat. "• 55- 30- Spica emersit. Finis occult. 12. 0. 39. Alt. Kog 26. 18. 0. 12. 2. c;. ii a 26. 3- 0. J 2- 36- 55- Alt. Lyrae 49. 39- 0. 12. 3<). 23. U l( 49. 5°- 0. Temp. (-'oil. II. M. H. 9. 56. 21. 9. 58. 32. 10. 47. 56. 11. 17. 25. 11. 57. 10. 12. 2. 14. 12. 4. O. 12. 39- 45- 12. 41. o. Hevei.iu.s <>iv('s altitude of Regulus 36. 18. o. at the moment of immersion; also, "Emersionsis ►Stollao aecuratissime deprehensum est". Tlie mean times computed from the altitudes compare with those of Heveluts as follows: — Mean Times. Diir. from IIliVELlUS. Clock-cor- rcclion. /* m s m s Ill s 9 54 52 — I 29 \- 2 7 y 57 30 — I 2 + 2 10 10 46 42 - 1 14: + I 9 12 1 9 - I 5 + 30 12 2 55 - I 5 + 46 12 3S 21 - I 24 + I 26 12 39 37 - I 23 + 14 Tlie mean result is that at ii"" 26™ the dock-correction was 4- 1™ 12". I shall admit a rate of — 24 seconds per hour. The results will then be : — Greenwich mean time of innnersion 9'' 32"' 25" ± 15' Greenwich mean time of emersion 10'' 41" 54" ± 15'- Page 564.— Occultation of Satiun, 167 1. June 1. mane. Tlie times are so discordant that the observations seem worthless. IFere 'lowever, are tlio observations: — Horolog. lunbnlftt. 'oinp. corr. 2. 49. 50. Altitudo Lyrao 71.0 8.' . 2.50.31. 2. 52. o, " " 70. S°' ...;./.. 2. S3. 44, 14 75 Ap, 2 io6 RESEARCHES ON THE MOTION OF THE MOON. 2. 53. 32. Altitudo Lyrao .... club. 70.0 32.' 2. 56. 51. 3. 38, 15. T? Tegiincipiebat 3-38.15. 3.38.39. ^ oraniiio tectiis; alt, J limb. inf. i6.° 57.' 3- 38. 39. 3. 46. .0. Alt. circa i.o o.' o." 3. 46. o. S-2i-2t " " 12.40 5.22. s- S- 26. 58 " «< 13. 17 s. 26. 38. S-3t-29 " " 13-42 5- 29- 42. Vage 61^.— OccttllaUo riejadum. 1672. Novem. 6. inauc. " • II. M. 8. HoroloR. amb. 12. 51. o. riejatluin praeccdens omnium a Num. tecta iY J. I. 2. 45. In cuapido occid. b Num. i it 5 tecta ad Stagnnm Miris V . supra Paludem Maraeotidem. I. 21. 31. Plejadnm Lucidam proximo praeccdens d tecta ad Montem. h. m. 8. Acabe & Paludem Arablae i. 24. o. 2.22. o. Altitudo Procyonls, 34.0 S9-' 2.24.15. 2- 24. 26. " " 35. 14 2. 27. 3. The altitudes of Procyon give: — : Mean Times. Uiff. from Hevklius. Clock-cor- rection. /; m . s 14 7 27 14 10 5 m s - 16 48 - 16 53 m s - 14 33 — 14 21 Tlie differences from IlEVELirs exceed the equation of time by 48' and 58' re- spectively. The clock-correction at 14'' 23'" is— 14'" 27"^ 17". The interval of one hour and more between this time and that of the occultations considerably increases the uncertainty. The resulting Greenwich times are : — Immersion of Coeleno 1 1"* 21"" 57'±3o' Immersion of Taygeta 1 1'' 33" 42'±28' Immersion of Maia 11'' 52'" 28'±25'. Page 628. — OccuUatio Pln%dum. 1673. Martii, 22. Die 5 , vesp. Horolog. amb. 7. 21. 30. Altitudo Psililicii . . . 35.° 50.' Temp. corr. 7.24.57. 7- SS- o. Praeccdens Num. I. 6. In cuspide Occidentali ■ PlejadumtlLuna. . . tegebatur 7. 58. o. 7.58. o. Plejadum una, sed Globo baud adscripta, tecta tuit 8. I. o. 8. 7. o. Altitudo Palilicii . . 29. 39 8. 10. 8. 8. 9. o. Alia PI, N. 4. ex illis arctioribus duabus prae- ccdens ... rursus tecta 8. 12. o. _ *; i V t , 8. 14. o. Ex bis posterior Num. 5. tecta fuit fere eo ipso J loco 8. 17. o. , Ai,= 8, 57. 10. Altitudo Procyouis . . 36.055.' 9. o. 52. RESEARCHES ON THE MOTION OF THE MOON. 107 Comparison of Hevelius's times with the mean times computed from the ahi- tudeB : — Mean Ti Diff. from Clock-cor- Hevelius. rection. h tn s m s m s 7 32 25 + 7 28 + 10 55 8 17 35 + 7 27 + 10 35 7 58 + 7 6 + 10 .48 The moan dock-correction is+ 10"' 46", and there is no evidence of any sensibh rate. Adopting this correction, tlie resuUs are : — Greenwich mean time of imnifrsion of Taygeta Greenwich mean time of immersion of m PI. . . . Greenwich mean time of immersion of Asterope . . Greenwich mean time of immersion of I PL . . . I'iige 658. — Occultatio I'leiadum 1674 Aiigusti 24. luiiiu! Die 9. 6'' 54™ ID" ±25" 7" 5'" lo'ias' 7'' 10'" IO»±25' Ilorolog. ainb. 12. 57- 30- 12. 59- 3°- I. 37- 0. 2. 4- 3°- 2. 21. 3°- 2. 28. 0. SIC. iO- 3°- 2. 47- 0. 2. 57- 0. 3- 0. 0. 3- 6. 40. 3- 12. 20. 3- 45- IS- 4- 3- 55- Altitiulo Aquilao 26. 51. dub. . tcini). cor. " " 26.31 St, inf. praecedens occultatii Praecedens omniuui N. i Lunaiii subiii- gressa Iiileriorum seq. N. 5. Luiiam subiit . . . Praecedens oinninni rnrsus in conspectam prodiit liucidam praecedens N. 4. circa linibura superiorem !) (ubi praectul. om.) tectaest Inferiorem praecedens sese rursiis sistebat. Lucida PI. sese subduxit Lucidani praecedens exiit ..... Altitudo Markab. Pegasi. 39.° 23.' . . . Inferiorem sequens eniersit Altitudo Capitis Audroniedae 54.° 12.' Lncida Plejaduni N. 6. rursus illuxit . . 59- 54- 2. 27. 40. o. 7- 30- 24. 30. 31- 2 39- 3°- 2 S°- 0. 3- 0. 3- 3- 3- 9- 3f 3- IS- 20 3- 48. 16 4. 6. S5 The results of the. altitudes are:- Mean Times. Diff. from Heveuus. Clock-cor- rection. A m s Ill s Ill s 13 I 38 + I 44 + 4 8 13 4 10 + I 43 + 4 40 15 II 10 + I 32 + 4 3'' ■5 49 52 ■h I 36 + 4 37 The mean clock-correction is -|- 4" 29', wliich I shall consider constant. The mean times thus resulting are given in a subsequent section. io8 RESEARCHES ON THE MOTION OF THE MOON. The equation of tiino is + '"' 57") «<> t'l'it the moan systematic ditterence from IIev£lius is about 20'. Pugo 684. — Oocultatlou duriiip lunar eviijisc, iG-j^, ? , .I.iiiiMi'y ii,ev. The clock-times are not given, but only those corrected. II. M. H. 8. o. 50. Stellula /> tectti alt. I\I. Koiiiii; simI cxiro illaii) noil ilepivliendi. 8. 35. 20. Stc'UiiIa snprema i\ Tergo rolliicis v oiiiiiiiio tecta, 8. 51. 25. Stellula (7 ad ipsiuii Liuibiuii iiiferiorein tecta. 9. 9. 10. Haec eadeiu Stella riirsns eiiuM si f. The altitudes from which the clock was corrected, taken before and after the eclipse, are given as follows: — Tuiiipiis sec. liurol. ; ex nltit. corr. h 111 s o , // 6 22 18 AltltudoCiiiulae Cygiii 6 25 4 AltitudoOaiulae (J.vgiii 10 58 35 Altitude Lucidac T 11 II 2i Altitudo Oapellac . . II 15 20 II 16 59 I. 18 37 u 3') 3 38 41 28 5^ 70 1 1 69 39 69 24 60 I ( The mean times computed from certain of these altitudes compare iis follows with the apparent times given by IIevelius : — Mkvelu's's App. Time. A m s Compnted Mean Time. A in s Eq. T inc. A PI . Time. App. Error of Ukvki.ius. m 1 Corr.to He- VKi.iiis on Mean Time. /// s m J A m s 6 22 iS 6 30 20 + s 55 6 21 25 + 53 + 82 f> 25 4 b 33 5 + 8 55 6 24 10 + 54 + 8 I 10 58 35 II 5 55 + S 59 10 i(> if> + I 39 + 7 20 II II 33 II 18 57 + 9 II 9 57 + I 56 + 7 24 II iS 37 II 26 + 9 II n + I 37 4- 7 23 The deviation of more than a minute from Hevelujs is embarrassing; but I can get no other result from his altitudes than that given. I shall* therefore take -f 7" 42' as the corrections to reduce the times given by IIevelius to mean time, from which we shall have: — Locul nionn time. Oncnwich mean time. 8'- 8'" 32' 6'' 53"' 56" Immersion of * ?> Immersion of * c (85 Geminor.) . . Immersion of * (^ - Emersion of * 0(85 Geminor.) . . Page fi^.— Solar eclipse of 1675, Juno 23, A. M. He seems to have used no clock at all, but to have got all his times from a sun- dial, giving only the minutes. 8" 43-" 2" 7" 28'» 26 8" 59" 7' 7" 44" 31 9'' t6"' 52" 8" 2'" 16 RESEARCHES ON THE MOTION OF THE MOON. 109 Piijjo 768. — /v'o//j>.vt.v iVt)/is. 1676. Die Jovis II Jiiiiii «h/c Hi ,'„. g. 45. 4>h 9...45. 25- 2.i. II. 35- 35. • II. 35. 20. .1 9. 54. 22. g. 54- 3!. II. 36. 59- II. 3f'- 55- l.paulo plus. 10. 3. 44. 10. 3. 22. ■ll. tl. 37- 55- II. 37. 53- Nondum Sol om. 10. 8. 30. • 10. 8. 20. 45. II. 33. 35- II. 33. 35. Nondum. 10. 18. 17. to. 18. 0. 4.!.fei6. II. 29. 15- II. 39- 15. Nondum. If. 39- 40. II. 39' 40. Finis Eclipscos, . . . 18. 10. 33- "• 18. 19. . . . • • • • 4. 20. 0. 32. 57. 20. 36. Obseri'cd Scmidiamcters of the Moon. H. .M. , „ 10. 0. 13- 53- to. 24. 14- 0. II. 0. 14- 50. Ultimo. 15- 0. Ilor. auib. I. 25. 3C. 39- 45- 47- 55- 25- 54- o. 19. 50. 43- 45- o. 24, 1- 3S- 4J. 1. 44. 7. 2. 46. 29. 2- S3- 35- 3. 18. 19. 3. 42. 20. Piige 774. — Occultatio Martin et quarundam Fixantm 1676 Sept. 1. mand. II. M. s. Alt. Ciuidiie Cygiii 57.° 40.' Temp. cor. i Mars i\ Luna oinuiiio tcctua Alt. Caiidae Cjgni S'- J7- Mars cniicnit; Finis lunniio occultationis . . Alia Stelliila Fi.xa b sub Marte cgrcditur . . Altitude Sehcat Pegasi. ... 45. 3. Fixa c ad Cuspidcm Lunae iuferiorem observata est, ; [Corresponds exactly with a MS. at the Paris Observatory.] Animadvertenda. De caetero notandum est, paallo post Martis egressuiu aliain insuper Stellulam Fixam b, Olobo nlitts nondum adscriptain, vix ad 3 Min. prima iufra Martcm versiis iVustrnm, Honl uimiruni no RESEARCHES ON THE MOTION OF THE MOON. 2 S3' 35" exiliisse circa Paludes Ainaras; qiiaiu quidoni Lunain siibiro baud aiiiinadverti; ctiin totus iu eo fueriin, ut Martis momeutum occultatioiiis praecisc deterniinareni : • * Tlie results of tlie altitudes are: — Mean Times. Ditr. from Hevklius. Clock-cor- rection. /; m s m s HI S 12 59 26 - 58 - I 59 13 43 26 — 41 - I 59 "5 17 30 - 49 — 2 20 The mean correction is — 2'" 6", which may be considered constant. The Green- wich mean times will then be : — Immersion of Mars 12'' 19™ 57" ^ 15' Emersion of Mars 13'' 31'° 12' ± 15' Immersion of h 13'' 38" i8'± 15' Immersion (?) of f 14'' 27'" 3' ±25". I have not succeeded in identifying the two stars. They are probably too small to be in the accurate catalogues. Pago ?>i^.— Occxdtatio duarnm Stelhilantm in Clara Orionis 1678. JIart. 28 5 veap. II. M. s. Hor. aiiib. 7. 31. o. 9. 16. o. 9. 17. o. 9. 19. o. Luna togit iniiecedentciii in Clava Orionis. Luuategitaliani Stclhilam bacteuua iucogn.* Alt, Procyoiiia 33. 18. o. " " 33. 4- o. Nam ilia praecedens in Clava Orionis hoc tempore anno sc. cuiTeiito 1678 dcgit secundum nostrum Catalogum in 24P 21' 10" □ & Lat. 30 1 1' 24" Anst; sic nt oninino ilia ipsa fuerit, quae priua fuit obtecta. At do altera posteriori dubito, an ca ipsa fiici it, ilia scilicet in clava Orionis sequeus; Latitudo quidera ejus, quae est 3° 21' 19" Aust. occultatin 1 iion piobibct omnino, sed nibilomi- nils adeoarctamSj'uodum cum priori Stellulanon concodit. * * • • 250 17 n & Lat. 3° 13' A. The clock-corrections resulting from the altitudes are, respectively, + 6™ 43" and + 7" I'; mean, -f e™ 52". The Greenwich mean times of the occiiltations will then be : — First star, B. A. C. 1867 (f) 6^ 23"' i6»±45" Second star, ;t* Orionis (?) 8'" 8™ 16' ±22". The two stars are those of the British Association Catalogue nearest the moon's limb; but it is doubtful whether they are really the occulted stars. "In the original MS. at Paris the minutes were first 14, and were changed to 16. RESEARCHES ON THE MOTION OF^THE MOON. From the Annus Clhnactericus of IIevelius, Gedmii, MDCLXXV. Page 7. — Occ • 'atio Lanck Amtrinae &c. 1^)79. Mart. 30. Mane. Ill Horol, amb. Distantiac et Alliludlncs. Quo instru- mcnto. Temp, corrcc. gr. m. s. I. 48. 30. Altitudo Roguli . . dub 23. 27. 0. Quadr. p. or. 2. 41. 0. Minor Stella occulcabalur 2. 45- 0. 2. 48. 40. Major Slell.T •egcli-'.tur . 2. 52. 40. 2. 55- 0. Alt. Arcturi .... 52.' II.' 2. 50. 15- 2. 58. 0. " " .... 5t. 57. 3. I. 0. 3. 16. 0. It ti 50. 3- 3. 21. iC. 3. 56. 40. Emcrsio Minorls Stcllulae 4- 0. 40. 4. 5- 15. Emcrsio Majoris Stcllulae . 4. 9- >5. 4. 34. 0. Alt. Arcturi .... 40. 46. 4' 38. 29. 4. 36. 0. " " • • • • 40. 24. • 4. 41. 14. Stel. diff. in long. 4.' 30." Lat. 3.' ft ri. Minor majorcm sequatur in mjijori. Lai. Bor. Long. ejus. 1660. 10. ° 16. 0." HI. et Lat. 0. 29. 30. B. 1 The results of tlie observed altitude.s are: — Rejecting the doubtful altitude, the clock-correction at 1 5*" 49" was -f 9" 30" ± 1 2*, which we shall suppose constant. Tliere may bo some suspicion of a gaining rate to the clock, but its effect on the mean of the observations would be small. The results will be : — Greenwich mean time of immersion of a} Libras Greenwich mean time of immersion of a^ Libne Greenwich mean time of emersion of a' Librse Greenwich mean time of emersion of oc^ Libra; 1 3' 3 5'" 54" ±2 2' i3'43"'34'±20» 14" 51" 34' ±15' i5'» o'" 9" ±16" I I 2 RE.SEARCIIES ON THE MOTION OF THE MOON. Piigo i8. — OccuUatio U, 1679. Juiiii 5. man6. ( rose at 15'' 35"'.) Hor. Ami). Dislanliac &i allitudincs. Tcropus correct. I. 18. 55. I. 29. 0. 4. 15. 40. 4. if.. 9. 4- 16. 35. 5. 14. 0. 5. 14. 20. 5. 14. 45- ID. 22. 30. 10. 27. 16. 10. 30. 8. 10. 38, 0. 10. 45. 28. All. Capitis Andromedac All. Arcluri Jupiler slringcbat J linibum " ad ceiilrurn usque occullabalur Jupiler lotus omnino tectus Jupiler denusexircvol.ibili parliculA videbatur Oimidius Jupiler exiveral Tolus Jupiler omnino prodiit Alliludino Solis II II 24. 52. • 3'. 3. . 53. 34. 40. 53. 59. 45. 54. 14. 0. 54- 53. 40. 55. 27. 20. II. M. S. I. 20. 54. I. 31. 24. 4. is. 5. 4. >8. 31. 4. 19. 0. 5. I&. 25. 5. 16. 45. 5. 17. 10. 10. 25. 2. 29. 42. 32. 26. 40. 26. 47. 4f>. Results of the observed .altitudes: Object. n Andromeda: Arcturus Sun . . Mt-an T inc. // m s >3 18 50 >3 29 4 10 22 44 10 27 9 10 30 12 10 37 54 10 45 13 Diir. from Hkvki.ius. 4 20 18 33 14 32 33 Clocli-cor- rcction. m — o + o + o — o + o — o — o 5 4 14 7 4 6 15 The niefiii dock-correction is — 2", without any sensible rate, mean times of the observed jihases are: — Immersion. Contact of limbs . Jupiter half covered Jupiter entirely hidden 1 5'' i 15" I' 15" I 2"dh7"- 3 1" ±7". 57" ±7"- KnierBion, Partly emerfyed . . Half emerged Entirely emerged The Greenwich 15" 59™ 2 2" ±7". 15" 59 42" ±7"- J 6'' o'" 7" ±7". RESEARCHES ON THE MOTION OF THE MOON. Page 27. — 1679, Jiiiiii 24. vesp, Oocultatio duarum atellidaruM in t . 113 Hor. ami). h. m. s. 10. 30- 55. 10. 41, 51, 11. o. 8. 11. 40. 55- 12. II. 48. 12. 13. 8. 12. 17, 25. 13. ig. ig. 12. 22. 52. Allitudo Arcluri Inilium occull.itionis j|< majoris Exitus ejus Stellae in / . Alt. Arcturi II II Alt. Lucidae Coronae ... Distantiae & altitudincs. Quo instruniL'nto. Tcmpus correct. 42. 42. 48. 31 • 30. 58. 2(). .15. 46. 9. 45- 53- 45- 23. Quad. p. or. 10. 44. 22, io. 46. 32. 11. 4. 28. 11. 45. 15. i'.^. 16. 20. 12. 17. 49. 12. 21. 42. 23. 36. 27 10. Major ilia Stella est media illi in praeccdente fascia, t . Results of the observed altitudes : Star. Mean Ti mes. Diff. from Heveuus. Clock-cor- reclion. A m s m s m s Arcturus 10 45 57 + I 35 + 6 2 " 10 48 5 + I 33 + 6 14 " 12 17 55 + I 35 + 6 7 " 12 19 26 + I 37 + 6 18 11 Corona) 12 22 25 + 43 + 5 " 12 24 •9 + 43 + 5 " 12 27 54 + 44 + 5 2 The difference of more than a minute between the ck)ok-corrGctions given by the two stars is quite embarrassinfi;', and the more so that IIeveliu.s's cah-uhition makes them nearly agree. The equation of time was i 45', so that the error, whatever it is, seems to be in the computations relating to a Coronic. The positions which I have adopted for the stars are ; — ! Arcturus, R. A. = 14'' i"" 4"; Decl. = + 20° 52'.5 ; aCoronaj, R. A. = 15'' 21™ 7"; DecL = + 27° 49'.5. In the observations of 1663, August 18, the same two stars were observed, and there Heveluis's computations agree with mine. At present, the only course seems to be to reject the altitudes of a Corona? entirely, and adopt the clock-correction +6'" 10" resulting from the altitudes of Arcturus, which, it will be seen, is only about 10'' greater than that resulting from Heveluis's computations of a CoroniB, when corrected for the equation of time. The results are then : — Greenwich mean time of immersion of p Sagittarii Greenwich mean time of emersion 15 75 Ap. 2 9" 51 42'±6» iqI. 2 a"- 29' ±6». 114 RESEARCHES ON THE MOTION OF THE MOON. Page no. — Occultatio Palilicii. i6Si. Jan. I. Hot. amb. ?• 37. 0. Stella occull.nta csl. alt. capitc Androm. 50. 3a. 7. 37- 33. 7. 46. 0- Altitudo Capitis Andromcdae . . , 49. 24. 7- 46. II. 7. 4q. 30- 48. 55- 7. 49. 8. 8. 46. 0. Paliliciiim rursiis afl'ulsit .... 8. 44- 0. 8. SI. 0. Alt. Cap. Androm. extitit .... 40. 22, 8. 49- 8. Results of tlie altitudes :- Mean Times. Dlff. from Clock-cor- Uevemus. rection. Ami m s m 3 7 4!» 37 + 5 4 + 5 37 7 51 14 + 5 3 + 5 14 7 54 53 + 5 45 + 5 23 8 55 55 + 6 47 + 4 55 Here again there seems to have been an error in Hevelius's computations of apparent time. But there is little doubt of the mean dock-correction -4-5™ 17' ±8"; applying which, we have : — Greenwich mean time of immersion e*" 27" 41' ± 20' Greenwich mean time of emersion 7'' 36"° 4'' i ''7'' Page 139. — OocuUatio Palilicii. 1683. Jaa. c). vesp, ,. ; H or. amb. 8. 54. 30. Alt. Pollucis .... . . 48. 43. Quad. p. or. 9- 0. 5. 8. 55- 15- " " .... . . 48. 53. 9- I. 22. 9- 42. 15- Initium occultationis . 9- 48. 15- 9- 30. 40. Alt. Reguli . . 24. 12. 9- 56. 35- 9- 54. 15- " . . 24. 40. 9- 59. 5«. 10. 55- 30. Finis occultationis Pal. . . • II. I. 30. 3. 58. Dist. Pal. ab occ. ([ limb. 7 rev. . 5- '9. 9- 58. 9. 10. " " " 10 . 7. 36. «5. 10. 13. 20. " 12 9. 7. 19. 20. 19. 12. Alt. Reguli . . 36. 16. II. 25. 32. 21. 2. . . 36. 22. . II. 26. 20. 23. 20. " " . . 36. 40. • II. 28. 46. RESEARCHES ON THE MOTION OF THE MOON. From tlio iiltitiulos wo havo : — 115 Star. Mean Ti IPCS. Dlff. from IIkvemus. Clock.cor- rcclion. h /« / m s m [t Pollux 9 8 «4 + 8 9 + "3 44 " 9 • 8 49 + 7 37 + «3 34 Rugulus 10 4 49 + 8 l» + »I4 9 " 10 8 4 + 8 .3 + 13 49 ' II 33 47 + 8 15 + >4 35 41 II 34 36 + 8 16 + 13 3t " II 37 3 + 8 47 + «3 43 Tlie niojin clock-corroction is +13'" 53'±6", vviiich sooins to Imvo been constaiit. Wo then havo: — Greenwich moan time of Immorsiou 8'' 41'" 3 2" ±8' Greenwich mean time of emersion Q*" 54™ 47' ± 8". Pago 145. — Occult, duarum * sub cornu aunt. 8 . 168,3. iipr. 2. vesp. Hor. arab. Tempus cor- rect. 9. 54. 30. 9- 53. 0. Initiuni occul. Sicllac Maj. A. 5. mag. . 10. 29. 36. " " Stcllac H. 6. mag. 10. 30. 36. 10. 52. 50. Finis occult. St. A. 10. 53. 50. II. 43- 30. Alt. Lyrae . 3i-° 25-' II. 44. 16. II. 45- 30. II K 3'. 44. . . . . . 46. 47- n. 46. 30. II II 31- 55. . . . . . 47- 42- II. 47. 30- ' 32. 6. . 49- 27- Tlie altitudes of a Lyrai give :- Mean Times. Diir. from Clock -cor- Hevemus. rection. h m s m s m s II 48 17 ■+■ 4 I 4- 4 47 II 50 40 + 3 53 -t- 5 '<> II 52 I + 4 19 •• 5 31 II 53 22 + 3 55 -»- 5 52 The mean correction is +5"' 20' ±14', which corresponds to the clock-time 1 1*" 46"'. We have no data for clock-rate ; but for several years it has appeared too small to be indicated by such observations as Hkvelius could make. Applying this correction to the occultations, the Greenwich mean times are: — Immersion of 119 Tauri 8" 43"" 44' ± 24' Immersion of 1 20 Tauri g"* 20" 20» ±20' Emersion of 119 Tauri 9" 43" 34' ±1 8'. ii6 RESEARCHES ON THE MOTION OF THE MOON, § ID. tS ()I!Si;i;VATIONS OF KCLII'HKS AND OCCIJLTATIONW MADK IIV ASl'IfONOMKUH OF TUK FltKN(;il HCIlOOIi ItKTWKKN 1670 AND 1750, AH FOI'NI) IN TlIK MANU SCmi'T IMiCOllDH OF TIIK PAIMS AND TIIK ^^^.KOV^^^ OKSKKVATOHIKH. Wc now i)iiss to a cliiss i)i' uliscrvutiuiiH imicli iimro siitisfnctory tliiiii tliono witli wliicli \v«' have ht'Oii tU'alinj;'. In llio latter part of tlic scxciitcciitli I'ciitiiry, I'icakd and otlior Kroncli astrononicns introduced the improved nietliod of dctcrnMuin;;' tliu time by eqnal altitudes of the Mun, of wliicli I have already spoken.* Their clocks were H(» far improved that tlusir j)rincipal chanj^es of rate were tliose due to ciian;^es of temper- ature. I include in tla^ present section all the (di.servatioiis for whicii the time was determined on this plmi, includin;^' those of Dei.isi.k in St. i'etersl)urj;'. They are for the most part nn|mlilished. The results of a few have indeed appeared in the (dd Memoirs of the French Aca'>"ks, that a condensed summary was absolutely necessary. These sunnnaries can always be distin<;uislied from verbatim copies by bein;;' written in Kni^lish. In printin the latter. The arrangement is made on the tbilowing plan: — The ob.servatif us are divided into four series, each of which aro made by one set of observers, or on a connnon plan, or with the same instruments. Perhaps it would be more accurate to say that the differ- ent series correspond to ditVerent sets of volumes found among tho archives of the Paris Observatory; certainly, this is the only real distinction I can now make between series I and series IV. Preceding each series is given such general discussion of tho observations as ajjplies to tho whole of it. Kacli series is divided into groups, each group comprehending such ol)servations as could bo conveniently discussed together, and the reduction ami discussion of tho observations of each group are given innue- diately after tho observations which belong to it. In tlio case of series IV, however, all the earlio'' observations are made and reduced on a plan .so nearly nnifonn that it has not been doomed nocessaiy to go into the separate details of reduction of each observation. It may happen that in some cases tho relation of the observations to each other, and the bearing of the remarks on them, will not bo clear. This is owing to several disadvantageous circumstances. Some of the archives examined were inisarranged through mistakes of the cataloguer; the copies were made during the reign of the Commune and tho siege o[ Paris by the national forces, and were therefore somewhat • In this connection, it may not Vic amiss to call attention to the widespread error, fuund even in Krench histories of astronomy, that Cassini 1. \v.is director nf the Paris Observatory. In fatr, iliisctalilishmcnt «a.* assigned to the common use of the astronomers of the Academy of Sciences, and no such office as that of director was known or recognized. The celebrity of Cassini seems to have given rise to ;he unfounded impression that he exercised a supervision over the work of the other astronomers. ii8 RESEARCHES ON THE MOTION OF THE MOON. hurried; in reading proof, no access to the originals could bo Iwul. These circuni stav.ctis are the only apology I can present for any crudity of arrangement which may bo noticed. • Examination of Manuscripts at the Paris Ohservatory. Series 1. . ■ - • . .^ . - /'- ■ ■ TliiTC are curious du] icate copies of the earlier ob.sorvationa at Paris, (i) We liavo a volume entitled Jlistoire Celeste de VOhservatoire Eoyal de Parin, vol. i, 1671-1675. Jiiit vol. 2, witli the eauie title, does not begin until 1783, and the similarity of the volumes following 2 to volume i seems to show that they were not prepared until a comparatively late date. (2) There is another volume, entitled Fragment des Releves des liegistresde VOhnervatoirr Royal de Vans, in which the observations of 1672, 1673, 1680-1684, 1700-1703, 1760-1767, are copied on j)rinte(l forms, with the beading Histoire Cdleste de VOhservatoire Royal de Paris, which was prepared by Cassini IV. for publication, but never published. These two volumes seem to be in the same handwriting, namely that of Cassini IV. Yet, while much of the matter in the two is common, each contains observations and remarks not given in the other. Fo> instance, in the case of the occultations of February 3, 1672, (2) says that the clock stopped about 5^ hours i). m,, and that it stopped very frequently about this period. There is no complaint of the clock at all in (i). Yet the observations agree perfectly. But of the alti- tudes for time copied from (i) only a very few are found in (2). More curious yet is the comparison of the accounts of an occultation in 1672 given in the two registers, which I copy verbatim. From (i), page 32. — " Le 2 Aoust. Vers Ic; J'', du soir la lune etoit proche d'une etoile fixe voisine d'Autar<5s qu'elle a eclyps(5e au moment de I'immersion (qu'ou a oublii; de maKpier sur le registre) la distance on la differ, de decliu. du bord austral de la lune et do I'etoile etoit do i' 3"." From (2), p. 42. — "Aoust le 2. Vers les 9''. du soir, la lune s'appro J..,.t d'une etoile voisine du coeur du Scori)ion que I'on a jug6 devoit 6tre eclypsde. Le parallelle de I'etoile parait quelques miuutes au raidi de la tache de Copernic. " 10''. 21'. 34". Occultation de I'stoile par la lune {10''. 2^'. n", T. vr.)" We find also that in (2) the use of the astrdnomica' "ly is introduced, instead of the old divisions " matin", "soir", and we have the following clock-errors ai'.d transits: — Aug. 2. 8" 22' 0' 12 17 5 14 44 15 13 9 56 'o 35 Pend. retard . o' 35" /9 versau au merid 34° 12' 55" Mars " " 32 57 30 Saturn " " 39 37 4° Pend. retard o' 42" a Aquilae. [In (x), 10'' 34' 40^' is giveu for the time of transit of a Aquilae.] But there is no indication how these clock-errors were obtained, and no obsers^atious in either book to fix clock errors at these times. I infer from this, and also from remarks of Gassini, that b(vt'« voluTties are simply excerpts from registers which cannot now be found, and that the observations of different i»ersons are mixed together. The clock-error would seem from what follows to be well determined, unless the InGtruments for determining it were erroneous. But the times of transits winch follow RESEARCHES ON THE MOTION OF THE MOON. 1^9 do not agree with this error at all. In fact, we have from the transits of /? Aqiiarii and a Aquilae : — 1672, Aug. 2. Aug. 3. h m e h 7n a Right ascension of star ... 21 14 17 19 34 48 : Mean time of transit .... 12 24 58 10 41 50 Apparent times 12 19 27 10 36 24 Clock-times 12 17 5 10 35 o Clock apparently slow 2 22 i 24. Either the meridian instrument was defective, and not used for clock-en'or, or observations with two clocks are mixed together. As the method of equal altitudes was known and practised at this time, I think we may take the clock-correction given as probably near the truth, .so that we shall have : — h m » Apparent time of an occultation of r Scorpii, 1672, Aug. 2 10 22 11. Equation of time 5 S'-^ Paris mean time . . . . ' 10 27 42.6 Greenwich mean time 10 18 21.6. In view of a certain probability that the clock-error was well determined, the probable en-or of this time may be estimated at ± 6"; but the probability of the error being, four times as large as this is much greater than would result from the applica- tion of the usual theory of errors to the supposed probable error. From (2). — 1680, April 4. 10'' 25' 7". Occultation d'uue etoilo par la lune. Midy le 2. 11'' 59' 36" Alaligne. 4. II 59 SS 6. o o 16. ' \Yo can only use this as apparent time. The discordant meridian transits of the sun which follow do not indicate any readily determined correction of the clock on apparent time. The equation of time being + 2'" 36", we have: — Paris mean time of occultation of Lalande 12 148 . . 10'' 27° 43' Greenwich lo" 18'" 22". The f»robable error may be ± 1 2'. The extraordinary coincidence between the mean times of this and the last occultation seems to be accidental. On 1^82, Feb. 15, we find the occultations of the Hyades recorded as follows :— ^59 2) Occultation des deux etoilesqu'on a observ^esapr^s la lune. 7 I 27 ) The times are marked in the column " Temps vray", which, however, contains elsewhere only clock-corrections. rreceiliiiK it we have a set of corresponding altitudes of for clock, evidently independent of those of La Hike, hereafter quoted, and {jiving a clock-correction of — 24'.3, nearly half a minute diilerent from the correction of La Uibe's clock. Yet the occultation must be that observed by LA Hire [given hereafter]. tso RESEARCHES ON THE MOTION OF THE MOON. For this dcM we have + 14™ 41' for the equation of time. This would make the moan times of the occultations, as reduced by the unknown computer : — h m s Oi Tauri 7 ^3 43 ©aTam-i 7 16 8 wliich are 9' less tlian those which we shall find to bo given by La Hire's observa- tions. This, then, may be regarded as tlie error of reduction in the present case. Observations hy Cassini and Makaldi. Tliere \» a series of registers, in small quarto, for the years 1683 onward, without original title or paging, containing rough notes of observations.* The only title is Observations du Solnil et den .EtoUen faites eii Jionlogne ct en Paris Pan 1683, H continuee^ e&H" 9 35 23 2 28 22 1 1 o o 12 o 31 1 Bord © 12 2 54 2 " " ■ . 2 23 12 I 34 Midy a la Marque Q 12 2 3 Midy a la .Marque D contre la Maraille. 12 1 sii Midy par les eorresp. 16 75 AP. 2 122 RESEARCHES ON THE MOTION OF THE MOON. A 2'' 40 I'liorloge orieiitale avaiuie 47" sur I'oec. J'ay oste deux iniiiutes a I'horloge oocideutale et j'ay mis avec elln I'orientale. Le 20 Bi'cenibie. 11 58 50 I Bord 12 I 12^ 2 " 9 S9 '8 10 I 28 10 3 38 2 42 a I 58 35^ 1 56 28 13 10 13 20 2 22J 13 3° ° 11 59 50 Midy par I'omb. 12 o 22 a la Marque D. [ judge that the following are altitudes of the sun observed on the monwiig of the 21st, with a mistake iu tlie hour, 2 being written for 9. There is a blank space lett for the corresponding Hltenioon altitudes. 2 32 4 33 55 ' 35 52 . ' 29 26 A midy nebuleux 43 20 47 13 S« '5 10 50 o 11 o 10 II 10 30 II 30 11 50 10 12 10 O 12 30 10 Le 21 Decembre. Coinmencemeut de I'eclipse 9'' 29' 8". '8 . . L'Btoile se cache derriere la hine. [Evidently a subsequent insertion.] 10'' 8' 58" L'Etoile paroist. [Under this another time is given for the same pheDomenon, appa rently 9' 10", but it is erased with the pen, and 8' 58" is substituted.] 35' 6" - 18 12 o II 1 Bord 12 2 34 n " 12 o 42 Midy a la Marque D. k lo* I'hor. oriental avance sur I'occ. 5". Le 22 Deceuibre. 9 14 46 9 10 o 18 5 doutense. 9 30 o dout«use. 21 31 9 50 o 24 57J 10 10 o 28 30 10 30 o 32 10 50 o Le 23 Di'cembre. Noon per siugle pair of altitudes, 12'' o™ 30", Lo 24 Deceinbre. 12 55 I B.ird du 9 14 52 2 46 54 9 10 12 3 15J 2 •' " " 18 II 2 43 34 ■J 30 12 34 Midy a la Marque Q 2- 37 2 40 8 9 50 12 I 16 Midy nou pass, a la Marque J) 25 '3 2 36 32 10 10 28 36 2 33 II 10 30 ■ 32 12 2 29 36 10 50 Tliese (tbservations from 1684, December 19 to December 24, are {jfiveii liere for the purpose of reducing the occultation of jn Geminorum, observed durinj'' an eclijjse of the moon, on tlie evening of December 21. The same occultation was observed by La Hirk, with a much more certain determination of clock-error; but I have .*^' RESEARCHES ON THE MOTION OF THE MOON. "3 thouf^lit it worth while to reduce these observations also, aUhougli there has been some difficulty in unravelling them, owing to the three meridian-marks or instruments on which the sun-transit was observed, and the general confusion of the records. The mode of proceeding has been as follows : — From the equal altitudes of the sun on December 20 and December 24 the index-error of the quadrant was derived. Taking this index-error for the altitudes observed on December 21 and December 7/ (a. m. civil time), the sun's hour-angle was computed for each of these observations. The clock-corrections thus deduced from the altitudes alone, reduced to noon, were : — Date. Corr. on Apparent Time. Equation T. Corr. on Mean Time. 1684. ■f m s s Dec. 19 + 8.0 — I 40.7 - 92-7 20 - 1-5 — I I0.5 — 72.0 31 - 17.0 — 40.4 - 57-4 22 — 24.0 — 10.3 - 34.2 23 — 30.0 + 20.0 — 10. 3' - 50.8 + 50.1 - 0.7 The correction of the clock for the phases of the occultation appears tf) be — 48^.2 and — 47'.3, with a j)robable error of perhaps 3'. There is no certain evi- dence that the clock used was the same with that with which tiie altittides were noted, but the close coincidence between the figures, — 1 8, written under the observed sec- onds of immersion, and the correction of the clock on apparent time, make it probable that the clocks were the same. The correction — 18' is that actually applied by Cassini, as appears from the publication of his result in the Memoirs of the Academy, vol. X, p. 674. The time there given is 9'' 34™ 48'. The emersion is to be received with suspicion owing to tiie double record, and the possibility that the observer did not catch the star when it first emerged. 1686, Apr. 10. Occultation of Jupiter observed, but no sufficient data for clock correction. Occultation of unknown star, 1686, June 25, 9^ 53' 51" p. m. clock. Juno 24, O altitudes. ID 3. o 59 20 ° 59 33 o j^ midy. ' ' ' ' 33 54 59 40 o I 54 • ' ' • 37 o ^o o o June 25. o S3 midy. 9 S3 5' une flxe dans la parte obscure J>. ' ^ ' June 26. haut. du bord du solei). II 58 48 - ,0 - 9 34 II 52 9 37 48 52 30 9 41 7 52 59 44 49 53 30 48 23 54 S cette derniere «e June 27. 'I 58 54 003 1( 1 centre (!). June 28. 9'" 33' 43" 5«° 5°' 10" 2>' 26' 26" 37 10 52 20 10 3 22 49 June 29. II 59 3 I 31 l( )l ■ 124 RESEARCHES ON THE MOTION OF THE MOON. The clock-times of apparent noon, as they follow from the meridian- nai'k and from the altitudes, are us follows : — Mark. Altitudes (corrected 1 June 24 0'' 0"' 43". 5 0" 0™ 38'- 5 25 0" 0" 53": 26 11" 59"' 57". 11" 59" 53' 27 0" 0" 3": 28 : • qI. Qm 2".5 29 I2» The clock appears to have been put back a minute on Jime 25, and there is no way of determining whether it was done before or after the occultation. The con-ec- tion on apparent time at 9''.9 was either — 51' or + 9'. The equation of time is _|_ 2™ 2'. We have therefore: — Cori'ection of clock on mean time Paris mean time of occultation Greenwich mean time .... + I™ II' or + 2" 11' 9' 55"' 2» or 9" se™ 2 9" 45'" 41" or 9'' 46" 41 The star is B. A. C. 3579. 1686. I Juillet. II ^i, 16J |( :''\: 1 35 )l o 25 I'oinbre a midy. L'horloge occ. retard i". 9 19 57 une etoile entre dans liiiie. 9 37 10 elle s'est sortie. 36 o elle estoit sortie. JuiDet 2. II 59 19 |( 26 a I'ombre. 1 36 )l Following this are observations rather difficuU to niiderstand, from which it is concluded that midnight on the 2d was at o'' o™ 28'; and on the 3d, midy was o* o"" 34*4. Using the correction of the meridian from the observations of June, we have : — Transit of©, July i, clock Transit of O, July 2, clock Cassini finds, July 2.5 . . Cassini finds, July 3.0 . . o*" o" o'' o" 12'' o™ o'' o™ 3 4". 5; meantime o*" 3 2i".0; meantime t *" 3™ 9'. 7. 22'.3; meantime o'' 3" 2r.2. 28"; meantime 12'' 3" 26'. 7. 3 2". 2. The clock-con-ection on mean time seems pretty well determined, and equal to -f 2" 59'. It seems possible that the clock used was the "horloge occidental", one second slower than the other; but the correction will still be less than 3"' o". We have, therefore : — Paris mean time of immersion of B. A. C. 5395 (?) Greenwich mean time of immersion of B. A. C. 5395 I 9'' 22" 9" 13" 56' 35'. RESEARCHES ON THE MOTION OF THE MOON. "5, I shall not attempt to use the emersion. 1689. Miii iS. 53 9 55 25 57 23 Mai 21. 52 59 53 JS 9 6 29 9 37 2 Mai 22. Mai 24. )| a I'oct. K )| Tiiis time is i)robal)ly 2"' early. lVi)y do la 'UJ au vcrticale 31 40 30. Iiniii. (I'liiic etoile de n pri-H <1« giiiiia'uli. 9 59 29J '? i)as8e par le vert. tlu. (!) I( II 54 o J miily. 52 52 55 9 55 40 |p liernier l)ui'd du iiii vert, de I'oetant. 9 231 I'epi ail vertical. 9 54 53 arcturiis pa.sse par le vert, du (jiiad. 9 30 42 49 30 30 14 59 46 33 I 49 50 27 53 14 )l a" V. 35 21 5° 'o 25 33 2 i6 9 o 28 I'epy au inerid. 9 52 46 arcturus au vert. Notes on the preceding observations, especially the list:— It is hard to say with certainty what instruments the transit of the sun was observed with. By induction, liowcver, I conclude that the signs |( and j| meant transits ol the suns's limbs over the meridian of the octant. Hut from the observations of May 21, it would seem that this could not have bi-en the case May 22. The following, however, are transits of O centre over something, and times of apparent noon from corresponding altitudes: — )1 1( Oct. Quad. Corresp. alt 1689. Mai 15. 11" 54' 8i" 56" 6» II 54 37 16. ' 54 II 17. 54 13 . 18. 11 54 17 56 15 21. II 'u. ^ 1 22. II 54 oj 54 32 23- 1 1 53 56 54 29 Olock adv. 6'". 24. 59 56 (?) 20 25- II 59 S4j 23 26. S4 The following are the altitinles of the sun for time :— May 15. a. ni. 9" 54' 50" 520 0' 57 34 52 20 10 2 58 53 5 47 i.3 20 837 S3 40 54 41 52 4 40 30 43 45 4° 55 May 23. ll8 53 56. + S2. II 56 12 + I 54 . S4 21 59 5&.: + 25.: II 56 17 - 4 4 The mean correction to the principal noon-mark being 4- 25', this quantity is applied to the clock-times of the transits of the sun on the 21st and 2 2d to obtain the clock-times of apparent noon. The clock-correction for the time of the occultation being +1"' 35", we have: — 38- 29" 37' ±i' 1 6'. 34 P- Paris mean time of occultation of Wkisse II, 1656 (?) . Greenwich mean time of occultation of Weisse II, 1 656 (?) OccultatioQS of 1690, Apr. 13 and July 3. 1690. Apr. 13. 11'' 37' 52" j'ay vu entre la fixe derriere le disque de 1» JUine par la lunette de The data for clock-correctious are: — 1690. h. ; /( / // Mar. 24 II 57 48 59 58 »S 58 23 32 27 57 33 59 41 29 56 21 58 30 30 56 13 58 22 (llock adv. 3'. Apr. 2 3 5 6 7 8 9 10 59 7 I 17 58 48* (!) 58 13 23 57 56 6 58 3 13 57 34i 59 44 57 10 56 43 * 58 53 Corresponding altitudes 0. Mar. 24. h. ' " h. ' " / 10 3 22 » 55 «9 37 6 42 5« 58 J 37 20 10 10 48 31 April 5. 37 40 9 38 33 2 20 3 38 30 42 21 17 14 38 5° 45 13 14 22 39 20 49 3« 10 I 39 40 52 29i 7 3J April 24. 40 per correspoudiug altitudes with- out correction . . SS"- 45' Interval . .... e* 45" ... >, t-li Apr. 23 • • II 57 »4 25 • • . II 57 25 * In this and the following observations, it is stated distinctly that the transits are over the vertical of the great quadrant. RESEARCHES ON THE MOTION OF THE MOON. lay Clock udv. 3'. Apr 12 . 59 6 13 58 40 ° S« »S 57 55 6 Jiiue II " 57 41 59 58 '3 57 45(»>c) 59 3 «4 58 25i(') 60 44 »S 58 "i 41 i6 58 " 39 July »i 59 '4 59 '8 30 28 3» 35 So oil Apr. 24 the correction wan about + 17'. June 13. b. in. // b. ' " / 9 50 56 284 54 20 53 '9 5 42 54 40 57 4 > 57 55 20 59 36 59 25 55 30 10 2 6 June 16. 55 5° li. ' */ b. ' " ' 9 22 22J 2 36 48 SO 20 24 36 34 32 40 26 5» 32 isi 5» 29 8J 29 s8 20 3' 25 27 40 July I. 40 9 27 56 - -. so 5° 5° 30 12J SI 10 32 30 5' 30 34 47 5" 5° 37 4 52 10 3 Juillet 3 s 25 nne fixe des Pleyades entre dans la luiie. We have first to find the corrections of the quadrant from the corresponding altitudes. The results are as follows: — Noon, from From Alti- Corr of Date. Quadrant. tudes. Quad. h m s m s / i6go, M.ir. 24 II 58 53- 59 3-0 + 10. Apr. 5 59 18. 59 30.8 + 12.8 •Apr. 24 57 «9.5 58 31.3 + 7«-8 June 13 58 54. : 59 28.6 + 34.6 June 16 59 30. 59 32-5 + a.5 July I 60 23. 6o. 35.1 + 3.1 We here meet the perplexing question whether these great changes in the position of the quadrant are real, or whether they arise from an accidental error of a minute in the record of April 24, and half a minute in tliat of June 13. There is clearly an error of one minute in one of the records of transit of the sun's limb on the latter date: I have assumed the error to be in the second limb. But no change in the minutes alone will reconcile the correction with the two following ones. For Ajjiil 24 I have copied nothing from the original record; the transit of the sun over the quadrant was not observed, but is deduced from those of the days preceding and following. For the con'espontling altitudes I took the mean of the actually observed times with the mean interval, the latter being required to compute the correction due to the change in the sun's declination. The remark about the con-ection being + ' 7° . A _ .— ™^— . (') J'avais replace le grand Q. auparavant I'observation. 128 RESEARCHES ON THE MOTION OF THE MOON. I !un now (juite unnblo to undcrwtaiKl. I Imvo iiHsumed tlio correction (»f the quiulrant to be +12" on April 13 iuul -f3" on July 3-4. Then, wo havo : — Date. i6go, Apr. •3 Apr. 15 July n July 3 July 4 Clock-lime of | ^Joon . A m s II 59 57 II 59 12 23 26 29 Mcau Time. A o m s o 18 59 47 3 22 3 33 3 44 Clock-cor- ri'ctloii, m + o + o -t- 2 + 3 + 3 J 21 35 59 7 •5 We thus deduce : — Clock-corrections at time of occultation Paris mean tiinen Greenwich mean times II' 11' April 3- July 2. + 24' + 3"" 4- 38'" 16' 15" 8"' 29" 28"' 55' 14" 59™ 8". The stars are sui)posed to be 136 Tauri and 27 Tauri. Assuming the (jnadrant to have been steady, the probable errors of these times do not exceed two or three seconds. If, howevei", the corrections to the quadrant on April 24 and June 13 were real, and the iiistrnmeut correspondingly unsteady, the times may be in error by twenty seconds or more, and are probably too great. Occultation of Aldebaran, 16^^, Aiig. 18. Aug. 19, A. M. I 38 44 I'etoile touclie. . . I 39 22 I'etoile entre. 2 17 12 I'etoile sorte do la Inne et paruit grosse. A correction of 1"' 6' is then ai)plie(l for clock-error ; but it is not possible to tell how it was obtiiined, and the confusion of the observations and of the two clocks is such tiiat the independent computation of a dock-correction is not po-ssible. Here, as in tiiu observations of 1684, we And comparisons between a "horloge oricntale" and "horloge occidentale ", but no indication as to the clock witli which any ])articnh)r observation was made. In examining the observations 1686-169P, I Und no indication that more than one clock was used. The last volume of the series from which the jneceding observations are copied, viz, vol. 19, is in a much nicer liandwriting, and is eviilently not a simple re<.'onl of observations, birt a mix- ture of observation and calculated results. An occultation of Aldebaran was observed 1701, Feb- ruary 16, but it is hard to tell what is meant. The duplicate series is bound in vellum, and is evidently a simple copy of the preceding in a fairer handwriting. As Ihe copy seemed to be quite correct, and to include everything, [ have sometimes employed it to copy from, nearly always, however, comparing with the original as I went along. This series is numbt»red 1009, and is bound in vellum. Vol. i is missing; at least, I conhi not find it. Vol. 2 commences with 1682, January i, but has no title whatever. On the inside of the cover of each volume is a rude index to the principal observations. The series con- tinues without interruption to 1795, but a number of volumes are missing. RESEARCHES ON THE MOTION OF THE MOON. tS9 From Iho iHHt cicftorlbetl nerioN, v(il. 0. Eclipse of 1734, May 22 f ObservatioiiH fiiiteft par Sarbl (f) daus tour iiifurieure uucideiitule. 5 55 24 com. decl. 6 49 10 Totalc. 51 52 recouv. de luro. S7 40 Un ne voit plus le Boleil. 7 39 o pend. sup. 7 39 ^^ peiid. inf. Observation falte par M. des Plages avec uiie lunette de 34 p'e'M" 8 i^ o comm. de I'Eclipse. lunette de 8 pieds, pend. iuf. et lunette de 34 pieds. 3 Doits • 5'1-i 6 '■■■ -^v-'v --':■ 10 d. i (sic) ' ' II II 6 4 17- 8 13 8 27 30 37 20 41 30 45 50 9 18 IS 20 12 40 SO 53 II 30 ■75 Ap. '30 RESEARCHES ON THE MOTION OE THE MOON. 17 16 23 o 28 30 »2 33 ° 32 55 t I Fin obHorvt'«5 u luiioite (!«' 8 [litMlM. Iioiitl. Hiip. pciitl. inf. OliHcrvntion f'aito 11 Miirly. (Uoconl in the Haino hand, and that u gouti one.) Le 2. May a 9'' 14' 6" H. 9 1685, Feb. 13 May 28 July 16 Sept. M Oct. 10 Oct. 117* Nov. 27* l6gq, Juno 2» Aug. 21 Sept. 13 Oct. 23 1706, May 6 1708, Sept. 16 1715, May 9 CUick-tin.e of Transit of "1 over Mcrid. of Instrument. A 12 12 12 II o o o s 23-<' 43-8 28.0 50.0 7.8 58.6 2.q o o II o o II II 1.8 4.0 A-5 17.2 16.5 38. o 26.0 .Mean '"lock- time off orres. Al'.ituiics. // 12 lU 12 II O o o ;;/ 5 9 6 59 o 4 I s 32.8 28.2 32.0 9-9 12.2 30.4 28.6 o 52.3 57 42.0 59 41-6 o 39.6 58 9.7 58 49.2 Mean Corr. for Interval. Mot. of 0. '" 50 22 I 32 «3 ! o 54 ; 16 ' s + 6.0 + 03 — 19.0 - 6.6 + 9-8 + 20 9 + 21.3 27 I 34 3' 49 20 + I5.3 + 18.7 + 20.7 - 13-5 + 21.0 - 13-5 Transit of over True Meridian. Corr. of /// s 5 38.8 9 28.5 6 13.0 59 3-3 22.0 4 51-3 1 49.9 Merid. In- ; Dec. of 0. strunient. 