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 uses utf-8 (unicode) file encoding. If you don't see 8 characters in the next line: α β γ ε λ ο ς ″ make sure your text reader's "character set" or "file encoding" is set to Unicode (UTF-8). You may also need to change the default font. As a last resort, use the latin-1 version of the file instead. 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_ (λ) 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_ (λ_0) of the radiation, also called (or nearly identical with) the _effective_ wave-length or the colour;