elocity (_W_),
apparent magnitude (_m_ or _m'_), absolute magnitude (_M_), spectral
type (_Sp_) or spectral index (_s_), and colour-index (_c_). Of these
the colour-index, the spectral type, the absolute magnitude and also (to
a certain degree) the radial velocity may be considered as independent
of the place of the observer and may therefore be considered not as only
apparent but also as _absolute_ attributes of the stars.

Between three of these attributes (_m_, _M_ and _r_) a mathematical
relation exists so that one of them is known as soon as the other two
have been found from observations.

FOOTNOTES:

[Footnote 1: Meddelanden fran Lunds Observatorium, No. 41.]

[Footnote 2: Meddelanden fran Lunds Astronomiska Observatorium, Serie
II, No. 14.]

[Footnote 3: Annals of the Harvard Observatory, vol. 50.]

[Footnote 4: In order to deduce from _M_ the apparent magnitude at a
distance corresponding to a parallax of 1" we may subtract 3m.48. To
obtain the magnitude corresponding to a parallax of 0".1 we may add
1.57. The latter distance is chosen by some writers on stellar
statistics.]

[Footnote 5: The best colour-scale of the latter sort seems to be that
of OSTHOFF.]

[Footnote 6: Compare H. A. 50 and H. A. 56 and the remarks in L. M. II,
19.]

CHAPTER II.

SOURCES OF OUR PRESENT KNOWLEDGE OF THE STARS.

18. In this chapter I shall give a short account of the publications in
which the most complete information on the attributes of the stars may
be obtained, with short notices of the contents and genesis of these
publications. It is, however, not my intention to give a history of
these researches. We shall consider more particularly the questions
relating to the position of the stars, their motion, magnitude, and
spectra.

19. _Place of the stars._ _Durchmusterungs._ The most complete data on
the position of the stars are obtained from the star catalogues known as
"Durchmusterungs". There are two such catalogues, which together cover
the whole sky, one--visual--performed in Bonn and called the _Bonner
Durchmusterung_ (B. D.), the other--photographic--performed in Cape _The
Cape Photographic Durchmusterung_ (C. P. D.). As the first of these
catalogues has long been--and is to some extent even now--our principal
source for the study of the sky and is moreover the first enterprise of
this kind, I shall give a somewhat detailed account of its origin and
contents, as related by ARGELANDER in the int