20.0 7.6 0.7 2.3 26.1 58 30.7 58 35-7 -t- 15-2 - '5-3 - 15.0 + 13-3 + 14-2 - 7-3 - 13.0 - 16.2 - 15-2 + 18.2 + 3-6 - 3-8 - 14-9 + 9.6 - 7-3 + 9-7 + 22 - 23 - 13 + 21 + 21 + 3 - 6 - 13 - 21 + 22 + 12 + 4 - II + 16 + 2 + 17 15 26 26 25 29 35 * For these three dales, I have accepted La IIirk's reduction of his corresponding altitudes, as his reductions were found in other cases to be correct. 132 RESEARCHES ON THE MOTION OF THE MOON. We now arrange these con-ections according io the sun's dechnation, putting in a separate cohimn those determined after the interval of 14 years between 1685 and 1699. We find them to be as follows: — )'8 Dec. 1684-5. 1699-1715. Porninla. a a I a -23 -15-3 . -157 — 21 -'5-2 • — 16.I -13 -15.0- 16.2 * — 14-9 — XI » - 14.9 -14. 1 - 7 - 13-0 ' * — 1 2.6 + 3 - 7-3 - 7-3 - 66 4 • - 3.8 - 5-7 12 ■■»■ + 3.6 . + 2.7 16 * + 9-6 + 8.0 n . + 9-7 + 90 '>i -^-^3^3 + 14.2 . + I5-I 2^ + 15.2 + 18.2 + 16.6 There seems to be no evidence of any change in the instrument during the whole period of the o]3,servations. Supposing the axis? on which it turned to be qtiite true, so that its deviation from the meridian arose only from errors of level, collimation, and azimuth, the correction nee essary to reduce the time of transit of an object over it to the true meridian could be expressed in the form m -\- c sec S -\-n tan 6, 6 being the declination of the object. The values of the constants which best repre- sent the above deviations are: — ni=: — i2i'.4 i c = -}- ii2".7 I r n = + 39'.8. ! The nunibers computed from these values of the constants are givca above in the last colunni They seem to represent the observed deviations within the probable errors of the observations. 'J'he following table shows the corrections computed from the formula ; — Decl. Correc- tions Diff. s s - 25 - 15.8 — 0. 1 — 20 - 15.9 + 0.6 - 15 - '5.3 1.3 — 10 — 14.0 2.2 - 5 — II. 3 3.1 + 5 - 8.7 - 4.8 3.9 4.8 10 15 0.0 + 5.9 5.9 7.0 30 + 12.9 + 8.7 S5 + 21.6 We shall use this table in reducing transits to the true meridian in order to obtain clock-con'ections. RESEARCHES ON THE MOTION OF THE MOON. Extracts from La Hire's Journal. Vol. 93, page 4. — La Hire's first occultation, observed at Observatory. m 1682, Feb. 15. 2- Mane. 9 I 49 '7 3^ Vesper. 2 58 40 Correct. 37^^. 11 etoit done inidy a 1 1 59 55 964 18 51 23>4 . :. 9 10 24 18 30 5° 2 Le 17 a midy I'horloge de.oit se tarder de 37. From altitudes of Cauda Leonis it seems the clock lost 28"" 52' on sidereal time between Feb- ruary 10 and 17, or 11"^ a day on mean time. Tbe following are the altitudes on the 17th : — 1682. Feb. 17. 4' 6" Alt. = 28° 30' 7 II 29 10 15 29 30 13 22 30 Doub. * Eclipse of Hyades par la Inne Feb. 15. 6 59 2 Emersion of «. ( According to Le Monniek, Hist. Coelente p. 257, the '< h. » appai ( 6 59 2 J 7 I 27 apparent times were 6 59 7 I 37- The corresponding altitudes of the sun give: — Clock-time of ©'s transit 23" 59™ 54".9, While mean time of 0's transit is -o'' 14™ 41". 7. Clock-correction + 14"' 46".8. The clock-rate being 1 1' 5 per d-iy, the error at the time of occultation would be -f 14"' 50".2. As a check upon thj rate, I have computed the correction from the alti- tudes of /? Leonis on February 1 7, and found, as the mean result from the four alti- tudes : — Feb. 17, 9" 9'" clock-time; correction = -f 15'" io".5. This gives a rate of 10" i)er day, and a ("orrection at the time of occultation o".4 less than that found above. I have, however, used + 14"' 50^.2, giving:— «| Tami. «' Taiiii. Paris mean times of occultation . . 7" 13'" 5 2". 2 f 16"' 17". 2 Greenwich mean times of occultation 7" 4"" Si'- 2 7" 6"' 5 6". 2. The equation of time being + 14"' 40".8, these result,s do not differ one second from those given by Le, Monnikk. The phase is actually immersion, not emersion. © Eclipse, 1684, July 12. Manuscript, vol. 93, page 287.— Observations of La Hire. 10 Julij. Altitudines superioris Limbi © pro horolog. Mauo. 7 32 S4i 31° 0' • 35 58 31 30 3S' 8" Correctio i2.i addenda 38 59 32 32 si 42 3 32 3° 29 2 45 5i 33 ° 4 25 59i . 134 RESEARCHES ON THE MOTION OF THE MOON. Meridies Inrologio indicante 12'' 5' 38" J Traiisiti 8 i)rioris Liiiibi 12 4 15^ Traii.situs posttTioris LiiuUi 126' 32" •■ •' ' ■ 2 i6f Transitns centri 12 s 23g Traiisitus per. ver Meridianuin 12 5 37 5 Traiisiius eeutrl 3h 6 32^ Traiisitus veri Temp, per vernui Merid. ...-...,. 3 o 55 U Traiisitus Centri 4'' i' 8" 11 Julij, : , Transitus prioris Liiiibi 12'" 4' 19" TrausituB posterioris Liuibi 12 6 35^ ■ . ' 2 16J Traiisitus centri 125 27J Altitude Merid. suiierioris Liiiibi 63 27 50 N Serpentarii Traiisitus 9 30 54J et tardavit(?) liorologiuin pro duobus diebus io"J 12 Julij. Altitudiuos superioris Limbi pro borolog. Manu. 5 36 5 21° 30' 39 H 22 o 42 14 22 30 45 ^^ 23 o Vespere Eclipsis Solaris. Plinses. TenipuH. I'LiiHcs. Tempus. 29' 56" 2" 3S' 59" II' 5" 3" 45' 49" 27 51 41 49 12 45 56 49 27 13 43 59 13 45 42 29 24 ss 49 59 14 39 69 23 36 53 49 16 14 10 49 22 '4 57 29 19 32 19- 39 19 55 3 3 49 , 21 23 24 19 17 56 9 59 23 36 30 39 16 14 16 29 . 26 46 37 39 14 I' 23 49 29 37 44 19 13 4 , . 27 9 It 48 34 9 Initiuin 2 31 6 tempore borolog. no 42 9 5 42 J corr. horol. aubt. Chordae. Tempiia. 13' 3°" 2'' 38' 19" 17 5 45 49 21 IS 55 9 22 s° 3 19 25 49 7 49 26 27 13 34 27 13 19 19 28 34 29 39 29 37 37 39 28 24 59 19 25 23i temp. vero. Cliordae. Tenipiig. 27' IS" 4" 8' i6' 23 55 22 19 22 20 26 39 19 5 34 12 45 43 9 RESEARCHES ON THE MOTION OF THE MOON. Fitiis totiiia Eclipseos, 4'' 49' 9". Pars illumiiiata 17' 44", 4'' 14' 49" Ditim. Ltinae 29' 39." Horologiuin acceleralmt tempore Eclipseos 5' 42"^. Fiiit igitur flnis veri temporis 4'' 43' 26"^. 13 Julij. Altitndines snperioris Limbi pro horologio. 135 Mane. 8 33 12 40O 30' 3 38 S Coirecitio addenda 12" 36 >9 41 34 58 39 28J 41 30 3> 49 4» 37 42 28 40 In meridie sole cxistente, horolog. indicavit 12 5 44 J. The clock-corrections for this eclipse are derived as follows : — The single altitudes observed on the morning of July 12 could be made avail- able for detennining the clock-con-ection on that day ; but the rate of the clock is so good that I have not deemed it necessary to go through the labor of discussing them. Interpolating between July 1 1 and 13, we find for the clock-error, before and after the eclipse: — July 12, 2^.1 Clock-correction, — 42^o. July 12, 5^3 Clock-correction, — 4i'.o. Occultation of /j. Oeminortim, 1684 December 21. 19 Deceinbris Mane HE Transitus T*" 25' 7" Alt. © sup. limbi pro horolog. Mane. Vespers. a* S3' 55" 6° o' 25™ 2' i" corroctio add. 56 54 6 20 22 2 '59 SS 6 40 19 2 9 2 57 70 3 IS 59 Oeutrum trafisivit per nicrid. indicante horolog 129 28^ 9 Trans'ius centri 96 55J Trau. prior, limbi 12 8 33 " posterioris " 10 54 J " centri 129 433 Ceti 08. transitus . 90 i Aldebaran " '° 3' 37 3) I " 10 33 46 136 RESEARCHES ON THE MOTION OF THE MOON. 20 Decembris. Betroactuiu est borolog. Io^ ® transitus I 11 59 o " " II 12 I 22 Cent. 12 o II 21 Decern bris. Ceti 08. transitus 8 42 4. Pro dnobus diebns tardavit horolog. 5". Inter '21 et 22 in media nocte accelerav horo!., 33". Accelerae lior. in media nocte 37". Vespere. Occultatio stellae /i II (i^'r^e eclipsata 93523 Einersio vel apimr. ejus • 10 9 2 Transitus Dl .... 121 44^ II 12 4 o^ 2 Decembris. 1 II S9S3i ; O II 12 2 16 : 16 8 Cent. 12 I 4| The clock-corrections derived from the transits of tlie sun fi-oni December 19 to 22, and tliose of the moon and a Ceti on the 21st, are shown in tabular form below. The first transit of the sun is that derived from the corresponding altitudes. The tabular right ascension of the moon probably requires an increase of two seconds of time; this correction has therefore been applied to its tabular right ascension at the time of transit to obtain the mean time of ti'ausit. Date. Object. Clock-time of Transit over Meridian In- strument. Corr. for Deviation. Clock-time of Transit over True Meridian. Computed Mean Time of Transit. Apparent Clock-cor- tion. 1684. A m s s m s m s m s Dec. ig © . . . 9 43.8 - 15-9 9 28.5* 58 19-3 — M g.2 20 © . . . II. - 15.9 59 55-" 58 49-4 - I 5.7 21 n Cell . 8 42 4. - 6.3 41 57-7 40 53-8 - I 3-9 21 Moon . 12 2 52.5 -1- I7-0 3 9-5 2 6.0 - I 3-5 22 © . . . 12 I 4.8 — 15.9 48.9 59 49.8 - 59.1 The occultation was observed between the transits of a Ceti and the moon. The agreement of the clock-corrections and the uniformity of the rate seem to indicate that the times can be determined within a second. Deriving the clock-correction from the transits of a Ceti and the moon, we have : — IiGmersion. Clock-corrections for occultation of /i Geminorum . . — i" 3".8 Paris mean times 9'' 34™ i9'.2 Greenwich mean times 9'' 24'" 58'. 2 Emersion. 10" 7'"58'.3 9" 58" 3r.3- ^From the corresponding altitudes. RESEARCHES ON THE MOTION OF THE MOON. 137 1685, Feb. 13. Altitudiiies sup. limb. O pro hor, Mune. Vespere. 8" 46' 14" 14O 20' 26' 51" 48 S3 14 40 24 10 Correct, subt. 38". SI 34 IS o ^ 21 29 54 17 'S 20 18 48 iSolis ueut. tetigit moridianuni, iiidicaute bor. 12 6 13. O transitus I II 7 3S Centri 12 6 28 On 1684, Dec. 2, the transit of © was i4>4" late, so that there can be no doubt of the correc- tion to La Hire's guonion. Here there is a lacune in Delisle's copy of La Hire, from which the preceding is copied ; this lacune is afterward filled up from La Hire's original. 1685. For correction of La Hire's meridian. P.M. 34029 i3j"corr. subt. ©Tr. 115742 A.M. Mfty 28 8 17 so 39 ° 20 S7 39 30 24 4 40 27 iij 40 30 6 20 56 24 2 39 3° 7 3*34 35 45 3856 42 6 7 18 42 7 48 21 5' 44 55 "^ 583s July 16. 19 30 20 22 30 Sept. 14. 17 '7 3° 18 1830 Sept. 13. 15 ° Oct. 10. 12 o 30 13 ° •3 30 37 22J 34 '6 3' 9 n 59 58 II 58 5° over mer. 1159 3 5 39 2<5 J !I ) . 21" add. 36 21 20 s8 19" add. + 13" © Tr. II 59 oi 12 o 16 12 o 73 43626 42" add. Sept. 13O 19 426 33 "6 J2 6 34 30 6 _. ^^^55 4," add, '='5 3° per ni. s 214 8A 45118 43" add. Sept.i6© 12 2 51^ S ° 12 3 55? 4 1438 , .,,■, Oct.9, ©tr. 12 I 22i ...3 "^^^ 332 4 23 12 2 27J Oct. II. O tr. 12 o 325 2 42* 18- -75 Ap. 2 12 I 37J t58 RESEARCHES ON THE MOTION OF THE MOON. Vol. 93, p. 429. Iiniiiei-sio stellae H Geiiiinoruin, 1685, Oct. 17. 9 52 29 Penil. Oct. 16 © cent, transit 11 59 38 17 Sclieat Fegiisi tr. 9 14 11 Markab. 9 15* 57 [• Le Monnier prints 14, which is rinht, but it is ck'aily 18 a Aquilai 5 57 45 15 in the MS.] Scheat Peg. 9 "o S Markab. 9 10 51 20 II 58 16.6 27 Correction of qnadrant per © — i6'J. Nov. 27 " " — iS'i- The clock-corrections from 1685, October 16 to October 20, are derived from the observations as follows : — Date. Object. Dec. Corr. for Deviation. Clock-time of Transit over True Meridian. Computed Mean Time of Transit. Apparent Clock-cor- tion. C. A. 1685. s h III s A III 1 m t s s Oct. ifi - 9-3 - 13.8 II 59 24.2 23 45 31.2 - 13 53.0 53.0 0.0 17 a Pegasi. + 26.3 + 23.9 9 14 34-9 9 48.5 - 13 46.1 39- « - 7-2 a Pegasi . + 13.5 + 4-0 9 15 II 9 I 20.4 -- 13 40-7 39-2 - 1.5 18 1 Aquilx. + 8.1 - '-9 5 57 43.1 5 44 14-4 - 13 28.7 30-5 + 1.8 li Pegasi . + 26.3 + 23-9 g 10 28. g 8 56 52.0 - 13 36.9 29.2 - 7.7 a Pegasi . + «3.5 + 4.0 9 10 550 8 57 23.9 - «3 311 29.2 - 1-9 20 © . . . - 10.7 - 14. 2 II 58 2.4 23 44 49.4 — 13 13.0 13.0 0.0 The discordance of clock-errors is perplexing. There is a seemingly systematic difference of nearly six seconus between the corrections from a and from /3 Pegasi. As the latter lies without the limits between which the deviation of the instrument was determined, the corresponding result is to be received with suspicion. If we determine the clock-correction and rate from the transits of the sun on the 16th and 2 1st, we have the results in colunms c' and A, the latter being the dif/erence between the computed error and that dei'ived from the intermediate observations. The most probable value of A for the tinu of the occultation may be estimated at — I'.o, with a probable error of 2". This .will give for the occultation of H Geniinorum: — Clock-correction Paris mean time of the occultation, October 1 7 Greenwich mean time of the occultation . . . 13" 38" 29^ 4g'.o 49".o 2810 ± 2'. Mane, 19 Augnst 1699. Imniersio Aldebarau i" 41"" 36' Eiuersio 2 19 37. Sed etiain in iiiunienio apimiuit niagna'et in disco d reflexionc luniinis tei The observed tninsit.s of were: — Ang. 15 II 57 38 '7 58 23 18 58 43 " 59 .S9 rae illnstratiie. U. 59 48J o 33 o 54 2 9 Cent. 58 43i 59 28 59 48i I 4 A. M. Aug. 19 ^ o 14 17 RESEARCHES ON THE MOTION OF THE MOON, 139 Aug. 21. Altitudines pro liorolog. 8 II I 30 30 3 S° 43i 14 14 31 47 30 17 28 31 30 44 18 (Joir. 3 20 39J 32 41 4i 23 S° 32 3° 37 48 L^iitrmn © perveuit ad Oiroulem lueridinniiiu iiidicmite lioroIo;;io 12'' i' 7"^. Qiiivre tiirdiit qiiiidrmis munilis in altitudiiimn 53° 12' ... . 3 J". On tlie 2d June preceding, he found iv coneotion to tlie quadnmt of +i8"4, as follows: — Tmnsit June i, o i 48 5. ° 2 55 Debui transire .... " 2, o 2 ijj Transit per alt. corresp o 2 20 Corr + i8i Again, Sept. 12, tlm correction w,is —4". Tlio change prohibly ilependa on the sun's Z. D. The derivation of clock-corrections from transits of the sun is as follows : — Clock-time 1 Date. Dec. Corr. of Transit over True Mean Time. Corr. of Clock. Hourly Rate. Meridian. I6g9, .f /( m s A m s ■ m s s Aug. 15 + 14-0 4- 4-7 II 58 47-9 3 55-9 + 5 8.0 1.42 17 13-4 4.0 59 32.0 3 31.8 3 59-8 1-37 l3 13.0 3-4 59 5"-9 3 18.9 3 27.0 1.62 2t 12.0 4- 2.2 61 7.2 2 37.5 I 30.3 In obtaining the time of the last transit, double weight has been given to the result from equal altitudes. Interpolating between the last two corrections, we liave; for the times of phases : — Clock-correction Paris mean time, 1 699, August 1 8 Greenwich mean time .... Irameraion. + 3"" 4'-8 i3''44'"46'.8 I3"35™i9'.8 EnierBion. + 3"° 3"-8 14" 2 2 '"40". 8 i9».8. 14" 13 Initium 8i'i3' 18" Dig. oj IS 43 I 18 28 14 22 19 ..• a 25 3° - . -»*- ■ 28 44 i 30 46 it 34 19 4 37 6 4i 40 4 S 43 «6 Si 46 55 23 Sept. © Eclipsi.**, 1699, luaue. Dig. 8 30 8 o 7 30 6 30 60 ;-:- 5 3° .-. , 5 ° 4 30 ' : ■ 40 *i 3 30 30 2 30 41 39 45 37 49 27 55 42 o 16 4 13 9 S 12 47 15 55 19 6 23 5 27* 4 • It seems as if the minutes first recorded were 26, and that they were afterward changed to 27. There is no evidence 10 show with certainty whether this was simply to make the ditferences run more smoothly or not. The change was evidently made after taking the differences. 140 RESEARCHES ON THE MOTION OF THE MOON. Dig. 6 8" so' 28" 6J 54 2 1 57 23 7 a* 9 I 20 8 5 " 8 30 9 12 9 14 6 Ditiir 93* 21 21 MHxiriia obsciiritiw. Teiiii 9 3° 28 57 9 » 35 S3 tr. I. II. Cent. Sept 12 II 57 59 9 58 4i 13 56 35 58 43 57 39 II 57 27 59 39 58 31 20 58 3oi o38i 59 21 . • i6i 59 114 22 57 45 59 524 58 48.? 23 57 20J 59 29 58 24.={ 26 56 8 58 17 57 «2i Oct, 22 59 8A I 20J i4i 23 59 " I 23J i7i 24 59 14 I 26 20 Oct. 23 Cent. tr. per iner. circ. ind. horol 12 ij Dig. 2 10 30 26 I 30 33 S3 I 37 '9 30 39 57 flni8 43 '8 Diiimeter cum micrometro 31' 58". Tempore observaliiiiiis liorolog. tanlebat i' 41' Sept. 12. Altitudines pro borol. et qua- (irantis muralis deviatione. 8" 12' S3" 25" 0' 42' 30" 22 s8 26 30 32 26 26 20 27 29 3 29 47J 27 30 25 37 33 15 28 22 9 36 '44 28 30 3 18 42 363 Oct. 23. 37 20 70 0' 22 2 40 46 7 30 18 i^ 44 15 80 15 7 47 45 8 30 4 II 4« Oorr. 40 J add. Quamobrem aufernndum iu mnralem. baec altitudiue 15"^ a traiiaitti centre per quadrantem The clock-coiTections are derived thus : — Date. Clock-time Mean Time Clock-cor- of Transit. of Transit. rection. 1699. h m s h m 1 m s Sept. 20 23 59 26.2 23 53 9.3 — 6 16.9 21 59 3-0 52 48.6 - 6 M.4 22 58 40.0 52 28.0 — 6 12. 23 58 15.8 52 7-5 - 6 8.3 26 57 2.8 51 7-0 - 5 55-8 The correction for the time of the ecHpse is — 6" 9'. . * 1701, 23 Sept. (mane). Aldebaran occultata a Luna 6 10 50 670 veri temp. Notandum quod stella jam supra discum Lunae quaiititatae i^ diainetri suae apparebat quando oninino evanuit, et circiter post 2" temporis ceiitri stellai' iminersiouis apparentis. (A similar lemark was made on the other occultation.) Emersio . . 6 57 8 Veri temporis 6 53 18. L'horloge tarde de 35" par jour. RESEARCHES ON THE MOTION OF THE MOON. I4I There are no corresponding altitudes given since those of Oct. 23, 1669, but he seems to know the errors of his quadrant e. g. 20 Sept. 1701 9 centri Transitus per Quad. mur. 11'' 7' 42". Trausitus per Q. M. veri temporis II 2 12^ altitudo ver. 50° n'. Transitus per V. merid. ver. temp. II 2 12. On the same day we find : — Trausitus centri © per vero inerid. 12 5 28, indicating a correction of — 6". Sept. 23 per ver. merid. 12 3 41. © tr. 1. II. Cent. 1 701, Sept. 19 12 S 7J 7' 16" 6 llj 20 4 30 6 38 5 34 21 3 35 6 3 4 59 23 * 43 4 5« 3 47 *4 2 8 4 16 3 '2 There are no altitudes within the two years following, aud no explanations of the data for deviation of the mural quadrant. The clock-corrections, as derived from the transits of the sun, are: — Date. ©•s Dec. Corr. Clock-time of Transit over True Meridian. Mean Time of Transit. Clock-correc- tion. Hourly Rate. 1 701. • 1 Am s h m s m s J Sept. 19 + 1.6 - 7-5 6 43 23 53 40.2 — 12 24.1 0.72 20 + 1.2 - 7-8 5 26.2 53 19.4 - 12 fi.S 21 + 0.8 - 8.1 4 50.9 52 58.6 - II 52.3 66 23 + 0.1 - 8.7. 3 38.3 52 '7-5 — II 20.8 0.62 24 - 0.3 - 8.9 3 3« 51 57-1 — II 6.0 Interpolating to the time of occultation, we have : — Immersion. Clock-correction for time of phase — ii" 24'. 7 Paris mean time, Sept. 22 Greenwich mean time 17" 59" if 50" 25"-3 4'.3 Emersion. — 11" 24'.2 18" 45"' 43».8 18" 36™ 22».8. 1706, ® Eclipsis, 12 Mali, mane, luitium circa 8'' 25" o" nam hora 8 25 10 jam apparebat Eclipsis quani proximo }i digit quod ad visum pertubum patebatur. Postea nubes frequentissimae nullas observationes habere permisferunt usque ad horam 8'' 48'. Observationes sequentes habitae sunt horologio ut se habet et non correcto. May 8'>48' 0" ,9' 59" 9 54 45 II 24 52 «7 49 56 10 12 2 55 ° '6 33 57 45 12 45 57 35 »5 17 59 30 13 23 9 20 ■4 I 50 14 I 10 II 24 2 25 14 39 7 »5 10 46 3 45 IS 17 8 40 10 8 5 15 IS 55 9 55 9 30 6 45 16 33 Transits of©. 4 II 59 37 I 49 12 43 S — I 3Si 29J 6 59 1° I 23 16^ 7 — I 10 3i 8 58 46 59 59 S2.i 9 5836 48i 59 42i lO 58 23 36 59 29i 142 RESEARCHES ON THE MOTION OF THE MOON. 9" 11' 10" 8' 52" 8 25 17 II Mii.v II II 58 10 »4 12 59 17 12 40 8 '4 9 45 «7 48 12 — 13 59 6 14 10 7 36 II 20 18 26 '4 57 43 59 56 58 494 '5 32 6 58 12 5° '9 5 17 10 6 20 14 «9 43 '8 33 5 42 14 55 20 21 6 Mail pro meridie deterniinaudo altitudiii 20 25 5 4 16 10 20 59 22 s 4 26 17 55 21 37 :' ■'' h / II / 24 s 3 48 «9 8 22 15 :'■■ 7 37 36 28 30 23 44 26 5 3 10 20 5° 22 S3 40 41 29 20 38 3« 2 45 22 '5 23 3' 43 42 29 30 »7 36 34 IS 3 10 25 15 24 47 46 49 30 14 30 36 JS 3 48 26 25 25 30 49 54 3° 3° II 27 38 26 4 26 27 52 26 8 52 S8i 31 4 8 20 40 5 4 59 10 26 46 41 38 S 42 30 20 27 24 Centrum tr. iud. horol. 12 26. 43 6 20 31 32 28 2 44 40 6 58 33 5 28 40 46 20 7 36 34 36 29 18 47 3° 8 14 36 5 29 56 49 S 8 52 37 40 30 34 50 25 9 30 40 24 flnis oclipsis accurate. • 52 10 8 53 30 10 46 Tempore eclipsis tardabat horologium 42". The results for clock-error, as derived from the transits of the sun, are as follows:- Date. Clock-time of Transit. Mean Time of Transit. Clock-cor- rection. 1706. Am s A m s m t May 10 23 59 39.0 23 55 59-5 - 3 39-5 II 59 26.3 55 56.8 - 3 30.0 12 59 16.2 55 54.7 - 3 21.5 J4 59 0.4 55 52.1 - 3 8.3 The resulting clock-correction at the beginning of the eclipse is —3"" 22'.7, and at the end — 3"' 21 '.9. trau. I II Ceut. pro merid. @ traus. I Cent. pro merid. 1708, 23 Februarii. II 59 8 12 I 21 5 Eclipsis a ([ Initinm 7 3 47 12 o 14J 12 O I Feb. 24. 11 59 2 12 I 13 12 o 7j n 59 54 Veri Temper is 7 3 48 Finis 7 3 57 7 3 58 RESEARCHES ON THE MOTION OF THE MOON. ^1 1708, Sept. 14. inn 110. Kclip.siH 0. In niediii eclipnis lioiolojjiuin tanlalmt ex tempore vero 35" He»l eorieeto posteii tempore per novas obNei'vationeH tardaliat 37". Ill sequeiitibiiH plnmihim teiiipiiH vernin iiotatum est. Sed ad 58' 30". Ergo, subt. sunt 8" in ait. 44". ■ Onines ipsae observatioues ope micrometri iiabitae fuerunt. Diameter post varias et repetitas observatioues per transitum per meridianum et mierome- trum lion excessit 31' 48". Hora 7'' 31' 52" linea ducta per cornua eclipsis distabat a limbo © iilustrato 25' 30" et baec liiiea ad sensuui horizonti erat equidistans. The clock- corrections are deduced as follows : — Clock-times of sun's transit over quadrant o' Clock-times of sun's true meridian . . . o' Mean time 23'' Clock-correction 708, Sept. 12. 1 708, Sept. 14. 0'" I 2 ".2 23" 59"' 24».8 0'" 6". 6 23" 59"' i8».6 55"" 59^9 23" 55"> lS^4 -4'" 6'.7 — 4"' 0".2 '44 RESEARCHES ON THE MOTION OF THE MOON. Tlu' coiTortinii on moan tinio is tlioroforo — 4'" i* (luring tlio crlipso; and as La MiKi: liiis alrojuly a|)|)lio(l -|- 35'i tlio total coiToction to liis timos Is — 4"'- ^6". Tlie (Mjuation (»f tlin(3 in —4'" 38", whicli agroos exactly with L\ lIiKu'a direction to udd 2' ni<»ii3 for rodnt'tion to apimront time. Till- ohHcrvntioiiM of tlio uclipHe of 17 10, 28tli Fob., are given only In digits and frnctious, and tliese only afti-r tliH middle, 17U. Transits of O's Centre. July 9 12 40J July 16 12 S2i (a 47 «7 S3i »♦ S°4 '9 S2i July IS, Vesper, Eclipsis. Iluroli (?•» Portio Ilium. KoaiJun Diiira. ^h jgtU 0" 30' 0" 7" 37"' 9" 19' 8" 21 »7 »S 38 23 18 30 24 45 25 30 39 37 17 52 28 30 23 36 40 51 17 14 3» 12 18 42 S >6 34 32 «4 21 40 43 18 '5 57 33 29 21 2 44 32 15 '8 ■ 34 42 20 24 45 46 14 40 35 SS 19 46 47 14 2 Tliese cannot be actual observations; the times and measures progress too uniformly.* "Journal des observations de M. De La Hire an mois do Decembre 1714. "L'erreur de sou Quad, etant sur la flu de l'ann»5e de 1 5" soustraire I'on aura les midis vrais comrae il suit." 17 14. Dec. 10 II 58 13 I Tbe obs. transits were 11 58 28 18 II 58 li I "3 58 i6>^ 1715. MaiJ 3. mane. Les observations de I'eclipse, tolles qu'olles font icy out este faites avec une horloge qui tardoit a I'egard de celle du cabinet de 21". Eclipsis © cum novo niicrometro. Digit. 8" 12" 16 '7 25 22 5" 27 54 32 25 36 20 41 36 44 3 46 45 49 16 52 6 54 56 57 30 Initium. 0' 0' I 2 3 4 4 3° 5 30 6 6 30 7 7 3° 8 8 30 Residuiiin. 9'' 26" ■ 0' 29 35 38 31 42 42 24 44 46 48 10 5° 50 54 56 51 59 22 2 10 8 32 Digit 10' 30" 10 9 8 30 8 7 30 7 6 30 6 5 30 5 4 30 3 30 " I am inclined lo think that the practice of "cooking " ohscrvalions was nuich more extensively practiced during the last century 'iian is generally supposed. jKAURAr must have been a great sinner in this respect. In the Memoirs of the French Academy for 1 779, he has a series of ol)servations of the Pleiades, which are sometimes considered authoritative, but which a very little examination shows to lie falirications of the clumsiest sort, so clumsy in fact that the author might be acquitted of intentional wrong-doing on that very ground. This is followed by a si'ries of meridian observations of Jupiter, including //lirfiYii cmisfcidiTf transits, which give a uniform motion to the geocentric position. Among the observers discussed in the present section I find none but I.A Hire guilty of the objectionable practice, and he only in two or three instances, of which the worst occurs in connection with the solar eclipse of 1 715' RESEARCHES ON THE MOTION OF THE MOON. H5 • I)i)i it. Kc'hIiImiiiii. .9'' 0'" 4" 9' 0" 10'' li" 14" 3' 0" 3 38 9 3° '4 3-' 2 30 6 3» 10 >7 9 2 9 40 10 "5° 22 28 I 'S 20 II 3 »s 33 30 22 1 1 10 iimx. 28 47 tin. Alia ubNiTvittU) [w liniigii ii8 u lllio. In Tjtbuluin (li\ i.siiii 1 HXHJ >ta poHt TulfscDitiuin Iiiitiiini. 8 12 16 9 2S 26 lOJ '7 I 29 7 10 20 tj • 32 »5 94 22 3 35 16 9 '5 »i 3« 40 «4 27 3 4> 47 8 . 3° 3i 44 30 74 33 4 47 48 7 36 44 5° 52 6i 38 S 53 4° 6 41* Si Sf' 43 s4 44 I "* 10 3 5 49 3 7 2 5° 44 52 23 74 6 4 SS 30 8 8 52 34 9 7 6 10 12 I 3 9 54 .04 17 28 t 14 27 II 32 30 I 18 S3 II 28 45 Iini8. Diiuneter © ope niicronietri 31' 45". t Toniporc observationis b()i'iil;;iiiniiiK ^vitli liiitiiiin 8 12 16, and ciidinu: with liiil.s 10 28 47, bnt, without any explanation wbatevcr cxci'pt "Oliservalioiici liinitatac ex niei.s .sod cum 5" pro defectn lioroloffii". Tlio times of tliodi|{it.s are, lio\vever,evidently smoothed ott, on the curve prin- ciple, for they could never have been observed so nicely. I therefore regard them as wortlile.s.s. The fourth and flfth tables are as follows : — Inilinm. 8 12 27 52 45 74 48 2. 7 '7 39 I 55 41 8 SI 21 rM 20 IS '4 9 « 10 54 II 6 22 SI 2 1 1 '5 lOj 56 56 54 25 27 24 14 38 1 1 59 46 5 28 7 3 19 4 1 1 10 2 48 44 3° 45 34 25 37 loi 6 4 33 24 4 29 I 10 9 10 34 36 S 44 32 23 94 13 10 3 38 46 5 35 43 9 17 42 2 41 29 54 3S 59 84 22 46 1 .44 13 6 42 1 1 8 28 s6 th\\». 49 5' 7 45 '7 74 ■ , II faut retraiKiber A, toutea ees observations 6". [Aftir writing this, 1 tind that this may not be the original journal of La Hire, and Hint the doubtful tables are not found in the original journal. The latter 1 did not discover till latci.] * 41 or 4a ; not legible. t This being 6" less than the real semidiaineter, the question arises whether the error is in the sc^ilo of tliu micrometer. 10 75 Af. 2 146 RESEARCHES ON THE MOTION OF THE MOON. Fifth tabic. 8 12 27 • nit'un . J? 43 I 20 23 'A 22 S3 2 2S 19 2I 28 7 ^ 3' 3i 33 38 4 36 28 4i 38 46 S 4t 25 S4 44 23 6 • 49 14 7 No ex[ilimatioii whatever Mh,v I 12 c 43 2 1 J 23i 3 12 5? 4 II 59 48 9 II 58 26. 52 34 ii 55 41 8 7 17 10 >o 5 loi «4 38 II 19 4 II 25 37 loj 29 18 10 32 26 9i 35 27 9 38 SI 8i 41 58 8 44 41 7J ■47 59 7 5» 3 6.i S3 5' 6 56 S4 s4 14 s 3 « 4* 6 II 4 9 3 3i J2 12 3 17 39 2 22 41 I 28 56 finis. iSmw'8 'Irandts, etc. May 9. 7 17 6 20 9 Sup. limb. Alt. © pro borolog. mane. 26 O I 40 33 II 58 36 26 30 I 4 37 29 i 11 58 35J Miiy 3 Tr. cent. pro. Merid. veri temporis 12 o 14. Correctiou 27" nuferenda a tempore seratino. Addenda igitur 10" tempori tranbitus centri O prociuadiHutem muralem in altiludinem centro q 58 26. The difficulty respecting the duplicate records is cleared up by a compari- son with La Hire's observations as printed in the ^' 3Icmoires" of the Academy for 1 715. The first two tables are the records of the original observations themselves, which have been entirely suppressed in pubiication. The fourth table gives the "cooked" results of the second set of observatio-is "par I'image du soleil", as printed in the Memoirs, and there is little doubt that the third set, « Inch I did not cojjy, is the same as the first published set "avec le micrometre". The origin of the fifth table does not seem worth investigating. The results for clock-error are as follows : — Date. Cluck-time of 0's Transit. A III s Mflan Time. Clock-cor- rection. 1715. A III s 1 III t 1 May I 48.9 23 5f) 51-9 - 3 bl-o 2 2g.8 56 4t-0 - 3 45.8 . 3 12.5 56 36-7 - 3 35-8 4 23 59 55.1 56 30.0 - 3 25." The error of the clock witli which the transits of the sun were observed may be supposed — 3" 37' during the eclipse. This clock, however, was not that with which the eclipse was observed: respecting the latter, we have only the statement that itwps 21 seconds slower. The correction of the clock actually used was therefore — 3"' i6*. RESEARCHES ON THE MOTION OF THE MOON. 147 1715, 25 July. Mane. Oticiilt. y a S ImincrHio liinlti ])riuri.s U in paiteni luiiiie liicidain . . liiiihi p().stui'ioi'i.s U Liinl)u» prioris U et tniii.sit iiiinierHioni.s linsterioris July 22. © centre transit n S9 584 23- 59 40.^ (( IhnU. poat 6 20 16 Veri tempore, (Jna. mur. . 6 20 34 per merit]. . 6 ' 3' 35 1 32 51 2 17 21 2 18 37 24. U tr. centri 7 true time per meridian 20 38 8 loj 29 39 [i. e., he adds 18" for clockcor- rt'ction and 4" for error of quadrant.] [So be considers the correc- tion 10".] © tr. centri . . . . . . n 59 25J per meridian >' 59 3li [Correction 12", it seems.] July 25. centre tr •' 59 7J • per meridian 11 59 rg I find no further data for the correction of the quadrant. From the transits of the sun v.'e have : — Date. G's Dec. Corr. Clock-time of Transit over True Meridian. Mean Time of Transit. Clock-cor- rection. m s H- 5 36-0 + 5 56-3 + 6 14- 2 + 6 33-9 Hourly Rate. July 22 23 24 25 + 20.3 20. 1 ly.g 10.7 + 13-4 131 12.8 12.5 /t in s 1 1 . () II 59 53.8 II 59 38.0 II 59 19-7 /i in s 5 17-9 5 50.1 5 52.2 5 53-6 s 0.84 0.75 0.S2 (3) (4) -f6"' 2 5».S +6 25".8 " 23" 46^.8 2'' 25'" 2^8 " 14'" 2 5".S 2" 15"' 41".; Interpolating between the transits of the sun on July 24 and 25, we find, for the times of the four contacts : — (9) -r6"' 2 5-.3 i" 39"" 1 6^3 i" 29'" 55"-3 1718, Sept. 9. 8 43 34 I'linmerNion d'une petite etoile par le corps de la lune. Sept. 5 tr. II 58 57.J 12 I 7 • 12 o 2J 8 57 32I 59 40A 58 36J >o 5(> 3Si 58 43* 57 39i The dock-corrections from the transits of the sun are : — (I) Clock-corrections +6'" 2 5".3 Paris mean times i'' 38'" o".3 Greenwich mean times i*" 28'" 39".3 Dale. ©■s Dec. Coir. 1718. s Sept. 5 + 6.8 - 3-3 8 5-7 4.2 j 10 4.9 4-" Clock-lline 01 Transii over True Meridian. A m .<■ 12 5.) 58..) 58 32.3 57 34 f- Mean Time of Transii. C'lock-cor- rection. m s - I 28.7 - . ..5 - 44,4 ilonrly Rate. // m s 23 58 30.2 57 30.8 5O 50.2 s 0.38 0.36 148 RESEARCHES ON THE MOTION OF THE MOON. - 49'-9 8" 42™ 44».i 8" 33''' 23'. I. We honce obtain : — Clock-correction foi* the time of immei'sion . . . Paris mean time, September 9 Greenwich mean time The star is li. A. C. 8184. Series III. Observations by Delisle at or near the Luxemburg. Volume 113, MS. No. 1012. Observations Astrononiiquea, fnit«s au Luxembourg par De I'Isle. (About 750 toises north of the Observatory.) 1 7 13, Noveiiibre 30. 011 gnomon Dec. I. " " " OecnItatioM ol' r Tauri (stli mag.), 2 Dec, matin Dec. 4- 3. on gnomon n 59 Sl'i o o 24J o 9 19 clock; o ?8 39^ t. vr. o I 22J o I 54 1713, June 21. Error of gnomon per e<(nal tiltitudes less than i". 17 14, .Tan. 26. ]\Iorning alt. 8'' 49"' o" = evening alt. 3'' 12'" 47'. ]\[ean of this autl 8 others gives transit of = (The correction tor change of dec. being —13'.) on gnomon o o 41.2 From the ol)servations on January 26, 17 14, the correction of the gnomon is abont +o".4. This correction may be considered as applicable to the transits of December 1 and 3 previons. AVe thns have: — 1713, Dec. I. Clock-times of 0's transit .... o'' o™ 24".9 Mean times . —10™ 2 7».o Clock-corrections — 10'" 5i".9 Clock-time of occnltation of r Tauri, Dec. i . . . . Clock-correction Paris mean tmie Ii'' 58"' 24^.3 Greenwich mean time 11'' 49'" 3''.3. 1714, Mar 20. Imm. of * U of 6th mag ... 9 6 50 clock. 9 8 21 t. vr. The star passcil only 4' within tht moon's southern limb. 1714, Marai. Iinin. of » Tauri, 6th mag. . . lo 15 54^ clock. 10 18 9^ t. v, Cette immersion a Hi'. ol)servee ,i I'observaloire a lo i8 9 t. vray. Mar 17. on meridian per equal altiintles (6 ill number) . . o 045^* " " " gnomon , 18. " " " 11 (. 11 1713, Dec. 3. Qh jm 23". 2 - 9" 39"-9 — n'" 3M. 1 2'' 9'" 19'. — lO™ 54"- 7 20. " " " mei'idian per 10 equal altituden 21. '' Limb on gnomon Transit of semidiameter from other davs o o 44i < 004^ 'I 58 45 >i 58 45-4 II 59 8 ' 5 " Le pendule a retardi de 23" dn le 20 au 21 snr le moien monve. ?i 58 3 du Soleil." 22. 011 gnomon "57 21J RESEARCHES ON THE MOTION OF THE MOON. 149 Applying +o'.7 for correction of gnomon, we have the following clock-correc- tions from transits of the snn : — Date. Clock-time of Transit of over True Meridian. "Mean Time of Transit. Clocli-cor- ! reclion. 1714- Mar. 17 h m s 45.2 h m s 3 41.2 m s + 7 56.0 ^ 18 5.2 8 23.4 + 8 18.2 20 II 58 45 -^ 7 46 . 8 + 9 1-4 21 II 5S 3-7 7 28.4 + q 24-7 22 II 57 22.2 7 9.8 + 9 47-<> j The clock-rate seems very good for this epoch. Interpolating the clock-correc- tions to the times of the occultations, we have : — 1714, Mar. 20, )|c B. 1714, Mar. 21, oTanri. Clock-times of occultation . . 9'' 6"' 50". 10'' 15™ 54».5 Clock-corrections -fg™ io'-2 +9"' 34-''4 Paris mean times 9'' 16"' o».2 10'' 25'" 28».9 Greenwich mean times .... 9'' 6"" 39^.2 10'' 16'" f.C). I have not certainly identified * B, but it is near B. A. C. 1373. 1714, April 7, Miitin. Imin. of I Sagittiirii (l)ii},'lit liinli). . • . 32048 dock. 3 24 22.J t. vr. (SiuUlenly to the JsL'coud), Einer.sion (ihiik liiiih). 1 u i.^ clock. 4 37 3''^ f- vr II y avoit (leja qnelques sei'oiuls (jik I'i'tolle avoit toiicli(/ le boul eclaire tie la luiio & elle paniLssoit se ineler avec I'oiidiilatioii (iiii w -nit tout autoiir dii bonl eciaiie. (Page 75.) He adds that at tbe Oliservato, 'lit' .ili.seivcd t iiiics were, Iiiimeision :; 19; Eiiier- sioii 4 37 25. He is surpiitied at the ditl'ereiiees ol 3' j and 1 -,% and enters into a Imm an onnt of his grounds for believing that the error is not on his snh- lie only weak point beinj; the want of a clock error between the 5th and 8th. He eonsiilers it possible, however, tluf In- may have forgotten to subtract the io» which he counted between tlie moment of eiiiersion and tn it of noting the clock- time; if 80, his time should be 4 37 28. Apr. 5. on gnomon, 11 57 32! 8. " " " II 55 30 9. " " " II 54 5° 10. " " " II 54 6 Applying -fo". 5 for gnomon, we have: — 1714, April 5. 17' ' iiril 8. Clock-times of O'rt transit . . 1 1" 57'" SS'o • '' ..V" 3o''-5 Mean times o" 2'" 48".; o" i"' 55».6 Clock-corrections +5'"' 5"- 7 4-6'" ? 5" i. Occultation of ^ Sagittarii, April 6 : — ' IniniLTHion. Emersion. Clock-times of observation . 15" 20'" 4.S' 16" 34"' I'.s Clock-corrections + 5'" 53"-6 + 5'" 54"-8 Paris mean times 15" 26'" 4r.6 16" 39™ 5 6". 3 Greenwich mean times . . . 15'' 17" 2o".6 ± 2» iG"- 30 35".3 ± 2'. I50 RESEARCHES ON THE MOTION OF THE MOON. These times agree so well with those noted at the Observatory (see jiost) that his opinion t>f o difFerence of ten seconds seems to be erroneous. La peudule a 6t6 avancde ile 2 minutes. La pend. a 6t6 avanc ' -> 2 > » J The clock-coiTections are derived as follows: — 1717, Sept. 25. 1717, Sept. 26. Clock-times of O's transit o'' o'" 37".2 o'' o'" 38".3 Mean times 23'' si"" 34^.6 23'' 51™ i4'.6' — 9"' 2".6 —9™ 23'.;. Occultation of a Tauri : — ImninrHion. Enicrsioii. Clock-times 9'' 12"' 15' 10'' 4'" 3 4". 5 Clock-coiTCctions —9"' lo".; —9'" ii".5 Paris mean times, Sej)tember 25 . . . 9'' 3"' 4^.3 9'' 55"" 23'.o Greenwich mean times 8'' 53™ 44^.0 9'' 46'" 2'./. But the immersion may be observed a little early. 1718, Jan. 16. i"" 27' 14". Immersion of ^ Geminorum (i5''.6, I think). Jan. 16. Tr. of sun per. (iorresp. altitudes (iincorr.) 0413.8 Mean interval, e"" i2"'corr. . u. Gnomon o'' 4' i".o = o 4 2.8 Jau. II. * = o 7 1 et 8' a 6te retrrtneh(5. Jan. 12. II 59 57 . 16. o 4 i.o la pendule a et6 retarde de 4'. 18, O 2 29.5 152 RESEARCHES ON THE MOTION OF THE MOON. Addiii}'' I' for gnomon, taking the time of transit for Jannary i6 from the corre- sponding altitndes (true correction — 1 1".6), and reducing the artificial changes in the clock to its state on Jannary 15, we have : — Date. ©'s Transit per Clock. Mean Time of Transit. Clock-cor- rection. m s Hourly Rate. 1718. h fPi s // in s. Jan. II 12 II 59 2.0 II 59 58.0 8 33.3 8 56.6 + 9 31-3 f 58.6 - i.3f' - 1.64 x6 18 4 2.2 6, 30.5 10 23.7 11 3-J 6 21.5 + 4 32.6 — 2.27 Interpolating the clock-correction to the time of observation, we have: — Clock-time of immersion of A Geminorum, 1718, Jan. 15 . . . 13'' 27" 14" Clock-correction +6" 41" Paris mean time 13" 33"' 55" Greenwich mean time 13'' 24" 34'. 7 ± 2". Page 127. — 1718, Feb. 9. Siiir. Inim. Aldebaraii • 6 19 44 = 6 16 48 t. vr., or 6 16 53? wliitili he thinks is more e.^at't, hecaiLse defived from trausits of stars as well as ©. Afterward he finds that 6 16 48 is after all tlie most probable time from tlie mean of all methods. The probable error does not seem to be .so iiuich as 2' Feb. 6. © on giioinoii 0841 Pend. ret. 9 inin. Clock has gained 5' since Feb. i, about 1' per day. Feb. 10. © on gnomon o 3 39 The correction to gnomon is -|- o'.y. Accepting Dkllslk's reduction, the equation of time being -f- 14"' 47*.4, we have: — Paris mean time of occnltation of Aldebaran, 1718, Feb. 9 . . 6'' 31"' 35".4 Greenwich mean time 6'' 22'" 15".! ± 2". Page 133. — "Looiiis, Feb. 14, soir, I'etoile a paru toucher dans son inniiersion la partieeclair<5e. J'ai ces.sd de i'apercevoir a 6 52 39 de la pendnle. Feb. 14. © on gnomon, o 7 43. 15. 08 43. It seems doubtful whether the immersion of n Leonis is worth using. The real occnltation was probably not seen. There is room for suspecting a change in the cor- rection to the gnomon. 1718. Sept. 9. 8'' 44' 49" Une etoile se cache sous le bord de la lune. 46 , Nov. 8. — 12 corr. alts. ©. Mean int. ... 6'' 23'" Uncorr. tuean . . 03 58.3 Corr +16 Aug. 19. Mean int. 11 28 Mean of 9 corr. alts, o i 32.1 Correction ... 20 8 45 35 Cent. Aug. 19. © tr. 0" 0' 45" 2' 56" ,' 5o"A Sept. 5. It 58 .7.1 26.J 59 2 2 J- 58 i.i 21 59 «63 8. 58 9 17 59 «3 10. 58 II 19 59 >5 Nov. 8. 3 8t 5 25 4 '6J •This same occnltation I)bi.isi.e says was observed at Toulon, "clans le Semenaire Royal de la Marine," by Le P. Laval. tnim. 64027, Lm. 74740, iJur. i 7 13; the clock being coriected by different corresiMnding heights of the sun on the 9lh and lolh. t Somewhat doubtful, from being obliged to use a watch in counting the seconds. RESEARCHES ON THE MOTION OF THE MOON. 153 T\\Q results for clock-error are flerived thus: — Date. Clock-time of ©'s Transit. Meai Time. Clock-cor- rection. Mou'ly Rate. 1718. A in s m s m s Sept. 5 II 59 32.5 58 30.3 - 52.2 + 0.72 : 7 17-3 57 50.7 1 26.6 + 0.67 ! 8; '3.5 57 30.8 I 42.7 + o.Sq ! 10 15-5 .. 50.2 - 2 25.3 1 We have: — Aug. 19. Correction of etju.'il altitudes +21'. 1 True transit o" i" 53". 2 Gnomon i'" So'-S Con-ection + 2".7, Nov. 8. Correction of equal altitudes +1 5'.8 I'nie transit 4'" i4".i Gnomon 4'" i6"-5 Correction . — 2^.4. I have used 4-o'.5. . We then have, for the time of occultation : — Clock-time, 1 718, September 9 8'' 44'" 49". Clock-correction —2'" 11 ".8 Paris mean time 8 42'" 37'.2 Greenwich mean time 8' 33" i6'.9J::2". I'agH 245. — 1719. Apr. 22, .soil'. Imui. A.kleb. dark limb, 7 44 44 clotiiv = 7 44 32 t. vr. Em. " brigbt " 8 34 24 =8 34 14 Daub cette observation I'etoile ii'etoit point encore detaclice dti boid eclaire de la hino. Apr. 22. True noon per 13 pairs equal altitudes o 031.7 © on gnomon o o 3^-5 23. " " " II S9 3'-S The results of the observations are : — Clock-times of sun's transit o'' Apr. Mean times 25" 58" Clock-corrections — 2' 3i'-7 ?5'.8 5"-9 Ajir. 23 II" 59 23" 58 — I 1" -if->' 13' '7' 4 ■3- Occultation of Aldebaran. Clock-time^' of phase, i 719, April 22 Clock-coiTections • . Paris mean times Greenwich mean tinier .... 20 75 Ap. 2 Iiiiiuei'siou. 7 44 44 — 1'" 50". 2 53'-8 33"-5 7" 42" 7" 33" Kiiiersioii. 8'' 34'" 24". — 1'" 4S».6 8'' 32™ J5'.4 8'' 23'" 1 5". I. 154 RESEARCHES ON THE MOTION OF THE MOON. I'li^o 249- — 1719, Auj?. 21. Iiiiin. y Libriis very exact, 7 41 31 nl. = 7 40 12 t. vr. . E(iiuil tiltittult's ot ©'« lower liiMl)(?). All''. 21. AH. 11O4.' '3 4?, •4 '5 20 J 5 =° 45 21 . A. M. 6 31 42A 44 °A 47 3 7 24 47 26 47 28.4 r. -M. 6 5 28J 5 53 '3 5° 3 12 32 10 32 837 Aiif;. 22. A. M. 16 43 28 58J 32 o Mean Aug. 22.0 Coir. . . Subtr. o 18 40 + 19 o !8 59 19 o 7 " 47i Aug. 22.0 . . . . 1 1 59 59 '352 Aug. 22.5. Mean of last 2, o 140 Correct 23 023 (.!l<>('k put b:!ck 19 tniiiutfs l)et\veeii Aug. 21, p. 111., aud Aug. 22, a. in. Owiiin 111 riouds ami fog, Dklisle rejects tlie tliiec top linca altogether. 1)em.slk's f nrrection for midnight seeiiLs all wrong. The corrections for noon and niidiiight are 4-'>*^'-6 and — 2 7".4 respectively, whence we obtain: — 1719, Aug. 21.0. 1719, Aug. 21.5. tiock-tiincH of siin'.^ transit, corrected lor change of 19'" 23'' 59'" 58".4 12'' i'" I2'.2 IVfean times o'' 2'" 51 ".2 12'' 2'"44'. i Clock-corrections +2"'52".8 4-i"'3i'.9 Clock-time of immersion of y Librif, 1719, Angnst 21 . 7'' 41'" 31". Clock-correction -|- 2'" i". i I'aris mean time 7'' 43'" 32".! Greenwich mean time z"" 34™ ii'-8. The dates Ang. 22.0 and Ang. 22.5 in my manu.script, and as printed above with- out change, are, without serious doubt, one day in error. 'I'iie computation is, how- ever, that f>f Dei-isle, ami it is evident that he has deduced his " Temps vray" from the erroneous deduction of the clock-time of midnigiit. I'.ige 259. — 1719, Oct. 3o(?) Iiiiinersiou of Altlebaran (inst.) 8 56 34 clock =9 2 54 t. vr. Emersion, dark limb. ... 9 S3 3j = 9 39 29^ Duration 56 29J Oct. 29. Efpial alt. ©. Oct. 30. 12 altitudes very accordant. 8 27 27 3 13 45 7" 47' 12" 70 25' 4'' i' i4"i 30 o II 9 ... . . ... 32 38 8 32 ... .- .. ... 35 214 S 49 ... . . ... 7,^ ik 3 5 8 13 56 us ' 3 34 29 40 46 o 24 Mean noon Oct. 29 n 5° 35 Mean of 12 i8i Correction Corrected u 5° 534 Clock advanced 60 II 54 12.9 + '9-5 II 54 32-S " 56 S3 J RESEARCHES ON THK MOTION OF THE MOON. 155 The coiToctioiis for motion of huh in ileclination I iimltD Uo + ''*^'6 mid + ig'.o. The rocUiction of the ol)s(>rvation.s thcrcfon' stiMids: — 1719, Ocl. 29. 1719, Oit. 30. Clock-timc'h i»f tninisit of O .... i i"" 56'" 53^.6 11'' 54'" 3i".9 Mean times i 1'' 43"" 58".o 11'' 43'" 54".8 (JU»ek-coiTeetions . — 12'" 55'.6 — 10'" 37".i. The elock-correittion nnist now he cari'ied forward eight hours with the rate derived from the observations of the two (hiyn. Occi(lt(itio)i of Alilcharnn. iDimoi'Hioii. EiUHrHiou. Clock-times of phase, 1719,00^30 . 8'' 56'" 34'. 9'' 53'" 3".5 Clock-correetions — 9"" 44^9 —9'" 39'.4 Paris mean times 8'' 46" 49". i g*" 43"' 24".! Greenwich mean times 3" 37'" 28".8 ±3" 9" 34™ i'-S ±3"- These times are 1" greater than those obtained 1»y eorrecting I)eli8i.i:'.s result for the equation of time, —16'" 6". The ditferenee arises from tiie change of o".5 in the correction for noon on October 30. Total I'ciipsf <>l ©, 1724, May 22.8 (?). 21! part of i)a},'i" 95. At the Royal Observatory, wliitlu-r lie had transpoitcil his iiistruiiifiits. J'ay (!OIiiiiioih:o a I'api'rct'voir a 5'' 53' 24" de ma peiidulc, inais le vray coiniiu'iicfiiiciit a pen arrivcr uii pini plustot, parceqai' jc iie ivKaiiiois pus dans ue teiiis hi pivcisemeiit i\ I'mdroit 011 la lime est entree, et que Je ne ni'eii siiis apeien (|iie lor.sriii'elle ocenpoit line petite portion ' 5^4 I have not yet reduced and discussed these observations. 1725, Feb. 19.5. liniu. of TiUiri, exii;t ilirk linr>. o"' 14' 24" = o'' 11' 18" t. vr. Correitious of Gnomon. TrRnsits of over Gnomon. s Jan. 8 o.o Feb. 17 o 2 44 Sept. 13 + ::.7 19 o 2 52.7 20 —0-7 2° ° 3 '9-' Assuming the gnomon to be correct, the reduction stands: — Keb. 19. Fell. -20. Clock-times of transit o" 2"' 5 2". 7 o" 3'" 19".! Mean times o" 14"' 18". 7 o'' 14'" i2".o Clock-corrections + 1 1-" 26".o +10™ 52-.9. '56 RESEARCHES ON THE MOTION OK THE MOON. ImtiHTsion of A' Tauri, clock-tinif, 1725, Feb. 19 ( 'lock-coiTectioii I'iiris inoiiii tiino Greciiwicli moan tiiuo 12'' 14"" 24". + 11'" 9".2 12'' 25'" 33". 2 12'' 16'" I2".Q. Serikm IV. Tliis is porliaps to some extent a ('(tntinuation of Series I., by tlie Cashinih and .M.\K.