The title of this essay will, perhaps, seem to certain persons in conflict with the philosophical opinions which I have all my life professed, as well as with the great school towards which the study of the sciences had led me even before I had heard the word of the master. Let such persons be reassured: the contradiction is but imaginary. Besides the Elements of Analytical Geometry, which his biographers omit to mention, I have accepted of Auguste Comte's writings only his Course of Positive Philosophy. And, furthermore, I have had to reject certain passages wherein were already revealed the familiar tendencies of the "High-priest of Humanity " - tendencies to be regretted in a work which will take rank among the chief ones of this age, and which I regard as the highest expression that philosophic thought has ever attained. This system of expurgation naturally traced my own programme, and the ideas I shall now set forth are as far removed from the dreams of mysticism as from the hallucinations of the spiritists.