a useful instrument, yet it cannot be classed among instruments of the highest order, nor can its results compare in accuracy with those obtained at the Royal Observatory at the Cape of Good Hope. It was therefore desirable to avoid as much as possible observing the same stars as had recently been, or would soon be observed, at the Cape of Good Hope. But, in the absence of information from thence, it was decided to observe, in addition to Nautical Almanac stars, only those stars of the 6th and 7th magnitudes which are given in the British Association Catalogue or in Lacaille's New Catalogue; and up to the end of 1859 the observations were limited to a space of 10° on each side of the zenith. But the equatoreal telescope, which has been ordered of Messrs. Merz and Son (7 inches French in aperture and 9 feet 8 inches focal length), and is in course of construction, when it arrives, may perhaps give a totally different direction to the efforts of the Observatory. Taschenbuch für Mathematik, Physik, Geodäsie, und Astronomie. Von Dr. Rudolf Wolf, dritte umgearbeitete und erweiterte mit 22 Tabellen und 5 Figurentafeln ausgestattete Auflage, 12mo. Bern, 1860, pp. 1-269. This little volume appears to be a most convenient handbook, comprising the utmost possible information for its bulk on the subjects to which it relates, and the author's name is a guarantee for the character of the work. Memoria sobre el Eclipso de Sol de 18 de Julio de 1860. Por D. Francisco de Paula Marquez, Capitan de Navio de la Armada, y Director del Observatorio de Marina de S. Fernando. Publicada de Orden Superior. 8vo. Madrid, 1861. The work contains an account of the Observations of the Eclipse, made at Oropesa, on the east coast of Spain, near the central line, by the Spanish Naval Commission under the command of D. F. Marquez, in company with the Portuguese Commission from Coimbra. It contains also an elaborate "Optical" theory of the Corona, Red Prominences, and other phenomena of the Eclipse, considered as arising from the diffraction and reflexion in our atmosphere of the light refracted at the border of the Moon's disk, and from the motion of the Moon. Beobachtung der totalen Sonnen-Finsterniss vom 18 (6) Juli, 1860, in Pobes. Nach den Berichten der einzelnen Theilnehmer zusammengestellt von Otto Struve. Mit 3 Tafeln. (From the Mém. de l'Acad. de St. Pét. t. iv. 1861.) The party from Pulkova who joined the Himalaya Expedition consisted of M. O. Struve, Dr. Winnecke, and the Portuguese Astronomer, Lieut. Oom, and the memoir contains an account of the observations of the Astronomer Royal, the three Pulkova Astronomers, and Herr C. Weiler, at or near Pobes, and of Herr Stenglein at Lodio, a few miles south of Bilbao. 23, 24 Mémoire sur l'intégration des Equations différentielles relatives au Mouvement des Comètes, établies suivant l'hypothèse de la force répulsive definie par M. Faye, et suivant l'hypothèse d'un Milieu résistant dans l'espace. Par Jean Plana. (Turin Memoirs, t. xxi. 1861.) This memoir, dated 12 Sept. 1861, replaces one with the same title presented to the Turin Academy, 26 May, 1861, the numerical results of which were erroneous, in consequence of an error of transcription in one of the formula. The conclusion arrived at is stated to be, that while the hypothesis of M. Faye gives results approaching those observed for the two periodic comets of 1205 days and 2718 days (Encke's and Faye's), a better agreement with the results of observation is obtained by the hypothesis of a resisting medium. The investigation relates exclusively to the motion of the centre of gravity of the comet. M. Faye's hypothesis, referred to in his paper, Comptes Rendus, 4 March, 1861, consists in supposing that there is a repulsive force emanating from the incandescent surface of the Sun, and, like the attractive force, varying as the inverse square of the distance, but which, in consequence of the finite velocity of propagation, acts in a direction inclined to that of the radius vector. Tabula Quantitatum Besselianarum quibus Apparentes Stellarum Positiones in Medias convertuntur, adhibitis Numeris Constantibus Pulcovensibus pro annis 1840 ad 1864 computatæ. Ed. O. Struve. 8vo. Pet. 1861. The tables are based on the formulæ and numerical values of the constants of precession, nutation, and aberration, given in Peters' well-known work, Numerus Constans Nutationis, &c., Pet. 1842. They contain for the 25 years to which they relate the logarithms of the quantities A, B, C, D, and the quantity for oh Pulkova sidereal time of each day. The quantity E, which varies very slowly, is given only for the last day of each month. Besides the logarithms of A, B, C, D, there are given, in the cases where the rapid variation of the logarithms renders it necessary for accuracy, the natural values of B, C, D. Arc du Meridian de 25° 20′ entre la Danube et la Mer Glaciale, mésuré depuis 1816 jusqu'en 1855. Sous la direction de C. de Tenner, Général d'Infanterie de l'Etat-Major Impérial de Russie, Chr. Hansteen, Directeur du Departement Géographique Royal de Norvège, N. H. Selander, Directeur de l'Observatoire Royal de Stockholm, et F. G. W. Struve, Directeur de l'Observatoire-Central-Nicolas de Russie. Ouvrage composé sur les différens Matériaux et rédigé par