\M>is. 1 liave not attempted to identify the individnal obHcrvers. The Hystom of oltscrvation was the same as before, the transits of the sun beinjr rejjfnhirly observed witli the niiirai (pnub-ant, and the true times of transit oec'asionally determined by corresi)ondin^ altitnth^s, and the eorrection of tlie qnacb'ant thence determined I have re-reduced all these observati 8.g 56 44.0 - 35.1 -16 25 1 July >) 23 58 31.9 4 33 - 18.2 + 4.3 58 3f).2 59 7-2 - 31.0 -f22 21 1 Sept. 12 23 58 26.0 4 47 - 57-4 + 16. y 58 42.9 59 18.0 - 35.9 + 4 4 1 17CH), Dec. 24 23 ?7 20.2 4 II + 2.y - 1 .2 57 19.0 57 53- - 34.0 -23 26 j 1710, Fel). ij 23 51 59- S 5 6 + .J8.i - 17.8 51 42.0 52 17.0 - 35.0 -14 43 i July 22 23 56 56.7 5 3 - 29.7 + 7.0 57 3-7 57 35-0 - 31-3 4- 20 20 Sept. 13 23 53 51.3 4 41 - 57-5 4- 16. q 54 8.2 54 47-5 - 39-3 + 3 5*1 Dec. 4 23 52 17- 4 10 - 20.3 + 8.1 52 25.1 53 I.O - 35-9 — 22 '4 ' 1711, Sept. 15 23 5" 39-5 4 If) - 57.8 + 17.0 50 56.5 51 33-2 - 36-7 + 3 1 '3 ! 1714, Mar, 16 23 57 57-2 4 44 + 59-2 - 18.7 57 38.5 — I 48 Mar. 20 23 57 q.o 6 1 + 59-3 - ig.2 56 49.8 57 28.5 - 38.7 — 13 1715, May 26 I 32.1 4 42 + 26.4 - 8.0 I 24.1 2 I. - 36.9 + 21 3 July 26 13.3 4 34 - 32.7 +- 7-5 20.8 I 0.0 - 39-2 + 19 33 Sept. 16 23 56 44.5 ■» 27 - 57-9 + ■7.3 57 1.8 57 43- - 41.2 + 2 50 Nov. 3 23 59 57.9 4 5 - 47.2 + «7-4 15-3 50.5 - 35.2 -14 56 RE.SEARCIIES'ON 'TUF. MOTION OF IIIF, MOON. 157 Itivesli^alwii of Conn'wns h> tlie l\ins Qiiailiniil, 1706-1758 — Continued. Date, < inrK-umi; 01 Mean of Com'spninlin.i; Alliliules. km i , Muan Ir)i(.rvat. h m iliiiiily Motion of Sun's Off . H Coir. Inl Motion. i <'lo,l< Tran M.-i III -tunc .il over ()ian. .r 1717, Sept 20 23 55" 48.7 1 4 20 - 58.4 + 17. f. 5f> Ifi. 4 42 -i- 3".o - f).8 9-2 May 28 23 '>'\ 4. 4 33 ■+ 23. s - 5..' 58 58.7 1727, Mar. 3 1 23 5') ->2.2 U + 5'). 3 - I.J. 2 59 3.0 1728, Feb. 13 23 53 IC). 4 12 4- 50.2 - 1S.2 53 0.8 Auk 30 23 4*< 11,. 5: 2 7 — 54.0 + 13.8 4S 33.3 «755.J»ly 18 S 7.7 5 54 + f>.5 ■S 14.2 1756, Dec. 13 1) 2; .2 5 33 - 9.2 + 3.7 9 249 Dor. 17 - 4.6 175a, Jan. 24 i) 22 6.2 5 2 + 36.4 - 14.2 21 52.0 ■:io(k -linu. of t fransii over 1 ^)iiailrani. ' i m s 56 45.0 I 12.5 10.5 45.0 59 35-5 59 44.2 53 45.0 49 17.2 8 10. 1 9 31.2 22 2.0 Corr, of Snn's De- Oiiadrant. 1 linalion. - 38.7 4- I 5 - 33.3 -23 2() - 43-6 34 - 35.8 (-20 ■7 - 36.3 + 21 33 - 41.2 ■r " 8 - 44-2 -13 31 - 43.9 -t- 8 52 + 4-1 - f'.3 -23 13 . -23 24 -19 It will be seen tliiit tlii' serio.>i of ofcultiitions which wo use beffiiis nine nioiitha before the iirsf detenniiiiition of the error of the quadrant, and that, diirinf-- the interval, the olistn-ver.s used a forroction for deviation nnich .smaller than that found from and after 1706, May 14. 'There is no way of determinin<>' whether there really was il change, or of dec,idin}>' liow the value actually used was obtained. 1 am strongly inclined to suHi)ect that tlu; value actufdly used was the result of some old determina- tion, which was fountl to be erroneous when equal altitudes began to be regidarly observed, and that the new value shouhl be used from the begiiming of the series. What has been tlone is to makts the reductions on each hypothesis in order that the results might bo comi)ared. , The deviations of the quadrant resnlting from the observations vary with the time and the declination in a niiinner which does not seem reducible to any e.xact law. T have therefore, in determining dock-corrections from the several transits, tried to execute a sort of double interpolation of the quadrant-error from observations each side of the date in time find each side of the declination in altitude. The con-ections thus deduced are »\w\\ u in the following table of individual dock-corrections. Instead of discussing each clock-correction separately, as in the former series of observations, I have in this series, owing to the uniformity of the processes, collected all the individufd residts into ii single tiible. Generally at least one determination is made on each side of the time of observing the occultation, and the correction for the time of observation is obtained by a simple interpolation. The table is as follows, and scarcely seems to noeti explanation. It may be remarked that the cidumn "^letm Time" gives the mciiu tabular time of transit of the sun over the true meridian, and is simply the equation of time, subtnicted from 24'' o'" o" when negative. The clock of which the corrections are here given Mas the "pendule superieure"; most of the occultations were actually observed with another clock, designated as "pendule inferieure", whidi was conqjared with the other soon after the occultation. 158 RESEARCHES ON THE MOTION OF THE MOON. Computation of Clotk-corrections from Transits of the Sun obstn7 45 ' - '4 to «9 59 26 58 51 45 45 - 13 6 1707, Apr. 4 . 50 9-7 3 .2,4 + 13 2.7 S 23 50 1.5 - 36.5 49 25.0 2 54 + '3 29 Sept. 3 33 55 7 -36 54 31 59 15 + 4 44 5 53 44 • • 53 8 58 36 + 5 23 1708, Feb. 33 23 57 26.5 - 35.0 56 5'. 5 '3 57.2 -1- 17 5-7 84 ' • 56 8.9 13 48.4 + «7 39.5 Sept. 5 *3 56 26.5 - 37-0 55 49. 5 58 21.5 -*- 3 33 7 54 31-5 53 54.5 57 41.8 + 3 47 1709, Apr. 30 *3 54 27 - 36 53 51 58 46 + 4 55 31 53 50 53 14 58 32 + 5 18 Sept. 13 23 52 >7-5 - 35 51 42 55 44.1 + 4 3 14 5t 33.0 50 48 55 23-4 - 4 35 15 50 36.0 49 51 55 2.5 5 II 16 49 3>-5 48 56.5 54 41-7 5 45 ]) 16 10 25 5 24 30 30 33 + 6 3 30 33 59 33 58 57 53 18 - 5 39 33 56 50 56 "5 52 «7 — 3 58 1710, Dec. 4 . . . 52 25 50 38.5 — I 46.5 5 33 52 59 - -Kt 52 23 51 3-4 — I 19.6 i7ll,Sept.3g 33 55 2r - 37 54 44 50 26 - 4 18 J 30.6 14 54 23 53 46 50 14 3 32 Oct. 3 53 0.5 • • 52 33 49 29 — 2 54 RESKARCHES ON THE MOTION OF THE MOON. Campii'iUioH of Clock-con eclions, etc. — Continued. IS9 Diilf. 1 CInck-tiinc of Transit over ^Juadranl. Correc- tion. Trana True IH It over Mcriil. Meat Time. Apparent Clock-cor- rection, 1 h m J 1 s s m s m t I7ia, May 15 j 024 - 33 1 3' 55 52 - 5 39 17 1 2 37 { 2 4 55 54 — 6 10 1714, Mar. 31 23 57 1'' - 39 5f< 37 7 28 + 10 51 23 , 57 5 1 56 36 7 10 + 10 44 Apr. 6 38 - 39 ! 59 59 3 31 + 2 33 "1 II 59 32 ■ 56 + 2 24 i7i5,Ji'ly 21 ; 45 - 38 7 5 44 + 5 37 33 48 • ■ 10 5 48 + 5 38 Aug. 9 16 - 40 59 36 5 4 + 5 28 10 7 • 59 27 4 56 5 29 16 23 58 57 58 '7 3 sft + 5 39 Oct, 7 23 58 18.5 - 39-5 57 39 47 59 - 9 40 10 58 34.5 57 55 47 10 - 10 45 Dec. 33 I 27 - 34 53 59 30 - I 23 30 4 37 4 3 2 58 - I 5 1716, Jan. 7 7 59 - 34 7 25 6 4' - 44 1717, Sept. 35 23 58 45.5 - 39.0 58 6.5 5> 34.6 — 6 33 s6 58 21.2 57 43.3 51 14.6 - 6 28 1 1718, Sept. 8 I 24 — 4' 43 57 30.8 - 3 H 10 34 59 53 56 50.3 - 3 3 I7lg, Apr. 22 23 58 49.5 - 41.5 58 8 58 25.8 + 18 23 58 27.5 57 46 58 131 + 37 Oct. 29 50 -40: ID 43 58 — 16 13 30 33 • 59 53 43 55 - 15 58 Nov. 36 23 58 32 - 37: 57 55 47 37 — 10 18 * 27 5S 38 58 1 47 57 — 10 4 1720, Apr. 16 23 59 52 - 40 59 12 59 38 + 36 30 58 7 57 27 58 42 « 15 33 56 51 56 II 58 4 + J 53 1727, Sept. 6 23 48 44 - 42 48 2 58 15 + 10 13 8 47 "3 46 31 \ 57 35 + 11 4 1738, Jan. 2 4 52 + 2 4 54 4 40 - 14 3 5 46.5 • • 5 48.5 5 7.8 — 41 Dec. 23 16 18.5 16 20.5 59 39-3 — 16 41 24 16 54 16 54 i 9-3 - "6 45 1739, Feb. 13 . 4 57-3 14 43-6 + 9 46.3 16 4 58.7 + J. 5 5 0.2 14 34-9 + 9 34-7 i6o RESEARCHES ON THE MOTION OF THE MOON. More observations, from the anonymous registers, accidentally oniitteil l)efore: — Occultrttion of .lupiter, July 27, 170... i'' 22' 34" '.)n jnge qu'il tonclioit par lit lunette ie 8. I 22 40 il comnieiicja A toucher le bord de I'D par la lunette de 18 pieds, 1 24 3 je crois I'avoir perdu de vue. 2 6 26 U est sort il moitie. 2 712 U tout sort. Tiansits of ©, etc. I. H. >r. II 58 55A I' II" 58 52 18 58 48 12 58 4oi o 55 58 38 o 52 He applies a correction of — 12" for instrument, but I ciinnot find on what this co rection depends. I find no data for such a correction till December 30, a. m., when we find: — 8 2 27, haut du bord suj*. du .soleil par M. d. ('. i^ 7' o". 8 6 39, le bord inf. a la inesme hauteur. Thermometer 25. Bar. 277A. r.y rough exau)ination of the temperature at ditferent seasons, the thermometer .seems to be that of Fahrenheit. The observed trans.'ts of O stre: — Cent. Midy. Dee. 25 o 4 7.3 o 3 50.3 30 o 5 4.5 04 47. J11I.V 25 26 27 38 29 c. ,Mi 80 it seems he now applies — 17" for error of instrument. It' this observation is worth rediicinj^-, it is nitlior to be ii.seil for deternuiiiiif^ tlie position of Juj)iter than that of the moon, 'i'he observetl ahittidc of the sun give.s a ciock-oon-eetion of — i'" 41", wiiicli is entirely ineoinpatibU' wi.h tiiat derived fntni the tnnsits. The only eoiir.se seems U> be to aecept the times of apiiareiit noon j^iveu by the observers, and correct the ohjoks accordin<,dy. The apparent times, deduced by np])lyiii<,^ a elork-correction of + i 7", are jfiven in the >[iMiioirs of tln^ Academy for 1 704, page 233. 1705, Aug. 5. (Aug. 4.6, astron. time.) 3'' 16' 40" Inunersion de I'etoilo dans la lune par la 'nnette ile 17 [lied.s. Je n'ay AiUI I 52 pas pu voir avec la lunette de 1 1 pieds. 3 18 32 9 9 5 S pend. sup 8 pend. inf. Uh after the occnltution. 08 Aug. tr. 1 1 58 o"i 3 © tr. II 57 43 o' IS" " 59 S '3 " 58 55 "'"''.v. 59 56 58 49i '3 1 1 58 36^ midy. II 58 16 midy (convert). RESEARCHES ON THE MOTION OF THE MOON. i6i ic II 58 50 'I 57 li D! I 21 59 15 • • 58 54 . • . . . II 58 8 '3 II 56 41 'I 57 SS • • ■ II 57 47 16 II 57 31 No altitudoH; no telling liow quadrant was corrected. The interval of six hours between the observation and the comparison of clocks renders the time more uncertain than usual, the difference — 8' being assumed constant for this time. The transit of the moon might be utilized for the dock-correction, but has not been. The results for local mean time of occultation will be: — Using Oas.sini's correction of quadrant, Aug. 4, is"" 23'" 58" . ^ Using ~35' 15'' 24'" 20" > . 1705, Sept. 2. II 46 11; itorl. inf. Futoile r de la 5' grandeur dans la Janibe uriental du Verseiui entre dans la piirtie obscare de la lune. 051 o riiorl. sup. o 51 39 I'liorl. inf. o 47 37 IV'toile sort. Sept. I tr. 11 56 " 55 28 58 12 57 38 'I 57 6 20 tr. II 56 46 I" 56 33 21 niidy 2 o pendule sup. 2 38 pendule inf. II 56 12 luidy. Sept. } o 38 tr. II 54 18 56 29. The hour of the last olock-comparison cannot be determined. 1706, Jan. 23, p. ni. II o 14 I'^toile entre dans la partie obscure de la lune par la lunette du 17 et par cctte de 1 1 p. 22 36 I'etoile entre par la lunette do II p. 23 19 par cette ile 17. II 32 29 I'etoile petite qui est entree la derridre sort de la lune 17 p. 32 34 par la lunette do 12 p. II 38 3 pendule inf. 38 o pendule sup. Les observations pr^ci^dentes de la 3> ont e8t6 faites & la pendule inf. Jan. 274, 1706. 12 21 3 l'6toile i, entre dans la lune du cott^ de la partie obscure. 12 25 22 pond. inf. 12 21 o pend. supr. 21 75 Ap. 2 |62 :>.,■■ RESEARCHES ON THE MOTION OF THE MOON. I. II. 1706, Jan. 21 tr. n 5836 054 n 59 45 17 II 59 28 midy. 44 58 8i 28 26 <£ tr. 10 22 45 25 4 27 11 57 28 59 49 , d II 17 8 19 27 aS II 57 19 59 38 II 58 29 1. II 58 12 midy. On January 23, the first inunersion isof w'Tauri the next two ai)i)ear to be two observations ot" the iunnersion of >r Tanri. All the observations are, however, dis- conlaut in a way which yives rise to the susi)icion that an eiTor of 3" was made in the com parison of clocks. 1706, April 21. Occnltatioii of ij Leonis. » 59 «5 Immersion de I'eloile derriere la lime supr. peiid. 9 « 45 Iniiiiersion ile IVioile r, diiiis le col dii Lion avee line lunette de 3 pieds . . . pend. inf. 9 « 47 avec line lunette de 2 pieds. 920 pendule supr. 9 4 28 pendnle infr. 9 55 20 Kuiersion de I'otoiie 1; de la lune par la liinett' 12' 11" 50° 0' 040 pend. su]i. 50 16 9 36 50 20 4 37 pend. inf. 52 50 71 ■ 50 40 55-9 4 30 5' ° 58 8 1 46 51 20 9 47 45 14 12 II 4 24 26 2 12 13 >' 59 .58 . 8 II 59 50 midy tl la pendule inf. 37 II 59 13 midy & la pendule supr. '"- S9_4_* 29 d<-elinaison de I'instr. May 14 11 59 4» «5 II 59 27 uiidy. This calculation refers to the transit of May 14. RESEARCHES ON THE MOTION OF THE MOON. 163 1706, May 24. 10 51 29 Ij'6toile eiitre dans le bord tie la J). Lu luiie sp couvre I'etoile. 11 3 S3 pend. inf. 10 51 39 (sic) II 00 pend. 8upr. 3 53 10 47 46 3 48 10 51 34 TrausitH and calciiiutiouN t'ur clock. May 23 iio 55' 50" 58' 6" 56' 58" 24 55 32 57 49 56 40—20 56 20 rnidy. «4 Id 9 52 41 I/ctoile 9 55 39 3 40 »S ,d 10 34 43 Dl 10 36 49 9 55 39 26 O' II 57 10 20 Aug. I © II 56 2 20 n 55 42 II 54 52 9 55 «9 3 48 9 59 7 57' 6" II 59 3° pond. 8upr. II 44 5 pend. inl'r. 15 25 Altitudes Aug. i. 8 26 30 2 53 II 6 26 41 3 >3 204 «■ 39 504 10 II 40 04 «5 25 " 55 25 inidy X la supr I' 55 59 8 26 30 - 53 'I 40 50 28 38 5' 4 41 10 33 2 46 38 41 50 35 8 44 32 42 10 34 dC'clinaiMoii. 1706, Nov. r8 a. in., 174 ast. time, o II 59 pend. inf. L'etoile h« cache de derhere In 5 en ligne droitc avecCopernic et o 17 30 pendnle aup. o 18 25 pendule inf. o 55 Nov. 16 tr. II 58 43 II 59 52 3° "7 Id 9 52 25 54 35 le vent. II 59 22 '9 © II 58 17 II 59 26 34 II 58 52 inidy. 164 RESEARCHES ON THE MOTION OF THE MOON. Sept. 19 '» 58 35 43 " 59 39 II 59 4 from alt. 35 '!«*'•• Alt. Sept. 19, 1706. 9 27 24 2 JO 6 33 " 31 40 25 .53 33 30 35 57 21 36 34 l)fc. 5, lyo*'. 9 39 40 2 18 3 12 40 43 35 14 13 , '3 ° : ',' 47 23 10 19 13 20 »7°7) April 4. S"" 8' r" pL'udule siipr. La petite etoile /> d'Aries est cachde par le bord obscure de la lune. | mill 10 6 9 7 41 peiul. iuf. 8 54 peiul. sup. Apr. I 3 5' 5'4 54 I tr. II 50 28J 52 48 49 43 5' 52 48 57 S' 6 «3 4« Apr. 4 4 5 Alt. ©. 9 33 " 36 7 duh. 38 59 4' 57 2 7 41 4 49 I S3 « 58 56 38 10 38 30 38 5° 39 10 9 33 " 2 7 41 4 34 30 2 17 »S II 50 26 «6 II 50 10 1 11 50 47J 37 diff. declinatio. 1707, June 18 © II 55 8 ' 57 25 S6 i6i »9 54 53 54 37 June 19. 57 " 56 55 Altitude G. 56 2 5546 9 2 4 37 48 48 26 46 17 48 48 20 • 7 44 5 '' '''" 48 40 9 II 41 54 49 II 23 39 4« 49 20 '3 36 37 29 49 40 From all which he seems to deUuce a correction of — 30" 1 ""or his instruments. I 707, Sei)t. 3. f transit by quadrant . . 23'' ss" 7^' 23'' 53'"' 44" Con-ections ol quadrant — 36.J' — 37' Clock-tinies of true transit 23" 54'" 31" 23" 53™ 7" Mean times 23" 59" 15" 58"" 36" Clock-corrections -f 4"' 44" -f- 5"' 29* Subtracting 2'" 57" for reduction from one clock to the other, the times of the phases are: — Iiuuiurtiiun. EnierHioii. Clock-times of occultation of Antares, 1 707, Sept. 3, 7'' 42'" 3': S*- 30" 14" Clock-corrections + 4'" 5'' + 4"' 52" Paris mean times •. . 7" 46™ 54": 8" 35'" 6" Greenwich mean times . . . • . ► . . • • 7" 37"' 33*: 8" 25"' 45" The first time may be considered as affected with a probable error of at least 10". 1708, Feb. 23, p. m. Occultation of Venus. 7 o 31 ? commence a entrer i^ la pend. inf. Lunette de 34. o 46 Kile entro entiiirement dans la lune. 7 o 23 9 commence ii toucher la luue par la lunette de 34. 038 V6nu8 eutre enti^rement A la lunette do 34 et de 12 pieds. . »dd 3' 19" 7 16 o i)eud. supr. Feb. 21 © tr. 11 57 45 59 57 7 16 9 pend. inf. 22 57 4 59 '5 33 56 20 58 33 • 9 H ■ ■ 55 38 57 50 25 54 49 57 « Feb. 24. Alt. ©. g^ 42' 45" .- 10' 6" 24O so' 46 8 " 6 jg 25 ,0 49 42 3 «3 25 30 ^ S3 «6 S9 3S *5 50 56 ii > 55 »7 »6 »o 1 66 RESEARCHES ON THE MOTION OF THE MOON. 1708, Sept. 6. Emersion de x Taurcau de la partie obscure de la Itine. peiidiilo inf. 9 32 S> 1070 1070 pendule supr. Sept. 3 000 tr. '« 57 15 59 24 9 50 52 33 48 40 38 43 33 46 3' 49 29 52 35 55 38 Sept. 12. 26 o 23 13 2 16 s [I 58 19J 34 1' 57 45 4 II 56 19 58 29 11 57 24 34 II 5f 5° S II 55 22 57 31 II 56 26 34 " 55 52 7 a. in. 1 7 © tr. 1 cent. 5 14 23i " 53 27 15 42i 55 36 II 54 31} 9 © tr 12 •I 57 58i II 58 14J 16 23 34 July Sept. 'I 53 57i 1708, J Illy 9. Alt. 0. 9" 37' 4" 39 27 4« 5' 44 »7 46 41 19' 57" 17 36 15 '3 12 50 2 10 23 51° 50' 52 10 523° 52 50 53 10 II 58 3ii 7 II 58 38* ■I 59 6J midy. midy. midy. 28 decl. ad. occid. 35 40 ^6 o 36 50 37 10 37 30* 37 50 38 10 38 30 1709, April 20. 7'> 52' 49" Immersion dans la luue de I'ctoilu t de la Lion. Tend, infer. 10 18 30 pend. inf. 10 II o pend. supr. 7 30 10 51 31 pend. inf. 44 o [tend. supr. 7 31 Apr. 19, H. m. 4 30 10 p. inf. 4 24 o p. sup. 6 10 5 » RESEARCHES ON THE MOTION OF THE MOON. 167 Apr. 17 tr. 18 19 " SS 19 S7 29 56 S« 56 II «i SS 46 3a '. . : II SS 14 ao II .S3 22 SS 33 II 54 28 »t «' S2 45 54 SS / 32 •I S3 56 niidy ^3 " 5' 34 S3 45 II 52 39 32 '■;■■■•■ ■ II 52 7 30 33" II SI 37 • 1709, September 17 (or 16J probably). )\ I'iioil. inf. Imniernion d« I'etoile a de la 5' gruudeur dans la partie obscure de la lune. Kile otoit en ligne droit avec H^lion et Timarcbus. 23 51 riiorl. iuf. 13 I'horl. aup. 9 45 44 1709, Dec. 24. 12° 20' 49 47 245° 40 10 s« Sept. 15 © tr. 16 II 49 22 II 48 27 5' 30 50 36 S3 59 58 IS 43 56 27 »3 »3 20 »8 »4 If' k Ti» pendule superieur Dec. 24 51 '3 10 24 3 p s'est arest^e. " .=;9 4 S3 24 58 43 1 1 S3 " 52 27 26 2 57 S3 57 ^' (CI eel. r ord qui manque.) 1710, Feb 9 '4 13 29 47 •7 25 26 33 ■ 20 37 23 23 23 54 2 20 6 17 10, July 9 '6 19 37 34 r . 22. •7" 18 18 18 47 SO' 10 30 5° 30 1710, Feb. 9 1151 10 July 22 II 56 27 1 1 1 1 32 «1 52 >7 57 35 II 57 3 20 51 25 32 28 23 48 48 20 SO • 3» 30 '4 35 23 39 2 '8 SS 49 5° 30 10 8 24 52 28 53 28 54 8 38 34 36 o 2 34 8 47 44 9 «« 5' 9 '4 24 Sept. 20 «3 1709, Sept. 23. Ocfuitation of Pleiades. Maia entre dans la Inne, lunette de 17 p. \ Talgcta entre lunette de 34 pieds. ' 1 Taigetu entre lunette de 17 p. pendule inf. pendule supr. s pend. infer. L'6toile marquee x putre L'^toilo X sort Maia sort O tr. II 58 28 i« 55 46 luuette do 17 p. peud. iuf. o' 57 36" 54 56 50 34 II 56 16 midy l« 2ad. ,68 RESEARCHES ON THE MOTION OF THE MOON. 1710, Deo. 4. Occ. Pleiades. 45012 Electra entre dans la lune. 7 36 retard horl. sup. ab. hor. var.t 6 12 1 24 add. ■ ' 54822 L'<5toiIe proche d'Asterope cache par la grande lunette. 5 56 58 Asterope entre dans la lune par la grande lunette. 6 9 50 ■}(• sort. 2328 Maia sort par le g. lunette. . • 6 59 9 pend. inf. S3 o pend. supr. * 69 , "/' . ^ ' Alt. © Sept. 13. Dec. 2 tr. n S« 59 54 21 9 29 6 18 4i 35° S^' 3 " " II 51 55 54 «6 3« 54 "5 48 36 10 3 |( " 9 56 58 59 4 34 45 '^ 5« 36 30 4 0" II 51 io 54 12 37 41 'o 4 3^ 3° 4 !( " 4 59 45 5 ' 58 > .- . 5 © " II SI S3 54 S Dec. 4- Sept. .3 ..5343 5S52A-39' -^^3, ,„, ,,Oo' 51 44 — 14 *o 11 52 17 + 8 = 11 52 25 1711, Oct. I. Occ. Pleiades (Oct. 0.6 astrou, time). 3 40 1 1 Maia est cach6e par la lune 4^' 40" add 6' 19" 48 10 Taigeta est cachee par la lune 54 39 4 50 55 Alcione esl cach6e par le bord olair de la lune ... 57 26 6 31 4 56 18 Maia sort 5 * 49 5 34 23 Alcione sort 4° 55 6 3J Alt. Sept. 15. Sept. 27 0tr. .155 53 58' 3" 9 36 5* * 4 '6 36° 3°' 28 I. 55 S ^7 '6 40 o I 24 36 50 ' a^ — 56 26 4253 5828 37 10 Corr. + 17. 45 59 55 «9 37 3° Oct. 0.6 Le ventre de la J 2 53 30 49 9 ' S» S 37 5° Jl SS «6 Oct. 2 II 51 56 54 5 Sept. IS II 5° 28i 52 38 Got. 2 II S3 o 32 II 52 28 midy. Ue seems to have used the same clock with which the transits of the © are ob8er^'ed. RESEARCHES ON THE MOTION OK illK MOON. 1712, Miiy is'/j. II 22 2 Imiiioi'Hion tliiii.s lit partiti oU.'4(;uru (1(> liv liiiie (lu ; I. ion. IVml. iiil. 169 Auf. 35" I >S Emersion < lu ht Itiii'tic cl iiie. 1 1 26 2 pi'iul. inf. II 27 U poiKl. )«-jp. M.iy 13 ti . I( 29 )| 2 42 2 4 '5 »7 57 3 '« 3 44 32 18 ° I 45 4 ' 32 " Lh 19 May iV e,'' ilii matin Mail. Oasttiiii est aucoiu-Jiru) il'iiiiu tillu i|iii a 6u'i ba|iti.s6o li> 27 ut nnininCtii Hiisiniiu Kraiiyoisu ", wliiuli perhaps acU')iiiitM tor our li.iviiii; no coi'i-a.-ip >:iilin^ iltilinhtH Hiiice last 8upteiiilier. 17 14, Jan. 19, p. III. S'' 46' 18" pond. iif. ImiiiRPsion dans I i (lartie obscure de la lime il'iuu' t'toile de.s PoiHSoiis. 6 34 o IV'toile fMrt do la [tartie ulaire de la luni'. 55 10 uiK^ autre <>toile, buaiiuoup plus petite, eiitre dans la partie ob.s<;iiic de la luiic vers sun bord sept. " IininerHioii en III lioril cliiirt". J S3 '7 3 46 13 .I'liy coinincMcc . o 39 36 tiinersion de i't'tiiile x- Jnly 26 tr. 11" 59' 52"* 2' 7"! AiiR. 9 10 16 Sept. 15 16 '7 9 36 S<5 26 9 50 20 39 '7 23 46 50 40 41 42 2 21 22 5' ° 44 9 18 56 51 20 - A list.). 3 Alt. July 26, '7«5- 9 39 '" 20 59 49« 40 43 17 19 50 10 46 51 2 «3 37 50 40 59 10 1 22 59 I — 57 5> 60 3 57 I 59 8 36 39 — 9 34 4» 38 5' 43 «3 47 49 S' -9 Sept. 16. '8 55 «4 36 10 II 5 39 I o .mm- II 58 26 1715, Oet. 9, p. ni. gii ,y/ 2" lY'toile veiioit d'fiititr diuiM In liord iiliw. de Irt liine. I'end. ill!'. Liiiietti' tlo 17 p. 8 24 22 ]i(>nd. inf. 8 23 o pend. sup. I 22 jh jg/ ,// pend. sup. Iniinersion de IVtoile x "l" Verseau. 7 *3 37 |>end. inf. Iuiiri('i>ioii de I'ctoile x-' tr. 7 »5 39 penU. tut. 7 30 pend. 8up. Dee. 23 30 1716, Jan. 7 10 15 * 39 3 26J 5 48 6 48 — 7 59 10 20 35 '° 35 40 36 10 36 40 37 - Alt. Nov. 3. Oct. 6 ir — 60 37 9 5° 44 9 23 20 20 t II 58 14 — 9 56 10 2 3 43 20 50 10 '« 57 30 59 39 to 59 5' 21 K) Nov. 3 'I 59 43 ■ 58 Dec. 30. !>• 4 2 in. ■ 55 S' 21 30 RESEARCHES ON THI. MOTION OF TIIF, MOON. tyi 1717, Sept. 25. (>i'rieure. 9 13 46 Alilebiiriiii cHt vmtM \mr In liiiit'. Hub. a' 14k" auf. »' 16" 9 JO 18 peiidiiU^ intV'riciirc. 9 16 o peiiiliile Hiipt'i'lviirt', 10 52 21 si^iiMl pciiil. inf. 10 48 o pciitl. Hiip. 4 18 10 69 AUlelxiraii sort tin bord obHCure tout *l'ini cuup. 1717, Dec. 19, Alt. 0. Sept. 24 tr. II 58 2 — corr. — 41" »5 "57 41 59 50 -4'" 26 '■ 57 «7i 59 25 Dec. 19 001 2 24 Sept. 20 if 55 4' 57 49 9 53 7 la 40 57 26 3' 55" "3 '° ' 3* 59 36 13 »o 6 -t '55 9 13 40 17 1 7, Sept. 20. 9 41 23 »o >3 34 30 44 3' 7 «o 34 5° 48 6 ilul). 4 1 35 '0 50 44 5' 35 30 a. III. 7 42 37 liiiineiKioii (rAlilebaruii tliiiis la lime f\ lu vne et en ineanie tempH avecia lunette. « 55 '-'. ■ '^ 7 44 32 8 32 II Aldebaran sort dn liord clair de la lime, • 56 8 34 7 8 34 58 Aldebaran sort et on Papperi^oit dans riimtaiil. 8 37 o la peudule. 8 39 52 pend. inf. 2 52 1718, Sept. 26 tr. 59 29 ■ 38 Alt. Sept. 27, ,7.8. *7 59 6 « '5 28 58 39 48 9 48 19 2 9 58 32° 30 1719, Apr. 22 «' 57 44 59 55 (•orr. -42" 51 31 6 46 3' 5° »3 57 22 59 33 -41 54 45 3 33 33 'o 17 19, Oct. 30, Oct. of Aldebaran. 9 58 57 a la peudule sup. Aldebaran sort ilii bord obscure. •lid o' 13" 1 7 19, Oct. 29 3° Nov. 3 6 Nov. 3 Nov. 26 tr. II 59 43 1' 57" o o 50 I 40 40 o 30 o 3? 13 II 57 59 o '5 o o 10 inidy. 8 3 58 — dii Verseaii an lixe. 7 14 30 IVtoile , I'll! re ilans le disqne de la luiie claire 1. 7 J p. 7 14 54 lY'toile r •'''"•" ''""'< '» '"'"' l'""" '** ^»nftU- de 17 |i. apres avoir paru quelcpies seconds aur le bord. 7 18 I pend. inf. 18 o |>end. sup. 172 RESEARCHES ON TIIK MOTION OF TIIK MOON. 170., Nov. 3.) ti' 57' '.V -5 — zf, 57 ^2 27 ^^ 28 )! • 59' .HJ S9 .^6 59 4» 1720, Mii.v 21, Alt. ©. 9 3> 57 49 'o 3S 3' 49 40 39 4 2 21 2« 5° '° 42 4< 50 40 S« 5° Sa ao 5» 49 30 53 '9 2° 1720, April -M, n. in. (20.5 iist.). 1720, May 28. o 22 i| pcriil. iiil'. Iiiiiii. ;-' \'ii(!iiii.s, 9 42 34 op. 2 15 34 op. o 22 4+ I'liM. (!»' /' Viijjiiiis. 46 14 op. — o 48 ifi l':iiii'i>liiii 43', so that this hypothesis is pnd»ably correct. But ho actually applies 50', seemingly out of carele».sno88 with regard to the RESEARCHES ON THE MOTION OF THE MOON. '73 iinitM of HecniidH, hiuI thuH obtaiiiH \m printed result 8'' 45"' 40*. Siipposiiifr, then, a (lifl'erenee of 33* between the ehiekn, the eorreetion on mean time wouifl be —3'" 3',)", and the mean time of oeenltation would be S'' 42'" 51". The oceultiitinn was* observed jiIho by La Hike^ and tlio three resultH nre: — Maiuldi 8" 42"' 38*. ■ La Hire 8" 42"' 44".! Cahhini 8" 42"' 51'. I mn inclined, under these eireumstunces, to uho La 11h{e'h observation only. The moon was totally eclipsed, and the oceidtation to«»k place at a ecmsiderable auffle, so that the results with respect to the phase of the moon are not so di.scordant as the times would indicate. 1727, Sept. 7. Occiillutioii of I'leiutlfs. li'et. lU'H i>l( Uii peu 48 15' •X gauche i 46 464 centre. 50 46 48 3° 45 52: The following table is given on the first page of volume 36, which contains the observations of 1732-33. It seems to be derived principall.v from observations in 1733 not toniid in the record, but this is not certain. I give the table in the order in which it is found. y * '■■■■. 174 RESEARCHKS ON THE MOTION OF THE MOON. I)6utii)HiMuii (111 qiitirt dii circle Itxc i|iii est iIhiim la tuur occiiltMituli- Htip, it I'i^gard du la ni<^ri- tlleiiiie. Hiiiiteiirg. 18° 40 sec. al. occ. ) *' ^°\ !• Tlii'80 lirst lour in a ditt'creut liaiulwrititiK from the utkers. 21 4» i "'84 5°' 43. SS 44 54 54 43 38 43 33 37 43 ■: ;., -v;.; ;. ••./ »3 54 4' >o «3 4« '. :; .;'; • 18 40 ,•■■".' 18 i9k 18 m , 30 If this table ret't^rs totlio iiistninn'iit with which the sun's transits wen* coinnionlv observcfl, the numbers wonhl s'.m'Iii to Ik; ton ^rn-at for use in previous years. Hut it confirms the siispieiou of an increase in the error of the (juathant. 1738, Jan. 2. Occiiltatiiiii of Aldehanui. 945 7 on 8, c'i>ck. Aldebaraii eutre — piirtie obscure 9 39 5' app. time. J 16 tub. II 6 24 Aldebaran sort. 11 16 app. time. Jan. I 0tr. 2 .(6} 5' 9" 4 52" Midy A la peadale. 2 3 41 — 4 S4 Mid.v vray. 3 04 36 6 57 5 46^ Midy pend. inf. 'o 37 fdtki Til -i-Sii rjX ^.,^^^___ tiaii. 2 VI ) ^^) 54a — I 4j 16 23i I ■'-,■* - ' ■ 9 3°° Aldebaran tr. 9 32 14 513 subtr. 16 25^ Mid,v. pend. sup. 1738, Dec. 23. Occult, ot .Mdebiinin. 5 50 35 Immersion partitM»l)scnic, Dec. 19 ® tr. 0'' 13' 53" 15' 15"} 16 28J 20 © ° '3 27 15 49 5 34 64 Inimersion lieuie vraye. 23 © '.S 74 >7 2oi Aldeb. 10 j8 51 6 50 36 Hmursioii. S 10 34 — I C 30 ■ T 1 f?\ IT f r 11 1 R 1 •4*^ 01541 10 J 6 34 6 Kmersion lieure vntvc. A great gnomon was established in the year 1729, and it niav be that the transits of the suD were observed over it after that dale, lint 1 iini by no nu'ans snr'. A correction of -|- 2' i.«, bow- ever, applied for error of nu'iidisin, and it seems to be well delerniined, though I do not know how. •739' ^''''''- '5 '' 5° 3-' I'lini. Arctiirns 6 30 » .Mii.v 5 + o'.6 •7 Arcttirus f, 26 10.8 Mil.N 26 + '••5 18 ArctiiniK 6 " '3 5 J) 7 53 JS-» .Ill l.v iS ( orroNp. altM. «9 7 '■' 9 2l4 -• 43 3 8 3'-S '755i -'"'.V 18 :Hioii of Alili'liiiiiiii. 8 II 29 <'. Copy winiplete and literal. 8 20 3 5 44 8 40 3 ' 54 9 5« 4.4 9 20 » SS 184 9 40 -• 5* 10 2 48 41 5 45 '*' Dec. 13 tr. 7 58 10 21.5 «3 a. HI. KeKuliiH 4 40 52.5 «3 © 8 20 10 42. 5 «S 9 6 - lb 9 30-S " 53 '7 © 9 54.5 12 16 IViil. 8" xoiist, 1758, F.'l). 17 10 36 js TmmcrHloti of ;- (ii'iniiiornm. Feb '5 0tr. 3 144 5 28 16 3 524 6 (' «7 I( 8 9 OJ 10 51 (ie viMitrc) r Gem. 8 14 594 18 < 8 59 ='4 «9 5 424 7 554 Jan. a3 20 47 23 (>i »♦ 20 s»4 23 "4 1756, Dec. 17. O ,0' 7 '54 7 10 20 7 40 13 304 8 ° 16 404 8 20 "9 534 8 40 Jan. 24. 1758. 9 47 52 14 10 2 ^(> 20 lioniif>. 51 14 14 30 2 52 S7 ""'''• 5441 14 50 249 3i 118.S1 /. lioniii', o 22 7j - '3 Did. iiiiiial (?) 74 176 RESEARCHES ON THE MOTION OF THE MOON. Sebieb V. OhiiervatloHt by Dklislb at St. Peterxburg. TIu>s(> nbservatioiiH have iievor been |niblished. 'IMio oriffiiml maunsi^riptH wei-e rcfainerl by Dki.imi.k wboii Iw rctiirn(«l to I'jtris about 1 749,aii(l wen> eveiitMally depoH- itiMl at ibc l^iris ( )b.s«ivatorv. In 1H44, tliey were claiiin'i! Jty th«» Uiissiaii (Jovcrii- inciit, (Iclivorod to Ottcj oTkiVE, ami dopoHiteil at tlio Piilkowa Observatory. A full rep(»rt upon (Iiein was made by Stkiivk, wIio called attention totbe poHHililo value of tlie ((bservatiouh ot" oceidtation.s of the I'leiades wbirh they eontained Tlu'se oecnlta- tions were discussed by Linshkk in 1.S64, who compared th«' observed times with those computed from IIansk.n'h iiUmir 'l'abh>s, showiiifr a in»u\ a<;r(fement. Desirous of inchidiu^- in the present iuvestitfation all that was vaiiial)l«' in I)k- msi.k's observations, I took occasion, dnrinjj a visit to Pulkowa, in .Manii, 1S71, to ask Stkl've's pormi.ssion to examint; the manuscripts, and make extracts for the purpose in vitnv. This was very kindly ;,'rantod, and the services of the secretary of the estab- lisluncMit, Mr. Lisokmaw, were placed at my disposal whihf en<^aein}jf iletermimnl frouj tin>e to tinui by correspondiuj^ altitutles of the sun before and after n<(on. rianc. of iiltservatioii, ()t)si>rvatuire laiixirial en iSiisile Ostrow. 1727, 1e 21 ft'ivrier, nouv. Hauteurs iln Holuil |>our I'liorloKe. MXin. 37 39 4' 44 ao* S» 8J 2ii 44 2 '4" 16 18 20 22 U 16 UniiUMirH, 13O 16' '3 46 •3 '4 <4 '4 S6 r> 16 26 rt<>ir. 2" 38" 3oi*' 32 «J *9 43 »7 »8J 2.S 9 " S^i 3 Ije a6, linutcurH du 8ol«il pour I'horloge. Milieu (Correct, tie NuUiuti Houst. Midi vrai ..... 26* 28 58 ■7" '3 '7 >7 •9 •9 21J 13° S6' 14 6 9'' aS" 2 3' «4 >4 • 4 «4 «4 16 26 36 46 S6 30 3» 35 37 39 44 I 9 '3 '5^ 6 «5 16 «S 26 •S 36 '5 46 «S 56 Ix> 27 Wvrier. Le soir li 8'> 42" II' (If l:> poriduli! iiumersion daus la partie obscurti de la lane il'ane forte petite etoile d(i la ((ueuf •III l>t:lier. II y avait 2 auin^s cette iinniersion d6duit des inidis le 21 et 28 f6vrier est 1^ 8'^ 40" 53*. RKSEARCHES ON THE MOTION Of' THE MOON. 177 l,«^ 28 (lisTicr. naiitfiii'H (III koIimI pour I'liorlogt . 9" 9" Muiiii. 29" 1 1 '3 '5 '7 '9 21 23 ^5 27 26 «3 '9 16 1 1 12 30 »7 314 lluiitciirH. 140 16' 14 2(1 14 I t '4 •5 15 '5 'S 36 .,r. 5''' 6 16 .■r, 36 29 27 IS 46 '5 56 i*» Mtiir. 2" S3'" 46' 5' 484 49 S«4 47 S'' 46 o 44 S 42 o 39 534 37 47 35 43 33 464 MiliiMi. •■" 374 ,1 llaiitiMir in^ti'iil. tin boni Niip. ilii sole o" ° ' 37i o ' 37i o • 374 o 1 38 o 1 36 o I 36 o I 3051 ° ' 37 ° « 37i ° « 37 22^ 17' 15" fort CXrtftt' MiliiMi sikim corrt'ctioii . . o'' < j)i'i'cciii)ii ilo Niuliits soimt. Midi \ rai o Midi vrui 1(? 21 o Difft-rt'iice pour 7 joiirn I'" 37" - 28 I 9 2 58 I 49 3 Iiisteatl nt" ilcpiMuliiif; on tliR i'lo»rk-rato tVom tlic alrirndcs of l'Vl»niai'v 21 iiuii Ft^liriiary 2S, I Imvi! iitili/cil those iiijuio on die inoriiintr of tim 26tli. By ronipntinj^ till' iiltitiidr tVoiii the cuiTcspoiKliiij;- oljscrviitioiis ol' Kchniarv 21 and 2S, it appoars tliat tlic allitiidi's as ;jivcii rciiniro m corivction oi" — 16'. 2 tor seini-diaint'tcr and index- error. Applyin}"' this, we liave an error of tdock 011 apparent time oi" i'" 4i'.5. We then find:-— Clock F.-isl. K'luaiion of Cluck-cor- I App Time. Time. rcclion. ./ » w / Fel. 35. »' ■» 1 41.5 38, 0.0 ' 8.0 + 13 35-3 . + I' 43-8 + 13 0.4 j 4- II 52.4 Fntorpohitini; to the time of the occnltation, we find : — Chick-time of oeciiltation of rr 'I'aiiri, 1727, Fehrnary 27 . . 8'' 42'" 12'. Ch)ek-correction ii"'4g*.8 Local mean time S"" 54"' r'.S Greenwirh mean time 6^ ^2'" ^K.t, ±2'. (kciiltatiiiiis of the Pleiades, 1729, Deamher 3. — Tlicsf oh.->frvatioiis licinjr jriveii, in extetiso, by Linhskk, in the |»aper already refernMJ to, I math' no copv of them, bur only eompared the orijiiiml here and there witli Linsskk's printed data. I- M'ems .siirtifient to present those of the results most likely to jiive ri.se to cpiestioiis. Lin.smeu }(ivos the followinjf resiilt.s for correction of the time of sun's transit over t!ie gno- mon.- — 1729, Nov. 23 -f l"S 1730, Feb. I -f 3'.8 1730, Mar. 4 4-8'.2. But ho makes no statement of the corr(>ctioii wiiich he actually iidopls, nor of his <,'roiind8 for ailoptiny; it, only remnrkin^f that it is interpolated from the above v.iliics By calculatinjf backward from his results for clock-error, imd his tabular data, he would seem to have adopted -|-i*.o. It would, therefore, seem that he coiisiriered the ;ja— 76 AP. 2 17S RI.SF.ARCHKS UN TlIK MOIIDN Ol' IHK MOON. t'orrectioii to varv witli tlic ilccliiiiitinii ><{' tlic .>«iin nitlicr tlmii with the thiu'. Hut whoii tlie results for several veins iH" plaeeil tojiether, they a|)|»ear to van only with the time. 1 therefore ailojited +2".5 for the correction. 'I'lu' addition of a slight dirterence in the ('([nation of time, arisin;-- iVom the |ieriodic |iertinl»ations of the sun's longitude, Iieing neglecte(l in my work, carries the ditVerence of computed mean times up to 2", an amount l>v whicli my mean times are less than those of I.inhski!. The following are mv independent results, alongside of which I place for comparison those of Ll.N'ssKK. The results are a mean of thos(t from the two (docks (J lUul D, which diti'er between themselves hy an auioimt varying fnun r.4 to l".o. /Mli; I7ay, Otifiiiher 3. «i" Sl;ir. Local Mean Tinir ol (>; iillation. l.inSMT Siduifal Tiimv (irt'uiiwirh i .Mean 'I'iinc. 1 // »t T s 1 : A m ' km 1 Uleclia 1(1 35 ??.') i') ' n 27 24. <) 14 34 444 Ccl'.una 41 yy(. 41? 33 7.(. 40 2(1 . 1 Maja 17 Id ■;...(i 58. S lo « 30 3 1 5 1543' Mfiop'' Jl 4-4 4<).7 23 23.'i 3" 33. y Alcyone 43 13 f ■5 '■ .1'» 52.7 47 0.3 Pleione l» J 2 "7 4 I'l 7 II .4 3-5 If) 31 3 g Alias . 37 3i.'- 37.7 M 29 22.6 3ft 22.1 1733, Ic 2 2 Mars. A iiiiili vrai li'iiniiKM'sioii est (loMC iirrivi'c. Anx iii'iiilillt'^'. All leiiiim \ iiiIm. (J l> N 27'" 4i.i" «" 3<'" 57" 7 2« 4 < h N C liiiiiicdiiitt'iiKMit ii|ir6s I'cmerHiiMi. 7'' 38"' o* 8'' 34™ 49" f I,il IXMldlllc K (\ CI INuifc (■'((• lUT«'t«?(', u» 54"" 47» 'o 58 59 003 " 52 i^ II 5.5 275 'o 55 48 «• 54 3'4 «« 53 7 RESEARCHKS ON TIIF, MOTION OF THE MOON 179 Ia' 25 Mars. A iiiiili vriii (' 1) N M "54 5 10 52 3? " 54 4' I I JO 29 Le 8»ir, occnltatiiui ilc « 5 ilaiiN iiii instant i\ 7'' 15'" i^'i <••" I" pfiKlnlt' •'• (• N i> AjUf's riiiiiiifrNion L'iniinHiHicin est ariivi-c. Aiix |>i>n5"' 444" I) 6 ..', ,84 N 7 '^' i<) 7'' irt"" o' 7" '« 44i" 6'' n)"< o" i \i>{ pi-mhilc .M 11 fic n-tardct' 27" on la rci-on [■ tant ct avani'i'-c 10 niiii. pour l'a|i[)roclier ilii I A' 27 .Mar.«* a luitl.v It'inps villi. 39 37^ 38 I Mil leu i Corrrfliiin r> 54 4-' o o 424 I)an« ci'N laltMiN dii iiMups vrai il ii',\ avail point (IVnciir ;\ la int-iitliennt'. (To ilt'torniiiu' tho ifvnn ol nu'iidian.) Lc io Mars. HanttMir> >lii lioid siipci i.'iir tin solcil. IVnil. Iv H'' 2,\"' If iS" 2>' 3" i.S'" <'7" "" 49'" M\'1 " ° 14 20 ; • 42 I I I 9 21 7 43 6 4 4 ■!•! - 44 I 6 .?9 ^S 57 40 I.C 2S Mais. UncorrtHJtt'il tiiin- ol appart'iil noon fioin (loiiUli- altitinK-.-s witli -lockt' Correal ion of KnU-r . . . > True noon pi-r clock C . . . • Hirtfii'iict' 111 (locks at noon 1 19 — ♦') , . . . . Iruc noon l>v dork I) ■ Traimit ol snii per rliMik 1> Coi«r»'«!lioii , , , Tlic results for convctinii of friioiitoii an- — 1733, Marrli 20 24 5« iS 3> 26 3'> r.S 4" 2« "4 i.S 5' ^9 55 '9 1 3' 32A '9 1 1 33 1 1 i<) 21 34 534 ■9 S> 3(> 3« '9 4< 3« 1 2 '9 5' 39 5' 20 I 4' ^x 20 1 1 l'' 49' 38" 11 '" -'9 39 3 •'^l ;. I'.iiiliilf I) 37.'! 37» 38 18 o 40 30 30 n 8 38 2 II 8 39 22 ('orretftion ilc la inc riilioniu- . . . 3 ii'' 53'" '4" 7 — 29. () «' 5* 45- ' I 9 57. o 10 42 48. 1 10 4) 4». 7 — 0.0 -l\S Mari-h tK —o'.h. riif vaJiK — I'.o 1ms i»i'i*i» a«lof«r, ami N, w*» tht»i» found to \tv as- fol!o»»:- At ii])]Mir<.Mit lUMiu, 1 1" 5IP.5 I ;■ 3".o 12" i8*.4 I) ■fb4'" 45V> 07" 46'. 3 73"" 36'.o 70"' 2y'4 82" 2 2*. 5 -i-Q'" 5*-.V b"' 4 2'. 5 I !'" 2 7".0 10'" 4 8*. 4 IcSo RtCSEARCHES ON THE MOTION OF THE MOON. ., \Ve tliiMi liavo the foll.nving results for moan time from the three clocks: — 1733, March 22. IiiiriitM-sioiis of I' ({cMiiii dock 7'' 21'" i8*.5 6'' 27"' 27'.o 7'' 24" 8'.5 ( lock-correct ions .... -f- i i'" 5o".7 i'' 5*" 41*4 I Mean lime.s y^'jT' 9".2 7^' 33'" 8'.4. . . 1733, March 25. Immersion of 'c Oancri, clock 7'' i5"'44".5 6^ 13" i8".5 7'' 16" 29'.o _l_ ,2-1. j;.^ ,h ,^M, ^Q,2 ,,,„ 2,, 2 7'' 27'" 49".8 7" 27"' 48".7 7" 27'" 5o".a. The mean of the limes jriven by the several clocks will be adopted, ■yj**! 'Vpril 14. Tiaiisit of sun's centre, ciock A, i' 3j'» iij*. l!oin|iiiiisou (if clock.s \I ,(. ,gin q» A ■ 35 '7 N 1 5a 43 liinni'isioii of Aldebunui instuntiineous at M, 11'' 56'" 30'. ArttTwanl ;yi ,,ii .gm q» A II 55 5 N o 13 »4j " LVrrenr

  • lii moi'iilienne est (i'envirnn 7" addftive." Times (if the innnersiuM. I'enJ o I' S4i 10 19 3«ij April 13. rtnn on meridian A i'' jc" J58* M ' 38 37i ^' ' 54 S4i Applying +b'.^ for error of ;.iUoiuoM, we have tlie following results for elocl - correction: — . A * M N April 14 Apparent noon —92'" 10". 7 —94'" 5 3". 7 — I09"'36".7 15. Apparent noon — 95'" 40".o _98'"5i".7 —115'" S".7. The mean time of the oliserved occiiltation is then found from each of the clocks as follows: — 1736, Aj.ril 14. A M K Clock-times of inmi. of n-Tauri 1 1'' 53'" 35". r i'' 56'" 3c". 12'' i i'" 54'.5 ('lork-ci.rrecfions . . . . — i'" 33'" 4o".7 — 1''^0"' 36".! —i^^i<»^g\j luteal mean times ... 10 ig™ 54".3 10'' 19'" 53*.9 10'' ic)'" 54'.8. RESEARCHKS ON THE MOTION OF THE MOON. i8i 1736, June 20, • TliP i!orru(!tioii of tlm iiii^riiliuii if) foun Im hiIiIimI to the ol>M>rv('il tinieH ol triiiiHit of the huh. AuK> ■• TriinNit of the huh I'eiiilulf iiouvflle, iifterwanl Hto|)|>cd A 8" 45- 34* M 8 41 58 [8 48 40] uouvclle. 8 48 22 HU|i(3ri«Mirf. 59"* 9i" 'o 59 A A 2'' 4 Next iiioniiiig iniiiifrsion of Alditltartiii very exact . . eitifrHJon ".le orois iiu'i'lli' lie fiiiMnii, ijue ile Hortir <|iiaii Apritit I'eiiierMioii liiiiiierHioM. M A Sup. Kinei'HioM, 4'' 0"' 4 12 39 26 A M Hup. Aug. 2. 2 3 Clock. 59'" 94" 55 29 ' 55 (6' True. ' 10" 34*1 6 10 25I 6 10 27^ CliM'k. 4*" 10™ 59' 4 7 20 4 "3 46 8uii uii iiierliliaii clock A M Sup. Truf. (7'' 2 2'" 56*] 7 22 47 7 22 484 8'' 49'" 2 2* « 45 5° 8 55 '5 1 Hiid 110 reiiaon given for rejecting clock A, ex(!ept its (liHconlaiue. I'rocecdiiitj: us usual, and adding + 9".2 fnr error of giininoii, wo liavo the fol- lowing resnltfj for «!oiTection of the three elocks, A, M, and Sup: — M. H"" 45'" 43'-2 S'' 42" ;'.2 Sup. 48"" .3 I '.2 15" 20' 5"' 46*.9 ■ 3"-7 8" 49'" 3 1*. 2 ,5- 23'" 39".; 8" 45'" 59" 2 >5" 8" >7" 52' o* .')•" 5" 16"' 2" 50" 42".9 •••.7 9" 5 is" 1 7"' 8'.o 2'' •5" 1 8" 4" •5" I' (/lock-times t»f traiiKit, AugiiHt 1 Mean tiin*' Clock-forrections Clock-tiniert of t<:iiiHit, .Vngnst 2 MoiUi tine . ,.♦».. (Jliwk-»"»>rrection» Imni«*si(vns .»f a 'raiiri, clock . ( 'hMik-«'o«Te*tioiis .. , . » . MewB Utm>» I H'' 1 6'" ) 7' 5 Ljn«isi.>TiH. ch>rk 4'' to'" $rMioii. IN'iidiilt'N. 6'' 6"' 1" 6 .. 6.^ L'iiiuiu'i'HJoii. I'uiiiliili'N. IViiipit \riki. A 4'' 50"' 58" 3'' o"' 32* M 4 47 6A 30 36 The (iatii for clmik-error lire Hoiiitnvliiit irrt>i;iilai'. We have: — 16 octobre Hiiii 011 iiioriilian (({iioinoii) A TraiiHit of sun over 5tli wire of mural sext. I'aHsajjo of diameter 2'" loj* Peiiihile A eiisnitc arnttee, et la peiuiiile M a>' .iieee 7 mlii. AfterwanI, tlie followiiit; transits over 5tli wire of the luiiral i|iia(lr.iiit iiiiiilM vriti. 4 «5 jC'' 1 r*" '9 JO" ni M ,ii ,«i., J J. Oct 18. 20. Hiiirs II limb . f A(|uliae . . a. Aquilae . . /S Aqiiilue . . Mars . . . . i^yk .... Bor. Cauil. Ceti Liicida T . . i» Hyad. . . ([ bord siiivaiit Aldubaraii . . Kigel . . . . Hollatrix . . Halt. Orion. At 23. rtun II Had) i I llera DEi.ihLB ' ' Bit;>iM)Ht'ii ri I III uf nierliltaii i W\ ^^\:\ oiiiU. f ^ Aquihe 7 .Inpiter 8 Nodi X o .Mars I La pendnle M a ('le ain-ti^e. Pendule A, Oet, Nov. 4. Hum's centre (mean of limbs) . . (iiiomon 34' 32 3''> 4' '5 37 5° 3 iK >9 r '7 21 26 • 3 ,v3 4' 42 .S3 o ' 4>!i' 44 59 2«i .S' .s° 3°^ 3-»i 28i ■■i 54 3S j 36M 25 ret M = A - 1 — ,;"' 52" at 4" 54" \ M - A = - 3" — 4 ssH' 9 Ditr [4' en la remontant. A . 2 3« 44.i -• 3« 30 + iii (sie) Till' itDiTfftioii ti> the tiinc ot' transit over the nuiriil sextant lor tlu' (Iccliwatioii id' tlie sun at thi« tini*' socnis to l»t' altout + 5'- ^^ «' Imve then tliii following roMiilts for correction of clo'.'k \: — I 736, October 1 8 'iVansit of © —ih^^"" 22. Transit of {{ij^cl —2'' 6'" 23. Tran.sitofO —2'' 7"' 34".5. '.■» -.1 7". 2 RESEARCHES ON TIIE MOTION Ul- Till: MOON. '«3 luteiitolatiii},'' to the time of occultntioii of Alil(l)artiii, we liavt' : — ► (Jlock- times 1 6'' 50'" 58" iS" 6'" I*. Cork-i-oiTcctioiis - 2" r,"' 5',6 - j'' 6'" 1 7".6 Mean tiiiK's 14" 44'" 52"4 i j" 59'" 43"-4- TlicHe results arc 10" less than those of Dkijsi.k, and more iiiicertain than usual. For cniii' III iiiciitliaii (^kikiiiioii), April 22, 1737. TruiiHit of SUM over stli wire, iiiaral HfMaiit . . A 1'' 57'" 46S" (^' = A 4- Mvritliaii ((;>>'**>>'>■>) S« Mi 8"' 30l" j'' 6 444 = (J Corrt'ciiiiii of si-xtaiit 278 Kroiu 13 pairs t-ipiiil altitudes with clock H, at a namii intiTval ol 5'' 42" Hull at Kicati-st luM^lit . Kuler's correction . . True transit of sun . . (," — 11 True tiaiisit per (! Oliserveil with ^{iioinoii Correction of k"*""*'*' ■ Correction of sextant 14'' 7'" 37.2* II 22.1 >4 •4 i4 6 + •S' 21.7 .S3-4 44.4 9.0 36.6 '737. ^'"i '• Transit of sun, mural sextant A .Meridian, k''**'"*"' (i. — a From 12 e(|ual altitudes ot the sun, interval 6'' 56". 2'' 33'" i'i' C = A 4- 2 3i 3Si '" 34 i(>i :C Mean for nieiidian . . Uitr. of clo(;ks (' and II . Apparent noon jier (' Kuler's eorrertion . . ('<>rre(;ted apparent noon Error of ^iH)nion Hrroi of sextant . . . + 3°* 14'' 38"' 23.8" II "2 3 >9-3 « 35 4'.S — 20.7 » 34 43-8 4- 7-° + 37-S 1737. •'^l".^ 7. s»»ir. Imiiiersion of ; Leuiiis (pietn<>"«)nie noon lt,\ the various clocks. 57'" »7' 2'' 58'" 2'.3 A 2" 53"^ 48.1' + 3-'-!' The immersion was at — CJDcliH TllW tillU'l-. .V 2'' 54"' 2>.,V (J 2 58 -'•3 M 2 5' 5-3 > II ■4 43 5 ''3 N 3 10 M3 \ After which C wi.s retarded 14' liy windint;. A 0'' 41'" 5* '»" 45"' '5f «! 44 45 9 45 '4 M 37 47 45 8^ 1 84 RESEARCHES ON THE MOTION OF THE MOON. " TnuiHiiiitN with iniini 1 Hexttiiit. Miiy 7. 8ii'itm A (yl> 30'" 50* 22 17 I'rocyoii 7 » I . . 9 9 S 34 SO S»A Cor. a . Cautlii il 1 1 3J S • Hpica . . 1 8 28^ ArcturiiH I 59 58 I'lMiiliile 11 U«;niiiKt!«l 3 or 3 HecoiuU Ity tliti conU. ▲ 6" 25"' o» 6 28 32 M 6 a« 434 Miiy 8. 8uii oil t;iioiiioii A 2 57 49-7 C 3 1 46.2 M a 54 24.7 • H •4 47 3-7 N 3 14 40.2 The scxdiiit 33*.5 sooiitT, Applying + 8".5 tor cornH-tion <»f' giioinoii, and taking t'roni cluck (,' on May 7 the 14* by which it wiisi rtitardod in winding, we Imve tlic lolhiwing resiihs tor chick- correction : — At traiinit of ©. Miiy 7. May 8. Clock A — 2" 58'" i7".9 - 3" !"• 50*4 C - 3" i"'44'.9 - 3" 5"'46'.9 M - 2" 55"' l".9 - 2" 58'" 2 5'.4 H -«4''47"'47'-9 -14" 51'" 4"4 N — 3" 14"' 20'.9 - 3" i8"'40'.9 The mean time of the occnltation, as given by the several clocks, is then as fol- lows ;— A M H N 9" 4'" 2 1 '.4 19'.! 2 2".4 n'-3- 20'.4 Mean 9* 41" 20».8 '737t ^^'*.v 20. Ten correspondiiiff pairs of sun'.t altitudes {five for thu correction of the gnomon -f- n'.j. 23, a. III. Occiiltatioij of Jupitor in daylight, •'npiter mo paraissait toucher le bord ccIairC' de la June. True tiluflS. le^ I" yi" > Jupiter me ot^raiHse tout entri^. May ■9" 58- 254' .1 10 •54 H 8 1 '94 A 8 3 22i 7 59 38* N 8 3 S'i M 16 I 94 16 I 9 16 584] 16 I 83 i RESEARI'HES ON THE MOTION OF THE MOON. 185 ClockH. liny at. Siui on Kiinrnon A 5'' jS™ Jo-S* II J 56 37'S M ^ SS 43-8 Mnml wxtiint A 3 57 41,0 O.-S 30-S Mny 23 Miiial sextant A 4'' i™ 36.5" C 4 J p.s (' M 4 3 41.0 H 3 59 »i-S N 3 5« 52-5 Le fll . Venus < .•'" 22" A A 1'' i;4"' o' Spica 13 3* *' ' 5 °i Arctiiius : s I M I 55 9 Pelisj.k's reduction is corrt'ct for dock II. Takiiif,' tin- menu of liis results, the apparent and niciui times of contact of linihH of Jupiter ami the moon will he: — First contact, apparent time 15" 59'" i9"-« (o(i.i=-3"' 47'-3) >"■ *■ = 'o" 55" 3>'-8 SocoikI contact, apparent time 16'' i'" 9".! is*" 57'" 2l'.8 Whence local niean time for centre of Jupiter .,...,... iS*" S^"" 26*8 1737, July 23, u. III. Occultiition of tf TiHiri. 01(H. llRiNMirs. Pkuslk flniU : Immersion of Star a (men.i.Moiinle)(i.i«-!.) A 9" 5'" .V*^' II (')-'■" 5'" ^4' 12" sr 36'.o Kinereioii of ft northerumost, ami A 9 38 h H 21 37 S3 ^3 3° °- ^ a A 9 50 46 II :i 50 31 13 42 36.6 Forelocks. July ai. Suti culii mean of 10 pair cKiresp. altitiules 8'' i'" 28.7' II Interval S'' o"'. Enler's conrcitiou + '3-8 l.ue upp. iHion 82 42.5 Clocks B — H 9 "'O True noon B. 7 53 *o-5 »,, Suu on gnomon, meridian 7 S3 '^-o " Correction of gnomon +8.5 ( Transit over 5tli will- oi' mural sextant 8'' i'" 33^" a norrectioii (G. — 8.) + 425 Jnlv .TV Sun on gnomon 7" 43'" 5°i' '^ ««■ ^ ('^ ''«' "*">** '^ Sextant 8 9 4 A = , jV 9' " Jul> -,. 