Among the theories proposed to explain the constitution of material substance, and to account for the facts relative to it disclosed by modern science, one developed in a recent work with the above title, by Rev. Joseph Bayma, of Stonyhurst, is specially worthy of notice for its ingenuity and the field which it opens to the mathematician. Whether it be true or not, it is at any rate such that its truth can be tested; and though this may be somewhat difficult, on account of the complexity of the necessary formulas and calculations, still the difficulty can probably be overcome in course of time, should the undertaking seem promising enough. It is briefly as follows. Matter is not continuous, even in very small parts of its volume, but is composed of a definite number of ultimate elements, each of which occupies a mere point, and may be considered simply as a centre of force. This force is actually exerted by each of them following the law of gravitation as to its change of intensity with the distance; but is attractive for some elements and repulsive for others, which is obviously necessary to preserve equilibrium. These elements are arranged in regularly formed groups, in which the balance of the attractive and repulsive forces is such that each group, as well as the whole mass, is preserved from collapse or indefinite expansion; these are what are known chemically as molecules; and in the simple substances they probably have the shape of one of the five regular polyhedrons. The simplest possible construction of a molecule would be one of the polyhedrons, with an element at each vertex, and one at the centre, whose action must be of an opposite character to that of those at the vertices; for these last must all exert the same kind of action, attractive or repulsive, for any kind of equilibrium to be maintained, and the centre must act in the opposite direction to prevent collapse or expansion of the mass. Furthermore, the absolute attractive power, or that which the molecule would have if all collected at one point, must exceed the repulsive, slightly at any rate, since the force exerted at distances compared with which its dimensions are insignificant is known to have this former character. This system admits of two varieties, according as the centre is attractive or repulsive. In either case, for the maintenance of equilibrium the force of the centre must always be less than half that of the vertices combined, as the author shows, (giving the values for each polyhedron;) and it would seem that the first supposition would therefore be untenable, since the attractive force in each molecule, as just stated, necessarily exceeds the repulsive. Equilibrium certainly cannot be maintained in this case; but this will not involve the permanent collapse of the molecule, but merely a continual vibration of its elements back and forward through the centre.