678 POPULAR SCIENCE MONTHLY. 



IN A WORLD HALF AS LARGE. 



By the Late M. J. DELBCEUF. 



LAPLACE says, in his Exposition du Systeme 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 sim- 

 plicity and its generality as rigorous. One of its remarkable prop- 

 erties is, that if the dimensions of all the bodies in the universe, their 

 mutual distances, and their velocities should be increased or dimin- 

 ished proportionately, they would describe curves like those they now 

 describe ; so that the universe, thus successively reduced to the small- 

 est 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 pro- 

 portionality of force and velocity, they are independent of the move- 

 ment 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 sim- 

 plicity 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 nu- 

 merous 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 dimen- 

 sions; that it is, in short, a purely geometrical universe, constructed 

 in a homogeneous space, of which the proportions have the same 