10 pair efpiftl altitudes, in'.erviil 7" 59"' give 8'' 15"' 44«.7 U Euler'M correction '5-5 ' App. noon 8 16 0.2 -• Dili', clocks, B — II o 41 18.8 App. noon clock B 7 34 4' -4 1* Meridian (gnomon) B 7 34 34-2 Correction of gnomon +7-2 24 75 AP. 2 IMAGE EVALUATION TEST TARGET (MT-3) 7 A O A :/. Ma LO U 1.25 ■ 50 "^ ^ ■^ aits 1^ ■2.5 ii 20 1.8 1.4 IIIIII.6 V] ^fj^^'s y >^ Photographic Sciences Corporation 23 WEST MAIN STREET WEBSTER, NY. 14580 (71 (») 872-4503 i 1 86 RESEARCHES ON THE MOTION OF THE MOOI^. Clochcomparisom. July 21 , noon. 22 soir. 22 soir. 23 a . m. 23 noon. i m / A m t A m t A m s A ni s 8 5 A 2 7 A 50 A 9 53 A 8 13 A 7 55 56 B I 47 25i B 19 49 47f H 21 52 46 H 7 47 5 B 3 6 [o 3 II 49 8 3 8 5 8 4 8 5 53i 45i 31 30 18 53 25 C D] E G H M N 2 6 5 2 z 10 30 3 7 46 C 56 D 54i E 57i G 4ii M 50 II N 9 53 loi N 8 ti >7 4 24 33 C 48J D 30 E 52 30 56 22i 7i A B C 9 9 [10 9 56 39 56 A 39 B I5i C]* 54 M 8 8 8 14 10 14 A 2 G 27* J II 54 47 I5i A D 9 58 A II »3 57 E I 51 I D 8 20 59i K 54 51 M I 16 3ii E 8 15 4 M 56 A 9 59 A 8 16 A 52 40 G 9 59 «3 J 3 >5 55 H 56 10 J 9 55 33i G 8 16 8 N II 56 3ii K * Afterward retarded 13* in winding. The clock-corrections have to be interijolated from the noons of July 21 and July 23. The system of proceeding will be this: — Taking clock A as a standard, we shall find the eiTors of the other clocks for the comparisons nearest the occultations, on the supposition that A is correct. The mean deviation being supposed to arise from changes in the rate of A, the latter will be corrected, so that the result shall be that given by the mean of all the clocks. We have, first: — •2 u B C E G H M N Other Clocks, miniit A, etc. (0 (2) 9° SO" A. July 21.0, 8" s™ A July 23.0, 8'' 14™ A Comp. Obs, A Comp. Obs. A m s — 9 4.0 + ' 53-5 + 224 31.0 — I 30.0 + 18.0 — 7.0 + 25.0 m s - 25 55.3 + 4 38.0 + 191 30.0 - 3 58.0 - 5.0 + I 4-0 + 8.0 Pt s - 21 35-3 + 3 55.8 ~ 3 20.2 + o.g + 45-7 + 12.4 s — 37-5 + (67.5) — 20.0 — 12.2 + 5'.o + II. s - 2.2 + 2.2 + 0.2 - J3.1 + 6.3 - 1.4 m s — 22 18.7 + 4 2.8 — 3 26.3 — o.i + 48.8 + II. 6 - 21.0 + 15.5 - 26.8 - 14.0 + 54.0 + 10.5 J - 2-3 + 2.7 - 0-5 - 13.9 + 5. a - I.I The 13 seconds by which C was thrown back is allowed for in columns A. The discordance of H seems to indicate that there is a mistake in its comparison for July 23.0. The general result is that the rate of A agrees very nearly with the mean of the other rates, while the discordance of H and M are such that it is impossible to say whether the correction to the position of A for July 22.5 should be positive or nega- MBIHI RESEARCHES ON THE MOTION OF THF MOON. 1 87 tive. We shall therefore suppose the rate of A correct ; its corrections will be found as follows: — July 21. July 23. Clock times of 0's transit (true mer.) . 8'' 2"" 24».5 8'' 9™ 53».3 Mean times o" 5" 49'.$ o" 5" 55'.4 Clock-corrections +4" 3"" 24".8 3" S^"" 2».i At the time of the occultation, the difference of clocks A and H was I3".3. It appears, therefore, that Heinsius observed the occultations about i'.5 earlier than Delisle. Taking the mean of the two observers, we have : — e, Imm. 01 Em. 61 Em. Clock-times by A 9" 5" 37'-9 9" 38" 7'-2 9" 50™ 45'. 2 Clock-corrections 3" sT" 44"-o 3' 57" 38'-9 3" 57™ 37'-i Mean times . . 13" 3" 21 '.9 13" 35™ 46'. i i3"48»22*.3 1738. Jan. 2. Occultation of Aldebaran and the Hyaiies. Immersion of /, instantaneous. fl' Tauri. e' Tauri. 2 observers diff. li*. Sec. of app. time. I II 4S B *94 2 21 30J 5a 6 26 2 D l8 7 3S 34i 5'J I 9 47J G tSJ 2 19 32J sij I 7 7 H ao 2 17 4j 54 I 10 28.5 J 18 2 20 I3J - S» I 3 16 K l81 2 12 S9J SI + 1- • The following are the apparent times from the mean of all the clocks, supposing Delisle to have applied the right clock-correction : — Immersion of / 6^ 15°' i8.'s 0' 7 24 52.0 — I* 0^ 7 28 8.0 —I" Aldebaran 12 18 46.0 — 0.5- Emers. 12" 58" 25'- Observer thinks right ; but the other m 8 46 16 observer is put down lo" later. 1737. Nov. 25. Transit of sun, sextant 4" 7"" 43'-' ^ gnomon 4 7 34 -S ^ G.-S - 8-6 1738. Jan. 3. Transit of sun, sextant 7" o- 7».6 B gnomon 6 59 59 -9 B G.— 8 -7-7 Febr. 25. Correction of gnomon from 6 pair altitudes . . +2'-7 March 19. " " " " • • +6-8 Jan. 2, a. m. Transits with sextant. Spica i" 14" 37* B Arcturus * ^ Si p.m. Algenib ° * 3»J Luc. T » SS 3 i» Hyadum 4 7 4* Aldebaran 4 23 4> Sirius 6 37 »3 1 88 RESEARCHES ON THE MOTION OF THE MOON. We h.avo to adopt Delisll's appsirent times. Tlio error of tlie gnomon is quite uncertain, so that tlie times are also uncertain. A})plying the equation of time, which ranges from +4" 45"- 5 to +4'° 52'.o, we have for the mean times of the phe- nomena :— 71 Tauri, immersion, 1738, January 2 6'' 20° 4".o 01 7''29"'38".5 , ©a ' 7*" 32" 54".5 ■ ' ■; * )», B. A. C. 1391 (f) 8''5i'" 3".5 ' :^ a Tauri la"* 23" 37".8 Em 13'' 3" i7'.8 1738. Febr. 2, aoir. Imrnersiou of / II at i?*" S'" 37' H 4 59 18 A 7" ss" 34» app. t. Api)arent time, mean of four clock.s ... 7'' 55'" 33" i But the guoinou is supposed correct. Sun on gnomon Febr. 2 9'' 2'" 27" A "3 9 6 30 A 1738, Aug. 3. Correction of gnomon + 7'-3 " 19- " " +5 .6 1738, Octb. 2, soir, occultation d'Aldebaran. Immersion, exact at 0'' 10"' 1.5' H. (2 observers.) Emersion i 10 27 H. Observer HErNSlus. '739) Outb. 24, matin, occultation tie I'etoile i de la sixieine grandeur que .Mr. FiasisI'EED appele la boroalo des trois qui suivent le bras droit des Jumeaux. Immersion dans la partie eclaire de la lune -X' 3'' 50°' 44» B ;! " Presqn'il la precision d'une seconde. Moment precise de I'emersion .... s"" i"" 37" B 1739, Octbr. 25, niiitin. Immersion <5Ciincri (within i sec.) 3" 24'" 58' B Emersion, instantaneous ... 4 31 32 B 1741, March 24. A midi I'on a commence a observer aujourdhui le passage du soleil il une non- velle mtiridicune filaire tracde daus le grand observatoire superieiire, pendule K comuie il suit o"' 12™ 404* Mean of 2. o 14 S98 2 19-5 The usual gnomon I J sec. earlier ... o 13 50.0 March 25, soir, immersion ij Oancri o'' 7'" 54" K (2 observers agree exactly). 1741, March 1. Oor. to meridian (gnomon) per double altitudes + ij" April 25 + 6^ Merid. superieuro + i'3 July II. Inf. +11,0 Sup + 39 Applying + 7'o for correction of gnomon, we find the correction of clock G on mean time to be; — August 8. At 8'' 55"' 2i».7 of G, con-. = +3'' 9" 49'.6 9. At 8" 58" 4o".2 of G, coiT. = +3" 6™ 23'.4 The clocks appear to agree so well that no reduction of the others is necessary. RESEARCHES ON THE MOTION OF THE MOON. 189 There is, however, .an obvious mistake of 4' in the time of immersion of Aldebaran, as given by G. Interpohiting clock-correction, we have the following local mean times: — 1738, Augusts. Immersionof 71 Tauri . . . . 15" 3" lo'.o Eir.rsionof 71 Tauri .... 15'' 59"" 5"-9 Immersion of (9, Tauri .... 16^ 21" so\7 Immersion of ©2 Tauri n Tauri Immersion of a Tauri 16" 22" 21" 18" r-7 5'4 22" 7"'49'-3- POSITIONS OF THE MOON PROM HANSEN'S TABLES, USED IN COMPARING THE PREOEDING OBSERVATIONS WITH THEORY. When a number of places of the moon are to be computed, several modifications may be made in the use of the tables, whereby the labor of computation will be diminished. " (i) Omission of terms unimportant on account of their minuteness. The older observations are so far from exact that there is no advantage in cairy- !ng the computation of the Fundamental Argument to the last degree of precision. Portions of the double-entry tables may, therefore, be omitted in comparing such observations with theory. The minuter terms are those contained in the twenty-seven tables of double-entry: all or a part of these tables may be omitted with the following results : — If the twenty-seven double-entry tables, XII to XXXVIII, are all omitted, and the sum of their constants, 0.0022240, substituti d, the probable deviation of the com- puted longitude from that given by a rigorous computation will bo ±i3"-6 If the seventeen tables, XXII to XXXVIII, are omitted, and the sum of their con- stants, 4290, substituted, the probable deviation will be ±2".7- If the nine tables, XXX to XXXVIII, are omitted, and the constant, 1 140, sub- stituted, the probable deviation of the result will be ±o".85.* (2) Modifications tvhen many places of the moon arc to he computed. These modifications refer principally to the formation of the arguments, and the introduction of the terms of long period. They are applicable when places of the moon are required for a series of dates in which there is no interval greatly exceeding a year. The following is a description of the method of forming the arguments actu- ally adopted for the years after 1632. The dates were divided into groups of not more than ten or twelve, except in cases where a number of dates were crowded together, when the number might be a little greater. A group always had to terminate when an interval of much more than one year was encountered. When no such interval occurred for several successive ' U is to lie remarked that in cases where an approximate position of the moon is rcquireil for any purpose.this plan of using Hansen's Tables, with the omission of the smaller terms (always taking care to include the constant terms of the omitted tables), is much better than that of using the older tables, the elements of which are affected with unknown systematic errors. IQO RESEARCHES ON THE MOTION OF THE MOON. groups, the same date was taken as tlie last of one group and the first of the group following. All the arguments were then computed for the limiting dates'; " each group in the usual way. Those of single entry, including g for the intermediate dates, were then found by adding to those for each date the interval in days between that and the date next following, and subtracting the greatest number of entire periods contained in the sum. The double-entry arguments are constant for each period of g, and change by a definite amount for every new period. To pass from those for one date to those for the date next following, it was only necessary to add or subtract a number depending on the number of periods of g which had terminated during the interval. To enable this to be done with the least labor, and risk of error, a long slip of paper was prepared for each number of periods of g. On the bottom of each slip was written, in regular order, the quantity by which each argument increased during the number of periods coiTesponding to the slip. On the opposite side and edge of the slip were written, in red ink, the complements of these numbei's; that is, the quantities by which they fell short of one period of the argument. Then, to pass from the values of the arguments from one date to those for the succeeding one, the number of entire periods of g which had been subtracted was noted, and the con-esponding slip taken. Being laid over the row of arguments, the red numbers were first subtracted in all cases where they were less than the argument. Then, turning the slip over, the black numbers were, added in all the remaining cases. When the end of the group was reached, the series of arguments thus obtained was compared with those derived by direct computation; and if they agreed, which was nearly always the case, the intermediate arguments wore all considered correct. The only way in which they could be erroneous would be by two opposite and equal errors entering into the same series. The computer who formed the arguments in this way was the Rev. Parker Phillips, whose conscientiousness and accuracy were such as to inspire entire confidence in his work. (3) Terms of long period produced by Ventis. The variation of these terms is so slow and regular that it is much easier to include their sum in the original computations of the arguments than to compute and add them for each date. Their sum was, therefore, computed for the beginning of every tenth year, and inteipolated to every year, as shown in the next table. Their product by the proper factors to form the corrections to Arguments 32 and 33 was also com- puted, and included in the same table. These arguments are farther to be corrected on account of the terms of long period con-esponding to Arguments 28 and 29; but the en'or from omitting these terms is so small, scarcely o". i in the mean, that they have been neglected. In place of them, the constant quantities -j- 200 and + 1 86 have been included in the table. The addition of these corrections to the three leading arguments necessitates a* correction corresponding to their change duriiig the interval between two consecutive dates, to be applied to that interval in order to find the total change of the argument. The amount of this change for 100 days in units of the last place in the argument is tabulated, and shown in the table next following that last described. RESEARCHES ON tHE MOtlON OF THE MOON. I9t The explanation of the several parts of the table is as follows: — Column A g gives, for the beginning of each year, the sum of Hansen's Venus-terms of long period, as derived from Tables XLI and XLII, Arguments 30 and 31, without any modification. The precepts of the tables direct that Arguments 32 and 33 be corrected by the sum of the four Tables XXXIX to XLII inclusive, multiplied by the factors o.i 1545 and 0.10717 respectively. The sum of the first two tables diff'ers so little from that of their constants, 1735, that we may use the latter; we have therefore put A 32 =0.11545 (Ar/ + 1735) =0.11545 A5f + 2oo A 33 = 0.10717 (A /7 + 1735) =0.10717 A (/ + 186. Arguments 32 and 33 are to be corrected by these quantities respectively. The change of g between two consecutive dates varies, not only in consequence of the variation of A g, but of tho secular acceleration. The change of the variation in the seventh decimal place of g for 100 days, in order to reduce it to the adopted period corresponding to the epoch 1800, as arising from both these sources, is as follows: — Date. Secular Term. Venus Terms. Date. Secular Term. Venus Terms. 1620 -103.31 - 4. II 1710 - 51.72 + 30.62 1630 - 97.58 + 4.06 1720 - 45.98 + 24.85 1640 - 91.85 + 12.23 J 730 - 40.24 + 17." 1650 - 86.12 + 1993 1740 - 34.49 + 8.04 1660 - 80.39 + 26.50 1750 - 28.74 - 1.71 1670 - 74.66 + 31.61 1760 — 22.99 — IJ.64 1680 - 68.93 + 34.79 1770 - 17.25 — 21.10 1690 -• 63.19 + 35.70 1780 — 11.50 - 29.46 1700 - 57.46 + 34.30 1790 - 5.75 - 36.09 1710 - 51.72 + 30.62 1800 0.00 - 40.50 The sum of these terms, interpolated to the beginning of each year, is given in the table as ^4^, while the corresponding terms for correcting Arguments 32 and 33 dt follow. To find the change of g and of Arguments 32 and 33 between the epochs < and < + A <, it is necessary to take out the values of these three derivatives for the time f + J A f, when we shall have: — - ChangeofArg. = A< + ^.-^-^^--iX Period; it being remarked that the second term is given in units of the last place of decimals. 192 RESEARCHES ON THE MOTION OF THE MOON. Date. 1630 31 32 33 34 35 36 37 38 39 1640 41 4« 43 44 4S 46 47 48 49 1650 5' 52 53 54 S5 56 57 58 59 1660 61 62 63 64 65 66 67 68 69 1670 71 7a 73 74 75 76 77 78 1679 3289 3304 3322 3343 3368 3396 3428 3464 3503 3545 3590 3637 3686 3738 3793 3851 3912 3975 4041 4110 4182 4257 4335 4416 4500 4586 4674 4763 4854 4947 5043 5141 524' 5343 5447 5554 5663 5774 5887 6002 6119 6237 6356 6476 6598 6721 6845 6970 7096 7223 Diff. 15 18 21 25 28 32 36 39 42 45 47 49 52 55 58 61 63 66 69 72 75 78 81 84 86 88 89 9> 93 96 98 100 102 104 107 109 tii "3 115 117 118 lig 120 122 123 124 125 126 127 128 A 32 580 581 583 585 588 591 595 600 604 609 614 619 624 630 637 644 651 658 666 674 683 6gi 700 709 7'9 729 740 750 761 772 782 793 805 817 S29 841 854 866 879 892 905 918 932 947 961 975 990 1004 1019 1033 'i 33 539 540 542 544 547 550 554 557 562 S66 571 576 582 587 593 599 606 613 620 627 635 643 651 659 668 677 687 696 706 7i6 726 737 748 758 769 780 792 805 817 830 842 855 867 880 893 907 920 933 947 960 St 36.5 35.7 34-9 + 8.1 8.1 + 8.1 rfA33 dt RESEARCHES ON THE MOTION OF THE MOON. '93 Date. A g 1680 81 82 83 I 84 i 85 86 87 88 89 l6go 91 92 93 94 95 96 97 i 98 I 1699 1700 01 02 03 04 05 06 07 08 09 1710 II 12 13 14 J5 16 «7 18 >9 1720 21 22 83 «4 as 26 27 28 1729 735> 7480 7609 7739 7869 8000 8131 8262 8394 8526 8653 8789 8920 9051 9182 9312 9442 957> 9700 9828 9956 10083 10209 10333 10456 10578 10698 10816 10933 11048 11161 1 1274 1 1 386 11495 1 1 602 11707 1 1 809 11909 12006 12101 12193 122S2 12369 12453 12535 I 12615 ; 12692 I 12767 I 12839 I 12908 Ui(T. 4 32 129 { 129 '■ 130 ' 130 i 131 ! 131 I 131 : 132 132 : 132 I 131 i i3> \ 131 131 130 i 130 '. 129 129 128 128 j 127 i 126 ' 124 123 122 I 120 I 118 117 115 113 113 112 109 107 105 102 100 97 95 92 89 87 84 82 80 77 75 72 69 66 1049 1064 1079 1094 I10() 1124 1 139 1154 1169 1185 1200 1215 1230 1245 1260 1275 1290 1305 1320 1335 1349 1364 1378 1393 1407 1421 1435 1449 1462 1475 1488 1500 1513 1526 1538 1551 1563 "574 1585 1596 4 33 973 987 ' 1001 1015 1029 1043 , 1057 1071 1085 1099 ; 1113 1127 1142 1156 j 1170 ' 1 184 1 1198 I 1212 1226 . 1240 I 1254 I 1263 ; I23l I 1295 \ 1308 i 1321 1334 1346 1358 1370 1382 1394 1406 1417 1423 1439 1450 1461 1471 1481 1607 j 1491 1617 I 1500 1627 \ 1510 1637 1519 1647 1528 1656 ! 1537 1665 j 1545 1673 I 1553 1682 i 1562 1690 1 1569 dt 341 33-4 32-6 319 31.2 30.5 29.9 29.3 28.7 23.1 27-5 1 ^ 7.0 6.9 6.9 6.8 6.7 6.6 6.5 6.4 6.3 6.2 6.1 6.0 5.9 5.8 5-7 5.6 5-5 •t- 2.1 2.1 2.1 2.0 2.0 2.0 2.0 1.9 1.9 1.9 1.9 1.9 1.8 1.8 t.7 1-7 1.6 1.6 1-5 1-5 1.4 1.4 ••3 5.3 1.3 5-2 1.3 51 1.2 5-0 I.I 4.8 I.O 4-7 I.O + 4.6 + 0.9 25- -75 Af. 2 194 RESEARCHES ON THE MOTION OF THE MOON. Date, Aa' Difr. A 32 A 33 at 7.32 ,11 ./ 33 lit 1730 12974 61 169/ 1576 - 23.1 + 4.4 + 0.8 3> 13015 58 1705 • 583 234 43 0.8 32 >3"93 1711 1590 23.7 4-3 0.7 33 13148 55 52 1718 1596 24.0 4.0 0.6 34 13200 1724 1601 24.4 3.9 "•5 35 3& 13249 13294 49 45 42 38 36 32 2B 1730 1735 1607 l6l2 24 .7 25.0 3-7 3.6 0.4 0.4 37 13336 1740 1616 25.3 3.4 0.3 38 13374 1744 1620 25.7 3.3 0.2 39 1740 "3410 13442 1748 1752 1624 1627 26.0 26.4 31 3.0 + 0.1 0.0 41 13470 24 21 17 14 1755 1630 26.3 2.9 - 0.1 42 13494 1758 1633 27.2 2.8 0.2 43 13515 1760 1635 27.6 2.6 0-3 44 13532 1762 1637 28.0 2.5 0.4 45 13546 1764 1638 28.4 2.3 0-5 46 13556 10 7 + 3 1765 1640 28.3 2.1 0.6 47 13563 1766 1641 29.3 2.0 0.7 48 13566 1766 1 64 1 29.7 1.8 0.3 49 13565 4 g 1766 1640 30.1 1-7 0.9 I--0 13561 1765 1640 30.5 1-5 1.0 51 '3553 12 1764 1639 30.9 1-4 I.I 52 '3541 1762 1638 31-3 1.2 1.2 53 13526 15 19 1760 1636 31.8 t.i 1-3 54 13507 1758 1634 32.2 0.9 1.4 55 13484 23 26 ■756 1631 32.6 0.8 1-5 56 13458 1753 1628 33-0 0.6 1.5 57 13428 30 1750 1625 33-4 0.5 1.6 58 13394 34 37 42 45 48 52 55 1746 1 62 1 33.8 0.3 1.7 59 13357 1742 1617 34-2 + 0.2 1.8 1760 13315 1737 1612 34.6 0.0 1.9 61 13270 1732 1608 35.0 — 0.2 2.0 62 13222 1727 1603 35-4 0.3 2.0 63 64 13170 13115 1721 17'5 1597 1591 35-8 36.1 0.5 0.6 2.1 2.2 65 13056 59 62 66 1703 1585 36.5 0.8 2.3 66 12994 170I 1578 36.9 0.9 2.3 67 12923 69 1693 •571 37.2 I.O 2.4 63 12859 1685 1564 37.6 1. 1 2.5 69 12787 72 76 80 83 86 89 1677 1557 38.0 1.2 2.6 1770 12711 1668 1549 38.3 1-4 2.7 71 1 263 1 165S "540 38.6 1-5 2.7 72 73 12548 12462 1649 163;, 1531 1522 38.9 39 2 1-7 1.9 2.8 2.9 74 12373 1629 1512 39.5 2.0 3.0 75 12281 92 1618 1502 39-8 2.1 3-0 76 12186 95 98 1607 1492 40.0 2.3 3.1 77 12088 1595 1481 40.3 2.5 3.2 78 79 1780 11987 11883 11776 lOI 104 -107 1584 1471 - 40.6 - 2.7 - 3-3 RESEARCHES ON THE MOTION OF THE MOON. •95 TliG tenn« oniittod were as follows: — For all the Aral)imi ul)S('rviiliniis and tor those! of I'toi.i.mv, nil the (hnihle-ciitry tables were omitted. From 1621 to 1666, Tiildes XXll to-'XXXVlII of doiil)le-(iitry were omitted. In all cases of such omission, the sum of the ('oustaiits inehided in the tables was added. From 167 1 onward, all tiui tables wt^re" included. Still another modification consists in the omission of the nutation. Since the comparison of the* place of the mooi: with that of the sun or star was made in lon- gitude, the ecpiinox to which each was referreil was indilfcreiit ; tlie mean eepiinox of the date has therefore been chosen. The nutation terms l)eino' given in 'I'aldes VII and IX of LoiifiUndc Vrai, these tables were omitted, amithe sum of the constants, o''. 00550, substituted. After the formation of the arguments, the computations of longitude, latitude, and parallax were made in duplicate Ijy two independent computers, and the work was then compared Ity myself Where differences of importance were found, the computer who was wr mg correlated his work without reference to tl-.at of the other. That these i)reeautions have secured al)solute freedom from error cannot bo asserted. Discrepancies of various sorts, which dctveloped themselves in the final results, led to the discovery of some errors which escaped all the i)reliminary examination, and which are wm-thy of mention as atlbrding hints to others. In one instance, an error of 20 days in forming an argument, though marked as wrong, failed to be corrected. About half a groiii) of laiitudes (dates 83 to 91) were in error from this cause. In another instance, some inadvertence in attemjiting to correct an error led to a connnon error in two computations. In a third instance, a typographical error in the tables led to both computations of longitude being wrong i)y about 20".* This last source of error is that which I now most fear. Througli sonui over- sight, some of the volmnes of tables used by the computers did not have tlu^ typo- gniphical errors corrected. Such errors in tiie longitude, if important, will admit of detection where two longitudes with the difl'erent variations are computed for the same day; and it was by comparing the difference of two longitudes with the variations that the mistake above nu'Utioned was found. _^ ^^ • In mv prelin.inarv paper in the .h„,;„,n, J,,m,.il of Sdaue nml Arh for S.-ptemher. 1870, tlie occuUation of Alde- baran on iftSo, Xovcmhor'?, appc.us as unaccjunUiWy.lUcor.lant. The ailTicully arose from a typ..i;r.->ph.cal error of i in the t«t)ular prineipal term of latitude. 196 RKSEARCHKS ON THE MOTION OK Till; MOON. Sun'n Ococcntric— .Mo(.n' s (ieoccniric — • Year. Dale. (ircenwieli Mean Time. I.onKilude. .'•enii- LoliKituile. Motlun in Paral. lax. Mean l",i|uin. dlnni. Mean E<|Uln. 0^.01. Laiiiuue. - 720 M.ir. 19 // m s 500 35" 31 3"-4 15 57 17" 59 3". 9 7 34 32 + " 3 39 55 44 - 719 Mar, 8 8 34" 41 49. 4 ifi If)" 30 31.7 7 6.02 T- 46 43 53 55 - 719 Sept. I 300 150 54 28.0 if) 329 55 25.4 9 4.97 - " 37 45 61 10 — 630 April 31 13 24 23 3f).8 15 49 3"4 If. 1 1 . 7 f'.78 + 53 50 54 a - 582 July 16 800 106 33 14,6 .5 48 38f) 37 13. 1 7 II . in " 4" 53 54 14 - 501 Nov. ") 800 231 54 14. f) If. 16 51 46 47.6 7 5 "2 + " 5" 43 53 51 — 490 April 25 7 38 31 35.9 15 49 207 55 48.9 8 7.91 + I I 36 57 48 - 3S2 Dec. 33 ' 16 2f>7 t 57-5 I6 17 8f. 4'. 52.5 8 42.95 _ " 57 49 59 52 - 38. June 18 400 80 37 49.9 .545 35947 0.2 7 i".34 + 46 38 54 " - 381 Dec. 13 600 35fl 9 56.4 If) 17 75 12 47-" 9 8.24 — 31 10 61 30 — aoo Sept. 33 5 I7f' 41.3 If. 4 356 2" 25.1 7 28.60 + 33 38 55 23 - 199 Mar. ■9 800 355 23 32. f) 15 58 173 5fi 33.8 8 16.66 + 4 54 58 19 — 199 Sept. II 10 165 I 43.1 If) 3 343 55 3-4 8 19.93 f 007 58 30 - 173 April 3" 10 35 40 6-5 15 49 314 45 55.5 9 4.43 — 35 42 61 5 - 140 Jan. 37 f) 304 3t 5fi-3 If) 13 123 2f. 23.7 9 8.10 + 46 34 61 30 + 125 April 5 600 14 ifi ir.9 15 54 194 2 38.5 8 18.60 + " 57 26 58 36 133 May 6 800 44 II 33.5 15 48 333 5f> 8.0 7 20.03 — 35 40 54 50 '3-) Oct. 20 8 :o6 15 f).3 16 II 35 54 53-2 7 33.38 — 36 45 55 40 ,36 Mar. 5 1200 344 36 35.8 16 3 163 51 50.9 8 53.37 — 53 II 60 28 829 Nov. 39 16 36 14 252 37 1.4 If) 15 251 37 35-6 7 51.53 + 33 7 56 54 829 Nov. 29 13 3fi 54 252 41 432 16 15 252 38 3.6 7 52.27 + 16 49 56 56 854 AUR. 1 1 12 I 7 143 35 32.2 15 52 321 40 199 8 48.28 + 18 14 60 16 856 June 31 12 21 58 04 10 31;. 2 15 45 273 34 3o-fi 8 15.06 - 45 13 58 14 923 June I b 56 33 74 43 21.5 15 4f> 255 29 5" .2 8 37-3" — 43 50 59 34 923 Nov. 10 16 21 8 23? 2(. 48.7 16 14 232 37 16.1 9 4.21 + 33 33 61 16 923 Nov. 10 17 32 32 233 29 49-5 16 14 333 33 33.0 9 407 + 38 14 61 II 935 April II 2 38 3(1 26 7 56.1 1554 304 16 46.0 a 25.73 + 36 51 58 57 925 April " 7 47 49 26 20 33.1 15 54 307 18 22.5 8 37.80 + 30 2 59 6 927 Sept. '3 12 50 46 175 II 58.9 16 354 38 43.6 9 5-48 + 51 14 61 17 928 Auk- ■7 15 39 29 149 36 57-7 15 53 149 7 31.6 7 51.39 — 13 10 56 54 929 Jan. 27 8 5 32 313 14 7-1 If. 13 131 48 27.9 8 30.55 + 30 37 59 17 933 Nov. A '3 17 45 227 48 52.7 If. 13 46 54 43-2 7 14.45 — 5 53 54 31 977 Dec. 13 18 19 2 367 I 39 If. 17 365 49 0.3 9 6.65 + 35 14 61 35 977 Dec. 12 30 36 10 2f)7 7 28.7 •16 17 367 16 6.3 9 6.38 + 27 16 61 35 978 June 8 33 39 81 4S SI.*-) 15 45 81 58 38.1 7 6.34 — 6 10 53 57 978 June 8 3 43 13 81 54 24.5 15 45 83 7 17-5 7 5.97 + 16 53 58 979 May 14 5 52 57 5f) 59.6 15 48 238 51 9-2 8 18.34 + 32 36 58 31 979 May 28 4 12 58 71 "5 6-9 15 46 ;i 47 32.3 7 36.34' + 39 3 55 55 979 Nov. 6 8 3 40 22Q 27 8. 9 16 13 48 42 43.9 8 18.33 - 37 36 58 34 979 Nov. 6 II 18 229 35 21.4 16 13 50 34 49" 8 17.30 — 27 15 58 38 980 May 2 14 26 47 31 iS-fi 15 49 228 24 21.3 7 38*20 _ 13 2 55 36 981 April 31 13 28 36 39 56-3 15 52 216 n 56.3 7 5.32 — 45 50 53 55 981 Oct. 15 14 7 208 I 33.9 16 8 27 24 21.5 9 2.06 + 46 36 61 7 983 Mar. I 9 55 346 13 '8.5 16 5 165 18 39.2 8 38.20 + 31 50 59 43 983 Mar. I 13 40 346 22 36.4 16 5 lf'7 33 37.9 8 36.75 + 19 34 59 35 985 July 20 2 56 30 122 17 35.7 15 47 132 43 17.6 8 10.32 + 15 4 58 I 985 July 20 4 iS 13 122 20 51.7 15 48 123 29 43.1 8 10.89 + 10 50 58 3 986 Dec. 18 '4 53 272 49 I.O 16 17 92 16 49.4 7 5.9" + 30 16 53 58 • 990 April 12 - 42 27 34 15.2 15 54 206 43 569 7 6.15 — 37 39 53 59 qjo April 13 4 27 42 24.7 15 54 200 23 26.7 7 5-94 — 38 17 53 59 993 Aug. 19 17 36 5 151 54 39.6 15 53 '5" 28 33.5 9 2.4" + 5 17 fil 4 1002 Mar. I 9 4r 18 346 35 57.9 lO 5 165 37 27.9 9 8.07 — 13 7 61 37 1004 Jan. 23 I 51 308 43 17.5 16 14 296 I 56.8 8 32.44 — I 2 7 59 20 1004 Jan. 24 I 5' 309 44 2.2 16 14 310 9 24.9 8 23.57 1 + 15 51 58 50 "■~T RESEARCIIKS ON THE MOTION OF THE MOON. ic I Motion In' No. I 9 3 4 A" i 6 7 8 9 10 II 13 13 J4 «5 lO "7 17" l8 >y 30 21 2 III 21J 22 23 24 25 26 27 2S 21) 30 3> 32 33 34" 34* 34 35 36 37 38 3y 40 41 42 43 Dale i (Irfi'iiwiili ^t(•:ln ; riCDCcnlrlc | Motion In ' Geocentt UiiiK-nlMu'iii. o''.oi. Lai. of Moon. Ifi2i, May 2o l623, July 5 1627. June 17 '• Sept. 18 1630. June 10 1632, Fel). 5 1633, Feb. 14 " Apr. 8 1634, Dec. 30 1635, Aug. 26 1637, Mar. 2() if';*, Jan. 24 '■ Dec. 20 1639, Apr. 7 " June I 1641, Apr. 13 1644, Nov. 14 1645, Aug. 21 " Oct. 7 " Oct. 8 1647, Jan. 20 " Apr. 12 1652, Apr. 7 " Apr. 8 1654, Aug. II 1656, Jan. 26 " Mar. I 1658,001. 14 t66o, Apr. 26 " June 17 1661, Mar. 2q " Mar. 30 " Aug. 3 1663, Mar, 14 " Aug. 18 1664, Mar. 31 1666, July I 1O71, Mar. 14 (ireenwi •li Mean ; Tiini'. A m s 1 18 3') 34 •7774768 : 31 5 10 .S7S787C) 1 9 24 '6 .3i)'85") 10 8 14 .4233843 10 39 30 4 48 o 7 12 o 1 5 o 11 20 4 4 48 o 5 43 44 () 34 32 37' .2(MMK_XX) . 3(KX)()l)<) .62504)00 .4722685 .2000000 .2387037 ' •3919'55 .375fKxx) • 3040394 .6720139 •3752431 . 1500000 ' .2500 65 40 39.2 99 '3 35^o 100 33 20,2 46 28 53.4 7 53.11 7 54.05 8 18.02 7 5'-53 7 1999 8 5^2l 8 6.25 7 58.98 7 22.32 7 53-90 8 11.76 8 3;. (XI 8 38.44 8 17.34 S 32.60 7 36.62 , 7 50.59 j 7 51.67 ! 7 5.41 t 9 403 8 7.94 8 6.94 3 52.87 8 49.06 o 48.26 9 9-47 8 38.18 8 48.80 8 48.08 8 24.22 8 23.28 7 433 7 4.30 7 44-94 7 4-01 8 21.52 7 41-30 8 59-10 8 58.50 8 50.64 8 49-53 7 35.10 8 37-57 7 4l^56 , 41.92 8 28.75 7 58.12 7 59.13 8 45^24 I'aii'llax. + o 45 36.4 + o 38 8.1 I - o 47 53.7 + I 25 49.9 H- 2 36 SI .8 + o 33 57.7 + o 40 33.9 + 4 58 31.; -t- 2 18 28.6 + O 12 4.5 + 4 46 35-3 - I 26 4.5 + 4 38 13.'' t 4 7 54-9 - o 15 9.0 + I 7 55-4 + o 43 53.6 + o 36 43,3 - I 58 40.0 - 5 o 36.6 4- o 51 18.0 + 1 o 31.5 - 5 4 6.1 - 4 49 3.7 +1 6 32.9 +1 7 '4 .6 + o 43 31.2 + O 51 34.3 + O 36 32.6 -+- o 28 40.1 1 1- o 47 56,6 4- o 55 24,2 -+- 4 54 8,4 + 8 6,6 4-2 8 20 I - I 16 33.8 4- o 37 16.9 4- o 39 0.8 - o 45 6.6 - o 53 30.8 +3 9 50.3 - 5 13 51.0 4- o 38 5.3 -H o 25 26.0 - 4 55 29.4 4- o 20 14.2 4- o 27 34.9 + 3 35 3».6 - 43- '9 - 43-38 + 43-42 + 40.95 - 34.76 + 44-54 + 44.49 ' - 4.52 + 35-28 + 43-74 . 4- 14.18 + 45.97 - 17.99 - 28.45 - 47.36 - 39.45 - 42.99 - 43.19 - 36.37 4- 1.70 + 44.41 + 44 07 4- 3^o8 4- 14.86 4- 49.66 4- 43.68 : 4- 48.40 I 4- 48.11 I - 46.33 I - 46.36 i I + 38.83 4- 38. 66 ! - 12.55 - 38.48 4- 42.38 4- 40.01 - 49.48 - 49-54 - 48.65 - 48.34 + 31-35 - . 5-63 - 43.46 - 42.57 4- 12.18 4- 44-OI + 44-07 + 35-52 197 Motion In <)''.oi. 56 58.5 57 1^9 58 42^7 57 5^9 i' 0.7 57 42.8 57 46.4 57 6.5 55 20.4 57 1-8 58 0.3 59 35^6 59 35^6 58 33-6 59 20.0 I 56 6.9 j 56 49.9 56 53-4 54 1-8 60 55.8 57 52.7 57 48.0 60 20. 1 60 4.2 61 28.5 59 >7^o 60 17.1 60 14. I 58 51.1 58 47-4 53 56.3 53 56.1 56 29.5 54 2,5 58 .10.5 56 30.8 60 51,9 60 49,8 60 24,6 60 20.7 55 28.4 59 33.8 j 56 16. r j 56 17^7 j 59 "•5 57 17^4 57 2KI 60 7,6 igS RESEARCHES ON THE MOTION OF THE MOON. (Jrecnwi cli Mean Geocentric Motion in Geocentric 1 Motion in Motion No. Date. Time. Long, of Moon. o''.oi. Lat, of Moon. O'l.OI. Parallax. ino''.oi. 44 1671, Mar. 14 // m s 8 37 .3590278 46 59 53^3 8 44^81 + 3 37 37^1 „ + 35-24 60 6.3 " 45 " Apr. 22 9 29 •3951389 198 38 41.2 7 5^02 — I 21 13.2 - 37-49 53 59-5 46 " " 10 39 .4437500 199 13 6.3 7 5^o2 — I 24 15.0 - 37-41 53 59-2 47 " May 31 14 21 .5979167 348 27 34.7 8 ig.36 — I 6 46.2 + 43-20 58 47-2 48 1672, May 18 IS 24 30 .7670139 320 33 46.2 7 29.06 — I 50 16. S + 36-84 55 46-1 40 " 20 3 30 ■8357639 321 25 5.9 7 29. 86 — I 46 2.1 + 37-22 55 49-0 50 " AiiR. 2 10 18 20 .4293982 246 54 50.5 7 7-97 ~ 5 13 26.2 + 0.18 54 10.8 51 " Sept. 25 10 7 36 •4219445 23S 50 21. I 7 16.61 - 5 10 27.3 - 4.88 54 41-6 52 " Nov. 5 II 30 .4791667 54 52 19^4 8 56^47 + 4 58 1.2 + 6.87 60 29.8 53 1673, Mar. 22 700 .2916667 55 35 37-f' 8 1 3. 06 + 5 10 53^3 + 0.66 53 23.2 54 1674, Aug. 23 12 36 .5250000 54 25 9^4 7 33^I7 + 4 42 45.4 - 17-43 55 51-S + 0-4 55 " 13 48 .575ocx)o 55 2 57.5 7 33^71 + 4 41 20.9 - 17-85 55 54.2 56 1675, Jan. II 700 .2916667 III 34 22.0 8 26.16 - 6 35.2 - 46^83 58 57-6 57 .. 8 12 .3416667 112 16 34.3 3 26.77 — 10 29.4 - 46.87 58 59-3 58 " Jimc22 16 0' .6666667 90 46 2.8 7 43^89 + 56 49.6 - 42.09 56 24.7 59 " 17 12 .7166667 91 24 43.2 7 44^26 + 53 I3.8 - 42.15 56 26.3 j 60 167b, I'd). 29 10 22 57 .4326042 169 3 17.1 8 38.29 - 4 56 59.6 -- 7. So 59 25-8 Ci " II 20 3 .4722570 169 37 32.6 8 3S.62 - 4 57 31.9 - 7-42 59 26.9 62 " Mar. IS 7 16 28 .3031019 47 5" o^3 7 5^74 +39 51.1 — 29.00 54 7.0 63 " Mar. 23 13 17 20 ■553703S no 50 36.5 7 32.52 — 2 4 28. 3 - 36-37 55 57-5 64 " June 10 20 ■S333333 80 13 23.4 7 3.10 + 13 46.0 - 39-58 54 l'-9 65 " " 22 24 •9333333 81 24 46.6 7 8.47 + 7 9.5 - 39-62 54 13-' 66 " June 29 II 29 59 •479'55I 334 57 26.9 3 0.24 + 5 I 25.2 + 13-30 57 25-3 67a " Aug. 19 8 24 .3500000 280 17 41.7 8 30.70 + I 43 7^6 + 42.61 59 18.2 1 67 " 1200 . 5000000 282 25 22.2 8 30.52 + 1 53 42^1 + 41-95 59 16.7 -1-0.2 1 68 " Aug. 31 1200 . 5000000 77 16 55^7 7 5-8i + 10 II..,' - 37.71 54 19-3 69 " 14 24 .6000000 78 27 55.5 7 6 . 02 + 3 54^3 - 37-79 54 20.3 + 0.0 3 70 " Sept. 26 17 30 24 •7294444 64 16 57^3 7 5^4l + I 3 17-4 - 36-91 54 '3-5 71 " Nov. 9 5 40 55 .2367476 2S1 53 33.0 8 42^3'> , 2 23 36.5 + 42.34 60 1.3 72 " 6 35 19 .2745254 282 26 25.5 8 41.89 -i- 2 31 16.0 + 42.06 59 59,8 73 1677, Mar. g 12 17 7 .511S8S6 64 39 50. S 7 10.02 + 16 32.4 - 38. C5 54 34-8 1 74 1678, Feb. 27 7 21 .3062500 63 40 50.7 7 30^25 — I 18 24.0 - 38.51 55 52-3 75 " 8 33 .3562500 64 l3 21.3 7 29.64 — I 21 36.7 - 38-40 55 50.1 76 " Mar. 28 3 ■3333333 8431 3-1 7 22.44 - 3 tl 13^0 - 31-55 55 >6-8 ^ 77 " Sept. 24 7 f) 32 . 2962038 284 49 30.4 8 24.43 + 4 48 9^2 + 17.43 58 54.0 78 " Oct. 29 8 35 38 •3580787 37 3 53.8 s 32.75 - 59.9 - 47-41 59 20.6 79 1679, ^'^f- 29 13 3f> . 5666667 220 9 55^3 7 16.28 +1 9 1.8 + 39-25 5446-5 1 80 " 16 .6666667 221 ^2 42.0 7 17.00 + I 15 34.0 + 39-13 54 48.7 *■ 81 " June 4 15 I 30 .6260416 30 4 4^o 8 34.62 - 17 59.6 - 46-33 59 32-9 82 " 1600 .6666667 30 33 54.6 8 34.55 - 21 7,6 - 46.28 59 32-6 83 " June 24 9 51 42 .4109028 284 41 24.6 8 i6.oi + 4 57 36.9 4- 7.89 58 8.5 ■ 84 " 10 32 29 •4392245 285 4 50^" 8 16.26 + 4 57 58.9 + 7-61 58 9-4 85 1680, Jan. 16 9 I 21 •3759375 128 15 55.5 7 55.78 1 - 4 31 28.2 + 17-99 56 56.7 86 " 10 7 I .4215394 128 52 2.9 7 55.16 - 4 30 05.0 + 1S.33 56 54-9 87 " Apr. 4 10 18 22 .4294213 91 23 1 1. 7 8 19.25 - 5 14 43^4 - 6.41 _ 58 33-3 88 " Sept. t3 15 53 .6256134 64 54 25.7 8 35^38 - 4 46 •■!9.7 - 20.27 59 30-0 89 " Nov. 7 7 50 43 .3268866 64 33 16. I 9 9^83 - 4 39 27.6 - 20.47 61 18.4 90 i68i,Jan. i 6 27 41 .2692245 64 53 53^2 8 53.16 — 4 45 23.1 - 15-37 60 40.3 9' „ .. 7 36 41 .3171412 65 36 5>^3 8 58^45 - 4 46 35^7 1 - 14-86 ■ 60 41.2 RESEARCHES ON THE MOTION OF THE MOON. 199 Grcuinvich Mean 1 Geocentric Motioning Geocentric Motion in : Motion ^'inll-iv ' No. Date. Time. Long, of Moon. ^ C'.oi. i ' Lai. of Moon. o''.oi. (iraii.ix. ino''.oi. j - 92 1682, Fell. 15 7 4 31 .2948033 1 1 63 27 54-5 8 21.37 i 1 — 5 17 40.1 + 0.80 58 40.! ■■ 93 " Mar. 14 9 -15 35 .4o'-655i " 61 48 36.0 8 14. 82 - 5 14 55.9 - 0-43 58 13.8 94 10 57 35 ■45(16551 62 29 50.4 8 15.14 - 5 14 56.7 + 0.03 f3 15.2 95 i6S3,Jan. y 8 41 32 . 3^21759 65 19 27.0 8 1S.13 - 4 54 29.8 _ + 15-99 58 25.3 96 9 54 47 .4130440 66 I 42.3 8 19.14 - 4 53 6.5 + 16.59 58 28.1 97 " Fell. 5 II 57 42 .4984027 61 51 25.5 7 58.01 - 5 3 33-0 + 13-24 50 20.7 ! 98 12 47 44 .5331482 62 19 7.6 7 58.66 - 5 2 46.4 + 13.63 57 22.7 - . 99 " Aiir. 2 8 43 44 .3f'37037 , 79 16 42.7 7 54.48 - 4 3 47-7 -1- 25. iS 57 7-8 : - . 100 9 43 34 .4052546 ■ 79 49 34-9 7 54-84 - 4 2 1.7 + 25.56 57 - • lOI " May 4 9 55 =3 .4134606 145 25 17- I 3 2987 + I 24 I.I j + 43-16 59 22.3 . . 102 10 40 55 .4450811 , 145 52 10.3 S 30.05 + I 26 17.7 1 -r 43.11 59 22.9 1 - . 103 1684, July 12 2 16 .0944444 : no 36 32.9 7 ^5.60 + 20 56.7 + 43.79 57 7-9 - • 104 4 40 .1944445 in 55 53-3 7 56.53 + n 28 15. i + 43-80 57 n-4 ' . . 105 " Dec. 21 ■ 9 24 59 -3923196 90 28 46.8 7 21. '-8 — 39 6.3 + 40.50 55 1.2 - . 106 10 59 .4173496 90 47 II. 7 21.83 - 37 24.8 + 40.58 55 I. 8 . . 107 l085,Oct. 17 9 29 28 .3954630 85 44 7.8 7 3-68 + 26 56.1 + 37-92 54 8.1 . . 108 ifi86, Apr. 10 93329 .39S2523 1 230 25.1 8 31.42 + I 51 9-8 ; - 42-7S 59 16.3 . ■ log 10 45 29 .44S2523 230 43 2.6 8 31.63 + I 47 35.3 i - 42.99 59 17.3 • • no " June 25 9 45 4' .4067245 ; 149 21 46.0 7 14-74 +58 36.7 , -r 7.17 54 35.3 \ ■ • . m " July 2 9 13 35 .3844329 j 240 53 20.4 8 42.11 + 49 10.9 ^ - 47.12 60 1 . 9 112 1 1O87, Mar. 28 13 30 37 . 56292S2 189 6 30.7 7 27. oS + 3 31 =2.9 - 29.07 55 15.7 . • 113 1 " May II 100 .0416667 51 17.9 8 3.84 - 3 55.5 + 44.69 57 38. I . . 114 .. 2 12 .0916667 51 40 36.1 8 3.30 - 12.1 1 + 44-63 57 36.2 . . 115 1689, May 21 9 29 11 .3952662 too 17 0.4 8 40.67 + 5 7 29.9 j + 2.94 59 42.1 116 " Sept. 13 3 20 .138SSS9 171 20 55.5 7 37-78 4- I 19 54-6 1 — 40.86 56 1.5 - • 117 4 32 .1888889 171 59 3-4 7 37-31 + 1 16 30.4 - 40.87 55 59.9 : . . IlS i690,Apr. 13 II 28 55 .4784143 86 7 20.7 8 41.57 + 5 12 56.4 1 + 0.17 59 47.8 . . 1 I'9 " July 2 14 59 9 .6244097 55 17 48.6 8 47.90 + 4 34 51-1 + 19.48 60 1 1 . . . 120 1699, Auk. iS '3 35 19 .5661921 64 56 16.9 8 27.31 - 4 57 48.5 1 — 14-50 59 1.6 121 14 13 :9 .5925S10 65 18 35-3 3 27.53 - 4 58 26.7 - 14.33 59 2.6 . . 122 " Sept. 22 20 .8333333 179 10 45.4 8 18.85 + 33 20.3 1 4- 45-83 58 31.4 . . 123 22 24 .9333333 180 33 48. 5 S 17. 88 -f 40 57.7 ; + 45-59 58 27.9 ; . . 124 I70I,Aug.23 12 .5000000 29 51 8.5 7 9-26 - 5 2 58.4 ; - II-I6 54 16. I . . 125 ,. 13 12 .5500000 30 26 54.8 7 9-44 - 5 3 53.5 •■ - 10-84 54 16.9 12f " Sept. 22 17 50 5 •7431134 65 49 31-4 , 7 23. 48 - 4 49 46-9 i + '3-67 55 n-9 - - 1 127 i 18 36 24 .7752778 66 13 21.0 1 7 23.63 - 4 49 2.1 • + 13-98 55 13-0 - • 128 1704, July 2^ I 20 .0555556 78 II 32.3 ' 7 12.29 - 14 15. 1 , + 39.03 54 36.0 - . . I2( 2 32 . .1055556 78 47 32.8 7 '2.04 - 10 59-8 ' ■+- 39-02 54 34-9 . • 1 131^ 1705, Aug. 4 >5 14 37 .63.^1505 313 iS 20.6 9 3.10 - 4 43 34,4 — 13-65 60 52.9 • • <3 ! ■• Sept. 2 II 39 35 .4858218 334 36 37-7 9 "-Si - 4 58 22.8 ! -f 6.23 61 22.6 • • 13; i7o6,Jan. 23 11 4 I4 .4612732 64 28 16.4 ■ 8 4-38 + I 10 23.3 + .,1.60 57 49-6 . . 13: ) II 40 14 .4862732 64 48 27.7 i 8 4-20 + 1 12 7-3 + 41.53 57 48.8 . . «3- 1 " Jan. 27 11 22 33 .4739931 117 2 23.9 1 7 38. 50 + 4 35 26.8 + 15-90 55 53-8 -0.39 >3 , " Apr. 21 8 51 49 -3693172 : 143 36 o.g ; 7 18.52 + 5 12 27.8 i - 6.32 54 53.5 . ■ • 3< 5 , " " 9 45 24 .4065278 ; 144 3 13-2 i 7 'S-30 + 5 12 3-9 - 6-58 54 52.4 . ■ »3 7 ! " May 11 20 30 .84; 2222 50 15 43-5 1 8 55.10 + 31 40.3 -t- 49-21 60 39.5 . . 13 3 ' " 22 44 .9472222 51 44 50.3 8 54.53 + 39 51-9 + 48-9S 60 37.2 . . J3 1 i " May 24 10 38 30 .4434028 ! 212 34 39-4 1 7 8-44 , + ■ 5 40-3 ' - 38.59 54 >6.9 > . . 14 1 j " Nov. 17 II 48 5 .4917246 ' 23 58 34-0 8 58.96 - 1 3 12.8 + 48.64 60 56.5 , ■ - 200 RESEARCHES ON THE MOTION OF THE MOON. Greenwich Mean Geocentric Motion in Geocentric Motion in Motion No. Date. Time. Long, of Moon. oii.oi. Lat. ol Moon. O'l.OI. Parallax. ino'f.oi. 141 1707, Apr. 4 A m s 8 II 52 .3415741 43 25 40.5 8 56.18 + I 33 35^o + 47.32 60 44.9 " 142 " Sept. 3 7 37 33 •3177431 245 43 I6.4 7 6.49 - 3 51 23.8 _ 25.90 54 14.7 143 ii (( 8 25 45 •3512153 246 7 3.8 7 6.42 - 3 52 50.3 25.68 54 14.6 144 1708, Feb. 23 7 8 22 .2974769 359 32 41 •& 7 52.93 - 46 37-3 + 42.52 56 59-5 145 " Sept. 6 9 27 6 •3938195 63 53 15^7 8 17.34 + 4 46 48.5 + 19.23 58 28.1 146 " Sept. 13 6 30 •2708333 162 55 38.5 8 38.18 + I 26 22.1 45^98 59 39.0 147 " 8 54 •3708333 164 21 55.5 8 37.46 + I 18 40.8 46^31 59 36.2 147a " 18 30 •7708333 170 5 36.7 8 33.83 + 47 36.2' - 46.90 59 24.2 I47i 20 54 •8708333 171 31 8.6 8 32.86 + 39 46.8 - 46.94 59 20.9 148 i7og, Apr. 20 7 41 6 .3202083 166 46 1 1. 2 8 34.73 + II 9.0 - 46.68 59 33.2 149 " Sept. 16 10 40 .4444444 331 3 52.5 7 4. So - 51 49.8 + 38.69 54 0.8 150 " " II 52 •4944444 33' 39 16.3 7 4.84 - 48 36.0 + 38.76 54 o.g 151 " Sept. 23 8 9 II ■3397106 54 59 50.1 7 40.33 + 5 4 3^8 + 11.07 56 10.2 +0.42 152 " " 8 57 II •3730439 55 25 25.5 7 40.55 + 5 4 40.2 + 10.78 56 II.4 153 " Dec. 14 500 •2083333 54 30 10.7 7 54.62 + 4 57 43.4 + 6.96 56 56.0 154 • 7 24 •3083333 55 49 26.6 7 56.03 + 4 58 48.3 + 6.02 57 0.4 155 1710, Dec. 4 4 32 58 . 1895602 54 42 23.6 7 19.78 + 4 58 13.0 6.47 54 44^0 156 " 5 44 58 .2395602 55 19 3.7 7 20.14 + 4 57 39-4 6.92 54 45^1 +0.23 157 1711, Sept. 30 15 20 .6388889 55 35 7^9 7 6.53 + 4 35 39.9 15.51 54 4^8 ■' 158 " 17 44 .738S889 56 46 13^8 7 6.42 + 4 33 0.8 - 16.20 54 4-7 159 1712, May 15 II 6 58 .4631713 170 24 29.7 8 1.54 - 4 36 20.2 - 18.88 57 32^9 160 " II 46 II .4904051 170 46 21.9 8 2. II - 4 37 II. 6 - 18.73 57 34^4 161 1713, Dec. I II 49 4 •4924074 68 5 59' 5 7 46.49 + 53 38. 8 - 42.47 56 33^6 l62 1714, Mar. 20 9 6 39 .3796180 65 15 35^8 7 57.47 + 32 12.2 - 41^93 57 29.7 163 " Mar. 21 10 16 9 .427S819 78 55 26.1 7 J 1. 20 - 40 13.7 - 40.50 56 32.6 164 " Apr. 6 15 17 21 .6370486 278 55 14.8 8 7.33 + 2 29 27.0 + 38.01 58 2.8 165 II 16 30 36 .6879167 279 36 37^2 8 7.87 + 2 32 40.6 + 37^82 58 4.9 166 " Sept. 27 9 40 .3754630 61 49 47.1 8 20.36 - 4 38.7 _ 44.79 58 49^7 167 " Oct. 2 14 37 51 .6096181 129 8 26.9 7 16 14 - 4 45 8.5 - 14.32 54 43-6 168 1715, May 2 19 12 .8000000 40 47 52.7 9 3.46 + 51 30.0 - 49.54 61 7.8 169 " June 22 200 .0830000 337 38 50.1 8 16.84 + 4 54 41.2 - 13.94 58 23.0 170 " July 21 14 49 43 .6178588 9 59 6.5 8 2g.oo + 3 4 20.6 - 35.77 59 14^0 171 II II 15 42 30 •6545139 10 30 13.4 8 29.08 + 3 « 9.2 - 35^98 59 14.3 172 " July 24 13 28 39 .5615625 51 34 10. 1 8 26.88 22 52.3 - 44^78 59 10.4 «73 II 14 14 26 •5933565 52 I 1.6 8 26.81 25 14.5 - 44.70 59 10. I «74 " Aug. 15 II 46 34 .4906713 335 28 18.4 8 36.13 + 4 41 49.5 - 15.78 59 21.0 «75 II II 12 31 41 .5220023 335 55 16^4 8 36.20 + 4 40 59.3 - 16.26 59 21.9 176 " Oct. 9 7 55 53 •3304745 335 21 17. 1 8 34.69 + 4 47 33.2 - 19.04 59 24.3 "77 " Dec. 30 7 17 35 •3038773 335 58 5-1 7 59.02 + 4 32 20.1 18.98 57 20.4 178 1717, Sept. 25 8 53 38 •3705787 65 5 39-7 8 14.12 - 4 36 58.0 - 22.10 58 13.9 179 " 9 45 58 •4069213 65 35 35^2 8 14.53 - 4 38 17^3 - 21.82 58 14.9 180 1718, Jan. 15 13 24 33 •5587153 105 54.2 9 7.74 - 4 49 15-7 + 14.69 61 9.9 I8l " Fel). 9 6 22 14 ■ 2654398 65 35 40.9 8 12.80 - 4 53 48.8 - I5^I3 58 12.6 182 " Feb. 14 6 50 .2847222 139 19 12.4 9 10.12 - 3 4 I5^8 +■ 40.38 61 25.9 ■83 " Sept. 9 8 33 19 .3564699 347 " 19^2 7 5-56 - 5 15.3 - 39 39 5» 1.4 184 1719, Apr. 22 7 33 37 .3150116 66 20 37.3 7 29.35 - 5 5 i^i + 0.79 55 22.4 185 (1 II 8 23 6 •3493750 66 46 21.3 7 29.60 - 5 4 57-6 + 1.08 55 23.3 186 " Aug. 21 7 34 50 •3158565 231 6 30.9 8 26.56 + 5 15 17^2 + 5.46 58 59.1 187 '" Oct. 5o 8 37 27 • 3593403 65 12 51.8 7 16.36 — 4 56 10.8 + 6.91 54 33.3 RESEARCHES ON THE MOTION OF THE MOON. 20 1 lkt„ Date. Greenwich Mean Geocentric Motion in Geocentric Motion in 1 Parallax. ,""" in c ,j tion No, Time, Long, of Moon o''.oi. Lat. of Moon. ■".oi. •I .01. 18S 1719, Oct. 30 9 33 45 ■3984375 65 4' W^7 7 16.50 - 4 55 43-1 4- 7-21 54 33-9 " I8y " Nov. 26 6 55 20 ,2884259 61 14 15,9 7 1S.70 — 4 56 4-9 + 6.15 54 36-9 • i 190 1720, Apr. 20 12 15 ,5104167 186 10 58.6 3 57.19 + 3 53 48.6 + 29.71 60 41.3 4-0.20 191 " 12 43 48 ,5304167 186 28 53,3 8 57^37 + 3 54 48-0 + 29-57 60 42. 1 +0.26 1 1(32 " Dec. 31 300 , 1250000 3" 24 1.9 8 36.24 — 1 2 7.0 - 46- 58 59 38-3 103 " 4 12 ,1750000 312 7 1^7 8 35^52 - I 5 59-6 - 46-34 59 35-6 I'M 1722, t)ec. S 1 30 .0625000 255 58 21,3 8 20.94 + 41 39.6 - 45-88 58 38.5 l>)S 1724, May 22 5 48 .2416667 61 59 10.6 8 56.4* — 34 1 1. 6 + 49-28 60 44,3 igf. " 700 .29ir)667 62 43 51,6 8 56.18 + 33 18.2 + 49.20 60 43.2 ■g? 1725, Fell. 19 12 16 12 .5112500 60 8 2,4 8 27.28 + I 44 5.5 4- 42.23 59 13.0 198 1726, Jan. 18 700 .2916667 128 5 17.2 9 4.72 + 4 49 53-6 - 12.09 61 0.4 •99 " 8 12 .3416667 128 50 40,8 9 4-25 + I 48 51-3 - 12,71 60 59,0 200 1727, Feb. 27 & 52 30 .28645S4 53 56 22,0 7 46^1 1 + 4 12 43^3 + 25,52 56 41.5 201 " Sept. 6 13 4'8 .5750000 55 5 0.6 7 <32 , 66 4- 4 44 10,5 + 18.62 55 48.8 +0.41 202 15 00 .6250 42 .2791667 64 33 38,9 7 14-41 — 5 6 ii.o 4- 2.41 54 27.8 2I() 9 f) .3791667 65 46 4,4 7 14-99 - 5 5 42.7 + 3.22 54 29.6 +0,16 217 " II 30 .4791667 66 58 35^5 7 15-56 - 5 5 6-1 4- 4.03 54 31-4 4-0.17 218 ■• Fi'h. 2 b 8 35 .2559607 109 32 40,8 7 42.06 — 3 24 10.2 4- 32,26 56 15..0 219 " Auk. S 13 00 .54l')W)7 63 13 7-1 7 7-57 - 5 9 18.1 -L 8,51 54 11.8 220 15 24 ,6416667 64 24 21,8 7 7^6l - 5 7 48.6 + 9-33 54 11. 8 221 .. 20 12 .8416667 66 46 51.8 7 7^6i - 5 4 25.7 4- 10.88 54 1 1. 