Intelligence and Miscellaneous Articles. 77 



To prove this : assume a perfectly homogeneous medium whose 

 parts exert forces varying as any function of the distance. Assume 

 in this an origin of coordinates, three coordinate axes, X, Y and Z, 

 and three constant elementary distances, dx, dy, dz. Conceive each 

 axis graduated by laying off its element successively from the origin 

 outward. Through each point of graduation on either axis pass a 

 plane parallel to the other axes : do this for each axis. The space 

 around the origin is thus divided into elementary parallelopipeds, 

 each of which contains a like portion of the homogeneous medium. 



The force of elastic tension or of cohesion is measured by the re- 

 sultant action on a unit of surface of the plane X, Y, by all the 

 forces acting in the positive direction of the axis Z, between the 

 parts on opposite sides of the plain X, Y. This resultant is balanced 

 by an equal one acting in the negative direction of the axis Z. To 

 make up this resultant, a certain number of the elementary portions 

 of the medium conspire. It may therefore be equated with a series, 

 each term of which expresses the positive component along the axis 

 Z, of the force exerted between two elementary portions of the me- 

 dium on opposite sides of the plane X, Y. 



If now the density of the medium be varied, each term of this 

 series will vary in the same ratio, since the quantity of matter in 

 each elementary volume varies as the density. The density thus 

 governs each term of the series,- by fixing the quantity of matter in 

 each elementary volume. If we call the ratio of the varying density 

 to a standard density N, each term of the series contains N as a 

 simple factor ; or the whole series varies as N. Hence the resultant 

 or entire elastic tension or cohesion varies as N, or as the density. 

 This result is entirely independent of any particular law of relation 

 between the forces and distances ; and will always be true so long 

 as the elementary volumes can be assumed as homogeneous. As 

 dx, dy, dz can always be taken indefinitely less than the radius 

 of sensible activity of any assumed force, the demonstration can 

 only fail by the parts failing to be homogeneous. 



It will be seen by the above, that any inference of the law of re- 

 pulsive force between ultimate atoms or molecules, cannot be cor- 

 rectly drawn from Mariotte's law, for this leaves the primary forces 

 involved wholly indeterminate. We are by no means authorized to 

 conclude, that in elastic fluids, where the pressure varies as the 

 density, the molecules repel each other directly as the distance. 



The demonstration now given has a singular bearing on the 

 atomic theory of material constitution. We know experimentally 

 that Mariotte's law does not prevail uniformly in elastic media, while 

 in liquids and solids it has no show of application. Hence we are 

 bound to infer non-homogeneousness. Now how can homogeneous- 

 ness be interrupted, except through something like an atomic con- 

 stitution of media ? A laminated, filamental, or molecular structure 

 alone can produce heterogeneousness. The two first would confer 

 special properties in certain directions, which are not found in fact. 

 Hence a molecular constitution of matter seems entailed as an in- 

 ference, from the bare fact that Mariotte's law is not universal. 

 According to the view now presented, the elasticity of gases varies 

 as the density, because the quantity of matter within the sphere of 



