On the Expansion of Elastic Fluids. 335 
When a finid passes by free expansion from one state of density 
to another, we should naturally suppose that it must pass throngh 
all the intermediate states of density that can be assigned between 
the two. Such appears to have been the notion of every writer 
who has made reference to this point; and at first view it would 
seem absurd to suppose that the fact could be otherwise. But 
such is not the way in which elastic fluids expand. On the con- 
trary the parts of the fluid successively and instantaneously change 
their density, to the extent of one half (when free to expand to 
that extent) without passing into the intermediate states. As 
vapor is thrown off from the surface of water in a tenuious state 
ab initio, and without having first passed into those states 0 
sity which are intermediate between the density of the water 
and that of the vapor, so a column of rarefied fluid is thrown off 
from the front of a denser column; each infinitesimal element of 
the highest order of the denser column, being successively and 
instantaneonsly transformed to the more rare state. And as the* 
change of density is instantaneous, so likewise the entire velocity 
due to that change is imparted instantaneously to each element 
successively. 
that we may be able to assign the precise state of the fluid, in 
Sent both the density and the elastic force. The force D acts 
during the first instant in every part of the column, and in every 
direction; and therefore during that instant every part of the 
column is kept in equilibrio except’ the first element. Conse- 
of motion in the second element ; also that motion will not com- 
mence in the second element until the density in front of it has 
been to some extent reduced. Let the ratio in which it is re- 
duced before motion begins in the second element be represented 
