and particularly if it is so great as it is with molecules of
one or two atoms, an isentropic curve, which enters on the side of the
liquid, however far prolonged, always remains within the heterogeneous
region. But in this case all isentropic curves, if sufficiently
prolonged, will enter the heterogeneous region. Every isentropic curve
has one point of intersection with the border-curve, but only a small
group intersect the border-curve in three points, two of which are to be
found not far from the top of the border-curve and on the side of the
vapour. Whether the sign of h (specific heat of the saturated vapour) is
negative or positive, is closely connected with the preceding facts. For
substances having k great, h will be negative if T is low, positive if T
rises, while it will change its sign again before Tc is reached. The
values of T, at which change of sign takes place, depend on k. The law
of corresponding states holds good for this value of T for all
substances which have the same value of k.

Now the gases which were considered as permanent are exactly those for
which k has a high value. From this it would follow that every adiabatic
expansion, provided it be sufficiently continued, will bring such
substances into the heterogeneous region, i.e. they can be condensed by
adiabatic expansion. But since the final pressure must not fall below a
certain limit, determined by experimental convenience, and since the
quantity which passes into the liquid state must remain a fraction as
large as possible, and since the expansion never can take place in such
a manner that no heat is given out by the walls or the surroundings, it
is best to choose the initial condition in such a way that the
isentropic curve of this point cuts the border-curve in a point on the
side of the liquid, lying as low as possible. The border-curve being
rather broad at the top, there are many isentropic curves which
penetrate the heterogeneous region under a pressure which differs but
little from p_c. Availing himself of this property, K. Olszewski has
determined p_c for hydrogen at 15 atmospheres. Isentropic curves, which
lie on the right and on the left of this group, will show a point of
condensation at a lower pressure. Olszewski has investigated this for
those lying on the right, but not for those on the left.

From the equation of state (p + a/v^2)(v-b) = RT, the equation of the
isentropic curve follows as (p + a/v^2)(v-b)^k = C, and from t