8 222 " Oct. 2 9 56 23.7 .4141632 65 41 42,6 7 S.65 - 4 54 25.3 4- 10.80 54 13,1 223 " 10 5& 44.3 .4560682 66 11 38,5 7 8.54 - 4 53 39-4 4- 11.09 54 12.9 224 " Dec, 23 5 24 32 .2253703 65 27 45,8 7 7.61 - 4 43 45-5 + ■5-23 54 0.7 225 " '1 24 33 .2670485 65 57 27,1 7 7^57 - 4 42 41-3 4- 15.54 54 0.5 225 reprint the observations in full; but we pi-esent the clock-errors resulting from the individual altitudes in the following table : — Imiivii/iial Corrections to Flamstcar s Clock, irs s^hrii h Altitudes, Dale. Greenwich Mean Time Coriec- tion. ' I! '" ' i + 12 4 ; Date. Gicenwich Muan Time. ("orrec- , lion. i tn s + 4 28 Dale. 1682, Mar. II Creenwich Mean Time. h HI f 21 30 4 1 Correc- tion. 1676, Mar. 18 /; m s 7 41 34 1676, .\ug. 30 20 12 2b 1 m s - 5 3" 44 II 12 I 1336 4 2O 33 5 3" • 47 41 12 6 14 45 4 30 : 35 54 5 24 Mar. 22 49 54 10 13 5') 12 4 + 4 12 Nov. y f, 4f, 51. 51 KJ - 3 40 1 3 42 : Mar. 14 II 37 2 23 - 5 42 5 42 17 18 20 43 3511 3 56 1 53 3' 1 3 41 ■ 4 25 6 32 5 43 5 44 23 10 3 58 ' 1677, Mar. (J 7 50 41 — 22 1O83, Fell. 3 6 13 24 - I 52 II 17 ly 3 47 j 51 56 23 "5 34 I 54 Mar. 24 7 57 38 8 7 29 + 4 18 4 14 53 "3 55 47 25 25 Fell. 5 17 44 9 5 4fi I 51 - 2 4| 8 17 12 4 27 Mar. It 7 20 - 7 7 54 2 4' June 26 30 5 23 28 4<; 48 28 5 2O 30 31 22 + fj II 6 16 6 20 + 8 47 8 46 I&7S, Oct. 28 7 "2 43 K) 12 22 27 2S 58 i - 5 51 ' 5 52 5 4^ : 5 54 Apr. I 10 1) 12 27 14 48 20 17 15 19 33 2 4 2 3 j 2 4 ! - 5 50 i 5 53 1 Aug. 19 3 3fi ') 33 27 + 5 43 5 44 • Oct, 29 II 25 5 28 22 - 6 II 1 - '' " fi 21 53 20 40 5 52! - 551 43 3 5 48 1O80, Jan. 1(1* 7 22 + II 16 30 20 5 - 6 I 20 25 8 + 5 23 27 15 II 23 M.ay 6 19 45 - 5 59 28 33 3U 51 5 19 5 15 ' 31 8 34 45 .125 j II 23 1686, \\ix. g 20 20 - S 34 35 31 5 18 . 38 9 i + II 21 20 20 - 12 52 1676, June o, 29.1 I, 5-6 * Clock losing alioul 32" per day on mean lime Clock-com'ctions for Fla.mstkeu's Ed'qms. -2 lo' 1 684, July 8, 5—4 28 1689, -I 46 12, 5 — 3 40 1687, May 6, 20.0 —12 25 1687, May II, 4-5—14 30 Sept. 5, 1.8 -f-i 29 Sept. 12, 3.9 -f-i 49 20.0 -\-2 5 RESEARCHES ON TIIK MOTION OF THE MOON. 203 Lonf^liidcs and Latitudes of Stars for 1850. Adoplfil <)lilii|uity for 1850, 23° 27' 3i".4. ' Name of star. Lon«., 1S50. 1 /,' /'I Lat., i"-o. j i B B" /'J t i iS Pisciimi .... 12 3 4.!>f> 5027.30 + 3-75 1 + 2 to 24.00 + 7-77 + 0.17 1 -- 7 - 33 " Pisciuiii .... 25 3S 41 . 10 5030.82 + 4-45 - I 37 54-1' + '7-45 + 0.14 - 7-7' I.alandc 4903 . /)' Arietis 44 4f) 28.02 5044.77 + 20.13 + I 10 34.52 + 0-95 -4- o.oS - 26. 88 B. A. C. 020 .. . t Ariclis 46 24 11). J2 5021.50 - 1-50 + 4 9 3l-fi5 + 37-45 + 0.08 — o.lS (i Arirlis 48 45 "0.1)5 5037.80 -+- 13-40 + I 48 35-3» + 35-01 + 0.07 - 3-75 Ariflis 49 51 '-50 5018.76 - 5-17 + 2 52 40.60 + 3'-99 + 0.07 - 7-27 / Taiiii 51 20 47-81 5028.22 + 0.40 - 5 55 55-7f' + 39-62 -\- 0.06 - 0.37 1) Taini 55 20 44.37 5020.02 - 2.80 + 3 42 22.55 + 35-94 + 0.05 - 5.62 16 ,(,r PIciadiim (Cclaeno) . 57 20 27.90 5023 . 46 — 0.21 + 4 20 58.47 + 36.30 + 0.04 — 6,01 17 // I'luiadum (Elcclral . 57 li) 04.12 5023.52 — 0.21 +- 4 10 27.23 + 36-29 + 0.04 - 6.01 m f'leiadiim .... 57 32 3f'.3f' 5023.20 — 0.20 + 4 52 3.00 + 36-37 + 0.04 — 6.01 i '9 (• Pleiadum (Taygita) . 57 28 14.20 5023.42 — 0.20 + 4 30 0-03 + 36.34 + 0.04 — 6.01 20 c PIfiaduin (Maia) . 57 35 10.4S 5023.47 — 0.20 + 4 22 27.82 + 36-38 ■ 1- 0.04 — 6.01 , 23 (1 Pleiadum (Meroiie) . 57 36 18.62 5023.63 — 0.20 + 3 56 24.61 +- 36-38 •)- 0.04 - 6.02 7 Tauri 57 53 53-58 5023.62 — o.ig + 4 2 6-9) + 36-49 + 0.04 — 6.02 27 / Pleiadiini (Atlas) . . 5S 15 42.32 5023.61 - 0.17 + 3 54 6-42 + 36.61 + 0.04 — 6.03 /( Plfiadiini . . . . 58 17 6.70 5023.68 - 0.17 + 3 58 55-08 -i~ 36.61 + 0.04 - 6.03 33 Tauri 51) 51 0. 18 5030.00 + 5-<>3 + 2 30 45-27 + 39-93 + 0.03 - 3-25 A' Tauri fit 21 28.80 5032.66 + 7-80 + I 14 40.04 ^ 33-68 + 0.03 - 008 53 Tauri 64 33 37-15 50^7.41 + 2 . 00 — !■ 56.08 + 38-81 4- 0.01 - 5-77 u- Tauri f)3 58 0.04 5010.68 - 5-7; - 46 3-73 4- 40-10 + 0.02 - 4-32 51 Tauri fi4 23 28 flQ 5033-50 + 8.40 + 10 23.27 + 3S-34 + 0.02 — 6.20 ) Tauri 63 42 22.34 5038.67 + 11.24 - 5 44 56-14 + 39 53 + 0.02 - 4-Sl 56 Tauri 64 42 2f).(lO 5026.36 + 1 .20 + 18 57.33 + 38-50 + 0.01 — 6.12 58 Tauri f>3 -18 36.36 5038.00 + 11.02 - 6 18 24. oS + 39- '7 ■t- 0.02 .- 5-21 V Tauri fif) 1 17.00 5027,84 + 3-5S +40 13.10 + 40-55 4- 0.01 - 4-30 »' Tauri 66 6 22.07 5032 . 00 + 7-81 + 36 38.01 + 37. .66 4- O.OI - 7-3' ^- Tauri 66 6 6.55 5035.08 + 10. 87 -1- 30 50-01 4- 36.87 + 0.01 — 8.00 70 Tauri 65 S 54.07 5034-35 + 7-f>5 - 5 40 14 05 + 40.8c + 0.01 - 3-92 71 Tauri .... 65 ifi 0-35 5036.06 ■\ 0-28 - 6 I 2.85 ■*■ 39-5' 4- 0.01 - 5-24 H. A. C. 1373 • • 66 36 10.67 5035 40 4- 10.21 - 4-80 + 36- 5f 4- 0.01 - 8. 52 1 f Tauri .... 66 21 58.47 5035.6, + 0-78 - 2 35 1-21 + 3? -7-1 + 0.01 - 6.10 (ii Tauri .... 65 51 22.57 5035 -30 + S.72 - 5 45 43-06 + ;o-4. S 4- 0.01 - 1-48 If- Tauri .... 65 5" 46. '3 5036.73 + 10.04 - 5 51 '0-42 + 40.7 + 0.01 - 4- '6 a A.c. 1341 • ■ 66 21 57.30 5033.81 t- 7-22 — 5 36 22.08 + 39-9 5 4- 0.01 — 5.10 (I Tauri .... 67 41 34.13 •5020.58 + 3-12 — 5 28 40.80 + 25.4 5 0.00 - 10.88 i r Tauri .... 70 3 34.50 5024.60 — 0.51 + 41 43-Si -t- 42-7 2 0.00 - 3->o' (1 Tauri ... So 24 6.36 5026.21 + o.oi — 1 18 30-46 + 45-2 5 - 0.04 - 1-77 Ill) Tauri .... St 18 3.38 5026.47 + 1. 00 - 4 42 10- '5 + 46-4 I — 0.04 — 0.64 120 Tauri .... 81 36 38. 28 5026.22 -4- 0.86 — 4 46 26. 7f + 47-4 4 : - 0.04 -+- 0.37 13(1 Tauri .... 86 25 24.56 5016.52 + l.io +49 44-95 + 46.0 2 ' — 0.06 — I .00 i i X^ Orionis .... . ' 86 42 50-3> 5024.11 1 - o.gs - 3 42 I3-3-) + 44-f 5 : — 0.06 — 2.36 : U Geminorum . . 88 51 7-05 5025. 18 — 0.06 — II I5.8f ) -f 36-f 6 — 0.07 — 10.21 3 Geminorum go 8 36.04 5025.07 1 - 0.14 - 10 34-4 + 45-' 4 - 0-07 - 1-7' Lalande 12148 • 1 1 ■ 1 i 204 RESEARCHES ON THE MOTION OF THE MOON. Longitudes and Latitudes of Stars for 1850 — Continued. /' Name of star. Long., 1850. /' /'I Lat., 1850. /r B" — 11-97 Gemiiioriim 93 12 18.48 5032.00 + 6.88 - 50 5.32 + 34-42 — 0.08 V Gotiiiiioruni QI 20 40. ql 5019-48 - 5.66 - 54 24.95 + 44-98 — 0.07 - 1.65 V Ceminonim Weisso II, lf)5f) 94 -12 30-93 5023.30 1.44 - 3 4 29.55 + 43-96 — 0.09 " 2.20 >. Oi'iiiiiioriim lof) 41 13.63 5019.62 - 3-74 - 5 39 4-(io + 37-54 — 0.09 "" 5.69 / Oeminoiiiin III 34 53.38 5022.17 - I.6i - 3 45 40-4' + 41-94 - 0.14 -1- 0-45 s Geminoriim . 112 5q 52. (J2 5017-39 - f'.77 - 2 39 43.70 + 33-82 - 0.14 - 7.10 85 Gemiiionim 114 57 20.30 5022.61 - 2.24 - 53 44.84 ■+■ 36-24 - 0.14 - 3-87 A Cancri . 119 43 15-34 5026.29 - 1.08 + 4 21 55.07 + 33-19 — 0. 16 4-72 it Cancri . 126 37 33-12 5029.15 4- 3. 87 +04 20.97 + 11.19 - 0.17 23.09 a Cancri . 131 32 49.20 5026.07 + 3-82 - 5 5 32-66 + 28.29 — 0. 18 - 3-12 K Cancri . 134 4 34-9■ Libra! . 233 2 25.27 5033.81 + 6.74 + 4 24 7.06 - 39.21 — 0.06 4- 1-42 !r Scorpii . 240 50 46.83 5022.08 - '-44 — 5 27 21 .05 - 43.53 — 0.03 - 5-04 ; /3' Scorpii . 241 5 43.84 5025.33 - 0.23 + I I 36.85 - 47.50 — 0.03 - 3-93 1 B. A. C. 5395 • 243 17 ig.io 5013.38 - 11.81 — 11 6.60 - 43-51 — 0.02 + 0.70 , 1 .) Scorpii . Sagittarii . 249 21 47.33 5024.37 -r- 0-55 — 6 6 1.12 49 99 0.00 — 4-30 , Sagitlarii . 281 21 19.59 5027.25 +- 2-44 -1- I 40 49.86 - 47-20 -1- 0. 11 - 2.41 : S.igiltarii- . 282 53 48.46 5030.00 + 5.00 -+- 52 52.20 - 51-68 +- O.ll . - 7-30 ^ TT Sagitlarii . . 284 9 28.01 5022.53 - 2.28 + I 27 24.42 - 47-84 + o.n - 3-83 : p' Sagittarii . . 2?7 21 25.77 5020.22 - 3-f'O -(- 4 14 26.80 - 42-93 + 0. 12 i + 0.08 ; /!'• Sagittarii . 287 19 4''-l'>3 5032. 85 + 8.87 + 3 47 '-6o - 54-20 + 0. 12 — U.17 33 Capricorni . 314 46 35.20 5022. 12 - f>.54 - 5 18 38.24 - 41.79 + 0.18 , - 12.41 ) Capricorni . 319 41 18.20 5043-47 + 16.61 - 2 32 35.89 - 30.24 + 0. 19 - 4." (^ Aijuarii 328 23 27.70 5030.25 -+- 4.81 1 - 16 28. f5 - 21.39 + 0.20 - 1-49 ' « Aipiarii 333 17 36-95 5023.39 - 2.79 1 '- I 13 13.67 - 18.11 -1-0.20 — 1-94 1 K A(|uarii 337 19 40-03 5010.35 - n.63 +47 8.56 - 21 .64 -1- 0.20 — 8. 62 i r' Afjuarii 336 30 1.80 5026.35 - 3-35 - 5 39 28.56 - 17-55 i ■1- 20 — 3-88 ; H. A. C. 81S4 . . 349 7 9-75 5035-12 + 8.95 j - I 7 49-10 — 33-16 + 0.20 — 28.66 NoTF..— These positions of the occulted stars are derived from standard catalogues are ruduced to the eical. excejit throu^ii each series. The ditl'erent .series are arranjied in the order of tlieir computation, as it did 1 it seem neee.ssary to run a risk of coid'usion in seeking' to make them more nearly clironolof^ical. 'i'he onlv serious displacement occurs in the case of Flamstkeo's observations, which, in strictness, should inmiediately follow those of lli;vr,i. us. The followin<>' are the only i)arts of the tabh- which .seem to need explanati( n. The data for local and (Ireenwich mean times have been already pretty fully o'iven, and, in most cases, the results are ^iven in precedinj;' sections, and are here simply copied from them. Small discn^pancies may be found in souh; cases, as the definitive discnssi \ Apr. 7 ■ 1641, I Apr. 13 j Apparent Position of Moon ami Slar. Longitudes, Latitudes. /■-/. M4 7 "S.d! +1-^ 34 25-8 4-0 27 ij.S 5 44 4 5 43 44 54 =4 14-8 o 20 33' . . . I +4 4fi 35-2 0- 42 I q o 21 ' 67 33 17.7 to 13 13' . . . ! +1 7 55.4 8 "3 4| 3 3 43 9 42 7 . . 144 39 4-1 54 44 5f)-'' 54 54 12.5 66 50 19.4! +0 36 9.7 — 99S.3 67 6 57.7 +0 40 13.4 - 243.7 63 13 57.0 I —2.28 30.91— 764.7 63 26 41.7 + 4 12 I5-<) - 555-9 + 4 o 49-7 + fi85-3 -2 36 23.0 + 472. .S" J} 938 .4 960.6 8S1.5 922.5 1028.6 838.2 898.0 © /.-0 86.3 58.4 279.2 '35.7 17.8 49-3 24.1 39-3 GASSENDUS. a Leonis, I. . [Digne.] ; Saeitlarii, L [Digne.J Mars, \. . . . [Paris.] j Mars, E. . ; Capricorni, \. . [Digne.] Pl.Electra,(/')L [Aix.] PI. Mal;„ {c) I. . r^l.Merope, (-OL 13 ! 1/ Tauri, I. PI. Merope, L jAix.l "5 '/ Tauri, I, [.\ix.] /i Geniinorum, L [Digne,] 1627, I June 17 1 1627, Sept. 18 1632, Feb. 5 1632, Feb. 5 1635, Aug. 26 1637, Mar. 29 I : 1637, ' M ar. 29 i 1637. I Mar. 29 ; '637. Mar. 29 1638, Jan. 24 1638. Jan. 24 . 1638, I Dec. 20 10 30 16 13 10 54 22 44 15 i3 12 21 15 47 12 50 10 5 3 10 29 20 15 9 >8 144 50 9 + 1 25 40 8 278 37 23 8 + 2 26 51 8 15 15 37 54 9 . . . *q 47 49 9 22 52 20 7 14 8 48 58 8 27 II 9 '8 49 9 22 9 52 9 J2 10 2 9 48 10 18 7 39 3 55 8 35 4 51 16 36 10 35 47 I 9 I o 43 : . . . I 21 9 10 34 30 9 27 7 7 17 47! I 10 , 8 13 23 42 i . . . 34 16 II 37 29: , . . 136 30 12.4 + 4 58 18.5 136 46 3.2 1 + 4 58 9-5 316 30 0.9 — I 26 9.6 54 54 41 -I + 4 38 53-2 55 14 58.4 + 4 38 II. o '55 20 43.7 + 4 37 59.0 55 30 38.3 +4 37 38.3 54 34 5-4 + 4 7 54-3 55 06 05.6 + 4 <■' 4-9 90 40 36.3 — o 15 22.0 144 24 50.8 I 144 39 41 277 59 43-8 I 278 15 14.9 j 136 14 12.2 1 136 23 41.2 136 27 35.81 136 23 25.3' 316 20 44.7 316 41 32. 3| 54 3 10.4 54 20 46.7 54 23 15,0 54 36 53-2 5429 6.2 54 38 I.I 54 39 20-2; 54 55 36-2! 54 23 5-6 54 39 3-9 54 45 30-0 i 54 S*) 38.9: 90 00 48. o 90 15 45.2 +0 34 51.0 +0 27 9.7 + 1 46 48.4 I 42 319 +4 20 32,8 + 4 33 30.6 + 4 18 16.0 + 4 33 30.6 — 2 19 36.7 —2 31 30.2 + 4 13 45,8 + 4 9 II-2 4-4 10 34.3 + 4 21 II. 6 + 4 9 37-1 + 3 55 8.4 + 4 7 58.6 + 4 o 50.5 + 3 49 '2-9 + 3 55 9-1 + 3 48 54-3 +4 o 51.2 -o 47 19-5 -o 51 18.4 - 853. + 4f'l- - 931. + 256. - 5fi9- - 777- 4- 250. - 914- - 887. 4- 713- -1056, + 274. - 8l8. - f>37. - 534. + 868, - 97f). 4- 428, - 958 - 356 - 668 - 716 - 897 4- 238 3 935 '4 3 970.0 1 903.0 5 965.4 o 945.1 8 ' 962 . 6 5; 944.3 6 948.0 6 982.3 5 11138.3 3 I 979.6 6 1088.6 2 '. 978.0 3 11035.4 977.6 1019.4 976.8 1063.6 .3 86.3 58.4 '75.6 102,7 316.6 179.8 '53-3 163, 9.4 45- 9.4 45-5 973 .3 304.9 109.7 2 i 1020. 3 9 I 972.6 9^ 979-4 .2! 979.2 9 ■ 928.4 304.9 iiio.o i 269.0 181.7 I *This local time should be increased by 2'" 23". See page 82. RESEARCHES ON THE MOTION OF THE MOON. Tabular Exhibit of Reduction of the Occultalious—Q.ovAmx^A., 207 HEVELIUS AT DANTZIG. 1 1 No. Star occulted.; Date. Local Mean and Sidereal Times. Greenwich Mean Time. 1 M J .a • Apparent Position of rt I Moon and Star. i i /.■-Ji - 993-2 I - 401.9 I 1 S' D © /-©, a Z ° s Loriv iludes. S Latitudes. i 1 17 « Tauri, I. 1644. Nov, 14 1 h m s h III s 14 50 9 '3 35 33 6 28 51 . • • 64 59 57-9 i 64 33 28.8 -5 50.5' 64 50 2.0 -5 36 ■4-f' -5 2Q 32.7 009.0 233.0 066.3 191. 8 1 i 18 a Tauri, E. . . I'i44. Nov. 14 15 50 39|l 7 29 31 : 4 3f' 3 <')5 38 3.4' fi5 4 39-"! -5 3f' 32-5 -5 " 43-5 f'4 5" 2.0 -5 29 32.7 f- ,S77. 0:1007.4 . . j - 419.8! 967.8 . . 1 ' ' 19 11 Tauri, I. 1645, Oct. 8 1 13 33 ()'i2 18 30J 2 44 4f> • ■ -1 f>4 27 23.1 f'4 33 49-9 -5 31 39-5 -4 51 50.4 fi4 50 40-4 -5 29 31-3 — I0I0.5 - 128.2 I 1 995-5 195-8 | 013.7 22q.O i 20 n Tauri, E. . if>45, Oct. S 14 43 '3 28 44 3 54 51 - • • I <>5 9 57-4 ''5 (> 45-1 -5 27 53-" -4 5" 37-9 f'4 5" AO.'\\ -5 29 31-3 + 964 -7 - 98.3 996.2 . . ' 965.2 . . ! 21 H. A. C. 920 . . 1656, Mar. I 8 34 45 7 15 3f' 7 20 () 44 7 19-2 43 25 48.1 -+-4 26 39-9 -h4 54 8.1 931.4 341.6 . . 1 62 i 22 53 Tauri, 1. . . 1 1058, Oct. 14 II 6 55 41 15' 9 52 19 61 25 40.1 61 42 17-8; -0 30 3-0 + 8 f).o f)I 53 43-8 -0 19 II. — 68fi.o| - 652.0 ; 893.0 '202. 5 946.4 219.4 23 ,j Scorpii, E. . 1660, Apr. 26 14 38 37' 17 I 22 13 24 I 238 38 45.5 23s 4" 1 1 -4 -f I II 54-5 + 2 8 20.5 238 27 14.5 +1 3 <•■- + 77f'-9 + 527-8 964.3 37.0 j 939.2 201.4 24 (I Virgiuis, 1. 1660, June 17 to 56 25 16 43 35 9 41 49 199 33.4 19S 54 19-0 -2 11 23.9 -I If) 33.4 199 (> 31-7 -2 I 43-8 - 732.7 — 580.1 927.7 1 87.0 934-4 112. I i 25 71 Tauri, 1. . . 1&63, Mar. 14 9 39 25 9 8 57 8 24 49 03 S 12.9 62 26 29.5 -5 51 7-f> — 5 14 0.6 O2 39 18.3 -f' 2 20.5 - 768. 8 + 672.9 9S0.4 354.0 1018.5 07.1 1 1 j 26 W Tauri, 1. . . 1663, Mar. 14 10 32 7 10 I 48 9 17 3" O3 39 46. f. fi2 5f' 45-4; -5 53 19-2 — 5 14 21.2 63 14 54-1 ; -5 52 37.4 -1088.7 - 41-8 978.3 - - I 1083.8 . . 1 1 27 y Tauri, 1. . - 1663, Mar. 14 10 35 7 I 10 4 48 9 20 31 i ' ■ ■ 63 4! 34. S 62 58 32.1, -5 53 27-f -5 14 22.4 63 14 33-0' -5 !7 0-5 — 960.9 - 387-1 978.2 . . , 1031.3 i . , 1 28 f' A(iuarii, I. 1663, .Aug. 18 9 15 37 19 4 4 1 .811 ! . , . 325 32 21.2 325 3') 9-8 -0 26 21.9 +0 25 5.0' 325 47 37-1 ! -0 15 47-5 - 687.3 - 634.4 924.2 145.6 j 935.2 180.2 1 29 • f' Aquaril, E. 1663, Aug.:8 10 5 31 19 54 6 8 50 55 325 59 "-5 325 57 8.2 -0 27 59. C + 02525.9 325 47 37-1 ' -0 '5 47-; '+ 571-I ;- 732-1 1 925.6; . . I i 928.8 1 . . .! 30 1 Tauri, 1. 1664, Mar. 31 9 24 20 Uo 3 51 ',8 9 44 1 65 31 39-9', f'4 49 3f'-S; -5 34 27-5 - 9f''J-4 -45542-3 f'5 5 43-2 -5 29 29.7'- 297.8 1 969.8 ' 11.6 ! 1007.2: 53.5 ; 31 (I Tauri, E. . 1664, Mar. 31 ! 10 16 t . 10 55 4! : 9 1 3U 1 b(> 2 S.9 652018.0 -5 35 55-2,+ 874.8 -45458.5' f'5 5 43-2 -52929.7-385-5 .967.8^ . . 1 1 952.3 - - 1 , 32 Not identified 1671, Mar. I. 19 3 3-1 \ 8 33 I ii 7 43 5f ; ) • - 4ft 30 41.8 45 43 50.9 +3 2 55.8 . . + 3 35 38.8 ' - 989.0 J354.O I . . 1 52.3 1 33 Not identified 1671, 1 Mar. I 1963 >.' 8 36 I ?^ 7 52 4f' 32 33-2 45 45 38-2 +3 2 57-3 + 3 35 4f>-3 • 988,91 . . ' ' " " i 34 Not identified ! 1671, ' Mar. I ! 9 55 2 4 9 25 I 5 8 40 4 5 • - 3 47 2 12.4; 40 15 0-5 +3 2 29. + 3 37 46.4 . • "I • ■ • 4 j 986.5 . 1 2o8 RESEARCHES ON THE MOTION OF THE MOON. Tabular Exhibit of Reduction of the Occultations — Continued, L_ HEVELIUS AT DANTZIG-Continued. i 1 1 INo. 1 1 1 Siar DCciiltrtl, nalo. i Local Mean and 1 Sidereal Times. Greenwich Me? Time. Moon's Tabular Geocentric Position. Apparent Position of ' Moon and Slar. /* — /, , *-* I.o[rgitU(k-s. 1 Latitudes, 5- i 35 (I ViiHinis, I. 1671, h in s 10 47 I i h m s 9 32 25 198 4n 21.9 199 50.5 -2 5 5.2 - 897,6 88g,4 — — - 32.4 i .•\pr. 22 12 50 45 . . , — I 21 22.1 199 15 48,1 -2 I 4f'.4 — 198,8 918.7 166,9 30 n Virgitiis, !■]. 1 67 1 , ! 11 5& 30 10 41 54 199 14 31.7 199 26 19,6 -2 II 39.2 4- 631.5' 889,1 ' 1 Apr. 22 14 26 . . . — I 24 22.7 199 15 48.1 1 -2 I 46.4 - 592.8 1 865,8 • • 37 I'l.Ccl., 16,4', I lf>72, 12 36 33 II 21 57 54 47 10.4 54 37 f'.jj +4 28 33.6 _ ,,2;. 7 l(X)4.S 223.9 Nov. ;; 3 4" 15 . . • t 4 57 574 54 52 32.2, 4-4 19 54.1 ;+ 5iq.5 1059.5 191-5 i38 I'l. Tay., 19 .■, 1. 1672, 12 4S 18 II 33 42 54 54 37.2 54 42 42.<>, +.1 29 2. oi— 1056.6 1004.7 , Nov, 5 3 52 s i . • . + 4 58 3.0 55 i3.6 4-4 29 4.6 - 2,6 '1053,4 39 PI, Mala, 20,-, I. 1672, 13 7 4 II 52 28 55 (J If). 2 1 1 54 51 39.7i +4 29 45.2 - 935.1 1004.6 . Nov, 5 4 10 51 . + 4 58 11.9 55 7 14.8 -t-4 21 23.3!-)- 501.9 [05S.3 • . 40 PI. Tay., I.J,-. 1. X'73, S 5 H. f) 51 I" 55 3" 31.7 54 49 24.9 -f 4 41 21.0 — 640.8 9f'3.3 2.5 ! Mai. 22 S S 51 , . . + 5 10 52.8 55 5.7 +4 29 6,0;.)- 735.0 974.5 52.5 41 PI. Tay., IS w, I. "f'TJ. S 8 4f) •■ 54 I" 55 32 15.8 54 50 58.8 +4 41 13,4 — 8()S.5 963.2; . . Mar. 22 S II 53 . . . + 5 10 53.0 55 4 27.3 +4 51 0.2 - 586.8 1 99f'.5 • ■ 42 I'l. .\51., 21 /•, 1. ■ C173, S 19 4C) 7 5 10 55 38 36.3 54 56 44.8 +4 40 45. oj- S31.2 962. 8 .Mar. 22 S 22 54 + 5 I" 53.4 55 10 36.0 44 32 5,1 + 519. y 978.2 . . ■••' PI. .Asl., 22 /, I. ■ '■73. S .24 4f) 7 10 10 55 41 29.1 545922.7 +4 40 31.1 i- 7f'4.5 9f'2.7 • • I Mar. 22 8 27 55 + 5 10 53. fi 55 12 7.2 +4 30 6.oj-t- 625,1 9S5.8' . . 44 PI. Kk-c, 17/., I. 1674, 13.41 29 12 26 53 54 20 22. f) 54 37 12. S +4 3 26.01- 907.3 923.4 150.6 Aug. 23 23 51 42 + 4 42 5f'-3 54 52 20.1 -1-4 9 24.4 - 35S.4' 973.4 264.3 45 1 Pl.Ccl.. 10^,1. lf'74. 14 8 59 12 54 23 54 34 48. 2 54 49 36.5 +4 4 38.5 - 247.4 9244 . . 1 ! Aug, 23 19 I& + 4 42 23.0 54 53 43.9 +4 I'J 55.9 - 917.4 949.5 . . 46 , PI, M.-i.,23./, I. ■f'74, 14 25 59 13 II 23 54 43 43.'i 54 56 5f'.3 +4 5 22.6 |- 758.3 925-0 j . . i AiiK.23 36 19 + 4 42 2.5 55 9 34-6 +3 55 22.1 4- 600.5 965.8' . . 1 , 1 47 PI. Cel., ifi^', E. if'74, 14 32 29 13 17 53 54 47 9.2 54 59 5f'.7 +4 5 42.6 + 372.8 925.1 : •■ . j 1 1 Aug. 23 42 50 + 4 41 58. 2 54 53 43-9 +4 19 55.9 - 853.3 929.0 j 4S ' PI, Maia, 2o,', I. 1674. 14 43 59 13 29 23 54 53 10.9 55 4 53.7 +4 f' 10.91- 212.8 925 . 5 ; Aug. 23 54 22 . . . + 4 41 44-0 5; S 26.5 4-4 21 25.3,- 914.4 938.4 1 • ! 4'J PI. Elcc, 17 /', E. If'74, 14 51 29 13 3f' 53, 54 57 72 55 S 6.3 4-4 6 29.2' 1 946.2 925.7! 1 1 Aug. 23 I I 53 • • ■ , + 4 41 34.7 54 52 20.1 4-4 9 24.4 . 175,2 959-8 . . 50 Pl,.\Icy.,25;;,T, ■''74, 15 I 29 13 4(i 53 55 2 22. f) 55 12 21.3 4-4 6 52.9 : 888. 3 926.0 j * ' 1 Aug. 23 I II 55 ! + 4 41 221 55 27 9.6 4-4 I 4.1 + 348.5 952.2 1 • • 1 51 PI. M.iia, 2or, !■:. If'74, '5 4 29 13 49 53 55 3 5f'.5 5? 13 3f'.5 +4 7 0.3 4- 310.1 926.1 \ 150.6 i A ug. 23 I 14 56 + 4 41 18. f) 55 8 26.4 4-4 21 25.3!- 865.0' 918.4' 264.5 52 PI. McT., 23 ./, E. If'74, 15 16 49 14 2 13 55 10 25.3 55 18 47.0 4-4 7 28.2 4- 552.5 926,4 . ! .\ui'.23 I 27 IS + 4 41 3.3 55 9 34.5 +3 55 22.1 4- 726.1 9tl,6 ■ '1 UI.SI,\K( lll> i)N nil. Mol'loN or Till, MOON. 7U/'ii.',ii l':.\hilnt oj Kcliulwfi i>j t/if Odiilln/wns—ViMwwwA. iii;vi;i.ii;.s at nANT/i«-r,)ritiiimd St;il CM illlllll. D.lll'. 3 U . ;2 S .2 ,, U .ui'iii I'liiiiiod of Mi)i>ii .111(1 Siar. LiiiigiliKli's. l.alitiKk'S. /. - /I aoy .V /,-0 53 I'l. Al.\,,3; V, K. 1(174 I A UK. 23 54 "'''■ |aii. II 55 85 (iciniiioiuiii, I. I'i75. |:in. II 5(j Aiiiim mills . . Hi??' Jan. II 57 85 Cfiuinuiiini, K. i'i7-' jail II 58 .Mars, 1. . . . i''7f'. Aiii; 31 5<> .Mars, I-:. . . . i<'l''. A 11.1?. 31 60 H, A. C. I7M? . '<''*'■ .•\ii,u;-3> 61 K'?-*. Mar. 28 f'3 (>^ f>5 fifi (>7 ()8 (>') 70 1 (Jiinnis. I. . 'i' Lilii'.c, 1 .;-■ I.iliix, 1. . d' l.ilirx, v.. . „■ I.ilila-, v.. . Ju|iiUT, 1. Iiipiter, K. I> Sagillarii, 1. Ifi7i^. Mar. 2S 1(171). Mar.2ij 16711, Mar.2() i''7'}. Mar.2<) i''7'). Mar.2(j I (.79. June 4 li'7<). JUIR' 4 1(171), 1 11 no 24 // /u s 1(1 ■> 24 2 II) I S 8 32 3 33 45 8 43 2 4 8 21 5 5) 7 4 2( 2() ') K' =2 4 42 l(' 13 34 33 18 2U 14 45 4S 1 2ij 46 14 52 54 I 3(1 54 7 37 52 8 3 43 y 22 52 ') 4'i " 14 50 30 15 2U 31 '/ /// V 14 53 4i> f) M ■■,'< 7 25 2() 7 44 3' S 2 1(1 12 I') 57 13 31 12 13 3'> I''' (1 23 111 "3 35 54 55 37 3'" + 4 3') 59-3 111 30 48. 8 -o (1 15.5 I II 51 1.7 -.1 8 7.7 112 027.5 — O () 0.0 55 3') 53'> +4 1) 12.2 t- 7(13.(1 55 27 1J.4 +4 1 4-4 + 4S7 S 113 (131.2 -u 31) 22. I 112 23 4().u — 4" 1 1 .S 112 31 Ml. 4 -o 54 4S.7 112 31 41.5 —1) 40 40. 5 447-4 87(1.1) 1)27. '1 . . <)f>4 . 5 • • i)74-" 21)1.4 . • 17')-') 1)74 5 • • 1,84.5 • ■ ')75.') • • 112 10 5 1 . 8 -i> ') 57-7 77 2f) 45-4 -o i> 11,. 3 78 I 52. 8 + 1. 6 12.7 78 5 22.7 + 5 54-1 S3 41 30. S -3 7 41.1 112 41) 15. J -n 41 Id.? + 53')-" ')7(i.5 • ■ 112 31 1(1.4 -I) 54 48.7 +- S12.2 i)7|.7 ■ ■ 77 53 31 ■" -->J 3' " " - y3--(' ''i)5-? l5')-3 78 11 3.(1 -o 28 U.4 - 1311.(1 (,41.0278.1 78 24 51.: -o 2., 33.1) f 873.(1 78 10 18. 1 —0 27 57. I - (,().8 73 27 5(j.3 -() 21) 31,2 . . 3(,7.l) S78.8 8()7.S S3 11, 58.1, -3 41. 14.2 1,14. '•3 75-4 14 58 10 13 43 34 15 28 13 ■ ■ ■ Id 10 14 51 34 If) 3(1 23 . . 1(1 14 4; 1(1 44 5') 1(1 ifi (1 21 1(1 311 4; 15 " ') 15 I 30 84 35 17.1 -3 11 3'i 221) 1) 52.1 +■1 (, 1.5 220 13 44-3 1- I 1) 22 . 4 220 48 4.1) + 1 12 28.0 220 52 25. S I- I 12 51.3 3(1 I 4.0 -o 17 51,. 6 84 4 44-3 -3 47 33-1 - 851. S 84 18 51). I -3 43 31 ■? - 241. (■ 220 II) 2(1.0 +0 iS 42.2 — 854.4 220 33 40.4 +0 24 12.5 — 330.3 220 22 18.5 +0 IS 4(1.7 — 83().3 2i(i 37 4.S +0 22 27.(1 — 220.(1 220 \i (,.5 +0 i(, 5(,.5 + S(i().i 220 33 JO. 4 t-o 24 12.5 — 253 " 220 51 2(,.2 -to 20 11.4 +- S(.4,4 220 37 4.8 -1-0 22 27.(1 — 13'i.2 30 K, 1.4 —111 57.0 II Sagillarii, K. . i(i;(), 1 11 (If 24 17 14 22 S 51 I : (. I S 17 i3 42 II 47 5 17 5'J 3*' 15 4') 41 I) 51 42 10 32 2() 3" 38 43-3 — 021 !<-() 2S4 41 24.5 + 4 57 3(J-') 2.-5 4 5'>-" t- I 57 58-') 254 50 22.3 -1-4 I 5i).7 284 5(, 8.5 -t-4 "5 40-2 255 8 8.5 -^4 2 1(1. 1) 284 51, 8.5 +4 15 40-2 1,1 1.(, . . 886.5 . . ()0 1 . 1 3 . (, (,16.4 211 .(1 ()0 1.1. (,13.2 . . (,00.5 . . (,05.3 . . 1,00 . 6 . S75.0 . (J7i)-i; 73 -'J . 3if).2 (,81.8 . . - 526.2 - h2().5 Jf 540.0 - S03.3 955-' ")3-" f)74-5 ")'-7 1,55.1, . . ,,67.2' . . -75 .\i'. J lU kl SI.Aki Ills O.N llll, MolKiN or llli: Moon. '/'ii/iii/iii h',\liil'il Hi kiilinliiiit ,ij till OiiiiltiUiims — (■ iiIumI, Til II TaiMi.!-:, 75 Mc) rauii, 120T; 77 ii:,n IIEVKI.IUS iK ll.\NT/l|>.M('III I'cisiiiiiii of Dale v! H /; III •t. V '7 MiMiM .iri.l Slar. LonKitiidi'ii. , Laliuulvii, /( III 1-1. \ .S" I h'-li ' I) /.-© l()Sl, Jan. 1 2 30 ij 1681. S 51 17 Jan. 1 ! 3 31J 20 7 42 IX 6 27 41 fM 53 53.2 fi5 2 4:'-a -5 2fj 08.8—1046,911005.4 . , [ -4 45 23.'.' (if ao 14.1 -5 20 22.7 t- 193,1) 1060.0 383. a 143.7 7 3'i 4' ''5 3f' 5'.3 <'5 3'' 23-4 -5 34 4"-4+ 969.31006.5 -4 46 35.7 65 20 14.1 —5 29 22.7+ 28i.3'l(x)5.o 1683, 9 56 ? 8 41 32 65 19 27. i] 65 4 42.4 -5 28 57.0-1031.81 968.3389.9 Jan. 9 1683, Jan. 9 5 i( -4 54 29.8 65 21 54.3 -5 29 a3.<>i-t- 25.01025.7135.4 II 9 23 9 54 47 '''1 ' 43-3| fiS 37 '7.1: -5 37 0.8 . . . -4 53 6.6 65 31 54. 3I -5 39 33.0 6 27 1683, I 9 58 20 Apr. 2 |i() 43 27 8 ,3 44 ■9 l'> 42.7 7S 41-) 7-4 -4 43 3<'."- -4 3 47.7 7» 58 17. 1&83, Apr. 3 1083, Apr. 2 10 31 5'' 2u 30 79 36 49. I! 7''' 5') 55-91 -4 43 35-5 -4 44 ^'S ,+ 'J32.9 967.9 + 141.3 1 928.6 — U189.6 g3<).7! +• 5.5 1086.2 — 1016. 2 938.0 13.3 66.0 133 10 58 10 9 43 34 M 43 27' . . . -4 2 42.(1, 79 16 52.1 -4 47 46.1 t- 2I9.3'I036.7 66.3 79 49 35"; 79 '2 5<'-u -4 44 3U.8+ 879.0; 937.8 . . -4 2 1.7: 78 58 <7.ul -4 43 35-5- 55.3i 878.2 66.5 TIIK CASSINIS .\.\l) OTllKUS .\T TllK I'AKIS OMSKKVATORY. '■% I r Scorpii, I. . I ! 79 85 Ccniiiionini So t' Lt'onis, I. . 81 I.conis, IC. 82 S.iiiirn, 1. 83 Saliirn, E. S4 I.alandu 1214S 85 86 J Tuiiri. 1. ," (".cininoniin, I. 1(172, 10 27 42.(110 iS 21.(1! 24(1 54 51.4 246 38 9.8 Auk. 2 "J 'f' 4'-'J ■ • • I -5 '3 26.2 246 53 25.3 1675, 8 18 iS 8 S 57 I(i7(>, 10 32 iS 10 22 5 Frii. 29 9 10 19.4 . 1676, II 29 24 II 20 Fel). 29 10 7 34.8 . 1678, 7 30 21 . . Feb. 27 6 2 1.3 . 1678, 8 42 21 . . Fel). 27 7 14 13.1' , 1680, 10 27 43 Uo 18 2 Apr. 4 II 23 50. 4I . . 1683, 12 13 50.6 12 42 Feb. 5 9 18 43' 5 • 16S4, 9 34 17.8 9 24 56.81 90 28 46.1 Ouc. 21 3 39 24.7: . . . I -o 39 6.3 112 14 47-4 02 53 11.7 — o 10 19. f 112 31 16.4 169 3 17.2 169 39 32.0 -4 5f> 59.7 'f") 5' 53-4 1O9 37 3J.(), 170 5 52.1 -4 57 3" 'V 'f") 5' 53.4 I ''J 4" 5<>.7l f>3 "7 51-9 - 1 iS 24.2! . 64 18 21.3 63 4() 19.3 -I 21 36.7; . . . . -6 4 47.5 -6 4 35.0 -o 38 25.4 -o 54 48.7 -5 3" 38-7 —5 42 13-4 'Jl5-5 887.: 12.5 910.. . .| 974.» 130.9 1 16.0 291.4 180 741.4 9S1.1 1340.8 + 694.7 'o'3-: -5 34 4'J-8 + -5 42 12.7 + -I 43 27.7: 838.7 983.' 445-9! 'J4^-' I <)25.< 3 11.3' 90 45 12.1 -1 47 15-8 -5 55 I7-fi -5 15 >3-5! ! 9.6' (11 55 11.7 -5 3 26.; 87 j // (.Jeiniiioruni, K. 1 16S4, 10 8 1.0.7! 9 58 49.7' 90 46 35.' Dec. 21 4 13 23.2: -o 37 31-4 fjl 10 41 .'. —5 35 1.2 61 22 22.1 , —5 46 4. I + 90 511 17.:., -I 5 55.1 90 -:4 17.'! -'J 51 2.4 1)1 3 8 . r - 1 315.3 ()o 54 17. S -o 51 2.4 700.8 662 . 9 - 240.5 923.; 963.4 943-0 962 . ^ 91 1. J 892.7! 924.1 530. 3j 912.1 732.9 904.5 189. 1 16.0 75-4 317-4 104.0 271 .0 179.9 Ri;si;.\uriii:s on nil. motion o|' iiii; moon, 'JUhiilar I:\IiiIhI oJ Kfifuitn'ii oj Hu- a,////'///'"/!— loiiiiiuicil 311 ITIK CAS'-INIS ,\N|l 01III;RS .\|- ITII: I'.\UIs OllM'RV a iokv ( 'lllltitlUI'll. ' ' 1 n 8 is. .\|p|i;iii'tM •iisiiiiui 1 f No. Still' itcciillt'd. D.iu-. Local Mian Sidereal Ti "■ '* ^ 5 - MiMJM ,iinl Sllll, LDiiKitllilts,, l.;iliniilrs. J : /-0 8» H. A. C. 357<), 1. lliHIi, // m » ') 55 3 // til V ') 45 41 UD 2" 4'i." I4'l 2 3' t4 18 5,, 1 - 75'i.l 8.)5 () ()4.'i June 85 If. IS 34.3 . . . + 5 8 3''.l' 14') 14 3».2 14 27 38.4 - 51'). 3 1)15 4 VI. (. g() B. A. r. nos K.Sf), 23 5f' <) l.» 35 2»o 53 20.4 241 3 45.7 -0 f) 3.2 (- 1(14.7 ')88 3 1(11 .3 July 1 16 7 5'J"' ■ • • t 41J li\.) 241 I I.I) -0 .) 55.5 t- 235.3 • . 13')- 7 QO \V. II, if.5'' . • lfi.8'), , IJ 38 37 May 31 113 39 II. 'J 1, 2.) l(. ■ i(«. r7 3.6 1-5 7 3"" W 42 8.1: — 4 2(1 42.3 . . i)S(i 2 'a. 1 . 3'^ ')' iifi Taiiri, K. Ifiqo, 11 38 Ifi II 23 55 85 7 2.1.7 84 23 5().( + 4 27 3').; . . ()8(i 3 24.4 Apr, 13 13 8 2|.2 + 5 12 5'i-4 .84 II 23.8 + 4 8 32. (> • 51) ■8 1)1 87 'riiiiii, 1. . Kiijo, 15 8 2() 14 5'J 3 55 17 4*." 55 4f' 38 '5 + 3 4f' 34''* - (j2(.i.7 ij)l (1 KlI .3 Inly 2 21 54 3'i.'l • • • + 4 34 51.2 50 I 53.3 + 3 53 7.1 - 3')2.3 l'>"7 (13I4.7 1 • j I 95 ! 96 I I ^' i i 98 99 93! «i Taiirl.I. . . I&83, 7 13 52.2' 7 4 3I.2| Feb. 15 4 ;8 1S.5 . . . i O'Taiiri, I. . . 1O82, 7 1(1 172 7 ^' 5f'-2 l-'cli. 15 5 (1 43.(j . . . /i (Jcmindinni, I, 1(184, () 34 ")-2 ') 24 58,2 Dec, 21 3 3() 26,1 . . , // (iLMiiinonim, IC. 1684, 10 7 58. 3 () 58 37-3 Dec. 21 4 13 II'. 8 . . . II Gemiiiorum, 1. i'i85, 'J 3* 4')" ') 2'j 28 Oct. 17 23 2fi 43.3 ... nTaiiri, I. . . ifxw, 13 44 4i'-8 13 35 'O-^ .\iig. 18 23 35 IJ-'' ■ • ■ aTauri, E. . idyi), 14 22 .|(i.S 14 13 ii).S ' Alls 18 (1 Tauri,!. . . I7i'i. 17 59 25.3 17 5o 4-3 Sept. 22 6 fi 41'- 8 - n Tauri, E- . . 17^1- 1845438183(122.8 Sept. 22 h 53 (i.ij . - Jupiter,!- . . 1715, 13 38 38-3 '3 2.j 17-3 Jill)' 24 Iupiter,E. . . 1715, 14 15 3-814 5 42-8 J"ly24 B- A. C. 8184, I. I 1718, 84244-' 83323.1 I Sept. 9 19 :(i 45^ ■ • 103 104 I.A HIRE. (>3 27 54. ('1 -5 17 4"-i| (13 13 44-5 63 30 34.7 -5 48 7-9-l'^l'->-2 -5 4(> 53-"- 74.7 973-3327 7 1008.2 95.8 63 29 18.8 -5 17 40.(1 63 14 45-8 (■>3 3" 55. f -5 48 4-8- 970-0 -5 52 31.8 + 2(17.(1 973-3 - • 1001. 3| . i ()(i 28 4fi.5 — 39 6.21 90 JO 17. 8, (JO 54 17.9 -1 5 55-1 - 2|0.1 -0 51 2.4 — 8(j2.7 911. 4 924.2 271 .11 17')') 9" 45 58.5 -11 37 31.5 91 3 7.4 9" 54 17 9 -I 315-3+ 529-5' — (1 51 2.4 — 73211 912.1 (J04 . 2 85 44 7-8 + 26 5(1- 1 86 18 38. 8 8fi 33 49-3 —I) 12 22.5 — 910.5 — 12 1(1.2 — (1.3 889. 1 205.2 910 5 241 .3 (14 56 17-2 -4 57 48-5 (15 25 52.2 fi5 35 3<>-3 -5 42 42.0- 578.1 -5 29 17.2 ■- 804. 8 (J72.5 146.1 (J89.5279.5 (■15 i3 35-8 . -4 58 2(1.7 65 4(1 3-1 (■15 35 31)- 3 -5 41 1S.4 t- (132. f -5 29 17.2 - 721.2 974-3 . ■ 957-4 - - fi5 49 34-8 -4 49 4(1.9 f)5 27 50.1 (15 37 27.4 -5 "7 15-4 - 577-3 — 5 29 1(1.8 + 721.4 914-3 i7')-5 922. 5 i*.i6. 1 6(1 13 21 .0 -4 49 2.1 (15 45 3'>-(i (15 37 27.4 -5 !(' 33-5 + 483.2 -5 29 1(1.8 ^ 763.3 9l3-( - ■ 902 . 2 . , 51 34 38.5 — 22 54.8 52 I 38.4 -I 12 28.8 . . 973.0 121. 1 . . 2(JO 5 51 55 54-5 (J74.; . ■ -0 24 47-4 347 <> 21-4 — 5 15-' 347 8 35.4 ' 347 '7 20.5 1 -0 55 5-1 - 525-' -I 7 6.3 h 721.: 888. 7 166.6 891 .() 1S0.7 i : 1 2 * RESKARCHES ON THE MOTION OF THE MOON, Tahilar Ex/il/rt of Rediutioii of f/ir Ortii//atlons — Co\\{m\M:A. CASSINI, ETC.-SERIESII . | N(i. j Star occulieil. Local Mean and Sider'.'al Times. (Ireenwich Mean Time, .2 S - ■ .Apparent Position of j2 S .= .Moon and Star. 1 1 /■-/. : .V /,_/,■ /) /,_0 ^ Longitudes Latitudes. ! i ^ 1 I // ni .' // HI s ° „ ro5 33 ('a|)ii<:orni, 1, 1705, 15 23 5S IS 14 57 313 'S 20.7 312 34 t?i).fi -5 30 7.4 —696.2 99S.2 . Aug. 4i 17 44- ■ • • : -4 4S 3I--I 312 a'' 5-? - S '7 37-' — 719.S 1021 . 1 . lijf) i r A(|uarii, I. 1705, ill 4S 5'i 1' 31) 35 334 3''' 37-7 334 >5 32. & -5 4<) '7-5 -837.31012.1 . i Sept. 2 22 36 27 ... —4 5S 2..? 334 2Q 30.1 —5 3() 2.1, — 614.6 1035.3, . 1 107 r .\(|uarii, I". 170;, 12 50 II) 12 40 5S 335 15 ,10. 1) 334 45 11. -S 44 2S.C + 940.9 loi 1.6 . 1 Sept. 2 23 3S 0.3 ... -4 57 5f'.- ■'34 2q 30.1 -5 3q 2.1) -325.6 991.3 . liiS (,' -laiiri, I, . . I7i;fi, II 13 34 II 4 13 ' 64 28 ili.o (,3 53 56. c +0 45 20.2 -713.9 956. 8 . Jai, 23 7 24 46. c . . . , +1 10 23.8 64 5 50.4 +0 35 44.8 + 575.4 916,.'. , 11)1) ' f'ani-ci, I, . . i7of., 12 31 ;t 12 22 33 117 34 14.5 117 21) 5(,.4 +4 12 Ii.c) -784.7 927.4 . Jan. 27 8 51) 5.0 . . . +4 3ft 33.1 117 43 4.1 +4 21 7.4 -535.5 94S.2 . 1 III ' // I.fclllis, I. . I7of), g I 1) 5 51 48 143 3fi 0.5 143 35 20. S +4 42 10.8 -771.7 9'".<' Apr.2i lio 58 56.7, . . . ■ +5 12 27. f 143 48 21 5 +4 50 Sf'.'J -526.1 931. S . The ahove limes 1 ave been computed usinj; C.vssiNi's coruction for deviation of quadrant if, instead of this , we use llie deviation found on and after May, 1706, the results will lie as follows: — 1 1 1 33 C'apricorni, I. 1705, 15 24 20 15 14 59 313 18 34.5 312 34 41.8 -5 30 6.6 ■ • . ,,c 998.! 32.1 AuR. 4 18 0.2 , . , , -4 48 34-7 3'2 4f) 5.S -5 17 37 < -740r 1012.3 30.7 112 ' A 47o 334 I5 3i.' - 5 49 17.0 —830. : IOI2.C f 0.0 Sept. 2 22 3f) 42.0 . . . 1 -4 58 22.7 334 2() 30. -1 -5 3() 2.1) -IJI4.I I02l).5 ■'4.5 "3 " Ai|iiarii, E. 1705, 12 50 34 12 4t 13 i 335 15 51)4 334 45 i8.^^ -5 41 27.3 + 948.2 101 1 .6 Sept. 2 23 38 15.3 . . . 1 —4 57 56.0 334 21) 30.1 -5 30 2.9 -324.4 997.5 IM *' Tanri, I. . . 1706, II 13 52 II. 4 31 I 042826.1 f)3 54 4.6 +0 45 19.2 -705.? 95'>.f 03.4 Jan. 23 7 25 4.6 . . . +1 10 24.f1 64 5 50.4 + 35 44.8 +574.4 ()0<).' 20.7 'I5 h' Tanri, I. . 1706, II 36 15 11 2f) 54 1 64 40 59 3 ()4 4 17. c) + c 45 46.6 - 72. f 956. c 1 Jan. 23 : 7 47 31.3 . . . +1 II 29.3 fi4 5 30.7 1 +0 30 6. 1 + 940.5 943-3 ilf) k- Tanri, I. . 1706, 113658 II 27 37 644123.5 64 4 37') Jan, 23 7 48 14.4; . , , +1 u 31,4 64 5 30.7 + 45 47.4 + 30 6.1 - 52.8 955.? +941. 3! 942. f ( ; ; 117 «-' Tanri, E. . ' 1 1706, tl 46 8 II 36 47 j 64 46 52.0 64 S 53.5 Jan. 23 7 C7 25.9 . . . +1 II 57.9 64 5 30.7 + " ^5 55-9 + 30 6. 1 + 202. f 055 -t + 949. f 97'. 2 • 118 / Cancri, I. . 1706, .12 32 12 112 22 51 117 34 24. Ij I 17 30 6.4 + 4 12 9.3 -777.7 927 4 07.5 Jan. 27 8 59 23.8 • • • -^4 3f> 33.4! 117 3 4.1 + 4 2" 7.4 -538.1 943.8 70.2 no n Lconis, I. . 1706, 9 I 29 8 52 8 143 36 10.5' 143 35 37.7 + 4 4^ 8.8 -;63.8| uio.c 31.2 Apr.2i 10 59 16,6 , + 5 12 27.7 143 48 21.? + 4 .= 1) 55.5 -526.7 925.7 12.6 120 ;/ Lconis, E. . . 1706, 9 55 5 1 9 45 44 144 3 23 3 143 5O 7..S + 4 38 5.7 + 466.3 908. c . . { Apr,2i jri 53 1,6 1 + 5 12 3.8 143 48 21.5 -r4 50 55.! -769.8: 899.2 t • 1 12t ?. Vir^inis, I. 1706, jio 47 51 10 38 30 212 34 3i)-4 212 43 0.9 + 18 36.5 - 518.5! S94.7 63.1 May 24 14 56 a. 5 + 1 5 40, 3j 212 51 39.4 + 30 1:4.7 - 738.2 902 . 2 ■49.8 kF.SKARClinS ON TIIK MOTION OF THE MOON. labular Exiiibit of Rcduition of tin- Occullatums — CloiUinued. 21' •ASSINI, ETC.— SERIES II— ("ontiniiecl. No. Sl;ir orculteii. 133 '34 1 i a H C I ~ H 122 " Pisciuni, 1. 123 /> Aiiclis. I. . 124 " Scorpii, 1. . 125 " Scorjjii, E. . 126 Venus. Ii. 127 Venus, I.. 12S ATauri.E. . . 12(; " Leonis, I. . t 130 " A<|uaiii, T. 131 PI. M;.ia, 20.-,I. 132 ri. Tay., 1,1 c. I. 22 !, I. 22 / E. 13; I'l. Mnia, 20 ,. E. 136 PI. Elcc, 11 Ik I. 137 22 /, 1. 138 PI. Asl., 21 k, I. 139 PI Ast , 21 /•, E .Apparent Posilion of .Moon anil Siai. Longiliuli's. Latiludus. /> - H h in 5 li 1)1 s i7ofi, 1 1 57 2t) 11 4S 5 Nov. 17 3 43 3')- 2 . . . 1707, 8 21 13 8 II 52 Apr. 4 'J I" 55.4 • • • 1707, 7 4f' 54 7 37 33 Sept. 3 'S 35 47-2 • • • 1707, 8 35 6 8 2; 45 Sept. 3 "3 -4 "•" . • ' 1706, 7 17 38 : S 17 Fell. 23 5 28 30.4 . . . 1708, 7 17 53 7 S 32 Feb. 23 5 2S 45 ... 1708, y 3f' >fi 9 2f> 55 Sept. 6 20 40 if) ... I7oq, 7 5" 27 7 4i <' Apr.20 9 45 10.2 . . . 1709, 12 I 48 II 52 27 Sept. If) 23 44 4»2 . . . 1709, S IS 32 8911 Sept. 23 20 28 23.4 . 1709, 8 22 34 8 "3 '3 Sept. 23 20 32 24 ... 1709, 8 41 24 S 32 3 Sept. 23 20 51 19. 1 . . . 1709, 9 5 32 8 56 II Sept. 23 21 15 3I-' • • ■ 1709, 9 8 5 8 5? 4) Sept. 23 21 IS 4.5 . . . 1710, 4 42 1') 4 32 5S Dec. J 21 34 29.f> . . . 171". 5 40 3> 5 3' i<) Dee. 4 22 32 5 I.I . 1710, 5 49 S 5 39 47 Dec. 4 22 41 49.5 . . . 1710, () 2 o 5 52 39 Dee. 4 22 54 23.7 . . . n /.-© 1008.5I235.0 1025 .7 148.6 996.01 14.3 1005.9 28.5 889.6'lf)0.5 905.3' 85. 2 23 58 34.0 23 22 46. S -I 32 54.4- 9'''9-5 -I 3 12. P 23 38 56.3 -I 38 30.3+ 335.9 43 25 52-S 42 34 '4.9 +' 2 43.7 - S96.3 + 1 33 3f'-i 42 49 ■'•2 +1 10 20.(1- 45f>-9 245 43 l'>-4 245 31 27.7 -4 43 36 3- 5f>9.9 -1 51 23.8 245 40 57-6 -4 31 51-5- 7"4.8 I 246 7 3-8 245 49 24-1 -4 43 54-2+ SOfi-SJ 888. 4j . I -3 52 50.3 245 40 57. fi —4 31 51.5- 722.7! 881.0, . . 359 32 39.2 358 41 23.2 -I II 2.1 - 842.8; 933-3|334-2 -o 46 37.1 358 55 26.0 -I 3 5'>-l - 432.0 947-1 24.7 359 32 47." 358 41 3<)-9 -1 " '•f'- 835.9; 933-3 -o 46 37. S 358 55 26.8 -I 3 50.0- 431-61 940-7 635322.1 64 19 54-1 +3 55 9-8+io'5-oi 958-IJ164-2 ; + 4 46 48.6 64 2 59.1 +3 59 16-4 - 246.6^!042.2'259.9 i i()6 46 11.3 167 15 49-3 -o 21 21.3- 69f'-9| 985. Sj 30.5 | -, ,) II 9.0 if-7 27 26.2 -o 33 22.5 + 721.2^1003.0:137.0 ' 331 39 29.6 331 10 8.5 —I 27 16.0- 622 4, 88g.S|i73.7 j -o 48 34.8 331 20 30.9 -I 12 49-2 - S66.8|lo67.0ji57.6 \ 54 59 50.1 55 24 II. 3 +4 14 8.6- 816.6 921.1180.5 | + 5 4 3-9 55 37 47-9 +4 21 35-f'- 447-0| 928.91235.1 \ 55 I 59.0 55 26 33.6 +4 14 24.1 - 2f)S.2J 921.3J180.5 ! + 5 4 7-" 55 3> '-8 +4 29 16.7- 892. 6| 93I.9i235-0 j I 55 12 I.o 55 37 311-8 +4 15 37-5- 332 -Sj 922.1 . . 1 + 5 4 21.4 55 43 3*' +4 30 16-''- 879-3! 939-9 ■ • ; 55 24 53.7 55 51 14-0 +4 "7 18.4+ 49"-4 923-2| - . + 5 4 39-5 55 43 3-f' +4 3" 16. 8- 778-4 9>9-2i • • 55 26 14.!^ 55 52 38.9 +4 17 29.4 + 891-0, 923-31 ■ • + 5 4 41.4 55 37 47-9 '4 21 35-f'- 246-2 922.0; . . 54 \2 23.6 55 8 13. 1 -^4 13 13-7- 836.4 899.9252.2 + 4 58 13-c 55 22 59.5 +4 9 36.8+ 216.9) 910.31163.2 55 12 1-7 55 37 30-5 +4 16 35-4- 401-3' 90*-4 + 4 57 46-0 55 44 il-8 +4 3" 18.9- >23-5! 915-4 55 16 25.3 55 41 40.0 +4 17 7-' - 60.6 902.7 + 4 57 41.0 55 42 40.6 +4 32 18.0- 910.9 9'2-9l 55 22 58. 4 55 47 46.8 +4 '7 55-5+ 3"6.2 903-1 + 4 57 35.7 55 42 40-6 +4 32 18.0- 862.5 915.2 214 RKSEARCIIES OS THE MOTION OF THE MOON. 7ir,'.,/(ir Kxhihit of Raitictioii of the Occiiltations — C'oiitiiiued. '53 Jiip'"-"''. '• i 154 : Jupiter, I. I 155 Jupiter, E. . 156 I Jiipiler, E. . i 157 (1 Ai|ii;>rii, 1. i i >7>5. '5 July 21 23 '715. '3 July 24 21 1715. "3 July 24 21 1715. 14 July 24 22 I7i5, 14 July 24 22 '7'5. " Auk. 15 2' 5" 5' 48 50. 37 59. ifi 2U. V) '5. ■17 42- 23 4f). 32 2o. 25 2. 33 37. 55 55 30 49. 15 42 31 > I . . . S13 2S 3S.S () . . . S r3 21) 54.8 S . . . 5 14 14 25-5 S . . . 5 14 '5 41-5 1 1 46 34 10 30 13-4 19 21 33-3 + 2 22 26.4 -t- 659-3 9S1.3 + 3 2 (J.I 10 10 34.0 + 2 10 13.3 + 733.1 985.? 5" 34 lf).(i 52 I J2. 1 -I 12 23.7 , , 973" — 22 52. !■ • • 51 35 0.() 52 I Jfl.l — I 12 28.7 , 973- > — 22 56.8 • • • 52 I \.U 52 27 fi.5 -1 12 14.0 974-9 — 25 '4-5 • • ■2 I 46.0 52 27 49.0 -I 12 13-2 . . 975.0 -0 25 IS. 4 " • • • . .1 335 28 18.4 335 IS 56.2 + 3 53 44. s - 532.9 980.4 142.2 H-4 41 49.5 335 27 49.I +4 7 37./ 832.9 9S3.oi( (3.3 RliSKARCllKS UN TIIK MOTION Ol" THK MOON. Tabular Exiiihil oj Kaliht'wn of tin- av////(///(W/j— Coiiliiuictl. CASSINI, ETC.— SERIKS II— ronliniicil. 215 No. Sl;ir occiillcd. Dale. c ■= ■g i J*" o .A|ip;ircnl I'osiiiiin u'f M Tauri, 1. . j 16S ; Virginis, I. l6g ) VitKinis, E, 171,), 7 42 58 7 33 37 Apr. 22 ij 43 54.3 ■ • ■ 1719, 8 32 27 S 23 6 Apr. 22 10 33 31.4 • • •■ 1711J, y 43 5 y 33 44 Oct. 30 o 17 23 . . . 1719, 7 4 40 <> 55 "J No-. 2() 23 24 58.9 . • • 1720, 12 24 2 12 14 41 Apr. 20 14 20 50.5 . . . 1720, 12 49 41) 12 40 28 Apr. 20 14 46 4" -8 . . . 170 PI. Elcc, 17 fc, I. 1727, '4 121 1352 Seiit. f) I 3 42.1 . . . 171 1>1. Cel., lO ,(,', I. 1727. '4 711 13 57 5" Sepi. 6 I 9 331 • ■ • 172 Pl.Tay., H)<-, 1. . 1727. '440 5 M 3" 44 Sept. 6 I 42 32-5 • ■ • 173 PI. Maia, 20 ,-, I. 1727. '4 42 ifi 14 32 55 Sept. (t I 44 43.8 . . ■ 174I PI. Elec, 17 /', E. 1727. >5 10 '5 '5 "54 Sept. (> 2 12 47-4 • • • 175' PI. Cel'., l(),i,', E. 1727. '5 20 39 15 11 "8 j ( Sept. 6 a 23 13- > • ■ ■ 335 55 i'>-3 +-4 4" 59-3 335 21 14.1 + 4 47 33-2 335 58 5-1 + 4 32 20. 1 65 5 53.6 -4 3<> 58.0 f>5 3: 34.9 -4 38 17-2 347 " '3-3 -o 5 15-3 66 20 37.3 -5 5 l-l 66 46 21.3 -5 4 57-''' 65 41 17.3 -4 55 43-' 61 14 15.3 -4 i<> 4.8 1S6 to 47.0 + 3 53 48.0 186 26 49.2 + 3 54 41-2 55 7 ('•4 + 4 44 15-7 55 10 9.8 + 4 44 23.2 55 27 25.5 + 4 45 5'7 55 28 34.0 + 4 45 8.3 55 43 14.5 + 4 45 43'9 55 48 42.1 + 4 45 57.' 335 38 53-9 335 27 49.1 335 14 4-7 335 27 52.5 335 12 49. S 335 27 3('-') 65 34 44-8 65 50 52. 8 66 6 26.0 65 50 52. S 347 8 32.3 347 17 20.4 65 38 20.2 65 51 45-8 66 3 25.8 6; 51 45-8 66 6 35.0 65 52 47-" 61 40 20.4 61 53 30.8 1S6 ti 16.5 186 16 53.8 186 23 53.4 186 16 53.8 55 21 32-1 55 3f> 47.7 55 23 55.9 55 38 II-5 55 37 II-4 55 45 57-8 55 38 3-3 55 52 54.') 55 48 59.6 55 S*) 47.7 + 3 55 37-0 + 4 7 37.7 + 3 58 40.0 + 4 7 39-" + 4 I 4'-7 + 4 7 39.1 -5 27 15.9 — 5 29 12.6 — 5 26 2().0 — 5 29 12.6 -o 55 4.9 -1 7 0.4 -5 3'' 44-1 -5 29 15.1 -5 38 46.1 -5 29 15.1 -5 35 3-4 — 5 29 12.9 -5 38 14-7 -5 45 47-7 + 3 4 44.3 + 2 49 1-7 -r 3 4 4-2 + 2 49 ' • 7 + 4 13 4-4 + 4 9 41.5 + 4 13 36.2 + 4 20 12.7 + 4 16 28. 9 + 4 29 23.1 + 4 If) 39'9 4-4 21 41.9 + 4 iS 57-8 + 4 9 41-5 + 664.S -720.7 -827.8 -539.0 -887.1 -357-4 -968.0 + 116.7 J- 933. 2 + 166.6 -52S.1 + 721.; — S05.6 — 449-0 + 700.0 — 571.0 + 82S.0 -350-5 -790.4 + 453.0 ■V /> l.-Q 981.0 . 979-4 • . 981.2 195.8 985.8139.7 j 942.S278.4 ; 954.2 57.1 953'4 182.5 970.6243.3 ^ 956.9 . . j 943-5 ■ • 858.7 166.6 894. 1 I So. 7 910.3 31.9 919.0 34.0 I qoS . 6 . 900.8 . 900.0 216.7 81)5.6 209.2 ' 899.5243.9 907.6 178.0 55 53 "-7 55 38 11-5 +4 19 47-1 +4 20 12.7 -337-3 + 942.6 + 419-') + 902 . 5 —915.6 + 202.9 -855.6 -39f'-5 -526.4 -774-2 -890.7' — 302.0 + 73I-9 + 55(J-3 + SS9.2' — 25.6 1003.2 31.2 tool. 0155. 1 1002.7 . 995.1 . . 924.9 164.0 935.4251.6 j 925.0 . 941.4 . ■ ' 926.0 . 935-2 . . 926 . . 93S.2 . . 926.6 164.0 917.6251.8 926.8 . 857.1 . . 2l6 UESIJARCllKS O.N TIIH MOIIO.N OF TIIK MOON. 'J'nhiiliu- Exliihil of Kcifuitioii (if the Ociultatunis — C'oiuiiuiud. C.XS.SINI. KTC— SKRir:S II— CiMiiiiiiud. No, 177 17S 179 I So 182 Star occulled. Dale. Local Mean and Sidereal Times. Greenwicli Mean Time. Moon's Tabulai Geocentric Position. .App.ircLiI I'ositiuti 1)1 .\Io ill ami Si.ir. Longitudes. Laliliides. I ~l. Ii-li 1 © /.-© // m X // /// s , , ., ., n . I'l. lay., Iij e, K. 1727. >5 35 5<) 15 26 38 55 56 44-3 55 58 5". 8 + 4 20 5(1.0 + 774. 927. 1 Scpi. 2 3S 35-7 + 4 4'J "''.5 55 45 57.8 -!-4 2y 23.1 -507.1 923.4 PI. Maia, 20<-, E, ■727, i() 38 15 51 17 5O <) 10.5 5O 8 12.7 + 4 22 40. t -^918.7 927.5 Sept. 6 3 3 >8.7 + 4 4f) 47.5 55 52 54.0 + 4 21 41. g + 58. g 9>7.9 . • 'I Taiiri, I. . 173S, <) 44 42 9 3; 21 (16 50.1^ 65 53 .12.1 -5 34 lS.2 -857.2 903.4 282.5 Jan. 2 4 33 51-4 • -5 5V1.' (•>() 7 5().3 -5 29 IO-4 -307.8 907.1 143.6 ti Tauri, E. . ■73S, 11 5 57 10 5f' 3f' 6() 41 44. (, W) 22 36. CJ -5 32 41.3 + 877.6 903.2 . Jan. 2 5 55 "J.S -5 5 "S-S f)6 7 5'). 3 --5 2g 10.4 — 2lo.g 8gS.5 . . (I Taiiri, I. 1738, 5 33 53 5 24 32 f>5 27 45. S f'5 54 44-? -; 24 2J.3 -845.3 88g.6 272.1 Dec. 23 23 41 5S.3 -4 43 45.5 fib S 49.8 — 5 2g og . 8 + 287.5 88.g.3 154." n Tauii, E. . ■ 738, f' 33 54 6 24 33 65 57 27.1 Of) 20 43.7 — 5 20 15.1 + 713.9 8g1.f1 . Dec. 23 42 9.2 -4 42 41-3 fifi 8 49. 8 -5 2g 10.0 ^ 534.9 88g.5 . • II Tauri 1731). 7 10 50 V) Vl 10 4>.4 59 2 40.0 -5 2g 58.5 327.0 Fcl). 15 4 4' 23.; -5 I 7-4 • • iii.g DELISLE .VT LU.XEMHOURG. 183 184! 185 186 187 18S 7 Tauri, 1. B. A. C. 1373. I. ') Tauri, 1. i Sagiltarii, I. f Sagiltarii, E. . I.)' Tauri, E. . 189 i '1 Cancri, E. 190 ' a Tauri, I. Igl ' 11 Tauri, E. . 192 1 / Geniinoriini, 1. 1713. Dec. 1 1714. Mar. 20 '7'4. .vlar. 21 1714. Apr. fi 17M, Apr. 6 1714. .Sept. 27 1714. Oct. 2 1717, II 50 4 4' g ifi 9 7 10 25 10 21 15 2fl Ifl 26 ifi 3g 17 40 g 10 21 34 14 47 3 32 9 3 Sept. 25 121 21 1717. I 9 55 Sept. 25 22 13 1718, 113 33 Jan, 15 I g 14 24.3 II 4g 1.5 , . o . 2 g f 1 55.2 . . 28. g 10 ifj 31. g . . 4I.fii5 '7 39.0 • • 56.316 30 5.8 . . o . 7 g o 56. S| . . 21.3 14 38 ss-(>: ■ ■ 4-3 S 53 10. g . 23. o' 9 46 38.2! . . 55.0I13 24 20.31 . . 3-3 39.2 7-9 35.3 39- 0.3 44.0 34.7 68 + 65 +0 27S + 2 279 + 2 61 I2g -4 65 -4 fi5 -4 105 -4 5 59 53 38 ■5 35. 32 12. 55 25. 40 13. 55 14 2g 27 36 36 32 40 49 47 4 38. 8 31. 45 8. 5 42. 30 58. 35 38. 38 18. '> 55 49 15 ,0 (.7 8 63 64 f'4 78 78 8 27g (1 27g .7 279 .6 279 . I 62 7 62 3 ■2g 6 1 2g 7 ('5 2 65 .2 104 .7 '04 59 '('■< 9 59-5 33 0.2 42 15.5 '5 54-9 30 ig.4 12 36.7 27 40.0 42 52.2 27 40.0 19 5.6 5 3.8 52 43-4 39 23. I 34 48.7 50 52.9 6 28.5 50 52.9 42 27.3 51 12.0 -t- o 2g 10.8 + 40 45.7 + " 3 ".71 — o 1^ 54.6! -1 13 24. J -1 ig 41.4 + 1 35 55-7 + 1 41 53.7 + 1 38 3.6 + 1 41 53.7 -o 54 23. g -o 46 57. g -5 12 53.9 -5 6 g.6 — 5 27 16.2 — 5 2g I2.fi| — 5 26 27.3 -5 29 12.6 -5 25 9.9 -5 39 54.0, -643.4 g3g. -6g4.g 946 -555. 3i g47 + 775-3 953 -864.5 g3i. + 377.0; 943- -903.3' 953. -35S.OJ g71. (■gl2.2: 955. — 230.1, 940. + 841.8 g65. -4 4".'' 952. + 8ix),3i 899. -404-31 893, -gf'4.2 g53. + 11O.4 966. + 935.6 956. + 165,3 946. -524.7 + 884.7 1014. 102b, 0249.4 8178.8 s 359.7 6 65 2 0.7 5 77. 8 4 16.5 4 262 3 • • 4 . . 4184.2 5237.9 7189.1 631x1.6 4182.5 9243.3 1 295 . 2 o 169.6 RESEARClll-S ON 1 llli MOTIDN OF THE MOON. Tahiitar E\lutnt of Kei/iiclioii <>/ tlif ar«/A;//,'//,(— CoiitimiL'il. 21/ DF.I.ISLE AT LUXK.MUOURCi— Conlinued. No, Sl.ir occiilU'd. Dan l'J3 Taiiri, I. 194 H. A. C. 8lS4, 1. ■')5 « Taiiri. I. Iij() a I'auri, 1'.. r()7 ; Lilir;o. I. I(j8 11 Tauri, I. Kji) 'I Tauri, K. 2o<) A' Taviii, 1. 203 20 ) 20() 207 2o3 209 9 Tauri, I. HI. Klcc, 17 I', 1- PI. Cfl., 16 .v. 1. f'l. Maia, 20 «, I I'i. >Kr,.23 ./, I. I'l. Alcy., ,,, 1. . Pl.l'lcio., 23//, I. IM. Alias, 27./, 1. r Cf.niiiorum, I. •3 . S « c .5 Ai)|>arcnl I'osition of Moon and Siar. /■-/, V-B h III Uonniludc-s. I.aliludus. /.-0 A /« 171S, ! f 31 35. f> 22 15.1 f)5 35 4>-5 Tell. 9 , 3 4) 252 . • . -4 53 48.7 iji.S, 3 42 37.2 3 33 16.9 347 o I3.3 f>5 35 '"'■5 -5 25 41- 65 51 7-9 -5 29 16. 347 3 31.9 -o 55 5. ) 5 I5-3i 347 17 20.6 -I 7 f>. I,i<), '■ 7 42 53-S; 7 33 33-5 «' 20 SS-fj f'S 3' '9-2 -5 3^' 44 Sept. 9 iiy sti 33.3: A|)r.22 : 9 43 ")•'); i.i] 65 5 r 45. S -5 2') 15 1719, ; 3 32 35.4 82315.1 (i(, 4fi 25.9I &0 331.1 -5 3'' 47 Apr.22 jio 33 3').S ... -5 4 57.f: (>5 5' 4--S -52915 1719, ! 7 43 32.1^ 7 34 ■'.*• 231 & 3.( 230 57 .4.1 t 4 20 39 Aui,'.21 117 41 3I-'' • ■ ■ +5 "5 I7-" 1719. 3 4fi 49- 1 8 37 2i.S O5 12 52 ' Oct. 30 1^3 20 57.!^ ... -45') lo-fe 231 13 2.() +4 24 5') 65 40 52.6 -5 33 l<) 65 52 46.9 -5 29 12 94324.1 9 31 3-*' fi5 41 27.0' 06 42.5 -5 35 17"). Oct. 30 I o 17 42.1: . . 1725, iI2 25, 33.2 12 16 l-i4. !9 jio 24 58.7, ■ • -4 55 42.',. .9 60 8 2.9 I +1 44 5.5 O5 52 46.9 —5 29 12. 59 20 55.2 +1 9 51 59 36 46.2 +1 13 59 1 -961.4 965.9320.6 2 + 215.1 93, .2 105.3 3 -525.7 888. 