ow Tc.

By far the majority of substances have a value of Tc above the ordinary
temperature, and diminution of volume (increase of pressure) is
sufficient to condense such gaseous substances into liquids. If Tc is
but little above the ordinary temperature, a great increase of pressure
is in general required to effect condensation. Substances for which Tc
is much higher than the ordinary temperature T0, e.g. Tc > 5/3 T0, occur
as liquids, even without increase of pressure; that is, at the pressure
of one atmosphere. The value 5/3 is to be considered as only a mean
value, because of the inequality of p_c. The substances for which Tc is
smaller than the ordinary temperature are but few in number. Taking the
temperature of melting ice as a limit, these gases are in successive
order: CH4, NO, O2, CO, N2 and H2 (the recently discovered gases argon,
helium, &c., are left out of account). If these gases are compressed at
0 deg. centigrade they do not show a trace of liquefaction, and therefore
they were long known under the name of "permanent gases." The discovery,
however, of the critical temperature carried the conviction that these
substances would not be "permanent gases" if they were compressed at
much lower T. Hence the problem arose how "low temperatures" were to be
brought about. Considered from a general point of view the means to
attain this end may be described as follows: we must make use of the
above-mentioned circumstance that heat disappears when a substance
expands, either with or without performing external work. According as
this heat is derived from the substance itself which is to be condensed,
or from the substance which is used as a means of cooling, we may divide
the methods for condensing the so-called permanent gases into two
principal groups.

Liquids as means of cooling.

In order to use a liquid as a cooling bath it must be placed in a
vacuum, and it must be possible to keep the pressure of the vapour in
that space at a small value. According to the boiling-law, the
temperature of the liquid must descend to that at which the maximum
tension of the vapour is equal to the pressure which reigns on the
surface of the liquid. If the vapour, either by means of absorption or
by an air-pump, is exhausted from the space, the temperature of the
liquid and that of the space itself depend upon the value of the
pressure which finally prevails in the space. From a practical point of
view the value of T3 may