Our knowledge of the stars is based on their apparent attributes, obtained from the astronomical observations. The object of astronomy is to deduce here from 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.