7 166.6 4 4-721.1 S94. 1 180.7 4 -Su6.6 910.3 3' -9 1 -449-3 920.2 3).o I + 705 .3 903. { . . 1 — 572.0 905.4 . . s — H-^o 97U.7 148.0 7 -259.9 980.6 83.2 -7I4.3 897.8 216.7 ') -546.1 S96.5 209.2 S 4-335.6 900.0 . 9 -349-9 902.4; . . .() -951.0 969.4331.5 •4 -247.8 982.4; S3. 1 DELISI.E AT ST. I'FTERSHIRG. .8 6 52 4S.3 53 50 3'.-* 53 22 13.0 -+-4 12 43. 8 53 37 53.0 1727. " 54 ' Fel).27 7 2-' 12.1 1729, 16 35 57 9|U 34 44-4 56 I 25.8 55 24 28. 3 Dfc. 3 9 27 24.9! ■ • ■ +■»-»* '-l^ 55 3S 54.4 1729, I6 41 39.614 40 26.1 56 4 15.3 55 27 15. » Dec. 3 9 33 7-5 - ■ ■ +-» 48 9-' 55 4o 17-3 1729, 17 16 56.615 15 43.1 50 21 45.5 55 44 4S-7 Dec. 3 10 8 30.3 ... -t-4 47 38.9 55 54 59-9 1729, 17 31 47--I 15 30 33-9 56 29 6.9 55 52 22.6 Dec. 3 10 23 23. ( ... +4 47 26.0 55 5(> 7-8 1729, .174313.81547 0.3 563716.5 5'' 052.7 Dec. 3 10 39 52.7 - • ■ ' +4 47 ii-7 5^ I3 42-8 . 1729, 18 32 17.4 '!■> 31 3-9', 56 59 8.0 56 24 16.1 j Dec, 3 11 2( 3-5 - • - +■» •»'^' 32-7 50 36 55-9 ' 1729, 18 37 35-1' 'f- 3!> 22.1 57 '45-3 5& 27 8.5 Dec. 3 11 29 22.6 . - - ■ +4 40 28-" 5f' 35 31-5 1733. 17 33 S.S 5 3" 55-3i 9258 9-i 92 48 4»-7 Mar.22l 7 33 55.(>i • • • i -2 3o 39-3 93 4 4f>.S 4-3 40 29.4 + i 41 39-7 + 4 13 23. 1 4-4 9 44-1 -1-4 13 7-0 -t-4 20 15.2 4-4 10 56.0 + 4 21 44-'i + 4 9 58.5 4-3 55 41.2 -1-4 S 53.6 -{-4 I 23 -0 4-4 5 54.9 4-3 5S 11.5 44 5 33.1 4-3 53 22.7 -3 8 12.4 -3 5 22.4 -940.C - 70.3 -566.1 4-224.C -7S2.3 -427. ( -611.2 -64S.( — 225.2 -I-S57.3 -770,1 -f450.c -759.8 4-4f>3-4 -503.' + 730-4 ■962, 1 936. t 940.7 8S8,e 892,4 833,6 8S9,( 887.1 890 . c 8S7 . ■: 886.2 886.8 S90.3 885.6 883. J 885.5 886.2 959.2 975.7 339.0 74.6 252.0 163 6 1O3.7 252.0 163.9 252.0 164.2 252.0 164.6 2-5 90 . 6 75 A I'. 'J 2l8 RESEARCHES ON THE MOTION OF THE MOON. Talnilar Exhibit of Reduction 0/ the Occitltations — C DKI.ISI.E .\T ST, PETERSBURG— Coniiuui'i out imicd. . 1 No. i i St.ir oci:uItc(-l. D.iti;. 1 Local Mean and Sidereal Times. Greenwich Mean Time. 1 Moon's 'I'abiilar 'J ■7 .\p|).irenl Position of .Moon and Star. Longitudes Latitudes. /) /.-0 1 /; HI .V // III X " 1 . .. 210 1. Cancri, I. . 173.'. 7 27 49. f) 5 2f) 3fi.l 131 5') 57.7 132 19 49 .S ~5 21 52.2 -43''. 7 940.6 5.4 .Mar. 2; 7 40 25.5 . . . --4 44 If). 9 132 27 fi.5 -5 35 30.1 + 817.9 926 . 2 1 26 211 11 Taiiri, 1. . 17,U'. 10 |i) 54.3 S iS 40. S ()6 2S 23. <>i 54 2 . J* — 5 19 5.0 -718.0 929.9 25.3 Apr. 1 1 11 52 54.3 ... -1 34 4 4 66 6 O.S — 5 29 II .0 + 606.0 937-1 40.8 212 It Tami, I. 173''. tS Id 12.2 Ifi 14 5S.7 fi; 47 53.'" '■5 ^0 41.7 ~5 26 4.0 -937.3 944.3 130.0 Au.^r. , 3 If.o ... -4 4; 7 ■ - 6f) 6 22.0 ~ 5 29 7.9 + 183.9 951 .0 296. 1 213* " Tauri, li. . 173''. 1') 27 5". 9 '7 2I1 37-4 ''(' 27 12.6 !>(> 21 51.0 '"5 25 29.5 -1-929.0 945.5 . . .•\ug. I 4 12 5.= . . . -4 4'> 27.7 (,(> 6 22.0 ~5 29 7.9 + 218.4 950.2 . . 2I^ CI Tauri. I. . >73!i. 14 44 52.412 43 3S.., f.(. 1 50.4 (>i 5' 26.5 ~5 23 59.3 -932.5 923.0209.9 Oct. 22 4 51 3^.1 ... -4 51 35.1 66 6 59-' -5 29 3.4 + 9. 1 928.3 216.2 2.5* n Tauri, E. . I73f'. '5 59 43.413 5;^ 29.9 (i(< 41 17.0 66 22 29.9 — 5 29 32.4 + 930.9 922.7 . . Oct. 22 6 6 41.4 ., . . -4 52 50.2 66 6 59." — 5 29 8.4 — 24.0 927.0 . .1 216 a Kconis, I. . 1737. 1) 41 ■-"■'^ - 40 7.3 137 52 4.(. 137 43 46. S -3 14 42.9 -927.7 959.7 47-5 May 7 12 43 57.9 ... -2 24 43.7 '37 59 't.5 ~3 10 0.6 -282.3 963.3 go. 5 217 Jupitei" . 1737. Mav 22 15 50 26. S 13 55 13,3 349 It; 5') 13. S . , . -0 23 23 4.0 23.4 349 23 3;. 7 -' 16 6 . 892.7 01.9 2t3 II' Tauri, I. . . 1737, 13 3 21.911 2 8.4 63 4.S '5.7 f'4 5 45.9 -6 35. S -f>77.7 903 . 1 20 . 2 I»ly 22 21 6 10.4 . . . — ; S 39.*' 0( 17 3.6 -5 46 27.0 -348.8 1084 304.1 219 "' Tauri, !•: . . 1737. 13 35 46.1 II 34 32. f) 64 4 51.3 f'4 23 30.4 — 5 59 54.7 1-386.8 903.9 . . July 22 21 3S 3').y ... -5 3 48. f. '>4 17 3.'> ~5 46 27.0 -807.7 894.7 . . 220 «- Tauri. F.. . . 1737. 13 4S 22.311 47 S.H ()4 II 22.(1 fM 30 16.2 — 5 59 3fi.5 + 7S3.S 904.3 . . July 22 21511.3.2. . . —5 8 52.1 (u 17 '2.4 — 5 52 4.7 -45'.8 901 . 1 . . 221 71 I'auri, I. . >73S. f) 20 4.0 4 IS 50. 5 63 21 44.4 (>3 33 34.3 ~5 49 41.7 -531-7 398.6282.5 Jan. 2 I S 21.3 ... -5 f) 30. S ''3 42 26.5 -6 1 45. 8 + 724.1 896.7141 1 . 222 "' Tauri. I. . . ■ 73S. 7 29 33.5 5 23 25.0 f:3 5f' 39.1 ('A 2 3'. 6 -5 47 3.0 — 909 . 2 ipo.o . , ' i 1 Jan. 2 2 l3 7-3 ... -5 f) 23.5 f>4 17 40.3 -5 4f) 29.8 -33.2 905.2 ... 223 ((• Tauri, 1. . . '738, 7 32 54.5 5 31 41.0 '13 5S "7.7 64 3 50.7 — 5 4f' 55-9 -852.2 goo. I . . j Jan. 2 2 21 23. S . . . -5 f) 23.0 f'4 18 2.9 -5 52 7.fi + 3'I.7 9»3.3 . - 224 a A. C. I3yi,I. '73?. S 51 3.5 (1 49 50.0 1)4 37 35.2 '>4 34 55.8 -5 44 21,0 -801.7 901. I . i Jan. 2 3 39 45. f' . • . , ~5 (> 9 7 'U |3 17.5 — 5 37 7.1 -433.9 908.2 . . ' 225 iis—Con\.\n\m\. 2 19 DELISLE AT ST. I'ETERSIUJRC— Conlinmd. No. Si;ir occullcil. 227 /lleniinoiuni, I. 228 71 Tauri, I. . 221) 71 Tauri, E. . ,230 «' Tauri, I. 231 "•' Taiiii. I. Date. .H £ \l>lKiioiil Position of Moon anil St.ir. / _ / .V G /■■ - /.' /) /,-0 )ngitn !• c ■= r. u< - 1 ►J (/■' A VI s h m s 8 <;43.5 S35.0 .09 3240. S U..J54 37.4 -4 "=5-7 -4"5.y ■)30.23l4-<> 5 „37., . . . -^32410,2 no 13,1.3 -3 4f' 2S.2 --837.5 934-'>>5f'-0 1738, 15 310.013 15''-: ('3 '4 4-S 63 2() 33-3 -55424.? -7'?I.2 8()3.2 . .j Aug. S 01222.3 ... -5 .) 17.0 634234.5 -'' ■ Jf.'l -^444.4 8,J5.. . .| 1733. 15 5y 5.0135752.4 f>3 4!45.l f'3 53 44.5 -5 5143.7 +670.0894.6 • • Aug. 8 1 S.27,3 . . . -^ 843.9 634234.5 -6 I 48.') +605.2895.1 . . ,738, .62150.7142037.= 6353 0.3 64 313.5 -55037.7 -S74.S 895.0136 2 Aug. S .3115.0. • ■ -5 8=9.1 64 .7 48. 3 -5 4626.3 -251.4 905.9288.. ,738, 1622 7.7.42054.2 6353 8.r 64 320,4 -55037.0 -S90.0 S95.0 . . Aug. 8 . 3> 32.9 . • • -5 8 29.0 64 .8 .0.4 -5 52 4.1 + 87. 1 S89.6 . . .738 21 18 5.4.9.651.9 6f, 1934.9 655846.4-54050.3-559.6895.7136.2 Aug.'s 628.9.3 ... -5 5 7.4 66 8 6.0 -529 7.4 -702.9 896.8289.9 173S, 22 749.320 635.8 66 44 I.. 4 66 .8 49. S -54026.0 +643.8 894.9 • • Aug. '3 7 .8 ...3 ... -5 429.8 66 8 6.0-529 7.4 -678.6933.7 • -I .73S, .1 57 37.2 9 56 23.7 65 4. .12.6 65 56 41.5 -5 38 .3.2 -7.0.. 894.3.89.6 0,1. 2 043 9.6 . . .' -45425.3 ''<' S3..6 -529 7.5 -545.7 892.9236.5 1738, .2 57 57.S.0 56 44.3 66 I. 38. 5 66 22 16.7 -5 35 II- I +825.1 895.5 • • Oct. 2 14340.0 . . . -4 53 39-3 66 8 3. .6 -529 7.5 -363.6 898.2 . . , .739, .34053.4.13939.9 .124142.4 1.3.053.3 -05855.8 -S56.5 895.32.0.2 OC..2J 34833.1 . - ■ -02438.1 1.325 9.8 -05424.6 -27..2 S9S.3263.2 4 5. 33.8.2 50 20.3 ..3 .6 26.1 113 40 6.7 -o 54 33.5 +896.9 896.8 . . : -o 21 34.3 113 25 9.? -o 54 24.6 - 8.9 S96.8 . . 1739 .•...^so.c. 943.0 .24.436.. 124 50 28. S +0 2 2.3 -882.9893.52.1.2 UCI.24 32227.8 . . +03632.6 .25 5 II. 7 +0 4 3.3 -126.0891.8273.9 ,7.9, .4 .7 IS. 4 12 16 4.9 124 47 15.2 .25 .9 58.0 +0 6 33-7 +886. 3 S95.4 - • Oct'^24 4 29 0.6 . . . +03924.6 125 511.7 +0 4 8.3 +145.4 898.2 . . ,746, 82040.061926.5 56.258.4 55 37 4-7 +4 8 6,8 -S94-7 896.7 6.2 Mar.26 83646.; - • - +4 41 2.6 55 5.59.4 +4 9 50.7 ->"3.9 898.4 49-7 .746, 8 33 7.0 6 36 53-5 56 2. .4.9 55 45 16.0 +4 7 48.2 -4S7.3 896.3 • • Mar 26 854.5.9- - • +4 -t' 24-7 555323.3+4=022.0-753.8896.9. . 1746, 9 751-3 7 637.8 563634.2 555933.3 +4 7 9.0 -580.5 895.7 . • Mar.26 924 5.1 . - - +4 42 2.0 56 913-8 +3 55 48.0 +68..0 893.9 - • .746, 93038.3 7 29 24. 8 56 47 57. 8 56.047.3+4 634.1 -S63.. 895.> • - Mar.26 94655.9. . ■ +44230.5 5625.0.4-^4 232.3 +241.8894.3. . .746, 93436.673323.1 564957.0 561246.3 M 627.6-847.8895.0'. . , Mar.26 9 50 54.8 . . 17J9. Oct. 23 4 59 25.2 + 4 42 35.4 56 26 54.1 +4 1 30.7 +296.9 896.3 • 220 RESEARCIIKS ON THE MOTION Ol' THE MOON. riilnihtr E \liilnt of Kctiiut'wn of lln- On iiltiitioiis — Coiitiiuit'd, DELI.SI.E AT .ST. PETERSHI;K( — Conliiuicc 1. 'osilion of id Slar. .\o. Star (icculleil. 1 1 Dale. i i Local mean and Sidereal Times. Greenwich Mean Time. M<»on's Tabular 'S 5 ■J lA .Apparent Mouii A 1 /-/, .S' t'-H J) / ^oni^iludes. I.alitiicles. 1 1 245 PI. Pleio.. 23 //, I. h I74f), 10 m s li III s ° 21 25.6 8 20 12.1 57 1 n ! 13 22.5 S<> 3*^ 44-4 . 1 " + 4 5 3.9 M ff O -797.fi 893,9 . . •Mar. 2f) III 37 51-5 ... +4 43 33.2 5fi 50 2.0 + 3 58 18.2 + 405.7 892.6 24f, I'l. Hessel S, I. . 1 74f'. ') I 43.7 7 30,2 5(, 33 30.3 55 5f> 34. f' +4 7 17-9 -877.7 895.8 . Mar. 26 <) 17 5fj-5 • • ■ +4 41 54.4 5'" 11 12,3 + 4 10 31.3 -193.4 896,5 247 I'l. Hesse! ,j, I. . I74. ') 11 40,8 7 10 27.3 5O 3S 28.9 5& I 25.4 + 4 7 3.7 -815.6 S95.5 Mar. 26 g 27 55-2 ... +4 42 6.8 5f' 15 i.o -t-4 13 20.9 -377.2 896.6 250 PI. Hessel 15, I. "74^1. 'J 28 2S.7 7 27 15.2 56 46 53,0 5f' 9 42,8 + 4 f> 37.7 -877.5 895. ll ( Mar. 26 44 45-9 ... 14 42 27.8 56 2( 20.3 -1-4 3 27. 8 + 189.9 895.7 251 PI. Hessel iS, I. 1746. y =<) 44-4 7 28 30. (J 56 47 30.9 50 10 20.6 +4 f) 35.6 -885.5 S95.I ] ! .Mar. 2f) y If' 1.8 .. . +4 42 29.4 5fi 25 f).i +4 3 57.5 + 158.1 897.31 i 1 252 PI. Bcssel 2. "> 9 20. 1 8 8 f).f) 57 7 19.4 5f) 30 26. S +4 5 26.8 -787.8 894.2 ( Mar. 26 10 25 44.0 ... +4 43 18.3 56 43 34.6 +4 12 32.1 -425.3 893.5 i 253 PI. Cel., 16 i'. I. 1747. '3 I 4S.511 35.0 5f, 23 11.7 55 Ad 42.0 +4 33 5.9 -464.3 892.5300.6 ' Jan. 20 9 I 27.7 ... +5 6 42.3 55 54 2f).3 +4 20 22.6 + 763.3 892.7115.3 254 PI. Tav., ly ,-, I. 1747, '3 3 55.5 11 2 42.0 56 24 14.f1 55 47 42,2 +4 33 1-5 -S70.5 892.5 . . i Jan, 20 9 3 35-1 ... +5 f' 43.3 5f) 2 12.7 +4 29 33.1 + 208.4 892.5 t 1 255 PI. .\st., 21 /.: 1. 17 13 25 4.4 I' 23 5", 9 5(> 34 43.3 55 57 49-2 +4 32 14. S -894.4 883.6 Jan. 20 9 24 47.4 ... +5 6 52. f) ?fi 12 43.6 +4 32 32.2 - 17.4 891.8 256 I'l. Mala, 20 ,, I. 1747. >3 2fi 21.5 11 25 8.0 56 35 21.5 55 5S 26... +4 32 1 1.9 -642.4 838.6 . j Jan. 20 9 1 2() 4.7 .. . +5 f) 53.1 5() 9 9,0 +4 21 51,8 + 620.1 891.5 257 22 /, I. , 1747. 13 2S 21.511 27 8.0 56 36 20,9 55 59 24.5' +4 32 7.2 -890.4 891.8 Jan, 20 9 2S 5.1 .. . +5 f' 54,0 5f' 14 14.9 -1-4 3" 33." -1- 94 .1 892 . 6 25S PI. Tay., ic, e, E. 1747, '3 15 12.5 11 13 59.0 56 54.0 5f) 17 10.9 + 4 27 3i'-7 + 887.1 892.5127.4 July 30 21 47 5f'." • . • 4-5 14 49-9 56 2 23.8 + 4 29 30.3 -119. 6 892.5288.6 254 PI. Hessel 4, IC. . 1747. '3 19 33.5 11 18 20.0 5f) 3 3.3 5f) 19 21.4 -1-4 27 43,4 + 783.5 892.6 . . j July 30 21 52 17.8 ... +5 14 49-9 5f' f> 17.9 +4 20 30.9 + 432.5 892.9 . . j 260 PI. Main, 20 r. K. 1747, 13 26 37.5 11 25 24.0 56 f> 33.4 56 22 52.2 4-4 28 4.5 + 812.2 892.8 . . 1 July 30 21 ' 1 59 23.0, ... +5 14 50.0 56 9 20.0 +4 21 49.1 + 375.4 892.6: . . ! • RESEARCHES ON TIIK MOTION (JF Till'. MOON. lii/nilar Jix/iihil oj lieiluclion oj the Oiiitllali<>iis—(\mU\mi^<. FLAMSTI'.r'.l) AT CRKHNWICIl. 22 1 A|]p;irfnl I'osilioii of Moiiii ;inil Si. II. ; No,' Slav occiilU'il. 261 C Arirtis, I. . 262 2S (i,) Ciem., I. ! 363 ! K A<|uarii, E i I ' 264 SiiKitlarii, 1. 205 Mars, I. . . 266 Mars, E. . . Dale. /■-/, .'-' A- -A /) /.-© J !^' l-oiigilmU'S. I.atitmlcs. 267 268 IT SaRittarii, I. Not itlenlifit'il 269'. /)-'Sagiltarii, 1. 270 ' Not iileiilitied 271 Lalaniit: 4()03 272 "■ Cancri, I. . 1 r . 273 a Cancri, b. . 274 " 'rami, I ! 275 n Taiiri, E. . 276 "■ Taiiri, I. 277 (1 Taiiri, E. 278 ; Tauri, I. /( m s h HI s l(,-li. 7 ''' 21) ... 47 5" "-I Mar. iS 7 4 ?7-'i ... +3 ') S'-' 1670, 13 17 3'J • • • "" 5" 4'-7 Mar.23 13 2f] 4<'.7 ... -24 28. 7 Ifi7f), II 3" 10 . . . 334 57 33" liiiiu2(j IS 5 25.5 ... +51 25.5 1676, 8 lf> 4b ... 2Sc) 13 24.'' Aug. IiJ iS 12 33.0 ... +1 42 4''-2 l07fi, 12 17 23 • • 77 25 2().S Aug. 31 23 I ')-2 . . +0 (} 26,0 1676, 13 18 10 ... 77 55 2S.0 AuK.31 i> 2 6.2 . . . . +0 4(1.4 1676, 5 40 55 . . • 2S1 53 32.1) Nov. 9 20 59 35 ... +2 jS 3(1.(1 1677, 12 17 7 . • ■ fi4 3'J 5"-8 Mar. 9 II 29 58-8 ... +0 16 32.4 1678, 7 6 32 ... 284 4') 3<).-l Sept. 24 19 22 10.0 ... +4 48 9.2 1678, 8 28 20 ... ... Oct. 29 1O78, 8 35 38 . . On. 29 23 9 30.1 . . 1(180, 9 I 24 . . Jan. lO 4 45 50.8 . . 1680, 10 7 5 . . Jan. ifi 5 51 A-''> ■ 1680, 15 o 53 Sept. 13 2 3() 28.7 . 1680, 16 9 12 Sept. 13 3 44 58.9 • 1680, 7 50 43 Nov. 7 23 I 58.(1 . 1680, 8 47 12 Nov. 7 23 58 36.9 1682, 9 45 35 Mar. 14 9 16 54.8 47 1' 24-2 47 25 29.3 1 Id 22 111.7 no 34 43.(1 335 1" 54-<' 334 S'; 1-4. 28(1 14 10.2 280 2S 45.3 77 55 41.3 7S 9 0.4 75 25 14.5 78 I" 27.7 281 29 45.2 2,Sl 44 23.2 64 o i().9 2S4 40 21.8 2S4 56 15.' + 2 45 29. S _ 845.1 S92.835S.7 + 2 51 45.7 - 375-') ')24.o 48.7 -2 50 21. 1 - 752.9 919.3 3-7 -2 40 44.5- i-('-<> <)AT.('to(<.<) -t-4 '■ 47.5 t- 952-f' 942.4 1)8.5 + 4 7 45.' - 57.5 95'.'J23fi.4 4(1 45 54."- 875.1 974.8 147.3 t-o 56 22.()— (■)28.9 107S.4 133.2 -d 32 5(1.(1— 71)9.1 892.6158.8 -o 2S 0.4— 21/1.2 852.2279.4 -o 32 7.(1 + SS6.8 8()4.9 . . -11 27 57.(1- 250.0 921.3 . . + 1 35 29.5- 938." 985.5227.9 + 1 28 47.9+ 401.61020.0 53. S — 02041.4 . . 893.9349.5 + 3 53 35-7- 953.3 969.2 181. 8 + 3 48 36.1 4- 21)9.6 ()97.2io3.i 216.4 37 3 53.8 — o o 59.0 128 15 55.5 -4 3' 28.3 128 52 5.1 -4 3" 4.9 I 64 54 25.7 -4 46 29.7 65 35 10.8 -4 48 6.0 64 33 16.0 -4 39 27.6 65 9 12.5 -4 40 47.7 61 48 36.0 -5 M 55-9 7 17 2.7 -o 47 5.6 37 123 55 21.3 129 10 50.5 129 25 .1.0 129 10 50.5: 65 3 44-4 65 19 48. 6 65 34 37.4 f,5 19 48.6 65 2 37. 8; 65 20 9.4; f,5 36 22.2 65 20 9.4; 61 5 4.0 61 21 23.0 980.7 -5 1 19.4- 929.2 939.3296.8 -5 6 20.1 + 300.7 973.2192.4 -4 59 48.9+ 853.5 940.8 . . -5 6 20.1 + 391.2 935.9 . . — 5 24 3.8— (J64.2 986,3172.2 — 5 29 22.1 + 31S.3 1011.2253.I -5 22 56.6 + S88.S 986.8 . . -5 29 22.1 + 3S5.5 965 I . . : — 5 29 14.3—1051.61008,9226.3 — 5 29 23.24- 8.91046.8198.8 — 5 27 36.54- 972.8101 1. 2 . -5 29 23.2 + 106.7 97.(.S . . -5 ,(9 6.8- 979.8 957.7 354-8 -5 46 4.3- 1S2.5 991.7 66.6 I 222 RKSEARCMES ON Till-. MOTION OK Till. MOON. Tabular Exlnhit of Reduclion of the Oaultalioiis — (.U)ii('luilcil, I'L.VMSTEKl AT ( iRKENWK' 1 — ronliiiued ] 'an and Times. i h Mean i'aliular j itric 1 ion. j 1 .Apparent F'osliion of Monn and Star. 1 -1. i" 1 No, Slar oceiilteil. Date. ^ ^ .i = ■ S .= S Sua. 1— . i/-n V /.-0 1 8 3 ii 5 - Longitiules. EalilUflcs, ■ ! h m s // m ,1- 279' y Taiiri, E. . . l6S2, ID 41 15 62 21) 28.8 61 31 0.3 -5 5' '5-5 +S76.5 055.7,354.8 .Mar. \\ to 12 .)3.(j i -5 14 sh.?! fji 2' 23.8 1 -5 4^1 4.3 —311,2 925.9 66.0 380 )■ Taiiri, I. . . lfiS3, II 57 41 1 61 51 25. i| fii ij 11,8 -5 3^ 41.8 — 700, s ■ 043.73I7.4 1 ' Veil. 5 ij 2 32.7 -5 3 33.0 61 22 2-;. I [ -5 4f' 41 + 5')2.3 067 . 1 1 04 . 281 ; Tauri, V.. . lf.83, 12 47 43 j f>3 10 7.1 '" 35 28-5 -5 37 42.4 + 786.4 042.3 • . Fell. 5 () 52 42.y — 5 2 46.4 fll 22 22. r --5 4''> 4-' + 501.7 920.6 . . 382 IK) Taiiri, I. . . 1683, S 4(1 .(O , V) is iy.3 7S 43 0.3 -4 3S 22.0 -Oif'.7 042.4 '3-3 Apr. 2 () 31 47.4 -■) 3 42. f' 78 5» 17.0 -4 43 38.0 + 315.7 966.6 65.7 283 I ig Tauri, V.. . 16S3, cj 27 54 70 40 58. 4 70 3 26, f) -4 33 55-4 •i-ooo-'i Apr. 2 10 13 8.2 -4 2 20.5 73 58 17,0 -4 43 33. (. + 283.2 040.8 . . 284 n Leonis, I. . l6fc3, ij 55 24 ' U5 25 17. f' 145 "4 4" + <) 30 I-O -7(17,2 081.8 44,6 May 4 12 46 52.4 + 1 24 I.I 145 25 51.2 + 27 ifi.f) + 705 -3 008,7 100. 3 1285 Ltonis, v.. . 1683, K) 40 i6 145 52 10 9 145 37 71 + 38 26.0 + fi75-0 080.5 . . i May 4 13 32 3' 9 ' + 1 26 17.7 145 25 51.2 + 27 I (1.6 + M1O.4 051.3 . . 1286 Jupiter, 1. . . 16S6, y 33 33 Apr. 10 . . , . . . . . . 21. .t 287 Jupiter, E. 16S6, 10 32 38 Apr. 10 . . . ' • • .... 24B: Saturn . . . 1687, 13 30 37 Mar, 28 . . . ' . . . • • • • • . -, 8.4 RKSEARciir.s ON tup: motion or thl: moon. 223 KCilJATIONH OK CONDITION OIVEN HY THI-} l»l{i:(!i:i)IN(} OCCULTATIONS OK STAKH. We may coiisiilcr it useless to attoiiipt to determine trnin these nldcr (iltHcrviitions any oluiiieiitM oi' tlio inoou's orl)it wliicli r*;iniiin eoiistiitit, and wliirli, tlKU'et'ore, ciin lie (letennined for any time t'nnii recent uliservatinns aioiie. Snch are tlie moon's ecceii- tricity, iiudination, semi-iliumeter, and parallax. Hut it may lie ad\ isalile to introduce the corroctious of those last two ohiuients intc the eijuatious, in order that when defin- itivo nuxhu'ii values are dod results for the values of the variations in (piestion. 'riie most imjiortant elenumt to be det(;rmined is the correction to the moon's mean loni^itnde, and it is to this that our attention will be principally devoted. The only elements whi(di we shall attempt to determine at the jiresent tini> 'vre the corrections to the inooi\'s mean lonji'itn'hter stars, snch as Aldebaran and S])ica, and, indeed, from the year 1680 onward, in the case of all stars bri;i'hter than the fourth maj^nitmle, no distinction of bright or thirk limb need be made, because siu-h stars can be readily seen at the brijiht limb with telescopes of moderate optical power. Observations of smaller stars at the bright limb are to be looked on with snspicion, and rejected entirely if there is no special reason to believe them accurate. All emersions are to be received with sus- picion, owing to the doubt whether the observer sa^v the star at the moment of its reapi)earance. They should be retained only when tlu;re is reason to believe that the observer did not record as gooil an observation which failed in this way. Besides these errors of observation, there may be a jiersonal error of a fraction of a second in estimating the tinie, which will necessarily elude discussion, and which, therefore, need not be farther considered. (/5) The errors in the elements may be divided into three classes: (i)tho.soof the lunar theory; (2) those arising from deviations of the moon from a spherical form; (3) those of the adopted po.sition of the occulted star. RKSKARCIIES ON Tllli MOTION OF THE MOON. (I ) III I'iirl III ut' I'jipm's piililislicd liy tlic 'Priuisit of N'fiiiis (Juiumissiiin, jicriodic cMiTcc'tioiis to II.wsi.n's 'riicory (irc! (iciliicdd. of wliifh tlio iiicaii vjiliu' will .sonit'wliat cxcouil one second. .Mr. Ni:i.>) can hardly he less than _V' 'n fhe most t"a\dral»le i-ascis, and may he {freiitcr to anv extent in niifavorahle ones. \\'lieii in the (roiirse of time the lunar theory is pcM'fected, and the proper motions of the stars are lietter determined, this prohahlo ei'ror may he considerahly diminished. \Vlieiie\' there was any means of estimating the pndiahle error of tlu* timo, that estimate is j^iscii in the following' list of eipiatioiis in the c(diiinn :^t. Its etl'eci is to 1)(! included in estiinatinn' the prohahle error. To eiiahle this to he done, the (dianf>'e of Ii ill one second of time is included in the eipiatioiis of condition. Tlie sij.;'nifi- cations of tin* indoteriiiinato (|Uantitiu.s in the eipiation.s are as follows: — fit, the correction to IEansion's mean loiij;itude of the moon at the date. '5/, the correction to the itii(le of peri<,''ee. <^0, the correction to the loiif^itnde of node. • ^ 'W;,,, the correction to the moon's latitude. A//, the correction to the moon's parallax. The mode of computing the coefficients of these (puuitities ha.s already heen descriheil in § 6, jiages 55 to 6S. The ahsohite tctrms of the e(|natious are tin values of l>—S', formed from the projier coluimi in the exhiliit of reductions already <;iven. In colinnn ± * i*^ f^iven the .supposed prohahle error of the observed times, (»rthe prohahle order of inagnitnde of ^^t. In the observations of Cassini, Series II, it may he assumed that the jirobahle error is always about 2" or 3". The phase (immersion or emersion) and the limb (bri<>'ht or dark) are indicated only in the unfavorable ca.ses, blank signifyin<^- an immersion or a phencmienon at the dark limb, while E indicates an emersion, ami \\ the bright limb. After the time of IlEvi'.Lirs, the jirobable errors of the equations ari.se almost entirely from the uncertainties ie the jiositions of the stars and the periodic inequali- ties of the moon, and are but slightl)' increased by the probable errors of the observed times. In the case of these obser>ations, the last column shows the relative weights which have been assigned in the provisional solutions of the ecjuations. KKSKARfllKS ON llli: MOTION ol Tllli MooN. 225 mi.l.lALDUi). lll'A'r.l.irS-rcmliniicil. l'.i|ii;iliiin. ii' Ycnr, i 4 F.ciii 0.031! ■ o.c)3 o.So ().23iW - 7i)-l ! • lf'35'0> - 0.47 +105. (j . i63i).3 - o.4» + 10.7 . i 1641.3 CASSKNDI^S. I 5.0 = j f) o - i 7 = I 8 o - I », — o 41 21 I') 27 5S 45 31} 60 3S 27 54 + O2.4 (■ 17.5 + 3-8 -MSfj.o + 10(|,(j + 57-4 4- 41.3 + Sf,.'' + 47.0 + f>.8 - 50. 8 ! 1627.5 1 . 1 1627.7' . ' 1632.1 1 . 1635. l637- 163?. 1631}. 17 o 18 o I ig o i 20 o 1 I 22 i24 ^25 126 127 :28 '29 — 1.07" + 1.04 — 1 . 10 + I. II — 0.51) + 0.()2 — o.3i : - 0.83 : — I.Oq : — I . 02 : — 0.65 : + 0.66 iir.vKLirs. I f -0.47,1/ + 57-3 35 i^'44- + 0.48 - 3'J.'' 35 - 0.47 + 17.5 35 If'-t5. + o.4() - 30.9' 35 — 0.30 + 53-5 25 ifisS- + 0.3S - 25.0 12 1660. — 0.37 + 6 6 20 1660. - 0.45 + 3S.I 40 I^'i3- - 0.58 +105. 5 25 -0.56 + 53-1 25 — 0.27 + II.O 12 1663, + 0.26 + 3.2 12 ^The final revision of tlie ohsciv 30 o = — 1.031W 31 () rr + o,l)7 35 o — — 0.86 36 o = + 0.71 37 o = — i.o • • 1 + 0.24 - 1.8 30 " I^ • - 0.45 4- 46.3 iS 1676.7 . H + 0.41 - 18.8 1 20 •■ E . — 0.40 — 25.4 72 1673.2 . - 0.35 -^- 15.3 22 1670.2 . U - 0.36 4- 12. 1 20 '' • H + 0.36 + 4.3 15 •■ E . + 0.38 - 24.4 16 " E . — 0.24 + 19.4 6? 1679.5 . , B 4- 0.22 1 II. 3 6? ■■ E 1 . - 0.43 + 54.6 20 16S1.0 . + 0.47 - 1.5 17 ■■ '■; » - 0.44 -t- 57.4 S 1683.0 . . + 0.44 - 39-3 8 " E U ) -0.53 4.146.5 25 1683.3 . . ■ ) -0.54 -r 9S.I 22 " . . + 0.56 — 59.6 2'' " E M e a vahic f,(/=4- I43''- 1 20- 75 Ap. 2 226 RESEARCHES ON THE MOTION OF THE MOON. CASSINI AND OTHERS, 8 a 'A 78 80 81 85 86 87 88 92 93 94 95 96 97 93 EjD -0.2S — 0.S4 4-0.33 -H 0.30 —1. 16 —0.24 —0.74 4-0.85 — 0.22 — 0.C2 —0.30 4-0.81 —0.14 4-0.21 4- o. '3 —0.32 4-0.84 —0.79 — 0.24 —1.30 4-0.76 4-0.76 —0.83 + 34.9 2 4- 28.0 2 4- 12.8 1 - 7.9 I 1 4- 21.4 2 i 4- 17.0 2 — 19.0 2 < 4- 8.2 2 - 11.4 2 4- 3-2 ^ 1682. I 1685.0 " E , 1685.8 . 1699.6 . j " E I70I.7 " E I7I8.7 • B B i B CASSINI, ETC.— SERIES II. 105 106 107 loS 109 110 o = — o.75(!f = - 0.95 = 4- l.oi 4- 0.44 0=r - 0.74 - 0.33 o = — 0.83 — 0.31 o = - 0.77 — 0.27 o.40ri/4- I.l6.-i(rj — 0.2l/(lW — o.76ii/io 4- 0.991! IT 4- 22.9 0.43 4- r.6o -1-0.07 —0.59 4-0.77 4-23.3 -1.86 4-0.04 —0.34 —0.23 —20.3 40.82 —0.68 -h 0.70 + O.IC) —40.0 — 0.52 4-0.21 —0.55 4-0.31 4- 2T.8 — 0.97 —O.oS — 0.5S 4-0.32 4-21.8 Tliese six equations result from using Cassini's correction to the (|uadrant, which is probahly incorrect, following these equations are given as lesulling from the new correction. - 0.76 - 0.59 - 0.34 4- 0.70 4- 1. 01 4 i.oi III 112 . 113 ! •14 115 tl6 117 118 119 120 121 122 123 0= - 0.75 0= - 0.95 0= -(- 1. 01 0= - 0.74 0=4- 0.01 o j= 4- 0.03 -= 4- 0.30 o = — 0.82 o = — 0.76 0-= + 0.49 c. = — 0.46 o = — 1.05 0.-= — 1.05 — 0.40 — 0.43 4- 0.44 — 0.33 — 0.02 — 0.01 ■f- O . I 1 — 0.30 — 0.27 4 0.2S — 0.13 — 0.43 — 0.56 ■i- 1.16 4- 1 . 60 - 1.86 4- 0.82 - O.OI - 0.04 - 0.33 - 0.50 - 0.95 -(- 0.62 - 0.98 4- 1.81 4- 1.84 - 0.21 4- 0.07 4- 0.04 - 0.63 - o.gS - 0.98 - 0.94 + 0.21 - 0.0" - 0.13 - 0.85 - 0.41 4- 0.36 + 0.96 ~ 0.55 - 0.59 - 0.36 - 0.87 4- 0.41 - 0.33 4- 0.99 4- 0.77 - 0.23 4- 0.19 - 0.39 - 0.41 - 0.57 4- 0.31 4- 0.32 4- 0.46 4- 0.62 4- 0.39 4- 0.99 1705.6 1705.7 « B ! ■' E B 1 706 . 1 1706.3 , In the * Cassini's recoril is 10" earlier than La Hiuk's. -r 14. 1 1705.6 . B 4- 17.5 1705.7 - 14.1 E B - 469 1 706 . 1 . - 12.7 - 13. 1 " -t- 15.6 " E B 4- 16.4 " + 15.7 1706.3 - 9.7 " E B 1- 7.5 1706.4 4 17.2 1706.9 + 9.9 1707.3 7« in solv "/■ ; t lis e(|ual on. ll RESEARCHES ON THE MOTION OF THE MOON. 227 CASSINI ETC.— SERIES 11— Continued. umber. 1 E( lu.ition. Year. ' 2 : £ ; i i i \ 1 ^ \ 1 1 124 = — 0.52(W — . 2 1 rl / — I . 1 () <• li :. — o.5fj/ii« - 0.821WV 4- o.Sg'-ll 4- 15-7 j 1707.7 ■ 1 _^ 1 1 i i 125 =: + 0.56 + 0.23 + 1.14 - 0.53 - 0.78 4- 0.59 — 6.3 : ' E B 1 I 1 126 1 = — 0.94 — 0.50 + 0.26 4- 0.38 - 0.33 -+• 0.99 4- 13-7 ' 1708. I j . U 1 127 1 = -0.93 — 0.50 4- 0.25 4- 0.38 - 0.38 4- 1. 00 4- 7-4 " s 128 : = + 1. 01 4- 0.61 — 1 .44 4-012 — 0.27 4-0.65 4- 84.1 1 1708.7 E ' .2q' = - 0.33 - 0.39 + r.3( 4-0.66 4- 0.66 — 0.74 4- 17-2 1 1709-3 : • • t \ 1 1 130 i 0= - 0.50 — 0.30 — 1.32 4- 0.75 — 0.7O 4- 0.57 4-177-2 1709.7 ■ . .3.' = - 0.S6 -0.54 -0.03 4- o.u — o.^6 4- 0.05 4-, 7-3 ' V, i 1 1 '32 0= — 0.30 — 0.22 — O.OI 4- 0.23 - 0.95 -h 0.71 4- 10.6 . V, i I 133 ; = — 0.3c — 0.26 — 0.01 4- 0.22 -• 0.93 4- 0.65 4- 17-8 ! " B ' ' 134 = + 0.50 + 0.25 + O.OI (- 0.21 - 0.S6 4-0.96 — 4-0 i E ! '35 = + o.i)3 + 52 + 0.02 4- 0.07 — 0.29 4- 0.63 - 1.3 1 " ^ 136 = — 0.91 — 0.50 —1.56 4- 03 4- 0.23 — 0.65 4- 10.4 1 1710.9 . I 1 >37 : = — . 40 — 0.2f) — O.O7 - 0.14 — 0.91 4- 0.47 4- ij-o " 1 t I 138 = — 0.05 - o.oS — 0.08 - 0.16 — I .o — O.JI - 0.50 4- 0.39 4- 17-5 . 1711.7 B i i 142 = — 0.20 — o.O(j - 0.44 — 0.42 - 0.99 4- 0.44 t- 12.6 " B * i 143 0= — 0.48 - 0.18 — 1.06 4-0.33 -h 0.36 — o.II 4- S.I : • B i 1 144 0= + 0.81 + 0.32 4- 1.80 - O.l'i — 0.46 — 0.20 4- 7-8 1 E , 145 0= + 0.48 4- 0.19 4- I.oS"> 4- <'.33 4- 0.85 — 0.60 ~ 6.3 E 146 = - n.56 — 0.30 4- 0..;, 4- 0.39 4-0. 84 - 0.68 4- ii.S 1712.4 I 147 = + 0.6O 4-0.28 -0.17 - 0.35 4- 0.77 -0.85 - 4-1 E B 1 1 148 o=»- 0.93 — 0.50 — 0.2G 4- 0.31 4- 0.32 t- 0.41 4- 12. 1 1714-2 I , i 149 0= — 0.98 — 0.40 — 1. 16 -h 0.26 — 0.30 -^- 0.06 4- 18.0 1714-3 •• 1 E 1 B ' r 150 0= + 0.98 -h 0.39 — I. 17 4- 0.28 - 0.32 ■y 0.34 - 14-9 ■ I 1 " 151 0= - 0.87 - 0.33 4-1.56 4- 0.48 4- 0.60 - 0.46 4- 13-9 1715.6 • j B I 152 0= + 0.O7 4-0.32 - '■") 4- 0.65 4- 0.80 — 0.60 4- 4-2 E ■ ! '57 0= — 0.56 - 0.27 4- 0.64 — 0.30 — 0.86 4-0.77 4- 7- 1715.8 . I • ! I 160 0= — o.gi -0.45 4-0.73 — 0.19 - 0.42 4- 0.93 4- II. 4 1716.0 ' I 1 161 0= - 1.04 — o.Ol 4- 1.34 4- 0.04 4- 0.08 — 0.60 4- 17.2 1717-7 • B I 1 162 = + 1.02 4- 0.59 - 1.32 4 o.io 4- 0.22 4- 0.37 - 13.4 " ! E 1 • ' I ' 163 0= — 0.60 -0.24 - 1.30 4- 0.7O 4- 0.76 -0.83 4- 5-4 1718.7 • • i 164 0= — 0.84 - 0.41 — o.fjo 4- 0.02 — 0.49 4- 0.95 4- 8.7 1719-3 • I ' i&S 0=4- 0.73 + 0.44 -t- •'■52 4- 0.03 ^ 0.64 -0.22 - 7-8 E B I 1 166 0= + 0.85 4- 0.38 + I.2f) 4- o.o3 - 0.41 4-0.69 - 4-4 1719.8 L i 167 0= — 0.80 - 0.37 - l.3f> — o.o3 4- 0.52 — 0.80 4- 8.1 1719-9 • • 1 I 168 o=- 0.33 -0.19 4-0.49 — 0.60 4- 0.97 — 0.76 — 2.2 1720.3 . • 169 0= + 0.54 4- 0.19 — 0.80 - 0.55 4- 0.89 — 0,78 — 7.6 : E B 170 o=- 0.93 -0.38 -0.39 — 0.12 4- 0.26 — 0.37 4- 10.5 1727.7 . B i • 7' = — 0.89 - o.jt -0.37 + 0.18 - 0.39 4- O.OI -1- 16.4 " • B k 172 0= - 0.57 — 0.29 — 0.23 -f- 0.36 — 0.32 -♦- 0.35 -f- 9.2 " • B '■ \ 173 = - 0.93 -0.40 —0.37 4- 0.13 — 0.29 0.00 4- 12.2 . .- - : B j i 22S tliSEARCHES ON THE MOTION OF THE MOON. CASSINI, ETC.— SERIES II— ContiiuKHl. s 3 Eciualion. i Year. | ! -g ^ .74 ^^ -f (J . 79 (5 1 + 0.351W + 0.31 , il J — 0.2f)/ wy + 0.58.5 A — 0.201' 1 9.0 1727.7 E 175 0= + 0.97 + 0.3S + 0.3S H- O.U3 — 0.07 + 0.09 - 39.7 E .76 -- + 0. 79 + 0.2S + 0.30 + 0.2f) - 0.59 + 0.28 - 3-7 E 177 = + 0.97 + 0.38 -(- 0.37 — D.OI + ".03 — O.Of) - 9.6 E 178 0= - 0.S8 - "■31 — 1 . 7 + 0.76 -t- 0.02 + f).i I7I4.2 185 0^ - J. 93 - 0.50 — i).26 + 0.31 + 0.32 + 0.41 + 12.3 ■' 1 186 0= - 0.9S — 0.40 1- 1 . 1() — . 2(i - 0.30 + O.Of) + iS.o i7t4-3 B .87 0= + 0.9S + 0.3S — 1. 17 +0.28 — 0.32 + 0.34 - 14.9 E i A ,VJ ^ -(- . 9S + 0.54 -0.93 -0.31J - 0-39 + 0.84 - 12.9 1714.7 1 i 180 = + o.8j + 0.40 + I.ll — 0.I() - 0.42 + 0.95 - 6.1 17148 E 190 = — t .04 — 0.61 + 1.34 + 0.04 + o.o5 — 0.f)0 + 13-5 1717-7 H igi = + 1 .112 + 0.59 — 1 .32 +0. 10 + 0.22 + "-37 - 10. " ; E , 192 = — 0.57 — 0.29 + 0.91 — 0.25 + 0.S7 - 0.35 + 13-9 1718.0 1 193 0= — 1.03 — 0.40 + o,<)4 + 0.07 4- 0. 19 — 0. 10 -t- ■5.3 171S.1 1 i "J-t = — . 60 — 0.24 — 0. If) +0.76 + 0.76 - 0.83 + 5.4 1718.7 i 195 = — 0.S4 - 0.41 — o.f>o + 0.02 - 0.49 + 0.95 + 9.9 1719-3 i I 196 0= + 0.73 + 0-44 -i- 0. 52 . -f 0.03 — u.fj4 — 0.22 - 3.2 E 1 B 107 = — 1 . 04 - 0.44 + 1.64 1- 0.03 — 0.2f) + 0.39 + 10. 1 1719.6 i I .98 0- - 0.75 — 0.42 — 1. 12 +0.12 — 0.60 + 0.06 - ■■3 1719-8 ; ^ I- 199 = -t- 0.85 + 0,3s +- 1.26 + 0.08 - 0.41 + 0.69 + 2.4 ] 2 200 — — i.o(> — 0.58 + 1.9S + O.lf) - 0.17 + 0.92 + 13.0 1725.1 1 I DELISLE AT ST. PETERSBURG. 201 = — 0.991! -0.47''/ + o.3[ t-itiJ + o.oi (■ (If — O.Oiil/' + 0.65^11 t- 4-7 I 1727.2 . 202 0-= — 0.88 - 0.48 — I .84 + 0.07 ■'- 0.23 + O.51) + 3.6 1729.9 203 = — 0.78 — 0.40 - i.f)3 - 0.15 -0.51 -I- 0.91 + I.O u ! 204 = — Oo - 0.35 - i.2fi - 0.23 -0.75 + o.9f) 4- 2.4 : 205 = — 0.25 - 0.18 — 0.53 +0.29 !- o.9fj — 0.50 - 1.0 i 206 (J = -«■ . 79 - 0.47 — I. Of) + 0. 15 + 0.48 + 0.22 + 3-5 ; 207 ■-= — 0.78 - 0.49 — I .f)4 +0. If) + 0.50 + O.lf) 4- 2.8 tl 208 0= - 0.53 — 0.30 — 1 . 1 1 -1- 0.25 -t- o.Sl — 0.26 4- 0.7 " 209 = — 1 . 00 - 0.43 -t- 1. 01 — U.23 — 0.20 + 0,27 4- :6.5 ■733-2 210 0-= - 0.49 - 0.23 -0.13 +0.34 -f- 0.88 — 0.76 - 14.6 211 0-= - ".79 — 0.5 J + 0.27 + 0.3U -t- o.f)i - U.05 4- 7.2 i73f>-3 212 = — 1 .00 - 0.42 — 0. 10 + 0.64 + 0. lO - 0.03 4- 6,7 1736-& B 213 = i- 0.98 + 0.42 + 0.08 + i).ii + 0.2; — 0-25 4- 4-7 i E 214 0-^ - 0.97 - 0.41 — U.43 - O.OI — 0.21 4- 0.19 4- 5.3 1736.8 B RESEARCHES ON THE MOTION OF THE MOON. 229 DELISLF. AT ST, VETERSBURG^ — Coiuimiu . ■ ' 1 1. i i mber. 1 E< iKllioil. 1 Year. £ 5 g •5 1 z ! . , 1 215 1 = + o.cjyiSf 4- 0.42''/ i- o.40i-ii..) o.oo/'l" O.O0(^ Ai — 0.32 (HI „ 1 1 ' •1- 4-3 i73fi.S E . j . 216 i = — 1.02 - 0.49 +- i.iS 4- 0. 19 — U.22 4- 0.39 4- S.f) 1737-4 • ■ ! ■ 1 219 i ^ + 0.41 4- 0.20 r- 0.64 — . 1 1 — 0.9" 4- 0.98 - 9.2 1737. & E • ! • 1 220 , :-= + 0.S2 4- 0.45 -h 1.26 - 0.06 - 0.49 + 0.76 221 = — 0.54 - 0.22 ■i- I. 17 — 0.01 i- 0.32 - 0.77 - 1.9 '73S.0 . • ' • 222 — — 0.93 - 0.41 - I.S5 i ) . 00 — 0.04 - D.OS +5.2 " 1 ■ ! • ! • ; 223 = — o.Sf) - 0.37 - 1-74 ~ o.or h 0.35 - U.35 4-3-2 !■:■;■ 1 224 ^= — 0.S2 -n.36 — 1 . 1 S 4- 0.02 -0.4S 4-0.38 + V.I •■ ^ • 1 • i • 225 o=-o.54 - 0.23 - 1. 05 4- O.Ot) - 0.S2 + 0.81 4-4.4 " • . ■ ■ • i -1.2 " E B 226 0= + ".5" -h 0.25 4- 0.97 (- 0.07 - 0.S5 4- 0.23 227 = — 0.50 — 0.24 - 0.37 4- 0.07 — 0.S7 4- 0.42 4- 4.4 173S.I 228 = — 0.73 — 0.36 - t-73 — 0. 1 1 4- 0.52 - o.6f, + 1.9 1738.6 . B T7 ' ' 229 = + 0.61) 4- 0.35 4- 1.52 - 0.15 -t- o.6f) - 0.37 4-0.5 , li B ' . ! „ , 1 230 = — 0.38 — 0.41 - 1-95 +- o.of) - 0.26 4- 0.04 4- 10.9 231 = — U.c)I — 0.42 — 2.U'1 — 0.1)3 4- 0.12 — 0. n - 5.4 " • ! " • ! 4-1.1 ■■ . , B ; . , 232 = — 0.53 — 0.25 - 1 . 29 + n.2I - 0.7S 4- 0.75 233 0=4-0.61 234 o=-o.74 ■+- 0.29 — 0.38 ■f- 1-35 — 1 .61 + 0.21 4- O.IS - 0.75 - 0.59 4- 0. if) 4- 0.2S 4- 3S-S " E . . ' . 1 - 1.4 173S.S . B . : I- ' 4- 3-0 I73'J.S . , B . ; 0.0 ■' E '. . . ; - 1.7 '■ . ' B . 1 4- 2.8 " E . . i 235 0=4-0.82 4- 0.35 4- I. So 4- 0.14 - 0.43 ■1- 0.49 236 o = — 0.8S - 0.43 — I . c/j 4- 0.22 - 0.22 — 0.32 237 -— •+- 0.90 -h ".40 4- 2.00 -(- . I (J — 0. 10 4- 0.44 238 0= - 0.90 — 1 ) . 4O - "-99 4- 0.05 — 0.05 - . sf) 239 = 4- 0.91) 4- 0.43 4- i.<)i — 0.07 4- 0.07 -f 0.50 240 = — 0.91 -0.46 - 1,48 4- 0.03 — 0.07 4- 0.73 + 1.7 i74f'-2 . ■ : ■ ] 241 0.-^-0.53 - 0.25 - 0.S5 4- 0.3: — 0.32 4- 0.37 4- O.f) " . . i . 242 = — 0.56 - "•3.1 - 0.91 - 0.35 4- 0.79 — 0.05 - I.S • 1 243 o=---o.87 - 0.4S - I .39 - 0.14 4- 0.31 4- 0.48 - 0.8 ; ; ; 1 244 = — 0.85 - 0.47 - i.3f' - O.lfj 4- 0.37 4 0.42 4- 1.3 " ; • i ' 245 --= — o.So - 0.47 — I . 2f) — 0.21 4- 0.49 4- 0.28 - '■' : • 1 1 ! 246 = — 0.90 - 0.4S - 1.45 -t- o.o3 - 0.18 4-0.80 4- 0.7 • • ' ■ 1 247 ; = — 0.()0 - 0.47 - 1-45 4- C.07 - 0.15 4- 0.79 4- 0.2 ! " ■ 1 • i ■ 1 248 = — 0.45 — 0.20 - 0.71 4- 0.39 - o.SS 4- 0.83 4- 0.8 ' " 1 ■ ! 1 249 i 0= - 0.84 - 0.44 - ..3f' 4- 0.17 - 0.39 4- 0.S9 4- I.I " ■ ; 250 ! = — O.S9 - 0.49 - 1.41 — o.ll 4- 0.25 4- 0.53 4- 0.6 ■ " . 1 , 251 , 0= - 0.89 - 0.49 - 1-42 — 0. 10 4- 0.22 + 0.55 + 2.2 ; " • j 252 = — 0.82 - 0.44 — 1.30 4- 0.19 - 0.44 -1- 0.93 - 0.7 ' " ! . 253 , = — 0.46 - 0,27 — I .01 - u.lfi 4- 0.S7 - i.iS 4- 0.2 I747-I 254 0= - 0.S8 — o.4() - 1.94 - o.Oi 4- 0.25 4- 0.51 0.0 " ,. 1 . . ! ,, 1 255 0= - 0.91 - 0.48 — 2.')"J . 00 0.00 4- o.()9 + ^■^ i • i • 1 ■ 256 = — 0.64 - 0.31 - 1.41 - (-.13 ■- o.7r 4- 0.04 + ^-o| 1 • 1 • ; • 257 0= — 0.90 - 0.4S - 1.95 - 0.23 4- 0. 12 4- 0.75 4- 0.3 " i • 1 • • 258 0= 4- 0.90 4- 0.49 4- 1. 89 0.00 - o.Ii 4- 0.42 0.0 1747.6 E • 259 0= 4- 0.79 4- 0.46 4- I.f>7 — O.OI 4- 0.49 — 0. 1() 4- 0.3 " "^ 1 • - 0.2 j " E 1 . 260 0=4- 0.82 4- 0.47 4- 1.73 - O.OI 4- 0.42 — 0.09 2 30 RESEARCHES ON THE MUTION OF THE MOON. FLAMSTEED. Si E s 2 Et|LKiti()n. 2fc: 262 ' 263 264 265 2f)6 267 I 26g ' 272 273 274 275 j 276 I 277 i o 278 = 279 = 280 = 281 = 2S2 = 283 = 284 = 285 := - o.Soilf - 0.71 + 1 .01 - o.'W - 0.81 + 0.S9 - o.yS - I. 01 - 0-95 + 0.93 - 1.05 + o.y() - l-"7 + I. If) - 1.03 + o.yS - o.Si + 0.87 - 0.93 + O.qS - 0.70 + 0.83 ■ 0.36 ■ 0.36 0.49 • 0.3S 0.47 0.44 0-39 • 0.39 0.43 o.4r ■ 0.43 0.41 0.61 ■ 0.58 ■ 0.52 0.50 0.43 0.43 0.4G 0.4S 0.36 0.36 U - i.78di^ — o.36/(W/ 0.57 — 0.62 + 0.03 + 0.48 - 0.43 — o. 19 0.05 1.48 1-77 I.I ■ I.d; 1. 41 0.25 0.27 1 .90 1. 78 2.00 1.99 i-3« "•33 0.26 0.29 0.65 0.69 1.28 '•52 — 0.17 4- o 12 + c ■' — 0.01 4- 0.05 + o.oi O.Oli — 0.18 — 0.13 — 0.23 — 0.15 — 0.74 — 0.62 o.47,l/'o + 0.67 + 0.09 + 0.52 + 0.43 - 0.18 T ■ 0.47 4- ■0.34 - 0-34 - ■ 0.38 •+- ■ 0.23 - 0.44 — ■ 0.03 — ■0.14 + ■ o. 19 0.34 0.61 ■ 0.52 0.38 0.25 0-77 •0.64 + Year. 6 VI 0, Limb. 0.S4I 11 + 31.2 1676.2 t 0.90 + 28.3 " I 0.29 + 9-5 1676.5 E . 0-55 + 103.6 1676.6 . 0.25 - 40-4 1676.7 B 0.72 + 26.4 " E 0.03 + 34-5 1676.8 . I 0.13 + 28.0 1678.7 . . I o.So + 33.9 1680.0 B I 0.33 - 4-9 E . 0.35 + 24.9 1680.7 B t 0.24 - 21.7 E • I 0.49 + 37.9 1 680 . 9 . B I 0.36 - 30-4 " E t 0,84 + 34-0 1682.2 t 0.51 - 29.8 E B 0.26 + 23.4 1683.1 I '•'■97 - 12-7 '■ E B 0.39 + 24.2 1683.3 • I 0.82 + 8.6 " E B 0.40 + 16.9 " . . I 0.75 — 29.2 " E ! 1 B , RESEARCHES ON THE MOTION OF THE MOON. 231 PROVISIONAL SOLirTION OF THE PRECEDING EQUATIONS. Observations of Bn.LiALDrs ami Gassendus. The only quantity which can bo obtained fn.ui tliese observations is a rough nicau correction to' the moon's mean h^i-ituih^ All the observations used were immersions at the .hirk limb, except in the case of the comparativel>- bri-ht star /* Gemuiorum, ot which the immersion was observed when the moon was full. The principal error to be feared is therefore in the determination of the time, which was derived by observin*' rr + 12" ±S". (li(iii[>, 165S-64. — 'Pile ciiuTsiou of fi Scoi'])!!, 1660. A))!'!! 26, Hevelus coiiMid- orod w(!ll obsorvcd, niid the result seems i;-ood. The other two oiiiersions I reject. The result thus o1)tin"ned is: — El)Ocli, 1662.0: AV ::r:-f.3S" ±4"; f?^' — 4-lS". (h-oiip, 1671-75. — The iuniiersioiis arc nil used, althouj^'h the oecultiitious of the I'leiiules 011 1674, .Vujiiist 23, were observed at the hrinht limh. 1 jud^c from the obser- vatious and other eousideratious that l[i;vi':i,irs could follow the stars of the iMi;iades elose up to the liudi of tlu- nioou. The emersions are all rejected, 'i'lie results are: Kpoch, 1673.9: '5f =z + 39".2i:3".4; St' — -{-22". drouji, 1676-83. — Here, althoii<>'h IIevelus's (dock-error seemed l)etter deter- niiiK'd than liefore, the observations exhibit anomalies which cannot be attributed to the apparent accidental errors ol' observation, and which, therefore, leave one in (h>ubt how the results should be treated. .\s the results cannot be worth a refined discussion, 1 shall simply state how I hav(^ used the e(piations. The emersions of Mars and of a Tauri have been retained, while, as Ixd'ore, all other emei'sions are rejected. The re- sults from ,v Orionis, 1678, .March 28, (Xo. 62), and fn.m the three .stars occulted 1683, April 2, (Xos. 75-77), have been rejected on account of discordance of residts. In the iirst case, the identity of the stai is still in doul)t, while in the second there was an interval of nearly two hours between the iirst occultation and the determination of (dock-error, du'-inn- which interval the error had to ha su)»posed constant. The results of the occidtations seem to indicate a large (dock-rate. Tliere remain nuie equations, of which the sum has been taken as a normal for determiinn;-' di. This e(|Uiition is: 8.44 .5* = 264" ±40"; and the result is EjKHdi, 1680.0: (5i r= + 3i"±5"; iit' —-\- 16". 'i'he (dose a,i>'reement of the four mean results derived from the oljsorvations of IIevemis is pundy accidental; the disconhuice of the individn.al etpiations in yeueral indicates that the [)robable errors we have assiniied may be satedy increased bv one third. Oh>icrv(if!i)iis of flic Froich (tstnDKimcr^t idhI of Fi.amstked. A preliminary examination of these ol)servations indicated that tliere was no sys- tematic difference lietweeii the results of the oecultiitious ob.served bv Klamstkeu aiid those (d)ser\ed by the French astronomers. They have thendbre been combined, and .solved so as to obtain corrections to the moon's mean longitude and to the longitude of the node. In effecting these s(diitions, we meet with the difficulty that the correc- ftfiSEARCHES ON THE MOTION OF THE MOON. 233 tlon to the tabular mean lon<,ntn(le cannot he re„ = + 2".,S6, wv]}rhi = 3.S. .Sucinid yiMiii), ( 'vssiM, La |[ii{i;, 1)i:i,i.si,k, 1699-1720. XiiniKil I'jiiififidiis. 31. 65 Sf — 2,32 I i'^0 + 0.753 '^''n — 466".S4 = o -2-321 +5-970 + 4.CS76 + 25"..S4:=o ^■753 +4-<'^76 +i7-^>3 — 29".3ir:o. Solul'imi. '5^ r=-f 14".7S, cpDcli 1712.5. 'V/„ zz + o".S2, wcinlit — 13.4. 'I'lic corrections i<)0 luivc a very siiifill weiglit iu botli equations. Occultations do not artbnl good data for dctcnniiiinj>- the correction to the moon's node, because, to he favorahh', an oltservation nuist l)e not too far from the node, and must not bo nearly central. A <>lance at the equations will show that the coelHcient of ifiO amounts to 0.5 in less than lialf the efjuations. Moreover, owinj)' to an accidental lack of .sym- metry in the occultations in each grou}), tlie value of t69 depends very largely on that oi' <%„, the approximate expres,sions being: — From the fir,st group, i(5(9— i".47 — 0.S5 f5?(„. From the second grouj), }60 z=. — 2''. 19 -f- 0.85 (%„. The actual value of 61)^ and (''519 should be consi„ — 4- i".2. Wlience we .shall obtain — From the first group, /''>^ = + o".2. I'Vom tile second group, iSOzz — i".2. To obtain a really definitive result, we nmst cond)inc both groups, suppo.sing the values of (h ind(>pendent, and putting — iSO., — 0.80 ;<')0„ Shn =0.80(5/;,, the subscript numerals distinguishing tlie values wliicli pertain to the two group.s. The coeflicient 0.80 presupposes that the position of the node and the tabular latitudes — 1-52 — 0.04 -|- 21.16 53S".27 = o — 4i".oo — o o".7^ = o. RESEAKClir.S ON Till: MOTION Ol' TIIK MOON. 2;,5 of t\w stars iuv com^ct nt tl.o cpccl. 1842, wind, is iilnrnt i.s - 1 „ hypctlu'sis as we (•nil nmkc. 'IMic (•(n.ilmii.ti.ni ..f tlit^ two j.'n.ui.s lias Ik-ou made on llic supposition that all tliooqimtionsofthosocou.l -n.np arc (irsl innltiplicl l.y ..25. and tliat ;''iO.,an.l dh,:uv, tluM. ivplar,(Mll)V0.8o^A-9, an.l 0.80 .W>, This conrs.- is tak.-n hccans.. th(, residuals show that tlu^ unit of woij-ht coiTcsponds to ii smaller pn.l.ahlc error ni the suc-ond i^Toiip than in the tirst. The conihint'd normals arc:— 39.56 , =:+ i".76 ±o".S; wei-ht = 2i. The prohiible error of each eipiatioii of wci-ht unity is about 3".6; and as all the o.piations of the second series were multiplied by tlw factor 1,25, the prol.ahle error of each observed distance of centre (.f moon from star would be alx.ut 3".o, which is the error already estimated from ern.rs of star-places and of the tabular p.M-turbations and from the irrejrularities of the moim's limb It i.s, therefore, from these sources, rather than from errors of the ..bserved times, that the errors of the ...piations arise, so that, when, in the course of time, the tal)ular perturbations and the places of the stars are more accurately d.^tenniued, more accurate results may be obtained troni these occultations. Obscrrations of CxsHis\ at Paris nml \)v.\axia: at St. I'rtrr.shtirf/, hrhrm, ly 20 anil 1750. i have not attempted any serious discussion of these observation^ having- merely sou<.-ht to obtain from them an approximate correction t.. the mean lon-itU(U> tbr some epoch near 1725. From the good observations between 1725 and 1730 inclusive, we ttnd:— Kpoch, 1728.5: (>)*—+ 7".3 (8 observations), a result I look upon with a snspicioii of its beiii- a little too large, owing to several of the observatums on whicdi it depends having been made at the moon's bright linilj. 23^> Ri;si;.\U(;iiKs ON tmk motion of tiii: moon. § 14. OI5SI':i!VATI()NS OK KCLIPHKS FROM ir.jo TO 1724. Tlu! tiihiiliir pliu'cs of tlio sun which aro used in the ruchictioii of tlioso uclipsos were iicc,i(hMitiilly oinittod in § 11, wIkm'u tlio corro.spondinir places of the moon aro {ifiven. Tlicy aro, tlicrcforc, };iven in the following tabh'. Thoy wore j^onorally coni- piitod for dirt'oront moan timos l>y dilforont coinpiiter.s, in order that the conipariHon of the resnUs nii<,dit serve as a cheek on the accuracy of the work. Tho ori^nnal results are all presented. Lon>;ilin/i-s of the Sun, from Hanskn's Tables. D.itc. Greenwich Mean Time. Longitude Mean Etjuinox. 1 Date, 1 Greenwich Mean Time. l.ongilude Mean E<|uinox 1, III s " h III s . . ., l62[. May 20 12 59 54 17.2 i()S4, July 12 no 46 12.2 " *' 18 39 34 6d 10 I7.5 " " 2 Id no 51 36.8 " 21 5 In f)() Id f..7 12 III 14 49-5 " " 24 Ck) 23 7.0 16S7, May II 50 48 33-9 1O33, .\|,i, 8 - 'J 21 IS 49 44-4 " I 50 50 58.0 " '* ■» 4S 1) !'J I 53-7 " " 12 51 '7 27-5 1639. Jl'"^ » 70 34 56.8 1689, Soi)l '3 171 14 54-4 " '* 3 3f' 70 43 33-2 " " 3 20 '-I 23 3-5 *' " 12 7' 3 33.7 " " 12 ■71 44 12.9 1645, Aug. 21 fj 143 34 I9-5 1699, Sept 22 12 180 8 18.3 1652, .\pr. 8 't 19 '3 46.4 " " 21 180 37 45-2 :f)5i, Aug. u 12 '39 14 52.0 1706, May II 12 50 42 54-2 .. 20 '39 34 4-9 " 20 20 u 5' 2 59-1 .. 24 139 43 42.3 24 51 II 4S.5 165(1, Jan. 2O 306 20 48. 4 1703, Sept. «3 12 171 9 S.o ,. 30 306 22 4.6 " 18 30 171 25 5-2 " 12 30f) 51 15. s 24 171 33 30.5 1675, June 22 II 91 33 18.9 ; 1715, May 2 12 19 12 41 42 51 8 20.2 45-5 l6f)i, Mar. 29 12 21 9 10 43 5 36.3 48.0 " • 24 42 20 22.2 1724, .May 22 61 2O 25.8 1&6O, July I 12 100 8 14.7 12 1) Oi 55 13-2 " 17 36 I(K) 21 35-2 " " 24 62 24 0.0 " 24 100 sft 50.3 1676, June 10 12 20 So 3o 40 59 27. S 33.3 . 24 81 9 6.0 The observations in question may be divided into two cla.sses: observations of contacts and of ])hases. The latter wore freuerally estimated l)y throwinjif the sun's imajio upon a screen so adjusted that the outline of the image should coincide with a circle drawn on the screen. The radius of this circle was divided into 12, 30, or 32 parts by concentric circles, so that the correspond! nj^ phases of the eclipse could be observed. The absolute maj^nitude of a phase thus determined is necessarily too RESEARCIIKS ON Till; MOTION OK Till; MooN -.■>/ iiiicertiiiii to ho rulii'd uii, iiwiii;;' to the nH'cct ot' irriulliitioii ami distortion of imiij;(^; hut, so far ns loiifj^itudo is coiiconu'd, this oll'oct will act in opposite dircctiinis hct'ore and aftor the tliuo of j;reatest eclipso. 