F. G. W. Struve. Publié par l'Académie des Sciences en St. Pétersbourg. Tome premier, Opérations géodésiques entre le Danube et le Golfe de Finlande, St. Pét. 1860. Tome deuxième, Opérations Géodésiques entre le Golfe de Finlande et la Mer Glaciale. St. Pét. 1857. Deux volumes, 4to. avec Atlas de 26 planches. The introduction to vol. i. contains the general history of this great geodetical undertaking. The total arc, comprised between Fuglences, lat. 70° 40' (near the North Cape), and Staro-Nekrassowka, lat. 45° 20' (near the mouth of the Danube), is 25° 20' in latitude. It is composed of 258 principal triangles, with 10 measured bases, not reckoning among the 258 triangles the triangles which effectuate the junction of the bases with the chain of triangles. The distance between the extreme points, measured on the great circle joining them, is 2700 versts = 2880 kilometers = 1552 geographical miles. The Observatory of Dorpat is about half-way between the extreme points, and may be considered as the meridian of the total arc. The total arc is divided into two principal portions, a southern and a northern arc, meeting at the Island of Hogland in the Gulf of Finland; in fact, the triangles of the two arcs form two distinct series, having a common point at MäkiPäälys in Hogland, but without any common side connecting the terminal triangles of the two arcs. There are on the total arc 13 points where the azimuth and latitude have been astronomically determined. The Observatory of Dorpat is the only point the longitude whereof has been determined with eminent precision, by the chronometric comparison in the year 1854, between Dorpat and Pulkova. In a statistic and chronological point of view, disregarding the observations of latitude which were in part repeated at a posterior epoch; the total arc may be divided into seven parts, which are arc. 26, 27 tions, or at least of certain specified astronomical stations, on the The question is discussed by M. Otto Struve in a paper in the Bulletins of the Academy of St. Petersburg (Feb. 1861), in which he maintains the contrary opinion, that this correction ought not to be made. Astronomical Observations made at the Observatory of Cambridge. By the Rev. James Challis, M.A. &c. Vol. xix. for the years 1852, 1853, and 1854. 4to. Camb. 1861. The volume contains the Observations made with the Transit and Mural Circle in the years 1852, 1853, and 1854, the Observations of Planets and Comets with the Northumberland Equatoreal in the same interval being reserved for separate publication with those of preceding years. The major part of the observations of the three years are directed towards the determination of the places of stars, and more especially such as are included in the list of 8000 zodiacal stars, observations of which were commenced in 1849. The observations of the Moon and Moon-culminating Stars were discontinued at the end of 1852. The Sun, the Planet Neptune, and the Minor Planets, were observed in that and the two following years. All these observations were compared calculated places, and if no Ephemeris was available for the purpose, the places were directly computed from elements of the orbits. 1845-1852 1845-1850 and the history may be divided into four periods, embracing 1. The origin of the undertaking, and the operations of MM. de Tenner and Struve relating to the arcs of Lithuania and the Baltic Provinces, united into a single arc of 8° 2'. The period terminates in 1831. 2. The period 1830 to 1844 comprises the continuation of the meridian northwards to Tornea, latitude 65° 50′, and the preparations for the Southern continuation as far as the Dniester. 3. From 1844 to the end of the year 1851, comprising the continuation southwards to the Danube and northwards to the Arctic Ocean. 4. The supplementary operation posterior in date to 1851, intended partly to reduce to uniformity and a higher degree of perfection the data requisite, as well for the union of the different partial arcs, as for the utilisation of this arc for the determination of the figure of the Earth. There is given, pp. cxli. to exliii., a chronological catalogue of the different publications in the Astronomische Nachrichten, the Memoirs and Bulletins of the Academy of St. Petersburg and elsewhere, in relation to the measurement of the arc of 25° 20′. The astronomically determined latitudes in the RussianScandinavian Arc of 25° 40′ are not, as in the English Ordnance Trigonometrical Survey, corrected for the deviations of the plumb-line due to the calculated attractions of the inequalities of the surface in the neighbourhood of the Station. It appears that in the opinion of General de Schubert, this correction should have been made; and with a view thereto, there should be a careful levelling of all the astronomical sta Astronomical and Meteorological Observations made at the Radcliffe Observatory in the year 1858. Under the Superintendence of Manuel J. Johnson, M.A., late Radcliffe Observer. Reduced and Printed under the Superintendence of the Rev. R. Main, M.A., Radcliffe Observer. Vol. xix. Published by order of the Radcliffe Trustees. 