Lectures on Stellar Statistics

Carl Vilhelm Ludvig Charlier
Lectures on Stellar Statistics, by

Carl Vilhelm Ludvig Charlier This eBook is for the use of anyone
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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

Produced by Susan Skinner and the Online Distributed Proofreading
Team at http://www.pgdp.net (The original copy of this book was
generously made available for scanning by the Department of
Mathematics at the University of Glasgow.)

[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],

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, .]

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
(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
([alpha][delta]) = (174435).
If [delta] is negative,
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