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( Communicated September 9, 1862.)

The object of the present Catalogue is to furnish (additional to the very accurate positions of the Berlin Jahrbuch) the means of reducing observations of right ascension with greater convenience and accuracy, and in a somewhat more systematic manner, than by the aid of former catalogues. It is divided primarily into two catalogues, the one of “polar stars,” the other of “ clock-stars,” so called ; with a supplementary list of stars which for large instruments are not commonly used in either capacity, but merely as tests of the accuracy of observation and reduction.

Excepting 25 “polar stars,” all the stars here given are found either in the Nautical Almanac Catalogue, or in that of the Berlin Jahrbuch.

This Catalogue contains, then, in the first place, the 47 stars of whose apparent places an ephemeris is given in the Jahrbuch; 2 of these being “polar stars,”

clock-stars,” and 9 of the supplementary list. In the second place, our Catalogue contains the 25 “polar stars ” -stars within 10° of the north pole — mentioned above.

In the third place, all the stars of the Nautical Almanac Catalogue are here given, except a Columbæ and 8 Sculptoris, & Ursæ Minoris, n Draconis, and y Cephei, and, also the stars below 45° of south declination.

The mean positions in this Catalogue of the 47 stars are derived from Wolfers's Tabulae Reductionum,* without further investigation. It will be often convenient to

36 66

* Tabulae Reductionum Observationum Astronomicarum ab anno 1860, usque ad 1880. Auctore J. Ph. Wolfers. Additur, Tabulae Regiomontanae ab anno 1850, usque ad 1860, ab Ill. Zech continuatae. Berolini, 1858.

have them in the form here presented, which differs from that adopted in those tables. The secular variations given for these stars are the same which Wolfers used, and which are taken from the Tabulae Regiomontanae.

Computation of the Mean Places of 25 Polar Stars.

In this discussion the following catalogues have been employed; to the name of each catalogue has been prefixed the abridgment by which it is cited in the course of the work : — Br. The Fundamenta Astronomiae (full title given in Vol. VIII. of the Memoirs

of the American Academy, Pt. I. p. 299). Gr. Groombridge (full title, loco modo citato). Str. 1815. F. G. W. Struve, Observationes Astronomicae institutae in Specula Univer

sitatis caesareae Dorpatensis. Vol. I. Pars II. Dorpati. 1817. 4to. Str. 1824. Stellarum Fixarum imprimis duplicium et multiplicium Positiones Mediae

pro Epocha 1830.0 deductae ex observationibus meridianis annis 1822 ad 1843 in Specula Dorpatensi institutis ; auctore F. G. W. Struve. Petropoli ex typographia academica, 1852. Fol. The positions which I have used

are a few for 1824.0 from the Introduction, page xxxxviii. et seqq. Schw. Schwerd's Beobachtungen von Circumpolarsternen in mittleren Positionen

1828.0. Von Wilhelm Oeltzen. Aus dem X. Bde der Denkschriften der Mathem.-Naturw. Classe der K. Akademie der Wissenschaften..... Wien,

1856. 4to. Arg. DLX Stellarum Fixarum Positiones Mediae ineunte Anno 1830. ... [auctore]

Argelandro. . . . Helsingforsiae, 1835. 4to. Pond. A Catalogue of 1112 Stars reduced from Observations made at the Royal Ob

servatory at Greenwich from the Years 1816 to 1833. London. ... . 1833.

Fol. Hend. Astronomical Observations made at the Royal Observatory, Edinburgh, by

Thomas Henderson. ..... Vol. III. for the Year 1837 [to V. for 1839].

Edinburgh. 1840 [-1843). 4to. [The same] reduced and edited by his successor, Charles Piazzi Smyth. Vol.

VI. for the Year 1840 (to X. for 1844 - 7]. Rob. Places of 5345 Stars observed from 1828 to 1854 at the Armagh Observatory,

by Rev. T. R. Robinson, D. D. ..... Dublin, 1859. 8vo. Airy. Airy's “Twelve-Year Catalogue,” “Six-Year Catalogue,” “Greenwich Observa

tions” from 1854 - 1858. (For full titles see Vol. VIII. of the Memoirs of

the American Academy, pp. 300, 301.) The “Greenwich Observations " for 1859 and 1860 have come to hand since the main part of these calculations were made. Joh. The Radcliffe Catalogue of 6317 Stars chiefly Circumpolar reduced to the

