e mentioned already, we find
for the value of the specific volume that gives the greatest cooling
the formula

RT1b 2a
---------- = ----,
(v1 - b)^2 v1^2

and for the value of the pressure
_ _____ _ _ _____ _
| / 4 T1 | | / 4 T1 |
p1 = 27p_c | 1 - / -- -- | | 3 / -- -- - 1 |.
|_ \/ 27 Tc _| |_ \/ 27 Tc _|

If we take the value 2Tc for T1, as we may approximately for air when
we begin to work with the apparatus, we find for p1 about 8p_c, or
more than 300 atmospheres. If we take T1 = Tc, as we may at the end of
the process, we find p1 = 2.5p_c, or 100 atmospheres. The constant
pressure which has been found the most favourable in Linde's apparatus
is a mean of the two calculated pressures. In a theoretically perfect
apparatus we ought, therefore, to be able to regulate p1 according to
the temperature in the inner spiral.

The critical temperatures and pressures of the permanent gases are given
in the following table, the former being expressed on the absolute scale
and the latter in atmospheres:--

Tc p_c Tc p_c

CH4 191.2 deg. 55 CO 133.5 deg. 35.5
NO 179.5 deg. 71.2 N2 127 deg. 35
O2 155 deg. 50 Air 133 deg. 39
Argon 152 deg. 50.6 H2 32 deg. 15

The values of Tc and p_c for hydrogen are those of Dewar. They are in
approximate accordance with those given by K. Olszewski. Liquid hydrogen
was first collected by J. Dewar in 1898. Apparatus for obtaining
moderate and small quantities have been described by M. W. Travers and
K. Olszewski. H. Kamerlingh Onnes at Leiden has brought about a
circulation yielding more than 3 litres per hour, and has made use of it
to keep baths of 1.5 litre capacity at all temperatures between 20.2
deg. and 13.7 deg. absolute, the temperatures remaining constant within
0.01 deg. (See also LIQUID GASES.) (J. D. v. d. W.)

CONDENSER, the name given to many forms of apparatus which have for
their object the concentration of matter, or bringing it into a smaller
volume, or the intensification of energy. In chemistry the word is
applied to an apparatus which cools down, or condenses, a vapour to a
liquid; reference should be made to the article DISTILLATION for the
various types in use, and al