Part 1 (1/2)

Lectures on Stellar Statistics.

by Carl Vilhelm Ludvig Charlier.

CHAPTER I.

APPARENT ATTRIBUTES OF THE STARS.

1. Our knowledge of the stars is based on their _apparent_ attributes, obtained from the astronomical observations. The object of astronomy is to deduce herefrom the real or _absolute_ attributes of the stars, which are their position in s.p.a.ce, their movement, and their physical nature.

The apparent attributes of the stars are studied by the aid of their _radiation_. The characteristics of this radiation may be described in different ways, according as the nature of the light is defined.

(Undulatory theory, Emission theory.)

From the statistical point of view it will be convenient to consider the radiation as consisting of an emanation of small particles from the radiating body (the star). These particles are characterized by certain attributes, which may differ in degree from one particle to another.

These attributes may be, for instance, the diameter and form of the particles, their mode of rotation, &c. By these attributes the optical and electrical properties of the radiation are to be explained. I shall not here attempt any such explanation, but shall confine myself to the property which the particles have of possessing a different mode of deviating from the rectilinear path as they pa.s.s from one medium to another. This deviation depends in some way on one or more attributes of the particles. Let us suppose that it depends on a single attribute, which, with a terminology derived from the undulatory theory of HUYGHENS, may be called the _wave-length_ (?) of the particle.

The statistical characteristics of the radiation are then in the first place:--

(1) the total number of particles or the _intensity_ of the radiation;

(2) the _mean wave-length_ (?_0) of the radiation, also called (or nearly identical with) the _effective_ wave-length or the colour;

(3) _the dispersion of the wave-length_. This characteristic of the radiation may be determined from the _spectrum_, which also gives the variation of the radiation with ?, and hence may also determine the mean wave-length of the radiation.

Moreover we may find from the radiation of a star its apparent place on the sky.

The intensity, the mean wave-length, and the dispersion of the wave-length are in a simple manner connected with the _temperature_ (_T_) of the star. According to the radiation laws of STEPHAN and WIEN we find, indeed (compare L. M. 41[1]) that the intensity is proportional to the fourth power of _T_, whereas the mean wave-length and the dispersion of the wave-length are both inversely proportional to _T_. It follows that with increasing temperature the mean wave-length diminishes--the colour changing into violet--and simultaneously the dispersion of the wave-length and also even the total length of the spectrum are reduced (decrease).

2. _The apparent position of a star_ is generally denoted by its right ascension (a) and its declination (d). Taking into account the apparent distribution of the stars in s.p.a.ce, it is, however, more practical to characterize the position of a star by its galactic longitude (_l_) and its galactic lat.i.tude (_b_). Before defining these coordinates, which will be generally used in the following pages, it should be pointed out that we shall also generally give the coordinates a and d of the stars in a particular manner. We shall therefore use an abridged notation, so that if for instance a = 17h 44m.7 and d = +35.84, we shall write

(ad) = (174435).

If d is negative, for instance d = -35.84, we write

(ad) = (1744{35}),

so that the last two figures are in italics.

[Transcriber's Note: In this version of the text, the last two figures are enclosed in braces to represent the italics.]

This notation has been introduced by PICKERING for variable stars and is used by him everywhere in the Annals of the Harvard Observatory, but it is also well suited to all stars. This notation gives, simultaneously, the characteristic _numero_ of the stars. It is true that two or more stars may in this manner obtain the same characteristic _numero_. They are, however, easily distinguishable from each other through other attributes.

The _galactic_ coordinates _l_ and _b_ are referred to the Milky Way (the Galaxy) as plane of reference. The pole of the Milky Way has according to HOUZEAU and GOULD the position (ad) = (124527). From the distribution of the stars of the spectral type B I have in L. M. II, 14[2] found a somewhat different position. But having ascertained later that the real position of the galactic plane requires a greater number of stars for an accurate determination of its value, I have preferred to employ the position used by PICKERING in the Harvard catalogues, namely (ad) = (124028), or

a = 12h 40m = 190, d = +28,

which position is now exclusively used in the stellar statistical investigations at the Observatory of Lund and is also used in these lectures.