Epoch 1845.0, formed from the Observations made at the Radcliffe Observatory under the Superintendence of Manuel John Johnson, M. A., late Radcliffe Observer. With Introduction by the Rev. Robert Main, M. A.,

Radcliffe Observer. Oxford. 1860. 8vo. Car. A Catalogue of 3735 Circumpolar Stars observed at Redhill in the years 1854,

1855, and 1856, and reduced to Mean Positions for 1855.0, by Richard

Christopher Carrington. London. 1857. Fol. LeV. Annales de l'Observatoire Impérial de Paris publiées par U. J. Le Verrier, Di.

recteur de l'Observatoire. Observations. Tome XII. (XIII.) Paris. 1860,

(1861). 4to. Tomes XIV., XV. were received later.

I found, when too late to use them, that Airy's Cambridge Observations contained two or three places which should have been inserted.

No use was made of the Histoire Céleste, or Fedorenko's Catalogue ; nor of Piazzi, nor Groombridge's right-ascensions. Any material from these sources is of uncertain accuracy; or would require insecure systematic corrections.

The method by which mean places for 1855, and proper motions referred to the ecliptic of the same year have been found, is as follows: The positions of the Fundamenta, where such existed, were reduced from 1755 to 1855 by the use of Struve and Peters's data. In some cases where there was no observed declination for 1755, a value for 1755 referred to the ecliptic of 1855 was assumed, and by a slight modification of the method given in the introduction (p. ix.) to the Tabulae Regiomontanae (see, also, Wolfers's Tabulae Reductionum, pp. lii., liii. of the Introduction) was made to serve the same purpose. For if (see the place just cited) $ be supposed

8' — (d' + d) known, we shall have ([32]) x =

In this case the declination for 1755

ßta corresponding to that assumed for the ecliptic of 1855, will be

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The indirect form of Bohnenberger's method which Bessel has given, and which has been transferred by Wolfers, is greatly preferable to the more direct one. It

We have now positions for 1755, referred to the ecliptic of 1855, which agree with all the data of the Fundamenta referring to these stars. We have also some modern observations referred with more or less accuracy to the ecliptic of the same epoch, or which we can easily refer to that ecliptic approximately. These give us the means of obtaining a formula which shall be of the form a= a + ho (t — 1755),

8=8° +1° 1 - 1755). Where ao so are (Bessel's) Bradley's positions of 1755, in cases where they are complete, referred to the co-ordinate-planes of 1855 ; or, in case the Fundamenta position of 1755 is incomplete, ao is the AR. for 1755 referred to the ecliptic and equator of 1855, by means of do, as explained above; so being here arbitrary within certain small limits: where again ho io are assumed proper motions referred to the ecliptic and equator of 1855, but so assumed as to nearly represent more modern observations. For stars not in the Fundamenta, ao go are both arbitrary.

In other words, if all observed positions are referred to 1855 by precession alone, the formula

a= a + etc.,

8= + etc.,

would represent those taken from the Fundamenta exactly, and all others nearly. But as certain positions are exceptionally incomplete, and others so as a rule, we shall not attempt so to refer them, but shall proceed in the opposite way. We shall compute theoretical places of each star for the epochs of the catalogues. This will be done most conveniently by computing places for epochs at equal intervals, which can then be tested, and afterwards interpolated ; thus saving labor, and securing accuracy.

Table I. contains the assumed values of ao go ho i°. For the stars contained in Bradley, the values of ao and do have been verified by Mr. A. Hall, now Aide at the U. S. Naval Observatory, Washington ; who has recomputed the positions referred to the ecliptic of 1755 from them.

From these values positions for 1810, 1830, 1850, 1870 were computed, and in some cases for 1820, 1840, 1860; using Struve and Peters’s constants. The positions for 1815 were computed independently, and also interpolated as a check. The proper motions (h' i'), and secular variation (in AR.) were computed for 1830 and 1850 ; the former by formulæ which will afterwards be cited with some modifications from Bessel, and the latter by the formula, 01.0284+04.1950 [tg 89 ++] sin 2 a'+0",4481 sin (a'+91°6') tg d'+0.01944 [h'tg d'cosa' ti' sec8" sin a'].

The secular variation in declination is

05.1950 tg 8 sin al? + 04.4481 cos (u' + 91° 6') — 04.01944 h' sin a'.

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