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1) The stars of Bradley from the north pole to declination —31° taken from Publ. 9 of the Astronomical Laboratory of Groningen. I have only rejected those stars between — 20° and — 310 which are also contained in Newcomb's catalogue of fundamental stars. There thus remain 2551 bradley-stars.

2) The fundamental stars of Newcomb ') between — 20° and — 40° of declination. In all 114 stars.

3) A number of 198 fainter stars of Taylor (nearly all magnitudes between 6 and 9), between — 20° and — 350 of deel., for which the proper motions have been derived by Prof. Kapteyn from the catalogue of Taylor-Downing (eq. 1835)") and that of Tucker (eq. 1900)8) (these proper motions have not as yet been published).

4) The fundamental stars of Newcomb between — 40° and — 520. In all 38 stars.

5) A number of 490 stars from the catalogue of astrographic standardstars by Sir David Gill (eq. 1900) *). The stars also contained in Newcomb's fundamental catalogue were excluded. Of the rest only the more reliable ones have been retained.

6) For the part of the sphere between — 520 and the south pole 225 stars of the „Fundamental-Catalog für die Zonenbeobachtungen am Südhimmel und südlicher Polar-Catalog für die Epoche 1900 von A. Auwers". 6)

The total number of stars is 3616.

The data required for the individual stars.

As may be seen from the formulae (4) it will be necessary to know for every star the following quantities:

a and 8, the right ascension and declination for a determined epoch, for which, in agreement with Publ. of the Lab. of Gron. n°. 9, we havechosen 1875; a and f*s, the proper motions in right-ascension and declination; (), the distance. lts estimation depends on the following quantities: m, the magnitude, reduced to the Potsdam scale;

(.i, the total proper motion in are of the great circle; ip, the angle of position of the total proper motion, taken in the sense, determined by the formulae on page 11 of Publ. 9;

A, the angular distance between the star and an approximate position of the apex which has been assumed in accordance with Publ. 9 «);

x) Catalogue of fundamental stars for the epochs 1875 an(* 1900 reduced to an absolute system by Simon Newcomb.

') General catalogue of principal fixed stars by Taylor, revised and edited by Downing, Edinburgh, 1901.

3) Catalogue of Southern Stars of Piazzi for the ep. 1900. Publications of the Lick-Observatory, vol. VI.

4) Gill, A catalogue of 8560 astrographic standard-stars between deel, —40° and — 520

for the eq. 1900, London 1906.

6) Astron. Nachr. n°. 3431—'32.

6) See page 8 of Gron. Publ. n°. 9.