The Deed of Foundation of the Shaw Fellowship provides that "it shall be in the power of the Senatus Academicus of the University of Edinburgh to require the holder of the Shaw Philosophical Fellowship, during the fourth or fifth year of his tenure of it, to deliver in the University of Edinburgh a course of Lectures, not exceeding four, on any of the subjects for the encouragement of the study of which the Fellowship has been founded." The following pages consist of four lectures delivered in the University of Edinburgh, in accordance with this provision, in the month of January 1884. Since their delivery, the argument of the lectures has been revised, and in some places enlarged. I have also thought it better to modify their original form by dividing the discussion into chapters.