Interpretation of Mariotte’s Law. 413 
each elementary volume varies as the density. The density thus 
goveins 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 
Nas a simple factor: or the whole series varies as NV. ence the 
resultant or entire elastic tension or cohesion varies as J, 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 homo-~ 
geneous. As dz, dy, dz, can always be taken indefinitely less 
than the radius of sensible activity of any assumed force, the dem- 
onstration can only fail by the parts failing to be homogeneous. 
It will be seen by the above that any inference of the law of 
repulsive force between ultimate atoms or molecules, cannot be 
correctly drawn from Mariotte’s law, for this leaves the primary 
forces involved, wholly indeterminate. We are by no means au- 
thorized to conclude that in elastic fluids where the pressure varies 
as the density, the molecules repel each other directly as the dis- 
tance. 
The demonstration now given, has a singular bearing on the 
atomic theory of material constitution. We know experimen- 
tally 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 homogeneousness be interrupted, except through something 
like an atomic constitution of media? A laminated, filamental, or 
parts would produce that homogeneousness from which Mariotte’s 
law becomes an inevitable inference. Such an inference, as ap- 
plied to media in general, being contrary to the fact, a limit to 
actual division of parts must be admitted. Any other theory 
than one of ultimate molecules, separated by spaces, seems to inn 
Pose inferences conflicting with facts, throwing us back irresistt- 
bly into the theory of true molecular structure. 
ton, April, 1850. 
