The last sentence is that to which my friend’s remark principally referred. XVI. _Nature of the Supreme Being._—The following striking expressions were made use of by M. Alexis, when entranced, in answer to a string of questions which I had sent to him on this subject. He declared, at the same time, that he had never before been led to consider it in his mesmeric state. I presume, therefore, that in his ordinary waking state he is a Spinozist, and that, in place of an intuition, he simply delivered an oracular announcement of his preconceived notions:— “Il n’y a pas de parole humaine qui peut donner une idée de la Divinité. Dieu c’est tout. Il n’a pas de personalité. Dieu est partout et nulle part. Dieu est le foyer qui allume la nature. Dieu est un foyer universel, dont les hommes ne sont que la vapeur la plus éloignée, la plus faible. Chaque homme est l’extremité d’un rayon de Lui-même. Il n’existe que Dieu.” LETTER XII. THE ODOMETER OR DIVINING-RING.—How come upon by the author—His first experiments—The phenomena an objective proof of the reality of the Od-force. “Qualis ab incepto” shall be the motto of this twelfth letter, the materials of which were undreamt of by me, when some three months ago I remitted the new and corrected edition of “the Letters” to England. The occasion which led me to the knowledge of the facts I have to mention, and their bearing, tally curiously with what has gone before. For it is again winter, with its long, solitary evenings, against the tedium of which I had to seek a resource; and I bethought me, this time, of occupying myself with looking into the higher mathematics. Accordingly I sent to Herr Caspari, professor of mathematics in the gymnasium at Boppard, to solicit him to give me the instruction and assistance which I needed. And he obligingly came, in the evening of the 31st of December, to sit by my side and converse with me. And I went over preliminarily my schoolboy recollections of the elements of mathematics, and was pleased at finding the remembered difficulties vanish before the explanations of my well-informed tutor. And I learned, to my vast delight, that the inability under which asymptotes labour to touch hyperbolas is a purely arbitrary one, like the legislative prohibition not to marry with one’s deceased wife’s sister; but that, unlike the latter, it can be evaded; inasmuch as an asymptote, by changing its name and forfeiting its properties, may at any time unite itself with the object to which it had before been infinitely near. Again, I found my boyish distrust and disbelief in sines and cosines replaced by an intelligent and well-satisfied acquaintance with them. And I even obtained a glimpse of the higher analysis itself, pointing with its unerring finger to the exact height, else unmeasurable, at which my candle should stand in the centre of my round table, to shed upon it its maximum of illumination.