'riierefore, hy snl)tiactitij^' from each other tlio correspondiiiff ol)servatioiis hoforc^ and after the middle, we slinll olitain results nearly frco from tlu; errors in (|iU'stion. This is the course which has hccMi ;^enerally adopted in tho discussion of these olworvatioiis. \VheU(!ver possihlc, ohservations at nearly 0(pial distances (m oadi side of tho niiddlo have alone heeii compared, the mean of two or more liein<; somotiuies comhined with a sin;;'le corrcspondin;^' one on tin- opposite side. When the ohservations were so lu'oken that there was no correspondence, the comhi- uation wiis made in the way which seemed adapted to "^ive tlu; most prolmhlo result. The details of reduction are presented pretty fully in the following;' forms; — I'nder the head of each eclipse is ijiven the apparent semi-diameter of the the moon as seen from the station at th»f l)e;;Mnnini;' and at the end of the eclipse, com|iuted with the same data and in the; same way as in the ease of occultatioiis. The sun's a])parent semi-diameter is c(unputed hy supposin;^' its value at distance unity to l)e 960". [n souuf cases, however, it may not exactly corres])ond to this constant, some \alue a little ditfereiit heinj-' used. Any small error in the semi-diamet<-r Ikmui^- in i^reat part eliminated fnmi the result, no fireat pains wen taken with it. The local mean times of the ohserved phases are, for the most ])art, derived from data already f,nven hy applyinji- the clock-corrections deriv(^d from altitudes or other sources. In the oliservations of (Ja.ssknius, the times are derived immediately from the observed altitudes. This tinu) heiui;- nsduced to Grecmwich nu^au tinu', the apparent position of the moon as seen from the station is computed in the .same way as for the occultatioiis, except that, instead of usiiij^- the parallax of tiu; moon, only the difference of parallaxes of the sun and moon ;ire emph)yed. I'Voiii this reduced pt)sitioii of the moon, and fnmi the f^^eocentric position of the sun, an; derived the tabular distance of the <'eiitres, which is (•■iveii in the c(dumii followinji' the mean times. To this taljular di.stance is added its ditfereiitial c'inuinj^', or the magnitude innuediately less than the hjast visible at ending. These two values of 111 are rejin^sontod l)y «, and a.., and in combining observations of contacts we have always supposed — At the same time, double weight is always given to an observation of ending, as com- pared with that of beginning, because the oljserver is less likely to fail in noting the lUCSKARCIIES ON Till. MOTION OF TIIK MooN. time wlicii tlu^ ('(tlipsc (lisM|i|(c;ii's tliini wlifu it ii|iit(':irs. \\\ tliis (■((iiildiiiitinii, flic nicjiii rcKiilt t'nmi tlio l»(',n'iiiiiiii;i' find ciid ot' iiii (u'li|»-ii' is iii(l('|)('ii(li'iit ut' die vuliic wliirli iiiny Iti' iissio'iit'il to (C,, iiml flicrct'nn' due-* nut i'c(|iiii-c iiiiy iiivcstiji'fitioii ii|' flic viiliK* ot lliiit (jiiiiiitity. Wi- iiiiiy sim|)i\- rc;;;inl a, and a^ as zero, iiiid ;^ivc doiildc wi-i^-'lit tu tlic oitscrviitioii of tilt' Olid ul' tluj f(di|)sc ms c.oiniiiinMl with tlint of hcifiiiiiiii;;'. Ill coiiihiiiiiiji' ohscrviifioiiH of coiitfift"* and phases to (ditaiii a mean result, it has lieeii supposed that one pair of eoiitacls is worth three or four pairs of ohser- lieiierallv iieeii sii vatioiis of phase, tlii' ]iroportioii varyiiiji' with the apparent accnratn" of the oliservi tioiis of phase. In a I'vw oases, wcijilits are assigned to the ol)s<;r\atioiis of phases; Itiit, ill f^-enernl, there arc no (hita for siudi an assi^iiinieiit. 'To facilitate the final discussion, the dillereiicc Ix-tweeii (iacli obsorved and tahiilar This ditVereiice is the ahsoliite term ion. distance is ^'iveii for ea(di separate o]»ser\at of an ('((nation c(nitaiiiin;;' . This combination is eliminattid from cacli pair of (d)scr\atioiis, at e(|iial distaJieos on imi' on errors ii each side of the middle, in tl le manner iilrea(l\- descri bed, leaviii;^' an e(piatioii in e aloiio. It has not been c(jnsidered necessary to write down the individual e(|iiations thus formed. The most probable rfjsnlts, (••eiierally (dttained bv citmbiniii^' tlie etpia- tioiis ill a suinmary maniier, appro.ximately, thoiifili not strictly by the iii('tho(l of leaj^t s(iiiares, are "i'iveii in connection with each set of obs(!r\ atioiis. Eclipse of 1621, .1/^f/y/ 20, ohsrrrcil hi/ (} asskndis ((t Air. |)parciit semi-diameter at bej^'iimiiiji' q36".4 Moon's apparent M-nii-diamettir at end 942". 7 Sun's apparent semi-diameter 949". o M 0011 Local .M. T., 19'' I'" S7"- Tabular distance if centre; 19S0 .7 — 1.00 '5* Observed distan(r(M>f centres . i,SS5".4 — n, 21'' 27"' I 7^ Tabular distance of centres . i57 •» Ohs. All. I.'x.il Mr T.ihul.ii DiM.ol Oil' III©. 15 : 21 33 20 .|8 •J.I 2( Icj 30 18 16 16 M 15 '5 3'J 1; 23 14 ?7 I I 22 13 44 34 II 3S II ic) I" I? c) 52 ') 5 lillK' 3 57 4 27-5 4 3'>-3 4 34. 'I 4 Jf'.'j 4 42-" 4 44-fi 4 41)-/ 4 5fi.') I.fi 5-1 10. S V 22.3 1 7. 1) II. s IJ.4 -0.8IJII -0.83 -0.58 -0.36 -o.2fi —0.04 4 +o.o3 12.7 +0.(18 13- 13- 14.5 + 0.71 + 11.74 15-7 +'J- 5 14.1 I7." +i>.'^4 s 17.2 i>.2 +0.S6 5 20.0 Ii>.4 +0.8S 5 20. ij II). 7 +0.88 5 23.0 20.6 +0.S1) 5 2(i. I 22.0 +0.()0 5 27.1) 22.7 +O.I)I 5 31.11 J4.I +o.i)2 5 36.0 2fi.3 +11.1)3 5 40.4 2S.4 +o.()5 5 4ri.i 31.07 +11.1)7 Disia II).. I : If) J. la.o II. f. '^•5 II.Ci 12.4 13-4 I5-" ifi.i) 17.4 lS.2 II). f) Tnliiila Disi. 2.7. 1-5 + 11 + 0.5 + 0.1 + 0.2 - '1.4 + 0.3 + 0.5 + 0.4 + "-4 \Vl. 23-5 H- 'o 24.3 I + I.fi 2f).2 2;.S + I-') 27.2 27.3 I + I." 21). I 21). fl j +1.1 31 .;o — "J I + ".4 I t Wlun-e two obsorved ' -.pp;irenl senii-diametui at beijinning . . . gsi/'.o Moon's a|... arum si.'mi-diamfti;r ai cTid <)35' -4 Sun's apian^nt scmi-diainctLT 945".*) No. of Obs. Alt. Local Mean Tabular Dist. of Obscr\ j Phase. of©. Tinii'. Centics. Dislan I 3f> 35 /; m s 3 48 04 I(j3f) - ,95,\t 18S5 - 2 33 51 4 f) 58 1449 - .9: 1450 3 3" 47 27 47 912 - .87 881 4 26 3r 5f' 49 343 + .02 360 5 25 58 5 27 348 + .3' 369 6 25 20 4 45 390 + -59 483 7 23 23 iS 668 + .91 748 S 21 38 29 58 987 + -97 1059 9 20 53 35 7 1132 -1- .98 1220 10 20 U 39 S<> 1270 -1- .98 1315 II 19 28 44 54 1415 + -99 1(46 12 iS 12 53 42 1676 -h .99 1700 13 17 2U 59 47 185S + .99 iSSi - Cor r. to Tal ular n is'. 51 H- 1 - 31 + '7 + 21 + 93 + 80 + 72 + 88 + 45 + 31 ■+■ 2J " 23 The contacts iilono here givo, <5f - + 33", wt. = 8. Phuse 2, coiuparcd witli tlio lueaii of 10, i [, and 12, <^'ivo.s the equation 1.92 Se=. + 32", wlience / iCf^f). yuni- i , obscn'cl by \\itv.v.o\. al or iinu- 7ik\I,//i l\iih. = 53 20 ; .1 — II'" 4S'.4 W. from C.iui-nwicli. Moon's apparent senii-diameler at begiiinini; . . 03') ■' . . • 03?"-" . . . 9-15".^' 241 Moon's apparent semi-diameter at end Sun's apparent semi-diameter . Corr, t(j ^ocal Mean Taliular Disl. of Observed .. ainilar Wt. Time. Centres. Distance. Dist. 1 h m s i " " 3 43 '8 ■ l()ii - .04'''' 1886 — "1 - 25 47 3 1817 - .04 1809* ! - 8 i 1 2 50 48 , 1722 - .04 if'O" i - 25 • 53 33 1652 - .03 if)2q ; - 23 2 59 3 1511 - -03 1 507 - 4 4 3 48 130" — -02 I38I 1 - 9 8 48 1262 — .0' 1255 i - 7 10 3 1231 - 0" 1223 ; - 8 • 12 18 1174 - •''0 1 1 60 - 14 17 33 1041 — .87 1002 - 39 ' 20 iS .)72 - .86 941 - 3' 2 ■It 3 827 - .81 813 - ^^ 32 3 f)S', - .75 &55 - 34 i 35 48 603 - .70 591 — 12 2 43 33 455 - -46 454 — I 2 48 3 307 - -2' 461 -i- 4 2 50 iS 381 - .05 38; ' + 4 57 18 307 + .44 417 -h 20 5 6 18 530 + -VO 559 + 20 2 9 33 610 + .84 1 622 + 12 t. «4 3 714 + -89 732 4- 18 2 21 33 ' 910 4 .05 037 -t- 27 2 24 3 ()76 + .ip I OCX) + 24 35 18 I2q2 + .98 I33f, + 44 38 33 1385 + -98 1441 + 56 41 33 ' 1472 + -90 1504 + 32 43 48 1537 + -00 1578 + 4> a 4f' 3 if)03 T- .90 1630 + 27 • 48 18 1 1670 + .99 1693 + 23 40 3 1692 -*- .09 ; 1725 + 33 54 33 184^1 + .99''' 1 1883 — nj + 37 •Derived from " rircnmferi'iilia r.iiip'-al.i" 33 The original observations are found in IIoRK'.ix's Ofiiis- aih Astiviiomici, London. lf)73. l>;l,^l■ 327. and asnin on I page 3S8. I '--ould not learn the exact position of I1"U- Rox: the longitude given aliove and employed is taken from a map, but the latitude is that given by Hokrdx. The separate results for reducing the clock to mean i iiuk as derived from altitudes are: — Cloi k T me. /( m ,f 2 30 I) 2 38 3 IS 45 4 '5 15 5 ■7 45 5 59 30 fi 5 45 (> / 15 b 8 45 f. lO 30 (1 12 45 fi 17 15 Correction. }it — 2 2fi - 2 37 2 37 — 5') — 1 5S — I 3 — 2 f> - 3 I - 2 4f' — 2 4f' — 2 20 - ' 55 Mean - 2 1 2 ± S« Tlie (••mtacts alone ji'ivc (5£_4-34; The obsorvatiou« of plias,. rS. = + 27 ( i 2 pairs); The phase from aiijjU' eclipsed . • • ■ • '^t — -\- ^' ■ The most pmibable mean from all the observations, r5f = + 27". .Tndo'ln- fnm. the .liseordance of the m. asnres, the probable error .tf this resnlt wo,.ld n,; exceed 3"; Lnt the possibility of systen,>.ie ern.r ,nnst ^ ^^.^.^. .^^^^. We can hardlv suppose a set of observations n,a,V> at tins epoeh to wne a p.ob.,1.1. error less than" <': ami when we a.Ul the nn^-rtainties respeetn.o' eh.ck-em.r ami «eo- Kraphicul position, the probable error may be in.'reased to S or 9 • ;n 75 A p. 2 24: RESEARCHES ON THE MOTION OF THE MOON. Rdipse (>f 1639, yiiw 1.2, (>/isit,vJ i'v C.assic.vdus iil Aix. '? = 43 32' ; >=2i"' 47" W. Moon's apparent semi-dianieler at beginning . 935".o Moon's apparent senii-ilianieler at end . . . ()3o".() V4/ J 1 '0 <0 1/) .2 , 1 Local Mean i Time. 1 Tabular Distance of Cei.tres. Observed Distance. Corr. to Tabular Dist. Obs. Alt. of 0. c s . 3 • Tabular Distance of Centres. Observed Distance. j ^ Corr. to 1 Tal)ular Dist. 1 ' // m 4 40.9 31. 8 — o.S9'W i 3"--l-"i -0.4-0, 19 -15 5 30.3 12. T — 0.44 (if II. 8 -"•3 28 10 ' A-i'i 30.8 - .88 31.4-O] 19 30 31-7 II. 7- .40 II. I -0.6 28 44.0 30. 5 - .SS 29.8 -0.7 19 25 32.2 1 1 . 6 - 37 10.8 -0.8 ' 27 -10 ■(5-9 29.6- .88 29.4 — 0.2 ■9 5 34.1 1 1 . 1 — .30 10.3 —0.0 1 27 20 47.8 2S.8 - .87 28.3 -0.5 .855 35-0 10.9— .26 10.2 -0.7 1 27 41)- 7 28.0- .87 27.7 -".3 13 36 36.8 .0.7 . . 9.9 -0.8 1 26 37 51.9 27.1 - .86 27.1 0.0 18 40.2 10. r . . lo.o —0. 1 , 26 to 54.3 26.0 — .85 -5-7 -0-3 17 16 44-4 10. . 9.9 —0.1 \ 26 2 55- 1 25-7 - -Ss 25,0 -0.7 16 40 47.8 ■.0.2 . . 9.S -0.4 ■ 25 30 58.0 24.4- .S4 24-5 +0.1 16 51.6 10.7 + .51 \ 10.5 —0.2 ! 25 24 5S.6 24.2- .84 23.7 -0-5 >5 30 54-5 II.3 + .f>2 , II. 7 +0.4 ; 25 " 5 o.S 23.2- .83 22. S -0.4 15 57-4 I 2 . I + .68 '2.7 +0.6 24 40 2-7 22.4 - .83 21. 9 -0.5 14 40 59-4 ■2.7 + .73 13.0 +0.3 i 2) 25 4.1 21.8 - .82 20.9 -0.9 13 5S 6 3.5 ■3-9 + -78 14.0 + 0.1 24 5 fl.O 21. I — .80 20.0 -I.I 13 35 5-7 14.9 1- Sl 14.9 0.0 23 40 S-3 20.1 — .78 19.4 -0.7 13 25 6.7 15.3 + -82 15.5 +0.2 23 .30 9.2 I';- 7- .77 19.0 -0.7 >3 5 8.6 16. 1 + .84 16.2 +0.1 23 20 10. 1 19-4 - .76 18.9 -0.5 12 48 10.2 16.7 + ,85 16. 8 + 0.1 23 u 12.0 IS. 6- .73 18.2 1 -0.4 II 18 19. 1 20.6 -f .91 21. 1 +0.5 22 55 12.5 18.4- .73 17.9 -0-5 [ II 20.9 21.5 + .9' 21.5 0.0 22 30 14. s ■7-5- .72 16.7 -0.8 10 37 23.1 22.5 )- .93 22.5 0.0 22 15 Ift.2 16.9— .70 r6.5 -0,4 ' 10 27 24.1 23-" + -93 22.8 —0.2 22 (1 17. f> 16.4 - .68 15.6 -0.8 ; 10 10 25.8 23. S+ .94 23.4 -0.4 21 2 23.0 14.4 - .60 14.0 -U.4 10 26.8 24.3 + -94 24.1 —0.2 20 30 2f).I 13-4- -55 12.4 — I.o 1 9 45 28.3 25.0 + .95 25.0 . 20 20 27.0 '3.1 - .53 II. 9 ! — 1.2 9 3" 29.7 25-7 + -95 26.2 +0.5 20 3 2S b 12.6 - ,49 „.8 1 -0.8 g 32.8 , 1 27-3 + -95 27.6 +0.3 The ('onstiuit error in tlie observjitioiis of phase would seem to l)e vei-y small. 1 have, therefore, used tlie tirst four certain observations of |)has(! by themselves, and in the ease of the remainder have combiiKid olwcrvatious after tht* middle with corre- sponding- ones before. The result is <5trz:+o'.3Sr= + RESEARCHES ON THE MOTION OK TlIK M(J()N. M,'^ Jiciipsr of 16,^9, yi'tu- I, ohcnrd l7-S 3i-i; — I . 00 ri 1 3I-39-"' 3i-4-"i + o.3-«, (1 in 23-9 2.9 4-o.99(^( 6.7 4.3 + 1.4 5 28.1 2f).0 — I . OU 2(1.3 25.8 —0.2 1 6 25-5 3.6 +0.99 7-1 4-7 + 1.1 5 J3-2 23-5 — I .00 24.8 24.1 +0.6 ; 6 26.9 4.3 +0.99 7-4 5-> + 0.8 5 38. (. 20. S — I . 0(.i 24.1 23-4 +2.6 t =8.6 5.1 +0.99 7-7 5-4 •t-0.3 5 42.2 IS.., — 1. 00 21.9 21.0 +2.1 6 30.1 5.8 +1.00 8.5 f>.3 + 0.5 5 45-7 17.2 -O.IJ9 20.0 18.9 -t '-7 6 32.6 7,2 + 1 . 00 10.7 8.7 + 1-5 5 48.2 I5.1) -I'-'W 19. 1 17.9 + 2.0 6 34.2 8 . (J + 1 . "O 11 .2 9-3 + 1.3 5 50-7 14. f. -o.yy 1S.5 17-3 + 2-7 6 3f'-i 9.0 +1.C0 12. 1 10.3 + 1-3 5 53-2 13-4 -o.gg 17.7 16.4 + 3-" 6 38.2 10.2 + I . 00 13 II. 3 + I.I 5 55-2 12.4 — . yS 15.6 14.1 + 1-7 6 40.1 1 1 . 1 -•- 1 .(,0 14.0 12.4 + 1-3 5 57-'> 1 I .2 -o.gS 14.0 12.3 + 1.1 fi 41.9 12.0 +1 00 i5-f> 14. 1 + 2.1 5 5i).f' 10. 2 — . yS 13.4 II. (> -+-1.4 6 44.2 13.4 + 1 . 00 17.2 15-9 + 2.5 f. 1.7 Q.I -o.yS 13-1 11.3 + 2.2 6 45.9 14.3 +1.00 18.1 16.9 + 2.6 6 4.1 7.9 -o.()7 12.5 10.6 + 2.7 6 49-3 16. 1 +1.00 .9.0 17.8 + 1.7 6 fi.o f...J -"•1)7 12.(1 10. 1 ; 4-3-2 6 5''- 7 16.9 + 1 . 00 19.7 18.6 + 1-7 (•) 8.0 5-y — . 7-4 5-" 1 "**' f, 57.8 i 20.8 +1.U0 22.5 21.7 + 0.9 (. 17.1 1.4 4.9 2.3 i+o 7 0.9 22.5 4 I. 00 22.8 22.0 -0.5 f) IS.I 1.2 3.f> 0.9 f -0.3 7 •-•5 23. fi +1.00 24.4 23.- — 0.1 U 10.3 I. I 4.0 1-3 + 0.2 7 -■3 24.9 4-i.'>o 25-0 24 1 - t)-5 6 21.0 1-5 -l-u.(j7 5.6 3-1 + 1.6 / ' :~.1 +1.00 26... 25.5 — 0.2 6 22.8 2.3 + 0.09 6.2 3.& ,...3 7 12. u ^ a8.<. +1.00 i 3...^ 31.3 (+ 2.7) IIevelii's i^'ives a immltor of (Irawiiiji's of jiliiises of this eclipse, sliuv il;- tliaf his iiLstnuiiciit was altoffethtT out of focus, the cusps of the sun Ix'iufj- .so rounded near the time of i^-reatest phase that tht* arc of sunli^'lit was of nearly ■ ,ual breadth throiifi'h- (lut For this reason, and also because tiie times depend entirely on some kind of a sun-dial which may not iiave been in the meridian, tliis eclipse was in the first place rejected entirely. (See p. SS for original note upon it.) Hut I afterward concluded to reduce it, if only to see what kind of a result would l)e obtain. om the worst set of observations found in his work. The irradiation seems, from the excess of abmit ;/ near the observations of ^^reat- est phase, to have been about one-tenth the sun's semi-diameter. In the column of corrected distances from observations, the observed eclipse is increased by its tenth part to allow for this. Owin^r to the uncerttiinty of the law of error, 1 have only combined observations of nearly etpuil phase on each side of the middle in the same way as with the eclipses of Gas.skmm s. The ontacts are rejected entirely, as there is clearly a mistake of several minutes in the observation of the end. The mean of 244 RESEAUCIIKS ON THE MOTION OF THE MOON. tlie lirst scvciittH'U abscvvutitms of pliaso .>/><(-r,'ci/ fiv Hevkliu.-^. Moon's semi-diaim-'tcr at beginiiini^ 10 22 1048 — 0.72 1039 - 9 15 12 1013 + 0.82 1078 + (.5 14 22 qSl — aji(> 1)60 — 21 18 22 1006 + o.Sf) 1117 + 51 II) 22 899 - 0.59 S80 - ly 22 2 1152 + 0.89 1 191 + 39 23 52 S35 - 0-50 S22 - 13 2f) 37 1226 4 0.91 1276 ¥ 50 24 52 322 — 0.48 Sot — 21 34 22 13S6 + 0.95 1434 + 48 27 52 7S4 - 0.41 781 - 3 50 22 1730 4- 0.98 1790 + 60 29 52 7(11 — 0.30 7(>2 + I 51 52 177" + 0.98 1830 + Oo 32 52 733.- 0.27 742 55 52 l^ifjl + o.gq igog— n.j + 4S-", A system of twelve equations of cniidition is formed l)v sul»tractiii"' the first twelve residuals from the last tw(dve, contact results excepted. The solution of these equations, .slightly greater weight being given to tht»se near the beginning and end of the eclipse, gives '5*- = +54". From the contacts we have: — Meginning End from which, supposing «, rr 2 a.,, we have 6t=^-\- 42". J t«ke, as the most probable result from this eclipse, '>'* = + 5'"- RKSEARCIIES ON TlUi MUTION OF TIIi: MOON. 245 Hrlipsa of 1652, April 7, ohscrri'il hi/ Gassexdi's ot l)i 32 : 18 30 21 2 22 52 24 4" 26 54 25 54 31 45 35 lo 37 32 3S 54 4f' 5 48 31 6 26 lOtq— 1. 101' f 1629— 1. 10 1558- 1. 10 I5i5-i.0() 1470— I .OIJ I4Ii)-I0i) I305-I.1KJ 1315 — 1.08 1245-1.07 1 1 ()2 — 1 . 0(1 1 104—1 .05 1072—1.04 qlo— 1.00 857 — 0.1)8 562-0.53 1955- 1O04 I53(> I5if' 1476 1436 138& 1317 1253 057 loi)7 1037 S.,I 838 578 1 579 1509 1487 1447 1 406 1356 1288 4-3f' -25 — 22 + I + & + 17 + 21 + 2 + 3 - 5 - 7 -35 -19 -19 + lfi + 36 -50 -4>J -28 -23 ->3 - 9 -27 9 9 12 34 14 15 27 55 30 17 39 f' 42 II 51 - 53 5 54 40 14 54 16 58 15 25 21 3 538-0.421!' 528—0.24 527-0.14 652 + 0.51 690 + 0.58 864+0.76 931+0.80 1136+0.89 1184+0. 91 1222+0.92 1731+0.99 1782+0.99 1821-^1.00 1887 + 1.00 509 459 499 638 69S 8ql 957 II97 1277 12S5 1795 1835 1895 1955- j-29 I -69 -28 -14 8 +27 +46 +61 +93 +63 1+64 1+53 1889 ', +74 + 67— nj 1780 1823 + 49 +41 + 68 + 67, Here, it is evident, the observed distances are sj-stcmatically too — 1400V) l,y applying which we torm the second column of observed di.stances and of correction to the tabular distances. Where this second column is not formed, we have corre- sponding observations betitre and after the midille of the eclii)se. (jonmienciiig n(»w with tlu^ consideration of the contacts, the considerable mag- nitude of the eclipse at the ol)serv('d moment of contact niuih-rs it suspicious; still, as 246 RESEARCllKS ON THE MOTION OF THE MOON. IlEVEi,n-s siivs, it Wiis (.1 (Served "accuratissiine", 1 luive not felt jiistilied in rejectinj-- it. Coinbininj-- the observution.s of first and last contacts in the usual manner, we find: '5f + 33", "t- = 2. The mean of the seven (djservatioiis following- lirst contact, nsin-i' the corrected distances, gives '5i rr + 26", \vt. =: i. The mean of the tin-ee observations precodin<>' last contact "-ives Sf - + 53", wt. = 2. The result of the intermediate observations, five on each side of the middle of the eclipse, in which the distaiu-e exceeds 890", tornied by takinj-' the differences of the correspoiuling- measures on each side, is: — '5i + 36", wt. = 3 ; the mean result of all tlie measures, '5f = + 3X". Considering the uncertainty of the times and of the measures, the probable error of this result cannot be uuu-h below 10". Eclipse of 1654, Aiii^itst 11, obscnr,! by Wai.tkkilis at Aix, Moon's somi-tliaiiielfr at licginnin),' . 970' Moon's si'mi-diainetcr at end . . . 973" Sun's semi-diamolcr g^g" Obs. All, Local Mian Tahnlar Dist. of Observed of 0. Tinii;. Ctiuris. Distanru. 35 30 38 39 41 41 42 43 45 47 48 49 50 30 15 35 45 10 35 35 b 35 "4 lo 7 20 // HI 2(1 24 g 32.0 - I .uoiW 32.0 211 29-3 30.2 - "■'W 29 -3 20 42-7 25-3 - 0.94 24.1 20 4'). 5 22.8 - 0.8,, 22. S 20 57.8 20.0 - 0.S2 21.5 21 "•3 13.3 - o.So IS.S 21 (1.2 17-4 - 0.72 17.5 21 9.3 16.5 - 0.67 If). 2 21 24-3 132 - 0.32 l3-f> 2r 34.9 12.2 -f- 0.04 12.3 21 40. y 12.4 + 0.25 10. () 21 47-2 13.0 + o.4f, I3.f' 21 55-3 1 ■ 4-3 + 0.66 ■4.9 ! Obs .All. Lo<:aI Mcai Talnilai DisI, of 1 Obsirvid of©. Time. f't'iilrcs. Distance. .i . . // w » ] - — 0.0 1 51 10 22 1,1 15.f1 T 0.781!) lfl.2 + o.f) 0.9 ■ 52 2 22 7.2 17-1 + 0.86 •7.5 + "•4, 1.3 52 2(, 22 10. 1 iS.o -)- 0.89 18. 8 + 0.81 0.0 i -^ 12 22 15.(1 '9-5 + u.y4 20.2 + 0.7' '0 1 53 50 22 20.6 21 . 1 -1- o.r)7 21.5 + 0.4 0.5 54 21 22 24.7 22.4 + I.otl 22.8 + 0.4 O.I 54 55 22 2i}.2 23-9 + 1.02 24.1 + 0.2 0.3 55 20 j 22 32.7 25.1 + 1.03 25-5 + 0.4 0.4 55 33 i 22 34.5 25.7 + 1.04 26.8 + I.I 0.1 55 58 i 22 38.0 26. S + 1 .^^ 20.1 + 1-3 4.5 5f> 18 22 41.0 27.9 + 1.05 21). 4 + ' 5 0.6 57 t 22 47.4 3<'l t- 1.07 3'i.7 f 0.6 O.f) j 57 20 1 22 50.4 31.2 + 1.07 32.0-n.. + 0.8 RESEARCHES ON THE MOTION OF THE MOON. 247 Tliorc is no (ivuliMV-o of systoinatic cmtr in tlio determiniition of tlu; pliascs. If wo tiiko tlio snni of all tlie o([nfttions in wiiicli tlic coolKcicMt oxccods 0.6, tlio cimtacts o.\('('j)tO(l, Avc have: — Sum of seven ('(jiiations near l)o-ive '5f = +o'.53. We may therefore [)iit, as the result of this eclipse, ,5t=4-3i". Er/i/'Sf of i66r, March 29-30, nhrnu-d hy IlKNKr.ius. Moon's appiirciil sonii-iliamcler ;\t licginniiii; . ii»0".o Moon's apparent s;Mni-cliaini'in al und . . i(x)6 ".5 Sun's apparent semi-diameter 059 -'J Local M ean Tahniar Dist. of Observed Corr. to Local M ean Tabular Dist. of Ol)Served Corr. to Time s 10 C( ntres. IQcjI — 1 .031I1 Distance. Iq()() — 'i| Tab. Dist. - 25 Time h lit 23 53 47 Centres. 1014 + o.SSih Distance. Tab. Dist. /; III 22 K) 967 - 47 20 33 KJ54 - 1.03 lq2() - 2S 4 30 1235 + o.yy 1247 + 12 21 I 11)44 - I -02 I l)Of) - 38 6 25 1274 + 1. 00 1307 + 33 22 5> Ii)03 — 1 .02 1 866 - 37 8 12 1312 + 1.02 1367 + 55 24 if) l8(jf) — I.OI 1826 - 40 '5 12 1472 + 1.05 1527 + 55 25 30 i32g — I.OI 1 7 24 1 706 — 0. i)() 1686 — 20 ■0 4 1561 + 1.07 1607 + 46 4' 30 1438-0.93 1447 + '0 1579 + 1.07 1627 + 48 50 >0 1236 — 0.86 1267 + 31 20 34 1596 + 1.07 1637 + 41 5S 50 i'54 - 0.75 1067 + 13 22 4 1632 + 1.07 1667 + 35 50 55 1035 - 0.74 1027 - 8 22 58 1654 + 1 .08 1687 + 33 23 I 40 1003 — 0.71 007 - 6 23 48 1674 + 1.08 1707 + 33 2 36 i)SS - 0.70 047 - 4t 25 6 1705 + I .oS 1727 + 22 4 32 055 -0.65 007 - 48 26 7 1730 + 1 .08 1767 + 37 2 S78 - 0.54 S47 - 31 26 45 1745 + i.oS 17S7 + 42 12 S 837-0.4P S37 27 5fi 1774 + I. 00 1S07 + 33 13 22 824 - 0.42 827 + 3 2S 53 1798 + I.oq 1847 t- 40 ■0 14 75S — 0.22 747 — II 30 21 1832 + 1 .10 1886 + 54 2t iS 744 -0.15 727 - 17 33 26 1907 f 1. 10 1966— '1 J + 50 40 41 8o() + 0.61 827 + 18 Combinin-;' the seven pha,.ses foUowin;^- the beginning' with the corresponding ones preceding the end, ve fnid ^5* — + 34". The contacts alone give <5f — + 48". Giving th(^ mean result from contacts the weight of two pairs of observations of i)hase, wo have: — Af = + 37". The other i)hase.s do not correspond to each other, and the agreement of the .sevtMi pairs we have used is .so good that it thtes not seem necessary to dist-uss them. 248 RESKARCUES ON THE MOTION OF THE MOON. Eclipse of 1666, yitly 1, ohscrrrd by Hkvki.us, Mdoh's .ippaicnt sunii-ilianicicr at lif.niiininR . 1)44". 8 Moon's appareni suini-cliaim'tci al v\v\ . . . fdiir observations follo\viii<>' first contact, combined with tho corrospondinfr t'oiu' precedin}^' last contact, ji'ive Se — -f 24. Tho remaining obsei'vations in which the distance exceeded 900" give f5£ = + 22", or <5i— +15", according as wo Inchido or reject the donbtfnl fifth observation of phase. Tho most ])robable resnlt o\' all tho observations is. <5*= + 25". RESEARCIIKS ON THF, MOTION OF THE MOON. Eclipse of 1C76, yiiiie 10, ohsi-ireil hy I'l.xMSi kid nt Giriin.'uh. Moon's apparent srmi-diamctir at first olisorvalion . S()4".() Moon's apparent senii-iliamuler at last i>l)si'rvalii)n . 8()f> "o Sim's senii-ilianieter i)-l5 ■" ' i Corr. to Mean Time ''«! «'l-'>- Dist. of Observed Dist. .,.^,,,,,^^ Centres. : (by cuspsj. ; |jj^, 249 h m 20 2 20 II 20 38 If) 4 32 "J 1751 — o.fifjiW 1655 ~ o.fM 1513 - oM 1244 — 0.22 20 16 2q 1447 — 0.551W 20 18 58 ' I416 — 0.53 20 25 53 \ 1339 — 0.40 20 26 53 ' I32q — 0.45 20 33 4 i 1277 - 0.3S I73f> 1 039 I4')5 1282 (liy dir. ineas.) 1433 14" 1361 1308 12S1 - 15 - If) - IS An exainiiiation of Fi.AM^i i;r.ii's ol)served semi- diameters of ilie sun shows that liis micrometer measures of that element rei|uirea correction of — 7". 5 for irradiation when ilie lonf? telescope was used. + 38 I and — 14 '.3 wlienthesliorl one wasused. Thesecor- rerlinns have lieen applied in llie colnmn of oliservcd _ ' distance when necessary. - 5 + 22 — 21 + 4 At the timtt of the bist meiisum of the (listancc of (Misps, the eclipse mis so far iidvaiieed that 110 rehahh; residt coiihl l)e obtained from tlie measure. .AForeover. the diseordaiice of the result is such as to indicate some mistake. The results from the other measui-es nuiy fairly receive the respective weio'hts 4, 3, and 2. The discord- ance of the third measure of phase is also so <>-roat as to <^-ive rise to a suspicion ot some error in the reciu'd. The error is in fact between 30" and 40", whereas the probable error of Fi.amstf.ek's measures of the sun's semi-dianu-ter tUtes not in gen- eral exceed 3" or 4". From the three first measures of distance of cusps with the wei<,'hts assifjued, we have, ''if rz+ 2 5".o. The suni of all the etpiations f = + ''^"• Rejectino- the third measure, we shall have, I.Ql ''if = + 36; .-. ''if = + 10". Tiie residts from measures of distance of cusps near the be«i,'innin<;- of an ecli|)se ought to 1)0 prettv accurate, while the discordance of the ineasiu'es of phase renders their results uiu'ertain. I t!;,-refore consider th(^ most probable result from thiN eclii)se to be. (5f = + 23" ±6' 32 T.J Ar. 2 250 RESEARCHES ON THE MOTION OF THE MOON. Eclipse of i()?>^, yuly \2, ohsencd by I'I.amstked. Moon's a|)p;irciit somi-diaiiR-ltr .11 hijjinniiiK . 946' .7 Moon's apparent scnii-diamctcr :it ciiil . . . 943". S Sun's suniiUiameler 944".6 Mean lime ■7 44 25 39 42 5') 47 Sf) I 1 = 5 21' 6 23 8 6 S 34 14 2 15 7 19 19 21 59 26 10 30 13 3fi 27 Tabular Dist. of Centres. 1891 — o.g&df 1654 - 0.94 1352 — 0.90 1252 — o.S; '))7 - ".75 937 - 0.70 923 — 0.69 899 — O.flf) St) I — 0.65 S21 - 0.54 781 - 0.45 770 - 0.42 754 - 0.33 73fi - 0.19 734 - 0.04 763 + 0.15 OI)served Distance. I8f)2 1655 1334* 1241 1005 945 90 1 * S69* SSfi 827 741* 7f>S 724* 73S 733 768 Corr. to Tabular IJisi. J! - 29 + I - 18 - 1 1 - 22 - 30 - 5 + ft - 37 - 2 - 30 + 2 + 4 + 5 Micrometer measures of "pars lucida", Mean ifiie. Tabular Disi, of Centres. Observed Distance. Corr. to Tabular Dist. // /// r „ M 3 39 35 786 + o.26(!i 797 + II 41 54 811 + 0.33 82ft + >5 46 21 8ft5 + 0.43 885 + 20 5" 39 931 + 0.53 944 + 13 53 4 973 + 0.57 io9 II48 + 0.70 tl8o + 32 5 5 1205 + 0.72 1240 + 35 12 52 ■377 + 0.78 '417 + 40 20 2S 155ft + 0.83 •SftSf + 12 20 40 1561 + 0.83 1594 + 33 23 34 1632 + 0.84 ift4of + 8 25 5f' iftgo + 0.85 1741 + 51 20 52 1714 -i- 0.S5 '736f + 22 29 2(1 1778 + 0.36 1829 + 51 32 42 1859 -r 0.87 1888 4- 29 f From measures of cusps. There is dearly ii systeiiiatie error in the measures ttf ])hase, renderinj^- it neces- sary to eonipare phases as nearly equal as possible (ni eaeh side of the middle. This comparison gives the etjuations, 0.87 rSi— 9", \.l2 6t — 22" 1.08 I.2-! 5 1-59 46 5 1. 78 43 I. Si 80. The solution of these equations gives t5.= + 25". Tlie micrometer measures of "pars lucidae" before the middle of the eclij)se give .5f = + 38". . The three measures of cusps near the end give .5. = +17". The most probable result fi-om all the observations is «Jfc = + 24"±4". RKSEARCHF.S ON THE MOTION OF THE MOON. Eclipsi' "/ 1684, yll/^ \2, ol'sarci hy La Hink iU I'um. MoDIl'.S ippaicnt seini-iliamcler at boRinninK . ()4f>".7 Moon's ippaienl senii-1 Mean "T Falnilir Distance Observed Corr.to Time. uf Centres. Distance. lab. Disl. ') "ime. i of Centres. Distance. I'ab. Dist. h in 2 30 s \ 23 i I(j34.8 - o.(j8 Uj l8qi.3 - 43-"! h 4 m s 18 57 ; 1130. 1 + o.73iI( II 1173 + 34 35 16 i.SaS.l -- o.(j7 ; I7<)8 - 30 23 37 ' 1244.4 + 0.77 1284 + 40 41 6 1 6()() . 4 — . ()6 1673 -26 20 57 , 1393.8 + 0.82 1417 + 23 43 16 1652. 1) — o.()6 lf>35 - '7 3'> 57 1566.5 +0.84 i 1607 + 40 4'J 16 1521.0- o.()5 1407 -24 43 37 1736.6 + 0. 87 ; 1778 + 4' 53 6 1433.6 - o.(j4 1418 — 21 48 27 ; 1862.8 + O.H9 1887. S From + 25 -flu 5f> 46 13?')-') - "-yJ 1325 - 35 1 1 meas. of 3 3 6 1227.0 - 0.90 iigb -31 1 j cnsps. 9 16 1102.3 - 0.87 1077 -25 37 Sf' 1776.4 —0.97''' 1707 -69 15 46 t)7(j. I — 0.81 075 - 4 45 f' 1611 .8 — 0.96 I5»7 - 25 23 6 852.4 — 0.71 841 ~ '2 54 2f' 1409,6 — 0.93 1304 - 16 26 26 603.2 — 0.65 , 784 1-19 50 3f) 12()9.8 — 0.92 1301 + I 33 26 7l(j.i -o.4() 1 708 -.. .; 3 7 6 1145.8 -0.88 1081 -65 41 26 66g.o — 0.22 ; 660 r '^ 12 51 1032.6 -0.83 1025 - 8 45 6 666.2 -O.oS 665 I- " , 4 21 37 119S.4 + 0.76 1229 + 31 56 7 736.4 +0.32 i 765 1 + 29 25 57 1298.4 + 0.79 1331 + 33 4 I 47 811. 6 + 0.47 835 ; + 13 33 18 1475.4 + 0.S3 1502 + 27 5 27 871.0 + 0.55 1 879 + 8 42 27 1706.6 + 0.87 1727 + 20 10 7 (J56.0 + 0.63 1 075 + >9 •i Trejitlng tlio contacts in the usual way, tlie result is, .^.= + 31". The sum of the eleven etiuations from phases following first contact in which the coefficient of 6e exceeds 0.5 is, 9.65 A-f= 244"-. .•.''^ = + 25"- The sum of seven phases preceding last contact, 5.21 r^f = 205": .-. '^f =r + 4o". The measures of cusps near begimiing, giving doul)le weight when /) > 1600", give the result, r5*zr + 37"- Those near end give '^f = + 32"- The most probable mean result is, Se- + Z2" ±2". RKSEARCIIICS ON THE MOTION UK Tllli MooN. Ei/i/'xr 0/ i6Sj, May w , ,th.u-nr,l hj Fiamsikkh. MiKin's a|)|i:M()iil senii-iliariii'ltr al liCKiniiiiiK , (^55".^ Miion's :i|i|iai('nl scnii-iliamcler al end . , i)54".3 Sun's ;i|i|iai(iii vciiii-diamcU'r iM4".'i MciM Tinic. Tahiilar Di-^lanic of Ciiiiiis. OhscrMcl llisiaiu'i'. Mrairiin.c. -lal.ul.u Dislan.c i.f (•.■iilrrs. "'""'"■'"I iJisiaticu. // m s " ' '3 3 "P5 . . 15 •JI 1885 - o.i8itf + i).ijS( ilH .871.2 17 ') 1S77 - 0.17 -1- 0.1)8 1S51J.7 22 5 HW - 0. 11 + 11. w 1G31.2 28 31 1825 - 11.1)2 + i>..)y lSift.7 31 53 iSr7 0.(J<) ■(- I. IK) 1810.5 35 27 I8l2 4- 0.07 t- 0.()CJ l8o4.y 3S 3 1812 + 0. lu + 0.(J() 1804.8 k m s t* ,, I 38 43 1812 (- (1. 1 1 il ' 1 . 9(j / il H 1804.8 411 4i> 1S13 i- 11.13 + n.,j,j 1807.4 44 47 1820 f 1). icj + 0.98 1816.7 48 3 1830 + 0.23 f o.()7 1832.0 54 1 1855 + 0.30 + 0.95 1858.9 55 43 1SO4 -f 0.32 -(- 0.95 1870.3 2 (J "3 1892 + 0.38 + o./'S,'nri/ /•¥ I. a IIikk ,1/ /'ii/is. 253 Mddii's sciiii-iliiitiii'ti'i :it lii'i(iiiiiiii.u MiKin's scriii-cliaim-liT ;il end . Sun's Sfiiii-ili;inH'ii'r I ')''3".5 c)W.".!i ,,5H'.4 Paris MiMn Tabular DiMam-iOl.scrvHli Corr. to ' Paris Mian 1 ..l.ulai I'i-^i.niM Ol.^dv,,! Curi.iu Tinii'. i.fCcMlrcs. Distanrr Tal.. Dist. , Tiitif. ..fCcnlM^^ DiMan.r lal., I)is|. JO ni 7 ') I(Jj0.2- I .01 1'' 11)21. () „ -14.3 -" ') 34 1872.1-1.')! 1842.1 -3".2 12 "') 1800.0— 1 .111 1 762 . 3 -37.7 I(J III ifi()().3 — 1 .1X1 16S2.5 -16.8 "J 21 1616.4 — 1 .00 1602.7 -13.7 22 35 1532.1j-1.iKi 1522. 1) -10.0 24 37 1480. 7-0. ()ij 1443.2 -37-5 2S 10 I3()0.3-o.c)8 I3f'3.4 -26.CJ 3" 57 1320. 1— o.ijS 1283.6 -36.5 33 55 1245. 4-0. y7 1203. (J -41.5 37 7 1166.0 — 0.1/1 1124.1 -41. IJ 41 > 4^' 1076.7-0.y5 1044.3 -32.4 44 ",i ()5.4 S'l 2 658.2-0.80 fi45.5 , -12.7 21 3 3 573.0-0.72 5''5 . 7 -12.3 7 57 4')I. ')-'>■ 51J 486.0 - $■<) 15 '7 402.5 — 0.23 406 . 2 ^■ 3.7 22 4» 38S.4+0.a6il' 406 . 3 + 17.9 2ij 14 450.2 + 0.63 486.3 + 36-1 35 30 538.CJ + 0.80 566.2 t-27.3 3') 28 61 1 .4 + 0. 88 646.1 + 34.7 43 18 I1S7.2 1 O.IJI 726.0 + 38. » 41) 33 818. 3+0.1)7 8S5.1) + 67.6 54 7 ijl8.o+o.i)ij 1J65.CJ + 47. 1) 5S 4 1005 .4 t- I. oil 1045. '< + 40.4 2 56 11 15. 2 + 1. 01 1125.7 + 10.5 6 3S Illji).3+l.l)2 1 205 . 6 + (.,3 >) 46 I27o.(j + i.o3 12S5.5 + 14-6 12 57 1344.4l-l.03 1 3^'? • 5 + 21. I 16 5(> 1435. 3+1.03 1445-4 + 10,1 2IJ 55 1504.0+ 1 .114 1525 3 + 21.3 24 17 16114. 8+1. o| 1605,3 • + 0.5 27 44 16S4.4 + 1.04 1685.2 + 0.8 3> 10 1763.7 + 1.04 1765.1 + 1.4 33 48 1824.6 + 1,04 1S45.0 + 20,4 37 9 lijoi .8 hi. 04 1IJ24.IJ + 23,1 Till) ruutacts give <5fzz -f 20". 2. 'I'hc 16 moiisuros uf pliii.sc followiuf-' lii'st L-oiitiiet, 15.23 '5f = 426"; .■.<'it = + 27".g. Tliu 16 uiuiLsures of pluisc procodiiij;- last coiitiict, 1 5.87 'Sf = 364"; .-. />sc>ra/ h I, a Hikk Paris Mean Talnilar f)isian-4 + I. 12 54 23 783,9 + 5f' S30.4 1. 13 701 19 5 18 tSo.; <■' 33 645.9 1.98 >-97 7 48 3 - 27 625 — 21 587 549 - 21 511 - 19 473 - 2T 435 - 17 398 - 19 57 28 860. () + 1.13 59 3 9"<)-3 + 1. 13 23 945.2 (-1.13 1 53 9S5-7 -t I- 13 3 23 1026. 4- I -.3 20 43 292 ■ 0.62 ■■■■7 38 256.6 — 0.44 214.0 + 0.20 31 53 ' 233-0 + 0.62 32 53 I 260.8 + 0.80 35 4 300-5 + o-9> 3C> 35 I 333-2 + 0.97 33 i6 ' 369.8 -(- 1. 01 30 38 j 401.7 + 1.06 41 18 j 442.3 + 1.06 42 58 [ 483. 8 + 1.07 44 8 I 513.6 + 1.08 45 43 ' 554-4 :- i-'>8 58().I + 1. 10 47 48 38 630.8 + 1. 360 322 284 246 246 284 360 39S 4j- 474 512 550 5S8 626 6&4 + 7 + 13 + 23 + 27 + 28 + 34 + 32 + 28 + 36 + 34 + 37 + 33 5 3 107' -4 f 1. 13 6 23 1 107. 3 + 1.13 7 58 1150.3 + 1.13 9 28 1190.9 + I. 13 10 38 1222.5 + I. 13 M 33 1247.2 + I. 13 12 48 12S1.1 f 1.13 14 33 132S.4 ^- 1.13 15 40 1301.3 ^ 1. 1 3 17 2S 1407.3 + I. 13 '8 53 1445-O r 1.13 2' 53 152O.7 + 1.13 23 3 1558. 1 f 1.13 24 30 1597-0 I 1.13 25 48 1632.0 + 1.13 26 58 1663.4 + I. 13 23 10 1O95.7 + 1.13 29 43 1737-3 t- 1.13 31 14 177S-I I I 13 32 43 1817-8 ^ 1.13 34 18 1860.7 •t 1. 13 37 2 1933.5 + I. 13 702 740 778 S22 860 897 936 974 1050 lo83 1125 II63 1240 1278 1315 1354 1302 1430 14O8 1544 1587 1O25 1O63 1739 1S15 ■S53 1891 1955 32 + 37 + 38 + 30 -)- 30 + 27 + 26 + 24 + 18 + >3 + I3 + 31 + 34 + 26 + 31 + 17 + 29 + 28 + 3" -- 18 + 43 + 40 ■t 37 ••- 35 + 31 As tliorci.s !i j,ar. of 23 iiiiniitcs in tlic ..hscrviithnis nftcr flic liC'riuniii.r w<. 1 (liiriiio: this iiitcrviil, 110 ob.Horvntidiis to ci.mpjirc witli tlic> correspt)!!!! 011(1. Tlu' sum of tlio 14 ('(|iiiiti(>iis after the hcoiui lavi' III"' (incs near the 13.65 fl^ —309' liny' IS, :+ 22". Tlic .siiiii of 24 (•(|iiati.ms most iicfirl\ (■om..s|) lino- to tlicm after the miV- + 2S".S. e IS, The remaiiiiii£ = + 27".4- RESEARCHES ON THE MOTION OF THE MOON. 255 1 think this result sliould l)e rojei-tod, iintl thiit we shi.iild tiikc, iis tlio result of the olisci'Viitioii, df = + 24".! ± 2". luUpSi- (■/ 1715, '^fin 2, ohii-iviil hy ///<■ Messrs. I,\ lliui. ,it J\iris. Moon's apparent senii-ili.imetcr at hcKiiminj; . Mx)7 -5 Moon's apparent sLMni-ilianiclcr al rnd . . ion ".2 Sun's a|iparem scnii-iliaineler <)5' -2 La Hirk, the father, using new micrometer. La llikK, the son, using Iniaxi; on screen. — ( .11-1 t n , ( 'orr. to ^oc.il Mean I'aliular V)\M. of '"'^^"^•^'' lahntar '-'" il Mean I'aliular Dis t. ol" Observed . 'alinlar Time. Onlres. Distance. Dlsl. 'iine. Centres. Distance. DiM. h HI s \ 20 1) t1j71.f1 — 1.151' 1958.7-", - 12.9 20 m X 9 1971.6 - 1. 5,1. 1058-7-ni — 12.9 >4 ') 1313.0 -1.15 1800.3 - 13. f. 14 6 lSio.4 — 1 . 15 1800.3 — 10. 1 ") 34 !f'4')-5 - 1. 15 1641.9 - 7.f' '■<> 5f' 1729.2- 1. 15 1 72 1.1 - S.I 24 39 I4i)f..S - 1.15 1433.5 - 13-3 19 21 lf)53 5-1. 15 1641.0 1 - 1 1. 6 31) 11 1361.7 — 1 . 15 1325.1 -.lO-f. 21 52 1570-0- 1- 15 1562.7 -17.2' 33 • 12(5.4 - 1.15 r.'45-o + 0.5 24 40 1405-7 - 1- 1; 14S3.5 — 12.2 38 30 uiijo,.^ —1.15 10S7.6 - 24 27 33 14<>).5 - 1. 15 1404.3 - 5.2^ 40 47 1018. - 1. 15 1008.5 - 9.5 30 u l33':-3- I. 15 1325-1 - 5-7 43 29 930-2 - 1.15 92<) . 2 — to.o 33 1 1246.8 - I. 1; 1245.0 1 - 0.9; 4f) 8f.f>.3 -I. I? S50.0 - 16.3 35 10 II78.8 - 1. If 1166.7 1 - 12. 1 4.S 5'> 7S».6 - I. 15 770.9 - 13-7 37 53 1 100.6 - 1 15 10S7.6 - 13.0 51 40 703.7 - lit 691.7 1 - 12.0 4" 5f' 1013.4 - I 15 1008.5 - 4.9 54 14 631.1 — 1 . 1 3 612.5 - 18.6 45 47 S72.5 - I 15 8 50.0 - 22.5, 50 4.S 559. .J - 1. 12 533-3 - 26.6 40 7 776.4 - I "5 770-9 - 5-5i 21 12 467.0 — t . 1 1 454-1 - 12.9 52 14 6S7.6 - I l| 691.7 + 4. J 3 16 336.1 - t.o6 374.0 - 11.2 21 3 50 371 .6 — I 05 374.0 + 3.3 f. 24 303.1 — !>) 293-7 - 12.4 6 33 302.6 — 87 295 - 7 - 6.9 197.1 -0.5S 208 . 9 + It. 3 11 11 209.9 -0 .69 216.7 -t- 6.8: I I? 41 201.6 + 0.50 19"- 3 - 11.3 15 3; 175.4 +0 .02 216.3 + 41-4 22 44 276.3 +o.St 296. <' -'- i'o.7 22 10 264.0 + .-s 29O . + 32-0 25 44 344.7 +0.92 375-3 ■t- 30.6 25 51 349.0 + .92 375.4 + 26.4 3» «5 1 5t2.o + 1.03 533-0 H 21.9 28 50 i 427.5 +" -00 ■ 454-8 + 27.3' 35 ali 596.7 4- 1.04 613.2 + 16.3 32 506.2 + t .03 534.1 + 27.9 V) 8 61/). 3 + '-"7 692.5 — 3.3 35 24 50f>-3 + « .04 613.4 + 17. 1 41 30 ^(to.2 + t.o3 771. 8 + 1 1 . 6 33 31 680. 1 + I .of> 692.8 + 12.7 44 54 852.5 4- t .09 85 I. 2 - 1-3 41 14 753-4 + I .08 772.1 + 18.7 ■»7 34 925.2 +11" 930 -f) + 5-4 44 32 842.3 t 1 .09 851.5 + 8.7 5" U 101 1. 1 + t. to loto. 2 — (Ml 47 3f' 926.1 (- . 10 030.9 1 + 4.8 I 53 35 108S.5 + I . to 1089.7 + 1.2 50 24 1002.1 ' . 10 1010.3 + 3.2 56 f> I157-I +1.11 116(1.2 4 12.1 53 27 1084.9 + . 10 1089.6 + 4-7 1 5S 54 1233.0 t- 1. 11 1243.5 + If. 5 5f> 47 !lt74.f> + . II 1169.0 - 5.6 22 ? If. I.t<>4.9 )- 1.12 1.407.0 ) 2.1 50 34 ■ 1251. t 4 . II 1248.3 - 2.8 t S 5S 1504.5 + 1.12 1486.8 -17-7 2 2 2 44 1336-8 + 1 . 12 1327.7 j- 0-. 11 5f> 1566.4 + I.I2 1566.0 - 0.4 5 36 14130 + t . 12 1407.0 i - 6.0 13 53 1636.7 f- 1 .12 1645. 1 + 9.4 8 45 ; 1408-7 + 1 12 1486.4 - 12.3 10 12 1779.2 t- 1.12 1803.8 + 24 -f) 14 12 1645- I t 1 . 12 1645- ' 0.0 22 17 IS6I.6 + I.I3 1883. I (- 21 .6 19 M 1780.0 + 1 . 12 1803.8 + 23-8 25 31 1947.8 + 1.13 t96j.|-'i, + 14.7 25 20 1 1946.9 (• 1.13 ' 11)62.4-0 i +«5.5 ^5^ RESEARCHES ON THE MOTION OF THE MOON. 'I'lio 1 6 iiioiisnres of the fatlior, t'ollovviii<>- first cfnitjict, <>iv(' .\Y flf 1715, }r,iy 2. ohanui lcal Mean Tahulai Oisiaiici- Ob Ti t)f t"i lived Co l)i rr. to Tah.Disi. 7 4" IiJ7f'-4 - 1. 1? 'I' 12 IS 1835.2 - 1.15 17 f> 168S.: - 1. 15 22 57 1512. 1 - 1.15 2() 2 I4lr).S — 1. 15 20 !< 1327-4 —1.15 34 15 I175I - l"5 3<) 44 ">i4-5 — • • '5 4; 2S I 847. () - I. 15 52 2 , f)58.5 - I. 14 5') 4y 52f'-5 -1.13 I3 3fjf).f) — I .()f) 219.0 i')5'J- i.?oo 1484 1405 1326 1 1 67 f.92 5.34 375 ai7 • >7- ■35 ■47 23 34 + 8 21 14 Ifi Ifiy.4 180.2 l!^ 3S 214. 8 ^■4 53 34').n + o.()2il 30 55 5o''i.S \- 1.03 37 54 f''}3.2 + 1.07 43 42 849.8 + i.oy 55 38 1174.5 f I. 13 38 I6fiu 1512.7 + 1. 12 h I. 12 177 177 21S 376 f>93 852 1 1 69 I48f) If. 8 1808.3 ^ 24 28 I951. t 1 . 13 45 1S03 Ii)f'2- + 8 + 3 + 28 -27 - 16 - 5 + 10 — (ij The .systematic errors in the .'stimates of phases are .so stronglv marked that oiih I'oiTesiHdKU ng ph lases can he coniomei d. Til tions, the siiiii of which give the eipiatimi 1 7.66 '*i^ — -f 70'' The obserxatioiis ot contact almic <>i\(' ■ic are in all eight pairs of such ol )ser\a- +v ''if rr + I 2' Owing to the extreme irregularity of the observations of phase, T think tl of contacts are entitled to as iiiiicli weight as tiie wl le pair phase. The result of these observations will then b( lole eight pairs of observations of ()* = + -S" ± 4' RESEARCHES ON THE MOTION OF THE MOON. 257 J'Jclipse of the Sun, 1715, Mai/ 2-3, as observed in England. Tills eclipse was total in Hiij^land, where a <^reat niiinher of observations were made, tlu* results of which were pnlilislu'd in the I'liilosophirnI Transaii'ions. I'nfor- tunatelv, in the lar- that it should have i)assed entirely luinoticeil and unused. In discussinji: this eclipsi*, we shall l)eratlu!red from a letter of Feamsteeh, printed by lUn.v in his Aiamtit of the Urr'. John Flainsfred, pp. 315-316. 'I'he followinj,' are the essential observations, giving times of transit over nuu-al quadrant, and iduises of eclipse: — Date. (Old styliM rior k Time. Truc.Vpp Tiiiit irenl Object. I7'5- Apr. 21 1 1 m I 8 24 30 J 7 31 23 3 h m s r Hooiis. 17 Bootis. K Virginis. n noolis. 20 II 45 20 5 54 Initiuin Eel. 0. 21 M 41 21 q Tdlalis obscuratis. >7 52 13 13 I.UX prima. >q 1 13 31 Venus transit. 23 25 32 33 ig 51 Finis. 2<< II II a8 • • 3.1— 75 Ar. 2 258 RESEARCHES ON THE MOTION OF THE MOON. Tho (liserppaii)- of ten socoiuls in tlie clock-correction for bojrinninjr I cannot certainly explain ; it exists in the MS., and may I)e a correction for phase. 'I'o di'dncv the chu-k-correction.s from the .star-transits, mc nui.st know tlio (kiviation <»f tile (piadrant from the meridian. In Kkikokh's doctoral dissertation, Ik Asrni- sioiiibiis Iterfis a l-'lim.strnUo (^mdiaiitis Muralis ope. ohscrrniis, lionn, 1854, is fonnd a di.scnssion uf the errors of the (juadrant in 1690, in which the following valnes of m are quoted from a dissertation l)y Ahoklaxdek: — 1690, aetate vernali w = 4- 26'.7 1690, aestate . . -f- aS'.g 1699, auctnmno • +35*-8 1713, mense Jnnio -f-69".4. These are the corrections to reduce the observed time of transit of an equatorial •star to the true meridian. Supposing the change to go on, the correction in 171 5 would have been about + -j^'. Neglecting, at first, the p(.lar deviation from the meri- dian, we have the following (dock-corrections from the star-transits: — May 7 - Bootis '/ Bootis « Virg'nis IC 55 - 7 33 9 U 2 41 21 49 - 8 14 + 20 ! 2 41 2 ') - <) "> -) 20 From this it may be concluded that the clock-correction for an e.|uatorial star on May 2 at i i''. i would have ln-en Applying AKtiiM-.vxoKK's m luigatively . Clock-error at 11''. i _g Change in 10 hours, daily rate being — 13" - 7- 42" -I"' 13" 111 r -^ 53 CI 5" ock-correction fin- middle of eclipse _g Another determination of the error of the quadrant has been attenq)ted, as follows:— On 1713, Jmie 16-27, the clock-time of transit of the su-. over tlie true meridian, as derived from morning and afternoon altitudes, was o'' 7'" 11", while the transit over the quadrant occurred at o'' 6'" 30", showing a correction of -{-41". Again, on 1718, August 29-Sipteml)er 9, the true transit was found in the same way to be wt o*" 3"' 5" dock-time, while the transit over the quadrant was marked at o'' i"' 54". We, therefore, have, for the corre(!tion to the (juadrant, I 713, at declination -f 23°: c rr-j-o"' 41". I 718, at declination -f 5°: c = -f i'" 1 1*. The mean declination of the three northern stars observed on May 2 was -f 19", and the uncorrected clock-correction was — 8"' 1 2". The correction of quadrant inter- RESEARCHES ON THE MOTION OF THE MOON. 259 polated to this declination is 4S^ making- for the trne clock-error — 9'" o". If we had taken all fonr stars, we slioiild have had: mean clock-correction, — S'" i"; mean decli- nation, -(-12'; correction for (piadrant, 59"; and the resnltinj;' clock-correction wonld still he — 9™ o". ( !orrectinrrection for the time of the eclipse is — 9'" 5". The correction to apparent time applied by Flaaimteki) is — 5'" 40", and the ecpia- tion of time is —3'" 23", so that the correction actnally nsed by Fla.mstkkd, of the derivation of which we have no knowledtrc!, is —9'" 3". \Ve have, then, the three fol- lowin;^ rc^snlts for the correction to Fi..vxisTEKJ>'s clock on mean time at the moment of total eclipse: — Usinn- Aii(iEi.ANnr.ii's m — 9" o". From an independent discnssiim .... — 9'" 5". Fr.AMSTKKi) actnally nsed — 9'" 3"- The value of Aroki.amikk's ih restinjf on an "extrapolation", and its applicability bein;,f (luestion;ible, not much weij^ht can be jriviiu to the first result. I think, there- fore, that we mayi)Ut the clock-correction on mean time at — 9'" 4-, and that the error can then hardly exceeil 3 oi- 4 seconds. Obserratioiis hif riAi-i-KV. — These were made at the rooms of the Uoyal Society in Crane Court, Fleet .Street, London. A re-reduction of his altitudes gives results scarce! v ditferinj^' from those he obtains. The correction of his clock on mean time is — 3"' 38". I have a.ssumed his position to be, A rz o'" 25" west. The longitude may be some seconds in error, Init it would be a useless rertnement to discuss it in connection with such oltservations. Ohsi-rrdtiniis liif I'or.ND. — Here we have nothing !)Ut apparent times, and can do nothing but apply —3'" 22', the etpiation of time, to his results. I'ouNu'.s pctsition was, ^ = 51° 34' A zr o» 8" east. Eh'iiiriil-t ilcriml frmn Tlicori/. — The liusselian elements of this eclipse are as follows: — Greenwich Mean Times \^lllles of .V ... Hourly variation . Values ol 1' Hourly variation . LoK sin 1/ . . . . Radius ol penuniljra . Radius of sliaduiv . A m K) t2 — t .5207(] + 0.56762 + lane of reference, passing through the 26o RESEARCHES ON THE MOTION OF THE MOON. centre of tlio earth ixTpeiulicular to tlie axis of tlie sliadow. Tlie value of n is tliat of //' (■oiTospoiKliii'r to tlio meridian of Greenwich. From these (hita we obtain tiie fonowinfr observed and computed local mean times: — Place. Observer. Total Phase. Beginning . Local .Mean Time ol)s. h m s 21 5 37 Local Mean Time conip. m s f) 34 Coireciion. Greenwich . Flanistted . 1 - 57 End . . . 21 S 48 9 32 - 44 London . Halley . . Beginning . 2' 5 39 6 I — 22 End . . . 21 t) 2 u the other hand, were it not for the e(pially yreat deviation of IIai.i.kv's obseivations from prolial»ility in the opposite direction, I might assign him a greater weight than i'oLXD, and the result would then l)e luit little altered.. I shall, therefore, adhere to the above weights. This combination will give, .Aleaii correction to beginning . . . 