8vo. Oxford, 1861. Instruments for Sale. The Radcliffe Observer is empowered to offer for sale the Transit Instrument and Meridian Circle which have been in use since the commencement of Mr. Johnson's directorship till the present time, but which are now unnecessary on the establishment of the Carrington Transit Circle. The Transit Instrument has an object-glass of 4 inches clear aperture, with a focal length of 8 feet, and is an excellent instrument of its class. Price 120l. without the piers. The Meridian Circle, by Jones, is 6 feet in diameter, and its telescope, of the same focal length, has a clear aperture of 4 inches. It cost about 1000l. Price without its piers 300l. The piers may be taken at a valuation at the discretion of the purchaser. The Astronomer Royal has been requested by the Rev. George Fisher to state that Commander Mansell's Comet observations (see page 16) were computed by the senior boys of the Nautical School, under the direction of John Riddle, Esq., Head Master of the Nautical School. 29, 30 Dr. WOLFERS: on the Right Ascensions and Declinations of the Radcliffe Catalogue. 30, 31 VOL. XXII. December 13, 1816. No. 2. Dr. LEE, President, in the Chair. Henry Worms, Esq., Park Crescent, Portland Place; and Rev. John Sargent, 6 Bentinck Terrace, Regent's Park, were balloted for and duly elected Fellows of the Society, Grant for a Hill Observatory in India. The following letter was received in answer to an application for the aid of Her Majesty's Government towards the establishment for a limited period, under the superintendence of Captain Jacob, of an Observatory in the neighbourhood of Bombay, at a considerable altitude above the sea. Treasury Chambers, 8th August, 1861. In reply to your application addressed to Lord Palmerston on the 24th June last, for a grant to the Royal Astronomical Society of 1000l. in aid of the proposed temporary maintenance of an observatory near Poonah, I am commanded by the Lords Commissioners of Her Majesty's Treasury to acquaint you that the sum of 100ol. having been voted in Parliament for the object described in your letter, My Lords will be prepared to issue the amount in such manner as you may desire, on the understanding that the Society will see to the proper application of the fund thus placed at its disposal. I have the honour to be, Gentlemen, Your obedient servant, The President and Treasurer of the Royal Astronomical Society, Somerset House. A letter was sent to his Lordship expressing the thanks of the Council for the promptness with which their application had been met. The foregoing grant was announced by the President at the November Meeting, and should have been mentioned in the last number of the Notices. On the Right Ascensions and Declinations of the Radcliffe Catalogue. By Dr. Wolfers. (Communicated by the Rev. R. Main.) The Radcliffe Trustees having presented to me the observations made at the Radcliffe Observatory, Oxford, vols. xviii. and xix., I have compared the places of stars contained in these two volumes with those contained in the Tabula Reductionum. Having combined these two series of differences with the earlier-obtained series (Astr. Nachr., No. 1181), I have obtained the table of comparisons which I now send. « Hydræ... & Leonis... 31, 32 Name of Star. Number of J.-W. Number of J.-W. 8 +0'10 3 -0.6 Mr. CAYLEY: on the Secular Acceleration of the Moon's Mean Motion. 33, 34 Moon, and taking the usual approximate expression of the disturbing function, the equations of motion are dt dt 6 I -0°2 1Ο -0°02 8 or writing 5 +0:03 4 -0.8 II 6 0'00 3 -0'7 d m2 n2 P, m2 n2 Q, 2 -1.8 dt 5 -2.8 -Ο ΟΙ 6 ... -2'4 where, for shortness, 3 + COS 2 V 2 - 20'), The notation is then changed by writing e' de', v' + d v', in the place of ', v'; using henceforward g', v', to denote the elliptic values of the solar co-ordinates, as calculated with the constant excentricity e'; and, moreover, ę + dę, v + dv, in the place of ę, v; using henceforward ę, v, to denote the values of the lunar co-ordinates obtained from the equations of motion by writing therein, v', instead of the complete values g+de, vv. Then putting or, integrating the second equation, and by means of such viz., it is assumed that the mean longitude at the time t is integral changing the form of the first equation, we have & + n t + n2 ť2 + &c. where ɛ, n, ny and, moreover, where C is to be determined by the condition that dt may contain no constant term (for otherwise nt would not be the whole term varying directly as the time, in the longitude vv). The values of g', v', de', do', are given by the theory of elliptic motion, and those of g, v, by the ordinary lunar theory, in which the excentricity of the solar orbit is treated as a constant; the integration of the last-mentioned equations leads to the values of de, dv, and then the radius vector and longitude of the moon are a (e + dę), v + dv, respectively. where it is to be noticed that the terms t cos arg. and t sin arg. arise from the substitution of e' + f' t for e' in the coefficients of the terms cos arg. and sin arg. in the ordinary values of g and v. The new periodic terms sin arg. in de and cos arg. in v agree as to the arguments g', 27, 27 g', 27+g', with those obtained by Prof. Adams; those for the other arguments 2 g, 2 T-2 g', 2 + 2 g', do not contribute to the formation of the term in m2 of the acceleration. The values in the first instance obtained for de, dv, are and |