When a simple mathematician reads and studies these astronomical discussions, he believes that the form and the number of the spheres are facts established by proof. But this is not the case; for the science of astronomy does not aim at demonstrating them, although it includes subjects that can be proved; e.g., it has been proved that the path of the sun is inclined against the equator; this cannot be doubted. But it has not yet been decided whether the sphere of the sun is excentric or contains a revolving epicycle, and the astronomer does not take notice of this uncertainty, for his object is simply to find an hypothesis that would lead to a uniform and circular motion of the stars without acceleration, retardation, or change, and which is in its effects in accordance with observation. He will, besides, endeavour to find such an hypothesis which would require the least complicated motion and the least number of spheres; he will therefore prefer an hypothesis which would explain all the phenomena of the stars by means of three spheres to an hypothesis which would require four spheres. From this reason we adopt, in reference to the circuit of the sun, the theory of excentricity, and reject the epicyclic revolution assumed by Ptolemy. When we therefore perceive that all fixed stars move in the same way uniformly, without the least difference, we conclude that they are all in one sphere. It is, however, not impossible that the stars should have each its own sphere, with a separate centre, and yet move in the same way. If this theory be accepted, a number of Intelligences must be assumed, equal to that of the stars, and therefore Scripture says in reference to them, “Is there any number of his armies?” (Job xxv. 3); for the Intelligences, the heavenly bodies, and the natural forces, are called the armies of God. Nevertheless the species of the stars can be numbered, and therefore we would still be justified in counting the spheres of the fixed stars collectively as one, just as the five spheres of the planets, together with the numerous spheres they contain, are regarded by us as one. Our object in adopting this number is, as you have noticed, to divide the influences which we can trace in the Universe according to their general character, without desiring to fix the number of the Intelligences and the spheres. All we wish to point out is this: in the first place, that the whole Creation is divided into three parts, viz. (1) the pure Intelligences; (2) the bodies of the spheres endowed with permanent forms—(the forms of these bodies do not pass from one substratum to another, nor do their substrata undergo any change whatever); and (3) the transient earthly beings, all of which consist of the same substance. Furthermore, we desire to show that the ruling power emanates from the Creator, and is received by the Intelligences according to their order; from the Intelligences part of the good and the light bestowed upon them is