'V, — — 44' .Mean correction to end .... . 'V^ :r — 31". Hy substituting the values of 'V, -^A, etc., in the etpwitioiis of coiulition, they become, 2.58 '^4 — 2.0 f^A — o. 1 34 'W — 44 1.76 <5* — 2.0 '5Zy-|- 0.1 79 (5 > — 31. RESEARCHES ON THE MOTION OF THE MOON. 261 Puttinif fSL, the correction to the .sun's lonjiitude, ecjuiil to zero, wo derive from those equations jcct of these researches. If we supimse no deviation in the mean motion of tlie mo(m except that which is due t(» the {fravitation of other boflies of our .system, this mcfan motion woidd l)c constant with the exception of a secuhir acceleration, the amount of wiiich has lu-cn accurately lixcd liy theory. Ft is, iiowevcr, well known that the secular acceleratiftn ^^ivcn l»v oljscrvation is not the .same as that deduced from theorv, and astronomers have jicnerally been ai'reed that the apparent dift'erence may lie due to a retardation of the earth's axial rotation. Thus, the apparent sccidar accel- eration will be made up of two parts, — the one a real acceleration; the other an a|)parent one, due to the chan ± 8 1 661.2 + 37 i 6 16C2.0 + 38 + 5 1666.5 + 25 ± 10 '673-9 + 39 + 4 1676.4 + 23 ± 6 1 680,0 + 3' + 5 1680.0 + 29.4 ^+ 1.0 1684.5 + 24 + 4 .6S4.5 ■^-3^ ± 2 1699.7 + 24-f i ± 2.0 1706.4 + 24- :l: 2.0 '7 '2-5 + 14.8 i 0.6 '7 '5-3 + 16.. '..i: 2.5 ■715-3 + 8 + 4 '7>5-3 -f 10. ?+ '-S 1728.5 + 7-3+ '-5 E(!li|tKe0, by Ukvelius. 4 |)ll)l^i(•H of u(tciillali(>nH, by Hkvklium. E(li|im'0, by JlKVELlus. Kiii|i.sc' 0, by IIKVKLIU8. K(!lipst' 0, liy VValtekius. Kcbpst' 0, by IlEVEMua. OcTiiltatioiis, by Hevemus. E(;li|).si' 0, by HkVKMUS. Occ.iiltiitiDiist, by Hevemus. Kclip-st' 0, by Flamstekd. Oiciiltatioiis, by Hevki.U's. Occiiltatioiis by Flamsieei) ami the PaiLs a.strouoiiierH. Kclipsc 0, by Flamsteeo. lM!lip.s('0, by La Hike. Fclips('0, by La Hike. Ei'lip.sc0. by La lIlRB. (Jciuiltiitimi.s, by tlio Paris astroiioiriiTs, FHip,sf0, by Fi-AMSTEEU, IIalley, and Pound, Kt'lipst'0, by Cassim, at Marly. Ki;lips»' 0, by the La Uikes, at ParJH. Oc'caltatioiiN, by Delisle, etc. The (lisconl.ances among the ohler results tire, on the wlioh', not greater than what we .should I'.xiiiK't from the probable errors assigned, i'.\c('|it in the case of the ellipse of 1639. In faet, if we suppose tiu' error of the tal)Ies to dimini.sh uniformly from 60", in 1620, to 30", in 16S0, tiie deviation of the result will in no case e.xceed t.5 X f''^' probable error assigned, except in the civse of the observations of the ecdip.se of 1O39, by (iAssKNDis and IIorkox, where the deviations are, respectivelv, 3.0 and 4.6 X prol»al)lc error. 'The ([Ui'stion whether the olhservations are (u- are not to be taxed with tliis apparent error cannot now be settled. 'I'd investigate the (piestions now under con.sideration, we nmst linve the correc- tion to II.usskn's Tables given by observations from 1750 to the ])resent time. From the comparisons piiltlislicil l»y 11.\nskn himself in the Mimthhi Xaticr.s of tlii' Itoi/al Ashniiiiiiiiiiil Sniicli/, it would appear that the correction from 1750 to 1S50, inclusive, is very nearly zero. The coiu'se of the ino<»n since 1S50 has been investigated in Part III of the J'dfxr.s piililislii'd hi/ Hir ('niiii)ii.ssinii 011 the TriiHnil of Voiks, from wliicdi it apjicars that, at the epoch 1S75.0, the meridian ob.servatiiuis at (Jreenwich and Wash- ington indicate a correction to the moon's mean htngitude of — 9". 7. Uut the occul- tatious about the same time give a correction nearly two seconds less, so that we nuiy consider the correction at this epoch to lie — 8". The iirst (piestion to l)e considered is how nearly the ob.servati(Uis can be repre- sented by thenry without any em|tirical correction. It is well kiu)wn that Hansen intro- duced into his tai)les a term depending <>n the argument 8 times the mean motion of Venus minus 13 times the mean motion of the earth, which is to be regarded as (;mpiri- cal, .since it has never been satisfactorily shown to have any theoretical existence. We RESEARCHES ON THE MOTION OF THE MOON. 263 must thcroforo rpmove tliis term from the tlicoi y to lie compiirfil witli oliscivjitioii. 'riic s(!<'iiliir iU'cclcnitioii i.s, however, to be left iirljitriiry, l)eciiiise it ilcjieiuls in |iiirt on the unknown ti(hil retimhition of the eiirth's rotiition. For convenience in solving"' tlie ('([niitions, we slmll nTiiphiciilly inter|M.hite the indivi(hml corrections to the moon's mean h>n;iitM(h' jnst coMected, so as to !*' = +33" 1650 + 39 ± 5 — 21.4 + 18 '675 + 32 ± — 16.8 + ■5 1700 + 21 ± — 5-2 + 16 1725 + 7 ± + 8.6 + 16 1750 rt + 18.9 + 19 1775 ± + 21.2 + 21 1800 ± + 14.7 + •5 1825 ± + 2.1 + 2 1850 ± — 1 1.4 — I I •875 — 8 ± — 20.1 -28 It is clear, without comimtation, that these residuals cannot be represented bv corrections to the epoch, mean motion, and secular acceleration. The onlv secular accelerati' the data, because the mean in (piestion does not admit of precise definition. The deviation during recent years is such that the secular acceleration will come out smaller the greater the weight we assign to the modern observations. T(» (d)tain the best residt from the ancienr and mo(leni obser- vations combined, it seems advi.sable to assign a minimum proliable error of 4" or 5" to each residual of the modern observations. The equations of condition given by the am-ient and modern corrections are as follow. In the.se ecpuitions we have i)ut ii p. 54. '|"lns anse.s tn.in tfic fact that .'.|iial wcijilit was ^ivcii to all the ccliiisc* in funiiiii;.- these e(|Matioiis. TIk- final result is snl)staiitially the .sanut on either system. Treatin^r ilie above equations by the method ..f leasi squares, we have the nor- njiils : — 20.02 (Sf + I 2.07 '5» -f- 20.62 Ss — 4- I 74.0 12.07 +20.60 — 9.66 zz-\- 15.2 20.62 — 9.66 +657.1 =—1687.0 The solution of whieh gives : — c5fr.+ I9".57^ Sh-=—\ 2".3 1 y Ei)och, I 700. '5.s=- 3".36> If we transfer the e[)och to 1800, the corrections will be: — ''>* =+ 3".90^ (Sh = — 1 9".03 [• Epoch, 1800. 6s =- 3".36^ If we sulwtituto these values of the unknown (|uantities in the equations of con- dition, we shall have the residuals ftjllowinj,-- the e(|uations. We .see that in the case of the modern observations the residuals are of an entirely inadini.s.sible niaf,niitudo; RESEARCHES ON THE MOTION OF THE MOON. 26s it \H tlicrffurc ocrtiiin tliat tin- cxistiii;.'- tlicurv will not roprcsciit ohsorvntions with any vmIiic wliatcvcr of tlic secular accclfratimi. Still, the comM'tioii which we havo (lediiced for the secular acceleration is clearly imlicated hy the conildnation of all thu obHervations. 1Ia\si;n',s adopted value Ix-iu}-- 12". 17, wo ure lod to tho vuluo s = 8".8 (IS that which, on the whole, hcHt satisfioH the obHorvati(»ns wliicli w(! have discussed. Uespectinjr the cause of the outstandinf^ deviations, wo may make two hvpo- the.se.s : — (1) That these deviations are only apparent ones, arisin*,' from ine(|Ualities in the axial rotation of the earth. The deviation of tlu* observed secular acceleration from tho theoretical value 6".i,S has lonjr boon attributed to a retardation of tho earthV rotation, and liy supposing- tliis retardation to be it.solf a varialtle (pnintitv, and indeed sometimes to chauf-c into an acceleration, we may completely account for the observed deviations. (2) We may suppo.se the deviations to ari.se from one or more incMiualitioH of long ]ieriod in tla^ actual mean motion of the moon. l.et us consider the.se two hypotheses in order. Wa have first to see what result.s foUow, if we suppose the theory of jrravitation to correitly account for all real clian;fes in tho mean motion of the moon, and attribute the observed deviations to chan>,'es in the earth's axial rotation, or the len;>th of the mean day. To Hud what the.so devia- tions really are, we inu.st take out tlicf eUect of IIanskn's increase of the secular acceleration as well as the empirical term due to the action of N'enus from the thoorv to be compared. The latter has been taken out wherever ne< cssary in the preceding eshil)it of the corrections to the nuton'.s moan loniiii/ ciirlli. Tlifxr niniilnrs mnsf tlirrrf'orr hr siihfidiird from the tiiiws indi- cated by asliiinoiniciil ohsi-rrations in order to ndmr tlnm to it idiijiiriu mvasnrr of time. -M7; ''* = + . 3X'.6, J ilz=— 70" -381 + " 9.9 - 18 — 1 89 + 9.6 - 17 + '34 + 3-5 — 6 846 — 0.2 926 + 2.1 - 4 986 — 1-3 + 2 1625 — 6".6 + 12* 1650 — 19.0 + 35 '675 — 18.6 + 34 1700 — '3-5 + 25 '725 — 8.6 + 16 1750 0.0 1775 + 8.4 - 15 1800 9-5 -17 1825 + 4-4 - 8 1850 0.0 '875 — 7.6 + 14 These corrections are so mimitc tliut tlicir iiidcpendont detection by existing ol)sprviitions is hiirelv |)ossil)l('. 'Plic most proniisiiijf moans of detection is atFoi'tled by the eclipses of tlu! first siitcllite of Jupiter, wiiicii lia\e been obscirved since 1670. Next in order coino meridian ttbservationK of Venus (hirin<; several months on each side of her superi(U' conjunction, the discussion of which would be extremelj' lal)orious, and would involve a complete re-e\aminatioii of tlu^ theorv of the motii>n of Venns. Transits of .Mercury also atl'ord some hope, but, unfortunately, |[.\i-i,Kv's excellent observation of the transit of 1678 is vitiated bv some defect in his ch»ck-error, which cannot be investif^ated for want of data. If the hypothesis in ([iiestion is correct, tins pr(d)lem of predicting; the nnxm'B motion with accuracy throujih lonj;- intervals of linu' nnist be re;.''arde(l as ho|ieless, since it cannot be expected that variations in the earth's axial rotation will conform to any determinable law. Suc(^ess in tracing;' the deviatii.ns in (piestion to the nuHiu itself and to the theory of firavitation is therefore a consnuunation to be hoped for. I'assiujf now to the second hypothesis, a ose an empirical correc- tion to Hanskn's first term dependin^;■ on the action of Venus, the ptniod of which is 273 ^ears. In this inquiry, we contine ourselves to the modern observations; and we mn.st introduce, in addition to the term sought, new corrections to the nu)on'8 ch and menu motion. Let ns ejiocl J)Ut A = iS F-i6i'- 9; RKSF.ARCIIE.S ON TIIK MOTION OF TIIF MOON. J67 riM-iiiy tlic iiK^iiii Iniij-itinlc (if V(;mis, /■; tliiit i.f tlic caitli, and // tin- mean anunialv ttf tiie moon. Tlio rcwiilual »oiii'('tiHn.s will then lir of tin- form At -\- Ti^n -\- ./• .sin J -|_ y (.,,s ^1. Cctiintinjf T'\\\ coiiturios from i3oo, tlio o(iuution.s of condition will bo: — rfe_ 1.75 ,S„_ 0.73x4- 0.68;/ = 4- 6".i \Vt.=: ^ (5f— 1.50 —0.24 4-0.96 =r— 6". 9 I 4-0.33 4-0.95 =- 7".4 j 4-0.79 4-0.62 =— 3".6 5 4- 1. 00 —0.09 =.— o".3 3 4.o,,SS —0.47 =4- 6".4 4 4-0.4.S -0.87 =4-i2".5 4 — 0.07 — 1. 00 1=4- 1 1 ".I 4 — 060 —080 — -f 3".o 4 — 0.94 —0.34 =:— 4".6 8 — 0.97 4-0.22 =:— I5".8 10 ^e— 1.25 ''>■« — 1. 00 «5f — 0.75 ^E — 0.50 < leads to tin normals: — 48.500 '5* — 6.375 A«_ 6.465./— 3.660// = — i22".55 — 6.375 4-27.401 -21.13S — 9.975 —— 89".26 -6.465 -21138 4-28946 4- 3.107 =4-i96".i7 — 3.660 — 9.975 4- 3.107 4-19.492 = — 182". 72. The solution of tho.se o(iuatioiis irives: — '^f = — 'U = - 5".o4) '5,< = -io".i4r'l'"'''' '^°°- XZZ — .09 y = - >5' ■49. The oiitstatidinj^- residuals iire: — 1625 + 3".9 1775 4- 1".6 50 - 2".2 1800 4- o".6 75 ~o".3 25 - •"•9 1700 4- i".o 50 4-0". 2 25 - o".8 '875 4-o".2. SO - o".8 The empirical iiltoratiou in (luestioii, therefore, ro]»roseut8 the observations quite satis- factorily. The additional dimiinition of 10" per century in the mean motion of the moon at the ))re.sent time will nece.ssitate a farther diminution of o".5 in the value of the secular acceleration in order that the ancient ob.scrvations mav still be well repre.sented. 'I'his will leave the moon's lonj^itudo unaltered by the last correction at the ei)oeh — 250. 268 RESEARCHES ON HIE MOTION OF THE MOON. To rcprcMeiit the Araliinn cbsL'i'ViVtion.s without Jiiiy iiu'ini rcsidiuil, tlu* diininntion .xhoiild he about .?", so that the observed secidar acc«'leratiiveii witli tlic acceleration 8".3- The total correction to tlio mean longitndo of Hansen's 'I'abU's now becomes - i".i4-29".i7r-3".86r*- F;,-o".09sin J - i5".49rosJ: V-i representinj;, as before, the empirical term (hie to the action of W-niis; A, the an + 339 + 40.4 60 35<).3 •(- 20.7 - 15-5 -t 32. 1 + 37-3 7" 12.4 + 18.5 - 15.1 + 30.2 1- 33.6 8.. 25.6 + 15.0 - 14.0 + 28,2 + 29.2 i)U 38.8 + 10.4 - 12.1 + 26.2 ■t- 24.5 t^ + 0.5 20 210. 2 - 4') i- 134 - 7i -(- 1.4 30 ar3.4 + 0.7 + 11.3 — 10,3 + 1-7 40 236.6 + 6.2 + 8.5 - >3.5 + 1.2 50 94Q.8 + II. 1 + 5-4 ^ l(..7 + <).i 60 263,0 + •5-7 + 1.9 — 20.0 - 2.4 70 276.2 + 19.0 - 1-7 - 23.4 - 6.1 80 289.4 + 20. (J - 5.2 — 26.9 - It. 3 0" 302 . () + 21.5 -- 8.4 - 30. 4 - "7 3 I()UO 315.8 + 20.6 - 11. 1 - 34' 24.6 -^ - — _ v-f. REsn-ARv-rrrEs on the motion of the moon. 269 It will he iiistriictivf f(i notice^ liow tlicsc rcsiiltiiiji- cnrrccfiniis ((iiiiiiiirf witli tlioso wliich liav(' Immmi iilnfjuly (lorliK-fd tVoni individiinl oltscrvatioiis ur jituiips of uhscrva- tioiis. This is sli.twii ill the foll(.\viii}r table. 'I'lic ohscrvcMl com't-tions ami tlic pn.ha- ItliMMTnirt -i- f arc taken without chaiij^v trmii the table ffiveii 35.7 1639.4 1645a I&45-6 1652.3 I6S4.6 1661.2 1662.0 iMA.i 1673.9 1676.4 16P0.0 II 1684.5 16W.7 1706.4 1712.5 •715.3 172S.5 • 78 35 53 57 34 23 »1 34 5" 38 31 37 38 »5 39 83 31 21). 4 34 3« 34.8 24.1 + 45 44 44 43 43 43 43 41 41 40 39 37 37 35 32 31 »9 39.0 37 »7 19.8 16.6 + 33 - 9 + 9 + 14 - 9 - 20 - 16 - 7 + 10 - 2 - 8 o + I - 10 + 7 - 8 + 2 + 0.4 - 3 + 5 ±' Wt. n '4 25 '3 9 II 9 5 1 10 8 10 8 6 5 10 4 6 5 i.u 4 2.0 14.8 '39 16.2 ■ 2.6 8.0 12.6 10.3 12.6 7.3 7.5 5.0 7-5 0.9 3.6 4.6 2.3 0,2 2 6 2 5 4 1 5 ' 5 6 3 4 too 6 35 »5 25 45 3 I 7 Hy conipann;,'- tlie corrections with the probalih^ errors it will be .seen tiiat The rcmdiials are loss than the probable error in 1 i eases; The re.sidtial". are eipial to the probable error in 2 ea.ses; The residuals ,ire ;;reater than the ]iroliable error in i.| cases If the theory were itself pert'e.t, this would imlieate that the |iiol)al)le errors assigned are, in the in<-an, .soinewhat too small in the ca.He of the eclipse of 1639, by iIoki>'o\, it may be re«rardcd as certain tint the assigned prolial)le error is too small, as, thron-li lnadvcrtein!e, proper accomit was not taken of the uncertainty of his clock-correction. 270 RESEARCHES ON THE MOTION OF THE [HOON. Tlio results arc divided iiitd jiroiips, iiiid the luoaii l»y wciiilits has boon taken. It will he remarked that each ;iroii|) has its own unit ot wei;>ht. The mean results for the corrections still uutstandin;^' will then ho as follows: — 1635.9, (5*— — 2".o ±4"-2 1649.5 — i"-2 ±4"-2 1662.3 -o".8±3".5 1681.7 +i".3±o".8 •6997 +5"-o±2"-o 1706.4 +7".5_t2".o 17 13. 1 +o".5±o".5 1728.5 -o".2±i".5. It will he seen that the results are, on the whole, as ;;ftod as could he expected except in the case of the solar eclipses of 1699 and 1706, where the ( duration inailo a short distance within. Sucli an observation is of especial value for deterininiujr the position of the moon's node. The ujode of treatiujf observations of this class is as follows: — I'uttiuj;' r,, for tlu; central duration correspondini,'' to the position of the ob.serv ;r, r fnr the ob.served duration, and ^j, for the radiu.s of the shadow, if we eompu e k from the formula the .shortest distance of tlit; observer fnnn the centre of the shadow will be A — p, cos k. The value of t^ is given by the formula r - 11^ . If iiirl\- (lue limit is ubserved, this result will be subjtxtt to errors of the semi- diameters of the sun and uKton; Imi these errors will be eliminateil from the menu observations made near the two limits. RESEARCHES ON THE MOTION OF THE MOON. 271 IIr' ahscrvatioiis \vc iii'c ikinv tu use nic loiiiid in Ham.kv's papor in tlic I'hilu- softiiiriil I ninsacfioiis \i)y 1715. I ho lixiiiy <>l the exact <((Mij>rapliifal pusitndis ot the ])lncc>H of (dmervatioii at lirst picsfritcd a dinicuhv , wliicli wascntirclv iciiiovcd tlimii^ili tlif kindness ul" ( Jeneral Sii' Hknhv .1 amks, ( 'liiet' nt' llie ( )rdnance Snrvev ut Kn^iand. wild sent me a i-omplele and aecnrate list nt' the positicms in (piestiun. Tlio I'oUowiiig ib u rtuiiiniiiry of all the i)l(serv!iti iir Sditlhcrt: Limit, 1. Norton ('ourt, ahont 10 miles this side < 'anterhniv . Oitserver, IJev. Dr. .Fdiin IIakkis, S. 'I". 1)., It. S. S., IVel)endary of Rochester. ' l>tn;ati«>n, one minute, or rather less. 2. Mocton. ahout midway hetweeii Norton ('oui*t and ('anterlmr\-. ( >liservers, the inhahitants. Kidipse, liardlr total, a small star lieinj;- left on the lower part of the sun at {greatest (dt>.enration. 3. (!ranl)rook, in Kent. Observer, Wii.i.iam 'i'KMri.r., Ks(|., U. S. .S. Sun extin- jfuislied for a monuint and then reappeared. 4. Wadhurst, h(ivond 'i'nrid»rid;ie Wells. 'I'otal, Init im duration jriven. 5. Ficwis. Kclipse total lor "sonu; short time". 6. Hri■^htlin;,^ Not (piite total. Tho followinjj; (juantities may he assumed as liuvin^ tlio same value for ail those stations: — \'alue of <^ or di>tanre from place of reference 0.658 Aujrmi'ntation of radius of sha-'ow 00305 Hadins (tf shadow on plane of reference 012.S4 K'adins of shadow at points of ohservation 015S9 Helative velocity, or >/ X-' + K'" ('-"Ji'O 9.6720 Duration on central line 243".4. Wi- now take the stations in the ordei- in \\Iiicli they are ^iivcn. 1. X'litiiii Ciiinl. — In all prohaiiility. the duration was iietweeii 52" an-? one minute.* If r = 52", then sin /,n 0.2 14; A =.01552. If r =()(/, thi'U sin /, =0.247; A =.01 540. The mean of thes<' two i-esnlts is .01546, with a prohahle error of les.s than 6 in the last place. 2. Horloii. — 'The sun could not have |ii-esented this iippearance at an\- appr, , lalile distance outside the slcidow. I'i'oliahly the point was exactly on the limit, the sun's lind) shinin■ .01589. * Al lilt' timi' ol writiiiij llils I iliil mil iiiilii;i.' ili.ii H u.l.KY eUttwIicre k^vc U.it.i siidwiiiK tin- iliir.ilinii lo he ex.ictly sip. 272 RESEARCHES ON THE MOTION OF THE MOON. Tln' cotupiirison of tht'sc n^siilts with tlio tahK's is as follows; the positions aro those t'liniisluMl by Sir IIknkv Jamks. Tlu' tiilHilar values of A, the iniiiiiiiuni distuiice of the point of ohserviitioii from the axis of the shadow, are coiiiputod by the forinuljc of v\ 7 :— l.ali imic. Longiludc. Tabular A. Oliservud li. rorrccllon. Norton ('oiin . 5' I y . f ) - •4i).4 + .')I5'>7 .01546 — .(HX)5I Hoclon . 5> 17 : - 'j7-4 .oif.7(, .1)1 fSt) — .000l)0 CranliiDok 51 5-7 - 3a-4 .Olf)83 .01531) - ■<'•")} Wailhutsi . M 3.8 - 20.5 .1)1624 .01589 minus. — .iKX)35 anil more. Lewis . 50 52.6 - 0.8 .i)i()5f) j .()I58() mit)us. ( .01577 — .txx)f)7 anil nioio. — .(XH)7i): HriKlolinR 5" 57-7 — aa.() .01740 .01589 plus. - .«m67 and less. The mean of the first three results, {fiviiiff double weiiflit to Xortoii Court, is .00071 J::.oooio. Hut sine*- the l.ewis o1)servatioM uives a iniiiiiiiuni limit of .00067, the most prol)al)le value of the eorrectiou may i)e estimated at — .00075 -4- .ooooS. IV — Stiidons near Noithnti Limit. 1. Haverford-\\'(!st. ()i)server. Rev. Uohkh I'kossku. Kclipse total a minute and a half 2. Shrew.sbiiry in Shropshire. ( Hiserver, Dr. IFoi.i.iNiis. Duration of totality, I ■" 40". 3. Darrin^ion, al)ouf 2 miles this siih' I'oiitefraet. ( )bs<'rver, TiiKoriiii.is Si!i;i,- ToN, Ks(|. The sun rtJilueed almost to a [toint resenildinj'- the planet .Mars, and then the li;iht iie^iiin to ineri-ase. 4. liariisdale, .'? miles south of DaiTinuton. The eclipse "just total". 5. IJadsworth. Authority, the Hev. and Learned .Mr. I).\iiu /.. The corona .se(ni, and iheret'ore the ecdipse total. 6. Witley, the seat of I.,ord Koi.KV. Duration, _5"' 15". \N'e ha\e from the (dements: — Hav. w. .Mean value of {>'.) g.6S62 Diiratiiin on central liiu* ^^.'".o 2;6".6 The t(dlowin;;' values of A are derived from the obsei-vatinns ; — I. Ihiri'ifind. — sin /' — .,5Sf^; Azr.oi44^ 2 Slirrirshiirif. — >iii /r — .423; A =: .01427. ;. IhiniiK/tdii. — Here the phenomenon corresponds almost (exactly t(> that at Hiirtnn in the south; we therefore put A rrradins of sh.idow — .01 575. 4. Iliiiiisdiilr. — Same vahu' of A. 5. liailmctnih. — A < 0^575, Init prol>ably very little less. h. W'itliy.—Hit far from the limit m to be entirely unreliable; the results, howovor, nre, sin /. = .825; A = .00891. OtlKTHt. 0.6,^2 .00291 .oi 28.1 ■01575 9.6805 RKSKAKCIIKS ON TIIK MoMoN c)| ||||; .MooN. 37.3 Kxl.ilHtiii- til,. hilMilar n-siilis in il,,. .saiiic lurm ;i.s tor llir m.iiiImtii limits, tlu-v will lie sli.iwii ;is Iwjluws: — Laritiutu. I.iinniciulr. T.ili. i. Olis j, Curr. lo^. "■'^' 'I W. 51 4S.1 f .) ;S.3 - .,,u,s _ .,,,4,3 .. .^^,35 Slii.wsl.uiy . 52 12.5 f 2 41.5 - ..,i2(.(. - .,,1427 I - .iKJlOi "•'"'"«'"" • 53 ^".5 ^ I I'..., - .nun - .,,1575 - ..^mXm "•""""'•'''•• • 53 3M • I ii; - ..>.ui - .'..5-i - ..«.I34 ll...lw..,il, . . 53 37. j;; H, ,s.„ -.01484 - .oisfM: - ,„j„So; ^^''''•'* • • • 52 Ki.ij 1 3 20. a - .0.701 - .U081JI: - .ooK^: Tllr llli'MII cnirrili I.livr,! iV.illl lll(. tirM turn- st.ltiulis is — .OOOC/). I'.llt til,. • •l«.s,TV:iiiuii ,.f tl.,. .■,.i.,.ii,i ill |Sa,iu..rtli w,.iil.l iii,li.'al.. a .■,.iT,.,-ti.n. inmuTi.alK less thai. .n,),),yi.u|,i,li, Ii.,u,.v,.i-. Nv,.,.amio| ivj^aid as cTtain, .Mt,.-,tl„.|.. I tliiiik u." may n o-anl — .oikkjo as ili,. m,,st pioltaMc ciHTcctioii. W ,. tlm^ li;i\,., lur til,. ,.<.i.i.,.,.ti,m 1,. the tal.iilar p-psiii,,,, ,,\' tli,. -Iia.i..\v-|iatli: From olt.sri'valioiis ,.f Miiitlitru limit, — .i>,ic)75 From l^lls(.|\,.^ti,lll^ 111' nortlKrn limit, — .ooocyo .Alcaii coiTt.i'ti,!!!, — .00082. Tlir ..,.i|.,.,.ti..ii ..xpn.ss,',! in 1,.|iiis of th,. yx-o,., iifri,- <.o-,.nliiiat,..v of th,. mo..ii. rt'lativo to tli,. smi, ami of the iiio,.ii-s |.anilla.\, is, in m.it.s ,,f tli,. 5tli [.lace of .l(.,.imals, — o..|4 -HA f j;.;, .H// i 1.5 <' + 0.4 i^L -f 2.4,) >'iO -j- 1 ; ■>// — — K>, ill., iiiiils of til,. .•oi.n.,ti,.n> l),.iiiii s,.,.,.ii,l> of an-, 'riic \alii,. oi -H^ -iv,.|i l.\ ;ill th,. ol.M.|.\atioiis of III,. ,.,li|,si. is f II .2. «hil».. th.. fonmila o.i\^.s -f 1 >'.(>, rii,. iii.iM |tfol)al.li. \alii,. is |K.||ia|)s the uiciin ..f tlu-s, two ivsiilK ^.i f 1 i".(,. W,. ii,.,.,..>aiil\ HiHijKWf <^L iiud -W/ njiial to ziTo, >o that ih.. Nairn- ,>f ')f> iov tlu> i-jmu'Ii will Ik. ,!!,'>-- iS"±5". From the ..,.,-iiliatioii>, u.. Ii.iv,. foKml (|>. 235), / *^^ = — o".i4 ^ i".2, wlii.li woiihl ^ivt' I li(. moHi ^Hojialili. aii-aii rtsuJt l«»r i;io is for 1S6S * I'll I 1 1 1 rf f^^ result, hnwfvcr, im n('i;ilit is ;;i\cii to tlic (tlisrrv;ilii>iis used liv IIanskn liiiiisclt. Allniifilicr, I tliiiik wf iiiiiy rcnjird llic most |ii'iili!ilili- currcctiiMi us nlnnit 1""- TIk' iiioliiiii n|' liic iiiiilc liciiiy- iicfiiitivc, this fMiTtM'tioii iliiiiiiiislii's hotli its illi>uli||c \;i|ilr mill lllr .lln lllliilit i>t' l:ltilllil<- li\ tllr i|ll;illlitV in' y, /' liriiiii cuiiili'il ill (tiiiiirii's I'iniii iS^ci, This icsiilt, thoiiiili iiciirlv (•ciliiiii with ifs|ircl til its iilycliijiir si^ii, ciiiiinit lie rc;i;iri|ii| lis t|i'tiliiti\ r, iis it will In- iitVcctcil liv any corn-ctiiiii tu Hansdn's viiliic (il'thc niiinirs pjiijilliix. foNCMiMNc i;i:m.m;ks on thk valik or tiik skculai: accklkuation IM.IH ( i;i» IN THIS I'AI'Ki;. Tlic aiitlmf Is ciiiisciuiis thill llicii' iiiav lie lunin t'nr iliirci'i'iiccs ul' ii|(iiiii>ii rcs|i('ct- iiu'- till' reality ot' the vcrx laru'e iliiiiiiiiitiiui nl' the seeiilar aeeeleratimi which is imli- e.ileil li\ the |irerei|i|i^- ilixMlssi. Hi. .\ e|(M|- >||| .irv ill' the eviilelli'e iili Imtli sides this iii\esti^ati<>ii. in the tiist jilaee, ii is to lie remarked that tiiele are three |iieees III' e\ ideliee, all of W hiell lllililale a;,;aillst till' dimilllllloil hen! di cjihed, and in raMirolthe lar^ie \,ihie round li\ IIaN'skn. Thev areas follows: — I . 'I'llc .s|||i|(osed ,iii(iinl lot.'il eelijises known res|ieetivelv as the «'cli|»M' ol' 'I'ltAt.Ks and the ellipse at i.aiissn If the total eelipse of— 5,S.|. Ala\- 2S, reallv |i;isseil over the icLiioii in wliieh the ei lelnated hallle descrilied liv IJKKoiions is sii|i|iosei| to liavo lieell lolloht, anil if the eilijise of — -^^f), Mjiy li,, was really total at the sll|i|iosed site ot' l.arissi, then no apiireeialile ehaiiii ' "I I1a.nsi:n's loiijiitiide of the moon diiriiij,' those times is admlssihle The reasons I',.r doiilitin^i- the realit\- of these eeli|isesare set forth .^o I'lilly in vN ;, that lliey lie 'd not he repeated here. -• 'I'lie hin.ir ellipse of — ,^Sj, reportiil as ohscrved at Haii\loii. It is certain tli.'it if this eclipse was le.illy seen at Hahyloii, no appreiialile diniiniitioii of IIan.skn's longitude at this time can he admitted. ;,. Those lunar eidipses cited l)y l'roLi;Mv without .i stateineiil oi' the phase .di>er\cd, !; lieiiiM hithcit,! ;issniiiei| tliat the times noted are those of the middle ol' the eclipse. Th'se eclipsi > are in e\cry way so iiiiceilain thai no i^reat stress can he laid iMion them. two ; The -oiirce.s of evidence uliicji indicate the diminiition here deduced are these (r. The I'loliniaic eclipses of the Afiiitir/r.s/, discussed in >> | ol this pajier. fi. 'Hie Araliian eclip.ses, discussed in v\ 5. |{ |(|(i-«l lie n marked that this is not a case in which the discordant data can he coml>im d hy uiijihts. The e\ idence iiu liidi d niider heads 1 and j is either coiiehisive, or false, and thei'ej'ore worthless, liither the ,so!;ir eclip.ses were total at the points Ki.sr.ARciir.s ON Tin; motion or Tin: moon. '■7> sup|Misc(l, or tlit'N were iHit. It' llicy were, we ciiiiiiitt ••li:niiii- IIanskn's Idimiliulc : it' tlicy were lint, we ciiii (Iciliicf ii(itlii:i;;' from tlicin.* 'The same rciiiark ii|i|ill till! liiimr t'rli|is(! of — _^Sj, iiccitnliiij:- to \\li('tln'r we sii|i|mis(' it to iia\ c liccii n-allv st'cii at liiilivl.iii or Hot. I >atii (r ami // do not admit of l)riii<>' disno.srd ot sd pirrixlv, Imt we c.Miiiot sii|i|io.sc till- accclcratioii imicli ^icatcr than S".:; willioiit sii|i|Misiiii;- systciiiatii- <-rrors wliicli sci-iii (jiiitf im|iiiilialil«'. '\\i hk- tlicsc errors srcm more iinprolmhh' tliiiii mistakes ill data i and j, and tlieriturc I re^aril the 'iiiall \alne there- fore of interest to know what sahie of the secnhir acceleration woidd lie olitaiiied li\ conil)iiiin;;' iIh-iii svith the modern olisei'\ atioiis. The nncertaintx n >|ieciinii' the inei|iialities of loii;^' period prevents iis t'roin dedinin;^' a precise n-snlt in this v\ay, Imt we may safeh' sa\' that it will ditfer very little t'rom 7', and will tliereloi-M he scarcely iai'^i-er than the theoretical \alne of the accideratioii. Let lis now view the (piestion from the opposite Ntaiidpoihl. ( Jiaiitini: tli" naiity of the prolilemalical total eclipses, and theiet'oie the corri'ctiiess of IIanskn's loiii;itiiile live or six centuries liefore ('iiKlsr, how w II llii' nndoiilited eclipses ot' I'rtn.KMV and the Arahians he represented .' In consider n;;' this ipiestioii, we must reiiieiiilier that this representation will not he the same as'hy II\\si:n'> iinalteivd talih s, incan-i' the modern (dtservatiims have show 11 that the latter need a correction to the mean motion of the moon at the present time, and the M-ciilar acceleration must he taken to accord with this chanjic It will he rememhered that II.Wsi'.n's \aliie of the secular ai-'elera- tioii has ill itself no foundation wliate\<'r eitli> r in oh.serxation or correct theory, ami iiia\' therefore l)e chaii'jed at jileasiire to til the toiindatioii which wa~- t'oiind for it after its deduction, iiameh , the ancient eclipses. Since it' we retain it iniaiiered, and admit the mean motion of the moon deduced tVoin niodiin oli^eivatioiis, the ancient eclipses will 110 loii^^er he repre-ellted. We lllllst, ;.> place its vallli- oil an\ I'ollllciat ion at ;ill, cliailfre it so that tlle>e eclipses shall he represented. 'The coirectioll to the centennial ineiiii iikotii'iii jrivcn li\ inodern ol(>ervalioiis we luive already loiiiid to he — j<> .2. If, tlu'u, we ivjireseiif hv »Vs flu- correction to IIanskn's .secular acceleration, tliu total ctmi'ctioii lo the moon'> mean i-iij^itiide '/'centuries alter iSoo \\\\\ lie To re|irt-.ent the ancient rotal "■cli|»«M'> as n-ipiired, tin- jiiantitv >lioiild he zero alioiil five anil a halt ceiiliiri- <'ii«|]tr. I'r lor T zz ~ -\v.V This condition will j^ive •J^r:— .25 ; = 10" *> tor ikv secuiiu aceeleia! whit . >»iU .• pn'>eiii at ihi -ami' time the mlv<-ni''.. UMil falMit aihl u'iiilllli'»lM'«* iiiuiTi In llii liisimii' ii.iriaiivt' j" hi iIi.iI ■.iiiii\'u 1 1 linn III llir iiiiM.illvi' III! uliirli llir litpnll" ''i'' '■! .1 Inl.il ii lijis,' K Inuiiili'il. .M.ikini; allowaiii r fni llii i K'aKi-i'i.iiiMh-. ,iiii| iinrcrlaiiilii's lo wliiili naiialuis arc liaMi' wlu-ii llirv jiass ilir<>iii;li iiniiiliial ntiinU. In rniisiiliis il iini .ii all iiii|>i>>lialM ' ii'spi liliiH llir li'iiiiiiiallnii \' il.iiknrss iiiav have oliuiiiali il Imiii ,i pailial n'li|isr (i( llii' sun, wliirli ii'rtllinl or iii.|iirssfil ilii' roinlial mis. rs|ir( iilly jl iliis n lijisr ivas aliiio-l loi.il wIiimi iIic smi srI. Ilciic'o, ronrriloin llial Ihr |)lwnoiiiiiioii iv.is irallv llu- !• lipvc mI -i''!, lii- I'misi.li is tli.il ilif ii.iii.iIk i- iloi s iioi enable us lu decide wluilici llic f lipsu wjs tulal ui |iailial. 276 ri:si:arch!.s on riir. moiion oi iiii. mkon. tiiiiis iiiiil till' li'Iiil (Mli|(M's III' 'riiAi.iis iiiiil l-iiri>sii. 'riic (•(irrtM'tioii In llic iiiuMirs iiicaii lMii;^itii(lc 7'ciutiirics mI'Iit iScio will llicn l)r - 7' (29'+ \".2S '/•). Wf now di'siri' to kimw limv tlii'sc cnrivi'tiaii-i will .iltcr tlic rcprcsiMitiilinii of tlic rtoli'iiiiiic iiml .\r:ilii:iii CI lipscs. I''i»r tlir tciniii'r. llic ii'|iri'>('iiliMinii will lie siiloliiii ti.ilK till' s ;!■> 1)\ tlir uii:illrri'(l till ill •> III' II \\si;\, litiimsc tlic I'iictui- 2()" -|- I ".J 5 T V.'lllislics ill llif rciiiisc III' till' iilisiTMltiiills. ir till' illirifllt siiljir i'cli|iscs illT ri'ill. wr iiiiist still >ii|i|iii>f tli.il till' •j:vf.{{ iii;is> III' I'loi.r.MN's iclipsi's :iii' iinii'c tliiiii liiill' .111 Imiir ill I'lTiir. I'"iil' till' Alilliiilll rrlijisrs, 7' IMllp-s rroill — <).7 tii -So, illlil tl|r r' i|isim|||i'1iI rnr- |•|•^li(lll^ In tllr l:llilll:ir llirMll 1( illilit l|i li - ill' till- llliinll fll'i' : For S29, (U r: -|- 2'.- VilV lOlXI, 'W n -f- 2'.-{. 'I'll Iiml Imw llir Ar.ilii.iii nli^iTviitiniis i(|iirsciit tlic rcviscil tlicnrv. wc iimst sii|i|iiisc tliiit ill tlic iiiiii|i;iri>iiiis ;^i\cii mi piiuc 5 ? tlic tnliiilnr litii;;itiiilc is iiirrciiscil Iiy these iiiiiiiinits licl'iirc liciii;,;' i'iiiii]i,iriil willi niiscrv .itinii. Wc iiuist tlicri'l'ttrc iijiply flicsc \illllc-< III 'W llcniltiv'i'K' til tlic ciilllliili Jl til iilit;iill the new eiilTertiiills. 'These new (■iiriciiiiiiis ;ire then cuiiMTteil iiitii time liy ili\ iiliiiL;- them liy the ruetnr /', whei'cliy we iilitiiiii the riilliiwiii;;' enn'cetiiiiis In the IiiImiIjii- times nixcn hy fill the Aniliiiin iiltscrxiitiuiis. Ill iinlci' In fncilitiite 11 iliscnssinii nl' the results, and the ileteetitni hI' imv s\stem!itie ermr iimnii^' the niiscrv jitimis, ;i tlireernlil cl;issilii;itiiiii is iiunle m eiinl- illi:- In whelhcr the eclipse Wils nl' the sun nr nf the liinnli, whether the he;,;innillji- '"■ ciiil w:is nli>er\ci|, mill whethei' the iiltitinlc mi which tli" time ilepeiuls niis iiliser\ci| ciist iirwcst III' the nil riili.in. 'The hitter ilistiiictimi is impiirtinit, heciiiise nny emi- sfnnt crrni- in ileterniiiiin^' the ;iltitiiiles will Iiiinc iippnsile ell'ecls on the two siih'.s of tile mci'iili.'iii. IIAGHAII. Vciir .S-0. K<'l. 0. iie.i:-., 'W-(( 5i"'i Alt. Iv S:i) Km! + -M ■^54 1) Mcjr. + >2 S5f, D itc--. h 9 923 1) Kiiil I 12 02;, Knil 1 ^:. 925 3^ He}.-. 1 1 925 D Knil -\' 7 927 1) r* • — s .,2.S Kuil -1- 16 9-9 1) 1 ten* (-33) 9:; 3 3) Hojf. + 7 i<: RESEARCIIKS ON Iiii; motion oi- mi. moon, CMI.'ii. Vi'jir 977, KrI, 0, |;,.o,, (.V), ,j/- j. If,'" .\|, |.; •/ / 'HI Kii.l -f- (.. 1;. 97.S 15.- (.S) f 31 W. 97s I'in.l + 9 w. 079 ),j Kii.l + 16 1 07') © |{'-. .S) + 15 w. 9;t> 2) !!'■;:. -f 8 H 979 ]) KimI -f- 1') \V. 9.S(0 2) Km.I + 10 ; 9S. 3) I'..-. ■\- 8 w. 98 r 2) Km.I + 3 » 981 ]) I5..0.. ■\- 20 w. 9«3 2) Kii.l + - \\. 9«5 li.- + 3<^ \\. 9S5 Km.I ■1- 10 w. 986 2) It.- (.V) -f-27 \\. 990 2) l'..r. — 20 v.. 993 II.-. -1- 6 K. 993 Ki^.l 4-25 K. li)02 2) li..n. + 6 v.. .'ihil f -10'" w. luu} !!<•;:•. f ir. \v. T.ikiMt; llic Mlc;lM> liy .liLssi's, \\r linil ; — I'VtIMI 0, 111 — illlliMli', Ml.'.lil Si— I |(/" 0, Kii.i, -)., is J), n(';iiiiMiny, 4- 6 ..r (-9'" 2), Kiinlnr ...■lip.s... Tli.. tun nu^nis H„- }* l..-inMiiM. ;mv • l.'rivc.l, till. „ii(! !.>• ivIniiiiM- mii.I tli.^ ..iIht l.y ivj.M-liM- tli.. .Iis,-,,n!.iMl ..l..s..rvri(inM of 990. Im III.' I!:.h',I.mI ...•Iii.s..s. ill,. al|ilM.l...s uviv all nhs.TV ,,1 \n lli,. rasf, su ||,al u.. sli.ml.l ..iMit ih.Mii .'iitiivly ill pariML; rasl aii.l wsl ..l..s..r\ali..Ms. Ki-hm tl... Cai,,, «'fli|iscs, we Iin\.' : — •^l'';iii ivsmIi Ir a^l ahiiiiil.s, A/ — | 7'" ..r | 12"', M.'cc.nliMi;- asllic .lisoiiilaiil ..liscrvatinii uJ'q.m. is ivtaliic.l nr ivjr..l..<| ; .Mean ri'.Milt Ir wc^t altitM.lcs, A/~ j-20'". That 111.' |H.,sltiv.' .-..nvftion ..f ten ,,r |ilt,.,. iiiiit...^ thus iii.li.at.'.l >Ii,.mI I 1... '""''•'' '^ '" '" ""• '"" '•'■ »'"' M"'-''I'"i II' ■ Ii.hI to ..s|,lalM Ihrir vality. tl,.. ni..sHialiiral way ..f .loin- so unul.l h.. t,. mi|i|m.>.. thai th.' .,l,s,.|\aliuMs vn-,-,. (a.n'iMav.l 27% UESRAuriiLs ON nil: moikin or nir. modn, with to -nil Millie lliiiiiy. r>iil llii> cNipl.-iiiiitiuii sicni- iiiiiiliiiis>ililr, lic(;iii>r llir tnii- sisti'iir\ with llic iiHMlirii iIkih'v nf tlic iiii'i|iiiiliti('s ol' till' siiii .'iiiil iiiiMiii is, I tliiiik, ;irfllt«'r tllilll lllllt ol'tllr lust llicmy tlir AllllliilllS nilllil li;i\r cnlislrilrtcil. 'I'llis cnll- sidiTjltinli seems tu me III lie (•(i||rlllsi\ e in tiUtir ii|' the ;;elillillelie^> ul' the Alilliiilll nils! rv.itlulis. 'I'm sil|i|iuse llie (lil]'el'eliees |ii result iVolll |ilirel\ ;i(eii|eiit;il eiriils seeing >ii |;ir Ii(\iiimI llie iiiHIllcU ( li re.'Isi iM;lI lie Jil'i ili.l liilit \ tlliit im ilisrll»iiili id'slleli :i |ini|i- • i^ilioll is lleces>iil\ . .\|i|i:irelitl\ , I liilel'i nc. we r.ili li.r-ill\ ;i\iiiil ;ie(e|itill^ ime ul' tlle-e |iritiii||> ; — l.itlier tlie recently ilece|ite(| Miillenl llie ,l( celer.lt Ic ill .'ilul tile llsiliil inlel'|ireliltii ill (i| llie illieielit si i|;ir eclipses ;ire In lie r;ii|ic;ill\ .lllereii, tlie edili'ie ul - ^ V Iml li:i\ ili^' lieeii tnliil !it Liiiissii, .iiiii lliiil nj — 5,S| nut Iiiixiii;^- lieeii tiital in .\>i;i .Minur; ( )|- tlie me.'in niiiliiMI ul llie muiili is, in the nmrse ut' celitnries, slllijecteil til dummies >u wide llial it is nut |ius-,il(le tu iissii^n a ilelinite \iiliie lu tlie secniiir Jicct I- enitiun. In cuiiclnsiun, it m:iy lie interestini;- lu iiKjiiin' what liy:lit uflur material tlian lliat ilisciiNseil in tlie |ireceilin^ |ia;i('s may throw on the ijuestioiis at issni'. The must iinpurtant >i| these i|iies|iuns is that ul' the niuon's mean lun;:'itnile tVum twcnix lu lweiit\ t'uiir ceiiliiries ai^ii, nil whicli iimsl iie|ieiii| uiir iiiter|ire|,itiuii ul' the ancient sular ecli|ises. I Mill awai'e ul' unl\ t w u classes ul' (lata which can lie reasunalih e\|iecteil tu thi'uw li^'lil ii|iun this i|iie>tiuii separate IVum an\ tlieuiv ul' the n n's uiutiuii ruiindeil uii iiiiiileiii uliserv atiuii>. The first ul' these are histurical tutal (•(•lip>es ile^criliiil ill uther writiiiL;s than iIium' ut' the (Jreek ainl liuiiiaii classic anthurs. Sume ul' the ( 'him >e eclipses were iliscnsseil li\ Srii.ii;i.i,i;i;i c in a paper preseiileil |u the Maiiisii Aca(leiii\ ul' Sciences aliunt 1S75. 'The remains ul' Ass\riaii talilet>. ili-cu\ereil ilnriiiL; the last lew \ears. conlain ilescriptiuns ul' ur allnsions to eclipses which iiia\ hereailer lie rc.iiiiil tu he luial. The uther class indniles tlieucciil- tatiuiis of stars, or the positions of the mu to iiliserv aliuii-- which cmild he received with suine appruach tu entire cunlideiice. I lad uther material lieeii admilted, the |trulial)le result wuiilil liav c lieon a ;:reat mass uf discurdaiit resiills, miicli ul' win di vvmild have tu lie rejected on accuunt ul' its iiicumjialihilily vvilii utlnr puiliun-. The result to he linallv accepted would then have depended very larticlv on what uliservaliuns were rejected ami what relaimd, and this wuiild necessarily have depended uii the indiiineiil uf the investi- jrator. it would hardly have h en jiossilile to have lorined ^mdi a jiidi;iiieiit without the suspicion of its lieiiii;- inlllleliced liy his i\ ishes or prejudices. It thereloie seemeil Itelter to avoid this necessity, as I'ar as jiossilile. hy einployin;^- no maleiial mi the jicn- eral relialiilitv ol' which tlie author vvuidd have I'elt niiwilliii;;- to stake the euirectness ul' his cum lusiuii, ur, speakini; mure |ilainly, which lie wuiild have meant to retain if il came out ii;;ht, and reject if it came out wruii;;-. It was, of cuiirse, im|iussiliU' tu Ul.si;.\K( 11 ^ (IN 1 I II Mill ION (II II II. Mm i\. r7«) liiiN'c MM ;i>>iii'aii('(' III cscrv iliiliiiii |ii'ii\iiiL: ('iiin|i;itilil<' >\itli iNcrs iitlicr niic, iis is ^liiii\ii li\ ilii' r('i«-('iiiiii 11111111' I'tii!. iiuiic Mini two nr ilii'ic AiMliiMii i'i'li|iM'>. Itiii tliis |ii'fiiiiii III rcji'i'li-il iiiMici'iiil scciii> siiiiill, niiisidcriiii; till' iicci '^.■>Ml°\ iiiiicrlMiiiiv uf till' I'liMimi'ls tliri»ii;^li wliii li tlic (ilisi rvMriiiiis Iimvc i'( iiclicil ii>. Niiw. ri-liiniiii;: ls, ilir (illjcclioll III lllr ll-s\riMll i'(!i|i-.i'^ wm- ■.lllislMllliMlK lllr ^Mlllr MS tllill III llic clif^sicMl l'cli||si ^: llir Ml rnlllil'' ills|iil'i'i| Ho I'I'MMIIIM lllc I'Cl'iMilll \ IIimI IIii- (■(•li|iscs were scvcimIIv I.iImI Ml (I( riiilli- |Miinls ul' ilic cMrtli's siii'Imcc. 'I'Iic (icriillMtiinis ciIimI 1i\- I'iKl.r.MV seemed Wnl'lllS ut' lilnl'e ciiuliileiK-e, Mini I Weill ^. i JMI' MS In iiimIm' il >iiiniiiMrv III l'iiii,i;\n's slMliineiil^, Inn tliey were -i. Imi- I'li'iii liein;^ preci-e iIimI -iiiie liesilMl.i \- WMS jell ill ileiidili;. wllethef tlleV Here Uollll elll|ilii\ illji'. I lillMlK' (•nil- cImiIi'iI ! ■ iiMlil tlleili iViilii llie ImcI iIimI lliev H'e ciled li\ |'|ii|.|:>n. lint fur tile |ini'|Mi>e III' |ireselllill;^' M (•ii||i|ilele series (if i •liserVMliii||>':, lillt |i> |i|ii\e li il llie elTnliei Ml> vmIiu- 111 llie ciill^lMlll 111' |irece-^iiill ilediiced lt\ Illll'Vlii III s, liMllli l\, iille decree ill M eell- llll\ , vvii.H Cdrfect. II. 'ill;; ill mII |ir(il'.tl(ilil \ selected I'nf fin |iii|-|mi- nl |iiii\ii|H i\\\ elTiilieiills li\ |iiitlie^is, it wm-^IimIiIK |i -silile In eilljiliiV lllelll willlnlll llie Ii'mIV MtiiHI mIiiiM- Mllildi'd In. tllMl tins' >lliilllil II' Mecepted nl' n iecled Meenrdiii;; Ms llieil' renlllts I'lid nr did lint M^^Tee Willi llliise i|eri\ed llnm iillier iImIM. The ecli|i>e (if 'rilKiiV WMs nliserscd in the Vcmt ;'i|. Ie>s tliMIl live eellfllfies Iw-fiire the ciimillelieenielll nf the series <,f ('('li|iMS i;i\ eii li\ IHill .I. Il m'cIIIs In IIU- sciircely WnrlllX III rnliliilellie. lie lieMin, |i\ •^iMlillii- IIimI he MCeltlMteh eMlelllMled the lime I if lH';>'illllil|i.', Mini fmilnl it in lie tWii limii > mi id lil'l \ lllillllte^, Mild then. tllMl liMN - in;^ fiirctiiily nliscrveil ilie time nf l»ejjiiiiiiii;;r, Ik niiiid it exMclly the smiiic. The lime nf elidiliy is ;;isell ii- •'►"^TVcd. Mild M> il WMS lini stMted In llMVC lieell liredieted, less >ii»jiieini>i may MllMeh i< it In Im Mlisenee III ;ui\ iiidieMlinii hnw hi- limes were deTtTlliilied, Mild ill llie l'>|ii('inil- e. liliiidillee nl ' 'iser\eil Mild enlll|illted time nl lie;:iimiii;r. Ii' ^m \ imlliiiii; nl m n rlMiii ii^^iniiess which runs thi'niitih lii> iiMrrMliNC, il seems III me tllMt We llMXC rcMsnli In |iImi '■ this ec|i|iS(' ill the SMIlle CMl('^ii|'\- with nlher rejected iMMteriMl. I Irillllill^i' lIlMt the .|llestinll W Inlhi-r II \N-I a LiIiIiImi iiIi'MII Inlli^ilnde nl llie mnnll dne,'% nr dues lint rei|ll!l' M lMr;ii i|i';4'Mti\(' Ci>rre( !iiill diirill;: the celllmies which i;re- cedeil the ('hiishMii eiM ^ which (|Me«li(>ii I>* tin rninlMmeiil.it 'Mie) reiiiMiiis undecided, the i|UeNiinn iiiMXMri-i- liiiw Mdeii-i\(' ;ni-\\er cMii lie ri-.tcln d. 'I'his (|e|M'iids iijinii whelhel';: cnl'I'ecl llienl'N' liiin. 'I'lle nlih colirse W ill lie In IMMke M ciilU|ilete re-l'XMlllin.ll inii nl mII M' flit ellipses Mild nlher (hltM wllicll lllMy llirnw liLlhl nil the i|Uestiiill, Mild In c II ipMl'e ll'»-lll with the I'oiill- iA' ihe Iwn , v pntheses : lir-t, tliMt I!an>k\'s T.-diles Mfe (in d diiriutf the perinil ill i|lle-linn: Mild, M'Cnlld, tllMt llle\' reiplil'e il cnrrectinll nl si\t( rl' IllillUteS, suljIrMclivi'. Shniild llie i'\ideiice pnt\u to \}c iiiMiidy in luMir of nne hypoti e.s'*, that 38o RESKAUrilKS ON llli: Mdllii.N oK llli: MDiiN. Il\ |iiithr^i> WiiIlM li;iM' to Iti' ;iri'('|ili'il ; ■i||it i| Im- lli>|)i'lt'.s^>l \ . ilisfitrilailt, I lie i|Ur»l lull Wniilil iTiiiiiili llliilcciili'il. 'I'liu illltllor winilil lie vorv >x\n>\ tn st-c the (|llcNliiiii cmimi iiiril ill tliis wiiv liy Hiiiiir iiiilf|ii'iiilfiil iiiitlmriiy. ir. nil till- utiicr Ii.'iimI, :i |ii rlrt't tlii'iirv of iill tlic iiii'i|ii.ililii's in tlic iiiiM>irH iiit'.iii iiiniinii I'.'iii III' I'lii'iiK'il iiiil('|ii'iii|i'iitly of iiliscrviiliiiiis, till- i|iirsiiiiii will, in nil |ii'iiliiiliil il\ , Miliiiil III' lirinti sitllnl liy llir iiitiilcni nlisiTvatiiMiH ainiii'. ( )ii |i;i;r<' 25 of tlic [trcH- fiil |i;i|ifr is ;;ivcii an fstiiiiatu sliiiwiii;; Imw acmralely, on llic liy|Mi|lifiis in (|ii('>liitii, till- Hci'iilar acceleration can lie ileterinineil wlieii the o1iser\ation.<< lielweeii iCiH) anil I 7^0 are siilistilnteil I'lir llie ancient olHervatioiis, ( 'oiii|iarin;i- the proltalilti errors there a>silllleil with lllii-e 111' the lilial re>llll< ;^i\('ll in the [ireceilin;; sections, it will lie Keen that while the results ol'ilie iitiseiN aliiMis near 1700 are perliaps a little less accu- rate than is there assnined, those lietweeii l();,o anil 1670 appear more accurate. Makin;; the most lilieial allowance I'ur iiiu'ertainty of every kiml, the prolialile error 111' the Mcniar acceleration u> lie ileri\eil Iriin the iiniileni iili>er\atiiiiis aloiie cuiilil searceK' ainolinl to 1" in the case silppnseil. ami \\ollhl lie colisiileialily leillHeil liy the iiliservations which will lie iiiaile lielore the emi of tin- present century. Since tlu- conipetinu' \aliies, S"..| ami !<)".(), dilVer I'roin each other liy ^".5, 11 result ilerived in llle^^a^ wi' ha\ c ile^crilieil wuiijil In llkel\ to ileriil liel ween them it It.' I I'll l.alih erro r was 1", ami woiiM he almost sure tu ilu sn il it iliil not exeeeil i)".5, which I think Wiilllil prove to lie the c; ( i, ' '-qV- / .,/•''< 7'^1