Lectures on Stellar Statistics

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Lectures on Stellar Statistics, by

Carl Vilhelm Ludvig Charlier This eBook is for the use of anyone anywhere at no cost and with almost no restrictions whatsoever. You may copy it, give it away or re-use it under the terms of the Project Gutenberg License included with this eBook or online at www.gutenberg.org
Title: Lectures on Stellar Statistics
Author: Carl Vilhelm Ludvig Charlier
Release Date: July 27, 2007 [EBook #22157]
Language: English
Character set encoding: ISO-8859-1
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[Transcriber's Note: This text is intended for users whose text readers cannot use the "real" (unicode/utf-8) version of the file. Characters in the Greek alphabet are represented as follows: [alpha], [beta], [gamma], etc.
In the original text, the units h and m, and ordinals th and st were printed as superscripts. For readability, they have not been represented as such in this file. Similarly for the + and - signs when used to describe intermediate stellar colours.
Other superscripts are indicated by the carat symbol, ^, and subscripts by an underline, .]

LECTURES ON STELLAR STATISTICS
BY
C. V. L. CHARLIER
SCIENTIA PUBLISHER LUND 1921
HAMBURG 1921 PRINTED BY LüTCKE & WULFF
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 space, 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 pass 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 ([lambda]) 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 ([lambda]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 [lambda], 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 ([alpha]) and its declination ([delta]). Taking into account the apparent distribution of the stars in space, it is, however, more practical to characterize the position of a star by its galactic longitude (l) and its galactic latitude (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 [alpha] and [delta] of the stars in a particular manner. We shall therefore use an abridged notation, so that if for instance [alpha] = 17h 44m.7 and [delta] = +35°.84, we shall write
([alpha][delta]) = (174435).
If [delta] is negative, for instance [delta] = -35°.84, we write
([alpha][delta]) = (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