| IN A WORLD HALF AS LARGE. |
By the Late M. J. DELBŒUF.
LAPLACE says, in his Exposition du Système du Monde: "The law of attraction inversely as the square of the distance is that of emanations starting from a center. It appears to be the law of all forces the action of which is perceptible at sensible distances, as we recognize in electrical and magnetic forces. This law, therefore, responding exactly to all phenomena, should be regarded in its simplicity and its generality as rigorous. One of its remarkable properties is, that if the dimensions of all the bodies in the universe, their mutual distances, and their velocities should be increased or diminished proportionately, they would describe curves like those they now describe; so that the universe, thus successively reduced to the smallest imaginable space, would always present to observers the same appearance. These appearances are, consequently, independent of the dimensions of the universe, since, by virtue of the law of proportionality of force and velocity, they are independent of the movement it may have in space. The simplicity of the laws of Nature thus permits us to observe and recognize only these relations."
This masterly page contains propositions of different natures. Some of them are of an exclusively mechanical order; as those which teach that attractive forces, emanating from a center, act in inverse proportion to the squares of the distances; that this appears to be the law of all forces acting at sensible distances; that its simplicity and generality should cause it to be regarded as rigorous; and that the consequence flows from it that we may conceive an infinity of universes mechanically alike—that is, built upon all imaginable scales. These propositions, even if they had not the support of Newton, would acquire an incontestable authority from the single fact that Laplace advanced them.
Other of these propositions lie in the domain of psychology and metaphysics. Such are those that assert that these infinitely numerous universes, built on different scales, enlarged or diminished, would always present the same appearances to observers; and that, consequently, these appearances are independent of the dimensions of the universe, because the simplicity of the laws of Nature permits us to observe and recognize only relations. From all this we are authorized to infer as a final consequence which Laplace does not deduce explicitly, but which was assuredly in his thought, that the universe has fundamentally no fixed, immutable, absolute dimensions; that it is, in short, a purely geometrical universe, constructed in a homogeneous space, of which the proportions have the same
