Eventually the position is given in galactic squares, as defined in [§2].
II. The apparent motion of the stars will be given in radial components (W) expressed in sir./st. and their motion perpendicular to the line of sight. These components will be expressed in one component (u0) parallel to the galactic plane, and one component (v0) perpendicular to it. If the distance (r) is known we are able to convert these components into components of the linear velocity perpendicular to the line of sight (U and V).
III. The intensity of the light of the stars is expressed in magnitudes. We may distinguish between the apparent magnitude (m) and the absolute magnitude (M), the latter being equal to the value of the apparent magnitude supposing the star to be situated at a distance of one siriometer.
The apparent magnitude may be either the photographic magnitude (m′), obtained from a photographic plate, or the visual magnitude (m) obtained with the eye.
The difference between these magnitudes is called the colour-index (c = m′-m).
IV. The characteristics of the stellar radiation are the mean wave-length (λ0) and the dispersion (σ) in the wave-length. The mean wave-length may be either directly determined (perhaps as effective wave-length) or found from the spectral type (spectral index) or from the colour-index.
There are in all eight attributes of the stars which may be found from the observations:—the spherical position of the star (l, b), its distance (r), proper motion (u0 and v0), radial velocity (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.